Numerical Modeling and Simulation of Flame Spread Over Charring Materials by Matthew T. McGurn December 14, 2012 A dissertation submitted to the Faculty of the Graduate School of the University at Buffalo, State University of New York in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Mechanical & Aerospace Engineering UMI Number: 3554478 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 3554478 Published by ProQuest LLC (2013). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 Acknowledgments I would first like to express my deepest gratitude to my advisor, Dr. Paul E. DesJardin, for his continuous support, encouragement, and guidance throughout my graduate studies. The research and life experience I gained from my association with him will stay with me for many years to come. I am grateful to Dr. Gary F. Dargush, Dr. James D. Felske, and Dr. Amjad J. Aref for their discussion and suggestions on my research and for serving on my dissertation commit- tee. I would especially like to thank all the current and past members of UB Computational Energy Transport (CET) Laboratory for their continued help, support, and friendship. My appreciation goes to all others who have helped on the research work, but the space is too limited to mention everyone. However, I would like to especially thank Dr. Amanda Dodd from Sandia National Laboratories, Dr. Jim Lua from Global Engineering and Materials and Dr. Brian Lattimer from Virginia Tech for their support on this work. I owe a great deal of gratitude to my entire family, especially my parents, Debra and Thomas McGurn, without whose unwavering love and support I would not be the individual I am today. Support for this work has been provided by the National Science Foundation (NSF) under Grant CBET-1033328. Matthew T. McGurn The State University of New York at Buffalo December 2012 ii Contents Acknowledgments . ii Abstract . x 1 Introduction & Background 1 1.1 Background . 1 1.2 Objective . 5 2 Porous Media Modeling of Charring Materials 7 2.1 Formulation . 8 2.2 Numerical Implementation . 10 2.2.1 Weak Formulation . 10 2.2.2 Numerical Integration in Time . 13 2.2.3 Numerical Integration in Space . 14 2.3 Carbon Epoxy Modeling . 14 2.3.1 Pyrolysis Rate Modeling . 15 2.3.2 Matrix Thermal Properties . 16 2.3.3 Composite Swelling . 17 2.3.4 Gas Properties and Exothermic Chemical Reactions . 20 2.3.5 Results . 21 2.3.6 Conclusions . 27 3 Fluid-Solid Coupling 36 3.1 Formulation . 38 3.1.1 Eulerian Model . 38 3.2 Numerical Formulation . 42 3.2.1 Efficient Level Set Initialization and Update . 43 iii CONTENTS iv 3.2.2 Ghost-Fluid Implementation . 47 3.2.3 Coupling Time Interval . 52 3.2.4 CFD Numerics . 53 3.3 Results . 54 3.3.1 Conservation Error Checks . 54 3.3.2 Flow Over a Cylinder . 55 3.3.3 Isothermal Plate Heat Transfer . 55 3.3.4 Surface Blowing . 56 3.3.5 Sublimation with Constant Densities . 57 3.4 Conclusions . 59 4 Flame Spread Simulations 70 4.1 Small Scale Simulations . 70 4.2 Large Scale Simulations . 72 5 Conclusion 84 5.1 Proposed Future Research . 86 A Balsa Wood Modeling 87 A.0.1 Thermal and Transport Properties . 88 A.0.2 Water Transport . 89 A.0.3 Balsa Results . 90 B Finite Element Domain Decomposition 97 B.1 Mathematical and Numerical Formulation . 99 B.1.1 Finite Element Methodology . 99 B.1.2 Domain Decomposition Methodology . 101 B.1.3 Numerical Integration in Time . 106 B.1.4 Reduced Interface Problem . 107 B.1.5 Solution Algorithm . 109 B.2 Coding Implementation . 110 B.2.1 Existing Framework . 110 B.2.2 Existing Multi-Threading . 111 B.2.3 Message Passing in Java . 112 B.2.4 Object Layout . 113 CONTENTS v B.3 Results . 115 B.3.1 Verification . 115 B.3.2 Performance and Scaling . 116 B.4 Conclusions . 123 Bibliography 124 List of Figures 1.1 Sketch of upward flame spread at an inclination angle, θ, showing the flame height, Sf , and pyrolysis length, Sp. ...................... 2 2.1 Illustration of element expansion process in 1D for (a) temperature and (b) reaction progress variable at t = 0 s and 180 s. 29 2.2 Coupon scale simulations showing (a) instantaneous snapshots of tempera- ture (solid lines) and α (dashed lines) at t = 775, 1775 and 2025 s for a 10 oC=min heating rate and (b) comparison of predictions of solid mass frac- tion (solid lines) to TGA data from Quintiere et al. (symbols) and their curve fit using a first-order Arrhenius rate model. 