An experimental and numerical study of the effects of heat loss and unsteadiness on laminar strained flames

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Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UM I a complete manuscript and there are missing pages, these w ill be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UM I directly to order. UMI Bell & Howell Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. AN EXPERIMENTAL AND NUMERICAL STUDY OF THE EFFECTS OF HEAT LOSS AND UNSTEADINESS ON LAMINAR STRAINED FLAMES by Hai Zhang A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Mechanical Engineering) May 1999 Copyright Hai Zhang Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DMI Number: 9933695 UMI Microform 9933695 Copyright 1999, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY OF SOUTHERN CALIFORNIA TH E GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 90007 This dissertaticnir written by under the direction of h,..lÆ.... Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of re quirements for the degree of DOCTOR OF PHILOSOPHY late StudUs Dean at Date DISSERTATION COMIvGTTEE Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENT Looking back over the years I have spent in my Ph.D. program in the Mechanical Engineering Department (ME) of the University of Southern California (USC), there are many people I would like to thank. Without their help, this dissertation would not have been possible. First, I would like to express my deepest gratitude to Dr. Fokion N. Egolfopoulos, chairman of my dissertation committee and my academic advisor, for his encouragement, support and guidance throughout aU my studies. It is my great honor to be his student, especially his first Ph.D. student. I gratefully acknowledge the other members of my dissertation committee. Dr. Paul D. Ronney and Dr. Theodore T. Tsotsis, for their simulating comments, valuable suggestions and kindness cooperation. I would like to thank Dr. Fletcher Miller for his great academic and personal support during my experimental visits in NASA John H. Glenn (Lewis) Research Center. I thank Dr. Satwindar S. Sadhal, Dr. Charles S. Campbell, Dr. Roy P. Choudhury and many other professors in USC for their academic teaching and advisement. I also thank Jacquette Givens, Teodora Valdez and aU other staff members in ME department for their helps. I especially thank Mr. Warren G. Haby who has offered so much help for my research and thesis writing. Besides, I thank Carrion Joe, Mike Johnson, Andy Jenkins and all other people in the 2.2-second Drop Tower Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ill Department in NASA Glenn Research Center for their assistance to conduct the microgravity experiments. I would like to thank Christine Vagelopoulos, Brad Cracchiola, Wenjun Qin, Jyh Y. Ren, Andac Gurhan, Zhengjie Zhang, Linton Honda, Sharif Jamal and all other colleagues for their help and cooperation during the research. Besides, I want to thank Xiaogang Qiu, Xingang Zhang, Yuyong Zhang, Yuhai Wang, Helen Tian, Biyong Chen, Hongwen Gao, Jiangchun Yi, Kun Li, Yidan Yang, Bing Zhang, James Jin and many other friends for their friendship and help during these years. It is never enough to thank my parents-in-law for their all-around support, especially for raising my son at the crucial stage of my study. At the same time, I would like to thank my grandma, my parents, my brother and my brother-in-law for their love and encouragement that motivated me all the time. Finally, I would like to contribute this dissertation to my wonderful wife, Hongmei Su and our lovely son, Jerry Zhang. I appreciate Hongmei from the deep of my heart to her loving forbearance, support, and scarification. I thank Jerry for his endless love and his smiling face, which always are the sources of my happiness. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV TABLE OF CONTENTS Chapter 1. INTRODUCTION 1 1.1 Significance and Overview 1 1.1.1 Flammability limits 4 1.1.2 Downstream conductive heat losses 8 1.1.3 Upstream conductive heat losses 10 1.1.4 Effect of unsteadiness on strained flames ..............................................11 1.2 Objectives 12 1.3 Organization of the Dissertation ........................................................................17 1.4 References 18 Chapter 2. EXPERIMENTAL APPROACH 26 2.1 Opposed-Jet Counterflow System 27 2.2 Single Jet-Wall Stagnation Flow System 29 2.3 Unsteady Counterflow System 30 2.4 Laser Doppler Velocimetry (LDV) .............................................31 2.5 References 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3. NUMERICAL APPROACH 39 3.1 Introduction 39 3.2 Governing Equations 41 3.3 Boundary Conditions 43 3.4 Thermal Radiation Models 44 3.4.1 The opticaUy-thin model ....................................................................... 44 3.4.2 The optically thick model ....................................................................... 45 3.5 References 46 Chapter 4. FULL RADIATION MODEL 49 4.1 Introduction and Objectives 49 4.2 The Full Radiation Model 51 4.2.1 Expression of the radiation source term' ............................................. 51 4.2.2 The RADCAL and spectral absorption coefficients 52 4.2.3 Computational implementation 53 4.3 Application of the FuU Radiation Model in 1-D Premixed Flames ....................54 4.3.1 Comparison of two optically thin models ............................................. 54 4.3.2 Optically thick limit 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VI 4.4 Concluding Remarks 61 4.5 Reference 62 Chapters. MICROGRAVITY EXPERIMENTS ON THE EXTINCTION OF NEAR-LIMIT, WEAKLY-STRAINED, PREMIXED FLAMES 75 5.1 Introduction of the Microgravity Experimental System 76 5.2 Experimental Sequences 81 5.3 Observation and Discussions 82 5.4 Concluding Remarks 86 5.5 References 87 Chapter 6. EXTINCTION OF NEAR-LIMIT PREMIXED FLAMES: RADIATION AND UPSTREAM HEAT LOSS EFFECTS 92 6.1 Introduction and Objectives 93 6.2 Results and Discussion 95 6.3 Concluding Remarks 104 6.4 References 105 Chapter 7. WALL EFFECTS ON THE PROPAGATION AND EXTINCTION OF STEADY, STRAINED, LAMINAR PREMIXED FLAMES 126 7.1 Introduction and Objectives 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vu 7.2 Results and Discussion .....................................................................128 7.2.1. No-slip condition effect .....................................................................128 7.2.2. Heat loss effect on flame extinction ...........................................130 7.2.3 Radical recombination effect on flame extinction ................135 7.2.4 Heat loss effect on flame propagation ...........................................138 7.3 Concluding Remarks .................................................................... 142 7.4 References .................................................................... 144 Chapter 8. UNSTEADY EFFECTS ON STRAINED NON-PREMDŒD LAMINAR FLAMES .......................................................................................................... 160 8.1 Introduction and Objectives .................................................................... 160 8.2 Results and Discussions........................................................................................... 161 8.2.1 Velocity profiles .................................................................... 161 8.2.2 Frequency response.............................................. ...........................................162 8.2.3 Extinction of unsteady non-premixed flames...............................................164 8.3 Concluding Remarks................................................................................................ 165 8.4 References..................................................................................................................166 Chapter 9. CONCLUDING REMARKS AND RECOMMENDATIONS ........ 173 9.1 Concluding Remarks.............................................................................................. 173 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V U l 9.2 Recommendations 176 Appendix: Derivation of the full radiation model 179 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IX LIST OF FIGURES Fig. 1-1 The definition of flame stretch ........................................................ 24 Fig. 1-2 The laminar fiameiet concept 25 Fig. 2-1 Schematic of opposed-jet counterflow configuration with twin premixed flames 33 Fig. 2-2 The definition of strain rate K and reference flame speed in the counterflow configuration 34 Fig. 2-3 Determination of laminar flame speed by linear extrapolation in counterflow configuration. 35 Fig. 2-4 Schematic of opposed-jet counterflow flow system 36 Fig. 2-5 Schematic of single jet-wall configuration for the upstream conduction heat loss effect study 37 Fig. 2-6 Schematic of opposed-jet counterflow system for the study of unsteady diffusion flames 38 Fig. 4-1 Schematic of full radiation model: a planar radiating medium bounded by two infinite botmdaries. 64 Fig. 4-2 Axial profiles of temperature and radiative species for three 1-D freely propagating, premixed methane/air flames at different (j)'s. ...65 Fig. 4-3 Distributions of Planck mean absorption coefficients predicted by the Tien's model and the RADCAL model for three 1-D freely propagating, premixed methane/air flames at different (j)'s. 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X Fig. 4-4 Distributions of Planck mean absorption coefficients for individual radiative species predicted by the Tien's model and the RADCAL model for a near-limit, 1-D freely propagating, premixed CH/air flames 67 Fig. 4-5 Distributions of divergences of radiative heat flux and generative heat flux by three different radiation models and for three 1-D freely propagating, premixed methane/air flames at different (j)'s......................68 Fig. 4-6 Distributions of normalized divergences of radiative heat flux for different radiation models and for three 1-D freely propagating, premixed methane/air flames at different (j)'s. Divergences of heat flux are normalized with that predicted by the RADCAL radiation model. ....................................................................................................................... 69 Fig. 4-7 Variations of normalized heat flux with equivalence ratio for premixed methane/air flames with different radiation models. 70 Fig. 4-8 Distributions of each term in the full radiation model for three 1-D freely propagating, premixed methane/air flames at different (j)'s.....................71 Fig. 4-9 Temperature profiles predicted by three different radiation model for three 1-D freely propagating, premixed methane/air flames at different (|)'s. 72 Fig. 4-10 Variations of maximum flame temperature with equivalence ratio predicted by different radiation models for 1-D freely propagating, premixed C H /air flames ..................................................................73 Fig. 4-11 Variations of the ratio of radiation/generation fluxes with predicted by different radiation models for 1-D freely propagating, premixed CH/air flames 74 Fig. 5-1 The schematic of the microgravity experimental system ................ 88 Fig. 5-2 Fuel concentration variation during the microgravity experiment ....................................................................................................................... 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XI Fig. 5-3 Variation of extinction strain rate with equivalence ratio for near-limit, weakly-strained, premixed methane/air flames .............................. 90 Fig. 5-4 Variation of extinction strain rate with equivalence ratio for near-limit, weakly-strained, premixed propane/air flames .............................. 91 Fig. 6-1 Variations of temperature gradient at the nozzle with the burner separation distance for near-limit, counterflow premixed flames with different imposed velocities 107 Fig. 6-2 Variations of temperature gradient at the nozzle with equivalence ratio for near-limit, weakly-strained, counterflow premixed flames as burner separation distance L= 1.5cm. 108 Fig. 6-3 Velocity profiles of near-limit, weakly strained premixed CH /air flames under a small burner separation distance and different imposed velocities. Thermal Radiation is ideally excluded. 109 Fig. 6-4 Temperature profiles of near-limit, weakly strained premixed CH/air flames under a small burner separation distance and different imposed velocities. Thermal radiation is ideally excluded................................... 110 Fig.6-5 Variations of extinction strain rate with equivalence ratio for near-limit, weakly strained, counterflow premixed C H /air flames with small burner separation distance. Thermal Radiation is ideally excluded................. I l l Fig. 6-6 Variations of flame temperature with global strain rate for near-adiabatic, near-limit, counterflow C H /air premixed flames as upstream heat losses are excluded. 112 Fig. 6-7 Variations of flame temperature with global strain rate for near-limit, counterflow CH^/air premixed flames. 113 Fig. 6-8 Variations of maximum flame temperature and temperature gradient at the nozzle with global strain rate for near-limit, counterflow CH/air premixed flames with different burner separation distances.................114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XU Fig. 6-9 Variations of global extinction strain rate with equivalence ratio for near limit, counterflow CH^/air premixed flames with or without upstream heat losses. 115 Fig. 6-10 Structures of near-limit, weakly strained, counterflow C H /air premixed flames with the upstream conductive heat loss. 116 Fig. 6-11 Variations of local extinction strain rate with equivalence ratio for near- limit, counterflow C H /air premixed flames with or without upstream heat losses. 117 Fig. 6-13 Comparison of numerical results and experimental data on the variations of global extinction strain rate with equivalence ratio for near-ümit, counterflow CH /air premixed flames. 118 Fig. 6-13 Variations of maximum flame temperature and temperature gradient at the nozzle with global strain rate for (j)=0.6, CH /air premixed flames. .......................................................................................................................119 Fig. 6-14 Variations of maximum flame temperature and temperature gradient at the nozzle with global strain rate for <{)=0.6, C^Hg/air premixed flames. 120 Fig. 6-15 Variations of flame location from the stagnation plane with global strain rate for counterflow, C H /air and QHg/air premixed flames as (|)=0.6. 121 Fig. 6-16 Variations of maximum flame temperature and temperature gradient at the nozzle with global strain rate for (j)=0.6, CgHg/air premixed flames when radiation heat loss is ideally excluded. 122 Fig. 6-17 Velocity profiles of weakly strained, (^0.6 premixed CgHg/air flames under low imposed velocities. Conductive heat losses are introduced. .......................................................................................................................123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XIll Fig. 6-18 Distances between the twin flames for near-extinction, counterflow, premixed C H /air and C^Hg/air flames as (()=0.6 124 Fig. 6-19 Comparison of numerical results and experimental data on the variations of global extinction strain rate with equivalence ratio for near-limit, counterflow CjHg/air premixed flames. ........................................125 Fig. 7-1 Variation of the numerically determined with K and extinction behavior of a <{)=0.70 CH4/air flame, for the opposed-jet and single jet- waU configurations under the adiabatic condition.................................. 146 Fig. 7-2 Spatial variations throughout the flame of the numerically determined (a) temperature and (b) radial velocity gradient G=dv/dr and density weighted radial velocity for a <|)=0.70 methane/air flame as K=859 sec ' for both the opposed-jet and single jet-wall configurations..................147 Fig. 7-3 Variation of the numerically determined Tmax with K and extinction behavior of a (j)=0.70 methane/air flame, for the opposed-jet single jet- wall configuration under adiabatic and T^,n=1500, 1400 and 400K conditions. 148 Fig. 7-4 Variation of the numerically determined (a) heat flux to the wall and (b) distance of the flame luminous zone from the stagnation plane (wall) as a function of K and T ^ , for a ({>=0.70 methane/air flame and the single jet- waU configuration. 149 Fig. 7-5 Comparison between the experimentally and numerically determined extinction strain rate K,,, for atmospheric methane/air flames under the single jet-wall configuration and = lOOOK. ............................150 Fig. 7-6 Comparison between the numerically determined extinction strain rate and the experimental data of Law et al. (1986) for atmospheric methane/air flames under the opposed-jet configuration....................... 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XIV Fig. 7-7 Variation of the numerically determined spatially integrated heat release rates in flames established in the opposed-jet configuration as function of strain rate and equivalence ratio. 152 Fig. 7-8 Variation of the numerically determined spatially integrated heat release rates in flames established in the jet-waU configuration with T^3y= 1 0 0 0 K as function of strain rate and equivalence ratio................................... 153 Fig. 7-9 Comparison between the experimentally and numerically determined extinction strain rate for atmospheric methane/air flames under the single jet-wall configuration and = 573K. .............................154 Fig. 7-10 For a < { ) = 0.70 CH^ /air flame and single jet-wall configuration: (a) Effect of H radical recombination at the wall on extinction under adiabatic and T^ai, = 1600 K conditions, (b) Variation with T^^,, of the ratio of with H radical recombination over without H radical recombination. .....................................................................................................................155 Fig. 7-11 Variation of the numerically determined reference flame speed with local strain rate K for ( { ) = 0.805 methane/air flame under the near- adiabatic opposed-jet and non-adiabatic single jet-wall configurations for L = 20 mm. 156 Fig. 7-12 Variation of the numerically determined reference flame speed with local strain rate K for ( j) = 0.805 methane/air flame under the near- adiabatic opposed-jet and non-adiabatic single jet-wall configurations for L= 20 mm. 157 Fig. 7-13 Variation of the numerically determined reference flame speed with local strain rate K for ( j) = 0.805 methane/air flame under the near- adiabatic opposed-jet and non-adiabatic single jet-wall configurations for L =9m m . 158 Fig. 7-14 Variation of the numerically determined spatial temperature profiles for a ( j ) = 0.70 methane/air flame and for the single jet-wall configuration with T^jii = 1000 K and L = 20 mm. 159 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XV Fig. 8-1 Axial velocity profiles along the centerline in the opposed-jet counterflow configuration for no-premixed flames with different coflow flow rates......................................................................................................167 Fig. 8-2 Axial velocity profiles along the centerline in the opposed-jet counterflow configuration for no-premixed flames with different burner separation distances. 168 Fig. 8-3 Variation of maximum flame oscillation displacement with the impinging frequency for unsteady non-premixed flames in the opposed- jet counterflow configuration with different oscillation amplitudes of the upstream velocity. .................................................................. 169 Fig. 8-4 Variation of flame oscillation displacement normalized by its value at 2Hz with the Stoke’s parameter for various unsteady non-premixed flames in the opposed-jet counterflow configuration. The upstream oscillation amplitude U q s ^ and aerodynamic strain rate K are measure by the LDV. 170 Fig. 8-5 Variation of amplitude normalized at its quasi-steady value with the Stoke’s parameter T |k defined in terms of the angular frequency CD and the aerodynamic strain rate K. [Egolfopoulos and Campbell, 1996]...........171 Fig. 8-6 Variations of maximum oscillation amplitude of the upstream velocity for flame extinction with the upstream oscillation frequency for unsteady non-premixed in the opposed-jet counterflow configuration................. 172 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XVI ABSTRACT A combined experimental and detailed numerical study was conducted on the effects of heat loss and unsteadiness on strained laminar flames at normal- and micro gravity. Results are of interest to a variety of fundamental combustion phenomena including flammability limits. Furthermore, valuable information is provided in the context of mrbulent combustion for conditions under which the fiameiet concept is applicable. The majority of previous studies on flamelets have been focused on steady and adiabatic conditions, even though unsteadiness and heat loss are inherently present in any realistic flowfield. The experiments included the use of the opposed-jet and single-jet configurations in which the strain rate is a well-defined and well-controlled parameter. Velocity measurements were conducted through the use of laser Doppler velocimetry at normal-gravity and extinction strain rates. The counterflow technique was also introduced in micro-gravity through an involved experimental apparatus that allowed for the study of extinction of near-limit flames under conditions that could not be assessed in normal-gravity. The C-shape response of the extinction strain rate vs equivalence ratio was quantified for Le<l flames by assuring that upstream heat losses were not present. For Le>l flames, a monotonie response was found. Experiments were also conducted at normal-gravity on the effect of downstream heat loss on the propagation and extinction of laminar strained premixed flames. The effect of monochromatic velocity unsteadiness was experimentally studied for non-premixed strained flames and theoretically derived scaling arguments were confirmed. Furthermore, the flames were found to resist to extinction at high frequencies, confirming again theoretical predictions. The experiments were modeled by using detailed description of chemical kinetics, molecular transport, and thermal radiation. The effect of various radiation models on the flame response was assessed. Such Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x v n models included the assumptions of optically thin and optically thick limits, as well as the mean Planck mean absorption coefficient and detailed narrow-band formulations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1 INTRODUCTION 1.1 Significance and Overview Flames can be classified as premixed or diffusion, depending upon whether the reactants (oxidizer and fuel) are initially mixed or not. If the reactants are mixed before the reaction is initiated, the flame is called premixed. Otherwise, the flame is defined as diffusion or non-premixed. Flames can be also classified as laminar or turbulent, depending upon whether the flow is laminar or turbulent. In a laminar flow, distinct streamlines exist for the bulk convective motion, whereas in a turbulent flow, such streamlines do not exist and at any point in space and time, the flow quantities fluctuate randomly. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In real combustion processes, flames are predominately subjected to the stretch, which is induced by three effects including flow non-uniformity, flame curvatiure, and flame motion. Shown in Fig. 1-1, at any point on an arbitrary surface S, the flame stretch is defined as the Lagrangian time derivative of the area logarithm of an infinitesimal element on the surface, K=(l/A)*dA/dx [e.g. Strehlow et al., 1978; Matalon 1982; Buckmaster, 1984; Williams, 1986; Law, 1988]. The surface S can be an isotherm within the flame structure. Within the boundary of this surface, elem ents move tangentially at the local tangential component of the fluid velocity; the stretch, K, has the unit of sec'*. Stretched laminar flames are of relevance to a number of flame phenomena, such as flame stabilization and flame front instabilities as well as to turbulent combustion under certain conditions. In most cases, shown in Fig. 1-2 [Ronney, 1994], a turbulent flame can be considered as an assembly of wrinkled laminar flamelets, the curvature and the motion of which are strongly related to the flame stretch [Peters, 1984, 1986]. Thus, extensive studies have been conducted on strained laminar flames and significant advances have been made in understanding the flame stretch and its influence on the flame structure [Law, 1988]. However, the majority of the studies are limited to adiabatic and steady systems, while the effects of unsteadiness and heat loss have not been adequately assessed in a rigorous and systematic manner. In practical combustors, flames are as heat sources, providing energy through the heat transfer in the forms of radiation, convection, and conduction. Because of the flame motion, flame curvature and the flow divergence, flames are also subjected to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. stretching. At the same time, the heat loss may induce flame temperature reduction, flame structure modification, and even flame extinction. Under conditions of weak burning, past studies [e.g., Ronney, 1988a, 1988b; Abbud-Madrid and Ronney, 1990; Law and Egolfopoulos, 1992; Maruta et al., 1996; Smooke et al., 1993] have shown that there is a strong couphng between stretch, chemical kinetics, and heat loss. Such processes have been considered as chiefly responsible for the existence of the experimentally observed flammability limits. Apparently, studies of non-adiabatic stretched flames are significant for the design of combustion devices. Additionally, the combustion takes place mostly in unsteady flows. Therefore, the flow unsteadiness introduces another time scale in the hydrodynamic zone and influences the flame structure and dynamics by coupling with the other properties such as strain rate, chemical kinetics, molecular diffusion, and heat loss. It is essential that the mechanisms for the flame response to the external unsteadiness are also understood, so that the conditions under which the results obtained from steady flames are of relevance to unsteady flames are specified. Given that a number of unsteady flame studies has been conducted theoretically and numerically, experimental validations are necessary. More details of the background theory are given below, with emphasis on flammability limits, and on the effects of upstream and downstream heat losses and flow field unsteadiness. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.1.1 Flammability limits In early studies, the term “flammability limits” has been loosely used to describe the failure of flame propagation. However, it is important to distinguish between “extinction limits” and “flammability limits”. Extinction limits are defined as the concentration limits beyond which flame propagation is not possible under the influence of external mechanisms. Flammability limits are defined as the concentration limits beyond which the use of the ideal one-dimensional, steady, laminar, near-adiabatic flame model is not possible [Williams, 1985]. It is clear that if fundamental flammability limits exist, they must be intrinsic mixture properties and do not depend on any external loss mechanism, other than the radiative losses, which are inherently present. The identification of fundamental flammability limits has been the subject of extensive investigations and the source of substantial controversy, as they are important from both fundamental and practical points of view. Traditionally, “flammability limits” were experimentally determined by using the standard flame tube [e.g.. Coward and Jones, 1952] or the spherical bomb [e.g., Ronney and Wachman, 1985]. Both approaches, however, introduced parameters that are external to the mixture and could not be systematically accounted for. Heat and radial losses, unsteadiness, strain rate, and ignition energy “memory effect” were among them. In these early studies, radiative loss was considered as the sole responsible for such limits. