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Experimental Study of Subcritical to Supercritical Mixing

Permanent Link: http://ufdc.ufl.edu/UFE0021034/00001

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Title: Experimental Study of Subcritical to Supercritical Mixing
Physical Description: 1 online resource (236 p.)
Language: english
Creator: Polikhov, Stepan Alexa
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Liquid jet injection into quiescent gaseous environment was investigated experimentally and analytically. This is the first comprehensive experimental study covering subcritical to supercritical conditions. The research was focused on investigating the surrounding gas pressure and temperature influence on the jet break-up mechanisms. Subcritical, transcritical and supercritical jet break-up mechanisms were observed. The map of break-up modes was plotted in the P-T space. Under the subcritical conditions first and second wind-induced break-up regimes were observed. The break-up in this case was controlled by surrounding gas inertia and surface tension forces. Apparent decrease of surface tension influence on the jet surface behavior was observed under transcritical conditions. Ligament formation was significantly reduced under these conditions with only occasional drop formation observed. A significantly different jet break-up was observed in the transcritical mixing region. Further increase of pressure and temperature led to supercritical break-up modes. This manifested through a smoothening of the liquid ? gas interface. Ligament formation was not observed under supercritical conditions; this indicates that surface tension did not play any role in the supercritical jet break-up. Despite the apparent absence of the surface tension, the density gradients values observed under supercritical conditions were comparable to those observed under subcritical conditions. A linear jet stability analysis was performed to gain physical insight into the jet break-up mechanisms. The results showed good correlation with experiments for subcritical mixing but did not match for the transcritical and supercritical regimes.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Stepan Alexa Polikhov.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Segal, Corin.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021034:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021034/00001

Material Information

Title: Experimental Study of Subcritical to Supercritical Mixing
Physical Description: 1 online resource (236 p.)
Language: english
Creator: Polikhov, Stepan Alexa
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Liquid jet injection into quiescent gaseous environment was investigated experimentally and analytically. This is the first comprehensive experimental study covering subcritical to supercritical conditions. The research was focused on investigating the surrounding gas pressure and temperature influence on the jet break-up mechanisms. Subcritical, transcritical and supercritical jet break-up mechanisms were observed. The map of break-up modes was plotted in the P-T space. Under the subcritical conditions first and second wind-induced break-up regimes were observed. The break-up in this case was controlled by surrounding gas inertia and surface tension forces. Apparent decrease of surface tension influence on the jet surface behavior was observed under transcritical conditions. Ligament formation was significantly reduced under these conditions with only occasional drop formation observed. A significantly different jet break-up was observed in the transcritical mixing region. Further increase of pressure and temperature led to supercritical break-up modes. This manifested through a smoothening of the liquid ? gas interface. Ligament formation was not observed under supercritical conditions; this indicates that surface tension did not play any role in the supercritical jet break-up. Despite the apparent absence of the surface tension, the density gradients values observed under supercritical conditions were comparable to those observed under subcritical conditions. A linear jet stability analysis was performed to gain physical insight into the jet break-up mechanisms. The results showed good correlation with experiments for subcritical mixing but did not match for the transcritical and supercritical regimes.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Stepan Alexa Polikhov.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Segal, Corin.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021034:00001


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1 EXPERIMENTAL STUDY OF SUBCRITICAL TO SUPERCRITICAL MIXING By STEPAN A. POLIKHOV A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DO CTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007

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2 2007 Stepan A. Polikhov

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3 To my wife Polina

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4 ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor Dr. Corin Segal for his patience and enthusiasm while guiding me through the educational process I am using this occasion to thank my colleagues in the combustion lab for providing a nice working environment. In particular, I owe a lot to Dr. Jonas Gustavsson for his expertise in Matlab and extremely optimistic attitude regarding the future he never hesitates to share with people around him. I am also thoroughly thankful to my pare nts and my wife Polina for their endless support and tenderness.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 NOMENCLATURE ................................ ................................ ................................ ...................... 13 Latin Symbols ................................ ................................ ................................ ......................... 13 Subscripts ................................ ................................ ................................ ................................ 15 Greek Symbols ................................ ................................ ................................ ........................ 15 Non dimensional Numbers ................................ ................................ ................................ ..... 16 ABSTRACT ................................ ................................ ................................ ................................ ... 17 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 19 Mixing and Atomization Processes ................................ ................................ ........................ 19 Mixing a nd Atomization in Applications Not In volving Combustion ................................ ... 19 Mixing and Atomization in Applications Involving Combustion ................................ .......... 21 Pressure Jet Atomizers ................................ ................................ ................................ .... 22 Plain orifice atomizers ................................ ................................ .............................. 23 Swirling pressure atomizers (Simplex) ................................ ................................ .... 26 Other types o f swirling pressure atomizers ................................ .............................. 29 Duplex and dual orifice atomizers. ................................ ................................ ........... 29 Spill return atomizers. ................................ ................................ .............................. 30 Air Assist and Air Blast Atomizers ................................ ................................ ................. 30 Air assist atomizers ................................ ................................ ................................ .. 31 Air blast and effervescent atomi zers ................................ ................................ ........ 33 Liquid Round Jet Break up ................................ ................................ ............................. 35 Droplet Deformation and Break up ................................ ................................ ................. 42 Features of Supercritical Mixing ................................ ................................ ..................... 46 Experimental works ................................ ................................ ................................ .. 50 Numerical simulations ................................ ................................ .............................. 55 Objectives of the Current Work ................................ ................................ ...................... 60 2 EXPERIMENTAL SETUP AND TECHNIQUIE ................................ ................................ .. 73 High Pressure Chamber ................................ ................................ ................................ .......... 73 Material Choice ................................ ................................ ................................ ............... 73 High Pressure Chamber Body Design. ................................ ................................ ............ 74 Optical A ccess Layout ................................ ................................ ................................ ..... 75 Lid and Injector Design ................................ ................................ ................................ ... 77

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6 Liquid/Gas Supply System ................................ ................................ ................................ ..... 79 Gas Supply Line. ................................ ................................ ................................ ............. 79 Liquid Supply Line. ................................ ................................ ................................ ......... 82 Data Acquisition Systems ................................ ................................ ................................ ....... 84 Data Acquisition and Control System ................................ ................................ ............. 84 Optical Data Acquisition System ................................ ................................ .................... 86 Experimental Technique ................................ ................................ ................................ ......... 88 FK 5 1 12 Thermodynamic and Spectral Properties ................................ ...................... 88 Image Processing ................................ ................................ ................................ ............. 90 Accurac y Analysis ................................ ................................ ................................ ........... 91 3 RESULTS AND DISCUSSION ................................ ................................ ........................... 112 Experimental Results ................................ ................................ ................................ ............ 113 Subcritical Mixing ................................ ................................ ................................ ......... 113 Transcritical Mixing ................................ ................................ ................................ ...... 114 Supercritical Mixing ................................ ................................ ................................ ...... 114 Theoretical Analysis ................................ ................................ ................................ ............. 116 4 CONCLUSIONS ................................ ................................ ................................ .................. 142 5 FUTURE WORK ................................ ................................ ................................ .................. 144 APPENDIX A DRAWINGS OF SET UP ................................ ................................ ................................ .... 146 B LABVIEW CODE AND OPERATIONAL PROCEDURES ................................ .............. 163 General Description ................................ ................................ ................................ .............. 163 Operational Procedure ................................ ................................ ................................ .......... 165 C MATLAB SCRIPTS USED TO PROCESS RESULTS ................................ .................... 177 D EXPE RIMENTAL RESULTS ................................ ................................ ............................. 191 LIST OF REFERENCES ................................ ................................ ................................ ............. 229 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 236

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7 LIST OF TABLES Table page 1 1 Practical applications of atomization ................................ ................................ ................. 61 1 2 Performance of various atomizers ................................ ................................ ..................... 62 1 3 Swirling pressure atomizers SMD empirical evaluation ................................ ................... 63 1 4 Numerical experiment conditions ................................ ................................ ...................... 63 2 1 Some properties of stainless steel, brass and copper ................................ ......................... 94 2 2 O ring sizes an locations ................................ ................................ ................................ .... 94 2 3 Curre ntly available gas/liquid injector geometries ................................ ............................ 94 2 4 Parameters and constants used in PRSV ................................ ................................ ............ 95 2 5 Uncertainties related to the d ata acquisition and control system ................................ ....... 95 3 1 Numerical experiment conditions ................................ ................................ .................... 128 B 1 Active channels in different operational modes .......................... 165

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8 LIST OF FIGURES Figure page 1 1. Ultrasonic atomizer. ................................ ................................ ................................ ........... 64 1 2. Spray triode atomizer. ................................ ................................ ................................ ........ 64 1 3. Plane orifice atomizer. ................................ ................................ ................................ ....... 65 1 4. Depen dence of discharge coefficient on Reynolds number. ................................ .............. 65 1 5. Typical pressure swirl atomizer design ................................ ................................ .............. 66 1 6. Different modifications of the swirl pressure atomizer. ................................ .................... 66 1 7. Different modifications of the internal mixing air assist atomizer. ................................ ... 67 1 8. Different modificat ions of the external mixing air assist atomizer ................................ .... 68 1 9. Different modifications of air blast atomizers, typical design of e ffervescent atomizer ... 69 1 10. Break up regimes of liquid round jet in quiescent surrounding gas ................................ .. 70 1 11. Qualitative dependence of jet break up length on Weber number ................................ .... 71 1 12. Mechanisms of break up of low viscosity liquid drops observed experimentally under atmospheric or lower initial pressure ................................ ................................ ....... 71 1 13. Qualitative phase diagram to illustrate supercritical injection. ................................ .......... 72 1 14. Nitrogen specific heat at constant pressure around critical point, ................................ ................................ ........................... 72 2 1. High pressure chamber overall view ................................ ................................ .................. 96 2 2. High pressure chamber overall view CAD drawings ................................ ........................ 97 2 3. Schematic of Liquid/Fuel supply system. ................................ ................................ .......... 98 2 4. Cross sectional CAD images of coaxial injector assembly. ................................ .............. 99 2 5. Liquid injector overall view. ................................ ................................ ............................ 100 2 6. Gas heater overall view. ................................ ................................ ................................ ... 101 2 7. Sponsler Lo Flo precision flow meter MF 125 MB PH A 4X N1 cal ibration curve. ... 102 2 8. Data acquisition system diagram ................................ ................................ ..................... 103

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9 2 9. Image acquisition system synchronization schematic ................................ ..................... 104 2 10 Circuit diagrams. A) heaters, B) solenoid valves ................................ ............................ 105 2 11. Image acquisition system schematics ................................ ................................ .............. 106 2 12. Beam profile. ................................ ................................ ................................ .................... 107 2 13. Liquid jet injection at STP conditions, ..................... 108 2 14. FK 5 1 2 Emission spectrum at STP conditions, excitation wave length .. 109 2 15. FK 5 1 2 Emi ssion spectra in the region of an interest at variety of pressures and temperatures, excitation wave length ................................ .......................... 110 2 16. FK 5 1 2 Phase diagram Labels on the curves are in atm. ................................ ............ 111 3 1. Proposed test matrix. ................................ ................................ ................................ ........ 129 3 2. Actual test matrix. ................................ ................................ ................................ ............ 130 3 3. Jet injection at STP conditions, injection velocity ................................ .. 131 3 4. Jet injection, Injection velocity ...................... 132 3 5. Jet injection Injection velocity ....................... 133 3 6. Jet injection, Injection velocity .................... 134 3 7. Jet injection, Injection velocity .................... 135 3 8. Jet injection, Injection velocity .................... 136 3 9. Jet injection, Injection veloci ty .................... 137 3 10. Spatial growth rate dependence on wave number. ................................ ........................... 138 3 11. Correlation between measured (vertical axis) and predicted wavelength. ...................... 139 3 12. Spatial growth rate dependence on wave number in case of supercritical mixing. ......... 140 3 13. Viscous flow above liquid surface ................................ ................................ ................... 141 A 1. Chamber body front view, all dimensions are in inches. ................................ ................. 146 A 2. Chamber body top view, all dimensions are in inches. ................................ .................... 147

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10 A 3. Chamber body, isometric view. ................................ ................................ ....................... 148 A 4. Chamber lid. A) front view, B) top view, all dimensions are i n inches. .......................... 149 A 5. Chamber top. A) Front view, B) top view, all dimensions are in inches. ........................ 150 A 6. Chamber lid, isometric view. ................................ ................................ ........................... 151 A 7. Chamber exhaust. ................................ ................................ ................................ ............. 152 A 8. Chamber exhaust, isometric view. ................................ ................................ ................... 153 A 9. Dummy Fla nge 12. A) front view, B) top view, all dimensions are in inches. ............... 154 A 10. Dummy Flange 12, isometric view. ................................ ................................ ................. 155 A 11. Dummy Flange 14. A) front view, B) top view, all dimensions are in inches. ............... 156 A 12. Dummy Flange 14, isometric view. ................................ ................................ ................. 157 A 13. Flange 12. Front view, sectioned. All dimensions are in inches. ................................ .... 157 A 14. Flange 12. A) top view, B) bot tom view, all dimensions are in inches. .......................... 158 A 15. Flange 12, isometric view. ................................ ................................ ............................... 159 A 16. Flange 14. A) top view, B) bottom view, all dimensions are in inches. .......................... 160 A 17. Liquid injector, all dimensions are in inches ................................ ................................ .. 161 B 1. F ront panel of hpchcontroller.vi ................................ ................................ ...................... 167 B 2. Diagram of hpchcontroller.vi, frame 0 overall view ................................ ........................ 168 B 3. Diagram of hpchcontroller.vi, frames 0.0 0.1 ................................ ................................ .. 169 B 4. Diagram of hpchcontroller.vi, frames 0.2 0.3 ................................ ................................ 170 B 5. Diagram of hpchcontroller .vi, frame 0.4 ................................ ................................ ......... 171 B 6. Diagram of hpchcontroller.vi, frame 0.5 ................................ ................................ ......... 172 B 7. Diagram of hpchcontroller.vi, frame 0.6 ................................ ................................ ......... 173 B 8. Diagram of hpchcontroller.vi, frame 1 overall view ................................ ........................ 174 B 9. Diagram of hpchcontroller.vi, frame 2 ................................ ................................ ............ 175 B 10 Diagram of hpchcontroller.vi, frame 3 ................................ ................................ ............ 176

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11 D 1. Jet injection at STP conditions, injection velocity ................................ .. 192 D 2. Jet injection, Injection velocity ...................... 193 D 3. Jet injection, Injection velocity ...................... 194 D 4. Jet injection, Injection velocity .................... 195 D 5. Jet injection, Injection velocity ................... 196 D 6. Jet injection, Injection velocity ................... 1 97 D 7. Jet injection, Injection velocity ..................... 198 D 8. Jet injection, Injection velocity ...................... 199 D 9. Jet injection, Injection velocity ..................... 200 D 10. Jet injection, Injection velocity .................... 201 D 11. Jet injection, Injection velocity .................... 202 D 12. Jet injection, Injection velocity ................... 203 D 13. Jet injection, Injection velocity .................... 204 D 14. Jet injection, Injection velocity ....................... 205 D 15. Jet injection, Injection velocity .................... 206 D 16. Jet injection, Injection velocity .................... 207 D 17. Jet injection, Injection velocity .................... 208 D 18. Jet injection, Injection velocity .................... 209 D 19. Jet injection, Injection velocity .................... 210 D 20. Jet injection, Injection velocity ................... 211 D 21. Jet injection, Injection velocity ...................... 212

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12 D 22. Jet injection, Injection velocity .................... 213 D 23. Jet injection, Injection velocity .................... 214 D 24. Jet injection, Injection velocity ................... 215 D 25. Jet injection, Injecti on velocity .................... 216 D 26. Jet injection, Injection velocity .................... 217 D 27. Jet injection, Injection velocity .................... 218 D 28. Jet injection, Injection velocity .................... 219 D 29. Jet injection, Injection velocity ..................... 220 D 30. Jet injection, Injection velocity ..................... 221 D 31. Jet injection, Injection velocity .................... 222 D 32. Jet injection, Injection velocity .................... 223 D 33. Jet injection, Injection velocity ..................... 224 D 34. Jet injection, Injection velocity .................... 225 D 35. Jet injection, Injection velocity .................... 226 D 36. Jet injection, Injection velocity .................... 227 D 37. Jet injection, Injection velocity .. ...................... 228

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13 NOMENCLATURE Latin Symbols cross section area [m 2 ] orifice area [m 2 ] ellipsoid of rotation minor semi axis [m] ellipsoid of rotation maj or semi axis [m] discharge coefficient heat capacity at constant pressure heat capacity at constant volume [ ] diameter [m ] jet initial diameter [m] pintle diameter of prefilming atomizer [m] potential energy [J] flow number [m 2 ] frequency [Hz] velocity coefficient wave number [m 1 ] length [m] molar weight [ ] mass flow rate [kg/s] pressure [Pa]

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14 critical pressure [atm.] reduced pressure pressure difference [Pa] gas constant [ ] universal gas constant [ ] radius [m] drop area [m 2 ] Sauter diameter [m] Sauter mean diameter [m] resonance temporal disturbance growth rate [s 1 ] critical temperature [K] reduced temperature initial temperature [K] liquid jet break up time [s] liquid film thickness [m] velocity [m/s] specific volume [m 3 kg 1 ]

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15 Subscripts critical droplet gas initial liquid orifice initial Greek Symbols heat transfer coefficient [ ] droplet deformation rate ellipsoid of rotation eccentricity thermal diffusivity [m 2 /s] disturbance magnitude [m] disturbance initial magnitude [m] semi vertex spray cone angle [rad] thermal conductivity [ ] wavelength [m] dynamic viscosity [ ] kinematic viscosity [m 2 /s] density [kg/m 3 ] surface tension [N/m]

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16 absorption cross sec tion [cm 2 molecule 1 ] characteristic droplet deformation time [s] droplet evaporation time [s] radial frequency [s 1 ] Non dimensional Numbers Weber numbe r [ ] Reynolds number [ ] Ohnesorge number [ ] Laplace number [ ]

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17 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 EXPERIMENTAL STUDY OF SUBCRITICAL TO SUPERCRITICAL MIXING By Stepan A P olikhov August 2007 Chair: Corin Segal Major: Mechanical Engineering Liquid jet injection into quiescent gaseous environment was investigated experimentally and analytically. This is the first comprehensive experimental study covering subcritical to super critical conditions. The research was focused on investigating the surrounding gas pressure and temperature influence on the jet break up mechanisms. Subcritical, transcritical and supercritical jet break up mechanisms were observed. The map of break up mo des was plotted in the P T space. Under the subcritical conditions first and second wind induced break up regimes were observed. The break up in this case was controlled by surrounding gas inertia and surface tension forces. Apparent decrease of surface te nsion influence on the jet surface behavior was observed under transcritical conditions. Ligament formation was significantly reduced under these conditions with only occasional drop formation observed. A significantly different jet bre ak up was observed i n the trans critical mixing region. Further increase of pressure and temperature led to supercritical break up modes. This manifest ed through a smoothening of the liquid gas interface. Ligament formation was not observed under supercritical conditions; th is indicates that surface tension did not play any role in the supercritical jet break up. Despite the apparent absence of the surface tension, the density gradients values observed under supercritical conditions were comparable to those observed under sub critical conditions. A linear jet stability

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18 analysis was performed to gain physical insight into the jet break up mechanisms. The results showed good correlation with experiments for subcritical mixing but did not match for the transcritical and supercriti cal regimes.