30 2.3 Time-to-ignition cases with simulated sealed and open right boundaries com- pared against time-to-ignition data provided by QWC. 31 2.4 One-sided heating cases with open right boundary showing heat release rate (HRR) comparisons for incident heat fluxes of (a) 25 kW=m2, (b) 50 kW=m2, (c) 75 kW=m2 and (d) 100 kW=m2........................ 32 2.5 One-sided heating cases with sealed right boundary showing heat release rate (HRR) comparisons for incident heat fluxes of (a) 25 kW=m2, (b) 50 kW=m2, (c) 75 kW=m2 and (d) 100 kW=m2........................ 33 2.6 Instantaneous snapshots of (a) T & α and (b) pg & K at t = 25, 50 and 75 s. Symbols denote position of FE nodes. 34 2.7 Comparisons of predictions of (a) V=Vo, Vg=Ve & Yrc and (b) Yrcf to data with increasing incident heat flux. 35 3.1 Classification of CFD nodes as either being defined as either inside (xp1, xp3, xp4) or outside (xp2) the projected volumes associated with the surface mesh. 60 vi LIST OF FIGURES vii 3.2 Identification of nearest node (xc) and attached surface elements for the calculation of the of level set function. 60 3.3 Illustrations of patch level growth starting from the original surface mesh. 61 3.4 Level set function initialization with patch levels of (a) 0 (original mesh), (b) -1, (c) -2 and (d) -3 for every node n the Eulerian mesh. Patches are indicated as different colored lines on the surface mesh (a rectangle). 61 3.5 Ghost-fluid mirroring showing the ghost-fluid node of interest, xG and its evaluation using linear extrapolation across the interface from the gas-phase at location, x.................................... 62 3.6 Flow over a moving 2D cylinder and a 3D sphere showing (a) vorticity con- tours around a cylinder, and (b) vorticity contours around a sphere with an isosurface at a vorticity of 5000 and contours of density. 63 3.7 Mass conservation errors for moving cylinder and sphere cases showing (a) mass conservation errors for high (dashed red) and low (black) resolution cylinder cases, and (b) mass conservation errors for high (dashed red) and low (black) resolution sphere cases. 64 3.8 Flow shedding over a stationary cylinder showing (a) Von Karman vortex streak, (b) cross-stream velocity along the centerline at 0:5 diameters down- stream and (c) pressure coefficient and percent error along the upper surface (0o corresponds to the upstream stagnation point). 65 3.9 Conjugate heat transfer for an isothermal plate showing (a) problem sketch, (b) instantaneous snapshot of temperature contours, (c) NuL vs. RaL for inclination angles of 30o and 60o. Green symbols are cases for which the mesh is aligned with the surface and the gravity vector changed. 66 3.10 One-dimensional diffusion test problem results showing (a) steady state mass fraction distribution and (b) L2 error for the \standard" ghost-fluid method, area modified ghost-fluid method, and exact interface treatment using an Eulerian method. 67 3.11 A sketch of the sublimation validation problem of section 3.3.5. 68 3.12 One-dimensional sublimation test problem results showing (a) the predicted interface location with grid refined compared to the analytical solution and (b) L2 relative error norm for the non-dimensional interface location, velocity, and heat flux. 69 LIST OF FIGURES viii 4.1 Fully coupled simulation showing the CFD and FE domains along with igniter. 76 4.2 The L2 relative error norm in average surface temperature and total heat to the surface for the fully coupled simulations in one and two dimensions. 77 4.3 Fully coupled simulations of the carbon-epoxy composite showing mass frac- tion of CH1:3O0:2, gas and composite temperatures after (a) 2:5 s (b) 3:5 s and (c) 4 s. .................................... 79 4.4 Fully coupled simulation showing the CFD and FE domains along with inert backer-board and igniter flame region. 80 4.5 Fully coupled simulations of the carbon-epoxy composite with an uniform applied heat flux of 14:2 kW=m2 after (a) 15 s (b) 30 s and (c) 45 s. 82 4.6 Time history of integrated heat flux over the composite surface for applied heat fluxes of 0:0, 10:0, 14:2, and 20:0 kW=m2. 83 A.1 Sketch of a balsa slab response to heating from a fire.