Oct 22, 2001 - Because of droplet shattering on the wire, the method is limited to flow velocities ...... Flowmaster 3S was equipped with image doubling optics.
ROGERIO GOMES PIMENTEL
MEASUREMENT AND PREDICTION OF DROPLET SIZE DISTRIBUTION IN SPRAYS
Thèse présentée à la Faculté des études supérieures de l'Université Laval dans le cadre du programme de doctorat en génie mécanique pour l'obtention du grade de Philosophiae Doctor (Ph.D.)
Département de génie mécanique FACULTÉ DE SCIENCES ET GÉNIE UNIVERSITÉ LAVAL QUÉBEC
2006
© Rogério Gomes Pimentel, 2006
Abstract As part of sustainable development policies in most developed countries, the requirement for improving the performance of energy génération Systems has motivated much research around the world. A field of particular interest is optimizing the use of nonrenewable liquid hydrocarbon fuels since their application in internai combustion engines and industrial burners is responsible for most of the energy production and air pollution around the world. However, due to the complex phenomena governing each aspect of the combustion of such fuels, better understanding of the processes involved is essential. Spray characteristics are considered to play the most important rôle from the standpoint of thermodynamic performance and the level of pollutant émissions in combustion. However, the mechanism of spray formation is not perfectly understood. The knowledge of the evaporation characteristics of the discrète phase in a convective environment must also be better understood. Expérimental studies hâve demonstrated to be indispensable in the development of complex Systems providing assessment of the fondamental aspects of phenomena involved and supporting the improvement in the accuracy of theoretical models implemented in numerical codes. Therefore, the purpose of this study was to improve the understanding of the atomization process through the development of more rational méthodologies to carry out droplet sizing in sprays, to predict the performance of liquid fuel atomizers and to détermine the evaporation characteristics of liquid fuel droplets. With thèse goals the following methods were proposed: i. Détermination of minimum sample size required to characterize sprays, ii. Non-intrusive technique to measure evaporation rate of free-falling liquid fuel droplets, iii. Generalised droplet size distribution to characterize sprays, using Pearson system, iv. Development of corrélation for planar SMD distribution in sprays, and v. Improved atomization model for CFD codes.
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The results obtained in this study were used to détermine the best fuel injection System, positioning, and operating conditions for the expérimental puise détonation engine developed by the Propulsion Group at Defence Research and Development Canada Valcartier. However, thèse results can be used, on a broader basis, to support the validation of computational fluid dynamics codes and the design of industrial combustion chambers.
Résumé Les politiques récentes de développement durable en vigueur dans la majorité des pays requièrent des améliorations significatives dans la performance des systèmes de génération d'énergie d'aujourd'hui et ont encouragé fortement différentes études à travers le monde au cours des dernières années. Un champ d'intérêt particulier concerne l'optimisation de l'usage des carburants liquides, car ils sont responsables pour les émissions polluantes dans le monde de part les applications dans les moteurs à combustion interne et les brûleurs industriels étant ainsi des sources non renouvelables d'énergie primaire. Cependant, les complexités inhérentes aux phénomènes qui gouvernent chaque partie du processus de la combustion demandent encore une meilleure compréhension. Entre ces complexités, la qualité de l'atomisation des carburants liquides joue un rôle major du point de vue de la performance thermodynamique et le niveau des émissions polluantes dans le processus de combustion. Néanmoins, le mécanisme de formation des aérosols n'est pas encore parfaitement compris. Un autre aspect qui demande des études plus approfondies pour une meilleure compréhension est la connaissance des caractéristiques d'évaporation de la phase discrète dans un environnement convectif. Au cours des dernières années, des études expérimentales ont démontré l'importance de la compréhension des aspects fondamentaux inhérents aux systèmes complexes en supportant l'amélioration de la précision des modèles théoriques implémentés dans les codes de simulation numérique. La présente étude est consacrée à améliorer la compréhension du processus d'atomisation pour un carburant liquide, par le développement de méthodologies plus rationnelles pour mesurer les tailles des gouttelettes dans des aérosols, pour prédire la performance d'atomiseurs de liquides et pour déterminer les caractéristiques de l'évaporation de gouttelettes liquides. Avec ces objectives les méthodes suivantes ont été proposées: i.
Détermination de la taille minimale requise par un échantillon pour la caractérisation d'un aérosol,
ii. Technique non-intrusive pour mesurer le taux d'évaporation des gouttelettes de carburants liquides,
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iii. Fonction général pour caractériser la taille de gouttelettes dans des aérosols selon le système Pearson, iv. Développement d'une corrélation pour la distribution du SMD dans un plan axial de l'aérosol, et v. Perfectionnement du modèle d'atomisation à utiliser dans des codes de modélisation numérique en fluide. Les résultats pratiques obtenus ont été utilisés pour déterminer les positionnements et conditions opérationnelles optimales, ainsi que le mode d'injection le plus approprié à être utilisé pour le prototype expérimental du moteur à détonation puisée qui a été développé par le Groupe de la Propulsion du centre de Recherche pour la Défense et Développement du Canada - Valcartier. Néanmoins, les résultats peuvent être utilisés d'une façon plus générale pour supporter la validation de codes de modélisation numérique et le projet de chambres de combustion industrielles.
