FLAME SPREAD AND EXTINCTION OVER SOLIDS IN BUOYANT AND FORCED CONCURRENT FLOWS: MODEL COMPUTATIONS AND COMPARISON WITH EXPERIMENTS

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1 FLAME SPREAD AND EXTINCTION OVER SOLIDS IN BUOYANT AND FORCED CONCURRENT FLOWS: MODEL COMPUTATIONS AND COMPARISON WITH EXPERIMENTS by SHENG-YEN HSU Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation adviser: Dr. James S. T ien Department of Mechanical and Aerospace Engineering CASE WESTERN RESERVE UNIVERSITY May, 9

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Sheng-Yen Hsu candidate for the Ph. D. degree *. (signed) Professor James S. T ien, EMAE (chair of the committee) Professor Yasuhiro Kamotani, EMAE Professor Chih-Jen (Jackie) Sung, EMAE Professor Chung-Chiun Liu, ECHE Dr. Gary A. Ruff, NASA Glenn Dr. David Urban, NASA Glenn Dr. Sandra L. Olson, NASA Glenn (date) /6/9 *We also certify that written approval has been obtained for any proprietary material contained therein.

3 Table of Contents Table of Contents.i List of Tables.v List of Figures....vi Nomenclature.. xiii Acknowledgements... xviii Abstract....xix Chapter 1: Introduction and Motivation Flame spread over solid fuels Overview of selected experimental works on concurrent-flow flame spread over solids Flame spread in buoyant flow Flame spread in forced flow.7 1. Overview of the model development at Case Western Reserve University Other similar models Motivation and organization of the dissertation..17 Chapter : Theoretical and Numerical Formulations...1 Theoretical model.1.1 Gas phase model..1. Solid phase model Radiation model... Numerical scheme. Property value..1 i

4 Chapter : Flame Spread in Buoyant Flow: Comparison between Model and Experiments...1 Results and discussions.1.1 Comparison with the experiments by Kleinhenz et al. (8) Three-dimensional flame structure Flame spread at different pressure and gravity levels Flame spread rate Flame structure Comparison with the experiment by Chu (1978) Comparisons of flame structure at centerline Effects of oxygen percentage and ambient pressure on spread rate and extinction limit Summary..68 Chapter : Flame Spread in Forced Flow: Comparison between Model and Experiments Computed results and comparison with experiments Forced-flow flame structure for a reference case.1.1. Effect of gap size upstream of the flame Effects of forced flow velocity, oxygen percentage and pressure 1. Summary 19 Chapter : Effect of Chemical Kinetics on Concurrent-flow Flame Spread over Solids Introduction...1 ii

5 . Computational results Comparison of flame and flow structures in two-dimensional forced and buoyant spreading flames Effect of chemical kinetics on two-dimensional spreading flames 1.. Three-dimensional (-D) buoyant upward flame spread 1. Summery 17 Chapter 6: Conclusion and Discussion 19 Appendix A: Comparison of the Two Sets of Pyrolysis Parameters.1 Appendix B: Radiation Emittance and Absorptance of Kimwipes...16 B.1 The formulation of the variable emittance and absorptance.16 B. The influence of varying emittance and absorptance 16 Appendix C: The Adjustment in Combustion Heat Release to Account for Products Dissociation...17 Appendix D: Sensitivity Tests...18 D.1 Flame spread sensitivity tests 18 D. The effect of gas-phase radiation on three-dimensional buoyant upward spreading flames.. 18 Appendix E: Pressure Limits of Non-Premixed Flame..19 E.1 Introduction...19 E. Stagnation-point diffusion flame...19 E. Side-stabilized diffusion flames.... E. Spherical diffusion flame.. iii

6 E. Remark on pressure limits in pure gaseous diffusion flames... E.6 Remark on pressure reaction order E.7 Experimental data on pressure limits E.8 Conclusions... 1 References iv

7 List of Tables Table.1: Fitting equations for Planck mean absorption coefficients for CO and H O. (p.) Table.: Polynomial relations for specific heat for O, CO, H O, N, and Fuel. (p.) Table.: Gas phase property values. (p.) Table.: Solid fuel property values. (p.6) Table.: Nondimensional parameters. (p.7) Table.1: The computed cases (1% O ) for the comparison with the experiments of Kleinhenz ea al. (8). (p.7) Table.: The computed cases for the comparison with Chu s experiment (1978). (p.71) Table.1: The computed cases for the comparison with Olson and Miller s experiment (9). (p.111) Table.1: Reference pair of concurrent-flow spreading flames at.-atm air (1% O ) used in two-dimensional comparison. (p.19) Table A.1: Two sets of parameters for the th order pyrolysis equation. (p.1) Table B.1: The experimental spectral-averaged emittance for Kimwipes at several temperatures and area densities measured by Pettegrew (6). (p.16) Table B.: The functional fit for Kimwipes emittance as a function of solid temperature and area density. (p.166) Table C.1: Values for constant a at different ambient conditions. (p.177) Table D.1: The values of the parameters for the base case and testing cases. (p.187) Table E.1: Properties and parameters from T ien (1986). (p.8) Table E.: The values of B ref according to the calibration procedure. The high stretch-stretch extinction (blowoff) occurs at a =1 s -1 at p =1 atm, Y oe =. and T ref =K. (p.1) v

8 List of Figures Figure 1.1: The classification of the types of flame spreads from Feier (). (p.19) Figure 1.: (a) Schematic of combustion chamber system and (b) Sample holding plates used in the experiment by Chu (1978). (p.) Figure 1.: Physical description of an upward spreading flame over a thin paper at p=.atm, X O =%. (a) Side view. (b) Front view. (Chu, 1978) (p.1) Figure 1.: Experimental setup for investigating flame spread in partial gravity. (Feier et al. and Kleinhenz et al., 8) (p.) Figure 1.: (a) Sample holder configuration. (b) Images of concurrent flame spread over -cm-wide Kimwipes at cm/s,. atm (6. psia), %O. (Olson and Miller, 8) (p.) Figure.1: -D flame spread configuration for buoyant cases in a large chamber. (p.8) Figure.: -D flame spread configuration for forced cases in a confined tunnel. (p.9) Figure.: Three-dimensional grid distributions for buoyant cases. (p.) Figure.: Three dimensional grid distribution for forced cases. (p.1) Figure.1: The computed reaction rate contours compare to the experimental side-view flame image for 1-cm-wide sample burning at 6-psia air and.16g e. (a) The reaction rate contours which are integrated across the width of the flame. (b) The experimental side-view image from Feier (1). (p.7) Figure.: The computed fuel thickness contours compare to the fuel surface image for 1-cm-wide sample burning at 6-psia air and.16g e. (a) The computed contours of the fuel thickness ratio to virgin one. (b) The experimental front-view image from Feier (1). (p.7) Figure.: The distributions on solid fuel surface. (a) Solid temperature (left side) and ratio of remained fuel thickness to virgin fuel thickness (right side). (b) Solid emittance (virgin emittance =.7). (p.7) Figure.: The cross-section planes present the flame and flow structures of a buoyant upward spreading flame over a 1-cm-wide solid sample burning at 6-psia air and.16g e. (a) Front view (Y=.cm). (b) Side view (Z=cm). (c) Top view (X=1cm). The left half shows the nondimensional temperature distribution (T=1 is K), the velocity vector and the streamline projections; the right half shows the fuel vapor reaction rates (unit: g/cm /s) and the fuel-vapor mass flux projections. (p.7) vi

9 Figure.: The oxygen mass fluxes, streamline projections, fuel-vapor mass fraction (left halves) and equivalence ratio (right halves). (a) Front view (Y=.cm). (b) Side view (Z=cm). (c)top view (X=1cm). (p.76) Figure.6: The vectors of projected radiative heat flux and the contours of radiative heat loss in the gas phase. (a) Front view (Y=.cm). (b) Side view (Z=cm). (c) Top view (X=1cm). (p.77) Figure.7: The distribution of the convective heat flux to solid surface. (p.78) Figure.8: The distributions of radiative heat fluxes over solid surface. (a) Outgoing radiative heat flux ( q r ) from solid surface. (b) Incident radiative heat flux ( q + r ) to solid + surface. (c) The total loss of radiative heat flux ( q r = q r q r ) from solid surface. (p.79) Figure.9: The distribution of net heat flux ( q net = q c q r ) to solid surface. (p.8) Figure.1: The experimental comparisons from Kleinhenz (6). (a) Front views at three gravity levels according to the equal flame spread rate (p 1.8 g). (b) Front views at three different gravity levels. ( psia) (p.81) Figure.11: The comparison of flame spread rates between the computed results and experimental data from Kleinhenz et al. (8). (p.8) Figure.1: The computational flame spread rates as a function of two pressure-gravity combinations. (a) p 1.7 g. (b) p 1.8 g. (g e =9.8 m/s ) (p.8) Figure.1: The flame spread rate versus pyrolysis lengths. (a) Numerical results. (b) Experimental measurement from Kleizhenz (6). (p.8) Figure.1: The comparison of side-view flame structures at three different gravity levels ( psia) Left half: the velocity vectors and fuel-vapor consuming rate (g/cm /s). Right half: nondimensional temperature and streamline projections. (p.8) Figure.1: The comparison of top-view flame structures at three different gravity levels. ( psia) Left half: the velocity vectors and fuel-vapor consuming rate (g/cm /s). Right half: nondimensional temperature and streamline projections. (p.86) Figure.16: The comparison of solid temperatures (left) and ratios of fuel thickness (right) at three different gravity levels. ( psia) (p.87) Figure.17: The comparison of side-view flame structures at three gravity levels according to the equal flame spread rate (V f =.7 ±. cm/s). (g e =9.8 m/s ) Left half: the velocity vectors and fuel-vapor consuming rate (g/cm /s). Right half: nondimensional temperature and streamline projections. (p.88) vii

10 Figure.18: The comparison of front-view flame structures at three gravity levels according to the equal flame spread rate (V f =.7 ±. cm/s). (g e =9.8 m/s ) Left half: the velocity vectors and fuel-vapor consuming rate (g/cm /s). Right half: nondimensional temperature and streamline projections. (p.89) Figure.19: The comparison of solid temperatures (left half) and ratios of fuel thickness (right half) at three gravity levels according to the equal flame spread rate (V f =.7 ±. cm/s). (g e =9.8 m/s ) (p.9) Figure.: Flame temperature distribution at centerline. (a) Computational result. (b) Experimental measurement from Chu (1978) (p.91) Figure.1: Solid temperature distributions at centerline. (a) Computational result. (b) Experimental measurement from Chu (1978). (p.9) Figure.: Conductive heat flux distribution at centerline. (a) Computational result. (b) Experimental measurement from Chu (1978). (p.9) Figure.: Additional information from numerical model. (a) Predicted visible flame from side view. (b) Solid temperatures (left) and ratios of solid thickness (right). (c) Solid emittance. (p.9) Figure.: Flame spread rate as a function of oxygen mole fraction. Experimental data is from Chu (1978). Model computations are at. atm in red and at. in blue. (p.9) Figure.: The cuts of flame structures at Y=.cm at. atm and different ambient oxygen fractions. (a) %. (b) %. (d) %. Left half: fuel vapor reaction contours (g/cm /s). Right half: non-dimensional temperature (T=1 is K) (p.96) Figure.6: The distribution of solid temperature (left half) and fuel thickness (right half) at. atm and different ambient oxygen fractions. (a) %. (b) %. (c) %. (p.97) Figure.7: Flame spread rate as a function of ambient pressure at % O. Experimental data is from Chu (1978). Model computation for sample A (in red). (p.98) Figure.8: The cuts of flame structures at Y=.cm at % O and different pressures. (a).atm. (b).atm. (d).atm. Left half: fuel vapor reaction contours (g/cm /s). Right half: nondimensional temperature (T=1 is K) (p.99) Figure.9: The distribution of solid temperature (left half) and fuel thickness (right half) at % O and different pressures. (a).atm. (b).atm. (c).atm. (p.1) Figure.1: The computed reaction rate contours compare to the experimental side-view flame image for a -cm-wide sample. (a) The reaction rate contours which are integrated viii

11 across the width of the flame. (b) The experimental side view image from Olson and Miller (9). The flow velocity is cm/s, the oxygen mole fraction is % (76% N ) and the ambient pressure is 6. psia. (p.11) Figure.: The computed fuel thickness contours compared to the fuel surface image. (a) The computed contours of the fuel thickness ratio to virgin one. (b) The experimental front-view image from Olson and Miller (9). The flow velocity is cm/s, the oxygen mole fraction is % (76% N ) and the ambient pressure is 6. psia. (p.11) Figure.: The cross-section planes present the flame and flow structures of a forced-flow flame spreading over a -cm-wide sample burning at cm/s, 6. psia and % O. (a) Side view (Z=cm). (b) Front view (Y=.cm). The upper halves show the nondimensional temperature distribution (T=1 is K) and the streamline projections and the lower halves show the fuel vapor reaction rates (unit: g/cm /s) and, the velocity vector projections. (p.11) Figure.: The The distributions on solid fuel surface (a) Solid temperature (T= 1 is K) (upper) and ratio of fuel remained thickness to virgin fuel thickness (lower). (b) Solid emittance. (p.11) Figure.: The flame spread rates as a function of gap size. (p.116) Figure.6: The flame spread rates as a function of forced flow velocity at % O and.69 atm (1. psia). (p.117) Figure.7: Flame spread rates as a function of oxygen mole percentage at cm/s and.69 atm (1. psia). (p.118) Figure.8: The flame spread rates as a function of pressure at cm/s and % O. (p.119) Figure.9: The computational flame spread rates as a function of the two parametric..6 correlations. (a) U ( X O.11) p. (b).7.6 U X O p. (p.1) Figure.1: The experimental flame spread rates as a function of the parametric. correlation ( U X p ) from Olson and Miller (9). (p.11) O. Figure.11: The computational flame spread rates plotted using U X O p in abscissa. (a) Compared with the best experimental fitting curves suggested by Olson and.6 Miller (9). (Solid: y =.x+.. Dashed: y =.676x ). (b) Best fits for the computational results. (p.1) Figure.1: The experimental flame spread rates plotted as a function of the best..6 correlations from computation results. (a) U ( X O.11) p. (b).7.6 U X O p. ix

12 (p.1) Figure.1: The experimental flame spread rates plotted as a function of. U ( X O.11) p. (p.1) Figure.1: Schematics of two concurrent-flow flame spreading models: with infinite-fast gas-phase kinetics (left) and with finite-rate gas-phase kinetics (right). Symbols: q : f, r radiative heat flux to solid from flame; q :convective heat flux to solid from flame; q : c s, r radiative heat flux from solid to surroundings; Q : radiative heat flux from flame to r surroundings. (p.1) Figure.: Flame structures and flow fields in the two-dimensional concurrent-flow flames. (a) Forced-flow flame with upstream velocity 1 cm/s (V f =1.6cm/s). (b) Buoyant-flow flame with. earth gravity (V f =1.19cm/s). The left side in each figure represents the temperature distribution (T=1 is K) and velocity vectors. The right side represents the fuel-vapor reaction rates (unit: g/cm /s) and streamlines. (p.11) Figure.: The distributions along the solid fuel surface. (a) Convective heat flux ( q c ) and net heat flux ( q net ). (b) Non-dimensional solid fuel temperature (T s ) and solid-fuel thickness (h). (c) Fuel mass flux. (solid line: forced flow; dashed line: buoyant flow) (p.1) Figure.: (a) Forced-flow flame. (b) Buoyant-flow flame. Left-half: distribution of fuel mass concentration. Right-half: distribution of equivalence ratios and the fuel mass fluxes. (p.1) Figure.: Fuel-vapor mass fluxes across X-sectional planes as a function of X. (p.1) Figure.6: The -D flame characteristics in forced and buoyant flows as a function of the ratios of pre-exponential factors (B g /B g,ref ). (Zero in the abscissa corresponds to the reference case.) (a) Percentage of escaped fuel vapor. (b) Flame and pyrolysis lengths. (c) Flame spread rate. (solid line: forced flow; dashed line: buoyant flow) (p.1) Figure.7: The maximum (induced) U-velocities at X-sectional planes as a function of X for two different kinetic rates. (p.16) Figure.8: Flame and flow structures of a buoyant upward spreading flame over a 1-cm wide solid sample. Air is at 6 psia and.16g e. B g = cm /g/sec ( B g,ref ). (a) The solid surface profiles. (b) The cross-section along the centerline of the solid sample (side view). (c) The cross-section at x=1cm (top view). For (a), the left side shows the non-dimensional temperature distribution (T=1 is K); the right side shows the non-dimensional fuel thickness. For (b) and (c), the left sides show the non-dimensional temperature distribution and the velocity vectors; the right sides show the consuming rates of fuel vapor (unit: g/cm /s) and the projections of fuel-vapor mass flux. (p.17) x

