1932

Abstract

Ablative thermal protection systems have experienced renewed interest in the past decade owing to the retirement of NASA's Space Shuttle fleet and the US presidential mandate to develop technologies that enable humans to explore space beyond low Earth orbit. Blunt body architecture for spacecraft and the use of ablators for thermal protection systems returned as the primary choice in mission planning. This review addresses current progress in modernizing predictive tools for ablative material response. Current theory development leverages progress made in the theory of flows in porous media. This development, combined with progress in experimental techniques and high-end computing, is enabling the development of 3D macroscale models with realistic closure coefficients derived from direct numerical simulations of 3D microscale geometries of actual materials. While flight data quantifying ablative material response remain sparse, the next decade will be one of exploration in which heatshield instrumented spacecraft will provide crucial flight data for refining and validating closure models.

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2024-01-19
2024-04-29
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Literature Cited

  1. Aavatsmark I. 2002. An introduction to multipoint flux approximations for quadrilateral grids. Comput. Geosci. 6:3405–32
    [Google Scholar]
  2. Allen HJ, Eggers AJJ. 1953. A study of the motion and aerodynamic heating of ballistic missiles entering the Earth's atmosphere at high supersonic speeds Tech. Rep. NACA RM A53D28 Natl. Advis. Comm. Aeronaut. Moffett Field, CA:
  3. Amar A, Calvert N, Kirk B. 2011. Development and verification of the charring ablating thermal protection implicit system solver Paper presented at 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition Orlando, FL: AIAA Pap. 2011-144
  4. Bachmat Y, Bear J. 1986. Macroscopic modelling of transport phenomena in porous media. 1: The continuum approach. Transport Porous Media 1:3213–40
    [Google Scholar]
  5. Bailey SC, Bauer D, Panerai F, Splinter SC, Danehy PM et al. 2018. Experimental analysis of spallation particle trajectories in an arc-jet environment. Exp. Thermal Fluid Sci. 93:319–25
    [Google Scholar]
  6. Bartlett EP, Kendall RM, Rindal RA. 1968. An analysis of the coupled chemically reacting boundary layer and charring ablator. Part 3 - nonsimilar solution of the multicomponent laminar boundary layer by an integral matrix method Tech. Rep. NASA CR-1062 Natl. Aeronaut. Space Adm. Moffett Field, CA:
  7. Bear J. 1988. Dynamics of Fluids in Porous Media New York: Dover
  8. Bear J, Bachmat Y. 1967. Generalized theory on hydrodynamic dispersion in porous media. Int. Union Geod. Geophys. Publ. 72:7–16
    [Google Scholar]
  9. Beavers GS, Joseph DD. 1967. Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30:1197–207
    [Google Scholar]
  10. Beck RA, Driver DM, Wright MJ, Hwang HH, Edquist KT, Sepka SA. 2014. Development of the Mars Science Laboratory heatshield Thermal Protection System. J. Spacecr. Rocket. 51:41139–50
    [Google Scholar]
  11. Bessire BK, Minton TK. 2017. Decomposition of phenolic impregnated carbon ablator (PICA) as a function of temperature and heating rate. ACS Appl. Mater. Interfaces 9:2521422–37
    [Google Scholar]
  12. Bhattacharya A, Das A, Moser RD. 2008. A filtered-wall formulation for large-eddy simulation of wall-bounded turbulence. Phys. Fluids 20:11115104
    [Google Scholar]
  13. Borner A, Panerai F, Mansour NN. 2017. High temperature permeability of fibrous materials using direct simulation Monte Carlo. Int. J. Heat Mass Transf. 106:1318–26
    [Google Scholar]
  14. Bose D, White T, Mahzari M, Edquist K. 2014. Reconstruction of aerothermal environment and heat shield response of Mars Science Laboratory. J. Spacecr. Rocket. 51:41174–84
