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Calibrating Pressure Sensitive Paints Using Proper Orthogonal Decomposition


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CALIBRATING PRESSURE SENSITIVE PAINTS USING PROPER ORTHOGONAL DECOMPOSITION By AHMED F. OMAR A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Ahmed F. Omar

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This dissertation is dedicated to my family.

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iv ACKNOWLEDGMENTS THOSE OF HIS SERVANTS ONLY WHO ARE POSSESSED OF KNOWLEDGE FEAR ALLAH; SURELY ALLAH IS MI GHTY, FORGIVING. (QURAN: SURAT FATIRR, VERSE 28) THEY ASK THEE CONCERNING THE SOUL SAY: THE SOUL IS OF THE AFFAIR OF MY LORD: OF KNOWLE DGE IT IS ONLY A LITTLE THAT IS COMMUNICATED TO YOU, (O MEN!) (QURAN: SURAT AL-ISRAAA, VERSE 85) I express my humility and gratitude before Allah for all the blessings and successes in my life. None of these accomplishments would have been possible without the grace and mercy of Allah. I would like next to th ank my parents and brother for all their sacrifices to help me in my educational pursuit. I owe them everything, and I know the world would not be enough to give to them. My fiance is owed sincere appreciation for her support and understanding. I would also like to thank Dr. Carroll, my a dvisor, for his support over the course of my Ph.D. pursuit. Special thanks are owed to Dr. Paul Hubner and Dr. Louis Cattafesta for their assistance and guidan ce in a time of desperate nee d. Further appreciation goes to the rest of my committee members, Dr. Ki rk Schanze and Dr. William Lear. Finally, I would like to thank all of those who helped me through the course of my Ph.D.: friends, colleagues, and university staff.

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v TABLE OF CONTENTS page LIST OF TABLES...............................................................................................................x LIST OF FIGURES.........................................................................................................xiii NOMENCLATURE......................................................................................................xxiii ABSTRACT...................................................................................................................xxvi CHAPTER 1 INTRODUCTION........................................................................................................1 Literature Review.........................................................................................................3 Preface...................................................................................................................3 Historical Perspective............................................................................................4 Photophysics of Luminescent Coatings.................................................................6 Statement of the Problem....................................................................................11 Research Efforts..................................................................................................14 Proper Orthogonal Decomposition (POD)..........................................................36 Motivation and Contribution......................................................................................41 2 LUMINESCENT COATINGS...................................................................................46 Overview.....................................................................................................................46 The Ozone Accident............................................................................................47 The Structure.......................................................................................................51 Paint Chemistry..........................................................................................................52 The Photophysics.................................................................................................52 The Temperature Dependence.............................................................................55 The Oxygen Factor..............................................................................................57 Paint Composition and Character........................................................................58 Which Luminescent Molecule?....................................................................58 Binder Polymers...........................................................................................59 The Undercoat..............................................................................................62 Measuremen t System..................................................................................................64 The Excitation Source.........................................................................................65 The Detection Device..........................................................................................66 Calibration Techniques........................................................................................67

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vi A Priori Calibration......................................................................................67 In situ Calibration.........................................................................................69 Hybrid Calibration........................................................................................70 PSP Calibration............................................................................................70 TSP Calibration............................................................................................74 3 PROPER ORTHOGONAL DECOMPOSITION.......................................................76 Overview.....................................................................................................................76 POD Analysis.............................................................................................................77 Introduction.........................................................................................................77 Mathematical Formulation..................................................................................78 Principle component analysis.......................................................................78 Target transformation...................................................................................82 POD Behavior.............................................................................................................84 Introduction.........................................................................................................84 Algorithm............................................................................................................85 Target transformation..........................................................................................86 Data generation....................................................................................................88 Noise.............................................................................................................90 Analysis......................................................................................................................9 3 Case One (Independent Emission)......................................................................94 Case One-A (Temperature Emission Amplified by 10)......................................96 Case One-B (Temperature Emission Broa dened to Overlap with Pressure).......97 Case One-C (Temperature Emission Greatly Broadened to Overlap with Pressure)...........................................................................................................98 Case One-D (Close Emission: Temper ature at 600nm and Pressure at 650 nm)...................................................................................................................99 Case One-E (Shot Noise Imposed on the Spectra)............................................100 Case One-F (Shot Noise Amplified by 10).......................................................102 Case One-G (Filtered Spectra with Shot Noise Amplified by 10)....................103 Case One-H (Filtered Noisy Spectra Using Only Two Filters).........................105 Summary............................................................................................................106 Case Two (Temperature Depe ndent Pressure Emission)..................................107 Calibration Surface Fitting.........................................................................107 Summary............................................................................................................114 4 LAMINAR CHANNEL FLOW...............................................................................115 Preface......................................................................................................................11 5 Isothermal Flow Solution Mathematical Derivation.........................................120 Assumptions/Justifications.........................................................................121 Boundary Conditions..................................................................................122 The Fully Developed Region (Poiseuille Flow).........................................122 Non-Isothermal Fully Developed Flow.............................................................127

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vii 5 EXPERIMENTAL SETUP......................................................................................132 Hardware Description...............................................................................................132 Channel..............................................................................................................132 Channel Deformation.................................................................................137 Optical Setup.....................................................................................................142 Image Registration.............................................................................................148 Thermal Expansion....................................................................................150 6 RESULTS AND ANALYSIS...................................................................................153 Procedure and Test Cases.........................................................................................153 Exposure Times.................................................................................................153 Data Matrix........................................................................................................154 POD Analysis....................................................................................................156 Calibration Matrix vs. Test Matrix.............................................................156 Image Filtering...........................................................................................160 Results.......................................................................................................................1 61 Case One (Isothermal Longitudinal Pressure Gradient)....................................162 POD Calibration.........................................................................................168 Case Two (Longitudinal Temperature Gradient)..............................................175 POD Calibration.........................................................................................178 Case Three (Simultaneous Longitudinal Pressure and Temperature Gradients)183 POD Calibration.........................................................................................186 Case Five (Perpendicular Temperature Gradient with Longitudinal Pressure Gradient)........................................................................................................194 POD Calibration.........................................................................................199 Case Seven (Oblique Temperature Gr adient with Longitudinal Pressure Gradient)........................................................................................................208 POD Calibration.........................................................................................211 The Case for POD.............................................................................................218 Curve Fit of the 650nm Intensity Data and Intensity Ratios.............................220 Case Three..................................................................................................221 Case Five....................................................................................................224 Case seven..................................................................................................228 Error Sources and Uncertainty..........................................................................231 Classification of Error................................................................................233 Uncertainty Analysis..................................................................................236 7 CONCLUSIONS AND FUTURE WORK...............................................................244 Conclusions...............................................................................................................244 Future Work..............................................................................................................246 APPENDIX A IMAGING SYSTEM................................................................................................249

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viii Measurement System................................................................................................249 The Excitation Source.......................................................................................249 Lasers.........................................................................................................250 UV Lamps..................................................................................................252 Visible Light Illumination LEDs................................................................253 The Detection Device........................................................................................253 CCD Cameras.............................................................................................254 Physical Construction.................................................................................255 From Light to Electrons.............................................................................256 Potential Wells...........................................................................................256 Charge Transfer..........................................................................................257 Digital Signal Processing...........................................................................259 CCD Chip Types........................................................................................259 Full-Frame CCD Chips..............................................................................259 Frame-Transfer CCD Chips.......................................................................260 Back-Thinned, Back-Illuminated CCD Chips...........................................261 CCD Artifacts.............................................................................................261 Charge Transfer Efficiency........................................................................262 Photon (Shot) Noise...................................................................................262 Pixel Gain Variations.................................................................................263 Read-Noise.................................................................................................264 Saturation...................................................................................................264 Thermal (Dark) Current.............................................................................264 Camera Resolution.....................................................................................266 Photomultiplier Tubes (PMTs)...................................................................266 Data Reduction..................................................................................................268 Correcting for Non-Idealities.....................................................................269 Dark Image Correction...............................................................................269 Illumination-Field Variation Correction....................................................269 Image-Registration correction....................................................................270 Flat-Field Correction..................................................................................271 Supplementary Topics..............................................................................................272 Lifetime Approach.............................................................................................272 Measurement Uncertainties...............................................................................275 Measurement Systems................................................................................276 Illumination source.....................................................................................276 CCD camera...............................................................................................276 Filtering/Spectral leakage...........................................................................277 Physical/Chemical Properties of Coating...................................................278 Displacement/Deformation of Model.........................................................278 Useful Definitions.............................................................................................279 Binning.......................................................................................................279 Blooming....................................................................................................280 Bit Depth of Camera Data..........................................................................280 Dynamic Range..........................................................................................281 Fill Factor...................................................................................................282

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ix Light Sensitivity.........................................................................................282 Linearity.....................................................................................................282 Signal to Noise Ratio (SNR)......................................................................283 B DERIVATION OF LAMINAR CHANNEL FLOW SOLUTION..........................285 Isothermal Flow Solution Mathematical Derivation.........................................285 Assumptions/Justifications.........................................................................285 Boundary Conditions..................................................................................286 The Fully Developed Region (Poiseuille Flow).........................................287 Non-Isothermal Fully Developed Flow.............................................................290 Uniform Temperature/Heat Flux Boundary Condition..............................290 C MATLAB codes for POD analysis...........................................................................301 Image Registration....................................................................................................301 Calibration Intensity/Pressure and Temperature Extraction.....................................305 POD Code.................................................................................................................311 D Derivation of Some Equations..................................................................................315 POD Analysis...........................................................................................................315 Derivation of Pressure Calibration Coefficients................................................315 LIST OF REFERENCES.................................................................................................318 BIOGRAPHICAL SKETCH...........................................................................................325

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x LIST OF TABLES Table page 1-1 Response time and temperature depe ndency of PtTFPP/FIB with different base coatings.....................................................................................................................18 1-2 Research effort trea ting PSP temperature effects.....................................................42 3-1 Conditions and their C elements..............................................................................93 3-2 Eigenvalues for case one..........................................................................................94 3-3 Eigenvalues for case one-A......................................................................................96 3-4 Calibration Error case one-A....................................................................................96 3-5 Eigenvalues for case one-B......................................................................................97 3-6 Calibration Error case one-B....................................................................................97 3-7 Eigenvalues for case one-D......................................................................................98 3-8 Calibration Error case one-C....................................................................................98 3-9 Eigenvalues for case one-D......................................................................................99 3-10 Calibration Error case one-D....................................................................................99 3-11 Eigenvalues for case one-E....................................................................................101 3-12 Calibration Error case one-E..................................................................................101 3-13 Eigenvalues for case one-F....................................................................................103 3-14 Calibration Error case one-F..................................................................................103 3-15 Eigenvalues for case one-G....................................................................................104 3-16 Calibration Error case one-G..................................................................................104 3-17 Eigenvalues for case one-G....................................................................................106

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xi 3-18 Calibration Error case one-G..................................................................................106 5-1 Coefficients of Thermal Expansion........................................................................151 6-1 Exposure times for the different filters..................................................................153 6-2 Pressure drift throughout the exposure times (case five).......................................154 6-3 Test matrix..............................................................................................................15 4 6-4 Temperature drift throughout the exposure times (case 5).....................................162 6-5 Case one: Test-points pressure resu lts. Actual represents pressure tap measurement and POD represents the cal culated pressure via POD calibration. The precision error of the Actu al readings is 0.006 psi......................................172 6-6 Case three: Test-points pressure re sults. Actual represents pressure tap measurement and POD represents the cal culated pressure via POD calibration. The precision error of the Actu al readings is 0.006 psi......................................189 6-7 Case five: Test-points pressure re sults. Actual represents pressure tap measurement and POD represents the cal culated pressure via POD calibration. The precision error of the Actu al readings is 0.006 psi......................................203 6-8 Case seven: Test-point s pressure results. Actual represents pressure tap measurement and POD represents the cal culated pressure via POD calibration. The precision error of the Actu al readings is 0.006 psi......................................215 6-9 Comparison of different calibration techniques.....................................................218 6-10 Case five: Comparison between test -points pressure results for POD and intensity-ratio Actual represents pressure tap measurement and POD represents the calculated pressure via POD calibra tion. The precision error of the Actual readings is 0.006 psi............................................................................................227 6-11 Case seven: Comparison between test -points pressure results for POD and intensity-ratio. Actual represents pressu re tap measurement and POD represents the calculated pressure via POD calibra tion. The precision error of the Actual readings is 0.006 psi............................................................................................230 6-12 Intensity error sources and values for Photometrics CH250A CCD camera (SI 502AB), 200 kHz, 14 bit A/D for a unity nominal gain value and a measured gain ( ) of 19.1 (e-/ADU).....................................................................................237 6-13 Shot noise uncertainty for all filters (case seven) with total precision uncertainty of 29.3cts................................................................................................................238

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xii 6-14 Intensity drift uncertainty for case se ven. Reference conditions are not included in the analysis as they are acquired under isothermal conditions. The total intensity bias uncertainty due to test conditions drift is 9.7cts...............................239 6-15 Uncertainty (95% confiden ce level) for key factors..............................................243 A-1 Error estimates for the 16 & 14-bit CCD cameras. Camera linearity error is 0.07% and ADU speed is 200 kHz.........................................................................277

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xiii LIST OF FIGURES Figure page 1-1 Stern-Volmer model for a range of qK......................................................................9 1-2 Jablonski energy-level diagram showi ng the absorption and emission processes for a typical luminescent molecule...........................................................................13 2-1 Coating Structure......................................................................................................51 2-2. Typical Absorption (left) and Emissi on (right) vs. Wavelength for PtTFPP in fluoroacrylic polymer binder (PtT FPP/FIB). (Bell et al. 2001)...............................52 2-3 Typical rate of gas permeation acros s a membrane (after Lu and Winnik, 2000)...60 2-4 Equipment Setup for Temperature Calibration........................................................65 3-1 Spectral emission for two independen ce processes: (A) Raw spectra (B) A single raw spectrum with dependence on th e higher wavelength factor and no dependence on the lower wavelength f actor (C) The normalized spectra...............79 3-2 P.C.A. Algorithm.....................................................................................................85 3-3 Target transformation algorithm..............................................................................87 3-4 Simulated spectral response of th e luminophors: (A) Frequency domain (B) Wavelength domain..................................................................................................90 3-5 Shot noise as a function of intensity.........................................................................92 3-6 Case one: Narrow spectrum with no overlap...........................................................94 3-7 Case one: Eigenvectors and calibration curves for pressure (left) at 79.8392 and temperature (right) at 13.6121................................................................................95 3-8 Case one-A: Temperature Emission Amplified 10 Folds........................................96 3-9 Case one-A: Eigenvectors for pressure (left) at 66.5546 and temperature (right) at 0.3275.................................................................................................................96 3-10 Case one-B: Emission spectra..................................................................................97

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xiv 3-11 Case one-B: Eigenvectors for pressure (left) at 75.592 and temperature (right) at 9.365...................................................................................................................97 3-12 Case one-C: Emission spectra..................................................................................98 3-13 Case one-C: Eigenvectors for pressure (left) at 72.783 and temperature (right) at 6.556...................................................................................................................98 3-14 Case one-D: Emission spectra..................................................................................99 3-15 Case one-D: Eigenvectors for pressure (l eft) at 78.15 and temperature (right) at 11.923.....................................................................................................................99 3-16 Case one-E: Emission spectra................................................................................100 3-17 Case one-E: Reconstructed spectra........................................................................100 3-18 Case one-E: Eigenvectors for pressu re (left) at 280.1082 and temperature (right) at 166.392..................................................................................................101 3-19 Case one-F: Emission spectra................................................................................102 3-20 Case one-F: Reconstructed spectra........................................................................102 3-21 Case one-F: Eigenvectors for pressu re (left) at 100.1556 and temperature (right) at 346.3815................................................................................................103 3-22 Case one-G: Emission spectra................................................................................103 3-23 Case one-G: Reconstructed spectra........................................................................104 3-24 Case one-G: Eigenvectors for pressure (l eft) at 79.79 and temperature (right) at 13.502...................................................................................................................104 3-25 Case one-H: Emission spectra................................................................................105 3-26 Case one-H: Eigenvectors for pressure (l eft) at 258.9 and temperature (right) at 192.68...................................................................................................................105 3-27 Case two: Emission spectra....................................................................................107 3-28 Case two: Eigenvectors rotated at the a ppropriate angle for te mperature (left) at 345.78 and pressure (right) at 106.44..................................................................110 3-29 Case two: Temperature calibration.........................................................................110 3-30 Case two: Second order pressure ca libration using the scorers from POD............111

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xv 3-31 Case two: Second order pre ssure calibration using the 2nd set of scorers and temperature.............................................................................................................111 3-32 Case two: Third order pressure ca libration using the scorers from POD at 193.46...................................................................................................................112 3-33 Case two: Pressure calibrati on using the scorers from POD at 193.46................112 3-34 Case two: Numerically filtered emission...............................................................113 3-35 Case two: Numerically filtered emissi on eigenvectors for pressure (left) at 106.6 and temperature (right) at 346.06..............................................................113 3-36 Case two: Second order pre ssure calibration using the 2nd set of scorers and temperature.............................................................................................................114 4-1 Channel flow schematic.........................................................................................116 4-2 Channel flow: flow developm ent and pressure distribution...................................117 4-3 Low-aspect ratio de veloping channel flow............................................................119 4-4 Fully developed velocity profile for an incompressible laminar channel flow......123 4-5 Hotwire and PIV measurement schematic in the channel......................................124 4-6 Isothermal case: Centerline pressure gradient along the channel showing the deviation of the experimental results from the theoretical prediction....................126 4-7 Non-isothermal flow schematic.............................................................................130 5-1 Mass flow contro ller (AALBORG)........................................................................133 5-2 Channel flow schematic: Top view of channel shown...........................................134 5-3 (A) Channel resting on heaters (B) Side view of channel showing the 1 inch glass plate (C) Backside of channel showing thermocouples, pressure taps, stagnation chamber and tubing connecting from the top water channel to the cooler......................................................................................................................136 5-4 Close-up of the beginning of the cha nnel showing the packaging and aluminum foam, thermocouples and pressure taps. Firs t two test pressure taps are circled in yellow.....................................................................................................................137 5-5 Channel deformation due to pressure for ces (modulus of elasticity for aluminum and glass is ~ 10.5 and 9.6 psi x 106, respectively)................................................138 5-6 Channel deformation due to pressure forces using Plexiglas comparing the theoretical pressure profile (green line) to experimental profile (blue circles)......139

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xvi 5-7 Calculated percentage channel hei ght deformation (relative to no-flow conditions of 0.01) along the centerline fo r 1 plate with a maximum flow rate of 100LPM, 23 psi static pressure at th e beginning of the channel and 0.01 channel height........................................................................................................140 5-8 Glass deformation (a comparison between theoretical and experimental results): 3/8 glass (top) and 1 glass (bottom) w ith percentage pressure deviation from theory in top-left corner of each plot. Flow from right to left................................141 5-9 Experimental optical setup showing th e relative position of the CCD camera and excitation sources with re spect to the channel.......................................................142 5-10 Pressure response of dual-lu minophor paint at 293K (Kose 2005)......................143 5-11 Temperature response of dual-lu minophor paint at 14.7 psi (Kose 2005).............143 5-12 First bandpass interference filter: 550 nm, 40 8 nm FWHM; dia. = 50 mm (www.mellesgriot.com)..........................................................................................144 5-13 Second bandpass interference filter: 600 nm, 40 8 nm FWHM; dia. = 50 mm (www.mellesgriot.com)..........................................................................................144 5-14 Third bandpass interference filter: 650 nm, 40 8 nm FWHM; dia. = 50 mm (www.mellesgriot.com)..........................................................................................145 5-15 Fourth bandpass interfer ence filter: 700 nm, 40 8 nm FWHM; dia. = 50 mm (www.mellesgriot.com)..........................................................................................145 5-16 Filters arrangement relative to paint spectral response to temperature (left) and pressure (right).......................................................................................................146 5-17 (A) Filter wheel (B) Blue LED ISSI LM2 (excitation source) (C) CCD camera and filter wheel assembly.......................................................................................147 5-18 Effect of image registration on SNR (A) Unregistered image (B) Registered image. Bottom plots show a horizontal section of the images above....................148 5-19 Pixel intensity shift on the CCD array...................................................................149 5-20 Pixel shift due to thermal expansion from bottom to top of the channel...............152 6-1 Stern-Volmer relation for dualluminophor (PtTFPP-Ruphen/PAN nanospheres in poly-t-BS-co-TFEM) at different temperature levels (Kose, 2005)...................155 6-2 Channel image showing thermocouples, calibration pressure taps and pressure test points taps........................................................................................................157

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xvii 6-3 Effect of adding rows instead of colu mns to the calibration matrix. Observe the direction of the main eigenvector (bl ack arrow) compared to the calibration eigenvector (orange arrow)....................................................................................159 6-4 Intensity percent error due to shot noise vs. numbe r of frames (14-bit CCD camera)...................................................................................................................160 6-5 Case one: Pressure profile (bottom), (a ) percent pressure deviation from theory (psi), (b) temperature profile (therm ocouples) over the plate (8 x 3).................163 6-6 Case one: Normalized intensity (Irun/Iref): 550nm [left] --600nm [right]...........164 6-7 Case one: Normalized intensity (Irun/Iref): 650nm [left] --700nm [right]...........164 6-8 Case one: Centerline pressure respon se of dual-luminophor at different bandpass wavelengths............................................................................................................165 6-9 Normalized intensity for case one (650nm) using N2 (left): (A) Reference image acquired with no flow and exposure ti me of 1500ms (B) Reference image acquired with nitrogen flow and exposure time of 185ms. Exposure time for run image is 1500 ms....................................................................................................166 6-10 Fluorescence image using epifluorescen ce microscope of Ruphen/PAN particles emission (dispersed into the PtTFPP / poly-t-BS-co-TFEM binder) at 560nm. The image shows the heterogeneous disp ersion of the Ruphen/PAN particles in the poly-t-BS-co-TFEM matrix (Kose 2005).........................................................167 6-11 Case one: Normalized intensity (Iref/Irun)................................................................168 6-12 Case one: Calibration eigenvectors at 174.56 degrees (left) and eigenvalues (right)......................................................................................................................16 9 6-13 Case one: Product of first (left) and second (right) eigenvectors and eigenvalues of calibration..........................................................................................................169 6-14 Case one: Product sum of eigenvectors and calibration eigenvalues showing 1 % variation at 550nm and 15% at 650nm...................................................................170 6-15 Case one: Calculated centerlinepressure profile by each eigenvector..................171 6-16 Area change due to chamfer in the glass plate at the exit......................................172 6-17 Case one: Calibration error, absolu te (left) and percentage (right)........................172 6-18 Case one: Calculated pressu re field from POD calibration....................................173 6-19 Case one: Calculated pressure from POD calibration vs. pixel index along the channel. Each curve represents a longit udinal line of pixels along the channel. Actual represents the actual pressure taps readings used for calibration...............174

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xviii 6-20 Case two: Temperatur e profile (thermocouples)....................................................175 6-21 Case two: Normalized intensity (Irun/Iref): 550nm [left] --600nm [right]...........176 6-22 Case two: Normalized intensity (Irun/Iref) : 650nm [left] --700nm [right]..........176 6-23 Case two: Centerline temperature response of dual-luminophor coating at different bandpass wavelengths.............................................................................177 6-24 Case two: Temperature linearity of dual-luminophor co ating at different bandpass wavelengths............................................................................................177 6-25 Case two: Normalized intensity (Irun/Iref)...............................................................178 6-26 Case two: Calibration fundamental spectra at 0.5 degrees (lef t) eigenvalues of calibration (right)....................................................................................................178 6-27 Case two: Product of first (left) and second (right) eigenvectors and eigenvalues of calibration..........................................................................................................179 6-28 Case two: Product sum of eigenvector s and calibration eigenvalues showing 28 % variation at 550nm and 18% at 650nm..............................................................180 6-29 Case two: Calculated temperatur e field from POD calibration (image)................181 6-30 Case two: Calculated temperature fi eld from POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual thermocouple readings used for calibration..........................182 6-31 Case three: Pressure profile (bottom), (a) percent pressure deviation from theory (psi), (b) temperature profile (thermocouples).......................................................183 6-32 Case three: Normalized intensity (Irun/Iref): 550nm [left] --600nm [right].........184 6-33 Case three: Normalized intensity (Irun/Iref) : 650nm [left] --700nm [right]........184 6-34 Case three: Centerline pressure and temperature re sponse of dual-luminophor at different bandpass wavelengths.............................................................................185 6-35 Case three: Inverse of normalized intensity (Irun/Iref).............................................186 6-36 Case three: Pressure calibration fundamental spectr a at 1 degrees (left) eigenvalues of ca libration (right)...........................................................................187 6-37 Case three: Product of first (lef t) and second (right ) eigenvectors and eigenvalues of pressure calibration........................................................................187 6-38 Case three: Product sum of eigenvect ors and pressure ca libration eigenvalues showing 18 % variation at 550nm and 27% at 650nm...........................................188

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xix 6-39 Case three: Temperature calibration f undamental spectra at 0 degrees (left) eigenvalues of ca libration (right)...........................................................................189 6-40 Case three: Product of first (lef t) and second (right ) eigenvectors and eigenvalues of temperature calibration..................................................................190 6-41 Case three: Product sum of eigenvector s and temperature calibration eigenvalues showing 23 % variation at 550nm and 26% at 650nm...........................................190 6-42 Case three: Calculated pressure field from POD ca libration (image)....................191 6-43 Case three: Calculated temperatur e field from POD calibration (image)..............192 6-44 Case three: Calculated pressure field from POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual pressure taps readi ngs used for calibration..................................................193 6-45 Case three: Calculated temperature field from POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual thermocouple readings used for calibration..........................193 6-46 Case five: Temperatur e profile (thermocouples)....................................................194 6-47 Case five: Pressure profile (bottom), (a ) percent pressure deviation from theory (top)........................................................................................................................19 5 6-48 Case five: Normalized intensity (Irun/Iref): 550nm [left] --600nm [right]...........196 6-49 Case five: Normalized intensity (Irun/Iref): 650nm [left] --700nm [right]...........196 6-50 Case five: Speckling in the 550nm imag e (left) and a comparison to the 700nm filter........................................................................................................................1 97 6-51 Case five: Centerline pressure and te mperature response of dual-luminophor at different bandpass wavelengths.............................................................................198 6-52 Case five: Centerlin e temperature profile..............................................................198 6-53 Case five: Inverse of normalized intensity (Irun/Iref)...............................................199 6-54 Case five: Temperature calibration funda mental spectra at 89 degrees (left) eigenvalues of ca libration (right)...........................................................................200 6-55 Case five: Product of first (left) and second (right) eigenvectors and eigenvalues of calibration..........................................................................................................200 6-56 Case five: Product sum of eigenvect ors and calibration eigenvalues showing 9.5% variation at 550nm and 17% at 650nm.........................................................201

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xx 6-57 Case five: Pressure calibration funda mental spectra at 11 degrees (left) eigenvalues of ca libration (right)...........................................................................202 6-58 Case five: Product of first (left) and second (right) eigenvectors and eigenvalues of calibration..........................................................................................................202 6-59 Case five: Product sum of eigenvector s and pressure calib ration eigenvalues showing 4% variation at 550nm and 16% at 650nm..............................................203 6-60 Case five: Calculated temper ature from POD calibration (image)........................204 6-61 Case five: Calculated temperature from POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual thermocouple readings used for calibration.................................................205 6-62 Case five: Calculated pressu re from POD calibration (image)..............................206 6-63 Case five: Calculated pressure fr om POD calibration (image). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual pressure taps readi ngs used for calibration..................................................207 6-64 Case seven: Temperatur e profile (thermocouples).................................................208 6-65 Case seven: Pressure profile (botto m), (a) percent pressure deviation from theory (top).............................................................................................................209 6-66 Case seven: Normalized intensity (Irun/Iref): 550nm [left] --600nm [right]........210 6-67 Case seven: Normalized intensity (Irun/Iref) : 650nm [left] --700nm [right].......210 6-68 Case seven: Inverse of normalized intensity (Irun/Iref)............................................211 6-69 Case seven: Temperature calibration f undamental spectra at 93 degrees (left) eigenvalues of ca libration (right)...........................................................................212 6-70 Case seven: Product of first (lef t) and second (right ) eigenvectors and eigenvalues of calibration.......................................................................................212 6-71 Case seven: Product su m of eigenvectors and calib ration eigenvalues showing 31% variation at 550nm and 28% at 650nm..........................................................213 6-72 Case seven: Pressure calibration fundamental spectra at 53 degrees (left) eigenvalues of ca libration (right)...........................................................................213 6-73 Case seven: Product of first (lef t) and second (right ) eigenvectors and eigenvalues of calibration.......................................................................................214 6-74 Case seven: Product su m of eigenvectors and calib ration eigenvalues showing 8% variation at 550nm and 5% at 650nm..............................................................214

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xxi 6-75 Case seven: Calculated temper ature from POD calibration (image).....................215 6-76 Case seven: Calculated pressu re from POD calibration (image)...........................216 6-77 Case seven: Predicted temperature from POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual thermocouple readings used for calibration.................................................217 6-78 Case seven: Predicted pressure fr om POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual pressure taps readi ngs used for calibration..................................................217 6-79 Temperature sensitivity (integrated inte nsity/K) of the temperature and pressure luminophors at 14.7 psi (Kose 2005).....................................................................220 6-80 Case three: Pressure calibrati on using intensity ratio at 650nm.............................221 6-81 Case three: Calculated pressu re using intensity ratio at 650nm.............................221 6-82 Case three: Pressure calib ration using intensity ratio (I550 / I650)............................222 6-83 Case three: Pressure calib ration using intensity ratio (I600 / I650)............................223 6-84 Case three: Calculated pre ssure using intensity ratio at (I600 / I650)........................223 6-85 Case five: Pressure ca libration using intensity (1 / I650).........................................224 6-86 Case five: Calculated pressure using intensity (1 / I650).........................................224 6-87 Case five: Pressure ca libration using intensity (I600 / I650)......................................225 6-88 Case five: Calculated pressure using intensity (I600 / I650)......................................225 6-89 Case five: Calculated pressure using intensity (I600 / [I650]2)..................................226 6-90 Case five: Calculated pressure using intensity (I600 / [I650]1.5)................................226 6-91 Case five: Calculated pressure: (A) Intensity I600 / [I650]1.5 (B) POD calibration...227 6-92 Case seven: Calculated pressure using intensity (1 / I650)......................................228 6-93 Case seven: Calculated pressure using intensity (I600 / I650)...................................228 6-94 Case seven: Calculated pressure using intensity (I600 / [I650]2)...............................229 6-95 Case seven: Calculated pressure using intensity (I600 / [I650]1.55)............................229 6-96 Case seven: Calculated pressure: (A) Intensity I600 / [I650]1.55 (B) POD calibration...............................................................................................................230

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xxii 6-97 Bias and precision error..........................................................................................233 A-1 Schematic of CCD imaging system.......................................................................254 A-2 CD Chip..................................................................................................................25 5 A-3 Potential Well Structure.........................................................................................257 A-4 CCD readout sequence...........................................................................................258 A-5 A schematic of a Photomultiplier tube...................................................................268 A-6 Timing sequence for lifetime measurement (frequency domain)..........................274 A-7 Timing sequence for lifetim e measurement (time dom ain)...................................275 A-8 SNR as a Function of Intensity..............................................................................284 B-1 Fully developed velocity profile for an incompressible laminar channel flow......289 B-2 Thermal boundary layer development in a laminar channel flow..........................291 B-3 Non-isothermal flow schematic.............................................................................298

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xxiii NOMENCLATURE A(T) Stern-Volmer first coefficient B Bias error B(T) Stern-Volmer second coefficient c Speed of light in vacuum (3.0 1017 nm/s) C Scores matrix pc Specific heats per unit mass at constant pressure vc Specific heats per unit mass at constant volume D Data matrix, Diameter Dp Luminophor diffusion coeffi cients in polymer Dq Oxygen diffusion coefficients in polymer e Electronic tE Energy transport rate dE Diffusion activation energy nrE Arrhenius activation energy fo r a non-radiative process EQ activation energy for oxygen diffusion in the binder f Frequency g Gravitational force h Channel height, enthalpy, Planks constant (6.626176 10-34 Js) I Luminescence intensity Ia absorption intensity D I dark charge intensity em I Emission intensity

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xxiv o I Luminescence intensity in the absence of oxygen ref I Luminescence intensity at reference conditions run I Luminescence intensity at run conditions k Thermal conductivity (W/mK), Boltzmans constant (1.381 10-23 J/moleculeK), nrk Non-radiative decay rate qK, qk Stern-Volmer constant rk Radiative decay rate L Polymer thickness (Chapter 2) m Mass flow rate readoutN Read out noise 2O Oxygen concentration Precision error 2OP Partial pressure of oxygen Pr Prandtl number ( Pr ) refP Pressure at reference conditions runP Pressure at run conditions Q Mass flow rate q energy generation within object wq heat flux (W/m2) R Universal gas constant (8.315 J/molK), Eigenvector matrix Re Reynolds number ( RemmVDVD ) S Gas solubility sT Solubility coefficient

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xxv ls linear solubility coefficient based on Henrys law nls non-linear solubility coeffici ent based on Langmuirs model t time T Temperature, Rotation matrix g T Glass transition temperature u x-component velocity U Uncertainty v y-component velocity mV Mean velocity w z-component velocity, width AW Wetted perimeter dw Channel width Z Squared data matrix T Coefficient of linear thermal e xpansion, affinity coefficient Gain Viscous boundary layer thickness T Thermal boundary layer thickness Error steady-state gas flux into polymer Wavelength, Eigenvalues Dynamic viscosity Kinematic viscosity quantum yield of luminescence, dissipation function in energy equation Density Standard deviation shot Shot noise em Emission lifetime of an excited molecule

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xxvi Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIBRATING PRESSURE SENSITIVE PAINTS USING PROPER ORTHOGONAL DECOMPOSITION By Ahmed F. Omar August 2006 Chair: Bruce F. Carroll Major Departme nt: Mechanical and Aerospace Engineering Pressure sensitive paints (PSP) have been gaining more popularity in experimental fluid mechanics and aerodynamic testing. A major problem with PSP pertains to its temperature dependence making the calibration process very difficu lt. Dual-luminophor PSP has an added temperature phosphor to provide temperature information for the calibration. Dual-luminophor systems still suffer from the inherent temperature dependence and possess added complications du e to spectral cross talk and overlap. However, to date there is no successful universal calibration technique for dualluminophor systems. Such calibration is needed for dual-luminophor PSP to become a practical experimental tool. With this aim, a statistical technique known as proper orthogonal decomposition (POD) is used to extract pressure and temperature information from intensity data. POD works by defining and separating the main f actors of any system and evaluating the proportional contribution of each factor. Th e calibration technique is examined by

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xxvii applying the dual-luminophor PSP in a channe l flow experiment. Before applying the calibration experimentally, a set of artificial data is examined using POD to provide a fundamental understanding of POD as a cal ibration technique. The experiment was designed to allow for different flow conditi ons and temperature gradients to interact, hence providing enough varia tion to examine the calibrati on technique. Seven cases are examined, with each case shedding light on a particular aspect of the calibration. The POD calibration is compared to the intensityratio calibration in order to emphasize the effectiveness of the technique. Finally, resu lts are evaluated for accuracy and a detailed uncertainty analysis is performed to fully assess the POD calibration.

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1 CHAPTER 1 INTRODUCTION This dissertation presents novel work in the characteri zation and calibration of dual-luminophor pressure sensitive paints using proper orthogonal decomposition (POD). The paint is additionally implemented in a ca nonical flow experiment, namely a laminar incompressible channel flow, to fully char acterize the paint and calibration procedure under flow-based conditions. The paint utilized in this work is PtTFPP-Ru(phen)/PAN /Poly-tBS-co-TFEM, developed by Kose (2005) and collaboratively tested under static (no flow) conditions with the author. Pressure sensitive paints (PSP) offer a promising and more effective tool for characterizing a nd resolving pressure fields over test-model surfaces in comparison to traditional pressu re measurement techniques. Traditional techniques can offer at best a discrete repres entation of the pressure field. In addition, there is a rise in cost and time of experiment ation, as well as restrictions on access to the entire model for pressure sensor placemen t. In contrast, PSP technology is relatively inexpensive and can be easily applied to a ny surface in very thin layers (~ 10 m). A typical pressure sensitive paint is composed of an oxygen sensitive luminophor embedded in an oxygen permeable polymer, whic h is then applied directly on the surface or on top of a primer layer to enhance light reflection. Exciting the paint with the appropriate wavelength, usually long ultravio let (UV) to blue wavelengths, energizes the paint electronically, which is then followe d by a deactivation process through different paths. The path characterizing the pain ts dependence on pressure is the oxygen quenching path. Nonetheless, other paths of deactivation compete with the oxygen

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2 quenching path, primarily radiati on. Radiation is the molecule emission of light at higher wavelength as a means of deactivation. The oxygen quenching process is directly proportional to the partial pressure of oxygen in the surrounding medium, hence the pressure of air. Accordingly, the intensity of the light emitted by the paint is inversely proportional to the pressure. However, as the luminophor is embedded in an oxygen permeable medium (polymer), the oxygen sorpti on and diffusion characteristics of such medium would obviously affect the quenching process. Intu itively, temperature would appreciably alter the permeability of the polymer, thus the oxygen sorption and diffusion characteristics. In addition, on the molecula r level there is an inherent temperature dependence related to thermal quenching. Th is defines a principal concern with PSP, which is an inherent te mperature dependence that necessitates a temperature compensation procedure, in combination with a typical pressure/intensity calibration, to account for temperature variations while colle cting pressure information. Compensating for temperature effects is rather challenging, and while various research efforts have attempted to resolve the issue with relative success, a robus t and universal procedure is yet to be born. Dual-luminophor PSP contains an added temp erature sensor, which typically emits at sufficiently different wavele ngths, usually lower, such that the temperature data can be collected simultaneously to provide both a temperature compensation technique as well as mapping the temperature distribution over the surface. However, this leads to a different problem, namely, cross talk between the two sensors, which makes it difficult to separate the independent f actors, pressure and temperatur e, through spectral filtration. Cross talk is an adverse effect that st ems from either one luminophor absorbing the

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3 emission of the other, a spect ral overlap between the two emissions, or both. This work examines and applies POD to resolve these problems. POD identifies and separates the main factors of any process and resolves th e relative magnitude, and hence importance, of each factor; in addition, it se rves as a noise rejection tool. The second part of this work focu ses on examining the dual-luminophor PSP technology under flow-based conditions. Static behavior of the dual-luminophor PSP has already been quantified by the author in collaboration with Kose (2005). Flow-based measurements using the dual-luminophor PSP would allow for a thorough evaluation of the paint and the analysis/calibration process. The paint is applied in a laminar channel flow experiment with an imposed temperat ure gradient varying in direction from longitudinal, transverse, and oblique relative to the flow direction. The channel flow experiment is chosen as it is a canonical flow with an ex isting analytical solution under laminar incompressible conditions. The details of the channel flow experiment including literature review and mathematical analysis ar e presented in Chapter 4 and Appendix-B. Literature Review Preface The aerodynamic design of any model en tails fundamental fluid mechanics experiments involving the char acterization of the surface pr essure distribution. These measurements are usually obtained to estimat e the aerodynamic forces (e.g., lift and drag) through an integration process. More crucia l is the identification and understanding of specific flow phenomena that profoundly affect the design criterion, such as boundary layer separation or shock wave impingem ent on the surface. O ccasionally, such phenomena may affect the structural aspect of the design. Additionally, computational fluid dynamics (CFD) continue to evolve and expand in appli cation, requiring full-field

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4 experimental techniques capable of provi ding more comprehensive validation. Typically, pressure measurements are perf ormed using traditional techniques that implement pressure taps and transducers. These devices are located on discrete points over the surface of the model. This approach has several shortcomings. The first and most obvious is the lack of a full field mapping of the pressure field, which can lead to ignorance of the flow field behavior near the surface in critical areas of the model. Further, even with prior knowle dge of specific locations on the model that are potentially critical, it is not always po ssible to practically install su ch devices in the model (e.g., sharp corners, thin edges). It is rather imprac tical for one to try to compensate for the lack of enough spatial resolution of traditional pressure measurement techniques by adding more taps as the task is quite expensive as well as time consuming, not to mention the physical implications on the structural inte grity and the inevitable compromise of the flow characteristics over the su rface. To provide the reader with an idea of the cost involved in model constructi on, a typical pressure-instr umented aircraft wind tunnel model can cost on the order of $500,000 to $1 million to construct (McLachlan 1995). These shortcomings led to aerodynamic testi ng being a fairly time consuming process that adversely added to the cost and time required for any design. Historical Perspective A paper published by Dickerson and Stedman (1979) initiated research efforts in the field of flow measurements using lumine scent molecules as they utilized ozone to visualize flow patterns. Ozone has excellent flow tracing characteristics due to its physical properties. A fluorescent screen w ith a turbulent flow passing over it was illuminated with UV, and as the ozone-air mixture passed over the screen, the ozone absorbed some of the UV, hence casting a sha dow that is directly proportional to the

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5 ozone concentration in the flow and the sp eed of the flow. By placing an additional fluorescent screen perpendicular to the flow, they were able to create a three-dimensional image of the turbulent plumes. This was the ea rliest recorded attempt to quantify a flow using luminescent dyes. Ironically, the whole idea was based on a mere accident as they were trying to measure the rate of photolysis of ozone in the atmosphere when some ozone leaked between a mercury lamp and a bl ack light poster, whic h then cast a shadow that looked like smoke plumes. As they sc rambled to find the source of the smoke, Dickerson realized it was the shadow of an ozone plume! The work of Dickerson and Stedman ( 1979) inspired a group at the National Institute of Health (Peterson and Fitzgera ld, 1980), to pioneer the concept of surface pressure characterization using luminescent coatings in the West. Nonetheless, the originality of the oxygen quenched lumi nescent molecules technology was first established by the German scientists Kautsky and Hirsch (1935). Peterson and Fitzgerald, (1980) described an experiment in which a surface was covered with a fluorescent dye (fluorescent yellow dye adsorbed on silica partic les) that was then excited by a blue light. The dye had photoluminescence characteristics th at allowed it to respond inversely to surrounding oxygen concentration. As flow over th e surface was initiated, either nitrogen or oxygen was injected into the flow through a static pressure tap on the surface. In the case of nitrogen injection, a bright str eak of luminescence was detected on the downstream side of the tap, while the oxygen injection resulted in a dimmer illumination downstream of the tap. The nitrogen decr eased the oxygen concentr ation downstream of the tap and hence increased the lumines cence of the paint in versely to the oxygen concentration. Even though the PSP used in th is experiment was not favorable to accurate

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6 and practical experimental implementation due to low oxygen sensitivity of the dye and the oxygen permeability of the binde r as well as other problems such as poor adhesion of the dye to the surface, it undoubtedly created the potential for the use of luminescent technology in aerodynamic testing. Concurrently, Russian scientists produced the first practical pressure sensitive coating. A year later they obtained pressure measurements with the same coating (Ardasheva et al., 1985). Around the same time a group from the Central AeroHydrodynamic Institute (TsAGI) in the former Soviet Union deve loped a new polymerbased PSP, which they applied to a cone-c ylinder model at supersonic mach numbers. Their results showed that the paint suffe red from very significant temperature dependence, hence establishing one of the fundamental probl ems with PSP that is still unresolved to this date. The Russian a dvancements in PSP technology was finally revealed in the West through a commercial a dvertisement for an Optical Pressure and Temperature Measurement System in the 1990 February issue of Aviation Week & Space Technology. Over the nineties PSP technology was commer cialized in the aerospace industries. Companies like McDonnell Douglas, Boei ng, British Aerospace, and government research institution such as NASA, Offi ce National dEtudes et de Recherches Aerospatiales (ONERA) in France, to na me a few, have widely implemented PSP technology into the design and testing of their products (Bell et al., 2001). Photophysics of Luminescent Coatings Pressure sensitive paints offer a potentially promising substitution to current standard pressure measurement technique s in aerodynamic testing. The PSP method allows one to obtain not only qua litative pressure images, but also quantitative absolute

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7 pressure values at the desire d locations on the m odel, without introduc ing flow-disturbing probes or affecting the struct ure of the model surface (Engler et al., 2000). PSP can alter the nature of the surface r oughness affecting flow transition. However, PSP can be applied in very smooth layers and with careful design of both the paint and paint application such effects can be minimized Photochemically excited molecules are embedded in an oxygen permeable binder, and once excited with the appropriate wavelength they deactivate th rough different mechanisms, such as a process known as oxygen quenching, hence affecting the degree of luminosity. By means of photodetectors, such as a CCD camera or through a photomultiplier tube (PMT), the emission of these molecules can be recorded and translated to yield the true pr essure field. Two measurement techniques are implemented in acquiring the intensity field, the first known as the intensity based method, the other know n as the lifetime method. The details and comparison of both techniques can be found in the following references (Bell et al., 2001; Hardil et al., 2002; Liu and Sullivan, 2004; Zele low et al., 2003). This work adapts the former technique and is discusse d in detail in Chapter 2. Although PSP technology has improved, it is s till in its premature stages and many problems and concerns need to be addressed in order for the technol ogy to gain a better acceptance and implementation in aerodynamic testing. More details about the history and development of the luminescent t echnology, chemical formulations, decay mechanisms, paint preparation, accuracy a nd calibration/measurement techniques and systems are presented in Chapter 2 and can be found in even greater detail in the following references: Bell et al., 2001; Engl er et al., 2000; Liu et al., 1997; Liu and Sullivan, 2004 and McLachlan et al., 1995.

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8 Pressure sensitive paint technology is ba sed on photoluminescence, which includes both fluorescence (emission ~ 10-8 10-6 s) and phosphorescence (delayed emission ~ 103-100 s). Probe molecules are embedded in an oxygen permeable binder when excited by incident light they deactivate through diffe rent mechanisms, namely oxygen quenching, radiation and thermal quenching. The oxyge n quenching mechanism can be generally modeled by the Stern-Volmer relation (Oglesby, 1995): 21o qOI KP I (1.1) In this relation I is the luminescence, o I is the luminescence in the absence of oxygen, 2OP is the partial pressure of oxygen, and qK is the Stern-Volmer constant. The valueso I and qK are both functions of temperature. Equation (1.1) indicates an inverse relation between the partial pr essure/concentration of oxygen; hence the pressure, and the intensity. The constant qK is a measure of the sensitivity of the dye to pressure. For high values ofqK high accuracy of the pressure measur ement is obtained at low pressure levels, while low values of qK yield higher sensitivity at high pressure levels (Oglesby, 1995). Observing Figure 1-1 it is apparent that for higher qK values, as the pressure increases the intensity ratio o I I gradient becomes smaller (i.e., less sensitivity). This could result in low signal-to-noise ratio, whic h is most certainly the case in low speed wind tunnel testing where pressure varia tions are relatively small and close to atmospheric conditions, which can be accommodated by using PSP with lowqK. Low speed wind tunnel testing with PSP is quite ch allenging, and more effort is needed to

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9 identify probes with appropriate qKvalues, which could perhaps be tailored to specific test conditions (Morris et al. 1993). Figure 1-1 Stern-Volmer model for a range of qK It is not typically practical to create a reference condition, o I ,by purging the oxygen in the test cell, hence a more practic al approach is to use a known condition-say atmospheric-as the reference condition as s hown below in equation (1.2). Equation (1.2) reiterates the temperature dependenc e in the intensity, as the slope B T and the intercept A T are both functions of temperature. The Stern-Volmer approximation does reasonably well under two conditions: first, the ra nge of the test pre ssures is adequately sensible (limited), and second, the reference condition is near the pressures of interest. Note that in equation (1.2) the reference a nd run intensity are under isothermal condition Oxygen Partial

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10 to cancel out the temperature dependence; however, this approach is intrinsically impractical. refrun run runrun runrefIT P ATBT I P (1.2) Photodegradation, an intrinsi c concern with luminescent molecules, is the loss of intensity due to exposure of th e sensor probe to light. Molecu les are much more active in their excited state than in ground state and can react to certain compounds to which they are indifferent in ground state. Addition of such compounds to a sample containing luminophor causes luminescence lifetime and in tensity to decrease, a process known as quenching of luminescence and thus such compounds are accordingly named luminescence quenchers. All luminophor que nching processes are to some extent irreparable and consequently intense and continuous illumination of luminophors degrades luminophors illumination (Vollan et al 1991). This is the result of the singlet oxygen molecules produced through the oxygen que nching process, which are extremely reactive. They bond with nearby molecules form ing either non-luminescent molecules or causing deformations in the polymer matrix that lower measured intensities. Recent advancements in luminescent molecules and polymer sciences have nearly eliminated photodegradation of luminophors (Kose, 2005). Coating the surface of a m odel with paint can potent ially alter the airflow characteristics over the model, making the pain t intrusive. This intrusion can be in the form of actual physical alteration such as a dding thickness to the surface of the model or an alteration to the effective shape of the model, e.g., altering the boundary layer development (Schairer et al., 1998). Physi cal alteration does not necessarily imply a change of the roughness of the su rface; on the other hand, eff ective alteration is a direct

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11 result of roughness change of the surface. For example, a rougher surface due to the paint would lead to premature transition of the boundary layer, or it could have the opposite effect if the paint forms a smoother contact-s urface with the flow relative to the actual surface. Further, paint could affect readi ngs from the calibration pressure taps by rounding square edges or forming a prot uberance (disturbance) around the opening. Schairer et al. (1998) assert that the latter was not obser ved and if it was to be a concern then it would be detected as a consistent offset between the paint-on and paint-off pressure readings at every location and c ondition. The issue is further addressed by Vanhoutte et al. (2000), as they examined th e effect of the pain t under low speed, low Reynolds number and high subsonic conditions for a swept wing. Low speed examination showed that an increased surface roughness due to the paint yielded higher drag forces due to the prevention of the occurrence of a bursting laminar separation bubble. High subsonic speeds testing indicated the in creased roughness induced significant drag increase, while increased thickness showed le sser, but considerable, drag increase. The reader interested in more of the details a nd mechanics of PSP intrusion is encouraged to read Vanhoutte et al. (2000) and Amer et al (2001), as the subject is merely addressed here for completion. Statement of the Problem A principal concern with pressure sensitiv e paints is their inherent temperature dependence, an issue that remains unresolved in the literature. Other issues include: accuracy, feasible environmenta l range of application, time response, invasiveness and cost-effectiveness (Weiss, 2002). The accuracy of PSP measurements is affected by several factors that include model deformation, paint self-illumination, excitation source stability, image registration, and photoblea ching. Nevertheless, temperature dependence

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12 continues to be the primary source of error in PSP measurements as innovations in the fields of CCD fabrication, di gitizers and data processors have greatly reduced related errors associated with measurements. Liu et al. (2001) investigated the different sources of error in PSP measurements and concl uded that temperature effects dominate PSP uncertainty. Therefore, a calibration technique th at is robust and accurate is essential for PSP applications. Schanze et al. (1997) examin ed the different sources of the temperature dependence in an attempt to pave the way for identifying the appropriate solutions. The polymer they employed is a typical PSP formulation comprising a luminescent polypyridine Ru (II) complex dispersed within a poly-dimethylsiloxane (PDMS) binder. The dye is excited with blue light (450 nmex ) and luminesces strongly in the red wavelengths (max620 nm ). The formulation was tested over the 0-14 psi range and yielded a Stern-Volmer quenching constant SVK of 0.70 psi-1. Mathematically the intensity,em I and natural emission decay lifetime,em can be expressed as follows (Bell et al., 2001). 2 r em rnrqCk I kkkO (1.3) 21rnrq emkkkO (1.4) where C is a constant that linearly relates th e intensity to the quantum efficiency; and rnrqkkk are the radiative, non -radiative and oxygen quenching first-order rate constants, respectively. The deactivation pr ocess yields light only through radiative decay, while the other two decay m echanisms yield temperature.

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13 Figure 1-2 Jablonski energylevel diagram showing the absorption and emission processes for a typical luminescent molecule. As illustrated by Hager et al. (1975a, 1975b), the radiative decay is typically temperature independent. Further, Van Hout en and Watts (1976) characterized the general temperature dependence of the non-ra diative decay rate behavior with an Arrhenius function. They attempted to physica lly separate these diffe rent effects through the experiment to identify the main source of luminescence and its relative magnitude. They eliminated the oxygen quenching path by reducing the pressure to vacuum or simply deoxygenating the paint with an inert gas, i.e., argon. In such a case the ratio of intensity-lifetime is simply dependent on the nonradiative (tem perature) decay ratenrk Conversely, oxygen diffusivity in the bi nder, which is directly related toqk was the main

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14 source of temperature dependence under oxygen rich conditions. Schanze et al. (1997) tested the dye embedded in two different mediums, namely ethanol and PDMS. They concluded that the intrinsic temperature dependence is no t strongly influenced by the medium under vacuum or degassed conditions However, in the presence of air the lifetime temperature dependence is substant ial for a PSP sensor dispersed in PDMS, while it is almost non-existe nt when ethanol is the medi um. This is because the oxygen quenching pathway is characterized by much lower activation energy for ethanol in contrast to PDMS, which has typical activ ation energies on the order of 11kJ/mol. Activation energy is often used to denote the minimum energy needed for a specific chemical reaction to occur. Further, in the presence of oxygen, they found that oxygen quenching is the predominant decay mechanism (> 90% of the total decay). Finally, by comparing the lifetime emission of the pol ypyridine Ru(II) /PDMS in vacuum and in oxygen rich environment, they showed th at oxygen quenching is the main factor influencing the temperature de pendence due to the larger temp gradient, further suggesting that in the absence of oxygen the lifetime temperature dependence is solely due to the nonradiative temperat ure dependence. These results indicate that in order to minimize the temperature dependence, the medi um (binder) used must possess the lowest possible activation energy for oxygen diffusivity. Research Efforts A paper by Puklin et al. (2000) exam ined a PSP probe, PtTFPP, embedded in copolymer of heptafluoro-n-butyl methacrylate and he xafluoroisopropyl methacrylate (FIB), possessing an activation en ergy of 1.5 kJ/mol, which satis fies the criterion set forth in the previous work by Schanze et al. (1997) for low temperature dependence in PSP

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15 (i.e., low activation energy). They introduced th e concept of an ideal paint, which they define as one for which the Stern-Volmer relation (intensity-r atio) under isothermal conditions for the run and reference condi tion is approximately independent of temperature, and the intensity ratio under isobaric conditions is approximately pressure independent. In a simpler sense, any paint ca n be described as ideal if all the SternVolmer plots for different temperatures co llapse to a single curve under isothermal conditions. Hence, an ideal PSP can be more conveniently corrected for temperature dependency; however, this de finition of ideality is applicable only for a limited temperature range (Puklin et al., 2000). Idea lity provides the ease of determining the pressure value if both the temperature da ta and the intensity ratio under isobaric conditions are known, thus decoupling temperat ure data from any pressure dependency. Using a lifetime measurement approach under static conditions, they examined the dye for different pressures between vacuum and atmospheric pressure under three temperature conditions (10C 30C & 50C). Th eir results showed -0.6%/ C temperature dependence in the PSP. In a follow-up paper, Gouin (2000b) investigat ed the feasibility of achieving an ideal PSP by annealing the pol ymer. As they noted, annealing the paint (PtTFPP) made the paint behave ideally w ith very small temperature dependence (0.52%/C) with an almost identical slope under vacuum and atmospheric pressure conditions. They also found that non-anneal ed samples exhibit higher temperature dependence with a varying slope between vacuum and atmospheric conditions (0.54%/C and -0.80%/C respectively). The ann ealing process has to take place above the glass transition temperature, g T, of the polymer to achieve th is ideal behavior. Heating a polymer network above g T has the effect of relaxing the chains, loosening the

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16 entanglements in the network, and allo wing the system to achieve thermodynamic stability. This will ease oxygen diffusion through the polymer as the relaxation of the network implies fewer entanglements leadi ng to easier diffusion and lower activation energy. A third publication by the same group at the University of Washington (Gouin, 2000c) examined the effect of using a second base coat under the PtTFPP/FIB paint. Such combination typically results in an increase in the response time and the temperature dependence of the PSP. The accur acy of the PSP measurements depends on many factors, one of which is the uniformity of the model surface, as the light emitted by the PSP is not totally captured by the photodete ctor (CCD, PMT, etc.). A determinant of how much light is captured by the photodetector is the intrinsic reflectivity of the model surface. Reflectivity is defined as the ratio of reflected light intens ity to incident light intensity at the surface of a material that is considerably thick such that the reflectance is independent of the thickness; thus commonly described as the intrinsic reflectance of the surface. Surface reflectance is Lambertian (di ffuse), Phong (specular) or a combination of both. Ideal Lambertian surface apparent reflect ance is independent of the observer; i.e., the object brightness is indepe ndent of the angle between the observer and the surface. This contrasts with glossy surfaces, as the apparent brightness is highest when the observing angle is equal to the source angle. Most real objects have some mixture of Lambertian and Phong qualities. As models t ypically incorporate different materials on the surface, ranging from the actual material of the model to wax and Bondo material, variation of the reflectivity of the surface i nduces significant error accordingly. For that reason, a uniform base, known as a base coat, is typically applied to the surface to create

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17 a homogeneous canvas. A base coat is gene rally a polymer which is embedded with a white substrate (pigments), e.g., titanium dioxide, which possesses a high index of refraction and good dispersion in the polymer (high hiding power), but can sometimes photoxidize organic compounds when irradiated with UV (< 390nm). Unfortunately, base coats have been shown to influence PSP functiona lity. This is partially attributed to the change of the dynamic oxygen equilibrium of th e PSP layer as it interacts mutually with the surrounding air as well as the base co at. The combination eventually reaches equilibrium after a certain response time. The eq uilibrium process is directly tied to the oxygen diffusion in the polymers. This effect is only imperative when performing high frequency or transient measurements, as res ponse time is important. The more prominent effect is the apparent influence of the base coat on the temperature dependency of the PSP layer, which in turn can potentially yield adverse affects to the desirable temperature dependency characteristics, mentioned previously of an ideal paint. They examined five different base coats: FIB, polymethylmethacrylate (PMMA ), polyacrylonitrile (PAN), polyvinyl acetate (PVA) and a silicone (SR-900). Gouin et al ., (2000c) found that oxygen diffusion in the polymer is the main factor influencing the temp erature dependency as vacuum results were almost identical. Furt her, the oxygen concentration gradient that exists between the base coat and the PSP layer is the reason behind the direct influence of the base coat on the temperat ure dependency of the PSP, as different base coats would hold different concentrations. Comparing perm eable polymers (FIB and silicon base coat) versus impermeable polymers (PMMA, PAN a nd PVA) showed significant increase in both response time and temperature dependency at atmospheric conditions for the latter polymers except for PAN; the results are tabul ated below for convenience. Their results

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18 assert the importance of choice of a speci fic base coat for eac h particular PSP. Table 1-1 Response time and temperature depe ndency of PtTFPP/FIB with different base coatings Base-Coat Polymer Response time (sec) Temperature dependence@ atm. (/C) No base coat 0.6 -0.52% FIB 0.8 -0.56% PMMA 15 -1.06% PVA 7 -0.75% (-2% above 35C) PAN 0.9 -0.7% Silicone (SR-900) (PVC) of 44 % 1.1 -0.69% In Table 1-1 Pigment Volume Concentra tion (PVC) is defined as Gouin et al. (2000c). of pigmentof pigment of pigmentof pigmentofbinderofbinder massdensity PVC massdensitymassdensity (1.5) Their last publication in the series, (Gouin, 2000d), demonstrates how non-ideal paints can be idealized through the addition of inorganic pigments. They show that the diffusion of oxygen is affected by the addition of 0pigments to the polymer and that the decay rate behavior of the paint is affected as well; however, not all the quenching rate constants were affected. They further noticed that a specific concentration of pigments made the paint act ideally. Using fine grade (1-5 m) aluminum oxide (Al2O3) with pigment volume concentration of 31% they we re able to closely match the temperature dependence of PtTFPP at vacuum, yielding an ideal paint. Again, it is important to note that such ideality is pertinent to limited te mperature ranges and is othermal conditions. Woodmansee et al. (1997) investigated th e issue of temperature dependence as they examined three different PSPs and two TSPs formulations as well as four different temperature compensation methods. The pain t was applied to a transverse-jet-in-

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19 crossflow experiment. As the behavior of the specific paint is not of relative importance to this work and is well documented in th eir paper, reduction methods will be discussed herein and only related paint behavior if n eeded. They compared four different reduction methods: isothermal, in-situ K-fit and temperature corrected pressure. The isothermal approach, as implied by its name, ignores te mperature variations by assuming that the temperatures at run conditions are identic al to the calibration run. The calibration coefficients are obtained through a static cal ibration of a specimen and then fitting the data in a least squares sense. This approach under-predicts the pressu re as it ignores the temperature drop due to the operation of th e tunnel. On average, the isothermal calibration had an 8.0%f.s. drop relative to th e pressure taps measurements and 2.8%f.s. root mean square (rms) deviation. Nonethel ess, the predicted pressures mapped a similar trend as the pressure taps, which makes such an approach good fo r qualitative purposes only. However, this approach may be useful quantitatively if th e run images have a steady and identical temperature distribution, in which case the reference image must be acquired immediately after the terminati on of the each run of the experiments. The second approach, in-situ accounts for the temperature variation by placing pressure taps on the painted surface and using that pressure information to evaluate the calibration coefficients. However, pressure taps need to be positioned in predetermined locations to ensure the coverage of the enti re domain of the pressure test range (i.e., lowest and highest pressure areas). To ensure this, a run test prior to installation of the pressure taps with the surface painted may be necessary to obtain a qualitative picture of the pressure field. Further, adequate numb ers of pressure taps need to be positioned through the intermediate range to secure accep table accuracy in the results. The overall

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20 results for this approach showed that the in-situ method had the smallest error of all methods with 1.0%f.s. mean and 0.55%f.s. RMS differences. A hybrid technique between the earlier te chniques is the K-fit approach. It is typically implemented when the model lacks enough pressure taps to cover a wide enough pressure range. It relies on the fact that the pressure vs. intensity curves collapse if the run and reference temperatures are both identical (i.e., isothermal). This of course limits the experiments allowed by many constraint s, such as air-flow speed, geometry of the model, steady conditions, etc. Neverthele ss, as mentioned previously, if a reference (wind-off) image is acquired immediately af ter the run image, temperature variations should vanish in the normalization process, unless temperature gradients are severe and change significantly between the two runs. The K-fit approach empirically scales the reference image to emulate a reference image at a different temperature condition. This approach is better than the isothermal techni que with a 4.7%f.s. mean and 2.7%f.s. RMS differences, yet it is still inferior to the in-situ calibration approach. The last examined technique, temperature-co rrected pressure calibration, utilizes a temperature sensitive paint (T SP) to calibrate the PSP measurements. The TSP is applied to the model after PSP experiments and then the two images are a ligned to sub-pixel accuracy. Knowing the intensity ratio and the te mperature at each pixe l, a 2-D surface is constructed with the pressure as a function of both intensity ratio and temperature. This method eliminates the need for an in-situ pressure tap data. Unfortunately, the authors did not have great success with this approach due to several predicted problems such as photodegradation, shelf-life degradation and calibration su rface effects. The authors conclude by recommending a multi-step in-situ calibration.