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Subsequent detailed numerical studies [Law and Egolfopoulos, 1990, 1992; Egolfopoulos, 1994b] revealed the internal mixture mechanisms which couple with the inherently present radiative losses and lead to the failure of propagation beyond certain concentration limits. The studies provided a unified thermal-chain theory for fundamental flammability limits by simultaneously emphasizing the importance of heat loss and chain termination. Furthermore, a turning-point behavior in terms of laminar flame speed vs. equivalence ratio was observed [Law and Egolfopoulos, 1992] when radiation was included in the one-dimensional, freely-propagating flame model. The sensitivity of flame response to the strain rate, radiative loss, and chemical kinetics was found to be heightened for near-limit flames [Egolfopoulos, 1994b]. For these weak flames, low activation energy termination reactions start competing strongly for the important H radical with the high activation energy main branching reaction H + O^— ^ OH + O , and a critical balance between them is required to sustain a vigorous burning. Experimentally, the opposed-jet counterflow technique was introduced [Law cc al., 1986] for the determination of extinction strain rates for various mixture compositions and subsequent determination of flammability limits at the limit of zero strain rate through linear extrapolations. This approach resulted in flammability limits which were comparable to the generally accepted values, as found from other system s. However, experiments for very weak mixtures were not possible in normal gravity because of the buoyancy-induced convection and instabilities. Microgravity (p.g) environment is required for the study of extinction characteristics of near-limits flames and flammability limits. Early jig studies adopted the use of the standard Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. flammability tube [e.g.. Coward and Jones, 1952] and the spherical bomb [e.g., Ronney and Wachman, 1985]. Recently, such p.g studies have been extended by using the meritorious counterflow technique [Maruta et al., 1996; Vagelopoulos et al., 1997]. The approach of the linear extrapolation to zero strain rate [Law et al., 1986] was challenged by the recent p.g experiments [Maruta et al., 1996]. In the experiments, very weak flames were established in microgravity and a C-shape behavior was observed in the extinction (global) strain rate vs. the equivalence ratio diagram for near-limit mixtures with a Lewis number less than unity (Le<l). Here, the Le number is defined as the ratio of the heat diffusivity of the mixmre over the mass diffusivity of the controlling (deficient) reactant. The findings suggest that the linear extrapolation is inappropriate for Le<l mixtures such as CH^/air. The |ig experimental results of Maruta et al. (1996) motivated numerical studies [Sung and Law, 1996] and the C-shape extinction behavior was reproduced numerically. The bifurcation was found to be caused the synergistic effect of radiative losses and the reduction of reaction intensity as the strain rate decreases for Le<l mixtures. The advantage of using the counterflow configuration is that the strain rate is well defined such that its effect can be systematically studied. However, limited microgravity experimental data available [Maruta et al., 1996] whose accuracy is also questioned because of the experimental methodology that was used. Although the results have been qualitatively reproduced by numerical simulations [Sung and Law, 1996], the quantitative agreement is rather poor. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In the experiments of Maruta et al. (1996), near-limit extinction data were obtained for a relatively small nozzle separation distance, e.g., L= 1.5cm. The estimation showed [e.g., Lakshmisha et al., 1990] that the thickness of near-limit premixed flames is of 0.5-1.0 cm. Given that the thickness is of the order L/2, it is apparent upstream conductive heat losses to the burner were unavoidable especially as the strain rate is reduced. Therefore, these experimental data may be contaminated by the upstream conductive heat loss. Moreover, fuel concentrations at the flame front were dynamically determined from the ones at the mixing point by a parameter called “the delay time”, which is difficult to measure precisely. In view of these considerations, one of the main objectives of the present study was to experimentally and numerically study the various loss effects on the extinction of near-limit flames. Experiments were conducted in microgravity and the data are free from such losses and, as a result, of fundamental interest. In laminar flame simulations, the radiation term has been generally calculated by using the Planck-mean absorption coefficients without considering the important gas phase radiation properties of wavelength dependence and re-absorption [e.g., Egolfopoulos and Law, 1992; Guo et al., 1996]. Namely, the radiation effect at the optically thick limit has not been sufficiently studied. In the present study, a full radiation model was developed and applied in the study of ideal one-dimensional freely propagating flames, for near-limit conditions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.1.2 Downstream conductive heat losses In many practical combustion processes, flames interact with the surrounding solid surfaces. The surface serve as both heat and radical sinks and can be either a namral boundary of a combustor, or an integral part of a heterogeneous reacting process. The interaction between the flame and the non-adiabatic solid wall modifies the transfer processes, which results in a variation of combustion efficiencies and pollutant formation [Charles et al., 1981; Hock et al., 1981]. Conductive/convective heat losses, unlike radiative losses, strongly depend on the geometry and boundary conditions of the system. In order to study the downstream heat loss effect on the strained flame, it is necessary to establish a model flame in which flow dynamics can be well described. A single jet-wall, stagnation flow configuration is an ideal environment for such studies. Many earlier applications of the single jet-wall configuration were primarily interested in the heat transfer, or heat losses [e.g., Anderson and Stresino, 1968; Beer and Chigier, 1968, Milson and Chigier 1973; Bankal and Gebhurt, 1995a, 1995b]. Smdies regarding the flame combustion have been conducted since the early 70's. Experimental and numerical results [Fang et al., 1971; Smith et al., 1971] showed that the flame standoff location and extinction depend on the impinging velocity and fuel concentration, and that the surface temperature is important to flame ignition. However, the straining effect in non-adiabatic flames was first studied in the early 80’s. Experiments were conducted by impinging a jet of lean QHg/air mixtures against a flat non-catalytic surface [Law et al., 1981]. The strain rate (velocity Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. gradient) was used as a measure to interpret the maximum flame temperature and flame location at extinction. It was reported that extinction limits were insensitive to the temperature of the surface. However, subsequent smdies [Sato and Tsuji, 1983; Law, 1988] showed that the above argument of the downstream heat loss on flame extinction is only valid for mixtures with Le>l. For those flames, the flame extinction occurs at a finite distance from the wall. The experimental studies with rich C,Hg/air mixtures [Ishizuka et al., 1982], and lean CH^/air mixmres [Ueda et al., 1993] concluded that for Le<l mixmres, the non-adiabatic surface introduces an additional factor for the flame extinction, and that the downstream heat loss on the flame extinction is more profound compared to Le>l mixmres. In these previous studies, the strain rates were determined globally so that they did not precisely quantify the straining effect. Furthermore, no corresponding modeling of the experiments was attempted. Recently, Vlachos and coworkers [1993, 1994a, 1994b, 1995] conducted rigorous numerical studies on the combustion of H,/air and CH^/air mixmres near the wall. The studies showed that the presence of the wall alters the extinction characteristics compared to the opposed-jet configuration, and that the flame extinction becomes sensitive to the radical wall destruction at high wall temperatures. While the smdies presented extensive information on the ignition and extinction phenomena, issues related to the steady burning, such as the flame speed, were not addressed. The global strain rate was imposed as a defined property from the far field, and its effect was quantified through the variation of the species profiles when the two Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 configurations were compared. Furthermore, no experiments were conducted in order to validate the simulations. 1.1.3. Upstream conductive heat losses The upstream conductive heat loss effect on the flame propagating has been addressed for flame propagation in a tube and a burner-stabilized flame. Due to the practical and fundamental interests, flame propagation in tubes has been studied extensively. A standard tube has been proposed as the means to experimentally determine the fundamental flammability limits [Coward and Jones, 1952]. However, as mentioned earlier, this determination is influenced by several external factors, such as the interaction between the tube and the surrounding hot gases and buoyancy. Thus the flames have been observed to be curved and stretched [e.g.. Levy, 1965; Buckmaster, 1982; Lee and Tsia 1995]. Furthermore, the conductive heat loss is induced and becomes important to flame propagation and extinction, coupling with other effects such as buoyancy, stretch, Lewis number, chemical kinetics [Buckmaster, 1982; Williams 1986; Wang and Ronney, 1993]. However, because the flame shape is not one-dimensional and varies during propagation, the strain rate and the conductive heat loss are difficult to be quantified [Egolfopoulos, 1993] By contrast, flames are one-dimensional when stabilized through heat loss on a porous flat burner. The upstream conductive heat loss not only acts as the mechanism for flame stabilization, but also influences the flame structure and dynamics. The laminar flame speed varies with the heat loss rate, and a dual flame Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Il speed response exists which is similar to the situation with only radiation heat loss [Spalding 1957; Botha and Spalding 1954; Spalding and Yumlu 1959; Ferguson and Keck 1979]. The dual flame speed response was further addressed [Chao and Law, 1988; Eng et al., 1991; Eng et al., 1995] by asymptotic analyses and experiments. Alternatively, the opposed-jet counterflow configuration with small separation distances between two nozzles is used in the present study, so that the stretch is well defined. With small separation distances, upstream conductive heat losses are introduced, similarly to the experiments of Maruta et al. (1996). Moreover, the heat loss is quantified as the temperamre gradient at the nozzle exit. The effect of upstream conductive losses has only been considered numerically. 1.1.4. Effect of unsteadiness on strained flames In realistic situations, flames are sustained predominantly in the turbulent regime. However, for a wide range of flow conditions, the flame thickness. Ip is smaller than the smallest turbulent eddy size, such as in the Kolmogorov scale, Consequently, the laminar flamelets concept can be applied. Namely, each segment of the reacting front can be treated as laminar flamelets which are subjected to various amounts of aerodynamic straining by the adjacent vortices [Peters, 1986]. At the same time, this effect of fluid mechanics on each individual flamelet is of unsteady nature. Thus, the fundamental understanding of the response of laminar flames to external unsteadiness is important to the better understanding of regimes of turbulent Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 2 combustion. In the mean time, it is important to the understanding of acoustic instability and combustion [Kim and William, 1994; Kistler et al., 1996]. Extensive theoretical and experimental studies have been motivated by the laminar flamelet concept and significant insight has been gained into the coupling between the aerodynamic straining and the elementary processes of molecular transport and chemical kinetics. However, the majority of the studies have been limited to steady flames. Though the steady state assumption constitutes a convenient approximation for the application of the flamelet concept in turbulent combustion, it ignores several features of relevance to turbulent combustion. For example, in a turbulent field, flames respond to the unsteadiness of not only the fluctuations of the local velocity and consequently the strain rate, but also the fluctuations of incoming reactant concentrations and temperature. The far field unsteadiness introduces additional time scales, and it affects the flame structure and dynamics by coupling with the time scales of convection, diffusion, and reaction. It has been found experimentally and analytically that the flame response strongly depends on the frequency of far-field unsteadiness [Strahle, 1965; Saitoh and Otsuka, 1976; Rutland and Fereiger, 1990; Stahl and Wamatz, 1991; Cetegen and Pine, 1992; Ghonien et al., 1992; Darabiha, 1992; Darabiha and Candel 1993; Kim and Williams, 1994; Im. et al., 1995; and Kistier et al., 1996]. At lower frequencies, flames respond in a quasi-steady manner. At higher frequencies, the amplitude of oscillation of all flame properties is reduced and a phase-shift is established with respect to the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 imposed signal. As the frequency of the imposed oscillations is further increased, the flames no longer respond. The physical explanation of the frequency response has been given in limited recent studies [e.g., Kim and Williams, 1994; hn. et al., 1995]. Analyses were conducted for each frequency regime. Namely, at low frequencies, the quasi-steady response was found to be attributed to the fact that the characteristic oscillation time scale is much longer that the diffusion time scale. At high frequencies, the failure of flame response was explained by the phase lag. The phenomenon of amplitude attenuation at high frequencies was explained from first principles by Egolfopoulos and Campbell (1996). An analogy between the upstream oscillation in diffusion flames with the Stokes’ second problem w as demonstrated by numerical simulations of counterflow unsteady diffusion flames with a detailed description of chemistry and transport. For the Stokes’ second problem, a plate oscillates within its plane under a stagnation fluid and the resulting fluctuating velocities “penetrate” into the fluid through momentum diffusion. Similarly, for diffusion flames subjected to oscillations of the far field temperature, concentration or velocity, these externally imposed variations propagate by diffusion into the main reaction zone. Thus, as the frequency increases, the physical penetration length for oscillations gradually becomes of the same order as the size of diffusion zone so that amplitude of oscillations is attenuated within the main diffusive zone. In the Stokes’ second problem, the amplitude of velocity flucmation is scaled with a non-dimensional coordinate, T].= z( ^ cû/2 v Ÿ'~, where z is the dimensional distance from the plate, û) = 2 ;çf the angular frequency, and n is the kinematic viscosity of the fluid. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 Analogously, a similar parameter, defined as the Stokes’ parameter, tj^, was proposed for unsteady diffusion flames [Egolfopoulos and Campbell, 1996], % =(n)/2AT)'^^, where c o is the angular frequency and K is the strain rate on the oxidizer side. The results of the variation of normalized amplitude T„,„ with the r;^ show that the is an appropriate parameter that controls the frequency response of the flame. It was also found that the drastic reduction of the normalized temperature amplitude initiates at 7 7, = 1 . Since the proposed criterion quantifies the transition between quasi-steady and transient regimes, it is important to test its validity through systematic experiments. 1.2 Objectives The above overview shows that the previous studies on the steady or unsteady laminar non- adiabatic flame are limited by the following: 1. Lack of rigorous numerical models. Mostly, detailed chemistry and transport descriptions were not used, while they were essential for understanding the detailed flame structure and intermediate formation (e.g., OH, H radicals; NOj). In addition, the radiation was mostly restricted to the optically thin model. 2. Lack of sufficient experimental data. Experiments were mostly conducted in normal gravity, such that near-limit and weakly-strained flames were not sufficiently assessed due to buoyancy effects. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 3. Lack of a comprehensive study. The previous studies were not consistently conducted in numerical simulation and experiments. The effects of the non- adiabaticity and the unsteadiness were not sufficiently assessed. Consequently, the main objectives of present smdy are focused on the effects of heat loss and unsteadiness on the propagation and extinction of strained, laminar flames and their implication on the existence of fundamental flammability limits. This investigation is carried out by both numerical simulations and experiments. Physical insights regarding the non-adiabatic, steady and unsteady flames are provided. More specifically, the numerical simulations focus on: 1. The development of a fuU radiation model. The model considers both the spectral wavelength dependence and the re-absorption in gas medium. Furthermore, it is incorporated into a I-D freely propagating flame code for the flammability limit study. 2. The propagation and extinction of the nearly-adiabatic premixed flames with emphasis on the near-limit and weakly-strained ones. 3. The upstream conductive heat loss effect. Studies are focused on the propagation and extinction of near-limit and weakly-strained flames in the counterflow configuration with small separation distances. 4. The downstream conductive heat loss effect. Studies are focused on the propagation and extinction of premixed flames in the single jet-w all configuration. The no-slip and wall temperamre effects are assessed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 The experiments focus on: 1. The development of a microgravity-compatible experimental system, using the opposed-jet counterflow technique. The system is applied to study the extinction characteristics of the near-limit, weakly-strained laminar flames. 2. The conduction of microgravity experiments. The experiments are focused on the extinction of near-limit, weakly-strained premixed flames, with mixmres of Le<l (e.g., lean CH^/air) and Le>l (e.g., lean C^Hg/air). 3. The propagation and extinction of nearly-adiabatic flames in normal gravity using the opposed-jet counterflow configuration. The LDV is applied to measure the velocity profile along the centerline and determine the local strain rate. 4. The downstream conductive heat loss effect. The single jet-wall stagnation flow configuration is applied and experiments are focused on the flame propagation and extinction characteristics. The results are compared to those from the opposed-jet counterflow configuration. 5. The effect of unsteadiness on the diffusion flame. The experimental system is modified from the conventional opposed-jet counterflow system. The experiments are focused on the validation of previous theoretical smdies. 1.3 Organization of the Dissertation In Chapter 2, the experimental methodology is described. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 In Chapter 3, the numerical methodology is described. In Chapter 4, a full radiation model is derived. The model is applied in an ideal one-dimensional, freely-propagating premixed flame for the study of fundamental flammability limits. In Chapter 5, a description of the microgravity experimental system is given. Experimental observations and data are reported. In Chapter 6 , the results of the numerical simulations of the counterflow configuration corresponding to microgravity experiments for CH^/air and C,Hg/air mixtures are presented. With small separation distances, the upstream conducted heat loss is introduced and its effect on the flame structure and extinction is addressed. In addition, the effect of Lewis number is assessed. In Chapter 7, the downstream heat loss effect is studied by both numerical simulations and experiments. The effect of no-slip and non-adiabaticity on flame propagation and extinction are addressed. An alternative method for the experimental determination of laminar flame speeds is introduced. In Chapter 8 , the effect of unsteadiness on the laminar diffusion flames is experimentally studied. Previous theoretical studies on the frequency response are experimentally validated. The flame extinction under free-stream velocity oscillations is also assessed. In Chapter 9, concluding remarks and recommendations for future studies are given. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 1.4 References Abbub-Mardir, A. and Ronney, P. D., (1990) 23rd Symp. (Inti) on Combus./Th& Combus. Insti., Pittsburgh, p423 Anderson J. E. and Stresino, E. P., (1968) J. Heat Transfer, 85(1) 49-54. Bankal C. E. and Gebhurt, B. (1995a) Combus. Sci. TechnoL, vol.104, pp339-357. Bankal C. E. and Gebhurt, B. (1995b) Combus. Sci. TechnoL, vol.104, pp359-385. Beer J. and Chigier, N. (1968) Combustion and Flame, 12: 575-586. Botha J. P. and Spalding, D. B (1954), Pro. R. Soc. Ser. {Land.) A 225: 71-96. Buckmaster, J. D. and Mikolaitis, D. (1982) Combustion and Flame, 45:109-122. Buckmaster J. D., (1984) J. Meek. Appl. Math. 35, 249 Cetegen B. M. and. Pine, D. S., (1992) Combustion and Flame, 91:141-152. Chao H. and Law, C. K. (1988) Combus. Sci. TechnoL, vol62: 211-237. Charles, A., Westbrook, K., A, Adamizyk and Lavoie, G. A. (1981) Combustion and Flame, 40:81-97. Coward H. and Jone, L. (1952) U. S. Bur. Mines Bull., 503. Darabiha, N., (1992) Combus. Sci. TechnoL, Vol. 8 6, ppl63-181, 1992. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 Darabiba, N. and Candel, S. (1993) Thirteen International Colloquium on Dynamics o f Explosion and Reaction System, Nagoya, Japan, 1991. Dynamics of G aseous Combustion, Vol. 151, edited by Kuhl et al., ppl73-187. Egolfopoulos, F. N., and Law, C. K. (1990) Combustion and Flame 80:7-16 Egolfopoulos, P. N., (1993) “ Aerodynamic, Unsteady, Kinetuc and Heat Loss Effects on the Dynamics and Structure of Weakly-Buming Flames in Microgravity”, Research Proposal, 1993. Egolfopoulos, F. N. (1994a) 25th Symp. (Intl.) on Combus.rïhe. Combus. Insti., Pittsburgh, pp 1365-1373. Egolfopoulos, F. N. (1994b) 25th Symp. (Intl.) on Combas.lTao. Combus. Insti., Pittsburgh, pp 1375-1381. Egolfopoulos, F. N. and Campbell, C. S., (1996) J. Fluid Mech., vol 318, 1-29. Eng, J. A. Egolfopoulos F. N., and Law, C. K. (1991) Heat Transfer in Fire and Combustion Systems, HTD-vol. 166, ASME. Eng, J. A., Zlhu D. L. and Law, C. K. (1995) Combustion and Flame 100: 645-652. Fang, M., Schmitz R.A., and Ladd, R. G. (1971) Combus. Sci. TechnoL, Vol 4, ppl43- 48. Ferguson C. R. and Keck, J. C. (1979) Combustion and Flame, 34:85-97. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 0 Ghoniem, A. F. Soteriou M. S. and Kino, O. M. (1992) 24th Symp. (Intl.) on Combus.lThe. Combus. Insti., Pittsburgh, p357. Hock, W., Peters N. and Adomeit G., (1981) Combustion and Flame, 41: 157-170. Im, H. G., Law, C. K., Kim, J. C., and Williams, F.A. (1995) Combustion and Flame, 100: 21-30. Ishizuka, S. Miyasaka K., and Law, C. K. (1982) Combustion and Flame, 45: 293-308. Kim, J. S., and Williams, F. A., (1994) Combustion and Flame, 98: 279-299. Kistler, J. S., Sung, C. J., Kreutz, T. G., Law, C. K., and Nishika, N., (1996) 26th Symp. (Intl.) on Combus.lTh& Combus. Insti., Pittsburgh, ppl035-1046. Lakshmisha, P. J., Paul K N. and Mukunda, H. S. (1990) 23rd Symp. (Intl.) on Combus.rihe. Combus. Insti., Pittsburgh, pp433-440. Law, C.K., Ishizuka S. and Mizomota, M. (1981) 18th Symp. (Intl.) on Combus./Tho. Combus. Insti., Pittsburgh, ppl791-1798. Law, C. K., Zhu. D. L, and Yu, G., (1986) 2 Ist Symp.(Intl.) on Combus./The Combus. Insti., Pittsburgh, pl419. Law, C. K. (1988), 22nd Symp. (Intl.) on Combus. /The Combus. Insti., Pittsburgh, P1381. Law C. K. and Egolfopoulos, F. N. (1992) 24th. Symp. (Intl.) on Combus.lTho Combus. Insti., Pittsburgh, p4 13-426. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 1 Lee S. T. and Tsai, C. H. (1994) Combustion and Flame, 99, 484-490. Levy, A. (1965) Proc. R. Soc. Ser. A 283, 134. Maruta, K., Yoshida, M., Kobayashi, H., and Niioka, T. (1996) Symp.(IntL) on Combus./Tho Combus. Insti., Pittsburgh, 26th . Symp. (Intl.) on Combus./Vae. Combus. Insti., Pittsburgh, p 1283-1294. Matalon, M. (1982), Combus. Sci. TechnoL, Vol. 131: 169-181. Milson A. and Chigier, N. A. (1973) Combustion & Flame, 21: 295-305. Peters, N (1984) Prog. Energy Comb. Sci., vol. 10, pp319-339. Peters, N. (1986) 21st Symp. (Intl.) on Combus.rïh& Combus. Insti., Pittsburgh, p p l2 3 1-1250. Ronney, P. D., (1988a), 22nd Symp. (Intl.) on Combus.rih& Combus. Insti., Pittsburgh, P1615. Ronny, PD, (1988b) Combus. Sci. TechnoL, Vol.59, 123. Ronny, PD, (1994) Modeling in Combustion Science Proceedings, Kapaa, Kuuai, Hawaii, Lecture Notes in Physics, Vol. 449 Springer-Verlag , Berlin, 1995. Ronny PD and Wachman, H. Y.(1985) Combustion and Flame 62: 107-133. Rutland, C. J., and Fereiger, J. H., (1990) Combus. Sci. TechnoL, Vol. 73, pp305-326. Saitoh, T., and Otsuka, Y., (1976) Combus. Sci. TechnoL, Vol. 12, ppl35-146. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 2 Sato Jun'ichi and Tsuji, Hiroshi (1983) Combus. Sci. TechnoL, Vol.33, pp 193-205. Smith, H- W., Schmitz R. A., and Ladd, R. G., (1971) Combus. Sci. TechnoL, Vol.4, ppl31-142. Smooke, M. D., Em, A., and Giovangigli, V., (1993) Joint Technical Meeting, Central and Eastern State Sections, The Combustion Institute, Paper 47 Spalding, D. B. (1957) Proc. R. Soc. Ser. A 240: 83-100. Spalding D. B. and Yumlu, U. S. (1959) Combustion and Flame, 3:553-556. Stahl, G. and Wamtz, J., (1991) Combustion and Flame, 85 :285- 299. Strahle, W. S., (1965) lOth Symp. (Inti) on Combus., ppl315-1325. Strehlow, R. A. and Svavge, L. D (1978) Combustion and Flame 31: 209-221 Sung, C. J. and Law, C. K (1986) 21st Symp. (Intl.) on Combus.rihç. Combus. Insti., Pittsburgh, p865,. Ueda, T., Yahagi Y., and Mizomoto, M. (1993) Turbulence and Molecular Process in Combustion, T., Taken (Editor), pp327-338. Vagelopoulos, C. M., Egolfopoulos F. N. and Law,. C. K. (1994) Symp. (Intl.) on Combus.nh& Combus. Insti., Pittsburgh, ppl341-1347. Vlachos, D. G., Schmidt L. D., and Aris, R. (1993) Combustion and Flame, 95:313- 325. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 Vlachos, D. G-, Schmidt L. D. and Aris, R. (1994a) AIChE J. Vol.40, No.6 ppl005- 1017. Vlachos, D- G., Schmidt L. D. and Aris, R. (1994b) AIChE J. Vol 40, No.6 pplOlS- 1025. Vlachos, D. G. (1995) Combustion and Flame, 103:59-75. Wang Q. and Ronney, P. D. (1993) “Mechanisms of Flame Propagation Limits in Vertical Tubes”, Spring Technical Meeting, Combustion Institute, Eastern &Central States Sections. Wüliams, F.A. (1985) Combustion Theory, 2nd Edition, Benjamin-Cummins, Menlo Park Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 C O ? t> II Î — II 3 « C *« u. G O u E ca c ■ a i C 3 E ,o c o s o 2 II V u E E a C O j= 0 1 ( U E CO c § 0) * t3 4 > L U Ü, Ü U Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O Q. C g Q. ■ D CD C/) C/) 8 ci' 3 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) Burned gas Unburned gas Integral scale eddy Kolmogorov scale eddy I I Distance or lime "Thin" flame (Re » 1, Ka « 1) Burned gas \ Kolmogorov scale eddy Unburned gas Integral scale eddy Distance or time "Distributed" flame (Re » 1, Ka » 1) Fig. 1-2 Laminar Flamelet Concept (Ronney, 1994] 26 Chapter 2 EXPERIMENTAL APPROACH In this chapter, the main methodologies and techniques of the experimental approach are introduced. In the first section, the widely-used counterflow system is briefly introduced. It provides an exclusive environment to study the strain flames, particularly the radiation effect. The system is applied in microgravity for the study of flammability limits, which will described in details in Chapter 5. In the second section, the single jet-wall system, which is used to study the downstream conductive heat loss effect is introduced. In the third section, the system for the study of unsteady diffusion flame is described. Finally, the LDV technique is briefly described. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 2.1 Opposed-jet Coimterflow System The opposed-jet counterflow system has been used for the flame as it offers the following advantages: ( 1) the stretch is well-defined; (2 ) the flame is flat and steady; (3) the upstream heat loss is eliminated; (4) the downstream heat loss can be eliminated or controlled; (5) the configuration degenerates to quasi-one-dimensional along the stagnation streamline, which allows for its convenient detailed modeling. Thus, the effect of stretch on flames can be systematically studied. Moreover, the configuration allows for the establishment of arbitarily low strain rates, which are of relevance to near-limit, weakly-burning flames, through which the issue of fundamental flammability limits can be assessed. The counterflow system includes two identical aerodynamically-shaped nozzles separated by a certain distance, L. Two identical streams are injected from the two nozzles against each other. Thus, upon ignition two symmetric flames are established. The system is also appropriate for the study of non-premixed flames that can be established by impinging a stream of oxidizer on a stream of fuel. Figure 2-1 depicts the schematic of the counterflow configuration with the twin premixed flames. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 Figure 2-2 depicts a typical velocity profile along the centerline measured by the laser Doppler velocimetry (LDV). The velocity gradient is near zero at the nozzle, and gradually increases to a maximum just before the velocity starts to increase as a result of the gas heating. This maximum velocity gradient in the hydrodynamics zone is defined as the imposed strain rate, K, and the minimum velocity as the reference upstream flame speed, S„ ^ For a given mixtiue, the variation of with the K is monitored, as shown in Fig. 2-3. By linearly extrapolating to zero K, the laminar flame speed, S„°, is determined [Wu and Law, 1984; Zhu et al., 1984; Yu et al., 1986; Egolfopoulos et al., 1989; Egolfopoulos et al., 1990]. As the exit velocity hom the nozzle increases the imposed strain rate K increases and eventually flame extinction occurs at a value In the present study, the opposed-jet counteflow system was designed for flame studies at both normal- and micro-gravity. Figure 2-4 depicts the schematic of the system as used in normal gravity. Two identical burners are facing each other. Each burner consists of a diffuser, a settling chamber with damping screens and a high-area-contraction nozzle. The burner is water-cooled to maintain the unbumed gas mixture at the ambient temperature. The coflow (e.g., N,) is generally applied in order to isolate the main flow from the quiescent ambient air, to m inim ize the vortex ring formation around the flame edges, and to keep the flame planar. The system is housed in a large plexigas chamber with continuous air ventilation. In normal gravity, the LDV technique is used to measure the axial velocity profiles. The seeding particles are aluminum oxide with 0.3|im in diameter. The strain rate is determined as the maximum velocity gradient before the flame as described Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 earlier. The mixture equivalence ratio, ((), depends on the flow rate ratio of the fiiel over that of oxidizer. Both air and fuel flow rates are measured by calibrated sonic nozzles. The individual flow rate can be adjusted by setting the upstream pressures of the sonic nozzles. The total flow can be modified by either adjusting the individual flow rates of both fuel and oxidizer or by using a bypass valve. The version of the system that is appropriate for microgravity studies is described in Chapter 5. 2.2. Single Jet-Wall Stagnation Flow System A single jet-wall stagnation flow configuration is used for the study of the downstream conductive heat loss effect. The opposed-jet counterflow system is modified by replacing the upper burner with a stainless steel plate. A single, planar premixed flame is thus established between the solid surface and the nozzle. The je t- wall flow configuration has the similar advantages as the opposed-jet counterflow one with the additional degree of freedom being the controllable downstream conductive heat loss. The system is illustrated in Fig. 2-5. The plate temperature is maintained at a desired temperature within the range of 500 K and 1300 K. Low plate temperatures are obtained by blowing cold air with adjustable flow rates against the non-interacting surface of the plate, while high plate temperatures are obtained by using an electric Si-C heater. The heater is installed on the non-interacting side of the plate and it provides uniform heating to the plate through thermal radiation. Desired high plate temperatures can be achieved by controlling the voltage on the Si-C heater. A refectory furnace is built to reduce heat Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 losses from the heater to the ambience. S-type thermocouples are used to measure the temperature at the gas-solid interface, by exposing the joint bean on the flame interacting surface around the plate center. The temperature uniformity around the plate center area is tested by using two thermocouples at different radial positions. The results demonstrated that the difference is of the order of I K/cm which assures that the assumption of uniform plate temperature, essential for the quasi-one- dimensional modeling, is valid [Egolfopoulos et al., 1997]. 2.3 Unsteady Counterflow Syetem Figure 2-6 depicts an experimental system for the study of unsteady strained diffusion flames. The system is similar to the conventional counterflow one as described earlier, except for the bottom burner. The unsteadiness is induced by the flow oscillation generated by a 16” woofer-type speaker, which is mounted under the nozzle on the fuel side. The speaker is driven by a lOOW amplifier according to a sinusoidal wave signal provided by a function generator. The frequency and amplitude of the upstream velocity oscillation are controlled independently. The mean flow rate is adjusted by the upstream pressure of sonic nozzles. The LDV is used to measure the axial velocity profile along the centerline when the oscillation is not imposed, and to measure the maximum and minimum axial velocities at the nozzle when the velocity oscillation is imposed. The difference between the maximum and the minimum values is defined as the oscillation amplitude of the upstream velocity. The flame displacements are observed by a telescope with a vertical displacement scale. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 2.4 Laser Doppler Velocimetry (LDV) In normal gravity, the LDV is used for the non-intrusive velocity measurement. The illumination source is a 4.0-Watt A+ continuous wave laser with a 514.5nm wavelength (green light). Dual beams and forward receiving mode are adopted. The seeding particles (AI2O3 with 0.3 microns in diameter) closely follow the gas phase and efficiently scatter the laser light. A photo-multiplier is used as a detector to convert optical signals into electrical ones. The Doppler burst rate is measured by using a frequency counter with 1.0 ns resolution. Generally, the axial profile is measured along the centerline of the main flow. The spatial step usually is within the range of 0.1 and 0.01 mm. A two-phase step motor or a manual handle with a micrometer was built and applied for the stepping. The data can be acquired by the acquisition time mode or the acquisition number mode. Statistical processes are completed with the software provided by the QSP Company. The axial velocity profiles are subsequently analyzed for the determination of the reference flame speed and the imposed strain rate. The strain rate is obtained by linearly fitting the velocity data in the hydrodynamic zone. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 2.5 References Egolfopoulos, F. N. (1990) “An Experimental and Computational Study on the Propagation and Kinetic Structure of Laminar Premixed Flames” Ph.D. dissertation. University of California, Davis. Egolfopoulos, F. N., Cho P., and Law, C. K (1989) Combustion and Flame, 76:375- 391. Egolfopoulos, F. N., Zhu D. L. and Law, C. K. (1990), 23rd Symp. (Intl.) on Combus. The Combus. Insti. Egolfopoulos, F. N., Zhang H., and Zhang, Z. (1997) Combustion and Flame, 109:237- 252. Vagelopoulos, C. M., Egolfopoulos F. N., and Law, C. K. (1994) 25th Symp. (Intl.) on Combus. / The Combus. Insti. pp. 1341-1347. Wu C. K. and Law, C. K. (1984) 20th Symp. (Intl.) on Combus. / The Combus. Insti., ppl942- 1949. Yu, G., Law, C. K and Wu, C. K. (1986), Combustion and Flame, 63:339-347. Zhu, D. L., Egolfopoulos F. N., and Law C. K, (1984) 20th Symp. (Intl.) on Combus. /The Combus. Insti., pp. 1537-1545. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 X Flame Stagnation Point Flame High Contraction nozzle - r Premixed Fuel and Oxidizer Fig. 2-1 Schematic of the opposed-jet counterflow configuration with premixed twin flames Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O Q . C g Q . " O CD C/) C/) 3. 3 " CD CD ■ D O Q . C a o 3 " O o CD Q . " O CD C/) C/) 250 Stagnation Plane Flow Direction 0 ISO > c V G 1 " u K=-du/dx 'u.rel 1.6 1.2 1.4 1,0 0,4 0.6 0.8 1.0 02 0.0 Distance from the N ozzle Exit, x, cm Fig. 2-2 Definilions of strain rate K and reference flame speed S„ in the stagnation configuration 4^ CD ■ D O Q. C g Q. ■ D CD C/) W o' 3 0 3 CD 8 ■ D ( O ' 3 " 1 3 CD 3. 3 " CD CD ■ D O Q. C a O 3 ■ D O CD Q. ■ D CD ( / ) ( / ) Karlovitz Number 35 30 20 □ A ° ' L=7 mm o , " % I u 'S P 14 mm co 22 mm S “, 1-D Code ( H 2 /Air, p = l atm, ({)=0.3^ 600 500 400 200 300 Hydrodynamic Strain, s ' 100 Fig. 2-2 The definition of strain rate K and reference flame speed S^^r in the counterflow configuration (from Vagclopoulo.s et al., 1994) W U \ 36 1.2—nozzles 3.4— straight tube 5.6— diffiisors 7— compressor 8.9— fuelmitrogen tank 10—laser 11—photomultiplier 12—computer 13—mixing chamber tX3 — valves G1.G2 — pressure gauges S1.S2 — sonic nozzles G 1 To Exhaust Plexiglass House conow (N ->) water in water out Fig. 2-4 The schematic of opposed-jet counterflow flow system Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 Thermometer To Power Supply Transformer Thermocouples Heatingn Element x= 0 Stagnauon Plane Prem ixed M ixture, Fig. 2-5 The schematic of single jet-wall configuration for the upstream conduction heat loss effect study Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 1,2—nozzles 3.4— straight tubes 5.6—diffiisors 7—compressor 8.9— fuel/nitroeen tank 10—laser 11—photomultiplier 12—computer C X ] — valves G1.G2 — pressure gauges S1.S2 — sonic nozzles Plexiglass House To Exhaust coflow (Nt) water m water out Funcuon Generator Amplifier Fig. 2-6 The schematic of the opposed-jet counterflow system for the smdy of unsteady diffusion flames Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 Chapter 3 NUMERICAL APPROACH 3.1. Introduction In this chapter, the numerical models, governing equations and associated boundary conditions used in the present study are described. The thermal radiation models are also briefly introduced The laminar flame speeds are determined by using the one-dimensional. Premix Sandia code [Kee et al., 1985] which allows for the modeling of freely- propagating flames. Strain rate effects are studied through the numerical simulations of the opposed-jet counterflow and the single jet-wall stagnation flow are conducted by solving the conservation equations of mass, momentum, species concentration. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 and energy along the system centerline. The integration includes the use of detailed description of chemical kinetics, molecular transport, and thermal radiation. The formulation of the stagnation-point flow has been a subject of extensive investigation for the past fifteen years, [Miller et al., 1984; Kee et al., 1988]. The governing equations and the appropriate boundary conditions have been well- established. Two parameters, i.e., the radial pressure curvamre J^l/r)(dP/dr) and the radial velocity gradient G=dv/dr=v/r are used to characterize the flow, where P is the dynamic pressure and v the radial flow velocity. The axial velocity, temperature and species concentration are assumed to be uniform in the radial direction. Under these assumptions, the parameter G is considered as a function of the axial coordinate, i.e., G=G(x). Simultaneously, the radial velocity v increases linearly with the radius, r [Kee et al., 1988]. The original code [Kee et al., 1988] allows for the solution in the opposed-jet, twin-flame symmetric configuration. The code was modified to account for both slip or no-slip conditions at the stagnation plane such that both the opposed-jet and the single jet-wall configurations could be assessed [Egolfopoulos et al., 1997]. The no-slip condition for the axial velocity in the opposed-jet configuration is allowed by setting the G equal to zero. Thus, the radial velocity at any point of the plane is zero. The counterflow and stagnation flow codes were further modified to allow for the one-point continuation, such that the turning-point behavior can be characterized [Zhang and Egolfopoulos, 1998]. This was implemented by an internal boundary condition for the temperature. The boundary condition for the flow velocity is eliminated and turned into part of the solution. The one-point continuation is used to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 characterize the extinction states of strained premixed flames; flame extinction is identified by the turning point behavior of the maximum flame temperature versus the imposed strain rate. The codes are linked to the Chemkin-II [Kee at al., 1989] and Transport [Kee et al., 1983] subroutine packages which provide detailed chemistry and transport information respectively. Two different chemical kinetic mechanisms are used. One is the hierarchically developed C, mechanism, referenced as EDL [Egolfopoulos, 1992]. The EDL satisfactorily predicts a wide range of the oxidation properties of hydrogen, carbon monoxide and C, and C, hydrocarbons. The second scheme is the recently developed GRI 2.1 [Bowman et al., 1995]. For the modeling of C^Hg/air flames, a C, su b mechanism [Pitz and Westbrook 1986] is added to the GRI 2.1 C, mechanism. 3.2 Governing Equations Governing equations used in the present study are consistent with that used in the previous studies [Kee et al., 1985; Egolfopoulos and Campbell, 1996]. The governing equations for 1-D, transient state flames in the opposed-jet counteflow configuration are: ^ + 2pG 4- ^ (pm) = 0 (mass conservation) ( 1 ) at dx Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 3C? 3G d dG —+ p « — —+ p G ^ + 7 — — (/z—~) = 0 (momentum conservation) (2) dr dx dx dx (energy conservation) (3) p - ^ + p u ^^+ ^(.p Y ^V ^.) — = 0 (species conservation) (4) dt dx dx with G = ^ = — = G(x) and J = — dr r r dr Where, t denotes the temporal coordinate, and x denotes the spatial coordinate perpendicular to the flame front; T denotes the temperature and P denotes the pressure; u and v are the axial and radial convective velocity component respectively; p, C p and X are the mass density, the constant pressure heat capacity and the thermal conductivity of the mixture respectively; K is the total number of species; and are the mass fraction and the molecular weight of the kth species; is the molar rate of chemical production per unit volume; h^ is the specific enthalpy; is the diffusion velocity; and V is the divergence of the net heat radiation flux. For open flames, since the velocity variation effect is dominant, the temporal pressure variation is reasonably neglected, i.e., ^ = 0 [Kim and Williams, 1994]. ot For steady flames, the terms regarding the temporal variation are eliminated. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 3.3 Boundary Conditions For premixed flames in the opposed-jet configuration x = 0 (stagnation plane): « = 0 , ^ ^ = 0 , — = 0 , — = 0 (5 - 1) dx dx dx ^ — ^ (exit): Y q ^ —X o ,.x= l^ ~ ^ c h^.x= l^ ~ ^ n..x= l' ( x — 0 (5-2) For premixed flames in the single jet-wall configuration, (5-2) remains but (5-1) becomes. x = 0 (stagnation plane): M = v = 0 , -^ ^ = 0, T = T^,G = 0 (6- 1) dx x= L (exit): Y q ^ —^o .,x= l- > ~ ^ c h,.x = l‘ < ~ ^ n..x = l’ > 6? — 0 (6-2) For diffusion flames in the counterflow configuration (assumed air is from the lower burner), x = 0 (lower): ^o,jc= o , 1^^^ —Yc h,.x = o’ ^v, ~^v,.x=o’ G = 0 (7-1) X = L (upper): F q , = , G = 0 (7-2) The unsteadiness is introduced by oscillating the axial velocity at the nozzle exit, by imposing sinusoidal variations of a given amplitude around a mean value [Egolfopoulos and Campbell, 1996], namely, ««/r = “e x « + sin(û)f) = sln (2 # ) (7-3) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 3.4 Thermal Radiation Models 3.4.1 The optically-thin model For an optically thin medium, the re-absorption in the gas medium is not considered. The divergence of the radiation flux is usually expressed as: V-q^ = -AKa^il) - g\T\V) - r ] (8) Where, a is the Stefan-Boltzmann constant; T is the local gas temperature; Tq is the ambient temperature; and is the Planck-mean absorption coefficient. As shown in Eq. 8 , at the optically thin limit the radiative transfer depends only on the local and ambient temperatures, and the local species concentrations. In the present study, two methods are adopted to calculate the Plank-mean absorption coefficient. (1) Empirical equations îov^ p The Planck mean absorption coefficients for each radiative species are given with the empirical equations in terms of temperature. The average Planck mean absorption coefficient, , is then calculated as where P- the partial pressure of species i. This method is the simplest and fastest in computation. The results, such as the flame speed and the extinction limit are found to be generally acceptable [e.g.. Law and Egolfopoulos. 1992; Guo et al., 1996; Sung and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 Law, 1996]. Since the empirical equations are from Tien (1967), the model is referred as the Tien’s model in this study. (2) Spectral integral for One of the major differences between the emissivities of gases and solids is in the spectral behavior. In general, for solid surfaces, the variation of the emissivity with wavelength is smooth. However, for gases, the variation of the emissivity with wavelength is irregular. In other words, the absorption and emission coefficients of gases significantly depend on the wavelength. Obviously, spectral properties are not accounted accurately in the empirical equations of Tien. Given the spectral properties, the Planck mean absorption coefficients can be calculated from the integration of the spectral absorption coefficients [Siegel and Howell, 1981; Grosshandler 1993] = (9) Where, 4(0 is the blackbody intensity, 4 (0 = 4 ^(0<7A = cfT '* (Z ) / ;r ? In our studies, the spectral data are from the RADCAL, a well-developed narrow-band radiation package [Grosshandler, 1993]. 3.4.2 The optically thick model As opposed to the optically thin model, the optically thick limit takes into account the re-absorption in the gas medium. Thus, a part of the energy emitted by Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 the radiative species at a location is absorbed by the radiative species at other locations within the domain of interest. Although the re-absorption effect is found not to affect the response of rigorously burning flames, it may be important for near- limit flames. Since the flames studied herein are one-dimensional, they can be described as planar radiating media bounded by two infinite, parallel, opaque surfaces. With the consideration of the re-absorption characteristics, a full radiation model is derived. The model directly provides the radiation term in the energy conservation equation. In addition, it uses the spectral absorption data from RADCAL. More details about the RADCAL and the full radiation model are given in the next chapter. 3.5 References Bowman, C. T., Frenklach, M., Gardiner, W. R. and Smith, G. (1995) The “GRI2.1” Chemical Kinetic Mechanism. Personal Communications. Egolfopoulos, F. N., Du, D. X and Law, C. K, (1992) Combus. Sci. and TechnoL, 83: pp33-75. Egolfopoulos, F. N., and Campbell, C. S. (1996) J. Fluid Mech., vol. 318, pp 1-29. Egolfopoulos, F. N., Zhang, H., and Zhang, Z. (1997) Combustion and Flame, 109:237-252. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 Grosshandler, W. L. (1993) “RADCAL: A Narrow-Band Model for Radiation Calculations in a Combustion Environment”, NIST Technical Note 1402. Que, H., Mamta, K., Niioka, T. and Yu. J (1996) 26th Symp. (Intl) on Combus. / The Combus. Insti., pp 1333-1344. Kee, R. J., Wamatz J., and Miller, J. A., (1983) “A FORTRAN Computer Code Package for the Evaluation of Gas-Phase Viscosities, Conductive, and Diffusion Coefficients” Sandia Report, SAND83-82G9. Kee, R. J, Grcar, J. P., Smooke, M. D. & Miller J. A. (1985) “A FORTRAN program for Modeling Steady Laminar One-Dimensional Premixed Flames”, Sandia Report, SAND85-8240. Kee, R. J., Miller, J.A., Evens, G. H., and Dixon-Lewis, G. (1988) 22nd Symp. (Intl.) on Combus., The Combus. Insti., pp. 1479-1494. Kee, R. J., Rupley, F. M., and Miller, J. A. (1989) “Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics", Sandia Report, SAND89-8009. Kim, J. S. and Williams, F. A. (1994) Combustion and Flame, 98:279-299. Law, C. K., and Egolfopoulos, F. N. (1992) 24th Symp. (Intl.) on Combus.J the Combus. Insti., pp. 137-144. Miller, J. A., Kee, R. J. Smooke, M. D. and Grcar, J. F., (1984) Spring Meeting o f Western States Section o f Combustion Institute, Paper WSS/CI 84-10. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 Pitz, W.A. and Westbrook, C. K., (1986) Combustion and Flame, 63:113-133. Siegel, R., and Howell, J. R., (1981) '''’ Thermal Radiation Heat Transfer", second Edition, Hemisphere Publishing Corporation. Sung, C. J., & Law, C. K (1996) 26th Sym.p. (Intl.) on CombusJ the Combus. Insti., Pittsburgh, PA, pp865. Tien, C. L (1967), Adv. Heat Trans. 5:253. Zhang, H. and Egolfopoulos, F. N. (1998) Spring meeting o f the western states section/ The Combustion Institute, Berkeley, CA. Paper WSS/CI 98S-041. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 Chapter 4 FULL RADIATION MODEL In this chapter, a full thermal radiation model for the planar flames is developed. The model is used in the simulation of extinction of near-limit, weakly-strained premixed flames and thereby the mechanism of flammability limits can be assessed. 4.1 Introduction and Objectives In laminar flame simulations, the thermal radiation term has been generally expressed in terms of the Planck-mean absorption coefficient, . As introduced in the Chapter 3, the was usually calculated by the empirical equations without considering the wavelength dependence and the re-absorption. Although, simulation results such as the laminar flame speed and the extinction strain rate, obtained by Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 using the optically thin assumption, compare favorably with the experimental data, it is reasonable to assume that the re-absorption in the gas medium can compensate at least partially the radiation heat loss. The hypothesis has been supported by previous studies. For example, the asymptotic simulations [Joulin et al., 1986, 1989] of a planar premixed flame in a gaseous mixture seeded with small and inert particles revealed that the radiative transport plays completely different roles according to different particle concentrations. When the particle concentration is high, a significant portion of emitted radiation may be reabsorbed within the gas. The re-absorption reduces the radiative heat loss and heats up the unbumed gases. The theoretical predictions were confirmed by the experiments in microgravity [Abbud and Ronney, 1990]. Recently, a considerable increase of the burning velocity and an extension of flammability limits were reported when the re-absorption was taken into account for 1-D freely propagating flames [Ju et al., 1998]. The radiative transfer equation was solved with the discrete ordinate method (DOM) and the S6 quadrates scheme. Additionally, the importance of re-absorption effect has been demonstrated by the theoretical analysis of stretched diffusion flames at high pressures, and especially in the very low strain rate regime [Vranos and Hall, 1993; Shan et al., 1995]. Results showed that the thermal field could substantially affect the flame temperature especially at low strain rates. Therefore, the rate of NG^ formation was foimd to be substantially affected by adopting the optically-thick analysis at low strain rates. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 As mentioned in Chapter 1, if fundamental flammability limits do exist, they should be independent of external mixture parameters. Thermal radiation is in general considered as a loss mechanism and then a controlling mechanism responsible for the existence of fundamental flammability limits. However, the re-absorption is a gain mechanism and it is important to assess its effect on near-limit flames. Thus, in the present study, a full radiation model is incorporated into the flame codes by accounting for the wavelength dependence and re-absorption. The spectral transport data are given by the RADCAL [Grosshandler 1993]. 4.2 The Full Radiation Model 4.2.1 Expression of the radiation source term Flames are assumed to be within a planar radiating medium bounded by two infinite parallel planes, which serve as boundaries, shown in Fig. 4-1. The medium is assumed isotropic, non-scattering and bounded with diffusion boundaries. The divergence of radiation flux, which is the radiation source term in the energy conservation equation is given below - K \lk l]a ^(.k J^d X (1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 The first two terms are related to the boundaries. Given that the boundaries are assumed to be at the ambient temperature, these terms are much smaller than the other terms. In the present study, boundary surfaces are simply treated as blackbodies. The third term pertains to the radiation fix>m the medium between a specified location x and the boundaries. The exponential function is a measure of the attenuation of the radiation emitted from an arbitrary location in the domain to the location x. The term oc^(Jc^) represents the local absorption ability with respect to the incident radiation at a wavelength X. The last term relates to the radiation source, and it approximately equals to the term used in the optically thin model. The details of the derivation are described in the Appendix of this thesis. 4.2.2 The RADCAL and spectral absorption coefficients The RADCAL [Grosshandler, 1993] is a well-developed radiation package which predicts the spectral structure of various combustion products over a wide range of temperature, pressure and path-length. It can be used to compute the spectral intensity, from a non-isothermal mixture of combustion gases and soot incident upon a volume element within or external to the environment. It solves the equation of transfer for an absorbing and emitting medium (no scattering) by breaking the line-of- sight into a number of uniform elements. It also uses molecular models and tabulated data for spectral absorption coefficients. The RADCAL provides the spectral absorption coefficients for the radiating species of CO^, ILO, CO, CH^ and soot particles. Since lean mixtures are major Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 concern for our study, the soot is excluded. However, the RADCAL is not directly applicable for flames in a double bounded medium. 4.2.3 Computational implementation The computational implementation of the full radiation model into the flame codes was done as follows: a. For given boundary conditions, the mass and species conservation equations are solved without coupling with the energy equation. The solutions of the temperature and species concentration profiles are used as initial guesses for the subsequent iteration with the energy equation. This treatment assures a more efficient convergent. Alternatively, temperature and species concentration profiles from optically thin models can be used as initial guesses. b. According to the given temperature and species profiles, the optical thickness of each layer is computed by the RADCAL, and thus the total optical thickness Atg^in the entire region is obtained. Simultaneously, the spectral absorption coefficient and the spectral emission intensity '-u - in each layer are computed. c. The divergence of radiative flux V is computed upon the expression ( 1). d. By substituting V - into the energy equation, new temperature and species profiles with the full radiation model are computed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 e. Solution is considered as converged if the change of all dependent parameters is within a user-specified error tolerance. f. Use the last results for next iteration and repeat step b, c, d and e until results are within the specified error tolerance. 