    [Google Scholar]
  15. Breugem W. 2005. The influence of wall permeability on laminar and turbulent flows: theory and simulations PhD Thesis Tech. Univ. Delft Neth.:
  16. Breugem W, Boersma B. 2002. The turbulent flow over a permeable wall. Proceedings of the Summer Program 2002215–28. Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  17. Breugem WP, Boersma BJ. 2005. Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach. Phys. Fluids 17:2025103
    [Google Scholar]
  18. Breugem WP, Boersma BJ, Uittenbogaard RE. 2006. The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562:35–72
    [Google Scholar]
  19. Candler GV. 2019. Rate effects in hypersonic flows. Annu. Rev. Fluid Mech. 51:379–402
    [Google Scholar]
  20. Chandesris M, d'Hueppe A, Mathieu B, Jamet D, Goyeau B. 2013. Direct numerical simulation of turbulent heat transfer in a fluid-porous domain. Phys. Fluids 25:12125110
    [Google Scholar]
  21. Chandesris M, Jamet D. 2006. Boundary conditions at a planar fluid–porous interface for a Poiseuille flow. Int. J. Heat Mass Transf. 49:13–142137–50
    [Google Scholar]
  22. Chandesris M, Jamet D. 2007. Boundary conditions at a fluid–porous interface: an a priori estimation of the stress jump coefficients. Int. J. Heat Mass Transf. 50:17–183422–36
    [Google Scholar]
  23. Chen YK, Milos FS. 1999. Ablation and thermal response program for spacecraft heatshield analysis. J. Spacecr. Rocket. 36:3475–83
    [Google Scholar]
  24. Chen YK, Milos FS. 2005. Navier-Stokes solutions with finite rate ablation for planetary mission Earth reentries. J. Spacecr. Rocket. 42:6961–70
    [Google Scholar]
  25. Darcy H. 1856. Les Fontaines Publiques de la Ville de Dijon: Exposition et Application des Principes à Suivre et des Formules à Employer dans les Questions de Distribution d'Eau. Un Appendice Relatif aux Fournitures d'Eau de Plusieurs Villes au Filtrage des Eaux, Vol. 1 V. Dalmont Paris: Librairie Des Corps Superiaux Des Pont et Chaussee et Des Mine
  26. Daryabeigi K, Cunnington GR, Knutson JR. 2011. Combined heat transfer in high-porosity high-temperature fibrous insulation: theory and experimental validation. J. Thermophys. Heat Transf. 25:4536–46
    [Google Scholar]
  27. Das A. 2004. A filtered-wall formulation for large-eddy simulation of wall-bounded turbulence PhD Thesis Univ. Illinois Urbana-Champaign:
  28. Davit Y, Bell CG, Byrne HM, Chapman LA, Kimpton LS et al. 2013. Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?. Adv. Water Resour. 62:178–206
    [Google Scholar]
  29. De Socio L, Marino L. 2006. Gas flow in a permeable medium. J. Fluid Mech. 557:119–33
    [Google Scholar]
  30. Driver D, MacLean M. 2011. Improved predictions of PICA recession in arc jet shear tests Paper presented at 49th AIAA Aerospace Sciences Meeting Orlando, FL: AIAA Pap. 2011-141
  31. Ferguson JC, Borner A, Panerai F, Close S, Mansour NN. 2022. Continuum to rarefied diffusive tortuosity factors in porous media from X-ray microtomography. Comput. Mater. Sci. 203:111030
    [Google Scholar]
  32. Ferguson JC, Panerai F, Borner A, Mansour NN. 2018. PuMA: the Porous Microstructure Analysis software. SoftwareX 7:81–87
    [Google Scholar]
  33. Ferguson JC, Panerai F, Lachaud J, Mansour NN. 2017. Theoretical study on the micro-scale oxidation of resin-infused carbon ablators. Carbon 121:552–62
    [Google Scholar]
  34. Ferguson JC, Panerai F, Lachaud J, Martin A, Bailey SC, Mansour NN. 2016. Modeling the oxidation of low-density carbon fiber material based on micro-tomography. Carbon 96:57–65
    [Google Scholar]
  35. Florio J Jr., Henderson JB, Test FL, Hariharan R. 1991. A study of the effects of the assumption of local-thermal equilibrium on the overall thermally-induced response of a decomposing, glass-filled polymer composite. Int. J. Heat Mass Transf. 34:1135–47
    [Google Scholar]