Forward This study was carried out to develop rational méthodologies to characterize liquid fuel sprays to be applied to the Canadian Puise Détonation Engine Program, as developed by the Defence Research and Development Canada - Valcartier (DRDC). It is the opportune time to demonstrate ail my gratitude to people I had the pleasure to share some years of work and life that contributed directly or indirectly in différent aspects of this study. I would like to thank to my thesis supervisor Dr. Alain deChamplain and my cosupervisor Dr. Robert Stowe to rely on me for this important task related to the Canadian Puise Détonation Engine and for their valuable advice during my graduate work. I would also like to thank very much my co-supervisor Dr. Detlef Kretschmer for his numerous catalytic comments that motivated me to obtain important accomplishments in the research. I was very grateful to hâve had the opportunity to contribute and to work together with the scientists from the Propulsion Group at DRDC, Mr. Paul Harris and Mr. Rocco Farinaccio. Thanks for their very proactive support and solid expériences in propulsion Systems. I am also in debt to the technicians in mechanics, computers and electronics from the Mechanical Engineering department, Jean-Claude Gariépy, Sylvain Ménard, Michel Tremblay, Patrice Gagnon, Mathieu Thomassin, André Chamberland and Michel Dominique to allow me to materialize many ideas to overcome several aspects of the expérimental part of the research. My spécial thanks to Yves Jean for his valuable support and discussions on instrumentation. Thanks to the administrative personnel of the Mechanical Engineering department, Mrs. Hélène Fafard, Mrs. Dominique Poulin, Mrs. Sylvie Brodeur, Mrs. Johanne Pouliot and Mrs. Lise Leclerc for their usual support and patience. I would like to thank Lande Vieira and Laurent Turgeon from the Engineering Physics department for lending us many optical instruments used in the research. I would like to thank Manuel Garcia from the Chemical Engineering department for his tireless support in the expérimental campaign. I would like to thank the encouragements received
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from my présent and former colleagues from the Energy Group at Laval University, PierreAntoine Rainville, Stéphane Mailhot, Nicolas Hamel and Vincent Harrison. I would like to thank Mrs. Bonnie McBride from NASA for her kind support providing me first hand the updated version of the CEA code and several thermodynamics properties for JP-1O, which were not yet available in the open literature at that occasion. Thanks to Dr. Constantino Tsallis from the Brazilian Centre of Researches in Physics (CBPF) and Dr. H. T. Huyin from the Electronic Engineering department who devoted a great part of their precious time to discuss and suggest aspects concerning statistical analysis. Thanks for Dr. Konstantin Kurbatskii from Fluent Inc. for the many suggestions about the implementation of user-defined functions. Thanks for Mr. Thomas Berg from LaVision GmbH for kindly provide me many droplet size data of sprays. Finally, I would like to thank the Defence Research and Development Canada Valcartier (DRDC), the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT) for their financial support. Rogério G. Pimentel
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To my wife Helaine, my children Igor and Julie and to my parents Antonio and Jadirfor their support, encouragement and compréhension during ail the time
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"Ifany macro-phenomenon isfound to be reproducible, then it jollows that ail microscopic détails that were not reproduced must be irrelevant for understanding and predicting it. " E. T. Jaynes, 1985