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19 CHAPTER 1 INTRODUCTION Mixing and Atomization Processes Atomization is defined as the disintegration of a liquid into small structures which can be either drops at subcrit ical pressures and temperatures Atomizati on is involved in a var iety of industrial applications such as internal combustion engines and liquid rocket engines. The importance of atomization for practical applications [1] is illustrated in Table 1 1. It worth to note that the goals in different app licat ions are significantly differ as well. A brief description of atomizers for various applications is given below. Mixing and Atomization in Applications Not Involving Combustion In the case of painting or powder production, for example, the main goal i s to obtain a spray consisting of drops with well defined and controlled diameter. Usually in this type of applications, the flow rate is constant and quite small; there is no gas supply readily available. Since t here are two types of forces presen t ine rtia and surface tension and the flow rat es are usually relatively small a balance between these forces is possible. There are many types of atomizers which take advantage of resonance lik e liquid behavior to produce drops of well controlled diameter In the late 70s Berger [2] et al. introduced an atomizer design which is now known as the ultrasonic atomizer and widely used in variety of applicati ons which require well controlled droplet diameter distribution at relatively small flow rates. The physics b ehind this device was established by Lord Kelvin in the 19 th century. It was shown that if a horizontal flat surface covered with a liquid film is vibrated in the vertical direction, at certain frequencies of vibr ation standing waves pattern is formed on t he liquid surface. These waves are known as capillary waves. If some critical amp litude of vibration is exceeded the waves are no longer stable and disintegrate producing small drops ejecting

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20 normally to the surface. If the wet ted surface is pointed downwa rd this kind of surface with some kind of liquid supply system can be used as an atomizer. The resulting drop diameter depends on the liquid surface tension fluid density and vibration frequency and can be estimated by [2]: (1 1) This physical phenomenon is utilized in ultrasonic atomizers; a schematic of such a device is shown in Figure 1 1. The standing wave pattern is formed on the atomiz ing surface 4, which is necessarily pointed downward. The total combined leng th of the front and back horns, m arked in the drawing as 1 and 2 res pectively, is proportional to the half wavelength for a given operating fre quency so the entire assembly is a q uarter wavelength resonator. Typically, these horns are made of titanium due to its excellent acoustical properties and corrosion stability. Piezoelectric discs are placed in the middle of the assembly at the pressure anti node i.e. velocity node to insure maximum energy supply to the system. The common plate between the piezoelectric discs is connected to one of the electrical input terminals; the other terminal to the assembly body. A reduction in the front horn diameter helps to amplify the acoustical vi bration magnitude. The typical vibration amplitude achieved with this type of devices is limited to tens of microns. Droplet diameters vary from 1 2 microns up to 0.1 mm. Maximum flow rates are limited to 5 7 l/hr. Probably, the most significant drawbacks of this atomizer are the susceptibility to environment pressure variations in time and the requirement that the atomizing surface has to be pointed downward; therefore it is impossible to implement it in turbine combustion chambers and internal combustion engines. Another type of atomizer widely used for applications such as painting or pesticide spraying is the electrostatic atomize r. In line with its name the main force exploited to disperse

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21 the liquid in this kind of atomizers is the electrostatic force. One of the most common designs was proposed by Kelly [3] and is shown in Figure 1 2. A liquid is supplied to a nonconductive cell 1 through the entrance 2. It flows around the highly conductive electrode 3 and gets collected on its tip. Since the high vol tage is applied between electrodes 3 and 4, liquid collected at the tip of the first (emitter) electrode disintegrates and accelerates toward the first and second electrodes. During the flight between first and second electrode, droplets are charged with t he same polarity; therefore, electrical repulsion forces ensure an excellent spray cone formation. The main portion of the static charge is removed at the second (blunt ) electrode which is a mesh made of highly conductive material. The rest of the charge i s removed at the third (collector) electrode. Hence, the design of this atomizer is actually similar to that of cathode ray tube (CRT) used in old fashioned TVs and computer monitors. The voltage applied between the first and second electrodes varies from 1 to 100 kV. Usually, an arra y of emitter electrodes is used so the flow rate can be as high as 30 l/h. The results of experiments w ith this kind of atomizers show that the resulting drop diameter depends on the applied voltage, emitter tip size, liquid fl ow rate and liquid electrical conductivity and dielectric constant. The re sulting drops diameters vary m to 1 mm. This kind of atomizers are generally used to disperse fluids with conductivity as low as 10 10 S/cm, for example paints, oil, pure water and pesticides. Due to its relative complexity and need for additiona l heavy equipment these atomizers are not used in ap plications involving combustion but they are the primary choice in applications such as painting. Mixing and Atomization in Applications Involving Combustion For interna l combustion and rocket engines a uniform drop size distribution is not a priority. The main goal in this case is effective gas phase comb ustion which depends on the quality of the gaseous mixture between fuel and oxidizer. As a result, atomization is used to

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22 provide the most efficient flu id vaporization and enhance its mixing with other propellan ts. Usually, the requirements to these atomizers are higher than to those used for uniform spray formation. The mixing has to be efficient over wide ranges of pressures and flow rates. Therefore, t he fine or resonance tuning of the jet atomizer is not a priority in this case; instead, more attention is paid to ensure good overall performance over as a wide range of conditions as possible. Different types of atomizers with some comments on their perf ormance and features [2, 4] are presented in Table 1 2. The goal of this work is to understand the processes related to jet decomposition and mixing in applications involving high pressures, e.g. internal combustion engines and liquid rocket engines. Alth ough combinations of individual injectors including atomization, swirling e.t.c. are used to enhance the performance in these applications, important physical features of jet break up and mixing under high pressure are still poorly understood. Therefore th is study involves single jet entering a quiescent atmosphere. Since only plain orifice and coaxial atomizers were tested in this work the emphasis of the following review will be placed on these types of atomizers while only key features of other types wil l be mentioned. However, it should be noted that the capabilities of the proposed technique are not limited to a specific type of atomizer. Pressure Jet Atomizers The simplest type of at omizer is the pressure atomizer where a liquid is discharged through a small orifice. The performance in this case is determined by the Bernoulli equation, (1 2) so that

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23 (1 3) where is a pressure difference across the atomizer is the fluid density and is the fluid velocity. The larger the pressure drop the better atomization can be achieved. In other words, the potential energy of the liquid is converted to kinetic energy. The difference betw een different types of pressure jet atomizers is related to the processes taking place during the acceleration. Several basic parameters are used to evaluate the performance of pressure atomizers [4] The effective flow area is usually described by the flo w number (1 4) where is a mass flow rate. A non dimensional parameter widely used to characterize the drag losses during the injection is the discharge coefficient (1 5) where is the actual orifice area. In fact, this coefficient is the sca led ratio between flow number, which is an effective flow area, and the actual orifice area (1 6) The discharge co efficient is the most commonly used parameter during the evaluation of overall hydrodynamic atomizer efficiency. Plain orifice atomizers The plain orifice atomizer is the simplest possible design for liquid disintegrati on and atomization. T hese atomizers a re widely used due to their simplicity and reliability. A schematic of the plain orifice atomizer is shown in Figure 1 3. The best known application of this kind of

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24 atomizers is in the diesel engine. The atomizer in this case works in a pulsing mode to inj ect fuel into the combustion zone during each power stroke of the piston. Since the pressure above the piston can be a s high as 30 40 a tm., the pressure at the liquid supply is usu ally in the range of 100 200 a 18 00 a tm. for the common rail design. The resulting injection speed varies from 200 to 700 m/s. Plain orifice atomizers are also used in jet engine afterburners. In this case, an assembly consists of tens of such injectors to provide the required flow rate a nd prevent orifice blockage. P lain orifice atomizers are used in rocket injectors as well In this case, oxygen and fuel jets are impinging on each other once they leave the injectors orifices. At low pressures and temperatures, the jets form a well define d and visible zone (sheet) where the mixing and disintegration take place. This sheet disappears at higher velocities of the fuel injection the disintegration takes place before the fuel and oxidizer reach the mixing zone. Despite the simple design the processes taking place inside and outside the pla in orifice are quite complex and cannot be predicted entirel y even with modern computational capabilities. Therefore, experiments are still widely used to investigate the injection processes taking place at given particular injection conditions for specific injector designs. Most authors agree that the flow inside a plain o rifice atomizer has an apparent similarity to the flow inside a pipe. Therefore, the transition between turbulent and laminar flows has a significant impact on the discharge coefficient. Also, different authors report that the transition between laminar and turbulent flow inside the plain orifice atomizer clearly affects the further jet disintegration pattern [4, 5] As may be expected, turb ulence greatly decrease s the jet disintegration length but the discharge coefficient tends to exhibit a reverse dependency on the Reynolds number, i.e.

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25 forces. Many authors report the dependency of the discharge coefficient [4, 5, 6, 7, 8, 9] on the Reynold s number as shown in Figure 1 4. It can be seen from the figure that for orifices with a length/diameter ratio ( see Figure 1 3) s maller than 0.7 an apparent extremum was observed for Reynolds numbers corresponding to the turbulence transition regime. There is no clear theoretical explanation for this behavior available in the literature. Qualitatively, this region corresponds to the transition between viscosity dominated laminar flow and inertia dominated turbulent flow [4, 5, 9] The distinguishing feature of the viscosity dominated flow is the formation of a vena contracta flow pattern where a separation bubble is formed i n the cas e of the short orifice T his bubble co mpletely takes over the orifice while it effectively disappears once the transition to the turbulent flow occ urs. At higher Reynolds numbers the turbulent friction losses dominate over the eff ect of the bubble disappea rance. H ence completely turbulent flow is characterized by a decrease of the discharge coefficient. For long enough nozzles the flow has a chance to reattach to the walls before leaving the orifice; therefore the disch arge coefficient does not exhibit a s pike at certain Reynolds numbers for T here is no quantitative theory able to predict the discharge coefficient over a wide range of Reynolds numbers. T herefore several empirical correlations have been proposed. Nakayama [9] pr oposed (1 7) which is accurate for and Asihmin 8 et al. suggested (1 8) which is valid for and with 1.5% accuracy. Finally, Lichtarowicz [6] et al. proposed

PAGE 26

26 (1 9) where (1 10) This expression is valid for and None of these expressions is able to predict the discharge coefficient for which underlines the complexity of the flow at these circumstances. Therefore it seems to be reasonable to keep this ratio above 2 2.5 to facilitate estimation of the discharge coefficient. Another complication arises in the case of pulsing or non stationary operation of plain orifices, e.g. diesel injectors. In this case the discharge coefficient does not follow the empirical expre ssions proposed for the stationary cases. Swirling pressure atomizers (Simplex) The disadvantages of the plain orifice atomizers, such as the relatively narrow spray angle, led to the development of the swirling atomizers. There are two types of swirling a tomizers : a s olid cone atomizers produce an even distribution of drops throughout the spray cone [10] These atomizers are mostly used for humidification in agricultural applications and domestic burners due to a relatively poor drop size distribution qual ity. Hollow cone atomizers [1, 4, 10] are capable of providing much better spray quality; therefore they are wi dely used in a variety of industrial burners, turbines etc. A schematic of the hollow cone swirling pressure atomizer with converging exit nozzle [10] is shown in Figure 1 5. The injecting liquid is forced under high pressure in th e tangential inlet passages inducing rotation in the swirling chamber. The liquid exits the swirl chamber through a nozzle and forms a thin conical sheet that surrounding an air core. The sheet rapidly disintegrates into small droplets. The main di sadvantage of this design is the low atomization quality at flow rates significantly lower than designed; i.e. if the pressure

PAGE 27

27 drop across the atomizer decreases significantly fo r any reason, the atomization quality degrades drastically. The analysis of the flow inside and outside the swirling pressure atomizer is a non trivial problem; an analytic solution is not easily availabl e. Modern CFD capabilities model this flow with reas onably good agreement with experimental results [11, 12] As for virtually all types of pressure atomizers, the discharge coefficient is one of the most important parameters for evaluating the performance of the swirl pressure atomizer. Several empiric rel ationships for the swirl pressure atomizer are available in literature. According to Taylor [13] in the case of an inviscid incompressible fluid, the discharge coefficient can be evaluated as (1 11) where is total liquid area of fuel supply slots, is the swirling chamber diameter and is the exit orifice diameter. This equation has obvious drawbacks: it does not take into account fluid propert ies and some geometrical parameters of the injector. Jones [14] offered the following expression for the discharge coefficient after comprehensive experimental research: (1 12) where is the dynamic viscosity of injected fluid and is the length of the swirling chamber. This equation is reported to be applicable for the following range of the non dimensional groups incorporated into it: and Another parameter of interest related to atomization quality is the liqui d film thickness. Lefebvre [4] proposed the following empirical expression for this parameter: (1 13)

PAGE 28

28 where the flow number is given by equation (1 14) These equations are reasonably accurate for all types of swirling pressure atomizers. Further, velocity coefficient (1 15) relates the actual injection velocity to the ideal one, which would be attain ed if the Bernoulli equation were valid. This coefficient was evaluated by Rizk et al. [15] as (1 16) where (1 17) is the ratio between air filled and liquid filled areas. Finally, according to Simmons et al. [16] the following equation can be used to find the semi vertex spray cone angle evaluation (1 18) The acc uracy of this equation is reported to be as good as To complete this brief description of the swirling pressure atomizers, several empirical equations for evaluating the Sauter mean diameter (SMD) of the drops forming the spray cloud are listed in Table 1 3. SMD is defined by following equation : (1 25)

PAGE 29

29 where represents the number of drops having some particular diameter. Basically SMD is a ratio between average dro p volume and average drop surface area. Therefore this parameter pro vide a great deal of information about the Other types of swirling pressure atomizers In general, as was pointed above, swirling pressure atomizers are capable of providing satisfactory mixture qualit atomizer is the quite narrow operational flow rate range; decreasing of the flow rate by just 10% ruins the mixture quality, and a turbulent liquid jet is injected instead of a hollow cone shaped thin liquid sheet. To provide good atomization over a wider range of operational flow rates a large number of swirling pressure atomizers modifications have been proposed by different authors. Some of the designs will be described briefly below. Dup lex and dual orifice atomizers A schematic drawing of a typical duplex at omizer is shown in Figure 1 6 A There are two different liquid supply passages in this design. The primary passages are open throughout the entire flow rate range of this atomizer an d the main purpose of these passages is to ensure good mixture quality at low flow rates. The liquid supply to the second set of orifices is provided by the same f uel pump as for the primary one but with a spring loaded pressurizing valve installed into th e secondary fuel supply line. This valve is preset to start opening once the pressure in the fuel supply system reaches a certain value. Thus, this atomizer is capable of providing the required mixing quality at flow rates as small as 10% of the maximum fl ow rate. The only

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30 drawback of this type of atomizers is a significant reduction of spray angle (up to 20 0 ) at transitional regimes of operation. The dual orifice atomizer takes advantage of the same idea as the duplex atomizer. The only difference, as show n in Figure 1 6 B is in the arrangement of fuel supply passages. In this case, each set of passages has its own swirling chamber, located coaxially. This design eliminates the spray angle change throughout a much wider range of flow rates. Spill return at omizers The spill return atomizer [10] ( Figure 1 6 C) is almost identical to the standard swirling pressure atomizer. The only difference is the presence of a return line, which is connected through an adjustable valve to the low pressure portion of the f uel supply system, i.e. the fuel tank. The main idea of this atomizer is to control the flow rate via adjustment of the return valve. The pressure and the flow rate of the fuel supplied to the atomizer are always high; therefore the atomization is almost i ndependent on the resulting flow rate allowing satisfactory atomization at flow rates as low as 1% of the maximum rate. Despite the obvious advantages, there are a few drawbacks associated with this design. The spray angle exhibits a reverse dependency on the flow rate, with a variatio n as high as 50 0 There are also difficulties measuring the actual flow rate for this type of atomizers since portion of a fuel returns to the fuel tank. Air Assist and Air Blast Atomizers All types of pressure atomizers are c haracterized by relatively simple design and quite robust performance but they have a significant and unavoidable disadvantage the liquid injection velocity, and as a result the mixing quality, is proportional to the square root of the pressure differenc e between surrounding and liquid supply line. Hence, to double the injection velocity the pressure difference across the injector must increase four fold. Usually, there are two components involved in the combustion process an oxidizer and a fuel. In the vast majority of

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31 practical applications one of these components is supplied to the combustion chamber in a liquid state while other is supplied as a gas. In applications where air is used as an oxidizer and hydrocarbons as a fuel the mass ratio between ai r and fuel can be as high as 20. This means that there is a significant flow of air supplied into the combustion chamber. It seems reasonable to use at least a portion of this gas flow energy to improve mixing quality. These atomizers are called air blast and air assist atomizers and are widely used in applications such as jet engines and rocket engines. Air assist atomizers There are two types of air assist atomizers. In the atomizers of the first type the initial mixing between liquid and gas takes place inside the atomizer ; hence this type of atomizer is usually ref erred to as internal mixing air assist atomizer s Several typical designs of these at omizers are shown in Figure 1 7 [1, 4] Internal mixing atomizers are capable of providing an excellent mix ing quality but the spray cone semi vertex angle has a reverse dependence on the gas flow rate. The interaction inside the mixin g chamber or volume is intensive; therefore internal mixing atomizers are usually used to disperse fluids with high viscosity a nd surface tension such as heavy oil and liquid slurries. A n inherent f the liquid and gas flows causing large energy consumption. The per formance of internal mixing air assist atomizers is completely defined by design features. Hence, it is almost impossible to suggest a general equation to evaluate a mixing quality, but the following expression [4] can be (1 26)

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32 where constant s and have to be evaluated experimentally in each particular case. This equation does not take into account fluid properties and mixing chamber geometry; therefore, it cle arly has a limited range of applicability. Due to the complicated design and poor fluid dynamics the application of these atomizers is restricted to la rge industrial boilers utilizing heavy residual fuel oil which cannot be atomized effectively through oth er methods. The second ty pe of air assist atomizers is the exte rnal mixing air assist atomizer [21]; several designs of th is device are shown in Figure 1 8. External mixing atomizers usually have better fluid dynamics properties and less complex design tha n internal mixing atomizers. Since t he resulting semi vertex spray cone angle d oes not depend on the flow rate there is virtually no chance of fluid penetra tion into the air supply system and these atomizers can only be used to disperse fluids with relativ ely low viscosity and surface tension. The performance of coaxial atomizers where liquid is injected in the center can be evaluated using several expressions offered by different authors. Elkotb et al. [22] proposed the following expression (1 27) Note that Weber and Reynolds number in this formula as well as throughout the manuscript, are ba sed on diameters and relativ e gas to liquid velocities. In an attempt to attain generality Simmons et al. [16] offered an equation whi ch is supposed to be valid for simple pressure atomizers as well. His data analy sis resulted in the following expression (1 28 )

PAGE 33

33 where the constant is defined by features of the atomizer design. In the case where liquid is injected through the outer passage the situation is quite different since the liquid tends to form a film around the gas stream. Inamura and Nagai [23] carried out a careful investigation of the performance of this type of atomize rs which resulted in the following expression: (1 29 ) Air blast and effervescent atomizers A ir assist atomizers require supply high pressure gas, which is not a problem in the case of a liquid rocket engine but is quite dif ficult to incorporate into a jet engine. Therefore, a slightly different type of atomizer, known as air blast atomizer, was implemented in applications w here only relatively low speed, usually up to 100 m/s, air supply is available. It is worth to note tha t in most applica tions where air blast atomize rs are used the air velocity is low but the total mass flow of air is greater than in applications where air assi st atomizers are used. This allows implementing such designs as prefilming atomizers. A typical d esign of such a n atomizer is shown in Figure 1 9 A The performance of prefilming air blast atomizers has been evaluated by many researchers. Rizkalla and Lefebvre [24] give the following expression to evaluate the drop distribution for a prefilming atomiz er: (1 30 ) The evaluation of plain jet atomize r mixture quality (see Figure 1 9 B) can be done using a variety of semi empirical formulas. Nukiyama and Tanasawa [25] offered the following equation:

PAGE 34

34 (1 31 ) Although this equati on is not dimensionally correct it still provides a tren d which can be useful as a preliminary evaluation of atomizer performance. For example, for low viscosity liquid and relatively small liquid/gas mass flow rates, SMD is inversely proportional to the gas liquid velocity difference. On the other hand, for high viscosity fluid and high gas liquid velocity difference, the SMD is defined by the liquid gas mass ratio. Rizk and Lefebvre 15 continued and expanded the previou s equation to make it dimensionally correct and came up with following relationship: (1 3 2 ) This equation exhibits an excellent correlation within 1.5 to 3% to the experimental data in the case of low viscosity liquids. Atomiz ers where a relatively small amount of fuel was introduced into a relatively high air flow rate were discussed so far. There is also a type of atomizers which inject s a gas into the fluid and only then form a jet. A schematic of an atomizer of this kind is shown in Figure 1 9 B. The gas is injected into the chamber filled with liquid; the two phase mixture is then injected into the combustion chamber. The apparent advantage of this atomizer is that quite a low pressure difference is required to obtain a rea sonably good quality of mixture. The resulting spray quality does not depend on the size of the passages; therefore the probability of blockage is low. This design has also proven experimentally to reduce soot formation. The only drawback is a tendency of the liquid to find its way into air supply system. SMD for this type of atomizers is reported to follow the trend [4] :

PAGE 35

35 (1 3 3 ) where is a gas orifices diameter. The key feature of this equation is an absence of the SMD dependence on the liquid orifice diameter and exit orifice parameters. Therefore, the risk of orifices blockage can be eliminated by simply increasing the passage diameters. Liquid Round Jet Break up Liquid jet break up has been studi ed extensively both as a fundamental and as an important applied problem. Pioneer theoretical works by Rayleigh [26] suggest that a round liquid jet is not energetically stable. Rayleigh suggested that the potential surface tension force can be referred as (1 34 ) where is a disturbance wavelength, Fou rier series number, any integer is a Fourier series expansion coef ficient. It should be noted that this theory rests o n three fundamental assumptions: T he liquid is inviscid. T he jet is laminar. The jet is quite slow ( i.e. surrounding air influence can be neglected) the jet is unstable if A s can be seen from the equation 1 34 for the liquid jet is unstable with respect to disturbances of wavelength longer than ; for all other disturbance numbers the jet is sta ble Assuming exponenti al disturbance growth rate Rayleigh showed that the fastest growing disturbance wavelength is Assuming that a segment of the jet with a length equal to the resonance frequency wavelength become s a s pherical drop where is the resulting drop

PAGE 36

36 diameter. Hence the break up characteristic drop diameter can be evaluated as Later experimental research conducted by Taylor [27] showed that and, c onsequently Hence the Rayleigh theory is quite accurate for predicting the break up lengt h as well as the resulting drop diameter distribution. T he jet break up length is determined from the disturbance growth rate equation and an assumption that the disturbance value is equal to the jet initial radius (1 3 5 ) where (1 36 ) and (1 37 ) Taking into account that break up length can be ex pressed as then, (1 38 ) The initial disturbance value d epends on the particular experimental conditions, but there are empirical equations to estimate it [4] e.g. (1 39 ) A criterion for this break up mechanism can be formulated as follows [1] In the literature, this break up regime is usually referred to as a Rayleigh break up or varicose

PAGE 37

37 break up mechanism [1, 4] The main features of the Rayleigh type liquid round jet break up mechan ism are shown in Figure 1 10 A Weber [28] attempted to increase increase the generality showing that the assumption regarding the liquid viscosity can be removed by taking viscosity into account: (1 40 ) while the shortest unstable wavelength is the same as Rayleigh suggested. This break up mode is shown in Figure 1 10 B Later experimental results reported by Haenleign [29] validated the relation 1 40 suggested by Weber. Weber also attempted to predict the resulting drop distribution an d a jet break up length, without significant success. To explain this setback, Lefebvre [4] suggested that the influence of the surrounding gas can be neglected only for the p ure Rayleigh break up mod e. Although at the initial stag es of the disturbance promotion the phenomena can be described via a balance betwee n viscosity and surface tension at the later stages the influence of the surrounding gas has to be taken into account. So, only semi empirical expressions can be used to evaluate the jet break up length and resulting drops size distribution under these circumstances. Grant et al. [30] suggested the equation (1 4 1) Sterling et al. [31] suggested a modified versio n of th is equation which is also applicable for up mechanism (1 42 ) where (1 43 ) and function can be evaluated as

PAGE 38

38 (1 44 ) Dan et al. [32] offered the following equation (1 45 ) where the empirical constant in many practical evaluation can be estimated as Since the average drop diameter does not exhibit an apparent correlation to the disturbance wavelength, there are few semi empirical relations suggested by different researchers to evaluate it. In the literature, this break up mechanism is usuall y referred to as the first wind induced or sinu ous wave break up mode. The conditions for this break up mode to become dominant are [1, 4] (1 46 ) T he influence of the surrounding gas as a separate parameter must me incorporated in the theory of the liquid jet break up. T he ga s liquid interaction in this case can be explained via Kelvin Helmholtz instability (KHI). This type of instability eventually leads to jet disintegration. The resulting drop diameter is not rela ted to the initial jet diameter but to the surface tension as well as to the liquid/gas velocity and density ratio. The first attempt toward application of an instability theory to a liquid jet injected into a gaseous environ ment was done by Taylo r [27] The formulation of the dispersion equation in the case of negl igible visc osity and gravitational forces i.e. high R eynolds and Froude numbers) appears as follows: (1 47 ) where k is a disturbance wave number and is a disturbance radial fr equency. The shear laye r in this case around the jet is always unstable when (1 48 )

PAGE 39

39 The resonance wavelength i n case of still surrounding gas is described by following equation (1 49 ) Thus, the resonance waveleng th is linearly proportional to the surface tension and inversely proportional to the velocity square. This analysis does note take viscosity into account. And, although this reduces the theory generality, recent investigations by Hongobok et al. [33] show that the presence of viscosity affect s more the resulting drop size distribution rather than the initial disturbances wavelength and growth rate. It is also worth to note, that in the limit ance wavelength so the Rayleigh instability domi nates in this case, as expected Comparison s between me asured disturbance wavelength and the present li near KHI analysis were found to be in good agreement for low viscosity fluids [33] This regime is usually named the second wind induced break up or a wave like break up regime with air friction. This regime manifests itself at [1, 4] (1 50 ) Incorporation of jet turbulence into the analytical investiga tion of the liquid round jet break up has not been as yet, successful. T he main reason is, probably, an absence of a detailed theory that would describe the turbulent shear layer with a good degree of accuracy. There are two turbulent regimes observed exp erimentally. In the first case, the jet is initially laminar. O nce the fluid leaves the nozzle infinitesimal disturbances unavoidably present in a flow, have a chance to grow. Eventually the jet beco me s turbulent. This break up mode is clearly illustrated by the photographs of Taylor and Hoyt. [34] Recen t numerical simulations presented by Hongobok [33] et al. suggest that, at the first stages, while disturbances are small, this case most likely can be described via KHI instability. However, the resulting d rops diameter is not related to the initial disturbance wavelength. This disagreement is related by authors to further jet

PAGE 40

40 turbulization as well as the e ffect of the liquid viscosity. There are a few empirical equations offered by different authors to eval uate the jet break up length. Sallam et al. [35] suggest that (1 51 ) where C and are empirical positive constants related to the injector design features. After a maximum value, break up length again t ends to decrease almost linearly with increasing injection velocity. Lin et al. [36] offer the following equation to evaluate this parameter under these circumstances (1 52 ) SMD distribution in this case was evaluated by Fae th et al. [35] as (1 53 ) where C is an empirical constant Wu et al. [37] evaluated it as This regime of jet break up was named as an atomization. The limits are [1, 4] a nd The upper limit of the Reynolds number is strongly dependent on features of the nozzle design. Atomization of initially laminar jet is illustrated in Figure 1 10 D. There are cases where a jet is t urbulent within a nozzle itself so the mixing is strongly influenced by the initial turbulence. As a result, KHI is not likely to be capable to describe any of the aspects of the jet break up in this case. Therefore analytical description of the turbulent jet break up is limited to the semi empirical evaluations with some dimensional analysis background. Fully developed liquid jet break up is illustrated in Figure 1 10 E. SMD in this case can be evaluated via a semi empirical equation offered by Tanasawa [38] et al.