  36. Gazarik MJ, Little A, Cheatwood F, Wright JM, Herath JA et al. 2008. Overview of the MEDLI project IEEE Pap. 2008-1510
  37. Giovangigli V. 1999. Multicomponent Flow Modeling New York: Springer Science+Business Media
  38. Gnoffo PA, Gupta RN, Shinn JL. 1989. Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium Tech. Rep. NASA-TP-2867 Natl. Aeronaut. Space Adm. Moffett Field, CA:
  39. Goldstein D, Handler R, Sirovich L. 1993. Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105:2354–66
    [Google Scholar]
  40. Goldstein HE. 1965. Kinetics of nylon and phenolic pyrolysis Tech. Rep. LMSC-667876 Lockheed Missiles Space Co. Sunnyvale, CA:
  41. Goldstein R, Eckert E, Ibele W, Patankar S, Simon T et al. 2005. Heat transfer—a review of 2002 literature. Int. J. Heat Mass Transf. 48:5819–927
    [Google Scholar]
  42. Gray WG, Lee P. 1977. On the theorems for local volume averaging of multiphase systems. Int. J. Multiphase Flow 3:4333–40
    [Google Scholar]
  43. He X, Apte SV, Finn JR, Wood BD. 2019. Characteristics of turbulence in a face-centred cubic porous unit cell. J. Fluid Mech. 873:608–45
    [Google Scholar]
  44. Helber B, Chazot O, Hubin A, Magin TE. 2015. Microstructure and gas-surface interaction studies of a low-density carbon-bonded carbon fiber composite in atmospheric entry plasmas. Composites Part A Appl. Sci. Manuf. 72:96–107
    [Google Scholar]
  45. Hornung U. 1997. Homogenization and Porous Media New York: Springer Science+Business Media
  46. Irmay S. 1958. On the theoretical derivation of Darcy and Forchheimer formulas. Eos Trans. Am. Geophys. Union 39:4702–7
    [Google Scholar]
  47. Jin Y, Kuznetsov AV. 2017. Turbulence modeling for flows in wall bounded porous media: an analysis based on direct numerical simulations. Phys. Fluids 29:4 045102.
    [Google Scholar]
  48. Kendall RM, Bartlett EP, Rindal RA, Moyer CB. 1968. An analysis of the coupled chemically reacting boundary layer and charring ablator. Part 1 to 6 Tech. Rep. NASA CR-1060 to CR-1065 Natl. Aeronaut. Space Adm. Moffett Field, CA:
  49. Kirk BS. 2007. Adaptive finite element simulation of flow and transport applications on parallel computers PhD Thesis Univ. Texas, Austin:
  50. Klinkenberg L. 1941. The permeability of porous media to liquids and gases. Drilling and Production Practices200–13. New York: American Petroleum Institute
    [Google Scholar]
  51. Krause M, Hausherr JM, Burgeth B, Herrmann C, Krenkel W. 2010. Determination of the fibre orientation in composites using the structure tensor and local X-ray transform. J. Mater. Sci. 45:4888–96
    [Google Scholar]
  52. Krygier MC, LaBonte T, Martinez C, Norris C, Sharma K et al. 2021. Quantifying the unknown impact of segmentation uncertainty on image-based simulations. Nat. Commun. 12:15414
    [Google Scholar]
  53. Lachaud J. 2006. Modelisation physico–chimique de l'ablation de matériaux composites en carbone PhD Thesis Univ. Bordeaux I, France:
  54. Lachaud J, Aspa Y, Vignoles GL. 2017a. Analytical modeling of the transient ablation of a 3D C/C composite. Int. J. Heat Mass Transf. 155:1150–65
    [Google Scholar]
  55. Lachaud J, Cozmuta I, Mansour NN. 2010. Multiscale approach to ablation modeling of phenolic impregnated carbon ablators. J. Spacecr. Rocket. 47:6910–21
    [Google Scholar]
  56. Lachaud J, Mansour NN. 2014. Porous-material analysis toolbox based on OpenFOAM and applications. J. Thermophys. Heat Transf. 28:2191–202
    [Google Scholar]
  57. Lachaud J, Scoggins J, Magin T, Meyer M, Mansour N. 2017b. A generic local thermal equilibrium model for porous reactive materials submitted to high temperatures. Int. J. Heat Mass Transf. 108:1406–17
    [Google Scholar]
  58. Lachaud J, van Eekelen T, Scoggins JB, Magin TE, Mansour NN. 2015. Detailed chemical equilibrium model for porous ablative materials. Int. J. Heat Mass Transf. 90:1034–45
    [Google Scholar]
