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Study of Soot Formation in an Iron-Seeded Isooctane Diffusion Flame Using In Situ Light Scattering


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STUDY OF SOOT FORMATION IN AN IRON-SEEDED ISOOCTANE DIFFUSION FLAME USING IN SITU LIGHT SCATTERING By KATHRYN ALLIDA MASIELLO A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2004

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Copyright 2004 by Kathryn Allida Masiello

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Dedicated to my best friend and husband. His encouragement and love have been invaluable throughout my academic career.

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iv ACKNOWLEDGMENTS This work would not have been possible without the vision, encouragement, and guidance of Dr. David Hahn. I am deeply grateful to him for teaching me the ins and outs of laser based diagnostics, and also for helping me to discover a field that captures my interest and leaves me filled with curiosity. I also thank my labmates, Allen Ball, Brian Fisher, Vincent Hohreiter, Kibum Kim, and Prasoon Diwakar. Allen was responsible for building the vaporization chamber used in my experiments. Thanks to his efforts, I could begin experimentation right away, without extensive setup. Brians role as resident answer man was greatly appreciated; as too were Vince, Kibum, and Prasoons insightful conversations and suggestions. I thank my family for their unending support. My parents, siblings, in-laws, and husband showed interest in my work, and in the excitement it brought me. And when things werent so exciting, or were overly frustrating, my husband was responsible for keeping me focused on my final goal. I thank him for helping me to reach for my highest potential.

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v TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Soot Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Production of Soot Precursor Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Particle Coagulation and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Particle Agglomeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Soot Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Metallic Fuel Additives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Additives in Premixed Flames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Additives in Diffusion Flames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Project Methodology and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2 ELASTIC LIGHT SCATTERING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Scattering Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Mie Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Rayleigh Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Systems of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Monodisperse systems of particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Polydisperse systems of particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 System Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3 EXPERIMENTAL METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Burner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Fuel Vaporization and Delivery System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

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vi Laser Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Photomultiplier tube linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Stray light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Vaporization of Soot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Micro-Raman System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 RESULTS AND DATA ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Elastic Light Scattering Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Transmission Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Soot Characteristics Determined from Mie Theory . . . . . . . . . . . . . . . . . . . . . . . . 74 Particle Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Number Density of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Particle Volume Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Micro-Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5 DISCUSSION AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 APPENDIX A COMPOSITION OF COMMON JET FUELS . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 B EXTINCTION COEFFICIENT DECONVOLUTION TECHNIQUES . . . . . . . . 111 C ERROR ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

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vii LIST OF TABLES Table page 3-1. Concentric diffusion burner dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3-2. Data collection heights and radial positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3-3. Flame operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3-4. Average unseeded and seeded flame diameters at each height. . . . . . . . . . . . . . . 41 3-5. Description of fuel vaporization and delivery system . . . . . . . . . . . . . . . . . . . . . . 41 3-6. Description of scattering system apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3-7. Differential scattering coefficient for methane and nitrogen at common incident wavelengths at 1 atm, 298 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3-8. Methane to nitrogen reference differential scattering coefficient ratio used for stray light calibration at common incident wavelengths, assuming ideal gases. . . 49 3-9. Number densities, differential scattering cross sections, and scattering coefficients for methane and nitrogen calibration gases at 1 atm, 344K. . . . . . . . . . . . . . . . . . 50 3-10. Average time-integrated calibration gas and stray light signals and range of signals seen over all scattering experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3-11. Description of transmission apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4-1. Average (N=10) time-integrated scattered signal from unseeded flame. . . . . . . . 61 4-2. Average (N=6) time-integrated scattered signal from iron pentacarbonyl seeded flame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4-3. Average (N=10) unseeded K' VV results and standard deviation of K' VV . . . . . . . . 63 4-4. Average (N=6) seeded K' VV results and standard deviation of K' VV . . . . . . . . . . . 63 4-5. Average (N=5) unseeded power measurements used in transmission study. . . . . . 67 4-6. Average (N=5) seeded power measurements used in transmission study. . . . . . . 67

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viii 4-7. Average (N=5) transmission through the unseeded flame. . . . . . . . . . . . . . . . . . . 68 4-8. Average (N=5) transmission through the seeded flame. . . . . . . . . . . . . . . . . . . . . 68 4-9. Average (N=5) unseeded extinction coefficients determined using a three-point Abel inversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4-10. Average (N=5) seeded extinction coefficients determined using a three-point Abel inversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4-11. Unseeded ratio of K' VV /K ext determined from experimental data. . . . . . . . . . . . . . 75 4-12. Seeded ratio of K' VV /K ext determined from experimental data. . . . . . . . . . . . . . . . 75 4-13. Complex refractive indices for soot from various sources. . . . . . . . . . . . . . . . . . . 76 4-14. Unseeded soot particle modal diameters determined from Mie theory and complex refractive index of m = 2.0-0.35 i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4-15. Seeded soot particle modal diameters determined from Mie theory and complex refractive index of m = 2.0-0.35 i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4-16. Unseeded soot particle mean diameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4-17. Seeded soot particle mean diameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4-18. Unseeded soot particle number densities determined from Mie theory and complex refractive index of m = 2.0-0.35 i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4-19. Seeded soot particle number densities determined from Mie theory and complex refractive index of m = 2.0-0.35 i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4-20. Unseeded soot particle volume fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4-21. Seeded soot particle volume fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4-22. Bulk iron oxide powder specifications used in micro-Raman study. . . . . . . . . . . 92 A-1. Composition of fuel oil no. 1 and JP-5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 A-2. Composition of surrogate JP-8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 A-3. Composition of shale-derived and petroleum-derived JP-4. . . . . . . . . . . . . . . . . 110 B-1. Unseeded extinction coefficients determined from onion peeling inversion. . . . 113 B-2. Seeded extinction coefficients determined from onion peeling inversion. . . . . . 114

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ix B-3. Unseeded extinction coefficients determined from linear regression technique with two flame geometries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 B-4. Seeded extinction coefficients determined from linear regression technique with two flame geometries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 B-5. Unseeded extinction coefficients determined using linear regression and a smoothing technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 B-6. Seeded extinction coefficients determined using linear regression and a smoothing technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 B-7. Unseeded extinction coefficients determined using a three-point Abel inversion. 123 B-8. Seeded extinction coefficients determined using a three-point Abel inversion. . 123 C-1. Error in K' VV and at unseeded height d, position 4. . . . . . . . . . . . . . . . . . . . . . 124 C-2. Curve fit parameters for Mie diameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 C-3. Curve fit parameters for C ext . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 C-4. Summary of experimental data and calculated parameters at height d, position 4 with error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 C-5. Unseeded particle diameters with error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 C-6. Seeded particle diameters with error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 C-7. Unseeded particle number densities with error. . . . . . . . . . . . . . . . . . . . . . . . . . 130 C-8. Seeded particle number densities with error. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 C-9. Unseeded particle volume fractions with error. . . . . . . . . . . . . . . . . . . . . . . . . . 131 C-10. Seeded particle volume fractions with error. . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

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x LIST OF FIGURES Figure page 1-1. Transmission Electron Microscope (TEM) images of propane soot. . . . . . . . . . . . 3 1-2. The H 2 -abstraction-C 2 H 2 -addition mechanism acting on a biphenyl molecule. . . . 6 1-3. Particle coagulation versus particle agglomeration. . . . . . . . . . . . . . . . . . . . . . . . . 8 1-4. Soot formation process showing stages of formation on molecular and particulate scales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1-5. Soot formation regimes in a diffusion flame, and radial soot concentration profile at an arbitrary flame height. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1-6. Chemical structure of isooctane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2-1. Light scattering response to an incident electromagnetic light beam. . . . . . . . . . . 21 2-2. Polar coordinate geometry for light scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2-3. K' VV /K ext versus modal particle diameter for a specific polydisperse system. . . . . 32 2-4. Diagnostic techniques for determining scattering and extinction coefficients for a system containing varied properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3-1. Concentric diffusion burner schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3-2. Data measurement heights and radii relative to the flame. . . . . . . . . . . . . . . . . . . 37 3-3. Fuel vaporization system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3-4. Alicat Scientific digital flow meters used for nitrogen coflow and oxygen. . . . . . 40 3-5. Light scattering system setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3-6. Sample scattering signals from methane, nitrogen, and flame. . . . . . . . . . . . . . . . 50 3-7. Transmission system setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3-8. Region of iron deposits on flame holder screen. . . . . . . . . . . . . . . . . . . . . . . . . . 56

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xi 3-9. Confocal micro-Raman schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4-1. Typical scattered signal response from photomultiplier tube measuring calibration gases and flame signal at a fixed height and radial position. . . . . . . . . . . . . . . . . 60 4-2. Baseline-subtracted scattered signals from calibration gases and flame at a fixed height and radial position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4-3. Seeded and unseeded differential scattering coefficients. . . . . . . . . . . . . . . . . . . . 64 4-4. Seeded and unseeded extinction coefficients determined using a three-point Abel inversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4-5. Soot particle modal diameters determined from Mie theory for m = 2.0-0.35 i and ZOLD parameter # o = 0.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4-6. Unseeded and seeded soot particle modal diameters. . . . . . . . . . . . . . . . . . . . . . . 79 4-7. Extinction cross section of soot particles determined from Mie theory for m = 2.0-0.35 i and ZOLD parameter # o = 0.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4-8. Unseeded and seeded particle number densities. . . . . . . . . . . . . . . . . . . . . . . . . . 85 4-9. Unseeded and seeded soot particle volume fractions. . . . . . . . . . . . . . . . . . . . . . . 89 4-10. FeO reference Raman spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4-11. Fe 2 O 3 reference Raman spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4-12. Fe 3 O 4 reference Raman spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4-13. Graphite reference Raman spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4-14. Carbon black reference Raman spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4-15. Reference Raman spectra of clean, unburned flame holder screen. . . . . . . . . . . . 95 4-16. Raman spectra of seeded flame holder screen and Fe 2 O 3 reference. . . . . . . . . . . . 96 4-17. Raman spectra of mixed bulk powders of FeO and Fe 2 O 3 . . . . . . . . . . . . . . . . . . 97 4-18. Raman spectra of two seeded flame holder screens. . . . . . . . . . . . . . . . . . . . . . . . 98 4-19. Raman spectra of unseeded flame holder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4-20. Raman spectra of seeded and unseeded screens taken at center of flame holders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

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xii 5-1. Soot volume through the growth regime (annular regions 3, 4, and 5) of the flame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 B-1. Geometry used for onion peeling inversion scheme. . . . . . . . . . . . . . . . . . . . . . 112 B-2. Geometries used for linear regression inversion scheme. . . . . . . . . . . . . . . . . . . 115 B-3. Example of smoothing algorithm used to determine extinction coefficients from linear regression results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 B-4. Flame geometry used for three-point Abel inversion. . . . . . . . . . . . . . . . . . . . . 120

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xiii Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science STUDY OF SOOT FORMATION IN AN IRON-SEEDED ISOOCTANE DIFFUSION FLAME USING IN SITU LIGHT SCATTERING By Kathryn Allida Masiello May 2004 Chair: David W. Hahn Major Department: Mechanical and Aerospace Engineering Elastic light scattering and transmission measurements were performed on a laboratory isooctane diffusion flame seeded with 4000 ppm iron pentacarbonyl. These measurements allowed the determination of the size, number density, and volume fraction of soot particles in the seeded flame. Comparison to an unseeded flame allowed the determination of the effects of the metallic additive on soot particle inception, growth, and oxidation. It was shown that while the additive may have had a slight soot-enhancing effect at early residence times, the growth of the soot particles was unaffected by the addition of iron to the flame. The greatest effect of the additive on soot perturbation is concluded to occur in the oxidation regime of the flame. In addition, confocal microRaman spectroscopy performed on the stainless steel mesh flame holders of the seeded and unseeded flames showed that the state of the iron present was the oxide Fe 2 O 3

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1 CHAPTER 1 INTRODUCTION Small particles in the air ranging in size from a few nanometers to tens of microns are described as particulate matter (PM). In 1997, the Environmental Protection Agency 1 established National Ambient Air Quality Standards (NAAQS) for PM less than 2.5 m (PM2.5) and revised the existing NAAQS for PM less than 10 m (PM10). Particulate matter less than 2.5 m is increasingly under study. The largest of this class of particles is approximately 1/30 the diameter of a human hair. Because of the small size of these particles, they are able to permeate and impact the deepest parts of the lungs. Increased incidences of asthma, chronic bronchitis, shortness of breath, painful breathing, and increased respiratory and heart disease have all been linked to PM2.5. 2 Children and the elderly are at greatest risk from PM2.5 inhalation. Often the immune systems of the elderly are weaker because of age, or they suffer from existing cardiopulmonary diseases. Children are at risk because their respiratory and immune systems are not yet fully developed. An average adult breathes 13,000 liters of air per day, while children can breathe up to 50% more air per pound of body weight than adults. Asthma in children is a common result of PM exposure. It is estimated that although children make up only one quarter of the population, 40% of asthma cases appear in this group. 1 Soot particles, rich in amorphous carbon and polycyclic aromatic hydrocarbons (PAHs), are a specific type of PM that are known to be mutagenic and carcinogenic. 3 4 Particulate matter has significant environmental effects as well. PM is the leading cause of reduced visibility or haze in the United States. In particular areas across the

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2 U. S., visibility has been reduced from natural conditions by as much as 70%. 1 In addition, PM from combustion processes includes sulfates and nitrogen oxides, which are responsible for acid rain, and greenhouse gases, responsible for global warming. 2 5 Further, as PM2.5 settles on soil and water, the nutrient and chemical balances of the ecosystem are disturbed. Water systems can become more acidic, threatening aquatic species, and soil nutrients are depleted, damaging sensitive crops and forests. Because of their small size, PM2.5 particles are able to travel long distances; thus their environmental and health impacts are felt hundreds of miles away from the source. 2 5 Because soot from combustion processes is a major source of PM, there has been significant interest in the formation of soot and methods of soot reduction. Reduction of soot would clearly improve the health of individuals exposed to PM. For example, ground crews on aircraft carriers are constantly exposed to high levels of PM in the effluent of jet engines. During jet takeoff, high fuel consumption is necessary, and soot emissions are at a maximum. The shortand long-term health effects of this exposure on ground crew personnel is a serious concern, and a means of reducing soot in turbine engines is of great interest. A balance must be maintained, however. Reduction of harmful PM emissions is desirable, but engine performance cannot be compromised. The process of soot reduction via fuel additives is being explored as a potential means of reducing harmful combustion byproducts, while having a minimal impact on the combustion characteristics. Soot Formation The oxidation of organic compounds leads to the formation of soot, which can be described as amorphous molecules containing mostly carbon and hydrogen. The actual

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3chemical structure is that of a multiple ring polynuclear aromatic compound. Palmer andCullis6 described the physical characteristics of soot in detail.The carbon formed in flames generally contains at least 1% by weight of hydrogen.On an atomic basis this represents quite a considerable proportion of this elementand corresponds approximately to an empirical formula of C8H. When examinedunder an electron microscope, the deposited carbon appears to consist of a numberof roughly spherical particles, strung together rather like pearls on a necklace. Thediameters of these particles vary from 100 to 2000 and most commonly liebetween 100 and 500 The smallest particles are found in luminous butnonsooting flames, while the largest are obtained in heavily sooting flames (p.265).Elementary soot particles exhibit a size distribution well modeled by a log-normaldistribution.7 The average diameter of 100 to 500 cited by Palmer and Cullis6corresponds to about one million carbon atoms. X-ray diffraction measurementsperformed on soot show randomly dispersed domains of graphite-like parallel layerswithin the particle, though the spacing between the layers is larger than that of graphite.Figure 1-1 shows Transmission Electron Microscope (TEM) images of propane soot attwo magnifications. Figure 1-1. Transmission Electron Microscope (TEM) images of propane soot. A) at0.2 m scale. B) at 100 nm scale. A B

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4 The process of soot formation can be described by four distinct stages: 1. Production of soot precursor molecules 2. Particle coagulation and growth 3. Particle agglomeration 4. Soot oxidation. Perturbations in sooting characteristics of a flame are due to changes in the mechanisms of soot formation. Thus, an understanding of these stages is essential to the study of soot reduction in flames and combustion systems in general. Production of Soot Precursor Molecules In the first stage of soot formation, soot precursor molecules are formed. These molecules act as nucleation sites for the formation of soot. It is widely believed that this stage is the rate-limiting step in the formation of soot. A number of mechanisms have been suggested to describe the formation of these nucleation sites. In general, all of these mechanisms involve small aliphatic (open chained) compounds that form the first aromatic rings, typically benzene, C 6 H 6 Acetylene, C 2 H 2 is abundant in the early stages of combustion, thus it is the most likely aliphatic compound to initiate this process. In later stages, benzene is thought to lead to the production of more complex PAHs. 8 One proposed mechanism, termed an even-carbon-atom pathway, involves the addition of acetylene to n-C 4 H 3 and n-C 4 H 5 by n C 4 H 3 + C 2 H 2 # $ # phenyl (1-1) n C 4 H 5 + C 2 H 2 # $ # benzene + H (1-2) Kinetic simulations of shock-tube acetylene pyrolysis suggest that the reaction in Eq. 1-1 is significant in forming the first aromatic rings, 9 while Bittner and Howard 10 suggested the reaction in Eq. 1-2 is an important pathway to aromatic ring formation at low temperatures. Miller and Melius 11 countered this even-carbon-atom mechanism,

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5 suggesting that n-C 4 H 3 and n-C 4 H 5 are too short-lived, thus, their concentrations would be too small to have a significant effect on aromatic ring formation. Instead, they suggest an odd-carbon-atom pathway involving the combination of more stable propargyl radials, C 3 H 3 + C 3 H 3 # benzene or phenyl + H (1-3) Recent Monte Carlo theoretical studies have, however, predicted the n-C 4 H 3 radical and n-C 4 H 5 isomer to be more stable than originally suggested, restoring the importance of the even-carbon-atom pathway described by the reactions in Eqs. 1-1 and 1-2 Yet another possible mechanism for the initial aromatic ring formation combines the stable propargyl radical with the abundant acetylene molecule to form a cyclopentadienyl radical by C 3 H 3 + C 2 H 2 # c $ C 5 H 5 (1-4) The cyclopentadienyl radical is then quick to form benzene. A comparison of reaction rates between Eq. 1-4 and Eq. 1-3 showed that the former was predicted to proceed faster than the latter by a factor of 2 to 10 3 8 Many more reaction mechanisms have been proposed to characterize this first stage in soot formation, though the mechanisms reviewed above are gaining wide acceptance. Clearly, the particle inception stage is subject to great debate. It is considered the most critical step in soot formation, yet the least understood. Particle Coagulation and Growth The transition from molecular to particle properties occurs at a molecular weight of about 10 4 amu, which corresponds to an incipient soot particle diameter of about 3 nm. This transition occurs during the second stage of soot formation, coagulation and particle growth. In this step, the initial surface area for particle growth appears. In the process of

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6coagulation, coalescent collisions of particles result in one larger, essentially sphericalparticle. This process dominates early soot particle growth, increasing particle diameterwhile decreasing particle number density (number of particles per volume). Coagulationis limited to very small particles, on the order of 18 nm or less. Coagulation transitionsinto chain-forming collisions when the viscosity of the particles increases past a criticalvalue due to dehydrogenation of the condensed phase.12Soot particle surface growth occurs as gas phase species attach to the surface of aparticle and become incorporated into the particulate phase. Frenklach8 describes thisprocess as H2-abstraction-C2H2-addition, in which H atoms are abstracted from aromaticcompounds, and gaseous acetylene is incorporated to bring on growth and cyclization ofPAHs. The process of H-abstraction-C2H2-addition is described by Ai+H" # Ai$+H2 (1-5) Ai"+C2H2# $ # products ,(1-6)where the notation Ai refers to an aromatic molecule with i peri-condensed rings, and Ai#is its radical. The reaction in Eq. 1-5 describes the removal of an H atom from thereacting hydrocarbon by a gaseous H atom. The second step, C2H2 addition, is shown inthe reaction of Eq. 1-6. Figure 1-2 shows H abstraction from a biphenyl molecule and thesubsequent addition of acetylene. Figure 1-2. The H2-abstraction-C2H2-addition mechanism acting on a biphenyl molecule.

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7 It is possible for the growth of aromatic compounds to occur via different mechanisms specific to the fuel and flame conditions, however, using numerical simulations Frenklach et al 9 showed that these alternate methods quickly relax to the acetyleneaddition mechanism. Soot surface growth will eventually cease. While once believed that the depletion of growth species was responsible for this phenomenon, it is now understood that the reduction of soot surface growth is due to a decrease in the surface reactivity of the soot. 13 14 The means by which the particle surface loses its reactivity are not yet fully understood, however, it is suggested that it is strongly tied to the ratio of C to H atoms in the soot as the particle ages. 13 15 This relationship has been described in both a chemical and a physical sense. Chemically, the growth of the particle relies on a radical site created by the abstraction of a H atom. Though, physically, if it is assumed that the hydrogen in the particle is contained only at the edges of the aromatic ring, it can be seen that the C to H ratio will increase as the particle grows. As a result, the number of possible growth sites decreases. While this method serves to describe the decay of soot surface reactivity, it is incomplete. One would expect a direct proportionality between the H to C ratio and surface reactivity with this model. However, it has been shown that the H to C ratio decays 2 to 3 times more slowly than the surface reactivity. 16 The molecular details of soot surface decay are under continued investigation to more accurately model this mechanism. Particle Agglomeration As the surface reactivity of the maturing soot decays, the third stage in soot formation, agglomeration of the nascent soot particles, becomes increasingly important. At this stage, coagulation has ceased as described above and collisions now result in the

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8sticking, or agglomeration, of particles together forming chain-like structures. Inagglomeration, the particles still retain their original identity as opposed to coagulation,in which the individual particles coalesce into one larger particle. Figure 1-3 illustratesthe difference between coagulation and agglomeration. Agglomerated soot particles maycontain 30-1800 primary particles and are well characterized by a log-normal sizedistribution.17 Figure 1-3.Particle coagulation versus particle agglomeration.Soot OxidationThe final stage in soot formation is soot oxidation, where the particles are partiallyor completely destroyed, yielding CO as a product. Oxidizing species in soot destructioninclude O atoms, OH radicals, and O2. Previous work has demonstrated that theconcentration of O atoms in sooting flames is relatively low, and so too is the probabilitythat a reaction will occur when an O atom hits the soot surface. Therefore it is assumedthat OH radicals and O2 are primarily responsible for the oxidation of soot particles.17 Anunderstanding of the process of soot formation is fundamental to studies in soot

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9reduction. The four stages of soot formation are illustrated in Figure 1-4, after thetreatment of Bockhorn.18 Figure 1-4.Soot formation process showing stages of formation on molecular andparticulate scales.Flames are a primary source of soot. There are two main classes of flames premixed and diffusion (or non-premixed). In a premixed flame, the fuel and oxidizer aremixed at the molecular level prior to combustion. An example of this type of flame is a

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10typical spark-ignition engine. The final stage of soot formation, soot oxidation, is lesspronounced in a premixed flame than in a diffusion flame because most of the oxidizingspecies are spent by the time soot particles reach maturity. It is at this critical time whenthe growth has waned that the oxidizer can begin to have a net destruction effect on theparticles, though there is little oxidizer available in a premixed flame at this point. In adiffusion flame, the reactants remain separate and react at the interface between the fueland oxidizer. A candle is a classic example of a diffusion flame. This type of flame hassignificant oxidation of soot at higher flame heights as oxygen diffuses into thecombustion zone and encounters mature soot particles. A diffusion flame can be dividedinto distinct regimes according to the stages of soot formation the inception regime, thegrowth regime (incorporating coagulation, chemical species growth, and agglomeration),and the oxidation or burnout regime.19 Figure 1-5 demonstrates these regimes as well asthe radial soot profile at an arbitrary flame height. Figure 1-5.Soot formation regimes in a diffusion flame, and radial soot concentrationprofile at an arbitrary flame height.

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11In the soot profile shown in Figure 1-5 it can be seen that small quantities of soot arepresent in the inception regime but peak formation occurs in the growth regime.Destruction occurs at the outer radii and at the flame tip as oxygen diffuses into thecombustion zone.Metallic Fuel AdditivesMetallic fuel additives have become commonplace in many combustionapplications. Starting in the early 1920s and through the 1970s, tetraethyl lead was apopular additive in gasoline to enhance octane levels and reduce engine knock. Elevatedlevels of lead in blood can have adverse health effects, ranging from anemia, mentalretardation, and permanent nerve damage. Because of these risks, the EnvironmentalProtection Agency began limiting the use of this additive from its inception, phasing itout in the 1980s and eventually completely banning leaded gasoline for on-road vehiclesin 1996. Another common fuel additive is methylcyclopentadienyl manganesetricarbonyl (MMT), manufactured by the Ethyl Corporation. MMT has been usedprimarily in Canada for over 25 years, though it is available worldwide. Similar to lead,this octane enhancer is a neurotoxin and can cause irreversible neurological disease athigh levels of inhalation.Metallic additives have also been used to alter the sooting characteristics of flames.The effects of the additives, as well as the mechanisms by which they alter flamecharacteristics, are under study. Common additives include alkali metals such as Li, Na,K, and Cs, and alkaline earth metals such as Ca, Sr, and Ba. Transition metals are also ofinterest, particularly Mn and Fe. Results from these studies vary significantly dependingupon fuel type, additives used, premixed versus diffusion flames, and flame conditions.Often studies of the same type of combustion system have yielded opposing conclusions.

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12 The review that follows will be limited to key studies of Mn and Fe in premixed and laminar flames. Additives in Premixed Flames Ritrievi et al. 20 studied a laminar premixed ethylene flame seeded with ferrocene, Fe(C 5 H 5 ) 2 for dopant concentrations of 0.005-0.14% Fe by weight of fuel and for flame C/O ratios of 0.71-0.83. In this study, they observed a decrease in initial particle diameter in the seeded flames, however these particles grew to a larger final size than those in the unseeded flames. Additionally, the number density of particles (number of particles per volume) increased in the seeded flames in early residence times, though this value decayed rapidly with an end result approximately equal to the unseeded flame. These results were supported by previous work performed by Haynes et al 21 Further, in the seeded flames, measurable volume fractions of soot (fraction of soot per sample volume) were found at an earlier residence time than in the unseeded flames, and the final volume fraction was always greater in the seeded flames. Overall, this study found an overall increase in soot yield for the seeded flames ranging from factors of 1.2-13.5 for the range of C/O ratios studied. For a constant ferrocene concentration they saw the enhancement of soot decline as the C/O ratio was increased. Additionally, growth rates for the seeded flames were measured to be lower at early residence times than in unseeded flames. Auger spectroscopy was used to determine the spatial distribution of Fe and C in extracted soot particles. They observed that the iron in the soot was concentrated at the cores of the particles while the outer surface was a thick carbon-rich layer. Mossbauer spectroscopy determined that the iron in the particles was in elemental form. Although

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13 metallic iron was found in the soot particles, FeO was expected to be the stable species present under the given flame conditions, based on thermodynamics. Ritrievi hypothesized that FeO homogeneously nucleated early in the flame before particle inception began. This explained the higher number densities, smaller size, and measurable volume fractions early on in the seeded flame, as well as the layering of Fe and C in the analyzed soot particles. Additionally, it was concluded that carbon deposited on the particles was used to reduce FeO to metallic Fe via direct reduction. The consumption of carbon at the surface explained the slower growth rates in the seeded flames and suggested that FeO is relatively inactive in promoting soot growth. However, metallic iron can catalyze carbon deposition on the particle surface leading to growth. Carbon then serves two roles in growth processes. First, the growth of soot particles in early residence times of the flame is determined by the ability of carbon to reduce FeO to the more active Fe, and by the degree that Fe is diluted on the surface by depositing carbon. In the later growth regimes, diffusion of Fe through the layers of depositing carbon determines soot growth rates. In studies of a similar premixed ethylene flame seeded with either ferrocene or cyclopentadienyl manganese tricarbonyl, (C 5 H 5 )Mn(CO) 3 Feitelberg et al. 22 also found that the additives had the effect of increasing the total amount of soot formed. For this study, C/O ratios from 0.74 to 0.80 were studied, similar in range to Ritrievis work. Iron was added to the fuel in 200 ppm concentrations by a molar basis (0.13% Fe by weight of fuel), and manganese was added in 140 ppm concentrations (0.10% Mn by weight of fuel). Overall, the iron additive tripled total soot volume fraction, while manganese increased this parameter by approximately 50%. The results of this study agreed with

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14 Ritrievis assessment that particle size and soot volume fraction increased at the later residence times in the flame and that the overall number densities were unchanged. Disagreement arises however near the burner lip where Feitelberg saw, within experimental error, conditions in both seeded flames equal to unseeded, contrary to Ritrievis earlier soot inception conclusion. An equilibrium analysis was employed to determine the states of the metal additives in the flame. Feitelberg concluded that at high flame temperatures, the iron would exist as free metal atoms. The iron would then precipitate out of the gas phase into metallic iron form near 1760 K, or at residence times between 3 and 5 ms. Though Ritrievi concluded that FeO was present in the flame, Feitelberg concluded that thermodynamically FeO was not expected to form in the fuel rich flame studied. As with the iron additive, manganese was predicted to exist in the gaseous phase as free metal atoms at high temperatures. At a slightly longer residence time, the manganese was expected to precipitate and form solid MnO. In analysis of the data, Feitelberg concluded that the metal additives had no effect on soot particle inception, rather their role was to increase the rate of gas-solid reactions that increase the total size of the soot while the number density of particles remained constant. Modeling of acetylene addition to soot particles indicated that the metal additive acts as a catalyst to carbon deposition via acetylene, thus increasing the final particle size. Hahn 23 studied a premixed propane flame seeded with iron pentacarbonyl, Fe(CO) 5 with fuel equivalence ratios of 2.4 and 2.5. Iron pentacarbonyl was added in concentrations of 0.16-0.32% by weight of iron to the fuel. Again, an overall increase in

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15 the total amount of soot produced was noted. The diameter of soot particles appeared to be the least affected by the iron additives, with an average increase in the seeded flames of only 1.9%. The number density of particles increased in the seeded flames in all regions of the flame, with the exception of the lowest heights studied in the richer flame. Overall this parameter saw a 16.9% increase. The seeded volume fraction and surface area of the soot particles were found to increase over all heights studied by an average of 22.9 and 20.5%, respectively. X-ray photoelectron spectroscopy was employed to determine the state of the iron additive in extracted soot particles. This analysis identified iron oxide in the form Fe 2 O 3 as the dominant species in the sampled soot particles, accounting for nearly 100% of all iron present. No significant quantities of elemental Fe or other oxides such as FeO were identified, discounting Ritrievis conclusion of FeO reduction and Feitelbergs analysis predicting elemental Fe. Hahns study had the advantage of experimentally determining the state of the iron in sampled particles, rather than using prediction models, although no in situ analysis was performed. It has been suggested that metal additives may accelerate the rate of soot oxidation in the burnout regime. 23 24 This regime is absent in premixed flames however, thus the full effect of the metal additive cannot be seen. Previous studies of premixed flames have demonstrated an overall increase in soot formation due to metallic fuel additives, either by catalysis of acetylene addition or by increasing the number of initial soot nucleation sites. With the addition of the burnout regime in diffusion flames, a complementary picture of the effect of additives can be investigated.

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16 Additives in Diffusion Flames In a study of an isooctane diffusion flame operating above its smoke point, Bonczyk 25 noted soot enhancing and suppressing characteristics of ferrocene added in concentrations of 0.09% Fe by weight of fuel. Similar to Ritrievis work, Bonczyk saw the appearance of soot earlier in the seeded flame. In early residence times in the flame, particle size and number density all increased, enhancing soot production. However, in later residence times, these parameters were decreased significantly when the soot reached the burnout regime of the flame. The net effect was a reduction in soot when compared to the unseeded flame, measured by these parameters and also visibly noted when the smoke plume, apparent in the unseeded flame, was eliminated in the seeded flame. Particles were collected post-flame and subjected to an Auger-type analysis to determine the species of iron present in the soot. This analysis indicated that Fe 2 O 3 was the condensate present with only trace amounts of carbon when the flame was seeded at the original concentration of 0.09% Fe by weight of fuel. However when this concentration was reduced to 0.03%, the principle condensate was identified as carbon, with less than 2% of elemental iron. Bonczyk concludes that the soot enhancement is due first to increased nucleation sites provided by solid Fe x O y particulates. Enhancement is then furthered by the same reduction reaction suggested by Ritrievi, Fe x O y + yC # xFe + yCO (1-7) The presence of Fe has a catalytic effect on the deposition of carbon on the particle surface, increasing particle surface reactivity. The reduction of soot in the burnout regime is also enhanced by the presence of the metal additive. Iron oxide catalytically

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17 enhances the removal of carbon by molecular oxygen, but this requires elemental Fe to diffuse through the soot matrix to the surface and its subsequent oxidation by xFe + 1 2 yO 2 # Fe x O y (1-8) Combining the reactions in Eqs. 1-7 and 1-8 shows the net oxidation of carbon due to the metallic additive, C + 1 2 O 2 # CO (1-9) Through the reaction in Eq. 1-9 carbon oxidation is enhanced by the additive and the result is a net reduction of soot in the burnout regime. This method of iron reduction and subsequent oxidation is also supported by Zhang and Megaridis, 26 who studied an ethylene diffusion flame seeded with ferrocene, as well as by Kasper et al 27 whose investigation included ferrocene seeded methane/argon and acetylene/argon flames. It is important to note that this conclusion is characterized by a more efficient burnout of soot particles in seeded flames, not an inhibition of soot formation by the additive. In fact, seeded flames see peak soot production levels higher than those in unseeded flames due to increased surface area for soot formation in the particle inception regime. The net reduction of soot is caused by efficient oxidation by catalytic means in the burnout regime. A second important observation regarding past research are the discrepancies in the identification of the state of the metallic additive in the flame. In the studies reviewed, analyses of soot species in the flame were performed outside of the flame. Ritrievi and Feitelberg relied on a thermodynamic analysis. Extraction techniques were used in Hahns and Bonczyks study, and although extraction techniques have been developed to

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18have a minimal impact on the flame, there is no way to ensure that these methods do notperturb the characteristics of the flame during sampling. The most effective method ofdetermining the state of the metallic additive is to use an in situ technique.Project Methodology and MotivationTo this authors knowledge, in situ measurements have not been performed toidentify the state of the metallic additive in the flame, although this diagnostic techniquewould eliminate the possibility of perturbing the flame and altering flame characteristics.Identifying the additive state in an annular region surrounding the flame is a step closer toin situ flame measurements and may be used to predict the state of the additive in theflame.This research focused on the effects of iron pentacarbonyl, Fe(CO)5, on a laminarprevaporized isooctane/oxygen diffusion flame. As compared with other fuel additivessuch as manganese and lead, which are known neurotoxins, iron has relatively lowtoxicity. In studies it has also been shown to be a highly effective soot suppressant.22,28In addition, iron pentacarbonyl is an organometallic solution that is soluble in liquidisooctane, allowing for a simple means of regulating and delivering the dopant to thecombustion system before vaporization of the fuel. These factors combined make ironpentacarbonyl an ideal additive for this study. Isooctane, C8H18, was of interest becauseit is an analog to high performance jet fuels and is characterized by a relatively lowboiling point. The compositions of a number of common jet fuels are listed in AppendixA. Figure 1-6 shows the chemical structure of isooctane. Operating a diffusion flameallowed for the effects of the additive to be observed throughout all regimes of the flame,from particle inception to the critical burnout regime, better representing gas turbineengines, for example.

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19 Figure 1-6. Chemical structure of isooctane. The laser diagnostic techniques of elastic light scattering and transmission were used to probe the flame. The light scattering and transmission studies allowed the characterization of the soot particles by determining particle diameters, number densities, and volume fractions. All of these methods were performed in situ so that the flame would not be perturbed and the results would paint a more accurate picture of the flame character. In addition, micro-Raman spectroscopy was used to identify the state of the iron additive deposited on the flame holder screens used for flame stability. The goals of this project were threefold. First, to implement novel laser based techniques to measure the size, number density, and volume fraction of soot particles in seeded and unseeded flames. Secondly, to fully characterize the seeded and unseeded flames spatially. And third, to determine the state of the metallic additive deposited during combustion in an annular region surrounding the flame, bringing the eventual in situ identification of the state in the flame closer to reach. These support the goals of exploring potential mechanisms for soot reduction using the information retrieved about soot particle growth and the state of the additive in the flame.

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20 CHAPTER 2 ELASTIC LIGHT SCATTERING Scattering Theory Laser light scattering is a diagnostic tool that can effectively extract information about a system of particles in situ while having a minimal or undetectable impact on the particles or the system overall. Electromagnetic radiation incident on a particle can be scattered or absorbed, or undergo a combination of the two. The way this electromagnetic radiation interacts with the scatterer is characteristic to the particular system. Information about the number and size of the particles can be extracted from the scattering response. In this study, elastic laser light scattering was employed to determine the profile of the scattering and extinction coefficients throughout the seeded and unseeded flames. These parameters were then employed to determine the size of the soot particles in the flame, as well as their number density and total volume fraction. Elastic scattering is based on the re-radiation of electromagnetic energy resulting from a heterogeneity in an incident electric field. For this research, the heterogeneity can be thought of as a particle of soot. As incident electromagnetic energy encounters a heterogeneity, the radiation creates an oscillating dipole moment in the particle. The acceleration and deceleration of electrons through the oscillating dipole moment acts as a source of electromagnetic energy of the same frequency as the incident radiation, which is then absorbed by the particle or radiated out as elastically scattered light. Figure 2-1 demonstrates this response.