13 Figure.9: The -D flame characteristics in buoyant flow as a function of the ratios of pre-exponential factors (B g /B g,ref ) for a 1-cm-wide solid sample. (Zero in the abscissa corresponds to the reference case.) (a) Percentage of un-burnt fuel. (b) Flame and pyrolysis lengths. (c) Flame spread rate. (p.18) Figure A.1: The burning rates as functions of temperature. (p.16) Figure A.: The flame structures of two different pyrolysis equations for 1-cm/s forced flow. (a) Old set. (b) New set. Air (1% O and 79% N ) at.atm. (p.17) Figure A.: The distributions of mass fluxes along the solid surfaces. (p.18) Figure A.: The distribution of heat fluxes along the solid surfaces. (p.19) Figure A.: The distributions of temperature along the solid surfaces. (p.16) Figure A.6: Spread rates vs. oxygen mole percentage. (p.161) Figure B.1: The comparison between the formulated model and the experimental data. (p.167) Figure B.: The various emittance as function of area density at several temperatures. (p.168) Figure B.: The flame structures at the centerline cross-section. (a) With constant emittance and absorptance. (b) With variable emittance and absorptance. Left side: reaction rate contours (g/cm /s) and flow velocity vectors. Right side: the flame temperature contours (T=1 presents K) and the projection streamlines. (p.169) Figure B.: The distributions of surface temperature (left) and the ratio of thickness to virgin one (right). T=1 represents K. (a) Constant fuel emittance (absorptance). (b) Variable fuel emittance (absorptance). (p.17) Figure B.: The distribution of emittance over the solid surface. (virgin emittance is.7) (p.171) Figure B.6: The flame spread rates as a function of the ratio of fuel absorptance to emittance. (p.17) Figure C.1: Adiabatic flame temperature vs. oxygen mole fraction at. atm. (p.178) Figure C.: Adiabatic flame temperature vs. pressure at 1% O. (p.179) Figure C.: The combustion heat release as a function of temperature with different a values. (p.18) xi

14 Figure C.: Flame spread rate as a function of oxygen mole percentage at.atm and normal gravity. (p.181) Figure C.: Flame spread rate as a function of oxygen mole percentage at 1% O and lunar gravity. (p.18) Figure D.1: The sensitivity tests for flame spread rate. (p.188) Figure D.: The upward flame spread rate as a function of the correction factor (CF) for the Planck-mean absorption coefficient. The test condition is at 6-psia air and lunar gravity (.16g e ) over a 1-cm-wide sample. ( Kleinhenz s experiment, 6) (p.189) Figure D.: The contours of reaction rate (g/cm /s) (left half) and flame temperature (right half). (a) With flame radiation (b) Without flame radiation. (p.19) Figure D.: The comparison of flow velocity between with and without flame radiation at the centerline cross-sectional plane. (p.191) Figure E.1: Pressure extinction limit as a function of pressure reaction order for (a) adiabatic cases ( a = s -1 ) and (b) non-adiabatic case with surface radiation loss ( a = s -1 and 1 s -1 ). Ambient oxygen mass fraction Y oe =.. (p.1) Figure E.: Non-dimensional maximum flame temperature vs. pressure for (a) n=1. and (b) n=.. ( a = s -1 and Y oe =.) (p.1) Figure E.: Comparison of the oxygen limits as a function of stretch rate for different fuel-to-oxygen exponent ratios (n f /n o ) at an equal overall reaction order (n=n f +n o =). ( p =1 atm) (p.16) Figure E.: Limiting oxygen mass fraction as a function of stretch rate at different pressures for (a) n=1. and (b) n=.. (p.17) Figure E.: Schematics of a side-stabilized diffusion flame and its flame stabilization zone. (p.18) xii

15 Nomenclature Roman Symbols A s Solid phase pre-exponential factor (cm/s) B g, B g Bo C Gas phase pre-exponential factor (cm /g/s) Boltzmann number Planck-mean correction factor C R Specific heat ratio: c * p c s c p Nondimensional gas phase specific heat c s Nondimensional solid phase specific heat Da D i Damköhler number Diffusion coefficient for species i (cm /s) E E g Nondimensional activation energy Nondimensional gas phase activation energy E s Nondimensional solid phase activation energy f i Stoichiometric mass ratio of species i to fuel g Gravity at negative x-direction (cm/s ) G Incident radiation (W/cm ) h Nondimensional solid fuel thickness I Radiation intensity in a given direction (W/cm ) k Nondimensional gas thermal conductivity xiii

16 L l f l p Le i Nondimensional latent heat of solid Flame length (cm) Pyrolysis length (cm) Lewis number of species i L R Reference length (i.e. the thermal length) (cm) M i Molecular weight of species i m m ˆn p Nondmensional solid burning rate (g/cm /s) Surface normal vector Nondimensional pressure p Ambient pressure (atm) Pr Q Prandtl number Nondimensional energy source term or dimensional heat flux o Δ H R Nondimensional heat of combustion Δ H R Nondimentional combustion heat release q r Nondimensional radiative heat flux q c Convective heat flux from flame to solid (W/cm ) q + r Incident radiative heat flux to solid surface (W/cm ) q r Outgoing radiative heat flux form solid surface (W/cm ) q q q ) + q r Total radiative loss on solid surface ( r = r r q The net heat flux from flame to solid surface ( q net = q c q r ) net xiv

17 r Re R u Position vector Reynolds number Universal gas constant (8.1 kj/kmole/k) s ŝ T T Geometric path length Unit vector Nondimensional gas temperature Ambient temperature (K) T s Nondimensional solid temperature u U R Nondimensional velocity in the x-direction Reference velocity (is equal tou ) (cm/s) U, U v V f, V f w X i Inflow velocity (cm/s) Nondimensional velocity in the y-direction Flame spread rate (cm/s) Nondimensional velocity in the z-direction Molar fraction of species i Y i Molar fraction of species i X Dimensional x-coordinate (equivalent to x ), or molar fraction Y Dimensional y-coordinate (equivalent to y ) Z Dimensional z-coordinate (equivalent to z ) Greek Symbols α Solid absorptance or thermal diffusivity xv

18 * α ε Γ Reference thermal diffusivity (cm /s) Solid emittance Nondimensional solid parameter κ Nondimensional absorption coefficient ( C κ P LR ) κ p Planck mean absorption coefficient μ Ω ρ Nondimensional gas dynamic viscosity Radiation solid angle Density or surface reflectance ρ s Solid fuel density (g/cm ) ρ g Nondimensional gas density ρ Ambient gas density (g/cm ) * ρ g Gas phase density evaluated at * T (g/cm ) σ Stefan-Boltzmann constant ( W/cm /K ) τ ω F Solid fuel half-thickness (cm) Dimensional fuel vapor consuming rate (g/cm /s) ω i Nondimensional sink or source term of species i Subscripts diff Diffusive F, f Refers to fuel or flame i L Species i Refers to latent heat xvi

19 O, O Refers to oxygen ref g s spec w, wall x y z Refers to reference case Refers to gas Refers to solid wall Specular Refers to wall Refers to the x or x direction Refers to the y or y direction Refers to the z or z direction Refers to ambient property Superscripts * Evaluated at * T =1K (Overbar) Dimensional quantity. Refer to per unit time xvii

20 Acknowledgements I would like to thank my dear parents for fully supporting my graduate education in the United States of America and thank my lovely wife, Li-Ya, for keeping company with me through this journey. I am indebted to my advisor, Professor James S. T ien, for his careful guidance, meticulous instructions, limitless patience and sustained encouragements throughout the entire course of this work. I appreciate everything Professor T ien has done for me from the bottom of my heart. Thank you to Drs. Shih and Feier for their excellent works on -D flame spread codes. I am also grateful to my defense committee members for their important and valuable comments. Special thanks to Dr. Olson for sharing her knowledge and experimental results with me. Last but not least, I would like to express my appreciation to all of the colleagues I have worked with in Case Computational Combustion Lab., Dr. Feier, Dr. Han, Dr. Kumar, Dr. Raju, Kevin, Ya-Ting and Makoto, for their help and discussion. This work was supported by NASA Glenn Research Center with Dr. Gary Ruff as the grant monitor. xviii

21 Flame Spread and Extinction Over Solids in Buoyant and Forced Concurrent Flows: Model Computations and Comparison with Experiments Abstract by SHENG-YEN HSU A detailed three-dimensional model for steady flame spread over thin solids in concurrent flows is used to compare with existing experiments in both buoyant and forced flows. This work includes (1) several improvements in the quantitatively predictive capability of the model, () a sensitivity study of flame spread rate on input parameters, () introduction of flame radiation into the buoyant-flow computations and () quantitative comparisons with two sets of buoyant upward spread experiments using cellulosic samples and a comparison with forced downwind spread tests using wider cellulosic samples. In additional to sample width and thickness, the model computation and experimental comparison cover a substantial range of environmental parameters such as oxygen percentage, pressure, velocity and gravity that are of interest to the applications to space exploration. In the buoyant-flow comparison, the computed upward spread rates quite favorably agree with the experimental data. The computed extinction limits are somewhat wider than the experimental limits based on only one set of older test data (the only one available). Comparison of the flame thermal structure (also with this set of older data) shows that the computed flame is longer and there is structure difference in the flame xix

22 base zone. This is attributed to the sample cracking phenomenon near the fuel burnout, a mechanism not treated in the model. Comparison in forced concurrent flows shows that the predicted spread rates are lower than the experimental ones if the flames are short but higher than the experimental ones if the flames are long. It is believed that the experimental flames may have not fully reached the steady states at the end of -second drop. The effect of gas-phase kinetic rate on concurrent flame spread rates is investigated through the variation of the pre-exponential factor. It is found that flames in forced flow are less sensitive to the change of kinetics than flames in buoyant flow; and narrow samples are more sensitive to the change of kinetics compared with wide samples. The rate of chemical kinetics affects the flame spread rates primarily through two mechanisms: the amount of un-burnt fuel vapors escaping the reaction zone and the induced velocity variation through flame temperature change in the case of the buoyant flames. xx

23 Chapter 1 Introduction and Motivation 1.1 Flame spread over solid fuels Flame spread over solids is a classical problem in combustion science and fire safety. Generally, it involves a diffusion flame over a solid fuel and complex interactions between the gas-phase flame and the solid fuel. The solid diffusion flames can either be stationary or spreading. A flame occurs because a part of the solid fuel is ignited. For the flame to advance, a forward heat transfer mechanism has to exist. The advancing flame front is established when the vaporized fuel produced by the forward heat transfer process and the ambient oxidizer form a flammable mixture at the pyrolysis front. This is a self-sustained process requiring proper coupling of heat and mass transfer mechanisms and chemical reactions. The spreading flames can be classified into two broad types according to the heat transfer mechanisms, see Fig Depending on the relative directions between the ambient oxidizer flow and the flame spread, it is divided into opposed flow where the spread direction is opposed to the oxidizer flow direction and concurrent flow where the spread direction is the same as the oxidizer flow direction. In this study, the focus is on concurrent-flow spreading flames. Since the ambient flow can be generated either by buoyancy or by wind, a distinction is made by classifying the flow types as forced flow (external source) and buoyant flow (gravity or body force). We will treat both forced and buoyant flows in this work. 1

24 The thickness of the solid fuel affects the heat-up rate of the solid and the type of solid heat transfer analysis needed in the model. Classically, a distinction of thermallythin and thermally-thick were used (de Ris, 1969). A solid is thermally thin if the heat conduction time across the sample thickness is much smaller than the solid heat-up time in the pre-heat zone. In such a case, the solid temperature is approximately uniform perpendicular to the surface. Also, when the solid sample is sufficiently thin, heat conduction in the direction parallel to the surface can be ignored. These approximations simplify the treatment of the solid and are adopted in this work. In addition, we assume that the sample thickness is much smaller than the flame standoff distance. So, even when the solid thickness is varying during combustion, the solid boundary conditions are always applied at the same location. This aerodynamically-thin approximation is similar to the mean-surface approximation used in thin airfoil theory (Shapiro, 19). A concurrent flame can spread in a steady or in an unsteady growing state. In a growing flame, the flame or pyrolysis length increases with time and the pyrolysis front moves in a non-constant rate. In steady spread, the solid achieves burnout and the burnout rate is the same as the rate of motion of the pyrolysis front so that the flame length and the spread rate are constants. Steady spread is most easily achieved for thin solids, narrow samples and in low speed flows. The limiting flame is relatively short and laminar. We will concentrate our present effort on steady flame spread in concurrent flows. Fire safety in spacecraft and space habitats introduces different constraints and conditions from those on earth environment (Ruff and Urban, 7). In a spacecraft, the gravity level can be nearly zero (microgravity) but the ventilated air can produce a low-

25 speed forced flow. To reduce weight plus other considerations, the atmosphere for future aircraft may be at low pressure but enriched oxygen (Ruff and Urban, 7). A space habitat on the Moon or Mars clearly has a gravity level less than that on earth. To understand flame spread for these applications, we will need to know the effects of the low-speed purely forced and the partial-gravity induced buoyant flows in the atmospheres with different pressures and oxygen percentages. Experiments to test solid material flammability characteristics in these unusual environments are difficult to perform. The difficulties include cost, opportunity, test duration and test facilities. For example, there are few experimental results on partial gravity solid-fuel flames because achieving partial gravity in a ground-based facility is not easy. The results that exist are limited to short-duration tests. One way to alleviate this situation is through modeling. If a good numerical model can be established, we may be able to use it to connect the material flammability performance in space environments to that on earth, which can be obtained more readily. Over the years, the group at Case Western Reserve University has been working on a numerical model for flame spread in concurrent flows that can also analyze the extinction limits. Although still limited in scope (e.g. steady spread over thin solids), the model has achieved enough sophistication that a detailed comparison with existing experimental data is possible. The purpose of the present effort is to (1) implement a number of enhancements on the model to improve the predictive capability and () make detailed comparisons with key experiments to assess the model capability and limitations. Since comparison with experiments is the main objective of this study, these relevant experiments will be reviewed next.