  59. Lachaud J, Vignoles GL. 2009. A Brownian motion technique to simulate gasification and its application to C/C composite ablation. Comput. Mater. Sci. 44:41034–41
    [Google Scholar]
  60. Le Foll S, André F, Delmas A, Bouilly J, Aspa Y 2012. Radiative transfer modelling inside thermal protection system using hybrid homogenization method for a backward Monte Carlo method coupled with MIE theory. J. Phys. Conf. Ser. 369:012028
    [Google Scholar]
  61. Lee S. 1989. Effect of fiber orientation on thermal radiation in fibrous media. Int. J. Heat Mass Transf. 32:2311–19
    [Google Scholar]
  62. Leonard A. 1975. Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18:237–48
    [Google Scholar]
  63. Leroy V, Goyeau B, Taine J. 2013. Coupled upscaling approaches for conduction, convection, and radiation in porous media: theoretical developments. Transport Porous Media 98:2323–47
    [Google Scholar]
  64. MacNeil JML, Ushizima DM, Panerai F, Mansour NN, Barnard HS, Parkinson DY. 2019. Interactive volumetric segmentation for textile micro-tomography data using wavelets and nonlocal means. Stat. Anal. Data Min. 12:4338–53
    [Google Scholar]
  65. Mahzari M, Braun RD, White TR, Bose D. 2015. Inverse estimation of the Mars Science Laboratory entry aeroheating and heatshield response. J. Spacecr. Rocket. 52:41203–16
    [Google Scholar]
  66. Marle C. 1967. Ecoulements monophasiques en milieu poreux. Rev. Inst. Fr. Pet. 22:101471–509
    [Google Scholar]
  67. Marle C. 1982. On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media. Int. J. Eng. Sci. 20:5643–62
    [Google Scholar]
  68. Marschall J, MacLean M, Norman PE, Schwartzentruber TE. 2015. Surface chemistry in non-equilibrium flows. Hypersonic Nonequilibrium Flows: Fundamentals Recent Advances E Josyula 239–327. Reston, VA: AIAA
    [Google Scholar]
  69. Marschall J, Milos FS. 1997. The calculation of anisotropic extinction coefficients for radiation diffusion in rigid fibrous ceramic insulations. Int. J. Heat Mass Transf. 40:3627–34
    [Google Scholar]
  70. Marschall J, Milos FS. 1998. Gas permeability of rigid fibrous refractory insulations. J. Thermophys. Heat Transf. 12:4528–35
    [Google Scholar]
  71. Martin A, Boyd ID. 2010. Non-Darcian behavior of pyrolysis gas in a thermal protection system. J. Thermophys. Heat Transf. 24:160–68
    [Google Scholar]
  72. Martin A, Zhang H, Tagavi KA. 2017. An introduction to the derivation of surface balance equations without the excruciating pain. Int. J. Heat Mass Transf. 115:992–99
    [Google Scholar]
  73. Matheron G. 1965. Les Variables Régionalisées et leur Estimation [Regionalized Variables and Their Estimation] Paris: Editions Masson
    [Google Scholar]
  74. Meurisse JB, Lachaud J, Panerai F, Tang C, Mansour NN. 2018. Multidimensional material response simulations of a full-scale tiled ablative heatshield. Aerosp. Sci. Technol. 76:497–511
    [Google Scholar]
  75. Milos F, Chen YK. 1997. Comprehensive model for multicomponent ablation thermochemistry Paper presented at 35th Aerospace Sciences Meeting and Exhibit Reno, NV: AIAA Pap. 1997-141
  76. Milos FS, Rasky DJ. 1994. Review of numerical procedures for computational surface thermochemistry. J. Thermophys. Heat Transf. 8:124–34
    [Google Scholar]
  77. Mittal R, Iaccarino G. 2005. Immersed boundary methods. Annu. Rev. Fluid Mech. 37:239–61
    [Google Scholar]
  78. Moyer CB, Rindal RA. 1968. An analysis of the coupled chemically reacting boundary layer and charring ablator: Part 2 - finite difference solution for the in-depth response of charring materials considering surface chemical and energy balances Tech. Rep. NASA CR-1061 Natl. Aeronaut. Space Adm. Moffett Field, CA:
  79. Murray VJ, Marshall BC, Woodburn PJ, Minton TK. 2015. Inelastic and reactive scattering dynamics of hyperthermal O and O2 on hot vitreous carbon surfaces. J. Phys. Chem. C 119:2614780–96