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21 Figure 2-1. Light scattering response to an incident electromagnetic light beam. Mie Theory The interactions of electromagnetic radiation and a particle are prescribed by Maxwells equations. For a single homogeneous sphere, Mie 29 developed the exact solution to this interaction in 1908. The notation and treatment given by Kerker 30 will be used in this study to describe scattering theory. Figure 2-2 illustrates the geometry for scattering by a single homogeneous sphere. Figure 2-2. Polar coordinate geometry for light scattering. A plane electromagnetic wave traveling in the positive z-direction incident upon a homogeneous sphere of radius a

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22 The incident electromagnetic wave has electric vector E linearly polarized along the xaxis, and magnetic vector B along the y-axis. The direction of propagation lies along the Poynting vector S The spherical, homogeneous particle has radius a and a complex refractive index of m = n i k where n denotes the refractive index and k represents the absorption coefficient. The surrounding medium has a refractive index of m o Typically the surrounding medium is air and m o is assumed to be unity. The scattered radiation S scat is oriented at a particular $ and % and the scattering plane is defined by the observation angle % and the forward direction, defined by the direction of propagation. Given an incident radiation intensity I o at wavelength & the intensity of the scattered radiation polarized perpendicular and parallel to the scattering plane, respectively, is given by I = I o # 2 4 $ 2 r 2 i 1 sin 2 (2-1) I = I o # 2 4 $ 2 r 2 i 2 cos 2 (2-2) where r is the distance from the particle and i 1 and i 2 are intensity functions defined by i 1 = 2n + 1 n( n + 1) n = 1 # a n $ n (cos % ) + b n & n (cos % ) [ ] 2 (2-3) i 2 = 2n + 1 n( n + 1) n = 1 # a n $ n (cos % ) + b n & n (cos % ) [ ] 2 (2-4) The parameters n and n in Eqs. 2-3 and 2-4 are the angular dependent functions of the associated Legendre polynomial, expressed as n (cos # ) = P n ( 1) (cos # ) sin # (2-5)

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23 n (cos # ) = dP n ( 1) (cos # ) d # (2-6) with the parameters a n and b n defined as a n = n ( # ) $ n ( m # ) % m n (m # ) $ n ( # ) & n ( # ) $ n ( m # ) % m n (m # ) $ & n ( # ) (2-7) b n = m n ( # ) $ n (m # ) % n (m # ) $ n ( # ) m & n ( # ) $ n (m # ) % n (m # ) $ & n ( # ) (2-8) The parameter m is termed the relative refractive index, and is defined as the ratio of the refractive index of the particle to the refractive index of the medium, namely m = m / m o The size parameter, ( is defined as = 2 # a $ (2-9) where again, a is the particle radius and & is the wavelength of the incident radiation in the medium. Prime notation in Eqs. 2-7 and 2-8 denotes differentiation with respect to the entire argument. The Ricatti-Bessel functions ) n and n are given by n ( z) = # z 2 $ % & ( ) 1 2 J n + 1 2 (z ) (2-10) n ( z) = # z 2 $ % & ( ) 1 2 H n + 1 2 (2) (z ) = n (z ) + i + n (z ) (2-11) where the parameter + n (z) is given by n ( z) = # $ z 2 % & ( ) 1 2 Y n + 1 2 (z ) (2-12) In Eqs. 2-10 2-11 and 2-12 J n+1/2 (z) and Y n+1/2 (z) are the half-order Bessel functions of the first and second kind, respectively, and H n + 1 / 2 ( 2) ( z) is the half-order Hankel function of the second kind.

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24 The differential scattering cross section, C' pp represents the energy removed from the incident beam path and scattered about a given solid angle in a given direction. The two-component subscript pp denotes the polarizations of the incident light and the scattered light, respectively. The differential scattering cross section for vertical, or perpendicular polarized incident light with perpendicular polarized scattered light would be denoted as C' VV Likewise, horizontal, or parallel polarized incident and scattered light would be denoted as C' HH For these two special cases, the scattering cross sections are given by C VV = 2 4 # 2 i 1 (2-13) C HH = 2 4 # 2 i 2 (2-14) which can be derived from Eq. 2-1 For spherical particles with linearly polarized incident radiation, the differential scattering cross sections C' VH and C' HV are zero. The differential scattering cross section for natural, or unpolarized light is the average of Eqs. 2-13 and 2-14 namely, C scat = 2 8 # 2 (i 1 + i 2 ) (2-15) The intensity of scattered light in terms of the differential scattering cross sections may be determined by from Eqs. 2-1 2-2 2-13 and 2-14 specifically, I VV = I o 1 r 2 C VV sin 2 (2-16) I HH = I o 1 r 2 C HH cos 2 (2-17) I scat = I o 1 r 2 C scat (2-18)

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25 Integration of Eq. 2-15 over all solid angles of 0 $ 2 and 0 % yields the total scattering cross section C scat This parameter represents the fraction of incident radiation scattered in all directions, and is expressed as C scat = 2 2 # 2n + 1 ( ) a n 2 + b n 2 ( ) n = 1 $ % (2-19) The absorption cross section C abs describes the fraction of incident energy absorbed within the particle. The sum of the absorption cross section and the scattering cross section describe the extinction cross section as C ext = C abs + C scat (2-20) The total amount of energy removed from an incident beam of intensity I o is then determined from the product I o C ext For a spherical particle, the extinction cross section is given by C ext = 2 2 # 2n + 1 ( ) Re {a n + b n } n = 1 $ % (2-21) Rayleigh Theory Mie theory provides a general solution to spherical scattering without limits on particle size. For large particles, Mie theory solutions converge to those attained by employing geometric optics. For small particles, Mie theory agrees with the theory developed by Rayleigh 31 in 1871. Rayleigh theory is an approximate solution to scattering for small, non-absorbing (k = 0 in the complex refractive index) spherical particles. While Mie theory can also accurately describe these particles, it is desirable to employ Rayleigh theory whenever possible due to the complexity of the Mie solution. A valid scattering solution using Rayleigh theory for a spherical particle may be obtained for the following conditions:

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261. The external electric field seen by the particle is uniform2. The electric field penetrates faster than one period of incident electromagneticradiation.These two conditions are satisfied for the case of "<<1 and |m |"<<1 where ( is thesize parameter defined previously, and |m |=(n2+k2)1/2 In the Rayleigh regime, thedifferential scattering cross sections for a single spherical particle are given as CVV'="24#2 $6m 2%1m 2+2 2 (2-22) CHH'=CVV'cos2" .(2-23)Note that the vertical-vertical differential scattering cross section is independent of theobservation angle %, while the horizontal-horizontal differential scattering cross sectionhas a minimum at 90 degrees. The Rayleigh scattering cross section and absorption crosssection are expressed as Cscat=2"23# $6m 2%1m 2+2 2 (2-24) Cabs="#2$ %3Imm 2"1m 2+2 & ( ) + .(2-25)As shown in Eqs. 2-24 and 2-25, the scattering coefficient scales with (6, while theabsorption cross section is proportional to (3. In the Rayleigh regime, the size parameteris sufficiently small (recall, ( << 1) thus for an absorbing particle, the contribution ofCscat to the total extinction cross section Cext can be neglected, and it is assumed thatCext = Cabs.

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27 Systems of Particles The theory presented above was specific to scattering from a single spherical particle. However, often the system of interest contains a large number of particles, such as an aerosol cloud. Mie theory, and its subset Rayleigh theory, can be used to describe a system of particles based on the scattering of single particles 32 provided that 1. The particles are spaced such that there are no electrical interactions between particles 2. Scattered light from one particle is not subsequently scattered from another particle 3. There is no optical interference between the scattered waves. Criteria 1 is satisfied if a distance of 2 to 3 diameters separate each particle. Defining the number density N as the number of particles per system volume, the maximum N allowable while still maintaining 3 diameters of separation between particles is N=2/(9 d 3 ). Criteria 2 is met if the optical mean free path is greater than the optical pathlength L of the system. The quantity 1/(NC ext ) is comparable to the optical mean free path, thus for Criteria 2 to be met, the product LNC ext must be less than 1. The last criteria in treating a system of particles based on the scattering of single particles is met when the system under consideration consists of a large collection of randomly oriented particles. In this case, the intensities of scattered light from each particle can be added directly to determine the total intensity of scattered light from the system. Monodisperse systems of particles A monodisperse system is characterized by uniformly sized particles. The overall scattering and extinction of light for such a system can be described by the differential scattering coefficient and the extinction coefficient, defined respectively as K pp = NC pp (2-26)

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28 K ext = NC ext (2-27) where N is the number density of particles (particles per volume), and again, the pp subscript refers to the polarizations of the incident and scattered light. The parameters C' pp and C ext are determined from either Mie theory, Eqs. 2-13 2-14 and 2-21 or Rayleigh theory, Eqs. 2-22 2-23 and 2-25 noting that for Rayleigh particles C ext = C abs + C scat with the scattering cross section neglected if absorption is present. The transmission of incident radiation I o through a system of particles for a particular wavelength is defined as = I transmitted I o (2-28) Complete transmission of incident light will result in a of unity. Conversely, a of zero will result if all of the incident light is absorbed and/or scattered by the particles. The Beer-Lambert law relates the transmission to the extinction cross section by = exp( # K ext L) (2-29) where L is the optical pathlength. The quantity K ext L is known as turbidity, a measure of the ability of the system to extinguish incident light. The volume fraction f v like the number density, is a useful parameter for characterizing the particles in a system. The volume fraction is defined as the volume of particles per unit volume. For a monodisperse system, the volume fraction is given by f v = 6 d 3 N (2-30) where d is the diameter of the scattering particle. It should be noted that the parameters d, N, and f v are not mutually exclusive. Knowledge of any two permits the calculation of the third.

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29 Polydisperse systems of particles A system containing non-uniform particles is termed polydisperse. A flame is an example of a polydisperse system as soot particles sizes can vary throughout the sample region. In order to characterize the scattering and extinction properties of a polydisperse system, information about the particle sizes must be taken into account. Often, continuous distribution functions are used to describe the probability that a particle size lies within a certain range. Espenscheid et al 33 proposed a zeroth-order lognormal distribution (ZOLD) to characterize a polydisperse system of particles. Unlike a Gaussian, or normal distribution, the ZOLD distribution is skewed to favor larger particle sizes, which typically models aerosol populations more accurately. Additionally, the domain of this distribution spans from zero to infinity, while the Gaussian distribution may predict unrealistic negative populations. The ZOLD is mathematically identical to a log-normal distribution, however its characteristic parameters are easier to specify for an aerosol population than are those of the log-normal distribution. The ZOLD function is defined as p( r) = exp( # o 2 2) 2 $ # o r m exp (ln r ln r m ) 2 2 # o 2 % & ( ) (2-31) where r is the particle radius, r m is the modal value of r, and o is a dimensionless measure of the width and skewness of the distribution. The mean radius r is related to r m by r = r m exp 3 2 o 2 # $ % & ( (2-32) and the true standard deviation of the ZOLD is related to o and r m by = r m exp( 4 o 2 ) # exp( 3 o 2 ) [ ] 1 2 (2-33)

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30 The extinction and differential scattering coefficients of a polydisperse system can now be determined using the ZOLD function and the mean extinction and differential scattering cross sections, C ext and C pp respectively, as K ext = N C ext (2-34) K pp = N C pp (2-35) The mean parameters describe the extinction and scattering for all spherical particles in the system, and are obtained by integrating the individual cross sections weighted with the distribution function over all radial values. Namely, C ext = C ext (r) p( r) dr 0 # (2-36) and C pp = C pp ( r) p(r) dr 0 # (2-37) Integration of Eqs. 2-36 and 2-37 requires numerical techniques for Mie theory. In the Rayleigh regime however, these integrals may be evaluated analytically. For a polydisperse system, the number density of particles is not directly affected by the size distribution. However, the characterization of volume fraction f v in a polydisperse system requires the ZOLD function to be taken into account, specifically, f v = N 4 3 r 3 p( r) dr 0 # $ (2-38) Substitution of the ZOLD function, Eq. 2-31 into the above and integrating yields f v = 4 3 N exp 15 2 # o 2 $ % & ( ) r m 3 (2-39)

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31 An interesting result of Eq. 2-38 arises when considering Rayleigh particles. In this regime, the mean extinction cross section of Eq. 2-36 can be written as C ext = 8 # 2 $ Im m 2 1 m 2 + 2 % & ( ) r 3 p(r) dr 0 + , (2-40) using the C ext parameter described by Eq. 2-25 and the definition of ( Combining Eqs. 2-38 and 2-40 the extinction coefficient K ext can be expressed in terms of the volume fraction by K ext = N C ext = 6 # f v $ Im m 2 1 m 2 + 2 % & ( ) (2-41) This expression allows for the determination of f v simply from transmission measurements. As it will be seen in the next section, this greatly simplifies diagnostics and allows for the characterization of an aerosol system without regard to the size distribution of the particles. System Diagnostics In the preceding analysis, the extinction and scattering coefficients could easily be determined provided that information about particle size, number density, and volume fraction is known. However in most scenarios, the inverse problem is faced given the extinction and scattering coefficients, characterization of the system in terms of the aforementioned parameters is desired. Referring to Eqs. 2-22 2-25 2-36 and 2-37 it can be seen that for either a monoor polydisperse system, the ratio of the differential scattering cross section K' pp and the extinction coefficient K ext is in general K pp K ext = NC pp NC ext = f ( # m d, $ ) (2-42)

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32 The values of & and % are dictated by experimental setup, and it is assumed that m is known based on a priori knowledge of the scattering particles. For a polydisperse system, can be determined by sampling particles from the aerosol, assuming a value, or by performing more advanced techniques such as dynamic light scattering, or photon correlation. For a monodisperse system, is zero. With these parameters in hand, only the diameter of the scattering particles is unknown (or the modal diameter for a polydisperse system), and it can easily be determined. Figure 2-3 shows the relationship between modal particle diameter and K' VV /K ext for a specific polydisperse system. Figure 2-3. K' VV /K ext versus modal particle diameter for a specific polydisperse system. For this case, & = 532 nm, m = 2.0 0.35 i and = 30.7 nm. With the particle diameter known from the above analysis, the number density and volume fraction can then determined. From the definition of the extinction coefficient given in Eq. 2-34

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33 N=KextCext ,(2-43)where Cext can be calculated using the previously determined particle size. The volumefraction for Mie particles is found from Eq. 2-39, or by rearrangement of Eq. 2-41 forRayleigh particles. Thereby the necessary parameters to characterize a system ofparticles, d, N, and fv, have been established.Deconvolution techniques. To this point, the scattering and extinction coefficientshave been assumed spatially constant for a given system. However, in many cases, suchas flame studies, these parameters may vary based upon the location in the system. Forexample, in Figure 1-5, the concentration of soot was shown to have high spatialdependence. To better characterize this type of system, areas of constant scattering andextinction coefficients are defined. For the case of a flame, concentric annular regionsabout the flame center are employed. As shown in Figure 2-4, laser light scattering datamay be collected at representative points to determine the scattering coefficient for eachregion. Figure 2-4. Diagnostic techniques for determining scattering and extinction coefficientsfor a system containing varied properties.

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34 Determination of the extinction coefficient for each region requires more attention however, as the transmission pathlength can intersect multiple regions. A variety of techniques have been developed to deconvolve line of sight measurements into the corresponding radial parameter. Onion peeling and three-point Abel inversion are two such schemes. Both techniques construct information about the radial parameters based upon information in neighboring sections. These schemes will be discussed further in Chapter 4

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35 CHAPTER 3 EXPERIMENTAL METHODS Burner For all experimentation, a concentric diffusion burner was used. A schematic of the burner is shown from side and top views in Figure 3-1 Isooctane and nitrogen flow through the center of the burner and are met at the burner exit by an oxygen flow, fed through an array of twelve inner ports. The dimensions of the burner are summarized in Table 3-1 Figure 3-1. Concentric diffusion burner schematic. Side and top views are shown. Isooctane and nitrogen flow through the inner tube, while oxygen enters the system through the outer array of ports.

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36 Table 3-1. Concentric diffusion burner dimensions. Inner Diameter (cm) Outer Diameter (cm) Outer tube 1.656 1.905 Inner tube 0.704 0.953 Inner array 0.254 A stainless steel mesh flame holder was placed 55 mm above the burner lip to promote flame stability. Because stainless steel is a poor conductor of heat, the region in the flame remained much hotter than the region outside of the flame. If the flame were to drift due to air currents, it would tend to recenter itself over the flame holder due to the temperature gradient in the mesh. The flame extended approximately 60 mm above the flame holder, however the observed height above the flame holder was subject to wide fluctuation. A new flame holder screen was used for each experimental run to assure that flame conditions were not significantly altered by a deteriorating screen. In addition to the flame holder, a shroud was placed around the burner to block ambient air currents. This shroud was 25.4 x 26.7 cm and made of 50% opaque Plexiglas, which also helped to block stray light from entering the scattering detection optics. A vertical translation stage allowed the burner to be raised and lowered, permitting light scattering and transmission data to be taken at various heights above the burner surface. Five heights were investigated and were designated with the letters b through f. These heights were consistently reproducible and corresponded to a number of specific rotations of the vertical stage knob. A sixth height designated a, 2.54 mm above the burner lip, was initially considered, though it was discarded due to interactions between the Gaussian tails of the laser intensity profile and the burner lip. These interactions introduced significant stray light into the system, thus this height was removed from consideration. Data were also collected at six equally spaced radial positions in the

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37 flame, ranging from the flame center to near the flame edge. A precision translation stage controlled by a micrometer allowed the collection optics to be adjusted to the these different positions. One revolution of the micrometer corresponded to 0.025 inches of linear motion. The flame was considered axisymmetric, and as discussed below, was divided into six concentric annular regions. The soot characteristics were assumed constant through these six concentric regions, defined by these radial positions. Table 32 summarizes these vertical and radial positions, and Figure 3-2 demonstrates the relative positions of these points in the flame. Table 3-2. Data collection heights and radial positions. Position Label Height Above Burner Lip (mm) Position Label Distance From Flame Center (mm) b 8.73 1 0 c 15.24 2 0.635 d 22.86 3 1.270 e 30.96 4 1.905 f 40.64 5 2.540 flame holder 54.60 6 3.175 Figure 3-2. Data measurement heights and radii relative to the flame.

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38 Fuel Vaporization and Delivery System Vaporization of the liquid isooctane fuel was necessary before the fuel could be delivered to the burner. This was achieved by flowing the fuel through a vaporization system. Three main sections characterize the vaporization system the preheat zone, the vaporization zone, and the delivery line. Figure 3-3 shows the vaporization system. Figure 3-3. Fuel vaporization system.

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39 All three regions of the vaporization system were wrapped with Omega heater tape and fiberglass insulating tape. The heaters were controlled with two PID controllers set at 100C, which was above the boiling point for the liquid isooctane. The preheat region consisted of a 0.625 inch diameter, 36 inch long 304 stainless steel tube packed with brass balls, which increased the surface area to promote heat transfer. A nitrogen coflow stream was introduced into the vaporization system at the head of the preheat zone at a rate of 0.8 L/min. The stream was heated and entered into the second region of the vaporization system, the vaporization zone, a 0.25 inch diameter, 36 inch long, 304 stainless steel tube. The liquid fuel was delivered to the vaporization region via a variable flow Fisher Scientific peristaltic pump at a rate of 1 mL/min. The warmed nitrogen aided in fuel vaporization as well as the transfer of the fuel through the vaporizer. The delivery line of the vaporization system consisted of approximately 50 inches of 0.25 inch diameter braided PTFE hose that delivered the nitrogen and vaporized fuel mixture to the burner. This line was also heated to eliminate any condensation of the fuel on the way to the burner. Prior to any experimentation, the vaporization system heaters were turned on and the nitrogen coflow was allowed to flow for at least half an hour. This ensured that the system was adequately heated before the fuel entered the system. At the burner exit the nitrogen/fuel mixture was met by a 9 L/min stream of oxygen. Alicat Scientific digital flow meters regulated the nitrogen and oxygen gas flow rates within 0.01 L/min for the nitrogen flow and 0.1 L/min for the oxygen. The accuracy of these instruments was 1% of full-scale. These flow meters can be seen in Figure 3-4

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40 Figure 3-4. Alicat Scientific digital flow meters used for nitrogen coflow and oxygen. Fuel and oxidizer flow rates were such that the unseeded flame operated just under the smoke point for isooctane. For the iron pentacarbonyl seeded flames, the dopant was added to the liquid fuel supply in 4000 ppm quantities by mass (~0.11% Fe per mass of fuel) and was delivered to the burner through the fuel stream. Table 3-3 summarizes the flame operating conditions. Table 3-3. Flame operating conditions. Stream Flow Rate (L/min) C 8 H 18 (liquid) 0.001 C 8 H 18 (vapor) 0.179 N 2 0.8 O 2 9.0 Fe(CO) 5 (seeded flame only) 4000 ppm Seeded and unseeded flames had an average diameter of approximately 7.8 mm at the burner lip. Flame diameters varied over the range of heights studied, and are summarized in Table 3-4 These diameters were measured graphically using still images of the flame. As can be seen from Table 3-4 the seeded flame diameters varied only slightly from the unseeded flame.

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41 Table 3-4. Average unseeded and seeded flame diameters at each height. Height Unseeded Flame Diameter (mm) Seeded Flame Diameter (mm) b 7.7 0.6 7.1 0.3 c 8.0 0.8 7.2 0.4 d 8.2 0.7 7.4 0.3 e 8.7 0.7 8.2 1.0 f 11.5 2.8 11.8 2.4 The overall equipment summary for the vaporization and delivery system is shown in Table 3-5 Table 3-5. Description of fuel vaporization and delivery system Device Manufacturer/Supplier Model Description Equipment Peristaltic pump Fisher Scientific 13-876-4 Variable flow peristaltic pump Heater tape preheat zone Omega SRT101-060 313 W Heater tape vaporization zone Omega SRT051-060 156 W Heater tape delivery line Omega SRT051-060 156 W Braided PTFE hose Swagelok SS-4BHT PTFE-lined stainless steel flexible hose Thermocouple Omega Type K Thermocouple Heater controller Omega CN9000A 2 PID controllers HEPA filter Gelman Laboratory 12144 2 HEPA filters Digital flow meter Alicat Scientific Used for N 2 coflow 0-1 SLPM, accurate to 1% of full-scale Digital flow meter Alicat Scientific Used for O 2 stream 0-10 SLPM, accurate to 1% of full-scale Fuel and Gases O 2 Praxair UN 1072 >99% pure N 2 Praxair UN 1066 >99% pure Isooctane Fisher Scientific O296-4 HPLC CH 4 (used for calibration) Praxair UN 1971 Ultrahigh purity, 99.97% pure

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42 Diagnostics Laser Light Scattering Laser light scattering techniques were employed to determine the scattering characteristics of soot particles in unseeded and seeded flames. Figure 3-5 shows the experimental setup for this scattering system. Figure 3-5. Light scattering system setup. A) Frequency doubled Nd:YAG 532 nm pulsed laser. B) Ultrafine-gauge wire meshes to attenuate laser. C) Dichroic mirror, R=99% at 45 and 532 nm. D) Aperture. E) Plano-convex lens, f=250 mm. F) Flame. G) Aperture. H) Beam dump. I-O) Scattering collection optics on translating stage. I) Neutral density filters. J) 532 nm bandpass filter. K) Vertical polarizer. L) Aperture. M) Biconvex lens, f=100mm. N) Aperture. O) Photomultiplier tube. P) Digital oscilloscope. Q) Precision high voltage supply.

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43An Nd:YAG pulse laser was operated in frequency doubled mode (! = 532 nm) at5 Hz. The laser intensity was first attenuated through a series of ultrafine-gauge wiremeshes and then turned with a 45 degree dielectric mirror optimized at 532 nm. Anaperture defined the pulse diameter as it passed through a focusing lens. The beam wasthen directed through the center of the flame and was terminated at a beam dump. Thescattering system collected scattered light at 90 degree angle from the incident beam.Scattered light first passed through a narrow aperture and a 532 nm band pass filter.Neutral density filters were added as necessary to the collection optics line of sight inorder to maintain signal linearity. A polarizer ensured that the scattered radiationobserved was only vertically polarized, matching that of the incident radiation emittedfrom the laser cavity. A second aperture at the rear of the collecting tube ensured thatonly a small scattering volume was observed and that stray light is minimized. Thescattered light was then incident on a photomultiplier tube and the signal was recorded ona digital oscilloscope.As illustrated in Figure 3-5, the scattering detection optics were mounted on amicrometer-controlled precision translational stage. One revolution of the micrometercorresponded to 0.025 inches of linear motion. The stage setup allowed the scatteredsignal to be observed at the six pre-defined radial positions summarized in Table 3-2.The photomultiplier tube was driven by a precision high voltage supply set to V.Thus, the signal displayed by the oscilloscope was negative. For simplicity, the signalspresented will be reported as absolute values. Table 3-6 summarizes the scatteringsystem apparatus in detail.

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44 Table 3-6. Description of scattering system apparatus. Device Manufacturer Model Description Equipment 532 nm frequency doubled Nd:YAG Laser Big Sky Lasers 230A8000 Q-switched, 5 Hz, Variable power, 100 mJ @ 10 Hz, 532 nm, 1 ns Beam dump Kentek ABD-2 Beam dump Photomultiplier tube Hamamatsu R2949 Photomultiplier tube Photomultiplier tube housing Products for Research, Inc. PR1402CE Photomultiplier tube housing Oscilloscope LeCroy LT 372, WaveRunner 500 Hz, 4 GS/s digital oscilloscope with 50 termination Precision high voltage supply Stanford Research Instruments PS325 Digital high voltage power supply Double shielded BNC cable Pasternack Enterprises RG-223/U Double shielded coaxial cable to reduce line noise Translational stage Mitutoyo Micrometer-adjusted translational stages Optics 532 nm dichroic mirror CVI Laser 45 degree, 532 nm dichroic mirror Aperture Newport ID-1.0 2 apertures Plano-convex lens Newport KBX079AR.14 BBAR coated, 430-700 nm, 25.4 mm diameter, 250 mm focal length Neutral density filters Optics for Research FDU-2.0 FDU-1.0 FDU-0.3 10 2.0 attenuation 10 1.0 attenuation 10 0.3 attenuation (nominal values) Polarizer Newport 532 nm line filter Newport 10LF10-532 T > 50%, 25.4 mm diameter Aperture ID-0.5 2 apertures in collection optics Biconvex lens UV coating, 100 mm focal length, 25.4 mm diameter

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45 Photomultiplier tube linearity A photomultiplier tube (PMT) is a high gain detector that converts photons into an electric signal by the photoelectric effect. The photoelectric effect is the phenomenon whereby electrons are emitted from a surface upon exposure to electromagnetic radiation. When an incident photon hits the PMT, a modest number of electrons in an electrode are released. These electrons hit another electrode, releasing additional electrons. A series of electrodes has a multiplicative effect on the number of electrons released and incident on the detector. PMTs are, in general, capable of outputting a linear response over several decades for a continuous signal source. However, a pulsed nanosecond-scale laser can easily invoke a non-linear response in the PMT due to the sudden flux of incident photons. It is common for a PMT to be limited to only one decade of linearity in such a system, hence attention must be paid to signal linearity. When the strength of an incident signal to a PMT exceeds the limits of linearity, neutral density filters can attenuate the signal and bring the PMT back into the linear response regime. A neutral density filter is characterized by a broad, steady transmission profile over a wide range of wavelengths. An x neutral density filter attenuates by a factor of 10 x These filters are available in a variety of attenuating strengths, thus maintaining the PMT in its linear regime is simply a matter of adding and removing filters from the PMT incident path. For the scattering experiments performed, filters were used in this manner, and the output of the PMT was maintained between 6 and 14 mV. Linearity was also checked periodically throughout the experiment by placing a 0.3 neutral density filter in front of the collection optics. A 0.3 filter should attenuate the signal by a factor of 10 0.3 or approximately 2, thus if the PMT response was indeed linear, the output signal was expected to drop by about one half.

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46 Calibration As detailed in Chapter 2 determination of the differential scattering coefficient K' pp is a necessary parameter in determining the size and number characteristics of the scattering particles. The scattering signal from the PMT is related to K' pp (recall that K' pp =NC' pp ) by S pp = I o # V #$ ( ) N C pp (3-1) where I o is the incident laser intensity, is the efficiency of the PMT detector and the collection optics, V is the scattering volume, and ., is the solid angle of observation. The parameters V, and may be measured, though to do so with great accuracy and precision is difficult. Rather, to extract K' pp from the scattering data, a calibration may be used. The ratio of the scattering signal to that of a known reference scatterer can be used to solve for the desired parameter K' pp namely, K pp = N ref C pp, ref S pp S pp, ref # $ % & ( ref ( # $ % & (3-2) where the transmission ratio accounts for any variation in the transmission of incident light between the reference scatterer and the scattering volume of interest. By taking the ratio of the reference scatterer signal to the signal from the scatterer of interest, the direct evaluation of the common terms ( V ) is avoided. Methane gas, CH 4 and nitrogen gas are commonly used as references for calibration purposes. At an incident wavelength of & = 694.3 nm, the differential scattering cross sections C' VV for each of these gases are 4.56E-28 cm 2 sr -1 and 2.12E-28 cm 2 sr -1 respectively. 34 A conversion may be performed to evaluate this parameter at the wavelength of interest by

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47 C vv, 2 = C vv, 1 1 2 # $ % & ( 4 n 2 ) 1 n 1 ) 1 # $ % & ( 2 (3-3) where n & is the wavelength-dependent refractive index. The number density of the reference scatterer can be approximated by the ideal gas law, or calculated with knowledge of the particle density and molecular weight. Table 3-7 lists the differential scattering coefficients for methane and nitrogen at three wavelengths characteristic of common laser systems. Table 3-7. Differential scattering coefficient for methane and nitrogen at common incident wavelengths at 1 atm, 298 K. Laser & (nm) K' VV at 1 atm, 298 K for CH 4 (cm -1 sr -1 ) K' VV at 1 atm, 298 K for N 2 (cm -1 sr -1 ) Ruby 694.3 1.12E-8 5.22E-9 Nd:YAG 532.0 3.33E-8 1.54E-8 Argon Ion 488.0 4.73E-8 2.18E-8 The reference scatterer for this study was methane gas. The calibration gas shared the delivery line of the vaporization chamber, as shown in Figure 3-3 thus the gas was expelled from the burner for calibration measurements. A series of brass plug valves were used to shut off the flow from the vaporization chamber during calibration, and vice versa during flame operation. The suppliers specifications of methane are listed in Table 3-5 Calibration of the scattering system with the known scattering characteristics of methane provided an absolute determination of the differential scattering coefficient for the soot particles in the flame. In addition, calibration also served as a means of determining and accounting for the amount of stray light present in the system, as discussed in the next section.

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48 Stray light Stray light is present in any real scattering system, and can take the form of reflected laser light from surfaces, or ambient light, for example. If unaccounted for, stray light can skew experimental data considerably. For example, the magnitude of stray light can easily be as large as the scattered light signal from the reference scatterer used to determine K' pp Since the relation between K' pp and S pp,ref is direct, any error in measuring S pp,ref is translated directly into error in K' pp Thus, it can be seen that reducing and accounting for stray light in a system is critical to obtaining accurate data for analysis. To minimize stray light from entering the scattering collection optics, a number of techniques were used. First, lenses and apertures in the collection optics were used to define a very small scattering volume. These apertures also served to block any stray light from outside the scattering volume line of sight from entering the PMT. Another stray light reducing method used was to minimize reflection of laser light from surfaces. Highly reflective surfaces, such as optical mounts, were either painted with matte black paint, or covered in thick black felt to reduce reflections. Whenever possible, these reflection sources were blocked from the PMT line of sight as well using opaque Plexiglas covered in black felt. Stray light minimization techniques are effective, however they cannot completely eliminate stray light from a system. To account for this, stray light may be quantitatively determined and then data may be corrected. Another calibration is employed for this effort. Similar to the scattering signal calibration, the stray light calibration relies on the known scattering characteristics of calibration gases. Employing methane and nitrogen, the ratio of these two gases reference scattering signals, R ref can be determined from Eq.

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49 3-1 to be the ratio of their differential scattering coefficients. This reference ratio is tabulated in Table 3-8 for the same incident wavelengths considered previously. Table 3-8. Methane to nitrogen reference differential scattering coefficient ratio used for stray light calibration at common incident wavelengths, assuming ideal gases. Laser & (nm) K VV,CH4 / K VV,N2 at 1 atm, 298 K Ruby 694.3 2.15 Nd:YAG 532.0 2.17 Argon Ion 488.0 2.17 The deviation in the measured calibration ratio from the reference ratio R ref is due to stray light in the system. Assuming that the stray light remains constant between methane and nitrogen measurements, an excellent assumption, this deviation can be expressed as R ref = K' pp, CH 4 K' pp, N 2 # $ % & reference = (S pp, CH 4 measured ) ( SL (S pp, N 2 measured ) ( SL (3-4) Where S pp,CH4 measured and S pp,N2 measured are the measured scattering signals of methane and nitrogen, respectively. With this relationship, the stray light in the system can be quantified as SL = R ref S pp, N 2 S pp, CH 4 R ref 1 (3-5) For the light scattering studies, stray light calibration measurements were taken prior to every flame study to determine an experiment-specific stray light value. The calibration gases flowed at a rate of approximately 13 L/min, controlled by a rotameter (GE700 Gilmont) flow tube. The temperature of the calibration gases exiting the heated fuel delivery line was measured with a type K thermocouple. On average, this value was 344 K. The number density N, differential scattering cross section C' VV and differential scattering coefficient K' VV for each gas was determined using this temperature. These

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50 parameters are summarized in Table 3-9 Number densities were calculated using isobaric density data tabulated by the National Institute of Standards and Technology. 35 Table 3-9. Number densities, differential scattering cross sections, and scattering coefficients for methane and nitrogen calibration gases at 1 atm, 344K. Gas N (cm -3 ) C' VV (cm 2 /sr) K' VV (cm/sr) Methane 2.14E19 1.35E-27 2.89E-8 Nitrogen 2.13E19 6.25E-28 1.32E-8 From Table 3-9 the reference calibration ratio R ref for methane to nitrogen at 344 K was determined to be 2.165. This value was used to determine the stray light contribution to the measured scattering signals from the calibration gases and the flame. Figure 3-6 shows the scattered signal from the calibration gases and the flame from a typical scattering experiment. Dark signals were recorded as well to normalize the baseline of the calibration gases and the flame. Figure 3-6. Sample scattering signals from methane, nitrogen, and flame. Flame signal is attenuated by a factor of 10 5 for signal linearity.

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51 For scattering analysis, the dark signals were first subtracted from the scattered signals. The signals were then integrated over a 90 ns full peak width. For the data depicted in Figure 3-6 the integrated signal for methane and nitrogen (including the influence of stray light) was found to be 0.64 mV-s and 0.38 mV-s, respectively, which yielded a calibration ratio of 1.67, a 23% deviation from the ideal R ref value of 2.165. This gives an indication to the magnitude of the stray light, which was responsible for skewing the calibration ratio. With the integrated calibration signals and the R ref value, Eq. 3-5 was used to calculate the stray light, which for this case, was determined to be 0.16 mV-s. The time-integrated measured flame signal determined from the data presented in Figure 3-6 was determined to be 0.38 mV-s. The average results of time-integrated calibration measurements over all experiments are shown in Table 3-10 along with the range seen in these values. The calibration ratio ranged from 1.59 to 1.79, with an average value of 1.70, a 22% deviation from R ref. Overall the stray light signal was approximately one-third of the nitrogen signal. Table 3-10. Average time-integrated calibration gas and stray light signals and range of signals seen over all scattering experiments. Average Signal (mV-s) Range in Signal (mV-s) Methane + SL 0.55 0.39 0.73 Nitrogen + SL 0.25 0.18 0.34 Stray Light 0.17 0.11 0.26 The true methane integrated signal is determined by subtracting the stray light from the integrated measured methane signal. Returning to the example data presented above, this yields a true integrated methane signal of 0.64 0.16 mV-s = 0.48 mV-s. The measured flame signal required a correction for any attenuation used to preserve PMT

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52 linearity. For the data presented above, a series of neutral density filters yielded an overall attenuation factor of 10 5 thus the true integrated flame signal was determined by (S flame,measured ) (10 5 ). The stray light signal may be subtracted from this signal, however because it is orders of magnitude smaller than the flame signal, it may be neglected without significantly altering the scattering results. All that remains to be determined in order to extract the differential scattering coefficient from the scattering data is the transmission of laser light through the calibration methane and the flame. The transmission through the methane was assumed to be unity. Determination of the transmission through the flame will be discussed in a later section; jumping to the results, for the flame height and position under consideration, this value was found to be 0.76. With this information, Eq. 3-2 was used to determine the differential scattering coefficient for the soot particles in the flame at height f, position 1. Specifically, K VV ht f pos 1 = (K VV CH 4 ) S VV flame 10 5 S VV CH 4 measured # SL $ % & ( ) 1 $ % & ( ) = ( 2.89E # 8 cm # 1 sr # 1 ) 0.37 10 5 mV + s 0.64 # 0.16 mV + s $ % & ( ) 1 0.76 $ % & ( ) = 2.2E # 2 cm # 1 sr # 1 Vaporization of Soot The degree to which laser energy is focused over an area is termed fluence. This parameter, measured as energy per area, was an important consideration in all experiments. At modest energies, a laser pulse can significantly heat soot particles and cause vaporization if the beam is focused to a small cross-sectional area. As shown by Dasch, 36 37 laser fluences greater than 0.2 J/cm 2 from a submicrosecond pulsed source can reduce the light scattering and extinction characteristics of soot by an order of magnitude

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53 due to vaporization. A typical laser cross sectional area is 1 mm 2 At this size, a laser energy of merely 2 mJ/pulse would significantly alter soot characteristics. For the flame studies performed, the lowest fluence that could be attained by simply reducing the laser pump energy was 0.4 mJ/cm 2 with an approximate beam cross sectional area of 0.013 cm 2 With any further reduction in laser pump energy, the laser pulse broadened in time and the scattering signal became difficult to detect. Therefore, rather than reducing the laser fluence by adjusting the laser pump energy, ultrafine-gauge mesh disks were placed in the beam path. As the beam passed through the meshes, the intensity of the beam was reduced to 0.42 mJ/pulse and an acceptable laser fluence of 0.03 mJ/cm 2 was attained. Because the laser beam was focused to a point at the burner, any shadow produced by the mesh could be neglected. This fluence was determined to produce no vaporization based on the observation of a steady scattering signal as the energy of the laser was further adjusted about this point. Transmission The experimental setup for the transmission system is shown in Figure 3-7 The optics encountered by the laser are identical in the transmission setup as those in the scattering system except rather than terminating at a beam dump, the transmitted radiation is monitored with a power meter. The optics and collection apparatus are mounted on two mechanically operated precision translation stages that direct the laser path through various positions through the flame. Forward scattered light was blocked from the detector by narrowing Aperture G, shown in Figure 3-7 to the beam width, and by placing the detection optics approximately 40 cm from the flame. These steps resulted in only a small solid angle of observation and limited the forward scattered light incident on the power meter.