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Table of contents Abstract Résumé Forward Introduction Chapter 1: The Atomization Mechanism Introduction 1.1 Liquid Dripping 1.2 Liquid Column/Jet Break-up 1.3 Disintegration of Liquid Sheets 1.4 Atomizers 1.5 Factors Influencing Atomization 1.5.1 Liquid Properties 1.5.2 Ambient Conditions 1.6 Summary of Atomization Mechanisms Chapter 2: Spray Diagnostics Introduction 2.1 Mechanical Methods 2.2 Electrical Methods 2.3 Optical Methods 2.3.1 The Laser Diffraction Method 2.3.2 The Phase Doppler Particle Analyzer 2.3.3 Shadowgraphy Technique 2.3.4 The Planar Droplet Sizing Technique 2.3.5 Particle Image Velocimetry and Particle Tracking Velocimetry 2.4 Summary of Spray Diagnostics Chapter 3: Mathematical Formulations to Characterize Sprays Introduction 3.1 Graphical Représentation of Droplet Distribution 3.2 Indicators of Position, Dispersion, and Symmetry 3.2.1 Indicator of Position or Central Tendency 3.2.2 Measurements of Dispersion 3.2.3 Measurements of Shape 3.3 Droplet Size Distributions in Sprays 3.3.1 Normal Distribution and its Dérivations 3.3.2 Chi Distribution and its Dérivations 3.3.3 Hyperbolic Distribution and its Dérivations 3.4 Information Theory and the Maximum Entropy Formalism 3.4.1 Application of MEF for Particle Sizing 3.5 Summary of the Mathematical Formulations to Characterize Sprays Chapter 4: Goodness-of-Fit Test Introduction 4.1 Graphical Methods 4.1.1 Overlaying Plots 4.1.2 Probability-Probability Plots
i iii v 1 7 7 8 9 11 13 16 16 18 19 21 21 22 24 25 26 29 30 31 33 34 36 36 36 39 39 43 45 47 49 51 54 56 57 59 61 61 62 62 62
4.1.3 Quantile-Quantile Plot 4.2 Statistical Tests 4.2.1 Chi-Square Goodness-of-Fit Test 4.2.2 Kolmogorov-Smirnov test 4.2.3 Anderson-Darling Test 4.2.4 Kullback-Leibler Distance - Relative Entropy and Mutual Information 4.2.5 Pearson Corrélation Coefficient (/?) 4.3 Summary of Goodness-of-Fit Tests Chapter 5: Possible Generalized Distributions Applied to Spray Systems Introduction 5.1 The Pearson System of Frequency Curves 5.2 Application of the Pearson System to Sprays 5.3 Summary of Possible Generalized Droplet Size Distributions in Sprays Chapter 6: Minimum Sample Size of Spray Systems Introduction 6.1 Factors Affecting Sample Sizes 6.2 Proposed Methodology 6.3 Statistics Applied to Sprays 6.4 Sprays Applied to Combustion 6.5 Conclusions Chapter 7: Previous Expérimental Results Introduction 7.1 Experiments at Laval University 7.1.1 Results for the Bosch System 7.1.2 Results for the BETE XA-PR200 Nozzle 7.1.3 Results with Delavan Atomizers 7.2 LaVision Measurements 7.3 Bhatia, Domnick, Durst and Tropea Experiments 7.4 Paloposki and Fagerholm Experiments 7.5 Lee and Tankin Experiments 7.6 Tishkoff s Experiments 7.7 Tate and Oison Experiments 7.8 Turner and Moulton Experiments 7.9 Houghton Experiments 7.10 Analysis of the Expérimental Data 7.11 Comparison of the Models 7.12 Summary of Previous Expérimental Work Chapter 8: Assessment of Planar Droplet Size Distributions in Sprays Introduction 8.1 Expérimental Facility 8.2 Calibration of the Planar Droplet Sizing Technique 8.2.1 Measurements with the Shadowgraphy Technique 8.2.2 Estimate of the Parameters 8.2.3 Measurements with the Planar Droplet Sizing Technique 8.3 Summary for the Assessment of a Droplet Size Distribution in Sprays Chapter 9: Investigation of Evaporating Properties of Liquid Fuels Introduction
63 63 64 66 67 68 69 69 70 70 72 78 80 81 81 81 82 85 90 92 94 94 95 98 100 102 104 106 108 110 112 114 116 118 119 120 146 148 148 149 152 155 166 168 176 178 178
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9.1 Expérimental Setup 179 9.2 Expérimental Data 181 9.3 CFD Simulation 182 9.4 Physical Properties 187 9.5 Results 189 9.6 Conclusions 190 Chapter 10: Improved Atomization Model for Computational Fluid Dynamics Codes. 191 Introduction 191 10.1 Multiphase Modeling 192 10.2 User-Defined Functions 194 10.2.1 Random Number Génération 195 10.3 Problem Description 196 10.3.1 The Continuous Phase Solution 197 10.3.2 The Discrète Phase Solution 199 10.4 Summary of Improved Atomization Model for CFD Codes 204 Chapter 11: Conclusions and Recommendations 205 Références 208 Bibliography 221 Annex A: User Defined Function to Generate Random Numbers A- 1 Annex B: Publications B- 1 -