26 1. Overview of selected experimental works on concurrent-flow flame spread over solids In this section, several selected experiments will be reviewed. All employ thin cellulosic solids as fuel. The experiments cover a variety of conditions so that they can be served as tests for the model capability Flame spread in buoyant flow Chu (1978) investigated the upward flame spread over narrow paper samples in normal gravity. The experiments were carried out in a large environmental chamber (total volume cm ) as shown schematically in Fig. 1.(a).The dimensions of the metal chamber are 61.cm.cm.6cm and the glass bell jar at the top is 61.cm long with inner diameter of.cm. The buoyant upward flames would not affected by the boundaries of the chamber. The chamber could be evacuated by a vacuum pump and loaded with desired oxygen/nitrogen mixtures from gas bottles, so the pressure and oxygen percentage could be varied as parameters in his experiment. Several paper samples of different thicknesses were tested. The fuel samples were attached by two aluminum holder plates, shown in Fig. 1.(b), which separated with narrow distances to create small scale flames. Steady flame spreads with limiting flame lengths and pyrolysis lengths were observed. The physical description of his observation on flame spread over papers is shown in Fig. 1.. The burnout shapes were zigzag and unburnt fuel residues were left near sample holders. The tests were conducted at ambient pressure from 1atm to extinction and oxygen percentage from 1% to extinction. The sample width effect was

27 tested between cm and the edge quenching limit. One-centimeter-wide samples were used in majority of his tests. In addition to spread rate and extinction limit data, Chu performed a series of detailed temperature measurement of the flame for one upward spreading case. In a given test, the thermocouple is placed at a given distance from the fuel surface. The temperature vs. time record is then translated into a temperature vs. distance record since the steady spread rate is also measured. By repeating a number of tests with the thermocouple placed at different distances from the fuel surface, a complete thermal structure of the flame along the centerline is obtained. This pain-staking procedure is needed because placing a thermocouple rack will quench the small flame. Chu also conducted several opposed flame tests. Since his experimental results will be used to compare with model prediction, they will be discussed later. To explore the space application, Feier (1), Feier et al. () and Kleinhenz et al. (8) experimentally studied the effects of pressure, gravity and sample width on upward flame spread over a thin cellulosic fuel (Kimwipes ). The experimental setup is shown in Fig. 1.. The dimensions of the chamber are cm in diameter and cm high. Although fuel samples of 1-cm, -cm, and -cm wide were tested, most data belong to the 1-cm wide sample. The samples were attached to the metal plates and were burned in air at pressures between.1 and.8 atm in partial gravity environments of.1g e,.16g e (Lunar), and.8g e (Martian) (g e is the normal gravity) on the NASA KC-1 aircraft flying a designed trajectory. They observed flame propagation speeds and pyrolysis lengths are approximately proportional to the gravity level. They also discussed the steadiness of the spread rates and narrow band infrared emission from the fuel surface.

28 In order to examine the idea of pressure-gravity modeling for upward spreading flames, Kleinhenz et al. (8) acquired more data on 1-cm wide Kimwipes at partial and normal gravities using the same experimental setup. They found that the spread rate data can be correlated with p 1.8 g. This is close to the Grashof number dependence on pressure and gravity, which yields a p g correlation. Photographic images of the flames at different pressure and gravity will be shown later in the comparison with model results. Other similar upward steady spread experiments have been carried out by Honda and Ronney () and Honda (1) in normal gravity using a larger chamber and covered a bigger pressure range. The pressure vessel is meter tall with cm in diameter. Similar to Chu s experiment, the solid fuel samples were held by two metal plates. They conducted tests for Kimwipes of wider widths up to about 8. cm at pressure between.atm and atm. The ambient oxidizers are between 1% and % diluted by He, N, SF 6, and CO. Using flow mixing and radiative loss as the mechanisms for reaching the limiting lengths in narrow and wide samples, the authors provided a spread rate correlation with pressure, oxygen percentage, flow velocity, gravity, diluents and sample width as parameters. This may be an attempt of too much ambition as the data have wide scatter around the correlating curve. It has also been discovered recently that in addition to the steady and growing (or decaying) spreads, a cyclic upward propagation can exist. Using Nomex fabric as the test sample fuel in enriched oxygen atmosphere in normal gravity, Kleinhenz and T ien (7) found that the upward spreading flame can break off into two flames and the secondary flame at downstream extinguishes but the upstream flame will grow over the partially pyrolyzed solid. When the flame reaches a limiting length, the flame again 6

29 breaks into two and the downstream flame extinguishes and cycle repeats. The authors attributed this cyclic phenomenon to the two pyrolysis temperatures of the Nomex fabric. 1.. Flame spread in forced flow To study flame spread in purely forced flow, a microgravity environment is needed. This is especially so if we are interested in flames in low-speed forced flows. There are several ways to reach microgravity condition, each with different microgravity duration: drop towers (-1 seconds), sounding rockets (minutes), shuttle (days), and Space Station (weeks or months). Although aircraft have also been used in a number of reduced gravity experiments or personnel trainings, their g-jitter level is too high to generate acceptable low-speed forced flows near a flame. Despite the existence of the rocket, shuttle and space station, the forced-concurrent-flow flame spreading data are all obtained from short-duration drop-tower facility because of the limitations of expense and opportunity. Grayson (1991) and Grayson et al. (199) studied low-speed concurrent-flow flames over a thin solid cellulosic sample (Kimwipes ) in the Zero Gravity.18 second drop tower at NASA Glenn. They studied the oxygen concentration between 1% and % at forced flow velocities from. to. cm/s. The forced velocity was obtained by translating the fuel sample through a quiescent chamber using a device originally designed by Foutch (1987). Because of the orientation of the translation device and the chamber diameter, not all the -second microgravity duration can be utilized at top velocity of cm/s. To improve this limitation, Pettegrew (199) re-designed a different 7

30 sample translation device to investigated ignition and flame growth over cellulosic paper fuels. The controlled relative flow velocities were increased to 1 cm/s. The oxygen concentration in Pettegrew s tests was fixed at 18% O. More recently, Olson and Miller (8) experimentally investigated the concurrent forced-flow flame spread in.18-second drop tower at NASA Glenn using a flow tunnel that can provide a much higher flow speed. The Kimwipes samples of -cm wide were burned in the combustion tunnel rig of diameter cm. The sample holder is cm wide and over cm long, extending 1.7cm upstream of the sample (Fig. 1.(a)). Fig. 1. shows the sample card and the sample mounting. In the tests, the forced flow velocity, the pressure and the oxygen percentage can be independently varied. The ranges covered are: velocity from -cm/s, pressure from.6-1.7psia (.-1.atm) and oxygen percentage from -8%. Fig. 1.(b) shows the images of concurrent flame for a case at cm/s, %O, 6.psia. The side-view image shows the significance of soot illuminating layer in the fuel-rich region. An interesting phenomenon was observed at intermediate values of concurrent forced flow velocity where flow/flame interactions produced a recirculation downstream of the flame, which allowed an opposed flow leading edge to form there. The experimental data chosen to be compared with model predictions are from Kleinhenz et al. (8) and Chu (1978) for buoyant flows and Olson and Miller (8) for forced flows. 1. Overview of the model development at Case Western Reserve University 8

31 In this section, the development of a detailed numerical model for concurrentflow flame spread over solids at Case will be reviewed. This review will serve as the background of the present modeling effort. Needed improvements to be implemented in the present work will also be mentioned. Models developed elsewhere will be briefly reviewed in a separate section. Ferkul (199) and Ferkul and T ien (199) formulated and solved the first concurrent-flow flame model at Case. The model is two-dimensional, steady-state and laminar using a mixed elliptic-parabolic formulation. Full Navier-Stokes elliptic solution is employed in the stabilization zone near the upstream solid burnout and a coupled parabolic solution is used downstream. The purpose of the mixed formulation is to save computational time. A one-step, second-order finite-rate Arrhenius reaction was assumed to model fuel vapor and oxygen reaction in the gas phase. A thermally and aerodynamically thin solid is assumed and heat conduction in the solid along the surface direction is ignored. The solid fuel is assumed to undergo a zeroth-order pyrolysis reaction so that burnout of the solid can occur in a finite time or finite distance. Solid radiation loss was considered and the solid emissivity and absorptivity were assumed constant over the entire solid surface. Since only the steady state solution is sought, the origin of the coordinate system is placed at the solid burnout point with a steady flame spread and the burnout rate is solved iteratively as the eigenvalue. This is the first time that a concurrent-flow flame spread model using an elliptic formulation. This formulation makes it possible to analyze extinction limits. Previous models have utilized boundary layer approximation (parabolic equations) that can not address the extinction question. 9

32 Ferkul applied this formulation to purely low-speed forced flows. Among the many solved results, it is noted that he identified the existence of the low-speed quenching limits due to the surface radiation loss and the existence of a fundamental low oxygen limit. He also showed that the flame spread rate is approximately proportional to the flow velocity. Several subsequent efforts improved and expanded Ferkul s model formulation although a number of the key elements stayed unchanged. Jiang (199) applied an elliptic formulation (Navier-Stokes equations) to the entire flame zone in the above concurrent two-dimensional model and introduced gasphase radiation. It turns out that the computational cost only increases modestly by the use of un-even expanded grids in this fully elliptic formulation but also makes the management of data and the treatment of gas radiation much easier. Jiang solved the radiation transfer equation using the S-N discrete ordinates method assuming a gray absorbing, emitting and nonscattering media. The radiation participating species consist of CO and H O only. He used the Planck-mean absorption coefficient of the CO and H O mixture as the absorption coefficient in the radiation transfer equation. The solution of the radiation transfer equation using the discrete ordinates method resolve the radiation flux distribution in the flame. Thus, both radiative heat loss and radiative heat feedback to the solid are accounted for. Jiang (199) found that gas radiation becomes increasingly important as forced-flow speed decreases; it plays an important role in the determination of the low-speed quenching limits. In a later paper, Jiang et al. (1996) applied the same model to two-dimensional upward spread over a thin solid. They found that two-dimensional steady spread (infinitely wide sample) can only be achieved when the gravity level is sufficiently low (<.1 g e ). 1

33 Shih () formulated and solved a three-dimensional flame spread model for thin cellulosic fuels of finite width but without including gas-phase radiation. He simulated forced-flow flame spread in microgravity in a flow tunnel and found many flame spread characteristics that could not be simulated by a two-dimensional model. He studied the effects of solid sample width, oxygen fraction, inflow velocity, sample holder strips and the condition of tunnel walls. Later, Feier et al. () simulated limited cases of buoyant-flow flame spread in a quiescent environment and suggested that the gasphase radiation should be included in the model for better agreement with the experiments. Feier (7) implemented a three-dimensional discrete ordinates gas-phase radiation code written by Dr. Bedir into Shih s three-dimensional forced-flow model in a flow tunnel. He performed coupled -D computations using a weighting factor as the free parameter to analyze the contribution of flame radiation. He found that the flame radiation in the three-dimensional model is more significant than in the two-dimensional model. However, he did not compare his numerical predictions with experiments, so the reliability of his -D model is unclear. Over the course of quantifying the contribution of radiation in flames, two issues came up. The first has to do with the use of Planck-mean absorption coefficient to estimate flame radiation and the second has to do with the proper value of emissivity or emittance that should be used for the thin solid fuel. Planck mean is the proper absorption coefficient at the optically thin limit. Our flames, in spite of only several-centimeter thick at most, are highly spectral with CO and 11

34 H O as the radiating species. Because of the self-spectral-absorption, these flames are not optically thin (nor are they optically thick). This was demonstrated by Bedir et al. (1997) in a systematic study comparing narrow-band, broad-band, gray-gas and optically-thin models in a one-dimensional flame. Since solving spectral radiation transfer equation in multi-dimensional flame spreading problem is not yet practical computationally, Rhatigan et al. (1998) proposed to use the gray-gas equation but with a correction factor in front of the Planck-mean coefficient. The value of this correction factor varies in the flame and has to be determined iteratively in the computation. This procedure has been applied to two-dimensional problems but a proper procedure has not been worked out in three-dimensional problem. In the present work a constant value for the correction factor is assigned to the three-dimensional flame spreading model. The second issue is on the value of radiation properties of the solid fuel. In all the previous works, an emissivity equal to.9 has been assigned to the solid fuel and this value is not changed in the pyrolysis zone. This value of.9 is taken from standard reference for sufficiently thick paper at room temperature. For many of the thin cellulosic samples (e.g. Kimwipes ) used in the microgravity experiments, the sample thickness is too thin and the solid emittance is less than.9. Note that we begin to use the word emittance rather than surface emissivity since the radiation emitted from the thin solid depends on the sample thickness, i.e. the volume of the solid (Siegel and Howell, ). So, surface emissivity can be a valid approximation only when the solid thickness is greater than the optical thickness. During pyrolysis, the solid fuel thickness or area density decreases. Therefore, the emittance should vary. In addition, there can be temperature dependence in the emittance. To resolve this issue, Pettegrew (6) 1

35 performed FTIR experiments on Kimwipes with different degree of burn in an integrated sphere and measured the sample s spectral absorptivity. By performing enough tests, he found that the absorptivity depends only on area density and temperature and is independent of the way the area density is achieved. Using Kirchoff s law, the solid spectral emittance is obtained. The wave length integrated mean solid emittance as a function of Kimwipes area density and temperature as listed in Appendix B. This realistic data will be implemented in our model computation. As will be seen in our sensitivity analysis (Appendix D), the flame spread rate is most sensitive to the solid emittance. Because the measured solid (Kimwipes ) absorptance is spectral in nature and the flame radiation from CO and H O is also spectral in nature, the mean absorptance of the solid from the flame radiation is not necessarily the same as the mean emittance. Pettegrew simulated flame spectra at a typical temperature to evaluate the mean Kimwipes absorptance and found it is about one half of that of the mean emittance. This value will be assumed in the model computation in this work. We note that this is just an approximation, but it will also be shown that solid absorption is not a very sensitive parameter in the computation (Appendix D). The second information from Pettegrew s experiment (6) is regarding the Kimwipes pyrolysis reaction rate constants (Appendix A). The data were collected since he needed to prepare partially pyrolyzed samples in a high temperature oven. He found that his data fit the zeroth order reaction well but the values of the activation energy and the pre-exponential factor are sufficiently different from those used in the 1

36 previous models (e.g. Ferkul, 199). This new set of data will be implemented in the present work to facilitate the comparison with experiments. One additional improvement needed for the model has to do with its application to the high oxygen environment. In the present model, the combustion products are CO and H O. In high oxygen environment, dissociation will occur and effectively reduce the enhancement of flame temperature. Since we do not know the detailed gas-phase reaction kinetics of the fuel vapors, the formation of intermediate and dissociated products will be avoided in our model. To account for the decrease of flame temperature, a procedure that effectively decreases the combustion heat release will be introduced (Appendix C). 1. Other similar models In this section, several flame spread models from other groups are described. The models are unsteady or having a quasi-steady gas phase, which were used to primarily investigate the transient phenomenon from ignition. Jiang and Fan (199) developed a three-dimensional unsteady flame spread model. Their gas-phase model included full Navier-Stokes equations and a six-flux radiation model. The combustion kinetics was simulated by a finite-rate single-step Arrhenius reaction between fuel and oxygen. The solid fuel model considered the heat conduction and the pyrolysis rate was modeled by a first-order Arrhenius relation. They predicted the flame spread process over cellulosic sheets from ignition in both forced flow (1 cm/s) and quiescent environments with gravitational acceleration ( g/ge) perpendicular and parallel to the fuel surface. For the case with gravity normal to the fuel, their 1

37 numerical simulations showed that the upstream flame spreading was faster than the downstream flame after a period of ignition. As the gravity was parallel to the fuel surface the flame spread was strikingly affected by the microgravity level. It should be noted that because of the large grid size used, the flame stabilization zone is unlikely to be modeled accurately. Di Blasi (1998) investigated the dynamics of concurrent flame spread over a thin charring solid in microgravity by using a two-dimensional, quasi-steady model (steady gas model and unsteady solid model). Her gas phase model was based on the laminar, reactive Navier-Stokes equations coupled with solid-phase enthalpy and mass conservation equations. The combustion kinetics was simulated by one-step finite-rate Arrhenius relation. No flame radiation was considered and black-body surface radiation loss was assumed. The simulations were made for forced flow velocities between.- 1cm/s, by decreasing the oxygen mass fraction below ambient value and by increasing the solid charring rate. Flame transition, flame quenching and blow-off were observed. McGrattan et al. (1996) developed a two-dimensional, time-dependent model to describe ignition and the subsequent transition to flame spread in microgravity. Their transient Navier-Stokes models included solid surface radiation loss with a constant emissivity, but no gas-phase flame radiation. The gas-phase oxidation reaction was simulated by a global one-step reaction between fuel and oxygen. The pyrolysis characteristic of the cellulosic sheet was modeled by two global thermal degradation reactions and a char oxidation reaction. The authors simulated a cellulosic sheet ignited in the central region with a slow, imposed wind. They found that the upstream opposed flame is stronger and faster with a greater supply of oxygen. However, the downstream 1