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54 Figure 3-7. Transmission system setup. A) Frequency doubled Nd:YAG 532 nm pulsed laser. B) Ultrafine-gauge wire meshes to attenuate laser. C-E) on translating stage. C) Dichroic mirror, R=99% at 45 and 532 nm. D) Aperture. E) Plano-convex lens, f=250 mm. F) Flame. G-I) on translating stage. G) Aperture. H) 532 nm line filter. I) Power meter receiver. J) Power meter display. The radial positions studied in the transmission flame corresponded to the same positions investigated in the scattering system. These positions were spaced at 0.635 mm intervals, beginning at the flame center and spanning to the flame edge. In addition, a reference position 1.65 cm outside of the flame was defined. The measured power of the laser through the flame was ratioed with the power measured at the reference position to give the transmission through the flame. From the Beer-Lambert law = I trans I o = exp( # K ext L ) (3-6) where I o is the incident intensity of the laser measured at the reference position, I trans is the transmitted intensity measured through the flame, and L is the optical pathlength through the flame. Table 3-11 describes the transmission instrumentation in greater detail.

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55 Table 3-11. Description of transmission apparatus. Device Manufacturer Model Description Equipment 532 nm frequency doubled Nd:YAG Laser Big Sky Lasers 230A8000 Q-switched, 5 Hz, Variable power, 100 mJ @ 10 Hz, 532 nm, 1 ns Translational stages Mitutoyo Micrometer-adjusted translational stages Power meter Molectron PM5200 PM3 Power meter Power meter head Optics 532 nm Dichroic mirror CVI Laser 45 degree, 532 nm dichroic mirror Aperture Newport ID-1.0 Aperture Plano-convex lens Newport KBX079AR.14 BBAR coated, 430700 nm, 25.4 mm diameter, 250 mm focal length 532 nm line filter Newport 10LF10-532 T>50%, 25.4 mm diameter Micro-Raman System After seeded combustion experiments were complete, rust-colored residue was apparent on the flame holders, indicative of iron deposits. This region of iron deposition can be seen in Figure 3-8 Confocal micro-Raman spectroscopy was used to investigate the flame holders to determine the state of the residual iron. Raman spectroscopy measures the inelastic shift in energy scattered from a particle as compared to the incident. The shift in energy is due to absorption of energy into vibrational modes in the molecule. As with electronic transition modes, the vibrational modes are quantized and can be used like a fingerprint to identify specific molecules. The confocal system combines Raman spectroscopy with a microscope objective, allowing the specimen under study to be observed with very high spatial resolution. The confocal micro-Raman system (LabRam Infinity, Jobin Yvon) is shown schematically in Figure 3-9

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56 Figure 3-8. Region of iron deposits on flame holder screen. Figure 3-9. Confocal micro-Raman schematic.

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57 The excitation wavelength was 632.8 nm, generated from a He:Ne continuous wave laser. The laser was focused on the flame holder using a 100x objective lens. Backscattered radiation from the sample was collected through a 500 m confocal aperture and dispersed over a 1800 grooves/mm grating onto a 1024-pixel CCD detector. The nominal output of the laser was 15 mW, but could be attenuated with neutral density filters. The Raman shift of the incident wavelength is determined from Raman = 1 # o $ 1 # scat % & ( ) (3-7) where & o is the incident wavelength, & scat is the wavelength of the scattered light, and Raman is the Raman-shifted wavenumber, usually measured in cm -1 The Raman shift is directly proportional to energy, thus a larger Raman corresponds to a larger shift in energy. Note that elastically scattered light, governed by Mie or Rayleigh theory, has zero shift since the wavelength of the incident matches that of the scattered radiation. A typical Raman spectra is plotted with the Raman shift as the independent variable. A positive value for Raman is termed a Stokes shift and is designated as Stokes For this case, energy is transferred to the vibrational bond mode, leaving a lower energy scattered photon. Conversely, a negative Raman shift is termed anti-Stokes and is designated as anti # Stokes Typically Stokes shifts are of much greater intensity than anti-Stokes shifts, and the Stokes-shifted Raman scattered light will appear at a lower wavenumber (higher wavelength) than the incident. Iron and iron oxides have characteristic Raman bands in the region of 200-1400 cm -1 which correspond to a wavelength of 640.9-964.3 nm relative to the 632.8 nm incident of the He:Ne laser. 38 The bandwidth of the confocal micro-Raman spectrometer was approximately 800 cm -1 thus multiple spectra were taken over the range of 150 to

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58 1800 cm -1 and combined to generate a single spectrum of the sample covering the wavenumbers of interest. The spectra were generally produced by averaging multiple integrations of the sample signal over 5 seconds.

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59 CHAPTER 4 RESULTS AND DATA ANALYSIS Experimental results are presented in this chapter. The results of the elastic scattering and transmission studies will be used to extract characteristic size, number density, and volume fraction data from the seeded and unseeded flames. Further, the results of the micro-Raman study to characterize the state of the iron deposited on the flame holder screen are presented. Elastic Light Scattering Results The laser cavity emitted vertically polarized light, and a polarizer at the head of the scattering collection optics ensured that only vertically polarized scattered light was captured. Thus the scattering parameter of interest was the vertical-vertical differential scattering coefficient, K' VV In order to extract this parameter accurately from the PMT signal output, two calibrations were used a methane calibration to relate K' VV to the signal S VV and a stray light calibration using methane and nitrogen to account for the extraneous signal induced by the reflection of laser light from various surfaces. The same methane signal was used for both calibration operations. A typical PMT response signal for the calibration gases and the flame signals are shown in Figure 4-1 The flame signal shown in Figure 4-1 has been attenuated by a factor of 10 5 to preserve linearity in the PMT response. Additionally, the baseline of each signal contains a steady noise signal attributed to electrical noise stemming from the laser flash lamp discharge. The laser was blocked from the detector and dark signals were taken for both the calibration gases and the flame signals, which are also shown in Figure 4-1 These

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60 dark current values were then subtracted from the signal response prior to any data analysis to give a steady baseline. The same three signals are shown in Figure 4-2 after baseline subtraction. Figure 4-1. Typical scattered signal response from photomultiplier tube measuring calibration gases and flame signal at a fixed height and radial position. Flame signal is attenuated by a factor of 10 5 to preserve signal linearity. Ten experimental data sets (N=10) over a number of days were collected for the unseeded flame conditions, and six data sets (N=6) were collected for the seeded flame. A summary of the scattered signal intensities integrated over the signal width of 90 ns are shown in Table 4-1 and Table 4-2 for the unseeded and seeded flames, respectively. These raw values are not corrected for stray light, nor have the attenuation factors of the neutral density filters been taken into account. The standard deviation of the integrated signal signal is included as well.

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61 Figure 4-2. Baseline-subtracted scattered signals from calibration gases and flame at a fixed height and radial position. Flame signal is attenuated by a factor of 10 5 to preserve signal linearity. Table 4-1. Average (N=10) time-integrated scattered signal from unseeded flame. Unseeded time-integrated S VV (mV-s) Radial Position Height 1 2 3 4 5 6 b 2245.76 3108.40 4183.01 12691.04 15937.38 15041.06 signal 1601.00 2810.04 3110.61 6562.52 7958.66 7438.60 c 6236.08 6465.53 10366.47 32509.15 41723.12 39680.84 signal 3477.99 3577.56 5307.95 16856.91 21804.01 20050.97 d 16207.65 17706.80 28749.58 48773.24 58366.89 54751.78 signal 13482.79 12178.86 14378.20 23296.32 27738.85 25777.34 e 32434.08 35615.65 47510.26 67200.75 74017.74 66607.10 signal 20374.19 21068.17 24583.19 34683.52 37557.89 34804.48 f 38000.86 40580.24 47743.01 53219.41 50690.26 50530.84 signal 20521.18 22170.80 26233.36 27501.84 25432.70 25982.58

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62Table 4-2. Average (N=6) time-integrated scattered signal from iron pentacarbonylseeded flame. Seeded time-integrated SVV (mV-s) Radial Position Height 1 2 3 4 5 6 b 4203.43 5689.80 9211.94 16924.39 19911.07 17847.25 !signal 2219.69 3892.45 4362.37 4460.29 6515.06 6028.36 c 9833.50 13848.86 35649.92 42231.29 49212.05 46287.00 !signal 5712.68 5690.52 16968.93 3703.77 8220.27 10710.66 d 22026.06 29478.17 42341.19 67974.13 77667.87 65318.91 !signal 6247.92 10078.33 13206.87 11121.29 16622.39 16005.66 e 28327.59 41352.14 63635.51 86432.04 89788.28 80665.76 !signal 13291.21 15986.79 23864.33 25076.68 20808.01 22100.59 f 47568.39 52784.64 60444.17 66742.23 67400.08 61121.52 !signal 10742.92 10862.32 13723.95 16993.14 11619.81 9383.93 As Table 4-1 and Table 4-2 show, the variation in the raw scattered light signalsvaried widely from day to day, as evident from the large standard deviations. However,this fluctuation is irrelevant so long as the relative scattered intensities between thecalibration scatterer, methane, and the scattered signal from the soot particles areconsistent with one another. The average K'VV for each radial position and height,corrected for stray light, are summarized in Table 4-3 and Table 4-4 along with thestandard deviation !Kvv. As shown in these summaries, the standard deviation for thedifferential scattering coefficient is much less than the standard deviation in the dailyabsolute signals. This indicates that while the absolute signal intensities may vary day inand day out, they still remain in relative agreement with respect to the methanecalibration signal. Therefore, the scattering data were characterized as remainingrelatively consistent and repeatable over all experiments.

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63 Table 4-3. Average (N=10) unseeded K' VV results and standard deviation of K' VV Unseeded K' VV (cm -1 sr -1 ) Radial Position Height 1 2 3 4 5 6 b 1.15E-04 1.55E-04 2.12E-04 6.66E-04 8.36E-04 7.95E-04 Kvv 5.67E-05 9.14E-05 9.53E-05 1.24E-04 8.71E-05 8.36E-05 c 3.33E-04 3.49E-04 5.56E-04 1.72E-03 2.20E-03 2.11E-03 Kvv 1.07E-04 1.22E-04 1.54E-04 3.81E-04 4.39E-04 4.37E-04 d 8.11E-04 8.99E-04 1.51E-03 2.59E-03 3.10E-03 2.92E-03 Kvv 4.55E-04 3.44E-04 2.49E-04 3.22E-04 5.09E-04 5.28E-04 e 1.70E-03 1.88E-03 2.50E-03 3.53E-03 3.90E-03 3.52E-03 Kvv 5.32E-04 5.72E-04 4.75E-04 4.90E-04 6.55E-04 6.49E-04 f 2.00E-03 2.13E-03 2.51E-03 2.82E-03 2.67E-03 2.66E-03 Kvv 3.53E-04 4.04E-04 5.18E-04 5.22E-04 3.48E-04 3.98E-04 Table 4-4. Average (N=6) seeded K' VV results and standard deviation of K' VV Seeded K' VV (cm -1 sr -1 ) Radial Position Height 1 2 3 4 5 6 b 1.97E-04 2.67E-04 4.40E-04 7.94E-04 9.21E-04 8.24E-04 Kvv 1.04E-04 1.84E-04 2.20E-04 1.86E-04 2.23E-04 2.07E-04 c 4.28E-04 5.99E-04 1.55E-03 1.89E-03 2.18E-03 2.05E-03 Kvv 2.29E-04 2.06E-04 6.42E-04 1.92E-04 2.11E-04 3.45E-04 d 9.28E-04 1.21E-03 1.77E-03 2.84E-03 3.22E-03 2.70E-03 Kvv 2.78E-04 3.47E-04 6.47E-04 3.12E-04 4.74E-04 5.13E-04 e 1.07E-03 1.58E-03 2.43E-03 3.33E-03 3.49E-03 3.13E-03 Kvv 3.54E-04 4.17E-04 5.71E-04 5.12E-04 4.44E-04 5.62E-04 f 1.92E-03 1.96E-03 2.25E-03 2.49E-03 2.53E-03 2.30E-03 Kvv 1.78E-04 2.19E-04 3.47E-04 4.78E-04 2.91E-04 2.95E-04 The results of the scattering experiments are also shown in Figure 4-3 for the unseeded and seeded flames. The seeded and unseeded differential scattering coefficients are plotted for each height over the burner with radial position as the independent variable. Note that data were recorded for only one radial direction, but are presented over the full burner for clarity.

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64 Figure 4-3. Seeded and unseeded differential scattering coefficients. A-E) Error bars represent one standard deviation. A) at height b. B) at height c. C) at height d. D) at height e. E) at height f. A B

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65 Figure 4-3. Continued. C D

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66 Figure 4-3. Continued.As Figure 4-3 shows, within experimental error, there is little deviation in thedifferential scattering coefficient between the seeded and unseeded flames. The mostsignificant deviation in K'VV appeared early in the flame at height c, shown in Figure 4-3B.Transmission ResultsAs discussed in Chapter 3, the transmission through the flame is described by theratio of the laser pulse power through the flame to a reference position outside of theflame. Transmission measurements were taken at six equally spaced line of sightpositions. These positions corresponded to the six radial positions investigated in thescattering experiments; namely position 1 crossed through the center of the flame and theremaining positions were spaced at 0.635 mm intervals outward. Table 4-5 and Table 4-6present the raw data for the power transmitted through the unseeded and seeded flames E

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67 and the standard deviation of the incident power signal power Note that the flame emission (no laser) was subtracted at each radial position. Table 4-5. Average (N=5) unseeded power measurements used in transmission study. Unseeded power measurements (mW) Line of Sight Position Height reference outside of flame 1 2 3 4 5 6 b 1.75 1.67 1.69 1.68 1.68 1.68 1.68 power 0.068 0.055 0.054 0.062 0.068 0.058 0.062 c 1.72 1.60 1.60 1.58 1.58 1.55 1.55 power 0.028 0.033 0.029 0.044 0.019 0.041 0.03 d 1.72 1.50 1.51 1.49 1.47 1.44 1.43 power 0.018 0.018 0.031 0.019 0.021 0.027 0.023 e 1.71 1.39 1.38 1.39 1.36 1.36 1.35 power 0.011 0.016 0.025 0.038 0.04 0.04 0.04 f 1.71 1.30 1.29 1.29 1.28 1.27 1.26 power 0.009 0.106 0.064 0.068 0.081 0.069 0.112 Table 4-6. Average (N=5) seeded power measurements used in transmission study. Seeded power measurements (mW) Line of Sight Position Height reference outside of flame 1 2 3 4 5 6 b 1.69 1.64 1.64 1.65 1.64 1.62 1.62 power 0.034 0.033 0.028 0.03 0.025 0.039 0.035 c 1.69 1.56 1.57 1.56 1.55 1.52 1.52 power 0.028 0.036 0.019 0.024 0.019 0.031 0.032 d 1.70 1.48 1.47 1.47 1.45 1.45 1.43 power 0.027 0.023 0.034 0.019 0.026 0.025 0.029 e 1.70 1.40 1.39 1.39 1.36 1.36 1.37 power 0.029 0.016 0.023 0.016 0.046 0.023 0.046 f 1.72 1.31 1.29 1.30 1.30 1.33 1.36 power 0.039 0.044 0.045 0.027 0.069 0.073 0.031 As seen in Table 4-5 and Table 4-6, the standard deviation in the transmitted power was relatively low. This precision in measured transmission translated into low standard deviation in the transmission, trans The transmission through the unseeded and seeded

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68flames is summarized in Table 4-7 and Table 4-8, and was determined from the ratio ofthe transmitted power to the reference power measured outside of the flame.Table 4-7. Average (N=5) transmission through the unseeded flame. Unseeded transmission, Line of Sight Position Height 1 2 3 4 5 6 b 0.95 0.97 0.96 0.96 0.96 0.96 "trans 0.007 0.008 0.008 0.01 0.008 0.01 c 0.93 0.93 0.92 0.92 0.90 0.90 "trans 0.006 0.006 0.011 0.007 0.011 0.009 d 0.87 0.88 0.87 0.86 0.84 0.83 "trans 0.01 0.011 0.01 0.009 0.018 0.013 e 0.81 0.80 0.81 0.80 0.79 0.79 "trans 0.006 0.011 0.019 0.019 0.022 0.023 f 0.76 0.75 0.75 0.75 0.74 0.74 "trans 0.059 0.036 0.04 0.047 0.038 0.064 Table 4-8. Average (N=5) transmission through the seeded flame. Seeded transmission, Line of Sight Position Height 1 2 3 4 5 6 b 0.97 0.97 0.97 0.97 0.96 0.95 "trans 0.014 0.008 0.01 0.008 0.014 0.006 c 0.92 0.93 0.92 0.92 0.90 0.90 "trans 0.015 0.005 0.013 0.011 0.016 0.006 d 0.87 0.87 0.87 0.85 0.85 0.84 "trans 0.011 0.013 0.012 0.014 0.009 0.015 e 0.82 0.81 0.81 0.80 0.80 0.80 "trans 0.02 0.015 0.013 0.022 0.016 0.025 f 0.76 0.75 0.76 0.76 0.77 0.79 "trans 0.019 0.023 0.017 0.032 0.034 0.003 The transmission measurements provided an overall extinction coefficient for theline of sight through the flame. In order to determine the individual extinctioncoefficients for each concentric radial region (i.e., annular region), a deconvolutiontechnique must be employed. A number of methods exist to approach the deconvolution

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69problem. In this work, three different techniques were tested onion peeling, linearregression, and a three-point Abel inversion, with the latter producing the best resultswith the least amount of error. A brief summary of the onion peeling and linearregression methods follow, while the results of the three-point Abel inversion will bepresented in full. A detailed description of all three of these techniques and their resultsare given in Appendix B.The onion peeling method is perhaps the simplest deconvolution technique.Working from the outer-most layer, or annular region, inward, the unknown parametersare successively determined one layer at a time. For this study, the sixth line of sightposition for the transmission data intersected only through annular region 6. Therefore, ifthe optical pathlength through the flame is known, Kext,6 may be determined from theBeer-Lambert law. Working inward, the extinction coefficient for region 5 is a functionof the transmission data through this line of sight, as well as the now known extinctioncoefficient of region 6. Through this manner of successive determination, the extinctioncoefficients for each annular region are calculated based on the values of Kext in the outerregions.Although onion peeling is straightforward and relatively simple, there is one majordrawback of the onion peeling method because this method relies on the successivedetermination of outer layer parameters, any error in these layers is compiled through thefield and can result in high errors in the inner regions. With relatively high overalltransmission values, this can easily lead to negative extinction coefficients as the sum ofthe Kext values for the outer regions exceeds the overall transmission recorded through the

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70entire path. In the onion peeling analysis performed for the present data, a number ofextinction coefficients were predicted to be negative valued. These are unrealistic valuesand evidence of the high imprecision in the sequential deconvolution scheme.In an effort to redistribute the error in the deconvolved variable, a linear regressionmethod with a least squares approach was used. In this technique, the exact extinctioncoefficient at a point was not explicitly determined. Rather, a regression fit determinedthe extinction coefficients in such a way that the overall error was minimized, whilebringing each of the individual extinction coefficients near, but not exactly to, their truevalue as predicted by the Beer-Lambert law. The values of Kext extracted from the linearregression analysis were in overall agreement with those from the onion peeling method.However, unallowed negative values for Kext still appeared in two positions in the seededresults. The median error in these values decreased by approximately one half over theonion peeling results.The final deconvolution technique employed, a three-point Abel inversion, wasmost successful in predicting a realistic extinction coefficient while minimizing the errorthroughout the flame field. Similar to the onion peeling method, this technique usesinformation from the outer layers to extract information from the inner regions.However, for more precision, the projection data is expanded as a quadratic function ofits neighboring points. More detail is presented in Appendix B and in the work ofMcNesby et al.39 Dasch provides a succinct summary of this technique as well.40 Theresults of this analysis are shown in Table 4-9 and Table 4-10.

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71 Table 4-9. Average (N=5) unseeded extinction coefficients determined using a threepoint Abel inversion. Unseeded K ext (cm -1 ) Three-Point Abel Inversion Radial Position Height 1 2 3 4 5 6 b 1.126E-01 3.574E-02 2.908E-02 4.086E-02 5.151E-02 9.783E-02 Abel 6.754E-02 3.928E-02 2.795E-02 2.724E-02 1.889E-02 1.855E-02 c 5.003E-02 5.546E-03 4.837E-02 6.601E-02 1.281E-01 2.420E-01 Abel 5.742E-02 2.906E-02 3.891E-02 2.161E-02 2.904E-02 1.814E-02 d 1.113E-01 4.769E-02 6.891E-02 1.169E-01 2.202E-01 4.221E-01 Abel 1.079E-01 5.731E-02 3.974E-02 2.730E-02 4.946E-02 2.700E-02 e 9.044E-02 1.855E-01 1.668E-01 2.285E-01 3.100E-01 5.462E-01 Abel 7.600E-02 6.425E-02 7.591E-02 6.487E-02 6.300E-02 5.070E-02 f 1.930E-01 2.373E-01 2.592E-01 2.940E-01 3.973E-01 7.099E-01 Abel 7.527E-01 2.198E-01 1.730E-01 1.707E-01 1.184E-01 1.525E-01 Table 4-10. Average (N=5) seeded extinction coefficients determined using a three-point Abel inversion. Seeded K ext (cm -1 ) Three-Point Abel Inversion Radial Position Height 1 2 3 4 5 6 b 1.825E-02 2.799E-02 3.357E-03 1.047E-02 4.993E-02 1.074E-01 Abel 1.356E-01 3.573E-02 3.443E-02 2.156E-02 3.275E-02 1.116E-02 c 8.781E-02 2.726E-02 4.017E-02 5.760E-02 1.278E-01 2.418E-01 Abel 1.561E-01 2.296E-02 4.467E-02 3.335E-02 4.214E-02 1.094E-02 d 4.238E-02 8.877E-02 9.598E-02 1.565E-01 1.963E-01 3.960E-01 Abel 1.159E-01 6.679E-02 4.634E-02 4.417E-02 2.469E-02 3.176E-02 e 8.668E-02 1.449E-01 1.484E-01 2.318E-01 3.221E-01 5.223E-01 Abel 2.379E-01 8.520E-02 5.443E-02 7.459E-02 4.601E-02 5.456E-02 f 1.738E-01 2.907E-01 3.050E-01 3.516E-01 4.081E-01 5.703E-01 Abel 2.380E-01 1.401E-01 7.486E-02 1.132E-01 1.025E-01 5.990E-03 The results of the three-point Abel inversion yielded realistic values for the extinction coefficients at each height and radial position while producing the lowest median error. Figure 4-4 compares the unseeded and seeded K ext for each height with respect to radial position. Note that data were recorded for only one radial direction, but are presented over the full burner for clarity.

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72 Figure 4-4. Seeded and unseeded extinction coefficients determined using a three-point Abel inversion. A-E) Error bars represent one standard deviation. A) at height b. B) at height c. C) at height d. D) at height e. E) at height f. A B

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73 Figure 4-4. Continued. C D

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74 Figure 4-4. Continued.In comparing the extinction coefficients over all radial positions and heights,Figure 4-4 shows that, in general, the extinction coefficients peaked at the outer-mostannular regions. Additionally, within experimental error, there was little change in thisparameter in the seeded and unseeded flames.Soot Characteristics Determined from Mie TheoryFrom the results of the scattering and transmission studies, the ratio K'VV/Kext forthe each radial position and height in the flame was calculated. These results are shownin Table 4-11 and Table 4-12. This ratio was then used to determine the size, numberdensity, and volume fraction of particles at each radial position and vertical height abovethe burner. E

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75 Table 4-11. Unseeded ratio of K' VV /K ext determined from experimental data. Unseeded K' VV /K ext (sr -1 ) Radial Position Height 1 2 3 4 5 6 b 1.06E-03 4.50E-03 7.55E-03 1.69E-02 1.68E-02 8.42E-03 Kvv/Kext 8.23E-04 5.62E-03 8.02E-03 1.17E-02 6.42E-03 1.83E-03 c 6.59E-03 6.21E-02 1.14E-02 2.58E-02 1.70E-02 8.61E-03 Kvv/Kext 7.85E-03 3.26E-01 9.67E-03 1.02E-02 5.13E-03 1.90E-03 d 6.76E-03 1.75E-02 2.04E-02 2.05E-02 1.31E-02 6.42E-03 Kvv/Kext 7.57E-03 2.21E-02 1.22E-02 5.43E-03 3.63E-03 1.23E-03 e 1.64E-02 8.83E-03 1.31E-02 1.35E-02 1.10E-02 5.60E-03 Kvv/Kext 1.47E-02 4.07E-03 6.44E-03 4.25E-03 2.89E-03 1.16E-03 f 8.38E-03 7.24E-03 7.83E-03 7.76E-03 5.44E-03 3.03E-03 Kvv/Kext 3.27E-02 6.85E-03 5.47E-03 4.73E-03 1.77E-03 7.94E-04 Table 4-12. Seeded ratio of K' VV /K ext determined from experimental data. Seeded K' VV /K ext (sr -1 ) Radial Position Height 1 2 3 4 5 6 b 1.08E-02 9.55E-03 1.31E-01 7.59E-02 1.84E-02 7.67E-03 Kvv/Kext 8.05E-02 1.39E-02 1.34E+00 1.57E-01 1.29E-02 2.09E-03 c 4.87E-03 2.20E-02 3.85E-02 3.28E-02 1.71E-02 8.47E-03 Kvv/Kext 9.04E-03 2.00E-02 4.57E-02 1.93E-02 5.86E-03 1.48E-03 d 2.19E-02 1.36E-02 1.85E-02 1.81E-02 1.64E-02 6.83E-03 Kvv/Kext 6.02E-02 1.10E-02 1.12E-02 5.49E-03 3.18E-03 1.41E-03 e 1.24E-02 1.09E-02 1.64E-02 1.44E-02 1.08E-02 5.99E-03 Kvv/Kext 3.43E-02 7.03E-03 7.13E-03 5.12E-03 2.07E-03 1.25E-03 f 1.10E-02 6.75E-03 7.38E-03 7.08E-03 6.19E-03 4.03E-03 Kvv/Kext 1.51E-02 3.34E-03 2.14E-03 2.66E-03 1.71E-03 5.19E-04 It is important to note the K' VV /K ext values at unseeded height c, position 2, and seeded height b, positions 3 and 4. The ratio K' VV /K ext is a non-monotonic function with a maximum value of 4.46E-2 sr -1 for the complex refractive index used in this study. However, the values in these three noted positions were much greater than this maximum value. In looking at the unseeded values for K' VV and K ext presented in Table 4-3 and Table 4-9 it is seen that at height c, position 2, the extinction coefficient is an order of magnitude smaller than that in neighboring sections. This value, combined with a modest

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76 K' VV at the same height and position, result in a very large K' VV /K ext ratio. Similar results are seen for the seeded case at height b, positions 3 and 4. As Table 4-4 shows, the K' VV at these locations is comparable to neighboring sections. However the K ext values predicted from the three-point Abel inversion summarized in Table 4-10 are much smaller than perhaps truly expected, thus resulting in an uncharacteristic K' VV /K ext ratio. As a result, these out-of-range K' VV /K ext values were discarded from the analysis and no information about particle size, number density or volume fraction was obtained for these three locations. The non-monotonic nature of K' VV /K ext is discussed further below. Particle Size Recall from Chapter 2 that the ratio of the differential scattering coefficient and the extinction coefficient can be used to determine the modal particle diameter, assuming a value of the complex refractive index m is known. For this study, a value of m = 2.00.35 i was used. A wide variation in the complex refractive index of soot has been reported in the literature. Table 4-13 summarizes the findings for m from key studies. Table 4-13. Complex refractive indices for soot from various sources. m = n k i Authors Type of soot Incident Wavelength (nm) n k Chippett and Gray 41 acetylene visible 1.9-2.0 0.35-0.50 Charalampopoulos and Chang 42 propane 457.9 488 514.5 1.58-1.82 1.57-1.82 1.54-1.71 0.65-0.83 0.65-0.85 0.67-0.87 Dalzell and Sarofim 43 propane 435.8 550.0 650 1.57 1.57 1.56 0.46 0.53 0.52 acetylene 435.8 550.0 650 1.56 1.56 1.57 0.46 0.46 0.44 Pluchino, Goldberg, Dowling, and Randall 44 carbon 488 1.6-1.8 0.06-0.19

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77 As Table 4-13 demonstrates, the range of m reported is wide, and no single value has been generally accepted. The value selected for this study is the value reported by Chippett and Gray, 41 which was based on a similar light scattering analysis with a heavily sooting fuel. In addition, it is noted that the ratio of the differential scattering coefficient to the extinction coefficient gives non-monotonic solutions for particle diameters beyond a certain range. The complex refractive index chosen for this study, along with a skewness parameter o of 0.2 from the ZOLD function, produced the best range in K' VV /K ext to fit the experimental data within the monotonic solution range. Using a Mie theory analysis, the modal soot particle diameter as a function of K' VV /K ext was plotted, as shown in Figure 4-5 and a polynomial curve fit was used to extract the particle diameter from the experimental results. Note the non-monotonic behavior of K' VV /K ext hence results for the diameter were limited to the monotonic region, corresponding to diameters less than 145 nm. Figure 4-5. Soot particle modal diameters determined from Mie theory for m = 2.00.35 i and ZOLD parameter o = 0.2.

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78Using the full Mie theory, the modal particle diameter for each radial section and ateach height was extracted. These diameters are summarized in Table 4-14 and Table 4-15 for the unseeded and seeded flames, respectively. Error in these calculations rangedfrom 4.4% (seeded height f, position 6) to over 300% (seeded height b, position 1), whilethe majority of the diameters calculated had error of less than 25%. A complete erroranalysis is presented in Appendix C.Table 4-14.Unseeded soot particle modal diameters determined from Mie theory andcomplex refractive index of m = 2.0-0.35i. Unseeded Particle Diameter (nm) Radial Position Height 1 2 3 4 5 6 b 22.89 40.76 47.95 67.33 67.20 49.74 c 45.94 N/A* 55.94 81.18 67.45 50.13 d 46.29 68.35 73.01 73.24 59.58 45.56 e 66.35 50.58 59.60 60.44 55.06 43.70 f 49.65 47.31 48.53 48.38 43.29 35.39 Value out of monotonic region.Table 4-15. Seeded soot particle modal diameters determined from Mie theory andcomplex refractive index of m = 2.0-0.35i. Seeded Particle Diameter (nm) Radial Position Height 1 2 3 4 5 6 b 54.74 52.06 N/A* N/A* 70.00 48.20 c 41.82 75.38 107.21 95.18 67.63 49.84 d 75.26 60.82 70.08 69.49 66.40 46.44 e 58.15 54.94 66.33 62.35 54.80 44.60 f 55.19 46.28 47.59 46.98 45.05 39.27 Value out of monotonic region.Figure 4-6 shows the unseeded and seeded soot modal particle diametersgraphically for all radial positions and vertical heights, excluding those locations wherethe monotonic limit was exceeded.

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79 Figure 4-6. Unseeded and seeded soot particle modal diameters. A) at height b. B) at height c. C) at height d. D) at height e. E) at height f. A B

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80 Figure 4-6. Continued. C D

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81 Figure 4-6. Continued. Recall that the ZOLD function describing the particle sizes is a skewed function, thus the mean diameter is larger than the modal diameter. The modal diameter is preferred for discussion over the mean, as it represents the most probable size of the particles. In contrast, the use of the mean particle size in analysis may result in confusion, if not clearly defined, due to the influence of the tail of the probability distribution. For completeness, the mean diameters are presented below in Table 4-16 and Table 4-17 however they will not be considered further in this analysis. As noted above, the skewness parameter o used for this work was 0.2. Thus, the average diameters were calculated from the ZOLD function by d mean =d modal exp(3 o 2 /2). For o =0.2, the multiplier is equal to 1.06. E

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82 Table 4-16. Unseeded soot particle mean diameters. Unseeded Particle Diameter (nm) Radial Position Height 1 2 3 4 5 6 b 24.31 43.28 50.92 71.49 71.36 52.82 c 48.78 N/A 59.40 86.20 71.62 53.23 d 49.15 72.58 77.52 77.77 63.26 48.38 e 70.45 53.71 63.29 64.18 58.46 46.40 f 52.72 50.24 51.53 51.37 45.97 37.58 Value out of monotonic region. Table 4-17. Seeded soot particle mean diameters. Seeded Particle Diameter (nm) Radial Position Height 1 2 3 4 5 6 b 58.12 55.28 N/A N/A 74.33 51.18 c 44.41 80.04 113.84 101.07 71.81 52.92 d 79.91 64.58 74.41 73.79 70.51 49.31 e 61.75 58.34 70.43 66.21 58.19 47.36 f 58.60 49.14 50.53 49.89 47.84 41.70 Value out of monotonic region. For comparison, the modal diameter of the soot particles in the center of the flame at height c was also calculated assuming the same skewness o but with a complex refractive index of m = 1.6 0.40 i a value in line with those determined by Dalzell and Sarofim. 43 From Table 4-14 and Table 4-15 the modal diameters calculated earlier at this position were 45.9 nm and 41.8 nm for the unseeded and seeded flames, respectively, with an unseeded/seeded diameter ratio of 1.10. With the alternate value of m these values were determined to be 63.3 nm for the unseeded flame, and 57.3 nm for the seeded flame, with a ratio of 1.10, which correspond to an average increase in particle diameter slightly higher than 30%. However, the relative diameters ( i.e. unseeded/seeded) are in exact agreement. Therefore, while the refractive index will influence the absolute values, the effect on relative comparisons between unseeded and seeded flames is minimal.

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83 Number Density of Particles A plot of Mie theory C ext versus K' VV /K ext allowed for the determination of the number density N from the relation N=C ext /K ext This plot is shown in Figure 4-7 Figure 4-7. Extinction cross section of soot particles determined from Mie theory for m = 2.0-0.35 i and ZOLD parameter o = 0.2. To accurately fit a polynomial curve to the C ext Mie data, the range of K' VV /K ext was divided into three sections K' VV /K ext < 3.0E-2, 3.0E-2 K' VV /K ext 4.0E-2, and K' VV /K ext > 4.0E-2. From this fit, C ext and therefore N, were easily determined at each height and radial position. The number densities resulting from this procedure are shown in Table 4-18 and Table 4-19 and plotted for each height in the flame in Figure 4-8 Error in these calculations ranged from 15.3% (seeded height f, position 6) to over 1000% (seeded height b, position 1), with the majority of number density errors less than 86%. More important than the magnitude of the absolute error in these measurements,

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84 however, is the relative agreement between the unseeded and seeded flames, as discussed above in the context of refractive indices. Table 4-18. Unseeded soot particle number densities determined from Mie theory and complex refractive index of m = 2.0-0.35 i Unseeded Number Density (particles/cm 3 ) Radial Position Height 1 2 3 4 5 6 b 2.695E+11 1.737E+10 7.418E+09 3.282E+09 4.166E+09 2.162E+10 c 1.519E+10 N/A 7.094E+09 2.381E+09 1.022E+10 5.191E+10 d 3.274E+10 3.624E+09 4.006E+09 6.696E+09 2.645E+10 1.325E+11 e 7.652E+09 3.849E+10 2.001E+10 2.625E+10 4.787E+10 2.033E+11 f 4.293E+10 6.384E+10 6.303E+10 7.234E+10 1.535E+11 5.485E+11 Value out of monotonic region. Table 4-19. Seeded soot particle number densities determined from Mie theory and complex refractive index of m = 2.0-0.35 i Seeded Number Density (particles/cm 3 ) Radial Position Height 1 2 3 4 5 6 b 2.873E+09 5.231E+09 N/A N/A 3.464E+09 2.682E+10 c 3.879E+10 1.371E+09 4.596E+08 1.141E+09 1.010E+10 5.300E+10 d 2.147E+09 9.994E+09 6.627E+09 1.117E+10 1.656E+10 1.150E+11 e 1.124E+10 2.253E+10 1.257E+10 2.412E+10 5.053E+10 1.789E+11 f 2.664E+10 8.563E+10 8.016E+10 9.736E+10 1.342E+11 3.164E+11 Value out of monotonic region.