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21 Hubner et al. (1997b) suggested a temper ature compensation model for PSP that was rather successful. Their work was motiv ated by the lack of a generic model of luminescent intensity in terms of pressure and temperature. They based their model on a Stern-Volmer with an Arrhenius-type temperature dependency. In general, oxygen sorption in an ideal and homogenous liquid is directly related to the partial pressure of the oxygen as described by Henrys law, assuming equilibrium between the oxygen within the binder and the oxygen above it: 22OOsTP (1.6) where sT is the solubility coefficient. Howeve r, as described by Hubner et al. (1997a), over expanded pressure ranges the solubility coefficient depends on pressure as well, 222,OOOsTPP (1.7) This leads to the redefining of the intensity -pressure calibration from equation (1.2) to extend it to higher order polynomial expansion, 2 refrun runrun runrefrefIT PP ATBTCT IPP (1.8) For limited pressure ranges, a linear solubi lity model can be used to estimate the pressure dependence. Large pressure ranges may be conveniently modeled with higher order polynomials; however, polynomials do not always adequately model the intensitypressure relationship. This is a result of the uneven dispersion of luminophors in binders, which leads to heterogeneous distribution of the luminophor within the binder causing molecular aggregation and consequently self -quenching of excited probes and multiple exponential decays (as opposed to single exp onential decays for luminophors dissolved in fluid solvent). Hubner et al. (1997a) propos ed a model based on sorption theory to

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22 compensate for these effects. For a given isotherm, the sorption model expands Henrys law by adding a non-linear term based on La ngmuirs model of penetrant immobilization, 2 2 221O lOnl OTP OsTPsT TP (1.9) where ls is the linear solubility coefficient based on Henrys law, nls is the non-linear solubility coefficient based on Langmuirs model and Tis the affinity coefficient ( of penetrantsabsorption desorption). Taking the limit of equation (1 .9) as the partial pressure of oxygen goes to zero and infinity reveal s a dual sorption (DS) model-equations 2 22 0limOlnl P OO ssT P (1.10) 2 22limOl P OO s P (1.11) Application of the DS model to equation (1.8) yields the prop osed model by Hubner et al. (1997a), 1ref ref runref refDPP I P ABC IP DPP (1.12) The coefficients (A, B, C & D) in this model are functio ns of both temperature and reference conditions. The model was applied to two PSP coatings and their results showed the superiority of their model rela tive to a second and even a third order polynomial, with a pressure ratio root mean square error (rmse)of 0.0004 and 0.001 for in-range and off-range data, respectively (PSP -A), which was also comparable to their second dye (PSP-B). The concern with this model is the difficulty in decoupling the

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23 temperature dependency of the sensitivity coe fficients as a direct result of the added nonlinear pressure terms, Hubn er et al. (1997b). This crea ted the motivation behind the subsequent work of Hubner et al. (1997b), as they proposed yet another model based on a Stern-Volmer with an Arrhenius-type temperature dependency. This model, unlike the DS model, has coefficients that depend only on temperature formulated from the radiative, non-radiative and quenching decay processes of the luminescence. They used a quadratic to model the solubility expansi on coefficient (i.e., PSP sorption). As they describe in their paper, the radiative decay is almost temperature independent and hence usually regarded as constant. On the other ha nd, the non-radiative de cay is significantly temperature dependent and is characterized by an exponential decay process in addition to an offset that is temperature independent. ,nrE RT nrnronrkkDe (1.13) The oxygen quenching process is governed by the sorption and the diffusion of the oxygen in the binder matrix, with Arrhen ius type decay approximation over small temperature ranges. This implies composite temperature dependence in Henrys law, namely the product of the oxygen concentration in the binder, 2O, and the Stern-Volmer constant, qk, hence the total activation energy is the sum of the activation energies of each process. Earlier in this review the work of Schanze et al. (1997) modeled the oxygen process as a simple exponential mainly depe ndent on oxygen diffusivity and established that oxygen quenching accounts for more than 90% of the total decay of the luminescent probe they used. The final form of Hubner et al. (1997b)s model is as follows:

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24 2 ref refrefI PP ABC IPP (1.14) where, ,,,,nrE RT ronronr refrefKKDe ATTP den (1.15) ,1,1,,qE RT q refrefDe BTTP den (1.16) ,2,2,,qE RT q refrefDe CTTP den (1.17) ,1,22 ,,,1,2qq nr refrefrefEE E RTRTRT ronronrqrefqrefdenkkDeDePDeP (1.18) The first coefficient, A, represents the radi ative and non radiative effects, while the second and third coefficients, B and C, characterize the oxygen quenching process. The coefficients are clearly a function of the r un as well as the reference temperatures. The activation energies, ,1,2,&nrqq E EE, the rate constants k, and the factors premultiplying the exponential decay terms are to be dete rmined by performing a standard emissionlifetime calibration. These coefficients are functions of the specific luminophor properties and binder characteristics. None theless, as stated already, run temperature information is still needed to evaluate the coefficients. Plot ting these coefficients as a function of the run temperature it was clear that the coefficient, A, was relatively temperature independent, while the other coefficients are noticeably te mperature dependent. The authors appeal to the need for dual-luminophor paint, a pa int containing two pr obes that measure pressure and temperature simultaneously a nd independently, which would provide the temperature information needed for calibration. Their model predicted the pressure with

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25 rmse of 0.011 and absolute pressure uncertain ty of 0.2 psi. Such high uncertainties in the measurements may not be tolerable in many applications, moreover; their results were based on 70 isotherms, underlining the difficulty in obtaining temper ature corrections for PSP measurements. Given the various limitations and requ irements for selecting a practical combination of an oxygen sensor and a suitable binder, another proposed solution included adding non-oxygen quenched temperat ure-dependent phosphor to the paint to map out the temperature field and correct for temperature dependence. Coyle and Gouterman (1999) attempted to correct for lif etime measurement usi ng such an approach. They defined a criterion for ideal TSP th at can be co-embedded with PSP in a dualluminophor formulation. The TSP criterions are: 1. Excite in the same spectral region as the PSP 2. Emit at a sufficiently different spectral region 3. Exhibit strong temperature dependence 4. Exhibit no pressure dependence The PSP sensor of their choice was pl atinum meso-tetra (pentaflurophenyl) porphtyin (PtTFPP), which emits around 650nm, as for the temperature sensor they utilized the phosphor La2O2S:Eu3+, which emits strongly at 514nm (Struck, 1970), both embedded in a (FIB) polymer. Both sensors are excited in the UV range, 337nm and 392nm for La2O2S:Eu3+ and PtTFPP respectively. The two dyes were prepared separately and the temperature dye was sprayed first a nd allowed to cure overnight and then the PtTFPP/FIB was sprayed on top of the existi ng film. Inspecting the emission spectra of both dyes separately one can obser ve that the emission of the La2O2S:Eu3+ overlaps with the excitation and emission of the PtTFPP, which could potentially lead to spectral interference. Maintaining a constant pressu re field across the sample, but varying the

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26 pressure between each run (0-1atm.), the te mperature emission was recorded and it was completely independent of the pressure be tween the range of 10-50C with a lifetime decay-to-temperature slope of 1.9%C and they were able to fit the emission to an Arrhenius function, as predicted by the theo ry. Their temperature calibration yielded a root-mean-square error of 1.11C for 20 differe nt data points. PtTFPP showed a lifetime decay temperature dependence of -0.3%/C under vacuum conditions. To calculate the pressure they used the following 2nd order relation: 2 vacvacPabc (1.19) Implementing the previous equation as th e calibration function to determine the pressure and temperature for fifteen differe nt environmental conditions, five pressures and three temperatures, their re sults yielded a maximum absolute error of 3.0C, with the error in the predicted temper ature increasing with the increase of temperature. The corrected pressure measurements had a maxi mum error of 4% and an average error of about 1%, while the non-corrected data had a maximum error of 16%. The authors argue that the difference between the emissions of PtTFPP and the combined dual-paint is not due to the interf erence of the 615nm emission of the La2O2S:Eu3+ with the PtTFPP emission, as they have observed La2O2S:Eu3+ emission at 625nm on the order of 400 s, while their observation of PtTFPP decay curv es fit to a double exponential model did not have a 400 s component, yet they fall short of offering an alternative explanation. Research at the University of Florida unques tionably indicates a cha nge in the intensity emission behavior of the PSP sensor with the addition of the TSP sensor; however, as our results are based on intensity measurements co mpared to lifetime measurements approach

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27 by Coyle and Gouterman (1999), the author de sists from disputing their rationale. In a paper presented by Ji et al. (2000 ) a temperature independent PSP based on a bichromophoric luminophor was de veloped and tested. In cont rast to prior work that typically utilized metalloporphyrins or polypyridine rythenium (II) complexes as the luminescent probes in formulating PSP, they used supramolecular assemblies. Supramolecular assemblies are two or mo re luminescent chro mophores that are chemically bonded together (Balzani et al., 1991), they often posses photophysical properties that are distinct fr om those of the isolated units. They used Ru-pyrene as the luminescent probe utilizing its very long-lived exited stat e (Simon et al., 1997). As illustrated by Hager et al. (1975a and 1975b), under vacuum conditions the radiative decay for PSP complexes is typically temperat ure independent. Furthe r, Van Houten and Watts (1976) successfully characterized the general temperature dependence of the nonradiative decay rate behavior for Rutheniu m complexes with an Arrhenius function. Under oxygen rich conditions, close to atmos pheric levels, the radiative and thermal (non-radiative) decay rates contribute insi gnificantly towards th e overall decay rate relative to the oxygen quenching. As described earlier in this revi ew by Schanze et al. (1997) this implies that under these conditions, the temperatur e dependence of the paint is mainly characterized by the temperature de pendence of the oxygen quenching decay rate (i.e., oxygen diffusivity in the binder), whic h is also commonly characterized by an Arrhenius type decay. Intermediate conditi ons between vacuum and atmosphere are characterized by a composite PSP temperat ure dependence behavior of the two previously mentioned states (i.e., vacuum and atmosphere). The probes excited state lifetime has moderate temperature depende nce; nonetheless a nearly temperature-

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28 independent Stern-Volmer calibration is co incidentally feasib le under isothermal conditions between the run and reference imag es (i.e., ideal paint). The Stern-Volmer relation is expressed as: ,0 1 ,orun qrun runITp KTp ITp (1.20) Differentiating this expression with respect to temperature and equating it to zero would set the condition needed to achieve a non-temperature dependent Stern-Volmer constantqK Through some mathematical ma nipulation and assuming that nrrKKthe condition yields 1d nrE E where E is the activation energy and subscripts d and nr refer to oxygen diffusion and non-radiative decay, resp ectively. In a simpler sense, if the temperature dependence of the oxygen diffusi vity in the binder and the temperature dependence of the non-radiative decay are nearly identical (i.e., slope), then the paint can be described as an ideal paint. They attempted to incorporate the sensor in PDMS as a binder, but the sensor had a poor emission, consequently they synthesi zed MPP acrylate polymer binder, which is relatively polar, hence able to dissolve polar transition metal salts contrary to PDMS. Subsequent to establishing the calibration cu rves and plotting the results, the SternVolmer plots, for temperatures of (25-55C) over a pressure range of 0.005 atm to 1 atm, coincided almost exactly, hence indicati ng that the Ru-pyrene/MPP Stern-Volmer calibration is temperature independent over the specified range of conditions. They reiterated the same examination using a diffe rent sensor, namely PtTFPP, with the same binder MPP and the results showed that th e temperature-independence Stern-Volmer behavior is unique to the Ru -pyrene/MPP system. Finally, they examined the lifetime

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29 emission (luminescent decay rate) to determin e the activation energies for each sensor under close to vacuum conditions and at 1 at m in order to separate the oxygen quenching and non-radiative decay channels. The Ru-pyr ene/MPP system had an equivalent decay rate, which is synonymous to equivalent ac tivation energies, t hus verifying their temperature-independence criterion stated in advance. On the other hand the PtTFPP/MPP system had different activation ener gies. This work showed that ideal paint formulations greatly hinge on the appropria te selection and matching of both the luminophor and the polymer. Another approach suggested in the lit erature is adding an environmentalconditions-independent sensor that is embedded within the formulation of a dualluminophor PSP to provide an internal referen ce, thus replacing the wind-off image, and using an intensity based approach to resolve the pressure and temperature. The feasibility of such a concept was investigated by S ubramanian et al. (2000 and 2001) where they implemented a non-pressure se nsitive paint (NPSP) sensor to utilize as a reference sensor. As the paper points out, it is nearly always the case that when two sensors are mixed together in the same paint matrix, spectral interference is inevitable. The sensor emitting in the lower part of the spectrum could influence the excitation and thus the emission of the other sensor emitting at higher wavelengths. This interference is very hard to resolve and could lead to more error in the data in addition to the already existing temperature dependence error. Theoretically, any added sensors to the PSP sensor should be excited in the same spectral domain and emit at the same wavelength, in order to eliminate multiple excitation sources and the need for a filter wheel on the camera, hence limiting the available choices of sensors. Th is can be accomplished by means of one of

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30 the following two methodologies. The same pressu re sensor can be utilized except that it would be embedded in an oxygen impermeable bi nder. This approach is impractical due to the infeasibility of crea ting a completely oxygen impe rmeable binder, knowing that any oxygen diffusion in the binder would certain ly lead to serious errors. The second approach is to utilize a sensor that is not quenched by oxygen and is temperature insensitive. This necessitates that such a se nsor emits at a different wavelength than any other sensor embedded in the same paint matrix in order for it to be entirely distinguishable from any other emission in th e spectrum. The emission from this sensor would then serve as the reference for each in dividual run and thus eliminating wind-off referencing. Further advantages to such an approach include: the potential of using the NPSP for correcting temperature dependence if it was possible to match the temperature effects of both PSP and NPSP, and the NPSP can be used as a target-marker for model deformation determination during wind-tunnel testing. Subramanian et al. (2001) avoided mixing the two sensors together, instead they applied the paints separately on different part s of their test specimen (disk) with a dark ring separating both dyes, conceivably to avoi d spectral interference; nonetheless, such a compromise may not be always tolerable. Th ey used six different combinations of PSPs, PSP binders, NPSPs and NPSP binders. The environmental range in which they conducted their experiments ranged between 0.001-2.7 atm and from 15-35C. Their results conclude that at c onstant temperature the NPSP wa s reasonably invariable with the change of pressure and that the PSP had an order of magnitude higher rate of change with pressure. However, upon imposing a temp erature gradient on the specimen, there was an obvious variation in the calibrati on curves, due to the inhomogeneity of the

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31 temperature dependence between PSP and NPSP sensors. The PSP showed temperature dependency even under isothermal conditions fo r the run and reference intensities. This fact forced them to concede th e infeasibility of their appro ach to correct for temperature dependence. They further investigated whethe r a spectral cross-talk exists between the two luminophors by eliminating the dark ring and it was not evident in some formulations, but it was significant in other formulations; nevertheless it was minimized when a dark ring separated the two luminophor s. They observed spectral leakage when the NPSP and the PSP had the same luminescent probe embedded in a different binder, non-oxygen and oxygen permeable binder, respectiv ely. However, they affirmed that none of the binders were absolutely oxygen impermeable. The department of chemistry at the Univer sity of Washington, Khalil et al. (2004), has collaborated with Innovativ e Scientific Solution Inc. (ISSI) and presented a paper in which they did similar work to that of S ubramanian et al. (2001). Khalil et al. (2004) point out in their paper that internal reference methods avoi d several problems that arise with intensity measurements such as light source changes, index of refraction, optical geometry variations and fluctuations in film thickness and dye concentration. They based their experiment on a technique called the yard stick, which is in essence similar to having two sensors, one of which is affected by a speci fic factor, e.g. pressure, while the other is independent of that factor. Th e latter then serves as a refe rence for corrections. For that they experimented with a near infrared porphyrin sensor, namely platinum tetra (pentafluorophenyl) porpholacton e PtTFPL. The sensor em its around a distant 733nm, allowing for another reference dye to be added without the concern of spectral interference. The reference dye of their choice was magnesi um tetra (pentafluorophenyl)

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32 porphine (MgTFPP), which luminesces at 650nm The two sensors were dispersed in a FIB polymer, taking advantage of its relativ ely low temperature dependence effects and its consistent temperature dependence at v acuum and atmospheric conditions. In their experimental setup, both dyes are excited at 460nm 10nm, with two CCD cameras equipped with the appropriate filters capturing the intensity emission. Their environmental operational range spanned temp eratures between 5 and 50C (the ideal range in which the PSP/FIB behave ideally) and a pressure ranging from 1 to 21 psi. Their results show that the pressure sensor and the reference dye exhibit temperature dependency. Nonetheless, by ta king the ratio of the referen ce sensor to the pressure sensor they were able to reduce the temp erature dependency to -0.1%/C, which is a significant reduction from 0.6%/Cfor the Pt TFPP embedded alone in the FIB polymer. As they concede in their work, these results would be close to unatta inable if there was any spectral interference be tween the two sensors, thus limiting the pool of sensor/reference/binder candidates available. Fu rthermore, these results are limited to a specific temperature range which imposes fu rther limitations on test ing conditions. In a subsequent work, Zelelow (2003), they replaced the reference sensor with a temperature sensor, namely tri ( -diketonate) phenanthroline europi um (Eu chelate complex), which is virtually an oxygen independent sensor that emits around 615 nm. The results closely matched their previous work with the temp erature sensor providing the potential to resolve temperature gradients as small as 0.001C. However, the luminescence intensity temperature coefficient for PtTFPL increased to 0.33%C. It is furthe r noted the cost of the material used in synthesizing both of thei r coatings is rather expensive relative to

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33 other available systems.1 They applied their formulation to an automotive model, Gouterman et al. (2004), and their results yi elded an rms of 0.06 psi for the in-situ calibration. As the TSP has -0.25%/C temperat ure sensitivity, they were able to reduce the temperature sensitivity of the PSP from -0.32%/C to -0.07%/C. However, they assess that the corresponding 33% percent improvement in temperature correction (reduction in rms) is below expectation for su ch reduction in the temperature sensitivity. They did not provide actual quantitative estim ates of their error, nonetheless, their Cp figure shows certain discrepancies between predicted and actual measurements. Their formulation suffered from considerable photode gradation (0.5%/hour at 1 bar and 40C). Their approach shows potential for dualluminophor PSP to resolve the temperature dependency issue, and a more robust data reduction and analysis technique would optimize results. Similar work presented by Mitsuo et al. ( 2003) utilizes a temperature sensitive dye for temperature compensation in dual-lumi nophor PSP. The temperature probe of their choice was Rhodamine B (RhB), which ab sorbs in the UV range and has a broad emission starting at 550 nm and extending to 750 nm, with peak emission around 580 nm. The PtTFPP peak absorbance overlaps with the tail emission of RhB, which couples the PtTFPP emission with the RhB emission. This phenomenon is known as cross talk, which makes decoupling pressure and temperature information from the spectral emission fairly complicated. They modeled th e temperature by a fourth order polynomial and the pressure by a third or der polynomial. By first compensating for the temperature effects in the emission intensity of the PtT FPP using the wind on temperature information 1 Personal communication with Kose

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34 and information from the PtTFPP calibration cu rves, they estimated pressure calibration coefficients that are temperature independe nt. The pressure sta ndard deviation was around 6%f.s., while the temperature estimat es incurred a 1.5 K error. Once more, resolving spectral interference using simple calibration procedure has proven to be insufficient for accurate results, and the need for a more profound mathematical approach is inevitable. Compensating for the temperature sensit ivity in PSP using a co-embedded TSP falls under two categories, compensation using absolute temperature measurements, or by matching the temperature sensi tivity of the PSP (Goss et al ., 2005). The later is obviously more convenient; however, it can only be app lied to ideal paint measurements as ideality indicates that the paint possesses constant te mperature sensitivity. Non-ideal paints have variable temperature sensitivity; hence absolute temperature information is needed for practical measurements. PtTFPP embedded in FIB, as mentioned previously, is classified as an ideal paint, thus most functional dua l-luminophor systems employ it as the pressure probe. A question that is recurrently raised when using luminescent coatings is whether to use intensity based systems or a lifetime decay approach. Hardil et al. (2002) asserts that intensity based systems are quite complicated due to the added excitation sources, windoff image and filtering system. They offer an alternative approach in which they have formulated a new oxygen-permeable sol-gel-based paint, cont aining both temperature and pressure luminophors. The fluorescence decay times of the two luminophors are separated by several orders of magnitude, which allows for the luminescent decay measurement to be separated in the time domain. In addition the two luminophors have

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35 been chosen such that they have similar ex citation and emission sp ectral regions to avoid multiple filtering regions and multiple excitation sources; hence image registration issues are completely avoided. Gouterman et al. ( 1997) explains the differe nce between the life time approach, adapted by Hardil et al. ( 2002) and intensity based approach, more commonly implemented and is the adapted tech nique in this work. The lifetime is an intrinsic property of the luminophor, which, unl ike intensity, is virtually independent of external perturbations; hence the requirem ent for a wind-off image is eliminated. Nonetheless, lifetime is still dependent on temperature and hence a correction is still required. Gartenburg et al. (1991), attempted to solve the problem by implementing an additional infrared camera to provide a temp erature correction for the pressure. Others (Alaruri et al., 1999 and Coyle and Gouterma n, 1999) added an additional temperature sensitive luminophor to provide the temperatur e data for correction, which still required added cameras, excitation sources and filters. Hardil et al. (2002) approach follows previous work done by Bedwell et al. (1998) with the exception that they implement an array of LEDs rather than a laser for excitati on. In addition, the work is specific for solgel-paints, [Ru (dpp) 3]2+. It is worth mentioning that the intensity ratio, defined in equations (1.1) and (1.20), is equal to the lifetime ratio, 0 except that the absolute value of the reference and run lifetimes are independe nt of external pertur bations. Hardil et al. (2002) lists three conditions for an ideal temperature luminophor: 1. It has the same excitation wavelength as the PSP luminophor 2. It is completely insensitive to oxygen 3. Has a significantly different decay time compared to the PSP luminophor

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36 Most two and three-component systems that have been developed satisfy the first two conditions, while the third condition is a disputed topic. The question then is how do the two measurement systems compare to each other? Unlike the intensity based method, lifetime approach requires that both the exc itation source and CCD camera be triggered with a delay shift between them, otherwise the CCD camera may incorporate extraneous light from the excitation source. This introduces complications into the control system, especially when decay times could be on the order of nanoseconds, and error could be easily introduced in the system if extraneous light is leaked into the measurement, which could be hard to detect as well. Not to me ntion the degree of sophi stication required in the CCD camera in order to be able to handle such short exposure times. Furthermore, for each condition, different exposure time for di fferent triggering cycles, usually on the order of 300 cycles, is required and need to be integrated in the same image frame. Other complications rise from the fact that in such a process, it is always assumed that the luminescence from the excitation source is absolutely constant and that the PSP luminophor decays to zero during the excitation sequence. The latter is not an issue for the intensity based system, while the effect of the drifting of the excitation source is not as nearly as significant compared to the lif etime system. As reported by Hardil et al. (2002), due to this drifting effect, their SNR was low enough to induce a temperature error of 3C. Proper Orthogonal Decomposition (POD) POD, also known as the Karhunen-Lov e expansion after Kari Karhunen and Michel Love, is a classical statistical technique that is often implemented to simplify/decompose a dataset. First introdu ced by Kosambi (1943), POD is a method of identifying patterns in data, and expressing th e data in a certain least squares optimal

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37 sense. Data patterns are often hard to identify, especially in dataset of high dimensionality, where graphical representa tion is unfeasible. It makes possible the reduction of multidimensional systems to lower-dimensional approximate descriptions (Chatterjee, 2000). Implementations of POD are mainly in dynamic testing, image processing, signal processing, and general data compression. Practical applications include identifying coherent structures in turbulence, vibration analysis, astronomy, combustion analysis, and chemical substan ce identification, to name a few. POD entails a mathematical procedure that transforms a number of potentially correlated variables into a smaller number of uncorrelated variables known as principal components. The first principal component fo rms an axis that acc ounts for the largest variance in the data, and each succeeding component accounts for as much of the remaining variability as possible. From a purel y mathematical perspective, it is a linear transformation that chooses a ne w coordinate system for the da ta set such that the greatest variance by any projection of the data set comes to lie on the fi rst axis, the second greatest variance on the second axis, and so on. In simpler terms, it provides a spatial basis for the modal decomposition of a system of functions. It enables the extraction of basis functions commonly called eigenfuncti ons. Quintessentially, it is an efficient procedure that captures dominant components of multidimensional systems and then reconstructing the system to the desired preci sion by using the relevant set of modes, effectively reducing the order of the system. POD entails two main objectives: the reduction, sometimes even characterization of the dimensionality of the dataset and recognition of fundamental fact ors (e.g. coherent structur es in turbulence, exhaust gaseous compositions, etc.).

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38 A key advantage of POD is its abilit y to generate an abstract modal decomposition that is data dependent wit hout any prior understanding of the process yielding the data. This enables the extracti on of the principal factors where a priori knowledge of the driving potential is insuffi cient to guide the basis function selection (Rathinam and Petzold, 1993). Moreover, unlik e traditional linear transforms, POD does not have a fixed set of basis vectors; rather its basis vectors depend on the data set. This means that POD can be used for reducing dime nsionality of the dataset without altering the key characteristics of the dataset that c ontribute most to its variance by eliminating the relatively less significant components. POD is often confused with one of its s ub-processes, namely Principal Component Analysis (PCA), which identifies the process by which raw eigenfunctions are established. The details are provided in Chapte r 3, nonetheless it is su fficient at this point to note that POD involves more than the basi c extraction of the moda l factors, it further works to transform this abstract solution to physically significant solution; however, this transformation then involves an intuition or feel for the expected reduced modes. A paper published by Carroll et al. (1999) explored the idea of using POD to separate the pressure and temperature information as well as for temperature compensation of the pressure calibration functions of measurements from dualluminophor coatings. As stated previously two main problems emerge with dualluminophor systems: spectral in terference between the two pr obes and cross talk between the two probes (i.e., emission overlap and abso rption of emission of the lower wavelength probe by the higher wavelength probe, resp ectively). As described previously, any spectrum contains different variations embedde d into it; nonetheless, one should be able

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39 to account for a finite number of independent parameters that constitute the spectrum (Carroll et al., 2002). These independent para meters would vary in the magnitude and range at which they contribute to the spectrum, hence allowing us to extract the main parameters that form the spectrum and easil y separating each parameter and identifying it with a physical parameter that we are intere sted in. Once these com ponents are obtained a new spectrum is constructed which contains the direct contribution of such parameters of interest omitting extra factors that may well be of no interest or inherently unwanted contributions such as noise. The process simply hinges upon finding the eigenvectors and eigenvalues of the data matrix Once these are established, the eigenvalues are compared and the largest n number of eigenvalues and their corresponding eigenvectors are used only to reconstruct the spectrum. The numbe r of eigenvectors selected depends on two aspects: how many factors one expects to be the main contributors and the relative expected ratio between the smallest eigenvalue, the factor with the least contribution and effect, to the largest eigenvalue. These cr iterions depend on the application and the degree of accuracy desired in the reprodu ced spectrum. A thorough description of the mathematical analysis is presented in Chapte r 3 and the reader is encouraged to read through Malinowski et al. (2002) for a full a nd comprehensive mathematical derivation and explanation of POD. Carroll et al. (1999) selected two luminophor s such that one is purely temperature dependent while the other is both pressure and temperature dependent. The full spectrum was collected through a spectrophotometer for c onstant temperature and varying pressure and vice versa, to ensure the behavior of each dye. They analyzed the full spectrum using the POD and yielded the need for three factor s to accurately reconstruct the raw spectra

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40 and to compensate for mutual interactions between the two lumi nophors. They managed to restrain the average percen t error in the retrieved envir onmental conditions to within 2%. However, the work did not perform the an alysis on a discrete set of data (using CCD camera), and they performed basic orthogona l rotation. The work presented initial characterization of POD, howev er, it stopped short of fully ev aluating POD application to dual-luminophor paints by applying it to variou s coatings with different compositions and implementing a real case experiment where more involved data are obtained. In a subsequent paper Carroll et al. (2001), reiterated their applic ation of the POD analysis to the same dye (Ruphen/Coumarin-7) they experimented with before and a new dye/polymer coating, namely PtTFPP/Diet hyloxadicarbocyanine iodide (DOCI). They concluded that unlike the Ru system, th e PtTFPP/DOCI data can be adequately represented with only two factors. Howeve r, their calibration curves for the DOCI showed some temperature dependence and they limited their calibration functions to a one-dimensional function. Further, they did not explore non-o rthogonal rotation or surface rotation. Their pressure calibration yi elded a percentage error between 0.32% and 1.3%. Nonetheless, they established the pot ential for POD to serve as data reduction technique for dual-luminophor PSP paints. Kose (2005) developed a dual-luminophor system (PtTFPP-Ru(phen)/PAN /PolytBS-co-TFEM) which was successful in providing accurate pressure and temperature information implementing POD to resolve the data. Mathematical characterization and implementation of the POD was develope d by the author and the calibration was collaboratively performed yielding very low e rror estimates of pressure and temperature. The main objective of the work was to fo rmulate a successful dual-luminophor system

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41 and to perform static testing to assess potential success in wind tunnel testing. Motivation and Contribution Pressure sensitive paints have been gaini ng acceptance in the practical market of aerodynamic testing; however, th e technology is still short of being easily and universally applicable due to several difficulties that re quire resolution for the technology to reach its full potential. The full scale and practi cal implementation of dual-luminophor PSP technology is hindered to a great extent by th e inherent temperatur e dependence of the paint. Aerodynamic testing can involve unavoidable and considerable temperature variations over the surface of the mode l and successful PSP implementation hinges on eliminating temperature effects that induces error in pressure field measurements. Various efforts have been addressing the issue in pursuit of satisfactory resolution including: PSP coatings with low temper ature dependence (Gouterman et al., 1997), various mathematical error reduction and calib ration models (e.g. isothermal and K-fit) (Hubner et al., 1997a; McLachlan et al., 1993; Woodmansee et al., 1997), simultaneous TSP imaging to provide a pi xel-by-pixel temperature compensation (Woodmansee et al., 1997), adding an environmentally independent sensor to replace wind-off reference (Subramanian et al., 2000 and 2001) and most promisingly a TSP luminophor that is coembedded in the same binder with the PSP in a dual-luminophor system.(Coyle and Gouterman, 1999; Khalil et al., 2004; Mits uo et al., 2003 ; Zelelow et al., 2003).

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42 Table 1-2 Research effort treating PSP temperature effects Calibration technique Advantages Disadvantages In situ isothermal calibration: Acquire wind-off images at atmospheric conditions The simplest approach Suitable for isothermal conditions Temperature effects can not be accounted for Calibration R.M.S. error on the order of 1.25 psi for PtTFPP/FIB (Bell et al, 2001) with pressure range of 29 72.5psi. Calibration r.m.s. error on the order of 0.2 psi for ODU PSP (Woodmansee et al., 1998), with pressure range of 1 15.4psi. In situ calibration: Acquire wind-off images immediately after wind-on conditions Easy technique Temperature effects absorbed in calibration coefficients Need to ensure temperature stability Wind tunnel must be turned off Limitation on number of images that can be acquired for reference condition, especially for long exposure times, due to temperature drift from wind-on conditions. Significant temperature variation between different parts of model require local calibration and pressure taps A priori calibration Few pressure taps scattered over the model are needed More controlled environment for calibration More efficient for practical applications (less time spent in the wind tunnel) Separate experiment for calibration in required Need to have a prior knowledge of expected pressure and temperature levels in the experiment to optimize the calibration process Pressure taps need to encompass the pressure range, and hence any sharp pressure gradients could be unobservable Temperature information must be obtained on the model using TSP (symmetric models with symmetric flow conditions). Asymmetric models or flow conditions can be mapped for temperature using dualluminophor systems Same batch of paint must be used for both calibration and experiment Calibration functions are typically biquadratic in pressure and

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43 Table 1-2 Continued Calibration technique Advantages Disadvantages temperature (Bell et al., 2001), necessitating a minimum of 9 points of calibration points with both pressure and temperature information Calibration r.m.s. error on the order of 0.021psi for OPTROD PSP (Bell et al., 2001), with pressure range of 0.75 14.7psi Ideal paints: Hybrid technique ( K -fit calibration) Simpler than a priori calibration (only one temperature condition is calibrated for a priori ) Useful for ideal paints when extrapolation beyond pressure taps range is needed Superior to in-situ isothermal calibration Inferior to in-situ calibration In some experiments, the K factor is pressure dependent, yielding a more complicated calibration Calibration r.m.s. error on the order of 0.99 psi for ODU PSP (Woodmansee et al., 1998), with pressure range of 1 15.4psi. Separate temperature measurement using IR camera Non-intrusive Reasonably accurate (standard uncertainty of 0.202 psi) given high temperature gradients Ineffective for Mach number less than ~ 0.75 (Kammeyer et al., 2002) Multiple cameras required to cover all surfaces Increased processing time Added uncertainty due to the IR camera system Separate temperature measurement using TSP Calibration procedure is simple Only two filters are needed In situ calibration, hence less cost No chemical interaction between P/TSP and no spectral interference Limited to symmetric models and conditions Thickness and roughness of PSP and TSP are difficult to match, hence surface flow conditions are typically different. PSP uncertainty limited by TSP uncertainty Thermocouples needed for TSP calibration

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44 Dual-luminophor systems have suffered from spectral interferen ce and cross-talk problem that yielded high errors in meas urements and difficulties in the calibration process. POD technique, first implemented to dual-luminophor systems by Carroll et al. (1999), showed the potential for resolving such issues mathematically. Nonetheless, full characterization and application of POD to pa int systems is yet to be carried out that would present a better unders tanding of the mathematical process and relate it to the physical properties of the paints, hence al lowing for optimal optimization and resolution of the data. Furthermore, a real-case test appl ication of the paint would serve to validate both the paint formulation and the analysis process and to furthe r address the various issues associated with acquiring measurem ent with dual-luminophor paints under flowbased conditions. A successful dual luminophor system has been developed by the Schanze group at the University of Florida (Kose, 2005), using the formulatio n PtTFPP-Ru(phen)/PAN /Poly-tBS-co-TFEM. The paint has been calibra ted and tested in collaboration with the author under static condition (vacuum cham ber), and POD method has been applied to correct for temperature effec tively. POD was capable of separating the pressure and temperature information with pressure and temperature 95% confidence error estimates of 0.1 psi and 0.4 K, respectively. Full char acterization and application of POD to paint systems is essential in order to completely understand the mathematical process and relate it to the physical prope rties of the paints, hence allo wing for optimal optimization and resolution of the data. Most importantly, full assessment of POD as a calibration technique is needed and a comprehensive an alysis including uncertainty estimates would establish the feasibility of POD a calibration technique.

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45 A channel flow experiment is utilized to evaluate the paint. The channel flow experiment provides a well controlled e nvironment with existing analytical solutions/approximations. A temperature gradient will be imposed both along and/or across flow direction to simulate seve ral cases of boundary conditions. The overall accuracy and uncertainty analysis will be assessed to evaluate POD as a calibration technique. Further, other calibration tec hniques are discussed and compared, when possible, to examine the effectiveness of PO D relative to existing calibration techniques.

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46 CHAPTER 2 LUMINESCENT COATINGS This chapter presents a fundamental de scription of pressure and temperature sensitive paints and the process of acquiri ng measurements and reducing and processing intensity data. The information presented herein is intended for readers acquainted with the subject. More detailed discussion a nd information is provided in Appendix-A. Overview Resolving the pressure and temperature fields is a typical requisite in nearly all experimentation in the field of fluid mech anics and aerodynamic testing. Surface pressure information is imperative in characterizing various flow phenomena from boundary layer separation/reattachment and sh ear layers to shock wave impingement on surfaces. It is further employed in computational fluid dyna mics (CFD) validation and perhaps more commonly in calculating the various aerodynamic loads such as lift, drag, wing torsion, etc. Temperature measurement is vital in supersonic and hypersonic flows and in flows involving significant heat transf er. Typically, holes are drilled in the surface to allow for pressure taps and thermocouples in orde r to measure pressure and temperature, respectively. Such practice could compromise th e structure of the model, the flow field, the accuracy of the measurements or the overall practicality of the experiment. Furthermore, the resolved field is only a di screte representation of the full field true distribution and hence an inte rpolation, or yet worse an extrapolation, procedure is required to resolve the full field leadi ng to added inaccuracies in the data.

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47 The Ozone Accident While working on a an experiment intended to measure the rate of photolysis of ozone in the atmosphere at the University of Michigan chemistry laboratory R.R. Dickerson stumbled on an idea that was de stined to inspire a new field for flow measurement (Dickerson and Stedman, 1979). As they were in the midst of running the experiment, some ozone seeped out and str eamed over a black light poster (UV sensitive fluorescent screen) that was illuminated by mercury lamp (i.e., UV radiation). The streaming ozone induced an illusion of sm oke plumes, which left the poor chemists scrambling for the source of the fire puffing the smoke. A short-lived thrill is broken by the realization of Dickerson th at the plumes are simply the shadow of the ozone over the black poster. The ozone absorbed some of the UV radiation as it passed over the black poster and hence lesser light intensity il luminated the black poster, thus lowering its emission intensity. At the time, helium bubble flow visualization techniques seemed fascinating, and smoke and density change t echniques were nothing short of a scientific marvelous. Compared to these techniques, ozon e was superior in many aspects, from its excellent tracing properties to its relative inexpensivene ss to its character as a nonintrusive technique. There is just only problem with ozone; it is totally invisible to the human eye, which might raise some eyebrows of skeptical experimental aerodynamicist. Dickersons observation surely provided a resolu tion to the issue, but more importantly, it inspired two biomedical engineers at the National Institutes of Health, Maryland to develop a new flow visualization techni que based on oxygen quenching of fluorescence (Peterson and Fitzgerald, 1980). John Peterson and Raphael Fitzgerald founded the field of flow measurement

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48 techniques using luminescent coatings The diminution of phosphorescence of luminescent dyes in the presence of oxygen was first discovered by Kautsky and Hirsch (1935). Luminescent molecules that are strongly quenched by oxygen are typically simple aromatic compounds and are easily ex ited in the longer wa velengths of UV range. The concern is their emission range and intens ity. Luminescence in the visible range of the spectrum is desired for practicality and we ll distinguishable emission from excitation is required for accurate measurements. Pete rson & Fitzgerald used Fluorescent Yellow dye adsorbed on silica particles for their meas urements, which has an excitation peak at 466 nm and emits strongly at 519 nm. Their technique measured flow patterns qualitatively and was rather simple; nonethel ess, it established th e potential for the technology. Few years after the publication of Peterson and Fitzgerald (1980), several research groups started developing paint systems and research advancements increased steadily. Among the most successful groups is the Gouterman group at the University of Washington (UW). They developed an oxygen-quenching porphyrin probe for oxygen concentration detection in blood that was ra ther successful. They managed to implement the technology qualitatively but effectivel y in pressure measurements on aerodynamic models by the late 1980s. The first quantita tive measurements took place in the summer of 1989 at the National Aeronautics and Sp ace Administration (NASA) Ames Research Center using the UW coating (Kavandi et al., 1990; McLachlan et al., 1993; Gouterman et al., 1997). On the other side of the northern hemisphe re, Soviet scientists were concurrently carrying out similar research. As early as the late 1970s, Soviet resear chers at the Central

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49 Aero-Hydrodynamic Institute (TsAGI) expl ored the possibility of using oxygenquenched luminophors for pressure measuremen ts in wind tunnel testing. Theoretical work initiated by Zakharov in the 1960s inspir ed two brilliant rese arches, Pervushin and Nevsky, to develop the first PSP formulation by 1981, which they successfully used to obtain initial experimental resu lts merely a year later (Ardasheva et al., 1985). By the mid 1980s another group at TsAGI de veloped an original polymer-based PSP formulation and tested it in supersonic flow s using a lifetime approach (see following sections). High temperature sensitivity of the PSP was the main drawback of their new system. Research continued with a shift towards intensity-based approach (see following sections), which led to a more practical system that was later commercialized by the Italian company INTECO (Volan and Alati, 1991). After a long period of ignorance and misrecognition by the Western research community, the early 1990s revealed the Soviet advancement, then former USSR, through a commercial a dvertisement in the 1990 February issue of Aviation Week & Space Technology The work of TsAGI was demonstrated experimentally by Deutsche Forschungsanstalt fur Luftund Raumfahrt e.V. (DLR) in Germany in January of 1991. Using intensity-based method, pressure fiel d measurements using the TsAGI coating in the high speed wind tunnel facility in G ttingen were acquired on a cropped delta wing model. The results were validated by pressure taps and oil flow visualization techniques in addition to temperature variations on the model surface (Engler et al., 1991). The paint was calibrated in a priori method and error estimated for the paint from temperature dependence was reported to be less than 0. 3% per degree by TsAGI. The paint layer experienced local temperature gradients less than 3C, while the overall temperature

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50 increased by as much as 12C. The temper ature was acquired through an infrared camera and just three thermocouples. They observed an increase in the pressure standard deviation following the application of the pain t. They experienced significant errors in their pressure estimates due to curvature e ffects that caused uneven reflection from the surface to the photodetector, which could have been accounted for by taking a reference image. However, the paint results were provided by INTECO and it appears that calibration and data processing techniques were still premature. Vo lan and Alati (1991) further elaborated on the TsAGI system and compared calibration techniques (see calibration section). At this point it is suffici ent to state that a calibration procedure is necessary for the paint involving the estab lishment of a relation between the property under investigation (e.g. pressure) and th e captured illumination of the paint, accommodating different variables affecting the calibration, such as temperature dependence and illumination degradation. Mo reover, error estimates greatly depend on the calibration technique, which in turn depends on the experimental setting (i.e., temperature variations/local gradients between run conditi ons, model movement, paint composition, etc.); hence, the degree of accuracy desired in the data is what eventually dictates the extent and complex ity of the calibration procedure. The 1990s brought prosperity to luminescent luminophor technology in wind tunnel testing. Major companies and organi zation competed to implement and further develop the technology to their advantage. Industrial institu tions such as NASA, Boeing Seattle, Boeing St. Louis (formerly McDonnell Douglas), British Aerospace in the United Kingdom, Office National dEtudes et de Recherches Aerosp atiales (ONERA) in France, National Aerospace Laboratory (NAL) in Japa n, Deutsche Forschungsanstalt fur Luft-

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51 und Raumfahrt e.V. (DLR) in Germany are am ong the main industrial implementers of the technology. Academic rese arch is encouragingly growi ng and has increasingly spread to many educational institutions around the globe. The University of Florida (UF), Purdue University and UW are among the le aders in current research advancements. The Structure Luminescent coatings contain a sensor mol ecule that is embedded in a transparent oxygen-permeable polymer binder, as in the cas e of Pressure Sensitive Paint (PSP), or oxygen-impermeable polymer binder, as in the case of Temperature Sensitive Paint (TSP), both of which can be dissolved in a vaporizable solvent a nd then sprayed on the surface, with a diffusely reflecting base undern eath (i.e., primer) as shown in Figure 2-1. Figure 2-1 Coating Structure These coating luminesces proportionally with pressure and temper ature levels when excited by electromagnetic radiation (light) of appropriate energy (i.e., wavelength). More accurately stated, the illumination of the coating is rather quenched by pressure and/or temperature. The illumination is then captured by a photodetection device, such as a charge-coupled device (CCD) camera or a photomultiplier tube (PMT) after passing the emission through appropriate filter(s) to separa te the various regions of emission in the Excitation Emission Binde r Base Coat Surface Oxygen Lumino p ho r

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52 spectrum. A typical absorption and emissi on spectrum for PtTFPP/FIB is shown in Figure 2-2. Figure 2-2. Typical Absorption (left) and Emission (right) vs Wavelength for PtTFPP in fluoroacrylic polymer binder (P tTFPP/FIB). (Bell et al. 2001). Paint Chemistry This section details the photophysical processes driv ing the luminescence of luminophors. Fundamental issues and concerns that arise and unfa vorably affect the luminophor emission are identified and addre ssed. Further, this section states the selection characteristics for each component of the paint system and the selected components for the dual-luminophor system implemented in this work. The Photophysics According to quantum theory, the electroma gnetic energy is transmitted in discrete amounts (i.e., in units or packets) called qua nta. A quantum of elec tromagnetic energy is called a photon. The energy carried by each photon is proportional to its frequency. An atom or molecule of a substance usually does not emit energy; it is then said to be in a low-energy or ground state. When an atom or molecule in the ground state absorbs a

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53 photon, it is raised to a higher energy state, and is said to be excited. The substance spontaneously returns to a lower energy state by emitting a photon with a frequency proportional to the energy difference between th e excited state and the lower state. In the simplest case, the substance will return di rectly to the ground state, emitting a single photon with the same frequency as the absorbed photon. Luminescence is often used to describe the cold emission of electromagnetic radiation at a different wavele ngth than that at which it is absorbed. Luminescence is triggered by the movement of el ectrons within the substance from higher energy levels to lower energy levels (i.e., deactivation). Lu minescence can initiate through various paths, from simple oxidation of the substance to complex processes such as chemiluminescence carried out by living organisms (e.g. Firef lies) in which chemi cal reactions induce luminescence. In the scope of pressure/tem perature sensitive paints, luminescence is more accurately referred to as photol uminescence. Photoluminescence is the instantaneous emission of light from a substa nce under the influence of optical excitation (Gfroerer, 2000). As a luminescent molecu le absorbs a photon of light a molecular photoluminescence (fluorescence and phosphores cence) radiative phenomenon follows. Fluorescence is a process that occurs when an electron in a molecule transitions from the lowest singlet state to the singlet ground state. While phos phorescence occurs when the electron transitions from the lowest excited trip let state to the singlet ground state. Unlike fluorescence, phosphorescence is a delayed emission with a longer lifetime and wavelengths (Liu et al., 1997). Upon excitati on an electron transition to a higher energy level, however, there are only two permitted states: The singlet state and the triplet state. At the excited singlet state an electron w ould posses more energy relative to an excited

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54 triplet state. Furthermore, it is more probable for an electron at the si nglet state to transit to another singlet state than to a triplet state (intersystem transition). Hence, after a molecule that is initially in the singlet ground state absorbs a photon it will most likely convert to an excited singlet state. Within picoseconds, the excited state relaxes to the lowest singlet state, without emission of radiation, through internal conversion. The remaining energy in the lowest singlet stat e may then be dissipated via radiation or through various radiationless mechanisms, such as thermal and oxygen quenching. In view of that, a luminescent molecule of an environmental sensor absorbs light and becomes electronically exc ited to an elevated energy state, which is followed by an energy emission to return to ground state. The absorption process takes place initially under thermal equilibrium state of the molecule then following excitation the molecule migrates to various vibrational levels of a new electronic state. As a result, there exists an energy deficit between emission and excitation energies, thus radiative emission occurs at longer wavelengths relative to absorpti on, a phenomenon known as the Stokes shift (Lakowicz, 1999).In general, the energy em ission (deactivation) is predominantly categorized under two groups: radiative-decay mech anisms in which energy is released as light and non-radiative-decay mechanisms in which energy is transferred to the surrounding medium (e.g. heat transfer). The pressure sensor molecules used in PSPs have an added feature that allows them to return to ground state by colliding with oxygen molecules, a process known as oxygen quenching Kautsky and Hirsch (1935). Therefore, as the ambient pressure increas es the partial pressure of oxygen in the air increases and thru sorption and diffusion, the oxygen concen tration within the bi nder increases. This leads to an increased quenching effect on th e sensor leading to a lower intensity. TSP

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55 coatings are typically embedded in oxyge n impermeable binders and function on the basis of the sensitivity of the lumines cent molecules (luminophor) to their thermal environment. The molecules reach an excite d state by absorption of a photon and then deactivates through the emission of a photon. A rise in temperature of the luminescent molecule will increase the proba bility that the molecule wi ll return to the ground state by a radiationless process, which is known as thermal quenching. However, TSP shows some apparent pressure, more accurately oxygen concentration, dependence, which is unavoidable as an absolutely oxygen impermeable binder is yet to exis t. Nonetheless, the pressure dependence in most TSP systems is rather insignificant relative to thermal quenching effects. The Temperature Dependence Unfortunately, PSP usually exhibits unde sired temperature dependence, which necessitates a correction to the calibration pr ocess. This dependability stems primarily from the fact that oxygen diffusion and solubi lity in the polymer depend on temperature, while the inherent temperature sensitivity of the luminescent molecules contributes to this dependability on a secondary basis (Schanze et al. (1997)). Recalling equations 1.3 and 1.4, the decay rate constants are temperat ure dependent except the radiative decay raterk 2 r em rnrqCk I kkkO (1.3) 21rnrq emkkkO (1.4) Henrys law states that for quasi-steady pr essure variations, the gas concentration in a medium is proportional to the gas concentration contiguous to the medium. Properties of the binder affect oxygen sorpti on and diffusion as well. These properties

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56 are: the solubility and diffusi on of the gas in the binder, th e density of the luminophor in the binder, the quenching efficiency, the luminophor(s) embedded within, the electronic state of the luminophor (triplet or singlet), and lastly the permeability of the binder (Bell et al., 2001). It should be noted that recalling th e discussion in the literature review of the work of Gouin (2000b), these properties can be appreciably altered by adjoining layers (i.e., primer). Temperature affects some of these properties, specifically, the solubility and diffusion of the gas in the binder and the permeability of the binder itself. Following Smoluchowskis model, the quenching second-or der rate constant can be described as (Szmacinski and Lakowicz, 1995) 4qPqkNpDD (2.1) where Dp and Dq are the diffusion coefficients of the luminophor and the oxygen in the polymer, N is the number of luminophor molecules per millimole in the binder and p is a factor characterizing the quenc hing mechanisms. The diffusion coefficients are functions of temperature, and can be related to temperature in an Arrhenius form over limited temperature ranges. eQE RT qD (2.2) where EQ is the activation energy for oxygen diffusion in the binder, R is the universal gas constant (8.315 J/mol.K) and T is the average thermodynami c temperature in K of the binder. The non-radiative first-order decay rate constant represents the intrinsic temperature dependence of the luminophor. It is further decoupled into two parts, a temperature-independent component and a thermally activated intersystem crossing function. The thermally activ ated component is usually modeled with an Arrhenius

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57 functions in a similar fashion to the diffusion coefficient in equation(2.2). The overall all temperature dependence of the paint is a composite function of both the intrinsic temperature dependence and the oxygen quenc hing rate constant. Typically, the oxygen quenching path is the more dominant; how ever, some formulations show opposite dependence (Liu et al. 1997). The Oxygen Factor Oxygen is a diradical molecule, that is it possesses a pair of equal energy molecular orbits and two unpaired electrons. Elec trons spin in orbits as they rotate about an axis passing through the electron. Molecule s whose outermost pair of electrons have parallel spins are in the triplet state; mol ecules whose outermost pair of electrons have anti-parallel spins are in the singlet stat e. Ground-state oxygen is in the triplet state its two unpaired electrons have pa rallel spins, a char acteristic that, according to rules of physical chemistry, does not allow them to r eact with most molecules. Thus, ground-state or triplet oxygen is not very reactive. However, triplet oxygen can be activated by the addition of energy, and transformed into re active oxygen species such as singlet oxygen. Singlet oxygen is produced as a result of th e absorption of light energy. When triplet oxygen absorbs sufficient energy to reverse the spin of one of its unpaired electrons, it forms the singlet state. Singlet oxygen though not a free radical it is highly reactive. When an excited luminescent molecule col lides with triplet oxyge n, energy transfer occurs and singlet oxygen is produced. As energy requirement for triplet oxygen transformation is rather low (1.0 eV), tr iplet oxygen is recogni zed as an excellent quencher. This is typically followed by a radiation deactivation process around 1240 nm and an intersystem crossing leading to vibra tional relaxation. They issue here is the lifetime of the singlet oxygen and its concentration relative to the triplet oxygen within

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58 the binder as it might react i rreversibly with the component s of the paint given enough time. The phenomenon is commonly as photobl eaching and is highly dependent on the surrounding environment and hence differs fr om one paint composition to the other. Paint Composition and Character As stated previously in this chapter, pa int system contains three major components, the luminophor, the binder and the primer. The binder accommodates the luminophor and regulates the interaction between the lu minophor and the surrounding medium, whereas the primer provides a homogenous base coat fo r the paint layer, which is advantageous for the overall performance of the paint. Which Luminescent Molecule? Luminophors are selected to have charac teristic such as: high quantum yield (defined later in this ch apter), long emission lifetime, photostability under extended excitation and a distinguishable Stokes sh ift (Bedlek-Anslow, 2000). Platinum porphyrins and ruthenium complexes are among the most u tilized sensors for PSP due to their high oxygen sensitivity and long lifetimes. When combin ed with a temperature probe in a dual luminophor system, self-quenching behavior is observed with increasing rate as the luminophor concentrations are increased, i. e., ~ 10nm molecular spatial separation distance, (Bell et al., 2001). Polymer binde rs must be robust enough to sustain skin friction and all other forces on the surface. In addition, they should be easy to apply in order to achieve a thin smoot h film on the surface (~ 10 m), thus ensuring that they would not change the aerodynamic or structural properties of the model and allow for a potentially fast dynamic response. The molecular pressure probe used in this work is PtTFPP, a fluorinated tetraphenyl porphyrin derivativ e which is extremely photosta ble (i.e., retains physical

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59 properties under exposure to light), posse ss a large phosphorescence quantum yield (90% in 3-methylpentane) and has a long lived triplet lifetime (120 s) (Zelelow et al., 2003). Its characteristic phosphorescence long lifetime allows enough time for oxygen quenching within the decay lifetime of lumi nophor in proper mediums. Absorption bands are observed at the long wave length UV range (390 nm), and in the low and high green wavelengths (506 nm and 540 nm). The green wavelengths absorption bands create a problem for dual-luminophor systems as TSP phos phors emits at that range. This leads to cross talk between the luminophors and an induc ed variation in the PtTFPP emission that is temperature dependent. Main emission of PtTFPP is in the red wavelengths spectral domain (651 nm) with a less significant em ission at the 712 nm wavelength, far enough from typical TSP emission. Spectral separati on of the PSP and TSP emissions is essential in dual-luminophor systems that implement intensity based measurement systems. The TSP phosphor is tris-(1,10-phenanthroline)ruthenium(II) dichloride (Ruphen). Strong absorbance is evident near the 450 nm ra nge while emission is near the 580 nm wavelength. Ruphen exhibits slight oxygen que nching properties due to its relatively long lived life time (0.6 s). To eliminate this dependence the Ruphen is encapsulated polymer-based nanospheres comprised of pol yacrylonitrile (PAN), which has extremely low gas permeability. Both the PSP and the TSP (encapsulated) are dispersed into poly-tBS-co-TFEM polymer. Binder Polymers Binders play the important role of me diating between the surrounding oxygen and the luminophor molecules (i.e., diffuse oxygen within). The charac teristics of the polymer are then crucial to the overall perfor mance of the paint. The diffusivity of a gas in a polymer medium is quantified by impos ing a specie gradient across the polymer and

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60 then measuring the gas flux across the polymer as a function of time, a procedure known as gas permeation across a membrane (Lu and Winnik, 2000). Initial gas diffusion is typically slow and exponential like, then follo wing some time lag a steady-state gas flux is manifested through the membrane (Figure 2-3). Figure 2-3 Typical rate of gas permeation across a membrane (after Lu and Winnik, 2000) The steady-state flux,, is linearly proportional to the gas diffusion coefficient in the membrane, D the gas solubility in the membrane under equilibrium state, S and the pressure gradient across the membrane, p and is inversely proportional to the membrane thickness, L DSp L (2.3)

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61 The diffusion of the gas in the polymer is permitted through the molecular-size voids into which the gas molecules can travel. As described by the free-volume model, formation of packets of free volume via thermal activation opens paths for molecular transportation within th e solid polymer, in contrast to diffusion through liquids which is driven by mere translational displacement. In trinsically, temperature will have the affect of increasing the volume of this free space l eading to enhanced diffusion. This diffusion enhancement is often characterized by an Arrhenius behavior. Temperature has a multifaceted effect on solid polymers. As the polymer bypasses the glass transition temperature, g T, thermal expansion becomes more si gnificant and the free volume of the system allows for large-amplitude molecula r motion of the polymer backbone, leading to more complex temperature dependence in gas diffusion. This is contrary to the temperature dependence of gas diffusion ch aracterized by a simple activation energy model under the glass transition temperature. Of ten, additives such as plasticizers are incorporated in polymers to lower thei r glass transition temperature. An ideal polymer will be completely temperature independent and possess excellent oxygen sorption and diffusion characte ristics. The first is yet to exist; however, Schanze et al. (1997) developed a realistic criterion for the se lection of polymers in order to minimize temperature dependency. Their resu lts indicate that in order to minimize the temperature dependence, the medium (binde r) used must posses the lowest possible activation energy for oxygen diffusivity. In other words, the lower the intrinsic resistance of the binder to oxygen diffusion, th e lesser temperature e ffects will be to the overall emission. Puklin et al (2000) developed a binder that satisfies the criterion set by Schanze et al. (1997). The group developed the FIB polymer, which exists in the glassy

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62 state at room temperature and holds a glass transition temperature of 70C. It has high pressure sensitivity relative to typical silicone resins, with robust and smooth application to surfaces and low temperature sensitivity (-0.6%/C). The Undercoat An undercoating, i.e., primer, coating is t ypically applied first on the surface before applying the paint. The primer coating cont ains white pigments embedded in a polymer, usually the same polymer used for the paint to minimize chemical alteration of the paint when applied on top of the primer, as the pain t will still be in aqueous form dissolved in the solvent which in turn once applied will dissolve and mix some of the primer layer with the paint. Having identical polymers fo r the paint and the primer layers further ensures that oxygen sorption and diffusi on are similar and hence avoiding oxygen gradient across the paint that could potentia lly change the paint characteristics (Gouin et al., 2000c). Primer layers are advantageous fo r various reasons. First, they posses high index of refraction and high hiding power. I ndex of refraction is a parameter used to describe the interaction of electromagnetic ra diation with matter. It indicates how much the light is slowed down while traveling thr ough a specific medium relative to vacuum. Whereas the speed of all electromagnetic radiat ion in vacuum is the same, it is a function of frequency in any medium. This index of re fraction is the ratio of the speed of sound to the phase velocity (the velocity at which the phase of any one frequency component of the wave will propagate) of the radiation wa ve, not to be confused with the envelop velocity (i.e., the velocity with which the overall shape of the waves amplitude propagates and is what dictates the rate at which information and energy may be transmitted by the wave). Thus index of refraction is typically bigger than one in proportion to the density of the ma terial, that is the denser th e material, the more the light

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63 is slowed down. That is advantageous as it provides more reflected light both back into the paint layer after penetrating it to the pr imer and from molecular emission back to the camera. Hiding power is defined as the ability of paint to obscure the surface over which it has been applied, which is strongly influen ced by the degree of dispersion of pigments in the binder media. The more the pigment particles agglomerate, the worse the hiding power becomes. Another advantage of primer coats is that they eliminate any intrinsic reflection of the surface due to various materials that compose the surface. The uniformity of the surface guarantees uniform reflection, which elim inates errors due to reflection variation that could be significant depending on the su rface material compos ition, and which can be further manifested as an error source if model movement occurs. However, primer coats, even with iden tical polymer as the paint, induce some undesirable effects as they interact with the paint layer. As shown by Puk lin et al. (2000) and Gouin et al. (2000c), primers can adversely alter the response tim e of the paint as well as the temperature dependence of the paint. Oxygen equilibrium across the paint layer is a deterministic factor for the quenching process, and a prim er that is oxygen permeable, especially one with a different permeability, induces an oxygen gradient across th e interface with the paint layer that affects the PSP characteris tics. Binders with low oxygen permeability provide a resolution to such problem, such as polyacrylonitrile PAN (Kose, 2005). A complete elimination of primer effects is not feasible because the white pigments (e.g. titanium dioxide) are known to affect the oxygen diffusion in the polymer, (Schappacher et al., 2003), in addition to other undesi rable effects such as photoxidation.

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64 Measurement System A schematic of the experimental setup for intensity based static measurement system is provided in Figure 2-4 show ing the different components and their arrangement. In this setup the specimen is placed inside a vacuum chamber, where the pressure can be precisely monitored and controlled, wedged betw een two rectangular aluminum blocks. The top block is heated, while the bottom is cooled imposing a quasione-dimensional temperature gradient along the length of the specimen, if desired. The specimen is excited with the proper light s ource (UV lamp, LED, laser, etc.) and the photonic emission is then passed through the appropriate filter(s ) then to the cooled CCD camera, which converts the photonic energy into electrical current. The Electronic Unit (E/U), which encloses an anal og-to-digital converter, amplifies and processes the current produced and passes it to the frame grabber car d installed in the PC for final processing by the test personnel. The pressure of the cham ber is measured via a pressure transducer and the temperature is measured through five equally-spaced thermocouples fitted on the back surface of the specimen.

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65 Figure 2-4 Equipment Setup fo r Temperature Calibration The Excitation Source Excitation source plays a key role influe ncing the accuracy and quality of data. Luminophors typically have multiple absorpti on peaks with modera te bandwidths, a desired character of the probe to avoid broad absorption and spectral overlap and interference. Therefore, the excitation source must provide sufficient and uniform illumination at these absorption bands to produce an output luminescence signal capable of saturating the detector in relatively short exposure ti me, thus taking advantage of detectors signal-to-noise (SNR) potential. However, the illumination should not be bright enough to cause photode gradation of the luminophor or overwhelm the detectors well depth (see useful definitions in Appendix-A). Further, the excitation source must have absolutely no emission at the lumi nophor spectral emission range. A spatially E/U unit CCD Camera Excitation Source Vacuum Chamber Cooled Base Heated Top Thermocouples 6.235 psi Pressure Transducer Filter wheel

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66 uniform illumination avoids the formation of local regions where the signal is low relative to the noise level with respect to the rest of the imaged field, inducing an inconsistent SNR field. If continuous illumination is desired, then a main character is the stability of the illumination output by th e source, while excellent pulsed excitation depends on repeatable excitation signal levels. Some of these induced variations can be accounted for in the calibration process such as inhomogeneous illumination fields (s ee calibration section), however, variations in the overall output signal level (source drif ting) is not easily accounted for. A drift in the excitation signal will have the effect of reducing the strength of the paint emission, falsely indicating higher pressu re/temperature levels. Consta nt monitoring of the output excitation signal, though possible, is quite impractical, especially when using multiple excitation sources. A suggested approach in th e literature is to embed an environmentalinsensitive probe in the paint (a multic omponent system) that depends only on the excitation signal. This approach provides an effective correction technique that eliminates excitation field variations; nonetheless, it is fa irly challenging to find a probe that will absorb in the same spectral range as the othe r probes and yet emits in an empty range of the spectrum not occupied by other luminophors, which becomes even more intricate in systems containing more than one probe (e.g pressure and temper ature dual-luminophor systems.) The Detection Device The detection device plays a deterministi c role in how accurate PSP measurements are and the degree of resolution obtainable. This could further impinge on the feasibility of certain experiments, such as low speed wind tunnel PSP measurements, where pressure variations are small and the corre sponding intensity vari ations are fairly

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67 diminutive. Accordingly, an understanding of the basic principles of operation of detection sources is fundamental for the comprehension of the setup and acquisition processes as well as error sources and uncertainty analysis. Calibration Techniques A calibration procedure is needed to tr anslate intensity information to the corresponding pressure and temperature. Howeve r, to establish the calibration re lations a prior knowledge of some environmental condition is required. This can be accomplished through an in situ or a priori approach or a hybrid a pproach. Each approach is defined in the following sections. A Priori Calibration This approach is based on static (n o flow) calibration procedure carried independently in a calibration chamber wher e the environmental conditions are well controlled and monitored. A coupon is coated with the paint and then imaged inside a pressure controlled environment, such as a vacuum chamber, and the intensity of the specimen is recorded as the pressure inside the chamber is varied, hence creating a relation between the two variab les. In applications where temperature variations are expected, a temperature gradient is imposed on the coupon and the pressure is varied while maintaining the temperature gradient and a calibration surface is produced where the pressure is a function of both the inte nsity and the temperature. The calibration relations are then utilized to retrieve pre ssure and temperature information from the actual test data, such as in a wind tunnel. Th e general form of the priori calibration is: 00 L LK ref k ij lkI paT I (2.4)

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68 It is usually sufficient to represent the pressure with a biquadratic function in equation (2.4) (i.e., L=K=2). The higher the order of the pressure calibration function the more points needed to solve for all the coe fficients, in this example, the biquadratic functions has nine coefficients and thus nine intensity and temperature measurements are needed. The range of the pressure and temp erature calibration conditions depends on the range of these conditions in the application as well as the accuracy needed. Extrapolation usually yield high errors, hence, the environm ental envelop should cove r all expected test conditions. The general behavior of the intensity within envelop should be known through spectroscopy analysis to determine th e resolution of the measurements desirable in each different region of the pressure and temperature ranges. A reference image is still needed to a ccount for spatial variation (i.e., paint thickness, illumination field, etc.); however, the reference condition in this case may or may not be identical to the reference conditi on in the actual tes ting environment (windoff). If the two conditions are not identical then the test normalized ratios are multiplied by the reference-to-wind-off intensity ratio before using equation (2.4). Priori calibration offers simplicity and convenience by eliminating the need for installing pressure taps and thermocouples in the model. Further, it allows for the full coverage of the environmental test range. This would be rather difficult if one attempts to installs pressure taps on the model surface, as no prior knowledge exists to provide information for optimal taps location or th e physical infeasibility of installing the pressure tap at these locations. In the form er case, the paint could be applied and a qualitative estimation of the pressure field is obtained to determine the best locations for installing pressure taps. Unfortunately, this approach may involve higher errors because

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69 of different camera and illumination source pos itions (Liu et al., 1997). Even though the same batch of paint is used to paint both the calibration coupon and the test model, variations still occur due to different app lication of the paint, environmental/surface containments, etc. Nonetheless, more often, this calibration technique is accurate enough for typical test environments with considerab le practicality. The results are exceptionally accurate if the calibration is carried in a wind tunnel where the static pressure and temperature can be controlled under wind-off co nditions (i.e., pressurized tunnels). In situ Calibration In this approach the calibration is carried in a wind tunnel under flow conditions. Pressure taps are installed in the model a nd the pressure variat ion over the model are recorded simultaneously with intensity values. The pressure function is typically a polynomial of the second-order, with a first-order represen tation sufficing many applications. 0 h H windoff h hI Pb I (2.5) The temperature effects are absorbed in the coefficients, which unless isothermal conditions are present, increases the standard deviation of th e calibration data and yields, in most cases, double-vale points that corres pond to different conditions. To compensate for this, thermocouples can be installed to record the temperat ure and the calibration curve is transformed to a calibration surface. The in situ approach may seem selfdefeating as it still requ ires pressure taps and thermocouples to be installed in the model, however, the number of calibration taps is si gnificantly less than the typical number of pressure taps required to map out the pressure field.