PAGE 41

41 (1 54 ) Since the spray is formed in the direct vicinity of the injec tor tip it is reasonable to introduce the spray angle as a parameter The simplest possible relation to evaluate a spray angle can be taken from the theory of turbulent jets [39] : (1 55 ) And Yokota et al. [40] provide the following equation based upon the regressive analysis of they experimental data (1 5 6 ) where is defined by, ( 1 57 ) Most researchers conclude that jet break up occurs in the direct vicinity to the injector tip, so the break up length in this case is equal to zero. Neverthe less th is hypothesis is not accepted unanimously. Hiroyasu et al. [41] evaluated break up length by measuring an electrical resistance of the spray in vicinity to the injector tip. T hey concluded that for 1 mm I D. nozzle, even at 20 MPa injection pressures the break up length is about 10 20 mm. The hypothesis of these researchers is illustr ated by t he blue dashed line in Figure 1 11 E. This regime, as the previous one, is referred as atomization and occurs for and To conclude the discussion on the liquid round jet break up in still air the qu alitative dependence of jet break up length on Weber n umber is given in Figure 1 11 with different regimes of jet break

PAGE 42

42 corresponds to the dripping mode; this mode occurs at extremely lo w flow rates and lies out side of the scope of interest for this work. As shown in the figure, initially the break up length is proportional to Weber number and this tendency holds for the Rayleigh and the firs t wind induced break up regimes plot. SMD in this range is comparable or even larger than the initial jet diameter. Once the surrounding gas starts affecting the jet disintegration, the disintegration length is inverse ly proportional to Weber number as shown in area marked in the pl ot. The resulting mixture quality is typically within the range: The trend is changing again with first signs of the turbulence onset. The location of the maximum is strongly dependent on injector design and can not be predicted the oretically; see the area marked Finally for the fully developed jet, the definition of the jet break up length is not quite clear the jet behavior is more or less sim ilar to that of the gas in the plot. Some re searchers, however, disagree with this theory and report results which suggest that even for a diesel atomizer, with a pressure difference across it as high as 20 MPa, the break up length is quite small, but finite. For both turbulent regimes In general, up, in particular, the turbulent mechanisms are still not quite clearly understood even on the qualitative level there are a large number of unresolved problems. Droplet Deformation and Break up Independent o f the atomizer design the final goal of atomization in combustion application s is to form the spray with characteristics most suitable for effective evaporat ion and combustion. To achieve this goal understanding of the drop/gas stream interac tion is a key parameter. This interaction is defined by liquid properties including viscosity, surface tension etc., droplet shape and diameter distribution and the gas flow velocity. The situation is

PAGE 43

43 complicated by the presence of the active heat exchange between droplets and surrounding gas. In general, droplet/gas interaction can be divided into two stages droplet deformation and its furth er disintegration. Both stages exert significant influence on the mass and heat transfer processes which in turn are affect the volumetric combustion rate and its overall efficiency. At the initial stages of droplet/gas interaction the drop is deformed to form an ellipsoid of rotation Usually the droplet deformation is charac terized by comparing major semi axis to an initial drop radius i.e. the deformation rate is stated as (1 58 ) Four major ways of droplet deformation influence the heat and mass exchange processes can be defined as foll ows: cross section A to tal area S hydrodynamic drag coefficient and heat exchange coefficient change. Cross section area is defined as (1 59 ) Its maximum value is define d by the maximal deformation rate which can be achieved without drop break up According to Wierzba [42] the maximum deformation rate can be estimated as ; therefore droplet cross section a rea variation relative to its initial spher ical shape can be as high as Total drop area can be estimated as (1 60 )

PAGE 44

44 where is a minor semi axis and For the maximal deformation rate the total to initial area ratio varies between 1.3 and 2.1. The h ydro dynamic drag coefficient exhibits a strong dependence on drop deformation as well. As has been shown in many studies, the drag coefficient of the deformed drop varies from 1.6 to 3.0 while its can be estimated as 0.42 if the drop keep s its initial spherical shape. According to Wadewitz [43] et al., the heat transfer coefficient of deformed drop s can be evaluated via following equation (1 61 ) where is a Sauter dia meter is an initial drop diameter and is a gas heat conduction coefficient. According to this equation heat transfer red for the deformed drop can be 3 to 5 times higher when for the spherical one. F rom this analysis, drag coefficient and cross section area increase will cause the drop accelerate and quickly reach a velocity of the surrounding gas and as a result the heat ex changed would be reduced. However, increasing the total area and heat transfer coeffici ent could promote the heat exchange processes. At the current state the resulting net effect of the droplet deformation on the heat exchange processes is not quite clear even for the single drop/gas interaction. Aerody namic droplet break up was extensivel y studied over the last 50 years due to its importance in practical applications. Earliest experimental works provided by Volhynsky [44] and Lane [45] concentrated mostly on the qualitative description of the distinguishing features of this phenomenon. Fur ther invest igations provided by numerous researchers [46, 47 48, 49]

PAGE 45

45 resulted in the development of a relatively complete description of droplet break up under a variety of conditions. The c ollected data were analyzed in several reviews [ 50, 51]. Several dimensionless parameters are commonly recognized as importan t for droplet break up phenomena : and Ohnesorge number, represents the ratio between viscosity a nd surface tension forces. For water and hydrocarbons droplets of ; therefore viscous forces can be neglected. Some authors use Laplace number instead of Severa l authors mention that changes of the gas flow velocity during the droplet break up appear to be one of the important parameters and introduce an addi tional dimensionless number [ 52] : (1 62 ) where (1 63 ) is a characteristic droplet deformation time. The c ritic al Weber number tends to increase with increasing G. It has been found that the Weber number is the most important parameter affecting the droplet deformation and break up process. Almost al l authors defi ne its critical value within 10 and 13. Dependence of the droplet disintegration regimes on Weber number in the case of small Ohnesorge number (or La >>1) is pr esented in the Figure 1 12. All disintegration and deformation modes begin from for ming the basic shape so Weber number s, Under these circumstances forces related to the surface tension and gas flow are compar able and the drop start s to oscillate. I f the disturbance related to the flow is strong enough break up occurs, producing 2 to 10 smaller drops Another break up regimes so break up or

PAGE 46

46 break up modes appear at Weber number within ; in this case the stagnation pressure is strong enough to force though the middle part of the drop and form a shape shown in the Fig ure 1 12 B. Increasing the flow speed processes related to the formation of the boundary layer start playing a key role in a droplet disintegration mode; therefore for droplet disintegration mode is significantly different from bag or vibration break up modes. So called stripping or shear break up mode is observed under these circumstances. Features of Supercritical Mixing To date, almost all theories and semi empirical evaluations of a liquid jet break up and further mixing processes have been relevant only for restricted range of experimental conditions. In particular, all the analyses presented above assume that the pressure and temperature of the liquid and the surrounding gas are well below critical values. As described above, analysis of mixing under sub critical conditions is heavily based on the assu mption that there is a clearly defined border between liquid and surrounding gas. Therefore, it is completely reasonable to assume that liquid temperature is nearly constant and limited by boiling temperature even if the surrounding temperature is much hig her. As a result, predictions of jet or droplet disintegration and further liquid/gas mixing are almost solely based upon such parameters as Reynolds, Weber and Ohnesorge numbers. There is a range of applications, however including automotive diesel engine s and liquid fuel rocket engines, where those assumptions are, obviously, not valid. All these applications require injection of a cold fluid into an environment with pressure and temperature significantly higher than the critical values for the pure fluid According to classical thermodynamic theory the main distinguishing feature of supercritical fluid is an impossibility of two phase region existence, i.e. typical assumptions on presence of two distinct regions liquid and surrounding gas with a clear s urface between them is not valid at these circumstances. It is

PAGE 47

47 evaporation but droplet mass losses due to diffusion. In fact numerical and experimental studie s show that even in a simplistic case single drop surrounded by still high pressure and temperature gas the drop evaporation process reveals significant changes. Sarvey [ 53] upon experimental observation of suspended on stainless steel wire decane dro ps, reported that the temperature distribution no longer has a discontinuity on the droplet border and there is no quasi steady state of the droplet temperature distribution, i.e. the droplet temperature increased throughout its lifetime. Similar behavior is found by Yang et al. in numerical simulations of liquid oxygen evaporation in an atmosphere of hydrogen [ 54, 55] Another interesting set of results is reported by Sato et al. [ 56] In their experimental work, the evaporation rate of an n heptane drop wa s evaluated over reduced pressure range of and reduced temperature range of The results suggest that there is an apparent minimum of the evaporation rate around critical point. Later experiments by Chauveau et al. [ 55, 56] and Morin et al. [57] with n heptane and methanol drops confirm this evaporation rate behavior around the critical point. The nature of this phenomenon is not quite clear. Chauveau et al. [56, 57] suggested that this non monotonic dependenc e can be explained by the combined effects of the decreasing diffusivity with increasing pressure. Both of these effects cause a high vapor concentration near the drop surface hindering emission and, as a result, increasing boiling point with pressure. The refore, the drop temperature increases and causes a reduction of heat transfer experimentally or numerically proven model demonstrating this evaporation rate minimum a round the critical point presented in the existing literature.

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48 Experiments with fluids injected into an environment with pressure and temperature exceeding the critical values of the injected fluid may, probably, illustrate the difference between sub criti cal and supercritical mixing, although the interpretation of results may not be straightforward. A qualitative picture of the thermodynamic transformations an injected fluid undergoes during injection can be illustrated with the simplified phase diagram sh own in Figure 1 13. Before entering the injecting nozzle the fluid is at supercritical pressure but sub critical temperature indicated by point 1 in the phase diagram. The pressure drop across an injector nozzle is quite small, therefore after injection, t he fluid has to change from its initial sub critical thermodynamic state to a supercritical one shown by point 2 on the phase diagram. Most authors suggest that after transition to the supercritical state the fluid further mixes with the surrounding; there fore its partial pressure drops below the critical value as shown by point 3 on the phase diagram. There is no clear opinion in the literature on the processes which take place during these thermodynamic transformations, although some points of overall agr eement can be found. First, the enthalpy of evaporation vanishes at these conditions; therefore the liquid gas mixing process is likely to be controlled by diffusion rather then evaporation [58, 59]. Additionally, Woodward and Talley [60, 61] pointed out t hat during mixing between liquid and surrounding gas the critical pressure can be several time higher than its value for a pure liquid. Hence, the critical pressure is not a fixed value but a dynamic parameter depending on local conditions. Finally, for lo cal mixtures near the critical point, thermal, mass and momentum transfer properties become nearly singular [54, 61]. The behavior of the specific heat of nitrogen during a transition from a sub critical to a supercritical state along the line with constan t pressure is shown in Figure 1 14 for nitrogen; other thermodynamic properties (e.g. ) have singularities around the critical point as well.

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49 Somewhat controversial suggestions exist in the literature regard ing the shear layer development and, as a result, the jet break up length. Chehroudi et al. [61] suggest that due to the disappearance of the surface tension and vanishing of evaporation enthalpy mixing between injected fluid and surrounding gas exhibits g as gas mixing like behavior once the critical values are achieved. These authors support their conclusions by experimental work done by Mayer et al. [62, 63] and they own experimental investigations of liquid nitrogen injection into a supercritical nitroge n environment [61]. Bellan et al. [64, 65, 66, 67] and Yang et al. [68, 69, 70] presented results of numerical simulations which suggest that as long as the gas/fluid density ratio is below 0.1, the supercritical jet exhibits significant differences to sub merged turbulent jet behavior. In particular, large density differences between fluid and the surrounding gas lead to turbulence damping and inhibition of the mixing rate. Due to these factors the jet has much longer unmixed core length compared to the wid e recognized and accepted turbulent gaseous jet theory summarized by Abramovich in his classical book on theory of the turbulent jets [71]. Abramovich also presented the theory of a heavy jet injected into lighter surrounding in case of absence of surface tension, e.g. a dust or droplet laden jet injected into a gaseous environment; however, this theory was not yet applied toward the supercritical jet. To justify the difference between numerical simulations and qualitative assumptions based on available exp erimental results, Bellan et al. [66] pointed out the limitations of experimental results using the shadowgraph technique. First, the method is integrative, the light has to pass through the entire jet, therefore the picture is an average throughout the je t. Secondly, the shadowgraph measures density gradient i.e. low density but highly turbulent regions can easily saturate the image. As a result, relatively low dense cloud of already mixed fluid, which indeed exhibits gas gas mixing features, can hide the high density core in the center of the jet. These suggestions are confirmed

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50 by visual comparisons of X ray images of sub critical, transcritical and supercritical mixing conducted by Birk et al. [72, 73] To support the somewhat general speculations discuss ed above, a review of available literature is given below. Experimental works The number of experimental works specifically addressing supercritical mixing, to the best 15 unrelated publications. Some of the re levant publications are described in detail below. An early experimental work intentionally devoted to obtaining some insight into supercritical mixing was done by Newman and Brzustowski [74] as early as 1971. Injection of liquid carbon dioxide into a cha mber filled with mixture of carbon dioxide with nitrogen was investigated. Three different chamber pressures were chosen: and The critical pressure of carbon dioxide is The researchers raised the reasonable question of whether the absolute pressure of the chamber or the partial pressure of carbon dioxide exhibits the stronger influence on mixing mechanisms; therefore three different sets of partial pressures o f carbon dioxide ranging from to 0.5 and up to 1 times its saturation value were used for each chamber pressure value. Finally, the temperature was varied from sub critical to supercritical values for each partial pressure of carbon dioxide. The injection velocity was varied from 2 to 4 m/s. The injector diameter and initial liquid temperature were kept constant for all experiments: and Simple photography was used to observe the jet be havior. For all experiments where the temperature of chamber was below the critical value for revealed a reverse dependence on chamber and partial pressure va lues. For experiments where the partial pressure of carbon dioxide was equal to its saturation pressure the droplet formation

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51 was no longer observed once temperature and pressure were exceeding the critical values. For experiments where the chamber was fil led with pure nitrogen at supercritical temperature gas/gas like jet mixing was observed only at sufficiently supercritical pressures, i.e. The dependence of jet mixing appearance on the partial pressure of injected fluid in the en vironment is one of the questions which have not been resolved even on qualitative level up to date. Another pioneering work was reported by Birk et al. [72, 73] This work is the only one where X ray imaging was utilized to obtain qualitative density fiel d of liquid jet. Among the apparent advantages of this technique is that beam steering is not a problem whereas for any optical technique this issue has to be addressed appropriately. Methyl iodine was used as a working fluid in these experiments due to it s appropriate X ray absorption cross section. Jet diameter was chosen to be equal to 1 mm; and the liquid injection velocity was varied around 40 m/s. Results, obtained via X ray imaging were compared with images obtained with high speed cinematography. Co mparison between X ray and regular images shows, that although the visible portion of the jet reveals apparent similarity to submerged turbulent jet, the liquid core is much less turbulent and reveals some similarity to low speed liquid jet behaviour. The authors report an apparent elongation of the unmixed jet core once the pressure and temperature exceed critical values. Clear disagreement is observed between liquid core length under supercritical conditions to semi empirical evaluations offered for sub c ritical mixing e.g. Equations 1 38, 1 41, 1 42, which is not surprising, since all of those equations are involve surface tension. Instead, an equation similar to that offered by Abramovich [71] to evaluate the potential core length of a turbulent submerge d jet (1 64)

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52 According to this evaluation, further increasing the chamber pressure caused reduction of the liquid jet core length this trend was confirmed experimentally. In general, despite its unavoidable integrative nature, t he X ray technique has potential for investigation of the mixing processes. A set of excellent experimental work on high pressure cryogenic jet mixing and combustion was published by Mayer et al. [62, 63] The investigations were done using shadowgraph for cold mixing and color photography for combustion. For some of the experiments images of OH distribution are presented among the results. The test chamber consisted of a head with a coaxial jet injector, an uncooled 40 mm ID variable length circular cross s ection combustion section and a variable profile exhaust nozzle. In most studies the combustion chamber was 400 mm long. Mixing and combustion was observed via two 25 mm visible diameter windows located across from each other, while another set of rectangu lar widows was mounted in the same cross section to access laser beam or sheet to the chamber when it was needed. All of the windows were cooled with nitrogen film during tests involving combustion. The coaxial injector was 12 mm long, the central post was made of 1 to 2 mm ID diameter 0.3 mm wall thickness tube. Co flow was supplied through a 2.8 or 3.5 mm diameter coaxial annulus depending on required experimental conditions. In all reported experiments liquid nitrogen or liquid oxygen were supplied to th e chamber in the center. In cold coaxial jet mixing investigations helium was supplied through the coaxial annulus. The velocity of injection through the central post was varied within The velocity of co flow was varied within In all cold mixing injected liquid temperature was set to 100 K while the chamber was set to room temperature. Results of several sets of experiments with single round jet were reported. Based on the results by Newman and Brzustowski [ 74], two sets of identical parameters for the chamber filled with nitrogen and hydrogen were reported. For all of

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53 these experiments, the liquid injection velocity was equal to 1 m/s. It was shown that in the case of the chamber filled with nitrogen transit ion to gas gas type of mixing appeared at chamber pressure equal to the critical nitrogen pressure. For the experiments where the chamber was filled with helium a supercritical mixing pattern was observed only if which is in agreeme experiments on injection of liquid nitrogen into the chamber filled with nitrogen with injection velocities of 5 and 10 m/s were reported. At 10 m/s transition to gas gas like mix ing was observed at pressure while in experiments with 5 m/s injection the transition was still observed at critical chamber pressure. An experiment with coaxial liquid oxygen/gaseous helium coaxial injection in general followed the trends revealed above with the only difference that transition to supercritical like mixing was observed at pressures which can be explained by the relatively high helium velocity, i.e. The influence of th e mixing mode on combustion was reported by this team as well. For sub critical pressures the presence of combustion caused drastic smoothening of the liquid portion of the jet. Droplet formation was also eliminated with the combustion. This behavior was e xplained by the gas density decrease around the jet due to the high combustion products temperature and, as a result, aerodynamic interaction between liquid jet core and its surrounding decreased significantly. The presence of combustion did not produce su ch a pronounced difference in jet appearance at supercritical conditions although certain laminarization of the jet was still observed. An interesting approach to obtain additional information on high pressure mixing was taken by Talley and Woodward [60] u sing Raman scattering. The authors suggested that, since the Raman scattering signal is proportional to density, the application of this technique is feasible