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85 Figure 4-8. Unseeded and seeded particle number densities. A) at height b. B) at height c. C) at height d. D) at height e. E) at height f. A B

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86 Figure 4-8. Continued. C D

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87 Figure 4-8. Continued. As seen in Figure 4-8 the soot particle number densities throughout the flame are nearly identical, within experimental error, for the seeded and unseeded flames. The sole exception being height b, position 1 ( Figure 4-8A ). However, upon closer investigation, it is seen that the C ext for this point is very small nearly five times smaller than the C ext determined for its neighboring point. Further, the K ext from the three-point Abel inversion was three times larger than the same neighboring point. Most likely the high number density calculated for this position is due to experimental error and is not a true measure of the soot condition. Particle Volume Fraction With the particle diameter and number density known, the particle volume fraction is determined from E

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88 f v = 4 3 N r m 3 exp 15 # o 2 $ % & ( ) (4-1) where r m and o are ZOLD parameters described in Chapter 2 These results are compiled in Table 4-20 and Table 4-21 Overall, the majority of the volume fraction calculations had errors less than or about a factor of 2. Seeded height f, position 6 had the lowest, with 20.3%, while seeded height b, position 1 was the highest, greater than one order of magnitude. The complete error analysis may be found in Appendix C Additionally, the soot particle volume fraction results are shown graphically in Figure 4-9 Table 4-20. Unseeded soot particle volume fractions. Unseeded Soot Volume Fraction (cm 3 /cm 3 ) Radial Position Height 1 2 3 4 5 6 b 2.283E-06 8.318E-07 5.779E-07 7.080E-07 8.936E-07 1.880E-06 c 1.041E-06 N/A 8.778E-07 9.002E-07 2.217E-06 4.622E-06 d 2.295E-06 8.181E-07 1.102E-06 1.860E-06 3.954E-06 8.860E-06 e 1.580E-06 3.519E-06 2.994E-06 4.095E-06 5.648E-06 1.199E-05 f 3.714E-06 4.780E-06 5.091E-06 5.791E-06 8.801E-06 1.718E-05 Value out of monotonic region. Table 4-21. Seeded soot particle volume fractions. Seeded Soot Volume Fraction (cm 3 /cm 3 ) Radial Position Height 1 2 3 4 5 6 b 3.332E-07 5.216E-07 N/A N/A 8.396E-07 2.123E-06 c 2.006E-06 4.150E-07 4.003E-07 6.956E-07 2.209E-06 4.639E-06 d 6.469E-07 1.589E-06 1.612E-06 2.649E-06 3.427E-06 8.139E-06 e 1.562E-06 2.641E-06 2.593E-06 4.132E-06 5.878E-06 1.122E-05 f 3.166E-06 5.998E-06 6.106E-06 7.136E-06 8.673E-06 1.354E-05 Value out of monotonic region.

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89 Figure 4-9. Unseeded and seeded soot particle volume fractions. A) at height b. B) at height c. C) at height d. D) at height e. E) at height f. A B

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90 Figure 4-9. Continued. C D

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91 Figure 4-9. Continued. In comparing the results for diameter, number density, and volume fraction shown in Figure 4-6 Figure 4-8 and Figure 4-9 it is seen that the seeded flames show little deviation from the unseeded flames in the regions studied, in consideration of experimental error. Micro-Raman Spectroscopy While there was little change in the size, number density, and volume fraction of soot particles in the seeded flames, significant differences between the unseeded and seeded flames were apparent at the flame holder. During combustion of the unseeded flame, soot particles slowly built up on the flame holder until reaching an equilibrium. However, with the addition of iron pentacarbonyl, no soot built up on the flame holder screen, and additionally, rust-colored iron deposits were left behind on the screen. E

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92 Micro-Raman spectroscopy performed on the flame holder screens was performed to determine the state of this iron. Figure 4-10 Figure 4-11 and Figure 4-12 show reference spectra of FeO, Fe 2 O 3 and Fe 3 O 4 These spectra were taken from bulk iron oxide powders pressed into 3 cm diameter disc, approximately 2 mm high. These spectra were in agreement with reported spectra presented by de Faria et al 38 Table 4-22 summarizes the manufacturers specifications of these pure iron oxides. Table 4-22. Bulk iron oxide powder specifications used in micro-Raman study. Oxide Supplier Catalog Number CAS # Description FeO Alfa Aesar 30513 1345-25-1 99.5% (metals basis) Iron (II) oxide, wstite Fe 2 O 3 Fisher Scientific I116-500 1309-37-1 Iron (III) oxide, hematite Fe 3 O 4 Fisher Scientific I119-500 1317-61-9 Iron oxide black, magnetite Figure 4-10. FeO reference Raman spectra.

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93 Figure 4-11. Fe2O3 reference Raman spectra. Figure 4-12. Fe3O4 reference Raman spectra.In addition, reference spectra for graphite and carbon black are shown in Figure 4-13 and Figure 4-14, respectively. Graphite consists of highly oriented sheets or layers of

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94 carbon, while carbon black consists of virtually pure elemental carbon in the form of amorphous structure with only very localized graphitic carbon. Figure 4-13. Graphite reference Raman spectra. Figure 4-14. Carbon black reference Raman spectra.

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95 Note that these two spectra depict two bands near 1325 cm -1 and 1575 cm -1 that are characteristic of carbon or soot structures. The intensity of the carbon black spectra is much less than that of graphite due to the aforementioned amorphous structure of carbon black compared to the ordered structure of graphite. Lastly, a spectra of a clean, unburned stainless steel mesh flame holder was taken. As Figure 4-15 shows, this Raman spectra is featureless. Figure 4-15. Reference Raman spectra of clean, unburned flame holder screen. A flame holder used during a seeded flame experiment was placed under the 100x objective of the micro-Raman spectrometer and a signal was integrated over 5 seconds and averaged over 8 cycles. The area of the screen studied corresponded to an annular region around the center of the screen, but at a radial distance larger than the flame diameter. The resulting spectra were consistent with the reference Fe 2 O 3 spectra, and both are shown in Figure 4-16 This spectra was also very consistent and repeatable throughout the annual region of the seeded screen.

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96 Figure 4-16. Raman spectra of seeded flame holder screen and Fe 2 O 3 reference. As demonstrated in Figure 4-16 Fe 2 O 3 is present on the seeded flame holder screen. An additional peak centered at 662 cm -1 is also apparent from the Raman spectra, which is uncharacteristic of Fe 2 O 3 The spectral resolution of the spectrometer was on the order of 1 cm -1 With this resolution in mind, the unidentified peak in Figure 4-16 is consistent with the FeO peak at 660 cm -1 shown in the reference spectra of Figure 4-10 Several interpretations are possible with respect to the 662 cm -1 peak. The Raman spectra of Figure 4-16 may suggest that FeO is also present on the flame holder screen. However, it was found to be quite difficult to obtain a reference spectra for FeO from the bulk powders. Specifically the spectra produced from the bulk FeO proved to be very sensitive, and in order to obtain a clear signal with relatively good signal-to-noise, a highly crystalline form of FeO had to be found under the microscope objective. This

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97 would suggest that if indeed, the unidentified peak in Figure 4-16 is characteristic of FeO, the form of the oxide on the screen must be highly crystalline in order to consistently produce such a peak in the Raman spectra in the presence of large quantities of Fe 2 O 3 To determine if perhaps the two iron oxide species could be present together on the screen, bulk FeO and Fe 2 O 3 were combined in approximately equal quantities and ground together using a mortar and pestle. The resulting spectra from this experiment is shown in Figure 4-17 Figure 4-17. Raman spectra of mixed bulk powders of FeO and Fe 2 O 3 Note the absence of the characteristic FeO peak. The presence of FeO in the mixture is not apparent from the spectra recorded in Figure 4-17 which is consistent with the apparent disparity between Raman signals of Fe 2 O 3 and FeO, with the latter being much weaker. This underscores the conclusion that FeO would have to be highly crystallized and in significant concentration in order to

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98 produce a strong Raman signal in the presence of the observed Fe 2 O 3 signal. Hence the identification of the 662 cm -1 peak as FeO is not ruled out but is not likely. The seeded screen used for the Raman study had been allowed to sit a number of weeks following combustion. To ensure that the iron on the screen did not oxidize over time, and to verify that the 662 cm -1 peak was not an aging artifact, a second screen was analyzed immediately following seeded combustion. Denoting the original screen as Screen A, and the new screen as Screen B, the spectra of these screens is shown in Figure 4-18 Figure 4-18. Raman spectra of two seeded flame holder screens. Screen A spectra was taken a number of weeks after combustion, Screen B spectra was taken immediately following combustion. Despite differences in relative intensity, the two spectra shown in Figure 4-18 are identical, indicating that the iron compound on the screens is stable and does not

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99 deteriorate or oxidize over time and that the 662 cm -1 peak is present on the screen during combustion. Another possibility for the 662 cm -1 peak is that it may have been an artifact from the mesh substrate. While the unburned stainless steel had no Raman character, as shown in Figure 4-15 during combustion the screen undergoes complex changes as the temperatures in the flame region can reach an excess of 1800 K. The spectra of an unseeded flame holder shown in Figure 4-19 tends to support this theory. This spectra was taken in the same annular region on the screen as the seeded spectra. Figure 4-19. Raman spectra of unseeded flame holder. The prominent peak shown in Figure 4-19 is consistent, within one wavenumber, with the 662 cm -1 peak present in the seeded screen Raman spectra, Figure 4-16 Recall the spectral resolution of the spectrometer was approximately 1 cm -1 Additionally, a few peaks characteristic of Fe 2 O 3 are visible just above the noise limit. The trace amounts of Fe 2 O 3 on the unseeded screen is most likely due to oxidation of iron present in stainless

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100 steel. It is noted, however, that these trace Fe 2 O 3 peaks are not comparable to the seeded flame screen peaks, and physical examination reveals no visible trace of rust, as seen with the seeded flame screens. The strength of the peak at 663 cm -1 is notable in comparison to the weak Fe 2 O 3 lines. As Figure 4-17 showed, small amounts of Fe 2 O 3 compared to FeO still produced dominant Fe 2 O 3 spectral lines. This indicates that the peak at 663 cm -1 in Figure 4-19 is not FeO, but an artifact of the stainless steel substrate, and it may further be presumed that the unidentified peak at 662 cm -1 on the seeded screen is due to the same characteristic artifact rather than FeO. Further evidence that artifacts arise on the screens due to deterioration of the stainless steel is presented in Figure 4-20 These spectra of unseeded and seeded screens were taken at the center of the flame holders where the stainless steel appeared most damaged. Figure 4-20. Raman spectra of seeded and unseeded screens taken at center of flame holders.

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101 With reference to Figure 4-13 and Figure 4-14 it is seen that the peaks shown in the spectra above are not characteristic of soot or carbon and are most likely artifacts from the flame holder. The seeded spectra shows two peaks at 678 cm -1 and 728 cm -1 This first peak corresponds well to the unseeded peak shown. These peaks however are different from the 662 cm -1 peak identified in the seeded and unseeded screens, where the Raman data was taken at a radial position outside of the flame center. The second peak shown in the seeded spectra of Figure 4-20 on the seeded screen is additional artifact of the substrate.

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102 CHAPTER 5 DISCUSSION AND CONCLUSIONS Discussion of Results The five heights studied in the unseeded and seeded flames were originally planned to span the inception, growth, and burnout regimes of a diffusion flame. It was anticipated that the addition of iron pentacarbonyl would result in a significant decrease in soot volume and soot particle size in the latter regions of the flame as oxygen diffused into the burnout regime. This is based on the working hypothesis that iron primarily affects soot in the oxidation or burnout regime. The results of the scattering and transmission studies however, indicate that the full range of soot particle inception, growth, and destruction was not realized. The heights studied thoroughly probed the growth regime, though burnout was not yet observed at the highest height investigated. Particle inception was not directly observable, however, the beginning stages of the growth regime observed did enable assessment of inception behavior in seeded and unseeded flames. It has been suggested that the addition of a metal additive to a flame results in earlier particle inception due to the presence of metallic nucleation sites in early residence times. 20 22 23 25 27 Because of interactions between the laser and the burner lip, the inception regime could not be probed to investigate this theory. However at the lowest flame heights b and c, an initial increase in soot particle size was observed, particularly near the center of the flame. At height b, position 1, the seeded soot particle size was nearly 2.5 times larger than the unseeded particles at the same location.

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103 Likewise at position 2 of height b, the seeded soot particles were approximately 30% larger than the unseeded particles. At height c, position 2, the seeded particles were close to 2 times the size of unseeded particles. This soot particle size enhancement tends to support an initial increase in soot loading due to metallic nucleation particles in the inception regime. With these seed particles present, soot growth may begin at an earlier residence time, thus explaining the larger particle size in comparison to the unseeded flame at the same location. This soot size enhancement quickly declines however, and as seen at the radial extremities and at the higher heights, the soot particle size of the seeded flames and the unseeded flames are comparable. At this point, soot particle growth dominates. The initial soot enhancing effects of the iron are overshadowed by the normal soot growth mechanisms. In investigating the particle number densities through the flame field it is seen that both seeded and unseeded flames were comparable on the basis of number of particles per volume. The number density was seen to remain nearly constant in the central regions across all heights as well. It is in these regions that the particles are in the growth regime. The number of particles is nearly fixed and only their diameter and volume fraction increase as mass is added to the particles. In the outer radial positions, the number density and volume fraction are shown to increase while the diameters decrease. This is to be expected as the soot particles are attacked and broken down by oxidizers diffusing into the outer radial positions of the flame. Pronounced oxidation of particles following the decay of soot surface growth was not observable in this study. Height f was the highest attainable position in the flame because the burner physically could not be lowered further. Although height f was 40.64

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104 mm above the burner lip, the region probed at this height was still characterized by soot particle growth, as revealed in the data. The total integrated soot in the growth regime (radial sections 3, 4, and 5) per differentially thick flame section over all heights is plotted in Figure 5-1 These radial positions correspond to the majority of soot formation at lower heights near the idealized annular region of fuel rich combustion. As this plot shows, the total volume of soot was still increasing up through height f, indicating that the oxidation regime had not yet been reached. Had the oxidation regime been reached, the soot volume would be expected to begin to decay in both unseeded and seeded flames, with the final soot volume being lowest in the latter. 22 Figure 5-1. Soot volume through the growth regime (annular regions 3, 4, and 5) of the flame. Although the soot suppressing effects of iron pentacarbonyl were not quantitatively measured in the burnout regime, a reduction in overall soot formation was observable

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105 during experimentation. The first observable effect was a reduction in the smoke point of the flame. The unseeded flame operated just under the smoke point for isooctane. Breakthrough smoke plumes were observed if the flame was disturbed, such as a disruption from an air current for example. Breakthrough soot was not apparent in the seeded flame however, indicating an overall reduction in soot formation. The soot suppressing effect of iron pentacarbonyl was observable on the flame holder as well. In unseeded flames, a slow but steady buildup of soot appeared on the flame holder screen. An equilibrium condition was eventually reached and a constant amount of soot was observable on the flame holder screen during unseeded combustion. With the addition of iron pentacarbonyl however, the flame holder screen remained free of soot during combustion. Thus, it is presumed that the burnout regime for the soot particles appears at or near the height of the flame holder, and that in this regime, the overall soot formation in the seeded flames was less than that of the unseeded flames. The results of this study, though lacking information about the effect of iron pentacarbonyl in the burnout regime, provide a thorough analysis of additives in the growth regime. Iron initially enhances soot particle growth at the lowest heights studied in the flame, presumably due to increased nucleation sites allowing for the formation of soot precursor molecules at earlier residence times. Further, as Figure 5-1 demonstrates, the soot volume through the growth regime in both the seeded and unseeded flames are essentially equal, within experimental error. These findings are in agreement with Zhang and Megaridis, 26 who saw an indistinguishable effect of iron pentacarbonyl on soot loading in a diffusion ethylene flame.

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106 Micro-Raman spectroscopy revealed interesting characteristics about the deposited iron on the flame holder screens. Iron in the form on Fe 2 O 3 was found in an annular region outside of the flame diameter on the seeded screens. An additional Raman peak appeared on these screens as well which is most likely considered an artifact of the substrate stainless steel mesh, although the presence of FeO cannot be ruled out. Iron was not detected on the flame holder in the center of the screen. Though temperature measurements were not taken in the flame, it is likely that the flame temperature at the screen was higher than 1565C, the melting point of Fe 2 O 3 Thus the temperature at the center of the flame holder was too high for iron oxide to deposit. Conclusions The addition of iron pentacarbonyl into a near-smoke point flame had the effect of reducing the smoke point of the flame and eliminating visible soot buildup on a stainless steel mesh flame holder. Light scattering and transmission data were used to extract particle size, number density, and soot volume fraction information for six concentric flame regions over five heights. These data support the theory that iron particles act as early nucleation sites for soot formation in the inception regime. This conclusion was drawn based on an increase in particle size at heights 8.7 and 15.2 mm above the burner. As the particles matured through the growth regime, it was seen that the size of unseeded particles matched those of the seeded particles, and by a height of 22.9 mm above the burner, these values were statistically indistinguishable. The number density and soot volume fraction over all heights studied were also statistically indistinguishable, indicating that any initial enhancing property of the iron pentacarbonyl in the seeded flame was muted by the soot growth processes active in both seeded and unseeded flames. Essentially, the iron species were quickly incorporated within the soot particles,

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107 giving way to a basically unseeded flame during the subsequent soot growth regime. Thus it is concluded that the effects of iron are most likely present in the soot oxidation regime. It is expected that if the oxidation regime of the seeded and unseeded flames had been probed, a rapid drop off in soot volume fraction would have been observed. Hence, it is anticipated that it is this regime in which the iron pentacarbonyl has the greatest effect on soot loading. Micro-Raman spectroscopy suggests that the state of the iron additive on the seeded flame holder was Fe 2 O 3 While this does not definitively identify the state of the iron inside of the flame, it provides insights into its character. At the flame boundary, soot particles incorporated with iron come into contact with oxidizers. As the carbon is removed from these particles, the gaseous iron diffuses outward due to the temperature gradient between the reaction zone and the ambient and eventually deposits onto the flame holder in an annular region surrounding the flame. The Raman study identified the state of this iron as Fe 2 O 3 throughout the annular region. This may suggest that Fe 2 O 3 is the state of the iron in the oxidized soot particle since it was identified in the region closest to the flame diameter. Future Work Flame stability was a significant factor in this study. As described above, measurements were taken through the end of the inception regime and throughout the growth regime. The burnout regime was higher in the flame, hence closer to the flame holder. However, due to flame stability issues, the flame holder could not be raised or removed to probe within this regime. Future studies in the burnout regime would allow for further characterization of the effects of iron pentacarbonyl on soot formation.

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108 Flame stability was also a factor for errors in the scattering and transmission measurements. A reduction in error in these measurements would translate into much greater precision in the calculated particle size, number density, and volume fraction. The current flame was characterized by a Froude number equal to 0.05, hence buoyancy effects dominated. For future studies, a momentum-driven flame (Fr > 1), less prone to instabilities due to buoyancy forces, would be ideal. In this case, the full effect of iron pentacarbonyl in the critical burnout regime could be examined. The transport of gaseous iron particles from the reaction zone to the annular region surrounding the flame on the flame holder screen was an interesting phenomenon observed in these studies. It was presumed that molecular diffusion led to the transport of iron species to the outer-flame regions, though it is unknown whether this iron underwent oxidation once outside of the reaction zone. Future in situ measurements outside of the flame in this diffusion region would be insightful and meaningful to the full picture of the effect of metallic fuel additives. In addition, in situ measurements inside of the flame would definitively identify the state of the additive in the flame. Thermodynamics, modeling, extraction techniques, and post-flame studies have been used in the past to predict the additive state. The use of in situ Raman spectroscopy or laser-induced fluorescence (LIF) are two novel laser-based techniques that have the potential to clearly identify the additive state. With knowledge of the correct additive state, the mechanisms of soot suppression or enhancement may be more closely investigated and better understood.

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109 APPENDIX A COMPOSITION OF COMMON JET FUELS Table A-1. Composition of fuel oil no. 1 and JP-5. Volume % Hydrocarbon type Fuel oil no. 1 45 JP-5 45 Paraffins ( n and iso-) 52.4 30.8 Monocycloparaffins 21.3 no data Bicycloparaffins 5.1 no data Tricycloparaffins 0.8 no data Total cycloparaffins 27.2 52.8 Total saturated hydrocarbons 79.7 no data Olefins no data 0.5 Alkylbenzenes 13.5 no data Indans/tetralins 3.3 no data Dinaphthenobenzenes/indenes 0.9 no data Naphthalenes 2.8 no data Biphenyls/acenaphthenes 0.4 no data Fluorenes/acenaphthylenes no data no data Phenanthrenes no data no data Total aromatic hydrocarbons 23.6 15.9 Table A-2. Composition of surrogate JP-8. Hydrocarbon type Weight % 45 Isooctane 3.66 Methylcyclohexane 3.51 m -Xylene 3.95 Cyclooctane 4.54 Decane 16.08 Butylbenzene 4.72 1,2,4,5-Tetramethylbenzene 4.28 Tetralin 4.14 Dodecane 22.54 1-Methylnapthalene 3.49 Tetradecane 16.87 Hexadecane 12.22

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110 Table A-3. Composition of shale-derived and petroleum-derived JP-4. Weight % Hydrocarbon type Shale-derived 46 Petroleum-derived 46 N-alkanes Heptane 4.73 15.76 Octane 7.48 6.60 Nonane 7.24 2.54 Decane 11.25 2.24 Indane 0.42 0.17 Undecane 16.62 4.17 Dodecane 11.49 5.25 Tridecane 6.07 4.71 Tetradecane 3.19 1.02 Pentadecane 0.96 1.35 Total 69.45 43.81 Monosubstituted alkanes 3-Methyl hexane 3.05 14.39 2-Methyl heptane 3.08 6.14 3-Methyl heptane 1.64 7.19 Total 7.77 27.72 Disubstituted alkanes 2,3-Dimethyl pentane 2,5-Dimethyl pentane 0.18 1.48 2,4-Dimethyl pentane 0.63 2.52 Total 0.81 4.00 Cyclohexanes Cyclohexane 1.52 2.13 Methyl cyclohexane 5.68 2.17 Ethyl cyclohexane Total 7.72 4.30 Monosubstituted aromatics Methyl benzene 3.77 3.41 Disubstituted aromatics (xylenes) m -Xylene 2.60 2.71 p -Xylene 1.70 1.63 o -Xylene 2.00 1.89 Total 6.30 6.23 Multisubstituted aromatics 1,3,5-Trimethylbenzene 1.52 1.09 1,2,4-Trimethylbenzene 2.00 3.52 1,2,3-Trimethylbenzene 0.30 1.04 Total 3.82 5.65 Overall total 99.12 95.12

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111 APPENDIX B EXTINCTION COEFFICIENT DECONVOLUTION TECHNIQUES In order to determine the individual extinction coefficients for each of the six concentric annular regions studied in the flame, a deconvolution technique was employed. A number of methods exist to approach the deconvolution problem. In this work onion peeling, linear regression, and three-point Abel inversion schemes were used, with the latter producing the best results with the least amount of error. The onion peeling technique is perhaps one of the simplest deconvolution techniques. In this scheme, the distribution of a parameter of interest throughout the field is determined by starting from the outermost annular region. The parameter is determined for this region from experimental data, and is used in determining the value of the unknown parameter in the next annular region. As information about each region is determined, it is peeled away until the entire field distribution is known. The layerby-layer approach is much like peeling away the layers of an onion, hence the techniques name. Along a line of sight the individual extinction coefficients in each region are additive, resulting in a total extinction coefficient. This parameter is measured as a function of the transmission along that line of sight. Figure B-1 depicts the geometry of the onion peeling inversion scheme.

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112 Figure B-1. Geometry used for onion peeling inversion scheme.As Figure B-1 demonstrates, the transmission measurements are a function of allthe radial section extinction coefficients crossing the line of sight. Namely, "1=fKext,1,Kext,2,Kext,3,Kext,4,Kext,5,Kext,6(),"2=fKext,2,Kext,3,Kext,4,Kext,5,Kext,6(),"3=fKext,3,Kext,4,Kext,5,Kext,6(),"4=fKext,4,Kext,5,Kext,6(),"5=fKext,5,Kext,6(),"6=fKext,6(). (B-1)As described, the onion peeling method relies on the successive determination of outlyingparameters. From the Beer-Lambert law, this implies

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113 K ext 6 = ln( # 6 ) 2 l 6 6 K ext 5 = ln( # 5 ) 2 l 5 6 K ext 6 2 l 5 5 K ext 4 = ln( # 4 ) 2 l 4 6 K ext 6 2 l 4 5 K ext 5 2 l 4 4 M K ext 1 = ln( # 1 ) 2 l 1 6 K ext 6 2 l 1 5 K ext 5 2 l 1 4 K ext 4 2 l 1 3 K ext 3 2 l 1 2 K ext 2 2 l 1 1 (B-2) where the (2 l x,y ) terms refer to the individual pathlengths each line of sight transmission measurement traverses through the radial sections. The individual pathlength terms are illustrated in Figure B-1 and are determined from geometry. Table B-1 and Table B-2 summarize the unseeded and seeded extinction coefficients for each annular region extracted using onion peeling. Table B-1. Unseeded extinction coefficients determined from onion peeling inversion. Unseeded K ext (cm -1 ) Onion Peeling Radial Position Height 1 2 3 4 5 6 b 1.986E-01 9.710E-03 2.658E-02 4.029E-02 3.391E-02 9.624E-02 onion 1.490E-01 7.722E-02 5.611E-02 5.523E-02 3.898E-02 3.619E-02 c 1.013E-01 -3.836E-02 5.827E-02 3.734E-02 1.028E-01 2.130E-01 onion 1.260E-01 5.712E-02 7.812E-02 4.382E-02 5.992E-02 3.540E-02 d 1.723E-01 1.740E-03 5.155E-02 8.115E-02 1.651E-01 3.545E-01 onion 2.370E-01 1.127E-01 7.977E-02 5.534E-02 1.021E-01 5.268E-02 e -5.302E-02 2.070E-01 9.426E-02 2.028E-01 2.102E-01 3.969E-01 onion 1.670E-01 1.263E-01 1.524E-01 1.315E-01 1.300E-01 9.892E-02 f 6.615E-02 1.643E-01 1.640E-01 1.705E-01 2.092E-01 3.201E-01 onion 1.655E+00 4.322E-01 3.473E-01 3.462E-01 2.443E-01 2.976E-01

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114 Table B-2. Seeded extinction coefficients determined from onion peeling inversion. Seeded K ext (cm -1 ) Onion Peeling Radial Position Height 1 2 3 4 5 6 b 1.990E-03 4.305E-02 -9.700E-03 5.360E-03 3.831E-02 1.472E-01 onion 2.981E-01 7.025E-02 6.912E-02 4.371E-02 6.758E-02 2.178E-02 c 1.586E-01 -2.060E-03 4.607E-02 4.065E-02 1.048E-01 3.103E-01 onion 3.432E-01 4.514E-02 8.967E-02 6.762E-02 8.696E-02 2.134E-02 d -1.888E-02 1.033E-01 6.121E-02 1.780E-01 1.146E-01 4.632E-01 onion 2.548E-01 1.313E-01 9.303E-02 8.954E-02 5.096E-02 6.198E-02 e -2.260E-03 1.530E-01 9.112E-02 2.200E-01 2.512E-01 4.318E-01 onion 5.231E-01 1.675E-01 1.093E-01 1.512E-01 9.494E-02 1.065E-01 f -2.473E-02 2.654E-01 2.097E-01 2.691E-01 2.762E-01 2.369E-01 onion 5.232E-01 2.754E-01 1.503E-01 2.295E-01 2.115E-01 1.169E-02 While the onion peeling deconvolution technique is straightforward and only requires simple geometry calculations to determine the pathlengths, this method has two drawbacks. First, because this method relies on the successive determination of outer layer parameters, any error in these layers is compounded through the field and can result in high errors in the inner regions. Secondly, oversampling, or spacing the line of sight measurements too closely, can result in high error in the deconvolution output. As the spatial resolution approaches the same magnitude as the error in the samples, the deconvolution becomes highly inaccurate. This was especially problematic with the onion peeling method where the error in the inversion scheme was significant. The second method of deconvolving the transmission data attempted to reduce the error in the inner regions by performing a least squares linear regression fit. In this technique, the exact extinction coefficient at a point was not explicitly determined. Rather, a regression fit determined the extinction coefficients in such a way that the overall error was minimized, bringing each of the individual extinction coefficients near,

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115 but not exactly to their true value as predicted by the Beer-Lambert law. Two geometries were employed for this method, as shown by Figure B-2 Figure B-2. Geometries used for linear regression inversion scheme. The linear regression approach was a two-step process. First, the extinction coefficients K ext,A through K ext,G were determined. Then a smoothing process was used to overlay the two geometries and convert K ext,A through K ext,G into the desired K ext,1 through K ext,6 parameters that correspond to the concentric regions studied in the scattering experiments. In each geometry, all six line of sight measurements were considered. The radial sections were defined such that there could be more than one transmission line through the section. Thus for each geometry the problem of inverting the transmission data to give the extinction coefficient was overprescribed. The Beer-Lambert law cannot be solved exactly for each point, however using linear regression allowed the extinction coefficients in each section to be approximated, while the error for each individual position was minimized. For each geometry, a system of equations describing the transmission and the extinction coefficient can be written as

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116 ln( # 6 ) ln( # 5 ) ln( # 4 ) ln( # 3 ) ln( # 2 ) ln( # 1 ) $ % & & & & & & & & & & ( ) ) ) ) ) ) ) ) ) ) = 2 l 6 7 0 0 0 2 l 5 7 2 l 5 5 0 0 2 l 4 7 2 l 4 5 0 0 2 l 3 7 2 l 3 5 2 l 3 3 0 2 l 2 7 2 l 2 5 2 l 2 3 0 2 l 1 7 2 l 1 5 2 l 1 3 2 l 1 1 $ % & & & & & & & & & & ( ) ) ) ) ) ) ) ) ) ) K ext D K ext C K ext B K ext A $ % & & & & & & ( ) ) ) ) ) ) (B-3) and ln( # 6 ) ln( # 5 ) ln( # 4 ) ln( # 3 ) ln( # 2 ) ln( # 1 ) $ % & & & & & & & & & & ( ) ) ) ) ) ) ) ) ) ) = 2 l 6 6 0 0 2 l 5 6 0 0 2 l 4 6 2 l 4 4 0 2 l 3 6 2 l 3 4 0 2 l 2 6 2 l 2 4 2 l 2 2 2 l 1 6 2 l 1 4 2 l 1 2 $ % & & & & & & & & & & ( ) ) ) ) ) ) ) ) ) ) K ext G K ext F K ext E $ % & & & & ( ) ) ) ) (B-4) With this information, a least squares linear regression was performed and values for K ext,A through K ext,G were extracted. Table B-3 and Table B-4 summarize these results. Table B-3. Unseeded extinction coefficients determined from linear regression technique with two flame geometries. Unseeded K ext (cm -1 ) Intermediate Linear Regression Values Geometry 1 Geometry 2 Height A B C D E F G b 1.872E-01 2.114E-02 3.692E-02 9.541E-02 5.595E-02 2.169E-02 7.850E-02 regr. 2.362E-02 4.400E-03 3.102E-03 2.577E-03 3.871E-02 1.980E-02 9.248E-03 c 5.080E-02 1.268E-02 7.468E-02 2.171E-01 6.799E-03 2.622E-02 1.825E-01 regr. 1.270E-01 2.365E-02 1.675E-02 1.263E-02 6.197E-02 3.169E-02 1.382E-02 d 1.526E-01 2.160E-02 1.252E-01 3.598E-01 4.981E-02 3.511E-02 3.063E-01 regr. 1.248E-01 2.325E-02 1.653E-02 1.178E-02 1.019E-01 5.212E-02 2.182E-02 e 1.602E-02 1.370E-01 1.997E-01 3.977E-01 1.373E-01 1.304E-01 3.568E-01 regr. 1.183E-01 2.203E-02 1.584E-02 9.687E-03 1.051E-01 5.383E-02 2.008E-02 f 7.097E-02 1.589E-01 1.892E-01 3.214E-01 1.508E-01 1.510E-01 3.041E-01 regr. 5.596E-02 1.043E-02 7.865E-03 2.844E-03 6.589E-02 3.426E-02 8.277E-03

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117 Table B-4. Seeded extinction coefficients determined from linear regression technique with two flame geometries. Seeded K ext (cm -1 ) Intermediate Linear Regression Values Geometry 1 Geometry 2 Height A B C D E F G b 3.822E-02 6.488E-03 1.909E-02 1.515E-01 3.603E-02 -1.414E-02 1.055E-01 regr. 7.829E-02 1.459E-02 1.024E-02 1.189E-02 4.968E-02 2.558E-02 1.476E-02 c 1.372E-01 1.967E-02 7.402E-02 3.165E-01 4.861E-02 1.317E-02 2.336E-01 regr. 9.540E-02 1.778E-02 1.247E-02 1.379E-02 9.840E-02 5.059E-02 2.839E-02 d -3.195E-03 8.673E-02 1.387E-01 4.562E-01 7.111E-02 8.089E-02 3.492E-01 regr. 1.167E-01 2.173E-02 1.525E-02 1.491E-02 1.684E-01 8.634E-02 4.494E-02 e 3.905E-02 1.111E-01 2.317E-01 4.341E-01 1.025E-01 1.391E-01 3.882E-01 regr. 8.257E-02 1.538E-02 1.093E-02 7.816E-03 9.756E-02 4.989E-02 2.094E-02 f 6.101E-02 2.952E-01 3.470E-01 6.216E-01 1.800E-01 2.555E-01 2.430E-01 regr. 5.595E-02 1.042E-02 7.312E-03 7.153E-03 4.549E-02 2.370E-02 5.505E-03 To determine the extinction characteristics in the same annular regions of the flame as studied in the scattering experiments, the linear regression data were combined and smoothed. In comparing the geometries shown in Figure B-1 and Figure B-2 it is seen that K ext,2 through K ext,5 are predicted by the value given by the linear regression for that region, as well as a weighted average of the values predicted from the regions which overlap the region of interest from the opposite geometry. Figure B-3 shows this smoothing formula graphically for determining the extinction coefficient of region 2. The fractions of overlap were calculated from the area of each region. K ext,3 K ext,4 and K ext,5 were calculated using the same technique. The extinction coefficients for regions 1 and 6 were assumed to be those predicted from the linear regression, namely K ext,1 = K ext,A and K ext,6 = K ext,D Table B-5 and Table B-6 summarize these smoothed results.