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70 Hybrid Calibration This technique combines the convenience of a priori approach with the accuracy of the in situ method. The pressure calibration is establis hed first in a static cell, and then the calibration is corrected for temperature variat ion between static and flow conditions via a factor K. The approach was explained earlier in the Literature Review Chapter. The technique relies on the very little temperature variations on the order of few degrees and a PSP coating exhibiting ideal behavior. Thus, this approach fails when significant temperature variation occur dur ing testing and with non-ideal paint/polymer systems. PSP Calibration In the presence of an oxygen-quencher a quantity known as the quantum yield of luminescence, more commonly known as the quantum efficiency, is modeled under oxygen rich conditions as: 2rate of luminescence emission rate of excitationr r arnrqk I k IkkkO (2.6) where I is the luminescent intensity, Ia is the absorption intensity and is the lifetime of an excited molecule. Under vacuum conditions, equation (2.6) becomes: 00 r r rnrk k kk (2.7) where 0and0 are the quantum efficiency and lif etime of the probe under vacuum conditions, respectively. Divi ding the quantum efficiency under vacuum by that under oxygen rich yields: 22 0 0 201 1rnrqq o rnrrnr o qkkkOkO I I kkkk I kO I (2.8)

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71 This form is known as the Stern-Volmer equation. It is not practical to pull a vacuum in order to estimate the vacuum lif etime of the sensor molecule, thus a known condition, such as atmosphere, is utilized in stead as the reference condition. Henrys Law relates the oxygen concentrati on to the partial pressure of oxygen as shown in equation (1.6). The intensity ratio with respect to an atmospheric reference condition is hence represented as: 2 2 22 2()() (1) (); (); rnrq rnrqO refatm run O rnrq rnrq ref q rnr O rnrqrnrqrefkkkO kkkP I ATBTP Ikkk kkkO k kk P ATBTP kkkkkkP (2.9) The general form of the Stern-Vo lmer equation is expressed as: 0 n N ref n n refI P AT IP (2.10) The coefficientsn A T are functions of temperature, as expected due to the temperature dependence in kD and kQ, and are to be determined through the calibration process, in which pressure and intensity da ta are acquired and then a least-square fit procedure is performed to determine th e coefficients. Typically a second order polynomial ( N = 2) is sufficient to accurately f it the experimental calibration data. The process of taking the ratio between the luminescence intensity and some reference intensity is essential in order to eliminat e illumination spatial non-uniformities, coating thickness variation and luminophor une ven dispersion in the binder.

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72 Temperature Compensation Models As described in Chapter 1, PSP exhibits temperature dependence primarily due to the dependence of the polymer binder permeabil ity on temperature, which in turn effects the oxygen diffusion and sorption in the binder. On a secondary level, under oxygen rich environments, the inherent temper ature quenching rate constant kD plays an insignificant role but becoming more significant as the oxygen concentration decreases until it constitutes the only temperature dependen ce at vacuum conditions. The temperature dependence can be modeled by a single expone ntially decaying function at vacuum and a multi-exponential decaying function around at mospheric conditions (Schanze et al., 1997). The proportionality constants and activa tion energies depend on the sensor probe and the polymer; however, up to the date of th is work, there has been no successful effort to globally model this dependence for a wi de range of pressures and temperatures. Calibration provides a mean to compensa te for the temperature dependence. In situ techniques have no explicit temperature depende nce; rather they absorb these effects in the calibration coefficients as the temperatur e spatial variations are averaged out among all points included in the cal ibration (Bell et al., 2001). Th is means that each set of coefficients correspond to a unique pressure and temperature condition. This approach is useful when temperature variations ar e small enough (~10-20 C depending on the PSP composition) to avoid double value points on the calibration surface that correspond to different pressure/temperature values. Furt her, extrapolating fo r points outside the calibration envelop entails high uncertainty. In wind tunnel experiments, the run image precedes the reference image as the referen ce image is acquired immediately after the termination of the run image to ensure id entical temperature di stribution throughout both images. This prohibits practical execution of long experiments as the tunnel must be

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73 stopped after each run to allow for the refere nce image. In the presence of significant temperature gradients on the model surface, a localized calibration is needed with enough pressure taps for each region. A priori calibration provides a more global calibration as the pressure is calibrated as a function of both normalized intensity and temperature. Nonetheles s, this necessitates that temperature field estimation on the mode l surface be performed. As this calibration approach offers a pixel-by-pixel temp erature compensation, the only reasonable temperature measurement technique would ha ve to be a TSP system. Early attempts suggested imposing a TSP layer either bene ath or on top of a PSP layer in order to simultaneously map out pressure and temper ature fields (Harri s and Gouterman, 1995; Oglesby et al., 1995). Latter attempts incorporat ed the two sensors in the same binder in a dual-luminophor system (Carroll et al., 1999) In either approach the convenience of having a second sensor to map-out the temper ature field comes with a highly undesirable consequence, namely spectral interference. Spectral interference occurs whenever two luminophors are co-embedded in the same binde r. The emission of the lower wavelength sensor probe, i.e., TSP, usually overlaps w ith part of the excitation region of the higher wavelength sensor probe, i.e., PSP. This adds to the temperature dependence complexity as the PSP emission is partially dependent on the intensity of the TSP emission. This makes the decoupling of the two effects rath er intricate using t ypical calibration and compensation techniques. Secondary detrimental effects include: spectral overlap due to broad emission of the lower wavelength luminophor, chemical in teraction, particles coagulation resulting in an uneven disper sion of the two luminophors in the binder and increased uncertainty in the temperature estimates as it is embedded in an oxygen

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74 permeable binder (TSPs possess finite oxygen sensitivity). This work utilizes a dual-luminophor system (Kose, 2005) and a mathematical statistical technique known as POD to provi de the calibration functions. POD is capable of separating the different factors constituti ng any dataset; further, it provides a physical insight into the various processes involved. A comprehensive discussion of the approach and calibration procedure is presented in Chapter 3. TSP Calibration TSP sensors are typically dispersed in an oxygen-impermeable polymer binder, thus the last term in the denominator of equation (2.6) can be eliminated reducing the equation to: 0r r arnrk I k Ikk (2.11) The temperature rate constant kD is modeled as an Arrhenius function of the form (Liu et al., 1997): expnrE k R T (2.12) where E is the Arrhenius activation energy and R is the universal gas constant. The Arrhenius behavior can be incorporated in the inverse of equation (2.11) to yield: exp 11arnrnr rrrE A Ikkk R T Ikkk (2.13) where A is a proportionality constant. Subtractin g two different temperature condition, with one of them chosen at absolute zero (T = 0) eliminates the unity constant.

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75 exp()0exp exp 0 0aa rE E A A R II RT ITITk exp r rk E A RT k (2.14) Dividing equation (2.14) by a reference temper ature condition, an approximate intensity ratio is realized as: 11 lnref refIT E RTT IT (2.15) In theory the plot of equation (2.15) is a straight line with slope of ER. However, from experimental observation this relation f its experimental data but only over certain temperature range which varies with different coating form ulations. Therefore, a more general form is required and can be expressed in the form: ref refIT T F T IT (2.16) where F is a general function that could vary from a polynomial, exponential or some other function that fits the experimental data over a certain temperature range.

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76 CHAPTER 3 PROPER ORTHOGONAL DECOMPOSITION This chapter presents the proper orthogonal decomposition (POD) analysis. It details all the involved steps and mathematical as well as physical implications. Artificial data are then examined and analyzed via P OD to characterize the POD and gain a more comprehensive understanding of the analysis process. Overview The idea of characterizing the pressure a nd temperature fields using specialized luminescent coatings (i.e., TSP or PSP separately) is presented in the previous chapters; however, the aforementioned approach is onl y capable of characterizing each field autonomously. The concept of formulating a coating containing both pressure and temperature sensors embedded in the same binder presented a rather fascinating supposition that is well worth investigating. Two obvious questions emerge through such concept: Are the two sensors (luminophors) going to interact and affect each other? Is it possible to identify and separate the emission from each sensor and consequently be able to accurately determine the pressure and te mperature? Even though the two questions are fundamentally tied together, the first is more of chemist subject, while the second is more of a question for a mathematician, hence my dilemma as an engineer! From a chemical prospective, the goal is find the proper combination of pressure and temperature luminophor such that they wi ll mix conveniently and disperse evenly in the binder without considerably changing th e chemical composition or the luminescent characteristics of each other. In addition they should possess a comparable wavelength

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77 excitation-region but distinguish able emission. Finally, any cross-talk between the two luminophor should be limited to minimal. Mathematically, the simplest approach is to ratio the emission of each luminophor to a fixed reference, such as a third luminophor that has a constant emission with respect to the environmental conditions but dependent on the excitation intensity level and paint thickness, or take the ratio of one emission to the other. The latter approach does not always yield accurate results and may perhaps be somewhat simplistic, especially when cross-talk is influential. A different math ematical approach, which is the approach adapted in this work, is to implement a mathematical technique known as proper orthogonal decomposition. POD Analysis The principal mathematical difficulty of the calibration process lies in three aspects: separating the pressure and temperature information, since a single field maps both parameters at the same time, accounting for the inherent temperature dependence in the pressure sensor and cross-talk between the two sensors, and most importantly establishing a calibration curve/ surface for each parameter. Introduction In general, a spectrum encompasses scores of diverse variations that derive from the quantities under investiga tion, intersystem relations and dependence, instrument variations (i.e., noise) and environmental c onditions. Nonetheless, such complex and correlated variations can usually be reduced to a set of finite nu mber of independent variations (factors) shaping th e spectral data. The criterion governing the possibility of such process of factorization is that the data matrix can be expressed as a linear sum of product terms (a.k.a. variation spectra). If it were feasible to calcu late such variation

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78 spectra, then this data could be used inst ead of the raw spectral data for building the calibration model. These variation-spectra, ofte n called eigenvectors or factors, are then used to reconstruct the original spectrum by multiplying each one by a different constant scaling factor, commonly known as eigenvalues or scores, and adding the results together until the new spectrum closely matches the or iginal spectrum. This method of breaking down a set of spectroscopic data into its most basic variations is a least-square technique known as Principal Components Analysis (PCA). PCA yields a form of a solution that is known as an abstract solution. Such soluti on has no physical signifi cance or implication by itself, thus further mathematical manipulati on is required in order to quantify the final solution as meaningful. Such process is known as Target Transformation (TA) and it involves rotating the newly constructed spectr um until a physically meaningful solution is realized. This rotation can be as simple as a two-dimensional orthogonal (single-axis) rotation or as complicated as an n-dimensional non-orthogonal rotation. Mathematical Formulation A full discussion of the mathematical aspect of the POD analysis is essential in the understanding of the process. Further, key as pects of the analysis are determined based on the process under investigation, and he nce a comprehensive discussion of the mathematical procedure is essential. Principle component analysis As mentioned previously, for POD to yield successful results, the data matrix must be expressible as a linear sum of product terms (eigenvalues and eigenvectors). This dictates that the data matrix must be square The different noise sources and the character of each noise were discussed in the previous ch apter. It was further noted that some errors increase proportionally with the magnitude of the signal such as shot noise, hence the

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79 need for a statistical normalization process. In order to give each column in the data matrix an equal statistical weight, each element is normalized by the square root of the sum of the squares of all the elements in its column. However, normalizing the data has an irrecoverable effect that may not be pr actical in certain processes. Luminescence application in fluid mechanics is one application that yields adverse effects when data is normalized. The source of the problem stems from the fact the normalization process causes a mutual dependence between all regi ons of the spectrum, hence imposing an additional complication to the analysis. Consider the simple case where a spectrum is a function of two independent fact ors that emit at two distinct wavelengths with no overlap as shown in Figure 3-1 Figure 3-1 Spectral emission for two independe nce processes: (A) Raw spectra (B) A single raw spectrum with dependence on th e higher wavelength factor and no dependence on the lower wavelength f actor (C) The normalized spectra A B C

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80 Each spectrum varies with only one factor at only one of the two emission regions, while remaining constant in the other region (i.e., invariant with the other factor). Upon normalization, the spectra show a new mutual dependence between th e two factors. The decomposition of the normalized spectra w ould still yield only two eigenvectors, however, the new dependence can not be easily re solved to retrieve the original spectrum. Therefore, the calibration f unctions are much more complicated and involved, which defeats the purpose of the POD as a model re ducing technique. The important question is then whether the analysis can be carried out without the normalization process while yielding accurate results. The answer to this question determines the potential for the POD analysis as a calibrator to a process. In the particular case of luminescent coatings, this calls for a thorough understanding of the error sources and thei r effect and scaling throughout the spectral range. Noise is shot no ise limited for high intensity levels (> few hundred electrons) and is preamplifier or dark current limited for low intensity levels and long exposure times, respectively. For most steady luminescent coatings a pplications in wind tunnel testing high intensity levels are present. Dynamic applica tions and low pressure applications, such as acoustics, do not enjoy such advantage. The experiment under investig ation in this work fortunately belongs to the former applications; hence noise is shot noi se limited. A typical scientific grade CCD chip has a FWC of about 330,000 e-, which yields shot noise of 0.17%, 0.25%, and 2.5% for FW, half-FW and 2,500 eintensity levels, respectively. This shows that noise variation between different regions of the spectrum can be effectively eliminated by using appropriate, but usually different, exposure times to utilize the FWC for each region of the spectrum.

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81 The next step in the analysis is to square the data matrix by obtaining the covariance matrix, Z, which is obtained by pre-multiplying the data matrix, D, by its transpose. Define the normalized data matrix as: ,,, 1n mnmjjn jDrcRC (3.1) here m corresponds to the number of wave lengths spanning the emission and n is the number of environmental conditions. Then the covariance matrix is given by: ,T nn Z DDZ (3.2) The next step is to extract the eigenvalues, and their corresponding eigenvectors, Q, from the covariance matrix. Utilizing a math solver such as MATLAB, the eigenvalues are extracted and arranged in a descending order with respect to their magnitude. The magnitude of these eigenvalues serves as a gauge for the importance of their corresponding eigenvectors. Accordingly, a criterion, such as a cutoff ratio of the eigenvalue to the largest eigenvalue, has to be set to determine the minimum acceptable eigenvector. The principal ei genvectors constitute an optimized, mutually orthogonal coordinate system. Each successive eigenve ctor accounts for the next maximum possible variance in the data. In the factor space, the largest eigenvector is oriented as to account in a least-square sense for the greatest possi ble variance in the data. Further, it passes through the greatest con centration of data points and de fines the best one-factor model for the data. While the first two factors define a plane passing through the greatest concentration of data points, with the second factor pointing in the direction that accounts for as much as possible of the variance not accounted for by the first factor. The eigenvalue extraction process is continued until all the significant eigenvectors are

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82 extracted. The remaining eigenvectors ch aracterize noise and insignificant factors embedded in the data and are consequen tly omitted. Now the new data matrix, Dw, can be reconstructed using the deduced eigenvalu es and eigenvectors. The mathematical sequence of this process is presented in equati ons (3.3) through(3.7). 1 jjkQZQ (3.3) jjj Z QQ (3.4) 1 TQQ (3.5) where, T TDUQ UDQR QC (3.6) wDRC (3.7) In equation(3.7), R is called the row matrix with an m x N dimension, where N is the number of factors, and C is called the column matrix with N x n dimension. Target transformation After extracting the principal factors of the da ta set, a rotation is usually required in order to transform the abstract solution to a physically meani ngful solution. We expect to have at least two principal components representing the two main variants in the data, namely pressure and temperature, neverthele ss, a third factor repr esenting cross-talk and/or mutual dependence could be notably influential. Hence, a discussion of threedimensional non-orthogonal rotation is essentia l. The following set of matrices express a three-dimensional non-orthogonal rotation applied to axis x, y, and z respectively.

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83 100 0cos()sin() 0sin()cos()xxxxx xxxxTab cd (3.8) cos()0sin() 010 sin()0cos()yyyy y yxyyab T cd (3.9) cos()sin()0 sin()cos()0 001zzzz zzzzzab Tcd (3.10) The coefficients multiplying the trigonometric functions, al, bl and cl, with l = x y and z are called the orthogona lity coefficients. Theses coefficients determine the degree of skewness imposed on each axes, with unit value imposing orthogonality. To carry out the transformation, the right hand side of equation (3.7) is multiplied by [ T ] and [ T ]-1 in the following manner: 1w w transformedtransformedDRTTC DRC (3.11) If the transformed solution ha s a physical significance, then a real solution has been established so that: real realrealDRC (3.12) A physical understanding of the proce ss under investigation is necessary to interpret the rotated data a nd determine a physically meani ng solution. For instance, in luminescent coating application, a pre-know ledge of the emissi on spectrum of the luminophor will aid in identifying the rotation process.

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84 POD Behavior The behavior of the POD as a model reduction technique an d a calibrator for luminescent data is examined in this section. Artificial data is utilized to provide as much insight in the original process being exam ined and hence the behavior of the POD analysis. Introduction In order to methodically understand and comprehend the POD analysis, a theoretical set of data will be created repr esenting a dual-luminophor emission. The data will have different distinct characteristics to evaluate the effect of each variation on the POD analysis. Two different case s of data will be analyzed: 1. The first set of data represents an ideal and simple spectroscopic emission, in which there is no mutual dependence be tween temperature and pressure. 2. The second set of data has the pressu re emission depending on temperature (spectroscopic). In addition, the following sub cases will be examined as well: The filtered and integrated emission. Shot noise will be imposed on the signal. Spectral overlap between f actors (i.e. cross-talk) Each set of data is utiliz ed to accentuate a particul ar feature of the POD The eventual goal is to examine whether the POD analysis is capable of extracting the main modes of the data even if other variations, such as noise, overlap, cross talk, etc., are present in the spectra. Furthermore, the anal ysis will assess the accur acy of the extracted modes as a function of SNR, degr ee of cross talk and overlap.

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85 Algorithm The following chart details the P.C.A. al gorithm and the vari ous steps involved. Figure 3-2 P.C.A. Algorithm Construct the covariance matrix Data Loop for the principal eigenvalues Calculate the largest eigenvalue and the corresponding eigenvector Subtract the product of extracted eigenvalue and eigenvector from the covariance matrix and set the matrix as the new covariance matrix Calculate the largest eigenvalue and the corresponding eigenvector of the new covariance matrix Check if the new largest eigenvalue is less than the predefined maximum-to-new eigenvalue ratio Reconstruct the data matrix by utilizing equation (3.7), and hence the abstract solution is established Terminate the loop

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86 Target transformation Equation (3.11) is used to perform a non-orthogonal rotation on the reconstructed data. The main focus of the rotation is on the C matrix. The elements in the C (eigenvalues) matrix are direc tly related to the environmenta l conditions. For example, if we hold the temperature constant for five spectra and vary only the pressure, after performing the POD we find a single eigenvector representi ng the general pressure variation, and each of the five elements in the C matrix scale that eigenvector according to the corresponding pressure le vel. Target transformation ma y not be needed at all in such case, as the variables are directly re lated. If the two parameters do not vary independently, then the rotation would be mo re involving to apply due to the mutual dependence between them. In such case we would have to solve two simultaneous equations with two unknowns, temperature and pr essure. Each equation states one of the environmental parameters as a function of th e eigenvalues. If only two factors are needed to constitute the data, then these equations represent surfaces in the eigenvalues plane. However, if three factors are needed to rec onstruct the data, then the equation lies in a four dimensional space. Figure 3-3 deta ils the target transformation process.

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87 Figure 3-3 Target transformation algorithm Reconstruct the data matrix from the extracted eigenvalues and eigenvectors Loop 360 for the rotation angle Loop for the orthogonality coefficients Fit the pressure and temperature to the eigenvalues in a leas t square sense and calculate the residual error Search for the minimum residual error and the corresponding rotation angle and orthogonality coefficients Rotate the data and reconstruct the rotated data matrix Terminate the coefficient loop Terminate the rotation loop

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88 Data generation To generate a theoretical data for dual-luminophor emission equations (3.13) through (3.16) are implemented to calculate th e peak values of each spectrum (Liu et al, 2001). In the following expressions ref I and refP are the reference luminescent intensity and pressure at a known temp erature, respectively. ref ref pressI P ATBT I P (3.13) 1ref nr ref refrefTT E ATAT RTT (3.14) 1pref ref refrefETT BTBT RTT (3.15) The pressure is represented by equation (3. 13), the Stern-Volmer relation, which is widely used as operational calibration rela tion for PSP measurements. The coefficients A(T) and B(T) are temperature-dependent, Enr is the Arrhenius activation energy for a non-radiative process, EP is the activation energy for oxygen diffusion, and R is the universal gas constant. Typical values of thes e coefficients for (Bath Ruth + silica gel in GE RTV 118) are: 0.13refAT 0.87refBT 2.82nr refE RT and 4.32p refE RT over a temperature range from 293K to 333K with the reference temperature is 298refTK. The temperature is characterized by the Arrhenius functions as follows: 11nr refE RTT ref tempI e I (3.16)

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89 The emission of the luminophors follows a Gaussian distribution in the frequency domain2. 222ffAI Ife (3.17) where AI is the amplitude-control c onstant of the intensity, is the standard deviation of the spectrum, f and f are the frequency and center frequency in Hz, respectively. This distribution is symmetric in the fr equency domain, however, upon transforming the spectrum to the wavelength domain it shows the familiar luminophor behavior of asymmetric spread. The transformation is guide d by observing that energy is related to the wavelength by the following relation: hc Ehf (3.18) here his Planks constant -34(6.626176 10 Js)and c is the speed of light in vacuum 17s(3.0 10 )nm. The spectrum can then be e xpressed in the wavelengths domain as: 222cAI Ie (3.19) This relationship will produce a spectrum that will tail off at the higher wavelengths and in consequences replicates the effects spectral ove rlap between the two emissions (i.e., TSP & PSP). 2 Personal communication with Dr. Schanze

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90 Figure 3-4 Simulated spectral response of the luminophors: (A) Frequency domain (B) Wavelength domain Noise There are two types of noise that will be introduced in the spectra, white noise and shot noise. White noise is a type of noise that spans al l different frequencies. The adjective white is used to describe this t ype of noise because of the way white light works. White light is made up of all of th e different colors (frequencies) of light combined together, in the same way; white noise is a combination of all of the different frequencies. At the CCD output the signal from the image sensor is converted from the charge domain to the voltage domain by means of a sense capacitor and a source-follower amplifier; this amplifier has a resistance that causes thermal noise. The effective resistance in this case is the output impe dance of the source follower. This type of thermal noise is sometimes called Johnson noi se, or as better r ecognized, white noise, since its magnitude is inde pendent of frequency. Frequency (Hz) Wavelength (nm) A B

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91 The noise in electrons can be described as: 4out white VkTBR V A N (3.20) where k is Boltzmans constant (J/K), T is the temperature (K), B is the noise power bandwidth (Hz) and R is the effective channel resistance ( ). To simulate this type of noise the rand function in MATLAB will be used to generate the random noise. A fundamental characteristic of white noise is its randomness. In performing the POD analysis, this change in different spectra, due to the different noise in each spectrum, necessitates a unique and different ro tation for each different set of data. This is due to the fact that the POD analysis doe s not eliminate noise from data regardless of its magnitude; rather it significantly damps the noise out. The magnitude of the change in the new rotation is related to the relative difference between the noises. Therefore, a different rotation is essential in order to obtain the most accurate calibration curves. Nonetheless, since the comparative change in no ise in each set of data is relatively small, given that the magnitude of the noise itself is usually small, the new rotation would be slightly differ from the original rotation, sparing us the hassle of repeating the 360 search. High-level noise in the data might on the other ha nd result in an irreversible distortion to the data that is unrecoverable by the POD Shot Noise is the noise associated w ith the random arriva l of photons at any detector, as described in Chapter 2. Since the time between photon arrivals is governed by Poisson statistics, the uncertainty in th e number of photons collected during a given period of time is: shot I (3.21)

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92 where shot is the shot noise and I is the intensity, both expr essed in electrons. So a 10,000-electron exposure will have a shot noise of 100 electrons. This implies that the best signal-to-noise rati o possible for a 10,000-electron signal is 10,000/100 = 100, accordingly, the maximum noise level is 1 % of the signal. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 10 20 30 40 50 60 70 80 90 100 IntensityShot noise Figure 3-5 Shot noise as a function of intensity

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93 Analysis In order to automate the process of findi ng the new rotation, one needs to perform a least square analysis on the surfaces rela ting the environmental conditions to the C matrix. Looking at Table 3-1, the temperature is varied for the first ten runs, while the pressure is held constant. The pressure is then increased and the same temperature variation is applied, resulting in a total of ninety conditions. Table 3-1 Conditions and their C elements Environmental Conditions C T matrix elements 3002 3073.5 3145 3216.5 3288 3359.5 34211 34912.5 35614 363 TP 1,12,13,1 1,22,23,2 1,32,33,3 1,42,43,4 1,52,53,5 1,62,63,6 1,72,73,7 1,82,83,8 1,92,93,9 1,2,3, nnnccc ccc ccc ccc ccc ccc ccc ccc ccc ccc The number of eigenvectors extracted for each case will determine the number of independent variables. We expect only two main independent factor s and perhaps a third factor that accounts for combined minor effects, such as noise and spectral interference.

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94 Case One (Independent Emission) This is the first examined case with no mutual dependence between the two emission regions. 450 500 550 600 650 700 750 800 0 0.5 1 1.5 2 2 5 Wavelength (nm)Intensity Figure 3-6 Case one: Narrow spectrum with no overlap The eigenvalues ( Table 3-2 ) show that only the first two factors shape the spectra while the third is 14 orders of magnitude smaller, and hence has no significance. Table 3-2 Eigenvalues for case one Eigenvalue Magnitude 1 3.23 e+003 2 1.40 e+002 3 -5.60 e-012

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95 450 500 550 600 650 700 750 800 -2 0 2 4 6 8 10 12 14 16 Wavelength (nm)Intensity -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 2 4 6 8 10 12 14 EigenvaluesPressure (psi) 450 500 550 600 650 700 750 800 -2 0 2 4 6 8 10 12 14 16 Wavelength (nm)Intensity -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 300 310 320 330 340 350 360 370 EigenvaluesTemperature (K) p Figure 3-7 Case one: Eigenvectors and calibrati on curves for pressure (left) at 79.8392 and temperature (right) at 13.6121 Pressure calibration is a li near fit while temperature was fitted via a quadratic expression. Absolute calibrati on error for the pressure is le ss than 2e-06 psi and for the temperature it is less than 0.1K. The two fact ors have a relative rotational angle of 66.2. Next, seven sub-cases are examined to shed light on specific issues pertinent to the understanding of POD with the results summar ized at the end of these cases.

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96 Case One-A (Temperature Emission Amplified by 10) The temperature emission is amplified by 10. 450 500 550 600 650 700 750 800 0 2 4 6 8 10 12 14 16 18 20 Wavelength (nm)Intensity Figure 3-8 Case one-A: Temperature Emission Amplified 10 Folds 450 500 550 600 650 700 750 800 -20 0 20 40 60 80 100 120 140 Wavelength (nm)Intensity 450 500 550 600 650 700 750 800 -20 0 20 40 60 80 100 120 140 160 Wavelength (nm)IntensityFigure 3-9 Case one-A: Eigenvectors for pre ssure (left) at 66.5546 and temperature (right) at 0.3275 Table 3-3 Eigenvalues for case one-A Eigenvalue Magnitude 1 1.24e+005 2 3.07e+002 3 -5.89 e-011 Table 3-4 Calibration Error case one-A Max. press. error 5.32e-006 RMS press. error 2.79e-005 Max. temp. error 0.095 RMS temp. error 0.595

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97 Case One-B (Temperature Emission Br oadened to Overlap with Pressure) The temperature emission is expanded to slightly overlap the pressure emission. 450 500 550 600 650 700 750 800 0 0.5 1 1.5 2 2.5 Wavelength (nm)Intensity Figure 3-10 Case oneB: Emission spectra 450 500 550 600 650 700 750 800 0 5 10 15 Wavelength (nm)Intensity 450 500 550 600 650 700 750 800 -2 0 2 4 6 8 10 12 14 16 Wavelength (nm)IntensityFigure 3-11 Case one-B: Eigenv ectors for pressure (left) at 75.592 and temperature (right) at 9.365 Table 3-5 Eigenvalues for case one-B Eigenvalue Magnitude 1 4.81e+003 2 1.89e+002 3 2.46 e-012 Table 3-6 Calibration Error case one-B Max. press. error 5.49e-005 RMS press. error 2.88e-004 Max. temp. error 0.095 RMS temp. error 0.595

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98 Case One-C (Temperature Emission Greatl y Broadened to Overlap with Pressure) The temperature emission is expanded to greatly overlap the pressure emission. 450 500 550 600 650 700 750 800 0 0.5 1 1.5 2 2.5 3 3.5 Wavelength (nm)Intensity p Figure 3-12 Case oneC: Emission spectra 450 500 550 600 650 700 750 800 0 5 10 15 20 25 Wavelength (nm)Intensity 450 500 550 600 650 700 750 800 -5 0 5 10 15 20 25 Wavelength (nm)IntensityFigure 3-13 Case one-C: Eigenv ectors for pressure (left) at 72.783 and temperature (right) at 6.556 Table 3-7 Eigenvalues for case one-D Eigenvalue Magnitude 1 1.17e+004 2 1.61e+002 3 -8.6e-012 Table 3-8 Calibration Error case one-C Max. press. error 1.77e-005 RMS press. Error 9.32e-005 Max. temp. error 0.095 RMS temp. error 0.595

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99 Case One-D (Close Emission: Tempera ture at 600nm and Pressure at 650 nm) The center frequencies of th e two emissions are close. 450 500 550 600 650 700 750 800 0 0.5 1 1.5 2 2.5 3 Wavelength (nm)Intensity Figure 3-14 Case one-D: Emission spectra 450 500 550 600 650 700 750 800 0 2 4 6 8 10 12 14 16 18 Wavelength (nm)Intensity 450 500 550 600 650 700 750 800 0 2 4 6 8 10 12 14 16 18 Wavelength (nm)IntensityFigure 3-15 Case one-D: Eigenv ectors for pressure (left) at 78.15 and temperature (right) at 11.923 Table 3-9 Eigenvalues for case one-D Eigenvalue Magnitude 1 4.97e+003 2 1.03e+002 3 -5.04e-012 Table 3-10 Calibration Error case one-D Max. press. error 6.08e-006 RMS press. error 3.19e-005 Max. temp. error 0.095 RMS temp. error 0.595

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100 Case One-E (Shot Noise Imposed on the Spectra) Shot noise randomized by multiplying it by a normalized random error (randn in MATLAB). 450 500 550 600 650 700 750 800 0 0.5 1 1.5 2 2.5 3 3.5 4 Wavelength (nm)Intensity Figure 3-16 Case one-E: Emission spectra 450 500 550 600 650 700 750 800 0 0.5 1 1.5 2 2.5 3 3.5 4 Wavelength (nm)Intensity Figure 3-17 Case one-E: Reconstructed spectra

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101 450 500 550 600 650 700 750 800 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 0 Wavelength (nm)Intensity 450 500 550 600 650 700 750 800 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 x 10 Wavelength (nm)Intensity Figure 3-18 Case one-E: Eigenv ectors for pressure (left) at 280.1082 and temperature (right) at 166.392 Table 3-11 Eigenvalues for case one-E Eigenvalue Magnitude 1 4.13e+003 2 1.79e+002 3 4.25e-003 Table 3-12 Calibration Error case one-E Max. press. error 0.02 RMS press. error 0.089 Max. temp. error 0.277 RMS temp. error 0.925

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102 Case One-F (Shot Noise Amplified by 10) Shot noise amplified by 10. 450 500 550 600 650 700 750 800 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Wavelength (nm)Intensity Figure 3-19 Case one-F: Emission spectra 450 500 550 600 650 700 750 800 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 Wavelength (nm)Intensity Figure 3-20 Case one-F: Reconstructed spectra

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103 450 500 550 600 650 700 750 800 -6 -4 -2 0 2 4 6 8 10 12 14 Wavelength (nm)Intensity 450 500 550 600 650 700 750 800 -6 -4 -2 0 2 4 6 8 10 12 14 Wavelength (nm)Intensity Figure 3-21 Case one-F: Eigenv ectors for pressure (left) at 100.1556 and temperature (right) at 346.3815 Table 3-13 Eigenvalues for case one-F Eigenvalue Magnitude 1 1.25e+005 2 5.43e+003 3 4.04e-001 Table 3-14 Calibration Error case one-F Max. press. error 0.028 RMS press. error 0.104 Max. temp. error 0.423 RMS temp. error 1.601 Case One-G (Filtered Spectra with Shot Noise Amplified by 10) Shot noise amplified by 10. 520 540 560 580 600 620 640 660 680 700 0 2 4 6 8 10 12 x 10 Wavelength (nm)Intensity Figure 3-22 Case one-G: Emission spectra

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104 520 540 560 580 600 620 640 660 680 700 0 2 4 6 8 10 12 Wavelength (nm)Intensity Figure 3-23 Case one-G: Reconstructed spectra 520 540 560 580 600 620 640 660 680 700 -1 0 1 2 3 4 5 6 7 Wavelength (nm)Intensity 520 540 560 580 600 620 640 660 680 700 -1 0 1 2 3 4 5 6 7 Wavelength (nm)Intensity Figure 3-24 Case one-G: Eigenv ectors for pressure (left) at 79.79 and temperature (right) at 13.502 Table 3-15 Eigenvalues for case one-G Eigenvalue Magnitude 1 8.87e+004 2 3.84e+003 3 2.35e-002 Table 3-16 Calibration Error case one-G Max. press. error 0.034 RMS press. error 0.116 Max. temp. error 0.487 RMS temp. error 1.540

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105 Case One-H (Filtered Noisy Spectra Using Only Two Filters) This case is intended to demonstrate the impact of using only two filters on the POD analysis. The ability to use less number of filters means more costly efficient experiment, less time required for data acquisi tion and analysis, and less time for test conditions to vary and hence improved accuracy. 520 540 560 580 600 620 640 660 2 3 4 5 6 7 8 9 10 Wavelength (nm)Intensity Figure 3-25 Case one-H: Emission spectra 520 540 560 580 600 620 640 660 -7 -6 -5 -4 -3 -2 -1 0 x 10 Wavelength (nm)Intensity 520 540 560 580 600 620 640 660 -6 -5 -4 -3 -2 -1 0 Wavelength (nm)IntensityFigure 3-26 Case one-H: Eigenv ectors for pressure (left) at 258.9 and temperature (right) at 192.68

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106 Table 3-17 Eigenvalues for case one-G Eigenvalue Magnitude 1 8.19e+04 2 3.62e+03 3 -0.09e-09 Table 3-18 Calibration Error case one-G Max. press. error 0.0328 RMS press. error 0.1269 Max. temp. error 0.4171 RMS temp. error 1.3858 Summary 1. Normalizing the data produces a third eige nvector that is 4 orders of magnitude lower than the first two, while in the raw data the third eigenv ector was 12 orders of magnitude lower. 2. Increasing the accuracy of the rotation angle increases the accuracy of the calibration (1 order of magnitude / decimal) 3. If the center frequencies of the two peak s and their widths are exactly matched (regardless of the relative magnitude) only one eigenvector emerges. Target transformation is not possible as there is only vector. Varying the width will produce a second factor, in pr actice it is almost impossibl e to have two emissions with the same exact emission freque ncy and broadness. Varying the center frequency by 1 nm will produce two eige nvectors. Error in all cases is not adversely affected. 4. Filtering nearly eliminates the noise from the filtered signal as the integration process acts as an averaging proces s and the results are comparable to spectroscopic results 5. Fitting the temperature data to an exponential fit doesn t produce accurate results as the data range is small and the fitting process fits within that domain, hence a bigger temperature range will improve the fitting process. Instead a quadratic calibration function suffices with good accuracy for small temperature ranges. 6. Non-orthogonal rotation produ ces rotation angles for pressure and temperature that are significantly close to each other. Or thogonal rotation produces better results (less error), however the rotation angles are significantly apart. 7. POD managed to separate the pressure and te mperature data effectively in all cases, except the case of identical center fre quencies and spectral emission width. 8. Adding noise to the signal is identified by POD as a th ird factor that is still relatively insignificant in ma gnitude compared to the first and second eigenvalues, but significantly higher than the case of no noise. Incr easing the magnitude of the noise increases the magnitude of the third eigenvalue.

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107 9. In all presented cases, only two factors were used. Using only two filters produced comparable results to using four filters. This significant result shows that the number of extracted factors determines the number of filters needed for calibration. Case Two (Temperature Dependent Pressure Emission) In this case the effect of temperature on pressure is examined. The temperature dependence is based on equations (3.13), (3.14) and (3.15). The same analysis performed on case one is carried out and yields similar results. Only the noise infected data, both spectroscopic and filtered, are presented. A summary at the end of this section addresses omitted results and provides discussion. 450 500 550 600 650 700 750 800 0 1 2 3 4 5 6 x 104 Wavelength (nm)Intensity Figure 3-27 Case two: Emission spectra Calibration Surface Fitting The intensity is calculated in the artificial data using 11nr refE RTT ref tempI e I The temperature can thus be retrac ted by the following equation. 11 lnnrrefref tempRI TEIT (3.22)

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108 Using 1,nC to represent ref tempI Iin the above equation the temperature is accurately calculated with a maximum absolute error of 4 x 10-5 K. In order to account for the temperature effects in the pressure calibration, a surface fit is needed with the pressure as a function of the tw o sets of scores C1,n and C2,n. The first set C1,n accounts directly for the temperature, in fact, the calibration below will show that they are interchangeable. Recalling the theoretical function for generating the pressure intensity data ref ref pressI P ATBT I P which is expressed in te rms of the pressure as: 1ref refI AT P PIBTBT (3.23) The first term is a function of both pressu re and temperature, while the second term is purely temperature dependent. These coeffi cients can be expressed in terms of the temperature via simple algebraic manipula tions of equations (3.14) and (3.15) (Appendix-b) to yield the following: 0.01 0.15 10.01AT T B TT (3.24) 11 0.0126122.8884BTT (3.25) The ratio of the constants AT B T is an order of magnitude smaller than the constant multiplying the intensity ratio 1 B T. The first term in equation (3.23) is a product of the intensity ratio and some function of temperat ure. Hence a product of the two sets of

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109 scores is appropriate to represent the first term. The second term can thus be represented in the calibration function by the temperature scores C1,n. These two representations are not necessarily linear. A second order calibra tion function for the pressure can then be represented by the following equation. 111121 121222222 111121 222 121222 222 1,11,12,1 1,11,12,1 22 2 1,1,2, 1,1,2,1 1 1 1nnn nnn nnn nnnCCCCCC CCCCCC a b c d e CCC CCCCCC CCC 1 2 1 n n P P P P (3.26) Solving for the coefficients yields a calibration surface for the pressure as a function of both sets of scores.

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110 450 500 550 600 650 700 750 800 -2 -1 0 1 2 3 4 5 x 105 Wavelength (nm)Intensity 450 500 550 600 650 700 750 800 -3 -2 -1 0 1 2 3 4 x 105 Wavelen g th ( nm ) Intensity Figure 3-28 Case two: Eigenvector s rotated at the appropriate angle for temperature (left) at 345.78 and pressure (right) at 106.44 0.06 0.07 0.08 0.09 0.1 0.11 0.12 300 310 320 330 340 350 360 370 EigenvaluesTemperature (K) Figure 3-29 Case two: Te mperature calibration The temperature calibration based on equati on (3.22) yielded a STD in the test points of 0.06K and a maximum absolute erro r of 0.17K. The pressure calibration is expressed by the following equation. 222 11211243.755 519.74 1088.4 160.15 0.44783PCCCCCC (3.27) C1

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111 -0.14 -0.12 -0.1 -0.08 -0.2 -0.1 0 0.1 0.2 2 4 6 8 10 12 14 C1 C2 Pressure (psi) Figure 3-30 Case two: Second or der pressure calibration us ing the scorers from POD 300 320 340 360 -0.2 -0.1 0 0.1 0.2 2 4 6 8 10 12 14 Temperature (K) C2 Pressure (psi) Figure 3-31 Case two: Second order pressure calibration using the 2nd set of scorers and temperature

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112 The third order calibration function is expressed by the following equation. 2 1121 22333 1211238.483 516.79 1036.8 93.442 163.64 11038 0.2689PCCCC CCCCC (3.28) -0.15 -0.1 -0.05 -0.3 -0.2 -0.1 0 0.1 0.2 2 4 6 8 10 12 14 C1 C2 Pressure (psi) Figure 3-32 Case two: Third order pressure calibration using the scorers from POD at 193.46 -0.15 -0.14 -0.13 -0.12 -0.11 -0.1 -0.09 -0.08 -0.07 2 4 6 8 10 12 14 C1 Pressure (psi) -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 2 4 6 8 10 12 14 C1 C2 Pressure (psi) Figure 3-33 Case two: Pressure calibra tion using the scorers from POD at 193.46

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113 A third order calibration sli ghtly improves the results from a STD of 0.02 for the second order fit to a STD of 0.012. P OD was capable of separating the two environmental conditions and retrieve the ch aracter of the original functions in the calibration functions. The filtered data exhibits the same results as shown below. 520 540 560 580 600 620 640 660 680 700 0 0.5 1 1.5 2 2.5 3 Wavelength (nm)Intensity Figure 3-34 Case two: Nume rically filtered emission 520 540 560 580 600 620 640 660 680 700 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 Wavelength (nm)Intensity 520 540 560 580 600 620 640 660 680 700 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 Wavelength (nm)Intensity Figure 3-35 Case two: Numerically filtered em ission eigenvectors for pressure (left) at 106.6 and temperature (right) at 346.06

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114 300 320 340 360 380 -0.2 -0.1 0 0.1 0.2 2 4 6 8 10 12 14 Temperature (K) C2 Pressure (psi) Figure 3-36 Case two: Second order pressure calibration using the 2nd set of scorers and temperature Summary 1. Remarks made for case one are applicable for case two 2. A calibration surface was required for the pressure. This is, however, should not be taken as universal for all paint formulations The artificial data was generated based on a particular paint charact eristics and other formula tions may should different characteristics that would allow for one dimensional calibration functions. Factors controlling this calibration are spectr al cross-talk, spectral overlap, PSP temperature sensitivity, and its mathema tical character (i.e., linear, exponential, etc.) 3. Accuracy of the calculated pressure using POD is a function of degree of cross-talk between the luminophors, degree of temper ature dependence in the PSP probe, and the magnitude of noise in the signal. Spect ral overlap is easily resolved by the POD as long as the higher wa velength emission does not absorb lower wavelength emission. If absorption occurs, then the problem is classified as cross-talk rather than simple spectral overlap.

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115 CHAPTER 4 LAMINAR CHANNEL FLOW This chapter presents theoretical discu ssion of the channel flow experiment. The chapter starts with the simple isothermal pr essure driven flow and then examines the nonisothermal solution. Only the isothermal case theoretical solution is presented. The nonisothermal cases are discussed and the governi ng equations for the solution are presented without solution. The non-isot hermal solution is presented as an aid for future work, Preface A channel flow experiment is employed in this work because it provides a well controlled environment allowi ng the calibration technique to be fully assessed. By controlling the boundary temperatures and the ma ss flow rate inside the channel, hence the pressure gradient, the pressure and temp erature fields can be predicted by theory. Fluid flows can be generally categorized as internal or external. Internal flows are entirely bounded by solid surfaces, while exte rnal flows are unbounded such as the flow over an airfoil. More precisely, in external flows boundary layer growth on a surface is not externally constricted (i.e., by a solid boundary), while such growth is eventually constrained in internal flows. An internal flow experiment, namely a channel flow, is utilized in this work as an application to demonstrate the feasibility of dual-luminophor PSP in dynamic testing. Internal flows can be classified as either laminar or turbulent depending on the Reynolds number Re. inertia forces Re viscous forcesVDVD (4.1)

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116 where and are the fluid density, dynamic and ki nematic viscosities, respectively, Vis the characteristic velocity of the flow, and D is the hydraulic diameter. Analytical solutions exist for various laminar internal flows including some cla ssical flows that are fundamental in any fluid mechanics text. Tu rbulent flows do not enjoy such simplicity, hence analytical solutions are not possible a nd empirical data and semi-empirical theories constitute our main understanding of such flows. Laminar and turbulent flows can be further subcategorized into compressibl e and incompressible. A channel flow can be often assumed to be two-dimensional by having a sufficiently large aspect ratio 1dw h; where dwis the channel width and h is the channel height, see Figure 4-2 below. The flow can be driven by a moving wall, gravity, or a longitudinal (flow direction) di fferential pressure with stationary walls or a combination of two or more driving potential s. The experiment utilized in this work is purely pressure driven, a classical flow known as Poiseuille flow in a rectangle channel. Figure 4-1 Channel flow schematic. Flow P1 P2 P1 > P2 Lower wall U pp er wall Incoming flow z y x h

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117 Figure 4-2 Channel flow: flow deve lopment and pressure distribution The following discussion is after (Fox and McDonald, 1998; Panton, 1996; Schlichting, 1979; White, 1974). Typically, th e received flow entering the channel is modeled as a slug flow (i.e., uni form parallel velocity) free of vorticity, which is rather difficult to establish in actual applications. In the experiment carried out in this work, the main difficulty lies in assuring a uniform ch annel height. The channel height is 0.25 mm, therefore, paint thickness variation and ch annel deformation are possible sources of channel height variation. Further, paint r oughness could alter the surface characteristics causing early transition in the channel. In ch annel flow, the center flow particles are accelerated by the pressure forces, and hence th e pressure must have a negative gradient l wd h Uniform f low Developing f low Fully developed f low P Pambinet P Lx Hydrodynamic length, LD Fully developed region h Flow u(x,y) x y u(y) x z y 1dw h

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118 along the flow direction while fluid particles adjacent to the solid boundaries experience viscous effects (i.e., friction) that cause a velocity deficit in the regions near the walls known as the boundary layers. These layers grow as the flow advances downstream deforming the initial uniform velocity profile. As the flow velocity is brought to zero at the wall by the no-slip condition and is gradua lly increased away from the wall, this velocity deficit dictates an increase in the centerline velocities for an incompressible flow to maintain a constant mass flow rate. Furt her, the development of this boundary layer causes a longitudinal reduction of the inviscid core of the flow. After a specific length known as the hydrodynamic entrance length th e two layers (top and bottom) merge forming the famous parabolic velocity profile. At this point, the flow has become completely viscid and has reached a fully deve loped stage. Velocity gradients in the axial direction of the flow vanish and the velocity reaches its maximum value at the centerline. Further, the pressure gradient is a constant in the axial direction as it balances the viscous forces in the developed region of the channel. This analysis is a reasonable approximati on under the condition that the aspect ratio is large enough. If the height of the channel is comparable to the channel width then four boundary layers, instead of tw o, interact and the hydrodyna mic entrance length may be longer and is determined by the longer dimension as shown in Figure 4-3 Furthermore, the axially fully developed flow would po ssess a lateral gradient and the maximum velocity would vary across the flow. In the case of the high aspect ratio channel the viscous effects would need a very long channe l length for the lateral boundary layers to diffuse and merge and hence relatively s hort channels can be modeled accurately neglecting end-wall effects.

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119 Figure 4-3 Low-aspect ratio de veloping channel flow A key dimensionless parameter of the fl ow is the Reynolds number. Experiments have shown that for typical engineering appl ications such a flow would transition from laminar to turbulent around Re14002300 for smooth circular channelsh. However, much higher transition values are attainable by careful fabrication of the channel surface to ensure the lowest friction coeffici ent possible and more importantly through meticulous attention to the incoming flow to prevent any disturbances in the upstream approaching flow. Further, the velocity profil e in the fully developed region is subject to the flow condition (i.e., lamina r or turbulent). Turbulent fl ows have fuller velocity profiles due to the mixing effect, which is the case for most practical channel flows except highly viscous flows. The hydrodynamic length is hence obviously a function of the Reynolds number and for laminar flow is (Shah and London, 1978): Hydrodynamic length Fully developed region wd

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120 0.50.05ReD hL h (4.2) This empirical relation shows that for lami nar flows entrance le ngths can be about 100 h. Turbulent flows, however, are indepe ndent of the Reynolds number (Incropera, 1981) and show much shorter entran ce length on the order of 25-40 h (Fox and McDonald, 1998), once more, due to the enhanced mixing. Although this classical problem may strike the reader as a simple fluid mechanics problem, research efforts are still ongoing to formulate a more accurate solution that accounts for entrance effects and turbulence as we ll as heat transfer issues. For example, in the design of flow-intake devices, accurate pre ssure loss analysis in the entrance region is detrimental. A more recent application that relies on accurate channel flow analysis is microchannels, where the length of the channel is shorter than the entrance length (Kohl et al., 2005; Muzychka and Yovanovich, 1998). Validating the dual-luminophor paint in the fully developed region will enable the extension of the paint application to the entrance lengths as well to more complicat ed flows/geometry. Isothermal Flow Solution Mathematical Derivation The governing equations for a channel fl ow in rectangular coordinates are: 0 continuity uvw txyz (4.3) Navier-Stokes equations for a Newtonian fluid with constant viscosity: 222 222 x x momentum uuuuuuuP uvwg txyzxyzx (4.4)

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121 222 222 yymomentum vvvvvvvP uvwg txyzxyzy (4.5) 222 222 zzmomentum wwwwwwwP uvwg txyzxyzz (4.6) Assumptions/Justifications 1. Two-dimensional flow with zero cross flow/gradients 0,0 w z : The aspect ratio of the channel 1dw h is large enough such that the flow is only in the x-direction and the channel length is relatively short, thus preventing viscous effects, due to the sidewalls, to laterally diffuse into the channel, except very near the sidewalls. 2. Parallel laminar incoming flow: The low velocity approaching flow is treated through a series of turbulence dampi ng layers (aluminum and packaging foam) to even and damp out any fluctua tions in the velocity and turbulence induced by the flow path. Further, th e mass flow rate is investigated experimentally (Chapter 5) showing a linear relation with respect to the pressure drop validating laminar conditi ons for the entire channel (Panton, 1996). 3. Steady laminar incompressible flow 0D Dt : Mass flow rate well controlled and measurements acquired under steady conditions (i.e., no transient measurements). Mass flow rate (as desc ribed in Chapter 5) is low enough that the Mach number is below 0.3 (incompr essible) and the Reynolds number is below 1400, ensuring laminar conditions. This further implies that the velocity divergence is zero (i.e., continuity equation) 4. Body forces are only due to gravity a nd act in the negative z-direction. Hence, the reduced system of equations is: 0uv xy (4.7) 22 22uuuup uv x yxyx (4.8)

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122 22 22vvvvp uv x yxyy (4.9) 0zp g z (4.10) Boundary Conditions The boundary conditions for a pressure driv en flow between two rigid infinitely wide parallel plates are: 0 @ 0&uvyh (4.11) The boundary conditions are the no-slip fo r the axial velocity component and no velocity penetration at the wall, i.e ., zero vertical ve locity component. The Fully Developed Region (Poiseuille Flow) In the fully developed region further simp lification allow for an exact solution for laminar flows. As the term fully-developed implies, the velocity profile ceases to vary in the flow directions. Only important equati ons/solutions are presen ted in this chapter. The details of the solution can be found in Panton (1996), White ( 1991), and Schlichting (1979) and is provided in AppendixB. The velocity solution is: 2 2 2 hPyy uy xhh (4.12) This is the famous Poiseuille parabolic profile with a maximum velocity value occurring at the centerline 2 h y 2 max8 hP u x (4.13) It is often convenient to non-dimensionaliz e the velocity by the maximum or mean velocity in order to have a universal representation of the velocity profile.

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123 2 max4 uyy uhh (4.14) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Normalized VelocityNormalized Channel Height Figure 4-4 Fully developed velocity profile for an incompressible laminar channel flow The channel height is 0.01 making any velo city measurement inside the channel to verify the velocity profile rather difficult. Anemometry probes (e.g. hotwire) would not be suitable due to flow inte rference. Although probes with wi re diameter on the order of micrometers exist; the probe itself is much larger in dimension and hence will impose on the flow. Particle Image Velocimetry (PIV ) measurements would also be close to impossible. Seeding particles on the order of micrometers are available allowing for PIV measurement without having concerns about th e relative size of th e seeding particles relative to the channel hei ght. Condensation on the glass is, however, a concern. Nonetheless, incense has been used successf ully in the literature to evade seeding particles problems (Holman, 2006). The main difficulty with PIV measurements in the channel is the optical alignment of the light sh eet. The measured sect ion of the channel is Normalized channel height Normalized velocity

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124 relatively long (10.18) and hence any slight mi salignment in the light sheet would result in an incorrect measurement of the flow field. As shown in Figure 4-5 if the light sheet is misaligned, the measured flow field would not correspond to the flow field at a certain channel elevation, u( y = constant), rather the flow fiel d inside the channel at different elevation, u( y constant). Figure 4-5 Hotwire and PIV measurement schematic in the channel Even though the velocity could have not b een measured experimentally, it can be estimated from the mass flow rate, which is a controlled variable in this experiment. Further, once the velocity pr ofile is known other quantitie s can be obtained via simple relations. The volume flow rate Q information is essential in the characterization of any fluid process. It is easily computed by inte grating the velocity over the cross sectional area. 3 0012whwhP Qudydz x (4.15) Wire (~2-7m) Probe (~150m) Lower wall Upper wall PIV light sheet Flow Top view of hotwire probe x y

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125 This relation will be used to validate la minar flow conditions in the channel flow and estimate the Mach and Reynolds numbers. As seen in the equation, the volume flow rate is linearly related to the pressure drop in the fully developed region for laminar flows. This linear behavior is not valid for turbulent flows (Panton, 1996). Once the volume flow rate is known, the mean velocity is readily obtained. 2 12mQhP u whx (4.16) Note that the average veloci ty is two-thirds the maximum velocity for a rectangular channel; however, the average velocity is only one-half the maximum velocity for circular cross sections. This is due to higher frictional for ces as result of the larger effective wetted perimeter. Equations (4.15) and (4.16) are utili zed to verify flow conditions. The latter provides a mean ve locity and hence the Mach and Reynolds numbers. At the maximum flow rate of 100LPM (0.0017 m3/sec) and standard conditions, the centerline pressu re gradient in the fully developed region (9.18) was measured experimentally to be 7.3 psi (50318 Pa), which yields an average velocity of: 2 20.00025 50318 12121.82e050.23317 62 secm mhP u x m u (4.17) Using the flow rate information: 0.0017 0.10160.00025 65 secm mQ u wh m u (4.18)

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126 The discrepancy in the calculated average velocity based on the measured mass flow rate and the centerline pressure gradient indicates that the channel is deforming (see Chapter 5), hence the pressure gradient is not constant across the channel. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 15 16 17 18 19 20 21 22 23 x/LPressure (psi) Experimental Theoretical Figure 4-6 Isothermal case: Ce nterline pressure gradient along the channel showing the deviation of the experimental resu lts from the theoretical prediction. Using equation (4.15), the calculated flow rate from the measured centerline pressure gradient is: 3 30.10160.00025 50318 12121.82e050.23317 0.00157 secwhP Q x m Q (4.19) This value is 6% lower than the experi mental measurement from the mass flow controller. There was some insignificant leak s between the aluminum and glass plates, however, the discrepancy is mainly due to channel deformation. Increasing the channel

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127 height from 0.25 mm to 0.25527 mm yi elds identical results for the flow rate calculated from equation (4.19) and the experimental va lue, and hence the two calculated mean velocity values from equations (4.17) a nd (4.18) are matched. The modified channel height represents an average channel height and is ~2% (5 m) higher relative to the noflow channel height. One possible way to accu rately estimate the channel deformation is to install an array of pressure taps at the beginning and end of the channel. The pressure taps will provide transverse pressure profile, which in tu rn will indicate any height variation. The calculated mean velocity based on the modified channel height is: 0.2552764.38 secm hmmm u (4.20) Thus, the nondimensional numbers are computed to yield: 0.2 M (4.21) Re1100 (4.22) These values confirm initial assumptions of incompressible and laminar flow, respectively. Further, the pressure gradient behavior was observed experimentally and showed a linear relation with respect to mass flow rate. Non-Isothermal Fully Developed Flow In the previous analysis isothermal conditions where assumed, but more importantly viscosity was presumed cons tant allowing for the decoupling of the momentum and energy equation (neglecting fr ee convection). The following analysis is based on Incropera (1981). The term fully -developed thermal region for flows with convection heat transfer is based on a non-di mensional temperature difference as opposed to the actual temperature. When this dimensionless temperature is independent of x the

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128 flow is termed fully developed. Hence th e fully developed thermal condition is: 0w wmTxTxy xTxTx (4.23) where wT is the wall temperature and mT is the flow mean temperature. If the boundary condition is a constant te mperature along the channel 0wT x then the fully developed condition reduces to: wm wmTTT T xTTx (4.24) while for a constant heat flux we obtain: wmTT x x (4.25) or alternatively: mT T x x (4.26) The foregoing results clearly show that know ing the mean temperature is essential in describing the temperature distribution throughout the fully developed region of the channel. The temperature distribution at the surface T x is the quantity sought after in this work as a mean of validating the m easured temperature profiles by the paint. However, the surface temperature is not cons tant due to forced convection effects and there is no heat flux at the surface, rather a constant heat flux at x = 0 and L and at z = 2dw The boundary conditions are clearly more involving than the simple cases of constant heat flux and consta nt temperature. A simple en ergy balance would yield the following expression for the mean temp erature in terms of convection.

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129 m A wm pdT W hTT dx mc (4.27) Obviously, this still calls for a known temp erature distribution or heat flux over the surface, which is neither available nor simple In order to estimate the surface and mean temperatures, the temperature profile ,Txy must be then determined by solving the energy equation. The energy equation for a Newt onian fluid in rectangular coordinates is: De pVkT Dt (4.28) where e is the internal energy per unit mass, where is customarily call ed he dissipation function and is always positive definite as viscosity dissipates energy from the system. For the fully developed viscous region in the channel flow problem, using the same assumptions used in the velocity deri vation, the energy equation reduces to: 2 22 22 pTTpTTu cuuk txxxyy (4.29) The temperature boundary and initial conditions are ( Figure 4-7 ): 0 , 12 1, @0, @0,0 @0, @0,0 @0; ,0w glassairwup metalairwbottomTxyTxy TxyTxxy Txy hhTTxyh y Txy hhTTxy y TxyTT Txtxy tL (4.30)

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130 Figure 4-7 Non-isothermal flow schematic These boundary conditions represent a ba lance between forced convection and conduction at the upper and lowe r walls, a uniform temperatur e profile at the beginning of the channel, while the lower wall havi ng an interface boundary condition with the metal. The problem is not easily reali zed because the bottom boundary condition (y = 0) is an interface boundary. This means that convection due to the flow and conduction in the metal are interfacing and constantly updating each other, he nce the two problems must be numerically solved simultaneously until steady conditions are realized. The conduction problem for the metal plate is gove rned by the general heat equation shown below. y x To Flow T1T2 T2 T1> T2 Tw Convection to air from metal and then from air into glass Conduction in metal Conduction in glass Side view Flow T2 T2 T1> T2 T3 > T2 Top view

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131 222 222pc TTTqT x yzkkt (4.31) where q represents energy genera tion within the plate. C onduction and radiation on the outside boundaries can be ne glected as forced convection in the channel is more significant. The two problems interface the terms T x and 2 2T x For each iteration equation (4.31) is solved first with the te mperature profile at the interface updated by the solution for one time step, then equation (4.2 9) is solved with the updated boundary and its solution updates the interface boundary. Th e numerical solution is reiterated until convergence occurs. The governing equations represent the 2-dinemsional solution in x and y coordinates. Realistically, the temperature is also varying in the z-direction, hence the problem is 3-dimansional. Besides the obvi ous intricacy of the problem, it is further beyond the scope of this work and thus is not further pursued. Nonetheless, the theory can be numerically solved to validate the experimental results for future work.