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54 due to the naturally high density of the investigated jet. The authors used a high pressure chamb er which sustains pressures up to 135 atm. The second harmonic (532 nm) of a Nd:YAG laser with an average pulse energy of 220 mJ was used to excite the Raman scattering. The laser beam was formed into 1 mm thick and 25 mm wide sheet. A notch filter with 60 7 nm center line was used to eliminate elastic scatter light. The main problem in these experiments was the low signal to noise ratio. To eliminate this problem, the authors averaged several pulses with limited success. The dependence of pressure values bo rdering sub critical/supercritical mixing appearance reported earlier by different authors was confirmed in this study. The presence of a high density core inside the gas gas like low density cloud was confirmed as well. Another set of shadowgraph investig ations of supercritical mixing as well as combustion at supercritical conditions was presented by Chehroudi et al. [61, 75, 76] The experimental facility of critical conditions for mixtures is worth mentioning. They suggest that some changes of the separation between supercritical and gaseous states behavior have to be clearly understood. The authors suggest that the first point on this line is defined by the heavy component of the mixture, i.e. for hydrogen/oxygen mixture the first point on the critical line is defined by the critical point of oxygen. Further increase of the mixture pressure reduces its critical temperature i.e. the line separating the supercr itical and gas states is no longer straight and has a positive slope. These changes can be attributed to the presence of a light component in the mixture. Although, for some systems, e.g. nitrogen/helium, such features are not reported the authors report r esults obtained with Raman spectroscopy and shadowgraph. Due to the extremely low Raman scattering intensity, averaging over 5 to 10 pulses was used. This probably affects the reliability of the data due to the high turbulence of the observed jet. Averagin g also makes it impossible to

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55 obtain reliable data on the density gradient field. Fractal analysis was applied to reveal whether the self similarity exist or not in this case. The resulting fractal dimension was reported to be approx. 1.25 for sub critical jet and 1.35 for a supercritical one. These results show good agreement with theoretical values for liquid and gaseous jet, correspondingly. A semi empirical equation to evaluate the jet spreading angle in case of supercritical mixing was offered as (1 65) where (1 66) Values of depend on the particular system being investigated. It was found that for liquid nitrogen to gaseous nitrogen injection, for into injection and for into injection. Numerical simulations There have been recent advances in numerical simu lations of these processes although there are still some apparent unresolved issues. First, the heat and mass transport properties, used in virtually all simulations presented in literature, have thermodynamic equilibrium as a fundamental assumption which is obviously not the case in this situation. One possible solution to this problem was offered by Bellan et al. [ 64, 65, 66, 67] fluctuation dissipation theory can be applied. The goal of this theory is to fill the gap bet ween molecular level approach, which is clearly difficult to apply at current level of numerical capabilities and the continuum assumptions. The second apparent problem worth careful consideration is the selection of the equation of state. Another problem arises from difficulties already pointed out above, as shown in Figure 1 14, as has quite a pronounced peak around

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56 the critical point. The thermal conductivity exhibits a similar behavior around the critical point. Therefore, the characteristic length scale has a tendency to increase during the transition through the critical point. But due to this characteristic length change, Navier Stokes equations, might be not valid. Therefore a careful analysis of the fu ndamental equations has to be conducted before relying on the results of numerical simulations of supercritical mixing. The problem of a single droplet in a stagnant supercritical environment was addressed by Lafon et al. [78], Yang et al. [68, 69] and Bel lan et al. [65]. Evaporation of liquid oxygen droplet exposed into hydrogen environment was investigated numerically by Yang et al. [68, 69] where the initial droplet temperature was chosen to be An extensive matrix of surrounding temperatures and pressures was covered: The Benedict Webb Rubin (BWR) equation of state was utilized (1 67) where constants , and are found in literature [79]. According to ex perimental results of Sychev et al. [80], this equation of state has 1.5% maximum relative error throughout the entire scope of temperatures at pressures. Semi empirical relations were used to evaluate transport properties. The locus of critical conditions was taken as a definition of droplet boundary. Droplet evaporation time was estimated as (1 67) where the correction factor was (1 68)

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57 No dependence of droplet lifetime on surrounding pressure was foun d. The same approach was applied to investigate the behavior of an n heptane droplet in air. Exponential decrease of the droplet lifetime with pressure increase was reported. In contrast to the liquid oxygen/gaseous hydrogen case, no temperature dependence of droplet lifetime was found. Lafon et al.[83] used the Peng Robinson equation of state to the study of liquid oxygen droplet drops in a hydrogen atmosphere. The overall view of the Peng Robinson equation of state is shown in the chapter 2, Equation 2 5. A semi empirical approach was used to estimate transport properties. Thermal diffusion was neglected in this investigation. Gas pressure and temperature was varied within a range and respectively. The i nitial droplet temperature was chosen to be Although qualitatively the results are in a good agreement with Yang et al. [68, 69], droplet evaporation time is underestimated up to 50%. Bellan et al. [64, 65] studied a heptane nitrog en system due to the availability of experimental data regarding this system. The Peng Robinson equation of state was chosen and dissipation theory was applied to evaluate the transport properties of the system. Since the loci of large density gradient were labeled as droplet boundaries in the available optical experiments by Morin et al. [59] and Sato et al. [56], it was decided to use the same definition in these numerical simulations as well. Comparison of these numerical simula tions results to available experimental data shows agreement of droplet radius dependence on time within 10%. Since all issues previously pointed out for droplet evaporation are present under these circumstances, only the results obtained with models prove n to work for single drop evaporation are reviewed.

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58 Yang et al. [68, 69, 70] published a set of numerical simulations results on supercritical mixing. These works extend the apparent success reached during investigation of single drop in stagnant surround ing to the case of drop exposed to uniform flow, then to 2 D shear layers and recently to 3 D jet mixing. Only the recent work on 3 D supercritical jet mixing is described here in detail. The work is covering performance of such devices as simple round, pr essure swirling and coaxial jet injectors. In all numerical experiments injection of liquid oxygen was investigated. Large eddy simulation technique with sub grid effects taken care of via the Smagorinsky eddy viscosity model was utilized to incorporate tu rbulence into the technique. Fluid transport properties such as viscosity and thermal conductivity were modeled utilizing extended corresponding state theory coupled with the Benedict Webb Rubin equation of state. Thermodynamic properties of the system, i.e. enthalpy, Gibbs energy and constant pressure specific heat, were evaluated via the Soave Redlich Kwong equation of state (1 69) where constants and are defined as and Environment and initial liquid temperatures for all experiments were chosen to be and cor respondingly. For the simple round injector two runs are described, both concerning the situation where liquid oxygen is injected from a 0.3 mm ID tube. The surrounding pressure of gaseous hydrogen in the first run was 69 atm. and 93 atm. in the second one The injection velocity was 15 m/s in both cases. The density, density gradient, vorticity, thermal diffusivity and compressibility fields were presented.

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59 Decreasing the jet liquid core length with increasing pressure was noticed. The high density gradie nt between the jet core and the surrounding gas was found to inhibit the turbulence development and, as a result, led to elongation of the liquid jet core. An equation to evaluate the spreading angle of the low density portion of the jet is offered: (1 69) where (1 70) This equation appears to be a modification of a semi empirical equation offered by Abramovich [71] to evaluate turbulent gas gas jet spread angle. The results of these numerical experiments were compared to experimental works of Chehroudi et al. [75, 76] which included liquid nitrogen/supercritical nitrogen. It appears that liquid nitrogen to supercritical nitrogen mixing exhibits some drastic differences to the l iquid oxygen/gaseous hydrogen mixing. After mixing, oxygen hydrogen mixture is sub critical which is not true for liquid nitrogen supercritical nitrogen mixing. Bellan et al. [64, 65, 66, 67] published results of shear layer simulations with 3 D effects fo r heptane/nitrogen and oxygen/hydrogen systems. The main parameters of these studies are given in Table 1 4. As is shown in the table, both components are supercritical, i.e. this is a case where both of mixing components are initially supercritical. Peng Robinson equation of state dissipation theory was used to evaluate transport and thermodynamic properties of the system. The fluctuation dissipation theory establishes a direct relation between the fluctuation propertie s of the thermodynamic system and its thermodynamic

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60 properties. The direct numerical simulation technique was used. Density, density gradient, vorticity, thermal diffusivity and compressibility fields are presented among the results. Kelvin Helmholtz in stability development was observed in all studies. High density gradient values were obtained; the authors conclude that the absence of experimental confirmation for this feature can be attributed to the absence of appropriate experimental techniques. The presence of high density gradient areas led to an apparent anisotropy on the energy dissipation, which in its turn disapprove the assumption of small scale similarity isotropy. Thus, the authors suggest that only direct numerical simulations can adequately solve this problem and question the reliability of other approaches, e.g. large eddy simulations which rely on the assumption of small scale similarity. The high density gradient region reported to be wider for than for heptane/nit rogen shear layers. Objectives of the Current Work This introduction was used to give a perspective of the liquid gas mixing problem in applications involving combustion. This problem has been actively approached by the research community, with signific ant success. Nevertheless, there are a few problems which did not attract enough attention so far supercritical mixing is one of them. Mixing at high pressures and temperatures appears in many applications including oil wells where pressure and temperatu re can easily exceed critical values for the oil, diesel engine etc. Yet, there is limited theoretical as well as conceptual understanding of the fundamental principles which are governing this process. As a result this topic has recently attracted signifi cant attention from the scientific community. The goal of this work is to expand the database of reliable experimental measurements of density distribution during the supercritical liquid/gas mixing as well as gain some insight into fundamental features of supercritical mixing under these conditions.

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61 Table 1 1 Practical applications of atomization Area Application Spray Drying Milk Powder Processing, Food Processing, Chemical Processing Spray Combustion Diesel Engines, Spark Ignition Engines, Gas Turbi nes, Rocket Engines, Industrial Furnaces, Domestic Heating Boilers Spray Cooling Cooling of Ingot in Continuous Casting, Cooling of Nuclear Cores, Cooling of Turbine Blades, Coke Quenching Spray In halation Vaporization of Volatile Anesthetic Agents and Medication Aerosol (Mist) Spray Humidification/Air Conditioning, Fire Fighting, Drenching Operations, Lubricating, Pollution/Dust Control Crop Spray Applying Agricultural Chemicals, Spray Irrigation Paint Spray Surface Finishing, Surface Coating Spray Cleaning Gas (Wet) Scrubbing, Gravel Washing, Vegetable Cleaning, Surface, Treatment, Car Washing Spray Atomization Dental Amalgams (AgSnCu Powders), Shot Blasting Grits (Still or Iron, Powders), Solid Rocket Fuels (Al Powder), Metallic Paints (Al, CuZn P owder), Filters (CuSn Powder), Solder Creams (PbSnAg, Bi 57 Sn 43 Powder), Strips for Diamonds Synthesis (Co Powder), Flares (Mg Powder), Jewellery Brazing Pastes (Pd, Au, Ag Powder), Dense Media for Minerals and Scrap Separation (FeSi Powder), Coating for We lding Electrodes (Fe, FeMn, FeSi Powder), Explosives (Al Powder), Food Additives (Fe Powder), Batteries (Zn Powder) Spray Deposition Spray Forming, Spray Casting, Spray Rolling Thermal Spray Plasma Spray, High Velocity Oxy Fuel (HVOF)

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62 Table 1 2. Perfo rmance of various atomizers Method Drop size (m) Application Advantage Drawbacks Pressure Atomization Plain Orifice 25 250 Diesel Engines, Jet engine Afterburners Ramjets Simple, Robust, Cheap Narrow Spray Angle, Solid Spray Cone Simplex 20 200 Gas Tu rbines, Industrial Furnaces Simple, Cheap, 180 0 Spray Angle High Pressure drop, Spray Angle Depends on Pressure Difference and Ambient Density Duplex 20 200 Gas Turbine Combustors Simple, Cheap, Good Atomization Over a Wide Range of Liquid Flow Rates Spr ay Angle Decreases With Increasing Liquid Flow Rate Dual Orifice 20 200 Gas Turbines Good Spray Atomization, Relatively Constant Spray Angle Poor Atomization in Transition Range, Complexity in Design, Susceptibility of Small Passages to Blockage Spill Return 20 200 Combustors Simple, Good Atomization Over Entire Range of Liquid Flow Rates, Low Risk of Blockage Varying Spray Angle with Liquid Flow Rate, Higher Power Requirements except at Maximum discharge Two Fluid Atomization Air Assist Internal Mixin g 50 500 Industrial Furnaces, Industrial Gas Turbines Good Atomization, Low Risk of Blockage, Ability to Atomize High viscosity Fluid Possible Liquid Back Flow Into Air supply Line, High Air pressure is Required, Auxiliary Metering Device is Required Ext ernal Mixing 20 140 Industrial Furnaces, Industrial Gas Turbines Good Atomization, Low Risk of Blockage, Ability to Atomize High viscosity Fluid, No Risk of Liquid Back Flow Into Air supply Line External Source of High Pressure Air is Required, Limited Liq uid/Air Ratios Two Fluid Atomization (Air Blast) Plain Jet 15 130 Industrial Gas Turbines Simple, Cheap, Good Atomization Narrow Spray Angle, Atomizing Performance Interior Pre filming Air Blast Type Pre filming 25 140 Aircrafts, Industrial Gas Turbines Good Atomization, Wide Spray Angle Poor Atomization At Low Air Velocities Effervescent Atomization 20 340 Combustors Simple, Reliable, Good Atomization, Low Risk of Blockage, Cheap Need for Separate Supply of Atomizing Air

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63 Table 1 3. Swirling pressure atomizers SMD empirical evaluation Source Expression Notes Radcliffe [17] (1 19) Jasuja [18] (1 20) Slightly modified version of Radliffe equation Babu et al. [19] (1 21) For Babu et al. [19] (1 22) For Kennedy [20] (1 23) Lefebvre [4] (1 24) Table 1 4. Numerical experiment conditions Parameter Veloc ity m/s 85.947 209.856 158.004 770.983 114.926 586.972 Density kg/m 3 259.487 20.141 96.764 3.965 197.317 8.050 Pressure atm. 60 60 100 100 100 100 Temperature K 600 1000 400 600 235 287 Reduced pressure 2.22 1.81 2.01 7.89 2. 01 7.89 Reduced temperature 1.11 7.92 2.58 18.08 1.52 8.65

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64 Figure 1 1. Ultrasonic atomizer. 1 atomizing horn, 2 reflecting horn, 3 piezoelectric discs, 4 atomizing surface. Figure 1 2. Spray triode atomizer. 1 nonconductive atomizer body, 2 liquid entrance, 3 first (emitter) electrode, 4 second (collector) electrode, 5 third (blunt) electrode. 1 2 3 4 Liquid Supply High Voltag e Source R Liquid Supply 1 2 3 4 5

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65 Figure 1 3. Plane orifice atomizer. Figure 1 4. Dependence of discharge coefficient on Reynolds number l 0 d 0

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66 Figure 1 5. Typical pressure swirl atomizer design Figure 1 6. Different modifications of the swirl pressure atomizer. A) Duplex atomizer B) Dual orifice atomizer C) Spill return atomizer Fuel slots Secondary fuel supply Primary fuel supply B Secondary fuel supply Primary fuel supply A Spill Fuel supply C

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67 Figure 1 7. Different modifications of the internal mixing air assist at omizer. A) Swirling liquid air assist atomizer, B) Perforated trumped multi air jet atomizer, C) air assist atomizer 1 Liquid supply Air supply A B Air supply Liquid supply C Air supply Liquid supply

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68 Figure 1 8. Different modifications of the external mixing air assist atomizer A) Plain jet atomizer, B) Coaxial atomizer, C) swirling air atomizer, D) swirling liquid atomizer Air supply Liquid supply Liquid supply Air supply Air supply Liquid supply Liquid supply Air supply A B C D

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69 Figure 1 9. Different modifications of air blast atomizers, typical design of effervescent atomizer A) Pre filming atomizer, B) Plain jet atomizer, C) Effervescent atomizer B Liquid supply A Air supply Pintle Air supply Liquid supply C Air supply Liquid supply

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70 Figure 1 10. Break up regimes of liquid round jet in quiescent surrounding gas A) Rayleigh mode B) First wind induced modes, C) Second wind induced mode, D) Atomization, initially jet is laminar, E ) Atomization, fully turbulent jet D L A B C D E

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71 Figure 1 11. Qualitative dependence of jet break up length on Weber number A) Dripping f low, B) Rayleigh and First wind induced mode C) Second wind induced mode, D) Atomization, initially laminar jet, E) Atomization, fully turbulent jet. Figure 1 12 Mechanisms of break up of low viscosity liquid drops observed experimentally under atmospheric or lower initial pressure A B C D E Jet Break up Length, L We

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72 Figure 1 13. Qualitative phase dia gram to illustrate supercritical injection. 1 2 3 supercritical mixing. 4 5 sub critical mixing Figure 1 14 Nitrogen specific heat at constant pressure around critical point, Temperature Pressure Vapor Solid Liquid Supercritical fluid Triple point Critical point ( ) 1 2 3 4 5

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73 CHAPTER 2 EXPERIMENTAL SETUP A ND TECHNIQUIE High Pressure Chamber The chamber design has to satisfy several somewhat conflicting requirements. The chamber has to provide maximal flexibility in terms of optical access and injectors configurations. Secondly, the chamber has to sustain high pressures and elevated temperatures to exceed critical conditions of working fluid. The design is shown in Figure 2 1 and Figure 2 2. The chamber consists of three main parts: (i) the upper component which incorporates gas and liquid supply, (ii) the body and (iii) the exhaust. After final assembly the chamber has been tested to sustain the pressure of 100 atm (1500 psi) and temperature of 200 0 C for 12 hours. Numerical simulation using Pro E mechanica revealed that the cham ber is capable of sustaining the pressures of up to 150 atm. (2200 psi) at temperature as high as 200 0 C. For operational safety the limit was set to pressures up to 70 atm. (1000 psi) and temperatures up to 250 0 C. The setup design allows for modification s that would convert this high pressure chamber into a combustion chamber with a minimum number of changes. It is most likely that during this possible modification the ducts for cartridge heaters will be transformed into the cooling channels and the exhau st will have to be redesigned completely while other parts of the chamber and gas/liquid supply systems would be maintained. Material C hoice The chamber has to sustain high pressures and elevated temperatures, provide fast enough heat transfer to prevent local overheating and insure uniform temperature from the injector tip to the chamber exhaust. Three materials were seriously considered during the design copper, stainless steel and brass. Essential properties of these materials are shown in Table 2 1. Copper has excellent thermal conductivity properties but is the worst in terms of max allowed yield

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74 stress, whereas stainless steel has good values of max yield stress, however, conduction properties are not acceptable. Therefore, brass has been selected. High Pressure Chamber B ody D esign The AutoCad drawing of the chamber is shown in Figure 2 2. A complete set of shop drawings is included in Appendix A. Three conflicting goals to reach during the chamber design are: a) the chamber has to sustain maximum possible pressure, b) optical access has to provide maximum field of view, and c) jet splashing from the chamber bottom should not reach the windows. To fulfill the requirements of maximum field of view the chamber was designed to be square instead of roun d which would have made it better from a structural point of view. To mitigate stress concentration and facilitate the machining, the chamber corners where rounded with 3.125 mm ( ) radii. To prevent highly undesirable liquid depositi on on the windows due to the jet flapping and splashing from the bottom, a ( ) cross section was chosen, which is considerably larger than the injector diameter kept around 1 mm The chamber is 228.6 mm ( ) long. The chamber is considerably long to prevent jet splashes from the bottom of the chamber from reaching upstream in the field of view. Another reason in favor of a relatively long chamber body is potential further investiga tions of the late stages of jet break up. Since one of the design goals is to investigate processes taking place at high temperature the heat flux through the chamber walls has to be minimized. This undesirable effect can be eliminated either via using wal ls insulation or through introduction of additional heat sources into the walls of the chamber body. The second solution was chosen here. Four round 6.6 mm ( ) diameter slots in the chamber body corners were drilled to insert four 152 .4 mm ( ) long Omega CIR 1060/240V cartridge heaters. Each heater is able to deliver 0.4

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75 kW. If the chamber is modified to a combustion chamber these slots can easily be transformed into cooling passages. The only change required in t his case is to provide these slots with low pressure fittings. The reason to place a NPT port at the bottom of the chamber body is to install a pressure transducer as well as pressure relief valve. The schematic diagram of the facility setup is shown in Figure 2 3. These pressure transducer and pressure relief valve are marked as 33 and 34 respectively in Figure 2 3. Omega PX303 1KG10V pressure transducers are used in the current setup configuration to measure the pressure in t he high pressure chamber liquid supply and gas supply line. A Swagelok SS 4R3A BU proportional pressure relief valve is mounted to this port as well. The valve is set up to open once the chamber pressure reaches 70 atm. (1000 psi). The purpose for placing a NPT port next to the port is to install the Omega K type KMTXL 125U 6 thermocouple. This thermocouple is marked with 32 in Figure 2 3. The thermocouple tip protrudes approximately 1.5 cm into t he chamber and it measures the gas temperature at the bottom of the chamber. Thermocouples of same type but different length are used to measure the temperature at all locations where the temperature is measured. To prevent leakages o ring type sealing is used. The grooves to place 2 152 size Parker silicone o rings are cut on the sealing face between the chamber body and window flange. Grooves cut on the chamber body bottom and top are designed to fit Parker 2 140 size o rings. The full list of o ring size s used throughout the set up is given in Table 2 2. Optical Access Layout Two requirements on the optical access ports were identified in addition to the capability of withstanding the required pressure. First, the windows have to provide access to the lat er

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76 stages of the jet break up. Secondly, the windows have to be flush with the inner side of the chamber to prevent the interference with the gas flow. As shown in Figure 2 1 and Figure 2 2, the chamber is provided with four cutouts to mount the windows. T wo different systems of window mounting are implemented and can be used depending on current research goals. The first system can be used for applications which do not require using laser light with wavelengths shorter 300 nm, therefore regular glass can be used. Standard Ilmadur size # 1 boiler borosilicate gage windows are used in this case [81]. These windows are designed to transmit close to 90% of the light with wavelength longer than 300 nm and are capable to sustain 200 atm. (3000 psi) at 400 0 C. These windows have 0.002 flatness and 0.003 parallelisms, which is good enough to transmit relatively high energy laser light. After the installation the actual field ose to withhold the windows in places is shown in Appendix A. The procedure to install the windows is as follows: a piece of wood having a cross section of the chamber internal cross section is inserted into the chamber body. Each window is covered with ta pe to protect it against contamination. After the window is inserted into its slot the clearance between window and slot is filled with 100% liquid silicone rubber. It takes about 2 hours for silicone rubber to dry an about 24 hours to form bond completely This installation procedure insures flush mounting and holds the windows in place firm enough to provide sealing between the window and the flange. The next step is to place the O ring into the grooves and mount window flanges. In cases where access for light with wavelength shorter than 300 nm is required the optical access design has to be changed. 96.52 mm ( ) long, 34.3 mm ( ) wide and 17.8 mm thick fused silica windows ar e used in this case. The clearance between flange and window is smaller than 0.3 mm ( ). The actual field of view for this optical access modification is

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77 ( ) which is almost th e same as in the previous case. The window is held in place by inserts located in the flange cavities. The squeezing force is created by tightening the socket screws and transmitted to the window via stainless steel insert which is inserted into the cavity To prevent glass damage a Teflon gasket is located between the stainless steel insert and the glass. Sealing between window and flange is ensured by a Parker size 2 149 o ring. Some pre stress during assembling is required to ensure sealing between glass and flange. The entire procedure replacing of all four windows takes approximately 1 hour which is a clear advantage of this type of optical access. In general this optical access configuration is easier from a maintenance point of view and provides wider capabilities in terms of wavelengths which can be used but the windows are custom made; therefore replacing scratched or broken window is more expensive and takes more time due to its manufacturing. Not all experiments require usage of all four windows. T o simplify the setup maintenance dummy flanges with no cuts for optical access were manufactured for these experiments. This way, unused cut outs can be easily and reliably blocked. Lid and Injector Design The top assembly design is shown in Figure 2 4. It incorporates the injector assembly and designed to provide the capability to study single liquid jet injection as well as coaxial injection. The liquid supply system is the same for both cases. The gas flow temperature is monitored via a thermocouple moun ted at the upper portion of the lid via a Swagelok NPT tube fitting. This thermocouple is marked with 30 in Figure 2 3. The temperature in the upper portion of the chamber is measured by a thermocouple inse rted into the chamber via a mm ( ) diameter duct drilled parallel to the gas supply annulus. This thermocouple protrudes

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78 approximately 1cm into the chamber and is marked as 31 in Figure 2 3. The lid is attached to the chamber body via 8 bolts. The connection is sealed with a 2 146 Parker o ring. A photograph of the liquid injector is shown in Figure 2 5. Liquid is supplied via Swagelok stainless steel tubing. The final injector diameter is defined by choosing the injector tip. The tip is 15.2 mm ( ) long and is soldered to the tubing so it can be easily changed according to the experimental needs. Standard size stainless steel hypodermic tubes are used to manufacture the injector tip. The injector is connected to the chamber lid via Swagelok tube NPT fitting. A honeycomb like structure welded to the injector just before the tip is used to straig hten the gas flow before injection into the chamber for the coaxial liquid/gas injection scheme of injector. An additional purpose is to reduce the injector post vibration. The clearance between the honeycomb like gas flow straightening structure and the g as supplying duct wall is only 0.02 mm ( ). A cross sectional CAD diagram of the liquid/gas injector assembly is shown in Figure 2 4 A. In general, the liquid/gas injecting system consists of three parts: the chamber lid itself, the liquid injector and the NPT plug with coaxial round duct drilled through it. This plug and outer side of the injector tip are forming the coaxial channel. Flush mounting between the plug and the lid must be insured. This design allo ws quick and easy change of the injector configuration. In the case of a single liquid jet injection, the internal diameter of the NPT plug is equal to the outer liquid injector tip diameter with a clearance smaller than 0.02 mm ( ).