4.3 Application of the full radiation model in 1-D premixed flames The radiation model was tested in one-dimensional freely propagating, atmospheric methane/air flames for conditions near the experimentally-observed flammability limits. In the future, this model will be tested for near-limit strained- weakly flames, dusty flames, landfill gas (high CO^ in composition) flames, and weakly-strained flames at high pressures. 4.3.1 Comparison of two optically thin models The radiation model is tested in three model flames using the narrow-band optically thin model. Figure 4-2 depicts the temperature and radiative species profiles for these three flames, including a stoichoimetric flame ((j)=1.0 ), a weak flame close to the flammability limit with (|)=0.51 and a flame with (f)=0.70. As indicated previously, the Planck mean absorption coefficient can be calculated by two methods. One is the Tien’s model since it uses the empirical correlation given by Tien (1978). The other one is the RADCAL model since it uses the narrow-band data from RADCAL. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 Figure 4-3 depicts the comparisons of Planck mean absorption coefficients calculated by the Tien’s model and the RADCAL model. It can be seen that the Tien’s model has very good agreement with the RADCAL model in the product regimes for 0=0.70 and 0= 1.0 flames, but it over-predicts the radiation more than 50% for 0=0.51 flame. Since the variations of molar fraction of the m ajor radiating species CO, and ILO are small in the product regimes (Fig. 4-2), the discrepancy depends on the temperature. Further comparisons of the absorption coefficients for H^O or CO^ species (Fig 4-4), it is seen that the two models are in good agreement for H ,0. The over-prediction is attributed to the correlation given for CO^ species especially in the low temperature regime. Shown in Fig. 4-4, the two models predict closely the CO absorption coefficient, and the Tien’s model slightly over-predicts the CH^ absorption coefficient. However, since the CH^ exists predominately in the low temperature zone, it plays a minor role in the overall observed discrepancy. As shown in Fig. 4-4, species CO^ and H^O chiefly contribute to the radiative transfer. Figure 4-5 depicts the axial distributions of the divergence of generation flux V-<3'y^„(x)and the divergence of radiation flux V-q^(x). It can be seen that the generation term is limited in a small domain of 0.5-1.0 mm where reactions are mostly completed. The radiative zone is much wider and includes both the reaction and product zones. The V • q ^x ) decreases as the temperature decreases. In the high temperature regime, the V-^^(x)predicted by the Tien’s model is close to that by the RADCAL mode, as expected. In the low temperature regime, V-q^(x) is significantly over-predicted by the Tien’s model. Figure 4-6 shows the ratio of V-q^(x) for these two optically thin models. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 43.2 Optically thick limit Radiation flux When the re-absorption in the gas medium is accounted for, the net radiation is significandy reduced for all three flames. Figure 4-5 depicts that in the unbumed zone a negative radiation term can be found. This indicates that radiation is a source instead of a loss in the energy equation. The radiation emitted by the downstream high temperature species is partially re-absorbed by CH4 in the unbumed zone. It can also be seen that the re-absorption effect becomes more significant in the product zone, where the temperature and concentrations of the radiating species are high. For vigorously burning flames, the V ■ q^x) is reduced about 50% in the product zone by the re-absorption. For near-limit flames, the re-absorption effect is more significant, especially downstream of the flame front. The V • q^x) in the far downstream region can be reduced down to about 1 /1 0 when re-absorption is considered. The total radiation flux can be calculated by integrating the V-^^(x) throughout the entire domain. Qr~j '^iXx^dx, where ^ = A and ^ correspond to the positions of the cold and hot boundaries respectively. Figure 4-7 depicts the variation of the total radiation flux with the equivalence ratio, < { ) , for the three radiation models. For all models, decreases with ((). This is reasonable given that the flame temperature is lower as ( { ) is reduced. Furthermore, the ratio of the total radiation fluxes between the two optically thin Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 models is close to unity within a wide range of < j ) ’s. However, the ratio is only around 0.5 for the optically thick model over the optically thin one. This indicates about 50% of the radiation emitted from the source is re-absorbed. The re-absorption effect becomes stronger as the flame becomes weaker. Figure 4-8 depicts the distributions of the four terms in the V - expression for the three typical model flames in a domain of L=10 cm. The four terms relate to the boundary, the upstream re-absorption, the downstream re-absorption and the source respectively. It can be seen, that all terms are strongly related to the temperature. Since the boundaries are at ambient temperature, their contribution to the total radiation is minor. The source term rapidly increases from nearly-zero to a maximum value at the flame front and then gradually decreases with the temperature. Furthermore, it is partially compensated by the re-absorption terms. The difference between the source term and the net radiation term indicates the importance of re absorption. In addition, as shown in Fig. 4-8, the upstream re-absorption term is close to zero in the unbumed zone. This is a result of the nearly-zero optical thickness and the low temperature in this region. The re-absorption term gradually increases in the high-temperature product regime as the optical thickness increases. Then it reaches a maximum at the right boimdary for most - flames except those close to flammability limits. Given that the radiative species concentration is nearly-constant in the product zone, the re-absorption depends on the local temperamre and the axial location. Along the axis, the absorption coefficient decreases with the temperature, while the upstream optical thickness keeps increasing. Consequently, the upstream Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 re-absorption term is reduced, as the temperature is reduced, while it is enhanced as the optical thickness increases. For the (|)=1.0 and ({>=0.7 flames, the temperature effect is dominated by the optical thickness effect. Therefore, the re-absorption term keeps increasing along the axis. However, for near-limit flames, e.g. <{)=0.51, the temperature is significantly reduced and the concentrations of the radiative species are low in the product zone. The optical thickness effect is dominated by the temperature effect, so that the maximum upstream re-absorption takes place close to the flame. The downstream re-absorption term is finite but small in the unbumed zone a s CH4 absorbs some radiation emitted from the downstream high temperature zone. The term increases rapidly to a maximum around the flame front where the concentrations of CO, and H ,0 , and temperature assume large values. In the product regime, as the temperature and the optical thickness decrease, the downstream re absorption gradually decreases and then becomes zero at the right boundary. For all three flames, the net radiation is significantly affected by re-absorption. Negative values in the unbumed zone indicate that a portion of the radiation emitted from the downstream becomes an energy source. The re-absorption in the unbumed zone slightly heats up the unbumed gases. In the reaction and product zones, the source term is substantially reduced by the two re-absorption terms. Especially for near-limit flames, the radiation in far downstream is mostly re-gained by the re absorption. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 Flame temperature Figure 4-9 depicts the flame temperature profiles of one-dimensional freely propagating flames simulated with the three different radiation models. Three flames are shown at different equivalence ratios, <^=l.O, ({)=0.7 and ({>=0.51. For the stoichoimetric flame, (#=1.0 , the temperature profiles for both optically thin models closely overlay on each other, and the both differ from the optically thick model especially in the reaction zone. In the far downstream region, the temperature predicted by the optically thick model is around lOOK higher than that by the optically thin ones. For the less strong flame, e.g. (#=0.7, the temperature predicted by the RADCAL model is slightly higher than that determined by Tien’s model. The maximum difference is about 50K in far downstream. It is of interest to note that for both (#=1.0 and (#=0.7 flames, the flame maximum temperatures, are not noticeably affected by the re-absorption. For near-limit flames, e.g. (#=0.51, the temperature predicted by the RADCAL model is higher compared to that predicted by Tien’s model within the entire product zone. The maximum difference is about 100 K far downstream. At the same time, the re-absorption compensates the source radiation more substantially. Therefore, the temperature noticeably increases in the product regime. The maximum difference is up to about 300 K far downstream. Furthermore, the three radiation models result in different maximum flame temperatures. Tien’s model predicts the lowest flame temperature while the optically thick model predicts the highest flame temperature. Compared with the results for the strong and weak flames, it was found that the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 radiation effect on the maximum flame temperamre is significant only for near-limit mixtures. Flammability limits Figure 4-10 depicts the variation of maximum flame temperamre, T ^ , vs. the equivalence ratio, < j ) for one-dimensional freely propagating flames and bifurcation behavior can be seen. On the upper branch the decreases as (j) decreases, while on the lower branch, the increases as 0 decreases. The point at which the two branches join is defined as the turning point. The upper branch is physically stable while the lower branch is unstable [Williams, 1985]. The fuel concentration at the burning point is defined as the fundamental flammability limit [Law and Egolfopoulos, 1992]. As shown in Fig. 4-10, the flammability limits calculated by three different radiation models are close to each other. The Tien’s and the RADCAL models predict * î > i i r a ~ 0-51. The optically thick model predicts 0,;^ = 0.50. Although the reduction of the downstream radiation flux is more than 50% (Fig. 4-7) when the re-absorption is considered, the reduction of flammability limits is less than 5%. This demonstrates that the extent of downstream radiation heat loss plays a minor role on flammability limits. This conclusion is consistent with that of the theoretical analysis [Williams, 1985]. Figure 4-11 depicts the variations of the generation heat flux and radiation heat flux for different ( { ) ’s. The results from the integration of the divergence of generation flux in the entire domain, i.e., Qr=\ ^ ^ ‘ • The results 6 om Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 the integration of the divergence of radiation flux in the entire domain, i.e., Qr — j ^V- It can be seen (Fig. 4-11) that the generation flux decreases with ({ ), as does the radiation flux (Fig.4-7). As < { ) becomes smaller than a critical value, the flame is not sustained. It can be also seen that close to this limit, the ratio of Qf/Qgen is around 0.7 for the optically thin model and around 0.45 for the optically thick one. Therefore, that rate of heat loss is found less than the rate of heat generation at the point beyond which flame propagation can not be sustained. This finding suggests that while the presence of thermal radiation is necessary for the existence of flammability limits, the actual failure of flame propagation is caused by kinetic mechanisms because of the temperature reduction. This was previously shown by Law and Egolfopoulos (1992). 4.4. Concluding Remarks A full radiation model accounting for the wavelength dependence and re - absorption was developed and incorporated into one-dimensional flame codes. For vigorously burning flames, the thermal radiation is similarly predicted by using the RADCAL subroutine package and the Tien’s model. However, for near- limit flames, the Tien’s model over-predicts the radiation significantly. It is found that the discrepancy is mainly attributed to the absorption coefficient given for the species CO,. In the low temperature regime, the discrepancy increases. It is also foimd that the re-absorption is significant for all flames if a large domain is considered. In the far Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 downstream region, accounting for re-absorption results in a reduction of the net radiative losses of about 50% for strong flames and about 80% for near-limit flames. As expected, the inclusion of re-absorption affects the flame temperature field. The temperature values in downstream region are significantly higher if re-absorption is considered. However, the maximum flame temperature is noticeably affected by radiation only for near-limit flames. Flammability limits derived from different radiation models differ slightly although the rates of downstream radiative transfer are significantly different. This suggests that the extent of the downstream heat loss plays a minor effect on flammability limits. Furthermore, it was shown that around the flammability limit the integrated radiative loss rate is only a fraction of the integrated heat generation rate. This suggests that the actual failure of flame propagation is caused by chain mechanisms as the flame temperature is reduced. 4.5 Reference Abbub-Mardir, A. and Ronney, P. (1990) 23rd Symp. (Intl.) on Combus. /The Combus. Insti., Pittsburgh, p423 Grosshandler, W. L. (1993) “RAJDCAL: A Narrow-Band Model for Radiation Calculations in a Combustion Environment”, NIST Technical Note 1402. Jouhn G. and Beshaies, B (1986) Combus. Set. Technol., Vol. 47 pp299-315. Jouhn G. and Eudier, M. (1989) 22nd Symp. (Intl.) on Combus. /The Combus. Insti. ppl579-1585. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 Ju, Y., Masuya G. and Ronney, P. (1998) 28th. Symp. (Intl.) on Combus. /The Combus. Insti., (to be presented August, 1999) Law, C. K L , and Egolfopoulos, F. N. (1992) 24th. Symp. (Intl.) on Combus. /The Combus. Insti. Shan, S. H., Pan X.C, and Aban-Ellail, M. M. M. (1995) “Flameiet Structure of radiating CH4- air Flames”, Combustion and Flame, 102, 438-446. Siegel, R-, and Howell, J. R. (1981) "''Thermal Radiation Heat Transfer", second Edition, Hemisphere Publishing Corporation. Tien, C. L (1967) Adv. Heat Trans. 5:253. Vranos A and Hall, R. J. (1993) Combustion and Flame, 93 230-238. Williams, F. A. (1985) Combustion Theory, 2nd Edition, Benjamin-Cummins, Menlo Park. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O a. c s Q . ■ D CD < / ) o' 3 CD 8 CD 3. 3 " CD CD ■ D O Q . C g o 3 " O o CD Q . ■ D CD C/) < /i _ Boundary 2 Absorbing, emmltting medium / \ _ Boundary I V- S - arbitrary path at angles 0 from the positive x-direction; radiation intensity, w.r.t. 0 ^ 0 ^ 90*^, D — thickness between two boundaries; i' — radiation intensity, w.r.t. 90^ ^ 0 ^ 180^ Fig. 4-1 Schem atic o f a planar radiating m edium bounded by two infinite boundaries 65 2500.0 H ^ O 0.16 2000.0 i 0.12 1500.0 I 0.08 U rn •i l O O O . O 0.04 - 500.0 0.00 0.0 g i Î J g 0.15 2000.0 0.12 1500.0 Z I 5? 0.09 § 1000.0 CH4 0.06 f i O " 500.0 0.03 .CO 0.00 0.0 04> 0.12 1500.0 4>=0.51 0.10 0.08 1000.0 0.06 C Q 0.04 500.0 0.02 0.00 0.0 O j O Axial Coordinate, xC cm ) 1.0 0.5 i Ï J* Fig. 4-2 Axial profiles of temperature and radiative species for three I-D freely propagating, premixed CH^/air flames at different ( j ) ’s. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 6 t I- B 1 2.0 2300.0 2000 . 0 1500.0 1.0 O C p • optically lO O O .O 500.0 C X Ion ) 0.0 0 .0 0.0 2. 0 - 2. 0 4.0 6.0 8.0 10.0 5 1 3 J cT r I 2. 0 2000.0 1300.0 1.0 1000.0 500.0 1 — o p tic a lly thin m o ^ e l (R -A ^ C A L ) 2 — o p tic a lly th in m o d e l CTien's) 0.0 2.0 -2.0 0.0 4.0 6.0 8.0 I 1500.0 •J* 3.0 1000.0 3 2.0 750.0 500.0 1.0 1— o p tic a lly th in m o d e l CRAJDCAL) 2 — o p tic a lly th in m o d e l (T ie n ) 250.0 0.0 p.o -2.0 2.0 0.0 4.0 A T r i al C oordinate, x(gzi) 10.0 6.0 8.0 Fig. 4-3 Distributions of the Planck mean absorption coefficients predicted by the Tien’s model and the RADCAL model for three I-D freely propagating, premixed CH^/air flames at different ( j ) ’s. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 (a) CO2 and radiation witb different models CK,/Air I-D premised 0=0.51 1 — Optically tliin model CTlcn) 2 — Optically thin model CRAX3CAL) o j > 2 J > * jo 6j > aa C i > ) CO radiation witb dlfTerent models 1500.0 1250.0 5 1000.0 a B 750.0 - 3 500.0 -4 250.0 0.0 o.ozo 1500.0 Methane/Air 1-D premixed 0=0-51_ _ _ _ _ _ _ _ _ _ S -g 0.015 1000.0 i I 0.010 750.0 500.0 «P o.oos Optically tHin model CTien) Optically thin model I 250.0 0.000 0.0 •2.0 0.0 2.0 4.0 6.0 8.0 (c) radiation witti different models 10.0 0.50 1500.0 Methane/A.ir 1-D prej 0=0.51 smixed 1250.0 A 0.40 Î g 1000.0 0.30 t 750.0 «■ 0.20 § 500.0 E Opitcally thin model (Tien) Optically thin model (Rj^JDCAL.) 0.10 250.0 s : 0.00 0.0 •2.0 0 .0 10.0 2.0 8.0 6.0 f Axial Coordinate. x(cm) Fig. 4-4 Distributions of Planck mean absorption coefficients for individual radiative species predicted by the Tien's model and the RADCAL model for a near-limit, 1-D freely propagating CH^/air premixed flame. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 8 •1 0 ■j « f i J e 1 0.0 2,0 4.0 8.0 10.0 6.0 S 1 o- I ^ S»M >« I 1. 2 = 3 = L Q g e n 1 — opôcally thin model CTien) 2 — optically thin model CRAOOAX^) 3 — optically thick model 2 * 4 - 1 0 2 f 16,10 2 9 5 * 4 - 0 9 ^ f 2. 0 4.0 6.0 8.0 t (^<t>=o.si) 1 — opticm JIy tliln model CTlcn) 2* * opdcmlly tMn modd (RADCAX.) 3 — optically thick model 4 e * 0 8 2 s 3c*08 cn f le ^ 8 S 6.0 O 10.0 Axial Coordinate, x(cm) Fig. 4-5 Distributions of divergences of radiative heat flux and generative heat flux by three different radiation models and for three 1-D freely propagating, CH^/air flames at different (j)’s. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 2. 0 2500.0 2000.0 Or.Tler/qrJ^ADCAL =e i l.O 2 5 1000.0 < îr.ihicfc^^JlADCAl. 500.0 0.0 0.0 0.0 6.0 - 2 . 0 2.0 8.0 10.0 2.0 2000.0 1500.0 qr.Tlci/OrJ^AOCAl. 1000.0 "S ^r.UUck/OrJO^DOAi- 500.0 0.0 0.0 0.0 2. 0 4.0 6.0 10.0 8.0 2. 0 1 500.0 f a Af.Tlcn/qfJUMXZAL 1000.0 1 . 0 500.0 Sr.TiiiG 3e/< ^JU irXZAl. 0.0 0.0 0.0 2.0 4.0 6.0 Axial Coordinate, x(cm) - 2 . 0 10.0 8.0 Fig. 4-6 Distributions of normalized divergences of radiative heat flux for different radiation models and for three 1-D free propagating, CH^/air premixed flames at different (|)’s. Divergences of heat flux are normalized by the values predicted by the RADCAL model. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O Q. C g O . ■ D CD C/) C/) 8 ■ D ( O ' 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD ( / ) ( / ) 1 g I I 3 0 1 3c+()8 1.4 Melhane/Air 1-D premixed 1.2 2c+08 1.0 Q r.R A D C A I. 0.8 lc+08 0.6 0.4 0.2 0.50 1.00 0.60 0.70 0.80 0.90 f f Equivalence Ratio, ^ Fig. 4-7 Variations o f normalized heat flux with equivalence ratio for premixed methane/air flames with different radiation models 71 " S h 3 e * 0 6 2 l< f* O S I • .le*C6. ■ -------------------------- - T « ^ 1 .0 0 ^ f A ^ ------------------ - r 5 - i 1 - T 1- - - - - ■ T _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _^ i 3.0 2500.0 2000.0 I 1 5 0 0 .0 ÿ a 1 1000.0 5 z * z 500.0 6.0 9.0 2000.0 I 1500.0 J l O O O . O 1 *s I 500.0 0.0 0.0 6. 0 3.0 1 2 . 0 9.0 I I 1500.0 1 • — boundary term: 2 — upstream re-absorpdon term; 3 — downstream re-absorpoon term: 4 . — source term: 5 — net radiation _ _ _ _ _ _ _ _ _ _ _ _ _ _ l O O O . O 500.0 0.0 0.0 1 2 . 0 9.0 2 2 I I ? Axial Coordinate. x(cm) Fig. 4-8 Distributions of each term in the full radiation model for three 1-D free propagating, premixed CH^/air flames at different < j > ’s. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 J CD ■ D O Q . C g Q . ■ D CD (/) W o' 3 0 3 CD 8 5 C 5 - 1 3 CD 3. 3" CD CD ■ D O Q. C g. o 3 "D O a o c % C/) (/) o' 3 g 1 H o > 2500.0 C liy A ir, I-D iixkIcI 2000.0 model 2 model 3 model 1500.0 model 1000.0 model 2 model 3 500.0 model I — narrow -banded opileally lliiek model model 2— narrow -banded opiically thin model model 3— T ie n ’s optically thin model 0.0 10,0 5.0 2.5 -2.5 0 .0 Axial C oorfliiialc, X(ciii) Fig. 4-9 Temperature profiles predicted by three different radiation models for three I-D freely propagating, premixed methane/air flames -4 to CD ■ D O Q. C g Q. ■ D CD C O C/) CD 8 CD 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) H 1 I 1700.0 1 -D Prem ixed Flam e C H ^ a ir, latm 1600.0 1 - T ien’s model (dashed line) 2 — R A D C A L model (solid line) 3 — Full Radiation model 4 " Radiation Excluded 1500.0 1400.0 1300.0 Optically Thcik Limit Optically Thin Limits 1200.0 i - 0.40 0.65 0.60 0.55 0.50 0.45 Equivalence Ratio, 4 > Fig. 4 -1 0 Variations o f maximum flame temperature with equivalence ratio predicted by different radiation m odels for 1-D freely propagating, premixed methane/air flames CD ■ D O Q. C g Q. ■ D CD C/) W o " 3 O 8 ci' 3 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) 1 -D Prem ixed F lam es CH^/air, 1 atm 0.8 1 - O ptically Thin M odel 0.6 2 - Optically Thick Model 0.4 « 3 0.2 0.0 0.9 0.6 0.7 Equivalence Ratio, < { ) 0.8 0.5 0.4 Fig. 4-11 Variations o f the ratio o f radiation flux over generation fluxes with equivalence ratio predicted by different radiation models for 1-D freely propagating, premixed CH^/air flames. 75 Chapter 5 MICROGRAVITY EXPERIMENTS ON THE EXTINCTION OF NEAR-LIMIT, WEAKLY- STRAINED, PREMIXED FT, A MES In the last chapter, the detailed numerical simulation of the radiation effect on o n e dimensional flames was conducted. In this chapter, the counterflow technique which was described in Chapter 3 is applied experimentally in microgravity to determine the extinction strain rates of laminar premixed flames. Given that external loss mechanisms were eliminated or minimized, the obtained results pertain to the concept of fundamental flammability limits. The experimental system and procedure are described in detail and the observations and results are reported. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 5.1 Introduction of the microgravity experimental system For near-limit mixtures for which the flame speeds are around 5-10 cm/s, the buoyancy-induced convection strongly affects the flame structure and dynamics. Under the influence of buoyancy, near-limit mixtures can not even be ignited. Therefore, microgravity environment is essential for the study of near-limit flames. The experiments on the extinction of near-limit, laminar, premixed flames were conducted in the 2.2 second drop tower facility at NASA-Lewis Research Center, on board of a stainless steel frame with 36"x33”xl8” dimensions. The counterflow configuration was established by impinging two identical mixtures on each other. In order to ensure that the flows exiting the nozzles are radically uniform, the nozzles were designed with an area contraction rate according to a 5'" order polynomial curve fitting [Vagelopoulos et al., 1994]. The nozzle separation distance was large enough so that upstream conductive heat losses were minimized. The schematic of the |ig apparatus is shown in Fig. 5-1. The apparatus consists of several sub-systems including power supply and distribution, mixture preparation, flow rate control and measurement, fuel concentration control, data acquisition, component action control, flame ignition, and flame visualization. (i) Power supply and distribution The power is supplied by two 28V rechargeable DC battery boxes, with each one independently being used by the ignition system. The power is distributed to the electronic components according to the required voltages. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 (ii) Mixture preparation In our first attempts, a mixture with a desired equivalence ratio was stored in a single tank (IL in volume). Extinction was induced by varying the flow rate (strain rate) for a fixed 6 . The major problems with this approach were the inability to ignite for very lean mixtures and a complicated mixture preparation procedure based on partial pressures. Alternatively, two tanks (IL in volume each) are used to store the high- pressure air and fuel independently. Air and fuel are mixed on the rig during the experiment. The desired < { ) value is easily obtained by properly setting the air and fuel flow rates. (ii) Flow rate control, measurement The values of both ( j) and the strain rate, K, are determined by the flow rates of air and fuel; all flow rates are measured by sonic nozzles. The sonic condition is satisfied by keeping the upstream pressure higher than about twice the ambient pressure, such that the flow rates vary solely with the upstream pressure in a linear manner. By adjusting/measuring the upstream pressure, we can control/obtain the flow rate. The nozzle calibration is done in normal gravity by a wet test meter or a bubble flow meter. The upstream pressure of sonic nozzle in the air line is maintained at a constant value during the test. This is done by pre-adjusting the pressure regulator between the tank and the sonic nozzle in normal gravity based on the desired total flow rate and the desired ( { ) value. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 On the other hand, the flow rate of fuel during the experiments is changed from high to low for ignition purposes with a PID (ER2000) control unit installed between the sonic nozzle and the fuel tank. The FID unit is a closed-loop electropneumatic controller with a rapid response time. By comparing the feedback signal with the reference, the PID adjusts the valve opening and hereby the fuel flow rate. Since the air constitutes the majority of the mixture and the change of fuel flow rate is generally less than 1% of the total flow rate, the strain rate is essentially maintained constant during each drop. iii) Fuel concentration setup and control Fig. 5-2 shows the variation of the fuel concentration during the experiments. The initial fuel flow rate is relatively high, so that flames are easily ignited in normal gravity. After ignition, the fuel concentration is reduced and eventually maintained at a constant value. If extinction does not occur at the second level, the experiment is repeated by lowering the second level at the same air flow rate. The maximum ( j ) at which flame can not be sustained is defined as the extinction limit, at the corresponding strain rate, K. By repeating the experiment for different air flow rates, the extinction response of (j)„t vs. K is captured. Although tedious, this approach results in more accurate values. While the ( { ) values can be accurately determined at the mixing, they can not be precisely determined at the flame front as the fuel flow rate varies. The approach of Maruta et Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 al. (1996) to calculate the ( ( ) at the flame front by using a constant delay time is questioned. In our experiments, the delay time was found to depend not only on the total flow rate but also on the fuel concentration. iv) Data acquisition and component action control Electronic pressure transducers are installed in the upstream of sonic nozzle in the air and fuel lines separately. A Tattletale-based microprocessor is used to record and store the pressure data. It is also used to control the action of all electronic devices, such as the ignition system, the PID unit and the video camera, by using programmable digital I/O lines instead of timers. The Tattletale is programmed with a BASIC dialect specially designed for portable and embedded logging/control applications. v) Flame ignition Initially, the ignition of premixed flame was designed to be performed in microgravity, at a near-limit concentration and by using an electrical spark. The spark was created by a spark generator designed by Ronney (1994). A series of capacitors were charged before the drop, and a high-voltage-generated spark was triggered between the cathode and anode during the drop. The spark intensity and the trigger timing were controllable. The electrodes were put into a proper position (close to stagnation plane) before the flow rates were initialized and were retracted out of the flame zone immediately after ignition. However, this ignition method appeared to have the following problems: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 (a) The available time for ignition was restricted by the microgravity time of 2 .2 seconds and this was not sufficient for the effective ignition of n ear limit mixtures; (b) (b) The spark generator was suspected to interfere with other electronic devices, such as the Tattletale microprocessor. Subsequently, ignition was modified in order to be performed in normal gravity at a relatively high fuel concentration through a combination of hot-wire and a pilot- flame lighter. In normal gravity, there are no time constraints. At the relatively high fuel concentration, ignition is easily achieved. Considered the poor reliability induced by the resistance variation of the hot wire, the pilot flame lighter was added. The pilot fuel was provided by a modified liquid fuel lighter with a remotely controllable solenoid mechanism. The gasified liquid fuel was ejected through a small ceramic tube into the high-temperature hot wire, and was easily and reliably lit as a pilot flame. Then the pilot flame was used to ignite the main flow mixture. The pilot flame was remotely controlled and it was shut off after the main flow was ignited. The hot-wire, pilot-flame lighter has several advantages. (a) It is simple and less expensive; (b) It is stronger ignition source and more durable than the spark as it provides not only thermal energy but also active radicals; (c) It minimizes the flow disturbance as the pilot flame can be placed outside the flame zone and the retractable arm is not needed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 1 (vi) Flame visualization A CCD video camera is used to visualize the flame. The flame behavior during the entire process is recorded. 