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118 Figure B-3. Example of smoothing algorithm used to determine extinction coefficients from linear regression results. Example shows the extraction of K ext,2 from K ext,E K ext,A and K ext,B Table B-5. Unseeded extinction coefficients determined using linear regression and a smoothing technique. Unseeded K ext (cm -1 ) Smoothed Linear Regression Radial Position Height 1 2 3 4 5 6 b 1.872E-01 4.777E-02 2.713E-02 2.615E-02 4.949E-02 9.541E-02 smoothed 2.362E-02 1.950E-02 1.200E-02 1.545E-02 2.392E-02 2.577E-03 c 5.080E-02 1.186E-02 1.621E-02 3.805E-02 9.959E-02 2.171E-01 smoothed 1.270E-01 3.347E-02 1.475E-02 2.756E-02 5.331E-02 1.263E-02 d 1.526E-01 4.298E-02 3.080E-02 5.945E-02 1.635E-01 3.598E-01 smoothed 1.248E-01 5.245E-02 1.847E-02 4.593E-02 8.808E-02 1.178E-02 e 1.602E-02 1.304E-01 1.348E-01 1.525E-01 2.538E-01 3.977E-01 smoothed 1.183E-01 5.386E-02 5.033E-02 7.116E-02 1.142E-01 9.687E-03 f 7.097E-02 1.500E-01 1.549E-01 1.641E-01 2.422E-01 3.214E-01 smoothed 5.596E-02 3.341E-02 5.650E-02 6.728E-02 1.058E-01 2.844E-03

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119 Table B-6. Seeded extinction coefficients determined using linear regression and a smoothing technique Seeded K ext (cm -1 ) Smoothed Linear Regression Radial Position Height 1 2 3 4 5 6 b 3.822E-02 2.302E-02 4.535E-03 -4.758E-05 3.356E-02 1.515E-01 smoothed 7.829E-02 2.604E-02 1.056E-02 1.407E-02 3.078E-02 1.189E-02 c 1.372E-01 4.067E-02 2.233E-02 3.272E-02 1.083E-01 3.165E-01 smoothed 9.540E-02 5.011E-02 1.280E-02 3.389E-02 6.647E-02 1.379E-02 d -3.195E-03 7.393E-02 8.218E-02 9.941E-02 2.010E-01 4.562E-01 smoothed 1.167E-01 8.501E-02 3.139E-02 6.242E-02 1.043E-01 1.491E-02 e 3.905E-02 1.028E-01 1.190E-01 1.613E-01 2.823E-01 4.341E-01 smoothed 8.257E-02 4.947E-02 5.001E-02 7.711E-02 1.236E-01 7.816E-03 f 6.101E-02 2.246E-01 2.628E-01 2.909E-01 3.464E-01 6.216E-01 smoothed 5.595E-02 2.342E-02 9.044E-02 1.203E-01 1.249E-01 7.153E-03 The use of a linear regression algorithm with a smoothing operation was novel, and produced satisfactory results, however, unrealistic negative values for K ext appeared in the seeded results at height b, position 4 and height d, position 1. Overall, the extinction coefficients agreed with those extracted using the onion peeling method, while the median error in these values decreased by approximately one half. The drawback of this method however is the use of the smoothing technique. There are many ways to overlay the data from the two geometries and different interpretations of the most effective smoothing algorithm exist. The three-point Abel inversion scheme proved the most effective deconvolution technique providing realistic extinction coefficient values with the lowest median error. The flame geometry used for this study is shown in Figure B-4

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120 Figure B-4. Flame geometry used for three-point Abel inversion. Dasch 40 provides a succinct description of the three-point Abel inversion scheme, while McNesby et al 39 provide a nice example of using a three-point Abel inversion with experimental data. In general, deconvolution techniques yield the distribution of the parameter of interest throughout the field by the following F(r i ) = 1 x D ij P(x j ) j = 0 # $ (B-5) where F(r i ) is the field distribution, P(x j ) is the projection data, and x is the spacing between projection data measurements. The indices j and i represent the projected and backprojected coordinates, respectively. D ij is a linear operator that acts on the projection data, and is specific to the type of deconvolution performed. Its coefficients are weighing factors on the projection data. For the case of determining the extinction coefficients illustrated in Figure B-4 the field distribution F(r i ) is the value of K ext in the six annular regions, and the projection data P(x j ) is the product of the extinction coefficient through

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121 the entire region and the optical pathlength through the flame. Thus from the BeerLambert law, P(x j ) may be interpreted as K ext,j L = -ln( j ), where L is twice the sum of the pathlengths l x,y depicted in Figure B-4 The spacing x is a constant value of 0.635 mm, thus Eq. B-5 becomes K ext, i = 1 x D ij ( # ln( $ j )) j = 1 6 % (B-6) The value of D ij varies depending on the deconvolution method used. For the three-point Abel inversion, D ij is expressed as D ij = 0 j < i 1 I i, j + 1 ( 0) I i, j + 1 (1) j = i 1 I i, j + 1 ( 0) I i, j + 1 (1) + 2I ij (1) j = i I i, j + 1 ( 0) I i, j + 1 (1) + 2I ij (1) I i j 1 (0) I i, j 1 ( 1) j # i + 1 I i, j + 1 ( 0) I i, j + 1 (1) + 2I ij (1) 2I i j 1 (1) i = 0, j = 1 $ % & & & & & & (B-7) where the functions I ij (0) and I ij (1) are given by I ij (0) = 0 j = i = 0 or j < i 1 2 ln [(2j + 1) 2 # 4i 2 ] 1 2 + 2j + 1 2j $ % & ( ) j = i 0 1 2 ln [(2j + 1) 2 # 4i 2 ] 1 2 + 2j + 1 [(2j # 1) 2 # 4i 2 ] 1 2 + 2j # 1 $ % & ( ) j > i + (B-8) and I ij (1) = 0 j < i 1 2 [( 2j + 1) 2 # 4i 2 ] 1 2 # 2jI ij (0) j = i 1 2 [(2j + 1) 2 # 4i 2 ] 1 2 # [( 2j # 1) 2 # 4i 2 ] 1 2 { } # 2jI ij (0) j > i $ % & & & & (B-9)

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122 Note that the expression for I ij (1) was reported incorrectly in Daschs work. In his summary, the j = i and j > i expressions were reported as + 2j I ij (0), while the correct form is 2j I ij (0). For this transmission study, six radial sections and six line of sight positions were used. Thus, the deconvolution operator D ij for this case was determined to be D ij = 0.525 0.293 0.101 0.039 0.021 0.013 0.104 0.207 0.165 0.049 0.023 0.014 0 0.074 0.154 0.113 0.035 0.018 0 0 0.061 0.129 0.091 0.029 0 0 0 0.053 0.113 0.078 0 0 0 0 0.047 0.101 # $ % % % % % % % & ( ( ( ( ( ( ( The coefficients of the D ij operator are independent of the data spacing, thus once this parameter has been determined, it need not be recalculated. The standard deviation in the deconvolved parameter may be determined by F ( r i ) = P ( x j ) # x D ij 2 j = 0 $ % & ( ) + 1 2 (B-10) where P(xj) for the transmission study was the standard deviation in the quantity ln( j ) and F(ri) was the standard deviation in K ext,i With the deconvolution operator determined, the extinction coefficient and its error may be determined from Eq. B-6 and Eq. B-10 The results of this analysis are shown in Table B-7 and Table B-8

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123 Table B-7. Unseeded extinction coefficients determined using a three-point Abel inversion. Unseeded K ext (cm -1 ) Three-Point Abel Inversion Radial Position Height 1 2 3 4 5 6 b 1.126E-01 3.574E-02 2.908E-02 4.086E-02 5.151E-02 9.783E-02 Abel 6.754E-02 3.928E-02 2.795E-02 2.724E-02 1.889E-02 1.855E-02 c 5.003E-02 5.546E-03 4.837E-02 6.601E-02 1.281E-01 2.420E-01 Abel 5.742E-02 2.906E-02 3.891E-02 2.161E-02 2.904E-02 1.814E-02 d 1.113E-01 4.769E-02 6.891E-02 1.169E-01 2.202E-01 4.221E-01 Abel 1.079E-01 5.731E-02 3.974E-02 2.730E-02 4.946E-02 2.700E-02 e 9.044E-02 1.855E-01 1.668E-01 2.285E-01 3.100E-01 5.462E-01 Abel 7.600E-02 6.425E-02 7.591E-02 6.487E-02 6.300E-02 5.070E-02 f 1.930E-01 2.373E-01 2.592E-01 2.940E-01 3.973E-01 7.099E-01 Abel 7.527E-01 2.198E-01 1.730E-01 1.707E-01 1.184E-01 1.525E-01 Table B-8. Seeded extinction coefficients determined using a three-point Abel inversion. Seeded K ext (cm -1 ) Three-Point Abel Inversion Radial Position Height 1 2 3 4 5 6 b 1.825E-02 2.799E-02 3.357E-03 1.047E-02 4.993E-02 1.074E-01 Abel 1.356E-01 3.573E-02 3.443E-02 2.156E-02 3.275E-02 1.116E-02 c 8.781E-02 2.726E-02 4.017E-02 5.760E-02 1.278E-01 2.418E-01 Abel 1.561E-01 2.296E-02 4.467E-02 3.335E-02 4.214E-02 1.094E-02 d 4.238E-02 8.877E-02 9.598E-02 1.565E-01 1.963E-01 3.960E-01 Abel 1.159E-01 6.679E-02 4.634E-02 4.417E-02 2.469E-02 3.176E-02 e 8.668E-02 1.449E-01 1.484E-01 2.318E-01 3.221E-01 5.223E-01 Abel 2.379E-01 8.520E-02 5.443E-02 7.459E-02 4.601E-02 5.456E-02 f 1.738E-01 2.907E-01 3.050E-01 3.516E-01 4.081E-01 5.703E-01 Abel 2.380E-01 1.401E-01 7.486E-02 1.132E-01 1.025E-01 5.990E-03 As seen in Table B-7 and Table B-8, the three-point Abel inversion provided extinction coefficient values for each height and radial position studied with no negative values. Further, the overall error in the deconvolution was less than that produced with the onion peeling and linear regression methods. The three-point Abel inversion was favored for its relative ease in computation and for its low error.

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124 APPENDIX C ERROR ANALYSIS A complete error analysis was performed for all data at each height and radial position. For illustrative purposes, the propagation of error through unseeded height d, position 4 is shown in this Appendix. The shorthand notation d4 will refer to this location throughout this analysis. From the light scattering study, the average K' VV calculated over all experiments (N=10) for location d4 was 2.40E-3 cm -1 sr -1 The standard deviation in these calculated values was 2.98E-4 cm -1 sr -1 or 12.4%. Similarly, from the transmission study, the average transmission (N=5) for this location was determined to be 0.855 with a standard deviation of 0.009, or 1.0%. From these two values, the particle diameter, number density, and volume fraction were determined, and all error in these calculated values resulted in a propagation of these initial standard deviations. Table C-1 summarizes these key values. Table C-1. Error in K' VV and at unseeded height d, position 4. Parameter Value Standard Deviation Percent Error (%) K' VV (cm -1 sr -1 ) 2.40E-3 2.98E-4 12.4 0.855 0.009 1.0 The first step in determining the characteristics of the soot particles was to determine the extinction coefficient K ext A three-point Abel inversion was used to deconvolved the transmission data and provide the K ext values throughout the flame field. The error in the deconvolved K ext at height d, position 4 is given by

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125 K ext d 4 = 1 # d 4 # d 4 $ x D 4 j 2 j = 1 6 % & ( ) + 1 2 (C-1) where x = 0.635 mm and is the spacing between transmission measurements, and D 4j is a linear operator used in the inversion scheme. The details of this scheme are given in Appendix B From the three-point Abel inversion results and Eq. C-1 the extinction coefficient and standard deviation for location d4 was determined to be K ext,d4 =0.117 cm -1 Kext,d4 =0.027 cm -1 In general, for a function x=f(a, b, y, z), the standard deviation in x, x is determined from the propagation of the errors of a through z. Namely, x = # x # a $ % & ( ) 2 a 2 + # x # b $ % & ( ) 2 b 2 + K + # x # y $ % & ( ) 2 y 2 + # x # z $ % & ( ) 2 z 2 (C-2) Thus, the standard deviation in the calculation of K' VV /K ext is determined from K' vv / K ext = 1 K ext # $ % & ( 2 K' VV ( ) 2 + ) K VV (K ext ) 2 # $ % & ( 2 K ext ( ) 2 (C-3) With the value of K ext in hand, the ratio of K' VV /K ext and its error may be determined. Thus, for location d4, K' VV K ext d 4 =2.05E-2 sr -1 K vv / K ext d 4 =5.43E-3 sr -1 The modal particle diameters were determined from a plot of Mie theory diameter versus K' VV /K ext A seventh order curve fit allowed the modal diameters to be determined from K' VV /K ext This curve fit was of the form x = M 0 + M 1 y + M 2 y 2 + + M n-1 y n-1 + M n y n (C-4) where n is the order of the fit. For the seventh order fit for the modal diameter calculations, the parameters M 0 through M 7 are given in Table C-2

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126 Table C-2. Curve fit parameters for Mie modal diameters. M 0 1.181E+01 M 1 1.245E+04 M 2 -2.094E+06 M 3 2.159E+08 M 4 -1.220E+10 M 5 3.782E+11 M 6 -6.030E+12 M 7 3.865E+13 From these parameters, the error propagated to the diameters from the error in K' VV /K ext was determined from d = M 1 + 2M 2 R + 3M 3 R 2 + 4M 4 R 3 + 5M 5 R 4 + 6M 6 R 5 + 7M 7 R 6 ( ) 2 K VV / K ext ( ) 2 (C-5) where R denotes the ratio K' VV /K ext For location d4, the modal diameter and error were determined to be d d4 =73.24 nm, d,d4 =8.09 nm. Similar to the diameter calculation, a curve fit of C ext versus K' VV /K ext gave the extinction cross section at each height and radial position. To best fit the Mie data, the plot of C ext versus K' VV /K ext was divided into three sections and each was fit with a polynomial curve. The curve fit parameters were of the same form of Eq. C-4 The coefficients for the fits are shown in Table C-3 Table C-3. Curve fit parameters for C ext K' VV /K ext < 3.0E-2 3.0E-2 K' VV /K ext 4.0E-2 K' VV /K ext > 4.0E-2 M 1 2.320E-14 M 1 9.173E-10 M 1 5.405E-06 M 2 3.461E-10 M 2 -1.210E-07 M 2 -4.931E-04 M 3 2.590E-08 M 3 6.054E-06 M 3 7.786E-03 M 4 -6.661E-07 M 4 -1.341E-04 M 4 5.473E-01 M 5 -2.166E+01 M 6 1.516E+02 M 7 1.615E+03 M 8 7.523E+04 M 9 -2.670E+06

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127 At location d4, the K' VV /K ext ratio of 6.76E-3 fell into the K' VV /K ext < 3.0E-2 curve fit range. Hence, the error in C ext was determined from C ext = M 1 + 2M 2 R + 3M 3 R 2 + 4M 4 R 3 ( ) 2 K VV / K ext ( ) 2 (C-6) Summarizing these results for location d4, the extinction cross section was determined as C ext,d4 =1.75E-11 cm -2 Cext,d4 =8.56E-12 cm -2 The particle number density was determined from the relationship between the extinction coefficient K ext and the extinction cross section C ext Namely, N= K ext /C ext The error in this calculation was determined from N = 1 C ext # $ % & ( 2 K ext ( ) 2 + ) K ext ( C ext ) 2 # $ % & ( 2 C ext ( ) 2 (C-7) Using the values for K ext and C ext listed above, the number density for location d4 was N d4 =6.70E9 cm -3 N,d4 =3.64E9 cm -3 Lastly, the particle volume fraction was calculated with knowledge of the ZOLD skewness factor o For this work, a o value of 0.2 was used. Thus the volume fraction was determined from f v = 6 Nd 3 exp 15 2 # o $ % & ( ) (C-8) and the error in this value was found from f v = # 2 Nd 2 exp 15 2 o $ % & ( ) + / 2 d ( ) 2 + # 6 d 3 exp 15 2 o $ % & ( ) + / 2 N ( ) 2 (C-9) With these functions in hand, the volume fraction of particles at location d4 was determined to be f v,d4 =1.86E-6 cm 3 /cm 3 fv,d4 =1.18E-6 cm 3 /cm 3

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128 Table C-4 summarizes the experimental data and calculated parameters for location d4, along with the propagated error and the percent error for each value. Table C-4. Summary of experimental data and calculated parameters at height d, position 4 with error. Parameter Value Standard Deviation Percent Error (%) K' VV (cm -1 sr -1 ) 2.40E-3 2.98E-4 12.4 0.855 0.009 1.0 K ext (cm -1 ) 0.117 0.027 23.4 K' VV /K ext (sr -1 ) 2.05E-2 5.43E-3 26.5 d (nm) 73.24 8.09 11.0 C ext (cm -2 ) 1.75E-11 8.56E-12 48.9 N (cm -3 ) 6.70E9 3.64E9 54.3 f v (cm 3 /cm 3 ) 1.86E-6 1.18E-6 63.4 As Table C-4 demonstrates, a low error in the initial experimental values of K' VV and can still translate into large errors in the calculated parameters. Thus it is important to minimize the error in the experimental measurements as much as possible. The error in particle size, number density, and particle volume fraction for the complete flame field at all heights and radial positions was calculated using the same methods outlined above. These results are summarized in the following tables, while the error for K' VV K ext and K' VV /K ext may be found in the text of Chapter 4

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129Table C-5.Unseeded particle diameters with error. Unseeded diameter (nm) Radial Position Verticalposition 1 2 3 4 5 6 b 22.89 40.76 47.95 67.33 67.20 49.74 "d 7.15 16.76 16.50 21.36 11.77 3.74 c 45.94 N/A* 55.94 81.18 67.45 50.13 "d 16.91 N/A 20.86 16.84 9.32 3.90 d 46.29 68.35 73.01 73.24 59.58 45.56 "d 16.12 38.83 18.30 8.09 7.79 2.68 e 66.35 50.58 59.60 60.44 55.06 43.70 "d 27.67 8.38 13.83 9.06 6.20 2.79 f 49.65 47.31 48.53 48.38 43.29 35.39 "d 67.04 14.23 11.22 9.70 4.37 3.57 Value out of monotonic region. See Chapter 4 for more detail.Table C-6.Seeded particle diameters with error. Seeded diameter (nm) Radial Position Verticalposition 1 2 3 4 5 6 b 54.74 52.06 N/A* N/A* 70.00 48.20 "d 172.46 28.92 N/A N/A 21.37 4.29 c 41.82 75.38 107.21 95.18 67.63 49.84 "d 24.86 28.89 101.43 42.42 10.59 3.03 d 75.26 60.82 70.08 69.49 66.40 46.44 "d 87.09 23.30 18.49 9.28 5.97 2.98 e 58.15 54.94 66.33 62.35 54.80 44.60 "d 74.06 15.08 13.44 10.63 4.44 2.85 f 55.19 46.28 47.59 46.98 45.05 39.27 "d 32.49 7.11 4.42 5.55 3.82 1.74 Value out of monotonic region. See Chapter 4 for more detail.

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130Table C-7.Unseeded particle number densities with error. Unseeded number density (cm-3) Radial Position Verticalposition 1 2 3 4 5 6 b 2.69E+11 1.74E+10 7.42E+09 3.28E+09 4.17E+09 2.16E+10 "N 2.66E+11 3.23E+10 1.25E+10 4.34E+09 3.03E+09 7.43E+09 c 1.52E+10 N/A* 7.09E+09 2.38E+09 1.02E+10 5.19E+10 "N 2.88E+10 N/A 1.03E+10 2.21E+09 5.61E+09 1.57E+10 d 3.27E+10 3.62E+09 4.01E+09 6.70E+09 2.64E+10 1.33E+11 "N 5.65E+10 8.83E+09 5.00E+09 3.64E+09 1.24E+10 3.32E+10 e 7.65E+09 3.85E+10 2.00E+10 2.62E+10 4.79E+10 2.03E+11 "N 1.29E+10 2.72E+10 1.72E+10 1.45E+10 2.02E+10 5.54E+10 f 4.29E+10 6.38E+10 6.30E+10 7.23E+10 1.53E+11 5.49E+11 "N 2.78E+11 9.77E+10 7.12E+10 7.12E+10 7.67E+10 2.02E+11 Value out of monotonic region. See Chapter 4 for more detail.Table C-8. Seeded particle number densities with error. Seeded number density (cm-3) Radial Position Verticalposition 1 2 3 4 5 6 b 2.87E+09 5.23E+09 N/A* N/A* 3.46E+09 2.68E+10 "N 3.67E+10 1.23E+10 N/A N/A 4.77E+09 9.90E+09 c 3.88E+10 1.37E+09 4.60E+08 1.14E+09 1.01E+10 5.30E+10 "N 1.11E+11 2.69E+09 2.33E+09 2.06E+09 6.65E+09 1.25E+10 d 2.15E+09 9.99E+09 6.63E+09 1.12E+10 1.66E+10 1.15E+11 "N 1.29E+10 1.42E+10 7.66E+09 6.61E+09 5.62E+09 3.16E+10 e 1.12E+10 2.25E+10 1.26E+10 2.41E+10 5.05E+10 1.79E+11 "N 5.47E+10 2.43E+10 1.00E+10 1.53E+10 1.53E+10 5.01E+10 f 2.66E+10 8.56E+10 8.02E+10 9.74E+10 1.34E+11 3.16E+11 "N 6.29E+10 6.79E+10 3.59E+10 5.64E+10 5.75E+10 4.84E+10 Value out of monotonic region. See Chapter 4 for more detail.

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131Table C-9. Unseeded particle volume fractions with error. Unseeded volume fractions (cm3/ cm3) Radial Position Verticalposition 1 2 3 4 5 6 b 2.28E-06 8.32E-07 5.78E-07 7.08E-07 8.94E-07 1.88E-06 "N 3.11E-06 1.86E-06 1.14E-06 1.15E-06 8.02E-07 7.73E-07 c 1.04E-06 N/A* 8.78E-07 9.00E-07 2.22E-06 4.62E-06 "N 2.29E-06 N/A 1.61E-06 1.01E-06 1.53E-06 1.76E-06 d 2.30E-06 8.18E-07 1.10E-06 1.86E-06 3.95E-06 8.86E-06 "N 4.63E-06 2.43E-06 1.60E-06 1.18E-06 2.42E-06 2.71E-06 e 1.58E-06 3.52E-06 2.99E-06 4.10E-06 5.65E-06 1.20E-05 "N 3.31E-06 3.04E-06 3.31E-06 2.91E-06 3.05E-06 3.99E-06 f 3.71E-06 4.78E-06 5.09E-06 5.79E-06 8.80E-06 1.72E-05 "N 2.83E-05 8.49E-06 6.75E-06 6.68E-06 5.14E-06 8.19E-06 Value out of monotonic region. See Chapter 4 for more detail.Table C-10. Seeded particle volume fractions with error. Seeded volume fractions (cm3/ cm3) Radial Position Verticalposition 1 2 3 4 5 6 b 3.33E-07 5.22E-07 N/A* N/A* 8.40E-07 2.12E-06 "N 5.30E-06 1.50E-06 N/A N/A 1.39E-06 9.67E-07 c 2.01E-06 4.15E-07 4.00E-07 6.96E-07 2.21E-06 4.64E-06 "N 6.78E-06 9.43E-07 2.32E-06 1.56E-06 1.79E-06 1.38E-06 d 6.47E-07 1.59E-06 1.61E-06 2.65E-06 3.43E-06 8.14E-06 "N 4.48E-06 2.91E-06 2.26E-06 1.89E-06 1.49E-06 2.73E-06 e 1.56E-06 2.64E-06 2.59E-06 4.13E-06 5.88E-06 1.12E-05 "N 9.66E-06 3.58E-06 2.60E-06 3.37E-06 2.28E-06 3.81E-06 f 3.17E-06 6.00E-06 6.11E-06 7.14E-06 8.67E-06 1.35E-05 "N 9.34E-06 5.50E-06 3.22E-06 4.84E-06 4.32E-06 2.75E-06 Value out of monotonic region. See Chapter 4 for more detail.

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133 11. Miller, J. A., and Melius, C. F. Kinetic and Thermodynamic Issues in theFormation of Aromatic-Compounds in Flames of Aliphatic Fuels. Combust.Flame, 91(1):21-39 (1992). 12. Prado, G., and Lahaye, J. Physical Aspects of Nucleation and Growth of SootParticles. Particulate Carbon (Siegla, D. C., and Smith, G. W. (eds.)). PlenumPress, New York, 143 (1981). 13. Harris, S. J., and Weiner, A. M. Surface Growth of Soot Particles in PremixedEthylene/Air Flame. Combust. Sci. Tech., 31:155-167 (1983). 14. Harris, S. J., and Weiner, A. M. Determination of the Rate Constant for SootSurface Growth. Combust. Sci. Tech., 32:267-275 (1983). 15. Haynes, B. S., Jander, H., and Wagner, H. Gg. The Effect of Metal Additives onthe Formation of Soot in Premixed Flames. 17th Symp. (Int.) Combust., 1365-1373, The Combustion Institute, Pittsburgh (1979). 16. Dasch, C. J. The Decay of Soot Surface Growth Reactivity and Its Importance inTotal Soot Formation. Combust. Flame, 61(3):219-225 (1985). 17. Warnatz, J., Mass, U., and Dibble, R. W. Combustion Physical and ChemicalFundamentals, Modeling and Simulation, Experiments, Pollutant Formation, 3rded. Springer-Verlag, Berlin (2001). 18. Bockhorn, H. (ed.). Soot Formation in Combustion: Mechanisms and Models.Springer-Verlag, Berlin (1994). 19. Turns, S. R. An Introduction to Combustion, 2nd ed. McGraw Hill, Boston (2000). 20. Ritrievi, K. E., Longwell, J. P., and Sarofim, A. F. The Effects of FerroceneAddition on Soot Particle Inception and Growth in Premixed Ethylene Flames.Combust. Flame, 70(1):17-31 (1987). 21. Haynes, B. S., Jander, H., and Wagner, H. Gg. Optical Studies of Soot-FormationProcesses in Premixed Flames. Ber. Bunsen. Phys. Chem., 84(6):585-592 (1980). 22. Feitelberg, A.S., Longwell, J.P., and Sarofim, A.F. Metal Enhanced Soot and PAHFormation. Combust. Flame, 92(3):241-253 (1993). 23. Hahn, D. W. Soot Suppressing Mechanisms of Iron in Premixed HydrocarbonFlames. Ph.D. dissertation. Department of Mechanical Engineering, LouisianaState University, Baton Rouge (1992). 24. Cotton, D. H., Friswell, N. J., and Jenkins, D. R. Suppression of Soot EmissionFrom Flames by Metal Additives. Combust. Flame, 17(1):87-98 (1971).

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135 39. McNesby, K. L., Daniel, R. G., Morris, J. B., and Miziolek, A. W. TomographicAnalysis of CO Absorption in a Low-Pressure Flame. Appl. Opt., 34(18):3318-3324 (1995). 40. Dasch, C. J. One-Dimensional Tomography A Comparison of Abel, Onion-Peeling, and Filtered Backprojection Methods. Combust. Flame, 31(8):1146-1152(1992). 41. Chippett, S., and Gray, W. A. The Size and Optical Properties of Soot Particles.Combust. Flame, 31:149-159 (1978). 42. Charalampopoulos, T. T., and Chang, H. In Situ Properties of Soot Particles in theWavelength Range from 340 nm to 600 nm. Combust. Sci. Tech., 59:401-421(1988). 43. Dalzell, W. H., and Sarofim, A. F. Optical Constants of Soot and TheirApplication to Heat-Flux Calculations. J. Heat Transfer, 91:100-104 (1969). 44. Pluchino, A. B., Goldberg, S. S., Dowling, J. M., and Randall, C. M. Refractive-Index Measurements of Single Micron-Sized Carbon Particles. Appl. Optics,19(19):3370-3372 (1980). 45. Agency for Toxic Substances and Disease Registry (ATSDR). Toxicology Profilefor Jet Fuels JP-5 and JP-8. U. S. Department of Health and Human Services,Public Health Service, Atlanta, GA (1998). 46. Agency for Toxic Substances and Disease Registry (ATSDR). Toxicology Profilefor Jet Fuels JP-4 and JP-7. U. S. Department of Health and Human Services,Public Health Service, Atlanta, GA (1995).

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136 BIOGRAPHICAL SKETCH Kathryn Allida Masiello was born, at home, in Oak Ridge, Tennessee in 1978, the third child of Earl and Nancy McDow. In 1985, she and her family moved to Florida, spending 4 years in Orange Park, and eventually settling in Gainesville. Kathryn attended the University of Florida as an undergraduate, and in 2001, she earned a Bachelor of Science degree in mechanical engineering, with highest honors. After marrying her college sweetheart, David, and a brief stint working as a process engineer at an environmental engineering firm, Kathryn returned to the University of Florida in 2002 to pursue a Master of Science in mechanical engineering under the advisement of Prof. David Hahn. This thesis is the culmination of the research conducted for this effort.




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Title: Study of Soot Formation in an Iron-Seeded Isooctane Diffusion Flame Using In Situ Light Scattering
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Copyright Date: 2008

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STUDY OF SOOT FORMATION IN AN IRON-SEEDED ISOOCTANE DIFFUSION
FLAME USING IN SITU LIGHT SCATTERING

















By

KATHRYN ALLIDA MASIELLO


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2004

































Copyright 2004

by

Kathryn Allida Masiello

































Dedicated to my best friend and husband. His encouragement and love have been
invaluable throughout my academic career.















ACKNOWLEDGMENTS

This work would not have been possible without the vision, encouragement, and

guidance of Dr. David Hahn. I am deeply grateful to him for teaching me the ins and

outs of laser based diagnostics, and also for helping me to discover a field that captures

my interest and leaves me filled with curiosity.

I also thank my labmates, Allen Ball, Brian Fisher, Vincent Hohreiter, Kibum Kim,

and Prasoon Diwakar. Allen was responsible for building the vaporization chamber used

in my experiments. Thanks to his efforts, I could begin experimentation right away,

without extensive setup. Brian's role as resident answer man was greatly appreciated; as

too were Vince, Kibum, and Prasoon's insightful conversations and suggestions.

I thank my family for their unending support. My parents, siblings, in-laws, and

husband showed interest in my work, and in the excitement it brought me. And when

things weren't so exciting, or were overly frustrating, my husband was responsible for

keeping me focused on my final goal. I thank him for helping me to reach for my highest

potential.
















TABLE OF CONTENTS
Page

ACKNOWLEDGMENTS ....................... ............. .....................iv

LIST OF TABLES ......... ........... ....... .................... ...........................vii

LIST O F FIG U R E S ....................................... ........................................................ x

A B S T R A C T ............................. ...............................................................................x iii

CHAPTER

1 INTRODUCTION ..................... ... .................................................. 1

Soot Form ation.................. ......... ......................... ..... ..................... 2
Production of Soot Precursor Molecules ............ ........................................... 4
Particle Coagulation and Growth..................... ................................................ 5
Particle Agglom eration...................................... ............ ........ ............ 7
Soot O xidation ....................... ..... ......... ................................ .............. 8
M etallic Fu el A dditives ............................................................. ........................ 11
A dditives in Prem ixed Flam es ........................................ ..................... 12
A dditives in D iffusion Flam es ........................................ ..................... 16
Project Methodology and Motivation............................................... 18

2 ELASTIC LIGHT SCATTERING................................................. ..20

Scattering Theory ...................... .. ... ........ ................ ..................... 20
M ie Theory...................... .......................... ............................. 21
Rayleigh Theory .......................... ................................ .................. 25
System s of Particles.............................. .............. .... .......................... 27
M onodisperse system s of particles ..........................................................27
Polydisperse system s of particles ..................................... ...................... 29
System D diagnostics ............................................ .......................................... 31

3 EXPERIM ENTAL M ETHODS .................................... ........... ........................ 35

Burner ................................... ...... ... .............. ........... ........... 35
Fuel Vaporization and Delivery System..............................................38
D iagnostics............................................. ....................................................... 42




v









Laser Light Scattering ............. ............. ..................... ..................... 42
Photomultiplier tube linearity ....................... .. .. ..................... 45
Calibration......................... ........... ....... ........................ 46
Stray light..................... .. ...... .. .. ......................... .................. 48
Vaporization of Soot........................ ........ ........................................... 52
Transm mission ........................... ................. ......... ..................... 53
M icro-R am an System ............................................. .............................. 55

4 RESULTS AND DATA ANALYSIS ......................................................................59

Elastic Light Scattering Results ...................................... ......... ........................ 59
Transm mission R esults.................................................... ........... ..................... 66
Soot Characteristics Determined from Mie Theory ........................................74
P article Size...................................................................... ................... 76
N um ber D ensity of Particles ................................................... ..................... 83
Particle V olum e Fraction .......................................... ....... ..................... 87
M icro-R am an Spectroscopy................................................................................... 91

5 DISCUSSION AND CONCLUSIONS........................................ 102

Discussion of Results ........................................ 102
C on clu sion s...................................................... ............................................... 106
Future W ork ............................. ................................................... 107

APPENDIX

A COMPOSITION OF COMMON JET FUELS ........................................... 109

B EXTINCTION COEFFICIENT DECONVOLUTION TECHNIQUES ............... 111

C ERR O R A N A LY SIS ............................................................. ..................... 124

LIST O F REFEREN CES.............................................................. ..................... 132

BIOGRAPHICAL SKETCH ........................................................ ..................... 136
















vi
















LIST OF TABLES


Table page

3-1. Concentric diffusion burner dimensions. ........ .................................................36

3-2. Data collection heights and radial positions................................................. 37

3-3. Flame operating conditions. ..................... ........................40

3-4. Average unseeded and seeded flame diameters at each height............................41

3-5. Description of fuel vaporization and delivery system ........................................ 41

3-6. Description of scattering system apparatus. ......................... .......... ........... 44

3-7. Differential scattering coefficient for methane and nitrogen at common incident
wavelengths at 1 atm, 298 K. ........................ ................. .......... ........ ...47

3-8. Methane to nitrogen reference differential scattering coefficient ratio used for
stray light calibration at common incident wavelengths, assuming ideal gases......49

3-9. Number densities, differential scattering cross sections, and scattering coefficients
for methane and nitrogen calibration gases at 1 atm, 344K.................................50

3-10. Average time-integrated calibration gas and stray light signals and range of signals
seen over all scattering experiments. .......................... ....................51

3-11. Description of transmission apparatus. ..................... ......................55

4-1. Average (N= 10) time-integrated scattered signal from unseeded flame. ..............61

4-2. Average (N=6) time-integrated scattered signal from iron pentacarbonyl seeded
flam e........................ ........... .................. ......... ........................ 62

4-3. Average (N= 10) unseeded K'vv results and standard deviation of K'vv............... 63

4-4. Average (N=6) seeded K'vv results and standard deviation of K'vv ................... 63

4-5. Average (N=5) unseeded power measurements used in transmission study..........67

4-6. Average (N=5) seeded power measurements used in transmission study. ............67









4-7. Average (N=5) transmission through the unseeded flame................................... 68

4-8. Average (N=5) transmission through the seeded flame....................................... 68

4-9. Average (N=5) unseeded extinction coefficients determined using a three-point
A b el inv version ................ .......................................................... ..................... 7 1

4-10. Average (N=5) seeded extinction coefficients determined using a three-point
A b el inv version ................ .......................................................... ..................... 7 1

4-11. Unseeded ratio of K'vv/Kext determined from experimental data.......................... 75

4-12. Seeded ratio of K'vv/Kext determined from experimental data............................... 75

4-13. Complex refractive indices for soot from various sources.....................................76

4-14. Unseeded soot particle modal diameters determined from Mie theory and complex
refractive index of = 2.0-0.35i ................................................................... 78

4-15. Seeded soot particle modal diameters determined from Mie theory and complex
refractive index of = 2.0-0.35i ................................................................... 78

4-16. Unseeded soot particle mean diameters. ............... ............. ..................... 82

4-17. Seeded soot particle mean diameters. ............................ .... ..................... 82

4-18. Unseeded soot particle number densities determined from Mie theory and complex
refractive index of = 2.0-0.35i. ...................................................................... 84

4-19. Seeded soot particle number densities determined from Mie theory and complex
refractive index of = 2.0-0.35i. ...................................................................... 84

4-20. Unseeded soot particle volume fractions ....................... .... ...................... 88

4-21. Seeded soot particle volume fractions......... ........................................88

4-22. Bulk iron oxide powder specifications used in micro-Raman study. ................. 92

A-1. Composition of fuel oil no. 1 and JP-5........... ................. ..................... 109

A-2. Composition of surrogate JP-8. ......................................... ...... .................... 109

A-3. Composition of shale-derived and petroleum-derived JP-4.............................. 110

B-1. Unseeded extinction coefficients determined from onion peeling inversion........ 113

B-2. Seeded extinction coefficients determined from onion peeling inversion. ........... 114









B-3. Unseeded extinction coefficients determined from linear regression technique
with two flame geometries. ........................................................... 116

B-4. Seeded extinction coefficients determined from linear regression technique with
tw o flam e geom etries. ....................................................... ..................... 117

B-5. Unseeded extinction coefficients determined using linear regression and a
sm nothing technique. ........................................................ ..................... 118

B-6. Seeded extinction coefficients determined using linear regression and a smoothing
tech n iqu e............................................... ....................................................... 1 19

B-7. Unseeded extinction coefficients determined using a three-point Abel inversion. 123

B-8. Seeded extinction coefficients determined using a three-point Abel inversion. ... 123

C-1. Error in K'vv and r at unseeded height d, position 4. ......................................... 124

C-2. Curve fit parameters for Mie diameters. ...................................................... 126

C-3. Curve fit param eters for Cext......................................................................... 126

C-4. Summary of experimental data and calculated parameters at height d, position 4
w ith error. ........................................... ................................................... 128

C-5. Unseeded particle diameters with error........................................................... 129

C-6. Seeded particle diameters with error ............................................................. 129

C-7. Unseeded particle number densities with error. ...................... ..................... 130

C-8. Seeded particle number densities with error..................... ............... ... 130

C-9. Unseeded particle volume fractions with error ................................................. 131

C-10. Seeded particle volume fractions with error ....................................................... 131
















LIST OF FIGURES


Figure pge

1-1. Transmission Electron Microscope (TEM) images of propane soot....................3

1-2. The H2-abstraction-C2H2-addition mechanism acting on a biphenyl molecule. .......6

1-3. Particle coagulation versus particle agglomeration. .......................................