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List of tables Table 1.1: Properties of some liquid fuels 18 Table 2.1: Receiver lens characteristics of the Malvern 2600 27 Table 3.1: Mean droplet diameters and their typical applications 42 Table 5.1: Breadth of droplet-size distribution obtained in atomization 79 Table 6.1: Influence of sample size for the accuracy of droplet size measurements 82 Table 6.2: Mean and Variance for the Rosin-Rammler Distribution 85 Table 6.3: Error in Percent for the Mean of Rosin-Rammler Distribution 85 Table 6.4: Expected Error in Percent for the Mean - Confidence Interval of 90% 86 Table 6.5: Expected Error in Percent for the Mean - Confidence Interval of 95% 87 Table 6.6: Expected Error in Percent for the Mean - Confidence Interval of 99% 88 Table 6.7: Expected Error in Percent for the Mean - Confidence Interval of 99,9% 89 Table 6.8: Comparison of the Predicted with Expérimental Data - % Error for the mean with 95% Confidence Interval 90 Table 6.9: Relationship between D32 and D| 0 for Some Distributions 91 Table 6.10: Comparison of the Statistical Method with Expérimental Data - % Error for the SMD with 95% Confidence Interval - Rosin-Rammler distribution 91 Table 6.11: Comparison of the Statistical Method with Expérimental Data - % Error for the SMD with 95% Confidence Interval - Nukiyama-Tanasawa distribution 92 Table 7.1: Operating Conditions for the experiments with the Bosch System 98 Table 7.2: Droplet size distribution for the Bosch System 99 Table 7.3: Operating conditions and sampling position for BETE XA-PR200 Atomizer.. 100 Table 7.4: Droplet size Distribution for the - BETE XA-PR200 Nozzle 101 Table 7.5: Operating Conditions for the experiments with Delavan Atomizers 102 Table 7.6: Droplet size distribution for Delavan atomizers 103 Table 7.7: Operating Conditions for the LaVision experiments 104 Table 7.8: Droplet size distribution for the LaVision experiments 105 Table 7.9: Operating conditions and sampling position for Bhatia et al experiments 106 Table 7.10: Droplet size distribution for Bhatia et al experiments 107 Table 7.11: Expérimental Conditions for the Paloposki and Fagerholm experiments 108 Table 7.12: Droplet size distribution for Paloposki and Fagerholm experiments 109 Table 7.13: Expérimental Conditions for the Lee and Tankin Experiments 110 Table 7.14: Droplet size distribution for Lee and Tankin experiments 111 Table 7.15: Expérimental Conditions for the Tishkoff Experiments 112 Table 7.16: The droplet size distribution for Tishkoff experiment ASTM10CL 113 Table 7.17: The droplet size distribution for Tishkoff experiment ASTM4P21 113 Table 7.18: Operating Conditions for Tate and Oison Experiments 114 Table 7.19: Droplet Size Distribution by Tate and Oison 115 Table 7.20: Operating Conditions for Turner and Moulton Experiments 116 Table 7.21: Droplet Size Distribution for Run 10 and 19 by Turner and Moulton 117 Table 7.22: Droplet Size Distribution for Run 39 and 66 by Turner and Moulton 117 Table 7.23: Droplet Size Distribution reported by Houghton 118 Table 7.24: Fitting of the Nukiyama-Tanasawa distribution to the expérimental data 143 Table 7.25: Fitting of proposed Beta distribution (Pearson Type I) to the expérimental data 144
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Table 7.26: Fitting of proposée Gamma distribution (Pearson Type III) to the expérimental data 145 Table 8.1: Equipments used in the shadowgraphy experiments 153 Table 8.2: Operating conditions and sampling positions - Shadowgraphy experiment 155 Table 8.3: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 2 156 Table 8.4: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 3 158 Table 8.5: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 9 160 Table 8.6: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 10.... 162 Table 8.7: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 12.... 164 Table 8.8: Components used in the laser sheet dropsize experiments 168 Table 9.1: Expérimental Data 181 Table 9.2: Liquid Properties of JP-10 187 Table 9.3: Vapour Properties of JP-10 188 Table 9.4: Other Properties of JP-10 188 Table 9.5: Validation of CFD Simulation 189 Table 10.1: Parameters of the Injection 200
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List of figures Figure 1: Spectrum of droplet sizes 1 Figure 2: Influence of fuel mean droplet size on soot formation 4 Figure 3: Influence of fuel atomization on NO émissions 4 Figure 4: Influence of fuel atomization on CO émissions 4 Figure 5: Influence of fuel atomization onUHC émissions 4 Figure 1.1: Droplet Formation via Dripping Mechanism 8 Figure 1.2 Droplet Beak-up of Cylindrical Liquid Jet 9 Figure 1.3: Corrélation for the maximum break-up length 11 Figure 1.4: The Wave Disintegration 11 Figure 2.1 : The laser diffraction experiment with the Malvern 2600 27 Figure 2.2: Optical Configuration with vignetting 28 Figure 