    [Google Scholar]
  80. Murray VJ, Minton TK. 2019. Gas-surface interactions of atomic nitrogen with vitreous carbon. Carbon 150:85–92
    [Google Scholar]
  81. Murray VJ, Recio P, Caracciolo A, Miossec C, Balucani N et al. 2020. Oxidation and nitridation of vitreous carbon at high temperatures. Carbon 167:388–402
    [Google Scholar]
  82. Natali M, Kenny JM, Torre L 2016. Science and technology of polymeric ablative materials for thermal protection systems and propulsion devices: a review. Prog. Mater. Sci. 84:192–275
    [Google Scholar]
  83. Nouri N, Martin A. 2015. Three dimensional radiative heat transfer model for the evaluation of the anisotropic effective conductivity of fibrous materials. Int. J. Heat Mass Transf. 83:629–35
    [Google Scholar]
  84. Nouri N, Panerai F, Tagavi KA, Mansour NN, Martin A. 2016. Evaluation of the anisotropic radiative conductivity of a low-density carbon fiber material from realistic microscale imaging. Int. J. Heat Mass Transf. 95:535–39
    [Google Scholar]
  85. Ochoa-Tapia JA, Whitaker S. 1995. Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development. Int. J. Heat Mass Transf. 38:142635–46
    [Google Scholar]
  86. Panerai F, Cochell T, Martin A, White JD. 2019. Experimental measurements of the high-temperature oxidation of carbon fibers. Int. J. Heat Mass Transf. 136:972–86
    [Google Scholar]
  87. Panerai F, Ferguson JC, Lachaud J, Martin A, Gasch MJ, Mansour NN. 2017. Micro-tomography based analysis of thermal conductivity, diffusivity and oxidation behavior of rigid and flexible fibrous insulators. Int. J. Heat Mass Transf. 108:801–11
    [Google Scholar]
  88. Panerai F, Martin A, Mansour NN, Sepka SA, Lachaud J. 2014. Flow-tube oxidation experiments on the carbon preform of a phenolic-impregnated carbon ablator. J. Thermophys. Heat Transf. 28:2181–90
    [Google Scholar]
  89. Panerai F, White JD, Cochell TJ, Schroeder OM, Mansour NN et al. 2016. Experimental measurements of the permeability of fibrous carbon at high-temperature. Int. J. Heat Mass Transf. 101:267–73
    [Google Scholar]
  90. Park C. 1976. Effects of atomic oxygen on graphite ablation. AIAA J. 14:111640–42
    [Google Scholar]
  91. Penide-Fernandez R, Sansoz F. 2021. Microscale Knudsen effect over the transverse thermal conductivity of woven ceramic fabrics under compression. Int. J. Heat Mass Transf. 171:121085
    [Google Scholar]
  92. Peskin CS. 1972. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10:2252–71
    [Google Scholar]
  93. Petrov VA. 1997. Combined radiation and conduction heat transfer in high temperature fiber thermal insulation. Int. J. Heat Mass Transf. 40:92241–47
    [Google Scholar]
  94. Poovathingal S, Schwartzentruber TE, Murray VJ, Minton TK. 2016. Molecular simulation of carbon ablation using beam experiments and resolved microstructure. AIAA J. 54:3999–1010
    [Google Scholar]
  95. Poovathingal S, Schwartzentruber TE, Murray VJ, Minton TK, Candler GV. 2017. Finite-rate oxidation model for carbon surfaces from molecular beam experiments. AIAA J. 55:51644–58
    [Google Scholar]
  96. Prata KS, Schwartzentruber TE, Minton TK. 2022. Air–carbon ablation model for hypersonic flight from molecular-beam data. AIAA J. 60:2627–40
    [Google Scholar]
  97. Price KJ, Panerai F, Borchetta CG, Hardy JM, Martin A, Bailey SC. 2022. Arc-jet measurements of low-density ablator spallation. Exp. Thermal Fluid Sci. 133:110544
    [Google Scholar]
  98. Puiroux N, Prat M, Quintard M. 2004. Non-equilibrium theories for macroscale heat transfer: ablative composite layer systems. Int. J. Thermal Sci. 43:6541–54
    [Google Scholar]
  99. Quintard M. 2015. Introduction to heat and mass transport in porous media. Porous Media Interaction with High Temperature and High Speed Flows O Chazot, F Panerai 42 Sint-Genesius-Rode, Belg.: von Karman Inst.