1-4. Soot formation process showing stages of formation on molecular and particulate
scales. ............................................ ..... ...... .... ..................... 9

1-5. Soot formation regimes in a diffusion flame, and radial soot concentration profile
at an arbitrary flam e height ............................................................................ ... 10

1-6. Chem ical structure of isooctane...................................................................... 19

2-1. Light scattering response to an incident electromagnetic light beam ...................21

2-2. Polar coordinate geometry for light scattering. ............................... .......... 21

2-3. K'vv/Kext versus modal particle diameter for a specific polydisperse system........32

2-4. Diagnostic techniques for determining scattering and extinction coefficients for
a system containing varied properties ..................................... ..................... 33

3-1. Concentric diffusion burner schematic ................................. .... .............. ....... 35

3-2. Data measurement heights and radii relative to the flame. .................................... 37

3-3. Fuel vaporization system ............................................................................... 38

3-4. Alicat Scientific digital flow meters used for nitrogen coflow and oxygen............ 40

3-5. Light scattering system setup.......................................................................... 42

3-6. Sample scattering signals from methane, nitrogen, and flame ..........................50

3-7. Transm mission system setup. ................................................. ...... ........................ 54

3-8. Region of iron deposits on flame holder screen. ........................................ 56









3-9. Confocal micro-Raman schematic.................... .......................................... 56

4-1. Typical scattered signal response from photomultiplier tube measuring calibration
gases and flame signal at a fixed height and radial position .............................. 60

4-2. Baseline-subtracted scattered signals from calibration gases and flame at a fixed
height and radial position. ......... ..... ................................. ................ ....... 61

4-3. Seeded and unseeded differential scattering coefficients......................... ............. 64

4-4. Seeded and unseeded extinction coefficients determined using a three-point Abel
inversion .............................................. ............................................... . 72

4-5. Soot particle modal diameters determined from Mie theory for m = 2.0-0.35i
and ZOLD parameter 0o = 0.2 ............... ........... ....... 77

4-6. Unseeded and seeded soot particle modal diameters ............................................79

4-7. Extinction cross section of soot particles determined from Mie theory for m =
2.0-0.35i and ZOLD parameter = 0.2. ......................................... .............. 83

4-8. Unseeded and seeded particle number densities......................... .................... 85

4-9. Unseeded and seeded soot particle volume fractions.......................................... 89

4-10. FeO reference Ram an spectra ..................................... ............... ..................... 92

4-11. Fe203 reference Raman spectra. ............................................................... .....93

4-12. Fe304 reference Ram an spectra. .........................................................................93

4-13. Graphite reference Raman spectra. ..................... ........................................... 94

4-14. Carbon black reference Raman spectra.......................................................... 94

4-15. Reference Raman spectra of clean, unburned flame holder screen......................95

4-16. Raman spectra of seeded flame holder screen and Fe203 reference.................... 96

4-17. Raman spectra of mixed bulk powders of FeO and Fe203................................ 97

4-18. Raman spectra of two seeded flame holder screens......... .............................. 98

4-19. Raman spectra of unseeded flame holder........................................................99

4-20. Raman spectra of seeded and unseeded screens taken at center of flame
holders. .............................................. ........ ...................... 100









5-1. Soot volume through the growth regime (annular regions 3, 4, and 5) of the
flam e ........................ .. ... ... ......................... .............. .......... 104

B-1. Geometry used for onion peeling inversion scheme......................................... 112

B-2. Geometries used for linear regression inversion scheme................................... 115

B-3. Example of smoothing algorithm used to determine extinction coefficients from
linear regression results. ............................................................ 118

B-4. Flame geometry used for three-point Abel inversion. ....................................... 120















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

STUDY OF SOOT FORMATION IN AN IRON-SEEDED ISOOCTANE DIFFUSION
FLAME USING IN SITU LIGHT SCATTERING

By

Kathryn Allida Masiello

May 2004

Chair: David W. Hahn
Major Department: Mechanical and Aerospace Engineering

Elastic light scattering and transmission measurements were performed on a

laboratory isooctane diffusion flame seeded with 4000 ppm iron pentacarbonyl. These

measurements allowed the determination of the size, number density, and volume

fraction of soot particles in the seeded flame. Comparison to an unseeded flame allowed

the determination of the effects of the metallic additive on soot particle inception, growth,

and oxidation. It was shown that while the additive may have had a slight soot-enhancing

effect at early residence times, the growth of the soot particles was unaffected by the

addition of iron to the flame. The greatest effect of the additive on soot perturbation is

concluded to occur in the oxidation regime of the flame. In addition, confocal micro-

Raman spectroscopy performed on the stainless steel mesh flame holders of the seeded

and unseeded flames showed that the state of the iron present was the oxide Fe203.














CHAPTER 1
INTRODUCTION

Small particles in the air ranging in size from a few nanometers to tens of microns

are described as particulate matter (PM). In 1997, the Environmental Protection Agency1

established National Ambient Air Quality Standards (NAAQS) for PM less than 2.5 [im

(PM2.5) and revised the existing NAAQS for PM less than 10 [im (PM10). Particulate

matter less than 2.5 pm is increasingly under study. The largest of this class of particles is

approximately 1/30 the diameter of a human hair. Because of the small size of these

particles, they are able to permeate and impact the deepest parts of the lungs. Increased

incidences of asthma, chronic bronchitis, shortness of breath, painful breathing, and

increased respiratory and heart disease have all been linked to PM2.5.2 Children and the

elderly are at greatest risk from PM2.5 inhalation. Often the immune systems of the

elderly are weaker because of age, or they suffer from existing cardiopulmonary diseases.

Children are at risk because their respiratory and immune systems are not yet fully

developed. An average adult breathes 13,000 liters of air per day, while children can

breathe up to 50% more air per pound of body weight than adults. Asthma in children is

a common result of PM exposure. It is estimated that although children make up only

one quarter of the population, 40% of asthma cases appear in this group.1 Soot particles,

rich in amorphous carbon and polycyclic aromatic hydrocarbons (PAHs), are a specific

type of PM that are known to be mutagenic and carcinogenic.3'4

Particulate matter has significant environmental effects as well. PM is the leading

cause of reduced visibility or haze in the United States. In particular areas across the

1









U. S., visibility has been reduced from natural conditions by as much as 70%.1 In

addition, PM from combustion processes includes sulfates and nitrogen oxides, which are

responsible for acid rain, and greenhouse gases, responsible for global warming.2

Further, as PM2.5 settles on soil and water, the nutrient and chemical balances of the

ecosystem are disturbed. Water systems can become more acidic, threatening aquatic

species, and soil nutrients are depleted, damaging sensitive crops and forests. Because of

their small size, PM2.5 particles are able to travel long distances; thus their

environmental and health impacts are felt hundreds of miles away from the source.2

Because soot from combustion processes is a major source of PM, there has been

significant interest in the formation of soot and methods of soot reduction.

Reduction of soot would clearly improve the health of individuals exposed to PM.

For example, ground crews on aircraft carriers are constantly exposed to high levels of

PM in the effluent of jet engines. During jet takeoff, high fuel consumption is necessary,

and soot emissions are at a maximum. The short- and long-term health effects of this

exposure on ground crew personnel is a serious concern, and a means of reducing soot in

turbine engines is of great interest. A balance must be maintained, however. Reduction

of harmful PM emissions is desirable, but engine performance cannot be compromised.

The process of soot reduction via fuel additives is being explored as a potential means of

reducing harmful combustion byproducts, while having a minimal impact on the

combustion characteristics.

Soot Formation

The oxidation of organic compounds leads to the formation of soot, which can be

described as amorphous molecules containing mostly carbon and hydrogen. The actual









chemical structure is that of a multiple ring polynuclear aromatic compound. Palmer and

Cullis6 described the physical characteristics of soot in detail.

The carbon formed in flames generally contains at least 1% by weight of hydrogen.
On an atomic basis this represents quite a considerable proportion of this element
and corresponds approximately to an empirical formula of CsH. When examined
under an electron microscope, the deposited carbon appears to consist of a number
of roughly spherical particles, strung together rather like pearls on a necklace. The
diameters of these particles vary from 100 to 2000 A and most commonly lie
between 100 and 500 A. The smallest particles are found in luminous but
nonsooting flames, while the largest are obtained in heavily sooting flames (p.
265).

Elementary soot particles exhibit a size distribution well modeled by a log-normal

distribution.7 The average diameter of 100 to 500 A cited by Palmer and Cullis6

corresponds to about one million carbon atoms. X-ray diffraction measurements

performed on soot show randomly dispersed domains of graphite-like parallel layers

within the particle, though the spacing between the layers is larger than that of graphite.

Figure 1-1 shows Transmission Electron Microscope (TEM) images of propane soot at

two magnifications.


Figure 1-1. Transmission Electron Microscope (TEM) images of propane soot. A) at
0.2 itm scale. B) at 100 nm scale.









The process of soot formation can be described by four distinct stages:

1. Production of soot precursor molecules
2. Particle coagulation and growth
3. Particle agglomeration
4. Soot oxidation.

Perturbations in sooting characteristics of a flame are due to changes in the mechanisms

of soot formation. Thus, an understanding of these stages is essential to the study of soot

reduction in flames and combustion systems in general.

Production of Soot Precursor Molecules

In the first stage of soot formation, soot precursor molecules are formed. These

molecules act as nucleation sites for the formation of soot. It is widely believed that this

stage is the rate-limiting step in the formation of soot. A number of mechanisms have

been suggested to describe the formation of these nucleation sites. In general, all of these

mechanisms involve small aliphatic (open chained) compounds that form the first

aromatic rings, typically benzene, C6H6. Acetylene, C2H2, is abundant in the early stages

of combustion, thus it is the most likely aliphatic compound to initiate this process. In

later stages, benzene is thought to lead to the production of more complex PAHs.8 One

proposed mechanism, termed an even-carbon-atom pathway, involves the addition of

acetylene to n-C4H3 and n-C4H5 by

n-C4H3 +C2H2 phenyl (1-1)

n-C4H5 + C2H benzene + H. (1-2)

Kinetic simulations of shock-tube acetylene pyrolysis suggest that the reaction in Eq. 1-1

is significant in forming the first aromatic rings,9 while Bittner and Howardo1 suggested

the reaction in Eq. 1-2 is an important pathway to aromatic ring formation at low

temperatures. Miller and Melius11 countered this even-carbon-atom mechanism,









suggesting that n-C4H3 and n-C4H5 are too short-lived, thus, their concentrations would

be too small to have a significant effect on aromatic ring formation. Instead, they suggest

an odd-carbon-atom pathway involving the combination of more stable propargyl radials,

C3H3 + C 3 ---benzene or phenyl + H. (1-3)

Recent Monte Carlo theoretical studies have, however, predicted the n-C4H3 radical and

n-C4H5 isomer to be more stable than originally suggested, restoring the importance of

the even-carbon-atom pathway described by the reactions in Eqs. 1-1 and 1-2. Yet

another possible mechanism for the initial aromatic ring formation combines the stable

propargyl radical with the abundant acetylene molecule to form a cyclopentadienyl

radical by

C3H3 + C2H2 c-C5H. (1-4)

The cyclopentadienyl radical is then quick to form benzene. A comparison of reaction

rates between Eq. 1-4 and Eq. 1-3 showed that the former was predicted to proceed faster

than the latter by a factor of 2 to 103.8 Many more reaction mechanisms have been

proposed to characterize this first stage in soot formation, though the mechanisms

reviewed above are gaining wide acceptance. Clearly, the particle inception stage is

subject to great debate. It is considered the most critical step in soot formation, yet the

least understood.

Particle Coagulation and Growth

The transition from molecular to particle properties occurs at a molecular weight of

about 104 amu, which corresponds to an incipient soot particle diameter of about 3 nm.

This transition occurs during the second stage of soot formation, coagulation and particle

growth. In this step, the initial surface area for particle growth appears. In the process of









coagulation, coalescent collisions of particles result in one larger, essentially spherical

particle. This process dominates early soot particle growth, increasing particle diameter

while decreasing particle number density (number of particles per volume). Coagulation

is limited to very small particles, on the order of 18 nm or less. Coagulation transitions

into chain-forming collisions when the viscosity of the particles increases past a critical

value due to dehydrogenation of the condensed phase.12

Soot particle surface growth occurs as gas phase species attach to the surface of a

particle and become incorporated into the particulate phase. Frenklach8 describes this

process as H2-abstraction-C2H2-addition, in which H atoms are abstracted from aromatic

compounds, and gaseous acetylene is incorporated to bring on growth and cyclization of

PAHs. The process of H-abstraction-C2H2-addition is described by

Ai + H--A_ + H2 (1-5)

Ai + C2H2 products, (1-6)

where the notation Ai refers to an aromatic molecule with i peri-condensed rings, and Ai-

is its radical. The reaction in Eq. 1-5 describes the removal of an H atom from the

reacting hydrocarbon by a gaseous H atom. The second step, C2H2 addition, is shown in

the reaction of Eq. 1-6. Figure 1-2 shows H abstraction from a biphenyl molecule and the

subsequent addition of acetylene.


j+ H + H2



0 + C2H2 + H


Figure 1-2. The H2-abstraction-C2H2-addition mechanism acting on a biphenyl molecule.









It is possible for the growth of aromatic compounds to occur via different mechanisms

specific to the fuel and flame conditions, however, using numerical simulations

Frenklach et al.9 showed that these alternate methods quickly relax to the acetylene-

addition mechanism.

Soot surface growth will eventually cease. While once believed that the depletion

of growth species was responsible for this phenomenon, it is now understood that the

reduction of soot surface growth is due to a decrease in the surface reactivity of the

soot.13,14 The means by which the particle surface loses its reactivity are not yet fully

understood, however, it is suggested that it is strongly tied to the ratio of C to H atoms in

the soot as the particle ages.13'15 This relationship has been described in both a chemical

and a physical sense. Chemically, the growth of the particle relies on a radical site

created by the abstraction of a H atom. Though, physically, if it is assumed that the

hydrogen in the particle is contained only at the edges of the aromatic ring, it can be seen

that the C to H ratio will increase as the particle grows. As a result, the number of

possible growth sites decreases. While this method serves to describe the decay of soot

surface reactivity, it is incomplete. One would expect a direct proportionality between

the H to C ratio and surface reactivity with this model. However, it has been shown that

the H to C ratio decays 2 to 3 times more slowly than the surface reactivity.16 The

molecular details of soot surface decay are under continued investigation to more

accurately model this mechanism.

Particle Agglomeration

As the surface reactivity of the maturing soot decays, the third stage in soot

formation, agglomeration of the nascent soot particles, becomes increasingly important.

At this stage, coagulation has ceased as described above and collisions now result in the








"sticking," or agglomeration, of particles together forming chain-like structures. In

agglomeration, the particles still retain their original identity as opposed to coagulation,

in which the individual particles coalesce into one larger particle. Figure 1-3 illustrates

the difference between coagulation and agglomeration. Agglomerated soot particles may

contain 30-1800 primary particles and are well characterized by a log-normal size

distribution. 17




0

particle coagulation







particle agglomeration

Figure 1-3. Particle coagulation versus particle agglomeration.

Soot Oxidation

The final stage in soot formation is soot oxidation, where the particles are partially

or completely destroyed, yielding CO as a product. Oxidizing species in soot destruction

include O atoms, OH radicals, and 02. Previous work has demonstrated that the

concentration of O atoms in sooting flames is relatively low, and so too is the probability

that a reaction will occur when an O atom hits the soot surface. Therefore it is assumed

that OH radicals and 02 are primarily responsible for the oxidation of soot particles.1 An

understanding of the process of soot formation is fundamental to studies in soot










reduction. The four stages of soot formation are illustrated in Figure 1-4, after the

treatment of Bockhorn.18


oxidation

agglomeration



coagulation and
growth



particle inception





formation of PAHs









soot precursor
molecules


OH 02 OH o2 0 OOH
02


* .S @-...* @. e*
*O* ,*o* *
0 a e 0 *
00 0 000


H2 H
C C
H2


particulate level





transition occurs
at 3 nm


molecular level


Figure 1-4. Soot formation process showing stages of formation on molecular and
particulate scales.

Flames are a primary source of soot. There are two main classes of flames -

premixed and diffusion (or non-premixed). In a premixed flame, the fuel and oxidizer are

mixed at the molecular level prior to combustion. An example of this type of flame is a










typical spark-ignition engine. The final stage of soot formation, soot oxidation, is less

pronounced in a premixed flame than in a diffusion flame because most of the oxidizing

species are spent by the time soot particles reach maturity. It is at this critical time when

the growth has waned that the oxidizer can begin to have a net destruction effect on the

particles, though there is little oxidizer available in a premixed flame at this point. In a

diffusion flame, the reactants remain separate and react at the interface between the fuel

and oxidizer. A candle is a classic example of a diffusion flame. This type of flame has

significant oxidation of soot at higher flame heights as oxygen diffuses into the

combustion zone and encounters mature soot particles. A diffusion flame can be divided

into distinct regimes according to the stages of soot formation the inception regime, the

growth regime (incorporating coagulation, chemical species growth, and agglomeration),

and the oxidation or burnout regime.19 Figure 1-5 demonstrates these regimes as well as

the radial soot profile at an arbitrary flame height.

Burnout regime
Burnout regime Soot concentration profile at an
arbitrary flame height

Growth regime


Inception regime


see ot \\
concentration -- --- -
profile at right 1




JI I

-1 0 1
relative radial position, r/ro
ro burner radius

Figure 1-5. Soot formation regimes in a diffusion flame, and radial soot concentration
profile at an arbitrary flame height.









In the soot profile shown in Figure 1-5 it can be seen that small quantities of soot are

present in the inception regime but peak formation occurs in the growth regime.

Destruction occurs at the outer radii and at the flame tip as oxygen diffuses into the

combustion zone.

Metallic Fuel Additives

Metallic fuel additives have become commonplace in many combustion

applications. Starting in the early 1920s and through the 1970s, tetraethyl lead was a

popular additive in gasoline to enhance octane levels and reduce engine knock. Elevated

levels of lead in blood can have adverse health effects, ranging from anemia, mental

retardation, and permanent nerve damage. Because of these risks, the Environmental

Protection Agency began limiting the use of this additive from its inception, phasing it

out in the 1980s and eventually completely banning leaded gasoline for on-road vehicles

in 1996. Another common fuel additive is methylcyclopentadienyl manganese

tricarbonyl (MMT), manufactured by the Ethyl Corporation. MMT has been used

primarily in Canada for over 25 years, though it is available worldwide. Similar to lead,

this octane enhancer is a neurotoxin and can cause irreversible neurological disease at

high levels of inhalation.

Metallic additives have also been used to alter the sooting characteristics of flames.

The effects of the additives, as well as the mechanisms by which they alter flame

characteristics, are under study. Common additives include alkali metals such as Li, Na,

K, and Cs, and alkaline earth metals such as Ca, Sr, and Ba. Transition metals are also of

interest, particularly Mn and Fe. Results from these studies vary significantly depending

upon fuel type, additives used, premixed versus diffusion flames, and flame conditions.

Often studies of the same type of combustion system have yielded opposing conclusions.









The review that follows will be limited to key studies of Mn and Fe in premixed and

laminar flames.

Additives in Premixed Flames

Ritrievi et al.20 studied a laminar premixed ethylene flame seeded with ferrocene,

Fe(CsH5)2, for dopant concentrations of 0.005-0.14% Fe by weight of fuel and for flame

C/O ratios of 0.71-0.83. In this study, they observed a decrease in initial particle

diameter in the seeded flames, however these particles grew to a larger final size than

those in the unseeded flames. Additionally, the number density of particles (number of

particles per volume) increased in the seeded flames in early residence times, though this

value decayed rapidly with an end result approximately equal to the unseeded flame.

These results were supported by previous work performed by Haynes et al.21 Further, in

the seeded flames, measurable volume fractions of soot (fraction of soot per sample

volume) were found at an earlier residence time than in the unseeded flames, and the final

volume fraction was always greater in the seeded flames. Overall, this study found an

overall increase in soot yield for the seeded flames ranging from factors of 1.2-13.5 for

the range of C/O ratios studied. For a constant ferrocene concentration they saw the

enhancement of soot decline as the C/O ratio was increased. Additionally, growth rates

for the seeded flames were measured to be lower at early residence times than in

unseeded flames.

Auger spectroscopy was used to determine the spatial distribution of Fe and C in

extracted soot particles. They observed that the iron in the soot was concentrated at the

cores of the particles while the outer surface was a thick carbon-rich layer. Mossbauer

spectroscopy determined that the iron in the particles was in elemental form. Although









metallic iron was found in the soot particles, FeO was expected to be the stable species

present under the given flame conditions, based on thermodynamics.

Ritrievi hypothesized that FeO homogeneously nucleated early in the flame before

particle inception began. This explained the higher number densities, smaller size, and

measurable volume fractions early on in the seeded flame, as well as the layering of Fe

and C in the analyzed soot particles. Additionally, it was concluded that carbon

deposited on the particles was used to reduce FeO to metallic Fe via direct reduction.

The consumption of carbon at the surface explained the slower growth rates in the seeded

flames and suggested that FeO is relatively inactive in promoting soot growth. However,

metallic iron can catalyze carbon deposition on the particle surface leading to growth.

Carbon then serves two roles in growth processes. First, the growth of soot particles in

early residence times of the flame is determined by the ability of carbon to reduce FeO to

the more active Fe, and by the degree that Fe is diluted on the surface by depositing

carbon. In the later growth regimes, diffusion of Fe through the layers of depositing

carbon determines soot growth rates.

In studies of a similar premixed ethylene flame seeded with either ferrocene or

cyclopentadienyl manganese tricarbonyl, (C5H5)Mn(CO)3, Feitelberg et al.22 also found

that the additives had the effect of increasing the total amount of soot formed. For this

study, C/O ratios from 0.74 to 0.80 were studied, similar in range to Ritrievi's work. Iron

was added to the fuel in 200 ppm concentrations by a molar basis (0.13% Fe by weight of

fuel), and manganese was added in 140 ppm concentrations (0.10% Mn by weight of

fuel). Overall, the iron additive tripled total soot volume fraction, while manganese

increased this parameter by approximately 50%. The results of this study agreed with









Ritrievi's assessment that particle size and soot volume fraction increased at the later

residence times in the flame and that the overall number densities were unchanged.

Disagreement arises however near the burner lip where Feitelberg saw, within

experimental error, conditions in both seeded flames equal to unseeded, contrary to

Ritrievi's earlier soot inception conclusion.

An equilibrium analysis was employed to determine the states of the metal

additives in the flame. Feitelberg concluded that at high flame temperatures, the iron

would exist as free metal atoms. The iron would then precipitate out of the gas phase into

metallic iron form near 1760 K, or at residence times between 3 and 5 ms. Though

Ritrievi concluded that FeO was present in the flame, Feitelberg concluded that

thermodynamically FeO was not expected to form in the fuel rich flame studied. As with

the iron additive, manganese was predicted to exist in the gaseous phase as free metal

atoms at high temperatures. At a slightly longer residence time, the manganese was

expected to precipitate and form solid MnO.

In analysis of the data, Feitelberg concluded that the metal additives had no effect

on soot particle inception, rather their role was to increase the rate of gas-solid reactions

that increase the total size of the soot while the number density of particles remained

constant. Modeling of acetylene addition to soot particles indicated that the metal

additive acts as a catalyst to carbon deposition via acetylene, thus increasing the final

particle size.

Hahn23 studied a premixed propane flame seeded with iron pentacarbonyl,

Fe(CO)5, with fuel equivalence ratios of 2.4 and 2.5. Iron pentacarbonyl was added in

concentrations of 0.16-0.32% by weight of iron to the fuel. Again, an overall increase in









the total amount of soot produced was noted. The diameter of soot particles appeared to

be the least affected by the iron additives, with an average increase in the seeded flames

of only 1.9%. The number density of particles increased in the seeded flames in all

regions of the flame, with the exception of the lowest heights studied in the richer flame.

Overall this parameter saw a 16.9% increase. The seeded volume fraction and surface

area of the soot particles were found to increase over all heights studied by an average of

22.9 and 20.5%, respectively.

X-ray photoelectron spectroscopy was employed to determine the state of the iron

additive in extracted soot particles. This analysis identified iron oxide in the form Fe203

as the dominant species in the sampled soot particles, accounting for nearly 100% of all

iron present. No significant quantities of elemental Fe or other oxides such as FeO were

identified, discounting Ritrievi's conclusion of FeO reduction and Feitelberg's analysis

predicting elemental Fe. Hahn's study had the advantage of experimentally determining

the state of the iron in sampled particles, rather than using prediction models, although no

in situ analysis was performed.

It has been suggested that metal additives may accelerate the rate of soot oxidation

in the burnout regime.23'24 This regime is absent in premixed flames however, thus the

full effect of the metal additive cannot be seen. Previous studies of premixed flames have

demonstrated an overall increase in soot formation due to metallic fuel additives, either

by catalysis of acetylene addition or by increasing the number of initial soot nucleation

sites. With the addition of the burnout regime in diffusion flames, a complementary

picture of the effect of additives can be investigated.









Additives in Diffusion Flames

In a study of an isooctane diffusion flame operating above its smoke point,

Bonczyk25 noted soot enhancing and suppressing characteristics of ferrocene added in

concentrations of 0.09% Fe by weight of fuel. Similar to Ritrievi's work, Bonczyk saw

the appearance of soot earlier in the seeded flame. In early residence times in the flame,

particle size and number density all increased, enhancing soot production. However, in

later residence times, these parameters were decreased significantly when the soot

reached the burnout regime of the flame. The net effect was a reduction in soot when

compared to the unseeded flame, measured by these parameters and also visibly noted

when the smoke plume, apparent in the unseeded flame, was eliminated in the seeded

flame. Particles were collected post-flame and subjected to an Auger-type analysis to

determine the species of iron present in the soot. This analysis indicated that Fe203 was

the condensate present with only trace amounts of carbon when the flame was seeded at

the original concentration of 0.09% Fe by weight of fuel. However when this

concentration was reduced to 0.03%, the principle condensate was identified as carbon,

with less than 2% of elemental iron.

Bonczyk concludes that the soot enhancement is due first to increased nucleation

sites provided by solid FexOy particulates. Enhancement is then furthered by the same

reduction reaction suggested by Ritrievi,

FexOy + yC-- xFe + yCO. (1-7)

The presence of Fe has a catalytic effect on the deposition of carbon on the particle

surface, increasing particle surface reactivity. The reduction of soot in the burnout

regime is also enhanced by the presence of the metal additive. Iron oxide catalytically









enhances the removal of carbon by molecular oxygen, but this requires elemental Fe to

diffuse through the soot matrix to the surface and its subsequent oxidation by

xFe + yO -- FexOy. (1-8)


Combining the reactions in Eqs. 1-7 and 1-8 shows the net oxidation of carbon due to the

metallic additive,

C+ 102-- CO. (1-9)


Through the reaction in Eq. 1-9, carbon oxidation is enhanced by the additive and the

result is a net reduction of soot in the burnout regime.

This method of iron reduction and subsequent oxidation is also supported by Zhang

and Megaridis,26 who studied an ethylene diffusion flame seeded with ferrocene, as well

as by Kasper et al.27 whose investigation included ferrocene seeded methane/argon and

acetylene/argon flames. It is important to note that this conclusion is characterized by a

more efficient burnout of soot particles in seeded flames, not an inhibition of soot

formation by the additive. In fact, seeded flames see peak soot production levels higher

than those in unseeded flames due to increased surface area for soot formation in the

particle inception regime. The net reduction of soot is caused by efficient oxidation by

catalytic means in the burnout regime.

A second important observation regarding past research are the discrepancies in the

identification of the state of the metallic additive in the flame. In the studies reviewed,

analyses of soot species in the flame were performed outside of the flame. Ritrievi and

Feitelberg relied on a thermodynamic analysis. Extraction techniques were used in

Hahn's and Bonczyk's study, and although extraction techniques have been developed to









have a minimal impact on the flame, there is no way to ensure that these methods do not

perturb the characteristics of the flame during sampling. The most effective method of

determining the state of the metallic additive is to use an in situ technique.

Project Methodology and Motivation

To this author's knowledge, in situ measurements have not been performed to

identify the state of the metallic additive in the flame, although this diagnostic technique

would eliminate the possibility of perturbing the flame and altering flame characteristics.

Identifying the additive state in an annular region surrounding the flame is a step closer to

in situ flame measurements and may be used to predict the state of the additive in the

flame.

This research focused on the effects of iron pentacarbonyl, Fe(CO)5, on a laminar

prevaporized isooctane/oxygen diffusion flame. As compared with other fuel additives

such as manganese and lead, which are known neurotoxins, iron has relatively low

toxicity. In studies it has also been shown to be a highly effective soot suppressant.22'28

In addition, iron pentacarbonyl is an organometallic solution that is soluble in liquid

isooctane, allowing for a simple means of regulating and delivering the dopant to the

combustion system before vaporization of the fuel. These factors combined make iron

pentacarbonyl an ideal additive for this study. Isooctane, C8H18, was of interest because

it is an analog to high performance jet fuels and is characterized by a relatively low

boiling point. The compositions of a number of common jet fuels are listed in Appendix

A. Figure 1-6 shows the chemical structure of isooctane. Operating a diffusion flame

allowed for the effects of the additive to be observed throughout all regimes of the flame,

from particle inception to the critical burnout regime, better representing gas turbine

engines, for example.









H


H H H
H-C --H
H H H


II I I H

H-C -H H-C -H

H H

isooctane
2,2,4-trimethylpentane
C8H18

Figure 1-6. Chemical structure of isooctane.

The laser diagnostic techniques of elastic light scattering and transmission were

used to probe the flame. The light scattering and transmission studies allowed the

characterization of the soot particles by determining particle diameters, number densities,

and volume fractions. All of these methods were performed in situ so that the flame

would not be perturbed and the results would paint a more accurate picture of the flame

character. In addition, micro-Raman spectroscopy was used to identify the state of the

iron additive deposited on the flame holder screens used for flame stability.

The goals of this project were threefold. First, to implement novel laser based

techniques to measure the size, number density, and volume fraction of soot particles in

seeded and unseeded flames. Secondly, to fully characterize the seeded and unseeded

flames spatially. And third, to determine the state of the metallic additive deposited

during combustion in an annular region surrounding the flame, bringing the eventual in

situ identification of the state in the flame closer to reach. These support the goals of

exploring potential mechanisms for soot reduction using the information retrieved about

soot particle growth and the state of the additive in the flame.














CHAPTER 2
ELASTIC LIGHT SCATTERING

Scattering Theory

Laser light scattering is a diagnostic tool that can effectively extract information

about a system of particles in situ while having a minimal or undetectable impact on the

particles or the system overall. Electromagnetic radiation incident on a particle can be

scattered or absorbed, or undergo a combination of the two. The way this

electromagnetic radiation interacts with the scatterer is characteristic to the particular

system. Information about the number and size of the particles can be extracted from the

scattering response. In this study, elastic laser light scattering was employed to

determine the profile of the scattering and extinction coefficients throughout the seeded

and unseeded flames. These parameters were then employed to determine the size of the

soot particles in the flame, as well as their number density and total volume fraction.

Elastic scattering is based on the re-radiation of electromagnetic energy resulting

from a heterogeneity in an incident electric field. For this research, the heterogeneity can

be thought of as a particle of soot. As incident electromagnetic energy encounters a

heterogeneity, the radiation creates an oscillating dipole moment in the particle. The

acceleration and deceleration of electrons through the oscillating dipole moment acts as a

source of electromagnetic energy of the same frequency as the incident radiation, which

is then absorbed by the particle or radiated out as elastically scattered light. Figure 2-1

demonstrates this response.










Elastically scattered light





e
Incident E
electromagnetic
wave
E

Induced dipole moment





l"incident = huscattered


Figure 2-1. Light scattering response to an incident electromagnetic light beam.

Mie Theory

The interactions of electromagnetic radiation and a particle are prescribed by

Maxwell's equations. For a single homogeneous sphere, Mie29 developed the exact

solution to this interaction in 1908. The notation and treatment given by Kerker30 will be

used in this study to describe scattering theory. Figure 2-2 illustrates the geometry for

scattering by a single homogeneous sphere.


E= m,





B


scat


Figure 2-2. Polar coordinate geometry for light scattering. A plane electromagnetic
wave traveling in the positive z-direction incident upon a homogeneous
sphere of radius a.









The incident electromagnetic wave has electric vector E linearly polarized along the x-

axis, and magnetic vector B along the y-axis. The direction of propagation lies along the

Poynting vector S. The spherical, homogeneous particle has radius a and a complex

refractive index of m = n ik, where n denotes the refractive index and k represents the

absorption coefficient. The surrounding medium has a refractive index of mo. Typically

the surrounding medium is air and mo is assumed to be unity. The scattered radiation

Scat is oriented at a particular and 0, and the scattering plane is defined by the

observation angle 0 and the forward direction, defined by the direction of propagation.

Given an incident radiation intensity Io at wavelength X, the intensity of the

scattered radiation polarized perpendicular and parallel to the scattering plane,

respectively, is given by


S= Io 2r2 i11 sin2, (2-1)

kr2x2
le = Io i2 cos2 (2-2)
4n2 r





i n(n + 1) (2-)

2n 1
i = + [a.-.(cos) + b..(cos)] (2-4)
nn(n + 1)

The parameters tn and -n in Eqs. 2-3 and 2-4 are the angular dependent functions of the

associated Legendre polynomial, expressed as

P1"(cose)
n,(cose)= -, (2-5)
sin









tz(cose) dP )(cs) (2-6)
dO

with the parameters an and bn defined as

SW(a)'(ma) mWn(ma)(a) (2-7)
n (a)',(ma) mWn(ma)('na)

Smw(ax)'(ma) (ma)(()
b = ( ((2-8)
mn (a)W' (ma) (ma)'n(a)

The parameter m is termed the relative refractive index, and is defined as the ratio of the

refractive index of the particle to the refractive index of the medium, namely m = m/mo.

The size parameter, a, is defined as

2na
ca (2-9)

where again, a is the particle radius and X is the wavelength of the incident radiation in

the medium. Prime notation in Eqs. 2-7 and 2-8 denotes differentiation with respect to

the entire argument. The Ricatti-Bessel functions Wn and .n are given by

/ \1/2
I'(z) = ( J1/2(z) (2-10)

/ \1/2
-(z) = H +/2(z) = W.(z) + ix,(z), (2-11)

where the parameter Xn(z) is given by

1/2
n(z) = Y.+l/2(z). (2-12)

In Eqs. 2-10, 2-11, and 2-12, Jn+v/2(z) and Yn+l/2(z) are the half-order Bessel functions of

the first and second kind, respectively, and H+ ,,(z) is the half-order Hankel function of

the second kind.









The differential scattering cross section, C'pp, represents the energy removed from

the incident beam path and scattered about a given solid angle in a given direction. The

two-component subscript "pp" denotes the polarizations of the incident light and the

scattered light, respectively. The differential scattering cross section for vertical, or

perpendicular polarized incident light with perpendicular polarized scattered light would

be denoted as C'vv. Likewise, horizontal, or parallel polarized incident and scattered

light would be denoted as C'HH. For these two special cases, the scattering cross sections

are given by


C'vv 11 (2-13)
4%2

C'HH 2, (2-14)
4j2

which can be derived from Eq. 2-1. For spherical particles with linearly polarized

incident radiation, the differential scattering cross sections C'VH and C'HV are zero. The

differential scattering cross section for natural, or unpolarized light is the average of Eqs.

2-13 and 2-14, namely,


Cscat- (i+i2). (2-15)
8n2

The intensity of scattered light in terms of the differential scattering cross sections may

be determined by from Eqs. 2-1, 2-2, 2-13, and 2-14, specifically,

1 2
Ivv = Io C'vvsin2 (2-16)
r

1
IHH o-CHHCOS2 (2-17)


Iscat = Io Cscat. (2-18)
r









Integration of Eq. 2-15 over all solid angles of 0 < < 2t and 0 < 0 < n yields the

total scattering cross section Cscat. This parameter represents the fraction of incident

radiation scattered in all directions, and is expressed as


Cscat 2 (2n + 1) an + b 2). (2-19)
nI=

The absorption cross section Cabs describes the fraction of incident energy absorbed

within the particle. The sum of the absorption cross section and the scattering cross

section describe the extinction cross section as

Cext = Cabs Cscat. (2-20)

The total amount of energy removed from an incident beam of intensity Io is then

determined from the product IoCext. For a spherical particle, the extinction cross section

is given by


Cext = (2n + 1)Re{a. + b,}. (2-21)
2lt ,

Rayleigh Theory

Mie theory provides a general solution to spherical scattering without limits on

particle size. For large particles, Mie theory solutions converge to those attained by

employing geometric optics. For small particles, Mie theory agrees with the theory

developed by Rayleigh31 in 1871. Rayleigh theory is an approximate solution to

scattering for small, non-absorbing (k = 0 in the complex refractive index) spherical

particles. While Mie theory can also accurately describe these particles, it is desirable to

employ Rayleigh theory whenever possible due to the complexity of the Mie solution. A

valid scattering solution using Rayleigh theory for a spherical particle may be obtained

for the following conditions:









1. The external electric field seen by the particle is uniform

2. The electric field penetrates faster than one period of incident electromagnetic
radiation.

These two conditions are satisfied for the case of a <<1 and m I a << 1, where a is the

size parameter defined previously, and I m I = (n2 + k2)1 2. In the Rayleigh regime, the

differential scattering cross sections for a single spherical particle are given as


C = 4- a 2 (2-22)
4JT2 !W + 2)

C'HH =C cos2. (2-23)

Note that the vertical-vertical differential scattering cross section is independent of the

observation angle 0, while the horizontal-horizontal differential scattering cross section

has a minimum at 90 degrees. The Rayleigh scattering cross section and absorption cross

section are expressed as

2 = 6--- -12 (2-24)
Cscat I am2_ (2-24)


Cabs = Im (2-25)
n f [m +2J

As shown in Eqs. 2-24 and 2-25, the scattering coefficient scales with a6, while the

absorption cross section is proportional to a In the Rayleigh regime, the size parameter

is sufficiently small (recall, a << 1) thus for an absorbing particle, the contribution of

Cscat to the total extinction cross section Cext can be neglected, and it is assumed that

Cext Cabs.