2.3: Components of the Phase-Doppler Particle Analyzer 30 Figure 2.4: Typical set-up of the shadowgraphy technique 31 Figure 2.5: The Laser Sheet Droplet Size Set-up 33 Figure 2.6: Typical PIV configuration 34 Figure 3.1: Normalized histogram 38 Figure 3.2: Normalized cumulative histogram 38 Figure 5.1: The Pearson Frequency Curves in the (fil, fil) Plane 77 Figure 5.2: Criterion to classify the Pearson curves 78 Figure 6.1: Z Curve 83 Figure 6.2: Expected Error in Percent for the Mean - Confidence Interval of 90% 86 Figure 6.3: Expected Error in Percent for the Mean - Confidence Interval of 95% 87 Figure 6.4: Expected Error in Percent for the Mean - Confidence Interval of 99% 88 Figure 6.5: Expected Error in Percent for the Mean - Confidence Interval of 99,9% 89 Figure 7.1: Set-up for the Bosch Common Rail System 97 Figure 7.2: Set-up for the BETE XA-PR200 Séries Atomizer 97 Figure 7.3: Measured Droplet Data in the (fiufii) Plane and Elderton &Johnson Diagraml 19 Figure 7.4: Bosch-Run#l 122 Figure 7.5: Bosch - R u n #2 122 Figure 7.6: Bosch-Run#3 123 Figure 7.7: Bosch -Run#4 123 Figure 7.8: XA-PR200 - Run#l 124 Figure 7.9: XA-PR200 - Run#2 124 Figure 7.10: XA-PR200 - Run#3 125 Figure 7.11: XA-PR200 - Run#4 125 Figure 7.12: XA-PR200 - Run#5 126 Figure 7.13: XA-PR200 - Run#6 126 Figure 7.14: XA-PR200 - Run#7 127 Figure 7.15: XA-PR200 - Run#8 127 Figure 7.16: XA-PR200 - Run#9 128 Figure 7.17: Delavan-Run#l 128 Figure 7.18: Delavan - Run#2 129 Figure 7.19: Delavan - Run#3 129 Figure 7.20: Delavan - Run#4 130
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Figure 7.21: LaVision - Run#l 130 Figure 7.22: LaVision - Run#2 131 Figure 7.23: LaVision - Run#3 131 Figure 7.24: Bathia et al - Run#4 132 Figure 7.25: Bathia et al - Run#5 132 Figure 7.26: Bathia et al- Run#6 133 Figure 7.27: Paloposki & Fagerholm - P208 133 Figure 7.28: Paloposki & Fagerholm - P209 134 Figure 7.29: Paloposki & Fagerholm - P210 134 Figure 7.30: Paloposki & Fagerholm - P211 135 Figure 7.31: Paloposki & Fagerholm - P212 135 Figure 7.32: Lee & Tankin - Run#l 136 Figure 7.33: Lee & Tankin - Run#5 136 Figure 7.34: Lee& Tankin - Run#6 137 Figure 7.35: Lee & Tankin - Run#7 137 Figure 7.36: Tishkoff- Run ASTM10CL 138 Figure 7.37: Tishkoff- Run ASTM4P21 138 Figure 7.38: Tate & Oison -Run#l 139 Figure 7.39: Tate & Oison - Run#2 139 Figure 7.40: Tate & Oison - Run#3 140 Figure 7.41: Turner & Moulton - Run#10 140 Figure 7.42: Turner & Moulton - Run#19 141 Figure 7.43: Turner & Moulton - Run#39 141 Figure 7.44: Turner & Moulton - Run#66 142 Figure 7.45: Houghton 142 Figure 8.1: XYZ positioning device 150 Figure 8.2 Fluorescent properties of JP-10 151 Figure 8.3: Transmittance of the optical filters 151 Figure 8.4: Calibration of the SprayMaster System 152 Figure 8.5: Calibration panel - SprayMaster System 154 Figure 8.6: Scale for calibration of microscope - 0 to 1000 ^im range 154 Figure 8.7: Typical image with shadowgraph setup - 2,5x2,0 mm FOV 154 Figure 8.8: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 2 157 Figure 8.9: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 3 159 Figure 8.10: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 9... 161 Figure 8.11: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 10.163 Figure 8.12: Droplet size distribution with - BETE XA-PR200 atomizer - Condition 12.165 Figure 8.13: Corrélation between the mode m and the operating conditions 167 Figure 8.14: Droplet mass distribution - condition 10 169 Figure 8.15: Droplet surface distribution - condition 10 169 Figure 8.16: SMD planar distribution - condition 10 169 Figure 8.17: Condition 2 170 Figure 8.18: Condition 3 170 Figure 8.19: Condition 9 170 Figure 8.20: Condition 10 170 Figure 8.21: Condition 12 170 Figure 8.22: Condition 2 171