    [Google Scholar]
  100. Rindal R, Flood D, Kendall R. 1966. Analytical and experimental study of ablation material for rocket engine application final report Tech. Rep. NASA CR-54757 Natl. Aeronaut. Space Adm. Moffett Field, CA:
  101. Saffman PG. 1971. On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50:293–101
    [Google Scholar]
  102. Salathé EP, Sirovich L. 1967. Boundary-value problems in compressible magnetohydrodynamics. Phys. Fluids 10:71477–91
    [Google Scholar]
  103. Saunders DA, Prabhu DK. 2018. BLAYER user guide Tech. Rep. NASA TM-2018-219749 Natl. Aeronaut. Space Adm. Moffett Field, CA:
  104. Scala SM, Gilbert LM. 1962. Thermal degradation of a char-forming plastic during hypersonic flight. ARS J. 32:6917–24
    [Google Scholar]
  105. Schrooyen P. 2015. Numerical simulation of aerothermal flows through ablative thermal protection systems PhD Thesis Univ. Cathol. Louvain, Belg.:
  106. Schrooyen P, Hillewaert K, Magin TE, Chatelain P. 2016. Fully implicit discontinuous Galerkin solver to study surface and volume ablation competition in atmospheric entry flows. Int. J. Heat Mass Transf. 103:108–24
    [Google Scholar]
  107. Scoggins JB, Leroy V, Bellas-Chatzigeorgis G, Dias B, Magin TE. 2020. Mutation++: MUlticomponent Thermodynamic And Transport properties for IONized gases in C++. SoftwareX 12:100575
    [Google Scholar]
  108. Semeraro F, Ferguson JC, Acin M, Panerai F, Mansour NN. 2021. Anisotropic analysis of fibrous and woven materials part 2: computation of effective conductivity. Comput. Mater. Sci. 186:109956
    [Google Scholar]
  109. Semeraro F, Ferguson JC, Panerai F, King RJ, Mansour NN. 2020. Anisotropic analysis of fibrous and woven materials part 1: estimation of local orientation. Comput. Mater. Sci. 178:109631
    [Google Scholar]
  110. Sirovich L. 1967. Initial and boundary value problems in dissipative gas dynamics. Phys. Fluids 10:124–34
    [Google Scholar]
  111. Sirovich L. 1968. Steady gasdynamic flows. Phys. Fluids 11:71424–39
    [Google Scholar]
  112. Stackpoole M, Sepka S, Cozmuta I, Kontinos D. 2008. Post-flight evaluation of Stardust sample return capsule forebody heatshield material Paper presented at 46th AIAA Aerospace Sciences Meeting and Exhibit Reno, NV: AIAA Pap. 2008-1202
    [Google Scholar]
  113. Stokes EH. 1995. Kinetics of pyrolysis mass loss from cured phenolic resin. J. Thermophys. Heat Transf. 9:2352–58
    [Google Scholar]
  114. Swaminathan-Gopalan K, Borner A, Murray VJ, Poovathingal S, Minton TK et al. 2018. Development and validation of a finite-rate model for carbon oxidation by atomic oxygen. Carbon 137:313–32
    [Google Scholar]
  115. Sykes GF. 1967. Decomposition characteristics of a char-forming phenolic polymer used for ablative composites NASA TN D-3810 Natl. Aeronaut. Space Adm. Moffett Field, CA:
  116. Torres-Herrador F, Coheur J, Panerai F, Magin TE, Arnst M et al. 2020. Competitive kinetic model for the pyrolysis of the phenolic impregnated carbon ablator. Aerosp. Sci. Technol. 100:105784
    [Google Scholar]
  117. Torres-Herrador F, Meurisse JB, Panerai F, Blondeau J, Lachaud J et al. 2019. A high heating rate pyrolysis model for the phenolic impregnated carbon ablator (PICA) based on mass spectroscopy experiments. J. Anal. Appl. Pyrolys. 141:104625
    [Google Scholar]
  118. Torres-Herrador F, Turchi A, Van Geem KM, Blondeau J, Magin TE. 2021. Determination of heat capacity of carbon composites with application to carbon/phenolic ablators up to high temperatures. Aerosp. Sci. Technol. 108:106375
    [Google Scholar]
  119. Trick KA, Saliba TE. 1995. Mechanisms of the pyrolysis of phenolic resin in a carbon/phenolic composite. Carbon 33:111509–15
    [Google Scholar]
  120. Trick KA, Saliba TE, Sandhu SS. 1997. A kinetic model of the pyrolysis of phenolic resin in a carbon/phenolic composite. Carbon 35:3393–401
    [Google Scholar]