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79 Additionally, before installation, the injector tip outer surface is covered with liquid silicone rubber. Therefore there is no gas flow through the annulus channel. Instead, the gas is supplied via four side channels drilled in th e lid body upstream of the honeycomb like structure. An additional advantage of this scheme is the gas flow in the direct vicinity to the windows thus preventing liquid deposition. However, this effect became less apparent in the runs where hot gas was sup plied. Schematics of the coaxial injector design and its overall view are shown in Figure 2 4 B and C. The internal diameter of the NPT plug is chosen according to the experimental needs. The NPT plugs are th readed into the aside gas channels, so all gas is supplied via the coaxial annulus. The dimensions of all currently available gas supplying annulus and liquid injector tips are listed in Table 2 2. The lengths to diameter ratio of the gas annulus as well a s the length of the injector tip were chosen to stay above 2.5 to avoid complications due to vena contracta flow pattern forming as described in chapter I. Liquid/Gas Supply System Gas Supply Line The liquid/gas supply system schematic is included in the diagram given in Figure 2 3. In cases with the simple round injector the gas supply is used to preheat the high pressure chamber and to maintain the required gas pressure and temperature during the experiment. In this applications gas is supplied far enou gh from the liquid injector from the chamber top to prevent gas flow liquid jet interaction. When the coaxial jet injector is used the system has to be able to provide the gas flow with well controlled temperature and velocity throughout the entire exper iment in addition to preheating and pressurizing of the chamber.

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80 Gas from the gas tank 1 is supplied to the gas line via pressure regulator 2. The maximum safe pressure in the gas supply line is 100 atm. (1500 psi). The gas supply to the gas line is contro lled via solenoid valve 3. All solenoid valves used in the setup are Omega SV 128, designed to operate within a pressure range of 0.3 100 atm. (5 1500 psi). The gas flow rate is controlled via needle regulator valve 4. Swagelok SS 4L MH needle valves are used in gas and liquid supply system of this setup [82] with the exception of exhaust valve 29 due to its high temperature requirements. These valves have a maximum flow coefficient Here, the flow coefficient for gases is defin ed based on (2 1) where if SI units are used (pressure units bars, temperature units Kelvin, flow rate units l/min), inlet pressure, pressure drop across a flow meter, (2 2) and is a volumetric flow rate. For liquids, the flow coefficient is defined as (2 3) where if SI units are used and It should be noted that the needle valves in the setup are used for control purpose only while flow rates are measured directly with flow meters. Downstream of the needle valve 4 shop air can be supplied to the line via check valve 5 The flow rate of the gas supplied to the chamber is measured by an Omega FLMG 12050SS MA flow meter. This flow meter has an operational range of 1 100 atm. in terms of pressure and 0 50 SCFM in terms of volumetric flow rates [83]. The flow meter has a frequency as well

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81 as voltage outputs. The voltage output with a range of 0 5 VDC is used here. The accuracy of the device is 4% of the full scale. The pressure in the gas line is measured with pressure transducer 7, mounted downstream of the flow meter 6. The desired gas temperature is achieved via electrical heater 8 located downstream of the pressure transducer 7. A photograph of the heater is shown in Figure 2 6. The drawings of the heater are shown in Appendix C. The heater consist of two parts the s made of SS316 stainless steel. The core is made of C 360 (ASTM B16) brass. The core is gas heat e Omega CIR 2121/240 cartridge heaters are inserted into the core. Each of the cartridge heaters has 1 kW heat power output, giving a total power output of 6 kW. The clear ance between sleeve while for steel it is only Taking to account initial sizes, evaluation of the temperature required to vanish the clearance between the core and sleeve can be formulated as (2 4) The sleeve is actually colder then the core, therefore this estimate is conservative. Thus, as soon as heater core exceeds the cl earance between the core and the sleeve is closed there and the gas has to follow the thread which improves the heat exchange efficiency. To prevent the NPT thread from overheating gas has to be supplied via the intake closest to it. The outer side of the heater as well as the line downstream are insulated with glass fiber tape. This heater is able to deliver 90% of its electrical power to the gas. The desired gas temperature is measured via thermocouple 9 inserted into the center of the heater core and the rmocouple 10 mounted into the

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82 chamber lid, so it measures the injected gas temperature with optimal precision. Additional measurements to evaluate the difference between the actual and desired injected gas temperatures have shown the difference to be less then 2 0 C. Heater operation and control are described in the data acquisition system description. Liquid Supply Line The purpose of this system is to provide liquid supply to the chamber. This system has to provide reliable control of the injected fluid t emperature and velocity. Liquid in the fuel tank 15 (see Figure 2 3) is pressurized with nitrogen supplied from the gas bottle 12 via pressure regulator 13. The maximum safe pressure on the low pressure side of the pressure regulator is 100 atm. (1500 psi) To facilitate pressure relief ball valve 14 is mounted on the upper side of the fuel tank. To prevent fuel leakage into the system as well as backpressure leakage into the fuel tank while filling the fuel tank ball valve 16 is mounted downstream of the f uel tank. Overall liquid supply is regulated via needle valve 17. Liquid flow meter is mounted just downstream of the needle valve. A turbine type Sponsler Lo Flo precision flow meter MF 125 MB PH A 4X N1 is used in this set up to measure the liquid flow r ate. This flow meter can provide frequency as well as voltage output. The precision of the flow meter if it works in the frequency output regime is reported to be significantly better than that for the voltage output. Therefore, in this application, freque ncy output was chosen. According to its specification, this flow meter has a measuring range of 5 to 100 cc/s with linearity [84]. The specific flow meter was additionally calibrated to ensure flow measurements precision. A cali bration curve is shown in Figure 2 7, where water was used to calibrate the device. An undesirable feature of this flow meter was its sensitivity to electromagnetic noise radiated by such devices as solenoid valves; solid state relays e.t.c., even if devic e connection and grounding is done according to the manual instructions. In particular, the location of a solenoid valve within 20 cm of the flow meter

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83 influence the measurements the actual flow signal is dominated by 60 Hz signal and its harmonics (120 Hz, 240 Hz etc.). Since these frequencies are overlapping with flow meter output frequencies it is virtually impossible to filter this noise out. To eliminate this noise all electronic devices were located at the distance greater than 40 cm from the liquid flow meter. Additionally, the entire flow meter was shielded for low liquid flow experiments. Two parallel lines are mounted downstream to the liquid flow meter. First line bypass line is controlled via bypass normally closed solenoid valve 21. Liquid flow through the bypass line is controlled via needle valve 23. The bypass line is designed to deliver liquid into the recuperation tank 27 without injection it into the high pressure chamber 11. The second liquid line is the main liquid line designed to d eliver a liquid into the high pressure chamber 11. Normally closed solenoid valve 20 is mounted just downstream of the liquid flow meter. Shop air at 14 atm. (200 psi) can be supplied into this line, when it required, via check valve 19. Liquid flow rate v ia this line is controlled via needle valve 22. Pressure in the liquid line is measured via pressure transducer 24. The liquid heater 25 is located downstream of the liquid line pressure transducer. The design of this heater is similar to that in the gas l ine. The only difference is the total heater length; it was chosen to be 127 mm ( ), so the actual heat exchange labyrinth length is 4 m ( ). Six 127 mm ( ) long Omega CIR 5051/240 c artridge heaters are inserted into the heater core. Each of these cartridges is able to deliver 0.5 kW of thermal power, so the total heater output is 3 kW. This design allows keeping the temperature of the injected liquid constant for 30 s at a flow rate of 50 cc/s. Therefore, the liquid heater can work only as heat storage and cannot provide continuous liquid heating for the entire range of possible liquid flow rates. The heater core temperature is measured with thermocouple 26, while the injected liquid temperature is measured with thermocouple 30.

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84 There are two reasons to choose a liquid supply system with bypass and main liquid lines. The main reason is a liquid supply system response time. It turns out that it takes about 5 seconds from opening the so lenoid valve until a constant flow rate settles up according to the flow meter readings. This delay can be attributed to the flow meter response time all calibration are done for steady flows or to the time which indeed required to set up the steady stat e flow through the liquid supply line. The second reason to setup a bypass line is fluid recuperation. For low temperature experiments, the recuperation ratio is about 80%. For high temperature runs, recuperation ratio falls down to 20 40%. In principle, providing the recuperation tank with a cooling jacket or some other appropriate means to reduce its temperature could bring the recuperation ratio to values of 80 90% throughout the entire range of flow rate and temperatures. Data Acquisition Systems Th e data acquisition system can be clearly divided into two parts: (i) the control of the experiment itself, i.e. pressure and temperature measurements, heaters control etc. and (ii) the optical data acquisition system. Synchronization is required between th ese systems. Data Acquisition and Control System A block diagram of the data acquisition and control system is shown in Figure 2 8. As is indicated in the scheme the system is operated from a PC via a NI AT MIO 64E 3 ISA data acquisition board [85]. This b oard has 32 analog 12 bit input channels in differential mode and 2 analog output channels. In the current setup the board is set to 10V analog input and output range so the input/output resolution is 2.44 mV. The maximum total sample rate is 500 ksamples/ s, which imposes some restrictions on the number of channels which can be used during the experiment. The data acquisition board is connected to the signal conditioner and channel multiplier NI SCXI 1100. As shown in the schematic there are three SCXI modu les involved in

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85 the data acquisition process. Data acquisition and control hardware is managed by a program written in the LabWiev 7.1 graphical programming environment. The listing of this program along with its general and operational procedures descript ions is given in Appendix B. Temperature is measured via an SCXI 1100 with an SCXI 1303 connection terminal. The module allows connecting 32 channels in differential mode. In the current configuration only six channels are connected. The locations and purp oses of thermocouples connected to this module are described above. In general, due to the limited data acquisition board capabilities in terms of sampling rate, the number of simultaneously used channels is kept to a minimum. The devices which have outpu t in a voltage range are connected via an SCXI 1140 module with an SCXI 1301 connection terminal. Six data acquisition channels are involved into the measuring process. Parameters monitored during the experiment are: liquid line pressure, gas line pressure chamber pressure, gas mass flow, liquid mass flow. The first channel is used for synchronization. The temperature, pressure and gas/liquid injection velocity may vary during the experiment; therefore during image processing the time reference is needed. The CCD camera used in the setup has an additional gate output which sends a 5V signal while an image is acquired. Since the typical camera exposure time is on the order of a few microseconds, this signal is too short to be picked up by the data acquisitio n system. To resolve this issue, the signal from the camera is first sent to the DG535 Stanford delay generator. This device increases the signal duration to 50ms and then send it to the synchronization channel of the data acquisition system. This strategy works as long as the pressure record is longer than the time when images are acquired, so the first or the last frame can be distinguished on the synchronization channel record. The wiring scheme for synchronization is shown in Figure 2 9.

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86 Control functio ns of the system are implemented via an SCXI 1124 module with an SCXI 1325 connection terminal. This module has 6 analog output channels; all of them are used in the current setup configuration and adjusted to output 5 V signals. The gas and liquid heaters consume 6 kW and 3 kW of electrical energy and require 240 VAC input. This type of heaters was preferred to heaters which have 110 VAC due to the higher energy per unit of area output. The control over power supply to each of these devices is done via 2 s olid state relays. The first relay is a Gordos G280D25 49 solid state relay operated from the setup output channel. The high voltage side of this relay is connected to a 110 VAC electricity source. The output of the first relay is connected to the input of the second one. The second relay is an Omega SSRL 240AC50 solid state relay. This device is able to control a 240VAC electric line with max current of 50 Amp. The output of the high voltage solid state relay is connected to the input of the electrical car tridge heaters. A schematic of the electrical connections is shown in Figure 2 10 A. All solid state relays involved in the control over gas line, liquid line and chamber heaters are housed within one box which is supplied with 110 VAC and 240 VAC. The val ves are controlled via much simpler system where only one Gordos G280D25 49 solid state relay is used to operate each valve. This system is also incorporated into one box which is supplied with 110 VAC. The schematic of the electrical connections is shown if Figure 2 10 B. Optical Data Acquisition System A schematic of the image acquisition system is shown in Figure 2 11. The system consists of following components: Continuum Surelite II Nd:Yag laser, a set of 3 laser mirrors, a set of cylindrical lenses to form a laser sheet, high pressure chamber, optical band pass filter and a Princeton Instruments PI MAX II CCD camera. The entire setup is mounted on an optical table to facilitate the optical acquisition system adjustment.

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87 The laser was tuned to its thir d harmonic which is a 355 nm wavelength. Average energy per single pulse was measured to be 100 mJ at 10 Hz. The laser pulse duration is 7 ns. Despite the tuning, the laser beam is still contaminated with some fraction up to 2% of total beam energy of ligh t with 532 nm wavelength i.e. the second harmonic. To eliminate this problem, a set of 3 laser mirrors was used to direct the laser beam into the chamber. According to the specification, the laser beam reflects only 10% of the light with 532 nm wavelength, while its reflection coefficient for light with 355 nm wavelength is estimated to be better than 99%. Therefore, after reflection off the three mirrors the laser beam contains only 0.002% of light with wavelengths different from 355 nm. The pulse to pulse energy variation was evaluated as 10% of the average pulse energy. Although for current calibration procedure such a high pulse to pulse energy fluctuation does not affect the resulting measurements precision, for other calibration procedures it can caus e problems. After reflecting off the mirrors, the laser beam is shaped into 25 mm wide and 0.1 mm thick sheet. A pair of 150 mm focal length cylindrical lenses and a 500 mm focal length plano convex lens is used for this purpose Typical beam profile is sh own in Figure 2 12. The laser sheet causes fluorescence of a fluid which is being injected into the chamber during the experiment. Images of the jet are recorded with intensified CCD camera. This camera has a resolution of 1024x1028 pixels and capable to a cquire the full frame images at rate of 7 Hz. The camera is equipped with Sigma normal 50 mm f/2.8 EX DG lens with Sigma 2x EX DG APO teleconverter and AI extension tube PK 12 allowing short focusing distance and effective light collection. Camera spatial resolution of 19 /pixel vertically and 18 /pixel and FWHM of 10 nm is used to eliminate elastic light scatter. The filter was incorporated into

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88 the camera lens. This approac h reduces overall light intensity without affecting useful portion of collected light. To ensure reliable operation and reduce a camera gating time, which is always favorable from the ambient light point of view, it is critical that the laser and camera ar e properly synchronized. Variable output from the laser Q switch was connected to the camera external synchronization input. Since the laser has to be adjusted to operate at 10 Hz to provide stable energy output and maximum camera full frame sample rate is only 7 Hz, this system is effectively forced to use every second laser pulse to acquire the image (i.e. actual sampling rate is 5 Hz). Since the camera is operated in gated mode this sample rate reduction does not cause any problems. Camera exposure time during the experiments was set to 10 s. Relatively short exposure time coupled with incorporation of the band pass filter into the camera lens allowed to reduce the background noise to the level that was essentially equal to the camera dark current noise. Camera controller sends out square pulse which is synchronized with actual exposure. Since the exposure time is too short comparatively to the data acquisition system sampling rate, output is connected to the input of delay generator DG 535 which increase the pulse duration to 50 ms and then sends it to the SCXI 1140 input. The image synchronization system is shown in Figure 2 9. Experimental Technique FK 5 1 12 Thermodynamic and Spectral Properties Fluoroketone 2 trifluoromethyl 1,1,1,2, 4,4,5,5,5 nonanofluoro pentanone or FK 5 1 12 [CF 3 CF 2 C(O)CF(CF 3 ) 2 ] has been chosen as the injected fluid for the planar laser induced fluorescence (PLIF) experiments. This fluid was chosen for several of reasons. It has relatively low critical parameters [ 86] This material has exceptional thermal

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89 stability 0 C. FK 5 1 2 exhibits strong absorption in the near UV, with peak abs orption located at At 355nm excitation wavelength the absorption cross section reduces quite significantly and is evaluated from the literature to be within a range of The upper end of this range would make it impossible to use the FK 5 1 12 for the PLIF at 355 nm excitation wavelength since the characteristic decay length for the liquid state of the fluid in this case is only 1.3 mm. A LIF image of the 0.84 mm liquid jet injected int o the still air is shown in Figure 2 13, with the light coming from the left side. It can be observed that there is no significant beam absorption over 1 mm. Some beam attenuation can be attributed to the beam steering effects rather than to the absorption phenomenon. A concern in the PLIF application is whether the emission depends on the pressure and temperature or not. Emission spectrum at STP conditions is shown in Figure 2 14. As it can be seen from the plot, the range of wavelength from 400 to 500 nm appears to be the most attractive in terms of fluorescence intensity. Behavior of emission spectra within this range of wavelengths depending on pressure and temperature is shown in Figure 2 15. The results indicate that there was no significant dependenc e of the emission spectra on the environment conditions for emission wavelength within a range of 400 500nm. Thus, based on the obtained emission spectra the center wavelength of the optical filter for PLIF measurements has been chosen to be 420 nm with 10nm FWHM width. In addition to good fluorescent properties the fluid has to have well documented thermodynamic properties [87]. The Peng Robinson Stryjek Vera (PRSV) equation of state can be used to predict FK 5 1 12 thermodynamic properties with 2 % uncertainty within a range of pressures and temperatures of and

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90 (2 5) All parameters used in this equation along with some key properties of FK 5 1 12 are given in Table 2 4. Due to considerable complexity of PRSV equation of state a special function named to calculate density for given pressure and temperature. The complete set of Matlab programs used for data processing is given in Appendi x C. The phase diagram plotted using this function shown in Figure 2 16. In actual processing this function is used to determine the fluid density upon known pressure and temperature. Image Processing A set of three images is required to obtain calibrated density distribution: the background image, the beam profile image and the actual experimental image. To obtain the laser sheet profile the chamber was closed preheated to temperature within a range of 50 100 0 C, and then half filled with FK 5 1 12. Once the equilibrium between liquid and vapor phases is achieved after approx. 30 min, the vapor phase was excited with laser sheet. 150 images were acquired and averaged to reduce possible noise. After appropriate processing, e.g. background correction averag ed image was used to obtain a laser sheet profile. Example of laser sheet profile is shown in Figure 2 14. Images of the field of view with no jet injection but with laser sheet were taken thus possible light scattering was taken into account. An image pro cessing was performed using a Matlab background image was subtracted. Second, the image was corrected for laser sheet unevenness (2 6) where and correspond to columns and rows respectively, pixel intensity after correction, uncorrected pixel intensity and intensity of the

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91 beam profile. Next, the image was calibrated to obtain the FK 5 1 12 density distribution. Since jet heating and evaporation takes time, it was assumed that in the direct vicinity to the injector face, fluid density can be calculated using the Matlab ed above. Chamber pressure and temperature measured with thermocouple 30 (see Figure 2 3) were used entire image can be processed to obtain the density distrib ution (2 7) where fluid density in the referred region and average intensity in the reference region which was 25X25 pixels area in the jet core, nearby the injection point. Spatial differentiation was applied to the density distribution to obtain the density gradient field The values of the density gradient were smoothened out with a pixels averaging filter to elimin ate the noise which is emerges as a result of numerical differentiation. Accuracy Analysis In general two types of the uncertainties hardly related to each over can be referred in this case. First type of uncertainties are related to data acquisition and c ontrol system. They eventually show up as a precision of injection velocity, gas/liquid temperature, chamber pressure etc. Another group of uncertainties is related to the features of the image acquisition system. The precision of these measurements eventu ally affects a precision of the density distribution. Uncertainties for different components of the data acquisition were discussed during their description given above. Summary of the precision for each component of the data acquisition and control system is given in Table 2 5.