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Figure 8.23: Condition 3 171 Figure 8.24: Condition 9 171 Figure 8.25: Condition 10 171 Figure 8.26: Condition 12 171 Figure 8.27: Fitting of LIF signal with Gaussian distribution - condition 10 172 Figure 8.28: Fitting of Mie signal with Gaussian distribution - condition 10 173 Figure 8.29: SMD profile 25,4 mm from injection 174 Figure 8.30: SMD profile 50,8 mm from injection 174 Figure 8.31: SMD profile 76,2 mm from injection 174 Figure 8.32: Radial SMD profile - Chigier 175 Figure 8.33: Radial SMD profile - Dodge 175 Figure 8.34: Radial SMD profile with PDS and PDA experiments - Domann and Hardalupas 175 Figure 8.35: Radial SMD profile with PDS and PDA experiments - Zimmer et al 175 Figure 8.36: Predicted SMD planar distribution - condition 10 176 Figure 9.1: Schematic of expérimental set-up for evaporation study - wetted porous sphère 178 Figure 9.2: Schematic of expérimental set-up for evaporation study 179 Figure 9.3: Stream of JP-10 droplets in free fall 180 Figure 9.4: Airflow velocity profile in the wind tunnel 181 Figure 9.5: Validation of the Evaporation Model in FLUENT® 5.5 189 Figure 10.1: Axial velocity profile 197 Figure 10.2: Radial velocity profile 198 Figure 10.3: Sampling Position 199 Figure 10.4: Set Injection Properties Panel in FLUENT® 200 Figure 10.5: Validation of injection model 201 Figure 10.6: Droplet size distribution - Center 1 202 Figure 10.7: Droplet size distribution - Center 2 202 Figure 10.8: Droplet size distribution - Center 3 202 Figure 10.9: Droplet size distribution - Middle 1 202 Figure 10.10: Droplet size distribution - Middle 2 203 Figure 10.11: Droplet size distribution -Middle 3 203 Figure 10.12: Droplet size distribution - Border 1 203 Figure 10.13: Droplet size distribution - Border 2 203 Figure 10.14: Droplet size distribution - Border 3 203
XV11
Nomenclature Man: "Hello, my boy. And what is your clog 's name ? " Boy: "I clon't know. We call him Rover. " Stafford Béer
ALR
Air/liquid mass ratio
CFD
Computational Fluid Dynamics
Cp
Constant pressure spécifie heat, J/(kg K)
d, D
Diameter, m
/ ( J C J ) Function of JC, g
Gravitational accélération, m / s 2
V(x)
Gamma function
k
Thermal conductivity, W/(m K)
m
Mass flow rate, kg/s
MMD Mass mean diameter, \im Nu
Nusselt number
p
Pressure, Pa
pdf
Probability density function
Pr
Prandtl number
Q
Volumetric flow rate, m/s
R
Individual gas constant, J/(kg K)
Re
Reynolds number
Se
Schmidt number
SMD Sauter Mean Diameter, ^m t
Time, s or film thickness, m
T
Température, K
M
Velocity, m/s
V
Volume, m3
We
Weber number
XVI II
Greek Alphabet
a
Thermal conductivity W/(m K)
/3
Beta function
A
Wavelength, nm
jU
Dynamic viscosity, kg/(m s) or mean of a statistical distribution
v
Kinematic viscosity, m 2 /s
6
Spray cône angle, deg
p
Density, kg/m
a
Surface tension, kg/s" or standard déviation of a statistical distribution
X
Chi distribution
Subscripts and superscripts
a f
anfuel
i
/th size class, direction, function, species or variable
L
Liquid
0
Orifice
P
Particle
R
Air relative to liquid
oo
Infinity
Introduction Liquid sprays consist of différent sizes of droplets dispersed in a gaseous médium. They are ail around us and indispensable for daily activities. They include natural phenomena such as rain, fog and waterfall mists, or are generated using mechanical devices like nozzles for différent applications such as in medicine (pulmonary drug delivery), in cosmetics, in various industries (painting and fuel injection), in agriculture (pesticide sprays), in fire suppression Systems (sprinklers) and in household applications (printers). A typical spectrum of droplet sizes from some natural phenomena and industrial applications is presented in Figure 1.
OIL FOG SMOKE
MIST
SEA FOG
CLOUDS
DRIZZLE
RAIN r
0.1
1
10
AEROSOLS
DROP SIZE,
100
SPRAYERS
SPRINKLERS
Figure 1 : Spectrum of droplet sizes Source: Lefebvre [63]
Most practical atomizers generate droplets that range in size from a few micrometers up to around 800 \im. The criteria for selecting a more suitable size and uniformity of droplets in various spray Systems dépend on the spécifie application. Médical sprays, for instance, could require droplets few micrometers in size in order to permit droplets to pass through small airways and reach the lungs. On the other hand, sprays for agricultural or fire suppression Systems require that droplets should be sufficiently large to hâve enough momentum and not to be carried away by the wind stream. In the case of combustion engines, a trade-off is required between the quantity of smaller droplets, needed to start a cold System and the quantity of larger droplets, needed to control flame stability. Therefore, the sole use of mean droplet diameter is not a satisfactory criterion to describe the spray from an atomization device. The knowledge of the entire distribution of droplets in the spray is mandatory.