  121. Valdés-Parada FJ, Lasseux D. 2021. A novel one-domain approach for modeling flow in a fluid-porous system including inertia and slip effects. Phys. Fluids 33:2022106
    [Google Scholar]
  122. Van Eekelen A, Lachaud J. 2011. Numerical validation of an effective radiation heat transfer model for fiber preforms. J. Spacecr. Rocket. 48:3534–37
    [Google Scholar]
  123. Vignoles GL, Turchi A, Bianchi D, Blaineau P, Lamboley X et al. 2018. Ablative and catalytic behavior of carbon-based porous thermal protection materials in nitrogen plasmas. Carbon 134:376–90
    [Google Scholar]
  124. Vincenti WG, Boyd JW, Bugos GE. 2007. H. Julian Allen: an appreciation. Annu. Rev. Fluid Mech. 39:1–17
    [Google Scholar]
  125. Weng H, Bailey SC, Martin A. 2015. Numerical study of iso-Q sample geometric effects on charring ablative materials. Int. J. Heat Mass Transf. 80:570–96
    [Google Scholar]
  126. Weng H, Düzel Ü, Fu R, Martin A. 2021. Geometric effects on charring ablator: modeling the full-scale Stardust heat shield. J. Spacecr. Rocket. 58:2302–15
    [Google Scholar]
  127. Weng H, Martin A. 2014. Multidimensional modeling of pyrolysis gas transport inside charring ablative materials. J. Thermophys. Heat Transf. 28:4583–97
    [Google Scholar]
  128. Weng H, Martin A. 2017. Development of a universal solver and its application to ablation problems Paper presented at 47th AIAA Thermophysics Conference Denver, CO: AIAA Pap. 2017-3355
  129. Whitaker S. 1986a. Flow in porous media I: a theoretical derivation of Darcy's law. Transport Porous Media 1:13–25
    [Google Scholar]
  130. Whitaker S. 1986b. Local thermal equilibrium: an application to packed bed catalytic reactor design. Chem. Eng. Sci. 41:82029–39
    [Google Scholar]
  131. Whitaker S. 1999. The Method of Volume Averaging Dordrecht, Neth.: Kluwer Acad. Publ.
  132. White C, Scanlon TJ, Brown RE. 2016. Permeability of ablative materials under rarefied gas conditions. J. Spacecr. Rocket. 53:1134–42
    [Google Scholar]
  133. Wiegmann A. 2007. Computation of the permeability of porous materials from their microstructure by FFF-Stokes Tech. Rep. Berichte Fraunhofer ITWM, Nr. 129 Fraunhofer Inst. Tech. Wirtschaftsmath. Kaiserslautern, Ger.:
  134. Wiegmann A, Bube KP. 2000. The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions. SIAM J. Numer. Anal. 37:3827–62
    [Google Scholar]
  135. Wong HW, Peck J, Assif J, Panerai F, Lachaud J, Mansour NN. 2016. Detailed analysis of species production from the pyrolysis of the phenolic impregnated carbon ablator. J. Anal. Appl. Pyrolys. 122:258–67
    [Google Scholar]
  136. Wood BD, He X, Apte SV. 2020. Modeling turbulent flows in porous media. Annu. Rev. Fluid Mech. 52:171–203
    [Google Scholar]
  137. Wood BD, Valdés-Parada FJ. 2013. Volume averaging: local and nonlocal closures using a Green's function approach. Adv. Water Resour. 51:139–67
    [Google Scholar]
  138. Wright M, Hughes MF, Barnhardt M, Calomino AM. 2015. An overview of technology investments in the NASA Entry Systems Modeling project Paper presented at 53rd AIAA Aerospace Sciences Meeting Kissimmee, FL: AIAA Pap. 2015-1892
  139. Wright MJ, Beck RA, Edquist KT, Driver D, Sepka SA et al. 2014. Sizing and margins assessment of Mars Science Laboratory aeroshell thermal protection system. J. Spacecr. Rocket. 51:41125–38
    [Google Scholar]
  140. Wright MJ, Candler GV, Bose D. 1998. Data-parallel line relaxation method for the Navier-Stokes equations. AIAA J. 36:91603–9
    [Google Scholar]
  141. Yang X, Gui Y, Tang W, Du Y, Liu L et al. 2018. Surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic martian gas flow. Acta Astronaut. 147:445–53
    [Google Scholar]
  142. Zhluktov SV, Abe T. 1999. Viscous shock-layer simulation of airflow past ablating blunt body with carbon surface. J. Thermophys. Heat Transf. 13:150–59
    [Google Scholar]
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