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92 Uncertainties associated with the image acquisition system are more complex. Sources that could provide a significant contribution to the density distribution uncertainty include camera pixel to pixel sensitivity variation, dark noi se, ambient light and laser sheet pulse to pulse intensity distribution variation. Pixel to pixel camera sensitivity was corrected via white field correction. Out of focus images of evenly illuminated white object were acquired. 50 images were acquired ave rage of these images was used for pixel to pixel sensitivity variation correction. Uncertainty of the white field correction was found to be An average of 100 images was captured before each series of experiments. The images were t aken with the laser light to correct for possible light scattering. The resulting background image was subtracted from the actual experiment image. The uncertainty of the ambient/background correction was estimated as 0.4%. The dark noise of the CCD was in vestigated via acquiring images with 20 exposures of 10, 100 and 500 each with the lid covering the camera lens. The resulting intensity was found to be independent on the exposure time and evaluated as 40 counts per pixel or 0.04% of the full scale sensitivity. The laser sheet profile pulse to pulse variation was estimated based on 100 images of evenly seeded with FK 5 1 12 vapors. Uncertainty, associated with this issue was estimated as 1%. Total uncertainty of the image acquisitio n system is estimated as 1.5% and has been obtained by taking the square root of sum of squared values of all mentioned uncertainties. However, it should be noted that there is an uncertainty related to the beam steering effects, which makes the main contr ibution to the resulting density uncertainty. To evaluate this problem the variation of the fluorescence intensity in the central portion was investigated. If 20 images during the

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93 experiment were acquired, this uncertainty was estimated as 5% of the initia l fluid density. Therefore total uncertainty of the technique can be evaluated as 5 to 7 % depending on number of images acquired during the experiment.

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94 Table 2 1. Some properties of stainless steel, brass and copper Material Thermal conductivity, W/m.K Yield Strength, Mpa Melting Point, 0 C Hardness, BHN Brass C 360 (ASTM B16) 115 124 900 100 Stainless Steel SS316 16.2 290 1400 217 Copper C110 388 69 1000 80 Table 2 2. O ring sizes an locations O ring size according to Parker catalog 2 146 2 154 2 152 2 149 Location Chamber body/lid, chamber body/exhaust interfaces Chamber body/flange interface Flange/window interface (Ilmadur windows) Flange/window interface (fused silica windows) Table 2 3. Currently available gas/liquid injector geometries G as supplying channel diameter, mm (in.) Liquid injector tip Inner diameter, mm (in.) Wall thickness, mm (in.) Small Parts catalog part # 2.16 ( ) 0.84 ( ) 0.4 ( ) U HTX 16HW 1.65 ( ) 3.56 ( ) 2.08 ( ) 0.22 ( ) U HTX 12 1/2

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95 Table 2 4. Parameters and constants used in PRSV Parameter or Thermodynamic Property Value Units 18 atm. 168 639 MW 316.1 g/mol 0.052 0.471 Table 2 5. Uncertainties related to the data acquisition and control system Parameter Precision Remarks Injected Liquid Temperature Injected Gas Temperature Chamber Pressure 0.17 atm. Liquid Injection Velocity Consists of Flowmeter and Fluid Density Evaluation Uncertainties Chamber Temperature

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96 Figure 2 1. High pressure chamber overall view C hamber up thermocouple Liquid injection port Gas injection port Gas temperature thermocouple Chamber pressure transducer Pressure relief valve

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97 Figure 2 2. High pressure chamber overall view CAD drawings

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98 Figure 2 3. Schematic of Liquid/Fuel supply system. Gas supply line : 1 = gas bottle, 2 = pressure regulator, 3 = solenoid valve, 4 = needle valve, 5 = shop air supply check valve, 6 = gas flow=meter, 7 = pressure transducer, 8 = heater, 9 = heater core thermocouple, 10 = gas temperature thermocouple. Liquid su pply line : 12 = gas bottle, 13 = pressure regulator, 14 = ball valve, 15 = fuel tank, 16 = ball valve, 17 = needle valve, 18 = liquid flow meter, 19 = shop air supply check valve 20 = main liquid line solenoid valve, 21 = bypass liquid line solenoid valve, 22 = main line needle valve, 23 = bypass line needle valve, 24 = liquid line pressure transducer, 25 = liquid line heater, 26 = liquid line heater core thermocouple, 27 = liquid recuperation tank, 28 = ball valve, 30 = liquid temperature thermocouple. Cha mber : 11 = chamber, 31 = chamber upper temperature thermocouple, 32 = chamber bottom thermocouple, 33 = pressure relief valve, 29 = exhaust needle valve, 34 = chamber pressure transducer. N 2 N 2 s s P T T T P s P T Liquid recovery Exhaust T T Liquid line Gas line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 23 24 25 26 27 28 34 29 30 31 32 33 19

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99 A) B) C) Figure 2 4. Cross s ectional CAD images of coaxial injector assembly. A) Overall view, B) Zoom into injector assembly, C) Drawing of the injector tip assembly Liquid injector tip Gas entrance port Chamber top thermocouple Gas annulus

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100 Figure 2 5. Liquid injector overall view.

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101 Figure 2 6. Gas heater overall view. Gas entrance Heater core th ermocouple Gas output

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102 Figure 2 7. Sponsler Lo Flo precision flow meter MF 125 MB PH A 4X N1 calibration curve.

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103 Figure 2 8. Data acquisition system diagram PC, Matrix DAQ AT MIO 64E 3 Chassis SCXI 1000 SCXI 1124 with SCXI 1325 ( analog output) SCXI 1140 with SCXI 1301 (voltage input) SCXI 1100 with SCXI 1303 (thermocouples) ch3, liq uid heater core T ch0, liquid T ch5, gas T ch1, chamber bottom T ch2 chamber up T ch4, gas heater core T ch6, chamber heater T ch0, reserve (power meter) ch 1 external synchronization ch 2 reserve ch 3 chamber pressure ch 6 liquid flow meter ch 7 gas flow meter ch0 gas solenoid valve ch 1 liquid bypass solenoid valve ch 2 liquid solenoid valve ch 3 chamber heater ch 4 liquid heater ch 5 gas heater ch 5 gas line pressure ch 4 liquid line pressure

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104 Figure 2 9. Image acquisition system synchronization schemat ic Standby AC Power ON LASER ON START/STOP SHUTT ER VOLTS Q SW DELAY Continuum Surelite II Control Unit SELECT RS232 EXTERNAL SINGLE SHOT IN VAR. SYNC. OUT FIXED SYNC. OUT FLASHLAMP SYNC. OUT Remote 2 Setting Aux. Ext. Sync. Scan Ready Camera Signal Camera PWR Detector TTL IN/OUT Aux. Serial COM Ext. Trig In Pre. Trig In T 0 Timing Gen. Aux. Trig. Out ON/OFF ON/OFF Ext. Trig T 0 A B A B A B C D C D C D To Data Acquisition System (SCXI 1140 ch 01) PI MAX II Controller Delay Generator DG535 Experiment Triggering Signal

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105 Figure 2 10. Circuit diagrams. A) heaters, B) solenoid valves 3 4 G280G25 49 1 2 3 4 SSRL240AC50 1 2 3 4 G280G25 49 1 2 3 4 G280G25 49 1 2 3 4 SSRL240AC50 1 2 ~ 240 V ~ 110 V 5V DC Ch5 ~ 240 V to gas heater ~ 240 V to liquid heater ~ 240 V to chamber heater 5V DC Ch4 5V DC Ch3 ~ 110 V to gas valve ~ 110 V to main liquid valve ~ 110 V to bypass liquid valve 5V DC Ch2 5V DC Ch1 5V DC Ch0 A B 3 4 G280G25 4 9 1 2 3 4 G280G25 49 1 2 3 4 G280G25 49 1 2 ~ 110 V

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106 Figure 2 11. Image acquisition system schematics CCD Camera Continuum Surelite II NdYag laser 355 nm laser mirrors Cylindrical lenses Test chamber Band pass filter 355 nm 355 nm + 532 nm

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107 Figure 2 12. Beam profile. Single shot image. Error 1.0%. Ba sed on this profile actual field of view was chosen to stay within

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108 Figure 2 13. Liquid jet injection at STP conditions, Light is coming fro m the left. Some beam attenuation can be attributed to the beam steering effects rather than to the absorption phenomenon.

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109 Figure 2 14. FK 5 1 2 Emission spectrum at STP conditions, excitation wave length

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110 Figure 2 15. FK 5 1 2 Emission spectra in the region of an interest at variety of pressures and temperatures, excitation wave length Based on these emission spectra the center wavelength of the optical filter for PLIF measurements has been chosen to b e 420 nm with 10nm FWHM width.

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111 Figure 2 16. FK 5 1 2 Phase diagram Labels on the curves are in atm.

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112 CHAPTER 3 RESULTS AND DISCUSSI ON A limited set of experimental data exists regarding supercritical mixing. Most researchers were using different variations of the shadowgraph technique with the only exception of data reported by Birk et al. [77, 78] who em ployed X ray. The shadowgraph technique cannot be used to investigate the liquid core behavior in cases where it is covered by vapor clouds. PLIF applied as described in the previous section is a most suitable approach. The low density sensitivity limit wa s set to be as high as 200 kg/m 3 since the max fluid density is 1600 kg/m 3 All experiments presented below investigated a round liquid injector with diameter The liquid was not preheated and the injection velocity was varied from 7 to 25 m/s. For these injection velocities, the Reynolds number was varied from 12000 to 40000. Since the flow was laminar before entering the injector turbulence does not have a chance to develop while the fluid is passing through the relatively short in jector tip. Nitrogen was used as a surrounding gas. Furthermore, the experimental results available in the literature cover a relatively narrow range of experimental conditions. Therefore, the goal of these experiments was to investigate the influence of s urrounding gas pressure and temperature on the liquid jet core behavior. To the supercritical liquid jet break up. Since it was not clear apriori at which exp erimental conditions transition from sub critical to supercritical mixing would appear, a relatively broad test matrix was proposed as shown in Figure 3 1. Thus, the temperature of the surrounding gas was varied within a range of i. e. 293 K 523 K where the upper limit is defined by the maximum working temperature of the facility. A pressure range of 1 to 35 atm was chosen based on the experimental results reported by Mayer et al. [62, 63] who suggested that typically supercritical mixing is observed once

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113 Experimental Results Experiments were conducted at the conditions shown in Figure 3 2. The quality of the data was excellent with minimal emission intensity decay inside the liquid core. The intensity fluctu ation seen in several experiments can be attributed to beam steering rather then to the decay due to absorption. As a result the validity of density distribution at the right side of the image is less reliable than the left side i.e. the beam entrance, par ticularly in cases where sub critical jet disintegration by atomization mechanism is observed. Three different types of jet break up were observed and are marked in Figure 3 2 as the sub critical, transitional and supercritical regimes. In principle it app ears to be possible to detect these regimes automatically through analysis of the density gradient matrices. The complete set experimentally obtained images is given in Appendix D. Subcritical Mixing The sub critical break up regime was observed for relati vely low temperatures and pressures. Surface tension and inertia forces are dominating under these circumstances. The well documented first wind induced, second wind induced and atomization break up mechanisms are observed under these experimental conditio ns, depending on the injection velocity and surrounding gas density. Since the observation was conducted in the direct vicinity to the injector face and the jet is initially laminar droplet formation was rarely observed. Nevertheless, occasionally observed droplets had an ellipsoid or round shape, i.e. the surface tension forces are relatively strong. The typical images of sub critical jet break up can be found in Figure 3 3 Figure 3 5. Both second wind induced and atomization break up mechanisms are char acterized by quite developed liquid surface. Pronounced ligament formation was observed under these conditions. The density gradient are high at these experimental conditions reaching 1.610 7 kg/m 4

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114 Transcritical Mixing A significantly different jet break up mode was observed in trans critical mixing region. The characteristic feature of this region is the apparent decreasing importance of surface tension. This manifests via smoothening of the liquid gas surface. Ligaments formation tends to decrease sig nificantly. The ligaments shape resembles the descriptions found in literature [62, like appearance. Once detached from the main jet body, liquid exhibits a dual beha vior. While in some experiments formation of round liquid drops was observed as seen, for example, in Figure 3 6, other experiments revealed a cluster like droplet formation which is reported in literature as a characteristic feature of supercritical mixin g such as shown in Figure 3 7. The typical images of sub critical jet break up can be found in Figure 3 6 and Figure 3 7. Supercritical Mixing Finally, with increasing pressure and temperature the jet behavior changes again. Typical images of supercritical mixing are shown in Figure 3 8 an Figure 3 9. Density gradient values decreased drastically and approached the values characteristic for a laminar jet at STP conditions as shown in Figure 3 3. This type of a liquid core behavior has not been observed in e xperimental results available in the current literature. However, it was reported in the numerical simulations by Bellan et al.[ 72, 73, 74, 75]. Qualitatively, this behavior can be explained as follows: since the temperature and pressure exceeds the criti cal values surface tension forces are no longer playing any significant role in the shear layer. As expected the jet mixing will eventually approach a liquid/liquid or a gas/gas like mixing at very high temperatures and pressures. But the gas/liquid densit y ratio has to be taken into account as well. Since in this case this ratio is 0.001 0.03, the momentum transfer across the liquid gas border is significantly inhibited. Probably, the situation can be compared to the phenomenon well recognized in

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115 acous decrease the energy transmitted by several orders of magnitude. Hence, in cases where effective transmission is desired a third media, i.e. a matching layer is introduced. Arguably, in case of sub critical jet mixing, the situation can be explained as follows: surface tension works as a storage of potential energy, i.e. the surface tension work as a spring in the spring mass system or as a capacitor in the LC circuit. The presence of characteristic disturbance wavelength described in the first chapter matches this description. The characteristic disturbance waves correspond to the resonant frequencies of the system, which consists of liquid and gas inertia and surface tensi on forces. But once the surface tension becomes insufficient some other means of energy transmission between liquid and gaseous phases have to manifest. The most obvious energy exchange mechanism is the Kelvin Helmholtz instability. According to Chandrasek har [88] the disturbance growth rate in this case can be expressed as: (3 1) since (3 2) which means that the large density difference between liquid and surrounding gas cau ses apparent inhibition of the Kelvin Helmholtz instability and, as a result, inhibit the turbulence development in the shear layer in the vicinity of the injector face. Therefore, despite an apparent decrease of the density gradient across the liquid gas surface damping of the turbulence development is observed. It should be noted that the energetic approach toward the

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116 understanding the jet stability has certain limitations as it can only describe quantitative behavior. Theoretical Analysis To gain some mo re quantitative as well as physically valuable insight into fundamentals of liquid jet behavior a linear stability analysis was performed. The Navier Stokes equations were used in a system of coordinates fixed with the jet The problem has to be divided in to the inner portion of the jet and the surrounding gas. First, the motion of surrounding gas should be considered. The gas is assumed to be initially quiescent. Gravity, compressibility and viscosity are neglected and the flow was considered axially symm etric. The Navier Stokes equations are written as follows : (3 3) T he flow around the jet is potential, therefore motion can be described via velocity potential : or in cylindrical system of coordinates: (3 4) T he general solution with assumptions regarding the harmonic behavior is where the first term corresponds to the solution far away from the jet and the second term is the system response on the harmonic disturbance : (3 5) and after substitution in the initi al equation it results in :

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117 (3 6) The solutions of Equation 3 5 are zero order modified Bessel functions of the first and second kind: (3 7) The solution has to be bounded everywhere, but if ; therefore should be discarded and solution remains : (3 8) Radial and axial components of velocity can be recovered via potential definition : (3 9) and (3 10) d ue to requirement for the velocity at infinity: (3 11) T he pressure dependence results as : (3 12) A ssuming that and using z momentum conservation equation: (3 13) After rearrangement gaseous pressure field can be referred as: (3 14)

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118 Once the flow outside the je t is resolved the flow inside the jet has to be defined. It is assumed that the flow is incompressible, gravity is neglected and the disturbances are small and symmetric. With these assumptions, the Navier Stokes equations look as follows: (3 15) T h e motion inside the jet can be divided into potential and viscous portions: (3 16) S ubstitution of these into equations of motions 3 14 lead to second order equations : (3 17) Again harmonic assumptions are implied : (3 18) Inserting Equation 3 17 into Equation 3 16 the system simplifies to : (3 19) Which has solutions as follows

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119 (3 20) where Again, the solution has to be bounded; therefore Thus, for velocities one could obtain: (3 21) Equations 3 21 can be simplified as follows: (3 22) with the pressur e relationship obtained via Bernoulli equation : (3 23) The solution of systems 3 3 and 3 15 contains 3 constants. These constants can be obtained via boundary conditions. First, the surface coordinate is expressed as : (3 24) where is the initial jet diameter and is the initial disturbance magnitude. This equation is the direct consequence of the harmonic assumption. The normal forces balance at the jet su rface provides the boundary cond ition which looks as : (3 25)

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120 where the second term reflects the influence of the liquid viscosity on the pressure inside the jet while the second one gives the surface tension a chance to manifest itself. Following relations are valid f or pressures and radiuses of curvature : (3 26) Substitution of relations 3 26 into normal stress balance Equation 3 25 yields : (3 27) Substituting Equations 3 14, 3 22 and 3 23, into 3 27 the solution is obtained as : (3 28) or (3 29) Finally, Equation 3 28 can be simplified as: (3 30) This equation is a dispersion relationship for the jet. The solution of this relationship allows evaluation of the most unstable disturbances wavelengths and their growth rates. This evaluation

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121 has only a first order accuracy; however it provides a reasonably good estimation of jet instability par ameters. It is necessary to define the constants and For the fluid inside the jet the boundary condition s are quite simple: (3 31) The first equation in the system 3 31 is the mass conservation equation while the second one represents the free boundary assumption and depictures the zero shear stress at the jet surface. After substitution of 3 22 and 3 24 into 3 31 and are obtained as: (3 32) For the gas surrounding the jet only one boundary condition is needed : (3 33) After substitution of Equations 3 9, 3 11 and 3 24 into 3 33 boundary condition looks as: (3 34) Finally, Equation 3 33 simplifies to: (3 35) A ll constants defined above can be substituted into the dispersion relationship 3 29:

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122 (3 36) After regrouping Eq uation 3 36 can be written as: (3 37) It is preferable to deal with non dimensional form of Equation 3 37. T o derive the non dimensional version of the eq uation, wavelength and wave number can be referred as where and represent non dimensional wave number and frequency. These transformations lead to following form of dispersion relationship : (3 38) Introducing the Weber and Reynolds numbers as and when the dispersion relation transforms as following : (3 39)

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123 Note that due to established traditions regarding the definitions in the jet sta bility theory literature this definition of the Weber and Reynolds numbers here differs to that given in the first chapter. In a l aboratory system of coordinates the dispersion r elation changes as follows: (3 40) this equation for the same boundary conditions was first derived independently in different forms by Ponstein [89], and Chandrasekhar [86]. Levich [90] has developed a very similar equation for slightly different boundary conditions. In case of and with the appropriate correction due to different system of reference dispersion relation simplifies to that first obtained by Rayleigh [26]: (3 41) Another simplification of the dispersion relationship 3 39, in particular in the case of non negligible gas to liquid density ratio but was considered by Weber: (3 42) Modifications of Ecuations 3 41 and 3 42 allow accurate estimation of the disturbance wavelen gth for relatively low values of Weber numbers. As mentioned, Equation 3 43 is valid within limits of while Equation 3 42 is valid as long as Note, that these Weber numbers are based on surrounding gas densi ty i.e.