Numerous scientific conférences and récent publications in the field attest to a renewed interest for atomization in the différent fields of science and engineering. The importance of spray Systems has also motivated the création of différent technical standards such as ASTM [3], [4], [5] and ISO [50] to normalize the information and terminology from différent researchers and to improve the processing of expérimental droplet size for analysis. A spécifie interest for the présent study is the development of liquid-fuel based puise détonation engine propulsion Systems. Therefore the présent study will be focused on spray Systems applied to combustion. Despite the spécifie interest of this research, the methodology developed and suggested herein is gênerai, and consequently can be used in many other applications of spray Systems.
Spray Applied to Combustion The interest in improving the performance of power génération Systems came from two well-defined sectors, namely environment and energy. From the environmental point of view, the American Air Pollution Control Act became law in 1955, followed by the Japanese Air Pollution Control Law No. 97 in 1968, and ultimately the European Council Directive 70/220/EEC in March 1970; they were the first government initiatives aimed at limiting émissions of pollutants in the atmosphère. Finally, the Environmental Crisis was officially recognized on April 22, 1970 as the first Earth Day, which motivated many discussions on the subject and culminated with the historical Kyoto protocol signed in 1997, viewed as the greatest world plan to date to combat global warming and improve the sustainable development of the planet. Despite its rejection by the United States, the biggest polluter in the world, the protocol was signed by 141 countries and came into force on February 16, 2005. The Kyoto protocol establishes goals aimed at the réduction of greenhouse gases, principally carbon dioxide. From the energy standpoint, the Energy Crisis became officiai with the first Arab oil embargo of 1973 and afterwards with the first and second Gulf War in 1991 and 2003, respectively. Since then, in the industrialized countries, the so-called sustainable development has been the motivation for several studies leading to législation. In this context, the
optimization of combustion Systems is very attractive, since the use of non-renewable liquid hydrocarbon fuels in internai combustion engines and industrial burners is responsible for most of the energy production and atmospheric émissions in the world. Therefore, improvements in the design and opération of this equipment are essential for current environmental and energy requirements. However, due to the complexities inhérent in each mechanism governing the combustion of liquid fuels, including atomization, air-fuel mixing, and chemical reactions in multiphase and turbulent flows, better understanding of such phenomena is critical to achieve optimal performance. Fuel spray characteristics are considered to play the most important rôle from the standpoint of thermodynamic performance, level of pollutant émissions, and acoustic instabilities in combustors as illustrated in Figures 2 to 5. McCreath and Béer [75] report that, in liquid sprays, droplet size frequency and spatial distributions control fundamental flame characteristics such as length, stability, radiant heat transfer, smoke, and the formation of nitrous oxides. The increased number of techniques available for droplet size measurements, such as the Laser Diffraction method [110], the Planar Droplet Sizing method [126] and the Phase/Doppler Particle Analyzer [8], attest to the importance of droplet size in the différent processes that utilize liquid sprays. As pointed out in Kretschmer [59] and Brophy et al [13], in actual applications that hâve been analyzed as promising technologies for flight Systems of this new century, such as liquid-fuel based Puise Détonation Engines (PDE) and Supersonic Combustion Ramjets (Scramjet), the characterization and control of the spray quality is a key issue in order to guarantee droplet sizes capable of evaporating and mixing in air, ail within the timescales typical of high speed propulsion Systems.
5.0 4.0-
FUEL - DF 2
FUEL=KER0SINE T3 - 573 K P 3 =1.52MPa
200
2.0-
•§ 100 CT 80
40
1.0 0.8
060.510
09 10 I.! EQUIVALENCE RATIO
IB
1.0
1.2
1.4
Figure 4: Influence of fuel atomization on CO émissions
FUEL-DF2 T3 =573K
16 g/kg fuel
0.8
EQUIVALENCE RATIO. 4>
Figure 2: Influence of fuel mean droplet size on soot formation
i
0.6
K
14
SMD.nm o 30
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12
A 70 • 110
10 8
.