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132 CHAPTER 5 EXPERIMENTAL SETUP This chapter describes the experimental setup and the data acquisition process, including hardware specificati ons and design. It starts by de scribing the hardware and the different devices utilized. Th e latter part presents the optical setup and key issues involved with the imaging system, such as im age registration due to thermal expansion. Hardware Description Channel The channel is comprised of two rectangular plates (14 x 6 x 1): one aluminum and the other is window (float)-glass for op tical access. The two plates are clamped together with a U-shape hard gasket sandwiched in between them creating the channel cavity. The thickness of the gasket determines the channel height; however, C-clamps are used to attach the aluminum and glass plates which would affect the channel height as well due to localized clamping profile instead of a uniform profile. The gasket used in this experiment is 0.01 (0.25 mm) thick, wh ich then constitutes the channel height. The channel height was chosen to maximize th e pressure gradient along the channel. Compressed air is supplied through two la rge tanks which are charged by a 300HP rotary screw compressor (Quincy QSI-1000) capable of supplying 950 SCFM at 200 psig. The compressor capacity well exceeds the required stagnation pressure of ~ 50 psi. Moisture in the compressed air is removed via dual-desiccant dryers (Hydronix). This is a crucial requirement as moist air could lead to condensation on the gl ass, especially when heating and cooling are applied. The air channels into the la b through a series of 3 and

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133 1 lines that lead to the mass flow controller MFC (AALBORG GF C471S). The mass flow controller plays a central role in th e success of the experimental work since maintaining constant flow rates, and conseque ntly pressure levels, is vital for accurate calibration. The MFC has a maximum flow rate of 3.531 SCFM or 100 SLM (Standard Liter per Minute). An excitation voltage of 12V is supplied to the MFC, while controlling the flow rate is accomplished via an analog output signal from a National Instrument (NI) 12-bit 100KS/sec data acquisition card (DAQP ad6020E) attached to an NI BNC 2120 board. The MFC has an input voltage range of 0-5V and a calibration constant of 0.05 V/SLM. A circuit attached to the MFC supp lies an output voltage providing feedback to monitor the stability of the flow rate. Figure 5-1 Mass flow c ontroller (AALBORG) Flow then enters a cylindrical PVC sta gnation chamber (2 D x 4 L) through the side where the incoming flow velocity is si gnificantly reduced on th e opposite wall of the cylinder before diffusing into the chamber. Th e chamber is mounted perpendicularly with respect to the channel and hence the flow at the exit of the chamber is forced to turn 90

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134 degrees. The chamber-to-exit area ratio is ~ 79, ensuring stagnation conditions in the chamber. A static and stagnation pressure ports are inserted into the chamber to ensure stagnation conditions and provide stagnation back pressure information. At the exit of the stagnation chamber a inch thick circular pie ce of packaging foam la ys flushed with the surface of the aluminum plate to abate any turbulence generation due to the 90 degrees turn. A rectangular strip of aluminum foam is embedded in a recessed area downstream of the packaging foam at the beginning of the channel to damp out any left over turbulence. Figure 5-2 Channel flow schematic: Top view of channel shown. 1 2 Calibration pressure tap Thermocouples Water channel for circulating antifreeze Heater strait housing electrical heaters Aluminum foam 14 6 10.18 4 2 3 2 Gasket Test pressure tap Flow

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135 Two cylindrical straits ahead of the fo am house two 120V 600W electrical heaters (Omega CHROMALOX CIR-2066) controlled by a variable voltage controller (POWERSTAT). Two water channels serve to circulate cold antifreeze providing temperature boundary control. One channel is longitudinally positioned at the top of the channel (relative to the Figure 5-2 ), while the other is perpendicularly laid at the very end of the channel. Anti-freeze is circulated in the water channels via a cooler (Haake G/D3). The entire assembly rests on three hot-pl ates (Thermolyne Cimarec 375 W) providing heat generation from the bottom side of the channel. The aluminum plate has twenty Ttype thermocouples (Omega) and seventeen 0.02 diameter pressure taps arranged on the surface as shown in Figure 5-2 All thermocouples and pressure taps are flushed with the surface and are free of burr. Thirteen pressure taps line up the cente rline of the channel and provide pressure information for calibra tion. Four additional pressure taps are utilized to examine the accuracy of the cal ibration and the two-dimensionality of the flow. The surface of the aluminum plate has a mirror-surface polish (600 grit) in order to prevent premature transition of the flow to tu rbulence. The paint is applied on top of the aluminum using an OPTIMA 5000 gravity sp ray-gun with a 0.25 nozzle head. No primer was used in the experiment to avoid more thickness uncertainty. After the paint is applied and allowed enough time to cure a Terry cloth is used to smooth the surface. The surface is further treated with compressed air to remove a ny residual paint or primer loose particles. The paint is manually app lied in a systematic and steady motion to minimize any surface thickness variation. Furt hermore, the amount of paint applied is optimized by applying just enough paint laye rs to yield enough intensity emission upon excitation without having an average thickne ss that would impact the overall channel

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136 height. The last two steps (i .e., uniform and optimal thickne ss) are important for ensuring the most agreement upon comparing the theoretical and measured pressure distributions. Figure 5-3 (A) Channel resting on heaters (B) Side view of channel showing the 1 inch glass plate (C) Backside of channel showing thermocouples, pressure taps, stagnation chamber and tubing connecting from the top water channel to the cooler. B A C

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137 Figure 5-4 Close-up of the beginning of the channel showing the packaging and aluminum foam, thermocouples and pressure taps. First two test pressure taps are circled in yellow. The above figure shows a close-up of the be ginning of the channel. As seen in the figure, the greatly decelerated flow from the stagnation chamber exis ts through a layer of packaging foam. The flow impinges on the glas s plate and is then forced to enter the channel through the aluminum foam strip. The flow is then accelerated inside the channel under differential pressure forces meeting am bient conditions at th e exit. The stagnation pressure is a function of the mass flow rate, channel height, and visc ous forces inside the channel. Channel Deformation In this experiment large pressure grad ients were sought to ensure significant intensity variation due to th e paints shallow gradient near and above atmospheric conditions. The pressure forces due to the flow inside th e channel caused the glass and aluminum plate to deform altering the eff ective cross sectional area of the channel. Thermocouples Packaging foam Pressure taps Aluminum foam

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138 Figure 5-5 Channel deformation due to pre ssure forces (modulus of elasticity for aluminum and glass is ~ 10.5 and 9.6 psi x 106, respectively) Several attempts were made before choosi ng 1 inch thick glass as the material for the optically accessible plate. A 3/8 inches wi ndow-glass piece was fitted in an aluminum frame and bonded to the frame by epoxy. The glass cracked upon clamping the aluminum frame to the other metal plate under flow-on conditions. It is conceivable that the local stress by the C-clamps combined with the pr essure inside the channel lead to glass cracking. The second attempt utilized Plexig las, as it a possesse s higher modulus of elasticity. Plexiglas, however, is more prone to scratching and is often coated with chemicals that luminesces upon excitation with blue/UV radiation. The Plexiglas proved durable and did not crack; none theless, Plexiglas has relatively high thickness tolerance ( 0.05 mm) and therefore created an une ven channel height which was clearly observable in the pressure distri bution along the fl ow direction ( Figure 5-6 ). Plexiglas would be the optimal choice if the channel height is large enough for such small surface d (x) Deformation line x Pstag Patm

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139 variations to be insignifican t. For that reason (i.e., surface flatness) a 3/8 inches glass plate was reused without inserting it into any frame, but rather a full size plate was directly clamped to the metal plate. 0 2 4 6 8 10 15 16 17 18 19 20 21 22 23 24 25 x-position (inch)Pressure (psi) Figure 5-6 Channel deformation due to pressu re forces using Plexiglas comparing the theoretical pressure profile (green line) to experimental profile (blue circles). The 3/8 glass deformed almost twice as much as the 1 glass as shown in Figure 5-8 This confirms that pressure deviation from theory is due to glass deformation. Using simple mechanics of equations (Beer a nd Johnston, 1981) one can deduce deflection profile as shown in Figure 5-7 The plate is modeled as a wi de beam fixed at one end and free at the other. This simplification is undert aken for two reasons: first, the deformation of the beam would be higher th an that of a plate clamped at three sides, hence this estimate would represent a worst case scenar io. Second, modeling the deformation of a plate is rather involved and re quires finite element calculations. The load (i.e., pressure) is modeled according to the theoretical Poiseuil le flow solution. For a 6 wide beam the

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140 deflection is maximum at the beginning of the channel, which is consistent with experimental observations. 0 2 4 6 8 10 12 01234567891011121314 Position (inch)Percent deflection Figure 5-7 Calculated percentage channel height deformation (re lative to no-flow conditions of 0.01) along the centerlin e for 1 plate with a maximum flow rate of 100LPM, 23 psi static pressure at the beginning of the channel and 0.01 channel height. Bernoullis equation pr edicts that the pressure scales as the velocity square and continuity predicts a linear relation between ve locity and area (i.e., channel height for a fixed width). Therefore the maximum vari ation from the figure above is ~ 3.2%. Figure 5-8 shows 4% maximum deviation in the pressure.

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141 Figure 5-8 Glass deformation (a comparis on between theoretical and experimental results): 3/8 glass (top) and 1 glas s (bottom) with percentage pressure deviation from theory in top-left corner of each plot. Flow from right to left 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.50.00 0. 10 0 .20 0.30 0. 40 0 .50 0. 6 0 0. 70 0. 80 0.90 1. 00x / LPressure (psi) actual theor y Pl(tl) -0.2 0 0.2 0.4 0.6 0.8 10.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00x / LDeviation from theory (psi) 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.50.00 0 .1 0 0.20 0 .3 0 0 .4 0 0 .5 0 0 .6 0 0 .7 0 0 .8 0 0 .9 0 1 .0 0x / LPressure (psi) theor y actual Pl(l) -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.40.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00x / LDeviation from theory (psi )

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142 Optical Setup A schematic of the optical setup for the experiment is shown in Figure 5-9 The CCD camera utilized is a Photometrics CH250A coupled with a 14-bit 200 kHz A/D converter (CE200A) for pixel voltage convers ion. The CCD chip (SITe502CB/AR-X) is 512 x 512 pixels thinned scientific grade array with a FWC of 329,000 e-. The camera head is thermoelectrically cooled to minimi ze thermal noise in the CCD chip output. In order to capture the entire channel with the CCD camera, a Nikon NIKKOR 50 mm lens is attached to the front of the camera. Sma ll focal lengths produce a fish-eye effect in the image observed as warping of the image biased towards the center of the image. Figure 5-9 Experimental optical setup showing the relative position of the CCD camera and excitation sources with respect to the channel Filter wheel CCD camera Excitation source Stagnation chamber Flow Heaters Heaters Aluminum p late Glass p late

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143 A filter wheel is positioned in front of th e lens to resolve the spectral range. In order to select the appropriat e filters a spectroscopic analys is of the paint emission is needed. The following two figures show the pa int spectral response due to pressure and temperature. Figure 5-10 Pressure response of dualluminophor paint at 293K (Kose 2005) Figure 5-11 Temperature response of dualluminophor paint at 14.7 psi (Kose 2005)

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144 Based on the spectral data above, four ba ndpass interference filters (Melles Griot) are selected. As shown in the following four figures, the four filters have a center frequencies of 550nm (03 FIV 044), 600nm (03 FIV 046), 650 nm (03 FIV 048), and 700nm (03 FIV 058). Figure 5-12 First bandpass interference filter: 550 nm, 40 8 nm FWHM; dia. = 50 mm (www.mellesgriot.com) Figure 5-13 Second bandpass interference filt er: 600 nm, 40 8 nm FWHM; dia. = 50 mm (www.mellesgriot.com)

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145 Figure 5-14 Third bandpass interference filter: 650 nm, 40 8 nm FWHM; dia. = 50 mm (www.mellesgriot.com) Figure 5-15 Fourth bandpass in terference filter: 700 nm, 40 8 nm FWHM; dia. = 50 mm (www.mellesgriot.com) Observing both the emission spectra and the bandpass filters plots, the first filter (550 nm) should only capture th e temperature emission. The second filter overlaps with the beginning of the pressure emission and hen ce is expected to observe some of pressure emission. The third and fourth filters (650 a nd 700 nm, respectively) capture the pressure emission due to pressure and temperature eff ects as well. The former overlaps with the

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146 main pressure emission, while the latter obs erves only the tail of the emission. This intensity variation between the different filt ers would necessitate different exposure times to maintain similar SNR th roughout the spectra. Figure 5-16 Filters arrangement relative to pa int spectral response to temperature (left) and pressure (right). The excitation sources are two blue super-bright LEDs by ISSI that is approximately centered at 465nm. The LEDs are c ooled with an internal fan to maintain lamp stability. LEDs were positioned far enough from the channel to create a more uniform illumination field and avoid sharp deviations in the intensity ensuring optimal SNR over the entire image. Care should be practiced to also avoid having the reflection of the LEDs on the image. This is si mply accomplished by locating the LEDs far enough laterally. All optical surfaces are cleaned with an appropriate solvent to remove any oil residue or dust particles. Data was collected using a Pentium III computer and NI LabView software. The software interfaced with Photometrics softwa re V++ to acquire the images. A NI SCXI 550 nm 600 nm 650 nm 700 n m

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147 1000 frame accessorized with a NI SCXI-1303 m odule was used to read all thermocouple data and a Mensor digital pre ssure gauge (Model 15000) collected pressure readings (f.s.: 25 psia and accuracy: 0.025% f.s.). A mechani cal pressure scanner was used to switch between the appropriate pressure channels. Figure 5-17 (A) Filter wheel (B) Blue LED ISSI LM2 (excitation source) (C) CCD camera and filter wheel assembly A B C

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148 Image Registration Image registration is the process of aligni ng two images to sub-pixel accuracy often utilized in PSP application in wind tunnels. In real experiments model movement is inevitable due to aerodynamic loads, t unnel vibration, and camera movement. PSP luminophors disperse inhomogenously in binders and tend to aggregate when embedded in nano-spheres in dual-luminophor systems (Kose, 2005). This creates sharp spatial gradients due to this uneven di spersion. As optical distorti on occurs, e.g. due to model movement, these variations create a rough image effect in the normalized image (run/ref), as shown in Figure 5-18 100 150 200 250 300 350 20 40 60 80 100 120 140 160 180 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 Pixel indexNormalized intensity 20 40 60 80 100 120 140 160 180 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 Pixel indexNormalized intensity Figure 5-18 Effect of image re gistration on SNR (A) Unregistered image (B) Registered image. Bottom plots show a horizontal section of the images above. A A B

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149 When an image moves, the intensity valu e of each pixel changes according to the following relation (ignoring pixel-to-pixel variations of the CCD array): ,1,21,1 11 0010 no shift n pixels shift, n=integer 0ijijij mIaIaI aa aan (5.1) where ij m I is the modified intensity value, 1a and 2a are the confidents of translation. The translation coefficients depend on the am ount of shift from the reference image. For a non-integer pixel shift 1n both coefficients are non-zer o and scale linearly with pixel shift, hence a linear interpolation is possible. For example, assume that an image moves 20% in the x-direction and 60% in the y-direction, Figure 5-19 with pixel intensities of 10, 100, 30, and 70 counts for pixels 1, 2, 3, and 4, respectively. Figure 5-19 Pixel intensit y shift on the CCD array 60% 20% x y 70 100 10 30 1 3 2 4

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150 The modified intensity of pixel 3 is a combination of the intensity values of pixels 1, 2, 3, and 4. Assuming homogenous electr on flux at each pixel surface, the relative contribution of each pixel to the shifted pixe l depends on the relative area of each pixel that overlaps with the shifted pixel multiplied by its intensity value. Therefore, for our example the modified intensity of pixel 3 would be: 3100.481000.12300.32700.0832mI (5.2) Model deformation is not limited to pure tran slation; models warp, rotate, and even stretch/shrink. For such deformations more complicated image registration routines are needed, such as projective and polynomial tran sformation. To enable initial prediction of type(s) of transformation need ed, models are fitted with reference points that map the frame of the model. Following image acquisi tion, image pairs are compared utilizing these reference points and appropriate tr ansformation can be determined. Thermal Expansion Materials undergo thermal expansion as their temperature increases. Experiments show that for small temperature chan ges (< 100C) the change in length L is directly proportional to the change of temperature T (Young, 1992). Further, the length of the object relates directly to th e amount of thermal expansion. The overall relation may be expressed as: 0LLT (5.3) where is the coefficient of linear thermal expansion (1/C) and 0L is the initial length of the object. It is important to note that th is relation is an approximation valid only for small temperature variations, while for higher temperature changes would depend on the initial temperature of the material and the relation ceases to hold its linearity.

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151 The channel is mated between aluminum and window-glass plates of equal thickness. The following table lists the values of for both materials, notice that for aluminum is an order of magnitude higher than for glass. Table 5-1 Coefficients of Thermal Expansion Material 610/ C Aluminum 24 Glass 4-9 The material of the channel experiences re latively small temperatures changes (~ 50 C), however, this change is sufficient to induce an unfavorable increase in both the length and width of the channel requiring image registration. The channel rests vertically on a series of hot-plates, and hence any increase in width will yield a spatial translation in the positive y-direction. Alum inum possess higher thermal expansion coefficients, we calculate the vertical shif t in the image to be: 624 152.4500.183mm 10yL (5.4) and similarly for the longitudinal length we obtain: 624 355.6500.426mm 10xL (5.5) The CCD camera produces a 512 x 512 pixe ls image and the imaged longitudinal portion of the channel is 10.2 inches, which yields a spatial resolution of: 512pixels 1.976 259.08mm (5.6) which translates to a maximum pixel shift of: 0.1830.362pixel 1.976 0.4260.842pixelmmy pixel mmx mm (5.7)

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152 Thermal expansion for free objects is zero at the geometric cent er and maximum at the peripheries. For our channel, each mm is equivalent to 0.988 pixels, and hence the bottom row of intensities co rresponding to the bo ttom side of the channel would not move, while the top row would move by a total of 0.362 pixels with a linear translation in between the top and bottom ro w. Therefore a linear transf ormation is required and a constant spatial shift is not sufficient. Im age registration effects are more pronounced for the temperature filters (i.e., 550nm and 600nm) due to the nature of the TSP probe and its dispersion in the binder. 50 100 150 200 250 300 350 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 row number (0=bottom)pixel shift (pixels) Figure 5-20 Pixel shift due to thermal expa nsion from bottom to top of the channel

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153 CHAPTER 6 RESULTS AND ANALYSIS This chapter presents the results of the experimental work an d provides discussion and analysis of the results. The analysis pr esented herein is based on the POD analysis presented in chapter 3. The data is anal yzed using the MATLAB codes provided in Appendix-A. Procedure and Test Cases The following sub-sections addr ess key aspects of the expe rimental procedure, data acquisition and the va rious test cases. Exposure Times In order to maintain similar SNR throughout the spectrum, different exposure times are needed to utilize the camera FWC at each wavelength. The following table shows the distinct variation be tween exposure times, note that the boundaries of the spectrum require the longest exposure times and hence possess the lowest intensity emission levels. Table 6-1 Exposure times for the different filters Filter 550nm 600nm 650nm 700nm Exposure time (ms) 3400 560 1500 3500 Sixteen frames were acquired per image to ensure low shot noise. Given the relatively long aggregate exposure times, it is essential that the environmental conditions do not drift during the acquisi tion process. Each case was allowed enough time to reach steady state conditions and the ma ss flow controller was able to maintain steady pressure levels throughout the experiment. In addi tion, the pre and post-run pressure and temperature values are recorded and are comp ared to ensure stabil ity of conditions for

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154 each run. The pressure deviation is shown in Table 6-2 through an entire set of measurement. Further, the first and last filt er conditions are compared to determine any variation, which would be accounted for in the uncertainty analysis. Table 6-2 Pressure drift throughout the exposure times (case five) Quantity/Filter 550nm 600nm 650nm 700nm Maximum absolute error (psi) 0 0.0063 0.012 0.016 Mean Error (psi) 0 -0.0028 -0.0076 -0.012 STD (psi) 0 0.0033 0.0044 0.005 Data Matrix Seven cases were examined to fully charac terize the paint and calibration process. The experiments have three variables: pressure (i.e., flow), temperat ure, and the direction of the temperature gradient with respect to the flow direction. Table 6-3 Test matrix Temperature Profile Flow OFF Flow ON None Reference Case 1 Longitudinal (flow direction) Case 2 Case 3 Transverse (perpendicular to flow) Case 4* Case 5 Oblique Case 6* Case 7 Results not shown to avoid redundancy The response of the pressure probe PtT FPP, i.e., Stern-Volmer relation (SV), Figure 6-1 shows a very shallow gradient of ~ 3 %-psi-1 near atmospheri c conditions, and Flow

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155 exhibits lower gradients when embedded in the dual-luminophor system (Kose, 2005). Kose (2005) did not characteri ze the response at higher than atmospheric pressure levels due to hardware limitations; however, the tre nd of the SV predicts an even shallower gradient. In order to ensure significant intens ity variations the pressu re gradient along the channel is preset and maximized by the mass flow controller to about 6.4263 .0087 psi (95% confidence level). Figure 6-1 Stern-Volmer relation fo r dual-luminophor (PtTFPP-Ruphen/PAN nanospheres in poly-t-BS-co-TFEM) at different temperature levels (Kose, 2005) Hardware and flow conditions imposed a limitation on the maximum obtainable temperature gradient. The cooler pump is not capable of circ ulating water fast enough to maximize heat transfer, in particular, in the case of temperature gradients perpendicular or oblique to the flow field. From Fourie r law of conduction (Equation 4.24) for constant heat flux and thermal conductivity coefficien t, as the length of the object along which

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156 heat is conducted increases, the temperature difference increases, and vice versa. This limited the maximum temperature gradient perp endicular to the flow at any given cross section to ~ 10 C for cases 4-7. POD Analysis The details of the POD analysis are presen ted in chapter 3. Only key elements of the analysis are discussed below for convenien ce. The analysis of the artificial data showed that in a spectral da taset depending on two independent factors (i.e., pressure and temperature) a base factor shapes the sp ectrum and a second complementary factor scales the different regions of the spectrum. The scores associated with the latter are thus used for calibrating the indepe ndent factors. The calibration functions are distinguished and realized by applying a diffe rent rotation to the compleme ntary factor and hence the scores. The complementary factor is extracted from a dataset that c ontains both intensity and corresponding environmental conditions, hen ce two calibration data sets are possible. Upon decomposing and rotating th e calibration dataset the coe fficients for the calibration function are extracted and a calib ration set of scores are determined. This set of scores is then implemented as the guiding calibrat or for unknown conditions. The intensity information for unknown environmental conditio ns is added to the calibration data and POD is applied to the entire data matrix. Only the first data columns containing calibration information are used to determin e the appropriate rotation angle. As the unknown conditions differ from the calibration conditions a different rotation angle is obtained by searching the data space in a 360 hunt. Calibration Matrix vs. Test Matrix The approach adapted by the author in establishing the calibration function via POD is based on an in-situ approach. Specific points on the channel surface contain

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157 pressure taps and thermocouples ( Figure 6-2 ). The normalized intensity values and environmental values from these calibration poi nts are utilized to estimate the calibration functions. The calibration matrix contains both the intensity values and the environmental values arranged as four rows corresponding to the four filters and n columns corresponding to the number of calibration poi nts. The test matrix contains intensity values (normalized) and its columns are adde d one full set (4 rows x 501 columns) at a time to the right of the calibration matrix columns. Figure 6-2 Channel image showing thermocouples calibration pressure taps and pressure test points taps. The entire matrix is processed by the POD analysis with curve/surface fitting reevaluated for each new combined matrix throughout the full rotation space (360) to optimize the calibration. The calibration and test matrix is shown below in equation (6.1). Flow

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158 1,1501,1 550nm 600nm 650nm 700nm 1 2. .\ ...... refrefrefref runrunrunrun refrefrefref runrunrunrun refrefrefref runrunrunrun refrefref runrunDnmD IIII IIII IIII III ref runrunI (6.1) The test set has to be coll ected along the same directi on as the calibration points. This means if there is a direction in wh ich the calibration points are collected (i.e., longitudinal or lateral) then the test points to be eval uated must be collected along that direction. Since the pressure calibration points span the l ongitudinal direction of the channel in order to maximize the calibration enve lope, test sets are chosen as the intensity values of the longitudinal lines along the channe l. This is important as the test set is added to the calibration matrix and prior to decomposing the combined matrix, it is squared by post-multiplying the matrix by its transpose. This can be thought of as inducing more weight around a specific portio n of the calibration data causing a false bias on the calibration, and consequently its orientation (i.e., the calibration eigenvector orientation). Therefore, if data points are concentrated around a specific value on the calibration curve, they will cause a shift in the orientation of the calibration eigenvector Calibration data Unknown conditions

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159 and hence the calibration scores. This rule is not a limitation on POD, rather it serves to optimize computational time only. Figure 6-3 Effect of adding rows instead of columns to the calibration matrix. Observe the direction of the main eigenvector (black arrow) compared to the calibration eigenvector (orange arrow). Consider case 3 with temper ature and pressure gradient s along the flow direction. Lines perpendicular to the flow direction have almost consta nt temperature and pressure values and hence the eigenvector will signifi cantly deviate from its calibration position if these data lines are inserted in the matrix (instead of line parallel to the flow). This becomes less of a problem as the environmen tal condition field encompasses significant multidirectional gradients (e.g. cases 6 and 7). 50 100 150 200 250 300 350 400 450 500 1 2 3 4 5 6 7 8 9 10 Normalized Intensity Pixel index (rows) Calibration rows (100 pts)

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160 Image Filtering Shot noise is the main cont ributor to noise associated with the imaging system. Sixteen frames were acquired per filter to minimize shot noise. For our 14-bit CCD camera, readout noise is 13.3 e-/frame (R.M.S.) at 200 kHz. The total readout noise is then equal to 13.3 x 16 = 212.8 e-. Averaging 16 frames at an average intensity of 191,000 e(10,000 counts) yields shot noise i.e., uncertainty, of 1748 e(91.5 counts). 0 5 10 15 20 25 30 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 Number of framesPercent error Figure 6-4 Intensity percent e rror due to shot noise vs. num ber of frames (14-bit CCD camera) Read out and shot noise for the CCD camer a are comparable at average intensity levels of 57300 e(3,000 counts). Lower intensity leve ls yield read-out-noise limited intensity and higher intensity levels are s hot noise limited. For this work, sufficient intensities, averaging 191,000 e(10,000 counts), make the data shot noise limited. The

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161 relative uncertainty for 16 frames is 0.057 %, compared to 0.08 % and 0.23 % for 8 and 1 frames, respectively. Therefore, very modest image filtering was required to smooth pixel variation after image registration. Unless ot her wise stated, the averaging square size utilized is 3 x 3 pixels. Results The following subsections detail the results for the different cases. The results are presented in more details in earlier cases a nd any repeated results or conclusions are briefly referenced back to pr evious cases. Each case represents a unique condition that examines a particular aspect of the POD calibration process. A general uncertainty analysis is presented at the end of this chapter. Temperature effects influence the accuracy of the pressure calibration, thus, the uncertainty in the pre ssure differs between cases due to the different temperature gradie nts orientation and ma gnitude. The pressure is examined at four discrete points on the surface of the channels containing pressure taps. The results are tabulated and compared to the theoretically predicted uncertainty at the end of the uncertainty section. Temperat ure uncertainty is not emphasized for each case as it remained constant for the various cases and it has been the observation of the author that typical uncertainty reported in th e literature for TSP paints are similar to the presently examined dual-luminophor syst em. Observed calibration temperature uncertainty (95% confidence) th rough the experimental work is 0.6C for cases 2 and 3, and 1.5C for cases 5 and 7. The thermocouples have an error of .5C or 0.4% f.s., whichever is greater, and a STD of 1C or 0.75% f.s., whichever is greater. This yields temperature uncertainty due to thermocouples of 2C. The error in temperature was independent of the pressure levels of each case, but varied with the orientation of the temperature gradient relative to pressure. Further, temperature accuracy of a degree or so,

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162 which is typical of TSP (Cattafesta et al, 1998) is more than suffici ent for most practical applications. However, dual-luminophor system s have shown higher errors (~2-3C) in the temperature estimates (Hardill et al, 2002, Mitsuo et al, 2003.) In addition to the previous temperature uncertainties, temp erature deviation during image acquisition ( Table 6-4 ) added to the total uncertainty. Table 6-4 Temperature drift thr oughout the exposure times (case 5) Quantity/Filter 550nm 600nm 650nm 700nm Maximum absolute error (psi) 0 0.52 0.49 0.59 Mean Error (psi) 0 -0.30 -0.34 -0.39 STD (psi) 0 0.16 0.17 0.23 Case One (Isothermal Long itudinal Pressure Gradient) The objective of this case is to isolate the pressure re sponse of the paint in the absence of temperature gradients ( Table 6-3 ). This will identify the spectral response of both luminophors (P/TSP) due to pressure and more importantly expose any pressure dependence in the temperature probe. Further, this will help guide the calibration process of the pressure in the presence of temperat ure gradients by identifying the main character (i.e., functional form of calibrati on) of the pressure response.

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163 0 0.2 0.4 0.6 0.8 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 x / LPercent deviation from theory 24.25 24.3 24.35 24.4 24.45 24.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 15 16 17 18 19 20 21 22 23 x / LPressure (psi) Experimental Theoretical Figure 6-5 Case one: Pressure profile (botto m), (a) percent pressure deviation from theory (psi), (b) temperature profile (thermocouples) over the plate (8 x 3) (a) (b) C Percent deviation from Theory (psi) Position (inch) 0.5 1 1.5 2 2.5 3 3. 5 0 1 2 3 4 5 6 7 8 Position (inch)

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164 0.982 0.984 0.986 0.988 0.99 0.992 0.994 0.996 0.998 0.94 0.95 0.96 0.97 0.98 0.99 1 Figure 6-6 Case one: Normalized intensity (Irun/Iref): 550nm [left] --600nm [right] 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.86 0.88 0.9 0.92 0.94 0.96 Figure 6-7 Case one: Normalized intensity (Irun/Iref): 650nm [left] --700nm [right]

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165 Figure 6-5 b shows a maximum temperature vari ation of 0.5C over the channel, which is within the thermocouple 95% confid ence uncertainty estimate of 2C, ensuring isothermal conditions. The pressure profile has a maximum deviati on of ~ 2% from the Poiseuille-flow theoretical solution. The deviat ion in the pressure is attributed to the bowing of the glass plate due to pressure forces As detailed in chapter 5, this was evident from the pressure profile using a 3/8 inches thick glass plate compared to the 1 inch plate used in the experiments. The de viation is still tolerable in terms of pressure variation. Nonetheless, a more important effect is observed in the intensity images due to the thickness of the glass and its deformation. As the glass plate deforms it creates different light transmission characteristics between th e paint and the CCD camera due to light refraction as the incident angle is non-zer o for the run images. The reference images suffer no such deformation and hence upon nor malizing the images false effects are observed, especially at the ends (inlet and ex it) of the channel where the incident angle is highest. These effects are shown in Figure 6-8 1 2 3 4 5 6 7 8 9 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 x-position (inch)Normalized intensity 550 nm 600 nm 650 nm 700 nm Figure 6-8 Case one: Centerline pressure response of dual-luminophor at different bandpass wavelengths

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166 The intensity level at the beginning of the channel doe s not decrease with the pressure increase; rather it is nearly flat at the higher wavelength and curves up at lower wavelengths. This observation was suspected to be due the SV behavior, however upon investigating lower pressures the effect persisted. An attempt was made to acquire reference conditions using nitr ogen to replicate the glass deformation without imposing a pressure field observable by the paint (the paint responds to oxyge n concentration not pressure as described in chapter 2). This attempt was not successful because the normalized image was terribly noi sy. This noise was not due to image registration or high shot noise in the signal. The results, Figure 6-9 show significant incr ease in the level of noise in the normalized image for whic h the reason is not apparently clear. 0.95 1 1.05 1.1 1.15 1.2 50 100 150 200 250 300 350 400 450 500 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 50 100 150 200 250 300 350 400 450 500 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 Figure 6-9 Normalized intensity for case one (650nm) using N2 (left): (A) Reference image acquired with no flow and expos ure time of 1500ms (B) Reference image acquired with nitrogen flow and exposure time of 185ms. Exposure time for run image is 1500 ms. A B

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167 The image suffers from a spottiness eff ect rather than a noisy grainy effect observed when image registration is an issue. Figure 6-10 shows the microscopic aggregation of the Ruphen/P AN particles in the PtTFPP / poly-t-BS-co-TFEM binder and the observed inhomogeneous dispersion. Kose (2 005) noted that this variation was barely obvious on the macroscopic scale. In the cha nnel flow experiment this was slightly observed in the normalized image of the 550nm filter ( Figure 6-6 ). It should be noted that the intensity false color resolution was refine d to show the inhomogeneity in the image. Further, an intensity variation of -1.6% is observed in the image due to convection. This intensity variation corresponds to ~1C (irresolvable by ther mocouples) according to the reported sensitivity value of -1.45%/C. The heterogeneous nature of oxygen/nitrogen diffusion in the binder matrix combined with small temperature variations are a plausible cause of the spottiness in the normalized image. It is rather impossible to remove all of the oxygen in the binder (Weaver et al, 1999) and hence any left over oxygen in the binder would yield spurious results. Figure 6-10 Fluorescence image using epif luorescence microscope of Ruphen/PAN particles emission (dispers ed into the PtTFPP / poly-t-BS-co-TFEM binder) at 560nm. The image shows the heteroge neous dispersion of the Ruphen/PAN particles in the poly-t-BS-c o-TFEM matrix (Kose 2005).

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168 Figure 6-8 shows less than 0.5% variation in the centerline temperature intensity (550nm) with pressure, while the 600nm filter ob serves some of the pressure variation. The 650 and 700nm filters, with more empha sis in the former (~12 % decrease in intensity), predominantly capture pressure in formation. This agrees with theoretical prediction of insignificant oxygen quench ing effects for the temperature phosphor. POD Calibration Intensity information is analyzed th rough POD yielding the following results: 550 600 650 700 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 Wavelength (nm)Normalized intensity Figure 6-11 Case one: Normalized intensity (Iref/Irun) POD extracted two eigenvectors as sh own in the following two figures. The spectrum in Figure 6-11 shows a very small intensity va riation of about 1.5% at 550nm compared to 16.5% 650nm. POD produces linear sum of factors, he nce two factors are needed, one to account for the main variant in the spectrum and another to shape and scale the overall spec trum throughout the spectral range. However, in the absence of temperature effects, both vectors can be used for calibration.

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169 550 600 650 700 25 20 15 10 -5 0 Wavelength (nm) R1 R2 1 2 3 4 5 6 7 8 9 -0.18 -0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.18 -0.16 C1 C2 Figure 6-12 Case one: Calibration eigenvectors at 174.56 degrees (lef t) and eigenvalues (right) 550 600 650 700 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 550 600 650 700 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Figure 6-13 Case one: Product of first (lef t) and second (right) eigenvectors and eigenvalues of calibration The two are identical in sh ape; however, the correspondi ng eigenvalues shape them differently. As seen in Figure 6-13 the first product (1st eigenvector) maps the main variant, i.e., pressure, while the second ads to it to reconstruct the original spectrum scaling the different regions of the spectrum as shown in the following figure. The second eigenvector is thus the calibration vector. P P Calibration point index Eigenvalue Eigenvector magnitude Wavelen g th ( nm ) Wavelen g th ( nm ) R1 x C1 R2 x C2

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170 550 600 650 700 1 1.05 1.1 1.15 1.2 1.25 Wavelength (nm)Normalized intensity Figure 6-14 Case one: Product sum of eigenv ectors and calibration eigenvalues showing 1 % variation at 550nm and 15% at 650nm The pressure calibration is a linear fit of the intensity data, equation (6.2) with the coefficients extracted at the appropriate ro tation angle. The calibration eigenvalues were recalibrated each time a run intensity column (501 data points) was inserted into the matrix to optimize the calibration. Higher-order even functions yielded erroneous results while odd powers indistinctly improved the calibration. 2253.492789.99 PabCC (6.2) P

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171 0 100 200 300 400 500 14 15 16 17 18 19 20 21 22 23 Pressure (psi) R1 R2 Actual Figure 6-15 Case one: Calculated centerlin e-pressure profile by each eigenvector Figure 6-15 shows the predicted centerline pr essure by both eigenvectors at the same rotation angle. The second eigenvector over-predicts the pressure below calibration range and slightly under-predic ts the pressure above the ca libration range. The intensity flat behavior near the inlet of the channel is evident in the calibration. The calibration adheres to low errors relative to the taps readings except near the entran ce. The rise in the predicted pressure near the ex it of the channel is expected as the flow experiences a positive area change forcing the flow to pl unge below atmospheric pressure to recover atmospheric conditions at the exit. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 x / L

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172 Figure 6-16 Area change due to chamfe r in the glass plate at the exit The calibration has an aver age error of 0.0638 psi (0.325 %) and a maximum error of 0.276 psi at the maximum pressure (22.022 psi) with the next highest absolute error of 0.114 psi and an R.M.S. of 0.0072 psi. The un certainty of the calibration is .19 psi. 0 2 4 6 8 10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 x-position (inch)Absolute Error (psi) 0 2 4 6 8 10 -0.5 0 0.5 1 1.5 x-position (inch)Percent Error (psi) Figure 6-17 Case one: Calibration error, abso lute (left) and percentage (right) Table 6-5 Case one: Test-points pressure re sults. Actual represents pressure tap measurement and POD represents the cal culated pressure via POD calibration. The precision error of the Actu al readings is 0.006 psi. Actual (psi) POD (psi) Absolu te error (psi) /Percent error 22.03 21.71 0.32 (1.45 %) 21.35 21.25 0.1 (0.47 %) 19.22 19.15 0.07 (0.36 %) 16.77 16.61 0.16 (0.95 %) The predicted pressure field is shown in Figure 6-18 Four test points are compared to the predicted values and the results show a maximum deviation of 0.351 psi from the actual values and an average erro r less than 0.72 % as shown in Table 6-5 Flow Glass Aluminum Area

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173 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0. 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / L Figure 6-18 Case one: Calculated pre ssure field from POD calibration psi

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174 14 15 16 17 18 19 20 21 22 Pressure (psi) Actual Predicted Figure 6-19 Case one: Calculated pressure fr om POD calibration vs. pixel index along the channel. Each curve represents a longit udinal line of pixels along the channel. Actual represents the actual pressure taps readings used for calibration. It is worthy of noting that columns that pass through high inte nsity points exhibit slightly higher errors. This is because th e direction of the calibration eigenvector is slightly altered because of the addition of this high intensity pixel value. These highintensity pixels correspond to points on the surface of the cha nnel with contaminants that luminesces highly relative to the paint (e.g. large primer particles lodged inside the spraygun) or points where paint particles have coa gulated and formed a high concentration of luminescent particles. These high-intensity points are not eliminated during the normalization process. In the reference image these points reach saturation but they do not in the run images, hence upon normalization they exhibit a different trend relative to surroundings pixels. Nonetheless, these points can be digitally filtered to resolve their adverse contribution. Calculated 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 x / L

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175 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0. 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / LCase Two (Longitudinal Temperature Gradient) The objective of this case is to isolate the temperature re sponse of the paint in the absence of pressure gradients. This will further identify the spectral response of the both luminophors (P/TSP) and more im portantly expose any temp erature dependence in the pressure probe, an expected outcome. Additi onally, this will help guide the calibration process of the pressure in the presence of temperature gradients by identifying the temperature dependence character in the pressure response. 32 34 36 38 40 42 44 46 Figure 6-20 Case two: Temperat ure profile (thermocouples) C

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176 0.75 0.8 0.85 0.9 0.95 1 0.8 0.85 0.9 0.95 1 Figure 6-21 Case two: No rmalized intensity (Irun/Iref): 550nm [left] --600nm [right] 0.81 0.85 0.9 0.95 1 1.035 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02 Figure 6-22 Case two: No rmalized intensity (Irun/Iref) : 650nm [left] --700nm [right]

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177 0 2 4 6 8 10 12 14 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 x-position (inch)Normalized intensity 550 nm 600 nm 650 nm 700 Figure 6-23 Case two: Center line temperature response of dual-luminophor coating at different bandpass wavelengths The temperature response of the paint show s a 26% percent vari ation relative to reference conditions in the intensity (550nm ) with temperature, while the 600nm filter observes 24% variation. The 650 and 700nm filters show a strong temperature dependence of 17% and 13.5%, respectively, as expected. The temperature effect on the intensity is linear in all spectral regions. 30 32 34 36 38 40 42 44 46 48 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Temperature (C)Norm alized intensity 550 nm 600 nm 650 nm 700 nm Figure 6-24 Case two: Temperature linearity of dual-luminophor co ating at different bandpass wavelengths

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178 POD Calibration Intensity information is analyzed th rough POD yielding the following results: 550 600 650 700 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Wavelength (nm)Normalized intensity Figure 6-25 Case two: No rmalized intensity (Irun/Iref) POD extracted two eigenvectors as sh own in the following two figures. The spectrum is shown in Figure 6-25 The two eigenvectors account for the temperature variation and the indirect temperature effect in the pressure spectral range. 550 600 650 700 0 5 10 15 20 25 Wavelength (nm) R1 R2 50 100 150 200 250 300 350 400 450 500 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 C1 C2 Figure 6-26 Case two: Calibrati on fundamental spectra at 0.5 degrees (left) eigenvalues of calibration (right)Pixel index Eigenvalue Eigenvector

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179 550 600 650 700 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 Wavelength (nm) 550 600 650 700 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 Wavelength (nm) Figure 6-27 Case two: Product of first (l eft) and second (right) eigenvectors and eigenvalues of calibration Similar to case 1, the two vectors are identical in shape; however, the corresponding eigenvalues scale them differently. As seen in Figure 6-27 the first product (1st eigenvector) maps the main variant, i.e., temperatur e, while the second scales the data in the pressure range inversely with respect to the temper ature range. The second eigenvector serves by enhancing the temperature effect at 550nm and to a lesser extent at the 600nm range, while reducing the temp erature effect at the 650 and 700nm wavelengths, with more damping in the la tter. The addition of the two eigenvectors retrieves the calibration spectrum shown below. T T R2 x C2 R1 x C1

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180 550 600 650 700 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 Wavelength (nm)Normalized Intensity (ref/run) Figure 6-28 Case two: Product sum of eigenv ectors and calibration eigenvalues showing 28 % variation at 550nm and 18% at 650nm The Temperature calibration is a linear fit of the intensit y data, equation (6.3), with the coefficient extracted at the appropriate rotation angle. The calibration eigenvalues were recalibrated each time a run intensity co lumn was inserted into the matrix to optimize the calibration. Once more, higher or der calibration functions with even powers yielded erroneous results wh ile odd powers insignificantl y improved the calibration. 1TTTabC (6.3) The linear character of th e calibration function suggest s a strong relation between the nature of the temperature field and the calibration character. The predicted temperature field is shown in Figure 6-29 with an average calibra tion error of 0.3 C. T 31.8 0.49C 35.3 0.25C 39.1 0.06C 43.0 0.09C 47.1 0.25C

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181 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / L Figure 6-29 Case two: Calcul ated temperature field from POD calibration (image)

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182 30 35 40 45 50 Temperature (C) Actual Predicted Figure 6-30 Case two: Calculat ed temperature field from POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual thermocouple readings used for calibration. As anticipated, the temperature calibration accuracy is superior due to the linear nature of the temperature field and the abse nce of significant noise interference. These result will guide the calibration for the followi ng cases keeping in mi nd to explore a more suitable calibration function to the temperature field. Calculate d 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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183 Case Three (Simultaneous Longitudinal P ressure and Temperature Gradients) The objective of this case is to study the effect of a parallel pressure and temperature flow fields on the calibration. The pressure and temperature are decreasing longitudinally and hence have an aggregate le ssening effect on the intensity rather than an opposing effect. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -1.5 -1 -0.5 0 0.5 1 x / LPercent deviation from theory 29 30 31 32 33 34 35 36 37 38 39 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 15 16 17 18 19 20 21 22 23 x / LPressure (psi) Experimental Theoretical Figure 6-31 Case three: Pressu re profile (bottom), (a) per cent pressure deviation from theory (psi), (b) temperature profile (thermocouples) (a) (b) C Position (inch) ii 0.5 1 1.5 2 2.5 3 3. 5 0 1 2 3 4 5 6 7 8 ii

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184 0.95 1 1.05 1.1 1.15 1 1.05 1.1 1.15 1.2 Figure 6-32 Case three: Normalized intensity (Irun/Iref): 550nm [left] --600nm [right] 1 1.05 1.1 1.15 1.2 1.25 1.3 1.05 1.1 1.15 1.2 1.25 Figure 6-33 Case three: Normalized intensity (Irun/Iref) : 650nm [left] --700nm [right]

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185 0 2 4 6 8 10 12 14 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 Normalized Intensity (ref/run) 550 nm 600 nm 650 nm 700 Figure 6-34 Case three: Center line pressure and temperatur e response of dual-luminophor at different bandpass wavelengths The temperature field in case 2 was expos ed to forced convection by the flow yielding case 3. The temperature field was shrunk from 18C to 11C difference along the flow direction. The corres ponding decrease in the intensit y is linear with the decrease in temperature in the 550nm range with a slope of ~1.45%/C. The intensity at 650nm decreased by 22 % compared to 12 % for th e adiabatic case, which translates to 1.1%/C, which is the value (at 14.7 ps i) reported by Kose (2005). As the paint characteristics were not char acterized at higher than atmospheric pressures by Kose (2005), there is no current reference for comparison, however, the values are in agreement with the trend of increasing temperature dependence with increasing pressure as reported by Kose (2005). Further, Kose ( 2005) used spectroscopi c results, while this work uses filtered (integrated) intensity data. The pressure profile still shows the bowing behavior but the temperature field has incr eased the thermodynamic pressure, increasing the pressure deviation from the ad iabatic theoretical solution. Calibration point index

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186 POD Calibration Intensity information is analyzed th rough POD yielding the following results: 550 600 650 700 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 Wavelength (nm)Normalized intensity Figure 6-35 Case three: Invers e of normalized intensity (Irun/Iref) POD extracted two eigenvectors, however unlike the previ ous two cases; two different rotation angles are needed to extrac t the pressure and temperature information. The rotation angles are 0degrees and 1 degree for the temperature and pressure, respectively. This is a significant result as it manifests the fact that the pressure and temperature fields are parallel. The spectrum in Figure 6-35 shows comparable intensity variation at 550n m and 650nm. 1 1 1 / Normalized intensity

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187 550 600 650 700 0 5 10 15 20 25 30 Wavelength (nm) R1 R2 1 2 3 4 5 6 7 8 9 -0.05 0 0.05 C1 C2 Figure 6-36 Case three: Pressu re calibration fundamental spect ra at 1 degrees (left) eigenvalues of ca libration (right) 550 600 650 700 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 Wavelength (nm) 550 600 650 700 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 Wavelength (nm) Figure 6-37 Case three: Produc t of first (left) and sec ond (right) eigenvectors and eigenvalues of pressure calibration As seen in Figure 6-36 the second eigenvector has a near zero value at 650nm, hence the scores associated w ith the first eigenvector mainly scale the pressure. From Figure 6-37 the contribution of the second produ ct at the 650nm wavelength is only 0.7% relative to the contribution of the first product. This is because the temperature and pressure gradients are in the same direct ion and hence the temperature effect on the pressure in this case can be thought of as a bias, particularly since temperature effects were observed from case two to be nearly linear in the pressure region. It is interesting to P P Calibration point index Eigenvector magnitude Eigenvalue R2 x C2 R1 x C1

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188 observe that the effect of th e second eigenvector is the sma llest at the 650nm, while it is comparable at the other wavelength, incl uding the 700nm wavelength. This emphasizes the fact that the pressure main emission is at the 650nm, while the 700nm captures only the tail of this emission. Furt her, it suggests a reemergence and extension of temperature probe emission at the higher wavelengths. 550 600 650 700 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 Wavelength (nm) Figure 6-38 Case three: Product sum of eigenvectors and pres sure calibration eigenvalues showing 18 % variation at 550nm and 27% at 650nm The pressure calibration is a linear fit of the intensity data, similar to equation(6.2), with the coefficient extracted at the appropriate rotation angle (6.1312, 562.6 ab ). The pressure calibration has an average erro r of 0.0295 psi and a maximum error of 0.129 psi at the maximum pressure (21.851 psi), with the next highest abso lute error at 0.0646 psi. The test points exhibit a maximum error of 0.241 psi (1.45 %) and average error of P Normalized intensity 1 1 1 / Normalized intensity

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189 0.153 psi (0.826 %). The predicted pressure e rror has not increased compared to case 1, further, high pressure (>21 ps i) accuracy has improved. Table 6-6 Case three: Test-points pressure results. Actual represents pressure tap measurement and POD represents the cal culated pressure via POD calibration. The precision error of the Actu al readings is 0.006 psi. Actual POD Absolute error (psi) /Percent error 21.85 21.77 0.08 (0.37 %) 21.17 21.09 0.08 (0.38 %) 19.03 18.82 0.21 (1.10 %) 16.62 16.37 0.25 (1.50 %) The Temperature calibration is acquired in a similar manner to pressure with a slightly different rotation a ngle. In this case the second eigenvector has insignificant contribution at the 600nm wavelength. Further, only the scores associated with the first eigenvector collapse to single line as shown below. The temperature error is similar to case 2. The eigenvector mapping the pressure had to be slig htly rotated by a degree to point towards the other variant, i.e., temperature. 550 600 650 700 0 5 10 15 20 25 Wavelength (nm) R1 R2 50 100 150 200 250 300 350 400 450 500 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 C1 C2 Figure 6-39 Case three: Temper ature calibration fundamental sp ectra at 0 degrees (left) eigenvalues of ca libration (right) Pixel index Eigenvector magnitude Eigenvalue

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190 550 600 650 700 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Wavelength (nm) 550 600 650 700 -2000 -1500 -1000 -500 0 500 1000 Wavelength (nm) Figure 6-40 Case three: Produc t of first (left) and sec ond (right) eigenvectors and eigenvalues of temperature calibration The reconstructed spectra is shown below. 550 600 650 700 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 Wavelength (nm) Figure 6-41 Case three: Pr oduct sum of eigenvectors a nd temperature calibration eigenvalues showing 23 % variat ion at 550nm and 26% at 650nm T T T R1 x C1 R2 x C2 Normalized intensity 29.43 0.43C 32.05 0.22C 34.5 0.05C 36.95 0.03C 39.16 0.37C 1 1 1 / Normalized intensity

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191 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / L Figure 6-42 Case three: Calc ulated pressure field fr om POD calibration (image) psi

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192 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / L Figure 6-43 Case three: Calc ulated temperature field fr om POD calibration (image) C

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193 0 100 200 300 400 500 15 16 17 18 19 20 21 22 23 Pressure (psi) Actual Predicted Figure 6-44 Case three: Calcul ated pressure field from PO D calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual pressure taps readings used for calibration. 0 100 200 300 400 500 28 30 32 34 36 38 40 Temperature (C) Actual Predicted Figure 6-45 Case three: Calcul ated temperature field from POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual thermocouple readings used for calibration. Calculated Calculated 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 x / L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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194 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / LCase Five (Perpendicular Temperature Gradient with Longitudinal Pressure Gradient) In this case the temperature gradient is im posed perpendicular to the flow direction. The temperature profile is nearly constant al ong each lateral station. This will allow the investigation of PODs ability to distinguish the relative a ngle between the pressure and temperature gradient. Further, the accuracy of the results would assess the ability of POD to fully separate the variables. Unlike case 3, the intensity variation would not be constant across the channel, while the pressure is assumed constant laterally, due to the temperature gradient. 38 39 40 41 42 43 44 45 46 47 48 Figure 6-46 Case five: Temperat ure profile (thermocouples) C

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195 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2.5 3 3.5 4 4.5 5 x / LPercent deviation from theory 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 15 16 17 18 19 20 21 22 23 24 x / LPressure (psi) Experimental Theoretical Figure 6-47 Case five: Pressure profile (bottom), (a) percen t pressure deviation from theory (top)

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196 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 Figure 6-48 Case five: No rmalized intensity (Irun/Iref): 550nm [left] --600nm [right] 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02 Figure 6-49 Case five: No rmalized intensity (Irun/Iref): 650nm [left] --700nm [right]

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197 It is observed that image registration is more important in this case compared to previous cases. This is due to the nature of the pressure and te mperature fields and thermal expansion as discussed in chapter 5. A constant image translation is not sufficient and a translation gradient is required. The metal expansi on is small enough that a linear gradient suffices. This is confirmed by the noise level in the different filtered images. The noise is highest at th e 550nm wavelength and lowest at the 750nm filter. The TSP particles are more pronounced (i.e., observed in the spectral images) at the lower wavelength and hence a lateral temperature grad ient effects on image registration is most observed at these wavelengths. The following figu re shows this effect, notice the speckles the 550nm image causing sharp gradients betw een neighboring pixels, thus making image misalignment more pronounced. Figure 6-50 Case five: Speckling in the 550nm image (left) and a comparison to the 700nm filter

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198 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.8 0.85 0.9 0.95 1 1.05 Normalized intensity 550 nm 600 nm 650 nm 700 nm Figure 6-51 Case five: Centerline pressure and temperature respons e of dual-luminophor at different bandpass wavelengths The centerline temperature pr ofile is evident across the spectral range. The 550nm filter reveals the extent of invariability in the temperature profile along the centerline station. Although the temperature profile is not exactly constant along each lateral station of the channel, it varies insignificantly enough (< 4C) for the charac ter of the POD to be fully distinguished. 1 2 3 4 5 6 7 8 9 40.5 41 41.5 42 42.5 43 x-position (inch)Temperature (C) Figure 6-52 Case five: Cent erline temperature profile

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199 POD Calibration Intensity information is analyzed th rough POD yielding the following results: 550 600 650 700 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 Wavelength (nm)Normalized intensity Figure 6-53 Case five: Invers e of normalized intensity (Irun/Iref) POD extracted two eigenvectors form th e temperature calibration matrix, shown below, similar to case 2. The eigenvectors re present the pressure and temperature as was the case before. At the minimum-error rotation angle the scores of the second eigenvector scale the temperature. The scores associated with the first eige nvector can also be used at the same rotation angle to scale the temper ature, however, produci ng nosier calibration. This is because this set of scores represent th e intensity variation in the pressure spectral range due to temperature change. 1 1 1 / Normalized intensity

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200 550 600 650 700 -25 -20 -15 -10 -5 0 5 Wavelength (nm) R1 R2 50 100 150 200 250 300 350 400 450 500 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 C1 C2 Figure 6-54 Case five: Temperat ure calibration fundamental spect ra at 89 degrees (left) eigenvalues of ca libration (right) 550 600 650 700 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Wavelength (nm) 550 600 650 700 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 Wavelength (nm) Figure 6-55 Case five: Product of first (l eft) and second (right) eigenvectors and eigenvalues of calibration The optimum rotation angle for calibration is 89 degrees and the mean calibration error is consistently 0.3C. The reconstruc ted temperature calibra tion spectrum is shown below. T T Pixel index Eigenvector magnitude Eigenvalue R1 x C1 R2 x C2

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201 550 600 650 700 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 Wavelength (nm)Normalized intensity Figure 6-56 Case five: Product sum of eigenv ectors and calibration eigenvalues showing 9.5% variation at 550nm and 17% at 650nm The temperature calibration is a quadratic fit of the intensity data, equation (6.4), with the coefficient extracted at the appropr iate rotation angle. A linear fit produced less accurate results. Further, the normalized image vectors must be taken in the direction of the temperature gradients (i.e., rows not colu mns) for the calibration procedure to yield correct values. 2 22TaCbCc (6.4) The pressure calibration yielded two eige nvectors with the calibration utilizing the first eigenvector. The calibration mean erro r was 0.061 psi with a maximum error of 0.24 psi. T

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202 550 600 650 700 -5 0 5 10 15 20 25 30 Wavelength (nm) R1 R2 1 2 3 4 5 6 7 8 9 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 C1 C2 Figure 6-57 Case five: Pressure calibration f undamental spectra at 11 degrees (left) eigenvalues of ca libration (right) 550 600 650 700 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Wavelength (nm) 550 600 650 700 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Wavelength (nm) Figure 6-58 Case five: Product of first (l eft) and second (right) eigenvectors and eigenvalues of calibration P P Calibration p oint index Eigenvector magnitude Eigenvalue R1 x C1 R2 x C2

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203 550 600 650 700 0.95 1 1.05 1.1 1.15 1.2 1.25 Wavelength (nm)Normalized intensity Figure 6-59 Case five: Product sum of eigenv ectors and pressure ca libration eigenvalues showing 4% variation at 550nm and 16% at 650nm The pressure calibration is a linear fit of the intensity data similar to previous cases. The results for the test points show a slight in crease in the predicted error relative to case 3 ( Table 6-7 ). The robustness of the POD analysis is evident in the re sults. The relative angle between the two calibrati on eigenvectors is 78 degrees showing the ability of POD to identify the relative orientation. The relativ e angle is less than 90 degrees because the temperature field was not c onstant along lateral stati ons as discussed above. Table 6-7 Case five: Test-points pressure results. Actual represents pressure tap measurement and POD represents the cal culated pressure via POD calibration. The precision error of the Actu al readings is 0.006 psi. Actual POD Absolute error (psi) /Percent error 22.48 22.34 0.14 (0.63) 21.81 22.05 0.24 (1.10) 19.62 19.40 0.22 (1.12) 17.04 16.89 0.14 (0.88) P 1 1 1 / Normalized intensity

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204 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / L Figure 6-60 Case five: Calculated te mperature from POD calibration (image) C

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205 0 50 100 150 200 250 300 350 400 450 500 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Temperature (C) Actual Predicted Figure 6-61 Case five: Calculat ed temperature from POD calib ration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual thermocouple read ings used for calibration. The temperature field in Figure 6-60 shows the angularity (i.e., relative angle between) of the temperature w ith respect to the flow direction. Observing the figure above, it is evident that the te mperature calibration was not able to accurately observe the sharp gradient between pixe l indices 165 and 265; however, the values are off by about 1.2C. The sharp gradient is caused by a 0. 5 gap between the hot-plates. A temperature gradient of 2C is possible within the 2 distance separating the two thermocouples. From Fourier law, a temperature gradient of 2C over a distance of 2 with thermal conductivity of ~200 W/m.K fo r aluminum, and a cross sectional area of 2 inch2, the wattage needed is about 10W. This show s that such gradient is possible as Calculate d 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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206 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / L Figure 6-62 Case five: Calculated pr essure from POD calibration (image) psi

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207 14 15 16 17 18 19 20 21 22 23 24 Pressure (psi) Actual Predicted Figure 6-63 Case five: Calculated pressure from POD calibration (image). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual pressure taps r eadings used for calibration. Observing the figure above, the pressure ca libration was able to observe the lateral increase in the pressure due to temperature increase. Idea l gas law predicts roughly 0.5 psi difference laterally due to thermodynamic effects. However, the calibration seems to slightly over predict the pressure close to the channel exit. Unfo rtunately, no pressure validation was available for ex it conditions; nonetheless, the calibration shows consistent accuracy within the calibration domain. Calculated 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 x / L

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208 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / LCase Seven (Oblique Temperature Gradient with Longitudinal Pressure Gradient) In this case the temperature gradient is ob lique relative to the flow direction. The temperature profile varies along each lateral station. This will further confirm the PODs ability to distinguish the re lative angle between the pressure and te mperature gradient. Further, the accuracy of the re sults would assess the ability of POD to fully separate the variable. This is the most challenging cas e for the POD calibration and would set the benchmark for its success. 45 50 55 60 65 Figure 6-64 Case seven: Temper ature profile (thermocouples) C

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209 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2 2.5 3 3.5 4 4.5 5 x / LPercent deviation from theory 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 15 16 17 18 19 20 21 22 23 x / LPressure (psi) Experimental Theoretical Figure 6-65 Case seven: Pressu re profile (bottom), (a) per cent pressure deviation from theory (top)

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210 0.45 0.5 0.55 0.6 0.65 0.7 0.45 0.5 0.55 0.6 0.65 0.7 Figure 6-66 Case seven: Normalized intensity (Irun/Iref): 550nm [left] --600nm [right] 0.5 0.55 0.6 0.65 0.7 0.75 0.55 0.6 0.65 0.7 0.75 Figure 6-67 Case seven: Normalized intensity (Irun/Iref) : 650nm [left] --700nm [right]

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211 POD Calibration Intensity information is analyzed th rough POD yielding the following results: 550 600 650 700 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 Wavelen g th ( nm ) 1 / Normalized intensity Figure 6-68 Case seven: Invers e of normalized intensity (Irun/Iref) POD results are in complete agreement w ith previous results and the extracted eigenvectors and eigenvalues are shown belo w. The calibration functions are once more linear for the pressure and quadratic for the temperature with similar calibration accuracy compared to case 5.

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212 550 600 650 700 14 12 10 -8 -6 -4 -2 0 Wavelength (nm) R1 R2 50 100 150 200 250 300 350 400 450 500 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 C1 C2 Figure 6-69 Case seven: Temp erature calibration fundamental spectra at 93 degrees (left) eigenvalues of calibration (right) 550 600 650 700 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Wavelength (nm) 550 600 650 700 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 Wavelength (nm) Figure 6-70 Case seven: Produc t of first (left) and sec ond (right) eigenvectors and eigenvalues of calibration T T Calibration p ixel index Eigenvector magnitude Ei g envalue R1 x C1 R2 x C2

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213 550 600 650 700 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Wavelength (nm) Figure 6-71 Case seven: Pr oduct sum of eigenvectors a nd calibration eigenvalues showing 31% variation at 550nm and 28% at 650nm 550 600 650 700 -40 -30 -20 -10 0 10 20 30 p@ Wavelength (nm) R1 R2 1 2 3 4 5 6 7 8 9 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Wavelength (nm) C1 C2 Figure 6-72 Case seven: Pressu re calibration fundamental spect ra at 53 degrees (left) eigenvalues of ca libration (right) T Normalized intensity Calibration p oint index Ei g envector ma g nitude Ei g envalue

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214 550 600 650 700 -1 -0.5 0 0.5 1 1.5 2 Wavelength (nm) 550 600 650 700 0 0.5 1 1.5 2 2.5 3 Wavelength (nm) Figure 6-73 Case seven: Produc t of first (left) and sec ond (right) eigenvectors and eigenvalues of calibration 550 600 650 700 1.4 1.6 1.8 2 2.2 2.4 2.6 Wavelength (nm) Figure 6-74 Case seven: Pr oduct sum of eigenvectors a nd calibration eigenvalues showing 8% variation at 550nm and 5% at 650nm POD successfully recognized the change of orientation between the pressure and temperature from 78 degrees in case five to 40 degrees in case seven. Further, the calibration accuracy is consis tent with previous cases. P P P R2 x C2 R1 x C1 1 1 1 / Normalized intensity

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215 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / LTable 6-8 Case seven: Test-points pressure results. Actual represents pressure tap measurement and POD represents the cal culated pressure via POD calibration. The precision error of the Actu al readings is 0.006 psi. Actual POD Absolute error (psi) /Percent error 23.28 23.42 0.14 (0.60) 22.51 22.54 0.03 (0.13) 20.01 19.76 0.25 (1.25) 17.10 16.88 0.22 (1.29) Figure 6-75 Case seven: Ca lculated temperature from POD calibration (image) C

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216 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 z / wx / L Figure 6-76 Case seven: Ca lculated pressure from POD calibration (image) psi

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217 50 100 150 200 250 300 350 400 450 500 40 45 50 55 60 65 Temperature (C) Actual Predicted Figure 6-77 Case seven: Pred icted temperature from POD calibration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual thermocouple readings used for calibration. 14 15 16 17 18 19 20 21 22 23 24 Pressure (psi) Actual Predicted Figure 6-78 Case seven: Predic ted pressure from POD calib ration (values). Each curve represents a longitudinal line of pixels along the channel. Actual represents the actual pressure taps r eadings used for calibration. Calculate d Calculate d 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 x / L

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218 The Case for POD A fundamental question that is inherently tied with the principle of using POD to calibrate the paint is why POD? What adva ntage does POD offer compared to simpler techniques? Such techniques could be as simple as a priori calibration that encompasses a wide range of temperatures expected duri ng the experiment. Other techniques suggested in the literature (Bell et al 2001, Woodmansee et al 1998) are presented again in Table 6-9 To assess the robustness and advantage/di sadvantage of using POD, two different calibration techniques are utilized. The first technique is a simple curve fir of the intensity data at the pressu re spectral emission region (650nm). The second technique uses an intensity ratio of the intensities from the temperature (550nm) and pressure spectral regions. Table 6-9 Comparison of diffe rent calibration techniques Calibration technique Advantages Disadvantages In situ isothermal calibration: Acquire wind-off images at atmospheric conditions The simplest approach Suitable for isothermal conditions Temperature effects can not be accounted for Calibration R.M.S. error on the order of 1.25 psi for PtTFPP/FIB (Bell et al, 2001) with pressure range of 29 72.5psi. Calibration r.m.s. error on the order of 0.2 psi for ODU PSP (Woodmansee et al 1998), with pressure range of 1 15.4psi. In situ calibration: Acquire wind-off images immediately after wind-on conditions Easy technique Temperature effects absorbed in calibration coefficients Need to ensure temperature stability Wind tunnel must be turned off. Limitation on number of images that can be acquired for reference condition, especially for long exposure times, due to temperature drift from wind-on conditions. Significant temperature variation between different parts of model

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219 Table 6-9 Continued Calibration technique Advantages Disadvantages require local calibration and pressure taps A priori calibration Few pressure taps scattered over the model are needed More controlled environment for calibration More efficient for practical applications (less time spent in the wind tunnel) Separate experiment for calibration in required Need to have a prior knowledge of expected pressure and temperature levels in the experiment to optimize the calibration process Pressure taps need to encompass the pressure range, and hence any sharp pressure gradients could be unobservable Temperature information must be obtained on the model using TSP (symmetric models with symmetric flow conditions). Asymmetric models or flow conditions can be mapped for temperature using dualluminophor systems Same batch of paint must be used for both calibration and experiment Calibration functions are typically biquadratic in pressure and temperature (Bell et al 2001), necessitating a minimum of 9 points of calibration points with both pressure and temperature information Calibration r.m.s. error on the order of 0.021psi for OPTROD PSP (Bell et al 2001), with pressure range of 0.75 14.7psi Hybrid technique ( K -fit calibration) Simpler than a priori calibration (only one temperature condition is calibrated for a priori ) Useful for ideal paints when extrapolation beyond pressure taps range is needed Superior to in-situ isothermal calibration Inferior to in-situ calibration In some experiments, the K factor is pressure dependent, yielding a more complicated calibration Calibration r.m.s. error on the order of 0.99 psi for ODU PSP (Woodmansee et al 1998), with pressure range of 1 15.4psi.

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220 Curve Fit of the 650nm Intensity Data and Intensity Ratios A simple approach to account for temperat ure effects in pressure measurements is to normalize the pressure emission by that of the temperature. This approach would effectively eliminate the temperature depende nce under the postulati on that both pressure and temperature luminophors show identical temperature sensitivity (i.e., percent intensity variation/C). The dual-luminophor system used in this work (PtTFPPRuphen/PAN / poly-t-BS-co-TFEM) shows a te mperature sensitivity of 1.4%/C and 1.1%/C for Ruphen (temperature) a nd PtTFPP (pressure), respectively. Figure 6-79 Temperature sensit ivity (integrated intensity/ K) of the temperature and pressure luminophors at 14.7 psi (Kose 2005). The proximity of the temperature sensitivity of the two luminophors makes the intensity-ration appro ach a reasonable approximation for run conditions for which temperature variations are sma ll (~3-5C) relative to reference conditions. However, this approach is not suitable for higher temperature variations from the reference condition.