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124 Equation 3 40 takes into account not only surface tension and gas to liquid density ratio but also the liquid viscosity and incorporates earlier developed Equations i.e. 3 41 and 3 42 as simplifications. Equation 3 39 doe s not have an analytical solution; therefore it was solved numerically in Matlab. The listing of the MatLab code used to obtaining the solutions for Equation 3 39 is given in Appendix C. Only spatial disturbances were considered i.e. frequency was assumed to be purely real while wave number was sough as The choice of spatial or temporal instabilities, as it was proven by Keller et al. [91] is not making any difference in case of high Weber number. To simplify the process of guessing of the initial roots they where chosen based upon the Gasler [92] theorem: (3 43) The roots of the Equation 3 39 were compared to the experimental results. The solution for jet injection at STP conditio ns is shown in Figure 3 11. As it can be inferred from the figure, the solution does no have a sharp maximum; instead, there is a relatively wide range of amplified wave numbers. It was assumed that wavelengths with amplification factor can be detected experimentally. Indeed, experimental results demonstrate quite a wide range of observed wavelengths for a given experimental conditions. As can be seen from Table 3 1 and Figure 3 12, the predicted wavelengths are in a reasonably good correlation with the measured ones for subcritical and trans critical cases. The significant discrepancy between experimental results and theoretical prediction was observed for the short wavelengths. For supercritical cases the typical solution is shown in Figure 3 13. This kind of behavior can be actually predicted analytically. For it is reasonably to assume that as

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125 well. Also, and With all these assumption s Equation 3 39 changes to: (3 44) With further simplifications: (3 45) In the supercritical cases there is no resonant wavelength, instead, all of the wav elengths shorter certain limit are equally promoted. This behavior does not appear to be physically valid. First, since Equation 3 45 was derived via small disturbance theory, the initial magnitude of the disturbance should be much smaller than the wavelen gth, i.e. Therefore, if this trend could have been compensated by but as shown in Equation 3 45 has a relatively big, yet, finite limi t. Another limitation of the developed analysis is due to elimination of the viscous shear stresses during the derivations. This affects the jet disintegration process either in cases where or for short wavelengths i.e. if This limitation was first pointed out by Sterling and Sleicher [31] in 1974. Many authors have legitimately pointed out this issue but it appears to be either impossible or extremely difficult to incorporate the shear stress into the analyt ical jet stability analysis. Sterling and Sleitcher [93] illustrated the significance of the shear stress elimination with the mathematical approach developed by Benjamin [94] in 1959. This author has presented exhaustive theoretical study on planar shear flow nearby liquid surface. Only shear stress fluctuations caused by the surface waviness are considered. To simplify the

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126 analysis shear stress and pressure fluctuation are averaged over the time. The planar approach is definitely valid as an asymptotic so lution in case of Described features of pressure and shear stress forces behavior can be easily recovered from Equations 3 46 and 3 47: (3 46) (3 47) where and all parameters here are non dimensional. The geometry of the problem is shown in Figure 3 44. The simplest linear boundary layer is assumed. As seen from Equations 3 46 and 3 47, the shear stress tends to be much smaller then the pressure fluctuation for long waves while dominating in case of Despite the simplistic approach this theory provides physically solid arguments against disregarding the surrounding gas viscosity during the stability analysis o f the jet in cases of short wavelengths. These formulas where used by Sterling and Sleicher [30] to justify certain modifications of the dispersion relationship. In their investigation of jet disturbances growth and disintegration length they introduced an empirical coefficient to reduce the influence of the term associated with gas to liquid density ratio. The value of the reducing factor was chosen to match the jet disintegration length. Although this technique allows matching between experimental results and theoretical predictions it still suffers from significant lack of fundamental arguments behind it. Also, this approach does not allow beforehand prediction of the resonant wavelength under different experimental conditions. The different theoretical analysis approaches towards the liquid jet disintegration under subcritial, trans critical and supercritical conditions can be summarized as follows. The linear

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127 stability theory allows prediction of the most promoted disturbance wavelengths under the range of the experimental conditions limited to the sub critical and some portion of the transcritical cases. The supercritical cases are not covered by up to date state of the linear stability analysis. There are some clear physical arguments indicating that d isregarding the surrounding gas viscosity is the major cause of this failure. An incorporation of the surrounding gas viscosity into the analytical stability analysis appears to be a formidable task and most likely is impossible. Computational fluid dynami cs (CFD) appears to be the only up to date available tool to predict the features of supercritical mixing. Currently, several CFD codes have been written to model the supercritical mixing. The apparent drawback of these numerical approaches is the lack of validating experimental results. This work contributes one of the first reliable experimental database in the supercritical mixing regime.

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128 Table 3 1 Numerical experiment conditions Chamber pressure, atm. ( ) Chamber temperature, K ( ) Injection velocity, m/s (predicted) Predicted wavelength, Measured wavelength 1 1.4 (0.054) 293 (0.66) 10.7 47 1.2 1.3 2 6.5 ( 0.35) 293 (0.66) 13.9 1.44 0.15 0.18 3 9.4 (0.51) 293 (0.66) 14.6 0.769 0.08 0.1 4 15.6 (0.84) 293 (0.66) 11.7 0.57 0.078 0.1 5 21.6 (1.17) 293 (0.66) 15.7 0.2 0.04 0.06 6 25.5 (1.38) 293 (0.66) 16.8 0.15 0.05 0.06 7 30.2 (1.64) 293 (0.66) 7.4 0.54 0. 1 0.12 8 6.9 (0.37) 361 (0.81) 11.8 1.6 0.15 0.16 9 9.8 (0.53) 364 (0.82) 22.6 0.28 0.055 0.07 10 19.6 (1.06) 363 (0.82) 15.3 0.23 0.055 0.05 11 27.1 (1.47) 363 (0.82) 11.4 0.23 0.06 0.06 12 30.7 (1.67) 357 (0.81) 14 0.14 0.055 0.065 13 34.3 (1.86) 3 60 (0.81) 13.3 0.13 0.055 0.06 14 7.3 (0.39) 407 (0.92) 9.2 1.65 0.09 0.1 15 13.4 (0.73) 404 (0.91) 14.1 0.3 0.07 0.06 16 17.7 (0.96) 409 (0.92) 15.3 0.15 0.05 0.06 17 23.5 (1.28) 416 (0.94) 15.3 0.09 0.04 0.06 18 25 (1.36) 412 (0.93) 16.1 0.08 0.038 0.045 19 30 (1.63) 411 (0.93) 15.3 0.07 0.038 0.042 20 35.7 (1.940 413 (0.93) 15.7 0.05 0.037 0.04 21 6.4 (0.35) 451 (1.02) 14.2 1.18 0.11 0.09 22 11.3 (0.61) 452 (1.025) 13 0.36 0.065 0.07 23 15.7 (0.85) 448 (1.016) 12.2 0.09 0.075 0.07 29 4.1 (0.22 ) 444 (1.00) 24.7 1.01 0.078 0.08 33 17.3 (0.94) 520 (1.18) 21.4 0.025 0.05 0.06

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129 Figure 3 1. Proposed test matrix. The temperature of the surrounding gas was chosen to vary within a range of i.e. 293 K 523 K where the upper limit is defined by the maximum working temperature of the facility.

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130 Figure 3 2. Actual test matrix. Three sufficiently different break up regimes were found. They are labeled as subcritical, transcritical and supercritical zones. sub critical mixing region transitional mixing supercritical mixing region

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131 Figure 3 3 Jet injection at STP conditions, injection velocity

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132 Figure 3 4. Jet injection, Injection velocity

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133 Figure 3 5. Jet injection, Injection velocity

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134 Figure 3 6. Jet injection, Injection velocity

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135 Figure 3 7. Jet injection, Injection velocity

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136 Figure 3 8. Jet injection, Injection velocity

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137 Figure 3 9. Jet injection, Injection velocity

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138 Figure 3 10 Spatial growth rate dependence on wave number.

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139 Figure 3 11 Correlation between measured (vertical axis) and predicted wavelength

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140 Figure 3 1 2. Spatial growth rate dependence on wave number in case of supercritical mixing.

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141 Figure 3 1 3. Viscous flow above liquid surface Y X

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142 CHAPTER 4 CONCLUSIONS A study of liquid jet injected into gaseous environment was undertaken under subcritical, transitional and supercritical conditions covering the range of i.e. 293 K 523 K and i.e. 1 1 This is the first comprehensive experimental study covering the entire range from subcritical to supercritical regime with the same fluid, facility and experimental method The analysis complements the existing solutions for subcritical liquid jet instability with comparision to the experimental results. A solution extension to the supercritical regime was also attempted. The results indicated the following: First wind indu ced, second wind induced and atomization break up mechanisms are observed under subcritical conditions with variations depending on the injection velocity and surrounding gas density. Pronounced ligament formation was observed under these conditions i.e. supercritical regime, when the density gradient tends to be the highest. At transcritical conditions a decreased importance of surface tension is apparent which manifests through the smoothening of the liquid tends to decrease significantly. The ligaments shape is similar to desc riptions available in computational solutions Once detached from the main jet, packets of liquid exhibit a dual behavior: in some cases the formation of rou nd liquid drops was observed as in the subcritical case, while in other cases a cluster like droplet formation was noticed, a feature characteristic for supercritical mixing. With increased pressure and temperature the jet behavior changed again with occas ional droplet formation observed under supercritical conditions only at relatively low temperatures. Density gradient values decreased drastically at supercritical conditions and approached the values characteristic for a laminar jet at STP conditions; thi s type of a liquid/gas interface behavior was described in previous computational results but not seen in previous experiments. A linear stability analysis was developed to gain additional insight into the physics involved into the jet disintegration and c ompare with the experiments.

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143 The analysis of the disturbance wavelength corresponding to the resonant frequencies of the system showed good correlation with experimental results for subcritical mixing The spatial growth rate dependence on the disturbance wavelength revealed a broad maximum. The location of this maximum was mostly defined by Reynolds and Weber number, while the values of the growth rate were mostly dependent on the gas/liquid density ratio. In case of transcritical and supercritical mixing the spatial growth dependence on the disturbance wavelength did not have a maximum. Instead, it was reaching the plateau with the growth rate values This can be obtained analytically assuming and This behavior was confirmed by solving the dispersion equation directly. The transcritical and supercritical regimes are not solved by the currently available analytical stability analys is primarily due to neglecting the surrounding gas viscosity. According to simplified analysis this should be the major force affecting the jet surface in cases where surface tension is not accounted for.

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144 CHAPTER 5 FUTURE WORK Several goals may be stated for future research. Capabilities of the technique can be expanded in terms of spatial resolution. With decrease camera focusing distance and current light intensity the spatial resolution can be increased two fold without loosing image quality of acquired images. It appears that most of the physically interesting processes during the supercritical mixing take place in the direct vicinity to the liquid/gas interface; therefore it is reasonable to zoom to thi s area. The current set of information acquired during the experiments is limited to the density distribution. Although this distribution can provide significant insight into the physics of the mixing phenomena, additional information is desirable. In part icular, fast imaging would capture the jet surface motion as well as the features of the evaporated fluid. These can be used later as references for the cross correlation analysis. This technique is limited since it cannot be used to obtain velocity distri bution inside the jet core, however, it provide information regarding the boundary layer around the jet. Therefore the mixing processes outside the jet can be better understood. This method would be particularly useful for investigation of the coaxial inje ction, where the majority of the physically interesting processes take place outside the jet core. A significant extension of this study would be the analysis of heated jet. The temperature should cover the range of transcritical to supercritical values. T his will also cover cases when supercritical jet enter a subcritical environment such as encountered in scramjet engines. The image post processing procedure as of now is relied on the assumption of known liquid density in the direct vicinity to the inject or tip. In the scope of the presented study the injected fluid was not preheated; therefore its density is known forehand with enough precision. But in cases where injected fluid has to be preheated the density might vary significantly even in the areas ne arby

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145 the injector tip. To avoid this possible source of uncertainty, direct calibration of the technique is required. To provide this calibration one should know following fluid parameters for a used laser light wavelength: light absorption efficiency, lig ht emission efficiency. Also the laser pulse to pulse intensity variation along with the laser beam profile should be controlled. The absorption and emission coefficients dependence on temperature and pressure should be accounted for in this study. A separ ate detailed analysis of the FK 5 1 2 fluorescence properties is recommended. Possibilities of expanding of the stability theory towards the supercritical jet break up were not completely explored in this work. In particular, there are boundary layers prof iles which could be incorporated in the linearized Navier Stokes equations as an initial velocity distribution, thus the shear layer features can be accounted during the stability analysis.

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146 APPENDIX A DRAWINGS OF SET UP Figure A 1. Chamber body front view, all dimensions are in inches.

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147 Figure A 2. Chamber body top view, all dimensions are in inches.

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148 Figure A 3. Chamber body, isometric view.

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149 A) B) Figure A 4. Chamber lid. A) front view B) top view, all dimensions are in inches.

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150 A) B) Figure A 5. Chamber top. A) Front view, B) top view, all dimensions are in inches.

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151 Figure A 6. Chamber lid, isometric view.

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152 A) B) Figure A 7. Chamber exhaust. A) Front and top view, B) Section A A an d bottom view, all dimensions are in inches.

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153 Figure A 8. Chamber exhaust, isometric view.

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154 A) B) Figure A 9. Dummy Flange 12. A) front view, B) top view, all dimensions are in inches.

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155 Figure A 10. Dummy Flange 12, isometric view.

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156 A) B) Figure A 1 1. Dummy Flange 14. A) front view, B) top view, all dimensions are in inches.

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157 Figure A 12. Dummy Flange 14, isometric view. Figure A 13. Flange 12. Front view, sectioned. All dimensions are in inches.

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158 A) B) Figure A 14. Flange 12. A) top view, B) bo ttom view, all dimensions are in inches.

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159 Figure A 15. Flange 12, isometric view.

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160 A) B) Figure A 16. Flange 14. A) top view, B) bottom view, all dimensions are in inches.

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161 A) B) Figure A 17. Liquid injector, all dimensions are in inches. A) Side view (injector tip and tube NPT fitting are not shown) B) Honeycomb like structure pattern.

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162 Figure A 18. Gas heater drawings, all dimensions are in inches.

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163 APPENDIX B LABVIEW CODE AND OPE RATIONAL PROCEDURES The goal of this appendix is providing comprehensive information on LabView 7.1 the experimental setup. Complete li sting of the program including user interface panel is given in Figures B 1 to B 10. General Description In general, there are two different setup operational modes. The first one is obviously an experiment itself. The experiment is usually last only 60 s or less. No control is required during this time i.e. there is no need to open or close any valve or turn on or off any of the heaters. Also, not all of the channels of registration are worth to acquire during this time e.g. liquid and gas heater core tem peratures are not necessarily worth to be known during the experiment active phase. From other hand, data acquisition sample rate has to be maximal during the experiment. Therefore number of active channels acquired during the jet injection is reduced to n ecessary minimum. Resulting sampling rate per channel is 11 ksample/s, list of active channels is given in Table B 1. The sampling rate is a critical value since the liquid flow meter has a frequency output within limits of 20 to 1200 Hz. To ensure accurat e measurements sampling rate has to be Figures A 2 5. Another setup operational mode is not as obvious as an active data acquisition, but nevertheless is necessary. The chamber has to be preheated, the desired pressure, gas flow rate and temperature have to be adjusted before the actual experiment can be started. This regime does not require high speed data acquisition; instead, a possibility of active con trol of the situation is necessary. Active control in this situation means possibility to control all devices

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164 incorporated into the data acquisition and control system via SCXI 1140 analog output module in the real time regime. To reach these goals, this p ortion of the program consists of three repeating steps: data acquisition, sending the signals to controlled units, waiting for a user response. The entire cycle turnaround time is 0.5 s. No data need to be saved while program is running in this mode. Para meters to achieve while this part of program is running: gas/liquid flow rates, gas/liquid temperature, temperature of the gas in the chamber. Procedure of gas/liquid flow rates adjustment is quite simple and described in the operational procedure. To cont rol the gas temperature, following strategy is used. The gas heater is controlled via gas temperature thermocouple and heater. The on/off state of the gas heater is depending in the temperatures in its core and injecting gas temperature. The threshold of t he heater core temperature to turnoff is set to be 800 0 C, practice shows, that this limit is typically not reached. The threshold of gas temperature to turn off the heater is preset to be equal to the desired gas temperature. It takes about 10 30 min to reach required gas and chamber temperature values. To prevent the excessive compressed gas waste the shop air is supplied into the system during the preheating. Obviously it is impossible to completely adjust the gas temperature during actual experiment s olely using only shop air. Therefore, before the experiment, the compressed air at desired pressure has to be used. The procedure of adjusting of the liquid temperature is quite similar to that for gas supply system with. Only difference in this case is a significant difference in gas and liquid heat transferring properties. Due to this issue actual liquid temperature is approximately 30 0 C higher than the gas temperature during the preheating process. List of active channels is also given in Table B 1. Lis 5 to B 7. There are to additional subroutines in the program. First subroutine is located between preheating mode and experimental mode. Listing of this part of the code is given in Figures B 7

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165 to B 8. this subroutine keep bypass liquid valve open for 5 to 10 s (depending on user decision) and then closes the bypass valve, opens the liquid valve and proceed to the experiment. Another subroutine is responsible for turning off all valves and heate rs before exiting the program. Listing of this part of code is given in Figure B 10. Table B Operational mode Voltage input (module SCXI 11 4 0 with SCXI 130 1 connection terminal) Therm ocouples, (module SCXI 1100 with SCXI 1303 connection terminal) ext ernal sync. chamb. P liq. line P gas line P liq. line flow meter gas line flow meter liq. line chamb. bottom chamb. up liq. heater core gas heater core gas Chamber heater ch1 ch3 ch4 c h5 ch6 ch7 ch0 ch1 ch2 ch3 ch4 ch5 ch6 Preheating Off On On On On On On On On On On On On Experiment On On Off On On On On On On Off Off On Off Operational Procedure The procedure described below is describing the case when liquid/gas preheating is req uired, if not corresponding actions have to be skipped. Also, not all of the procedures are needed to be done for each experiment, but they are still listed in the manual. All devices numbers are inline with Figure 2 10. 1. ram, make sure that all valves and heaters are off 2. Initiate the control interface 3. preset for how long bypass liquid valve will be open, sampling rate during the experiment and number of samples per channel to acquire 4. Provide the shop air supply into the sy stem 5. Preset desired temperatures for liquid and gas supply 6. Run the heaters

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166 7. Start the laser, laser shutter is off to prevent possibility of damaging the optics 8. Close the ball valve 16 and open ball valve 14 9. Fill the liquid tank 15 10. Close the ball valve 14 11. Op en the valves on the pressurized gas bottles 12. By adjusting the pressure regulators, assure that pressure at the low pressure side of regulators is more or equal to 1500 psi 13. Once the desired temperatures are achieved, stop the shop air supply to the gas lin e 14. Open the solenoid gas valve 3 15. Adjusting needle valves 4 and 29 reach desired chamber pressure and gas flow rate 16. Open the needle valves 22 and 23 to approx of they max value 17. open the ball valve 16 18. Open main liquid solenoid valve 20 and adjust the needle valve 17 to achieve the required liquid flow rate 19. Close main liquid solenoid valve 20 20. Open bypass liquid solenoid valve 21 and adjust the needle valve 23 to achieve the required liquid flow rate 21. Close bypass liquid solenoid valve 20 22. Initiate the image acq uisition system 23. Click the run button, simultaneously initiate the laser shutter to open 24. Once the image acquisition is over, close the laser shutter 25. Once the experiment is over resume the shop air supply to prevent the overheating of the heaters cores 26. If pl anning no experiments, initiate the control panel, turn off the heaters wait until heaters core temperature decrease below 200 0 C then click skip the run button and stop shop air supply to the system

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167 Figure B 1. Front panel of hpchcontroller.vi

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1 68 Figure B 2. Diagram of hpchcontroller.vi, frame 0 overall view

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169 Figure B 3. Diagram of hpchcontroller.vi, frames 0.0 0.1

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170 Figure B 4. Diagram of hpchcontroller.vi, frames 0.2 0.3

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171 Figure B 5. Diagram of hpchcontroller.vi, f rame 0.4

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172 Figure B 6. Diagram of hpchcontroller.vi, frame 0.5

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173 Figure B 7. Diagram of hpchcontroller.vi, frame 0.6

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174 Figure B 8. Diagram of hpchcontroller.vi, frame 1 overall view

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175 Figure B 9. Diagram of hpchcontroller.vi, frame 2

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176 Figure B 10. Diagram of hpchcontroller.vi, frame 3

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177 APPENDIX C MATLAB SCRIPTS USED TO PROC ESS RESULTS Once taken, experimental data has to be processed. Several different scripts were written to process results: 5 1 12. During data process ing the script is used as a subroutine to calculate FK 5 1 12 LabView program described in appendix A. The script outputs plots of pressure, temperature and flow rates du ring an experiment, also saves these data for further usage runs at once

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178 function density=goodeqn(To,Po) %PRSV.m %Peng Robinson Stryjek Vera equatio n of state applied to fluoro %ketone FK 5 1 12mmy2. Parameter values from Owens, J, "PHYSICAL %AND ENVIRONMENTAL PROPERTIES OF A NEXT GENERATION EXTINGUISHING %AGENT", Proceedings of HOTWC 2002 12th Halon Options Technical %Working Conference, Albuquer que, NM, April 30 May 2, 2002 %Modified through introduction of kappa variable replacing old %variable alpha now in accordance with original PRSV model in %Stryjek&Vera (1986) T=(0:1:600)'+273.15; R=8.3144; Tc1=441.81; Pc1=18.646E5; rhoc1=639; omega1= 0.471; kappa11=0.052; Mw1=.316046; %FK properties molar weight kg/m^3 Tc2=748; Pc2=40.5E5; rhoc2=315.29; omega2=0.30295; kappa12=0.03297; Mw2=.12817; x1=1; x2=0.0; % molar fractions Mw=x1*Mw1+x2*Mw2; rho=0.1:1:1800; V=Mw./rho; %m3/mole b1=0.077796*R*Tc1/Pc 1; b2=0.077796*R*Tc2/Pc2; Tr1=T/Tc1; Tr2=T/Tc2; kappa01=0.378893+1.4897153*omega1 0.17131848*omega1^2+0.0196554*omega1^3; kappa02=0.378893+1.4897153*omega2 0.17131848*omega2^2+0.0196554*omega2^3; kappa1=kappa01+kappa11*(1+Tr1.^0.5).*(0.7 Tr1); kappa2=kappa 02+kappa12*(1+Tr2.^0.5).*(0.7 Tr2); alpha1=(1+kappa1.*(1 Tr1.^0.5)).^2; alpha2=(1+kappa2.*(1 Tr2.^0.5)).^2; a1=alpha1*0.457235*(R*Tc1)^2/Pc1; a2=alpha2*0.457235*(R*Tc2)^2/Pc2; a=x1^2*a1+2*x1*x2*sqrt(a1.*a2)+x2^2*a2; b=x1*b1+x2*b2; p=R*T*(1./(V b)) a*(1./(V .*(V+b)+b*(V b))); pb=p/10^5; To=To+273.15; [ vl ,Ind ]=min(abs(T To)); for i=length(pb(Ind,:)): 1:1 if (pb(Ind,i) Po)<0 break end end density=rho(i)*.97; %pb(i,Ind)

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179 continued % % figure(1) % [c,h]=contour(rho .03*rho,T 273.15,p b,[0:1:60]); % clabel(c,h); % shading flat; % xlabel(' \ rho, kg/m^3'); % ylabel('T, C'); % grid minor % % figure(2) % % C = contourc(rho,T,pb,[25]);