5.2 Experimental Sequence The main experimental sequence is as follows; (a) Test in normal gravity, check the program, setup the air flow rate and the reference signal for fuel, charge batteries etc.; (b) Load the experimental rig into the enclosed frame, connect the fiber cable for camera; (c) After the whole system is lifted to the top of the drop tower, load the program and check the video system and be ready for remotely control the whole apparatus; (d) Initialize the flow at relatively high fuel concentration for a few seconds; (e) Activate the ignition system; (f) After ignition, shut off the hot wire and pilot fuel, reduce the fuel flow rate and record the pressure data of both air and fuel; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 (g) When the twin flames closely merge, drop the system, and monitor the flame behavior in microgravity; (h) Shut off all the flows and power when the rig encounters the ground air bag; (i) Load the recorded data and prepare for the next drop; Steps (d) to (h) are controlled by programming the tattletale. If the flame assembly is not extinguished, repeat the experiment at lower final fuel concentration while maintaining the same flow rate of air. 5.3 Observation and Discussions After weakly-strained twin flames are ignited and established in normal gravity (1-g) at a relatively high 0, the drop is initiated. Stable twin flames are sustained in |ig when 0 is higher than the extinction limit, 0 „^. Generally, in 1-g a near-limit, weakly-strained flame is influenced by buoyancy such that its edge is curved while its center is planar. In |ig, the entire flame front becomes planar as the buoyancy effect is m in im ized . In the experiment, as 0 decreases for both CH^/air and C^Hg/air the twin flames approach each other as they are stabilized at locations at which the local flow velocity equals the flame speed. As 0 decreases, the flame speed decreases, and therefore, the flame moves Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 closer to the stagnation plane where the flow velocities are lower. As ( f ) is further reduced, flame extinction is induced. The extinction behavior of near-limit CH^/air mixtures was found to be consistent with the observations in the previous study of Maruta et al. (1996). As < j ) decreases, extinction was observed after the twin flames merged at the stagnation plane, as expected for mixtures with L e<l. However, an interesting extinction behavior was observed for QHg/air flames. At the same separation distance and global’ CjHg/air flames were closer to the burner compared to CHj/air flames. This is because the C^Hg/air mixtures have higher flame speeds. It was also found that at low strain rates, the edges of CjHg/air flames were more curved than those of CH^/air flames. The fiiUy flat flame fronts were not developed within 2.2 seconds jig duration. It was observed that the flame extinction occurred when the twin flames were at a finite distance, as expected for mixtures with Le>l. Experimental data of the variations of extinction strain rate vs. the equivalence ratio for CH^/ air and C.Hg/air mixtures are shown in Figs. 5-3 and 5-4 respectively. The previous jig experimental data [Maruta et al., 1996; Maruta et al., 1995] are also shown for comparison. The global strain rates are used because laser diagnostics was not available in the present microgravity study. Figure 5-3 depicts a C-shape extinction response of vs. ( j) for CH^/air mixtures, which qualitatively agrees with the previous results of Maruta et al. (1996). The mechanisms for the C-shape extinction response were explained by previous studies [e.g., Maruta et al., 1996; Sung and Law, 1996]. The extinction Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 limit on the upper branch is caused by the incomplete reaction resulting by the sufficiently strong straining. Therefore, the upper branch is called the strain-rate- induced extinction limit. The flame with a higher equivalence ratio can be sustained at a higher strain rate, given that the radiation is not a major effect on the upper branch. The extinction limit on the lower branch is caused by the synergistic effects of thermal radiation. Le number, and strain rate. For Le<l mixmres, as the strain rate increases, the flame burning is enhanced [Law, 1988]. Therefore, flames can be sustained at a lower equivalence ratio as the strain rate increases. The main mechanism for the lower branch is radiation. For Le>l mixtures, such C-shape response is not found since the decrease of strain rate results in the increase of burning rate. It can be seen that the limits from the present study and the study of M aruta et al. are less than the value obtained from the 1-D freely propagating flames [Law and Egolfopoulos, 1992]. This results is consistent with the findings of Ronney (1985, 1988), who reported that Le<l flames under the ideal 1-D limits are possibly sustained by the effect of flame curvatmre. As shown in Fig. 5-3, the present data are shifted to lower ( { ) values, as the present experiments are nearly-adiabatic while the experiments of Maruta et al. (1996) were affected by upstream heat losses; the effect of upstream heat loss will be presented in Chapter 6 . It is also important to note that the present data are closer to the numerical results. More details wiU be given for the comparison between experimental data and numerical results in Chapter 6 . Figure 5-4 depicts that the extinction response of CjHg/air mixtures exhibits a monotonie, instead of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 C-shape behavior, in qualitative agreement with the experimental data of Maruta et al. (1996). The minimum global strain rate, which can be reached in present experiments is around 6 -7 sec '. At lower strain rates, flames are neither possible to be ignited in normal gravity nor possible to be established symmetrically between the two opposed nozzles in microgravity. In order to achieve ignition, a minimum initial equivalence ratio, ( ( ) ; is required, and in order to obtain the symmetric flames in microgravity, flow rates from the upper and lower burners are kept identical. At low strain rates, given they are ignited at (j)j in normal gravity, flames are strongly influenced by buoyancy such that the twin flames approach the upper burner. When the is very low. flame flashback occurs as a result of an asymmetric effect of buoyancy on the flow field. For CH^/air mixtures, within the achievable strain rate range, the C-shape turning point behavior of extinction response has been captured. However, for QHg/air mixtures, though the C-shape behavior was not found, more data at the ultra-low strain-rate regime are needed in order to validate the monotonie response argument. It is interesting to note the lower radiation-induced extinction branch has been found even for Le>l mixtures (Ju et al., 1998). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 6 5.4 Concluding Remarks An experimental system and methodology have been established for the extinction studies of near-limit, weakly-strained, premixed flames in microgravity. Experiments included the use of the counterflow technique and an improved approach for the accurate determination of the mixture composition. Furthermore, special care was taken in order to minimize upstream heat losses by using large nozzle separation distances; such losses were present in the similar previous microgravity experiments of Maruta et al. (1996) (This will be further address in Chapter 6 ). The experiments were conducted for CH^/air and C^Hg/air mixtures so that the Le number effect was assessed. A remotely controllable, hot-wire pilot-flame lighter was developed and successfully employed for the ignition of the counterflow flames in microgravity. The twin premixed flames were ignited at 1-g and stabilized in |ig. The extinction behavior was quantified in Lig. For both CH^/air and C,Hg/air mixtures, the flames approach the stagnation plane as < { ) decreases. For CH^/air flames, extinction happens after the twin flames merge. For CjHg/air flames, extinction happens before the twin flames merge. The extinction response for L e<l mixtures exhibits a C-shape behavior, while for Le>l mixtures, it exhibits a monotonie one. In order to further clarify the Lewis number effect, further experiments at ultra-low strain-rates are necessary. This can be achieved if the experiments are conducted in environments in which larger p.g time is available s o that ignition is achieved at p.g instead of 1-g. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 5-5. References Law, C. K. (1988), 22nd Symp. (Intl.) on Combus. /The Combus. Insti., Pittsburgh, P1381. Law, C. K. and Egolfopoulos, F. N. (1992) 24th. Symp. (Intl.) on Combus./Th& Combus. Insti., Pittsburgh, pl37-144. Ju., Y.. Guo. H.. Maruta., K., and Nhoka, T., (1998) Combustion and Flame, 113:603- 614. Maruta, K.. Yoshida. M.. Kobayashi, H., and Niioka, T., (1996) ) 26th Symp. (Intl.) on Combus./The Combus. Insti., Pittsburg, pl283. Maruta. K.. Yoshida. M.. Kobayashi, H., and Niioka. T., (1995) Proceeding of the 24th Japanese Symposium on Combustion, Tokyo, pp. 414. Ronney. P. D.. (1985) Combustion and Flame, 62:121-133. Ronney, P. D., (1988) Combus. Sci. TechnoL, Vol. 59. pp 123-141. Ronney, P. D., (1994) Personal Communication. Sung, C. J. and Law, C. K. (1996) 26th Symp. (Intl.) on Combus./The Combus. Insti., Pittsburg, pp865. Vagelopoulos, C. M., Egolfopoulos, F. N., and Law, C. K, (1994) 25th Symp. (Intl.) on Combus./The Combus. Insti., Pittsburg, pp.1341-1347. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ O O Q . C g Q. ■ D CD C/) C/) 8 ■ D CD 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) Reference Signal G E PIDUnIt ^ a n s d u c e r Nozzle Micro-processor Nozzle ansducer Upper Burner Hot-Wire Lighter Camera Flames Lower Burner Recorder Pilot Flame Lighter Fig. 5-1 T he Schem atic o f the M icrogravity E xperim ental System 00 00 CD ■ D O Q. C g Q. ■ D CD C/) o " 3 O 8 ■ D 3. 3 " CD CD ■ D O Q. C a O 3 ■ D O CD Q. ■ D CD C/) C/) I 8 S U 3 Variation ai the Mixing Point Flame Ignition Variation at the Flame Front Drop Starts Drop Ends 2.2 sec ► ► 9.0 12.0 15.0 0 3.0 6.0 TIME (sec) F ig.5-2 Fuel concentration variation during the m icrogravity experim ent 00 V O CD ■ D O Q. C g Û . ■ D CD C/) C/) 8 ■ D CD 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) s i I I 1 1 3 o O 25.0 20.0 15.0 10.0 5.0 0.0 g □ m Cl 14/Air, Premixed Counlerflow Microgravity g □ □ □ # □ □ present study (L=5cm) # M aruta et al. (1996) □ : 0.450 0.460 0.490 0.500 0.470 0.480 Equivalence Ratio, ( ( ) Pig.5-3 Experimental data in micorgravity for the variation of extinction strain rate with equivalence ratio for near-limit and weakiy-strain premixed methane/air flames. S CD T D O Q . C g Q . " O CD C/) C/) 8 " D ( O ' 3. 3- CD CD ■ D O Q. O 3 ■ D O & ■ D CD % O 3 40.0 V ÎS 1 3 I I I C T ) 1 13 3 ^ 30.0 20.0 1 0.0 0.0 0.45 t 1 # 1 1 « 1 1 « * 1 1 1 > CgHg/air, Premixed Counterflow M icrogravity V J / \ A # Present Data □ Marutal et al., (1995) y : ° ................. m ................... 1 .......... LJ • » • : □ : 0.50 0.55 0.60 0.65 Equivalence Ratio, ( { ) Fig.5-4 Experimental data in microgravity for the variation of extinction strain rate with equivalence ratio for near-limit and weakly-strained premixed propane/air Flames. V O 92 Chapter 6 EXTINCTION OF NEAR-LIMIT PREMIXED FLAMES: RADIATION AND UPSTREAM HEAT LOSS EFFECTS The radiative heat loss effect was addressed Chapters 4 and 5. However, in Chapter 4, the flames were considered as one-dimensional and stretchless, which is not consistent with the flames in the microgravity experiments. In this chapter, numerical simulations are conducted in the counterflow configuration. At the sam e time, the effect of upstream (conductive) heat loss is assessed. The results are valuable to interpret the previous experimental results and to design future experiments. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 6.1 Introduction and Objectives Simulations of the extinction of near-Umit, counterflow premixed flames have been already conducted [e.g.. Sung and Law, 1996; Guo et al. 1996, 1998; Egolfopoulos, 1994b]. However, such simulations have not been consistent with the exact conditions used in the microgravity experiments [e.g., Maruta et al., 1996; Zhang and Egolfopoulos, 1998]. More specifically, the nozzle separation distance, L, in the simulations has been larger than those used in the experiments. It has been shown [Egolfopoulos, 1994b] that the magnitude of Lean affect the flame response for the same local strain rate. Namely, with the same strain rate in the hydrodynamic zone, the flame is subjected to higher straining in the main reaction zone for smaller L. In addition, for small L, upstream heat losses can be introduced as the flame thickness increases for near-limit flames. Thus, by ignoring such effects a descripancy may exist between experiments and simulations as is the case between the experiments of Maruta et al. (1996) and the simulations of Sung and Law (1996). In the present study, numerical simulations were conducted with various separation distances, especially within a range allowed by the space limitations of the experimental rig. The simulations provided more physical insights into the effects of finite domain and upstream heat loss. At the same time, they provide appropriate interpretion of the previous microgravity extinction data of near- limit flames and suggest valuable instructions for future experiments and simulations. Numerical simulations of the counterflow were conducted by solving the conservation equations of mass, energy and species concentrations along the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 Stagnation streamline. The assumption that the gases leave the nozzles without radial variations in velocity, temperature, and concentrations was used. The one- point continuation approach was applied to capture the turning-point behavior of the maximum flame temperature versus the imposed strain rate. The pertinent equations and boimdary conditions were reported in Chapter 4. Solutions were obtained in a finite-domain configuration with various nozzle separation distances, L, allowing for upstream conductive heat losses. The boundary value of the temperature at the burner exit was kept at the ambient value, given the interaction between unbumed gas and burner is sufficiently short. Simulations were conducted for the fuel-lean CH^/air (Le<l) and QHg/air (Le>l) mixtures. The GRI 2.1 [Bowman et al., 1995] kinetic scheme was used for the CH^/air flames. For the CgHg/air flames a Cg [Pitz and Westbrook, 1986] mechanism was added. These two kinetic mechanisms are shown in the Appendix of this chapter. Simulations were focused on near-limit and weakly-strained flames and the extinction mechanisms were assessed. The flames were assumed optically thin and thermal radiation heat loss was calculated from the primary radiating species of CO,, H ,0, CO, and CH^. The upstream conductive heat loss is quantified in terms of the temperature gradient at the nozzle, (dT/dx)^^. More details on the radiation formulation can be found in Chapters 2 and 4. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 The numerical simulation results were compared with the experimental data obtained in microgravity by Maruta et al. (1996) and in the present study as described in Chapter 5. 6.2 Results and Discussion Finite-domain effects on extinction can become important for near-limit flames as the flame thickness scales inversely proportional to the mass burning rate. Although for the near-stoichiometric conditions a typical flame thickness, 5, is of the order of a fraction of millimeter. For near-limit flames 5 can be of the order of a centimeter. If the nozzle separation distance L is of the same order with Ô , upstream heat loss to the burner can be substantial especially as the strain rate is reduced and the flame approaches the burner. Figure 6-1 depicts the variation of the temperature gradient at the nozzle, (dT/dx)^, with L for a (j)=0.50 flame and for three different nozzle velocities, u^^s. Results show that for large L ’s, the (dT/dx)^ is zero. This indicates that there is no interaction between the flame and the nozzle. For lower L’s, a finite (dT/dx)„^ value is found. As the u^^ becomes smaller, the (dT/dx)^ becomes larger. This is reasonable given that as the u^, is reduced, the flame approaches the nozzle. On the other hand for the same u^j, the (dT/dx)^, increases as L is reduced, given that no space is allowed for the flame to be stabilized as adiabatic. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 Figure 6-2 depicts the variation of (dT/dx)^ as function of ( |) at different K g io b ai’s for L=1.5 cm, which corresponds to the experimental condition, used by Marata et al. (1996). It can be seen that for all values of Kgj^,, the (dT/dx)^^ is slightly reduced with < { ) , and eventually extinction is induced at an equivalence ratio, '^exv beyond which convergence is not possible. The reduction of (dT/dx)^ with ( j) is a result of the reduced flame temperature and the fact that the flame moves away horn the burner as the mixmre becomes progressively leaner and the propagation speed is reduced. It is of interest to note that the is initially reduced and subsequently increases as the (dT/dx)^^ increases. As the increase above 5 s' conductive heat losses are substantially reduced, but at the same time, the flames were found to approach the stagnation plane and the extinction is strain-rate- induced. For lower Kg,^ values, upstream heat losses to the nozzle through conduction are substantial. As the K g ,g b a j increases the amount of conductive heat loss is reduced and thus a leaner flame can be sustained. It can be seen that an increase of with K g io ^ a ] when upstream heat losses are present is similar to the one obtained based on the radiation argument for otherwise adiabatic flames. The upstream conduction heat loss effect on the flame structure and extinction is further addressed by deliberately eliminating the radiation term in the energy conservation equation. For L=1.5 cm, when the flames are weakly strained, upstream heat loss becomes important. Figure 6-3 depicts the axial velocity profiles of non-radiative flames of ({)=0.47 at different imposed velocities u^^/s. It can be seen that at higher u^/s, the axial velocity foUows a typical profile as described in Chapter 3. The velocity gradient is nearly-zero at the nozzle, and gradually Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 increases to a maximum value just before the minimum velocity point at which the heating starts. However, when the u^^, is less than a critical value, the axial velocity starts increases at the nozzle exit resulting in the disappearance of the pure hydrodynamic zone. Figure 6-4 depicts the temperature profiles of the non-radiative flames as shown on Fig. 6-3. It can be seen that the high-temperature product zone becomes thicker as the u^^ decreases. At the same time, the unbumed gas zone with zero temperature gradient becomes thinner. When the u^j is small enough, the flame is located close to the nozzle. The temperature gradient close to the nozzle becomes large and there is no hydrodynamic zone. Figure 6-5 depicts the variation of the extinction strain rate with equivalence ratio, ( j) for non-radiative flames for L=1.5 cm. The curve ABC corresponds to the strain rate induced extinction limit. Given radiation is excluded, it seems the zone below the ABC curve are flammable. However, it is of interest to note that as the is below the curve CBD, no hydrodynamic zone exists. The flame can be only sustained by the heat loss mechanism as the flame on the flat burner [Eng et al., 1996]. The strain rate below the curve CBD is meaningless. If the burners are not ideally the flat ones, it is reasonable to assume that the extinction of the flames with low exit velocities for short L’s is contaminated by conductive heat loss. Calculations were also conducted for L=10 cm which is quite large for any upstream conductive heat loss to be present. Representative results are shown for (j)=0.48 and (j)=0.50 flames in Fig 6 -6 , in which the variation of maximum flame Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 temperature, T ^ , with the can be seen. Similar to the results of Sung and Law (1996), a closed loop is formed which is characterized by two extinction points. The one corresponding to the right end of the loop (at the higher is caused by the strain rate, while the one corresponding to the left end of the loop (at the lower K giobaix»)) caused by the synergistic effects of thermal radiation. Le number, and strain rate. For Le<l mixmres, the reaction intensity decreases with the strain rate [Law, 1988]. At near-limit (j)'s, radiation plays a crucial role on the chemical reactions, as it affects the balance between the low activation energy termination reactions for the important H radical and the high activation energy main branching reaction H + O ^-^O H + O. As expected, the strain-rate-induced extinction limit is characterized by a larger value, while the radiation-induced extinction limit is characterized by a lower K g,^ 3 , value. This indicates the importance of lowering the strain rate to extinguish a stronger flame by radiation. Similar extinction results for various < j) ’s and for L=4 cm are shown in Fig. 6-7. It is apparent that the leaner is the mixmre, the narrower is the flammable range. Figure 6 -8 depicts the variation of T ^ and (dT/dx)^^, with the K g,^ for a (j)=0.48 mixmre at different L’s. Results revealed that for the larger L, e.g., L=10 cm, the flame response is nearly-adiabatic as the upstream losses are zero. For the small L, e.g., L=1.2 cm, it can be seen that at high K g,^bai's the flames are adiabatic while at low K g i^b aj’s the upstream heat losses are finite. Thus, the upper extinction limit K g,obai^t is an adiabatic one while the lower one is a non-adiabatic one. For L=0.7 cm, it can be seen that the flame suffers from the upstream heat losses for the entire Kg,3^ 3, range. Therefore, both extinction limits are non-adiabatic. It should be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 noted that when upstream heat losses are present the turning-point extinction is not observed [Eng et ai., 1991]. The complete extinction vs. ( { ) diagram is shown in Fig 6-9 for L=10 and 1.5 cm. While results for L=10 cm correspond to nearly-adiabatic flames and are of fundamental importance, results for L=1.5 cm, as used by Maruta et al. (1996), include the upstream heat loss as the B C g ,o b a i decreases. Adiabatic (i.e. no upstream heat losses) flames calculated for L=10 cm exhibit the anticipated C -shape extinction behavior as shown by Sung and Law (1996) who used L= 6 cm. The upper branch represents the strain-rate-induced extinction and the lower branch represents the radiation-induced extinction. For L=1.5 cm, the extinction limits induced by strain rate at the same ( j) are lower compared to those for L=10 cm because of the finite domain effect. However, the lower branch for L=1.5 cm is not shown because the notion of strain rate is meaningless given that there is no pure hydrodynamic zone. This phenomenon was described in Fig. 6-5. Figure 6-10 further shows the structure of a non-adiabatic flame. It can be seen that the flame struture is similar to the ones shown in Fig. 6-4 and Fig. 6-5 when the radiation is excluded. The results of Fig. 6-9 were also determined in terms of the local pre-flame extinction strain rate, and are shown in Fig 6 - 1 1. Comparing the results for L=10 cm with that for L=1.5 cm, we can find while differences of the values are about 20-30% while differences of the values are of the order of 2-3. This observation raises questions regarding the validity of the as a measure of the strain rate and the derivation of results with direct implication to the concept of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 0 flammability limits. The need of using Laser diagnosis for the detailed mapping of flow field is apparent. The numerical results are compared with the microgravity experimental data obtained by Maruta et al. (1996) and the present study, as shown in Fig 6-12. It can be seen, that numerical predictions of the extinction are in general agreement with the experimental data for L = 5cm. The C-shape extinction behavior for near-limit, weakly-strained premixed CH^/air flames agrees with the experimental results. The upper branch represents the strain-rate-induced extinction for adiabatic flames. For L = 5 cm flames, the lower branch corresponds to adiabatic flames and the extinction is radiation-induced. For L=1.5 cm flames, the lower branch is not shown because the hydrodynamic zone for the flames does not exist as we explained before. The Lewis number. Le, is used to characterize the mixture’s preferential diffusion. By definition. Le is the ratio of thermal diffusivity of the mixture to mass diffusivity of the deficient species in the unbumed mixture. It has been found [e.g.. Law, 1988] that the flame responds to the variation of the strain rate in different ways for Le>l mixtures from Le<l ones. However, the previous studies were generally limited to the relatively large strain rates, at which the buoyancy effect is not significant. At low strain rates, the flame thickness becomes relatively large, resulting in a large volume for thermal radiation. For Le<l mixtures at low strain rates, the thermal radiation is important. It affects the flame structure and dynamics and even leads the flame extinction. However, the radiation effect for Le>l flames at low strain rates has not been sufficiently studied. It is of interest to know whether Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 1 the radiation plays the same role for Le>l flames as it does for Le<l flames. Fuel- lean C^Hg/air mixtures have Le>l and were studied herein as well. Figures 6-13 and 6-14 depict the variation of the maximum flame temperature and the temperature gradient at the nozzle (dT/dx)^^ with the strain rate K for CH^/air and CgHg/air flames respectively. Results were obtained for (j)=0.60 and L=5.0 cm. Figure 6-13 depicts the vs. K variation. A maximum is found at a critical strain rate. On the right side of the critical strain rate, the decreases a s the K increases and the flame is extinguished when the strain rate exceeds a limit value, The reduction and the extinction are induced by the strain rate. The behavior of ((>=0.6 flames at large strain rates is similar to that of near-limit flames shown in Fig. 6-9 and 6-10. However, on the left side of the critical strain rate, the behavior differs hom that of the near-limit flames. The O-shape enclosed loop of T ^ vs. K is not seen. The response of T ^ vs. K shows three different trends. First, the T ^ decreases gradually as the K decreases from the critical value. This response is due to the Lewis number effect, which was discussed for near-limit flames earlier. Namely, the lower is the strain rate, the lower is the burning rate, thereby the T ^ _ Secondly, as K is further reduced, the T ^ variation becomes slower and even increases slightly. The third trend of the response is that the T^^^ rapidly decreases when the K is very small. The flame is extinguished as the strain rate is further reduced. This trend is caused by the upstream heat loss that can be represented in terms of (dT/dx)^. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 2 In the low strain rate regime, as shown in Fig. 6-13, the reduction occurs as (dT/dx)^>0, and the decreases rapidly as (dT/dx)^ increases. While near- limit flames are extinguished by radiation, strong flames are extinguished by the upstream heat loss. To clarify the mechanisms for the stage-type response shown in Fig. 6-13, the flame location (the maximum of H radical) is examined and shown in Fig.6-15. It can be seen that around the transition, the flame is rapidly moved from the stagnation plane vicinity to the nozzle. Although a wide high-temperature product zone is present, the response is not attributed to the downstream thermal radiation as discussed in Chapter 4. Instead, the response is still attributed to the Lewis number effect. When the global strain rate (exit velocity) decreases, the flame moves closer to the nozzle and the local strain rate increases. For a Le<I mixture, the increase of strain rate enhances the burning intensity and Figure 6-14 depicts the variation with the global strain rate for CjHg/air flames. It can be seen that the flame is extinguished by the stretch in the large strain rate regime as it does for the CH^/air flames. For conditions far from extinction, the gradually increases as the K decreases because longer resident time is available for the reactions to complete. Neither the O-shape response nor the three-trend response is seen in the low strain rate regime. The T ^ continuously increases until the upstream heat loss is present. When the K is smaller than a critical value, the T ^ suddenly decreases rather than gradually increases, corresponding to a substantial increase of the (dT/dx)^. As K is further reduced, no convergence is possible. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 Also shown in Fig. 6-15, as the strain rate increases, the twin flames approach each other. For CH^/air mixtures, extinction occurs after the twin flames merge at the stagnation plane, while for QH g/air mixtures, extinction occurs when twin flames are separated by finite distances. It is also seen that the variation of the distance with the strain rate is more sensitive for CjHg/ air flames. Figure 6-16 further depicts the results of T ^ ~ K and (dT/dx)„^~K at low strain rates for QHg/air flames with and without the thermal radiation. It can be seen that the response with radiation is similar to that without radiation. This indicates that at a low K, the upstream conductive heat loss is the mechanism for extinction rather than the radiation. Figure 6-17 depicts the representative results of temperature profiles for the weakly strained C^Hg/air flames. The phenomena are similar to those for the CH^/air flames as discussed earlier. Compared to CH^/air flames, the T ^ variation with K is more profound and the extinction strain rate is smaller for the CjHg/air flames. At the same <t)=0.60, CjHg/air flames are located closer to the nozzle as compared to CH_,/air flames, since they have higher laminar flame speeds. The axial profiles of H radical close to the extinction are shown in Fig.6-18. The peak values indicate the flame locations. It can be also seen that at extinction, the twin flames are located at the stagnation plane for the CH^/air mixture while they are located at finite distances from the stagnation plane for the C^Hg/air mixture. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 Experiments of C^Hg/air flames at low strain rates were conducted in microgravity using the 2.2-second drop tower. The methodologies and observations of the experiments were reported in Chapter 5. Figure 6-19 depicts the variation of extinction strain rate vs. equivalence ratio, (f), as determined from experiments and simulations. It can be seen that the response of the extinction strain rate with the equivalence ratio exhibits a monotonie behavior as opposed to the C-shape response for CH^/air mixtures. The results demonstrate that for Le>l mixtures, thermal radiation is not a dominant mechanism for flame extinction in the low strain rate regime. The discrepancies that are observed between experiments and simulations may be a result of inaccuracies associated with the chemical schemes. 6.3 Concluding Remarks A combined experimental and detailed numerical investigation was conducted on the extinction characteristics of near-limit laminar, premixed flames. The study aimed to provide insight into phenomena that are of importance to the experimental and theoretical determination of extinction and flammability limits. The numerical simulation included the use of the Chemkin-based opposed-jet reacting flow code. The code was modified by introducing a one-point continuation method to capture the turning point behavior when extinction conditions are prevailing. Consistent with the previous studies, a C-shape extinction response, caused by synergistic effect of strain rate and radiation, was found. The simulations were conducted for a wide range of nozzle separation distances. It was found that when Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 the separation distance is small, the upstream heat losses can become significant and the extinction diagram is not of fundamental importance. Coincidentally, a C - shape extinction response is found when (upstream) conductive and radiative heat losses are independently considered. When upstream heat losses are excluded by using large L ’s, the lower branch of the C-shape curve corresponds to the radiation induced extinction. When upstream heat losses are introduced by using small L ’s, the lower branch corresponds to the extinction induced by a combined effect of radiation and upstream heat losses. Even when the radiation was eliminated, the C - shape curve was still found and its lower branch corresponds to the extinction caused by pure upstream conductive heat losses. Furthermore, when upstream heat losses are present, the characterization of the fluid mechanics through reference to “strain rate” is incorrect. The Le number effect was addressed by studying both fuel-lean CH^/air (Le<l) and C^Hg/air (Le>l) flames. For CH^/air mixtures, the variation of vs. K g io b a ] shows a three-trend response in the low strain-rate regime. For CgHg/air mixtures, this response is not found. However, for both mixtures, flames are extinguished by upstream heat losses when the strain rate is low. For CH./air mixtures, flame extinction occurs after the twin flame merge at the stagnation plane, while for C^Hg/air mixtures flame extinction occurs when the twin flames are separated by a finite distance. Futhermore, a monotonie response of Kg,, vs. < { ) was found for QHg/air mixtures. This response differs from the C-shape one for CH^/air mixtures. The numerical results qualitatively agree with the experimental data. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 6.4 References Bowman, C. T., Frenklach, M., Gardiner, W. R. and Smith, G. (1995) The “GRJ2.1” Chemical Kinetic Mechanism. Personal Communications. Egolfopoulos, F. N., (1994a) 25th Symp. (Intl.) on CombusJThe Combus. Insti., Pittsburg, Pittsburgh, pp.l365. Egolfopoulos, F. N., (1994b) 25th Symp. (Intl.) on Combus./The Combus. Insti., Pittsburg, P ittsburgh, pp. 1375-1381. Eng, J., Egolfopoulos, F. N., & Law, C. K (1996) HTD-vol. 166, Heat Tranter in Fire and Combustion System, P.35, ASME. Guo, H., Ju, Y., Maruta, K., & Niioka, T., (1996) 26th Symp. (Intl.) on Combus./The Combus. Insti. Law, C. K. (1988) Dynamics of Stretched Flames, 22th Symp. (Intl.) on Combus./The Combus. Insti., Pittsburg, ppl381 Maruta, K., Yoshida, M., Kobayashi,H., and Niioka, T., (1996) 26th Symp. (Intl.) on Combus./The Combus. Insti., Pittsburg. P1283 Pitz, W. A. and Westbrook, C. K., (1986) Combustion and Flame, 63:113-133. Sung, C. J. and Law, C. K. (1996) 26th Symp. (Intl.) on Combus./The Combus. Insti., Pittsburg, pp865. Zhang, H. and Egolfopoulos, F. N. (1998), Spring meeting of the western states section/ The Combustion Institute, Berkeley, CA. Paper WSS/CI 98S-041. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 3 CD " O O Q. c 8 Q . ■ D CD C/) ( /) CD 8 " O ( O ' 3. 3 " CD CD ■ D O Q . C a O 3 " O o CD Q . ■ D CD ( /) ( /) 6 i I xi c s I 1 0 0 > 1 I H 4 0 0 .0 3 0 0 .0 200.0 100.0 0.0 100.0 0.0 CH^/Air ( j ) = 0.50 “ exit = 6.0 cm/s - ■ - Ugxit = 9.0 cm/s - - - U gxK = 15.0 cm ^ 0.5 1.0 1.5 2 .0 2.5 3.0 Burner Separation Distance, L (cm) 3.5 4 .0 Fig. 6-1 for near Variations o f temperature gradient at the nozzle with the burner separation distance llimit, counterflow premixed flames with different imposing velocities 3 CD " O O Q . C g Q . ■ D CD C/) o' 3 O 8 " O ( O ' 3. 3 " CD CD ■ D O O . C a O 3 ■ D O CD Q . " O CD CO ( / ) g 10000 i 1 I § ■ A A 1000 2.0 3.3 c u 1 z ( U 5 I 0 1 4.7 100 6.0 § I 0.490 0.500 0.480 0.470 0.460 450 E quivalence R atio, < { ) Fig. 6-2 Variations o f temperature gradient at the nozzle with equivalence ratio for near-limit, weakly-strained, counterflow premixed flames as burner separation distance L=15m m CD " O O Q . C 8 Q . ■ D CD C/) C/) CD 8 " O ( O ' 3. 3 " CD CD ■ D O Q . C a O 3 " O o CD Q . " O CD ( / ) CO KM) Î 3 i c a Metliaiic/Air <))=0.47, L=1.5 cm Radiation Excluded Stagnation Plane “ exll = O ° = 2.5 cm/s Nozzle Exit Axial Coordinate, x(cm) Fig. 6-3 Velocity profiles o f near-limit, weakly-strained prem ixed CH^/air flam es under a small burner separation distance and different imposed velocities. Thermal radiation is ideally excluded S CD ■ D O Q . C g Q . ■ D CD C/) C/) 3. 3" CD CD ■ D O Q . C a o 3 ■ D O CD Q . ■ D CD C/) C/) 1500.0 I a I I 1000.0 M ethane/Air (j)=0.47 L=1.5cm \R adiation E x c lu d e ^ 500.0 0.0 Stagnation Plane Nozzle Exit A - O 0- 0.0 “ exit = ^ Clii/s "exit = 6.0 ciii/s ^ «exit = 5.0 C H I/S Ugxn = 4.0 ciii/s O O = 2.5 cin/s 0.2 0.4 Axial Coordinate, x(cm) 0.6 0.8 Fig. 6-4 Temperature profiles o f near-limit, weakly-strained premixed CH ^air flames under a small burner separation distance and different imposed velocities. Thermal radiation is ideally excluded. CD ■ D O Q. C g Q. ■ D CD C/) W o' 3 O 8 ■ D 3. 3 " CD CD ■ D O Q. C a O 3 ■ D O CD Q. ■ D CD C/) C/) 36.0 Mc(liaiie/Air, prcniixcd Oppo.sed-jct Counterflow L=î.5 cm Radiation Excluded 32.0 28.0 - S A B C — Strain rate extinction 16.0 1 “ 8.0 4.0 Free hydrodynam ic zone region 0.0 ■ — 0.40 0.42 0.44 0.46 0.48 0.50 0.52 Equivalence Ratio, « ( ) Fig. 6-5 Variation o f extinction strain rate with equivalence ratio for near-limit, weakly- strained, counterflow premixed CH^/air flames with small burner separation distance. Thermal Radiation is ideally excluded. CD ■ D O Q. C g Q. ■ D CD C/) C/) 8 ■ D CD 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) H a i g a 1500.0 1450.0 1400.0 I 1350.0 H a i E 1300.0 1250.0 1200.0 0.0 R adiation Induced Extinction Limits = 0.50 Stretch Induced Extinction Lim its CH^Air P= 1 atm L= 100 m m Optically T h ii^ 10.0 20.0 30.0 40.0 G lobal S tra in R ate, (1/sec) 50.0 Fig. 6 - 6 Variation o f flame temperature with global strain rate for near-adiabatic, near- limit, counterflow CH^air premixed flames as upstream heat losses are excluded CD ■ D O Q. C g Q. ■ D CD C/) C/) 8 ci' 3 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD 0 0 C/) I o > ! I ( U I E G 1500.0 1450.0 1400.0 1350.0 1300.0 1250.0 1200.0 0.0 (j) =0.50 Stretch Induced Extinction Limits C H j/A ir L=40 mm Radiation Induced Extinction Limits 10.0 20X) ' 3 0 l) ' 40.0 G lobal S tra in R ate, K g|„|,a|(I/sec) 50.0 Fig. 6-7 Variation o f (lame temperature with global strain rate for near-limit, counterflow CH^/air premixed flames CD ■ D O Q. C g Q. ■ D CD C/) C/) 8 ci' 3 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) H § a 1500.0 1450.0 1400.0 I 1350.0 H « G 1300.0 1250.0 1200X 1 2000.0 800.0 0L = 7 mm □ L=12m m AL=100 mm CH^/AIr 4 » =0.48 1600.0 1400.0 1200.0 1000.0 ' L=7 mm \ --------------- m L=i2 mm ! 3 t % f i f s 10.0 15.0 20.0 25.0 Global Strain Rate, Kg|o|,g| (1/sec) Fig. 6 - 8 Variations o f maximum flame temperature and temperature gradient at the nozzle with global strain rate for near-limit, counterflow CH^/air premixed flames with different burner separation distances CD ■ D O Q. C g Q. ■ D CD C/) W o " 3 O 8 ■ D 3. 3 " CD CD ■ D O Q. C a O 3 ■ D O CD Q. ■ D CD C/) C/) 2 5 .0 L=100 mm radiation induced L= 15 mm I I 15.0 C H 4 /A ir Optically Thin C /3 fl 10.0 o % strain rate induced ■§ Free hydrodynam ic zone below this curve 3 0.470 0.480 0.490 0.500 0.460 Equivalence Ratio, t j ) Fig. 6-9 Variations o f global extinction strain rate with equivalence ratio for near-limit, counterflow, CH^/air premixed flames with or without upstream heat losses CD ■ D O Q. C g Q. ■ D CD C/) C/) 8 ■ D 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) 1 4 0 0 .0 1200.0 1000.0 g 8 0 0 .0 I Nozzle Exit Stagnation Plane 1.0 G. 6 0 0 .0 CH^/Alr ( |) = 0.460 L=15 mm Optically Thin 4 0 0 .0 rlow Direction 200.0 Fig. 6-10 The structure o f a near-limit, weakly-strained, counterflow CH^/air premixed flame with the upstream conductive heat loss CD ■ D O Q. C g Q. ■ D CD C/) W o " 3 O 8 ■ D CD 3. 3 " CD CD ■ D O Q. C a O 3 ■ D O CD Q. ■ D CD C/) C/) 4 0 .0 y (A i 3 0 .0 CH^/AIr Optically Thin i I 20.0 L=15 mm • X 3 L=100 mm a 1 10.0 M 1 3 ^ & 4 5 0 0 .4 6 0 0 .4 7 0 0 .4 9 0 0 .4 8 0 Equivalence Ratio, < { ) 0 .5 0 0 Fig. 6-11 Variations o f local extinction strain rate with equivalence ratio for near-limit, counterflow CH ^air premixed flames with or without upstream heat losses CD ■ D O Q. C g Q. ■ D CD C/) C/) 8 ■ D 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) 25.0 g 1 20.0 Present Sinitihilion (L=1.5cin) Present Sim ulation (L=5.0cm) Sung & Law (1996) (L=6.0cm) • Present data (L=5cni) □ M aru ta et ai. (1996) . I I C A § i M I r 15.0 10.0 Opposed-Jet Countetflow CH^/air, Premixed 5.0 0.0 0.43 0.44 0.45 0.46 0.47 0.48 Equivalence Ratio, ( { ) 0.49 0.50 0.51 Fig. 6-12 Comparison o f numerical results and experimental data for the variations o f extinction strain rate with equivalence ratio for near-limit, counterflow, premixed CH^/air flames 0 0 CD ■ D O Q. C g Q. ■ D CD C/) C/) 8 ci' 3 3 " CD CD ■ D O Q. C g O 3 " O O CD Q. ■ D CD C/) C/) 1700.0 1650.0 1 0 > G I 1600.0 1550.0 1500.0 Opposed-jet Counterflow CH^air Premixed (j)=0.60, L=5.0cm (dT/dx)„,| Conduction induced Extinction Limit 0.0 100.0 Strain Rate Induced Extinction Limit. I __ 200.0 U i _ 8000.0 6000.0 4000.0 2000.0 0.0 300.0 - 2000.0 Î I % g I I I Global Strain Rate, Kg,g|,g|(sec-1) Fig. 6-13 Variations o f maximum flame temperature and temperature gradient at the nozzle with global strain rate for (j)=0.6, CH^air premixed flames V O 7 J CD ■ D O Q . C 8 Q . ■ D CD (/) W o' 3 0 5 CD 8 ■ D 3 . C Û 3 " 1 3 CD P - 3 " CD CD ■ o O Q . C a O 3 ■ o O & o c " 8 H % i I H I U h E I ' i IKOO.d * — • 're n ip c ra lu re (îriH lii'iil a( tlifN(»7.7,K* • > f> Maximum Flame iVmpcralure 2000.0 Kxlinclion limi( l>y coiuliu'doii ICxUiictiuii limil hy slruiii rale 60.0 80.0 20.0 0.0 f O § s S' n I ( /) Ç 2 o' 3 <;i()hsil Slrsiiii lliile, Isec' ) I m. (>-14 Varialioiis ol m ax im u m llam c tem peraluie and lem peraliiie gradient at the nozzle with global strain rate for (j)=0.6, C’^Hs/air prem ixed flam es ë CD ■ D O Q. C g Q. ■ D CD C/) W o " 3 O 3 CD 8 ■ D ( O ' O 3. 3 " CD CD ■ D O Q. C a O 3 ■ D O CD Q. ■ D CD ( / ) ( / ) 1.0 ~ 0.8 O p p o sed -jel P rem ixed F lam es é = 0 .6 0 L = 5 .0 cm M 0 .6 0.2 C liy a ir 0.0 0.0 100.0 200.0 . 100.0 (ülohal slraiii raie, (.sec * ) Fig. 6-15 Variations ol llamc location Iroin the stagnation plane with global strain rate for counterflow, CH^/air and C^Hg/air premixed flames at (})=0.6 CD " O O Q. C g Q. ■ D CD C/) 2 2 o " 3 O 8 ■ D ( O ' 3. 3 " CD CD " O O Û . O 3 ■ D O CD Û . ■ D CD ( / ) ( / ) H aï I O i G I 5000.0 1800.0 C^IlH/air, O pposed-jet (|)=().6(), L =5.0cm 4000.0 "S 1700,0 3000.0 2000.0 % G— G Maximum Flame Tem perature Max. Flame Tem perature without radiation #— # Tem perature (Gradient at Nuzzle with Radiation Tem perature G radient at Nozzle without Radiation 1600.0 B xliiiclion limits induced by condiilive heat loss 1000.0 g: 0.0 1500.0 20.0 10.0 15.0 5.0 0.0 C lo b a l S tra in R ate, K g|„,„| (.sec ') rig. 6-16 Variations of inaxiiniiin flatne temperature and tempeiatuie gradient at the nozzle with global strain rate for weakly-strained, (j)=0.6, CgHg/air premixed flames when radiation is ideally excluded CD ■ D I 8 Q . " O CD CD 8 ■ D C 5 - 3 CD C 3. CD ■ D I C a O 3 ■ D S & O c % o 3 H I I O ) 2000.0 1500.0 1000.0 Propane/air Opposed-jet L=5.0 cm (j)=0.60 o o »exn = 116 cm/s □— a Ucxit = 13.1 cm/s o O U exU = 16.1 cm/s A — A U gxK = 21.1 cm/s V — V = 40.0 cm/s 500.0 'exit 0.0 2.0 0.0 1.0 3.0 Distance from the Stagnation Plane, X(cm) Fig. 6-17 V elocity profiles o f weakly-strained, (j)=0.6 premixed C^Hg/air flam es under low imposed velocities. CD ■ D O Q. C g Q. ■ D CD C/) C/) 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Û . ■ D CD C/) C/) 3e-05 O pposed-jet P rem ixed F lam e (j)=0.60 X=5.0cm 1 2e 05 t M *0 I I le-05 0.5 1.0 0.0 1.0 -0.5 D istance from the stagnation plane, x(cm) Fig. 6-18 Distances between the twin flames for near-extinction, counterflow, premixed CH4/air and CgHg/air flam es as (j)=0.6 CD ■ D O Q. C g Q. " O CD C/) C/) 8 ■ D CD 3. 3 " CD CD ■ D O Q. C a O 3 " O O CD Q. ■ D CD C/) C/) 40.0 Present Simulations Present 0-g Experiments Present 1-g Experiments 0-g Exp. Marata et al.(1995) 30.0 r - 1 K i (S 20.0 a co 'ë O 10.0 0 . 0 L - 0.45 0.65 0.55 0.60 0.50 Equivalence Ratio, < } > Fig. 6-19 Comparison o f numerical results and experimental data on the variations o f global extinction strain rate with equivalence ratio for near-limit, counterflow C^Hg/air premixed flames 1 2 6 Chapter 7 WALL EFFECTS ON THE PROPAGATION AND EXTINCTION OF STEADY, STRAINED, LAMINAR PREMIXED FLAMES In the last three chapters, the radiative heat loss and upstream heat loss were addressed. For a systematic undersatnding of the heat loss effect of the strained flames, the downstream (conductive) heat loss effect is studied in this chapter. The jet-wall configuration that was introduced in the Chapter 2 is used. The study includes both numerical simulation and experiments. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127 7.1 Introduction and Objectives The significance and theoretical background of downstream conductive heat losses on strained flames was introduced in Chapter 1. In this Chapter, a combined numerical and experimental investigation is presented on the interaction between a chemically inert solid wall and steady, strained, laminar, premixed atmospheric CH^/air flames. Numerical simulations were conducted by solving the conservation equations of mass, energy, species along the stagnation streamline in both opposed-jet and single jet-wall configurations. The effects of no-slip condition and wall temperature were assessed. Detailed description of chemical kinetics and molecular transport, and thermal radiation was used. Two different chemical kinetic mechanisms were applied. One of them was a hierarchically-developed C^ mechanism [Egolfopoulos, Du, and Law, 1992], referenced as EDL. The EDL mechanism satisfactorily predicts a wide range of oxidation properties of hydrogen, carbon monoxide, methane, ethane, ethylene, acetylene, and methanol. The other mechanism was the GRJ 1.2 mechanism. As introduced in earlier chapters, the single jet-wall configuration system, shown in Fig. 3-3, resuite from the opposed-jet counterflow system by replacing the upper burner with a stainless steel plate. A cooüng/heating system was used to maintain the plate at desired temperatures. The laser Doppler velocitmetry was used to measure the velocity profile along the centerline, hence the local strain rate was determined. Experiments were conducted in both the opposed-jet and single Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 2 8 jet-wall configurations, such that the no-slip effect was experimentally assessed. The experimental data were compared with the numerical predictions.7.2 Results and Discussions. 7.2 Results and Discussion 7.2.1. No-sIip condition effect The effect of no-slip condition at the stagnation plane was examined by detailed numerical modeling of both the opposed-jet (slip condition) and single je t- wall (no-slip condition) configurations. A fixed separation distance of 9 mm between the nozzle and stagnation plane L was chosen. Figure 7-1 depicts the variation of maximum flame temperature T^^ with the strain rate K for adiabatic conditions at the stagnation plane. The variations are for the (j)=0.7 CH^/air flames in both configurations. It is apparent that the wall no-slip condition leads to a substantial increase of extinction strain rate This result is in agreement with the finding of Vlachos et al. (1993). Physically, the presence of wall leads to a thicker momentum boundary layer compared to the opposed-jet configuration, and results in the modification of the flame structure. This is shown in Fig. 7-2a in which the spatial temperature variation is shown for the flames of Fig. 7-1 with K=859 s '\ It is seen that for the same hydrodynamic strain rate K, the no-slip velocity condition results in a flame displacement from the stagnation plane. This is physically reasonable given that the flame has to move further upstream in order to be stabilized at a location where the flame speed equals the local fluid velocity. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 129 Further analysis showed that for the same K, the no-slip condition causes a lower strain rate throughout the flame zone compared to the opposed-jet configuration (slip condition). This is shown in Fig. 7-2b, in which the local strain rate and the density, p, weighted strain rate p*G are shown throughout the domain. The local strain rate K is represented by the radial velocity gradient G (K=2G in the hydrodynamic zone). While the G is a measure of local straining in the velocity field, the p*G provides a more physical picture. The p*G accounts for the radial mass flux gradient which balances the 9(pu)/9x term in the continuity equation, therefore, it better relates to the local burning rate. It is clear that for the same K. both the G and the p*G are systematically lower inside the main reaction zone for the single je t- wall configuration. This is caused by the requirement that they both become zero at the wall. Therefore, in this configuration, the wall causes an overall reduction of the values of G and p*G in its vicinity and the flame is displaced upstream. Close to extinction the effect of straining is weakened (compared to the opposed-jet configuration) inside the main flame zone. The reduction of straining leads to a higher temperature at the wall vicinity. Thus, extinction occurs at a higher K value in the single jet-wall configuration compared with the opposed-jet one. Tlie analysis indicates that the extinction behavior is directly controlled by the strain rate distribution within the reaction zone rather than by the hydrodynamic zone. This should be expected, given that intermediate species, which are important for the fuel oxidation including the H, O and OH radicals, are present only within the flame zone. The magnitude of local strain rate directly affects the species transport. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 130 This point has not been addressed in previous extinction studies and it is central to assess the validity of comparison between experiments and numerical simulations. 7.2.2. Heat loss effect on flame extinction The effect of of heat loss to the wall was assessed by varying the wall temperature, Twaii, and monitoring the T^ax variation with K. In Fig. 7-3, such results are compared under adiabatic and non-adiabatic wall conditions. The presence of the heat loss leads to a substantial reduction of Kext between the adiabatic and the highest Twaii=1500 K cases, and the subsequent reductions of K ext corresponding to the lower values of T^aii are more gradual. This sensitivity to the heat loss is due to the fact that when the flame is highly strained, it is stabilized closer to the wall and the heat loss directly affects the processes of the main reaction zone causing thus noticeable T^ax reduction. When the flame is close to the critical state of extinction, its response becomes particularly sensitive to any Tmax reduction. It should be noted that while the Kext under adiabatic conditions is larger than the Kext at Twaii=1500 K condition by a factor of six, the Kext's for Twaii=1500 and 400 K differ only by a factor of two. This indicates that as long as finite heat loss is present, the effect of Tw aii is not as important. The Le number effect on such behavior was found not to be as important, given that results for rich methane/air (Le>l) flames showed similar sensitivity to the heat loss. However, the extent of Kext reduction between the adiabatic and non-adiabatic conditions, was found to be somehow lower compared to the Le<l mixtures. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 131 The heat loss flux to the wall, q^, and the distance of the flame luminous zone from the wail, X f, are shown in Fig. 7-4 as functions of the aerodynamic strain rate, K, and the wall temperature, Twaii- In Fig. 7-4a, was determined by calculating the term A,(dT/dx) in the gas phase right next to the wall; X is the gas conductivity. It can be seen that for the same K, qw is larger for lower values of Twaii which is physically reasonable. For all values of Twaii, it can be seen that qw increases w i± K simply because the flame approaches the wall and the temperature gradients at the wall are augmented. For values of K close to extinction, the rate of increase of qw with K was found to reduce given that the flame temperature starts reducing substantially right before extinction. In Fig. 7-4b the location of the flame luminous zone has been defined as the one at which the concentration of CH is maximum. It can be seen that for the same K, X f increases as Twau increases. This is physically reasonable given that as Twaii increases the thermal expansion at the wall vicinity will be more profound and this results in the upstream displacement of the flame. For all values of Twaii it can be seen that Xf decreases with K. This is also physically reasonable given that the flame is pushed closer to the wall. It is also of interest to note that the Xf at extinction is about the same for all values of Twaii • The result is in agreement with the previous experimental findings [Yahagi et al., 1992]. Furthermore, the X f at extinction assumes values of the order of 2.5 mm (for the conditions of Fig. 4) for all values of Twaii • This indicates that the flame does not have a chance to reach the stagnation plane, as it would be typically anticipated for adiabatic flames with Le<l. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 Fig. 7-5 depicts the experimental data and numerical results of the variation of with (|) for non-adiabatic flames as T^3,,=I0 0 0 K. For CH^/air flames corresponding to O .8< 0<1.2 experiments were conducted with L=10 mm. For the weaker flames corresponding to 4x 0 .8 and 4» 1.2 , experiments were conducted with L =20 mm, at which better flame stability was assured. Numerical simulations were conducted for the L’s used in experiments. The predicted values agree in general with the experiments with the exception being the over-prediction observed in the range of l.O < 0 < 1 .2 , especially with the use of the GRI mechanism. It is also of interest to note that the maxima of both experimental and numerical K^^’s occur around 0 = 1.05, which corresponds to the maximum adiabatic flame temperature and laminar flame speed. Previous experiments [e.g.. Law et al., 1986] and simulations [e.g., Egolfopoulos, 1994] on the flame extinction in the opposed-jet configuration have shown that for CH^/air mixtures, the peaks on the lean side of stoichiometry at about (p ~ 0.95. This has been explained on the basis of stretch and preferential diffusion characterized by Le<l [Law et al., 1986]. In the present study, this point was further assessed by modeling the opposed-jet extinction data of Law et al. (1986) by using the EDL and GRI mechanism. The results are shown in Fig.7-6. Simulations were conducted with the nozzle separation distances used in the experiments, which was L = 7 mm for ^ and L=14 mm for (jxO.7 and 4» 1.3. The results of Fig. 7-6 indicate that both EDL and GRI 1.2 mechanisms predict closely the experiment data; the GRI 1.2 mechanism over-predicts somewhat the experimental data for ^ ~ ^ . However, both mechanisms produce maximum Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 133 K„, values at around (p ~ 0.95, which is in agreement with the experiments. The quantitative and qualitative agreements support the validity of the various components of the modeling including the kinetics and molecular transport. The maximum occurs at < p~ 0.95 for the (adiabatic) opposed-jet configuration. For lean CFL/air mixtures Le<l so that the positive straining results in a higher flame temperature and the flame becomes more resistant to extinction [Law at al., 1986; Egolfopoulos, 1994]. The coupling between the straining and preferential diffusion {Le^l) is particularly strong at high strain rates and/or large deviations of Le from the value of unity. Therefore, flames subjected to positive straining become the most resistant to extinction at a 4) value, which on one hand is close to stoichiometric condition ( j > ~ 1.0, and on the other hand is characterized by Le<l. For C H /air mixtures, this occurs on the lean side of the stoichiometry at about 0 = 0.95. For the case of a non-adiabatic wall, flames at high strain rates are located close to the wall and their responses become very sensitive to the heat loss. Therefore, they cannot be strained at sufficiently high rates because extinction will be induced due to the temperature reduction. Furthermore, the Le number of the lean CH /air mixture is slightly less than unity. Thus, the flame response and extinction are more sensitively controlled by the downstream heat loss rather than by the coupling between the straining and preferential diffusion. This point is consistent with the results shown in Fig.7-4: as the downstream heat loss is introduced, the extinction occurs before flames reach the wall surface for Le<l mixtures. As a result, flames characterized by the highest burning intensity will be the most Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 134 resistant to extinction. Consequently, for CH^/air flames with downstream heat losses, the maximum occurs around (p - 1.05 which corresponds to the maximum flame temperature. The numerical results in Figs. 7-7 and 7-8 further support the arguments stated in the two previous paragraphs. The (spatially) integrated heat release rates are shown as functions of ( j ) and K for the adiabatic, opposed-jet and the non- adiabatic, single jet-wall configurations respectively. In Fig. 7-7 it can be seen that as K increases towards its extinction value, the <p=0.95 mixture sustains a higher value of integrated heat release leading to a larger B C e x t value compared to all other stoichiometries. On the other hand, the results of Fig. 7-8 show that in the presence of a non-adiabatic wall, the strain rates of interest are substantially lower compared to those of Fig. 7-7. Furthermore, as K increases the heat loss starts controlling the extent of heat release reduction. For all K's, however, the integrated heat release has consistently higher values for the ({>=1.05 mixture leading, thus, to higher Kext value compared to all other stoichiometries. It should be also noted, that results on the maximum heat release rate have a similar behavior with the integrated heat release rates shown in Figs. 7-7 and 7-8. Fig. 7-9 shows experimental data and numerical predictions for the of fuel-lean mixtures for T,^^, = 573 K. The experimental data with higher (j)’s were not available because the plate temperature was difficult to be maintained at such low values. It can be seen, again, a good agreement between experiments and numerical simulations is reached. Compared to the data shown in Fig. 7-5, it is of interest to note that the values for T^au=573K are close to the ones for T„^,=1000K. This Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 135 indicates that as long as the heat loss controls the extinction, its magnitude does not affect significantly. The result is in agreement with the one shown in Fig.7-3. The above qualitative and quantitative discrepancies between the results for flame extinction with and without heat loss suggest that the conclusion obtained from adiabatic flame studies must be used with caution in realistic conditions in which heat losses are present. 7.2.3 Radical recombination effect on flame extinction The effect of radical recombination at the wall surface was also considered by allowing the H radicals to completely recombine to upon collision with the wall. By doing so. we examined the limit behavior of complete H destruction; in reality the flame response should be bounded between the zero and complete radical recombination limits. The implementation of this boundary condition into the code was done by setting the mass fraction of H equal to zero at the wall and by accounting for the production through the H recombination reaction in the mass flux balance for the computational cell which is adjacent to the wall. The recombination of H radicals was considered because of their importance on both flame propagation and extinction. In Fig. 7 -10a, results are shown for a (^=0.7 CH^/air flame under adiabatic and Twaii=1600 K conditions. It can be seen that while the radical recombination has a drastic effect under adiabatic conditions by reducing B C e x i by a factor of 4, its effect is substantially diminished when heat losses are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136 present, and was found to be completely unimportant at lower values of Twaii- This result is in qualitative agreement with the findings of Vlachos et al. (1993). In Fig. 7-10a. results for Twaii < 1600 K are not shown because the calculations with and without H radical recombination are nearly-indistinguishable. Furthermore, the studies for Twaii > 1500 K do not lead to the classical "turning point" behavior of the T^ax with K. As K increases, the Tmax is reduced with an increasing slope which is indicative of the effect of the heat losses to the wall. However, when the Tmax is reduced close to the Twaii value, then the slope of Tmax i s reduced and Tmax approaches asymptotically the Twaii value and some chemical activity is present especially when H recombination is not included. This can be seen in Fig. 7 -10a for the Twait=1600 K case. Under such conditions, the complete H radical recombination leads to a more rapid approach of the Tmax towards the T^aii value given that the chemical activity caused by the relatively high wall temperature is arrested by the imposed H radical destruction. At the limit of no H radical recombination, Tm ax approaches T^aii m a more gradual manner. This behavior is observed because temperatures above 1500 K can lead to the (local) ignition of the mixtures studied herein. For these cases, Kext was defined as the strain rate at which a noticeable change of the slope of Tmax with K is observed. Thus, the effect of the non-adiabatic wall on the reduction of the gas phase chemical activity is isolated. Under adiabatic conditions the wall temperature is maintained at high enough values and in the absence of heat loss, the radical loss mechanism becomes dominant in a system which is otherwise free of any externally imposed loss Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137 mechanisms. Furthermore, at high wall temperatures, which is the case of the adiabatic wall, H radicals survive at the immediate vicinity of the wall only to be destroyed at the surface. The H radical destruction leads to lower chain branching which affects the overall exothermicity and. therefore, T^ax. and eventually facilitates extinction. When the Twaii is reduced, the H radicals recombine in the gas phase at the wall vicinity, their recombination at the surface becomes less important, and the heat loss becomes the dominant mechanism for the T^ax reduction and the eventual extinction. A careful examination of the variation of the maximum H radical concentration, [H ]m a x > with the strain rate K for the cases shown in Fig. 7-IOa further supported the arguments presented in the previous paragraph. For example, for a (j)=0.7 methane/air flame and under adiabatic conditions without H recombination, it was found that as K increases, [ H ] m a x increases until reactant leakage becomes important close to extinction and [H]max is reduced, as it is anticipated; the initial increase of [ H ] m a x is a result of the Le<l of the mixture [ 1 1 ]. For adiabatic conditions with H recombination, it was found that as K increases, [Hlmax monotonically decreases as a result of the flame approaching of the flame to a wall which acts as a sink of H radicals. These two different trends lead to a vastly different extinction responses. For the TwaU=1600 K case with and without H recombination, it was found that for the entire range of K, the [ H J m a x is lower compared to the adiabatic case given that the thermal losses to the wall lead to reduced chain branching. This is more obvious for the higher values of K for which the flame approaches the wall and the heat losses directly affect the structure of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 138 flame zone. For the Twaii=l600 K case without H recombination, the [H]max reduction with K was found to be arrested when the K^xt value is reached and some chemical activity is induced by the wall as discussed earlier. For the Twaii=1600 K case with H recombination, the [Hjmax reduction with K was found to be similar to that when there is no H recombination for low B C . For high values of K, the [H]max reduction with K was found to be greater when H radicals recombine with [H]max attaining near-zero values when the Kext value is reached. The difference, however, between the Kext values obtained with and without H recombination for TwaU=lbOO B C were found to be smaller compared to the adiabatic case. This suggests that in the presence of heat losses the effect of radical recombination on extinction is of secondary importance. A detailed picture of the effect of H recombination is shown in Fig. 7-10b as a function of Twau- Its importance on extinction is apparent for Twaii>1600 K since at these high temperatures the H radicals survive the gas phase recombination. It should be noted that the present discussion pertains only to 0=0.7 methane/air flame which is used herein as a test case, and it is possible that for other mixture initial conditions, the T w aU below which radical recombination is unimportant on extinction may be different than 1600 K. 7.2.4. Heat loss effect on flame propagation In the single jet-wall configuration, the extinction for CH^/air flames is controlled by the strain rate and the downstream heat loss. The significant downstream heat loss is introduced at a high strain rate as the flame is pushed to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 139 the vicinity of the non-adiabatic wall. However, at low strain rates, the flame is located close to the nozzle rather than to the wall, and it is sustained far away from the extinction conditions. In this case, the presence of wall and the effect of downstream heat loss on the elementary processes taking place inside the main reaction zone may be reduced. One of the goals of the present study is to investigate the wall effect on the flame dynamics at the limit of low strain rate. Flame speed was used as the property for comparisons, and it was determined at the upstream boundary of the preheat zone. It is known [Williams, 1985] that flame speed is more sensitive to upstream heat losses than downstream ones. Therefore, it is implied that under low strain rates, the flame propagation will be minimally affected by conduction at the wall. This implication could be important to developing an alternative experimental method to determine the laminar flame speed. As described in Chapter 2, Law and co-workers introduced the opposed-jet technique for the determination of the laminar flame speed S„° by systematically determining the dependence of upstream reference flame speed, on K and extrapolating the data to zero K. While the technique offers unique advantages as discussed before, it also offers a number of challenges. The challenges include the jet and flame stability, the significant fuel consumption and the complex upper burner design in order to avoid the overheating. Although these problems can be resolved, the use of a lower burner and a plate could be a simpler method since very stable flames are obtained, less fuel is used, and the upper burner is eliminated. In fact, true laminar speeds can be obtained by using the counterflow technique only if the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 140 nozzle separation distance is large such that very low strain rates are achievable [Vagelopoulos et al., 1994]. The dependence of on the K for a wide range of conditions at the stagnation planewas studied numerically and experimentally, and representative results are shown in Fig. 7-11 and Fig. 7-12 respectively with ç =0.805. Numerical simulations are conducted by using the updated mechanism of GRI 2.1. It can be seen that both experiments and numerical simulations show that the downstream heat loss affects the flame extinction. The higher the plate temperature is, the higher is the strain rate that the flame can be sustained. The experimental flame speed and extinction data are slightly higher than but still agree reasonably well with the numerical predictions. At low strain rates, results confirm that the presence of plate and heat loss has a negligible effect on the ^ compared to the data obtained in the opposed-jet configuration. The discrepancy is within the order of the uncertainty of the Laser Doppler Velocimetry used in the experiments. Therefore, the extrapolated values to K = 0 would lead to similar values S„° for both approaches. It is also seen that the numerical results closely agree with the experimental data. Consequently, it is proposed that the single jet-wall configuration can be used as an alternative technique for the determination. However, cautions are required to assure that the flame is not affected by the wall as indicated by the “bending” of ^ profiles. The data over a wide range of K are required to obtain as small as possible in order to assume a more meaningful extrapolation. This can be accomplished by using a high wall temperature and a large nozzle-wall separation distance. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 Additionally, similar numerical results on the dependence of on K are shown in Fig. 7-13 for L=9 mm. It can be seen extinction strain rates at the same ^ 6 systematically higher compared to that for L=15 mm. This again is physically explained as the finite domain effect. Namely, strain rates inside the main reaction zone with small L’s are higher than those with large L’s. The finite domain effect in the single jet-wall configuration is consistent with that in the opposed-jet configuration [Egolfopoulos. 1994]. Fig. 7-14 further illustrates the reduced sensitivity of burning rate on downstream heat losses. Temperature profiles for different strain rates are shown for the case of a non-adiabatic wall at T,^^„ = 1000 K, and for a separation distance of L = 2.0 cm. Results show that at low and moderate strain rates, flames are far away from the wall. A convection zone with the thickness of the order of many flame thickness is established between the main reaction zone and the non-adiabatic wall. The main reaction zone is confined around the region in which temperature has its highest curvature just before the equilibrium zone. Therefore, as long as a downstream convective zone of substantial thickness is present, there is no physical mechanism through which the main reaction zone will effectively "sense" the downstream losses, and only a minor reduction of the maximum flame temperature is observed. As a result, the main chemical processes, such as the high activation energy, endothermie main branching reaction H + O ^ ^ OH-hOH, are minimally affected by the presence of the waU at low strain rates. It should be noted that in the first attempt to experimentally determine the S„°, Wu and Law (1984) used the single jet-wall configuration. However, no Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 142 reference was made to the implications of the possible momentum and thermal interactions between gas phase and wall. In addition, in such an early stage, no comparison was made between the single jet-wall and opposed-jet counterflow configurations. The latter configuration became a standard one for determining the given that the nearly adiabatic condition is satisfied for a wide range of B C Furthermore, no systematic assessment was done on the heat loss effect, which is important on propagation, especially at high strain rates. 7.3 Concluding Remarks The wall effect on the dynamics and extinction of steady, strained. laminar premixed flames was investigated both experimentally and numerically. The experiments included the use of both the opposed-jet and the single jet-wall configurations. Laser Doppler Velocimetry (LDV) was used for the detailed mapping of velocity fields and the determination of the extinction strain rates and propagation speeds of CH^/air mixtures. Detailed numerical simulations were conducted in a finite domain for both configurations. The simulation was conducted under atmospheric pressure for various methane/air mixtures and wall temperatures, and the complete recombination of the H radicals at the wall surface was also considered. For the single jet-wall configuration, a wide range of wall temperature was used in experiments and simulations. Results show that the presence of wall influence the flame response in various ways. First, the no-slip condition causes the modification of flow field in the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 143 wall vicinity. With the same hydrodynamic strain rates, simulation results showed a reduction of strain rate within the main reaction zone is induced by the no-slip condition in the adiabatic single jet-wall configuration compared to the opposed-jet one. Therefore, extinction strain rates determined in the adiabatic single jet-wall configuration are different from those in the opposed-jet one, and the former ones are of larger values. Secondly, any wall non-adiabaticity causes a substantial reduction of extinction strain rate compared to the adiabatic value, and the dependence of extinction strain rate on the wall temperature is rather weak. Furthermore, the complete recombination of H radicals at the wall surface causes a significant reduction of the extinction strain at high wall temperatures. For lower temperatures, the H radicals recombine in the gas phase, their concentration is reduced close to the wall, and the heat loss becomes the dominant mechanism causing flame temperature reduction and eventually extinction. Finally, it was found that the combined effect of straining and preferential diffusion on flame extinction is dominated by the heat losses as long as they are present. Experimental results on flame extinction under various conditions of heat losses were also obtained, and the experimental extinction strain rates were predicted satisfactorily by the numerical simulations supporting thus the validity of the various assumptions and models which were implemented Both the experimental and numerical results confirm that the effect of the wall on the flame speed is quite unimportant at low strain rates. Given that the flame is not close to the stagnation plane, the downstream heat loss is not efficiently sensed in the far upstream. The predictions are further confirmed by experimental results Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 144 with and without wall. Thus, the single jet-wall configuration is suggested as an alternative technique for the determination of laminar flame speeds. 7.4 References Egolfopoulos. F.N., Du, D. X., and Law, C., K. (1992), Combust. Sci. TechnoL 83:33- 75. Egolfopoulos. F. N.. (1994) 25th Symp.(IntL) on Combus./The Combus. Insii., Pittsburgh, pp. 1375-1381. Egolfopoulos, F. N., Zhang H. and Zhang, Z., (1997) Combustion and Flame, 109:237-252. Law, C.K., Ishizuka S. and Mizomota, M. (1981) 18th Symp.(IntL) on Combus./The Combus. Insti., pp 1791-1798 Law, C. K., Zhu, D. L., and Yu, G., (1986) 21st Symposium (International) on Combustion, The Combustion Instimte, Pittsburgh, pp. 1419. Matalon, M. (1982), Combust. Sci. TechnoL, 131: 169-181. Vagelopoulos, C. M., Egolfopoulos, F. N., and Law, C. K, (1994), 25th Symp.(IntL) on Combus./The Combus. Insti., The Combustion Institute, Pittsburgh, pp. 1341-1347. Vagelopoulos, C. M., Egolfopoulos, F. N., and Zhang, H., (1996), “Dynamic and Stability Effects of Weakly-strained Counterflowing Laminar Premixed Flam es”, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 145 presented at the Fall Meeting o f the Western States Section/ the Combustion Institute, USC, Los Angeles. Vlachos, D. G-, Schmidt, L. D., and Aris. R, (1993) Combustion and Flame, 95:313- 335. Williams, F. A., (1985) Combustion Theory, 2nd ed., Benjamin/Cummings, Inc., Menlo Park, CA. Yahagi, Y., Ueda, T., and Mizomoto, M., (1992) 24th Symp.(IntL) on Combus./The Combus. Insti., Pittsburgh, 992. pp. 537-542. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O Q . C g Q . ■ D CD C/) C/) 8 ■ D CD 3. 3" CD CD ■ D O Q . C a O 3 " O o CD Q . ■ D CD C/) C/) 1900 (L ) 1850 U B cd M 1800 (U 6 1750 (U H u 1700 B cd ïi: 1650 1 1600 G 1550 1500 (C H 4 /Air,(|) = 0 .7 0 ) (Adiabatic)^ Jet-Wall Opposed-Jet (Adiabatic)^ ■ ■ I 200 400 600 800 1000 1200 1400 1600 1800 2000 Aerodynamic (Hydrodynamic) Strain Rate, K, s Fig. 7-1 Variation o f the num erically determ ined Tmax with K and extinction behavior of a (j) = 0.70 m ethane/air flame, for the opposed-jet and single jet-w all configurations u n d e r a d ia b a tic c o n d itio n . 147 2000 1800 1600 - -t.» 1200 1000 CH4 /Air, (j)= 0.70 K = 8 5 9 s' Single Jet-W ail (Adiabatic) Opposed Jet (Adiabatic) (D ■ O " 1 a O p p o sed -^ t (Adiabatic) 0.6 c •S ce O O (U > "S ca O C 600 400 200 - 0.5 Single Jet-W all (Adiabatic) 0 .4 B o %, 0 .3 £ - 0 .2 O * 0.1 Œ ) .0,0 0.00 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0.3Ô Distance from Stagnation Plane, cm Fig. 7-2 Spatial variations throughout the flame of numerically determined (a) temperature and (b) radial velocity gradient G=dv/dr and density weighted radial velocity gradient p* G for a é =0.70 m ethane/air flam e as K=859 s e c f o r both the opposed-jet and single jet-wall configurations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD - O O Q . C g Q . " O CD C/) C/) CD 8 T D ( O ' 3. 3 " CD CD " O O Q . C a O 3 " O O CD Q . " D CD ( / ) < /i 1900 0) } H 3 Cj 1800 1 H (D P4 s (D H 0) 1700 e cd E 3 1600 1 1500 (C H ^ /A ir , (|)= O .T O ) ( Single Jet-Wall ) T w aii.= 400 K T » .„ = 1 4 0 0 K T w3 „ ? 1 5 0 0 K A d ia b a tic 200 400 600 800 1000 1200 1400 1600 1800 A e r o d y n a m ic (H y d r o d y n a m ic ) Strain R ate, K, s ' Fig. 7-3 Variation o f the num erically determined Tm ax with K and extinction behavior o f a (|) = 0 .7 0 methane/air flam e, for the single jet-w all configuration under adiabatic and = 1500, 1400 and 400K conditions à 149 C / 3 w all — 4 0 0 K w all — ^00 K 3.0e+ 2.0e+ Twaii = 1200 K ' c CS 0.40 Tw aii = 1400 K = 0.35 Li. 0Û " w a ll = 1200 K 0.30 'w all = 400 Twaii = 600 ^ 50 100 150 250 200 Aerodynamic (Hydrodynamic) Strain Rate, K, s' ^ Fig. 7-4 Variation of the numerically determined (a) heat flux to the wall and (b) distance of the flame luminous zone from the stagnation plane (wall) as a function of K and Twaii for $ = 0.70 methane/air flames and the single jet-wall configuration. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O Q . C g Q . ■ D CD C/) C/) 8 ■ D ( O ' 3. 3 " CD CD ■ D O Q . C a O 3 " O O CD Q . ■ D CD ( / ) ( / ) 1000 c /) o •S m 800 % 600 400 c o § 200 ----- T" I I 1 1 1 Numerical Data 1 i 1 1 1 — t — 1 Numerical Data (GRI 1 .2 -scheme)' ' ' EL scrternle) Present Ex 3 t. Da ta- J ' 1 n 11 k 11 Ï X — / CH, /Air, p = l atn Single Jet - Wall Flame Extinctiot Twall= 1000 K 1 I— i i 1 1 L i — m . 1 ----- : 1 1 1 1 1 1 Equivalence Ratio, < ! > Fig. 7-5 C om parison betw een the experim entally and num erically determ ined extinction strain rate Kg*, for atm ospheric m ethane/air flam es under the single jet-w all configuration and T w a ir ^000 K. 7 3 CD " O O Q . C g Q . ■ D CD C/) o " 3 O 8 ■ D CD 3. 3 " CD CD ■ D O a. c a o 3 " O O CD Q . ■ D CD C/) C/) t/] b 00 a o o o % w 2000 1600 r 1400 1200 P i q 1000 800 600 400 200 8 < T “ ~r -r--~i 1 — " f " T - r — - Numerical Results - (GRI 1.2-scheme) ' a J I r - [J 1 1 1 1 1 1 1 ExDt. Data 1 g • M 9 t " m J ( L a ^ e t al. (19& !■ V ■ N ■ . pAciilfc__ I a j V üUL-scnemej 1i 1 < ) ■ rCH 4 /Air, p=l atm Opposetj-Jet I Flame Extinctior I 1 1 1 I I I I \ r % 1 1 O m ■ t, ■ y I T" ■ " I I 0.6 0.7 0.8 0.9 1.0 1.1 Equivalence Ratio, ^ 1.2 1.3 1.4 1.5 1.6 Fig. 7-6 C om parison betw een the num erically determ ined extinction strain rate Kexi and the experim ental data o f Law et al. (1986) for atm ospheric m ethane/air flam es under the opposed-jet configuration. L A CD - O O Q . C g Q . T D CD C/) C/) CD 8 ( O ' 3. 3 " CD CD " O O Q . C a O 3 " O O CD Q . O C ■ D CD ( / ) ( / ) 9.0e+8 c/) * ol o (/) g “ fli c§ (L ) r* 4 (S % ( U m T3 (L ) c d bî) < u B.Oe+8 7,0e+8 6.0e+8 ^ Opposed-Jet (Adiabatic) ^ = 0 .9 5 (|)=0.90 C H 4 /Air, p=l atm GRI 1.2-scheme 800 1000 1200 1400 1600 1800 2000 - 1 Aerodynamic (Hydrodynamic) Strain Rate, K, s Fig. 7-7 Variation of the num erically determ ined spatially integrated heat release rate in flam es established in the opposed-jet configuration as function o f strain rate and equivalence ratio. CD ■ D I I % CD 8 5 C 5 - 3 CD CD ■ D I C g o 3 & O c 1.1e+9 t GO * rj I O * t/3 (U c/3 C j (U p< cd (U w T3 (U cd W ) ( L ) 1.0e+9 9.00+8 8 .00+8 7.00+8 6 .00+8 C H 4 /Air, p=l atm GRI 1.2-scheme Single Jet - Wall Twall = 1000 K 200 400 600 800 1000 Aerodynamic (Hydrodynamic) Strain Rate, K, s ‘ Fig. 7-8 Variation o f the num erically determ ined spatially integrated heat release rates in flam es established in the single jet-w all configuration with = 1000 K as function o f strain rateand equivalence ratio. 12 CD ■ D O Q . C g Û . ■ D CD C/) C/) CD 8 CD 3. 3" CD CD ■ D O Q . C g O 3 " O O CD Q . - O CD C/) C/) ^ 4 0 0 C /! ) r > w u M (D cd P< O - a co u •s w 300 200 100 Numerical Results (GRI 1.2-scheme) 0.6 0,7 Present Expt. Data CHj /Air, p = l atm Single Jet - Wall Flame Extinction ^ T w a II= 573 K 0.8 0.9 Equivalence Ratio, a Fig. 7-9 C om parison betw een the experim entally and num erically determ ined extinction strain rate Kext for atm ospheric m ethane/air flam es under the single jet-w all configuration 155 .1900 (U 2 <U1800 CL E u g 1700 C Q Adiabatic /Air, (j)= 0.70^ ( Single Jet-Wall) E =3 1600 - H Recombination X CO 1500 H Recombination , %,3it = 1 6 0 0 K — A° 1000 1200 1400 1600 1800 .1 Aerodynamic (Hydrodynamic) Strain Rate, K, s'l = 1.00 - o 0.80 ■ S 0.70 g 0.50 P 0.30 E 0 .2 0 - i 0.10 200 400 600 800 1000 1200 1400 1600 1800 2000 Wall Temperature, Twaii, K ^ = 0.70 CH^/air flame and single jet-wall configuration: (a) Effect of H radical recombination at the wall on extinction under adiabatic and T waii=1600 K conditions, (b) Varaition with Twaii of the ratio of Kext with H radical recombination over K^xt without H radiacal recombination. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 ) CD ■ D O Û . C g a ■ D CD C/) C/) 8 ■ D CD 3. 3 - CD CD ■ D O Û . C g o 3 " O o CD Û . ■ D CD C/) C/) 50.0 I c /f 40.0 'd ' C& 35.0 Q j E O ) u i 20.0 □ □ Single J e l-W a ll, I\v„„ = 573 K , L = 2.0 cm Single J e t W all, = 1000 K , L = 2.0 cm A A O p p o s e d -Je t, L = 2.5, 4cm CH^/AIr ( } ) = 0.805 N um erical Sim ulation G R I 2 .I 30.0 25.0 - Ke„ = 330s-' K , „ = 3 7 0 s - ' 0.0 100.0 200.0 300.0 400.0 500.0 Hydrodynamic Strain Rate, K (sec *) Fig. 7-11 V ariations oi' the num erically determ ined reference flam e speed, Su^rel» w ith the hydrodynam ic strain rate K for ( { ) = 0.805 C H ^/air flam es under the near-adiabatic opposed-jet and non-adiabatic single jet-w all configurations. ;d CD ■ o 5 Û . C g Û . T 3 CD g 8 " O e g - 3 CD 3. 3" CD CD T D O Q . C g o 3 " O o CD Q . " O CD C/) C/) U I ! C T ) 'd 0) a A {/) Q ) § E cu s I 5 0 4 5 4 0 3 5 3 0 2 5 20 r > / Premixed melhane/Air, O Single Jet-WaIl,T^=573K, L=20mm P = 1 atm, ( |) = 0.805 n Single Jet-Wall, T ^ - lOOOK, L-20mm Nozzle Diameter D =14mm A Opposed-Jet, L=25mm J O o g a i ' ▲ AA n o eoei K ext= 280 I/see = 320 1/sec 0 100 4 0 0 5 0 0 2 0 0 3 0 0 Local Strain Rate K, 1/sec Fig. 7-12 Variation of the experimentally determined reference flame speed, Sy ref» with local strain rate K for < { » = 0.805 methane/air flames under the near-adiabatic opposed-jet and non- adiabatic single Jet-wall configurations. CD ■ D O Q . C g Q . ■ D CD C/) C/) 8 " O C Q ' 3. 