38 concurrent flame dies out due to oxygen shadow caused by the upstream flame. They also concluded that the ignition time and the transition time to steady flame spread respectively mainly depend on the peak flux of external radiation and the broadness of the efflux distribution. Kashiwagi et al. (1996) extended the two-dimensional model of McGrattan et al. (1996) to a three-dimensional model. The three-dimensional, timedependent model included carefully measured solid-phase kinetic constants, but the gasphase reaction constants, which the ignition and transition of flame spread is sensitive to, were properly chosen to produce results in rough agreement with observed phenomena. As comparing their resulting char patterns with experiments, the -D transient model captured the qualitative features of the effect of wind from ignition. Mell and Kashiwagi (1998, ) studied the dimensional effects on the transition of flame spread from ignition in an imposed wind in microgravity by using the above two-dimensional and three-dimensional models. In 1998, they studied the effect of imposed forced velocity on the flames and compared the -D and -D transient flames. They found significant oxygen diffusion from the sides for the -D flame and an enhancement of -D quenching limits as compared to the -D case. In the study, Mell and Kashiwagi modeled a setup very similar to Shih () and Feier (7): a thin cellulosic solid mounted between the edges of a steel or paper sample holder. They studied the effects of the sample width on the flame transition from ignition to steadystate spread. The heat loss effects at the interface of sample and sample holder were also tested by varying thermal-physical properties of the sample holder. 16

39 There is also a recent work on simulating upward flame spread over PMMA (polymethyl-methacrylate) at various gravities by Nishiki et al. They presented it as a poster in nd International Symposium (8) on Combustion. 1. Motivation and organization of the dissertation The motivation of this dissertation is to improve and assess the capability of a three-dimensional flame spread and extinction model that is intended to be used as a tool to evaluate material flammability for space application. One key element of a useful tool is to be able to relate the fire performance of materials in normal gravity to that in microgravity and partial gravity. In addition to introducing a number of enhancements to the model to improve its predictive capability, we will make detailed comparisons with key experiments to assess the model capability and limitations in both forced and buoyant flows. The organizations of the dissertation are as follows: Chapter 1: Introduction Chapter : Presentation of the numerical model Chapter : Comparison between model and experiment in buoyant flows. Two sets of experiments are chosen (a) Kleinhenz et al. (8) with pressure and gravity as parameters and (b) Chu (1978) with pressure and oxygen percentage as parameters. Chapter : Comparison between model and experiment in forced flows. The set of experiments are from Olson and Miller (8) with velocity, pressure and oxygen percentage as parameters. 17

40 Chapter : A study on the sensitivity of the gas-phase combustion kinetic rate in concurrent-buoyant-flow and concurrent-forced-flow flame spreads is presented. Chapter 6: Conclusion and discussion. Various appendices cover sensitivity study of material properties, radiation properties, pyrolysis rate constants, solid radiation data and an analysis of the effect of reaction order on pressure extinction limits. 18

41 19 Figure 1.1: The classification of the types of flame spreads from Feier ().

42 (a) (b) Figure 1.: (a) Schematic of combustion chamber system and (b) Sample holding plates used in the experiment by Chu (1978).

43 (a) (b) Figure 1.: Physical description of an upward spreading flame over a thin paper at p=.atm, X O =%. (a) Side view. (b) Front view. (Chu, 1978) 1

44 Chamber lid Fuel sample holder ( Sample card ) Fuel sample Port for filling and evacuating the chamber Infrared camera Front window Side window Side view camera Front View camera Z Y Hot wire igniter X Chamber light Pressure transducer Accelerometer assembly Figure 1.: Experimental setup for investigating flame spread in partial gravity. (Feier et al., and Kleinhenz et al., 8)

45 cm Sample Holder 7.cm cm 1cm ~cm 1.7cm Forced flow (a) gap Front view Side view (b) Figure 1.: (a) Sample holder configuration. (b) Images of concurrent flame spread over -cm-wide Kimwipes at cm/s,. atm (6. psia), %O. (Olson and Miller, 8)

46 Chapter Theoretical and Numerical Formulations The numerical model is for a three-dimensional, steady and laminar concurrentflow flame spread in purely forced, purely buoyant or mixed flows. In addition to the Navier-Stokes conservation equations, gas radiation heat transfer equation is included. They are coupled with the conservation equations in the thin solid fuel. The coordinate system moves with the flame. Iteration is needed to find the steady-state solution..1 Theoretical model The governing equations and boundary conditions for the steady three-dimensional concurrent-flow spreading flames will be presented. Many of the equations are similar to the ones used in previous works (Shih, ; Feier, 7). They are presented here for completeness. The new features adopted in this work will be pointed out in due course. Variables with an overhead bar,, are dimensional, and without bar are nondimensional. The governing equations are nondimensionalized based on the thermal length in the upstream flame stabilization zone, L R * = α UR. The reference velocities, UR = for forced flow and = ( ) U R 1 * * F for buoyant flow, are used as U g ρ ρ α ρ the reference velocities. The thermal length defined this way characterizes the size of the upstream flame stabilization zone. This is a small region in concurrent flow especially at higher speeds. But it is crucial in determining flame extinction and stabilization characteristics. Since part of the present work is to study the extinction conditions, the

47 structure in this zone needs to be resolved. We should note that there are other relevant length scales in concurrent flame spread. For example, the pyrolysis length or flame length are larger scales and they will be discussed when we present the computed results. The thermal and transport properties used in the above expressions are evaluated at the reference temperature T * =1K. In the following, temperature is nondimensionalized by the ambient temperature T (K) and the nondimensional pressure is given by * ( ) ρ p = p p U R..1.1 Gas phase model The gas phase model includes three-dimensional, steady, laminar, full Navier- Stokes equations for the conservation of mass, momentum, energy, and species. The species equations are for fuel vapor, oxygen, carbon dioxide and water vapor. A one-step, finite-rate Arrhenius reaction between fuel vapor and oxygen of second order is assumed. Continuity: ( ρu) ( ρv) ( ρw) + + = x y z (.1) X-direction momentum: u u u p 1 u u v w ρu + ρv + ρw = + μ + + x y z x Re x x x y z. (.) 1 u v u w ( ρ - ρ) + μ + + μ Gr * Re y y x z + + z x ( ρ - ρ )

48 where * g( ρ - ρ ) LR Gr = and * * ρν ρ U L =. μ * R R Re * Y-direction momentum: v v v p 1 v u v w ρu + ρv + ρw = + μ + + x y z y Re y y x y z 1 u v v w + μ + + μ + Re x y x z z y. (.) Z-direction momentum: w w w p 1 w u v w ρu + ρv + ρw = + μ + + x y z z Re z z x y z. (.) 1 u w v w + μ μ Re x z x y z y Species: Yi Yi Yi 1 Yi Yi Yi ρu ρv ρw + + = ρdi + ρdi + ρdi + ωi. (.) x y z Lei x x y y z z where the species i = F, O, CO and HO, and the reaction is modeled by the one-step second-order finite-rate Arrhenius reaction: E ω = f ( Da) ρ Y Y T i i g F O exp g, (.6) where Da, the Damköhler number, is proportional to the ratio of the flow time to the chemical reaction time within one thermal length in the stabilization zone: Da αρ B * * = LR UR g g * * ρg ρg B = g U. (.7) R 6

49 The stoichiometric oxygen and cellulose combustion reaction is assumed to be: 1 X O 1 X O CH 6 1O + 6 O + N 6CO + HO + 6 N. (.8) X O X O Therefore, the stoichiometric mass ratios ( f i ) between species i and fuel vapor are f F = 1, f O = 1.18, f CO = and f HO =.6. Energy: T T T k T k T k T ρu + ρv + ρw = + + x y z x cp x y cp y z cp z k cp T cp T cp T ρdc i pi Yi T Yi T Yi T cp x x y y z z i Lec + + i p x x y y z z. (.9) Q qr + c c Bo p p The source term from the chemical reaction is: Q=Δ H ω, (.1) R F where Δ H R is the sum of the heat of combustion and the enthalpy change due to variable specific heats: with T R R T = 1 p Δ H =Δ H + Δc dt (.11) Δ c = fc. (.1) p i pi i However, the above combustion heat release applied in the one-step overall forward reaction usually over predicts the flame temperature, especially for the cases at high oxygen environments (due to products dissociation). To compensate for this deficiency, 7

50 the combustion heat release is adjusted to account for products dissociation by modifying the enthalpy change (Appendix C). The purpose is not to resolve the correct amount of dissociated species but to obtain a more reasonable flame temperature. The Boltzmann number (Bo) indicates the importance of convective versus radiative heat fluxes: ρ c U Bo =. (.1) * * g p R σt To specify the boundary conditions, the experimental configurations to be simulated need to be given. Fig..1 and Fig.. respectively show the configurations for the buoyant-flow and the forced-flow cases. The buoyant-flow experiments were conducted in large chambers where the chamber walls were expected to have negligible influence on the flame behavior. Correspondingly, in the numerical simulation, an unbounded domain is assumed and the ambient boundary conditions are specified at sufficient distances away from the solid sample. On the other hand, the forced-flow experiment was carried out in a more confined flow tunnel so the boundary conditions will be specified according to the exact dimensions of the setup. One more comment that needs to be made here is related to the coordinate system. Following previous formulations (e.g. Ferkul, 199), the origin of the coordinates system is located at the fuel burnout point on the solid surface. Thus it is a moving system with respect to the laboratory system. Using this coordinate, a flame spreading at a steady rate ( V f ) can be treated using the steady equations. The steady spread rate is an eigenvalue in this formulation which is determined iteratively in the numerical scheme. 8

51 Referring to Fig..1, the boundary conditions for the buoyant flow case are: At x = x (upstream boundary), in u V U F =, R T Y v =, w =, =, i = x x ( i F, O, CO, H O) =. At x = x (downstream boundary), out u v w T Y =, =, =, =, i = x x x x x ( i F, O, CO, H O) =. At z = z (side boundary), side u V U F =, R w v =, =, z Yi If w<, T = 1, YO = Y,,, O, = i = F CO H O z T Yi If w>, =, = ( i = F, O, CO, HO) z z ( ). At y = y (top boundary), top u V v = F =, U R y, w =, Yi If v<, T = 1, YO = Y, (,, ) O, = i= F CO H O y. T Yi If v>, =, = ( i= F, O, CO, HO) y y 9

52 Note that, through numerical tests, the distances of the upstream, downstream, top and side boundaries are chosen to be large enough so that the flame solutions are not affected by the domain size. At z = (centerline symmetry plane), u v T Y =, =, w =, =, i = z z z z ( i F, O, CO, H O) =. At y = (symmetry plane on the solid fuel surface), u V U = F R, v vw ρdf YF =, w =, T = Ts, my Fw, = m + Le F y, w my iw, ρd Y ( i O, CO, H O) i i = Le i y w =. The blowing velocity v w, the fuel vapor mass flux m, and solid temperature T s are determined as a function of x and z from the coupled equations of the gas and solid phases. At y = (symmetry plane on the inert strip plates), Y u = VF UR, v =, w =, T = Ts, i = y ( i F, O, CO, H O) =. At y = (symmetry plane on the gap and upstream of the solid burnout), u w T Y =, v =, =, =, i = y y y y ( i F, O, CO, H O) =.

53 conditions are: Referring to Fig.. for the forced-flow flame spread in a tunnel, the boundary At x = x (upstream inlet), in u V U F = 1, R v =, w =, T = 1, Y = Y, i O O, Y = ( i F, CO, H O) =. At x = x (downstream tunnel exit), out u v w T Y =, =, =, =, i = x x x x x ( i F, O, CO, H O) =. At z = (centerline symmetry plane), u v T Y =, =, w =, =, i = z z z z ( i = F, O, CO, H O) At z = z (side wall), wall u V U F =, R Y v =, w =, T = 1, i = z ( i F, O, CO, H O) =. At y = y (top wall), wall u V U F =, R Y v =, w =, T = 1, i = y ( i F, O, CO, H O) =. 1

54 At y = (symmetry plane on the solid fuel), u V U = F R, v vw ρdf YF =, w =, T = Ts, my Fw, = m + Le F y, w my iw, ρd Y ( i O, CO, H O) i i = Le i y w =. At y = (symmetry plane on the metal plates), u V U F =, R Y v =, w =, T = Ts, i = y ( i F, O, CO, H O) =. At y = (symmetry plane on the gap between the burnout and plates), u w T Y =, v =, =, =, i = y y y y ( i F, O, CO, H O) =..1. Solid phase model In the three dimensional experiments, inner strip plates were used at the edges of solid fuel as sample holders, as shown in Figs. 1.(b), 1. and 1.(a). The area thermal inertia ( ρs h cs ) of the inert plates is assumed to be a thousand times that of the solid fuel in the model. Therefore, the temperature of the plates essentially stays at the ambient value during the passage of the spreading flames. The solid fuel is assumed to be 1% cellulosic fuel, i.e. Kimwipes (C 6 H 1 O ), and the solid can burn out completely with no residue. The solid fuel is assumed to be both thermally and aerodynamically thin in the model. The solid mass conservation is given by:

55 dh m = ρ. (.1) svf dx The density of solid fuel is assumed constant, but the thickness is allowed to change during pyrolysis. The fuel surface mass flux is assumed to follow a zeroth-order pyrolysis relation (Ferkul, 199): Asρ s E s m= exp v * = ρ ρgur Ts w, (.1) with a zeroth-order pyrolysis relation, a complete burnout of the fuel is possible. The blowing velocity, v w, the gas density at the surface and the fuel mass burning rate are to be solved together. Combining the above equations (Eq. (.1) and (.1)) with the conservation of mass for the solid fuel gives: dh A s E s = exp. (.16) dx V f Ts Since the solid fuel is thermally thin (no temperature gradient perpendicular to the solid surface), the energy equation for the solid is: ( ) r w s qc + q +Γ d ht =Γ dh ( 1 CR) TL + ( L) + CRTs Bo dx dx, (.17) ρscv s f where Γ=, * * ρ cu g p R C R * cp =, c s L L =. ct s The conductive heat flux is given by q c dt = k and the net radiative flux q r comes dy w w from the computation of the radiative heat transfer equation to be presented later. The last term on the left side of the energy equation is the heat-up term of the bulk solid. The right

56 side of the equation expresses the energy change due to the latent heat of vaporization. The fuel latent heat L is evaluated at T L = K. These solid equations are coupled with the ones in the gas phase via the boundary conditions at the fuel surface. The boundary conditions for the solid fuel are: At the downstream edge (x = x out ), dt s dx =, τ h =. LR.1. Radiation model The three-dimensional concurrent flame spread model coupled with gas-phase radiation was developed by Feier (7). The three-dimensional radiation model, originated from Bedir s research efforts (1998), was an extension of Jiang s twodimensional S-N discrete ordinates radiation model (Jiang, 199). The model here assumes emitting and absorbing gray media with no scattering, and the radiative transfer equations are solved by the S-N discrete ordinates method. A complete description of radiative transfer equation and the S-N discrete ordinates method can be found in several texts (Modest, 199; Siegel and Howell, for example). But a brief outline will be presented here using the notation from Modest (199). The presentation also enables us to point out the parts of unique radiation treatment used in this work.