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180 % 08/24/06 % Shows graphs of sensory data to check experimental validity % To make sure tar get temperature's and pressure's have been hit % Saves data in proceessed and meaningful form to 'ProcessedData.txt' % This program must be run before full processing can be done % Folders must be organized prior to running this program % Extremely similar to process_n_plot7.m % 1~time 2 3~temperature 4 ext sync 5 6~pressure 7~flow liquid % 2~post liquid heater 3~chamber top % 5~pressure chamber 6~pressure liquid line clear all [filename, pathname] = uigetfile('*.*','Find run to process','E: \ stepan \ HPCHe xperiment \ '); location=[pathname filename]; fid = fopen(location); data = fscanf(fid,'%f %f %f %f %f %f %f',[7 inf]); % It has seven rows now. data = data'; % Transpose to 7 columns fclose(fid); % Close the file, all relavant data has been stored samples=l ength(data); % Total number of samples time=data(:,1); % First column of data represents time in steps step=time(2); % This position is first step from time(1)=0 fs=1/step; % Sample rate % PROCESSING LIQUID FLOW DATA column 7 NofB=20; % Numb er of blocks that will be fit in total time delta=step*floor((samples 1)/NofB); % length in time of block chunk=floor((samples 1)/NofB); % indexed size of block for i=1:NofB Block(:,i)=data(chunk*(i 1)+2:chunk*i+1,7); BlockTime(i)=delt a*(i 1/2); % at center of block end for i=1:NofB [Pxx,f] = pwelch(Block(:,i),[],[],[],fs); [val,ind]=max(Pxx); domfreq(i)=floor(f(ind)); end liqflow=.0808*domfreq+1.5095; % DOUBLE CHECK THIS EQUATION!!!!!!!!! % PROCESSING TEMP AND PRES DATA columns 2,3,5,6 Fc = fs/200; % Carrier frequency F = Fc/fs; % Change F to vary the filter's cutoff frequency. [num,den] = butter(6,F); % Design Butterworth filter. scrsz = get(0,'ScreenSize'); h=figure('Name','Sensor output plots','NumberTit le','off','Position',[2 2 scrsz(3) scrsz(4) 70]); spot=filter(num,den,data(:,2)); % temporary variable to filter data subplot(2,2,1);plot(time,spot,'r') data(:,2)=spot;

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181 continued hold on % All temperature's appear on same plot spot=filter(n um,den,data(:,3)); plot(time,spot,'b') data(:,3)=spot; title('Temperature Readings') xlabel('Time (s)') ylabel('Temperature ({ \ circ} C)') legend('Liquid','Chamber top',1) subplot(2,2,2);plot(time,data(:,5),'r')%spot) hold on % All pressures appear on the s ame plot plot(time,data(:,6),'b') title('Pressure Readings') xlabel('Time (s)') ylabel('Pressure (atm)') tempmax=max(data(:,6)); % following finds max pressure so to scale axis START if max(data(:,5))>tempmax tempmax=max(data(:,5)); end ymax=1.1*tem pmax; % max found so axis is pretty END axis([0 1 0 ymax]) axis 'auto x' legend('Chamber','Liquid',1) subplot(2,2,3);plot(BlockTime,liqflow)%spot) for q=1:NofB data(chunk*(q 1)+1:chunk*q,7)=liqflow(q); end data(chunk*q:end,7)=liqflow(q); title('L iquid Flow Meter data') xlabel('Time (s)') ylabel('Flow (cc/s)') ymax=1.1*max(liqflow); axis([0 1 0 ymax]) axis 'auto x' subplot(2,2,4);plot(time,data(:,4),'g')%spot) title('Camera Sync output') xlabel('Time (s)') ylabel('Voltage (V)') hgsave([pathname 'PD I_' filename(9:end) '.fig']); newloc=[pathname 'ProcessedData.txt']; eval(['save newloc data ascii tabs']);

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182 % run_processor % 08/17/06 % NOTE: need to have background, LaserWeight, and ProcessedData % prior to running this progr am. % Liquid flow must be in final units in ProcessedData.txt kg/m^3 % STEPS: % 1 initialize all variables at beginning (make changes here to DONE % save time searching for all instances of each variable) % 2 prompt w/ ui for run data file DONE % 3 open & save ProcessedData.txt DONE % 4 open & save LaserWeight DONE % 5 open & save background DONE % 6 set location of test.TIF DONE % 7 open & save mymap DONE % 8 analize ext sync & save time at each frame DONE % 9 enter loop for each frame availibl e with sensory data DONE % 10 read & save frame from test.TIF into matrix of type double DONE % 11 subtract background.mat from matrix DONE % 12 apply weight to matrix (laser) DONE % 1 3 find reference intensity near nozzle DONE % 14 run checks on viablility of creating contour reject bad frame DONE % 15 obtain reference density with goodeqn() the PRSV EOS DONE % 16 calculate density slope and apply t o matrix DONE % 17 find sensory data index associated with time of frame USELESS % 18 calculate velocity in frame DONE % 19 apply ceiling(liq density) and floor(cutoff) to allow DONE % contour to run smoothly % 20 check different area if cutoff valid, increase if not DONE % 21 contour with low level for speedy processing time n<=10 DONE % 22 label axis & give all properties in title DONE % 23 a pply custom color map mymap.txt DONE % 24 save figure as bitmap with frame # as name DONE % 25 save matrix with frame # as name DONE % 26 save properties as text with frame # a s name DONE % 27 end loop DONE % x=id(1,1);y=id(2,1);scrntop=id(3,1);scrnbot=id(4,1); % camHz=id(5,1);Timech=id(6,1);LTch=id(7,1);CTch=id(8,1); % CPch=id(9,1);LPch=id(10,1);LFch=id(11, 1);datacol=id(12,1); % flowvalid=id(13,1);scrnres=512; % Leaving out scrntop and scrnbot for now since may not be needed clear all % VARIABLE INITIATION! DataCols=7; CamHz=5; %

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183 x=0.0187; % mm per one pixel y =0.0188; % mm per one pixel IntThreshold=2000; % UNKNOWN MUST OBTAIN value for which it is assumed no jet of interest maximumden=2000; % JetDia=0.08382; % UNKNOWN MUST OBTAIN cm Noz=40; % pixel dist of noz TimeCol=1; % Col stands for column, in ProcessedData.txt LiqTempCol=2; % ChmTempCol=3; % ExtSyncCol=4; % ChmPresCol=5; % LiqPresCol=6; % LiqFlowCol=7; % TotalFrames=55; % ExtSyncSpikeLev=3; % mingrad=.1*10^4; maxgrad=4*10^4; ContourLevel=50; % [filename, pathname] = uigetfile('*.*','Pick ProcessedData.txt file for data run to Process','E: \ stepan \ HPCHexperiment \ '); % if filename==0 % fprintf('A file must be chosen, this program will end \ n') % return % end %%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% pathname='E: \ stepan \ HPCHexperiment \ '; count=0; while true [filename, pathname] = uigetfile('*.*','Pick ProcessedData.txt file for data run to Process',pathname); if filename==0 if count==0 return end break end count=count+1; paths(count,:)=cellstr(pathname); files(count,:)=cellstr(filename); end clear pathname filename fprintf('These are the %d file locations you have chosen: \ n',count) Locations=strcat(deblank(char(paths)), deblank(char(files))) fprintf('If this is in error press ''Ctrl+c'' to cancel \ n')

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184 pause(3) fprintf('There will be %d contour levels calculated \ n \ n',ContourLevel) clear Locations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=1:count pathname=deblank(char(paths(i))); filename=deblank(char(files(i))); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% location=[pathname filename]; fid=fopen(location); Pdata = fscanf(fid,'%f',[DataCols inf]); Pdata = Pdata'; % Pdata is short for ProcessedData fclose(fid); % Close the file, all relavant data has been stored samples=length(Pdata); % Total number of samples step=Pdata(2,TimeCol); % This position is first step from time(1)=0 location=[pathname(1:39) 'laser _bckgrd \ LaserWeight.txt']; fid = fopen(location); weight = fscanf(fid,'%f',[1 inf]); % It has one row now. weight = weight'; % Transpose to 1 column fclose(fid); % Close the file, all relavant data has been stored location=[pathname(1:3 9) 'laser_bckgrd \ background.mat']; eval(['load location background']) ImageLocate=[pathname 'test.TIF']; location=[pathname(1:39) 'laser_bckgrd \ mymap.txt']; fid = fopen(location); mymap = fscanf(fid,'%f %f %f',[3 inf]); % It has thr ee rows now. mymap = mymap'; % Transpose to 3 columns fclose(fid); clear location fid % Pull out number of images and index of each image Frame=0; LengthCounter=0; check=0; for i=1:samples if Pdata(i,ExtSyncCol)>=Ext SyncSpikeLev LengthCounter=LengthCounter+1; IndexOfSpike(LengthCounter)=i; check=1; else if check==1 Frame=Frame+1; FrameIndex(Frame)=round(mean(IndexOfSpike)); check=0; LengthCounter=0; clear IndexOfSpike

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185 end end end clear LengthCounter check i % check if there are any images present if Frame==0 fprint f('There are no images associated with this data. \ n') fprintf('Check test.TIF and External Sync Channel in DAQ \ n') return %break end % check if last image is definitely present if (Pdata(samples,TimeCol) Pdata((Frame),Ti meCol))<1.1*(1/CamHz) fprintf('The last image may not be present in this run \ n') fprintf('Check test.TIF or no synchronization is possible \ n') return %break end InitialFrame=TotalFrames Frame+1; ScreenSize=double (imread(ImageLocate,1)); X=0:x:(length(ScreenSize(1,:)) 1)*x; % mm Y=0:y:(length(ScreenSize(:,1)) 1)*y; % mm clear ScreenSize scrsz = get(0,'ScreenSize'); %h=figure('Name','Density/Gradient Plot Window','NumberTitle','off','Positio n',[2 2 scrsz(3) scrsz(4) 70]); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if strcmp(pathname(40:53),'09_06_06_12_02'); Frame=32; elseif strcmp(pathname(40:53),'09_14_06_10_16'); Frame=48; elseif strcmp(pathname(40:53),'09_14_06_ 11_58'); Frame=40; elseif strcmp(pathname(40:53),'09_14_06_12_06'); Frame=29; InitialFrame=8; elseif strcmp(pathname(40:53),'09_14_06_10_30'); InitialFrame=31; elseif strcmp(pathname(40:53),'09_14_06_10_44'); InitialFrame=52; elseif strcmp(pathname(40:53),'09_14_06_12_20'); InitialFrame=17; elseif strcmp(pathname(40:53),'10_02_06_13_31'); Frame=28; end

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186 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for p ic=1:Frame %h=figure('Name','Density/Gradient Plot Window','NumberTitle','off','Position',[2 2 scrsz(3) scrsz(4) 70]); Current=InitialFrame+pic 1; if Current>55 break end ImageMatrix=double(imread(ImageLo cate,Current)); ImageMatrix=ImageMatrix background; if strcmp(pathname(31:38),'09_10_06') ImageMatrix=ImageMatrix(1:500,:); Y=0:y:(length(ImageMatrix(:,1)) 1)*y; end for i=1:length(ImageMatrix(:,1)) % ImageMatrix(i,:)=ImageMatrix(i,:)/sqrt(weight(i)); ImageMatrix(i,:)=ImageMatrix(i,:)/weight(i); end clear i maxfield=ImageMatrix((Noz+31):(Noz+50),:); [C I]=max(maxfield); [C J]=max(C); I=I(J); right=min(J+2,length(maxfield(1,:))); left=max(1,right 5); bottom=min(I+2,length(maxfield(:,1))); top=max(1,bottom 5); RefInt=mean(mean(maxfield(top:bottom,left:right))); clear C I J right left bot tom top maxfield if RefInt
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187 inued DY(:,i)=smooth(DY(:,i),7); end for i=1:length(DX(:,1)) DX(i,:)=smooth(DX(i,:),7); DY(i,:)=smooth(DY(i,:),7); end GradMatrix=sqrt(DX.^2+DY.^2); clear DX DY CutOff=400;%mean(me an(DensMatrix((length(DensMatrix(:,1))/25):(length(DensMatrix(:,1))/2 +5),(length(DensMatrix(1,:)) 15):(length(DensMatrix(1,:)) 5))))+100; for i=1:length(DensMatrix(1,:)) for j=1:length(DensMatrix(:,1)) if DensMatrix(j,i) maximumden DensMatrix(j,i)=maximumden; end end end clear i j for cnt=1:20 Area=mean(mean(DensMatrix((length(DensMatrix(:,1)) 15):(length(DensMatrix(:,1))5),(length(DensMatrix(1,:)) 15):(length(DensMatrix(1,:)) 5)))); if Area>0 CutOff=CutOff+50; for i=1:length(DensMatrix(1,:)) for j=1:length(DensMatrix(:,1)) if DensMatrix(j,i)0 jnum=jnum+1; jind(jnum)=samp; end end if isempty(jind)==1

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188 Origin=370; else Origin=round(median(jind)); end clear jind jnum X=X X(Origin); % final=[zeros(scrntop noz,scrnres);final]; % final=final(:,origin side: origin+side); % Y=[Y (Y(end)+y):y:(scrnbot scrntop 1+(scrntop noz))*y]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=1:length(GradMatrix(1,:)) for j=1:length(GradMatrix(:,1)) if GradMatrix(j,i)maxgrad GradMatrix(j,i)=maxgrad; end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% h=fig ure('Name','Density/Gradient Plot Window','NumberTitle','off','Position',[2 2 scrsz(3)scrsz(4) 70]); contourf(X,Y,DensMatrix,ContourLevel,'linestyle','none') axis ij axis square colormap (mymap); colorbar; xl abel('Distance (mm)') ylabel('Distance (mm)') bet=strcat('Density = ',int2str(RefDen),' kg/m^3 Velocity = ', num2str(Velocity,'%.1f'),'m/s Liquid Temp = ',int2str(LiqTemp),' C Chamber T = ',int2str(ChmTemp),' C Chamber P = ',num2str(ChmPres ,'%.1f'),' Atm Frame = ',int2str(Current),' Time = ',num2str(Time,'%.2f'),' s'); title(bet) % saveloc=strcat(pathname,'figures \ ',int2str(frame),'.fig'); % hgsave(saveloc) if Current<10 saveloc=strcat(pa thname,'ProcessedFiles \ ',int2str(0),int2str(Current),'d.bmp'); saveas(h,saveloc) eval(['save pathname 'ProcessedFiles \ int2str(0) int2str(Current) 'd.mat DensMatrix X Y']); else saveloc=strcat(pathname,'ProcessedF iles \ ',int2str(Current),'d.bmp'); saveas(h,saveloc) eval(['save pathname 'ProcessedFiles \ int2str(Current) 'd.mat DensMatrix X Y']); end

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189 close(h) clear DensMatrix h=figu re('Name','Density/Gradient Plot Window','NumberTitle','off','Position',[2 2 scrsz(3) scrsz(4) 70]); contourf(X,Y,GradMatrix,ContourLevel,'linestyle','none') axis ij axis square colormap (mymap); g=colorbar; set(g,'YTickLabelMode','manual'); num=get(g,'Ytick'); dem=get(g,'YtickLabel'); div=num(1)/str2num(dem(1,:)); NumZero=0; while true if div>=10 div=div/10; NumZero=NumZero+1; else break end end NumZeros=NumZero+3; bet=strcat('Gradient *10^ ^',int2str(NumZeros),' kg/(m^4) Vel= ', num2str(Velocity,'%.1f'),'m/s Liq T= ',int2str(LiqTemp),' C Cham T= ',int2str(ChmTemp) ,' C Cham P= ',num2str(ChmPres,'%.1f'),' atm Frame= ',int2str(Current),' Time= ',num2str(Time,'%.2f'),' s'); title(bet) xlabel('Distance (mm)') ylabel('Distance (mm)') if Current<10 saveloc=strcat(pathname,'Pro cessedFiles \ ',int2str(0),int2str(Current),'g.bmp'); saveas(h,saveloc) eval(['save pathname 'ProcessedFiles \ int2str(0) int2str(Current) 'g.mat GradMatrix']); else saveloc=strcat(pathname,'ProcessedFiles \ ',int2 str(Current),'g.bmp'); saveas(h,saveloc) eval(['save pathname 'ProcessedFiles \ int2str(Current) 'g.mat GradMatrix']); end if Current<10 fid = fopen(strcat(pathname,'ProcessedFiles \ ',int2str(0),int2str( Current),'t.txt'), 'w'); fprintf(fid, bet); fclose(fid); else fid = fopen(strcat(pathname,'ProcessedFiles \ ',int2str(Current),'t.txt'), 'w');

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190 fprintf(fid, bet); fclose(fid); end close(h) clear GradMatrix end clear Frame FrameIndex InitialFrame scrsz end

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APPENDIX D EXPERIMENTAL RESULTS

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192 Figure D 1 Jet injection at STP conditions, injection velocity

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193 Figure D 2. Jet injection, Injection velocity

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194 Figu re D 3. Jet injection, Injection velocity

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195 Figure D 4. Jet injection, Injection velocity

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196 Figure D 5. Jet injection, Injection velocity

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197 Figure D 6. Jet injection, Injection velocity

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198 Figure D 7. Jet inje ction, Injection velocity

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199 Figure D 8. Jet injection, Injection velocity

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200 Figure D 9. Jet injection, Injection velocity

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201 Figure D 10. Jet injection, Injection velocity

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202 Figure D 11. Jet injection, Injection velocity

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203 Figure D 12. Jet injection, Injection velocity

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204 Figure D 13. Jet injection, Injection velocity

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205 Figure D 14. Jet injection, Injection velocity

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206 Figure D 15. Jet injection, Injection velocity

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207 Figure D 16. Jet injection, Injection velocity

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208 Figure D 17. Jet injection, Injection velocity

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209 Figure D 18. Jet injection, Injection velocity

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210 Figure D 19. Jet injection, Injection velocity

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211 Figure D 20. Jet injection, Injection velocity

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212 Figure D 21. Jet injection, Injection velocity

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213 Figure D 22. Jet injection, Injection velocity

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214 Figure D 23. Jet injection, Injection velocity

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215 Figure D 24. Jet injection, Injection velocity

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216 Figure D 25. Jet injection, Injection velocity

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217 Figure D 26. Jet injection, Injection velocity

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218 Figure D 27. Jet injection, Injec tion velocity

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219 Figure D 28. Jet injection, Injection velocity

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220 Figure D 29. Jet injection, Injection v elocity

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221 Figure D 30. Jet injection, Injection velocity

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222 Figure D 31. Jet injection, Injection velocit y

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223 Figure D 32. Jet injection, Injection velocity

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224 Figure D 33. Jet injection, Injection velocity

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225 Figure D 34. Jet injection, Injection velocity

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226 Figure D 35. Jet injection, Injection velocity

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227 Figure D 36. Jet injection, Injection velocity

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228 Figure D 37. Jet injection, Injection velocity

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229 LIST OF REFERENCES 1. Huimin, L., Science and Engineering of Droplets: Fundamentals and Applications. William Andrew Publishing, Inc., New York, 1999. 2. Berger, H. L., Paul, A., William J. B., Unitary Axial Flow Tube Ultrasonic Atomizer with Enhanced Sealing. U nited States Patent # 4978067, Dec. 18, 1990. 3. Kelly, J. A., Electrostatic Atomizing Device. United States Patent # 4255777, Mar. 10, 1981. 4. Lefebvre, A. H., Atomization and Sprays, Hemisphere Publishing Corporation, New York, U.S.A., 1989. 5. Lichtrarowicz, A. Incompressible Non J. Mech. Eng. Sci., Vol. 7, No. 2, 1965, pp. 210 219 6. Proc. Inst. Mech. Eng., Vol. 173, No. 25, 1959, pp. 661 665 7. Oil Ind. Moscow, 1961, 9 8. icrometer: First Report, Characteristics of Bull. Jap. Soc. Mech. Eng., 1961, p. 4 9. NACA TR 373, September 11, 1930 10. O www.delavaninc.com/pdf/Fuel_Nozzles_for_Burners.PDF 11. Hansen, K.G. A Computational and Experimental Study of the Internal Flow in a Scaled Pressure M.Sc. Thesis Aalborg University Esbjerg 2001 12. Atomize Newtonian Fluid Chem. Eng. Sc. 55, pp. 4339 4348, 2000 13. Q. J. Mech. Appl. Math., Vol. 3, Pt. 2, pp. 129 139, 1950 14. Jet Atomizer for Powe Proceedings of the 2 nd International Conference on Liquid Atomization and Spray Systems, Madison, Wis., pp. 181 185, 1982

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230 15. AIAA J. Propulsion and Power, Vol. 1, No 3, pp. 193 199, 1985 16. Simmons, H.C. and Harding, C.F., Some Effects of Using Water as a Test Fluid in Fuel Nozzle Spray Analysis, ASME Paper 80 GT 90, March 1980 17. Radcliffe, A., The Performance of a Type of Swirl Atomizer, Proceedings, Insti tution of Mechanical Engineers, Vol. 169, pp. 93 106, 1955 18. ASME J. Eng. Power, Vol. 101, No. 2, pp. 250 258, 1979 19. Babu, K. R., Nara simhan, M. V. and Narayanaswamy, K. iction of In Proceedings of 2nd International Conference on Liquid Atomization and Spray Systems Madison, Wisconsin, 1982, pp. 99 106 20. ASME Paper 85 GT 37 1985 21. NASA, CR 2000 210467 2000 22. Atomizer Proceedings of the 1 st International Conference on Liquid Atomization and Spray Systems Tokyo, pp. 109 115, 1978 23. Mixed Twin Proceedings of the 3 rd International Conference on Liquid Atomization and Sprays, London, pp. IIC/2/1 11, 1985 24. ASME J. Fluids En g., Vol. 97, No. 3, pp. 316 320, 1975 25. Trans. Soc. Mech. Eng. Jpn., Vol. 5, pp. 68 75, 1939 26. Rayleigh L. Proc. London Math. Soc. 1 0:4 13 1879b. 27. Batchelor, G. K. (editor), Collected Works of G. I. Taylor Cambridge U. P., 1958, Cambridge, England 28. Journal of Applied Mathematics and Physics, Vol. 11, pp. 1931 29. NACA TN 659 1932

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236 BIOGRAPHICAL SKETCH Stepan A. Polikhov was born in Navoi in the republic Uzbekistan in the former Soviet Union. in 1978. A few years later his family moved back to Russia and settled down in the small town Torbeevo in the republic of Mordovia. After finish ing high school in 1995 Stepan A Polikhov enrolled in Moscow Engineering Physicists Institute (MEPhI). At this technical university he received a degree of Engineer Physicist in the area of high speed processes in 2002. A year prior to graduation, he start ed working at the N. N. Semenov Chemical Physics Institute as a Research Engineer in the combustion lab where he was involved in research on pulse detonation engine (PDE) projects. In 2003 he enrolled in the PhD program in Mechanical Engineering at the Uni versity of Florida.