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221 Case Three First we attempt fitting pressure intensity data from the 650nm range to pressure tap data. This approach is an in-situ isothermal approach for which temperature effects are not accounted for in the calibration. 1.05 1.1 1.15 1.2 1.25 1.3 15 16 17 18 19 20 21 22 1 / Normalized IntensityPressure (psi) Calibration data Linear fit Figure 6-80 Case three: Pr essure calibration using in tensity ratio at 650nm 0 100 200 300 400 500 12 14 16 18 20 22 24 Pixel indexPressure (psi) Figure 6-81 Case three: Ca lculated pressure using intensity ratio at 650nm 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4 x / L

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222 For case three, this approach yielded comp arable results to POD calibration results, but only within the calibration range. This is because the temperature gradient is decreasing linearly along the flow direction, thus the overall outcome is a DC offset to the intensity field. Next we try normalizing the 650nm data by the other two temperature wavelengths (i.e., 550nm and 600nm). 1.07 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 15 16 17 18 19 20 21 22 Normalized Intensity (I550nm / I650nm)Pressure (psi) Figure 6-82 Case three: Pressure calibration using intensity ratio (I550 / I650) The ratio (I550/I650) exhibits a double-value behavior for higher pressures and hence is not valid as a calibration scheme On the other hand, the ratio (I600/I650) exhibits no such behavior and could be possibly valid for calibration. Results of this calibration are shown in Figure 6-84 and show the inaccuracy of the calibration, especially at high pressure levels and outside the calibration envelope.

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223 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 14 15 16 17 18 19 20 21 22 23 Normalized Intensity (I600nm / I650nm)Pressure (psi) Calibration data Quadratic fit Figure 6-83 Case three: Pressure calibration using intensity ratio (I600 / I650) 0 50 100 150 200 250 300 350 400 450 500 10 15 20 25 30 35 40 45 50 Pixel indexPressure (psi) Figure 6-84 Case three: Ca lculated pressure using intensity ratio at (I600 / I650) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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224 Case Five 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 1.22 16 17 18 19 20 21 22 23 Normalized Intensity (1 / I650nm)Pressure (psi) Figure 6-85 Case five: Pressure calibration using intensity (1 / I650) 0 50 100 150 200 250 300 350 400 450 500 6 8 10 12 14 16 18 20 22 24 26 Pixel indexPressure (psi) Actual Calculated Figure 6-86 Case five: Calculated pressure using intensity (1 / I650) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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225 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 15 16 17 18 19 20 21 22 23 24 Normalized Intensity (I600nm / I650nm)Pressure (psi) Calibration data Quadratic fit Figure 6-87 Case five: Pressure calibration using intensity (I600 / I650) 0 50 100 150 200 250 300 350 400 450 500 10 12 14 16 18 20 22 24 26 Pixel indexPressure (psi) Actual Calculated Figure 6-88 Case five: Calculated pressure using intensity (I600 / I650) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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226 0 50 100 150 200 250 300 350 400 450 500 14 16 18 20 22 24 26 Pixel inde x Pressure (psi) Actual Calculated Figure 6-89 Case five: Calculated pressure using intensity (I600 / [I650]2) Figure 6-88 and Figure 6-89 show an inte resting trend of improved accuracy by changing the power of the denominator (I650). 100 200 300 400 500 14 15 16 17 18 19 20 21 22 23 Pixel indexPressure (psi) Figure 6-90 Case five: Calculated pressure using intensity (I600 / [I650]1.5) Actual Calculated 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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227 Figure 6-91 Case five: Calculat ed pressure: (A) Intensity I600 / [I650]1.5 (B) POD calibration. Table 6-11 Case five: Comparison between te st-points pressure results for POD and intensity-ratio Actual represents pressure tap measurement and POD represents the calculated pressure via POD calibration. The precision error of the Actual readings is 0.006 psi. Absolute error (psi) /Percent error Actual POD I600 / [I650]1.5 POD I600 / [I650]1.5 22.48 22.34 21.80 0.14 (0.63) 0.68 (3.02) 21.81 22.05 21.76 0.24 (1.10) 0.05 (0.23) 19.62 19.40 19.37 0.22 (1.12) 0.25 (1.27) 17.04 16.89 17.39 0.14 (0.88) 0.35 (2.05) The results show a maximum absolute error of 0.68 psi, which is much higher than the POD calibration. Evidently, the simple in tensity-ratio technique is not capable of accounting and compensating for temperature e ffects in the pressure data. The only case for which the technique yielded comparable resu lts was case three. N onetheless, even in A B psi

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228 such simple interaction between pressure and temperature (case three), the intensity-ratio technique yields notably inaccurate re sults outside the calibration range. Case seven 0 50 100 150 200 250 300 350 400 450 500 5 10 15 20 25 30 Pixel indexPressure (psi) Actual Calculated Figure 6-92 Case seven: Calculated pressure using intensity (1 / I650) 0 50 100 150 200 250 300 350 400 450 500 12 14 16 18 20 22 24 26 28 30 Pixel indexPressure (psi) Actual Calculated Figure 6-93 Case seven: Calculated pressure using intensity (I600 / I650) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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229 0 50 100 150 200 250 300 350 400 450 500 12 14 16 18 20 22 24 Pixel inde x Pressure (psi) Actual Calculated Figure 6-94 Case seven: Calculated pressure using intensity (I600 / [I650]2) 50 100 150 200 250 300 350 400 450 500 14 16 18 20 22 24 Pixel indexPressure (psi) Actual Calculated Figure 6-95 Case seven: Calculated pressure using intensity (I600 / [I650]1.55) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x / L

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230 Figure 6-96 Case seven: Calculated pressure: (A) Intensity I600 / [I650]1.55 (B) POD calibration. Table 6-12 Case seven: Comp arison between test-points pr essure results for POD and intensity-ratio. Actual represents pressure tap measurement and POD represents the calculated pressure via POD calibration. The precision error of the Actual readings is 0.006 psi. Absolute error (psi) /Percent error Actual POD I600 / [I650]1.55 POD I600 / [I650]1.55 23.28 23.42 22.35 0.14 (0.60) 0.93 (3.99) 22.51 22.54 22.22 0.03 (0.13) 0.29 (1.28) 20.01 19.76 19.48 0.25 (1.25) 0.53 (2.65) 17.10 16.88 17.74 0.22 (1.29) 0.64 (3.74) The results of case seven are comparable to the previous case (case five). This shows the robustness and effectiveness of the POD approach in calibrating dualluminophor paints. The calibration approach is universal and is thus applicable to any flow conditions without any fundamental restrictions. Ho wever, the POD is more involved, both mathematically and physic ally, and must be we ll understood to yield A B psi

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231 accurate results. The main issues pertinent to the success of the POD approach were discussed in previous sections. Next we turn our attention to the uncertainty analysis to complete the analysis and assess the accu racy of the POD approach. Although POD results showed high potential for the approach without identifying th e accuracy of the calibration and the results the overall succe ss of the POD would not be complete. Error Sources and Uncertainty The first question facing any experimental calibration techniqu e is: how accurate are the results? A calibration approach such as POD is rather involving and hence may contain many sources of errors. Combined, these errors could yield any calibration technique futile. We start by defining error, its sources and then c onclude by presenting the uncertainty analysis. The term error re fers to the magnitude of deviation in the measured value from the true value, or more specifically the estimat ed value of the true value. Of course, one can never estimate the error in any measurement without knowing the true measured value. On the other hand, th e true value is something that we can never know without measuring it, which is inherent some scale of error due to equipment, the experiment, or the experimentalist. One can conclude then that we can never actually measure the true value, and hence we can neve r know the exact error, either. This makes the entire argument seem circ ular! However, we can usuall y estimate the likelihood that a measuring error exceeds some specific value (Beckwith 1993). Experimentalists rely on tools such as statistics to quantify such likelihood within a specific confidence level, say 95%. This means that 95% of the time, we can claim the measurement error of that instrument to be bounded by some limit, while 5% of the time the error exceeds those limits. The error bounds on the measurement are commonly called the unc ertainty of that measurement. Error is defined as:

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232 mtrueErrorxx (6.5) where m x and true x are the measured and true value of the measurement, respectively. The uncertainty bounds to within a certain confidence level are thus: xxUU (6.6) where xU is the uncertainty in the measurement. Equivalently, the uncertainty can be expressed as: mxtruemx x UxxU (6.7) The first step in quantifying the uncertainty is to identify the various sources of errors. Despite the diversity of error sources, most errors can be placed into two general classes: bias and precision errors. Bias errors are systematic by nature, meaning they repeat themselves with the same magnitude and in the same direction every time a measurement is recorded. Therefore, they can be usually accounted for easily by subtracting this offset from any reading. However, to recognize bias error, a more accurate measuring instrument is needed to quantify its value in the instrument under investigation. Precision errors are inhere ntly random and differ for each successive measurement in both magnitude and direction. Fortunately, this type of error typically averages to zero if enough measurements are recorded. The readings will cluster around a central (i.e., mean) value and spread to some limit around this value creating a distribution. Enough readings ar e needed to define such di stribution. Upon defining the distribution of the error, stat istical analysis is employed to estimate the bounds of such error.

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233 Figure 6-97 Bias a nd precision error Classification of Error In general, error categories may overlap and are at times ambiguous. Some errors behave as precision in one case and as bias in others; further, some do not clearly fit into either category. However, we can generally classify errors as follows: 1. Bias errors (systematic) Calibration errors Consistent human errors or defective equipment System resolution limitations Loading errors 2. Precision errors (random) Fluctuating experimental conditions (e ither inherent to measured quantity or due to external factors) Insufficient system sensitivity 3. Alternating errors (sometimes bias and sometimes random) Instrument backlash, friction, hysteresis Calibration and or test envi ronmental conditions drift Variations in experimental procedure or definitions true x m x Bias error Total error Precision error Distribution of combined bias and precision error

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234 We know shed more light on some of these errors that pertain to our experiment starting with bias errors. Calibration errors are an obvi ous source and are evidently important to this work. A zero-offset is ty pically required to tare the equipment. For instance, the pressure transducer used in measuring the various pressures throughout the experiment is validated for calibration bias against a more accurate instrument (DRUCK), which has some bias itself, but rather much smaller. If the calibration offset is not accurate, then a bias value will be added to all measured values. Moreover, if the instrument is not checked for such bias regul arly, such bias error could slip unnoticed. On the other hand, thermocouple readings were simply validated agai nst each other. The channel has 20 thermocouples, and if under no-flow isothermal conditions a thermocouple reading is off by a specific valu e relative to the remaining thermocouples, then such error is recorded. However, thermocouples usually have a significant STD, and hence deviations within this precision uncer tainty fall in the ambi guous category as they may be sometimes random and other times systematic. Resolution limitation can induce a bias error equal to one-half the minimum possible resolution. In our experiment, the imaging system was superior to pressure and temperature instruments, with the temperature system possessing the poorest reso lution. An important sub-category of bias error is the loading error. Loading error re sults from equipment interference with the measured value. For instance, paint, pressu re taps, thermocouples and the glass plate used in this experiment influenced, to some extent, the flow characte ristics. Nonetheless, in our experiment the actual flow was not unde r investigation, rath er, the paint and the calibration procedure. Therefore, such errors can be tolerated in this case, but most definitely not in actual experiments.

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235 Precision errors vary in their sources, but exhibit a different tra it than bias errors. Fluctuating experimental c onditions can cause such erro r. CCD camera systems are typically cooled to maintain steady output a nd low noise. If the camera system is turned on and not allowed enough time to reach steady state conditions, such as the A/D unit which needs to reach the operating temperature of ~ -25C, precision errors will be introduced into the measured signal. The sa me argument goes for test cases were a temperature gradient was imposed on the channel. For that reason, environmental conditions were monitored throughout the experime nt. It is important to note that, strictly speaking, drifting test conditions are not errors, rather a lim itation of the design or an inherent feature of the phenomenon under inve stigation. However, the same statistical techniques can be applied and such va riations can be treated as errors. The most difficult error type is alternati ng error due to the ambiguity of the error source and hence the error processing proce dure (i.e., subtract a bias, average large enough sample, etc.). In our experiment, the main alternating error was due to temperature effects on the imaging system and the test conditions. Relatively long exposure times were used (~ 8 minutes) fo r which temperature variation occurred and affected the measurement to some extent. Th e imaging system had to be calibrated for every case to estimate dark current noise by taking an image with the excitation sources off. The heated flow exhausted into an en closure that included the CCD camera system and the channel itself. The increased temperat ure could have influen ced the dark current reading and thus the bias calib ration. Conversely, the variat ion of the temperature during such long acquisition time would induce a ra ndom error on the measurement. Only the latter was quantified, as its outcome is much higher with respect to dark noise error.

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236 Uncertainty Analysis As with any experiment, the accuracy of the predicted environmental conditions are limited by the uncertainty in those measurements. The total uncertainty defined in an r.m.s. fashion is: 22xxxUB (6.8) 1.96 95% for 30x xm m (6.9) where B is the bias error, is the precision error roughly es timated as twice the standard deviationx and mis the number of samples. For a linear function y of n independent variables xi the total uncertainty is then defined as: 2 22 1212y nnxxxyyy UUUU xxx (6.10) Sajben (1993) discussed predicted pre ssure measurements via PSP and concluded seven variables (from the Stern-Volmer relati on) contributing to th e uncertainty in the pressure. ,(,,,,,,) P refaarefrefrefUfIIIITTP (6.11) where P U is the total pressure uncertainty, I is the run intensity, the subscripts ref and a denote reference and excitation conditions, respectively, and T is the temperature. Each variable may have two types of noise embe dded within, bias or random. Observing the variables, they can be lumped into three va riables, intensity, temperature, and pressure. We start by examining the uncertainty in the intensity. Intensity uncertainty stems mainly inherent sources: shot noise, dark current, digitize r bias, and readout noise and external sources that are due to signal drift pertinent to test conditions drift. Other minor

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237 sources not addressed in this analysis include paint photodegrad ation, digitizer resolution, pixel-gain variation, and image registration. All main error sources are precision errors except for dark current noise. Dark current and readout noise are estimated from the camera specification, while digitizer bias is accounted for by subtracting a dark image from both the reference and run images. Table 6-13 Intensity error sour ces and values for Photomet rics CH250A CCD camera (SI 502AB), 200 kHz, 14 bit A/D for a unity nominal gain value and a measured gain ( ) of 19.1 (e-/ADU) Error sources Average Value Error Type Bias (B)/Precision (P) Dark current (e/pixel/sec @ -25C) 6 P Digitizer bias (cts) ~110 B Readout noise (e-/RMS) 13.3 P Shot noise (cts for m number of images) I P The total dark current uncertainty dU is exposure time dependent and hence is computed as: 2222163.460.5661.563.5 1.961.961.961.96 16161616 0.79 d dU Ucts (6.12) Shot noise follows Poisson statistics and is effectively reduced by averaging multiple images. The uncertainty due to shot noise for a single frame is then characterized as the square root of the collected electrons, equation (6.13). eUeI (6.13)

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238 The uncertainty in the intensity is thus: e IU I U (6.14) For multiple frames, the precision uncertainty (95%) is thus expressed as (Mendoza, 1997): 1.961.96I IU I m m (6.15) where is the ADU gain (=19.1 e-/ADU for our camera). Sixteen frames were acquired to minimize the uncertainty in the intensity measurement. As each case has a different intensity level due to different enviro nmental conditions, case 7 was chosen for uncertainty calculation as it possesses the lowe st run intensity leve ls, hence the highest uncertainty. The following table summarizes the intensity statistics for case 7. Table 6-14 Shot noise uncertainty for all filters (case seven) with total precision uncertainty of 29.3cts Intensity Data 550nm 600nm 650nm 700nm Mean (cts) 5256.1 5782 7017.8 6444.1 Average shot noise (cts) 72.5 76 83.8 80.3 Run I (cts) 8.1 8.5 9.4 9 Mean 10147 11129 12162 10252 Average shot noise (cts) 100.7 105.5 110.3 101.2 Reference I (cts) 11.3 11.8 12.4 11.4 All precision errors in Table 6-14 are then summed in an r.m.s. approach yielding a total precision uncertainty due to shot noise .3cts. Ignoring excitation source and photodegradation intensity drift, test condition intensity dr ift is only considered. The longest exposure time for an image is 3.5 s econds, and as environmental conditions (i.e.,

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239 pressure and temperature) were monitored, pressure drift was smaller than the precision of the pressure transducer of 0.00625psi. Te mperature variation was more difficult to assess because temperature drift (~ 0.08C) wa s smaller that its uncertainty. This falls into the ambiguous error category were it could be due to manuf acturer specification error limits (i.e., bias) of 0.5C or the STD limit of 1C. In the worst case it would contribute as a bias error, and hence it will be treated as such. For the 550nm emission, a 1C change caused a decrease in intensity of about 76cts, thus 0.08C error would yield a precision error of ~6 cts. The intensity drift for all filters are shown in then table below. Table 6-15 Intensity drift un certainty for case seven. Re ference conditions are not included in the analysis as they are acquired under isothermal conditions. The total intensity bias uncertainty due to test conditions drift is 9.7cts Intensity Data 550nm 600nm 650nm 700nm Temperature drift (C) 0.08 0.04 0.08 0.06 Temperature sensitivity (cts/C)* 76.2 80.9 77.2 46.4 I (cts) 6.1 3.2 6.2 2.8 *Based on average intensities from Table 6-14 Additional contributor to total error originated from image registration due to CCD pixel-to-pixel gain variations. To correct for th is bias error a flat field image is needed to normalize the registered image. Flat fi eld images are acquired using a uniform illumination source. As described by Catta festa et al (1998), a uniform source is assembled by using an integrating sphere in conjunction with a bandpass filter identical in its optical charac teristics to the bandpass filter us ed for luminescence detection. Cattafesta et al (1998) reported 1% variation due to this effect. The uniform excitation source was not available for this experiment; co nsequently a value of 1% will be added to the total intensity uncertainty to accommodate this effect.

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240 The total uncertainty in the measur ed intensity is thus given by: 22 IIIUB (6.16) The total bias error is: IdbBN 2 2 209.7 9.7 ctsid IN B (6.17) The total precision error is computed by th e r.m.s. of all precision errors, noting that dark current is multiplied by a factor of two to account for both run and reference images, and the readout noise is multiplied eight times to account for all filters in both run and reference conditions: 222 22228 29.320.7981.15 29.5 ctsIshdrd I INNN (6.18) In the above expressions, N is the noise and the subscripts d rd db and id denote dark current, readout, digitizer bias, and inte nsity drift, respectivel y. The digitizer bias noise was omitted as it was subtracted from both run and reference images. The total uncertainty in the intensity is thus given by: 229.729.5 31.1 ctsI IU U (6.19) It is often more convenient to express su ch uncertainty as a percentage with the mean intensity of all filters for both run and reference images as follows:

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241 31.1 (100) 8524.1 0.36% 95%I IU I U I (6.20) The uncertainty in the calculated pressu re from POD calibration has a fundamental difference from a simple Stern-Volmer rela tion. The coefficients of the linear fit produced by the POD for pressure calib ration are temperature independent. 1, &(,)nrefPabCabfTT (6.21) This is a significant and important result for two reasons. First, it shows that POD successfully fully compensated for the temperat ure effects in the pressure. Second, as a result, run and reference temperature uncerta inties, other than intensity drift, do not contribute to the pressure uncer tainty. Further, both the STD and the pressure drift for the run pressure are an order of magnitude sma ller than the pressure transducer accuracy (0.006psi), thus only the latter value need to be added to the total uncertainty of the pressure. The pressure calibration throughout a ll the cases was a linear function of a set of scores from the POD calibration, which carries the same uncertainty of the intensity ratio ref I I thus the overall uncertainty with 95% confidence level is then characterized as: 2 2PPrefI IP UUB I (6.22) Excitation source errors are omitted in this analysis. The excitation sources used have been characterized and observed to be ve ry stable with time and were always left on, but covered between runs to avoid photobleach ing effects, to avoid the initial drift in the source. Therefore, it will be assumed as an insignificant contributor to the total

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242 uncertainty. The total pressure uncertainty from POD calibration is then: 22 220.360.025 0.361% 95%PIP P PUUB U U (6.23) Similarly, the temperature uncertainty is computed and is tabulated below. The uncertainty analysis corroborates the r obustness and accuracy of POD calibration compared to other techniques reported in the literature. Mitsuo et al (2003) reported a percent uncertainty of 5-8% (at ~ 4-6psi) in the calculated pressure using PtTFPP/Rhodamine B(RhB)/Poly-IBM-co-TFEM dual-luminophor system. They used a simple Stern-Volmer calibration with temperat ure independent coefficients correcting for temperature effects only into the reference image. POD calibration has been shown to produce excellent results for dual-luminophor systems. Further, POD provides extends beyond the mathematical envelop providing physical insight into the process under investigation. This conclude s the analysis chapter. A su mmary of the results, final thoughts and future work are presented in the following chapter.

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243 Table 6-16 Uncertainty (95% conf idence level) for key factors Variable Average Value Bias Error3 Random Error (STD) 3 Uncertainty 95% confidence limits I 1 5256cts DiB=0.0cts 2 RoN=0.7cts 4 ShN=8.3cts 5 DkN=1.07cts 6 .4cts 2 Iref 1 10147cts DiB=0.0cts 2 RoN=0.7cts 4 ShN=11.5cts 5 DkN=1.07cts 6 .6cts 2 Tthermocouple 30-70C 0.5C 1C .55C 7 Ptap 23-16psi 0.00625psi 0.0003psi .00626psi Pref 14.72psi 0.00625psi 0.0003psi .00626psi Tpsp 30-70C 0.808C 1.193C .86C Ppsp 24-14.5psi 0.025% psi 0.36% psi .361% psi 1Case 7, filter 550nm 2After subtracting the dark image 3RoN=Readout noise, ShN=Shot noise, Dk N=Dark noise, DiB=Digitizer bias 4A/D frequency = 200 kHz 5Gain = 19.1 e-/ADU 6Dark current = 6 e-/pixel/second 7Number of samples = 64

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244 CHAPTER 7 CONCLUSIONS AND FUTURE WORK This chapter provides a summary of the work presented in this dissertation. It also provides direction for future work and possible research paths. Conclusions Pressure sensitive paints have been steadily advancing as a measurement technique in various engineering applications. Th e technology has been hindered since its emergence by several drawbacks. One of the main difficulties with PSP is the calibration process. PSP formulations have always suffered from an inherent temperature dependence causing spurious pressure measurem ents. Different calibration techniques are presented in the literature which attempt to compensate for the temperature dependency of PSPs. These techniques lack the universality and offer mo dest accuracy, particularly when temperature gradients are significant. Se veral research efforts investigated the idea of combining two luminophors that measure pressure and temperature simultaneously, hence providing temperature information for pressure calibration. These dual-luminophor systems exhibited undesirable behaviors such as cross-talk and spectral interference making the extraction of pressure and temper ature information more complicated. This work presented a calibration technique usi ng POD which was capable of separating the pressure and temperature information from ra w intensity data and fully compensate for temperature dependence in the pressure emi ssion. Furthermore, the technique extends beyond the mathematical envelope of calibra tion and provides physical insight into the process under investigation. POD calibrati on is not limited to isothermal conditions

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245 between run and reference conditions, small/moderate temperature gradients, similar temperature sensitivity of bot h luminophors or spectrally inde pendent emission. Further, it adds as a noise reduction techni que and a modal analysis tool. A channel flow experiment provided severa l test conditions to evaluate POD as a calibration technique. The first and second cases showed the paint response to pressure and temperature independently. The rest of the cases examined different mixed conditions between pressure and temperature. The analys is revealed the various advantages and provided a measure for the accu racy of POD as a calibration technique. The following is a summary of the main advantages of POD. 1. POD fully separates pressure and temperature information: This was evident in the pressure calibration func tions. All pressure calibrati on functions were linear and the calibration coefficients were c onstants (i.e., temperature independent). Temperature calibration was a quadratic fit. 2. The calibration functions are simple: Kose (2005) used POD to calibrate the paint in a priori approach. The calibration function we re nonlinear second order surfaces with no obvious relation to the know n pressure and temperature behavior as a function of intensity data. This wo rk examined the behavior of POD as a calibrator using artif icial data, which provided a f undamental understanding of the analysis. The calibration function were li near and quadratic for pressure and temperature, respectively. These calibrati on functions agrees with the theoretical prediction of the paint behavior. 3. POD provides physical insight about the pressure and temper ature field: The eigenvectors are extracted at an appropr iate rotation angles. These angles are related to the orientation of the pressure and temperature fields relative to each other. For instance, in case three, the pressure and temperature gradients were longitudinal, and the relative angle betw een the two eigenvectors was 1 degree. For case five the temperature gradient was mainly in the transverse direction, the relative angle between the cal ibration eigenvectors was 78 degrees. The last case, case seven, had an oblique temperature grad ient relative to the pressure gradient and the relative angle was 40 degrees. 4. Accurate results: The results of the te st points and the uncertainty analysis demonstrated the accuracy of the POD calibration. Absolutes errors averages ~0.2 psi for the test points with an uncertainty of .36% psi. This is far superior to results for similar dual-luminophor systems with uncertainty estimates of -7% psi, Mitsuo et al (2003). Furtherm ore, since POD calibration produced

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246 temperature independent calibration coe fficients, pressure uncertainty is temperature independent, yielding improve d pressure accuracy. The results were also compared to relatively rudiment ary calibration techniques using direct intensity-ratios of two diff erent wavelengths spectral data. The ratio technique had am average absolute error of 0.6 psi for case seven, with maximum error of ~ 1 psi near the calibration limits. The intensit y-ratio error increases significantly as the temperature gradient increases. This is evident by comparing the results for case five and case seven. On the other ha nd, POD error is steady and independent of the temperature field. Furthermore, POD calibration was accurate even outside the calibration envelope. The intensity ra tio approach fails significantly even within the calibration envel ope at high pressures. 5. POD calibration eases the constraints on paint formulations: The capability of POD to spectrally separate pressure and te mperature information allows for larger pool-of-candidates of dual-luminophor system s. Several research papers in the literature investigated vari ous pressure and temperatur e luminophors in an attempt to find the best combination with minimal cross talk and spectral interference. This limits the number of viable dual-luminophor systems. POD opens the door for more luminophors to be used and more importantly, perhaps, for the possibility of tailoring the formula tion to different applications. Future Work The potential for dual-luminophor PSP in expe rimental applications is yet to be fully realized due to the difficulty of the ca libration process. The work presented herein presented a successful techni que for calibrating dual-lumi nophor PSP. The next step would be to apply the paint and calibration in more involving applications, such as wind tunnel testing. Several wind t unnel applications exist in th e literature which are well established and can be utilized to further validate the paint/calibration system. Airfoil applications for different flow conditions w ould be of great importa nce to the validation process. In particular, an application with high pressure and temper ature gradients would serve to substantiate the capab ility of POD to separate pressure and temperature effects and provide accurate results. In addition, a lo w speed case with small pressure gradients would emphasize the accuracy aspect of the POD calibration. Several issues need to be addressed in either case. First, the number of calibration points need ed as a function of

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247 the environmental conditions range. Second, the extent of the calibration accuracy beyond the calibration envelope is a key factor th at needs to be further addressed. Third, different paint formulations should be used to fully assess the success of POD as a calibration technique. An interesting case to investigate would invol ve a non-directional temperature gradient, such as that from a h eat source in the middle of the channel. This will identify a key aspect of POD behavior, which is whether POD would still be successful under non-obvious grad ient orientation conditions. PSP is relatively and significantly less in trusive compared to traditional pressure measuring techniques. There are many intricat e applications in wh ich dual-luminophor PSP can be implemented and proven superior co mpared to traditional techniques. A case that is currently under investig ation at the University of Fl orida examines the flow over porous media used as injector face plates inside rocket engines combustion chambers. Such application would trul y establish dual-luminophor tech nology in both the academic and commercial sectors a nd provide more potential fo r the technology. A second application would be micro-ch annel flows. Such experiment would examine key aspects of the paint and calibration as well. Several issues can be investigated using a microchannel experiment: the intrusiveness of th e paint would be greatly emphasized, the number of calibration points needed, and the accuracy and sensitivity of both the paint and the calibration process. More practical app lications involve rotati ng airfoils, such as turbine or compressor blades. Dual-luminophor systems would prove superior in such application, following success of PSP, with an added bonus of mapping temperature variations as well. There is also considerable demand for high-temperature (>400 K) dual-luminophor systems. The development of such system is curre ntly ongoing at the

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248 University of Florida (Schanze group). Du al-luminophor would be a very robust and successful tool for CFD validati on. Instead of typical discrete information to validate the numerical simulation, leavi ng many areas in the flow i nvalidated; dual-luminophor PSP would provide for a full field validation.

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249 APPENDIX A IMAGING SYSTEM This appendix provides comprehensive de tails about the different component of imaging system. The information is primarily directed to reader s with little to no background in imaging system. Measurement System Various components come together to create an imaging system including excitation source, imaging device, and s upporting components. The following sections discuss each component and various issues pe rtinent to its applica tion in luminescence imaging. The Excitation Source Excitation source plays a key role influe ncing the accuracy and quality of data. Luminophors typically have multiple absorpti on peaks with moderate bandwidths, a desired character of the probe to avoid broad absorption and spectral overlap and interference. Therefore, the excitation source must provide su fficient and uniform illumination at these absorption bands to produce an output luminescence signal capable of saturating the detector in relatively short exposure ti me, thus taking advantage of detectors signal-to-noise (SNR) potential. However, the illumination should not be bright enough to cause photode gradation of the luminophor or overwhelm the detectors well depth (see definitions in the supplementar y topics section). Further, the excitation source must have absolutely no emission at the luminophor spectral emission range. A spatially uniform illumination avoids the forma tion of local regions where the signal is

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250 low relative to the nois e level with respect to the rest of the imaged field, inducing an inconsistent SNR field. If continuous illumination is desired, then a main character is the stability of the illumination output by th e source, while excellent pulsed excitation depends on repeatable exc itation signal levels. Some of these induced variations can be accounted for in the calibration process such as inhomogeneous illumination fields (s ee calibration section), however, variations in the overall output signal level (source drif ting) is not easily acc ounted for. A drift in the excitation signal will have the effect of reducing the strength of the paint emission, falsely indicating higher pressu re/temperature levels. Consta nt monitoring of the output excitation signal, though possible, is quite impractical, especially when using multiple excitation sources. A suggested approach in th e literature is to embed an environmentalinsensitive probe in the paint (a multic omponent system) that depends only on the excitation signal. This approach provides an effective correction tech nique that eliminates excitation field variations; noneth eless, it is fairly challenging to find a probe that will absorb in the same spectral range as the othe r probes and yet emits in an empty range of the spectrum not occupied by other luminophors, which becomes even more intricate in systems containing more than one probe (e.g pressure and temper ature dual-luminophor systems.) Lasers Laser (Light Amplification by the Stimulated Emission of Radiation) is an optical oscillator, which is made out of a solid, li quid or gas that emits uniform and coherent light. Unlike ordinary light s ources, coherent light produced by a laser is made up of waves of the same wavelength and in phase. Lase rs have the capability of delivering pure light in an almost-perfectly parallel beam (collimated), of one or more discrete

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251 frequencies. Laser emission can be continuous or pulsed and is used in a myriad of applications. A laser is an optical oscillator which is made out of a solid, liquid or gas with mirrors at both ends. Lasers also implement luminescence principles in their functionality. The lasing material is excited with appropriate energy, thus electronically energizing the atoms, causing them to jump to higher orbits, creating a population inversion. When a photon with a frequenc y corresponding to the energy difference between its excited state and its ground state strikes an excited atom, the excited atom is stimulated to emit a second photon of the same frequency and in phase with the striking photon. The striking photon and the emitted phot on may then each strike other excited atoms, stimulating further emissions of phot ons, all of the same frequency and all in phase. The light is then passe d through a laser medium between two mirrors. The mirrors continue to reflect the light b ack and forth; this process incr eases the intensity of the light waves and induces a chain reaction. The co mbination of spontaneous emission first, which is followed by stimulated emission, causes the laser to lase, which means it generates a coherent beam of light of a single frequency. Lasers are of great advantage in cer tain PSP applications. Their narrow-band emission can be easily tailored for each sp ecific luminophor, though not practical, and is easily distinguished in the spectrum. They ar e most advantageous in applications where optical access is difficult, such as imaging tu rbine blades inside the engine. Using fiber optics, laser beams can be funneled into comp lex structures to provide illumination for the paint. Moreover, lasers, as already stated can be pulsed with ve ry short illumination windows (~ 10 ns), making them ideal fo r unsteady measurements and rotating machinery. On the other hand, it requires cautious and continual surveillance of the

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252 spectrum and energy output intensity to avoi d excitation induced errors. Lasers are, however, unsuitable for applications requiring uniform illumination fields and always pose a safety concern as coherent lig ht sources due to high energy beams. UV Lamps Ultraviolet electromagnetic radiation occupies wavelengths shorter than that of the visible region on the spectrum. It can be subdivided into near UV (380 nm wavelength) and vacuum UV (200 nm). While invisible to the human eye; illuminating certain materials (i.e., lumines cent molecules) with UV radiation prompts the visible emission of fl uorescence and phosphorescence. Ga s discharge lamps, in particular mercury vapor discharge lamp s, are among the most common source of continuous ultraviolet source. The proportion of ultraviolet emitted by a mercury vapor lamp varies considerably with current density, but the operating pressure of the lamp mainly governs the spectral qua lity. Low-pressure mercury vapor lamps possess a very sharp and discrete emission at 254nm, which is significantly below typical PSP excitation range. High-pressure lamps are the typical c hoice for luminescent probes applications as they emit well within the excitation range of most practical probes with a characteristic peak output at 365nm and secondary peaks at 334nm and 313nm. Excitation via mercury-lamps is principall y at discrete wavelengths, narrowing the potential pool of compatible probes. UV sources with more continuous emission spectra include xenon arc lamps (commonly used as s unlight simulators), deuterium arc lamps, mercury-xenon arc lamps, metal-halide arc lamps, and tungsten-halogen incandescent lamps. UV lamps require considerable time to warm up and produce significant heat emission, which might induce errors in the measurement if the lamp is close enough to the test model. It is of an utmost impo rtance for researchers using UV radiation to

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253 practice safety by shielding themselves, espe cially under elongated exposure times, as UV exposure of the skin or eyes is fairly hazardous. Visible Light Illumination LEDs Some luminophors have excita tion absorption bands in the blue range of the spectrum (e.g. ruthenium complexes). Light Emitting Diodes (LEDs) are used in many electrical and elec tronic product on the market, from a tiny on/off light to digital readouts, flashlights, traffic lights and peri meter lighting. LEDs are more efficient and require considerably less power compared to incandescent bulbs. Assembled out of arrays of semiconductor diodes, high-quality LEDs are capable of emission at a single wavelength of light when charged with electri city. Lesser quality LEDs have lower purity compounds, hence possess a broader emission, yet are still practical for most engineering applications. LEDs have very long durable life and are available in various colors depending on the material used for the tips of the probes. Red and yellow LEDs utilize aluminum indium gallium phosphide (AlInGaP ), green and blue utilize indium gallium nitride (InGaN) and with the addition of phosphor, white LEDs are produced. Blue LEDs are the most widely used excitation source in luminescent probes applications due to the excitation range of most luminophor s that lies in the blue rang e of the spectrum. They are relatively expensive to buy (~ $ 2,500), but are rather practical over a wide range of applications, possess low-drifting intensity characteristics and emit low temperature relative to incandescent bulbs. The Detection Device The detection device plays a deterministi c role in how accurate PSP measurements are and the degree of resolution obtainable. Th is could further impinge on the feasibility of certain experiments, such as low speed wind tunnel PSP measurements, where

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254 pressure variations are small and the corre sponding intensity vari ations are fairly diminutive. Accordingly, an understanding of the basic principles of operation of detection sources is fundamental for the comprehension of the setup and acquisition processes as well as error sources and uncertainty analysis. CCD Cameras A charge-coupled device (CCD) is a sensor for recording images consisting of an integrated circuit containing an array of linked/coupled, cap acitors. Controlled through an external circuit, each capacito r can transfer its electric charge to one or other of its neighbors producing a stream of charges that is then passed to other components for further processing. Figure A-1 Schematic of CCD imaging system When a lens on the CCD array projects an image, it results in an accumulated electric charge on the capacito rs that is proportiona l to the local light intensity. Once the array has been electronically charged, a control circuit caus es each capacitor to shift its contents to its neighbor in a systematic way. The last capacitor in the array unloads its charge into an amplifier that converts the charge into a voltage. The process continues ADC A/D 01001 DSP Voltage Signal Digitized Signal 011001110110011 CCD Array Lens Light Pixel

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255 until the entire contents of the array are mappe d as voltage field. The electric voltage is then sampled, digitized and stored in memory for processing. CCDs contain grids of pixels and widely used in digital cameras, optical scanners and vi deo cameras as lightsensing devices. They typically have a light response of 70% to incident light making them by far superior and more efficient than photographic film, which have typical light response of 2%. Physical Construction A standard CCD device is composed of metal oxide semi-conductor (MOS) capacitor, a composite structure of doped se mi-conducting substrate and combination of aluminum or heavily doped polysilicon fuse d with an electrical connector (commonly known as an etched electronic gate) that is insulated in the middle by a layer of silicon dioxide (SiO2), and various s upporting electronics. Combined they work to collect, store and then digitize the analog information for computer processing. Figure A-2 CCD Chip The MOS capacitor (pixel) constitutes the building block of the CCD. The CCD array consists of two areas: th e sensing area, the region of pi xels exposed to light, and the serial register, a segment of pixels coated w ith an opaque material. As a voltage bias is applied to each pixel gate, it cr eates a potential well, thus tr iggering these pixels to accept

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256 and collect the electrons gene rated via the incoming electrom agnetic radiation in direct proportion. These collected char ge packets are then stored and transferred from the sensing area to the serial register, which in turn shifts each charge packet orderly for subsequent readout by the analog-t o-digital (A/D) electronic unit. From Light to Electrons Silicon crystalline enjoys favorable el ectronic properties under exposure to electromagnetic radiation in the visible spectrum. Thr ough photoelectric effects and thermal agitation of the silicon crystal lattice, output electric charge packets are generated in proportion to the inco ming electromagnetic radiation. The la tter effect is actually is an undesirable source of error known as thermal noi se or more famously dark current. As explained earlier, an electron can be elevated to a higher energy level as a photon strikes the atom, occasionally causing the freeing of the electron from the atom. Similarly, as light strikes the CCD surface, it frees el ectrons from the covalent bonds between neighboring atoms to move ar ound, which accumulate in the capacitors. Several factors influence the probability of a photon collision causing an atom to release an electron. The two central factors are: bloc kage by circuits on the CCD su rface prohibiting light from entering and the wavelength of the incide nt light (longer wavelengths photons can infiltrate to certain depths of the CCD arra y without colliding with atoms, while some shorter wavelengths may simply reflect off the surface.) Potential Wells Quantifying the number of photons that fa ll on the photoreactiv e surface resulting in a release of an electron is a true representation of the CCDs sensitivity. The ratio of incident photon to collision-i nduced electron release is known as the quantum efficiency and is often reported as a percentage. The pr ocess of quantifying th e number of electrons

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257 takes place in potential wells. A potential well is a thin layer of silicon dioxide, encrusted with a conductive gate structure, grown on a silicon layer. As a positive electrical potential is applied to these gates, a depleti on region is created provi ding a well to store the photon-induced free electrons. FigureA-3 Potential Well Structure The well collects the electronic charges unt il it reaches its full capacity, which is typically on the order of a million electrons. The well is indiscriminate to electrons regardless of their source, hence electrons generated from thermal agitation and high energy particles add to the total stored charge. Charge Transfer The CCD array is configured into multiple vertical shift registers and usually one horizontal shift register, both requiring differe nt clock patterns. Af ter the electrons are collected by the pixels in the potential well, they are then shifte d along the CCD array by the action of regular electroni c pulses. The register coll ects one line at a time and transports the pixel charges in a serial manner to the on-chip output stage. A circuit that deposits the electrons from each pixel into a sense capacitor counts the electrons. Farads law states that the potential diffe rence across a capacitor is equal to the e e e e e e e e e Electrical Connection Polysilicon gate Silicon dioxide Silicon Potential well Incident light

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258 electric charge accumulated inside the capac itor divided by its capacitance; accordingly a charge will develop a voltage acr oss the sense capac itor proportional to the incident light intensity collected by the corre sponding pixel. The output volt age is a series of stepped DC voltages. The circuitry measures this voltage and amplifies it then drains the capacitor. This procedure provides an effec tive grayscale image of how much light has fallen on each individual pi xel in the CCD array. Figure A-4 CCD readout sequence Each pixel retains three different voltage levels: the reset feed -through, the reference level, and the pixel level. The opaque pixels have the voltage level representing black that is utilized as reference voltage to adjust the signal offset. The reset feedthrough voltage is the potential applied to se t the sense capacitor to the initial reference voltage. The reference voltage can be relatively high, up to 12V but after the decay of this feed-through potential the capacitor will refl ect the reference voltage level. Once the capacitor has been reset, a switch opens and the pixel charge is transferred to the capacitor, altering its voltage. 1. Charges accumulate on the parallel-register due to light exposure 2. Charges are shifted from the parallel register (1st column) to the serial register 3. Charges in the first block of the serial register are shifted into the output node 4. Charges at the output node are collected for signal processing 5. Steps 3 & 4 are repeated till the entire serial register is read 6. Steps 1 through 4 are repeated till all the parallel registers are read

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259 Digital Signal Processing The voltage output of the CCD array is amplified and passed to the analog-todigital converter (A/D ). The A/D converter divides th e electronic charges of the CCD pixels that are readout from the chip by a certain factor (i.e., the conversion factor) thus delivering a digital signal measured in count s (or gray levels). The maximum possible conversion factor would be the full-well cap acity divided by the b it depth (i.e., maximum possible intensity range.) However, quite ofte n the conversion factor is lower than this theoretical value. The conversion factor prov ides a mean of contro lling the digitization process. For example, for low light level experiments a lower c onversion factor is desired, which implies a higher bit A/D. This allows for faster saturation as fewer electrons are needed, while the light-to-gray scale digitization is finer (i.e., fewer electrons per count) and hence the resolution of the image is improved allowing for the detection of smaller variations. An example would better illustrate the concep t. The CCD camera used in this work has a full-well capacity of 330,000 electrons a nd is coupled with a 14-bit A/D converter. This means that the well can collect up to 330,000 electrons before reaching its capacity, and the A/D converter has a saturation limit of 16,384 counts, which in turn implies that at the CCD saturation point the smallest resolvable variation by the A/D converter, ignoring noise, is on the orde r of 20 electrons. A 16-bit A/D converter would ideally be able to resolve variations of only 5 el ectrons for the same CCD camera. Noise undesirably reduces the dynamic range and t hus the resolution of the image. CCD Chip Types Full-Frame CCD Chips This type is has a lower sensitivity in the spectral range and has the simplest

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260 architecture, hence less expensive and a dvantageous in applications where high sensitivity measurements is not influentia l. Full-frame CCD chips consist of a highdensity array of photodiodes that convert the incoming photons into electrical potentials according to the process described previously. Their advantage lies in their very high fill factor, values of 97-99 % are typical, which means that the entire surface is functional with very little space be tween the photodiodes that is not functional in radi ation detection and hence lesser photons are lost. This CCD type requires a mechanical shutter or synchronized illumination to avoid image smearing artifacts that occur as a result of the continuous illumination during pa rallel regist er readout. Frame-Transfer CCD Chips This type compensates for the full-frame CCDs inability to simultaneously detect light and perform the readout process. This is accomplished by using a two-part chip in which one half is exposed to light and co llects photons while th e other serves as a temporary data storage only and is masked to protect it from incide nt photons. During the exposure of an image, the data of the previ ous image are readout fr om the storage array via the serial shift register through an output amplifier and the A/D converter. As soon as exposure and readout of the old image are completed the newly accumulated charges are very rapidly moved across the CCD array; this process is thus termed "frame transfer." The process of transferring data between the two parts of the CCD is relatively shorter compared to the readout process. This allo ws for faster image processing as each cycle yields an acquired image and as well as a simultaneously readout immediately preceding image, compared to only one acquired and read image per cycle. Unlike the full-frame CCD chips, a frame-transfer CCD chip can operate continuously w ithout a shutter at a high rate.

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261 Back-Thinned, Back-Illuminated CCD Chips A rather expensive and delicate type of chips for high-end scientific-grade CCD cameras, this type is superior due to its high quantum efficiency exceeding 80% between 450 and 650 nm, compared to only 65% for regul ar CCD chips. Polysilicon layers, as mentioned previously, compose the gates for the parallel register s and are relatively transparent at long wavelengths but becomes opaque at wave lengths shorter than 400 nm, thus attenuating light at the la tter wavelengths. As shown in Figure A 3, light enters the parallel register through thes e gates in standard CCDs, however, in back-thinned CCDs the back is thinned by acid etching down to about 10 m so that it becomes transparent allowing for light to enter from the back (sil icon side) where there is no gate structure. These sensors have a substantially improved sensitivity extending from the soft x-ray to the near infrared range as compared to sta ndard CCD chips. A substantial downside of this chip type is a readout noise that is usua lly considerably higher than that of standard chips even at slow digitization speed. Higher dark noise is typi cal for these CCDs as well. CCD Artifacts Inherently, CCD imaging in corporates noise (artifact s) as a result of the manufacturing and operation of the CCD device and the intrinsic nature of electromagnetic radiation. Th e four principal noise levels are the signal photon shot noise, dark current noise, dark bias noise and read noise. Artifacts superimposed on data obtained with CCDs are either multiplicative or additive. Multiplicative artifacts are corrected for via a division process, while additive artifacts are accounted for through subtraction. CCD Artifacts include: 1. Charge Transfer Efficiency 2. Photon (Shot) noise

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262 3. Pixel gain variations (flat field) 4. Read-noise 5. Saturation 6. Thermal (Dark) Current Charge Transfer Efficiency CCD imagers rely on efficient charge tran sfer from one pixel to the neighboring pixel during the readout process. As charges from distant pi xels relative to the output amplifier undergo many transfers, on the or der of hundreds or even thousands depending on the CCD size, the efficiency of this proce ss is vital for the overa ll performance of the CCD operation. Charge transfer efficiency (C TE) is defined as the fraction of electrons that are successfully passed onto the next position during the horiz ontal and vertical shifting associated with th e readout process. Typical CCDs exhibit a CTE of 0.99999; still, this can leave a significant portion of the charge in downstream pixels. For example, a CCD chip with a FWC of 330,000 electrons a CTE of 0.99999 and a chip size of 512x512 would loose 1,685 electrons during the transfer for the furthest pixel. This is only about 0.5% of the tota l charge; however, if the chip size is expanded to 2048x2048, then the lost charge is 6689 electrons or 2% of the tota l charge. A CTE of 0.99995 would yield a charge loss of 32,120 electrons or 10% of the total charge for a 2048x2048 chip size. Lost charges are thus a function of lo cation and the further away from the output amplifier the higher the relative loss. Relativ ely low CTE values result in minor smearing effect with the smears pointing away from the readout edge of the CCD. Photon (Shot) Noise Shot noise derives from the stochastic nature of the photon flux, thus is a fundamental property of the quantum nature of electromagnetic radiation. A steady

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263 illumination source emits photons according to a Poisson distribution over any time interval. Accordingly, the ch arge collected by the CCD chip exhibits the same Poisson distribution with a characteristic noise equal to the square ro ot of the intensity. Thus, in order to reduce shot noise, higher signal is required. For instance, a signal of 100 photons has a shot noise of 10 photons or 10%, while a signal of 10,000 photons has a shot noise of 100 electrons or 1%. Since this noise is cau sed by the natural statis tical variation of the light, it is independent of the camera hardwa re or design. Combining intensities of adjacent pixels, on the expense of lower spatia l resolution, during the readout process, a procedure termed binning, reduces the shot no ise. This is especially beneficial in low intensity applications where a sacrifice in the spatial resolution is tolerable. In general, the term shot noise is ap plied to any noise component reflecting a Poisson statistical variation, or uncertainty in measurements of the number of photons collected during a given time interval. Pixel Gain Variations This is multiplicative noise source that st ems from various causes. It is a gain variation from pixel to pixel the can be s een as a non-uniform canvas known as a flat field image. Causes include: quantum effi ciency variation between pixels due to wavelength dependence, fringi ng problems, which are wavelength dependent interference creating global interference patterns, dust partic les in the optical path that cause visible and repeatable patterns on the data frame, and quantum efficiency hysteresis that is a function of exposure history. In order to accoun t for gain variations a calibration flat field frame is captured to scale the gain in each pixel to the average gain of the CCD via a normalization process.

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264 Read-Noise Read noise, also known as pream plifier noise, is a direct result of the process of measuring the amount of charge in a give n pixel by time integr ating the measured current. Quoted in number of electrons, read-n oise is considered a mean quantity for the CCD array. Read noise can be effectively reduced by averaging multiple frames and the attenuation goes as the square ro ot of the number of frames. Saturation Saturation is reached when either the potenti al wells are filled or the A/D converter reaches the maximum digitizati on value equal to 2^(number of bits) 1. When saturation is reached information at that pixel is lost and even worse as the release of electrons continues by incident photons extra charge spills over to neighboring pixels (usually above and below as the potential barriers ar e smaller in the verti cal direction.) Most systems are designed so that the A/D converter saturates be fore the CCD wells saturate, in other words the CCD full well is much la rger than the A/D c onverter maximum count capacity. This results in the added benefit that one remains within the linear response range of the CCD until A/D saturation occurs. Another problem with saturation is emphasized when the illumination field is si gnificantly inconsistent or surface geometry is such that light reflection is greatly dive rgent (e.g. substantial surface curvature.) This creates localized regions where pixels are sa turated while other pi xels have very low intensity near noise levels. Increasing exposure time to fill up low intensity pixels would only lead to more sa turated pixels. Thermal (Dark) Current Breaking covalent bonds to free electrons can be initiated by thermal effects in addition to photonic collisions. This adds a false charge to the overall charge

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265 accumulated by the potential wells; hence thermal current is an additive noise. Dark noise arises from statistical variation in the number of electrons thermally generated within the silicon structure of the CCD, which is inde pendent of photon-induced signal, but highly dependent on device temperatur e. It arises mainly from two sources: general background heat from supporting electronic s and locally hot pixels. Th e former induces quite low noise contribution (few electrons per hour), while the latter displays vastly higher rates of thermal electrons generation. For both, the accumulation rate of electrons is proportional to exposure time and sensitive to temperature with a decaying exponential pattern. If a pixel reaches saturation on the time scale of the read-out process, known as Super-hot pixels, it creates a hot column, as pixel values downstream in that column pass through the hot pixel during the read process. Theoretica lly, dark current is linear with time and is accounted for by acquiring data frames with the shutter closed w ith integration time equivalent to run frames. Dark noise follows a Poisson relationship to dark current, and is equivalent to the square-root of the number of thermal electron s generated within the image exposure time. The theoretical dark current follows the following relationship, 3 2 2gE kTnATe (A.1) where n is the dark current, A is proportio nality constant, T is the temperature in degrees Kelvin, k is Boltzmanns constant a nd Eg is the silicon band gap energy (about 1.2 eV.) Cooling the CCD reduces th e dark current dramatically, and in practice, highperformance cameras are usually cooled to a temperature at which dark current is negligible over a typical exposure interval. Roughly, an 8-10 C decrease in temperature

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266 reduces the dark current by about half. Camera Resolution Camera resolution is an important parameter for any CCD camera. Digital images are composed of pixels representing the ch arge level of the miniature photodiodes on the CCD chip. Each photodiode inte grates the intensity of a ti ny area of the image and hence the size of the photodiode relates directly to the image resolution. The overall size of the CCD chip and the size of the focused imag e on the CCD chip also contribute to the overall resolution. It should be noted, how ever, that even though small CCD pixels improve the resolution, they also reduce th e dynamic range of the CCD because the fullwell capacity is dependent on the photodiodes size. Furthermore, increased resolution generally equals higher readout speed, which in turn dictates the requirements for faster and more elaborate subsequent electronics. For scientific grade CCDs, pixel size coul d be as small as few micrometers to 48 m, with total imaging area in the range of 1 to 24 cm2. In order to avoid signal acquisition defects, such as aliasing, moir, or heat frequencies, each resolution element in the image plane must be covered by at least two pixels on the CCD. Photomultiplier Tubes (PMTs) A PMT is an extremely sensitive electronic detector composed of a vacuum tube that converts incident light into electrical current and amplifies it. Photomultiplier tubes are advantageous in some applications becau se they are more sensitive to light than standard CCD elements with a wider range of frequencies as well (i.e., ultraviolet, visible and near infrared spectrum.) PMTs are capab le of multiplying the signal produced from the incident light to such an extent that de tection of single photons is possible. The main construction of a PMT is a glass tube wh ich houses a series of dynodes and an anode

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267 under vacuum conditions (Figure A 5). Vacuum is necessary to faci litate movement of electrons through the tube and prevent electron scattering by air particles. When photons strike the photocathode mate rial, a thin depos it on the entry window of the device, electrons are freed due to the photoelectric effect, in a manner similar to that of CCD chips. These photons are direct ed by the focusing electrode towards the electron multiplier (i.e., dynode), where elect ron multiplication occurs. A dynode is an electrode arranged in a series assembly with each dynode possessing a more positive charge than its predecessor. Electron collision instigates secondary emission at the surface of each dynode. Such an arrangement is able to amplify the infinitesimal current emitted by the photocathode by (typically) many hundreds of millions. Electrons past the photocathode are accelerated towards the firs t dynode due to the potential difference causing a bombardment of electrons on the dynode surface. This releases more electrons from the dynode surface that are then accelerat ed to the next dynode. The geometry of the dynode chain is such that a cascade occurs w ith an ever-increasing number of electrons being produced at each stage. The whole pr ocess is repeated with more and more electrons being generated. A 12 stage dynode PMT will typically generate a gain of incoming charge on the order of 10 million. Ev entually, the spawned electrons arrive at the anode and induce a surge of voltage pul se corresponding to in cident photon on the photocathode.

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268 Figure A-5 A schematic of a Photomultiplier tube The combination of high gain, low noise, high frequency response and large area of collection makes PMTs ideal for low intensity radiation applicati ons. PMTs operation is based on two principles: the particle(s) to be detected have to be converted to electrons by the photocathode before the amplification pr ocess initiates and th at the amplification is caused by a cascade of acceleration elec trodes (i.e., dynodes) cap able of accelerating the electrons to enough speeds allowing for the generation of more than one new electron upon impact of the dynode. Data Reduction Using intensity or lifetime measurement sy stem, intensity information is recorded in the form of image planes. The intensity information needs to go three processes to finally yield pressure and/or temperature information in the spatial domain. The data reduction processes are: 1. Correcting for non-idealities in the da ta originating during data acquisition 2. Creating calibration cu rves or surfaces 3. Transforming the 2-D calibrated intensity in formation in the calibrated image to the actual 3-D model Scintillator Photocathode Focusing electrode Dynodes PMT Anode Incident photon Electrical connector

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269 Correcting for Non-Idealities Dark Image Correction As explained earlier, heat in the camera sy stem induces a dark current that adds to the total collected signal. In addition, char ge drainage from the CCD and the amplifier offset is typically imperfect, hence adding to the measured signal. The existence of ambient light will also add to the noise tota l. A dark image is typically acquired to compensate for such problems. An image w ith the shutter closed with an identical exposure time as run images indicates the o ffset charge imposed on the data, and through a simple subtraction of this offset charge associated noise is significantly reduced. In cases where considerable ambien t light is present, the shutter should be opened, with the excitation source off, to better account for the noise. Illumination-Field Variation Correction Illumination-field variation stems from tw o sources: variations due to the uneven distribution of light on the model and mode l movement that changes the illumination field character. The former is easily co mpensated for by acquiring a reference image and normalizing the run images by it. A refere nce image is acquired under no-flow (a.k.a. wind-off) condition, such that all the intensity variations are due to the physical setup. The latter source, model movement, is much harder to compensate for. The most successful effort implemented a reference sens or incorporated in the paint composition. The reference sensor is only responsive to i llumination intensity and thus independent of environmental changes. It usually is excite d in the same spectral range as the other luminophors but emits at lower wavelengths (~ 510 nm). The emission of the reference sensor is utilized to normalize the raw inte nsities. It further ha ve the advantage of

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270 eliminating the need for a wind-off imag e as well as significantly reduce model movement error, especially if the detection device is equipped with a filter screen that allows for simultaneous acquisition of di fferent wavelengths. A potential for these referencing probes is their implementation in temperature compensa tion for PSP sensors. It is hypothesized that if th e reference probe and the pressu re probe can be matched for their temperature dependency, then normaliz ing the pressure emission by the reference emission would eliminate the temperature erro r. Unfortunately, findi ng such a probe is yet to be accomplished and further problems emerge whenever a probe is embedded in the binder such as spectral cross-talk. Image-Registration correction In wind-tunnel testing models move due to the aerodynamic loads acting on them. Such movement/warping deformation leads to significant errors in the necessary normalization process. Spatially, samples exhib it sharp gradients due to the nature of the paint mixture and the applic ation process. These gradie nts could be sharp enough to devastate the normalized images. A simple way to reduce these spatial variations is to either slightly defocus the image or implement some filtering/smoothing algorithm to the raw images prior to normalization. This is us eful only when spatial variations are modest, however, significant spatial gradients require image registration algorithm. Image registration is a process in which two images are matched via translation, rotation and resizing/warping. The objective of the process is such that when the two images are laid on top of each other pixels will exactly match. The registration process could be a simply rigid-body transformation (i.e., projective) invol ving only translation and rotation, or it could inco rporate physical deformation corrections (polynomial). Bell & McLachlan (1996) presented th e transformation models from the (x,y) coordinates to

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271 the (x,y) as: Projective: '''' 123123 '''' 1212, 11axayabxbyb xy cxcycxcy (A.2) Polynomial: '''' 0000, MNMN nmnm nmnm mnmn x axyybxy (A.3) These coefficients are determined by meas uring the centroid c oordinates of some target points on both images. The target poi nts should be well defined and easy to identify and contain few pixels to suppress deviation of the centroid. They should also be distributed over the surface of the model st rategically to ensure proper transformation. Rigid-body transformations require at least f our points, while polynomial transformations require as little as three points for a firstorder polynomial and te n points for third-order transformations. The degree of accuracy needed increases with the decrease in pressure and temperature gradients, fortunately, model movement decreases as well. Flat-Field Correction Camera lenses generate an inhomogeneous light field as they deposit more light near the focal point and lesser light near th e periphery of the image. Additionally, the pixel gain variation, discusse d in the CCD artifacts section, adds to the non-uniformity of the image. This correction is needed when model movement and/or deformation occurs; otherwise these variations vani sh in the normalization process. As local pixel variations could be quite significant, an image regist ration procedure is first needed. The process involves acquiring a flat-fiel d image and normalizing the run images by this image after subtracting the da rk image from both images. The flat-field image is collected via imaging the inside of an integrating sphere or capturing any image through several layers

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272 of diffusing opal glass (Bell et al. 2001). Unsurprisingly, an image added to the overall correction process means an increase in the tota l shot noise contributi on. The increase in shot noise is quantified by Mendoza (1997) as: no. summed data images 1 no. summed flat-field images (A.4) This dictates the acquisition of five times as many flat-field images as the number of raw images to reduce the shot noise to 10% of the theoretical minimum uncertainty. This relation goes by a factor of ten, that is to reduce the shot noise to 1%, 50 flat-field images are required. Supplementary Topics Further issues concerning data meas urement and reduction are discussed and detailed in the following subsections. Lifetime Approach The lifetime of luminescence is defined as the time required for the luminescence intensity to decay from some in itial value to 1/e of th at initial intensity. As lifetime is an intrinsic character of each specific molecule the emission is independent of illumination field variations, molecule concentration, phot odegradation, paint thickness or any other non-intrinsic character of the molecule. Howeve r, temperature depende nce is an intrinsic behavior of luminescent molecules, and hence temperature effects still persist in lifetime measurements. Lifetime measurements employ very short integration times on the order of few microseconds (2~5 s) as the entire decay process of the emission is typically less than 20 s. Mechanical shutters are incapaci tated under these demanding conditions, hence special imaging systems such as PMTs phase-sensitive cameras and intensified CCD cameras with pulsed excitation sources. Lifetimes can be measured by phase

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273 fluorimetry (phosphorimetry). Measurements of the phase shift between a harmonic, say, a sinusoidally modulated excitation signal and the emitted signal, luminescence intensity time decay (lifetime) of the sensor molecule can be quantified as follows (Liu et al. 1997): exp2dII Aift dt (A.5) where A is absorption amplitude of the em ission and is the frequency of the excitation signal. The solution to this relation is: 222exp2arctan2 14 iftf IA f (A.6) If the modulation frequency is fixed, the lifetime can be expressed as: tan 2 f (A.7) where is the phase shift. The emission has a phase shift delay relative to the excitation signal that increases with increased emission. Phase-sensitive cameras or lockin amplifiers are used to capture the excitation and emission signals during two gated intervals. The first gate is phase locked with the excita tion signal and the second gate captures the emission after excitation with a delaying phase shift. The process is better illustrated in the following diagram:

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274 Figure A-6 Timing sequence for lifetime measurement (frequency domain) Another approach is to measure the lifetime decay in the time domain. The specimen is excited by radiation, at which time the shutter of the camera is closed. The molecules absorb the radiation and reach a ma ximum intensity peak, then the excitation is turned off and the emission of the molecules st arts to decay. The first time gate opens as soon as the excitation source is turned off and the first decaying emission is captured. Excitation is initiated again but with a time de lay in the exposure cycle relative to the end of the excitation cycle under identical exposure times. This is the second exposure gate, and the process is repeated with an incremen tal constant delay between the excitation and the exposure cycles. Typically, two or three ga tes suffice to determine the lifetime of the molecule. Excitation signal gates Emission signal gates time Intensity ON ON OFF OFF

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275 Figure A-7 Timing sequence for lifetime measurement (time domain) The intensity of the emission follows an exponentially decaying behavior, thus lifetime can be related to the integrated intensity and the exposure times as follows: exp 1 2ln t I I (A.8) Even though the lifetime approach provides certain advantages compared to the intensity approach, it still lacks the simplicity and practicality of the latter approach. Sophisticated equipments are needed and noise is more influe ntial in lifetime measurements, rendering it not favorable for practical use. Measurement Uncertainties Uncertainties stem from three main sour ces: measurement systems, Physical and Chemical properties of coating, and disp lacement/deformation of the test model. ON OFF ON OFF Exposures Luminescence signal Excitation texp texp texp tdelay= t tdelay=2 t I1 I2 I3

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276 Measurement Systems This includes the illumination source, detectors and filtering/spectral leakage. Illumination source In order to avoid introducing noise to the measurement the illumination source must produce uniform and steady illumination at the proper excitation wavelengths for the luminophor. It should also be adequately bright to produce a luminescence signal that could saturate the detector, hence utilizing the full capacity of the detectors signal to noise ratio (SNR) potential. However, it should not be overly bright such that it will cause utter saturation or lead to excessi ve photodegradation of the luminophor. CCD camera The four principal noise sources are shot noi se, dark current noise, dark bias noise and readout noise. Shot noise is a statistical variation that stems from the nature of the uncertainty of electromagnetic radiation, causing the number of photons per unit time collected by the CCD to conform to Poisson st atistical distribution. The rms of the shot noise is then characterized as hence the SN R is also and SNR is highest when the fullwell capacity of the CCD is exploited thr ough longer exposure times or higher intensity illumination source. Such noise can be substantially reduced by averaging multiple images. Dark current is a thermally induced charge resulting in an accumulation of electrons in the detector. It ha s an rms of where is the dark charge intensity level. Conveniently, it can be noticeably reduced by simply cooling the CCD head. Dark bias noise is simply a zero-offset bias in the di gitizer that can be easily corrected for by subtracting a dark image (image with the shut ter closed with the same exposure time as the run images) from all the run images. Readout noise is a function of the data transfer frequency, the higher the data transfer fr equency the higher the noise, however through

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277 careful design of the readout electronics of th e detector it can be minimized. These four noise sources result in either random error, which can be reduced via acquiring numerous readings, or bias error (fixed and systematic error). Thus, the total uncertainty Utotal with 95% confidence level is e xpressed as (Mendoza 1997): 2 222random totalbiasu uu m (A.9) where m is the number of samples (i.e., images). The bias error includes dark bias and readout noise, and random error include s shot noise and dark current noise. Table A-1 Error estimates for the 16 & 14-bit CCD cameras. Camera linearity error is 0.07% and ADU speed is 200 kHz Error Source Photometrix Camera (16 bit) CH 350A/SI502 Photometrix Camera (14 bit) CH 250A/SI502AB Shot noise I @FWC SITE502 CCD, ADU cts/frame 256 128 Dark current noise e-/pixel/sec @ 25C 2.8 6 Dark bias noise, ADU cts 130 110 Gain e-/ADU (gain= 1 / 2) 5.2 / 1.3 19.1 / 4.8 Readout noise @ 200kHz e-/RMS (gain=1 / 2) 17.5 / 13.3 13.3 / 10.3 Filtering/Spectral leakage Filters must be utilized to separate the different regions of the spectrum and to separate the illumination source from the illumination signal of the coatings. Adequate absorption filter(s) should be inst alled in front of the light source to cutoff the excitation light after the end of the ab sorption region and before the emission region. Interference filter(s) are installed in front of the camera to precisely resolve the various regions in the spectrum and to stop leakage from the light source at the lower wavelengths. Allowing

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278 light leakage from the excitation source would have the effect of reducing the resolution available, since the CCD camera is blind to wavelengths, it captures the reflected light regardless of its spectral origin, and thus a reflected light from the excitation source would be added to the total signa l acting as a bias error. Physical/Chemical Properties of Coating One of the main problems with lumine scent coatings is photodegradation which could lead to a drifting signa l leading to incorrect intensity levels and the need for recalibration. Depending on the luminophor and the binder used the luminescence intensity of the coating will decay at a certain rate. Therefore, care should be practiced in both choosing a good luminophor/binder combina tion and acquiring data over elongated periods of time. Cross talk between diffe rent luminophors embedded in the same binder is prompted when a luminophor quenches the other by absorbing the emission from the lower-emitting luminophor, hence inducing error in the emission intensity of the quenched luminophor. Other e rror sources incl ude temperature dependence in PSP coatings, variation in paint thickness, une ven dispersion of the luminophor(s) in the binder and pressure and temperature hysteresis, a process that leads to a change in the calibration curve due to the transition of the polymer from a hardened state to a rubbery state when it is first heated above its glass temperature leadin g to a change in the thermal quenching rate. Displacement/Deformation of Model Subjected to aerodynamic loads, especi ally at high speeds (higher dynamic pressures), models can deform or even displ ace from their original position. To correct for this bias a process known as image regist ration is required. Image registration is the process of aligning the run image with the reference (wind-off) image, before

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279 normalizing them to even out all the physical non-uniformities in the coating, such that all the corresponding pixels are in perfect a lignment. The extent of how perfectly the alignment should be performed depends on the magnitude of illumination gradients and the desired pressure and temperature accura cy. If the model disp laces in a nonlinear manner then a third-order polynomial coordi nate transformation is unavoidable. An alignment procedure consists of allocating phys ically fixed points on the model to use a reference, usually called registration dots; these dots should cover few pixels on the image. The centroid of these registra tion dots is located and matched, via shifting/warping of the image, between all the images to sub-pixel accuracy. Useful Definitions Binning Binning, also called on-chip integration, is a process intended to improve the signal-to-noise ration by primarily reducing shot noise and secondarily readout noise through a process of combining charges of neighboring CCD pixels and during readout. The result is an increased signal and thus an improved sensitivity and an improved signalto-noise ratio. Binning is achieved first by th e addition of charges from neighboring wells of the serial register into a super-pixel (serial binning) followed by subsequent superposition of rows of data in the serial sh ift register (parallel binning). This allows for shorter exposure time, thus less photodegr adation of the specimen, less smearing in applications involving vibrati on and better dynamic response. Th is is accomplished at the expense of spatial as information is lost between pixels. The binning factor is modifiable in both the global and local levels It can be varied across the CCD width or more globally for the entire chip. Pixels are always aggregated in a square pattern to avoid image distorti on. Readout time is shor tened as one over the

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280 square root of the binning factor. Time saved in the serial register is limited to the serial binning only which takes place after the data ha ve been readout into the output node prior to being passed on to the output amplifier, wh ile parallel binning occurs on the actual CCD chip. Binning can also be done after image acquisition in the computer image memory, however, this approach does not improve neither readout time nor noise. Blooming Overexposed pixels with saturated potentia l wells observed in br ight regions of the image can spill their excess charge in neighboring pixels. This imposes an artificial additive intensity value for the receiving pi xels that are virtually impossible to be accounted for. This condition is termed blooming. Many chip designs incorporate overflow drain structures, also known as pot ential barriers, to pr event spilling from saturated pixels. These barriers are typically less effective in the column direction relative to the row direction. Even though it might be obvious that lowering exposure time or illumination intensity would resolve the problem, it is quite common to have bad pixels that exhibit high intensity le vels that would prevent ad equate exposure durations. Bit Depth of Camera Data The bit depth is a reflection of the binary range of the possible grayscale values available for the image. It is the process in which the analog signal (voltage) output is digitized by the A/D converter of the camera. It is similar to the dynamic range of the CCD chip, which represents the exploitable capacity of the potential wells. Higher bit depth provides a finer scali ng of the produced image during the digitization process. Bit depths range from 8 to 16 bit, that is, an 8-bit A/D converter has a maximum deviations of 2^8 = 256 available grayscales, while th e 16-bit A/D converter would offer 2^16 = 65,536 possible grayscale levels for the same signal. The theoretical pixel-per-grayscale

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281 value is determined by dividing the fullwell capacity by the ma ximum A/D converter deviations. For instance, a CCD chip with a full-well cap acity of 330,000 electrons when coupled with a 16-bit A/D converter w ould yield 330,000/65,536 = 5.035 electrons per grayscale. In simpler terms, the A/D convert er would be able to distinguish intensity gradient as small as 5 electrons in the imag e, but lesser variations would go undetectable. Sometimes the binary range is given in decibels with one bi t equaling 6 dB (i.e., 8-bit = 48 dB, 12 bit = 72 dB, etc.) Dynamic Range Potential wells collect charges indu ced through electromagnetic radiation; nonetheless, other charges are i nduced via other sources (e.g. thermal agitation) that are also collected in the potentia l well. These false charges eat into the dynamic range of the CCD chip by imposing a dc offset. It is quantified as the FWC divided by the additive noise. The higher the dynamic range the more reliable is the quantification of differences between the dimmest and the brightest intens ities of an image taken. The dynamic range (Dr) is sometimes measured in deci bels: Dr = 20 x log (FWC/Noise). Consider a CCD with a full well capacity of 330,000 electrons, a nd a read noise of 9 electrons per pixel at the sp ecified read-out rate and an average dark current of 16 electrons per pixel, the dyna mic range would be 330,000/(9+16), or 13200. In order to utilize the full dynamic range of the CCD, a ca mera incorporating 14 -bit analog-to-digital conversion is required, having the ability to detect 16,384 (2 to the 14th power) grayscale levels (or 0.805 electrons per gray-level step). If 12-bit A/D conversion is used, only 4,096 gray levels can be displayed, corres ponding to 3.22 electrons per grayscale step. On the other hand, a camera having 16-bit A/D conversion, which has the capability of discriminating 65,536 gray levels, will be limited by the dynamic range (4500 electrons

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282 per pixel) of the CCD, and will not offer improvement over the 14-bit A/D converter. A primary goal in the manufacture of scie ntific-grade CCD cameras is to maximize the signal available and minimize the noi se, resulting in maximum dynamic range. Cooling the CCD minimizes thermal noise, as well as optimizes clocking, sampling, and other read-out electronics, consequently, th e noise associated with each read-out cycle would been reduced in some high-performance scientific grade CCD cameras to as little as 3-5 electrons per pixel at typical read-out rates of approximately 1 MHz. Fill Factor Pixels do not always possess a 100% photon-active surface where photonic energy is transferred to electrons. The ratio of th e active area to the overall pixel area is known as the fill factor. In cases where the fill fact or is less than ideal, pixels exhibit moir structures as inactive areas on the pixel surface yield no information for the corresponding regions on the focused image. This becomes an issue for images with small spatial dimension. Further, as a porti on of the incident light is not utilized, the quantum efficiency of the CCD array will be decreased. Light Sensitivity Light sensitivity is a quantity represen ting the minimum number of electrons detectable by the CCD chip within the impos ed noise. It is characterized by the number of photons needed to generate enough electr ons to produce a unity signal-to-noise ratio (SNR). It is mathematically defined as the ra tio of the SNR to the quantum efficiency of the CCD chip. Light sensitivity is wavelength dependent as the quantum efficiency is wavelength dependent as well. Linearity A crucial characteristic of CCD camera is the time pe rformance of the chip. The

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283 intensity history in the time do main should exhibit a linear be havior to ensure accurate response to the measured radiation. Non-lin ear behavior would either lead to quick saturation of the high intensity regions leaving the lower intensity regions with very little count levels in the digitized image, or w ould magnify lower intensity gradients on the expense of the higher intensities gradients, which would create augmented uneven error distribution as errors such as shot noise s cale with the intensity. Scientific grade CCD systems have a very linear response with nonlin earities in the range of a few tenths of a percent. Signal to Noise Ratio (SNR) High SNR is imperative for accurate CCD imaging. The main noise sources affecting the SNR are: shot noise, dark current and readout noise. Ma thematically, this is expressed as: 222 2 D readout DreadoutII SNR IIN IIN (A.10) It is apparent from the above equation that at high intensity levels shot noise is the main contributor to the overall SNR since dark current noise and the readout noise are quite constant and are relatively small. Therefore, at high intensity levels the SNR is: I SNRI I (A.11) This implies that for high SNR values, the potential wells must be exploited to their limit. The following figure shows a graphica l representation of the above equation for CCD chip with a FWC of 330,000, showing that at the FWC the noise is less than 0.2% of the total signal while at 10,000 el ectrons the relative noise is 1%.