57 The gas medium is assumed to be radiatively absorbing, emitting, but nonscattering. The radiative participating gases are carbon dioxide and water vapor. The equation of radiative heat transfer is: di ds (, ) ( ) (, ) (, ) = sˆ I r sˆ = κ r I ˆ ˆ b r s I r s, (.18) where I is the radiation intensity, s is the geometric path length, ŝ is a unit vector into a given direction, r is the position vector, κ is the dimensional absorption coefficient, and I b is the blackbody intensity. Note that in Eq. (.18), the radiation intensity is wavelength-averaged. The possible spectral effect will be discussed when one select the gas mean absorption coefficient and the solid fuel radiation properties. The boundary condition for an opaque, diffusely emitting and diffusely reflecting solid surface is: ( ) ε ( ) ( ) ( r ) ρ I r, sˆ = r I r + I ( r, sˆ ) nˆ sˆ dω + ρ r I r, sˆ ( ) ( ) diff w ' ' w w b w w spec w w s π ' nˆi sˆ < (.19) with ε as the surface emissivity, ρ is the reflectivity, ˆn is the unit surface normal vector pointing away from the surface and into the gas medium, ŝ ' is the unit vector from any incoming direction, ŝ is the outgoing direction of interest, Ω ' is the solid angle of the incoming radiation, and s ˆs is the direction from which a specular ray must enter to be reflected into the ŝ direction. Equation (.19) is applicable to all solid surfaces including the sample holder and the solid fuel. But since the solid fuel can be thinner than the radiation absorption depth as demonstrated by Pettegrew (6) in his experiment using thin cellulose (i.e. Kimwipes ), the solid may not be opaque. So the use of Eq. (.19) needs a new interpretation. In a thin solid such as the ones used in the experiments

58 (Kleinhenz et al., 8, Chu, 1978; Olson and Miller, 8), part of the incident flame radiation is transmitted through the solid fuel. But since the flame is symmetric with respect to the solid (i.e. on both sides of the solid), the transmitted radiation is equivalent to reflected radiation. To be consistent, we assume that both the transmitted and reflected radiations are diffusive in nature. So Eq. (.19) is still applicable to our thin solid experiments as long as we use ρ = 1 α, i.e. the incident radiation which is not diff absorbed is treated as reflected. Since it is more appropriate to treat the thin solid as a radiation volume rather than a surface, we follow the terminology suggested by Siegel & Howell () that ε will be referred to as the solid emittance rather than surface emissivity and α as the solid absorptance rather than surface absorptivity when applied to the solid fuel. The emittance and absorptance are volumetric properties and are a function of sample thickness or area density as demonstrated by Pettegrew (6) for Kimwipes. In Pettegrew s experiment, the solid sample spectral transmittance and reflected radiation are measured and the spectral absorptance is deduced. Kirchhoff s law states that the spectral emittance is equal to spectral absorptance at a given direction and a given temperature (Modest, 199). In the present radiation model, we can not afford a spectral treatment and only spectrally integrated (mean) quantities are needed. Specifically, for a black surface ε = 1, the diffusive and/or specular reflectivity is ρ( r ) α( r ) ε( r ) = 1 = 1 =. However, for most combustion cases the spectral w w w nature of the radiative exchange between the solid and gas means that the total absorptivity is often different from the total emissivity due to the transmittance (Pettegrew et al., ). In this work the walls are black ( ε = α = 1). 6

59 The radiative heat flux at a surface or inside the medium is given by: q( r) = I ( r, sˆˆ ) sdω wi ( ) ˆ i i r si. (.) π i= 1 Also, the incident radiation G is: π i= 1 n n Gr ( ) = I( r, sd ˆ) Ω wi i i( r), (.1) and the divergence of heat flux (dimensional) is: n qr ( ) = κ( r) σt ( r) Gr ( ) = κ( r) σt ( r) wi i i( r). (.) i= 1 Non-dimensionalizing the incident radiation G by σ T, and κ by 1 L R, the nondimensional divergence of the radiation heat flux in the energy equation is: 1 1 σt q = κ ( T G). (.) cbo c cu r * * p p ρ p R Higher temperatures indicate that the radiation becomes more important due to the T term. Also, a lower Boltzmann number enhances the radiation effect (e.g. low speed flows where U R is low). Note that the Bo number is still important for the solid equations even if the gas radiation participation is absent. The dimensional absorption coefficient used in Eq. (.) is assumed to be: κ = C κ, (.) P where κ p is the Planck mean absorption coefficient of the mixture given by: ( ) κ = X κ + X κ p. (.) p CO P CO HO P HO 7

60 where X i is the is the molar fraction of species i and p is the ambient pressure in atmospheres. Note that only carbon dioxide and water vapor are treated as the radiation participating species in the gas mixture. Table.1 lists fitting equations for the Planck mean absorption coefficients ( κ andκ data from C. L. Tien (1968). P _ CO P _ HO ) for water and carbon dioxide using the The constant C ( 1) in front of κ p in Eq. (.) provides a correction of the flame radiation flux to the solid surface and the value is predicted by the Planck mean absorption coefficient. As discussed previously, because of the spectral self-absorption of CO and H O, the flame is not optically thin as represented by the Planck mean absorption coefficient. In the present three-dimensional computation C is assumed to be.. Note that in two-dimensional flames, a more elaborate scheme has been employed so that C varied along the downstream direction in T ien et al. s work (1) according to a procedure suggested by Rhatigan et al. (1998). The nondimensional absorption coefficient is obtained by multiplying by the reference length L R, κ = κ L = C κ L. (.6) R P R are as follows: The radiation boundary conditions at the enclosure boundaries and solid surfaces At x = x, in ε = 1, ρ = 1 ε =, T = T = K. diff 8

61 At x = x, out ε = 1, ρ = 1 ε =, T = T = K. diff At z = z, wall ε = 1, ρ = 1 ε =, T = T = K. diff At z = cm, ε =, ρ = 1, T = from gas phase solution. spec At y = y, wall ε = 1, ρ = 1 ε =, T = T = K. diff At y = cm symmetry plane (metal plates or inner strip plates), ε =.9, α =.9, ρ = 1 α, T = Ts. At diff y = cm symmetry plane (gap), ε =, ρ = 1, T = from gas phase solution. spec On the solid fuel surface at y = cm, the emittance is a variable depending on both the local solid thickness and temperature. The data for cellulose (Kimwipes ) from Pettegrew (6) is used here: ε = variable, ε α =, ρdiff 1 = α, T = Ts. 9

62 Note that using this set of realistic data has a major impact on the quantitative results because the thin virgin Kimwipes has an emittance value substantially lower than the ordinary quoted value of.9 for thick paper at room temperature (see Appendix B). The thickness of the partially-vaporized solid in the pyrolysis zone is even less, which further decreases the emittance. In addition, there is a temperature influence on the value of the emittance.. Numerical Scheme The SIMPLER algorithm and hybrid grid scheme are used for the fluid flow. The gas-phase equations are linearized by using finite-difference technique and the linear matrixes are solved by using Strong Implicit Procedure (SIP). Solid-phase equations are coupled to gas-phase flow field. The bisection method is used in the solid-phase equations to determine the steady flame-spread rate iteratively. The radiation routine is solved by using the S-N discrete ordinates method (Modest, 199; Siegel and Howell, ). The two-dimensional S scheme with 1 ordinate directions (Jiang, 199) and three-dimensional S8 scheme with 8 directions (Feier, 7) are used in the computations. A non-uniform mesh is constructed in the flow field. The grid points are clustered in the flame base stabilization zone to capture the drastic changes in the flame and then expanded upstream and downstream away from the solid burnout point by a factor of 1.1. The smallest cell size is one-tenth of the thermal length in the stabilization zone. In running the two dimensional cases (D code), the number of grid points are typically 7. In the x-direction, the calculation domain extends to 1 thermal

63 lengths downstream and thermal lengths upstream (measured from the burnout point); in y-direction, it extends to thermal lengths from the solid surface. For the three dimensional cases (D code), the computational domain is specified dimensionally. For buoyant flow cases (Fig..1), in the x-direction, the distances are cm upstream and 7cm downstream, which are measured from the burnout point on the central line on the solid surface; in the y-direction, the distance is cm from the solid surface; in the z-direction, it is cm from the central line on the solid fuel surface. The grid distribution for the buoyant-flow cases is shown in Fig... The model is to simulate flame spreads over thin samples in a large room. The calculation domain is found to be sufficiently large for this purpose. For the forced-flow cases with tunnel configuration (Fig..), the grid distribution is shown in Fig... One should note that because of symmetry, only one quarter of the domain needs to be computed.. Property Values The thermal and transport properties here are similar to the models from Jiang (199), Shih (), Tolejko (), Kumar () and Feier (7). Recall that overbar,, is used to denote dimensional properties and the absence of an overbar means nondimensional properties. (1) The gas density is evaluated using the equation of state: p = ρ R T g u, i F, O, CO, HO, N Yi M i i =. () The diffusion transport quantities, μ, k/ c p, and ρ gdi have a power law dependence following Smooke and Giovangigli (1991): 1

64 .7 μ = T, k c = T.7, p D T i = F, O, CO, H O, N..7 ρ g i =, () The specific heat is a function of mixture composition and temperature: c = Yc, i = F, O, CO, HO, N. p i p, i i Here c pi,, nondimensionalized by * c p, is a function of temperature. The approximations of c pi, are listed using polynomial relations in Table. (Hoffman, 1976; Lefebvre, 198). () The species have different but constant Lewis numbers. Gas phase property values, solid phase property values, and nondimensional parameters are listed in Tables.,., and., respectively. () Table B.1 lists the emittance at normal incidence for Kimwipes for several temperatures and area densities (Pettegrew, 6) and the fitting equations for variable emittance for celluloses as a function of area density and solid temperature are listed in Table B..

65 Table.1: Fitting equations for Planck mean absorption coefficients for CO and H O. κ p = a+ b T + c T (1/cm/atm) with T being the nondimensional temperature. Gas medium a b c Temperature range CO.89E-1.98E E-1.7E E- -.88E E- -.99E E-.168E- T < T.7.7 < T.8.8 < T H O 1.71E-1.618E E E-1 -.9E E E-.691E-.17E E- T < T.7.7 < T.8.8 < T

66 Table.: Polynomial relations for specific heat for O, CO, H O, N, and Fuel. ( ) cpi, = a + bt + ct + dt + et f.187 J/g/K pi, ( ) c = a + bt + ct + dt + et f cal/g/k with T in degrees Kelvin. Species a b 1 c 1 6 d 1 9 e 1 1 f 1 Temp. Range (K) O N CO H O Fuel

67 Table.: Gas phase property values. Symbol Value Units Reference * T 1 K Ferkul (199) ρ g/cm Ferkul (199) * g * μ g/cm/s Ferkul (199) * J/cm/s/K k ( Ferkul (199) ) (cal/cm/s/k) * c 1.8 J/g/K p Ferkul (199) (.) (cal/g/k) * α.1 cm /s Ferkul (199) 8. J/gmol/K R u Ferkul (199) (1.987) (cal/gmol/k) T K Ferkul (199) ρ g/cm Ferkul (199) P 1 atm Ferkul (199) T F K Ferkul (199) J/gmol E g B g Δ H R (.7 1 ) (cal/gmol) Ferkul (199) Ferkul (199) cm /g/s Current model J/g Frey and T ien (1979) (-. 1 ) (cal/g)

68 Table.: Solid fuel property values. Symbol Value Units Reference T L K Ferkul (199) -7.6 J/g L Ferkul (199) (-18) (cal/g) Ferkul (199) τ cm Pettegrew (6) ρ s.6 g/cm Ferkul (199) c 1.6 J/g/K s Frey and T ien (1979) (.) (cal/g/k) (. 1 Ferkul (199) ) J/gmol E s.86 1 (cal/gmol) (.9 1 Pettegrew (6) ) Ferkul (199) A s. 1 7 cm/s Pettegrew (6) ε variable Pettegrew (6) Pettegrew et al.() α ε /(variable) Pettegrew (6) 6

69 Table.: Nondimensional parameters. Symbol Value Parameter Reference Pr.7 * * v α Ferkul (199) * * Le F 1. α D F Jiang (199) Le O 1.11 * α * Smooke & Giovangigli (1991) Le CO 1.9 Le HO.8 Le N 1. D O * * D CO * * D H O * * D N E g. ( ) g u E s Es ( RT u ) α Smooke & Giovangigli (1991) α Smooke & Giovangigli (1991) α Smooke & Giovangigli (1991) E RT Ferkul (199). Ferkul (199) 6.8 Pettegrew (6) * * Δ HR cpt Frey and T ien (1979) Δ H -. ( ) R L -. L ( ct s ) Ferkul (199) Da variable * * αρ B U - Γ variable ( * * ) scv s F cu p R g R ρ ρ - 7

70 inert sample holder plates solid fuel X pyrolysis region flame g Y Z Figure.1: -D flame spread configuration for buoyant cases in a large chamber. 8

71 1 X (cm) Y (cm) 1 cm 7.cm 7.cm Flame Fuel metal plate gap metal plate cm 1cm Z (cm) Figure.: -D flame spread configuration for forced cases in a confined tunnel. 9

72 Y(cm) Z(cm) X (cm) X (cm) Y (cm) Z(cm) 7 6 X (cm) Z (cm) Y (cm) Figure.: Three-dimensional grid distributions for buoyant cases.

73 1 Y(cm) X(cm) 1 Z(cm) X(cm) 1 Y(cm) 1 X (cm) 1 Y (cm) 1 Z(cm) -1 Z (cm) 1 Figure.: Three dimensional grid distribution for forced cases. 1

74 Chapter Flame Spread in Buoyant Flow: Comparison between Model and Experiments Two sets of experimental data (Kleinhenz el al., 8 and Chu, 1978) are selected to compare with the model in buoyant flows. They are chosen because both have achieved steady spread conditions and have covered a range of environmental conditions that are of interest to space application. In addition, these experiments reported enough details (spread rate, extinction limits, flame images and temperature profiles) that enable more critical comparisons..1 Results and discussions In this chapter, two sets of numerical computations are carried out for purely buoyant upward flame spread in: (1) partial gravity and reduced pressure air according to the conditions in Kleinhenz el al. s study (8) and () enriched oxygen, reducedpressure atmospheres in normal gravity according to the conditions in Chu s work (1978). Note that in both sets of experiments, narrow cellulosic samples were employed (1-cm wide). Kimwipes were used in Kleinhenz el al. (8), and adding machine tapes and index cards were used in Chu (1978). Wherever experimental data are available, comparisons between numerical results and experimental data are made. These may include steady flame spread rates, extinction limits, and flame dimensions and shapes. In addition to these global quantities, the computed results contain detailed flame structures

75 such as flow pattern, species and temperature distributions and solid pyrolysis distributions. Thus the numerical results provide additional insight into the threedimensional flame spreading processes..1.1 Comparison with the experiments by Kleinhenz et al. (8) Three-dimensional flame structure In the following, a detailed computed three-dimensional flame structure will be presented and compared for the following experimental conditions. The ambient air is 1% oxygen and 79% N at 6-psia (.8-atm) ambient pressure and lunar gravity (.16g e ). The solid fuel sample (Kimwipes ) is 1-cm wide with both sides attached to strips of inert metal holder plates, each 1.-cm wide, as shown in Fig..1. The thermal inertia of the inert plates is one thousand times greater than that of the solid fuel. So they effectively serve as heat sinks for the flame. In this case, the experimental and computed flame spread rates are respectively 1.6 cm/s and 1.7 cm/s. The difference is less than %. Fig..1 shows a comparison of the side view of the flame shapes between the computation and the experiment. In the numerical model, the visible flame is best represented by the fuel vapor reaction rate contours. Since the side (edge) view flame photo image is along lines of sight (Fig..1(b)), the computed contours to be compared in Fig..1(a) is chosen to be the fuel vapor reaction rate integrated along the lines of sight (z-direction) from the threedimensional flame data. Fig..1(b) shows that the experimental visible flame length is