Systems of Particles

The theory presented above was specific to scattering from a single spherical

particle. However, often the system of interest contains a large number of particles, such

as an aerosol cloud. Mie theory, and its subset Rayleigh theory, can be used to describe a

system of particles based on the scattering of single particles32 provided that

1. The particles are spaced such that there are no electrical interactions between
particles

2. Scattered light from one particle is not subsequently scattered from another particle

3. There is no optical interference between the scattered waves.

Criteria 1 is satisfied if a distance of 2 to 3 diameters separate each particle.

Defining the number density N as the number of particles per system volume, the

maximum N allowable while still maintaining 3 diameters of separation between particles

is N=2/(9nd3). Criteria 2 is met if the optical mean free path is greater than the optical

pathlength L of the system. The quantity 1/(NCext) is comparable to the optical mean free

path, thus for Criteria 2 to be met, the product LNCext must be less than 1. The last

criteria in treating a system of particles based on the scattering of single particles is met

when the system under consideration consists of a large collection of randomly oriented

particles. In this case, the intensities of scattered light from each particle can be added

directly to determine the total intensity of scattered light from the system.

Monodisperse systems of particles

A monodisperse system is characterized by uniformly sized particles. The overall

scattering and extinction of light for such a system can be described by the differential

scattering coefficient and the extinction coefficient, defined respectively as

K'p = NC,, (2-26)
pp pp









Kext = NCext (2-27)

where N is the number density of particles (particles per volume), and again, the "pp"

subscript refers to the polarizations of the incident and scattered light. The parameters

C',p and Cext are determined from either Mie theory, Eqs. 2-13, 2-14, and 2-21, or

Rayleigh theory, Eqs. 2-22, 2-23, and 2-25, noting that for Rayleigh particles Cext= Cabs +

Cscat, with the scattering cross section neglected if absorption is present.

The transmission of incident radiation Io through a system of particles for a

particular wavelength is defined as

I = transmitted (2-28)
Io


Complete transmission of incident light will result in a of unity. Conversely, a of zero

will result if all of the incident light is absorbed and/or scattered by the particles. The

Beer-Lambert law relates the transmission to the extinction cross section by

= exp(-KextL), (2-29)

where L is the optical pathlength. The quantity KextL is known as turbidity, a measure of

the ability of the system to extinguish incident light.

The volume fraction fv, like the number density, is a useful parameter for

characterizing the particles in a system. The volume fraction is defined as the volume of

particles per unit volume. For a monodisperse system, the volume fraction is given by


f, d N, (2-30)
6

where d is the diameter of the scattering particle. It should be noted that the parameters

d, N, and fv are not mutually exclusive. Knowledge of any two permits the calculation of

the third.









Polydisperse systems of particles

A system containing non-uniform particles is termed polydisperse. A flame is an

example of a polydisperse system as soot particles sizes can vary throughout the sample

region. In order to characterize the scattering and extinction properties of a polydisperse

system, information about the particle sizes must be taken into account. Often,

continuous distribution functions are used to describe the probability that a particle size

lies within a certain range. Espenscheid et al.33 proposed a zeroth-order lognormal

distribution (ZOLD) to characterize a polydisperse system of particles. Unlike a

Gaussian, or normal distribution, the ZOLD distribution is skewed to favor larger particle

sizes, which typically models aerosol populations more accurately. Additionally, the

domain of this distribution spans from zero to infinity, while the Gaussian distribution

may predict unrealistic negative populations. The ZOLD is mathematically identical to a

log-normal distribution, however its characteristic parameters are easier to specify for an

aerosol population than are those of the log-normal distribution. The ZOLD function is

defined as

exp(-o2) -(In r In r)2'
p(r) = exp 2 (2-31)


where r is the particle radius, rm is the modal value of r, and Oo is a dimensionless

measure of the width and skewness of the distribution. The mean radius r is related to rm

by

r= rm exp (a, (2-32)


and the true standard deviation o of the ZOLD is related to 0o and rm by

r = r[exp(4od) exp(3o2)]1/2. (2-33)









The extinction and differential scattering coefficients of a polydisperse system can

now be determined using the ZOLD function and the mean extinction and differential

scattering cross sections, Cext and Cpp, respectively, as

Kext = NCext (2-34)

KP,= NCpp. (2-35)

The mean parameters describe the extinction and scattering for all spherical

particles in the system, and are obtained by integrating the individual cross sections

weighted with the distribution function over all radial values. Namely,


xt = Cext(r)p(r)dr, (2-36)
0

and


Cp = JC (r)p(r)dr. (2-37)
0

Integration of Eqs. 2-36 and 2-37 requires numerical techniques for Mie theory. In the

Rayleigh regime however, these integrals may be evaluated analytically.

For a polydisperse system, the number density of particles is not directly affected

by the size distribution. However, the characterization of volume fraction fv in a

polydisperse system requires the ZOLD function to be taken into account, specifically,

4
f = Nf -arp(r)dr. (2-38)
0 3

Substitution of the ZOLD function, Eq. 2-31, into the above and integrating yields

4 15 ,(
f = -nNexp r. (2-39)
32









An interesting result of Eq. 2-38 arises when considering Rayleigh particles. In this

regime, the mean extinction cross section of Eq. 2-36 can be written as


o X m +2J

using the Cext parameter described by Eq. 2-25 and the definition of a. Combining Eqs.

2-38 and 2-40, the extinction coefficient Kext can be expressed in terms of the volume

fraction by

S -6nf ru1
Kxt = NCext = Im 2. (2-41)
X lm +2J

This expression allows for the determination of fv simply from transmission

measurements. As it will be seen in the next section, this greatly simplifies diagnostics

and allows for the characterization of an aerosol system without regard to the size

distribution of the particles.

System Diagnostics

In the preceding analysis, the extinction and scattering coefficients could easily be

determined provided that information about particle size, number density, and volume

fraction is known. However in most scenarios, the inverse problem is faced given the

extinction and scattering coefficients, characterization of the system in terms of the

aforementioned parameters is desired. Referring to Eqs. 2-22, 2-25, 2-36, and 2-37, it

can be seen that for either a mono- or polydisperse system, the ratio of the differential

scattering cross section K'pp and the extinction coefficient Kext is in general

K' NC'
= = f(,,Em,,d,o). (2-42)
Kext NCext









The values of X and E are dictated by experimental setup, and it is assumed that m is

known based on apriori knowledge of the scattering particles. For a polydisperse

system, o can be determined by sampling particles from the aerosol, assuming a value, or

by performing more advanced techniques such as dynamic light scattering, or photon

correlation. For a monodisperse system, o is zero. With these parameters in hand, only

the diameter of the scattering particles is unknown (or the modal diameter for a

polydisperse system), and it can easily be determined. Figure 2-3 shows the relationship

between modal particle diameter and K'vv/Kext for a specific polydisperse system.




4.0001 0 50.00 10.. 0 150. 0 200. 0















.00010For this case, ------- 532 nm, 2.0-------- 0.35i, and ----- ---------30.7 nm.






With the particle diameter known from the above analysis, the number density and

volume fraction can then determined. From the definition of the extinction coefficient

given in Eq. 2-34,










N=Kxt (2-43)
Cext

where Cext can be calculated using the previously determined particle size. The volume

fraction for Mie particles is found from Eq. 2-39, or by rearrangement of Eq. 2-41 for

Rayleigh particles. Thereby the necessary parameters to characterize a system of

particles, d, N, and fv, have been established.

Deconvolution techniques. To this point, the scattering and extinction coefficients

have been assumed spatially constant for a given system. However, in many cases, such

as flame studies, these parameters may vary based upon the location in the system. For

example, in Figure 1-5, the concentration of soot was shown to have high spatial

dependence. To better characterize this type of system, areas of constant scattering and

extinction coefficients are defined. For the case of a flame, concentric annular regions

about the flame center are employed. As shown in Figure 2-4, laser light scattering data

may be collected at representative points to determine the scattering coefficient for each

region.


Kvy K 3 Kext 3


1o I "1)-


10 tc

T-f(Kext,I, Kext,2 Kextr)
Iscat.I 'scat,2 seat.3 Tb=f(Kext2, Kextl3)
r=f(Kex3)

Figure 2-4. Diagnostic techniques for determining scattering and extinction coefficients
for a system containing varied properties.






34


Determination of the extinction coefficient for each region requires more attention

however, as the transmission pathlength can intersect multiple regions. A variety of

techniques have been developed to deconvolve line of sight measurements into the

corresponding radial parameter. Onion peeling and three-point Abel inversion are two

such schemes. Both techniques construct information about the radial parameters based

upon information in neighboring sections. These schemes will be discussed further in

Chapter 4.














CHAPTER 3
EXPERIMENTAL METHODS

Burner

For all experimentation, a concentric diffusion burner was used. A schematic of

the burner is shown from side and top views in Figure 3-1. Isooctane and nitrogen flow

through the center of the burner and are met at the burner exit by an oxygen flow, fed

through an array of twelve inner ports. The dimensions of the burner are summarized in

Table 3-1.









7
02



outer array



inner tubeuter tube

T outer tube
isooctane +
N2
burner side view burner top view

Figure 3-1. Concentric diffusion burner schematic. Side and top views are shown.
Isooctane and nitrogen flow through the inner tube, while oxygen enters the
system through the outer array of ports.









Table 3-1. Concentric diffusion burner dimensions.
Inner Diameter (cm) Outer Diameter (cm)
Outer tube 1.656 1.905
Inner tube 0.704 0.953
Inner array 0.254

A stainless steel mesh flame holder was placed 55 mm above the burner lip to

promote flame stability. Because stainless steel is a poor conductor of heat, the region in

the flame remained much hotter than the region outside of the flame. If the flame were to

drift due to air currents, it would tend to recenter itself over the flame holder due to the

temperature gradient in the mesh. The flame extended approximately 60 mm above the

flame holder, however the observed height above the flame holder was subject to wide

fluctuation. A new flame holder screen was used for each experimental run to assure that

flame conditions were not significantly altered by a deteriorating screen. In addition to

the flame holder, a shroud was placed around the burner to block ambient air currents.

This shroud was 25.4 x 26.7 cm and made of 50% opaque Plexiglas, which also helped to

block stray light from entering the scattering detection optics.

A vertical translation stage allowed the burner to be raised and lowered, permitting

light scattering and transmission data to be taken at various heights above the burner

surface. Five heights were investigated and were designated with the letters b through f.

These heights were consistently reproducible and corresponded to a number of specific

rotations of the vertical stage knob. A sixth height designated "a," 2.54 mm above the

burner lip, was initially considered, though it was discarded due to interactions between

the Gaussian "tails" of the laser intensity profile and the burner lip. These interactions

introduced significant stray light into the system, thus this height was removed from

consideration. Data were also collected at six equally spaced radial positions in the









flame, ranging from the flame center to near the flame edge. A precision translation

stage controlled by a micrometer allowed the collection optics to be adjusted to the these

different positions. One revolution of the micrometer corresponded to 0.025 inches of

linear motion. The flame was considered axisymmetric, and as discussed below, was

divided into six concentric annular regions. The soot characteristics were assumed

constant through these six concentric regions, defined by these radial positions. Table 3-

2 summarizes these vertical and radial positions, and Figure 3-2 demonstrates the relative

positions of these points in the flame.

Table 3-2. Data collection heights and radial positions.
Height Above Distance From
Position Label Burner Lip (mm) Position Label Flame Center (mm)
b 8.73 1 0
c 15.24 2 0.635
d 22.86 3 1.270
e 30.96 4 1.905
f 40.64 5 2.540
flame holder 54.60 6 3.175


Figure 3-2. Data measurement heights and radii relative to the flame.






38


Fuel Vaporization and Delivery System

Vaporization of the liquid isooctane fuel was necessary before the fuel could be

delivered to the burner. This was achieved by flowing the fuel through a vaporization

system. Three main sections characterize the vaporization system the preheat zone, the

vaporization zone, and the delivery line. Figure 3-3 shows the vaporization system.


HEPA


02 frtrn
supply tank


pcristaltic pump liquid isooctane




E,


N2 from
supply tank

HEPA
filter


preheatzone


filter [

N2 from
supply tank


Figure 3-3. Fuel vaporization system.


m.ooctane vapor
+ N2 or
calibration gases
S to burner


Al


calibration gases









All three regions of the vaporization system were wrapped with Omega heater tape

and fiberglass insulating tape. The heaters were controlled with two PID controllers set

at 100C, which was above the boiling point for the liquid isooctane. The preheat region

consisted of a 0.625 inch diameter, 36 inch long 304 stainless steel tube packed with

brass balls, which increased the surface area to promote heat transfer. A nitrogen coflow

stream was introduced into the vaporization system at the head of the preheat zone at a

rate of 0.8 L/min. The stream was heated and entered into the second region of the

vaporization system, the vaporization zone, a 0.25 inch diameter, 36 inch long, 304

stainless steel tube. The liquid fuel was delivered to the vaporization region via a

variable flow Fisher Scientific peristaltic pump at a rate of 1 mL/min. The warmed

nitrogen aided in fuel vaporization as well as the transfer of the fuel through the

vaporizer. The delivery line of the vaporization system consisted of approximately 50

inches of 0.25 inch diameter braided PTFE hose that delivered the nitrogen and vaporized

fuel mixture to the burner. This line was also heated to eliminate any condensation of the

fuel on the way to the burner. Prior to any experimentation, the vaporization system

heaters were turned on and the nitrogen coflow was allowed to flow for at least half an

hour. This ensured that the system was adequately heated before the fuel entered the

system.

At the burner exit the nitrogen/fuel mixture was met by a 9 L/min stream of

oxygen. Alicat Scientific digital flow meters regulated the nitrogen and oxygen gas flow

rates within 0.01 L/min for the nitrogen flow and 0.1 L/min for the oxygen. The

accuracy of these instruments was 1% of full-scale. These flow meters can be seen in

Figure 3-4.



























Figure 3-4. Alicat Scientific digital flow meters used for nitrogen coflow and oxygen.

Fuel and oxidizer flow rates were such that the unseeded flame operated just under the

smoke point for isooctane. For the iron pentacarbonyl seeded flames, the dopant was

added to the liquid fuel supply in 4000 ppm quantities by mass (-0.11% Fe per mass of

fuel) and was delivered to the burner through the fuel stream. Table 3-3 summarizes the

flame operating conditions.

Table 3-3. Flame operating conditions.
Stream Flow Rate (L/min)
C8H18 (liquid) 0.001
C8H18 (vapor) 0.179
N2 0.8
02 9.0
Fe(CO)5 (seeded flame only) 4000 ppm

Seeded and unseeded flames had an average diameter of approximately 7.8 mm at

the burner lip. Flame diameters varied over the range of heights studied, and are

summarized in Table 3-4. These diameters were measured graphically using still images

of the flame. As can be seen from Table 3-4, the seeded flame diameters varied only

slightly from the unseeded flame.









Table 3-4. Average unseeded and seeded flame diameters at each height.


Height


Unseeded Flame
Diameter (mm)


Seeded Flame
Diameter (mm)


b 7.7 0.6 7.1 0.3
c 8.0 + 0.8 7.2 0.4
d 8.2 0.7 7.4 0.3
e 8.7 0.7 8.2 1.0
f 11.5 2.8 11.8 2.4


The overall equipment summary for the vaporization and delivery system is shown

in Table 3-5.

Table 3-5. Description of fuel vaporization and delivery system
Device Manufacturer/Supplier Model Description
Equipment
Peristaltic pump Fisher Scientific 13-876-4 Variable flow peristaltic
pump
Heater tape Omega SRT101-060 313 W
preheat zone
Heater tape Omega SRT051-060 156 W
vaporization
zone
Heater tape Omega SRT051-060 156 W
delivery line
Braided PTFE Swagelok SS-4BHT PTFE-lined stainless
hose steel flexible hose
Thermocouple Omega Type K Thermocouple
Heater controller Omega CN9000A 2 PID controllers
HEPA filter Gelman Laboratory 12144 2 HEPA filters
Digital flow Alicat Scientific Used for N2 coflow 0-1
meter SLPM, accurate to 1%
of full-scale
Digital flow Alicat Scientific Used for 02 stream 0-10
meter SLPM, accurate to 1%
of full-scale
Fuel and Gases
02 Praxair UN 1072 >99% pure
N2 Praxair UN 1066 >99% pure
Isooctane Fisher Scientific 0296-4 HPLC
CH4 (used for Praxair UN 1971 Ultrahigh purity,
calibration) 99.97% pure










Diagnostics

Laser Light Scattering

Laser light scattering techniques were employed to determine the scattering

characteristics of soot particles in unseeded and seeded flames. Figure 3-5 shows the

experimental setup for this scattering system.


DE


G H


Figure 3-5. Light scattering system setup. A) Frequency doubled Nd:YAG 532 nm
pulsed laser. B) Ultrafine-gauge wire meshes to attenuate laser. C) Dichroic
mirror, R=99% at 45 and 532 nm. D) Aperture. E) Plano-convex lens,
f=250 mm. F) Flame. G) Aperture. H) Beam dump. I-O) Scattering
collection optics on translating stage. I) Neutral density filters. J) 532 nm
bandpass filter. K) Vertical polarizer. L) Aperture. M) Biconvex lens,
f=100mm. N) Aperture. O) Photomultiplier tube. P) Digital oscilloscope.
Q) Precision high voltage supply.









An Nd:YAG pulse laser was operated in frequency doubled mode (, = 532 nm) at

5 Hz. The laser intensity was first attenuated through a series ofultrafine-gauge wire

meshes and then turned with a 45 degree dielectric mirror optimized at 532 nm. An

aperture defined the pulse diameter as it passed through a focusing lens. The beam was

then directed through the center of the flame and was terminated at a beam dump. The

scattering system collected scattered light at 90 degree angle from the incident beam.

Scattered light first passed through a narrow aperture and a 532 nm band pass filter.

Neutral density filters were added as necessary to the collection optics line of sight in

order to maintain signal linearity. A polarizer ensured that the scattered radiation

observed was only vertically polarized, matching that of the incident radiation emitted

from the laser cavity. A second aperture at the rear of the collecting tube ensured that

only a small scattering volume was observed and that stray light is minimized. The

scattered light was then incident on a photomultiplier tube and the signal was recorded on

a digital oscilloscope.

As illustrated in Figure 3-5, the scattering detection optics were mounted on a

micrometer-controlled precision translational stage. One revolution of the micrometer

corresponded to 0.025 inches of linear motion. The stage setup allowed the scattered

signal to be observed at the six pre-defined radial positions summarized in Table 3-2.

The photomultiplier tube was driven by a precision high voltage supply set to -830 V.

Thus, the signal displayed by the oscilloscope was negative. For simplicity, the signals

presented will be reported as absolute values. Table 3-6 summarizes the scattering

system apparatus in detail.









Table 3-6. Description of scattering system apparatus.
Device Manufacturer Model Description
Equipment
532 nm frequency Big Sky Lasers 230A8000 Q-switched, 5 Hz,
doubled Nd:YAG Variable power, 100 mJ
Laser @ 10 Hz, 532 nm, 1 ns
Beam dump Kentek ABD-2 Beam dump
Photomultiplier Hamamatsu R2949 Photomultiplier tube
tube
Photomultiplier Products for PR1402CE Photomultiplier tube
tube housing Research, Inc. housing
Oscilloscope LeCroy LT 372, 500 Hz, 4 GS/s digital
WaveRunner oscilloscope with 50 Q
termination
Precision high Stanford Research PS325 Digital high voltage
voltage supply Instruments power supply
Double shielded Pasternack RG-223/U Double shielded coaxial
BNC cable Enterprises cable to reduce line
noise
Translational stage Mitutoyo Micrometer-adjusted
translational stages
Optics
532 nm dichroic CVI Laser 45 degree, 532 nm
mirror dichroic mirror
Aperture Newport ID-1.0 2 apertures
Plano-convex lens Newport KBX079AR.14 BBAR coated, 430-700
nm, 25.4 mm diameter,
250 mm focal length
Neutral density Optics for Research FDU-2.0 102.0 attenuation
filters FDU-1.0 101.0 attenuation
FDU-0.3 100.3 attenuation
(nominal values)
Polarizer Newport
532 nm line filter Newport 10LF10-532 T > 50%, 25.4 mm
diameter
Aperture ID-0.5 2 apertures in collection
optics
Biconvex lens UV coating, 100 mm
focal length, 25.4 mm
diameter









Photomultiplier tube linearity

A photomultiplier tube (PMT) is a high gain detector that converts photons into an

electric signal by the photoelectric effect. The photoelectric effect is the phenomenon

whereby electrons are emitted from a surface upon exposure to electromagnetic radiation.

When an incident photon hits the PMT, a modest number of electrons in an electrode are

released. These electrons hit another electrode, releasing additional electrons. A series

of electrodes has a multiplicative effect on the number of electrons released and incident

on the detector. PMTs are, in general, capable of outputting a linear response over

several decades for a continuous signal source. However, a pulsed nanosecond-scale

laser can easily invoke a non-linear response in the PMT due to the sudden flux of

incident photons. It is common for a PMT to be limited to only one decade of linearity in

such a system, hence attention must be paid to signal linearity.

When the strength of an incident signal to a PMT exceeds the limits of linearity,

neutral density filters can attenuate the signal and bring the PMT back into the linear

response regime. A neutral density filter is characterized by a broad, steady transmission

profile over a wide range of wavelengths. An x neutral density filter attenuates by a

factor of 10x. These filters are available in a variety of attenuating strengths, thus

maintaining the PMT in its linear regime is simply a matter of adding and removing

filters from the PMT incident path. For the scattering experiments performed, filters

were used in this manner, and the output of the PMT was maintained between 6 and 14

mV. Linearity was also checked periodically throughout the experiment by placing a 0.3

neutral density filter in front of the collection optics. A 0.3 filter should attenuate the

signal by a factor of 100.3, or approximately 2, thus if the PMT response was indeed

linear, the output signal was expected to drop by about one half.









Calibration

As detailed in Chapter 2, determination of the differential scattering coefficient K'pp

is a necessary parameter in determining the size and number characteristics of the

scattering particles. The scattering signal from the PMT is related to K'pp (recall that

K'pp=NC'pp) by

Spp = Io0 (AVAQ)NCpp, (3-1)

where Io is the incident laser intensity, r is the efficiency of the PMT detector and the

collection optics, AV is the scattering volume, and AQ is the solid angle of observation.

The parameters r, AV, and AQ may be measured, though to do so with great accuracy

and precision is difficult. Rather, to extract K'pp from the scattering data, a calibration

may be used. The ratio of the scattering signal to that of a known reference scatterer can

be used to solve for the desired parameter K'pp, namely,


K'- = N reC pp P re f (3-2)
P- refCpp0re --
SSpp,ref

where the transmission ratio accounts for any variation in the transmission of incident

light between the reference scatterer and the scattering volume of interest. By taking the

ratio of the reference scatterer signal to the signal from the scatterer of interest, the direct

evaluation of the common terms YI(AVA2) is avoided.

Methane gas, CH4, and nitrogen gas are commonly used as references for

calibration purposes. At an incident wavelength of = 694.3 nm, the differential

scattering cross sections C'vv for each of these gases are 4.56E-28 cm sr and 2.12E-28

cm sr respectively.34 A conversion may be performed to evaluate this parameter at the

wavelength of interest by










C' v --C', X n I A 1 (3-3)
X2 nX, 1


where nx is the wavelength-dependent refractive index. The number density of the

reference scatterer can be approximated by the ideal gas law, or calculated with

knowledge of the particle density and molecular weight. Table 3-7 lists the differential

scattering coefficients for methane and nitrogen at three wavelengths characteristic of

common laser systems.

Table 3-7. Differential scattering coefficient for methane and nitrogen at common
incident wavelengths at 1 atm, 298 K.
K'vv at 1 atm, 298 K K'vv at 1 atm, 298 K
Laser X (nm) for CH4 (cm'sr-1) for N2 (cm'sr-1)
Ruby 694.3 1.12E-8 5.22E-9
Nd:YAG 532.0 3.33E-8 1.54E-8
Argon Ion 488.0 4.73E-8 2.18E-8

The reference scatterer for this study was methane gas. The calibration gas shared

the delivery line of the vaporization chamber, as shown in Figure 3-3, thus the gas was

expelled from the burner for calibration measurements. A series of brass plug valves

were used to shut off the flow from the vaporization chamber during calibration, and vice

versa during flame operation. The supplier's specifications of methane are listed in Table

3-5. Calibration of the scattering system with the known scattering characteristics of

methane provided an absolute determination of the differential scattering coefficient for

the soot particles in the flame. In addition, calibration also served as a means of

determining and accounting for the amount of stray light present in the system, as

discussed in the next section.









Stray light

Stray light is present in any real scattering system, and can take the form of

reflected laser light from surfaces, or ambient light, for example. If unaccounted for,

stray light can skew experimental data considerably. For example, the magnitude of stray

light can easily be as large as the scattered light signal from the reference scatterer used

to determine K'pp. Since the relation between K'pp and Spp,ref is direct, any error in

measuring Spp,ref is translated directly into error in K'pp. Thus, it can be seen that reducing

and accounting for stray light in a system is critical to obtaining accurate data for

analysis.

To minimize stray light from entering the scattering collection optics, a number of

techniques were used. First, lenses and apertures in the collection optics were used to

define a very small scattering volume. These apertures also served to block any stray

light from outside the scattering volume line of sight from entering the PMT. Another

stray light reducing method used was to minimize reflection of laser light from surfaces.

Highly reflective surfaces, such as optical mounts, were either painted with matte black

paint, or covered in thick black felt to reduce reflections. Whenever possible, these

reflection sources were blocked from the PMT line of sight as well using opaque

Plexiglas covered in black felt.

Stray light minimization techniques are effective, however they cannot completely

eliminate stray light from a system. To account for this, stray light may be quantitatively

determined and then data may be corrected. Another calibration is employed for this

effort. Similar to the scattering signal calibration, the stray light calibration relies on the

known scattering characteristics of calibration gases. Employing methane and nitrogen,

the ratio of these two gases' reference scattering signals, Rref, can be determined from Eq.









3-1 to be the ratio of their differential scattering coefficients. This reference ratio is

tabulated in Table 3-8 for the same incident wavelengths considered previously.

Table 3-8. Methane to nitrogen reference differential scattering coefficient ratio used for
stray light calibration at common incident wavelengths, assuming ideal gases.
KVV,CH4/ KVV,N2
Laser X (nm) at 1 atm, 298 K
Ruby 694.3 2.15
Nd:YAG 532.0 2.17
Argon Ion 488.0 2.17

The deviation in the measured calibration ratio from the reference ratio Rref is due

to stray light in the system. Assuming that the stray light remains constant between

methane and nitrogen measurements, an excellent assumption, this deviation can be

expressed as


Rf = K'pp,CH4 1 (Spp,CH4measured) SL (3-4)
SK'pp, N reference (Spp,N measured) SL

Where Spp,CH4 measured and Spp,N2 measured are the measured scattering signals of methane and

nitrogen, respectively. With this relationship, the stray light in the system can be

quantified as


SL= RrefSppN, SppCH4 (3-5)
Ref-1
Rref I

For the light scattering studies, stray light calibration measurements were taken

prior to every flame study to determine an experiment-specific stray light value. The

calibration gases flowed at a rate of approximately 13 L/min, controlled by a rotameter

(GE700 Gilmont) flow tube. The temperature of the calibration gases exiting the heated

fuel delivery line was measured with a type K thermocouple. On average, this value was

344 K. The number density N, differential scattering cross section C'vv, and differential

scattering coefficient K'vv for each gas was determined using this temperature. These










parameters are summarized in Table 3-9. Number densities were calculated using

isobaric density data tabulated by the National Institute of Standards and Technology.35

Table 3-9. Number densities, differential scattering cross sections, and scattering
coefficients for methane and nitrogen calibration gases at 1 atm, 344K.
Gas N (cm3) C'vv (cm2/sr) K'vv (cm/sr)
Methane 2.14E19 1.35E-27 2.89E-8
Nitrogen 2.13E19 6.25E-28 1.32E-8

From Table 3-9, the reference calibration ratio Rref for methane to nitrogen at 344 K

was determined to be 2.165. This value was used to determine the stray light

contribution to the measured scattering signals from the calibration gases and the flame.

Figure 3-6 shows the scattered signal from the calibration gases and the flame from a

typical scattering experiment. Dark signals were recorded as well to normalize the

baseline of the calibration gases and the flame.

N2 -CH4 -flame w/ 10^5 ND filter attenuation
----- calibration dark -flamc dark

0.01 I


0.008


0.006 -


0.004 I
I-

0.002


0 -


-0.002. **..* I
4.156 10's 4.161 10-s 4.165 10-s 4.169 10'"

time (s)

Figure 3-6. Sample scattering signals from methane, nitrogen, and flame. Flame signal
is attenuated by a factor of 105 for signal linearity.









For scattering analysis, the dark signals were first subtracted from the scattered

signals. The signals were then integrated over a 90 ns full peak width. For the data

depicted in Figure 3-6, the integrated signal for methane and nitrogen (including the

influence of stray light) was found to be 0.64 mV-s and 0.38 mV-s, respectively, which

yielded a calibration ratio of 1.67, a 23% deviation from the ideal Rref value of 2.165.

This gives an indication to the magnitude of the stray light, which was responsible for

skewing the calibration ratio. With the integrated calibration signals and the Rref value,

Eq. 3-5 was used to calculate the stray light, which for this case, was determined to be

0.16 mV-s. The time-integrated measured flame signal determined from the data

presented in Figure 3-6 was determined to be 0.38 mV-s.

The average results of time-integrated calibration measurements over all

experiments are shown in Table 3-10 along with the range seen in these values. The

calibration ratio ranged from 1.59 to 1.79, with an average value of 1.70, a 22% deviation

from Rref. Overall the stray light signal was approximately one-third of the nitrogen

signal.

Table 3-10. Average time-integrated calibration gas and stray light signals and range of
signals seen over all scattering experiments.
Average Signal Range in Signal
(mV-s) (mV-s)
Methane + SL 0.55 0.39 0.73
Nitrogen + SL 0.25 0.18 0.34
Stray Light 0.17 0.11 0.26

The true methane integrated signal is determined by subtracting the stray light from

the integrated measured methane signal. Returning to the example data presented above,

this yields a true integrated methane signal of 0.64 0.16 mV-s = 0.48 mV-s. The

measured flame signal required a correction for any attenuation used to preserve PMT









linearity. For the data presented above, a series of neutral density filters yielded an

overall attenuation factor of 105, thus the true integrated flame signal was determined by

(Sflame,measured) (105). The stray light signal may be subtracted from this signal, however

because it is orders of magnitude smaller than the flame signal, it may be neglected

without significantly altering the scattering results. All that remains to be determined in

order to extract the differential scattering coefficient from the scattering data is the

transmission of laser light through the calibration methane and the flame. The

transmission through the methane was assumed to be unity. Determination of the

transmission through the flame will be discussed in a later section; jumping to the results,

for the flame height and position under consideration, this value was found to be 0.76.

With this information, Eq. 3-2 was used to determine the differential scattering

coefficient for the soot particles in the flame at height f, position 1. Specifically,


SVV, ht.f, posl (KVVCH4) SV 1ame 1 1
SVV,CH4, measured SL \

= (2.89E-8 cm-'sr-)( 0.37x105mV- 1
0.64-0.16mV-s 0.76
= 2.2E-2 cm-'sr-.

Vaporization of Soot

The degree to which laser energy is focused over an area is termed fluence. This

parameter, measured as energy per area, was an important consideration in all

experiments. At modest energies, a laser pulse can significantly heat soot particles and

cause vaporization if the beam is focused to a small cross-sectional area. As shown by

Dasch,36,37 laser fluences greater than 0.2 J/cm2 from a submicrosecond pulsed source can

reduce the light scattering and extinction characteristics of soot by an order of magnitude









due to vaporization. A typical laser cross sectional area is 1 mm2. At this size, a laser

energy of merely 2 mJ/pulse would significantly alter soot characteristics.

For the flame studies performed, the lowest fluence that could be attained by

simply reducing the laser pump energy was 0.4 mJ/cm2, with an approximate beam cross

sectional area of 0.013 cm2. With any further reduction in laser pump energy, the laser

pulse broadened in time and the scattering signal became difficult to detect. Therefore,

rather than reducing the laser fluence by adjusting the laser pump energy, ultrafine-gauge

mesh disks were placed in the beam path. As the beam passed through the meshes, the

intensity of the beam was reduced to 0.42 mJ/pulse and an acceptable laser fluence of

0.03 mJ/cm2 was attained. Because the laser beam was focused to a point at the burner,

any "shadow" produced by the mesh could be neglected. This fluence was determined to

produce no vaporization based on the observation of a steady scattering signal as the

energy of the laser was further adjusted about this point.

Transmission

The experimental setup for the transmission system is shown in Figure 3-7. The

optics encountered by the laser are identical in the transmission setup as those in the

scattering system except rather than terminating at a beam dump, the transmitted

radiation is monitored with a power meter. The optics and collection apparatus are

mounted on two mechanically operated precision translation stages that direct the laser

path through various positions through the flame. Forward scattered light was blocked

from the detector by narrowing Aperture G, shown in Figure 3-7, to the beam width, and

by placing the detection optics approximately 40 cm from the flame. These steps resulted

in only a small solid angle of observation and limited the forward scattered light incident

on the power meter.




























Figure 3-7. Transmission system setup. A) Frequency doubled Nd:YAG 532 nm pulsed
laser. B) Ultrafine-gauge wire meshes to attenuate laser. C-E) on
translating stage. C) Dichroic mirror, R=99% at 45 and 532 nm. D)
Aperture. E) Plano-convex lens, f=250 mm. F) Flame. G-I) on translating
stage. G) Aperture. H) 532 nm line filter. I) Power meter receiver. J)
Power meter display.

The radial positions studied in the transmission flame corresponded to the same positions

investigated in the scattering system. These positions were spaced at 0.635 mm intervals,

beginning at the flame center and spanning to the flame edge. In addition, a reference

position 1.65 cm outside of the flame was defined. The measured power of the laser

through the flame was ratioed with the power measured at the reference position to give

the transmission through the flame. From the Beer-Lambert law

Ita
S- exp(-KextL), (3-6)


where Io is the incident intensity of the laser measured at the reference position, Itrans is

the transmitted intensity measured through the flame, and L is the optical pathlength

through the flame. Table 3-11 describes the transmission instrumentation in greater

detail.









Table 3-11. Description of transmission apparatus.
Device Manufacturer Model Description
Equipment
532 nm frequency Big Sky Lasers 230A8000 Q-switched, 5 Hz,
doubled Nd:YAG Variable power, 100
Laser mJ @ 10 Hz, 532
nm, 1 ns
Translational stages Mitutoyo Micrometer-adjusted
translational stages
Power meter Molectron PM5200 Power meter
PM3 Power meter head
Optics
532 nm Dichroic CVI Laser 45 degree, 532 nm
mirror dichroic mirror
Aperture Newport ID-1.0 Aperture
Plano-convex lens Newport KBX079AR.14 BBAR coated, 430-
700 nm, 25.4 mm
diameter, 250 mm
focal length
532 nm line filter Newport 10LF10-532 T>50%, 25.4 mm
diameter

Micro-Raman System

After seeded combustion experiments were complete, rust-colored residue was

apparent on the flame holders, indicative of iron deposits. This region of iron deposition

can be seen in Figure 3-8. Confocal micro-Raman spectroscopy was used to investigate

the flame holders to determine the state of the residual iron. Raman spectroscopy

measures the inelastic shift in energy scattered from a particle as compared to the

incident. The shift in energy is due to absorption of energy into vibrational modes in the

molecule. As with electronic transition modes, the vibrational modes are quantized and

can be used like a fingerprint to identify specific molecules. The confocal system

combines Raman spectroscopy with a microscope objective, allowing the specimen under

study to be observed with very high spatial resolution. The confocal micro-Raman

system (LabRam Infinity, Jobin Yvon) is shown schematically in Figure 3-9.



































region of Fe deposits

Figure 3-8. Region of iron deposits on flame holder screen.


Mirror He:Ne laser
632.8 nm





Spectrometer

Beam splitter


Confocal Roman
notch filter CCD camera


Microscope objective


Figure 3-9. Confocal micro-Raman schematic.









The excitation wavelength was 632.8 nm, generated from a He:Ne continuous wave laser.

The laser was focused on the flame holder using a 100x objective lens. Backscattered

radiation from the sample was collected through a 500 [im confocal aperture and

dispersed over a 1800 grooves/mm grating onto a 1024-pixel CCD detector. The nominal

output of the laser was 15 mW, but could be attenuated with neutral density filters. The

Raman shift of the incident wavelength is determined from


VRaman = 1cat ), (3-7)


where Xo is the incident wavelength, Xscat is the wavelength of the scattered light, and

VRaman is the Raman-shifted wavenumber, usually measured in cm-1. The Raman shift is

directly proportional to energy, thus a larger V~aman corresponds to a larger shift in

energy. Note that elastically scattered light, governed by Mie or Rayleigh theory, has

zero shift since the wavelength of the incident matches that of the scattered radiation. A

typical Raman spectra is plotted with the Raman shift as the independent variable. A

positive value for VR aman is termed a Stokes shift and is designated as vStokes. For this

case, energy is transferred to the vibrational bond mode, leaving a lower energy scattered

photon. Conversely, a negative Raman shift is termed anti-Stokes and is designated as

Vanti-Stokes. Typically Stokes shifts are of much greater intensity than anti-Stokes shifts,

and the Stokes-shifted Raman scattered light will appear at a lower wavenumber (higher

wavelength) than the incident.