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284 0 10 20 30 40 50 60 70 80 90 100 0 100 200 300 400 500 600 FWC (%) SNR Figure A-8 SNR as a Function of Intensity In low intensity applications where long exposure times are u tilized, dark noise increases, which in turn affects the dynamic ra nge and to a much lesser extent the SNR. If short exposure times are utilized, both dark noise and readout noise become significant contributors to the total noise. It is important not to confuse the actual intensity collected by the CCD chip with the digi tized signal output of the A/D converter. Using a higher bit A/D converter would not increase the intens ity, rather the resolu tion of the processed signal.

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285 APPENDIX BEquation Chapter 2 Section 1 DERIVATION OF LAMINAR CHANNEL FLOW SOLUTION This appendix provides the details of th e derivation for the laminar channel flow solution for both the isotherm al and non-isothermal cases. Isothermal Flow Solution Mathematical Derivation The governing equations for a channel fl ow in rectangular coordinates are: 0 continuity uvw txyz (B.1) Navier-Stokes equations for a Newtonian fluid with constant viscosity: 222 222 x x momentum uuuuuuuP uvwg txyzxyzx (B.2) 222 222 yymomentum vvvvvvvP uvwg txyzxyzy (B.3) 222 222 zzmomentum wwwwwwwP uvwg txyzxyzz (B.4) Assumptions/Justifications 1. Two-dimensional flow with zero cross flow/gradients 0,0 w z : The aspect ratio of the channel 1dw h is large enough such that the flow is only in the xdirection and the channel length is relative ly short, thus preventing viscous effects, due to the sidewalls, to laterally diffuse into the channel, except very near the sidewalls.

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286 2. Parallel laminar incoming flow: The low velo city approaching flow is treated through a series of turbulence damping layers (a luminum and packaging foam) to even and damp out any fluctuations in the velocity and turbulence induced by the flow path. Further, the mass flow rate is investigat ed experimentally (Chapter 5) showing a linear relation with respect to the pressure drop validati ng laminar conditions for the entire channel (Panton, 1996). 3. Steady incompressible flow 0 D Dt : Mass flow rate well controlled and measurements acquired under steady conditi ons (i.e., no transient measurements). Mass flow rate (as described in Chapter 5) is low enough that the Mach number is well below 1400. This further implies that the velocity divergence is zero (i.e., continuity equation) 4. Body forces are only due to gravity a nd act in the negative z-direction. Hence, the reduced system of equations is: 0 uv xy (B.5) 22 22uuuup uv x yxyx (B.6) 22 22vvvvp uv x yxyy (B.7) 0zp g z (B.8) Boundary Conditions The boundary conditions for a pressure driv en flow between two rigid infinitely wide parallel plates are: 0 @ 0& uvyh (B.9) The boundary conditions are the no-slip fo r the axial velocity component and no velocity penetration at the wall, i.e ., zero vertical ve locity component.

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287 The Fully Developed Region (Poiseuille Flow) In the fully developed region further simp lification allow for an exact solution for laminar flows. As the term fully-developed implies, the velocity profile ceases to vary in the flow directions, hence: 0 u x (B.10) This assumption reduces equation (B.5) to: 0 v y (B.11) Integrating the last expression once yields a constant vertical velocity component with respect to y and that at most it is a function of x However, the solid wall boundary condition necessitates that the v vanishes at the wall, hence 0 v everywhere in the fully developed region. The y -momentum equation reduces to: 0 p y (B.12) Thus, constyp (B.13) The flow is pressure driven with the pressure gradient in the x -direction, thus the pressure is a function of both x and z Since vertical pressure variations are due to the hydrostatic forces, it follows upon integrating equa tion (B.8) that: ,z p xzgPx (B.14) Notice the change in the sign of the body force term zg as the force acts in the negative direction. In the previous equation Px is the pressure along the bottom wall. Substituting for the pressure in the x -momentum equation (B.6):

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288 2 20 uP yx (B.15) The last expression reiterates that for pr essure driven laminar incompressible flow in a rectangular channel shear stress is ba lanced by the pressure forces in the fully developed region. The velocity, and hence th e shear stress, is so lely a function of y while the pressure term is only a function of x Thus: 2 21 const uP yx (B.16) Integrating twice and applying the no slip boundary condition: 2 2 2 hPyy uy xhh (B.17) This is the famous Poiseuille parabolic profile with a maximum velocity value occurring at the centerline 2 h y 2 max8 hP u x (B.18) It is often convenient to non-dimensiona lize the velocity by the maximum or mean velocity in order to have a universal representation of the velocity profile. 2 max4 uyy uhh (B.19)

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289 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Normalized VelocityNormalized Channel Height Figure B-1 Fully developed velo city profile for an incompre ssible laminar channel flow Once the velocity profile is known other quantities can be obtained via simple relations. Volume flow rate Q information is essential in th e characterization of any fluid process. It is easily computed by integrating the velocity over the cross sectional area. 3 0012whwhP Qudydz x (B.20) This relation will be used to validate la minar flow conditions in the channel flow. As seen in the equation, the volume flow rate is linearly related to the pressure drop in the fully developed region. This linear behavior is not valid for turbulent flow (Panton, 1996). Once the volume flow rate is known, a mean velocity is readily obtained. 2 12mQhP u whx (B.21) Note that the average velo city is two-thirds the maximum velocity; however, the average velocity is only one-half the maximum velocity for circular cross sections. This is due to higher frictional forces as result of the larger effective wetted perimeter.

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290 Non-Isothermal Fully Developed Flow In the previous analysis isothermal conditions where assumed, but more importantly viscosity was presumed cons tant allowing for the decoupling of the momentum and energy equation (neglecting free convection). In this section, we solve the same problem under non-isothermal conditions. Uniform Temperature/Heat Flux Boundary Condition Consider the same channel with both lower and upper walls 0; yyh at some constant temperature higher than the flow mean temperaturewTT where the subscript w indicates the lower wall, or have a cons tant heat flux, which is commonly defined using Fouriers law of conduction expressed as: wT qk x (B.22) where wq is the heat flux and k is the thermal conductivity whic h is a characteristic of the wall material. Inside the channel, convection heat transfer occurs and a thermal boundary layer begins to develop in a way similar to th e viscous boundary layer. If either a constant temperature or constant heat flux is maintained at the wall, fully developed thermal conditions are eventually attained.

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291 Figure B-2 Thermal boundary layer devel opment in a laminar channel flow The thermal entrance length,TL for laminar flows is experimentally observed to be (Incropera and Dewitt, 1981): 0.05RePrT hL h (B.23) where Pris the Prandtl number defined as: viscous diffusion rate Pr thermal diffusion ratepc k (B.24) The Prandtl number provides a measure of the relative effectiveness of momentum and energy diffusion via diffusion in th e viscous and thermal boundary layers, respectively. This nondimensional number solely involves fluid properties with no dependence on the flow geometry or veloci ty. For gases, it is near unity, hence momentum and energy transfer by diffusion are comparable. It is a significant parameter in heat-transfer applications as it compares the rate of mo mentum diffusion to that of energy. It follows that the value of Pr dictates the relative growth of the viscous and thermal boundary layers and can be approximated as: Thermal entrance length, LT Fully developed region h T T(x,y) x y T(x,y) T0 = const

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292 Prn T (B.25) where n is a positive integer, and T are the thicknesses of the viscous and thermal boundary layers, respectively. Thus, for gasses th e extent of growth (i.e., thickness) of the two layers is approximately equal. It is imperative to note that the concept of a mean temperature is not as simple as the mean velocity. First, to estimate the mean temperature, mT we integrate the product of the mass flux u and the internal energy per unit mass vcT over the cross section of the channel to yield the thermal energy transport ratetE That is, tv AEucTdA (B.26) For which the general expression for the mean temperature is: v t A m vvucTdA E T mcmc (B.27) For an incompressible flow in a rectangular du ct it follows that the mean temperature is: vc 0 h d vwuTdy mc dw 0 huTdy mduw h (B.28) 01 h m mTuTxydy uh (B.29) In forced convection internal flows, heat transfer is conti nuous along the entire length of the channel and hence temperat ure increases/decreases longitudinally. Therefore, the temperature is always a function of both x and y and flow direction

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293 gradients never vanish, unlike the velocity. This is also different from the case of external flows as the temperature is cons tant in the flow direction. It might then seem contradictory to use the term fully-developed thermal region for flows with convection heat transfer. Howeve r, in such flows the term fully developed is based on a non-dimensional temperature difference as opposed to the actual temperature. To realize the dimensionless temperature we need to introduce Newtons law of convection, which is: wcwmqhTT (B.30) where ch is the local convection he at transfer coefficient 2WmK Newtons law states that a temperature difference must exis t for heat transfer to occur, thus, it is reasonable to use a temperature difference to express the temperature. Utilizing all the known temperatures (wall, mean, and flow), we reach the dimensionless temperature: ,w wmTTxy TT (B.31) When this dimensionless temperature is independent of x the flow is termed fully developed. Hence the fully developed thermal condition is: 0w wmTxTxy xTxTx (B.32) If a constant temperature boundary condition is imposed on the flow, then the fully developed conditions depend only on the mean and flow temperatures. We can gain further insight in the fully developed region by differentiating the temperature difference with respect to y and evaluating the derivative at the wall.

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294 (), 1yh w wmwm yhfxTxy TxTxy yTxTxTTy (B.33) At the wall, there exists no fluid motion due to the no-slip condition; the only path for heat transfer is conduction (or radiation, not included here). Substituting Fouriers and Newtons Laws of conduction and c onvection, respectively yields: constch k (B.34) Thus for a constant properties flow, ch is constant in the thermally fully developed region. The convection coefficient ch strongly depends on the wall temperature gradient, which is in turn heavily dependent on condi tions in the thermal boundary layer. Further, this implies that ch must vary prior to fully developed conditions, reaching its maximum value at the channel entrance and0T then it decays rapidly approaching a constant value in the fully developed region. If we expand fully developed condition, equation (B.32), we get: 22 20 0 0ww wmwmwm wmwm w wmwwm wmwm wm w wmw wm w wTTT T xTTxTTTT TTTT T T TTTTTT xxxx TTTT TT T T TTTT xxx TT TT T T xx 0wm wmTT TTx (B.35)

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295 wwm w wmTTTT T T xxTTx (B.36) If the boundary condition is a consta nt temperature along the channel 0wT x then the fully developed condition reduces to: wm wmTTT T xTTx (B.37) and for a constant heat flux we first recall that ch is constant and from equation (B.30) we find: wmTT x x (B.38) Substituting back in equation (B.36): mT T x x (B.39) The foregoing results clearly show that know ing the mean temperature is essential in describing the temperature distribution throughout the fully developed region of the channel. The temperature distribution at the surface T x is the quantity sought after in this work as a mean of validating the measur ed temperature profiles by the paint. In our experiment, the surface temperature is not cons tant due to forced convection effects and there is no heat flux at the surface, rather a constant heat flux at x = 0 and L and at z = 2dw The boundary conditions are clearly more involved than the simple cases of constant heat flux and consta nt temperature. A simple en ergy balance would yield the following expression for the mean temp erature in terms of convection.

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296 m A wm pdT W hTT dx mc (B.40) Which can be further simplified for the cas es of constant heat flux and constant temperature at the surface yielding equations (B.41) and (B.42), respectively. wA mmoutlet pqW TxTx mc (B.41) ,expwm A wminlet pTT Wh x TT mc (B.42) In the previous equations, AW is the wetted perimeter area and h is the average value of h from the channel inlet to x Obviously, this still calls for a known temperature distribution or heat flux over the surface, whic h is not available nor simple. In order to estimate the surface and mean temp eratures, the temperature profile, Txy must be then determined by solving the energy equation. The energy equation for a Newtonian fl uid in rectangular coordinates is: De pVkT Dt (B.43) where e is the internal energy per unit mass, where is customarily cal led he dissipation function and is always positive definite as viscosity dissipates energy from the system. Using Stokes hypothesis from the definition of the mechanical pressure is expressed as: 222 22 2 22 2 3 uvwvuwv x yzxyyz uwuvw zxxyz (B.44)

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297 The total derivative D Dt and the divergence operator are expressed as: D V Dtt (B.45) x yz (B.46) From thermodynamic relations and for an ideal gas: p he (B.47) p vdhcdT decdT (B.48) where h is the enthalpy, pc and vc JkgK are the specific heats per unit mass at constant pressure and volume, respectivel y. Using the above equations, employing the general continuity equation, equation (B.1), to substitute for the velocity divergence in equation (B.43) and assuming constant ther mal conductivity, the energy equation can be rewritten as: 222 222 pTTTTpppp cuvwuvw txyztxyz TTT k xyz (B.49) For the fully developed viscous region in the channel flow problem, using the same assumptions used in the velocity deri vation, the energy equation reduces to: 2 22 22 pTTpTTu cuuk txxxyy (B.50)

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298 The temperature boundary and initial conditions are: 0 , 12 1, @0, @0,0 @0, @0,0 @0; ,0w glassairwup metalairwbottomTxyTxy TxyTxxy Txy hhTTxyh y Txy hhTTxy y TxyTT Txtxy tL (B.51) Figure B-3 Non-isothermal flow schematic y x To Flow T1T2 T2 T1> T2 Tw Convection to air from metal and then from air into glass Conduction in metal Conduction in glass Side view Flow T2 T2 T1> T2 T3 > T2 Top view

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299 These boundary conditions represent a ba lance between forced convection and conduction at the upper and lowe r walls, a uniform temperatur e profile at the beginning of the channel, while the lower wall havi ng an interface boundary condition with the metal. The problem is not easily reali zed because the bottom boundary condition ( y = 0) is an interface boundary. This means that c onvection due to the fl ow and conduction in the metal are interfacing and constantly updating each other, he nce the two problems must be numerically solved simultaneously until steady conditions are realized. The conduction problem for the metal plate is gove rned by the general heat equation shown below. pTTTT kkkqc x xyyzzt (B.52) where q represents energy generation within the plate. Assuming constant thermal conductivity: 222 222 pc TTTqT x yzkkt (B.53) Conduction and radiation on the outside bounda ries can be neglected as forced convection in the channel is more signif icant. The two problems interface the terms T x and 2 2T x For each iteration equation (B.53) is solved first with the temperature profile at the interface updated by the solution for one time step, then equation (B.50) is solved with the updated boundary and its so lution updates the interface boundary. The numerical solution is reiterat ed until convergence occurs. Besi des the obvious intricacy of the problem, it is further beyond the scope of this work and thus is not further pursued.

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300 Nonetheless, the theory can be numerically solv ed to validate the e xperimental results for future work.

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301 APPENDIX C MATLAB CODES FOR POD ANALYSIS Image Registration % Program to perform image registrati on and compare theoretical and % experimental pressure values clear all clc % Channel Parameters L=9.18*2.54/100; % length w=4*2.54/100; % width mu=1.82*10^(-5); % dynamic viscosity h=0.00025; % channel height x=(1:2/3:9); % x-spacing for the centerline pressure taps % Looping for the four filters for i=44:2:50 gstd=10000; for al=0.232:0.01:0.232 % Reading images run=double(imread(['c1CHNL_',num2s tr(i),'_PT2.tif'])); ref=double(imread(['c1CHNL_',num2str(i),'_ref.tif'])); dark=double(imread(['c1CHNL_',num2str(i),'_dk.tif'])); % Rotating images run2=imrotate(run,-al,'bicubic'); run=run2; runn=run; ref2=imrotate(ref,-0.25,'bicubic'); ref=ref2; reff=ref; [mm,nn]=size(run); % ################################################## % image registration

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302 % horizontal shift aa=1; for hs=0.76:0.01:0.76 bb=1; ref=reff; for j=2:nn ref2(:, j)=ref(:,j-1)-(ref(:,j-1)-ref(:,j))*hs; end ref2(:,nn)=ref(:,nn); ref4=ref2; % Vertical shift for vs=0.08:0.01:0.08 for j=1:nn-1 ref 2(j,:)=ref4(j,:)-(ref4( j,:)-ref4(j+1,:))*vs; end ref2(:,nn)=ref(:,nn); ref=ref2; ratio1=run./ref; bb=bb+1; ratio=run./ref; % computing the STD of two di agonal areas on the image to % optimize rotation and image registration gg=std(std(ratio(100:150,180:230)))+std( std(ratio(400:450,280:330))); if gg < gstd ratioC=ratio; gstd=gg; alpha=al; vsC=vs; hsC=hs; end ref=ref4; end aa=aa+1; gg end end

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303 % ############################################# ratio=run./ref; % Loading pressure and temperature information D=load(['c1CHNL_',num2str(i),'_PT2.txt']); Tmp=D(2:22,[1 3]); % Temperature Tmpstd=D(2:22,[2 4]); % STD for Temperature T=mean(Tmp,2); % Average Temperature Tstd=mean(Tmpstd,2); %Average STD for Temperature % Rearranging the temperature matrix for plotting for j=4:-1:1 T1(5:-1:1,5-j)=T(1+(j-1)*5:5+(j-1)*5,1); end Prss=D(23:42,[1 3]); % Pressure Prssstd=D(23:42,[2 4]); % STD for Pressure P=mean(Prss,2); % Average Pressure Pstd=mean(Prssstd,2); % Average STD for Pressure Q=mean(D(1,[1 3]),2)*20*0.0000166666666666666; % Average mass flow dP=-Q*(12*mu)/h^3/w*L; % Theoretical Poiseuille Pressure Gradient P0=P(20,1)*101325/14.7-dP; % Pressure offset Ptheory=dP/L*([x 10.18]-1)*2.54/100+P0; % Theoretical Poiseuille Pressure % Fitting the pressure to a polynomial [P1,S] = POLYFIT(x',P(1:13,1),2); P2=P1(1,1)*[x 10.18].^2+P1(1,2)*[x 10.18]+P1(1,3); % Setting the background color for the images a=min(min(ratioC(10:505,210))-0.02); b=max(max(ratioC(10:505,210))+0.02); c=(b-a)/3+a; run(:,1:123)=b; run(:,315:512)=b; ref(:,1:123)=b; ref(:,315:512)=b; ratio(:,1:132)=c; ratio(:,323:512)=c;

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304 ratio(1:8,:)=c; ratio(512:517,:)=c; % Plotting the run, reference and normalized images figure(1) imagesc(run) colorbar figure(2) imagesc(ref) colorbar figure(3) imagesc(ratioC, [a b]) title(['filter ',num2str(i),' PT2 hs= ', num2str(hs),'vs= ', num2str(vs)]) colorbar % Plotting temperature contours from thermocouple information figure(4) contourf(T1,256,'linestyle','none') colorbar % Plotting the theoretical and experimental pressure figure(5) clf plot(x, P(1:13,:),'o-') hold on plot([x 10.18], Ptheory*14.7/101325,'o-r') plot([x 10.18], P2, 'm') grid on xlabel('x-position (inch)') ylabel('Pressure (psi)') % Plotting pressure percen t deviation in pressure figure(6) plot((P(1:13,:)'-(Ptheory (1,1:13)*14.7/101325))./P(1:13,:)'*100,'o-') xlabel('x-position (inch)') ylabel('Percent deviation from theory') grid on pause end

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305 Calibration Intensity/Pressure and Temperature Extraction % Program to extract calibration matrices for pressu re and % temperature clear all clc % Channel Parameters L=9.18*2.54/100; % length w=4*2.54/100; % width mu=1.82*10^(-5); % dynamic viscosity h=0.00025; % channel height x=(1:2/3:9); % x-spacing for the centerline pressure taps % Looping for the four filters for i=44:2:50 gstd=10000; for al=0.232:0.01:0.232 % Reading images run=double(imread(['c1CHNL_',num2s tr(i),'_PT2.tif'])); ref=double(imread(['c1CHNL_',num2str(i),'_ref.tif'])); dark=double(imread(['c1CHNL_',num2str(i),'_dk.tif'])); % Rotating images run2=imrotate(run,-al,'bicubic'); run=run2; runn=run; ref2=imrotate(ref,-0.25,'bicubic'); ref=ref2; reff=ref; [mm,nn]=size(run); % ################################################## % image registration % horizontal shift aa=1; for hs=0.76:0.01:0.76 bb=1; ref=reff; for j=2:nn ref2(:, j)=ref(:,j-1)-(ref(:,j-1)-ref(:,j))*hs; end ref2(:,nn)=ref(:,nn);

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306 ref4=ref2; % Vertical shift for vs=0.08:0.01:0.08 for j=1:nn-1 ref 2(j,:)=ref4(j,:)-(ref4( j,:)-ref4(j+1,:))*vs; end ref2(:,nn)=ref(:,nn); ref=ref2; ratio1=run./ref; bb=bb+1; ratio=run./ref; % computing the STD of two di agonal areas on the image to % optimize rotation and image registration gg=std(std(ratio(100:150,180:230)))+std( std(ratio(400:450,280:330))); if gg < gstd ratioC=ratio; gstd=gg; alpha=al; vsC=vs; hsC=hs; end ref=ref4; end aa=aa+1; gg end end % ############################################# % Initializing the matrices averaging runs=run; refs=ref; % Specifying the averaging square size sqsize=5;

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307 % Smoothing the run and reference images length=(sqsize-1)/2; for js=131:322 for is=[sqsize:517-sqsize] runs(is,js)=sum(sum(run(is-lengt h:is+length,jslength:js+length)))/(sqsize^2); refs(is,js)=sum(sum(ref(is-length:is+ length,jslength:js+length)))/(sqsize^2); end end % ######################################## % Writing the test data matrix ratio=runs./refs; [sm,sn]=size(ratio); sm=sm-16; sna=131; snb=322; sma=9; smb=509; for si=1:snb-sna+1 ratioCCD((si-1)*(smb-sma+1)+1:si*(smb-sma+1),d)= ratio(sma:smb,si+sna-1); end % Loading pressure and temperature information D=load(['c1CHNL_',num2str(i),'_PT2.txt']); % Environmental data Tmp=D(2:22,[1 3]); % Temperature Tmpstd=D(2:22,[2 4]); % STD for Temperature T=mean(Tmp,2); % Average Temperature Tstd=mean(Tmpstd,2); %Average STD for Temperature % Rearranging the temperature matrix for plotting for j=4:-1:1 T1(5:-1:1,5-j)=T(1+(j-1)*5:5+(j-1)*5,1); end Prss=D(23:42,[1 3]); % Pressure Prssstd=D(23:42,[2 4]); % STD for Pressure P=mean(Prss,2); % Average Pressure Pstd=mean(Prssstd,2); % Average STD for Pressure Q=mean(D(1,[1 3]),2)*20*0.0000166666666666666; % Average mass flow

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308 dP=-Q*(12*mu)/h^3/w*L; % Theoretical Poiseuille Pressure Gradient P0=P(20,1)*101325/14.7-dP; % Pressure offset Ptheory=dP/L*([x 10.18]-1)*2.54/100+P0; % Theoretical Poiseuille Pressure % Fitting the pressure to a polynomial [P1,S] = POLYFIT(x',P(1:13,1),2); P2=P1(1,1)*[x 10.18].^2+P1(1,2)*[x 10.18]+P1(1,3); % matrix size n x n (n=temp thermocouple size m=pressure tap size) n=5; m=5; % coordinates (upper=U) (lower=L) (R=row) (C=column) UR=74; UC=149; dR=101; dC=50; dP=33; wdth=4; % width of outer rectangle n1=(n-1)/2; m1=(m-1)/2; nj=(n1+wdth); mi=(m1+wdth); % ####################################### % Temperature loop % % % % ................................ mi % : | : wdth % : ..........|.......... : m1 % : : | : : % : : | : : % --------------------------------% wdth UR/UC % % nj n1 ######################################### % Extracting temper ature intensity calibration b=1; c=1; for j=3*dC+(UC):-dC:UC

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309 a=1; for i=UR:dR:4*dR+(UR) Top=mean(mean(ratio(i-mi:i-m1,j-nj:j+nj))); Bot=mean(mean(ratio(i+m1:i+mi,j-nj:j+nj))); Lft=mean (mean(ratio(i-m1:i+m1,j-nj:j-n1))); Rgt=mean(mean(ratio(i-m1:i+m1,j+n1:j+nj))); InT(a,b)=(Top+Bot+Lft+Rgt)/4; IT(c,d)=(Top+Bot+Lft+Rgt)/4; a=a+1; c=c+1; end b=b+1; end %###################################################### % % Pressure Extraction (calibration) % Test Points PNT1C=floor(UC+(dC/2)); PNT1R=UR+4*dR; PNT2C=floor(UC+3*dC); PNT2R=floor(UR+3*dR+(dR/2)); PNT3C=floor(UC+(dC/2)); PNT3R=UR+2*dR; PNT4C=floor(UC+(dC/2)); PNT4R=floor(UR+(dR/2)); % ##################################################### % Calibration Points a=1; for i=4*dR+(UR):-33:UR IP(a,d)=mean(mean(ratio(i-mi:i+mi,f loor(UC+dC*1.5)mi:floor(UC+dC*1.5)+mi))); a=a+1; end IP(a,d)=mean(mean(ratio(PNT 1R-mi:PNT1R+mi,PNT1Cmi:PNT1C+mi))); IP(a+1,d)=mean(mean(ratio(P NT2R-mi:PNT2R+mi,PNT2Cmi:PNT2C+mi))); IP(a+2,d)=mean(mean(rat io(PNT3R-mi:PNT3R+mi,PNT3Cmi:PNT3C+mi))); IP(a+3,d)=mean(mean(ratio (PNT4R-mi:PNT4R+mi,PNT4Cmi:PNT4C+mi))); %###################################################### d=d+1;

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310 end % Plotting Calibration Curves figure(3) plot(IT(1:13,:),'o-') grid on title('Temperature') legend('550 nm','600 nm','650 nm','700 nm') figure(4) plot(IP(1:13,:),'o-') grid on title('Pressure') legend('550 nm','600 nm','650 nm','700 nm') % Calibration Parameters % Centerline Pressure data PCNTR=mean(P(1:13,:),2); % X and Y coordinates of the temperatu re thermocouples starting from the % top right of the plate (looki ng at the image from Matlab) a=1; for i=1:20 Tx(i,1)=a; if mod(i,5) == 0 a=a+1; end end a=1; for i=1:20 Ty(i,1)=a; a=a+2; if mod(a,11) == 0 a=1; end end % Fitting temperature to a surface to calculate centerline temperature % at the centerline along the pressure taps (TCNTR) Tf=[Tx.^2 Ty.^2 Tx.*Ty Tx Ty ones(20,1)]; TCof=linsolve(Tf,mean(T(1:20,:),2)); % TCof=(Tf\mean(T(1:20,:),2)); Ty=x; Tx=2.5;

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311 TCNTR=flipud(TCof(1,1)*Tx.^2+TCof( 2,1)*Ty.^2+TCof(3,1)*Tx.*Ty+TCof(4,1)*T x+TCof(5,1)*Ty+TCof(6,1)); PCalbMatrix(1,:)=TCNTR; PCalbMatrix(2,:)=PCNTR'; PCalbMatrix(3:6,:)=IP(1:13,:)'; % Temperature Calibration matrix TCalbMatrix(1,:)=mean(T(1:20,:),2)'; TCalbMatrix(2:5,:)=IT'; % Writing data matrices and calibration matrices dlmwrite('TCalbMatrix.txt',TCalbMatrix, 'delimiter','\t','precision','%.12f'); dlmwrite('PCalbMatrix.txt',PCalbMatrix,'delimiter','\t','precision','%.12f'); dlmwrite('dataMatrix.txt',ratioCCD,'d elimiter','\t','precision','%.12f'); POD Code % Program to extract pressure and temperature using POD clear all clc % Test parameters % (2) (1,84) % (1) (2,32) % (3) (2,234) % (4) (1,353 not 86) % 19:128:147 % Number of calibration points to use np=13 % Loading data data=load('PCalbMatrix.txt'); D2=1./data(3:6,(13-np)+1:13); Wavelength=(550:50:700); T=data(1,:); P=data(2,(13-np)+1:13); ImgData=(flipud(load(' dataMatrix.txt'))); ird=1; iar=501; % Loop to calculate pressure/tempera ture field (195 columns of 501

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312 % rows data) for ir=1:195 D2(1:4,np+1:iar+np)=1./ImgD ata((ir-1)*iar+1 :iar*ir,1:4)'; [mm,nn]=size(D2); % Initiating POD Lambda1=0; RR=zeros(n,n); Z=D'*D; CC=zeros(m,n); Rc=zeros(m, n); HH=zeros(m,n); e=1; Vec=0; p=1; while e > 0 if p > 1 Z=RR; end % calculating the eigenvectors and eigenvalues RR=Z-Lambda1*Vec*Vec'; [Q,Lambda]=eig(RR); Lambda1=max(max(Lambda)); if p ==1 maxii=Lambda1; end for y=1:n for t=1:n if Lambda1 == Lambda(t,y); x=y; end end end Vec=Q(:,x); % Terminating the loop if the eigenvalue is le ss than 0.00001 of % the Maximum eigenvalue if Lambda1 > maxii*0.00001 HH=D*Q; Rc(:,p)=HH(:,x); CC(p,:)=Vec'; else e=0; end p=p+1; end % Reconstructing the R & C matrices

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313 R=zeros(m,p-2); C=zeros(p-2,n); for aa=1:p-2 R(:,aa)=Rc(:,aa); C(aa,:)=CC(aa,:); end R1=R; C1=C; % Plotting the reconstructed spectra figure(2) clf plot(Wavelength,R*C) title('Reconstructed Spectra') xlabel('Wavelength (nm)') ylabel('Intensity') grid on PerrMn2=100000; a=1; % Target Transformation for phii=0:360 phi=phii*pi/180; % Rotation Matrix Tr=[cos(phi) -sin(phi); sin(phi) cos(phi)]; R=R1*Tr; C=inv(Tr)*C1; % Plotting the eigenvectors and eigenvalues figure(3) plot(Wavelength,R(: ,1),'o-b',Wavelength,R(:,2),'o-r') title(['Fundemental Sp ectra @ theta = ',num2str(phii)]) xlabel('Wavelength (nm)') legend('R1','R2') grid on figure(4) plot((1:2/3:9),C(1,1:13)','o-b',(1:2/3:9),C(2,1:13)','o-r') legend('C1','C2') grid on % Fitting the pressure calibration data to the calibration % function of order N N=1; Pcof=polyfit(C(1,1:np),P,N); N=N+1;

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314 for i=1:N Prss1(i,:)=Pcof(1,i)*C(1,:).^(N-i); End Prss=sum(Prss1); % Calculating the erro r parameters for the calibration Perr(a,:)=(P-Prss(1,1:np)); PerrMn(a,1)=m ean(abs(P-Prss(1,1:np))); PerrMx(a,1)=max(abs(P-Prss(1,1:np))); % Condition of minimum error if PerrMn(a,1) < PerrMn2 PP=Prss; PerrMn2(a,1)=PerrMn(a,1); PerrMx2(a,2)=phii; PerrMn(a,1)=PerrMn(a,1); end a=a+1; pause(0.05) end % Writing predicted pressure data PMatrix(ird,:)=PP(1,np+1:np+iar); ird=ird+1; end % Plotting the predicted values and image and writing data np=13; P=data(2,(13-np)+1:13); figure(1) plot((73:33:481-(34*abs(np-13))),fliplr(P),'ok') hold on plot(flipud(PMatrix'),'g') ylabel('Pressure (psi)') grid on figure(2) imagesc(PMatrix, [min(PMatrix(:,95)) max(PMatrix(:,95))]) colorbar dlmwrite('PImage.txt',PMatrix,'\t')

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315 APPENDIX D DERIVATION OF SOME EQUATIONS POD Analysis Derivation of Pressure Calibration Coefficients Starting with the Stern-Volmer relation and the definition of the temperature dependent coefficients: 1ref refI AT P PIBTBT (D.1) 1ref nr ref refrefTT E ATAT RTT (D.2) 1pref ref refrefETT BTBT RTT (D.3) Taking the ratio of the coefficients: 2.82 4.321 1 1 1ref refref ref ref nr ref refref pref ref ref refref refnr ref p refa bTT T TT E AT RTT AT AT BT ETT BT BT TT RTT TE RT E RT (D.4) 1 1 111refref refref refrefref refrefrefTTTT aa TT AT BT TTTTTT bbb TTT (D.5)

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316 1 11 1 11 1ref ref refref refrefrefaa b ba Ta T aT AT a b B TbbTbbT Tb T (D.6) 11 1 111 refref refrefref refaTa AT aa b BTbbTbbTbbT b T (D.7) Substituting the values for the different constants: 1.82 4.32 AT BTT 0.009463 1 0.014496 T (D.8) In the ratio AT B T the first ratio 1.82 4.32 T is two orders of magnitude smaller compared to the second term 0.009463 1 0.014496 T therefore the consta nts can be replaced with a unity value 1 1 T with the same results as the ra tio is still preserved due to the triviality of the constant in the denominat or compared to the temperature. The second term can be replaced as follows 0.01 1 0.01 T with the same results (slightly different rotation angle). Replacing the ac tual values makes it easier to simulate real data as the constants are a function of the luminophor. 1.820.009463 1 4.32 0.014496T T (D.9)

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317 0.0094630.01 1 10.01 0.014496AT T B TT T (D.10) 0.01 10.01 AT T B TT (D.11) The second coefficient can be similarly expressed as: 4.32 0.87111 11prefref refref refrefrefBT ETTTT BTBTb RTTT (D.12) 111bref Trefref refref ref ref refref ref BB BBT TT BTBTb BTb T B TTBTb T (D.13) 111refbTrefTref BB B TBBBTBBBT (D.14) 11 0.0126122.8884BTT (D.15) The ratio 11 0.0126122.8884BTT can not be approximated, as the calibration results would be less accurate because the temperat ure product is comparable in magnitude to the free constant in the denominator.

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318 LIST OF REFERENCES Alaruri, S., Bonsett, T., Br ewington, A., McPheeters, E., and Wilson, M., Opical laser Engineering Vol. 31, 1999, pp. 345-351. Amer, T. R., Liu, T., and Oglesby, D. M., C haracterization of Pressure Sensitive Paint Intrusiveness Effect on Aerodynamic Data, AIAA Journal paper 2001-0556 Vol. No. 2001. Ardasheva, M. M., Nevsky, L. B., Pervus hin, G. E., Measurement of Pressure Distribution by Means of Indicator Coatings, Journal of Applied Mechanics and Technical Physics 4:24 1985. Balzani, V., and Scandola, F., Supramolecular Photochemistry Ellis Horwood, New York, 1991. Beer, F. P., Johnston, E. R., Mechanics of Materials 2nd edition, McGraw-Hill International Editions, Mechanical Engineering Series, New York 1981. Beckwith, T. G., Marangoni, R. D., and Lienhard V, J. H., Mechanical Measurements 5th ed, Addison Wesley, Massachusetts, 1993. Bedlek-Anslow, J. M., Development and Characterization of Luminescent Oxygen Sensing Coatings, Ph.D. Thesis, Department of Chemistry, University of Florida, 2000. Bedwell, Davies, and Dunleavy, Pressure and Temperature Extraction from a Single Dye/Polymer, 6th Annual PSP Workshop unpublished, 1998. Bell, J. H., Schairer, E. T., Hand L. A., and Mehta, R. D., Surface Pressure Measurements Using Luminescent coatings, Annual Review of Fluid Mechanics Vol. 33, 2001, pp.155-206 Carroll, B. F., Abbitt, J. D., Lukas, E. W., a nd Morris, M. J., Step Response of PressureSensitive Paints, AIAA Journal Vol. 34, 1996, pp. 521. Carroll, B. F., Hubner J. P., Schanze K. S., Bedleck-Anslow J. M., and Morris M., Pressure and Temperature Measuremen t with a Dual-Luminophor Coating, ICIASF99 Toulouse, France, June 13, 1999.

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321 Hubner J. P., and Carroll, B. F., Applicati on of Dual Sorption Theory to PressureSensitive Paints, AIAA Journal Vol. 35, No. 2, Feb. 1997a, pp. 1790-1792. Hubner J. P., Carroll, B. F., and Schanze, K.S., Temperature Compensation Model for Pressure-Sensitive Paint, American Society of Mechanical Engineers FEDSM973470 1997b. Incropera, F. P., and Dewitt, D. P., Fundamentals of Heat Transfer John Wiley & Sons, Inc. New York 1981. Ji, H-F., Shen Y., Hubner, J. P., Carroll, B. F., Schmehl, R. H., Simon, J. A., and Schanze, K. S., Temperature-Independent Pressure-Sensitive Paint Based on a Bichromophoric Luminophore, Applied Spectroscopy Vol. 54, No. 6, Feb. 2000. Kammeyer, M., Donovan, J., Kelble, C., Benne, M., Kihlken, T., and Felter, J. A., Accuracy Assessment of a Pressure-S ensitive Paint Measurement System, AIAA Journal 2002-0530, 40th Aerospace Sciences Meeting & Exibit, 14-17 January, 2002, Reno, Nevada. Kautsky, H., and Hirsch, H., Detection of Minutest Amounts of Oxygen by Extinction of Phosphorescence, Journal of Inorganic and General Chemistry 1935, pp. 222:126. Kavandi, J., Callis, J., Gouterman, M., Khalil, G., Wright, D., Green, E., Burns, D., and McLachlan, B., Luminescent Barometry in Wind Tunnels, Review of Scientific Instruments Vol. 61, No. 11, 1990, pp. 3340. Khalil, G. E., Costin, C., Crafton, J., Jones G., Grenoble, S., Gouterman, M., Callis, J. B., and Dalton L. R., Dual-Luminophor Pressure-S ensitive Paint I. Ratio of Reference to Sensor Giving a Small Temperature Dependency, Sensors and Actuators B 97, 2004, pp. 13-21. Kohl, M. J., Abdel-Khalik, S. I., Jeter, S. M., Sadowski, D. L., An Experimental Investigation of Microcha nnel Flow with Internal Pressure Measurements, International Journal of Heat and Mass Transfer 48 (2005), 1518-1533 Kosambi, D. D., Statistics in Function Space, Journal of Indian Math Society Vol. 7, 1943, pp. 76-88. Kose, E. M., Multi-Luminophore Coatings for Pressure Sensitive Paint Applications, Ph.D. Dissertation, Department of Chem istry, University of Florida, 2005. Lakowicz, J. R. Principles of Fluor escence Spectroscopy; 2nd ed.; Kluwer Academic/Plenum Publishers: New York, 1999. Liu, T., Campbell, B. T., Burns, S.P., and Sullivan, J.P., Accuracy of Pressure Sensitive Paint, AIAA Journal paper Vol. 39, No. 1, January 2001.

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322 Liu, T., Campbell, B. T., Burns, S.P., and Sullivan, J.P., Temperature and Pressure Sensitive Luminescent Paints in Aerodynamics, Applied Mechanics Review Vol. 50, No. 4, April 1997. Liu, T., Sullivan, J.P., Pressure and Temperature Sensitive Paints Springer, New York, 2004. Lu, X., and Winnik, M.A., Luminescence Quenching by Oxygen in Polymer Films, University of Toronto, Toronto, Canada, 2000. Malinowski, E. R., Howery, D. G., Factor Analysis in Chemistry ; 3rd ed., John Wiley & Sons, New York, 2002. McLachlan, B. G., and Bell, J. H., Pressu re Sensitive Paint in Aerodynamic Testing, Experimental Thermal and Fluid Sciences Vol. 10, 1995, pp. 470-485. McLachlan, B. G., Kavandi, J. L., Callis, J. B., Gouterman, M., Green, E., and Khalil, G., Surface Pressure Field Mapping Using Luminescent Coatings, Experiments in Fluids Vol. 14, 1993a, pp. 33-41. Mendoza, D. R., An Analysis of CCD Camera Noise and its Effect on Pressure Sensitive Paint Instrumentation System Signal-to-Noise Ratio, Presented at international congress on instrumentation in aerospace si mulation facilities, 17th, Pacific Grove, CA, 1997. Mitsuo, K., Asai, K., Hayasaka, M., and Ka meda, M., Temperature Correction of PSP Measurement Using Dual-Luminophor Coating, Journal of Visualization Vol. 6, No. 2, April 2003. Morris, M. J., Donovan, J. F., Kegelman, J. T ., Schwab, S. D., Levy, R. L., and Crites, R. C., Aerodynamic Applications of Pressure Sensitive Paint, American Institute of Aeronautics and Astronautics Vol. 31, No. 3, March 1993. Muzychka, Y. S., and Yovanovich, M. M., M odeling Friction Factor s in Non-Circular Ducts for Developing Laminar Flow, AIAA 1998. Oglesby, M. D., Wind Tunnel Baro metry by Means of Fluorescence and Phosphorescence Quenching Inter0American Photochemical Society Newsletter, Vol. 18(2), November 1995. Panton, R. L., Incompressible Flow second edition, John Wile y & Sons Inc., New York 1996. Peterson, J. I., and Fitzgerald, V. F., N ew Technique of Surface Flow Visualization Based on Oxygen Quenching of Fluorescence, Review of Scientific Instruments Vol. 51, No. 5, May 1980, pp. 670-671.

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325 BIOGRAPHICAL SKETCH The author was born on February 20th 1977, in the city of Salmiya, Kuwait. He grew up in the Persian Gulf, spending most of his teenage years in Bahrain. He graduated from high school at the age of sixteen and then joined the mechanical engineering Department at the University of Bahrain, Bahrain. He earned an associate degree in mechanical engineering and then joined Em bry-Riddle Aeronautical University, Daytona Beach, Florida, earning a Bachelor of Science in aerospace engineeri ng in the Spring of 1999. He continued his graduate school at ERAU earning a Master of Science in aerospace engineering in the Spring of 2001. In the fall of 2001, Dr. Omar moved to Gainesville, Florida, joining the Mechanical and Aerospace Engineering Department. He worked under the supervision of Dr. Bruce Ca rroll working on several research projects, earning his Ph.D. in the summer of 2006.


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Title: Calibrating Pressure Sensitive Paints Using Proper Orthogonal Decomposition
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Copyright Date: 2008

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CALIBRATING PRESSURE SENSITIVE PAINTS USING PROPER ORTHOGONAL
DECOMPOSITION















By

AHMED F. OMAR


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006





























Copyright 2006

by

Ahmed F. Omar
































This dissertation is dedicated to my family.














ACKNOWLEDGMENTS


THOSE OF HIS SERVANTS ONLY WHO ARE POSSESSED OF KNOWLEDGE
FEAR ALLAH; SURELY ALLAH IS MIGHTY, FORGIVING. (QURAN: SURAT
FA'TIRR, VERSE 28)

THEY ASK THEE CONCERNING THE SOUL. SAY: "THE SOUL IS OF THE
AFFAIR OF MY LORD: OF KNOWLEDGE IT IS ONLY A LITTLE THAT IS
COMMUNICATED TO YOU, (O MEN!)"
(QURAN: SURAT AL-ISRAA'A, VERSE 85)


I express my humility and gratitude before Allah for all the blessings and successes
in my life. None of these accomplishments would have been possible without the grace
and mercy of Allah. I would like next to thank my parents and brother for all their
sacrifices to help me in my educational pursuit. I owe them everything, and I know the
world would not be enough to give to them. My fiancee is owed sincere appreciation for
her support and understanding.
I would also like to thank Dr. Carroll, my advisor, for his support over the course of
my Ph.D. pursuit. Special thanks are owed to Dr. Paul Hubner and Dr. Louis Cattafesta
for their assistance and guidance in a time of desperate need. Further appreciation goes to
the rest of my committee members, Dr. Kirk Schanze and Dr. William Lear. Finally, I
would like to thank all of those who helped me through the course of my Ph.D.: friends,
colleagues, and university staff.
















TABLE OF CONTENTS



L IS T O F T A B L E S ............................ .... .... ..... .................................. .. .............. ... x

LIST OF FIGURES .............. ......... .. ... ........ .... ............ .. ............. xiii

N O M E N C L A T U R E ......... .................. ........................................ ............................ xxiii

ABSTRACT ............. .................................................................. xxvi

CHAPTER

1 IN TR O D U C T IO N ............................................................. .. ......... ...... .....

L literature R review ................................................................ 3
P re fa c e .................................................................. ................................ . 3
H historical Perspective .......................................................... .. .................. .4
Photophysics of Luminescent Coatings..............................................................6
Statement of the Problem .............. ......................... ..... ............... 1
R research E efforts ................ .... .......... ................... 14
Proper Orthogonal Decomposition (POD) ................................. ...............36
M otivation and C contribution ............................................................. ....................4 1

2 LU M INESCEN T COA TIN G S ............................................................ ............... 46

O overview .................................... ..................... ........................... 46
T he O zone A accident ............................................................ .. ....................47
T h e S tru ctu re .................................................................................................. 5 1
P aint C h em istry ................................................................52
The Photophysics.............................................. 52
The Tem perature D ependence............................................. 55
T h e O x y g en F acto r ......................................................................................... 5 7
Paint Com position and Character ................................................................... 58
Which Luminescent Molecule? ..........................................................58
B inder P olym ers ........................................................... .. ....... ..... .. ... 59
T he U ndercoat................................................. ............... .............. 62
Measurement System .................. .................. .................................. 64
The Excitation Source .............. ...................... ......................... 65
T he D election D vice ...................................................................... ............... 66
C alibration Techniques ............................................................ ............... 67


v









A P riori C alibration ........................................................... ............... 67
In situ C alibration ......... ................................................ .. .. ..............69
H ybrid C alibration ......... .............................................. ...... ......... 70
P SP C alib ration ........................ .. ...................... .... ...... .... ..... ...... 70
TSP Calibration ................. .... ...... .. .. ...... .... ..... ......... .... ...... 74

3 PROPER ORTHOGONAL DECOMPOSITION ........... .....................................76

O v e rv ie w ............................................................................................................... 7 6
P O D A naly sis ....................................................... 77
In tro d u ctio n ................................................................................................... 7 7
M them atical Form ulation ............................................................................ 78
Principle com ponent analysis.................................... ....................... 78
Target transformation...... ......... ........... .......... 82
POD Behavior........................................84
Introduction .....................................84

T arget transform ation ................................................ .............................. 86
D ata generation............................................. 88
Noise ........................ ........................90
A n a ly sis ......................... .............................................................................................9 3
Case One (Independent Emission) ...................................................... 94
Case One-A (Temperature Emission Amplified by 10)................................. 96
Case One-B (Temperature Emission Broadened to Overlap with Pressure).......97
Case One-C (Temperature Emission Greatly Broadened to Overlap with
Pressure) ......................... ............................... ..... ........... 98
Case One-D (Close Emission: Temperature at 600nm and Pressure at 650
nm ) .......................... ....... .... ..... ..... ........... ..... ..... ...... .......... 99
Case One-E (Shot Noise Imposed on the Spectra)...................................100
Case One-F (Shot N oise Am plified by 10) .................................................... 102
Case One-G (Filtered Spectra with Shot Noise Amplified by 10)....................103
Case One-H (Filtered Noisy Spectra Using Only Two Filters)......................105
Sum m ary .............................. .. ........ ... ................ ...... .... 106
Case Two (Temperature Dependent Pressure Emission) ...............................107
Calibration Surface Fitting ...................................................................... 107
Su m m ary ...................................... ............................. ................ 1 14

4 LAMINAR CHANNEL FLOW ............................... ....................115

P reface ............. .. ......... ......... ................... ........... .............. 115
Isothermal Flow Solution Mathematical Derivation .............. ...............120
Assumptions/Justifications..... .................... ...............121
B boundary Conditions........................................................................... 122
The Fully Developed Region (Poiseuille Flow)...................................122
N on-Isotherm al Fully D developed Flow ............................................................127









5 E X PER IM EN TA L SE TU P ........................................................... .....................132

H ardw are D description ...................................................... ...................................132
C channel ................... ................... ...................2..........
Channel D eform ation ............................................................. ..... .... 137
O p tical S etu p ...............................................................14 2
Im age R registration ........ ........................................................ .... .......148
Therm al Expansion ............................................................................. 150

6 RESULTS AND AN ALY SIS.................................................................................153

P procedure and T est C ases ........................................................................... .... 153
Exposure Tim es .................. ............................ .. ...... ................. 153
D ata M a trix .................................................................................................. 1 5 4
POD Analysis ................................. ........................... ...........156
Calibration M atrix vs. Test M atrix .......................................... .................156
Im age Filtering ..................................... ........... ...... ........ ..... 160
R results ............................................................................. ........ 16 1
Case One (Isothermal Longitudinal Pressure Gradient)..................................162
POD Calibration................... ......... ......... 168
Case Two (Longitudinal Temperature Gradient) ...........................................175
P O D C alib ration ............................................. .......... .... ................17 8
Case Three (Simultaneous Longitudinal Pressure and Temperature Gradients)183
P O D C alibration ............... ......... ............ .... ....... .. ...... ........ ... 186
Case Five (Perpendicular Temperature Gradient with Longitudinal Pressure
Gradient) ........................................................................... .......................... 194
P O D C alibration ................. .... ... .... .... .. ................. .............. .. 199
Case Seven (Oblique Temperature Gradient with Longitudinal Pressure
G ra d ie n t) .................................................................................................. 2 0 8
P O D C alibration ......... .......................................... ...... .... .............. 2 11
The Case for POD ................... .. .......................... .... ... ..... .... ............... 218
Curve Fit of the 650nm Intensity Data and Intensity Ratios................................220
C ase T three .................................................................................. 22 1
Case Five .................................... .......................... ... .........224
C ase seven ................... ...................2.............................8
E rror Sources and U uncertainty ................................... ..................................... 231
C classification of E rror .................................... .... ................ ........... .....233
U uncertainty A analysis ............................................................. ...............236

7 CONCLUSIONS AND FUTURE WORK ....................................... .................244

C o n clu sio n s................................................... .................. 2 4 4
F future W ork ........................................................................246

APPENDIX

A IM A G IN G SY STE M ........................................................................ ..................249









M easurem ent Sy stem ................................................................................ ........ .... 24 9
The E xcitation Source ............................................... ............................ 249
L a se rs ...............................................................2 5 0
UV Lamps ................................................ 252
Visible Light Illum nation LED s.................................... ............... 253
The D election D evice ......................................................... ............... 253
C C D C am eras........... ...... .................................. .............. .. .... ...... 254
Physical Construction.................... ....... ........................... 255
From Light to E lectrons ........................................ ......... ............... 256
P potential W ells ..................... .. ...................... ... .... .. ...............2 56
C h arg e T ran sfer............ .............................................. ........ .... .......... 2 57
D igital Signal Processing ........................................ ........ ............... 259
CCD Chip Types .................................... ......... .... .. ............. 259
Full-Fram e C CD Chips ........................................ ......................... 259
Fram e-Transfer C C D C hips ............................................ .....................260
Back-Thinned, Back-Illuminated CCD Chips .......................................261
C C D A artifacts .................................................................. .................... 2 6 1
Charge Transfer Efficiency ............................................. ............... 262
Photon (Shot) N oise ............................................................................262
Pixel G ain V ariations ..........................................................................263
Read-N oise ................................................................ .. ......... 264
S atu ratio n ..............................................................2 6 4
Therm al (D ark) Current ........................................ ......... ............... 264
C am era R solution .............................. ............................... ............... 266
Photomultiplier Tubes (PM Ts)........................................ ............... 266
D ata R education .............. ............................................................ ........ 268
Correcting for N on-Idealities ........................................ ............... 269
D ark Im age Correction.................................................... ...... ......... 269
Illumination-Field Variation Correction .......................................... 269
Im age-Registration correction......................................... ............... 270
Flat-Field Correction ............................................................................ 271
Supplem entry T opics ........................................... .................. ............... 272
L ifetim e A pproach............ ... ...................................................... .... .... ....... 272
M easurem ent U uncertainties .................................................... ........ ....... 275
M easurem ent System s ........................................................... ............... 276
Illum nation source............. ...................................... .... .... .............. 276
CCD cam era ............................................................... ......... 276
Filtering/Spectral leakage....................................................... 277
Physical/Chemical Properties of Coating............................278
Displacement/Deformation of Model.................................... ................ 278
U seful D definition s .............................. ........................ .. ........ .... ............279
Binning ............... ... ......... ................. 279
Blooming ...................... ...................... 280
Bit Depth of Camera Data.....................................................280
Dynamic Range ................................. ........ ... .. ................. 281
F ill F acto r ......... ......... ...........................................2 8 2



viii









Light Sensitivity ......................... ..... .... .. .. ... ...............282
Linearity ................................................. 282
Signal to N oise Ratio (SNR) ........................................... ............... 283

B DERIVATION OF LAMINAR CHANNEL FLOW SOLUTION .......................... 285

Isothermal Flow Solution Mathematical Derivation .......................................285
Assumptions/Justifications...... .................... ...............285
B boundary Conditions........................................................................... 286
The Fully Developed Region (Poiseuille Flow)...................................287
Non-Isothermal Fully Developed Flow...................... ..................290
Uniform Temperature/Heat Flux Boundary Condition.............................290

C M ATLAB codes for POD analysis...................................... ......................... 301

Im age R egistration........................................................ .... .. ... .. .......... 301
Calibration Intensity/Pressure and Temperature Extraction.....................................305
P O D C o d e ...................................................................................... 3 1 1

D D erivation of Som e E quations...................................................................... .... 315

P O D A n aly sis ........................................ ..... ................................................... 3 15
Derivation of Pressure Calibration Coefficients .............................................3.15

L IST O F R EFER EN CE S ......... .................................... ........................ ............... 18

B IO G R A PH IC A L SK E T C H ........................................ ............................................325
















LIST OF TABLES

Table p

1-1 Response time and temperature dependency of PtTFPP/FIB with different base
c o atin g s ....................................................................... 1 8

1-2 Research effort treating PSP temperature effects...............................................42

3-1 Conditions and their C elem ents ........................................ ......................... 93

3-2 E igenvalues for case one ........................................................................... ...... 94

3-3 E igenvalues for case one-A ......................................................................... ... ... 96

3-4 Calibration Error case one-A ......................................................... ............... 96

3-5 Eigenvalues for case one-B ............................................. ............................. 97

3-6 C alibration E rror case one-B ........................................................................ .. .... 97

3-7 E igenvalues for case one-D ......................................................................... ... ... 98

3-8 C alibration E rror case one-C ........................................................................ .. .... 98

3-9 E igenvalues for case one-D ......................................................................... ... ... 99

3-10 Calibration Error case one-D ......................................................... ............... 99

3-11 Eigenvalues for case one-E ....................................................... ............... 101

3-12 C alibration E rror case one-E ...................................................................... .. .... 101

3-13 Eigenvalues for case one-F .............................................................................. 103

3-14 Calibration Error case one-F ............................................................................ 103

3-15 Eigenvalues for case one-G ......................................................... ............... 104

3-16 Calibration Error case one-G ............ ..................... ............104

3-17 Eigenvalues for case one-G ......................................................... ............... 106









3-18 Calibration Error case one-G ........... .............. ............... 106

5-1 Coefficients of Thermal Expansion............................. ................... 151

6-1 Exposure tim es for the different filters ...................................... ............... 153

6-2 Pressure drift throughout the exposure times (case five) ............ ............... 154

6 -3 T est m atrix ........................................................................................... .... 154

6-4 Temperature drift throughout the exposure times (case 5).....................................162

6-5 Case one: Test-points pressure results. Actual represents pressure tap
measurement and POD represents the calculated pressure via POD calibration.
The precision error of the Actual readings is 0.006 psi ................................. 172