76 about.6cm. If we choose the integrating reaction rate equal to 1 -. g/cm /s to present the visible flame, we see that both the flame shape and flame length are close to those in the experimental image. Please also note that the downstream flames become approximately parallel to the solid surface, this is different from spreading flames in purely forced flows where they are observed to diverge from the solid in the downstream direction. The computed nondimensional fuel thickness (h) contours are shown in Fig..(a) (thickness of the virgin solid is equal to one). The shapes of these contours reflect the three-dimensional feature of the flame over a narrow sample. The experimental frontview photo image of the solid fuel surface is shown in Fig..(b). The boundary of the blackened part of the surface is an indicator of the pyrolysis front. If we choose h =.9 as the pyrolysis front in the model, we see that both the model and the experiment have a similar shape and the pyrolysis length is around.cm. One also notices that near the edges close to the inert plates, there are two strips of solid un-burnt or partially burnt in Fig..(a), which are also found in the experiments. This is due to the quenching effect by the inert plates. Being able to predict quenching is the result of using a finite-rate chemical reaction in the model. The solid burnout contour is given by h = in Fig..(a). Comparing with that in Fig..(b), we note that while the two burnout shapes are similar in most locations, there is a noted difference. The burnout shape in the model is smooth and symmetric (as assumed); the experimental burnout in Fig..(b) contains a crack on the right-hand side. Cracks are observed regularly in the burning of thin celluloses. They occur because the solid material often contains a residue stress when manufactured. When the solid is burnt

77 to a thin char, it can no longer resist the stress and a crack is created. Of course, a crack does not always occur symmetrically and the cracked shape and length are also somewhat random. At the present time, we do not have an element in the model to account for the cracking phenomenon. So when we compare the model performance this should be noted. As an example, the side view of the flame photo in Fig..1(b) shows a more extended flame base as compared with that of the model in Fig..1(a). This is because of the crack that induces a local flamelet (seen in Fig..(b)). When side-view line-of-sight photo is taken, the flame there appears to be thickened. The left side of Fig..(a) shows the predicted solid temperatures. Their distributions are similar to those of the solid thickness shown on the right side of Fig..(a). The pack of isotherms close to X = -1cm is actually the gas temperatures on the same plane. These are located slight upstream of the peak flame temperature. Their locations give an indication of the thermal thickness there which is of the order of 1cm. Fig..(b) shows the emittance of the solid. These are computed based on experimental data of Kimwipes from Pettegrew (6). The distributions reflect the dependence of emittance on both the solid thickness and the temperature (See Appendix B). Note that they are quite different from the uniform distribution with a value equal to.9 used in most previous works (e.g. Feier, 7). The above comparisons indicate that the computational results can predict the experimental measurements quite well. In addition, the numerical simulation provides more details such as the three-dimensional flame structure, the flow field and the heat flux distributions. These pieces of information, not always obtained in experiments, offer further insight into the flame spreading processes and are presented below.

78 Fig.. shows a typical three-dimensional flame structure in a buoyant flow by three cuts. Because of symmetry, the results are presented in one half of the crosssectional planes. Fig..(a), (b) and (c) show the cut at Y=.cm (front view), the crosssection along the centerline of solid fuel Z=cm (side view), and the cut at X=1cm (top view) respectively. The left halves present the flame temperature contours, the flow velocity and streamline projections; the right halves show the reaction rate contours and the fuel vapor mass fluxes at selected locations. The side cut at the symmetry plane (Z=cm) in Fig..(b) gives profiles similar to those in the two-dimensional model (Jiang et al., 1996). The temperature and reaction rate profiles are somewhat similar because a robust reaction rate requires the presence of fuel vapor and oxygen at an elevated temperature. The thermal plume, however, extends further downstream than the reaction rate because of the consumption of fuel vapor and the sensitivity of reaction rate to temperature. The fuel flux distributions on the right side of Fig..(b) show, however, there is a small amount of fuel vapor escaping from the reaction zone. This will be explored further in Chapter. Figs..(a) and.(c) clearly show the three-dimensional features of the flame. Both show that the extent of the flame spills over beyond the width of the sample (-.cm < Z <.cm) due to lateral thermal expansion. Fig..(a) shows the flame is an elongated tear drop in the front view. Fig..(c) shows that oxygen is drawn into the flame and a quenching zone above the solid fuel and the sample holder allows the escape of fuel vapor un-reacted. Fig.. shows some of the mass transfer aspects of the flame in three crosssectional planes. The oxygen mass fluxes and the streamline projections are presented in the figures. Besides, the left sides present the fuel-vapor mass fraction contours; the right 6

79 sides present the distribution of local equivalence ratio. The local equivalence ratio is defined as the ratio of fuel vapor to oxygen divided by the stoichiometric fuel vapor to oxygen ratio. The figures show there is a small fuel-rich region above the pyrolysis surface, while in the downstream it s mostly fuel-lean. The closeness of the localequivalence-ratio contours near the solid burnout location suggests large fuel and oxygen gradients and intense reactions, consistent with those shown in Fig... Note that the oxygen mass fluxes are not always parallel to the streamlines due to molecular diffusion. While there is little oxygen near the solid pyrolysis zone, there is plenty of oxygen downstream due to buoyant induced flow that draws oxygen from the ambient into the flame and thermal plumes. Figs present the heat transfer aspect of the flame. Fig..6 shows the radiative heat fluxes (Eq. (.)) and the contours of radiative heat loss (Eq..) in the gas phase on three cross-sectional planes. Only half of the planes are presented due to the symmetry. Figs..6(a) and (c) show that, in this narrow flame configuration, the radiation is highly three-dimensional in nature. Figs..6(b) and (c) show that the radiative flux on the solid surface is pointed outward, i.e. radiation is heat loss from the surface. This is because the solid emission and reflection is greater than the incident flame radiation. Far from the flame, the radiative heat fluxes decrease in magnitude because of the effect of three-dimensional geometry. Heat transfer profiles on the solid surface are presented in Figs Fig..7 shows the distribution of the convective heat flux q c to solid which resembles the flame profiles shown in Fig..(a). Just downstream of the solid burnout, the constant flux lines have valleys at the center line that gradually vanishes further downstream. Fig..7 also 7

80 shows that the sample holder plates receive a large amount of convective heat flux, especially near the burnout. This is due to the spilling-over of the flame beyond the fuel surface as a result of the lateral thermal expansion action mentioned previously (see Fig..(c)). In addition to the low temperature of holder plates (thermal sink), the fact that the magnitudes of the heat flux are larger at the holder plates than those at the fuel surface is because at the fuel surface the pyrolyzed fuel vapor pushes the flame away (transpiration cooling effect) while there is no such effect at the inert sample holder plates. As a result, the flame standoff distance at the edge of the flame is smaller than that at the centerline (Fig..(c)). Fig..8 gives the distributions of the surface radiative heat fluxes. Fig..8(a) shows the distribution of the outgoing radiative heat flux q r (Eq. (.19)) from solid. The outgoing radiative heat flux is the sum of solid emission and reflection. For most small scale flames, the solid emission, which is proportional to the solid emittance and the forth power of surface temperature, usually dominate the outgoing radiative heat flux. Hence, because the solid emission strongly depends on surface temperature (see Fig..(a)), significant outgoing radiative heat flux only exists in the fuel pyrolysis zone. Furthermore, due to the variable emittance (see Fig..(b)) the high outgoing radiative heat flux is close to the pyrolysis front, where the area density has not substantially reduced (still high emittance). This indicates the difference of solid radiation response between using the experimentally variable emittance and a constant value. Fig..8(b) shows the distribution of incident radiative heat flux q + r (Eq. (.1)) to the solid surface, which is mainly from the radiative heat feedback from flame (the remaining is the ambient background radiation), Note that the magnitude of the incident radiation is about one- 8

81 order of magnitude smaller than the outgoing radiation. Consequently, the total loss of + radiative heat flux ( q r = q r q r ) on the solid surface shown in Fig..8(c) is very similar to that in Fig..8(a) for q r alone. It should be mentioned again that in the computation, the solid absorbance is assumed to be one half of the solid emittance (See Appendix B). Fig..9 presents the net heat flux ( q net = q c q r ) from gas phase to solid. This is a superposition of Fig..7 and Fig..8(c). The convective heat flux is larger than the surface radiative flux, but the latter is of sufficient magnitude that can not be ignored. Also, although flame radiation feedback appears to be of secondary importance in this example, it may not be ignored in other situations where convection is further suppressed as demonstrated in low-speed purely-forced flows (Jiang, 199 and Kumar, ) and in buoyant flow at much lower gravity levels (Jiang el al., 1996) Flame spread at different pressure and gravity levels Flame spread rate In this section, the flame spread model is employed to compute the steady upward spread rate as a function of pressure and gravity level and to compare with the experimental data by Kleinhenz et al. (8). The experiments were performed in an aircraft flying parabolic trajectories to achieve the reduced gravity of Lunar (.16g e ) and Martian (.8g e ) levels. In addition, Earth (1g e ) level gravity experiments were carried out using the same flight hardware on ground. From these experimental data and based on the consideration of preserving Grashof number, it is suggested that flame spread rates and pyrolysis lengths can be correlated using p 1.8 g as a variable. More precisely, the 9

82 flame spread rate (cm/s) is equal to.1 p 1.8 g ( p is in kpa and g is in g e (Earth gravity) ) for Kimwipes. Furthermore, when p 1.8 g is approximately the same, the flame sizes and shapes are similar to one another as shown in Fig..1(a). This is in contrast to the case when only gravity is varied (Fig.1(b)). The purpose of the numerical simulation in this section is to see the performance of the model when the pressure and the gravity levels are varied. Table.1 shows the computed cases that are carried out for the comparison with the experiments of Kleinhenz et al. (8). Fig..11 shows the flame spread rates at the three concerned gravity levels as a function of pressure. The experimental data and the computational results are both shown in the figure. One can see that the computed results favorably agree with the experimental data both qualitatively and quantitatively. However, the experimental data have large scatter, especially in the high pressure region at.16g e. In contrast, the uncertainties of the computed results are less than %. The computed pressure exponents of flame spread rate at different gravity levels are displayed (all of the three curves pass the origin). It shows the pressure exponents range from 1. (.16g e ) to 1.9 (1g e ). Fig..1 shows the computational spread rate as a function of two pressure-gravity combinations. Although p 1.7 g (Fig..1(a)) gives the best fit with R =.988 for the numerical results, p 1.8 g (Fig..1(b)) with R =.986 also shows an excellent correlation. We like to mention here that the pressure exponent has a slight gravity dependence which has also been found independently by Shih (9) albeit in lower gravity levels. Shih used a two-dimensional model so that steady spread can be achieved only when the gravity is sufficiently low. 6

83 Fig..1(a) shows the predicted spread rate as a function of pyrolysis length (pyrolysis front at 9% of virgin fuel thickness). It shows that the spread rates at differential gravity levels are all approximately linearly proportional to the pyrolysis length. The three lines are close to one another but do not collapse into a single line. By comparison, the experimental data are within one band given the margins of data scatter Flame structure Fig show the comparisons of the computed flame structures at three different gravity levels at -psia pressure. Figs..1 and.1 respectively show the side view and the front view (Y=.cm) of the flame structures and flow fields for the three cases. The flow velocity vectors indicate the magnitudes of the induced flow velocities are quite different because of the gravity level. This affects the convective heat flux from flame to solid, and consequently results in three drastically different flame lengths. The flame spread rates are respectively. cm/s, 1.76cm/s and.9 cm/s at the gravity levels, 1g e,.8g e and.16g e. Fig.16 shows the contours of solid temperatures and fuel thicknesses. It shows the pyrolysis lengths are also of very different scales. These computed flames compare favorably with the experimental flame photos shown in Fig..1(b), except the 1g e case. One can see from Fig..1 that the computed pyrolysis length for 1g e cases is substantially shorter than the experimental data especially at fast flame spread rates. A different way to compare the flame size and structure is to vary both the pressure and gravity in such a way that the flame spread rates are equal. This was the basic idea of the pressure-gravity modeling in Kleinhenz et al. (8) and the 61

84 experimental comparison is shown in Fig..1(a). Note that in this figure the p 1.8 g values are close but not exactly equal due to experimental constraints; consequently the flame spread rates are also only approximately equal. In the present modeling work, we can iterate to compare the three cases with almost equal spread rates. Fig show the comparisons of the cuts at centerline (Z=cm), the cuts of Y=.cm above the solid surface, solid temperature and solid thickness among three different gravity levels according to the equal flame spread rate (.7 ±. cm/s). Although the three flame sizes (Fig..17,.18) and pyrolysis lengths (Fig..19) are comparable, similar to the experimental images shown in Fig..1(a), the higher resolution of the computed plots reveals some minor differences. One sees that at higher gravity level the flame and pyrolysis lengths are slightly smaller than those at low gravity levels. This is difficult to judge from the experimental photos. It also suggests the pressure-gravity model is only approximate in nature..1. Comparison with the experiment by Chu (1978) An older set of upward flame spread experimental data over narrow paper samples is from Chu s thesis (1978). The experiments were carried out in normal gravity with pressure and oxygen as varying parameters. The samples tested are adding machine paper and index cards. In addition to the steady flame spread rates, the gas-phase flame and solid surface temperatures along the centerline were measured using thermocouples. In this section, they are compared with the numerical simulation. 6

85 .1..1 Comparisons of flame structure at centerline Chu measured the flame spread over a 1-cm-wide adding machine paper sample at normal gravity (1g e ) and.-atm pressure. The ambient gas mixture is % oxygen and 7% nitrogen. The sample used (referred to as Sample A by Chu) has an area density equal to.9 mg/cm, which is much thicker than that of Kimwipes. To use Pettegrew s correlation of cellulose emittance with fuel thickness, his relationship has to be extrapolated to a thicker solid with the virgin solid emittance equal to.9 (See Appendix B). All the other parameters are kept the same as in the previous section. For the case considered, the computed and experimental spread rates are.9 cm/s and 1.9 cm/s respectively. The predicted spread rate is 1.6% slower. Next, we will compare the predicted and the measured flame thermal profiles. Fig.. shows the predicted and experimental gas-phase temperature isotherms at the centerline. The maximum predicted flame temperature and flame length are respectively about ºC higher and 1.-time longer, and the predicted flame standoff distance is also higher than the experimental measurement. The predicted flame is stronger than the actual flame. Near the burnout, the predicted maximum flame temperature occurs at the leading edge of the flame; however, the experimental measurement shows it s above the solid surface. To help explain the discrepancy in this model-experiment comparison, let us first review how the gas-temperature was measured and other relevant experimental observations. The gas-phase temperatures were measured using a fine thermocouple. (The fine-wire thermocouple probes are made of Pt/Pt-1%Rh and the diameters of the 6

86 wire and the (non-catalytic) silica coated junction are.cm and.1cm respectively.) The thermocouple is inserted into the flame from the ambient vertically (i.e. perpendicular to the solid surface). Because of heat conduction through the leads, it is expected that very close to the surface, the measured temperature will be higher than the actual value but the flame temperature and oxygen side temperature will be lower than the actual ones due the conductive loss. The radiative loss from the thermocouple tip has not been included either. These may partially explain the measured flame temperature is lower and why the measured surface temperature is higher (also see Fig..1). One also sees that there is a difference of the thermal structure in the flame base zone between the model and experiment. In the model (region X < cm in Fig..(a)) the highest temperature for a given x is located on the plane Y = cm, the isotherms are compact. On the other hand, in the experiment (upstream region of point c) the highest measured temperature is at several millimeters above the plane and the isotherms are less compact within a stabilization zone at least twice as long as the theory predicts. This is explained by noting that thin cellulosic fuel typically develops cracks near the burnout region. We mention fuel crack briefly in Section when we examined the image of Kimwipes pyrolysis zone. Because of its thinness and its fiber structure, the cracks developed in Kimwipes usually are small and shallow. With other cellulosic samples, deeper cracks can result. Fig. 1.(b) is a drawing by Chu to illustrate the crack he saw in the burning of his adding tape samples. The crack changes the shape of the solid burnout profile. With the burnout shape as in Fig. 1.(b), it is difficult to explain the gas-phase thermal structure shown in Fig... Note that we do not have a crack mechanism in our 6