3 " CD CD ■ D O Q . C a O 3 " O O CD Q . ■ D CD C/) C/) 50,0 J» S 40.0 ^ Single Jet-W all, T„„„ =573K, L = 9 mm □ Single Jet-Wall, =1000K, L = 9 mm ) Opposed-jel, L = 18 mm Numerical Simulation GRi 2.1 CHVAIr ( { ) = 0.805 A 35.0 K .., = 328 s* K _. = 295s 200.0 500.0 H y d ro d y n am ic S tra in R ate, K (sec ') F ie 7 -1 3 V ariations o f the num erically determ ined reference flam e sp eed , S„ „f> '"‘f*’ the hydrodynam ic strain rate K frir 4, = 0 .8 0 5 C H ^ air flam es under the near-adiabatic op p osed -jet and non-adiabatic sin g le jet-w a ll configurations. U \ 00 ;d CD ■ D O Q . C g Q . -o CD C/) C/) 8 T D ( O ' 3. 3 " CD CD " O O Q . C a O 3 " D O CD Û . ■ D CD ( / ) o' 3 K = I7 0 s K =90s K =60s K = 130s 1000 A CH. /Air 4 ) K =190s Distance from Stagnation Plane, cm Fig. 7-14 Variation of the numerically determined spatial temperature profiles for a < j ) = 0.70 methane/air flame and for varies Ks, for single jet-wall configuration with T 1000 K and L = 20 mm. wall % 160 Chapter 8 UNSTEADY EFFECTS ON STRAINED N O N PREMIXED LAMINAR FLAMES 8.1 Introduction and Objectives An experimental study was conducted on the effects of far field velocity oscillations on the response of strained non-premixed flames. The experimental system was described in Chapter 2. The nozzles diameters were 14 mm. The burners were water-cooled in order to keep the unbumed gas at the ambient temperature. The nitrogen coflow was used in order to isolate the reactant flow from the ambience, to eliminate the oscillation-generated vortex rings, and to adjust the flame location. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 161 CH^/air non-premixed flames were studied. The fuel flow was diluted by nitrogen. The fuel was supplied ftom the bottom burner while the oxidizer was supplied from the upper burner. 8.2 Results and Discussions 8.2.1 Velocity profiles The velocity profiles were measured along the centerline by using LDV, and typical results can be seen in Fig. 8-1 and Fig.8-2. In general, the location of the non-premixed flame is determined by the requirement for stoichiometric supply of the reactants. In the present study, the lowest CH^ concentration was 25% in the CH4/N2 stream, while the O, concentration was 2 1 % in the oxidizer stream (air in all cases). For such conditions, the non-premixed flame is located on the air side of the stagnation plane, and the velocity profiles on the air side differ from those on the fuel side. It can be seen that on the air side, the velocity decreases as the flame is being approached and it reaches a minimum at the location where the heating starts. On the fuel side, the velocity simply decreases towards zero at the stagnation plane. The hydrodynamic strain rate K of a steady non-premixed flame was applied to characterize the upstream average straining for oscillating flames and its value was determined by the local velocity gradient before the flame as described in Chapter 2. The K was determined on the air side because the convective velocities of the oxidizer are directly associated with the oxygen leakage through the flame. The Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 162 leakage can lead to a temperature reduction and eventually to extinction [e.g. Egolfopoulos and Campbell, 1996]. Figure 8-1 depicts the influence of coflow flow rate on the axial velocity profile. It can be seen that as the co-flow increases on the air side, the velocity profile is moved towards the fuel nozzle. This indicates the flame is located closer to the fuel nozzle. Furthermore, the velocity at the nozzle exit increases on the fuel side but decreases on the air side. Fig. 8-2 depicts the velocity profiles at different nozzle separation distances. After shifting the profile of L = 10 mm to that of L = 15 mm by having the same stagnation points, one can find that the two velocity profiles closely overlay on each other at the flame vicinity. This indicates that the changes of local strain rate on the air and fuel sides are not significant, while the change of global strain rate is 50%. 8.2.2 Frequency response One of the major goals of present smdy was to experimentally quantify the frequency response to the upstream velocity oscillations. It was observed that the flame responds to the upstream oscillation in different maimers depending on the oscillation frequency. Namely, the amplitude of oscillation is substantially reduced at higher frequencies, while at low frequencies the flame responds to the oscillation in a quasi-steady manner. In the present study, the oscillation was induced by the temporal variation of u^j and its frequency was set up by the signal generator while its amplitude, A^, was determined at the nozzle. The LDV was used in the temporal mode to monitor the velocity oscillation amplitude and frequency at the no2:zle exit. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 163 The difference between the measured peak and trough velocity values is defined as the A^. This method was used for the first time and it quantified the amplitudes directly and more precisely compared to the method based on the modeling of the speakers vibrating chamber [Kistler et al., 1996]. Furthermore, the flame response is represented in terms of displacement of the luminous flame zone. Representative results of the response in terms of flame oscillation displacement, are shown in Fig. 8-3. For a fixed fuel concentration and a fixed mean exit velocity, a substantial attenuation of A^^^ is observed as the frequency increases. It can be also seen that at low frequencies, a larger upstream oscillation amplitude leads to a higher Ajj^^ value, as expected. It was also observed that when the imposed oscillations are characterized by low amplimdes and for low frequencies, the flame oscillates symmetrically about its original, unpermrbed location. At high frequencies or large amplitudes, the flame oscillates around a location close to the air nozzle rather than the original one. In order to quantitatively validate the theoretical predictions, experiments were conducted with various strain rates, various upstream oscillation amplitudes and various frequencies. The amplitudes of flame oscillation, Af,^^s were normalized by the corresponding quasi-steady values at 2 Hz for each case. (At f=l Hz the speaker did not work v/ell). The variation of the normalized A „ ^ with the Stokes’ parameter. Tit [Egolfopoulos and Campbell, 1996] is shown in Fig. 8-4. In agreement with the simulation results shown in Fig. 8-5, the experimental data under different conditions collapse into a single curve. This finding constimte an experimental validation that the Tit is the appropriate scaling parameter. The drastic Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 164 reduction of the normalized amplitude starts as 7 7^ = 0.6, which differs ftom the prediction of 77^ = I . The difference may be attributed to the fact that the oscillation was only induced on the fuel side in the experiments while it was induced ftom both sides in the simulations. It may be also caused by inaccuracies associated with the measurement of small oscillation amplitudes of the luminous zone at high frequencies. Nevertheless, this difference is not significant to alter the underlying physical conclusions. 8.2.3. Extinction of unsteady non-premixed flames A diffusion flame can be extinguished as the imposed oscillation amplitude of nozzle exit velocity exceeds a critical value, A^ Fig. 8-6 depicts the experimental results of the variation of the A^ with the frequency for various fuel concentrations. For a given frequency, as A^ increases, the flame oscillation displacement A ^,^ increases. At the same time, the increase of A„ facilitates the O, leakage, which leads to a temperature reduction and eventually flame extinction. It can be seen that for a fixed fuel concentration, as the frequency increases, the extinction occurs at a larger A^ value. In Fig.8-6, it can be also seen that the extinction limits strongly depend on the fuel concentration. At a fixed frequency, higher fuel concentration results in flames that are more resistant to extinction that occurs at a larger While the increase of the extinction A ^^ value as the fuel concentration increases is obvious, the increase of the extinction A^ value with frequency is a result of the transient and complicated nature of the process of extinction. Under Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 165 Steady conditions an increase of the nozzle exit velocity will result in a corresponding increase of the strain rate and as a result in increased reactant leakage that can lead to extinction. Extinction is a transient phenomenon and in order for it to be completed, a finite time is required which is of the order of the inverse of the strain rate as it corresponds to the time required for convective cooling. If during that time a favorable strain rate is imposed the flame can be re - ignited and burning is sustained [Egolfopoulos, 1994]. Thus, at high frequencies a larger amplitude of oscillations is required for extinction to be completed. 8.3 Concluding Remarks An experimental study was conducted on the response of unsteady non- premixed flames. Velocity oscillations were imposed on the bottom fuel burner by using a speaker, and the amphtude and frequency were controlled independently. . The local strain rate and the velocity oscillation amphtude at the nozzle exit were determined by using LDV, and the displacement of luminous zone movement w as quantified with a telescope. The flame response was represented by the oscillation amplitude of the luminous zone position. This response was smdied at various amphtudes and frequencies, under various mean free stream velocities (strain rates) and fuel concentrations in the fuel stream. The extinction behavior under the presence of unsteadiness was also assessed. Experiments confirmed that at low frequencies, the flame responds to the extemal oscillation in a quasi-steady manner. However, at high frequencies, the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 166 flame responds in a transient manner, and at very high frequencies, the flame no longer responds to the extemal oscillations. By scaling the flame amplitude response with the Stokes’ parameter, all data were found to collapse into a single curve which is in agreement with the recently developed scaling argument of Egolfopoulos and Campbell (1996). Furthermore, it was found that non-premixed flames are extinguished when the extemal oscillation amplitude is large enough at low and high frequencies. However, the extinction condition strongly depends on the frequency for a fixed fuel concentration in the fuel stream. Flames at higher frequencies were experimentally found to resistant to higher strain rate amplitudes, which is also in agreement with numerical predictions. Physically, this is a result of the transient nature of the extinction process and the unsteady nature of the imposed strain rate. 8.4 References Egolfopoulos, F. N. (1994) 25th Symp. (Intl.) on Combus./The Combus. Insti. ppl375-1381. Egolfopoulos, F. N. and Campbell, C. S. (1996) J. Fluid Mech., vol 318, 1-29. Kistler, J. S., Sung, C. J., Kreutz, T. G., Law, C. K., and Nishika, N. (1996) 26th Symp. (Intl.) on Combus./ The Combus. Insti. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD ■ D O Q . C g Q . ■ D CD C/) C/) 8 3. 3" CD CD ■ D O Q . C a O 3 ■ D O CD Q . ■ D CD C/î C/) ( A I I U u 'I 1 3 C H j /(N 2+CH4)=25% in mole D =14 mm, L=IO mm ^ o ia T cc/s, Fuel Side Coflow Changes on Air Side O C o f l o w Q |, Q| > Q 2 □ Coflow Q 2 . Q | < Q 2 A Collow Q , , Shiflcd ide ^ Air Side □ "W Fuel Side ^'^^0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Axial Coordinate, x (cm) Fig.8-1 Axial velocity profiles along the centerline in the opposed-jet counterflow configuration for non-premixed flames with different coflow flow rates 3 : : d CD ■ D O Q . C s Q . ■ D CD ( / > C/) CD 8 ■ D ( O ' 3. 3 " CD CD ■ D O Q . C a O 3 " O o CD O . " O CD ( / ) ( / ) 0.60 C ^ j /(N2+CH4)=25% in mole D =14 mm, with colfow Q= 60 cc/s, Fuel Side Q= 68 cc/s, Air Side LJ L=l5mm O L=IOmm A L= 10mm, Shifted % Fuel Side % 0.00 0 .2 5 0 .5 0 0 .7 5 1.00 Axial C oordinate x (cm) 1.25 1.50 F ig .8 -2 A xial velocity profiles alo n g the cen terlin e in the o p p o sed -jet co u n terflo w c o n fig u ratio n fo r n o n -p re m ix e d flam es w ith d ifferen t b u rn er sep aratio n distances. a > ■ D o û. c g Q . ■ D CD ( / ) C/) 8 CD 3. 3 " CD CD ■ D O Q . C a O 3 " O O CD Q . ■ D CD C/) C/) I S I U 0 1 c o â 'u ifi 0 > I k 3.5 3.0 2.5 2.0 1.5 1.0 .5 0.5 0.0 1 --------- f f - CI^/(N2+CH4)=25% in mole D =14 mm, I. = 15 mm u„i, = 0.21 m/s V □ % f ■ 0 Jpstrcai 1 oscillai ion ampiiluJc U o55 0.2 5 m/s 0 I ] ] u Upstream oscillation amplitude U.J6 m/s V ^ / f ) [ o f ; ] 1 [ [ ] ( ) 1 --- » — ( 0 10 90 100 110 120 20 30 40 50 60 70 80 Impinging Frequency, f (Hz) Fig.8-3 Variations of maximum flame oscillation dispalcemenl with impinging frequency for unsteady non-premixed flames in the opposed-jet counterflow configuration with different oscillation ampitudes of the upstream velocity. $ CD ■ D I 8 Q . ■ D CD C /) o' 3 CD 8 ■ D C 5 - 3 CD C 3. CD ■ D I C g. o 3 ■ D S & O c a 4 - 1 a 'a « .a 1 3 I 0 % s 1 § (J 0 1 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 C l(| /(N2 +CH^ )=25% in mole D=I4 mm, L= 15 mm □ K = 65 .s' Ug^j, = 0,21 m/s, i\«c = 0,25 m/s A K = 6 5 s ’* , Uexii = 0-2I m/s, ii„sc = 0,36m/s O K = 50 s '! u e^j,= 0,18 m/s, «osc= 0,25/n/s © K = 75s'*, u exii = 0,30 m/s, uosc = 0.25 m/s H K = 87 s ■ II exit = 0,39 m/s, uosc = 0,25 m/s .01 .1 Stokes' Param eter = (to /2K) Fig.8-4 Variations of flame oscillation dispalcemenl normalized by its value at 2Hz with the Stoke's param eter for various unsteady non-premixed flames in the opposed-jet counterflow configuration. Tlie upstream oscillation amplitude U o sc and aerodynamic slran rale K are measured by the LDV. CD ■ D I 8 Q . ■ D CD C /) o' 3 CD 8 ■ D C 5 - 3 CD C 3. CD ■ D I C a O 3 ■ D S & O c " O CD 1.00 O i "d I 0.80 0.60 I I o iz: 0.40 0.20 0.00 Numerical Results ° Flame I ^ Flame II • Flame III J . { — P-- E l '.01 .1 ^ 1 / 2 (0 Stokes' Parameter \ = (O)/2K) Fig.8-5 Variations of the Tinax am plitude norm alized by its quasi-steady value with the Strokes' param eter T ] defined in term s o f the angular frequency, o ) , and the aerodynam ic slran rate, K (Egolfopoulos and Cam pbell, 1996]. CD ■ D O Q . C g Q . ■ D CD C/) C/) 8 ■ D 3. 3 " CD CD ■ D O Q . C a O 3 " O O CD Q . ■ D CD C/) C/) □ C H ^ /(N 2 +CH^) = 25% in mole O CH^ / (N2 + CH^) = 28% in mole A CM4 / (N 2 + CH4 ) = 32% in mole O CH4 / (N 2 + CII4 ) = 35% in mole O CII4 / (N ] + CH4 ) = 38% in mole CH4 / (N2 + CH4 ) = 42% in mole > Opposed-Jet, Diffusion Flame D =14 mm, L = 15 mm U i, = 0.40 m/s 0.00 10 100 1000 Oscillation Frequency of Im pinging Flow (Hz) Flg.8 - 6 Varialions o f m axim um oscillation am plitude of the upstream velocity at w hich flam e extinction occurs with the upstream oscillation frequency for unsteady non-prem ixed flames in the opposed-jet counterflow configuration. 10000 w 173 Chapter 9 CONCLU DENG REMARKS AND RECOMMENDATIONS 9.1 Concluding Remarks The present dissertation research has made the following contributions towards understanding of the effects of gravity, heat loss, and unsteadiness on the structure and dynamics of strained laminar flames: 1. Experimentally determined the extinction strain rate for various near-limit, premixed mixtures in the opposed-jet counterflow configuration under microgravity. The Lewis number effect was assessed for mixtures with Le< 1 (e.g., lean CH„/air) and Le>l (e.g., lean C^Hg/air). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 174 2. Experimentally smdied the wall effect on flame propagation and extinction by using the single Jet-wall configuration. 3. Experimentally studied the propagation and extinction of nearly adiabatic flames in normal gravity by using the opposed-jet counterflow configuration. 4. Numerically smdied the experiments for neariy-adiabatic flames. 5. Numerically studied the upstream and downstream conductive heat loss effects on the propagation and extinction of strained premixed flames. 6. Developed a full radiation model, considering both the spectral wavelength dependence and the re-absorption in gas medium. 7. Experimentally studied the effect of unsteadiness on the dynamics and extinction of non-premixed flames. The introduction of the counterflow technique in microgravity is essential in addressing mechanisms responsible for the flammabihty limits. A microgravity- compatible experimental system was developed. The experiments capmred the C - shape extinction behavior for Le<l mixtures and the monotonie one for Le>l mixmres. Since the numerical results show that upstream heat losses could be induced with small separation distances, large separation distances were used. In addition, an improved method was proposed and used for the determination of the fuel concentration at extinction. Therefore, the present data are of fundamental interest compared to the previous microgravity data in which upstream heat loss was present. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 175 The numerical simulations were conducted by solving conservation equations of mass, momentum, species concentration, and energy along the centerline of the stagnation flowfield. A detailed description of chemical kinetics, molecular transport and thermal radiation was used. The simulations were conducted for finite domains that were compatible to the ones used in the experiments. The simulations and experiments provided physical insight into the mechanisms controlling flame extinction in the presence of strain rate and various types of heat losses. A full radiation model considering the wavelength dependence and the re- absorption in the gas medium was also developed. The results were compared with the ones obtained by using the optically thin assumption. The full radiation model was included into the one-dimensional Premix code. Results showed that the maximum temperature is noticeably affected by radiation only for near-limit flames, and that flammabihty limits derived from different radiation models differ slightly although the downstream radiation are significantly different. A single jet-wall configuration was developed in normal gravity for studying the downstream heat loss effect. Both experiments and numerical simulations were conducted. The effects of no-shp condition, wall temperature, and H radical recombination were assessed. It was found that the downstream heat losses minimally affect the experimentally determined laminar flame speeds at the limit of zero strain rate. Thus, this configuration is recommended as an alternative technique for the determination of laminar flame speed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 176 Finally, the effect unsteadiness on the structure and extinction of non- premixed flames was studied in a modified opposed-jet configuration allowing for the oscillation of the flow velocity at the nozzle exit. Experiments confirmed the generally predicted frequency repsonse and the recent theroretical scaling arguments regarding the transition from quasi-steady to fully transient flame response. It was also found that the extinction condition for non-premixed flames strongly depends on the frequency for a fixed fuel concentration in the fuel stream. Flames at higher frequencies were experimentally found to be more resistant to higher strain rate amplitudes. 9.2 Recommendations The present study is a first effort to rigorously quantify and understand the effects of heat loss and unsteadiness on the flame structure, dynamics and extinction 6om both numerical simulations and experiments. Many problems of interest must be further addressed and are indicated in the following: 1. Using the current microgravity system directly or with some minor modifications, many interesting studies can be done, e.g., with Helium-diluted mixtures for general Le number effect and with CO^-diluted mixmres for r e absorption radiation effect. 2. The present research has unambiguously demonstrated that the global strain rate is not accurate or even not appropriate to quantify the straining effect for the flame. Thus, the use of Laser diagnosis in micro gravity is essential. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 177 3. Another major limitation in the present microgravity experiments is that the achievable minimum strain rate (global) is around 6-7 s'". Although the C- shape extinction behavior for Le<l (CH^/air) mixtures and the monotonie one for Le>l mixtures were captured as expected by numerical and theoretical predictions, data at ultra small strain rate are still required. In order to achieve ultra-low strain rates, experiments are suggested be conducted in environments in which larger microgravity time is available so that ignition is performed at microgravity instead of normal gravity. 4. The discrepancy between the experimental and simulation results for the QHg/air flames may be caused by deficiencies of the chemical kinetic mechanisms. The results suggested that appending the C, sub-mechanism on the GRI mechanism may be improper. Given that chemical kinetics is a dominant mechanism for flammabihty limits, a better full Cj mechanism is required for the CjHg/air simulations. 5. The application of the full radiation model in one-dimensional freely propagating flames showed that the inclusion of re-absorption affects the flame temperature field. It is interest to use the model to study the pollutant formation, which strongly depend on the temperature. In addition, it is interest to further extend the integration domain to larger in order to complete the study of the upstream re- absorption effect. It is highly recommended that the model is used in the studies of strained flames with high CO, addition. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 178 6. The experimental study on the effect of unsteadiness did not provide any information regarding possible couplings between unsteadiness and heat loss. It is recommended that such studies are conducted for weakly-burning, weakly-strained flames which will require microgravity conditions. Furthermore, such studies must be extended to premixed flames as only non- premixed flames were studied herein. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 179 Appendix The Derivation of Full Radiation Model 1. Equation of Transfer As shown in the schematic diagram. Fig. 4-1, flames are assumed to be within a planar radiating medium bounded by two infinite parallel planes, which serve as boundary con ditions. In Fig. 4-1, .S denotes the arbitrary path at angles 0 from the positive x-direction; r* " denotes the radiation intensity, w.r.t. 0 < 9 < 90^ ; f denotes the radiation intensity, w.r.t. 9 0 < 0 < 180^ ; and D denotes the thickness between two boundaries. The temper ature and properties of the medium vary only along the x-direction (1-D). The optical depth ky^{x) is defined along the x-direction as: (1) The optical depth k^{S) is defined along the S-direction as: K = (2) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 180 According to the relation between and : k\(.S) = k^{x)/cosQ (3) the equation of transfer along the S-direction is: (4) where: Py^ik^, C ù ) is the source of intensity along the optical path from both emission and incoming scattering. For an isotropic scattering medium, the f is a function of (a dk-)^ is the optical differential thickness, f ^ is the radiation intensity. Applying the equation (4) to and f, then cose . 6) = e ) (5-1) Let |i = C O S 0 , then we have 3 /" * * H 1 1 ) = 1 1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 181 3î* p. ■ H) = H) (6-2) The above system of equations are integrated subject to the boundary conditions; = il{0 ,\i)^tky_ = 0 (7-1) i'xik^, |i) = I ’ xCfcox, M -) at (7-2) where. ^DX- + (8) — extinction coefficient, = + — spectral absorption coefficient — spectral scattering coefficient According to the non-scattering assumption, = 0 and . So, the integrated forms of equation o f transfer under the b.c become: K) = '1(0, li)exp(^-^^ + K)exp(^ ^ (9-1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 182 M-)exp(^— (9-2) In (9-2), 0 e [ it/2 ,7c] and p. e [- 1 ,0 ] . 2. Radiative Flux The total radiative energy flux in the positive x direction equals to the integral over all wavelengths of the spectral flux: q ,(x) = ( 10) Note that for a fixed x the will vary with X since is a function of X . The spectral energy flux in the positive x direction from is fJt/2 + - = r /T(it.,e)cos027csin0d0 (11) a A . - > 6 = 0 Similarly, the spectral flux in the negative x direction arising from is ■ ■ = -2 ti\ (it., 0)cos0sin0d0 (12) dX Je= 7t/2 The net flux in the positive x direction is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 183 (13) Substituting |i= cos0 yield. — = 2îC it(0, ^ L ) e x p - 2 î c - M - ) e x p p) exp -27c J^]^“V x(A :^ x , -p)exp(^^% ^]dk*;,^p. (14) 3. Divergence of Flux For the use in the energy equation, the term is needed. For the plane layer, depend only on x so that, with dkj^ = Kyjix)dx this becomes V.CM) = (16) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 184 and (17) There are six terms in the divergence form. The first two are related to the bound ary conditions. The last four terms are related to the source function. The third and fourth terms are related to the incident in positive x direction. The last two terms are related to the incident in the negative x direction. 4. Source function Source function |i) defined as P-) = (^ - ^ 0 % ) ^ J ^ C 0 j - ) O ( A „ C ù , © , ) d C û , - ( 1 8 ) ( Ü , = 4 rc where, is the albelo for scattering Qni = -z^= -----— — , for scattering 0^ “ x + cr.x alone 1 while for absorption alone Q.q^ 0 ; 4>(?i,(a,CD,-) is the phase function Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 185 for scattering, for isotropic scattering 0(X,oo,(o,) -i- 1 ; and f is the spectral inci dent intensity. So the source function for the non-scattering, isotropic (independent of p.) medium: = (19) S.Radiative flux of non-scattering and isotropic mediums Substituting (19) into (17), we have = -2 îtJ^ x (0 ’ M-)exp(^-^ydp.-2itj\x(/:ox. ~li)exp(^- ,2 dkydX (I) (ID A z /:)- t* x \ dk*\ - 2 ^ ^ fx£.(^üexp[— - — d\i + 2 jtj^ z \,( ^ x ) # a m (IV) (V ) (Y D (20) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 186 (/V) + (W ) = - (21) Introduce the exponential integral function, £’ „(^) E„(Ç) = j ‘ p" "= x p (l^ )d p (23) then. ' t = * ^*X ) (24) a m = - 2 k i\i,(*:*x)£i (*x - *:*x)<**x (25) simiariy. (V) = - 2 iz f° \'^ ( ^ k * ^ ) E ,( k * ^ - k ^ ) d k \ (26) " ( x ±erefore. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 187 (.III) + (.V)= -2nj^“ ru(*»i)£,C |«rx-<:*x|)**>. (27) Substituting (21) and (27) into (20), we have. - 2îcJ^“ (|*x - **x| )<*•».+ ( 2 8 ) 6. Diffusion Boundaries For the diSusion boundaries. f'lCO, p.) = :I(0) (29-1) ‘x(*0X. -n ) = 'l(tp x ) 09-2) then = -27iit(0)E2(A:0 (30) and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 188 = -2îtix(^Dx)^2(^DX-*x) (31) so, (28) can be rewritten as: d - 2 > tJ^“ ■\i.C **x)£'i ( ! < :;. - < ^ * x | )**x + *-^‘ ' x b W 0 2 ) 7. Divergence of radiative flux ^ t h diffusion boundaries, for non-scattering and isotropic mediums, the diver gence of radiative flux, which can be directly applied to the energy equation becomes, - t*x|)dt*x] • a x (tx ))'A + '* " J T '\/^ x ) ' «x(&x)'f)- (33) * ' 0 Kb Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 189 Numerically discreted form is i = l i = N r / j = i — I -27c X z (‘ ■'xi(**x.y)fi/(|fcx-**i.i)A t*x.y) i = 0Iv y = 0 i = N r r j = JJ -2 " Z Z (‘ ■■u(**x,/)£,(|fcx-t*x,yl)^x.y) 1 = 0 ^\y = ( + i is N : = 0 (34) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IMAGE EVALUATION TEST TARGET ( Q A - 3 ) / Vf % 1 . 0 l.l 1.25 #2.8 ys L: L â Ü làâ 1.4 m |2.2 2.0 1 . 8 150mm V c p o / A /A P P L IE D A IIVHGE . In c 1653 East Main Street Rochester. NY 14609 USA —— . ^ s Phone: 716/482-0300 - ^ = * - = Fax: 716/288-5989 0 1 9 9 3 . A p p lie d Im a g e , In c .. A il R ig h ts R e s e rv e d Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Zhang, Hai (author)

Core Title An experimental and numerical study of the effects of heat loss and unsteadiness on laminar strained flames

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Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, aerospace,engineering, chemical,engineering, mechanical,OAI-PMH Harvest

Language English

Advisor Egolfopoulos, Fokion N. (committee chair), Ronney, Paul D. (committee member), Tsotsis, Theodore T. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c17-431009

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