Iron and iron oxides have characteristic Raman bands in the region of 200-1400

cm-1, which correspond to a wavelength of 640.9-964.3 nm relative to the 632.8 nm

incident of the He:Ne laser.38 The bandwidth of the confocal micro-Raman spectrometer

was approximately 800 cm-1 thus multiple spectra were taken over the range of 150 to






58


1800 cm'1 and combined to generate a single spectrum of the sample covering the

wavenumbers of interest. The spectra were generally produced by averaging multiple

integration of the sample signal over 5 seconds.














CHAPTER 4
RESULTS AND DATA ANALYSIS

Experimental results are presented in this chapter. The results of the elastic

scattering and transmission studies will be used to extract characteristic size, number

density, and volume fraction data from the seeded and unseeded flames. Further, the

results of the micro-Raman study to characterize the state of the iron deposited on the

flame holder screen are presented.

Elastic Light Scattering Results

The laser cavity emitted vertically polarized light, and a polarizer at the head of the

scattering collection optics ensured that only vertically polarized scattered light was

captured. Thus the scattering parameter of interest was the vertical-vertical differential

scattering coefficient, K'vv. In order to extract this parameter accurately from the PMT

signal output, two calibrations were used a methane calibration to relate K'vv to the

signal Svv, and a stray light calibration using methane and nitrogen to account for the

extraneous signal induced by the reflection of laser light from various surfaces. The

same methane signal was used for both calibration operations. A typical PMT response

signal for the calibration gases and the flame signals are shown in Figure 4-1.

The flame signal shown in Figure 4-1 has been attenuated by a factor of 105 to

preserve linearity in the PMT response. Additionally, the baseline of each signal contains

a steady noise signal attributed to electrical noise stemming from the laser flash lamp

discharge. The laser was blocked from the detector and dark signals were taken for both

the calibration gases and the flame signals, which are also shown in Figure 4-1. These










dark current values were then subtracted from the signal response prior to any data

analysis to give a steady baseline. The same three signals are shown in Figure 4-2 after

baseline subtraction.

SN2 -CH4 flame w/ 10^5 ND filter attenuation
calibration dark -flame dark

0.01 ..... --............................

0.008

IV

0.006


I 0.004 -

I-I
0.002 -





-0.002
4.156 10"5 4.161 10"5 4.165 10-5 4.169 10"5

time (s)

Figure 4-1. Typical scattered signal response from photomultiplier tube measuring
calibration gases and flame signal at a fixed height and radial position.
Flame signal is attenuated by a factor of 105 to preserve signal linearity.

Ten experimental data sets (N=10) over a number of days were collected for the

unseeded flame conditions, and six data sets (N=6) were collected for the seeded flame.

A summary of the scattered signal intensities integrated over the signal width of 90 ns are

shown in Table 4-1 and Table 4-2 for the unseeded and seeded flames, respectively.

These raw values are not corrected for stray light, nor have the attenuation factors of the

neutral density filters been taken into account. The standard deviation of the integrated

signal osignaI is included as well.










- N2 flame w/ 10^5 ND filter attenuation
CH4


0


-0.002


Figure 4-2.






Table 4-1.


4.156 10" 4.161 10- 4.165 10"5 4.169 10"

time (s)


Baseline-subtracted scattered signals from calibration gases and flame at a
fixed height and radial position. Flame signal is attenuated by a factor of
105 to preserve signal linearity.



Average (N=10) time-integrated scattered signal from unseeded flame.


Unseeded time-integrated Svv (mV-s)
Radial Position
Height 1 2 3 4 5 6
b 2245.76 3108.40 4183.01 12691.04 15937.38 15041.06
signal 1601.00 2810.04 3110.61 6562.52 7958.66 7438.60
c 6236.08 6465.53 10366.47 32509.15 41723.12 39680.84
signal 3477.99 3577.56 5307.95 16856.91 21804.01 20050.97
d 16207.65 17706.80 28749.58 48773.24 58366.89 54751.78
signal 13482.79 12178.86 14378.20 23296.32 27738.85 25777.34
e 32434.08 35615.65 47510.26 67200.75 74017.74 66607.10
Osigal 20374.19 21068.17 24583.19 34683.52 37557.89 34804.48
f 38000.86 40580.24 47743.01 53219.41 50690.26 50530.84
Osigal 20521.18 22170.80 26233.36 27501.84 25432.70 25982.58









Table 4-2. Average (N=6) time-integrated scattered signal from iron pentacarbonyl
seeded flame.
Seeded time-integrated Svv (mV-s)
Radial Position
Height 1 2 3 4 5 6
b 4203.43 5689.80 9211.94 16924.39 19911.07 17847.25
Signal 2219.69 3892.45 4362.37 4460.29 6515.06 6028.36
c 9833.50 13848.86 35649.92 42231.29 49212.05 46287.00
Signal 5712.68 5690.52 16968.93 3703.77 8220.27 10710.66
d 22026.06 29478.17 42341.19 67974.13 77667.87 65318.91
Signal 6247.92 10078.33 13206.87 11121.29 16622.39 16005.66
e 28327.59 41352.14 63635.51 86432.04 89788.28 80665.76
Signal 13291.21 15986.79 23864.33 25076.68 20808.01 22100.59
f 47568.39 52784.64 60444.17 66742.23 67400.08 61121.52
Signal 10742.92 10862.32 13723.95 16993.14 11619.81 9383.93

As Table 4-1 and Table 4-2 show, the variation in the raw scattered light signals

varied widely from day to day, as evident from the large standard deviations. However,

this fluctuation is irrelevant so long as the relative scattered intensities between the

calibration scatterer, methane, and the scattered signal from the soot particles are

consistent with one another. The average K'vv for each radial position and height,

corrected for stray light, are summarized in Table 4-3 and Table 4-4 along with the

standard deviation cKvv. As shown in these summaries, the standard deviation for the

differential scattering coefficient is much less than the standard deviation in the daily

absolute signals. This indicates that while the absolute signal intensities may vary day in

and day out, they still remain in relative agreement with respect to the methane

calibration signal. Therefore, the scattering data were characterized as remaining

relatively consistent and repeatable over all experiments.









Average (N=10) unseeded K'vv results and standard deviation of K'vv.


Unseeded K'vv (cm'sr-)
Radial Position
Height 1 2 3 4 5 6
b 1.15E-04 1.55E-04 2.12E-04 6.66E-04 8.36E-04 7.95E-04
OKvv 5.67E-05 9.14E-05 9.53E-05 1.24E-04 8.71E-05 8.36E-05
c 3.33E-04 3.49E-04 5.56E-04 1.72E-03 2.20E-03 2.11E-03
OKvv 1.07E-04 1.22E-04 1.54E-04 3.81E-04 4.39E-04 4.37E-04
d 8.11E-04 8.99E-04 1.51E-03 2.59E-03 3.10E-03 2.92E-03
OKvv 4.55E-04 3.44E-04 2.49E-04 3.22E-04 5.09E-04 5.28E-04
e 1.70E-03 1.88E-03 2.50E-03 3.53E-03 3.90E-03 3.52E-03
OKvv 5.32E-04 5.72E-04 4.75E-04 4.90E-04 6.55E-04 6.49E-04
f 2.00E-03 2.13E-03 2.51E-03 2.82E-03 2.67E-03 2.66E-03
OKvv 3.53E-04 4.04E-04 5.18E-04 5.22E-04 3.48E-04 3.98E-04

Table 4-4. Average (N=6) seeded K'vv results and standard deviation of K'vv.
Seeded K'vv (cm'sr')
Radial Position
Height 1 2 3 4 5 6
b 1.97E-04 2.67E-04 4.40E-04 7.94E-04 9.21E-04 8.24E-04
OKvv 1.04E-04 1.84E-04 2.20E-04 1.86E-04 2.23E-04 2.07E-04
c 4.28E-04 5.99E-04 1.55E-03 1.89E-03 2.18E-03 2.05E-03
OKvv 2.29E-04 2.06E-04 6.42E-04 1.92E-04 2.11E-04 3.45E-04
d 9.28E-04 1.21E-03 1.77E-03 2.84E-03 3.22E-03 2.70E-03
OKvv 2.78E-04 3.47E-04 6.47E-04 3.12E-04 4.74E-04 5.13E-04
e 1.07E-03 1.58E-03 2.43E-03 3.33E-03 3.49E-03 3.13E-03
OKvv 3.54E-04 4.17E-04 5.71E-04 5.12E-04 4.44E-04 5.62E-04
f 1.92E-03 1.96E-03 2.25E-03 2.49E-03 2.53E-03 2.30E-03
OKvv 1.78E-04 2.19E-04 3.47E-04 4.78E-04 2.91E-04 2.95E-04

The results of the scattering experiments are also shown in Figure 4-3 for the

unseeded and seeded flames. The seeded and unseeded differential scattering coefficients

are plotted for each height over the burner with radial position as the independent

variable. Note that data were recorded for only one radial direction, but are presented


over the full burner for clarity.


Table 4-3.
















0.003500



0.003000



0.002500



0.002000



0.001500



0.001000



0.0005000


0.000 -I I
-3.81 -3.17 -2.54 -1.90 -1.27


0.003500



0.003000



0.002500



0.002000



0.001500



0.001000



0.0005000


-0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


- unseeded c
-4 seeded c


0.000 -I I I
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)



Figure 4-3. Seeded and unseeded differential scattering coefficients. A-E) Error bars
represent one standard deviation. A) at height b. B) at height c. C) at
height d. D) at height e. E) at height f.

















0.003500



0.003000



0.002500



0.002000



0.001500



0.001000



0.0005000


- unseeded d
-4 seeded d


0.000 I 1 1 1
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


0.003500



0.003000



0.002500



0.002000


0.001500



0.001000



0.0005000



0.000
-3.81 -3.17 -2.54 -1.90 -1.27 -0635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


Figure 4-3. Continued.







66



unseeded f
seeded f
0.003500


0.003000



0.002500-

0.002000


0.001500


0.001000


0.0005000


0.000-- -
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81

Radial position (mm)


Figure 4-3. Continued.

As Figure 4-3 shows, within experimental error, there is little deviation in the

differential scattering coefficient between the seeded and unseeded flames. The most

significant deviation in K'vv appeared early in the flame at height c, shown in Figure 4-

3B.

Transmission Results

As discussed in Chapter 3, the transmission through the flame is described by the

ratio of the laser pulse power through the flame to a reference position outside of the

flame. Transmission measurements were taken at six equally spaced line of sight

positions. These positions corresponded to the six radial positions investigated in the

scattering experiments; namely position 1 crossed through the center of the flame and the

remaining positions were spaced at 0.635 mm intervals outward. Table 4-5 and Table 4-6

present the raw data for the power transmitted through the unseeded and seeded flames









and the standard deviation of the incident power signal Opower. Note that the flame

emission (no laser) was subtracted at each radial position.


Average (N=


=5) unseeded power measurements used in transmission study.


Unseeded power measurements (mW)
Line of Sight Position
reference
outside
Height of flame 1 2 3 4 5 6
b 1.75 1.67 1.69 1.68 1.68 1.68 1.68
power 0.068 0.055 0.054 0.062 0.068 0.058 0.062
c 1.72 1.60 1.60 1.58 1.58 1.55 1.55
power 0.028 0.033 0.029 0.044 0.019 0.041 0.03
d 1.72 1.50 1.51 1.49 1.47 1.44 1.43
power 0.018 0.018 0.031 0.019 0.021 0.027 0.023
e 1.71 1.39 1.38 1.39 1.36 1.36 1.35
power 0.011 0.016 0.025 0.038 0.04 0.04 0.04
f 1.71 1.30 1.29 1.29 1.28 1.27 1.26
power 0.009 0.106 0.064 0.068 0.081 0.069 0.112


Table 4-6.


Average (N=5) seeded power measurements used in transmission study.


Seeded power measurements (mW)
Line of Sight Position
reference
outside
Height of flame 1 2 3 4 5 6
b 1.69 1.64 1.64 1.65 1.64 1.62 1.62
power 0.034 0.033 0.028 0.03 0.025 0.039 0.035
c 1.69 1.56 1.57 1.56 1.55 1.52 1.52
power 0.028 0.036 0.019 0.024 0.019 0.031 0.032
d 1.70 1.48 1.47 1.47 1.45 1.45 1.43
power 0.027 0.023 0.034 0.019 0.026 0.025 0.029
e 1.70 1.40 1.39 1.39 1.36 1.36 1.37
Power 0.029 0.016 0.023 0.016 0.046 0.023 0.046
f 1.72 1.31 1.29 1.30 1.30 1.33 1.36
Power 0.039 0.044 0.045 0.027 0.069 0.073 0.031

As seen in Table 4-5 and Table 4-6, the standard deviation in the transmitted power was

relatively low. This precision in measured transmission translated into low standard

deviation in the transmission, trans. The transmission through the unseeded and seeded


Table 4-5.









flames is summarized in Table 4-7 and Table 4-8, and was determined from the ratio of

the transmitted power to the reference power measured outside of the flame.

Table 4-7. Average (N=5) transmission through the unseeded flame.
Unseeded transmission, T
Line of Sight Position
Height 1 2 3 4 5 6
b 0.95 0.97 0.96 0.96 0.96 0.96
Otrans 0.007 0.008 0.008 0.01 0.008 0.01
c 0.93 0.93 0.92 0.92 0.90 0.90
Otrans 0.006 0.006 0.011 0.007 0.011 0.009
d 0.87 0.88 0.87 0.86 0.84 0.83
Otrans 0.01 0.011 0.01 0.009 0.018 0.013
e 0.81 0.80 0.81 0.80 0.79 0.79
Otrans 0.006 0.011 0.019 0.019 0.022 0.023
f 0.76 0.75 0.75 0.75 0.74 0.74
Otrans 0.059 0.036 0.04 0.047 0.038 0.064


Average (N:


=5) transmission through the seeded


Seeded transmission, -T
Line of Sight Position
Height 1 2 3 4 5 6
b 0.97 0.97 0.97 0.97 0.96 0.95
Otrans 0.014 0.008 0.01 0.008 0.014 0.006
c 0.92 0.93 0.92 0.92 0.90 0.90
Otrans 0.015 0.005 0.013 0.011 0.016 0.006
d 0.87 0.87 0.87 0.85 0.85 0.84
Otrans 0.011 0.013 0.012 0.014 0.009 0.015
e 0.82 0.81 0.81 0.80 0.80 0.80
Otrans 0.02 0.015 0.013 0.022 0.016 0.025
f 0.76 0.75 0.76 0.76 0.77 0.79
Otrans 0.019 0.023 0.017 0.032 0.034 0.003

The transmission measurements provided an overall extinction coefficient for the

line of sight through the flame. In order to determine the individual extinction

coefficients for each concentric radial region (i.e., annular region), a deconvolution

technique must be employed. A number of methods exist to approach the deconvolution


Table 4-8.


flame.









problem. In this work, three different techniques were tested onion peeling, linear

regression, and a three-point Abel inversion, with the latter producing the best results

with the least amount of error. A brief summary of the onion peeling and linear

regression methods follow, while the results of the three-point Abel inversion will be

presented in full. A detailed description of all three of these techniques and their results

are given in Appendix B.

The onion peeling method is perhaps the simplest deconvolution technique.

Working from the outer-most layer, or annular region, inward, the unknown parameters

are successively determined one layer at a time. For this study, the sixth line of sight

position for the transmission data intersected only through annular region 6. Therefore, if

the optical pathlength through the flame is known, Kext,6 may be determined from the

Beer-Lambert law. Working inward, the extinction coefficient for region 5 is a function

of the transmission data through this line of sight, as well as the now known extinction

coefficient of region 6. Through this manner of successive determination, the extinction

coefficients for each annular region are calculated based on the values of Kext in the outer

regions.

Although onion peeling is straightforward and relatively simple, there is one major

drawback of the onion peeling method because this method relies on the successive

determination of outer layer parameters, any error in these layers is compiled through the

field and can result in high errors in the inner regions. With relatively high overall

transmission values, this can easily lead to negative extinction coefficients as the sum of

the Kext values for the outer regions exceeds the overall transmission recorded through the









entire path. In the onion peeling analysis performed for the present data, a number of

extinction coefficients were predicted to be negative valued. These are unrealistic values

and evidence of the high imprecision in the sequential deconvolution scheme.

In an effort to redistribute the error in the deconvolved variable, a linear regression

method with a least squares approach was used. In this technique, the exact extinction

coefficient at a point was not explicitly determined. Rather, a regression fit determined

the extinction coefficients in such a way that the overall error was minimized, while

bringing each of the individual extinction coefficients near, but not exactly to, their true

value as predicted by the Beer-Lambert law. The values of Kext extracted from the linear

regression analysis were in overall agreement with those from the onion peeling method.

However, unallowed negative values for Kext still appeared in two positions in the seeded

results. The median error in these values decreased by approximately one half over the

onion peeling results.

The final deconvolution technique employed, a three-point Abel inversion, was

most successful in predicting a realistic extinction coefficient while minimizing the error

throughout the flame field. Similar to the onion peeling method, this technique uses

information from the outer layers to extract information from the inner regions.

However, for more precision, the projection data is expanded as a quadratic function of

its neighboring points. More detail is presented in Appendix B and in the work of

McNesby et al.39 Dasch provides a succinct summary of this technique as well.40 The

results of this analysis are shown in Table 4-9 and Table 4-10.









Table 4-9. Average (N=5) unseeded extinction coefficients determined using a three-
point Abel inversion.
Unseeded Kext (cm1) Three-Point Abel Inversion
Radial Position
Height 1 2 3 4 5 6
b 1.126E-01 3.574E-02 2.908E-02 4.086E-02 5.151E-02 9.783E-02
OAbel 6.754E-02 3.928E-02 2.795E-02 2.724E-02 1.889E-02 1.855E-02
c 5.003E-02 5.546E-03 4.837E-02 6.601E-02 1.281E-01 2.420E-01
OAbel 5.742E-02 2.906E-02 3.891E-02 2.161E-02 2.904E-02 1.814E-02
d 1.113E-01 4.769E-02 6.891E-02 1.169E-01 2.202E-01 4.221E-01
OAbel 1.079E-01 5.731E-02 3.974E-02 2.730E-02 4.946E-02 2.700E-02
e 9.044E-02 1.855E-01 1.668E-01 2.285E-01 3.100E-01 5.462E-01
OAbel 7.600E-02 6.425E-02 7.591E-02 6.487E-02 6.300E-02 5.070E-02
f 1.930E-01 2.373E-01 2.592E-01 2.940E-01 3.973E-01 7.099E-01
OAbel 7.527E-01 2.198E-01 1.730E-01 1.707E-01 1.184E-01 1.525E-01

Table 4-10. Average (N=5) seeded extinction coefficients determined using a three-point
Abel inversion.
Seeded Kext (cm1) Three-Point Abel Inversion
Radial Position
Height 1 2 3 4 5 6
b 1.825E-02 2.799E-02 3.357E-03 1.047E-02 4.993E-02 1.074E-01
OAbel 1.356E-01 3.573E-02 3.443E-02 2.156E-02 3.275E-02 1.116E-02
c 8.781E-02 2.726E-02 4.017E-02 5.760E-02 1.278E-01 2.418E-01
OAbel 1.561E-01 2.296E-02 4.467E-02 3.335E-02 4.214E-02 1.094E-02
d 4.238E-02 8.877E-02 9.598E-02 1.565E-01 1.963E-01 3.960E-01
OAbel 1.159E-01 6.679E-02 4.634E-02 4.417E-02 2.469E-02 3.176E-02
e 8.668E-02 1.449E-01 1.484E-01 2.318E-01 3.221E-01 5.223E-01
OAbel 2.379E-01 8.520E-02 5.443E-02 7.459E-02 4.601E-02 5.456E-02
f 1.738E-01 2.907E-01 3.050E-01 3.516E-01 4.081E-01 5.703E-01
OAbel 2.380E-01 1.401E-01 7.486E-02 1.132E-01 1.025E-01 5.990E-03

The results of the three-point Abel inversion yielded realistic values for the extinction

coefficients at each height and radial position while producing the lowest median error.

Figure 4-4 compares the unseeded and seeded Kext for each height with respect to radial

position. Note that data were recorded for only one radial direction, but are presented


over the full burner for clarity.














unseeded b
-- seeded b
0.8000



0.7000



0.6000-



0.5000 -


S 0.4000 A










0.1000
0.31000 -



0.2000-







-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)



e unseeded c
-- seeded c
0.8000-



0.7000



0.6000



0.5000



0.4000 B



0.3000






0.1000


0.000
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)



Figure 4-4. Seeded and unseeded extinction coefficients determined using a three-point

Abel inversion. A-E) Error bars represent one standard deviation. A) at

height b. B) at height c. C) at height d. D) at height e. E) at height f.















9 unseed
-* -seededd


-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


unseeded e
-* seeded e

0.8000- -



0.7000



0.6000 -



0.5000 -



0.4000



0.3000


0.2000 -

0.1000- -- --*-" -- -- --- -_

0.1000

0.000 --


-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


Figure 4-4. Continued.











unseeded f
seeded f
0.8000 -


0.7000


0.6000 -




0.5000 ________


0.3000- --- -- ,-- -;-- :-- _-- __-I--- ---


0.2000- -


0.1000 -


0.000
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81

Radial position (mm)


Figure 4-4. Continued.


In comparing the extinction coefficients over all radial positions and heights,


Figure 4-4 shows that, in general, the extinction coefficients peaked at the outer-most


annular regions. Additionally, within experimental error, there was little change in this


parameter in the seeded and unseeded flames.


Soot Characteristics Determined from Mie Theory

From the results of the scattering and transmission studies, the ratio K'vv/Kext for


the each radial position and height in the flame was calculated. These results are shown


in Table 4-11 and Table 4-12. This ratio was then used to determine the size, number


density, and volume fraction of particles at each radial position and vertical height above


the burner.









Table 4-11. Unseeded ratio of K'vv/Kext determined from experimental data.
Unseeded K'vv/Kext (sr1)
Radial Position
Height 1 2 3 4 5 6
b 1.06E-03 4.50E-03 7.55E-03 1.69E-02 1.68E-02 8.42E-03
OKvv/Kext 8.23E-04 5.62E-03 8.02E-03 1.17E-02 6.42E-03 1.83E-03
c 6.59E-03 6.21E 02 1.14E-02 2.58E-02 1.70E-02 8.61E-03
OKvv/Kext 7.85E-03 3.26E- 0 9.67E-03 1.02E-02 5.13E-03 1.90E-03
d 6.76E-03 1.75E-02 2.04E-02 2.05E-02 1.31E-02 6.42E-03
OKvv/Kext 7.57E-03 2.21E-02 1.22E-02 5.43E-03 3.63E-03 1.23E-03
e 1.64E-02 8.83E-03 1.31E-02 1.35E-02 1.10E-02 5.60E-03
OKvv/Kext 1.47E-02 4.07E-03 6.44E-03 4.25E-03 2.89E-03 1.16E-03
f 8.38E-03 7.24E-03 7.83E-03 7.76E-03 5.44E-03 3.03E-03
OKvv/Kext 3.27E-02 6.85E-03 5.47E-03 4.73E-03 1.77E-03 7.94E-04


Table 4-12.


Seeded ratio of K'vv/Kext determined from experimental data.


Seeded K'vv/Kext (srf)
Radial Position
Height 1 2 3 4 5 6
b 1.08E-02 9.55E-03 -.31E- -O 7.59E 02 1.84E-02 7.67E-03
OKvv/Kext 8.05E-02 1.39E-02 1.34+00 1.57E 01 1.29E-02 2.09E-03
c 4.87E-03 2.20E-02 3.85E-02 3.28E-02 1.71E-02 8.47E-03
OKvv/Kext 9.04E-03 2.00E-02 4.57E-02 1.93E-02 5.86E-03 1.48E-03
d 2.19E-02 1.36E-02 1.85E-02 1.81E-02 1.64E-02 6.83E-03
OKvv/Kext 6.02E-02 1.10E-02 1.12E-02 5.49E-03 3.18E-03 1.41E-03
e 1.24E-02 1.09E-02 1.64E-02 1.44E-02 1.08E-02 5.99E-03
OKvv/Kext 3.43E-02 7.03E-03 7.13E-03 5.12E-03 2.07E-03 1.25E-03
f 1.10E-02 6.75E-03 7.38E-03 7.08E-03 6.19E-03 4.03E-03
OKvv/Kext 1.51E-02 3.34E-03 2.14E-03 2.66E-03 1.71E-03 5.19E-04

It is important to note the K'vv/Kext values at unseeded height c, position 2, and seeded

height b, positions 3 and 4. The ratio K'vv/Kext is a non-monotonic function with a

maximum value of4.46E-2 sr-1 for the complex refractive index used in this study.

However, the values in these three noted positions were much greater than this maximum

value. In looking at the unseeded values for K'vv and Kext presented in Table 4-3 and

Table 4-9, it is seen that at height c, position 2, the extinction coefficient is an order of

magnitude smaller than that in neighboring sections. This value, combined with a modest









K'vv at the same height and position, result in a very large K'vv/Kext ratio. Similar results

are seen for the seeded case at height b, positions 3 and 4. As Table 4-4 shows, the K'vv

at these locations is comparable to neighboring sections. However the Kext values

predicted from the three-point Abel inversion summarized in Table 4-10 are much

smaller than perhaps truly expected, thus resulting in an uncharacteristic K'vv/Kext ratio.

As a result, these out-of-range K'vv/Kext values were discarded from the analysis and no

information about particle size, number density or volume fraction was obtained for these

three locations. The non-monotonic nature of K'vv/Kext is discussed further below.

Particle Size

Recall from Chapter 2 that the ratio of the differential scattering coefficient and the

extinction coefficient can be used to determine the modal particle diameter, assuming a

value of the complex refractive index m is known. For this study, a value of m = 2.0-

0.35i was used. A wide variation in the complex refractive index of soot has been

reported in the literature. Table 4-13 summarizes the findings for m from key studies.

Table 4-13. Complex refractive indices for soot from various sources.
Type of Incident m = n ki
Authors soot Wavelength (nm) n k
Chippett and Gray41 acetylene visible 1.9-2.0 0.35-0.50
Charalampopoulos propane 457.9 1.58-1.82 0.65-0.83
and Chang42 488 1.57-1.82 0.65-0.85
514.5 1.54-1.71 0.67-0.87
Dalzell and Sarofim43 propane 435.8 1.57 0.46
550.0 1.57 0.53
650 1.56 0.52
acetylene 435.8 1.56 0.46
550.0 1.56 0.46
650 1.57 0.44
Pluchino, Goldberg, carbon 488 1.6-1.8 0.06-0.19
Dowling, and
Randall44







77


As Table 4-13 demonstrates, the range of m reported is wide, and no single value


has been generally accepted. The value selected for this study is the value reported by


Chippett and Gray,41 which was based on a similar light scattering analysis with a heavily


sooting fuel. In addition, it is noted that the ratio of the differential scattering coefficient


to the extinction coefficient gives non-monotonic solutions for particle diameters beyond


a certain range. The complex refractive index chosen for this study, along with a


skewness parameter Oo of 0.2 from the ZOLD function, produced the best range in


K'vv/Kext to fit the experimental data within the monotonic solution range.


Using a Mie theory analysis, the modal soot particle diameter as a function of


K'vv/Kext was plotted, as shown in Figure 4-5, and a polynomial curve fit was used to


extract the particle diameter from the experimental results. Note the non-monotonic


behavior of K'vv/Kext, hence results for the diameter were limited to the monotonic


region, corresponding to diameters less than 145 nm.

5o0oo 0l . ll . ,.II. . .I


40(0010Z



4000 10'



2.000 10



1.000101



fNI)IX n


0.000 50.00 100.0 150.0 200.0 250.0

modal diameter (nm)


Figure 4-5. Soot particle modal diameters determined from Mie theory for m = 2.0-
0.35i and ZOLD parameter oo = 0.2.


Inversion reglor


moo~klimit









Using the full Mie theory, the modal particle diameter for each radial section and at

each height was extracted. These diameters are summarized in Table 4-14 and Table 4-

15 for the unseeded and seeded flames, respectively. Error in these calculations ranged

from 4.4% (seeded height f, position 6) to over 300% (seeded height b, position 1), while

the majority of the diameters calculated had error of less than 25%. A complete error

analysis is presented in Appendix C.

Table 4-14. Unseeded soot particle modal diameters determined from Mie theory and
complex refractive index of m = 2.0-0.35i.
Unseeded Particle Diameter (nm)
Radial Position
Height 1 2 3 4 5 6
b 22.89 40.76 47.95 67.33 67.20 49.74
c 45.94 N/A* 55.94 81.18 67.45 50.13
d 46.29 68.35 73.01 73.24 59.58 45.56
e 66.35 50.58 59.60 60.44 55.06 43.70
f 49.65 47.31 48.53 48.38 43.29 35.39
Value out of monotonic region.

Table 4-15. Seeded soot particle modal diameters determined from Mie theory and
complex refractive index of m = 2.0-0.35i.
Seeded Particle Diameter (nm)
Radial Position
Height 1 2 3 4 5 6
b 54.74 52.06 N/A* N/A* 70.00 48.20
c 41.82 75.38 107.21 95.18 67.63 49.84
d 75.26 60.82 70.08 69.49 66.40 46.44
e 58.15 54.94 66.33 62.35 54.80 44.60
f 55.19 46.28 47.59 46.98 45.05 39.27
Value out of monotonic region.

Figure 4-6 shows the unseeded and seeded soot modal particle diameters

graphically for all radial positions and vertical heights, excluding those locations where

the monotonic limit was exceeded.












- unseeded b
-seeded b


-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


Unseeded c
-- -seeded c


100.0---- -








.O I _
60.00




40.00




20.00 -
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


Figure 4-6. Unseeded and seeded soot particle modal diameters. A) at height b. B) at
height c. C) at height d. D) at height e. E) at height f.












-- unseeded d
-- -seeded d


-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


Figure 4-6. Continued.


e unseeded e
-- -seeded e







81


- unseeded f
- seeded f


1UU.U



80.00-



60.00- E




40.00- _



20.00
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81

Radial position (mm)


Figure 4-6. Continued.

Recall that the ZOLD function describing the particle sizes is a skewed function,

thus the mean diameter is larger than the modal diameter. The modal diameter is

preferred for discussion over the mean, as it represents the most probable size of the

particles. In contrast, the use of the mean particle size in analysis may result in

confusion, if not clearly defined, due to the influence of the tail of the probability

distribution. For completeness, the mean diameters are presented below in Table 4-16

and Table 4-17, however they will not be considered further in this analysis. As noted

above, the skewness parameter Oo used for this work was 0.2. Thus, the average


diameters were calculated from the ZOLD function by dmean=dmodalexp(3oo2/2). For


0o=0.2, the multiplier is equal to 1.06.









Table 4-16. Unseeded soot particle mean diameters.
Unseeded Particle Diameter (nm)
Radial Position
Height 1 2 3 4 5 6
b 24.31 43.28 50.92 71.49 71.36 52.82
c 48.78 N/A* 59.40 86.20 71.62 53.23
d 49.15 72.58 77.52 77.77 63.26 48.38
e 70.45 53.71 63.29 64.18 58.46 46.40
f 52.72 50.24 51.53 51.37 45.97 37.58
Value out of monotonic region.

Table 4-17. Seeded soot particle mean diameters.
Seeded Particle Diameter (nm)
Radial Position
Height 1 2 3 4 5 6
b 58.12 55.28 N/A* N/A* 74.33 51.18
c 44.41 80.04 113.84 101.07 71.81 52.92
d 79.91 64.58 74.41 73.79 70.51 49.31
e 61.75 58.34 70.43 66.21 58.19 47.36
f 58.60 49.14 50.53 49.89 47.84 41.70
Value out of monotonic region.

For comparison, the modal diameter of the soot particles in the center of the flame

at height c was also calculated assuming the same skewness Oo but with a complex

refractive index of m = 1.6 0.40i, a value in line with those determined by Dalzell and

Sarofim.43 From Table 4-14 and Table 4-15, the modal diameters calculated earlier at

this position were 45.9 nm and 41.8 nm for the unseeded and seeded flames, respectively,

with an unseeded/seeded diameter ratio of 1.10. With the alternate value of m, these

values were determined to be 63.3 nm for the unseeded flame, and 57.3 nm for the seeded

flame, with a ratio of 1.10, which correspond to an average increase in particle diameter

slightly higher than 30%. However, the relative diameters (i.e., unseeded/seeded) are in

exact agreement. Therefore, while the refractive index will influence the absolute values,

the effect on relative comparisons between unseeded and seeded flames is minimal.







83


Number Density of Particles

A plot of Mie theory Cext versus K'vv/Kext allowed for the determination of the

number density N from the relation N=Cext/Kext. This plot is shown in Figure 4-7.



3.000 10- -


2 .50 0 10 ............................................ ............................ .................................................................................... ................................


2.000 10- o


1.500 1 .......... ........... ....................................................................... ......... ...


1.000 10 --- -


5.000 10-11


0.000
0.000 100 1.00 10 2.000 10. 3-000 10 4.000 102 5.000 10

K'vKext


Figure 4-7. Extinction cross section of soot particles determined from Mie theory for
m = 2.0-0.35i and ZOLD parameter Oo = 0.2.

To accurately fit a polynomial curve to the Cext Mie data, the range of K'vv/Kext was

divided into three sections K'vv/Kext < 3.0E-2, 3.0E-2 < K'vv/Kext < 4.0E-2, and

K'vv/Kext > 4.0E-2. From this fit, Cext, and therefore N, were easily determined at each

height and radial position. The number densities resulting from this procedure are shown

in Table 4-18 and Table 4-19, and plotted for each height in the flame in Figure 4-8.

Error in these calculations ranged from 15.3% (seeded height f, position 6) to over

1000% (seeded height b, position 1), with the majority of number density errors less than

86%. More important than the magnitude of the absolute error in these measurements,









however, is the relative agreement between the unseeded and seeded flames, as discussed

above in the context of refractive indices.


Table 4-18.


Unseeded soot particle number densities determined from Mie theory and
complex refractive index of m = 2.0-0.35i.


Unseeded Number Density (particles/cm3)
Radial Position
Height 1 2 3 4 5 6
b 2.695E+11 1.737E+10 7.418E+09 3.282E+09 4.166E+09 2.162E+10
c 1.519E+10 N/A* 7.094E+09 2.381E+09 1.022E+10 5.191E+10
d 3.274E+10 3.624E+09 4.006E+09 6.696E+09 2.645E+10 1.325E+11
e 7.652E+09 3.849E+10 2.001E+10 2.625E+10 4.787E+10 2.033E+11
f 4.293E+10 6.384E+10 6.303E+10 7.234E+10 1.535E+11 5.485E+11
Value out of monotonic region.

Table 4-19. Seeded soot particle number densities determined from Mie theory and
complex refractive index of m = 2.0-0.35i.
Seeded Number Density (particles/cm3)
Radial Position
Height 1 2 3 4 5 6
b 2.873E+09 5.231E+09 N/A* N/A* 3.464E+09 2.682E+10
c 3.879E+10 1.371E+09 4.596E+08 1.141E+09 1.010E+10 5.300E+10
d 2.147E+09 9.994E+09 6.627E+09 1.117E+10 1.656E+10 1.150E+11
e 1.124E+10 2.253E+10 1.257E+10 2.412E+10 5.053E+10 1.789E+11
f 2.664E+10 8.563E+10 8.016E+10 9.736E+10 1.342E+11 3.164E+11
Value out of monotonic region.









































-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


unseeded c
-* seeded c
6.000 10"


5.000 10" --



4.000 10"



3.000 10" -


2.000 10"1



1.000 10" 1


0.00081 -31 2 27 1.90 2.54 3.17 381
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


Figure 4-8. Unseeded and seeded particle number densities. A) at height
c. C) at height d. D) at height e. E) at height f.


b. B) at height














Unseeded d
seeded d
6.000 10'1


5.000 10"



4.000 10"



3.000 10"1


2.000 101 -



1.000 1011



000 -- --= -


-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17


Radial position (mm)



Unseeded e
-* -seeded e
6.000 10" ,


E

- 3.000
CL
z


3.81


-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81


Radial position (mm)


Figure 4-8. Continued.























3.0001011 E

z
2.000 1011 .


1.000 101. -,


0.000
-3.81 -3.17 -2.54 -1.90 -1.27 -0.635 0.00 0.635 1.27 1.90 2.54 3.17 3.81

Radial position (mm)


Figure 4-8. Continued.

As seen in Figure 4-8, the soot particle number densities throughout the flame are

nearly identical, within experimental error, for the seeded and unseeded flames. The sole

exception being height b, position 1 (Figure 4-8A). However, upon closer investigation,

it is seen that the Cext for this point is very small nearly five times smaller than the Cext

determined for its neighboring point. Further, the Kext from the three-point Abel

inversion was three times larger than the same neighboring point. Most likely the high

number density calculated for this position is due to experimental error and is not a true

measure of the soot condition.

Particle Volume Fraction

With the particle diameter and number density known, the particle volume fraction

is determined from