87 present model and our predicted solid burnout boundary is smooth everywhere (see Fig..), quite different from that shown in Fig. 1.(b) Fig.1 shows the solid temperature profiles along the centerline of solid fuel compared with the experimental measurement using thermocouple touching the surface. Both profiles show approximately uniform temperatures over the pyrolysis region. The experimental temperature profile (Fig..1(b)) at the pyrolysis front is somewhat higher than in the middle of pyrolysis zone, which is not shown in the numerical results (Fig..1(a)). The predicted pyrolysis temperature is about 1 ºC lower than Chu s measurement. We believe that the higher measured temperature shown here is due to the reason just mentioned, i.e. the heat conduction gain from the flame with the way the thermocouple was deployed. The computed pyrolysis temperature is around 7K which is at the upper end of the reported range for cellulose. As discussed before, near the burnout (Fig..1) the predicted flame profile shows a sharper temperature gradient from flame to solid surface along the centerline; and the predicted flame region is mm narrower than the experiment. The predicted temperature is ºC higher. Chu defined the inflection point of the surface temperature in the downstream as the pyrolysis front. One can see that the predicted pyrolysis length is approximately 1cm longer. Without the surface temperature information, Kleinhenz et al. adopted the blackened front on the solid surface as the pyrolysis front. Fig. shows the conductive heat flux on the solid surface along the centerline. Similar to the surface temperature profiles (Fig..1), approximately uniform heat fluxes exist in the pyrolysis zone. The predicted value is approximately 1% (~.1 W/cm ) higher than the experiment. Note that the measured heat flux is deduced from the 6

88 temperatures (one on the surface and the other adjacent to it). Any error on temperature measurement and estimated heat conduction coefficient will affect the comparison. Near the burnout, the predicted values increase drastically. No experimental data point this close to the burnout was given. It is not known at the present time that whether the rapid rise of conductive heat flux there is real (i.e. experimentally observable) or is the consequence of assumed solid pyrolysis relation (zeroth order) in the model. Fig.. provides additional flame profiles form the model computation. There is no corresponding experimental measurement. Fig..(a) shows the contour of the integral fuel consumption rate across the width of flame. The visible flame length is.cm using 1 -. g/cm /s as the visible flame contour. Fig.(b) shows the contours of solid temperature and fuel thickness. The predicted burnout shape is smoothly rounded which is different from the observed burnout contour that has a crack in Chu s experiment. Fig..(c) shows the contour of the solid emittance..1.. Effects of oxygen percentage and ambient pressure on spread rate and extinction limit In this section, computed results on the effects of ambient oxygen fraction and ambient pressure on flame spread rate and extinction in normal gravity will be presented together with a comparison with Chu s experiments. Table. shows the computed cases that are carried out for this comparison. Using the material properties of Chu s Sample A, the computed flame spread rates at.atm and.atm as a function of ambient oxygen mole fraction is shown in 66

89 Fig... The computed results are plotted over Chu s experimental graph to facilitate comparison. The general trend of the computed spread rate agrees with the experimental results quite well over the entire range of oxygen percentages. Below % O for. atm and % O for.atm, the quantitative agreement is quite good (the model gives V f ~ X.11 O for.atm and V f ~ X.6 O for. atm). Above % O for. atm and % for. atm, the prediction is higher but is still reasonable; however, the discrepancy of prediction tends to increase with pressure. The predicted low oxygen extinction limits are around % O for. atm and 17% for. atm, which are lower than the experimental measurement. Extinction limits are sensitive to the values of the chemical kinetic parameters used. As listed in Table., the pre-exponential factor used in this work is 1.6 times of that used in previous works (e.g. Ferkul, 199). A increased kinetic rate is needed because when using the old rate constant, samples in served conditions in the partial gravity experiments (Kleinhenz et al., 8) become non-flammable. However, there are not enough experimental data on extinction limits for upward spreading flames to calibrate the kinetic constants. In Chapter, a study on the sensitivity of chemical kinetic rate on flame spread rates in concurrent flows was given. Kinetic rate has little influence on spread rate in forced flow but it has a finite but small influence on upward spread rate in buoyant flow. Several computed flame profiles at different oxygen percentages are given next. Fig.. shows the cuts of flame structures at Y=.cm at oxygen mole fractions equal to %, % and %. One can see that the flame becomes longer and the maximum temperature at a given height is greater when oxygen is increased. Fig..6 shows that the burnout shape changes from concave to convex at the center line (Z = cm) as ambient 67

90 oxygen fraction is increased. This is not reported in Chu s thesis. The occurrence of crack near the fuel burnout in the experiment is expected to complicate the comparison with this prediction. Fig..7 shows the flame spread rate as a function of pressure at % O. The computation stops at.atm. For pressure above this value, the flame becomes very long and is likely to be partially turbulent in reality. Computationally, it also becomes very expensive since the ratio of flame length to thermal distance at the flame base is very large. In our model, the flame base structure is resolved. In Chu s experiment, data points above this pressure are also marked differently, either because steady rate has not reached or because he felt there is interference of the chamber top wall. Within the computed range, the predicted spread rates agree with the experiment quite well. The numerical results show the spread rate is proportional to 1.98 power of pressure, slightly higher than that of the experiment (~1.8). The predicted low-pressure limit is around.1atm, which is lower than experimental value. Fig..8 shows the cross-section views at Y=.cm and Fig..9 shows the distributions of solid temperature and fuel thickness at pressures equal to.atm,.atm and.atm. One can see that as increasing pressure, the changes of flame structure and pyrolysis region are similar to that as increasing the oxygen mole fraction (Figs.. and.6).. Summary In this chapter, the three-dimensional concurrent-flow flame spread model has been applied to buoyant upward steady spread over cellulosic samples of narrow width 68

91 (1cm). The conditions computed correspond to two separate sets of experiments; one using Kimwipes as fuel and the other using adding machine paper tape. The environmental parameters varied include pressure, oxygen percentage and gravity level. The flame characteristics used in the comparison with experiments include: steady spread rate, extinction limits (wherever data are available), flame and pyrolysis shapes and lengths and flame and solid temperature profiles (wherever data are available). This is the first time we are aware of that such a detailed quantitative comparison has been made. The model, with its present input properties, appears to predict the steady upward spread rate quite well for both fuels as a function of pressure, oxygen percentage and gravity level. The computed flame and pyrolysis shapes and lengths are comparable with the Kimwipes data but are longer than those of the adding machine paper. The computed flammable ranges are also somewhat larger than the adding machine paper data (no data for Kimwipes ). One observation is that, for the adding machine paper, rather deep tearing cracks developed near the solid burnout zone. This alters the flame structure at the flame stabilization zone. Its effect on extinction limits and flame length is uncertain. At the present time we do not have a cracking mechanism in the model. The model predicts a higher flame temperature than that measured in the adding machine paper experiment. This may due to the way the thermocouple is deployed in the flame. Unfortunately, the experiment was carried out in 1978; many details have been lost and it is hard for us to make the proper data corrections. 69

92 Table.1: The computed cases (1% O ) for the comparison with the experiments of Kleinhenz ea al. (8). 1-cm-wide Kimwipes (Area density=1.8mg/cm ) Pressure Spread rate l p (h=.9) (psia) (cm/s) (cm) Gravity level (g e :9.8cm/s ) l f (1 -. g/cm /s) (cm) 7

93 Table.: The computed cases for the comparison with Chu s experiment (1978). O 1-cm-wide adding machine paper (Area density=.9 mg/cm ). atm, 1g e. atm, 1g e % O, 1g e Spread rate O Spread rate Pressure Spread rate (%) (cm/s) (%) (cm/s) (atm) (cm/s)

94 1 - g/cm /s X(cm) Y (cm) (a) (b) Figure.1: The computed reaction rate contours compare to the experimental side-view flame image for 1-cm-wide sample burning at 6-psia air and.16g e. (a) The reaction rate contours which are integrated across the width of the flame. (b) The experimental sideview image from Feier (1). 7

95 .99.9 X(cm) Z(cm) (a) (b) Figure.: The computed fuel thickness contours compare to the fuel surface image for 1-cm-wide sample burning at 6-psia air and.16g e. (a) The computed contours of the fuel thickness ratio to virgin one. (b) The experimental front-view image from Feier (1). 7

96 Solid Fuel Solid emittance X(cm) X(cm) Z(cm) Z(cm) (a) (b) Figure.: The distributions on solid fuel surface. (a) Solid temperature (left side) and ratio of remained fuel thickness to virgin fuel thickness (right side). (b) Solid emittance (virgin emittance =.7). 7

97 1 Front View (Y=.cm) L: 7.7 cm/s R: 1x1 - g/cm /s 1 Side View (Z=cm) L: 7.7 cm/s R: 1x1 - g/cm /s E X(cm) X (cm) 1E Z (cm) E-6 1E-6 1E-.1 Y(cm) E-6 1E Y (cm) 1 Top View (X=1cm) L:.17 cm/s R: 1x1 - g/cm /s Z (cm) (a) (b) (c) Figure.: The cross-section planes present the flame and flow structures of a buoyant upward spreading flame over a 1-cm-wide solid sample burning at 6-psia air and.16ge. (a) Front view (Y=.cm). (b) Side view (Z=cm). (c) Top view (X=1cm). The left halves show the nondimensional temperature distribution (T=1 is K), the velocity vector and the streamline projections; the right halves shows the fuel vapor reaction rates (unit: g/cm /s) and the fuel-vapor mass flux projections. 7

98 Front View (Y=. cm) Side View (Z= cm) Oxygen mass flux (1 - g/cm /s) 1 1 Oxygen mass flux (1 - g/cm /s) Y(cm) Z (cm) Y (cm) Z (cm) (a) (b) (c) 1 Oxygen mass flux (1 - g/cm /s)...1 X(cm) X (cm) Top View (X=1cm) Figure.: The oxygen mass fluxes, streamline projections, fuel-vapor mass fraction (left halves) and equivalence ratio (right halves). (a) Front view (Y=.cm). (b) Side view (Z=cm). (c)top view (X=1cm). 76

99 7 Radiative heat flux (1 W/cm ) Front View (Y=.cm) 7 Side View (Z=cm) Radiative heat flux (1 W/cm ) W/cm.1 W/cm Radiative heat flux (1 W/cm ) Top View (X=1 cm).1 W/cm Y(cm) 1. W/cm 1W/cm 1. W/cm 1W/cm X (cm) X (cm). W/cm 1. W/cm W/cm Y(cm) 1 Y(cm) 1W/cm 1 Z(cm) (a) (b) (c) Figure.6: The vectors of projected radiative heat flux and the contours of radiative heat loss in the gas phase. (a) Front view (Y=.cm). (b) Side view (Z=cm). (c) Top view (X=1cm). 77

100 . q c (W/cm ) X(cm) Z(cm) Figure.7: The distribution of the convective heat flux to solid surface. 78

101 (a) (b) (c) Figure.8: The distributions of radiative heat fluxes over solid surface. (a) Outgoing radiative heat flux ( ) from solid surface. (b) Incident radiative heat flux ( ) to solid surface. (c) The total loss of radiative heat flux ( ) on solid surface. 79

102 . q net (W/cm ) X(cm) Z(cm) Figure.9: The distribution of net heat flux ( q net = q c q r ) to solid surface. 8

103 (a) (b) Figure.1: The experimental comparisons from Kleinhenz (6). (a) Front views at three gravity levels according to the equal flame spread rate (p 1.8 g). (b) Front views at three different gravity levels ( psia). 81

104 8.16 ge exp. data.8 ge exp. data 1 ge exp.data.16 ge model 8 ge model 1 ge model Vf (cm/s) y =.x 1.97 R =.998 y =.16x 1.71 R =.9996 y =.17x 1.9 R = Pressure (psia) Figure.11: The comparison of flame spread rate between the computed results and experimental data from Kleinhenz et al.(8). 8

105 8 7 6 y =.91x R R =.988 Vf (cm/s) 1.16 ge.8 ge 1 ge p^1.7*g (psia^1.7*ge) (a) y =.6x R R =.986 Vf (cm/s) 1.16 ge.8 ge 1 ge p^1.8*g (psia^1.8*ge) (b) Figure.1: The computational flame spread rate as a function of two pressure-gravity combinations. (a) p 1.7 g. (b) p 1.8 g. (g e = 9.8 m/s ) 8

106 7 6 Vf (cm/s) 1.16 ge.8 ge 1 ge lp (cm) (a) (b) Figure.1: The flame spread rate versus pyrolysis length. (a) Numerical results. (b) Experimental measurement from Kleizhenz (6). 8

107 1 1g e psia 1E E- 1E-.1. X(cm) g e psia cm/s X(cm) 1E- 1E E- 1E- X(cm) Y (cm) g e psia Y(cm) Y(cm) Figure.1: The comparison of side-view flame structures at three different gravity levels ( psia). Left half: velocity vectors and fuel reaction rate contours (g/cm /s). Right half: nondimensional temperature contours and streamline projections. 8

108 1 1g e psia E-.1.16g e psia.1 cm/s 1E-.1. X(cm) X(cm) E Z(cm).8g e psia 7.1 1E X(cm) Z(cm) Z(cm) Figure.1: The comparison of top-view flame structures at three different gravity levels ( psia). Left half: velocity vectors and fuel reaction rate contours (g/cm /s). Right half: nondimensional temperature contours and streamline projections. 86

109 . 1 1g e psia X(cm) g e psia.8 X(cm) Z (cm) X(cm) 1-1.8g e psia Z (cm) Z (cm) Figure.16: The comparison of solid temperatures (left half) and ratios of fuel thickness (right half) at three different gravity levels ( psia). 87

110 E- 1E-.1 X(cm) g e 8psia cm/s E- X(cm) 1E g e psia Y (cm) E- 1E-.1 X(cm) g e.9psia Y (cm) Y (cm) p 1.7 g (psia 1.7 ge) p 1.8 g (psia 1.8 ge) p g (psia ge) Figure.17: The comparison of side-view flame structures at three gravity levels according to the equal flame spread rate (Vf =.7 ±. cm/s). (ge=9.8 m/s ) Left half: velocity vectors and fuel reaction rate contours (g/cm /s). Right half: nondimensional temperature contours and streamline projections. 88

111 g e psia 1E- X(cm).1 1E Z (cm) g e 8psia cm/s E- X(cm).8g e.9psia 1E-.1 X(cm) 1 1E E Z (cm) Z (cm) p 1.7 g (psia 1.7 ge) p 1.8 g (psia 1.8 ge) p g (psia ge) Figure.18: The comparison of front-view flame structures at three gravity levels according to the equal flame spread rate (Vf =.7 ±. cm/s). (ge=9.8 m/s ) Left half: velocity vectors and fuel reaction rate contours (g/cm /s). Right half: nondimensional temperature contours and streamline projections. 89

112 1g e psia 7.8g e.9psia 7.16g e 8psia X(cm) X(cm) X(cm) Z (cm) Z (cm) Z (cm) p 1.7 g (psia 1.7 ge) p 1.8 g (psia 1.8 ge) p g (psia ge) Figure.19: The comparison of solid temperatures (left half) and ratios of fuel thickness (right half) at three gravity levels according to the equal flame spread rate (Vf =.7 ±. cm/s). (ge=9.8 m/s ) 9

113 Y(cm) Flame temperature distribution at centerline 1-cm-wide sample (Sample A) normal gravity(1g). atm % O and 7%N T max =1791 C X (cm) (a) (b) Figure.: Flame temperature distribution at centerline. (a) Computational result. (b) Experimental measurement from Chu (1978). 91

114 Surface temperature distribution at centerline 1 1-cm-wide sample (Sample A) normal gravity(1g). atm % O and 7%N T( C) 1 burnout pyrolysis front X (cm) (a) (b) Figure.1: Solid temperature distributions at centerline. (a) Computational result. (b) Experimental measurement from Chu (1978). 9