6-6 Case three: Test-points pressure results. Actual represents pressure tap
measurement and POD represents the calculated pressure via POD calibration.
The precision error of the Actual readings is 0.006 psi ................................. 189

6-7 Case five: Test-points pressure results. Actual represents pressure tap
measurement and POD represents the calculated pressure via POD calibration.
The precision error of the Actual readings is 0.006 psi .................................. 203

6-8 Case seven: Test-points pressure results. Actual represents pressure tap
measurement and POD represents the calculated pressure via POD calibration.
The precision error of the Actual readings is 0.006 psi .................................. 215

6-9 Comparison of different calibration techniques...............................................218

6-10 Case five: Comparison between test-points pressure results for POD and
intensity-ratio Actual represents pressure tap measurement and POD represents
the calculated pressure via POD calibration. The precision error of the Actual
readings is 0.006 psi .................. ............................ .. .. .. .... .. ........ .... 227

6-11 Case seven: Comparison between test-points pressure results for POD and
intensity-ratio. Actual represents pressure tap measurement and POD represents
the calculated pressure via POD calibration. The precision error of the Actual
readings is 0.006 psi .................. ............................ .. .. .. .... .. ........ .... 230

6-12 Intensity error sources and values for Photometrics CH250A CCD camera (SI
502AB), 200 kHz, 14 bit A/D for a unity nominal gain value and a measured
gain ( ) of 19.1 (e A D U )....................... ......... .......................... ............... 237

6-13 Shot noise uncertainty for all filters (case seven) with total precision uncertainty
of 29.3 cts ................ ......... ..........................................238









6-14 Intensity drift uncertainty for case seven. Reference conditions are not included
in the analysis as they are acquired under isothermal conditions. The total
intensity bias uncertainty due to test conditions drift is 9.7cts.............................239

6-15 Uncertainty (95% confidence level) for key factors ...........................................243

A-1 Error estimates for the 16 & 14-bit CCD cameras. Camera linearity error is
0.07% and ADU speed is 200 kHz ............................. .... ... ............... 277















LIST OF FIGURES


Figure page

1-1 Stern-Volmer model for a range of K .............................................9

1-2 Jablonski energy-level diagram showing the absorption and emission processes
for a typical luminescent molecule..................................................13

2-1 C eating Structure ........... .................. .. ......... ........ .. ...... 51

2-2. Typical Absorption (left) and Emission (right) vs. Wavelength for PtTFPP in
fluoroacrylic polymer binder (PtTFPP/FIB). (Bell et al. 2001). ............................52

2-3 Typical rate of gas permeation across a membrane (after Lu and Winnik, 2000) ...60

2-4 Equipment Setup for Temperature Calibration ................................. ............... 65

3-1 Spectral emission for two independence processes: (A) Raw spectra (B) A
single raw spectrum with dependence on the higher wavelength factor and no
dependence on the lower wavelength factor (C) The normalized spectra ..............79

3-2 P .C .A A lgorithm ......................... ........................ .. .... ...... .. ........... 85

3-3 Target transform ation algorithm ........................................ ......................... 87

3-4 Simulated spectral response of the luminophors: (A) Frequency domain (B)
W av length dom ain ........... ...... ............................................................. ..... .... .. 90

3-5 Shot noise as a function of intensity......................................................... .. ........ 92

3-6 Case one: Narrow spectrum with no overlap ................................. ............... 94

3-7 Case one: Eigenvectors and calibration curves for pressure (left) at 79.83920 and
tem perature (right) at 13.6121 .......................................................................... 95

3-8 Case one-A: Temperature Emission Amplified 10 Folds .....................................96

3-9 Case one-A: Eigenvectors for pressure (left) at 66.55460 and temperature (right)
at 0 .3 2 7 5 ........................................................................................9 6

3-10 Case one-B : Em mission spectra ........................................ ............................ 97









3-11 Case one-B: Eigenvectors for pressure (left) at 75.5920 and temperature (right)
at 9.3650 ...................................... .................. ............. 97

3-12 C ase one-C : Em mission spectra ............................................ ........... ............... 98

3-13 Case one-C: Eigenvectors for pressure (left) at 72.7830 and temperature (right)
a t 6 .5 5 6 .........................................................................................9 8

3-14 Case one-D : Em mission spectra........................................... ........................... 99

3-15 Case one-D: Eigenvectors for pressure (left) at 78.150 and temperature (right) at
1 1 .9 2 3 0 ..........................................................................................9 9

3-16 Case one-E : Em mission spectra ........................................ .......................... 100

3-17 Case one-E: Reconstructed spectra ............................................. ............... 100

3-18 Case one-E: Eigenvectors for pressure (left) at 280.10820 and temperature
(right) at 166.3920 ....................... .................. ... .... ................. 101

3-19 Case one-F: Em mission spectra ........................................... ......................... 102

3-20 Case one-F: Reconstructed spectra ............................................. ............... 102

3-21 Case one-F: Eigenvectors for pressure (left) at 100.15560 and temperature
(right) at 346.3815 .................. .. ...................... ..... ............ 103

3-22 Case one-G : Em mission spectra......................................... ............ ............... 103

3-23 Case one-G: Reconstructed spectra.................................................104

3-24 Case one-G: Eigenvectors for pressure (left) at 79.790 and temperature (right) at
1 3 .5 0 2 0 ........................................................................................ 1 0 4

3-25 Case one-H : Em mission spectra.......................................... ........... ............... 105

3-26 Case one-H: Eigenvectors for pressure (left) at 258.90 and temperature (right) at
1 9 2 .6 8 0 .......................................................................1 0 5

3-27 Case tw o: Em mission spectra......................................................... ............... 107

3-28 Case two: Eigenvectors rotated at the appropriate angle for temperature (left) at
345.780 and pressure (right) at 106.440................. ........................................ 110

3-29 Case two: Tem perature calibration...................................................................... 110

3-30 Case two: Second order pressure calibration using the scorers from POD............111









3-31 Case two: Second order pressure calibration using the 2nd set of scorers and
tem perature ....................................................................... .......... 111

3-32 Case two: Third order pressure calibration using the scorers from POD at
19 3 .4 6 ........................................................................... ........................................ 1 12

3-33 Case two: Pressure calibration using the scorers from POD at 193.460 ..............112

3-34 Case two: Numerically filtered emission ............. ............................................... 113

3-35 Case two: Numerically filtered emission eigenvectors for pressure (left) at
106.60 and temperature (right) at 346.060...................................................113

3-36 Case two: Second order pressure calibration using the 2nd set of scorers and
tem perature ............................................................... ... .... ......... 114

4-1 C channel flow scheme atic. .......................................................................... ....... 116

4-2 Channel flow: flow development and pressure distribution................................117

4-3 Low-aspect ratio developing channel flow .....................................................119

4-4 Fully developed velocity profile for an incompressible laminar channel flow......123

4-5 Hotwire and PIV measurement schematic in the channel.................................... 124

4-6 Isothermal case: Centerline pressure gradient along the channel showing the
deviation of the experimental results from the theoretical prediction .................. 126

4-7 N on-isotherm al flow schem atic ........................................ ........................ 130

5-1 Mass flow controller (AALBORG)................. .........................133

5-2 Channel flow schematic: Top view of channel shown ................ ............... 134

5-3 (A) Channel resting on heaters (B) Side view of channel showing the 1 inch
glass plate (C) Backside of channel showing thermocouples, pressure taps,
stagnation chamber and tubing connecting from the top water channel to the
c o o le r ...................................... .................................................. 1 3 6

5-4 Close-up of the beginning of the channel showing the packaging and aluminum
foam, thermocouples and pressure taps. First two test pressure taps are circled in
y yellow ..............................................................................137

5-5 Channel deformation due to pressure forces (modulus of elasticity for aluminum
and glass is 10.5 and 9.6 psi x 106, respectively)................................................138

5-6 Channel deformation due to pressure forces using Plexiglas comparing the
theoretical pressure profile (green line) to experimental profile (blue circles)......139









5-7 Calculated percentage channel height deformation (relative to no-flow
conditions of 0.01") along the centerline for 1" plate with a maximum flow rate
of 100LPM, 23 psi static pressure at the beginning of the channel and 0.01"
channel height. ......................................................................140

5-8 Glass deformation (a comparison between theoretical and experimental results):
3/8" glass (top) and 1" glass (bottom) with percentage pressure deviation from
theory in top-left corner of each plot. Flow from right to left.............................141

5-9 Experimental optical setup showing the relative position of the CCD camera and
excitation sources with respect to the channel ............................ .................. 142

5-10 Pressure response of dual-luminophor paint at 2930K (Kose 2005)................143

5-11 Temperature response of dual-luminophor paint at 14.7 psi (Kose 2005).............143

5-12 First bandpass interference filter: 550 nm, 40 + 8 nm FWHM; dia. = 50 mm
(w w w .m ellesgriot.com ) .......................................................... ............... 144

5-13 Second bandpass interference filter: 600 nm, 40 + 8 nm FWHM; dia. = 50 mm
(w w w .m ellesgriot.com ) .......................................................... ............... 144

5-14 Third bandpass interference filter: 650 nm, 40 + 8 nm FWHM; dia. = 50 mm
(w w w .m ellesgriot.com ) .......................................................... ............... 145

5-15 Fourth bandpass interference filter: 700 nm, 40 + 8 nm FWHM; dia. = 50 mm
(w w w .m ellesgriot.com ) .......................................................... ............... 145

5-16 Filters arrangement relative to paint spectral response to temperature (left) and
pressure (right). .................................................................... 146

5-17 (A) Filter wheel (B) Blue LED ISSI LM2 (excitation source) (C) CCD camera
and filter w heel assem bly ................................................................................. 147

5-18 Effect of image registration on SNR (A) Unregistered image (B) Registered
image. Bottom plots show a horizontal section of the images above. .................148

5-19 Pixel intensity shift on the CCD array ....................................... ............... 149

5-20 Pixel shift due to thermal expansion from bottom to top of the channel .............152

6-1 Stern-Volmer relation for dual-luminophor (PtTFPP-Ruphen/PAN nanospheres
in poly-t-BS-co-TFEM) at different temperature levels (Kose, 2005).................155

6-2 Channel image showing thermocouples, calibration pressure taps and pressure
test points taps. .......................................................................157









6-3 Effect of adding rows instead of columns to the calibration matrix. Observe the
direction of the main eigenvector (black arrow) compared to the calibration
eigenvector (orange arrow ). ........................................... ............................ 159

6-4 Intensity percent error due to shot noise vs. number of frames (14-bit CCD
cam era) .................................... .......................... .... ..... ......... 160

6-5 Case one: Pressure profile (bottom), (a) percent pressure deviation from theory
(psi), (b) temperature profile (thermocouples) over the plate (8" x 3")...............63

6-6 Case one: Normalized intensity (Irn/Iref): 550nm [left] --- 600nm [right] ...........164

6-7 Case one: Normalized intensity (Irn/Iref): 650nm [left] --- 700nm [right] ...........164

6-8 Case one: Centerline pressure response of dual-luminophor at different bandpass
wavelengths .............. ..... ........... ...... ............... ....... ......... 165

6-9 Normalized intensity for case one (650nm) using N2 (left): (A) Reference image
acquired with no flow and exposure time of 1500ms (B) Reference image
acquired with nitrogen flow and exposure time of 185ms. Exposure time for run
image is 1500 ms ......................... .. .............. ......... 66

6-10 Fluorescence image using epifluorescence microscope of Ruphen/PAN particles
emission (dispersed into the PtTFPP / poly-t-BS-co-TFEM binder) at 560nm.
The image shows the heterogeneous dispersion of the Ruphen/PAN particles in
the poly-t-BS-co-TFEM m atrix (K ose 2005) ...................................................... 167

6-11 Case one: Normalized intensity (Iref/Irun)................................ ..........................168

6-12 Case one: Calibration eigenvectors at 174.560 degrees (left) and eigenvalues
(right) ........................................................................ ........... 169

6-13 Case one: Product of first (left) and second (right) eigenvectors and eigenvalues
of calibration ..... ..................................... ................ 169

6-14 Case one: Product sum of eigenvectors and calibration eigenvalues showing 1 %
variation at 550nm and 15% at 650nm........ ......... .......... ....... ............... 170

6-15 Case one: Calculated centerline-pressure profile by each eigenvector ................71

6-16 Area change due to chamfer in the glass plate at the exit .....................................172

6-17 Case one: Calibration error, absolute (left) and percentage (right)........................172

6-18 Case one: Calculated pressure field from POD calibration..................................173

6-19 Case one: Calculated pressure from POD calibration vs. pixel index along the
channel. Each curve represents a longitudinal line of pixels along the channel.
Actual represents the actual pressure taps readings used for calibration .............174









6-20 Case two: Temperature profile (thermocouples)....................................................175

6-21 Case two: Normalized intensity (Irun/Iref): 550nm [left] --- 600nm [right]...........176

6-22 Case two: Normalized intensity (Irun/Iref) : 650nm [left] --- 700nm [right] ..........176

6-23 Case two: Centerline temperature response of dual-luminophor coating at
different bandpass w avelengths ........................................ ......................... 177

6-24 Case two: Temperature linearity of dual-luminophor coating at different
bandpass w avelengths ................................................. ............................... 177

6-25 Case two: Normalized intensity (Irun/Iref) ................... ......... ....................178

6-26 Case two: Calibration fundamental spectra at 0.50 degrees (left) eigenvalues of
calib ration (right).......................................................................... ............... 17 8

6-27 Case two: Product of first (left) and second (right) eigenvectors and eigenvalues
of calibration ..... ..................................... ................ 179

6-28 Case two: Product sum of eigenvectors and calibration eigenvalues showing 28
% variation at 550nm and 18% at 650nm ................................... .................180

6-29 Case two: Calculated temperature field from POD calibration (image) ..............181

6-30 Case two: Calculated temperature field from POD calibration (values). Each
curve represents a longitudinal line of pixels along the channel. Actual
represents the actual thermocouple readings used for calibration.....................182

6-31 Case three: Pressure profile (bottom), (a) percent pressure deviation from theory
(psi), (b) tem perature profile (therm ocouples).................................... ................ 183

6-32 Case three: Normalized intensity (Irun/Iref): 550nm [left] --- 600nm [right].........184

6-33 Case three: Normalized intensity (Irun/Iref) : 650nm [left] --- 700nm [right]........184

6-34 Case three: Centerline pressure and temperature response of dual-luminophor at
different bandpass w avelengths ........................................ ......................... 185

6-35 Case three: Inverse of normalized intensity (Irun/Irf) ..................... .....................186

6-36 Case three: Pressure calibration fundamental spectra at 10 degrees (left)
eigenvalues of calibration (right) .............. ..... .......................................... 187

6-37 Case three: Product of first (left) and second (right) eigenvectors and
eigenvalues of pressure calibration .............. ................................................ 187

6-38 Case three: Product sum of eigenvectors and pressure calibration eigenvalues
showing 18 % variation at 550nm and 27% at 650nm..................................... .....188


xviii









6-39 Case three: Temperature calibration fundamental spectra at 00 degrees (left)
eigenvalues of calibration (right) .............. ..... .......................................... 189

6-40 Case three: Product of first (left) and second (right) eigenvectors and
eigenvalues of tem perature calibration ........................................ .....................190

6-41 Case three: Product sum of eigenvectors and temperature calibration eigenvalues
showing 23 % variation at 550nm and 26% at 650nm..................................... .....190

6-42 Case three: Calculated pressure field from POD calibration (image)....................191

6-43 Case three: Calculated temperature field from POD calibration (image) ............192

6-44 Case three: Calculated pressure field from POD calibration (values). Each curve
represents a longitudinal line of pixels along the channel. Actual represents the
actual pressure taps readings used for calibration ..............................................193

6-45 Case three: Calculated temperature field from POD calibration (values). Each
curve represents a longitudinal line of pixels along the channel. Actual
represents the actual thermocouple readings used for calibration.......................193

6-46 Case five: Temperature profile (thermocouples).................... ...............194

6-47 Case five: Pressure profile (bottom), (a) percent pressure deviation from theory
(to p ) ...................................... ................................................... 1 9 5

6-48 Case five: Normalized intensity (Irn/Iref): 550nm [left] --- 600nm [right]..........196

6-49 Case five: Normalized intensity (Irn/Iref): 650nm [left] --- 700nm [right].......... 196

6-50 Case five: Speckling in the 550nm image (left) and a comparison to the 700nm
filte r ....................................................................................... 1 9 7

6-51 Case five: Centerline pressure and temperature response of dual-luminophor at
different bandpass w avelengths ........................................ ......................... 198

6-52 Case five: Centerline temperature profile ................................... ............... 198

6-53 Case five: Inverse of normalized intensity (Irun/Iref).....................................199

6-54 Case five: Temperature calibration fundamental spectra at 890 degrees (left)
eigenvalues of calibration (right) ........................................ ....................... 200

6-55 Case five: Product of first (left) and second (right) eigenvectors and eigenvalues
o f calib ratio n ..................................................................... 2 0 0

6-56 Case five: Product sum of eigenvectors and calibration eigenvalues showing
9.5% variation at 550nm and 17% at 650nm ............................... ............... .201









6-57 Case five: Pressure calibration fundamental spectra at 110 degrees (left)
eigenvalues of calibration (right) ........................................ ....................... 202

6-58 Case five: Product of first (left) and second (right) eigenvectors and eigenvalues
o f calib ratio n ..................................................................... 2 0 2

6-59 Case five: Product sum of eigenvectors and pressure calibration eigenvalues
showing 4% variation at 550nm and 16% at 650nm .............................................203

6-60 Case five: Calculated temperature from POD calibration (image) ......................204

6-61 Case five: Calculated temperature from POD calibration (values). Each curve
represents a longitudinal line of pixels along the channel. Actual represents the
actual thermocouple readings used for calibration.............................. .............205

6-62 Case five: Calculated pressure from POD calibration (image)...........................206

6-63 Case five: Calculated pressure from POD calibration (image). Each curve
represents a longitudinal line of pixels along the channel. Actual represents the
actual pressure taps readings used for calibration ............................................207

6-64 Case seven: Temperature profile (thermocouples)............................... 208

6-65 Case seven: Pressure profile (bottom), (a) percent pressure deviation from
theory (top) ...................................................................... ..........209

6-66 Case seven: Normalized intensity (Irun/Iref): 550nm [left] --- 600nm [right]........210

6-67 Case seven: Normalized intensity (Irun/Iref) : 650nm [left] --- 700nm [right].......210

6-68 Case seven: Inverse of normalized intensity (Irun/Iref)..................... ..................211

6-69 Case seven: Temperature calibration fundamental spectra at 930 degrees (left)
eigenvalues of calibration (right) ........................................ ....................... 212

6-70 Case seven: Product of first (left) and second (right) eigenvectors and
eigenvalues of calibration ......................................................... .............. 212

6-71 Case seven: Product sum of eigenvectors and calibration eigenvalues showing
31% variation at 550nm and 28% at 650nm .................................. ............... 213

6-72 Case seven: Pressure calibration fundamental spectra at 530 degrees (left)
eigenvalues of calibration (right) ........................................ ....................... 213

6-73 Case seven: Product of first (left) and second (right) eigenvectors and
eigenvalues of calibration ......................................................... .............. 214

6-74 Case seven: Product sum of eigenvectors and calibration eigenvalues showing
8% variation at 550nm and 5% at 650nm ................................... .................214









6-75 Case seven: Calculated temperature from POD calibration (image) ...................215

6-76 Case seven: Calculated pressure from POD calibration (image) .........................216

6-77 Case seven: Predicted temperature from POD calibration (values). Each curve
represents a longitudinal line of pixels along the channel. Actual represents the
actual thermocouple readings used for calibration.................... ... .............217

6-78 Case seven: Predicted pressure from POD calibration (values). Each curve
represents a longitudinal line of pixels along the channel. Actual represents the
actual pressure taps readings used for calibration ............................................217

6-79 Temperature sensitivity (integrated intensity/K) of the temperature and pressure
lum inophors at 14.7 psi (K ose 2005). ................................................ ..............220

6-80 Case three: Pressure calibration using intensity ratio at 650nm.............................221

6-81 Case three: Calculated pressure using intensity ratio at 650nm.............................221

6-82 Case three: Pressure calibration using intensity ratio (I550 / I650)............................222

6-83 Case three: Pressure calibration using intensity ratio (1600 / 1650)............................223

6-84 Case three: Calculated pressure using intensity ratio at (1600 / 1650)........................223

6-85 Case five: Pressure calibration using intensity (1 / I650)..................... ............... 224

6-86 Case five: Calculated pressure using intensity (1 / 1650) .....................................224

6-87 Case five: Pressure calibration using intensity (1600/ I650).................................225

6-88 Case five: Calculated pressure using intensity (1600 / 1650)................................. 225

6-89 Case five: Calculated pressure using intensity (1600 / [650]2)...............................226

6-90 Case five: Calculated pressure using intensity (1600/ [650]15)..............................226

6-91 Case five: Calculated pressure: (A) Intensity 1600/ [6501.5 (B) POD calibration...227

6-92 Case seven: Calculated pressure using intensity (1 / I650) ...............................228

6-93 Case seven: Calculated pressure using intensity (1600/ I650o)................................ 228

6-94 Case seven: Calculated pressure using intensity (1600 / [650]2).............................229

6-95 Case seven: Calculated pressure using intensity (1600/ [I650]1.55)........................... 229

6-96 Case seven: Calculated pressure: (A) Intensity 1600/ [650]1.55 (B) POD
c a lib ratio n ...................................... ............................................... 2 3 0









6-97 B ias and precision error............................................................... .....................233

A-i Schem atic of CCD im aging system ............................................ ............... 254

A -2 C D C hip........................................................................................... 255

A -3 P potential W ell Structure .............................................................. .....................257

A -4 CCD readout sequence ........................................................................ 258

A-5 A schematic of a Photomultiplier tube .........................................................268

A-6 Timing sequence for lifetime measurement (frequency domain) ........................274

A-7 Timing sequence for lifetime measurement (time domain) ................................275

A-8 SNR as a Function of Intensity ......................... ......... ......... .....284

B-1 Fully developed velocity profile for an incompressible laminar channel flow......289

B-2 Thermal boundary layer development in a laminar channel flow........................291

B-3 N on-isotherm al flow schem atic ........................................ ........................ 298















NOMENCLATURE


A(T) Stern-Volmer first coefficient
B Bias error
B(T) Stern-Volmer second coefficient
c Speed of light in vacuum (3.0 1017 nm/s)
C Scores matrix

Cp Specific heats per unit mass at constant pressure

C, Specific heats per unit mass at constant volume
D Data matrix, Diameter
Dp Luminophor diffusion coefficients in polymer
Dq Oxygen diffusion coefficients in polymer
e Electronic

E Energy transport rate

Ed Diffusion activation energy

E,, Arrhenius activation energy for a non-radiative process

EQ activation energy for oxygen diffusion in the binder
f Frequency
g Gravitational force
h Channel height, enthalpy, Plank's constant (6.626176 10-34 JS)
I Luminescence intensity
Ia absorption intensity

ID dark charge intensity

Iem Emission intensity


xxiii










Io Luminescence intensity in the absence of oxygen

Iref Luminescence intensity at reference conditions

Iu, Luminescence intensity at run conditions

Thermal conductivity (W/m-K), Boltzman's constant (1.381 10-23
k
J/molecule-K),

knr Non-radiative decay rate

Stern-Volmer constant
Kq kq

k, Radiative decay rate

L Polymer thickness (Chapter 2)

m Mass flow rate

Nreadout Read out noise

[02 ] Oxygen concentration

P Precision error

Po2 Partial pressure of oxygen

V
Pr Prandtl number (Pr = )
a

Pref Pressure at reference conditions

P,,n Pressure at run conditions

Q Mass flow rate

q energy generation within object

q" heat flux (W/m2)
R Universal gas constant (8.315 J/mol-K), Eigenvector matrix
pV D V D
Re Reynolds number (Re= "- D VD)
/d v

S Gas solubility

s(T) Solubility coefficient


xxiv









S1 linear solubility coefficient based on Henry's law

Sni non-linear solubility coefficient based on Langmuir's model

t time
T Temperature, Rotation matrix

Tg Glass transition temperature

u x-component velocity
U Uncertainty
v y-component velocity

Vm Mean velocity

w z-component velocity, width

WA Wetted perimeter

Wd Channel width

Z Squared data matrix

a (T) Coefficient of linear thermal expansion, affinity coefficient

P Gain
3 Viscous boundary layer thickness

68 Thermal boundary layer thickness

E Error
3 steady-state gas flux into polymer
2 Wavelength, Eigenvalues
I/ Dynamic viscosity
v Kinematic viscosity
(D quantum yield of luminescence, dissipation function in energy equation
P Density
c Standard deviation

Shot Shot noise

Tme Emission lifetime of an excited molecule

















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

CALIBRATING PRESSURE SENSITIVE PAINTS USING PROPER ORTHOGONAL
DECOMPOSITION

By

Ahmed F. Omar
August 2006
Chair: Bruce F. Carroll
Major Department: Mechanical and Aerospace Engineering

Pressure sensitive paints (PSP) have been gaining more popularity in experimental

fluid mechanics and aerodynamic testing. A major problem with PSP pertains to its

temperature dependence making the calibration process very difficult. Dual-luminophor

PSP has an added temperature phosphor to provide temperature information for the

calibration. Dual-luminophor systems still suffer from the inherent temperature

dependence and possess added complications due to spectral cross talk and overlap.

However, to date there is no successful universal calibration technique for dual-

luminophor systems. Such calibration is needed for dual-luminophor PSP to become a

practical experimental tool.

With this aim, a statistical technique known as proper orthogonal decomposition

(POD) is used to extract pressure and temperature information from intensity data. POD

works by defining and separating the main factors of any system and evaluating the

proportional contribution of each factor. The calibration technique is examined by


xxvi









applying the dual-luminophor PSP in a channel flow experiment. Before applying the

calibration experimentally, a set of artificial data is examined using POD to provide a

fundamental understanding of POD as a calibration technique. The experiment was

designed to allow for different flow conditions and temperature gradients to interact,

hence providing enough variation to examine the calibration technique. Seven cases are

examined, with each case shedding light on a particular aspect of the calibration. The

POD calibration is compared to the intensity-ratio calibration in order to emphasize the

effectiveness of the technique. Finally, results are evaluated for accuracy and a detailed

uncertainty analysis is performed to fully assess the POD calibration.


xxvii














CHAPTER 1
INTRODUCTION

This dissertation presents novel work in the characterization and calibration of

dual-luminophor pressure sensitive paints using proper orthogonal decomposition (POD).

The paint is additionally implemented in a canonical flow experiment, namely a laminar

incompressible channel flow, to fully characterize the paint and calibration procedure

under flow-based conditions. The paint utilized in this work is PtTFPP-Ru(phen)/PAN

/Poly-tBS-co-TFEM, developed by Kose (2005) and collaboratively tested under static

(no flow) conditions with the author. Pressure sensitive paints (PSP) offer a promising

and more effective tool for characterizing and resolving pressure fields over test-model

surfaces in comparison to traditional pressure measurement techniques. Traditional

techniques can offer at best a discrete representation of the pressure field. In addition,

there is a rise in cost and time of experimentation, as well as restrictions on access to the

entire model for pressure sensor placement. In contrast, PSP technology is relatively

inexpensive and can be easily applied to any surface in very thin layers (- 10 [im).

A typical pressure sensitive paint is composed of an oxygen sensitive luminophor

embedded in an oxygen permeable polymer, which is then applied directly on the surface

or on top of a primer layer to enhance light reflection. Exciting the paint with the

appropriate wavelength, usually long ultraviolet (UV) to blue wavelengths, energizes the

paint electronically, which is then followed by a deactivation process through different

paths. The path characterizing the paint's dependence on pressure is the oxygen

quenching path. Nonetheless, other paths of deactivation compete with the oxygen









quenching path, primarily radiation. Radiation is the molecule emission of light at higher

wavelength as a means of deactivation. The oxygen quenching process is directly

proportional to the partial pressure of oxygen in the surrounding medium, hence the

pressure of air. Accordingly, the intensity of the light emitted by the paint is inversely

proportional to the pressure. However, as the luminophor is embedded in an oxygen

permeable medium (polymer), the oxygen sorption and diffusion characteristics of such

medium would obviously affect the quenching process. Intuitively, temperature would

appreciably alter the permeability of the polymer, thus the oxygen sorption and diffusion

characteristics. In addition, on the molecular level there is an inherent temperature

dependence related to thermal quenching. This defines a principal concern with PSP,

which is an inherent temperature dependence that necessitates a temperature

compensation procedure, in combination with a typical pressure/intensity calibration, to

account for temperature variations while collecting pressure information. Compensating

for temperature effects is rather challenging, and while various research efforts have

attempted to resolve the issue with relative success, a robust and universal procedure is

yet to be born.

Dual-luminophor PSP contains an added temperature sensor, which typically emits

at sufficiently different wavelengths, usually lower, such that the temperature data can be

collected simultaneously to provide both a temperature compensation technique as well

as mapping the temperature distribution over the surface. However, this leads to a

different problem, namely, "cross talk" between the two sensors, which makes it difficult

to separate the independent factors, pressure and temperature, through spectral filtration.

Cross talk is an adverse effect that stems from either one luminophor absorbing the









emission of the other, a spectral overlap between the two emissions, or both. This work

examines and applies POD to resolve these problems. POD identifies and separates the

main factors of any process and resolves the relative magnitude, and hence importance,

of each factor; in addition, it serves as a noise rejection tool.

The second part of this work focuses on examining the dual-luminophor PSP

technology under flow-based conditions. Static behavior of the dual-luminophor PSP has

already been quantified by the author in collaboration with Kose (2005). Flow-based

measurements using the dual-luminophor PSP would allow for a thorough evaluation of

the paint and the analysis/calibration process. The paint is applied in a laminar channel

flow experiment with an imposed temperature gradient varying in direction from

longitudinal, transverse, and oblique relative to the flow direction. The channel flow

experiment is chosen as it is a canonical flow with an existing analytical solution under

laminar incompressible conditions. The details of the channel flow experiment including

literature review and mathematical analysis are presented in Chapter 4 and Appendix-B.

Literature Review

Preface

The aerodynamic design of any model entails fundamental fluid mechanics

experiments involving the characterization of the surface pressure distribution. These

measurements are usually obtained to estimate the aerodynamic forces (e.g., lift and drag)

through an integration process. More crucial is the identification and understanding of

specific flow phenomena that profoundly affect the design criterion, such as boundary

layer separation or shock wave impingement on the surface. Occasionally, such

phenomena may affect the structural aspect of the design. Additionally, computational

fluid dynamics (CFD) continue to evolve and expand in application, requiring full-field









experimental techniques capable of providing more comprehensive validation.

Typically, pressure measurements are performed using traditional techniques that

implement pressure taps and transducers. These devices are located on discrete points

over the surface of the model. This approach has several shortcomings. The first and most

obvious is the lack of a full field mapping of the pressure field, which can lead to

ignorance of the flow field behavior near the surface in critical areas of the model.

Further, even with prior knowledge of specific locations on the model that are potentially

critical, it is not always possible to practically install such devices in the model (e.g.,

sharp corners, thin edges). It is rather impractical for one to try to compensate for the lack

of enough spatial resolution of traditional pressure measurement techniques by adding

more taps as the task is quite expensive as well as time consuming, not to mention the

physical implications on the structural integrity and the inevitable compromise of the

flow characteristics over the surface. To provide the reader with an idea of the cost

involved in model construction, a typical pressure-instrumented aircraft wind tunnel

model can cost on the order of $500,000 to $1 million to construct (McLachlan 1995).

These shortcomings led to aerodynamic testing being a fairly time consuming process

that adversely added to the cost and time required for any design.

Historical Perspective

A paper published by Dickerson and Stedman (1979) initiated research efforts in

the field of flow measurements using luminescent molecules as they utilized ozone to

visualize flow patterns. Ozone has excellent flow tracing characteristics due to its

physical properties. A fluorescent screen with a turbulent flow passing over it was

illuminated with UV, and as the ozone-air mixture passed over the screen, the ozone

absorbed some of the UV, hence casting a "shadow" that is directly proportional to the









ozone concentration in the flow and the speed of the flow. By placing an additional

fluorescent screen perpendicular to the flow, they were able to create a three-dimensional

image of the turbulent plumes. This was the earliest recorded attempt to quantify a flow

using luminescent dyes. Ironically, the whole idea was based on a mere accident as they

were trying to measure the rate of photolysis of ozone in the atmosphere when some

ozone leaked between a mercury lamp and a black light poster, which then cast a shadow

that looked like smoke plumes. As they scrambled to find the source of the "smoke,"

Dickerson realized it was the shadow of an ozone plume!

The work of Dickerson and Stedman (1979) inspired a group at the National

Institute of Health (Peterson and Fitzgerald, 1980), to pioneer the concept of surface

pressure characterization using luminescent coatings in the West. Nonetheless, the

originality of the oxygen quenched luminescent molecules technology was first

established by the German scientists Kautsky and Hirsch (1935). Peterson and Fitzgerald,

(1980) described an experiment in which a surface was covered with a fluorescent dye

(fluorescent yellow dye adsorbed on silica particles) that was then excited by a blue light.

The dye had photoluminescence characteristics that allowed it to respond inversely to

surrounding oxygen concentration. As flow over the surface was initiated, either nitrogen

or oxygen was injected into the flow through a static pressure tap on the surface. In the

case of nitrogen injection, a bright streak of luminescence was detected on the

downstream side of the tap, while the oxygen injection resulted in a dimmer illumination

downstream of the tap. The nitrogen decreased the oxygen concentration downstream of

the tap and hence increased the luminescence of the paint inversely to the oxygen

concentration. Even though the PSP used in this experiment was not favorable to accurate









and practical experimental implementation due to low oxygen sensitivity of the dye and

the oxygen permeability of the binder as well as other problems such as poor adhesion of

the dye to the surface, it undoubtedly created the potential for the use of luminescent

technology in aerodynamic testing.

Concurrently, Russian scientists produced the first practical pressure sensitive

coating. A year later they obtained pressure measurements with the same coating

(Ardasheva et al., 1985). Around the same time a group from the Central Aero-

Hydrodynamic Institute (TsAGI) in the former Soviet Union developed a new polymer-

based PSP, which they applied to a cone-cylinder model at supersonic mach numbers.

Their results showed that the paint suffered from very significant temperature

dependence, hence establishing one of the fundamental problems with PSP that is still

unresolved to this date. The Russian advancements in PSP technology was finally

revealed in the West through a commercial advertisement for an "Optical Pressure and

Temperature Measurement System" in the 1990 February issue of Aviation Week &

Space Technology.

Over the nineties PSP technology was commercialized in the aerospace industries.

Companies like McDonnell Douglas, Boeing, British Aerospace, and government

research institution such as NASA, Office National d'Etudes et de Recherches

Aerospatiales (ONERA) in France, to name a few, have widely implemented PSP

technology into the design and testing of their products (Bell et al., 2001).

Photophysics of Luminescent Coatings

Pressure sensitive paints offer a potentially promising substitution to current

standard pressure measurement techniques in aerodynamic testing. The PSP method

allows one to obtain not only qualitative pressure images, but also quantitative absolute









pressure values at the desired locations on the model, without introducing flow-disturbing

probes or affecting the structure of the model surface (Engler et al., 2000). PSP can alter

the nature of the surface roughness affecting flow transition. However, PSP can be

applied in very smooth layers and with careful design of both the paint and paint

application such effects can be minimized. Photochemically excited molecules are

embedded in an oxygen permeable binder, and once excited with the appropriate

wavelength they deactivate through different mechanisms, such as a process known as

oxygen quenching, hence affecting the degree of luminosity. By means of photodetectors,

such as a CCD camera or through a photomultiplier tube (PMT), the emission of these

molecules can be recorded and translated to yield the true pressure field. Two

measurement techniques are implemented in acquiring the intensity field, the first known

as the intensity based method, the other known as the lifetime method. The details and

comparison of both techniques can be found in the following references (Bell et al., 2001;

Hardil et al., 2002; Liu and Sullivan, 2004; Zelelow et al., 2003). This work adapts the

former technique and is discussed in detail in Chapter 2.

Although PSP technology has improved, it is still in its premature stages and many

problems and concerns need to be addressed in order for the technology to gain a better

acceptance and implementation in aerodynamic testing. More details about the history

and development of the luminescent technology, chemical formulations, decay

mechanisms, paint preparation, accuracy and calibration/measurement techniques and

systems are presented in Chapter 2 and can be found in even greater detail in the

following references: Bell et al., 2001; Engler et al., 2000; Liu et al., 1997; Liu and

Sullivan, 2004 and McLachlan et al., 1995.









Pressure sensitive paint technology is based on photoluminescence, which includes

both fluorescence (emission 10-8 10-6 s) and phosphorescence (delayed emission 10-

3-100 s). Probe molecules are embedded in an oxygen permeable binder when excited by

incident light they deactivate through different mechanisms, namely oxygen quenching,

radiation and thermal quenching. The oxygen quenching mechanism can be generally

modeled by the Stern-Volmer relation (Oglesby, 1995):


S=1+ P (1.1)


In this relation I is the luminescence, Io is the luminescence in the absence of

oxygen, P0o is the partial pressure of oxygen, and Kq is the Stern-Volmer constant. The

valueslo and K are both functions of temperature. Equation (1.1) indicates an inverse

relation between the partial pressure/concentration of oxygen; hence the pressure, and the

intensity. The constant K is a measure of the sensitivity of the dye to pressure. For high

values of K, high accuracy of the pressure measurement is obtained at low pressure

levels, while low values of Kq yield higher sensitivity at high pressure levels (Oglesby,

1995). Observing Figure 1-1 it is apparent that for higher Kq values, as the pressure
I
increases the intensity ratio gradient becomes smaller (i.e., less sensitivity). This
Io

could result in low signal-to-noise ratio, which is most certainly the case in low speed

wind tunnel testing where pressure variations are relatively small and close to

atmospheric conditions, which can be accommodated by using PSP with lowK Low

speed wind tunnel testing with PSP is quite challenging, and more effort is needed to










identify probes with appropriate Kq values, which could perhaps be tailored to specific


test conditions (Morris et al. 1993).



0.9 -- I I I I




0.7 ------ -------------- -------------------









SI l l I I I
0.8




0.2 --f------------------ ---------- ------ ------









0 10 1. 20 2. 30 35 40 45 00
0.1 ------ ---------- ----i --- ----- I
I I














0 5 10 15 20 25 30 35 40 45 50
Pressure (psia)

Figure 1-1 Stern-Volmer model for a range of K,


It is not typically practical to create a "reference" condition, I ,by purging the

oxygen in the test cell, hence a more practical approach is to use a known condition-say

atmospheric-as the reference condition as shown below in equation (1.2). Equation (1.2)

reiterates the temperature dependence in the intensity, as the slope B(T) and the


intercept A(T) are both functions of temperature. The Stemrn-Volmer approximation does


reasonably well under two conditions: first, the range of the test pressures is adequately

sensible (limited), and second, the reference condition is near the pressures of interest.

Note that in equation (1.2) the reference and run intensity are under isothermal condition
0 10 15 20 5 30 5 40 5 5
irssr (ps Iia)I
Figur 1- Str-Vle moe fo a rag of K
,, I I I
Iti o yial racial raea"eeec"codtoI b ugn h
oxyge in th tes cel hec a oepatclapoc st s nw odto-a
atosheica the reeec codto as sonblwieqaio(12.Eutn(.)
reitrate th teprtr deedec in th nesta hesoeBT n h
inerep A (T ar ohfntoso eprtr.Th tr-omrapoiainde

reaonbl well----c--c under.---~- tw cniton:fis, herng f hetstprsursisadqatl

sesbl lmie) adscod he reeec cnito isnarte rsursofiteet
Note tha in- eqain(.)te eeec n u itniyaeud r iotema cnito









to cancel out the temperature dependence; however, this approach is intrinsically

impractical.



rI Pef
A (I-nj + B P (1.2)
run ref

Photodegradation, an intrinsic concern with luminescent molecules, is the loss of

intensity due to exposure of the sensor probe to light. Molecules are much more active in

their excited state than in ground state and can react to certain compounds to which they

are indifferent in ground state. Addition of such compounds to a sample containing

luminophor causes luminescence lifetime and intensity to decrease, a process known as

"quenching of luminescence" and thus such compounds are accordingly named

"luminescence quenchers." All luminophor quenching processes are to some extent

irreparable and consequently intense and continuous illumination of luminophors

degrades luminophor's illumination (Vollan et al. 1991). This is the result of the singlet

oxygen molecules produced through the oxygen quenching process, which are extremely

reactive. They bond with nearby molecules forming either non-luminescent molecules or

causing deformations in the polymer matrix that lower measured intensities. Recent

advancements in luminescent molecules and polymer sciences have nearly eliminated

photodegradation of luminophors (Kose, 2005).

Coating the surface of a model with paint can potentially alter the airflow

characteristics over the model, making the paint intrusive. This intrusion can be in the

form of actual physical alteration such as adding thickness to the surface of the model or

an alteration to the effective shape of the model, e.g., altering the boundary layer

development (Schairer et al., 1998). Physical alteration does not necessarily imply a

change of the roughness of the surface; on the other hand, effective alteration is a direct









result of roughness change of the surface. For example, a rougher surface due to the paint

would lead to premature transition of the boundary layer, or it could have the opposite

effect if the paint forms a smoother contact-surface with the flow relative to the actual

surface. Further, paint could affect readings from the calibration pressure taps by

rounding square edges or forming a protuberance (disturbance) around the opening.

Schairer et al. (1998) assert that the latter was not observed and if it was to be a concern

then it would be detected as a consistent offset between the paint-on and paint-off

pressure readings at every location and condition. The issue is further addressed by

Vanhoutte et al. (2000), as they examined the effect of the paint under low speed, low

Reynolds number and high subsonic conditions for a swept wing. Low speed examination

showed that an increased surface roughness due to the paint yielded higher drag forces

due to the prevention of the occurrence of a bursting laminar separation bubble. High

subsonic speeds testing indicated the increased roughness induced significant drag

increase, while increased thickness showed lesser, but considerable, drag increase. The

reader interested in more of the details and mechanics of PSP intrusion is encouraged to

read Vanhoutte et al. (2000) and Amer et al. (2001), as the subject is merely addressed

here for completion.

Statement of the Problem

A principal concern with pressure sensitive paints is their inherent temperature

dependence, an issue that remains unresolved in the literature. Other issues include:

accuracy, feasible environmental range of application, time response, invasiveness and

cost-effectiveness (Weiss, 2002). The accuracy of PSP measurements is affected by

several factors that include model deformation, paint self-illumination, excitation source

stability, image registration, and photobleaching. Nevertheless, temperature dependence









continues to be the primary source of error in PSP measurements as innovations in the

fields of CCD fabrication, digitizers and data processors have greatly reduced related

errors associated with measurements. Liu et al. (2001) investigated the different sources

of error in PSP measurements and concluded that temperature effects dominate PSP

uncertainty. Therefore, a calibration technique that is robust and accurate is essential for

PSP applications. Schanze et al. (1997) examined the different sources of the temperature

dependence in an attempt to pave the way for identifying the appropriate solutions. The

polymer they employed is a typical PSP formulation comprising a luminescent

polypyridine Ru (II) complex dispersed within a poly-dimethylsiloxane (PDMS) binder.

The dye is excited with blue light (A ex 450 nm) and luminesces strongly in the red

wavelengths (Amax 620 nm). The formulation was tested over the 0-14 psi range and

yielded a Stern-Volmer quenching constant Ks, of 0.70 psi-1. Mathematically the

intensity, Im,, and natural emission decay lifetime, e,,, can be expressed as follows (Bell

et al., 2001).

Ck
I k k (1.3)
k, +k +k [02


=k +k +k [02] (1.4)


where C is a constant that linearly relates the intensity to the quantum efficiency;

k, k, and kq are the radiative, non-radiative and oxygen quenching first-order rate

constants, respectively. The deactivation process yields light only through radiative

decay, while the other two decay mechanisms yield temperature.










Vibrational level
- Electronic State


Ir



A,.
I k


Internal Conversion
Intersystem Crossing

Vibrational Relaxation

Absorption

Emission

Oxygen Quenching


A4sorptipn


Jores(

kf


kisc

A


- U I


ence


Phosp


lores4

kp


; I I I 1


:ence

knr


kq[(0]
COn

kg[O]


2


So 1 X X _

Figure 1-2 Jablonski energy-level diagram showing the absorption and emission
processes for a typical luminescent molecule.

As illustrated by Hager et al. (1975a, 1975b), the radiative decay is typically

temperature independent. Further, Van Houten and Watts (1976) characterized the

general temperature dependence of the non-radiative decay rate behavior with an

Arrhenius function. They attempted to physically separate these different effects through

the experiment to identify the main source of luminescence and its relative magnitude.

They eliminated the oxygen quenching path by reducing the pressure to vacuum or

simply deoxygenating the paint with an inert gas, i.e., argon. In such a case the ratio of

intensity-lifetime is simply dependent on the nonradiative (temperature) decay rate kn.

Conversely, oxygen diffusivity in the binder, which is directly related to kq, was the main









source of temperature dependence under oxygen rich conditions. Schanze et al. (1997)

tested the dye embedded in two different mediums, namely ethanol and PDMS. They

concluded that the intrinsic temperature dependence is not strongly influenced by the

medium under vacuum or degassed conditions. However, in the presence of air the

lifetime temperature dependence is substantial for a PSP sensor dispersed in PDMS,

while it is almost non-existent when ethanol is the medium. This is because the oxygen

quenching pathway is characterized by much lower activation energy for ethanol in

contrast to PDMS, which has typical activation energies on the order of 1 lkJ/mol.

Activation energy is often used to denote the minimum energy needed for a specific

chemical reaction to occur. Further, in the presence of oxygen, they found that oxygen

quenching is the predominant decay mechanism (> 90% of the total decay). Finally, by

comparing the lifetime emission of the polypyridine Ru(II) /PDMS in vacuum and in

oxygen rich environment, they showed that oxygen quenching is the main factor

influencing the temperature dependence due to the larger r/temp. gradient, further

suggesting that in the absence of oxygen the lifetime temperature dependence is solely

due to the nonradiative temperature dependence. These results indicate that in order to

minimize the temperature dependence, the medium (binder) used must possess the lowest

possible activation energy for oxygen diffusivity.

Research Efforts

A paper by Puklin et al. (2000) examined a PSP probe, PtTFPP, embedded in

copolymer of heptafluoro-n-butyl methacrylate and hexafluoroisopropyl methacrylate

(FIB), possessing an activation energy of 1.5 kJ/mol, which satisfies the criterion set forth

in the previous work by Schanze et al. (1997) for low temperature dependence in PSP









(i.e., low activation energy). They introduced the concept of an "ideal" paint, which they

define as one for which the Stem-Volmer relation (intensity-ratio) under isothermal

conditions for the run and reference condition is approximately independent of

temperature, and the intensity ratio under isobaric conditions is approximately pressure

independent. In a simpler sense, any paint can be described as ideal if all the Stem-

Volmer plots for different temperatures collapse to a single curve under isothermal

conditions. Hence, an ideal PSP can be more conveniently corrected for temperature

dependency; however, this definition of ideality is applicable only for a limited

temperature range (Puklin et al., 2000). Ideality provides the ease of determining the

pressure value if both the temperature data and the intensity ratio under isobaric

conditions are known, thus decoupling temperature data from any pressure dependency.

Using a lifetime measurement approach under static conditions, they examined the dye

for different pressures between vacuum and atmospheric pressure under three

temperature conditions (100C 300C & 500C). Their results showed -0.6%/o C temperature

dependence in the PSP. In a follow-up paper, Gouin (2000b) investigated the feasibility

of achieving an ideal PSP by annealing the polymer. As they noted, annealing the paint

(PtTFPP) made the paint behave ideally with very small temperature dependence (-

0.52%/C) with an almost identical slope under vacuum and atmospheric pressure

conditions. They also found that non-annealed samples exhibit higher temperature

dependence with a varying slope between vacuum and atmospheric conditions (-

0.54%/C and -0.80%/oC respectively). The annealing process has to take place above the

glass transition temperature, Tg, of the polymer to achieve this ideal behavior. Heating a

polymer network above Tg has the effect of relaxing the chains, loosening the









entanglements in the network, and allowing the system to achieve thermodynamic

stability. This will ease oxygen diffusion through the polymer as the relaxation of the

network implies fewer entanglements leading to easier diffusion and lower activation

energy.

A third publication by the same group at the University of Washington (Gouin,

2000c) examined the effect of using a second base coat under the PtTFPP/FIB paint.

Such combination typically results in an increase in the response time and the

temperature dependence of the PSP. The accuracy of the PSP measurements depends on

many factors, one of which is the uniformity of the model surface, as the light emitted by

the PSP is not totally captured by the photodetector (CCD, PMT, etc.). A determinant of

how much light is captured by the photodetector is the intrinsic reflectivity of the model

surface. Reflectivity is defined as the ratio of reflected light intensity to incident light

intensity at the surface of a material that is considerably thick such that the reflectance is

independent of the thickness; thus commonly described as the intrinsic reflectance of the

surface. Surface reflectance is Lambertian (diffuse), Phong (specular) or a combination of

both. Ideal Lambertian surface apparent reflectance is independent of the observer; i.e.,

the object brightness is independent of the angle between the observer and the surface.

This contrasts with glossy surfaces, as the apparent brightness is highest when the

observing angle is equal to the source angle. Most real objects have some mixture of

Lambertian and Phong qualities. As models typically incorporate different materials on

the surface, ranging from the actual material of the model to wax and Bondo material,

variation of the reflectivity of the surface induces significant error accordingly. For that

reason, a uniform base, known as a base coat, is typically applied to the surface to create









a homogeneous canvas. A base coat is generally a polymer which is embedded with a

white substrate (pigments), e.g., titanium dioxide, which possesses a high index of

refraction and good dispersion in the polymer (high hiding power), but can sometimes

photoxidize organic compounds when irradiated with UV (< 390nm). Unfortunately, base

coats have been shown to influence PSP functionality. This is partially attributed to the

change of the dynamic oxygen equilibrium of the PSP layer as it interacts mutually with

the surrounding air as well as the base coat. The combination eventually reaches

equilibrium after a certain response time. The equilibrium process is directly tied to the

oxygen diffusion in the polymers. This effect is only imperative when performing high

frequency or transient measurements, as response time is important. The more prominent

effect is the apparent influence of the base coat on the temperature dependency of the

PSP layer, which in turn can potentially yield adverse affects to the desirable temperature

dependency characteristics, mentioned previously, of an ideal paint. They examined five

different base coats: FIB, polymethylmethacrylate (PMMA), polyacrylonitrile (PAN),

polyvinyl acetate (PVA) and a silicone (SR-900). Gouin et al., (2000c) found that oxygen

diffusion in the polymer is the main factor influencing the temperature dependency as

vacuum results were almost identical. Further, the oxygen concentration gradient that

exists between the base coat and the PSP layer is the reason behind the direct influence of

the base coat on the temperature dependency of the PSP, as different base coats would

hold different concentrations. Comparing permeable polymers (FIB and silicon base coat)

versus impermeable polymers (PMMA, PAN and PVA) showed significant increase in

both response time and temperature dependency at atmospheric conditions for the latter

polymers except for PAN; the results are tabulated below for convenience. Their results









assert the importance of choice of a specific base coat for each particular PSP.

Table 1-1 Response time and temperature dependency of PtTFPP/FIB with different base
coatings
Base-Coat Polymer Response time (sec) Temperature dependence@ atm.
(/oC)
No base coat 0.6 -0.52%
FIB 0.8 -0.56%
PMMA 15 -1.06%
PVA 7 -0.75% (-2% above 350C)
PAN 0.9 -0.7%
Silicone (SR-900) 1.1 -0.69%
(PVC) of 44 %

In Table 1-1 Pigment Volume Concentration (PVC) is defined as Gouin et al.

(2000c).


PVC 0 (mass ofpigment/density ofpigment) (1.5)
(mass of pigment/densiy of pigment) + (mass of binder/desiy of binder)

Their last publication in the series, (Gouin, 2000d), demonstrates how non-ideal

paints can be idealized through the addition of inorganic pigments. They show that the

diffusion of oxygen is affected by the addition of Opigments to the polymer and that the

decay rate behavior of the paint is affected as well; however, not all the quenching rate

constants were affected. They further noticed that a specific concentration of pigments

made the paint act ideally. Using fine grade (1-5 [tm) aluminum oxide (A1203) with

pigment volume concentration of 31% they were able to closely match the temperature

dependence of PtTFPP at vacuum, yielding an ideal paint. Again, it is important to note

that such ideality is pertinent to limited temperature ranges and isothermal conditions.

Woodmansee et al. (1997) investigated the issue of temperature dependence as they

examined three different PSPs and two TSPs formulations as well as four different

temperature compensation methods. The paint was applied to a transverse-jet-in-









crossflow experiment. As the behavior of the specific paint is not of relative importance

to this work and is well documented in their paper, reduction methods will be discussed

herein and only related paint behavior if needed. They compared four different reduction

methods: isothermal, in-situ, K-fit and temperature corrected pressure. The isothermal

approach, as implied by its name, ignores temperature variations by assuming that the

temperatures at run conditions are identical to the calibration run. The calibration

coefficients are obtained through a static calibration of a specimen and then fitting the

data in a least squares sense. This approach under-predicts the pressure as it ignores the

temperature drop due to the operation of the tunnel. On average, the isothermal

calibration had an 8.0%f.s. drop relative to the pressure taps measurements and 2.8%f.s.

root mean square (rms) deviation. Nonetheless, the predicted pressures mapped a similar

trend as the pressure taps, which makes such an approach good for qualitative purposes

only. However, this approach may be useful quantitatively if the run images have a

steady and identical temperature distribution, in which case the reference image must be

acquired immediately after the termination of the each run of the experiments.

The second approach, in-situ, accounts for the temperature variation by placing

pressure taps on the painted surface and using that pressure information to evaluate the

calibration coefficients. However, pressure taps need to be positioned in predetermined

locations to ensure the coverage of the entire domain of the pressure test range (i.e.,

lowest and highest pressure areas). To ensure this, a run test prior to installation of the

pressure taps with the surface painted may be necessary to obtain a qualitative picture of

the pressure field. Further, adequate numbers of pressure taps need to be positioned

through the intermediate range to secure acceptable accuracy in the results. The overall









results for this approach showed that the in-situ method had the smallest error of all

methods with 1.0%f.s. mean and 0.55%f.s. RMS differences.

A hybrid technique between the earlier techniques is the K-fit approach. It is

typically implemented when the model lacks enough pressure taps to cover a wide

enough pressure range. It relies on the fact that the pressure vs. intensity curves collapse

if the run and reference temperatures are both identical (i.e., isothermal). This of course

limits the experiments allowed by many constraints, such as air-flow speed, geometry of

the model, steady conditions, etc. Nevertheless, as mentioned previously, if a reference

(wind-off) image is acquired immediately after the run image, temperature variations

should vanish in the normalization process, unless temperature gradients are severe and

change significantly between the two runs. The K-fit approach empirically scales the

reference image to emulate a reference image at a different temperature condition. This

approach is better than the isothermal technique with a 4.7%f.s. mean and 2.7%f.s. RMS

differences, yet it is still inferior to the in-situ calibration approach.

The last examined technique, temperature-corrected pressure calibration, utilizes a

temperature sensitive paint (TSP) to calibrate the PSP measurements. The TSP is applied

to the model after PSP experiments and then the two images are aligned to sub-pixel

accuracy. Knowing the intensity ratio and the temperature at each pixel, a 2-D surface is

constructed with the pressure as a function of both intensity ratio and temperature. This

method eliminates the need for an in-situ pressure tap data. Unfortunately, the authors did

not have great success with this approach due to several predicted problems such as

photodegradation, shelf-life degradation and calibration surface effects. The authors

conclude by recommending a multi-step in-situ calibration.









Hubner et al. (1997b) suggested a temperature compensation model for PSP that

was rather successful. Their work was motivated by the lack of a generic model of

luminescent intensity in terms of pressure and temperature. They based their model on a

Stern-Volmer with an Arrhenius-type temperature dependency. In general, oxygen

sorption in an ideal and homogenous liquid is directly related to the partial pressure of the

oxygen as described by Henry's law, assuming equilibrium between the oxygen within

the binder and the oxygen above it:

[02] = s(T)P (1.6)

where s(T) is the solubility coefficient. However, as described by Hubner et al. (1997a),

over expanded pressure ranges the solubility coefficient depends on pressure as well,

[02= s(T, Po )Pi (1.7)

This leads to the redefining of the intensity-pressure calibration from equation (1.2) to

extend it to higher order polynomial expansion,


ef ( =A(T)+B(T) P +C(rT)p +... (1.8)
'run \ ef j Vef

For limited pressure ranges, a linear solubility model can be used to estimate the

pressure dependence. Large pressure ranges may be conveniently modeled with higher

order polynomials; however, polynomials do not always adequately model the intensity-

pressure relationship. This is a result of the uneven dispersion of luminophors in binders,

which leads to heterogeneous distribution of the luminophor within the binder causing

molecular aggregation and consequently self-quenching of excited probes and multiple

exponential decays (as opposed to single exponential decays for luminophors dissolved in

fluid solvent). Hubner et al. (1997a) proposed a model based on sorption theory to









compensate for these effects. For a given isotherm, the sorption model expands Henry's

law by adding a non-linear term based on Langmuir's model of penetrant immobilization,


[02]= s (T) Po, + ,, (T) P (1.9)
I(+)an(T)Po,

where s, is the linear solubility coefficient based on Henry's law, s,, is the non-linear

solubility coefficient based on Langmuir's model and a (T) is the affinity coefficient

absorption
( of penetrants). Taking the limit of equation (1.9) as the partial pressure of
desorption

oxygen goes to zero and infinity reveals a dual sorption (DS) model-equations


Sa[O2]
lim C = s + snIa (T) (1.10)



lim = s (1.11)
P02 8Po,

Application of the DS model to equation (1.8) yields the proposed model by Hubner et al.

(1997a),


'ref A+ B + C D) (1.12)
I, ^ 1+D (P/Pr

The coefficients (A, B, C & D) in this model are functions of both temperature and

reference conditions. The model was applied to two PSP coatings and their results

showed the superiority of their model relative to a second and even a third order

polynomial, with a pressure ratio root mean square error (rmse)of 0.0004 and 0.001 for

in-range and off-range data, respectively (PSP-A), which was also comparable to their

second dye (PSP-B). The concern with this model is the difficulty in decoupling the









temperature dependency of the sensitivity coefficients as a direct result of the added

nonlinear pressure terms, Hubner et al. (1997b). This created the motivation behind the

subsequent work of Hubner et al. (1997b), as they proposed yet another model based on a

Stern-Volmer with an Arrhenius-type temperature dependency. This model, unlike the

DS model, has coefficients that depend only on temperature formulated from the

radiative, non-radiative and quenching decay processes of the luminescence. They used a

quadratic to model the solubility expansion coefficient (i.e., PSP sorption). As they

describe in their paper, the radiative decay is almost temperature independent and hence

usually regarded as constant. On the other hand, the non-radiative decay is significantly

temperature dependent and is characterized by an exponential decay process in addition

to an offset that is temperature independent.


k = ko +De (1.13)

The oxygen quenching process is governed by the sorption and the diffusion of the

oxygen in the binder matrix, with Arrhenius type decay approximation over small

temperature ranges. This implies composite temperature dependence in Henry's law,

namely the product of the oxygen concentration in the binder, [02 and the Stern-Volmer

constant, kq, hence the total activation energy is the sum of the activation energies of

each process. Earlier in this review the work of Schanze et al. (1997) modeled the oxygen

process as a simple exponential mainly dependent on oxygen diffusivity and established

that oxygen quenching accounts for more than 90% of the total decay of the luminescent

probe they used. The final form of Hubner et al. (1997b)'s model is as follows:










=A+ B P +C (1.14)
I \ ref \ Pre

where,
En/
K r+K +D e RT I
A (T,Te f,Pef) ro nro nr(1.15)
d n (1.15)
den


BD De R~
B (,TfPre)=f De (1.16)
den


D q2e RT
T, r ref ,,) den(1.17)
J den


den = k, +k +D e R +D 1e RT +DqI R (1.18)

The first coefficient, A, represents the radiative and non radiative effects, while the

second and third coefficients, B and C, characterize the oxygen quenching process. The

coefficients are clearly a function of the run as well as the reference temperatures. The

activation energies, En, Eq, & Eq,2, the rate constants k, and the factors premultiplying

the exponential decay terms are to be determined by performing a standard emission-

lifetime calibration. These coefficients are functions of the specific luminophor properties

and binder characteristics. Nonetheless, as stated already, run temperature information is

still needed to evaluate the coefficients. Plotting these coefficients as a function of the run

temperature it was clear that the coefficient, A, was relatively temperature independent,

while the other coefficients are noticeably temperature dependent. The authors appeal to

the need for "dual-luminophor" paint, a paint containing two probes that measure

pressure and temperature simultaneously and independently, which would provide the

temperature information needed for calibration. Their model predicted the pressure with









rmse of 0.011 and absolute pressure uncertainty of 0.2 psi. Such high uncertainties in the

measurements may not be tolerable in many applications, moreover; their results were

based on 70 isotherms, underlining the difficulty in obtaining temperature corrections for

PSP measurements.

Given the various limitations and requirements for selecting a practical

combination of an oxygen sensor and a suitable binder, another proposed solution

included adding non-oxygen quenched temperature-dependent phosphor to the paint to

map out the temperature field and correct for temperature dependence. Coyle and

Gouterman (1999) attempted to correct for lifetime measurement using such an approach.

They defined a criterion for ideal TSP that can be co-embedded with PSP in a dual-

luminophor formulation. The TSP criterions are:

1. Excite in the same spectral region as the PSP
2. Emit at a sufficiently different spectral region
3. Exhibit strong temperature dependence
4. Exhibit no pressure dependence

The PSP sensor of their choice was platinum meso-tetra (pentaflurophenyl)

porphtyin (PtTFPP), which emits around 650nm, as for the temperature sensor they

utilized the phosphor La202S:Eu which emits strongly at 514nm (Struck, 1970), both

embedded in a (FIB) polymer. Both sensors are excited in the UV range, 337nm and

392nm for La202S:Eu3+ and PtTFPP respectively. The two dyes were prepared separately

and the temperature dye was sprayed first and allowed to cure overnight and then the

PtTFPP/FIB was sprayed on top of the existing film. Inspecting the emission spectra of

both dyes separately one can observe that the emission of the La202S:Eu3 overlaps with

the excitation and emission of the PtTFPP, which could potentially lead to spectral

interference. Maintaining a constant pressure field across the sample, but varying the









pressure between each run (0-latm.), the temperature emission was recorded and it was

completely independent of the pressure between the range of 10-50C with a lifetime

decay-to-temperature slope of 1.9%/ C and they were able to fit the emission to an

Arrhenius function, as predicted by the theory. Their temperature calibration yielded a

root-mean-square error of 1.11 C for 20 different data points. PtTFPP showed a lifetime

decay temperature dependence of -0.3%/C under vacuum conditions. To calculate the

pressure they used the following 2nd order relation:


P = ra j b +b j +c (1.19)


Implementing the previous equation as the calibration function to determine the

pressure and temperature for fifteen different environmental conditions, five pressures

and three temperatures, their results yielded a maximum absolute error of 3.0C, with the

error in the predicted temperature increasing with the increase of temperature. The

corrected pressure measurements had a maximum error of 4% and an average error of

about 1%, while the non-corrected data had a maximum error of 16%. The authors argue

that the difference between the emissions of PtTFPP and the combined dual-paint is not

due to the interference of the 615nm emission of the La202S:Eu3+ with the PtTFPP

emission, as they have observed La202S:Eu3+ emission at 625nm on the order of 400 ps,

while their observation of PtTFPP decay curves fit to a double exponential model did not

have a 400 ps component, yet they fall short of offering an alternative explanation.

Research at the University of Florida unquestionably indicates a change in the intensity

emission behavior of the PSP sensor with the addition of the TSP sensor; however, as our

results are based on intensity measurements compared to lifetime measurements approach









by Coyle and Gouterman (1999), the author desists from disputing their rationale.

In a paper presented by Ji et al. (2000) a temperature independent PSP based on a

bichromophoric luminophor was developed and tested. In contrast to prior work that

typically utilized metalloporphyrins or polypyridine rythenium (II) complexes as the

luminescent probes in formulating PSP, they used supramolecular assemblies.