y»
f
6 0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
EQUIVALENCE RATIO, *
0.6 Q8 I.O EQUIVALENCE RATIO
Figure 3: Influence of fuel atomization on NO émissions
Figure 5: Influence of fuel atomization on UHC émissions
Source: Lefebvre [64]
Objectives The accurate knowledge of droplet size distribution and the capability of its prédiction can permit the development of evaporation models for liquid sprays, as in the studies of Cooper [20] and Probert [93]. Furthermore, the ability to predict spray évolution based on limited expérimental characterization of injectors is a key issue in research and development and quality control applications. The présent study aims at the development of a rational methodology to predict the spatial droplet size distribution in liquid sprays based on the operating conditions of the injection System. An expérimental facility was designed to handle the complexity of the phenomena, and a liquid fuel atomization study was carried out for two types of fuel injection devices. They were air-assist and pressure atomizers. Four possibilities to improve the body of knowledge on spray characterization and modelling were identified. Thèse included: 1. the détermination of minimum sample size of droplets to achieve a given précision [90], 2. the investigation of the parameters affecting droplet size [88], 3. the development of a more suitable mathematical expression to characterize droplet size distribution based on statistical analysis, and 4. the capability to predict droplet size distribution in sprays under any given operating condition. As part of the study, the evaporation characteristics of individual liquid fuel droplets were determined and the evaporation model implemented in a commercial CFD code and validated to further support the implementation of more realistic fuel injection Systems [89].
Scope The study is divided into eleven chapters as follows. In Chapter 1, a brief review of the various mechanisms of droplet formation, such as liquid dripping, liquid column/jet break-up, liquid ligament break-up, liquid sheet/film break-up, and liquid free-surface break-up is presented. Chapter 2 présents a brief review of some of the particle sizing
techniques that hâve been used over the past years, as well as détails of three important non-intrusive optical diagnostic techniques available for this study carried out in the Combustion Laboratory at Laval University: the Laser Diffraction Analysis, Laser Sheet Dropsizing, and Shadowgraphy. Additionally, the Phase Doppler Particle Analyzer is introduced. In Chapter 3, a summary of the main empirical models previously presented in the literature to characterize sprays, as well as some statistical parameters used to support the study are reviewed. In Chapter 4, some goodness-of-fit techniques are presented. A goodness-of-fit test vérifies the capability of theoretical models to agrée with expérimental data and assist with the sélection of the most suitable model to characterize spécifie phenomena under study. In Chapter 5, a possible method is proposed to generalize particle size distributions as applied to spray Systems. In Chapter 6, a methodology is proposed to support the détermination of the minimum sample size for a spécifie accuracy as applied to spray Systems. Chapter 7 présents previous expérimental studies and results used to validate the model for particle sizing in spray Systems proposed in Chapter 5. In Chapter 8, a corrélation to assess droplet size distribution in a plane of a solid cône spray is obtained. In Chapter 9, a new non-intrusive methodology to study evaporation of liquid is proposed. In Chapter 10, the atomization model implemented in the commercial Computational Fluid Dynamics code FLUENT® is improved with parameters from expérimental measurements. Finally, conclusions and suggestions for future studies are given in Chapter 11.
Chapter 1:
The Atomization Mechanism "In theory, there is no différence beîween theory and practice. But, in practice, there is. " Jan van de Snepscheut
Introduction Atomization is the process in which a bulk of liquid is disintegrated into droplets by internai and/or external forces as a resuit of the interaction between the liquid and the surrounding médium. The disintegration, or break-up, occurs when the disruptive forces exceed the liquid surface tension forces. The consolidating effect of liquid surface tension tends to pull a liquid into a form that exhibits the minimum surface energy, while the stabilizing effect of liquid viscosity tends to oppose any change in liquid geometry. The initial break-up process is often referred to as primary break-up, primary disintegration, or primary atomization. The larger droplets produced in the initial disintegration process may be unstable and undergo further disruption into smaller ones. This process is usually termed secondary break-up, secondary disintegration, or secondary atomization. The final droplet size distribution produced in the atomization process is determined by the liquid properties in both primary and secondary disintegration. In this part of the study, a brief review of the various mechanisms proposed for droplet formation, such as liquid dripping, liquid column/jet break-up, liquid ligament break-up, liquid sheet/film break-up, and liquid free-surface break-up is presented. A more complète discussion on the atomization mechanism can be found in Bayvel [10] and Lefebvre [63], [64].
1.1
Liquid Dripping The most elementary mode of droplet formation is liquid dripping from an orifice
where droplets are formed quasi-statically under the action of gravity, as illustrated in Figure 1.1. The dripping mechanism occurs when the gravitational force on the liquid exceeds the attaching surface tension. Due to low flow velocity of the liquid in the dripping mechanism, the gravitational and surface tension forces on the droplets govern the formation process of the droplet and détermine the droplet mass and size.
Figure 1.1: Droplet Formation via Dripping Mechanism Source: D'Innocenzo et al, 2002 [22] The prédiction of droplet diameter [Dp) formed by dripping liquid from a small orifice and based on the force balance is as follows:
(U)
where: 0 générâtes a normal random variable with pdf:
l /(£>)
= •
a
exp
la2
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-oo0, we take the range of x as x>-a/b;
if b