115 .. q c (W/cm ) q c X (cm) (a) (b) Figure.: Conductive heat flux distribution at centerline. (a) Computational result. (b) Experimental measurement from Chu (1978). 9

116 .7 Solid Fuel Solid emittance g/cm /s X(cm) X (cm).9.8. X(cm) Y (cm) Z (cm) Z(cm) (a) (b) (c) Figure.: Additional information from numerical model for upward flame spread over 1-cm-wide adding machine paper at. atm, % O and 1ge. (a) Predicted visible flame from side view. (b) Solid temperature (left) and thickness (right). (c) Solid emittance. 9

117 Figure.: Flame spread rate as a function of oxygen mole fraction. Experimental data is from Chu (1978). Model computations are at. atm in red and at. in blue. 9

118 E E- 1E-.1 X(cm).1 6 X(cm) X(cm) E- 1 1E (Unit: g/cm /s) T max =6.69 (Unit: g/cm /s) T max =7. (Unit: g/cm /s) T max = Z (cm) Z (cm) Z (cm) (a) (b) (c) Figure.: The cuts of flame structures at Y=.cm at. atm different ambient oxygen fractions. (a) %. (b) %. (d) %. Left half: fuel vapor reaction contours (g/cm /s); right half: non-dimensional temperature (T=1 is K). 96

119 X(cm) X(cm) X(cm) Z (cm) Z (cm) Z (cm) (a) (b) (c) Figure.6: The distribution of solid temperature (left half) and fuel thickness (right half) at. atm and different ambient oxygen fractions. (a) %. (b) %. (c) %. 97

120 Figure.7: Flame spread rate as a function of ambient pressure at % O. Experimental data is from Chu (1978). Model computation for sample A (in red). 98

121 E E- 1E X(cm) X(cm) E E X(cm).1 6 1E (Unit: g/cm /s) T max =6.6 (Unit: g/cm /s) T (Unit: g/cm max =6.9 /s) T max = Z (cm) Z (cm) Z (cm) (a) (b) (c) Figure.8: The cuts of flame structures at Y=.cm at % O and different pressures. (a).atm. (b).atm. (d).atm. Left half: fuel vapor reaction contours (g/cm /s); right half: non-dimensional temperature (T=1 is K). 99

122 X(cm) X(cm) X(cm) Z(cm) Z(cm) Z(cm) (a) (b) (c) Figure.9: The distribution of solid temperature (left half) and fuel thickness (right half) at % O and different pressures. (a).atm. (b).atm. (c).atm. 1

123 Chapter Flame Spread in Forced Flow: Comparison between Model and Experiments As mentioned in the introduction section, flame spread in purely forced flow requires the elimination of gravity. This is especially true in low speed forced flows. The existing forced-concurrent-flow flame spread data that have enough details to be compared with computations are all from NASA GRC s -second drop tower (Grayson et al., 199; Pettegrew, 199; Olson and Miller, 8). We choose the experiment by Olson and Miller for the present comparison because it covers a range of pressures, oxygen percentages and velocities that are of interest to the efforts of planned space exploration. The experiment is carried out in a flow tunnel. The sample holder for the solid Kimwipes is shown in Fig. 1.. During the flame spreading process, the incoming forced flow first encounters the leading edge of a metal holder followed by a gap before reaching the solid fuel. The gap is formed because of the solid burnout. The velocity profile that the flame base sees is therefore not a uniform one and it varies with time when the gap distance increases during flame spreading. Therefore, in addition to the concern of limited test duration (i.e. seconds), the experiment can not be truly steady because of this varying velocity profiles in this setup. In the experiment, only flame images were recorded and it was difficult to separate this velocity effect due to the large scatter of data. Since our present model is steady state, we can not resolve the transient development of the flame. But we can assume different gap distances to perform steady 11

124 computations. This will give the upper and lower bounds of the flame characteristics during the spreading process in the experiment. In the experiment by Olson and Miller (8), the forced flow velocities were varied from 1 to cm/s at 1. psia and % O, the ambient oxygen mole fraction altered from %-% at 1. psia oxygen and cm/s and the pressures were changed from -1. psia at % oxygen and cm/s. They observed an interesting phenomenon at intermediate values of concurrent forced flow velocity where flow/flame interactions produced a recirculation downstream of the flame, which allowed an opposed flow leading edge to form there. From their experimental data, they concluded that the concurrent flame spread rate is proportional to the product of oxygen model fraction to the firest power, forced flow velocity to the firzst power and of the squire root of the. ambient pressure ( V U X p ). f O.1 Computed results and comparison with experiments Before performing the parametric studies, a detailed comparison of the flame structure with experiment for a specific reference case is presented first. Then, the effect of the entrance gap distance is also investigated to demonstrate its influence on the flame spreading process. Table.1 shows the computed cases for the comparison with Olson and Miller s experiments (9)..1.1 Forced-flow flame structure for a reference case In this section, the -D computational results of a steady forced-flow flame for a reference case will be compared with the experimental images at the end of the -second 1

125 drop. The sample width is cm wide and the gap distance is set cm before ignition, as shown in Fig... The solid fuel is Kimwipes (1.8 mg/cm ). The flow velocity is cm/s, the oxygen mole fraction is % (76% N ) and the ambient pressure is 6. psia. In this model computation, the gap distance is fixed at cm. The computed and experimental flame spread rates are 1.81 cm/s and 1.81 cm/s respectively. The predicted flame spread rate is about 17% faster. Fig..1 shows the predicted side view of the fuel consumption rates (integrated across the flame). If we take fuel consumption rates equal to 1 -. g/cm s as the visible flame, its length is.8cm (Fig..1(a)) which is slightly longer than the experimental flame (Fig..1(b)) (of course, the experimental image depends on the sensitivity of the camera). Note that, the experimental image in Fig..1(b) shows a more complex structure than the model result. A luminous soot layer appears in the fuel rich region between the flame and the solid. The effect of the soot layer on flame spread in microgravity is not clear. The current model does not have the soot formation mechanism. It should also be mentioned that near-limit microgravity flames are typically soot-free. The present case which has % O is quite far away from the extinction limit for Kimwipes. Fig.. shows the predicted thickness distribution in the pyrolysis region and the front-view image from the experiment. In the previous comparison with flame spread in buoyant flow, we used the thickness contour (h=.9) to define the theoretical pyrolysis front. In Fig..(b), however, the soot layer on top of the solid surface smears the image and a clear outline of the pyrolysis front can not be identified. The burnout contour is smooth in the model prediction (Fig..(a)), but local small cracks are clearly present 1

126 near the experimental burnout front to create a somewhat irregular profile. The overall comparison appears to be reasonable. It should be noted that Pettegrew (199) found from previous tests that the burnout contours at the end of -second drop are very sensitive to the ignition method used. Whether the contour shape is still evolving at the end of the experiment is not completely certain. Additional computed flame structures and solid profiles are shown in Figs.. and.. A fan-shape flame structure is predicted, which is similar to those found in Shih () and Feier (7). Fig..(a) shows the cut of the flame structures at Z=cm (centerline of solid fuel). The fan angle is smaller in the present case because the flow velocity is greater. The velocity profiles from X = -cm to X = cm show the velocity development in the open gap between the sample holder and the burnout front of the solid fuel. The velocity profile before X = -cm obeys the no-slip boundary condition; its shape reflects the experimental setup with a metal holder 1.7cm long upstream of the un-ignited fuel. With the release of no-slip boundary condition X > -cm (A -cm gap is assumed in this computation), the velocity near Y = cm is no longer zero and changes with distance. Therefore, what the velocity profile the flame base encounters will depend on the gap width which is varying with time in the experiment. Fig..(b) shows the cut of the flame structures at Y=.cm. The threedimensional nature of the flame is obvious. Because of thermal expansion, the flame spills over the width of the sample (-.cm < Z <.cm). Fig..(a) shows the solid temperature and thickness and Fig..(b) shows the distribution of solid emittance. 1

127 Additional characteristics about -D forced concurrent-flow spreading flames, including the effects of sample width and gas-phase radiation can be found in Shih () and Feier (7)..1.. Effect of gap size upstream of the flame As mentioned before, the distance between the upstream sample holder and the solid burnout (referred to as the gap size) (Fig..) can affect the flow velocity profile entering the flame base zone. Therefore, it can influence the flame spread rate during the.18 seconds experimental duration. In this section, the gap size is treated as a parameter to investigate the range of the steady flame spread rates that may be measured in the Olson and Miller s experiments (8). Fig.. shows the computed flame spread rate versus the gap size at cm/s, % (76% N ) and. atm (6. psia). One can see that as the entrance gap distance varied during flame spread, the spread rate can be significantly affected. However, in Olson and Miller s experiments, the total sample length is only 1 cm. If the quasi-steady flame spread rates were measured as the gap size developed, say, from to 8 cm, the numerical results in Fig.. shows that the variation of flame spread rates is only.%. This is less than the experimental uncertainty..1.. Effects of forced flow velocity, oxygen percentage and pressure In Olson and Miller s experiments, three parameters were tested, forced flow velocity, oxygen percentage and pressure. They tried to derive the dependencies of flame spread on these parameters and then build up the relationship between flame spread rate 1

128 and the combination of the parameters. A similar exercise is performed here using the computed data and then a comparison will be made with the experimental correlation. Fig..6 shows the flame spread rate as a function of forced flow velocity at % O,.69 atm (1. psia) and a -cm gap size. Comparing with experiment, the predicted flame spread rates are higher at high forced velocities, but lower at low forced flow velocities, although the experimental data shows uncertainty. The experimental data from Olson and Miller (8) do not include the intermediate values of forced flow velocity between 11 and cm/s. That is because in that forced-flow velocity region, the authors observed that a recirculation downstream of the flame is produced, probably due to the flow/flame interactions; and this allowed an opposed flow leading edge to form there. Because of the short -second microgravity duration, it is not certain that this is just a transient ignition phenomenon or a persisting steady state. Our model predicts a steady solution that is quite different from that observed during and at the end of the drop in this velocity range. One can see from Fig..6 that the computed flame spread rate is approximately linearly proportional to the forced flow velocity. The straight line drawn in the figure, V f (cm/s) =.17 U (cm/s), passes through the origin which says V f is zero when U is zero. In reality, there is a low velocity limit as indicated in Fig..6. Also note that the near-limit points have the largest deviation (percentage-wise) of spread rate from the linear plot. Fig..7 shows the flame spread rate as a function of oxygen mole percentage at cm/s and.69 atm. The predicted flame spread rates are higher than experimental data 16

129 by about %. The predicted low oxygen limit is about 1%; however the experimental limit is not provided. Two numerical fits for the computational results are shown in Fig..7. Firstly, a fit that is forced to go through the origin is given by the dashed curve, referring to Olson and Miller s correlation (9). We note that the three computed data points in the near limit region fall way below the curve. This curve gives V f =.69 X.691 O. The R value was computed without including the three near-limit points. The second fit (solid curve) includes all the points and is given by V f =.96 (X O -1.86).81. It has a R value close to unity. When oxygen percentage equals to 1.86 (close to the low oxygen limit), the spread rate is zero according to this fitting curve. In combustion theory, the extinction limit is normally defined by a turning point and at the limit the spread rate is small but finite. Also at the turning point, the slope is infinite so a simple power law fit without including limit information will miss the near limit data. The lower branch of the flame response curve beyond the turning point is unstable so that it can not be obtained from the presented numerical method. It is plotted in Fig..7 (dotted line in red) just to illustrate the turning point behavior. Comparing the two fits, the second one is preferred as it approximates the near-limit behavior better (although not perfect). To obtain the second fit, however, we need limit and/or near limit information. Fig..8 shows the flame spread rate as a function of ambient pressure at cm/s and % O. At higher pressure, the predicted flame spread rates are faster than the experimental ones, but there are not enough experimental data to be compared at the lower pressure region. The predicted low pressure limit is about.atm, which is lower than experiment (~.atm). The fitting curve passing through the origin gives V f (cm/s) = 17

130 .6 p.68 (atm). It does not contain limit information. Again, a dotted line is given to illustrate the possible turning point behavior. According to the above individual dependences on forced flow velocity, oxygen mole percentage and pressure, two correlations of the numerical data are formulated. The..6 first is V ~ U ( X.11) p as shown in Fig..9(a) (note that we used only one f O decimal point for the exponents). This correlation gives a very high R value (=.998). The low pressure and low velocity limits are not in this formulation. The second.7.6 correlation is V ~ U X p as shown in Fig..9 (b). Again we note that the three f O points near the low oxygen limit are below the correlation line and are not included in evaluating the value of R (=.99). In Fig..1, Olson and Miller (9) plotted their recent experimental spread rate data together with previous data from Grayson et al. (199) and Pettegrew (199) using U X p. O as the abscissa. A linear fit and a non-linear fit are presented. The non-. linear fit appears to do better when U X p is small, i.e. near the limit. But the O percentage deviations in this region are still substantial, reflecting the more complicated flame behavior near the extinction limit. To see how well the correlation works with the computation results, Fig..11. shows the computational results using ( U X p ) as abscissa. The two experimental fitted curves from Fig..1 are plotted in Fig..11(a). The large discrepancy reflects the O 18

131 difference between the computed and experimental data. Two new fitted curves (one passing through the origin and the other does not) which fit the computed data better are shown in Fig..11(b). They are better correlations than that in Fig..11(a) but are worse than those in Fig Next, we test the model parameters, U ( X O.11) p and.7.6 U X O p, using the experimental data. These are shown in Fig..1 (a) and (b) respectively. The data scatter more than those in Fig..1. Both the linear and power fits have lower R value than those in Fig..1. The linear fit lines (dotted line) from the numerical data are even worse. Finally, we apply ( X.11) in Olson and Miller s experimental correlation. O. Fig..1 shows the experimental data plotted as a function of U ( X O.11) p. One can see that the power-fit cure is improved near the extinction region (compared with Fig..1) and gives the value of R equal to Summary In this chapter, numerical computations of flame spread in forced concurrent flows were performed to compare with recent experimental results obtained in the - second drop tower. The fuel sample is -cm-wide Kimwipes and the environmental parameters varied include velocity, pressure and oxygen percentage. Although the model produces all the trends observed in the experiments, quantitative comparison is not as good as in buoyant flow using narrower 1-cm wide samples. The discrepancies may come from the limitations of the experiments, the model or both. For example, comparing with model predictions, the experimental spread rates 19

132 are higher when the flame is short and lower when the flame is long. One possible interpretation is that due to the limited microgravity testing time, the igniter affects the shorter (slow) flames and boosts the burnout rate, while the longer flames need more time to reach their steady state. The wider -cm samples also produce a less regular pyrolysis front that create data scatter. On the other hand, the model does not contain soot which is observed in the experiment in higher oxygen environment. Because of the differences of these data, the correlated relations between the model and the experiment differ from each other. These correlations for the flame spread rate are not valid near the extinction limits. The lack of experimental extinction limit data prevents a more rigorous test of the model. 11

133 Table.1: The computed cases for the comparison with Olson and Miller s experiment (9). Flow velocity Oxygen Pressure Spread rate (cm/s) (%) (atm) (cm/s)

134 Y(cm) -1 - Unit: g/cm s X(cm) (a) 1 cm (b) Figure.1: The computed reaction rate contours compare to the experimental side-view flame image for a -cm-wide sample. (a) The reaction rate contours which are integrated across the width of the flame. (b) The experimental side view image from Olson and Miller (9). The flow velocity is cm/s, the oxygen mole fraction is % (76% N ) and the ambient pressure is 6. psia. 11

135 1 Z(cm) X (cm) (a) 1 cm (b) Figure.: The computed fuel thickness contours compared to the fuel surface image. (a) The computed contours of the fuel thickness ratio to virgin one. (b) The experimental front-view image from Olson and Miller (9). The flow velocity is cm/s, the oxygen mole fraction is % (76% N ) and the ambient pressure is 6. psia. 11