Supramolecular assemblies are two or more luminescent chromophores that are

chemically bonded together (Balzani et al., 1991), they often posses photophysical

properties that are distinct from those of the isolated units. They used Ru-pyrene as the

luminescent probe utilizing its very long-lived exited state (Simon et al., 1997). As

illustrated by Hager et al. (1975a and 1975b), under vacuum conditions the radiative

decay for PSP complexes is typically temperature independent. Further, Van Houten and

Watts (1976) successfully characterized the general temperature dependence of the non-

radiative decay rate behavior for Ruthenium complexes with an Arrhenius function.

Under oxygen rich conditions, close to atmospheric levels, the radiative and thermal

(non-radiative) decay rates contribute insignificantly towards the overall decay rate

relative to the oxygen quenching. As described earlier in this review by Schanze et al.

(1997) this implies that under these conditions, the temperature dependence of the paint is

mainly characterized by the temperature dependence of the oxygen quenching decay rate

(i.e., oxygen diffusivity in the binder), which is also commonly characterized by an

Arrhenius type decay. Intermediate conditions between vacuum and atmosphere are

characterized by a composite PSP temperature dependence behavior of the two

previously mentioned states (i.e., vacuum and atmosphere). The probe's excited state

lifetime has moderate temperature dependence; nonetheless a nearly temperature-









independent Stern-Volmer calibration is coincidentally feasible under isothermal

conditions between the run and reference images (i.e., ideal paint). The Stern-Volmer

relation is expressed as:

lo (T p = 0)
(T= 1+M, Kp (M( ) (1.20)
I (T ) K(, P)

Differentiating this expression with respect to temperature and equating it to zero

would set the condition needed to achieve a non-temperature dependent Stern-Volmer

constant K Through some mathematical manipulation and assuming that Knr > Kr the


condition yieldsd- d 1, where E is the activation energy and subscripts d and nr refer to
Er

oxygen diffusion and non-radiative decay, respectively. In a simpler sense, if the

temperature dependence of the oxygen diffusivity in the binder and the temperature

dependence of the non-radiative decay are nearly identical (i.e., slope), then the paint can

be described as an ideal paint.

They attempted to incorporate the sensor in PDMS as a binder, but the sensor had a

poor emission, consequently they synthesized MPP acrylate polymer binder, which is

relatively polar, hence able to dissolve polar transition metal salts contrary to PDMS.

Subsequent to establishing the calibration curves and plotting the results, the Stern-

Volmer plots, for temperatures of (25-55C) over a pressure range of 0.005 atm to 1 atm,

coincided almost exactly, hence indicating that the Ru-pyrene/MPP Stern-Volmer

calibration is temperature independent over the specified range of conditions. They

reiterated the same examination using a different sensor, namely PtTFPP, with the same

binder MPP and the results showed that the temperature-independence Stern-Volmer

behavior is unique to the Ru-pyrene/MPP system. Finally, they examined the lifetime









emission (luminescent decay rate) to determine the activation energies for each sensor

under close to vacuum conditions and at 1 atm in order to separate the oxygen quenching

and non-radiative decay channels. The Ru-pyrene/MPP system had an equivalent decay

rate, which is synonymous to equivalent activation energies, thus verifying their

temperature-independence criterion stated in advance. On the other hand the

PtTFPP/MPP system had different activation energies. This work showed that ideal paint

formulations greatly hinge on the appropriate selection and matching of both the

luminophor and the polymer.

Another approach suggested in the literature is adding an environmental-

conditions-independent sensor that is embedded within the formulation of a dual-

luminophor PSP to provide an internal reference, thus replacing the wind-off image, and

using an intensity based approach to resolve the pressure and temperature. The feasibility

of such a concept was investigated by Subramanian et al. (2000 and 2001) where they

implemented a non-pressure sensitive paint (NPSP) sensor to utilize as a reference

sensor. As the paper points out, it is nearly always the case that when two sensors are

mixed together in the same paint matrix, spectral interference is inevitable. The sensor

emitting in the lower part of the spectrum could influence the excitation and thus the

emission of the other sensor emitting at higher wavelengths. This interference is very

hard to resolve and could lead to more error in the data in addition to the already existing

temperature dependence error. Theoretically, any added sensors to the PSP sensor should

be excited in the same spectral domain and emit at the same wavelength, in order to

eliminate multiple excitation sources and the need for a filter wheel on the camera, hence

limiting the available choices of sensors. This can be accomplished by means of one of









the following two methodologies. The same pressure sensor can be utilized except that it

would be embedded in an oxygen impermeable binder. This approach is impractical due

to the infeasibility of creating a completely oxygen impermeable binder, knowing that

any oxygen diffusion in the binder would certainly lead to serious errors. The second

approach is to utilize a sensor that is not quenched by oxygen and is temperature

insensitive. This necessitates that such a sensor emits at a different wavelength than any

other sensor embedded in the same paint matrix in order for it to be entirely

distinguishable from any other emission in the spectrum. The emission from this sensor

would then serve as the reference for each individual run and thus eliminating wind-off

referencing. Further advantages to such an approach include: the potential of using the

NPSP for correcting temperature dependence if it was possible to match the temperature

effects of both PSP and NPSP, and the NPSP can be used as a target-marker for model

deformation determination during wind-tunnel testing.

Subramanian et al. (2001) avoided mixing the two sensors together, instead they

applied the paints separately on different parts of their test specimen (disk) with a dark

ring separating both dyes, conceivably to avoid spectral interference; nonetheless, such a

compromise may not be always tolerable. They used six different combinations of PSPs,

PSP binders, NPSPs and NPSP binders. The environmental range in which they

conducted their experiments ranged between 0.001-2.7 atm and from 15-35C. Their

results conclude that at constant temperature the NPSP was reasonably invariable with

the change of pressure and that the PSP had an order of magnitude higher rate of change

with pressure. However, upon imposing a temperature gradient on the specimen, there

was an obvious variation in the calibration curves, due to the inhomogeneity of the









temperature dependence between PSP and NPSP sensors. The PSP showed temperature

dependency even under isothermal conditions for the run and reference intensities. This

fact forced them to concede the infeasibility of their approach to correct for temperature

dependence. They further investigated whether a spectral cross-talk exists between the

two luminophors by eliminating the dark ring and it was not evident in some

formulations, but it was significant in other formulations; nevertheless it was minimized

when a dark ring separated the two luminophors. They observed spectral leakage when

the NPSP and the PSP had the same luminescent probe embedded in a different binder,

non-oxygen and oxygen permeable binder, respectively. However, they affirmed that

none of the binders were absolutely oxygen impermeable.

The department of chemistry at the University of Washington, Khalil et al. (2004),

has collaborated with Innovative Scientific Solution Inc. (ISSI) and presented a paper in

which they did similar work to that of Subramanian et al. (2001). Khalil et al. (2004)

point out in their paper that internal reference methods avoid several problems that arise

with intensity measurements such as light source changes, index of refraction, optical

geometry variations and fluctuations in film thickness and dye concentration. They based

their experiment on a technique called the yardstick, which is in essence similar to having

two sensors, one of which is affected by a specific factor, e.g. pressure, while the other is

independent of that factor. The latter then serves as a reference for corrections. For that

they experimented with a near infrared porphyrin sensor, namely platinum tetra

(pentafluorophenyl) porpholactone PtTFPL. The sensor emits around a distant 733nm,

allowing for another reference dye to be added without the concern of spectral

interference. The reference dye of their choice was magnesium tetra (pentafluorophenyl)









porphine (MgTFPP), which luminesces at 650nm. The two sensors were dispersed in a

FIB polymer, taking advantage of its relatively low temperature dependence effects and

its consistent temperature dependence at vacuum and atmospheric conditions. In their

experimental setup, both dyes are excited at 460nm + 10nm, with two CCD cameras

equipped with the appropriate filters capturing the intensity emission. Their

environmental operational range spanned temperatures between 5 and 50C (the ideal

range in which the PSP/FIB behave ideally) and a pressure ranging from 1 to 21 psi.

Their results show that the pressure sensor and the reference dye exhibit temperature

dependency. Nonetheless, by taking the ratio of the reference sensor to the pressure

sensor they were able to reduce the temperature dependency to -0.1%/OC, which is a

significant reduction from 0.6%/Cfor the PtTFPP embedded alone in the FIB polymer.

As they concede in their work, these results would be close to unattainable if there was

any spectral interference between the two sensors, thus limiting the pool of

sensor/reference/binder candidates available. Furthermore, these results are limited to a

specific temperature range which imposes further limitations on testing conditions. In a

subsequent work, Zelelow (2003), they replaced the reference sensor with a temperature

sensor, namely tri (P-diketonate) phenanthroline europium (Eu chelate complex), which

is virtually an oxygen independent sensor that emits around 615 nm. The results closely

matched their previous work with the temperature sensor providing the potential to

resolve temperature gradients as small as 0.001C. However, the luminescence intensity

temperature coefficient for PtTFPL increased to 0.33%OC. It is further noted the cost of

the material used in synthesizing both of their coatings is rather expensive relative to









other available systems. They applied their formulation to an automotive model,

Gouterman et al. (2004), and their results yielded an rms of 0.06 psi for the in-situ

calibration. As the TSP has -0.25%/oC temperature sensitivity, they were able to reduce

the temperature sensitivity of the PSP from -0.32%/oC to -0.07%/oC. However, they

assess that the corresponding 33% percent improvement in temperature correction

(reduction in rms) is below expectation for such reduction in the temperature sensitivity.

They did not provide actual quantitative estimates of their error, nonetheless, their Cp

figure shows certain discrepancies between predicted and actual measurements. Their

formulation suffered from considerable photodegradation (0.5%/hour at 1 bar and 400C).

Their approach shows potential for dual-luminophor PSP to resolve the temperature

dependency issue, and a more robust data reduction and analysis technique would

optimize results.

Similar work presented by Mitsuo et al. (2003) utilizes a temperature sensitive dye

for temperature compensation in dual-luminophor PSP. The temperature probe of their

choice was Rhodamine B (RhB), which absorbs in the UV range and has a broad

emission starting at 550 nm and extending to 750 nm, with peak emission around 580

nm. The PtTFPP peak absorbance overlaps with the tail emission of RhB, which couples

the PtTFPP emission with the RhB emission. This phenomenon is known as cross talk,

which makes decoupling pressure and temperature information from the spectral

emission fairly complicated. They modeled the temperature by a fourth order polynomial

and the pressure by a third order polynomial. By first compensating for the temperature

effects in the emission intensity of the PtTFPP using the wind on temperature information


1 Personal communication with Kose









and information from the PtTFPP calibration curves, they estimated pressure calibration

coefficients that are temperature independent. The pressure standard deviation was

around 6%f.s., while the temperature estimates incurred a 1.5 K error. Once more,

resolving spectral interference using simple calibration procedure has proven to be

insufficient for accurate results, and the need for a more profound mathematical approach

is inevitable.

Compensating for the temperature sensitivity in PSP using a co-embedded TSP

falls under two categories, compensation using absolute temperature measurements, or by

matching the temperature sensitivity of the PSP (Goss et al., 2005). The later is obviously

more convenient; however, it can only be applied to ideal paint measurements as ideality

indicates that the paint possesses constant temperature sensitivity. Non-ideal paints have

variable temperature sensitivity; hence absolute temperature information is needed for

practical measurements. PtTFPP embedded in FIB, as mentioned previously, is classified

as an ideal paint, thus most functional dual-luminophor systems employ it as the pressure

probe.

A question that is recurrently raised when using luminescent coatings is whether to

use intensity based systems or a lifetime decay approach. Hardil et al. (2002) asserts that

intensity based systems are quite complicated due to the added excitation sources, wind-

off image and filtering system. They offer an alternative approach in which they have

formulated a new oxygen-permeable sol-gel-based paint, containing both temperature and

pressure luminophors. The fluorescence decay times of the two luminophors are

separated by several orders of magnitude, which allows for the luminescent decay

measurement to be separated in the time domain. In addition the two luminophors have









been chosen such that they have similar excitation and emission spectral regions to avoid

multiple filtering regions and multiple excitation sources; hence image registration issues

are completely avoided. Gouterman et al. (1997) explains the difference between the life

time approach, adapted by Hardil et al. (2002) and intensity based approach, more

commonly implemented and is the adapted technique in this work. The lifetime is an

intrinsic property of the luminophor, which, unlike intensity, is virtually independent of

external perturbations; hence the requirement for a wind-off image is eliminated.

Nonetheless, lifetime is still dependent on temperature and hence a correction is still

required. Gartenburg et al. (1991), attempted to solve the problem by implementing an

additional infrared camera to provide a temperature correction for the pressure. Others

(Alaruri et al., 1999 and Coyle and Gouterman, 1999) added an additional temperature

sensitive luminophor to provide the temperature data for correction, which still required

added cameras, excitation sources and filters. Hardil et al. (2002) approach follows

previous work done by Bedwell et al. (1998) with the exception that they implement an

array of LEDs rather than a laser for excitation. In addition, the work is specific for sol-

gel-paints, [Ru (dpp) 3]2+. It is worth mentioning that the intensity ratio, defined in


equations (1.1) and (1.20), is equal to the lifetime ratio, except that the absolute value
Z-

of the reference and run lifetimes are independent of external perturbations. Hardil et al.

(2002) lists three conditions for an ideal temperature luminophor:

1. It has the same excitation wavelength as the PSP luminophor
2. It is completely insensitive to oxygen
3. Has a significantly different decay time compared to the PSP luminophor









Most two and three-component systems that have been developed satisfy the first

two conditions, while the third condition is a disputed topic. The question then is how do

the two measurement systems compare to each other? Unlike the intensity based method,

lifetime approach requires that both the excitation source and CCD camera be triggered

with a delay shift between them, otherwise the CCD camera may incorporate extraneous

light from the excitation source. This introduces complications into the control system,

especially when decay times could be on the order of nanoseconds, and error could be

easily introduced in the system if extraneous light is leaked into the measurement, which

could be hard to detect as well. Not to mention the degree of sophistication required in

the CCD camera in order to be able to handle such short exposure times. Furthermore, for

each condition, different exposure time for different triggering cycles, usually on the

order of 300 cycles, is required and need to be integrated in the same image frame. Other

complications rise from the fact that in such a process, it is always assumed that the

luminescence from the excitation source is absolutely constant and that the PSP

luminophor decays to zero during the excitation sequence. The latter is not an issue for

the intensity based system, while the effect of the drifting of the excitation source is not

as nearly as significant compared to the lifetime system. As reported by Hardil et al.

(2002), due to this drifting effect, their SNR was low enough to induce a temperature

error of 3C.

Proper Orthogonal Decomposition (POD)

POD, also known as the Karhunen-Loeve expansion after Kari Karhunen and

Michel Loeve, is a classical statistical technique that is often implemented to

simplify/decompose a dataset. First introduced by Kosambi (1943), POD is a method of

identifying patterns in data, and expressing the data in a certain least squares optimal









sense. Data patterns are often hard to identify, especially in dataset of high

dimensionality, where graphical representation is unfeasible. It makes possible the

reduction of multidimensional systems to lower-dimensional approximate descriptions

(Chatterjee, 2000). Implementations of POD are mainly in dynamic testing, image

processing, signal processing, and general data compression. Practical applications

include identifying coherent structures in turbulence, vibration analysis, astronomy,

combustion analysis, and chemical substance identification, to name a few.

POD entails a mathematical procedure that transforms a number of potentially

correlated variables into a smaller number of uncorrelated variables known as principal

components. The first principal component forms an axis that accounts for the largest

variance in the data, and each succeeding component accounts for as much of the

remaining variability as possible. From a purely mathematical perspective, it is a linear

transformation that chooses a new coordinate system for the data set such that the greatest

variance by any projection of the data set comes to lie on the first axis, the second

greatest variance on the second axis, and so on. In simpler terms, it provides a spatial

basis for the modal decomposition of a system of functions. It enables the extraction of

basis functions commonly called eigenfunctions. Quintessentially, it is an efficient

procedure that captures dominant components of multidimensional systems and then

reconstructing the system to the desired precision by using the relevant set of modes,

effectively reducing the order of the system. POD entails two main objectives: the

reduction, sometimes even characterization of the dimensionality of the dataset and

recognition of fundamental factors (e.g. coherent structures in turbulence, exhaust

gaseous compositions, etc.).









A key advantage of POD is its ability to generate an "abstract" modal

decomposition that is data dependent without any prior understanding of the process

yielding the data. This enables the extraction of the principal factors where a priori

knowledge of the driving potential is insufficient to guide the basis function selection

(Rathinam and Petzold, 1993). Moreover, unlike traditional linear transforms, POD does

not have a fixed set of basis vectors; rather its basis vectors depend on the data set. This

means that POD can be used for reducing dimensionality of the dataset without altering

the key characteristics of the dataset that contribute most to its variance by eliminating

the relatively less significant components.

POD is often confused with one of its sub-processes, namely Principal Component

Analysis (PCA), which identifies the process by which raw eigenfunctions are

established. The details are provided in Chapter 3, nonetheless it is sufficient at this point

to note that POD involves more than the basic extraction of the modal factors, it further

works to transform this abstract solution to physically significant solution; however, this

transformation then involves an intuition or "feel" for the expected reduced modes.

A paper published by Carroll et al. (1999) explored the idea of using POD to

separate the pressure and temperature information as well as for temperature

compensation of the pressure calibration functions of measurements from dual-

luminophor coatings. As stated previously, two main problems emerge with dual-

luminophor systems: spectral interference between the two probes and cross talk between

the two probes (i.e., emission overlap and absorption of emission of the lower wavelength

probe by the higher wavelength probe, respectively). As described previously, any

spectrum contains different variations embedded into it; nonetheless, one should be able









to account for a finite number of independent parameters that constitute the spectrum

(Carroll et al., 2002). These independent parameters would vary in the magnitude and

range at which they contribute to the spectrum, hence allowing us to extract the main

parameters that form the spectrum and easily separating each parameter and identifying it

with a physical parameter that we are interested in. Once these components are obtained a

new spectrum is constructed which contains the direct contribution of such parameters of

interest omitting extra factors that may well be of no interest or inherently unwanted

contributions such as noise. The process simply hinges upon finding the eigenvectors and

eigenvalues of the data matrix. Once these are established, the eigenvalues are compared

and the largest n number of eigenvalues and their corresponding eigenvectors are used

only to reconstruct the spectrum. The number of eigenvectors selected depends on two

aspects: how many factors one expects to be the main contributors and the relative

expected ratio between the smallest eigenvalue, the factor with the least contribution and

effect, to the largest eigenvalue. These criterions depend on the application and the

degree of accuracy desired in the reproduced spectrum. A thorough description of the

mathematical analysis is presented in Chapter 3 and the reader is encouraged to read

through Malinowski et al. (2002) for a full and comprehensive mathematical derivation

and explanation of POD.

Carroll et al. (1999) selected two luminophors such that one is purely temperature

dependent while the other is both pressure and temperature dependent. The full spectrum

was collected through a spectrophotometer for constant temperature and varying pressure

and vice versa, to ensure the behavior of each dye. They analyzed the full spectrum using

the POD and yielded the need for three factors to accurately reconstruct the raw spectra









and to compensate for mutual interactions between the two luminophors. They managed

to restrain the average percent error in the retrieved environmental conditions to within

2%. However, the work did not perform the analysis on a discrete set of data (using CCD

camera), and they performed basic orthogonal rotation. The work presented initial

characterization of POD, however, it stopped short of fully evaluating POD application to

dual-luminophor paints by applying it to various coatings with different compositions and

implementing a real case experiment where more involved data are obtained. In a

subsequent paper Carroll et al. (2001), reiterated their application of the POD analysis to

the same dye (Ruphen/Coumarin-7) they experimented with before and a new

dye/polymer coating, namely PtTFPP/Diethyloxadicarbocyanine iodide (DOCI). They

concluded that unlike the Ru system, the PtTFPP/DOCI data can be adequately

represented with only two factors. However, their calibration curves for the DOCI

showed some temperature dependence and they limited their calibration functions to a

one-dimensional function. Further, they did not explore non-orthogonal rotation or

surface rotation. Their pressure calibration yielded a percentage error between 0.32% and

1.3%. Nonetheless, they established the potential for POD to serve as data reduction

technique for dual-luminophor PSP paints.

Kose (2005) developed a dual-luminophor system (PtTFPP-Ru(phen)/PAN /Poly-

tBS-co-TFEM) which was successful in providing accurate pressure and temperature

information implementing POD to resolve the data. Mathematical characterization and

implementation of the POD was developed by the author and the calibration was

collaboratively performed yielding very low error estimates of pressure and temperature.

The main objective of the work was to formulate a successful dual-luminophor system









and to perform static testing to assess potential success in wind tunnel testing.

Motivation and Contribution

Pressure sensitive paints have been gaining acceptance in the practical market of

aerodynamic testing; however, the technology is still short of being easily and universally

applicable due to several difficulties that require resolution for the technology to reach its

full potential. The full scale and practical implementation of dual-luminophor PSP

technology is hindered to a great extent by the inherent temperature dependence of the

paint. Aerodynamic testing can involve unavoidable and considerable temperature

variations over the surface of the model and successful PSP implementation hinges on

eliminating temperature effects that induces error in pressure field measurements.

Various efforts have been addressing the issue in pursuit of satisfactory resolution

including: PSP coatings with low temperature dependence (Gouterman et al., 1997),

various mathematical error reduction and calibration models (e.g. isothermal and K-fit)

(Hubner et al., 1997a; McLachlan et al., 1993; Woodmansee et al., 1997), simultaneous

TSP imaging to provide a pixel-by-pixel temperature compensation (Woodmansee et al.,

1997), adding an environmentally independent sensor to replace wind-off reference

(Subramanian et al., 2000 and 2001) and most promisingly a TSP luminophor that is co-

embedded in the same binder with the PSP in a dual-luminophor system.(Coyle and

Gouterman, 1999; Khalil et al., 2004; Mitsuo et al., 2003 ; Zelelow et al., 2003).









Table 1-2 Research effort treating PSP temperatui
Calibration Advantages
technique
In situ isothermal The simplest
calibration: Acquire approach
wind-off images at Suitable for
atmospheric isothermal conditions
conditions


In situ calibration:
Acquire wind-off
images immediately
after wind-on
conditions


A priori calibration *


Easy technique
Temperature effects
absorbed in
calibration
coefficients







Few pressure taps
scattered over the
model are needed
More controlled
environment for
calibration
More efficient for
practical applications
(less time spent in the
wind tunnel)


re effects
Disadvantages


* Temperature effects can not be
accounted for
* Calibration R.M.S. error on the order
of 1.25 psi for PtTFPP/FIB (Bell et
al, 2001), with pressure range of 29
72.5psi.
* Calibration r.m.s. error on the order
of 0.2 psi for ODU PSP
(Woodmansee et al., 1998), with
pressure range of 1 15.4psi.

* Need to ensure temperature stability
* Wind tunnel must be turned off
* Limitation on number of images that
can be acquired for reference
condition, especially for long
exposure times, due to temperature
drift from wind-on conditions.
* Significant temperature variation
between different parts of model
require local calibration and pressure
taps
* Separate experiment for calibration
in required
* Need to have a prior knowledge of
expected pressure and temperature
levels in the experiment to optimize
the calibration process
* Pressure taps need to encompass the
pressure range, and hence any sharp
pressure gradients could be
unobservable
* Temperature information must be
obtained on the model using TSP
(symmetric models with symmetric
flow conditions). Asymmetric
models or flow conditions can be
mapped for temperature using dual-
luminophor systems
* Same batch of paint must be used for
both calibration and experiment
* Calibration functions are typically
biquadratic in pressure and









Table 1-2 Continued
Calibration
technique


Advantages


Disadvantages


temperature (Bell et al., 2001),
necessitating a minimum of 9 points
of calibration points with both
pressure and temperature
information
Calibration r.m.s. error on the order
of 0.021psi for OPTROD PSP (Bell
et al., 2001), with pressure range of
0.75 14.7psi


Ideal paints: Hybrid
technique (K-fit
calibration)









Separate
temperature
measurement using
IR camera




Separate
temperature
measurement using
TSP


* Simpler than a priori
calibration (only one
temperature condition
is calibrated for a
priori)
* Useful for ideal paints
when extrapolation
beyond pressure taps
range is needed
* Superior to in-situ
isothermal calibration
* Non-intrusive
* Reasonably accurate
(standard uncertainty
of 0.202 psi) given
high temperature
gradients


* Calibration procedure
is simple
* Only two filters are
needed
* In situ calibration,
hence less cost
* No chemical
interaction between
P/TSP and no spectral
interference


* Inferior to in-situ calibration
* In some experiments, the K factor is
pressure dependent, yielding a more
complicated calibration
* Calibration r.m.s. error on the order
of 0.99 psi for ODU PSP
(Woodmansee et al., 1998), with
pressure range of 1 15.4psi.



* Ineffective for Mach number less
than 0.75 (Kammeyer et al., 2002)
* Multiple cameras required to cover
all surfaces
* Increased processing time
* Added uncertainty due to the IR
camera system

* Limited to symmetric models and
conditions
* Thickness and roughness ofPSP and
TSP are difficult to match, hence
surface flow conditions are typically
different.
* PSP uncertainty limited by TSP
uncertainty
* Thermocouples needed for TSP
calibration









Dual-luminophor systems have suffered from spectral interference and cross-talk

problem that yielded high errors in measurements and difficulties in the calibration

process. POD technique, first implemented to dual-luminophor systems by Carroll et al.

(1999), showed the potential for resolving such issues mathematically. Nonetheless, full

characterization and application of POD to paint systems is yet to be carried out that

would present a better understanding of the mathematical process and relate it to the

physical properties of the paints, hence allowing for optimal optimization and resolution

of the data. Furthermore, a real-case test application of the paint would serve to validate

both the paint formulation and the analysis process and to further address the various

issues associated with acquiring measurement with dual-luminophor paints under flow-

based conditions.

A successful dual luminophor system has been developed by the Schanze group at

the University of Florida (Kose, 2005), using the formulation PtTFPP-Ru(phen)/PAN

/Poly-tBS-co-TFEM. The paint has been calibrated and tested in collaboration with the

author under static condition (vacuum chamber), and POD method has been applied to

correct for temperature effectively. POD was capable of separating the pressure and

temperature information with pressure and temperature 95% confidence error estimates

of 0.1 psi and 0.4 K, respectively. Full characterization and application of POD to paint

systems is essential in order to completely understand the mathematical process and

relate it to the physical properties of the paints, hence allowing for optimal optimization

and resolution of the data. Most importantly, full assessment of POD as a calibration

technique is needed and a comprehensive analysis including uncertainty estimates would

establish the feasibility of POD a calibration technique.






45


A channel flow experiment is utilized to evaluate the paint. The channel flow

experiment provides a well controlled environment with existing analytical

solutions/approximations. A temperature gradient will be imposed both along and/or

across flow direction to simulate several cases of boundary conditions. The overall

accuracy and uncertainty analysis will be assessed to evaluate POD as a calibration

technique. Further, other calibration techniques are discussed and compared, when

possible, to examine the effectiveness of POD relative to existing calibration techniques.














CHAPTER 2
LUMINESCENT COATINGS

This chapter presents a fundamental description of pressure and temperature

sensitive paints and the process of acquiring measurements and reducing and processing

intensity data. The information presented herein is intended for readers acquainted with

the subject. More detailed discussion and information is provided in Appendix-A.

Overview

Resolving the pressure and temperature fields is a typical requisite in nearly all

experimentation in the field of fluid mechanics and aerodynamic testing. Surface pressure

information is imperative in characterizing various flow phenomena from boundary layer

separation/reattachment and shear layers to shock wave impingement on surfaces. It is

further employed in computational fluid dynamics (CFD) validation and perhaps more

commonly in calculating the various aerodynamic loads such as lift, drag, wing torsion,

etc. Temperature measurement is vital in supersonic and hypersonic flows and in flows

involving significant heat transfer. Typically, holes are drilled in the surface to allow for

pressure taps and thermocouples in order to measure pressure and temperature,

respectively. Such practice could compromise the structure of the model, the flow field,

the accuracy of the measurements or the overall practicality of the experiment.

Furthermore, the resolved field is only a discrete representation of the full field true

distribution and hence an interpolation, or yet worse an extrapolation, procedure is

required to resolve the full field leading to added inaccuracies in the data.










The Ozone Accident

While working on a an experiment intended to measure the rate of photolysis of

ozone in the atmosphere at the University of Michigan chemistry laboratory R.R.

Dickerson stumbled on an idea that was destined to inspire a new field for flow

measurement (Dickerson and Stedman, 1979). As they were in the midst of running the

experiment, some ozone seeped out and streamed over a black light poster (UV sensitive

fluorescent screen) that was illuminated by mercury lamp (i.e., UV radiation). The

streaming ozone induced an illusion of smoke plumes, which left the poor chemists

scrambling for the source of the fire puffing the smoke. A short-lived thrill is broken by

the realization of Dickerson that the plumes are simply the "shadow" of the ozone over

the black poster. The ozone absorbed some of the UV radiation as it passed over the

black poster and hence lesser light intensity illuminated the black poster, thus lowering its

emission intensity. At the time, helium bubble flow visualization techniques seemed

fascinating, and smoke and density change techniques were nothing short of a scientific

marvelous. Compared to these techniques, ozone was superior in many aspects, from its

excellent tracing properties to its relative inexpensiveness to its character as a non-

intrusive technique. There is just only problem with ozone; it is totally invisible to the

human eye, which might raise some eyebrows of skeptical experimental aerodynamicist.

Dickerson's observation surely provided a resolution to the issue, but more importantly, it

inspired two biomedical engineers at the National Institutes ofHealth, Maryland to

develop a new flow visualization technique based on oxygen quenching of fluorescence

(Peterson and Fitzgerald, 1980).

John Peterson and Raphael Fitzgerald founded the field of flow measurement









techniques using luminescent coatings. The diminution of phosphorescence of

luminescent dyes in the presence of oxygen was first discovered by Kautsky and Hirsch

(1935). Luminescent molecules that are strongly quenched by oxygen are typically

simple aromatic compounds and are easily exited in the longer wavelengths of UV range.

The concern is their emission range and intensity. Luminescence in the visible range of

the spectrum is desired for practicality and well distinguishable emission from excitation

is required for accurate measurements. Peterson & Fitzgerald used Fluorescent Yellow

dye adsorbed on silica particles for their measurements, which has an excitation peak at

466 nm and emits strongly at 519 nm. Their technique measured flow patterns

qualitatively and was rather simple; nonetheless, it established the potential for the

technology.

Few years after the publication of Peterson and Fitzgerald (1980), several research

groups started developing paint systems and research advancements increased steadily.

Among the most successful groups is the Gouterman group at the University of

Washington (UW). They developed an oxygen-quenching porphyrin probe for oxygen

concentration detection in blood that was rather successful. They managed to implement

the technology qualitatively but effectively in pressure measurements on aerodynamic

models by the late 1980s. The first quantitative measurements took place in the summer

of 1989 at the National Aeronautics and Space Administration (NASA) Ames Research

Center using the UW coating (Kavandi et al., 1990; McLachlan et al., 1993; Gouterman

et al., 1997).

On the other side of the northern hemisphere, Soviet scientists were concurrently

carrying out similar research. As early as the late 1970s, Soviet researchers at the Central









Aero-Hydrodynamic Institute (TsAGI) explored the possibility of using oxygen-

quenched luminophors for pressure measurements in wind tunnel testing. Theoretical

work initiated by Zakharov in the 1960s inspired two brilliant researches, Pervushin and

Nevsky, to develop the first PSP formulation by 1981, which they successfully used to

obtain initial experimental results merely a year later (Ardasheva et al., 1985). By the mid

1980s another group at TsAGI developed an original polymer-based PSP formulation and

tested it in supersonic flows using a lifetime approach (see following sections). High

temperature sensitivity of the PSP was the main drawback of their new system. Research

continued with a shift towards intensity-based approach (see following sections), which

led to a more practical system that was later commercialized by the Italian company

INTECO (Volan and Alati, 1991). After a long period of ignorance and misrecognition

by the Western research community, the early 1990s revealed the Soviet advancement,

then former USSR, through a commercial advertisement in the 1990 February issue of

Aviation Week & Space Technology.

The work of TsAGI was demonstrated experimentally by Deutsche

Forschungsanstalt fur Luft- und Raumfahrt e.V. (DLR) in Germany in January of 1991.

Using intensity-based method, pressure field measurements using the TsAGI coating in

the high speed wind tunnel facility in Gottingen were acquired on a cropped delta wing

model. The results were validated by pressure taps and oil flow visualization techniques

in addition to temperature variations on the model surface (Engler et al., 1991). The paint

was calibrated in a priori method and error estimated for the paint from temperature

dependence was reported to be less than 0.3% per degree by TsAGI. The paint layer

experienced local temperature gradients less than 3C, while the overall temperature









increased by as much as 120C. The temperature was acquired through an infrared camera

and just three thermocouples. They observed an increase in the pressure standard

deviation following the application of the paint. They experienced significant errors in

their pressure estimates due to curvature effects that caused uneven reflection from the

surface to the photodetector, which could have been accounted for by taking a reference

image. However, the paint results were provided by INTECO and it appears that

calibration and data processing techniques were still premature. Volan and Alati (1991)

further elaborated on the TsAGI system and compared calibration techniques (see

calibration section). At this point it is sufficient to state that a calibration procedure is

necessary for the paint involving the establishment of a relation between the property

under investigation (e.g. pressure) and the captured illumination of the paint,

accommodating different variables affecting the calibration, such as temperature

dependence and illumination degradation. Moreover, error estimates greatly depend on

the calibration technique, which in turn depends on the experimental setting (i.e.,

temperature variations/local gradients between run conditions, model movement, paint

composition, etc.); hence, the degree of accuracy desired in the data is what eventually

dictates the extent and complexity of the calibration procedure.

The 1990s brought prosperity to luminescent luminophor technology in wind

tunnel testing. Major companies and organization competed to implement and further

develop the technology to their advantage. Industrial institutions such as NASA, Boeing

Seattle, Boeing St. Louis (formerly McDonnell Douglas), British Aerospace in the United

Kingdom, Office National d'Etudes et de Recherches Aerospatiales (ONERA) in France,

National Aerospace Laboratory (NAL) in Japan, Deutsche Forschungsanstalt fur Luft-









und Raumfahrt e.V. (DLR) in Germany are among the main industrial implementers of

the technology. Academic research is encouragingly growing and has increasingly spread

to many educational institutions around the globe. The University of Florida (UF),

Purdue University and UW are among the leaders in current research advancements.

The Structure

Luminescent coatings contain a sensor molecule that is embedded in a transparent

oxygen-permeable polymer binder, as in the case of Pressure Sensitive Paint (PSP), or

oxygen-impermeable polymer binder, as in the case of Temperature Sensitive Paint

(TSP), both of which can be dissolved in a vaporizable solvent and then sprayed on the

surface, with a diffusely reflecting base underneath (i.e., primer) as shown in Figure 2-1.


0
O O0 Oxygen O
Excitation 0 0 oxygen Emission


Luminph 0 0 0 0 0 00 0 Binder


NB- ase Coat


Surface

Figure 2-1 Coating Structure

These coating luminesces proportionally with pressure and temperature levels when

excited by electromagnetic radiation (light) of appropriate energy (i.e., wavelength).

More accurately stated, the illumination of the coating is rather quenched by pressure

and/or temperature. The illumination is then captured by a photodetection device, such as

a charge-coupled device (CCD) camera or a photomultiplier tube (PMT) after passing the

emission through appropriate filter(s) to separate the various regions of emission in the









spectrum. A typical absorption and emission spectrum for PtTFPP/FIB is shown in

Figure 2-2.



1.5E+05
-1
0.8 1"
1.OE+05
S0.6
Z-1

I 5.0E+04 0.4
W 0.2

0.0E+00 0
350 450 550 650 750
S(nm)
Figure 2-2. Typical Absorption (left) and Emission (right) vs. Wavelength for PtTFPP in
fluoroacrylic polymer binder (PtTFPP/FIB). (Bell et al. 2001).

Paint Chemistry

This section details the photophysical processes driving the luminescence of

luminophors. Fundamental issues and concerns that arise and unfavorably affect the

luminophor emission are identified and addressed. Further, this section states the

selection characteristics for each component of the paint system and the selected

components for the dual-luminophor system implemented in this work.

The Photophysics

According to quantum theory, the electromagnetic energy is transmitted in discrete

amounts (i.e., in units or packets) called quanta. A quantum of electromagnetic energy is

called a photon. The energy carried by each photon is proportional to its frequency. An

atom or molecule of a substance usually does not emit energy; it is then said to be in a

low-energy or ground state. When an atom or molecule in the ground state absorbs a









photon, it is raised to a higher energy state, and is said to be excited. The substance

spontaneously returns to a lower energy state by emitting a photon with a frequency

proportional to the energy difference between the excited state and the lower state. In the

simplest case, the substance will return directly to the ground state, emitting a single

photon with the same frequency as the absorbed photon.

Luminescence is often used to describe the cold emission of electromagnetic

radiation at a different wavelength than that at which it is absorbed. Luminescence is

triggered by the movement of electrons within the substance from higher energy levels to

lower energy levels (i.e., deactivation). Luminescence can initiate through various paths,

from simple oxidation of the substance to complex processes such as chemiluminescence

carried out by living organisms (e.g. Fireflies) in which chemical reactions induce

luminescence. In the scope of pressure/temperature sensitive paints, luminescence is

more accurately referred to as photoluminescence. Photoluminescence is the

instantaneous emission of light from a substance under the influence of optical excitation

(Gfroerer, 2000). As a luminescent molecule absorbs a photon of light a molecular

photoluminescence (fluorescence and phosphorescence) radiative phenomenon follows.

Fluorescence is a process that occurs when an electron in a molecule transitions from the

lowest singlet state to the singlet ground state. While phosphorescence occurs when the

electron transitions from the lowest excited triplet state to the singlet ground state. Unlike

fluorescence, phosphorescence is a delayed emission with a longer lifetime and

wavelengths (Liu et al., 1997). Upon excitation an electron transition to a higher energy

level, however, there are only two permitted states: The singlet state and the triplet state.

At the excited singlet state an electron would posses more energy relative to an excited









triplet state. Furthermore, it is more probable for an electron at the singlet state to transit

to another singlet state than to a triplet state (intersystem transition). Hence, after a

molecule that is initially in the singlet ground state absorbs a photon it will most likely

convert to an excited singlet state. Within picoseconds, the excited state relaxes to the

lowest singlet state, without emission of radiation, through internal conversion. The

remaining energy in the lowest singlet state may then be dissipated via radiation or

through various radiationless mechanisms, such as thermal and oxygen quenching.

In view of that, a luminescent molecule of an environmental sensor absorbs light

and becomes electronically excited to an elevated energy state, which is followed by an

energy emission to return to ground state. The absorption process takes place initially

under thermal equilibrium state of the molecule then following excitation the molecule

migrates to various vibrational levels of a new electronic state. As a result, there exists an

energy deficit between emission and excitation energies, thus radiative emission occurs at

longer wavelengths relative to absorption, a phenomenon known as the Stokes shift

(Lakowicz, 1999).In general, the energy emission (deactivation) is predominantly

categorized under two groups: radiative-decay mechanisms in which energy is released as

light and non-radiative-decay mechanisms in which energy is transferred to the

surrounding medium (e.g. heat transfer). The pressure sensor molecules used in PSPs

have an added feature that allows them to return to ground state by colliding with oxygen

molecules, a process known as oxygen quenching Kautsky and Hirsch (1935). Therefore,

as the ambient pressure increases the partial pressure of oxygen in the air increases and

thru sorption and diffusion, the oxygen concentration within the binder increases. This

leads to an increased quenching effect on the sensor leading to a lower intensity. TSP









coatings are typically embedded in oxygen impermeable binders and function on the

basis of the sensitivity of the luminescent molecules (luminophor) to their thermal

environment. The molecules reach an excited state by absorption of a photon and then

deactivates through the emission of a photon. A rise in temperature of the luminescent

molecule will increase the probability that the molecule will return to the ground state by

a radiationless process, which is known as thermal quenching. However, TSP shows

some apparent pressure, more accurately oxygen concentration, dependence, which is

unavoidable as an absolutely oxygen impermeable binder is yet to exist. Nonetheless, the

pressure dependence in most TSP systems is rather insignificant relative to thermal

quenching effects.

The Temperature Dependence

Unfortunately, PSP usually exhibits undesired temperature dependence, which

necessitates a correction to the calibration process. This dependability stems primarily

from the fact that oxygen diffusion and solubility in the polymer depend on temperature,

while the inherent temperature sensitivity of the luminescent molecules contributes to this

dependability on a secondary basis (Schanze et al. (1997)). Recalling equations 1.3 and

1.4, the decay rate constants are temperature dependent except the radiative decay rate kr.


I Ckr (1.3)
k, + k,,, + [02


= + k +k [02] (1.4)


Henry's law states that for quasi-steady pressure variations, the gas concentration

in a medium is proportional to the gas concentration contiguous to the medium.

Properties of the binder affect oxygen sorption and diffusion as well. These properties









are: the solubility and diffusion of the gas in the binder, the density of the luminophor in

the binder, the quenching efficiency, the luminophor(s) embedded within, the electronic

state of the luminophor (triplet or singlet), and lastly the permeability of the binder (Bell

et al., 2001). It should be noted that recalling the discussion in the literature review of the

work of Gouin (2000b), these properties can be appreciably altered by adjoining layers

(i.e., primer). Temperature affects some of these properties, specifically, the solubility

and diffusion of the gas in the binder and the permeability of the binder itself. Following

Smoluchowski's model, the quenching second-order rate constant can be described as

(Szmacinski and Lakowicz, 1995)

k = 42Np(D, +D) (2.1)

where Dp and Dq are the diffusion coefficients of the luminophor and the oxygen in the

polymer, Nis the number of luminophor molecules per millimole in the binder andp is a

factor characterizing the quenching mechanisms. The diffusion coefficients are functions

of temperature, and can be related to temperature in an Arrhenius form over limited

temperature ranges.

-E
Dq a e R (2.2)

where EQ is the activation energy for oxygen diffusion in the binder, R is the universal

gas constant (8.315 J/mol.K) and Tis the average thermodynamic temperature in K of

the binder.

The non-radiative first-order decay rate constant represents the intrinsic

temperature dependence of the luminophor. It is further decoupled into two parts, a

temperature-independent component and a thermally activated intersystem crossing

function. The thermally activated component is usually modeled with an Arrhenius









functions in a similar fashion to the diffusion coefficient in equation(2.2). The overall all

temperature dependence of the paint is a composite function of both the intrinsic

temperature dependence and the oxygen quenching rate constant. Typically, the oxygen

quenching path is the more dominant; however, some formulations show opposite

dependence (Liu et al. 1997).

The Oxygen Factor

Oxygen is a diradical molecule, that is, it possesses a pair of equal energy

molecular orbits and two unpaired electrons. Electrons spin in orbits as they rotate about

an axis passing through the electron. Molecules whose outermost pair of electrons have

parallel spins are in the "triplet state;" molecules whose outermost pair of electrons have

anti-parallel spins are in the "singlet state." Ground-state oxygen is in the triplet state its

two unpaired electrons have parallel spins, a characteristic that, according to rules of

physical chemistry, does not allow them to react with most molecules. Thus, ground-state

or triplet oxygen is not very reactive. However, triplet oxygen can be activated by the

addition of energy, and transformed into reactive oxygen species such as singlet oxygen.

Singlet oxygen is produced as a result of the absorption of light energy. When triplet

oxygen absorbs sufficient energy to reverse the spin of one of its unpaired electrons, it

forms the singlet state. Singlet oxygen though not a free radical it is highly reactive.

When an excited luminescent molecule collides with triplet oxygen, energy transfer

occurs and singlet oxygen is produced. As energy requirement for triplet oxygen

transformation is rather low (1.0 eV), triplet oxygen is recognized as an excellent

quencher. This is typically followed by a radiation deactivation process around 1240 nm

and an intersystem crossing leading to vibrational relaxation. They issue here is the

lifetime of the singlet oxygen and its concentration relative to the triplet oxygen within









the binder as it might react irreversibly with the components of the paint given enough

time. The phenomenon is commonly as photobleaching and is highly dependent on the

surrounding environment and hence differs from one paint composition to the other.

Paint Composition and Character

As stated previously in this chapter, paint system contains three major components,

the luminophor, the binder and the primer. The binder accommodates the luminophor and

regulates the interaction between the luminophor and the surrounding medium, whereas

the primer provides a homogenous base coat for the paint layer, which is advantageous

for the overall performance of the paint.

Which Luminescent Molecule?

Luminophors are selected to have characteristic such as: high quantum yield

(defined later in this chapter), long emission lifetime, photostability under extended

excitation and a distinguishable Stokes shift (Bedlek-Anslow, 2000). Platinum porphyrins

and ruthenium complexes are among the most utilized sensors for PSP due to their high

oxygen sensitivity and long lifetimes. When combined with a temperature probe in a dual

luminophor system, self-quenching behavior is observed with increasing rate as the

luminophor concentrations are increased, i.e., 10nm molecular spatial separation

distance, (Bell et al., 2001). Polymer binders must be robust enough to sustain skin

friction and all other forces on the surface. In addition, they should be easy to apply in

order to achieve a thin smooth film on the surface (- 10 pm), thus ensuring that they

would not change the aerodynamic or structural properties of the model and allow for a

potentially fast dynamic response.

The molecular pressure probe used in this work is PtTFPP, a fluorinated

tetraphenyl porphyrin derivative which is extremely photostable (i.e., retains physical









properties under exposure to light), possess a large phosphorescence quantum yield (90%

in 3-methylpentane) and has a long lived triplet lifetime (120 [ts) (Zelelow et al., 2003).

Its characteristic phosphorescence long lifetime allows enough time for oxygen

quenching within the decay lifetime of luminophor in proper mediums. Absorption bands

are observed at the long wavelength UV range (390 nm), and in the low and high green

wavelengths (506 nm and 540 nm). The green wavelengths absorption bands create a

problem for dual-luminophor systems as TSP phosphors emits at that range. This leads to

cross talk between the luminophors and an induced variation in the PtTFPP emission that

is temperature dependent. Main emission of PtTFPP is in the red wavelengths spectral

domain (651 nm) with a less significant emission at the 712 nm wavelength, far enough

from typical TSP emission. Spectral separation of the PSP and TSP emissions is essential

in dual-luminophor systems that implement intensity based measurement systems. The

TSP phosphor is tris-(1,10-phenanthroline)ruthenium(II) dichloride (Ruphen). Strong

absorbance is evident near the 450 nm range while emission is near the 580 nm

wavelength. Ruphen exhibits slight oxygen quenching properties due to its relatively long

lived life time (0.6 is). To eliminate this dependence the Ruphen is encapsulated

polymer-based nanospheres comprised of polyacrylonitrile (PAN), which has extremely

low gas permeability. Both the PSP and the TSP (encapsulated) are dispersed into poly-t-

BS-co-TFEM polymer.

Binder Polymers

Binders play the important role of mediating between the surrounding oxygen and

the luminophor molecules (i.e., diffuse oxygen within). The characteristics of the

polymer are then crucial to the overall performance of the paint. The diffusivity of a gas

in a polymer medium is quantified by imposing a specie gradient across the polymer and







60


then measuring the gas flux across the polymer as a function of time, a procedure known

as gas permeation across a membrane (Lu and Winnik, 2000). Initial gas diffusion is

typically slow and exponential like, then following some time lag a steady-state gas flux

is manifested through the membrane (Figure 2-3).






__--_--_-_r --_-- _--_-- _-_-r --_ --- -- ----- --

SL I I I I I I______ ______- -









time la Time











Figure 2-3 Typical rate of gas permeation across a membrane (after Lu and Winnik,
2000)

The steady-state flux, 3, is linearly proportional to the gas diffusion coefficient in

the membrane, D, the gas solubility in the membrane under equilibrium state, S, and the

pressure gradient across the membrane, Ap, and is inversely proportional to the

membrane thickness, L.


3 =D (2.3)
2 i i sa
i i L









The diffusion of the gas in the polymer is permitted through the molecular-size

voids into which the gas molecules can travel. As described by the free-volume model,

formation of packets of free volume via thermal activation opens paths for molecular

transportation within the solid polymer, in contrast to diffusion through liquids which is

driven by mere translational displacement. Intrinsically, temperature will have the affect

of increasing the volume of this free space leading to enhanced diffusion. This diffusion

enhancement is often characterized by an Arrhenius behavior. Temperature has a

multifaceted effect on solid polymers. As the polymer bypasses the glass transition

temperature, Tg, thermal expansion becomes more significant and the free volume of the

system allows for large-amplitude molecular motion of the polymer backbone, leading to

more complex temperature dependence in gas diffusion. This is contrary to the

temperature dependence of gas diffusion characterized by a simple activation energy

model under the glass transition temperature. Often, additives such as plasticizers are

incorporated in polymers to lower their glass transition temperature.

An ideal polymer will be completely temperature independent and possess

excellent oxygen sorption and diffusion characteristics. The first is yet to exist; however,

Schanze et al. (1997) developed a realistic criterion for the selection of polymers in order

to minimize temperature dependency. Their results indicate that in order to minimize the

temperature dependence, the medium (binder) used must posses the lowest possible

activation energy for oxygen diffusivity. In other words, the lower the intrinsic

"resistance" of the binder to oxygen diffusion, the lesser temperature effects will be to the

overall emission. Puklin et al. (2000) developed a binder that satisfies the criterion set by

Schanze et al. (1997). The group developed the FIB polymer, which exists in the glassy









state at room temperature and holds a glass transition temperature of 700C. It has high

pressure sensitivity relative to typical silicone resins, with robust and smooth application

to surfaces and low temperature sensitivity (-0.6%/oC).

The Undercoat

An undercoating, i.e., primer, coating is typically applied first on the surface before

applying the paint. The primer coating contains white pigments embedded in a polymer,

usually the same polymer used for the paint to minimize chemical alteration of the paint

when applied on top of the primer, as the paint will still be in aqueous form dissolved in

the solvent which in turn once applied will dissolve and mix some of the primer layer

with the paint. Having identical polymers for the paint and the primer layers further

ensures that oxygen sorption and diffusion are similar and hence avoiding oxygen

gradient across the paint that could potentially change the paint characteristics (Gouin et

al., 2000c). Primer layers are advantageous for various reasons. First, they posses high

index of refraction and high hiding power. Index of refraction is a parameter used to

describe the interaction of electromagnetic radiation with matter. It indicates how much

the light is slowed down while traveling through a specific medium relative to vacuum.

Whereas the speed of all electromagnetic radiation in vacuum is the same, it is a function

of frequency in any medium. This index of refraction is the ratio of the speed of sound to

the phase velocity (the velocity at which the phase of any one frequency component of

the wave will propagate) of the radiation wave, not to be confused with the envelop

velocity (i.e., the velocity with which the overall shape of the wave's amplitude

propagates and is what dictates the rate at which information and energy may be

transmitted by the wave). Thus index of refraction is typically bigger than one in

proportion to the density of the material, that is the denser the material, the more the light









is slowed down. That is advantageous as it provides more reflected light both back into

the paint layer after penetrating it to the primer and from molecular emission back to the

camera. Hiding power is defined as the ability of paint to obscure the surface over which

it has been applied, which is strongly influenced by the degree of dispersion of pigments

in the binder media. The more the pigment particles agglomerate, the worse the hiding

power becomes.

Another advantage of primer coats is that they eliminate any intrinsic reflection of

the surface due to various materials that compose the surface. The uniformity of the

surface guarantees uniform reflection, which eliminates errors due to reflection variation

that could be significant depending on the surface material composition, and which can

be further manifested as an error source if model movement occurs. However, primer

coats, even with identical polymer as the paint, induce some undesirable effects as they

interact with the paint layer. As shown by Puklin et al. (2000) and Gouin et al. (2000c),

primers can adversely alter the response time of the paint as well as the temperature

dependence of the paint. Oxygen equilibrium across the paint layer is a deterministic

factor for the quenching process, and a primer that is oxygen permeable, especially one

with a different permeability, induces an oxygen gradient across the interface with the

paint layer that affects the PSP characteristics. Binders with low oxygen permeability

provide a resolution to such problem, such as polyacrylonitrile PAN (Kose, 2005). A

complete elimination of primer effects is not feasible because the white pigments (e.g.

titanium dioxide) are known to affect the oxygen diffusion in the polymer, (Schappacher

et al., 2003), in addition to other undesirable effects such as photoxidation.









Measurement System

A schematic of the experimental setup for intensity based static measurement

system is provided in Figure 2-4 showing the different components and their

arrangement. In this setup the specimen is placed inside a vacuum chamber, where the

pressure can be precisely monitored and controlled, wedged between two rectangular

aluminum blocks. The top block is heated, while the bottom is cooled imposing a quasi-

one-dimensional temperature gradient along the length of the specimen, if desired. The

specimen is excited with the proper light source (UV lamp, LED, laser, etc.) and the

photonic emission is then passed through the appropriate filter(s) then to the cooled CCD

camera, which converts the photonic energy into electrical current. The Electronic Unit

(E/U), which encloses an analog-to-digital converter, amplifies and processes the current

produced and passes it to the frame grabber card installed in the PC for final processing

by the test personnel. The pressure of the chamber is measured via a pressure transducer

and the temperature is measured through five equally-spaced thermocouples fitted on the

back surface of the specimen.












L tf-_ 1 Pressure
Transducer
Filter wheel CCD Camera




[ E/U unit


1/ Excitation Source
Cooled Base 0
Thermocouples 0 0









Figure 2-4 Equipment Setup for Temperature Calibration

The Excitation Source

Excitation source plays a key role influencing the accuracy and quality of data.

Luminophors typically have multiple absorption peaks with moderate bandwidths, a

desired character of the probe to avoid broad absorption and spectral overlap and

interference. Therefore, the excitation source must provide sufficient and uniform

illumination at these absorption bands to produce an output luminescence signal capable

of saturating the detector in relatively short exposure time, thus taking advantage of

detector's signal-to-noise (SNR) potential. However, the illumination should not be

bright enough to cause photodegradation of the luminophor or overwhelm the detector's

well depth (see useful definitions in Appendix-A). Further, the excitation source must

have absolutely no emission at the luminophor spectral emission range. A spatially









uniform illumination avoids the formation of local regions where the signal is low

relative to the noise level with respect to the rest of the imaged field, inducing an

inconsistent SNR field. If continuous illumination is desired, then a main character is the

stability of the illumination output by the source, while excellent pulsed excitation

depends on repeatable excitation signal levels.

Some of these induced variations can be accounted for in the calibration process

such as inhomogeneous illumination fields (see calibration section), however, variations

in the overall output signal level (source drifting) is not easily accounted for. A drift in

the excitation signal will have the effect of reducing the strength of the paint emission,

falsely indicating higher pressure/temperature levels. Constant monitoring of the output

excitation signal, though possible, is quite impractical, especially when using multiple

excitation sources. A suggested approach in the literature is to embed an environmental-

insensitive probe in the paint (a multicomponent system) that depends only on the

excitation signal. This approach provides an effective correction technique that eliminates

excitation field variations; nonetheless, it is fairly challenging to find a probe that will

absorb in the same spectral range as the other probes and yet emits in an empty range of

the spectrum not occupied by other luminophors, which becomes even more intricate in

systems containing more than one probe (e.g. pressure and temperature dual-luminophor

systems.)

The Detection Device

The detection device plays a deterministic role in how accurate PSP measurements

are and the degree of resolution obtainable. This could further impinge on the feasibility

of certain experiments, such as low speed wind tunnel PSP measurements, where

pressure variations are small and the corresponding intensity variations are fairly









diminutive. Accordingly, an understanding of the basic principles of operation of

detection sources is fundamental for the comprehension of the setup and acquisition

processes as well as error sources and uncertainty analysis.

Calibration Techniques

A calibration procedure is needed to translate intensity information to the

corresponding pressure and temperature. However, to establish the calibration relations a

prior knowledge of some environmental condition is required. This can be accomplished

through an in situ or a priori approach or a hybrid approach. Each approach is defined in

the following sections.

A Priori Calibration

This approach is based on static (no flow) calibration procedure carried

independently in a calibration chamber where the environmental conditions are well

controlled and monitored. A coupon is coated with the paint and then imaged inside a

pressure controlled environment, such as a vacuum chamber, and the intensity of the

specimen is recorded as the pressure inside the chamber is varied, hence creating a

relation between the two variables. In applications where temperature variations are

expected, a temperature gradient is imposed on the coupon and the pressure is varied

while maintaining the temperature gradient and a calibration surface is produced where

the pressure is a function of both the intensity and the temperature. The calibration

relations are then utilized to retrieve pressure and temperature information from the

actual test data, such as in a wind tunnel. The general form of the priori calibration is:

LK ( )
p ak re (2.4)
1-0 k0 \ )









It is usually sufficient to represent the pressure with a biquadratic function in

equation (2.4) (i.e., L=K=2). The higher the order of the pressure calibration function the

more points needed to solve for all the coefficients, in this example, the biquadratic

functions has nine coefficients and thus nine intensity and temperature measurements are

needed. The range of the pressure and temperature calibration conditions depends on the

range of these conditions in the application as well as the accuracy needed. Extrapolation

usually yield high errors, hence, the environmental envelop should cover all expected test

conditions. The general behavior of the intensity within envelop should be known

through spectroscopy analysis to determine the resolution of the measurements desirable

in each different region of the pressure and temperature ranges.

A reference image is still needed to account for spatial variation (i.e., paint

thickness, illumination field, etc.); however, the reference condition in this case may or

may not be identical to the reference condition in the actual testing environment (wind-

off). If the two conditions are not identical then the test normalized ratios are multiplied

by the reference-to-wind-off intensity ratio before using equation (2.4).

Priori calibration offers simplicity and convenience by eliminating the need for

installing pressure taps and thermocouples in the model. Further, it allows for the full

coverage of the environmental test range. This would be rather difficult if one attempts to

installs pressure taps on the model surface, as no prior knowledge exists to provide

information for optimal taps location or the physical infeasibility of installing the

pressure tap at these locations. In the former case, the paint could be applied and a

qualitative estimation of the pressure field is obtained to determine the best locations for

installing pressure taps. Unfortunately, this approach may involve higher errors because









of different camera and illumination source positions (Liu et al., 1997). Even though the

same batch of paint is used to paint both the calibration coupon and the test model,

variations still occur due to different application of the paint, environmental/surface

containments, etc. Nonetheless, more often, this calibration technique is accurate enough

for typical test environments with considerable practicality. The results are exceptionally

accurate if the calibration is carried in a wind tunnel where the static pressure and

temperature can be controlled under wind-off conditions (i.e., pressurized tunnels).

In situ Calibration

In this approach the calibration is carried in a wind tunnel under flow conditions.

Pressure taps are installed in the model and the pressure variation over the model are

recorded simultaneously with intensity values. The pressure function is typically a

polynomial of the second-order, with a first-order representation sufficing many

applications.


P = bh windoffh (2.5)


The temperature effects are absorbed in the coefficients, which unless isothermal

conditions are present, increases the standard deviation of the calibration data and yields,

in most cases, double-vale points that correspond to different conditions. To compensate

for this, thermocouples can be installed to record the temperature and the calibration

curve is transformed to a calibration surface. The in situ approach may seem self-

defeating as it still requires pressure taps and thermocouples to be installed in the model,

however, the number of calibration taps is significantly less than the typical number of

pressure taps required to map out the pressure field.









Hybrid Calibration

This technique combines the convenience of a priori approach with the accuracy of

the in situ method. The pressure calibration is established first in a static cell, and then the

calibration is corrected for temperature variation between static and flow conditions via a

factor K. The approach was explained earlier in the Literature Review Chapter. The

technique relies on the very little temperature variations on the order of few degrees and a

PSP coating exhibiting ideal behavior. Thus, this approach fails when significant

temperature variation occur during testing and with non-ideal paint/polymer systems.

PSP Calibration

In the presence of an oxygen-quencher a quantity known as the quantum yield of

luminescence 0, more commonly known as the quantum efficiency, is modeled under

oxygen rich conditions as:

rate of luminescence emission I k_ (2.6)
= k,T (2.6)
rate of excitation I k +k + k[02 ]
where I is the luminescent intensity, Ia is the absorption intensity and r is the lifetime of

an excited molecule. Under vacuum conditions, equation (2.6) becomes:


(Do =- k= o (2.7)
k +k

where OD and r0 are the quantum efficiency and lifetime of the probe under vacuum

conditions, respectively. Dividing the quantum efficiency under vacuum by that under

oxygen rich yields:

0 I k + k,, + k[0] [k1 [02]

( I
Sk 1+k k (2.8)


-o =I [o
D I









This form is known as the Stem-Volmer equation. It is not practical to pull a

vacuum in order to estimate the vacuum lifetime of the sensor molecule, thus a known

condition, such as atmosphere, is utilized instead as the reference condition. Henry's Law

relates the oxygen concentration to the partial pressure of oxygen as shown in equation

(1.6). The intensity ratio with respect to an atmospheric reference condition is hence

represented as:

I fk,+k, +k,[O2]}. k +k +k P
refatm x g l_ r nr q 0, = A(T) +B(T)P0
I kr +k,,n +kq [O2 r k +k, + k (1)

(2.9)
k +k k P
A(T)= kr ; B(T) k Po = p
k, +knr + k kk +kn1 +kq Pf

The general form of the Stern-Volmer equation is expressed as:


A (T)
n=0 (2.10)
The coefficients An (T) are functions of temperature, as expected due to the

temperature dependence in kD and kg, and are to be determined through the calibration

process, in which pressure and intensity data are acquired and then a least-square fit

procedure is performed to determine the coefficients. Typically a second order

polynomial (N = 2) is sufficient to accurately fit the experimental calibration data. The

process of taking the ratio between the luminescence intensity and some reference

intensity is essential in order to eliminate illumination spatial non-uniformities, coating

thickness variation and luminophor uneven dispersion in the binder.









Temperature Compensation Models

As described in Chapter 1, PSP exhibits temperature dependence primarily due to

the dependence of the polymer binder permeability on temperature, which in turn effects

the oxygen diffusion and sorption in the binder. On a secondary level, under oxygen rich

environments, the inherent temperature quenching rate constant kD plays an insignificant

role but becoming more significant as the oxygen concentration decreases until it

constitutes the only temperature dependence at vacuum conditions. The temperature

dependence can be modeled by a single exponentially decaying function at vacuum and a

multi-exponential decaying function around atmospheric conditions (Schanze et al.,

1997). The proportionality constants and activation energies depend on the sensor probe

and the polymer; however, up to the date of this work, there has been no successful effort

to globally model this dependence for a wide range of pressures and temperatures.

Calibration provides a mean to compensate for the temperature dependence. In situ

techniques have no explicit temperature dependence; rather they absorb these effects in

the calibration coefficients as the temperature spatial variations are averaged out among

all points included in the calibration (Bell et al., 2001). This means that each set of

coefficients correspond to a unique pressure and temperature condition. This approach is

useful when temperature variations are small enough (-10-20 C depending on the PSP

composition) to avoid double value points on the calibration surface that correspond to

different pressure/temperature values. Further, extrapolating for points outside the

calibration envelop entails high uncertainty. In wind tunnel experiments, the run image

precedes the reference image as the reference image is acquired immediately after the

termination of the run image to ensure identical temperature distribution throughout both

images. This prohibits practical execution of long experiments as the tunnel must be









stopped after each run to allow for the reference image. In the presence of significant

temperature gradients on the model surface, a localized calibration is needed with enough

pressure taps for each region.

A priori calibration provides a more global calibration as the pressure is calibrated

as a function of both normalized intensity and temperature. Nonetheless, this necessitates

that temperature field estimation on the model surface be performed. As this calibration

approach offers a pixel-by-pixel temperature compensation, the only reasonable

temperature measurement technique would have to be a TSP system. Early attempts

suggested imposing a TSP layer either beneath or on top of a PSP layer in order to

simultaneously map out pressure and temperature fields (Harris and Gouterman, 1995;

Oglesby et al., 1995). Latter attempts incorporated the two sensors in the same binder in a

dual-luminophor system (Carroll et al., 1999). In either approach the convenience of

having a second sensor to map-out the temperature field comes with a highly undesirable

consequence, namely spectral interference. Spectral interference occurs whenever two

luminophors are co-embedded in the same binder. The emission of the lower wavelength

sensor probe, i.e., TSP, usually overlaps with part of the excitation region of the higher

wavelength sensor probe, i.e., PSP. This adds to the temperature dependence complexity

as the PSP emission is partially dependent on the intensity of the TSP emission. This

makes the decoupling of the two effects rather intricate using typical calibration and

compensation techniques. Secondary detrimental effects include: spectral overlap due to

broad emission of the lower wavelength luminophor, chemical interaction, particles

coagulation resulting in an uneven dispersion of the two luminophors in the binder and

increased uncertainty in the temperature estimates as it is embedded in an oxygen