An implicit ablation and thermal response program is presented for simulation of one-dimensional transient thermal energy transport in a multilayer stack of isotropic materials and structure that can ablate from a front surface and decompose in depth. The governing equations and numerical procedures for solution are summarized. Solutions are compared with those of an existing code, CMA, and also with arcjet data. Numerical experiments show that the new code is numerically more stable and solves a much wider range of problems compared with the older code. To demonstrate its capability, applications for thermal analysis and sizing of aeroshell heatshields for planetary missions of Stardust, Mars Microprobe (Deep Space II), Saturn Entry Probe, and Mars 2001, using advanced lightweight ceramic ablators developed at NASA Ames Research Center, are presented and discussed. Nomenclature a = absorption coef cient, m ¡1 B 0 = dimensionless mass blowing rate, P m=½ e u e C M B a = pre-exponential constant in Eq. (8), s ¡1 C H = Stanton number for heat transfer C M = Stanton number for mass transfer c p = speci c heat, J/kg-K E a = activation temperature in Eq. (8), K F = view factor g = outward pyrolysis mass ux, kg/m 2 -s h = enthalpy, J/kg N h = partial heat of charring, de ned in Eq. (6), J/kg I 0 = radiation source function in Eq. (2), W/m 2 -sr i C = radiant intensity in Cx direction, W/m 2 -sr i ¡ = radiant intensity in ¡x direction, W/m 2 -sr K = extinction coef cient, a C ¾ s , m ¡1 k = thermal conductivity, W/m-K P m = mass ux, kg/m 2 -s P = pressure, N/m 2 q C = conductive heat ux, W/m 2 q R = radiative heat ux, W/m 2 R = universal gas constant, J/kmol-K s = surface recession, m P s = surface recession rate, m/s T = temperature, K u = velocity, m/s x = moving coordinate, y ¡ s, m y = stationary coordinate, m Z ¤ = coef cient in Eq. (9), de ned in Ref. 10 ® = surface absorptance 0 = volume fraction of resin " = surface emissivity µ = time, s · = optical thickness · D = optical thickness for path of length Ḑ = blowing reduction parameter ½ = density, kg/m 3 ¾ = Stefan-Boltzmann constant, W/m 2 -K 4 ¾ s = scattering coef cient, m ¡1 ¿ = mass fraction of virgin material, de ned in Eq. (5) 9 = decomposition reaction order in Eq. (8) Subscripts c = char e = boundary-layeredge g = pyrolysis gas i = density component (A, B, and C ) j = surface species v = virgin w = wall

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A general theory is presented for ablation thermochemistry of thermal protection materials with multiple surface species. The theory includes capability for simultaneous ablation, pyrolysis, surface-element constraints, nonequilibrium surface reactions, and material failure. Numerical procedures for solution of the equations are described and incorporated into the Multicomponent Ablation Thermochemistry code. The theory and code are extensions of traditional methodology for generating dimensionless ablation tables. Solutions for materials containing silicon and carbon are presented and discussed. The results compare favorably with arcjet, ablation data for the Shuttle Orbiter reinforced carbon-carbon oxidation protection system which contains sodium silicate, silicon carbide, silica, and carbon. (Author) Abstract A general theory is presented for ablation thermochemistry of thermal protection materials with multiple surface species. The theory includes capability for simultaneous ablation, pyrolysis, surface-element constraints, nonequilibrium surface reactions, and material failure. Numerical procedures for solution of the equations are described and incorporated into the Multicomponent Ablation Thermochemistry code. The theory and code are extensions of traditional methodology for generating dimensionlcss ablation tables. Solutions for materials containing silicon and carbon are presented and discussed. The results compare favorably with arcjet ablation data for the Shuttle Obiter reinforced carbon-carbon oxidation protection system which contains sodium silicate, silicon carbide, silica, and carbon. Nomenclature B = Reaction constant, SI units B' = m/p,.u e C M , dimensionless mass flux C H = Stanton number for heat transfer C M = Stanton number for mass transfer cj. n = Atoms of element k in species n d = Constrained normalized stoichiometric coefficient E = Vector of equation errors E -Reaction activation temperature, K F = Equilibrium modification factor h = Static enthalpy, J/kg / = Number of gas-phase species J = Jacobian matrix j -Diffusion mass flux, kg/m 2 -s K = Number of elements 1C = Equilibrium constant, pressure units L -Number of condensed-phase species M = Molecular weight, kg/kmol m = Surface mass flux, kg/m 2 -s N = Molecular formula for a species P = Pressure, kg/m-s 2 T = Temperature, K u = Boundary layer velocity, m/s V = Surface-normal velocity, m/s R -Net reaction rate, kmol/m 2 -s f = Forward reaction rate, SI units X = Vector of unknowns X = Surface mole fraction Y = Element mass fraction Z* = Element diffusive fraction, Eq.(3) Zjt = Moles of element k per mole of char H = Reaction stoichiometric coefficient i/ ku = Molecules of base species k in species n

An implicit ablation and thermal response program is presented for simulation of one-dimensional transient thermal energy transport in a multilayer stack of isotropic materials and structure which can ablate from a front surface and decompose in-depth. The governing equations and numerical procedures for solution are summarized. Solutions are compared with those of an existing code, the Aerotherm Charring Material Thermal Response and Ablation Program, and also with arcjet data Numerical experiments show that the new code is numerically more stable and solves a much wider range of problems compared with the older code. To demonstrate its capability, applications for thermal analysis and sizing of aeroshell heatshields for planetary missions, such as Stardust, Mars Microprobe (Deep Space n), Saturn Entry Probe, and Mars 2001, using advanced light-weight ceramic ablators developed at NASA Ames Research Center, are presented and discussed. Nomenclature a B' F g h h I' K k rh = absorption coefficient, m"' = rh / p e u e C M , dimensionless mass blowing rate = pre-exponential constant in Eq.(8), s" 1 = Stanton number for heat transfer = Stanton number for mass transfer = specific heat, J/kg-K = activation energy in Eq.(8), J/kmol = exponential integral function = view factor = outward pyrolysis mass flux, kg/m 2 -s = enthalpy, J/kg = partial heat of charring, defined in Eq.(6), J/kg = radiation source function in Eq.(2), W/m 2 -sr = radiant intensity in +x direction, W/m 2 -sr = radiant intensity in -x direction, W/m 2 -sr = a + o s , extinction coefficient, m" 1 = thermal conductivity, W/m-K = mass flux, kg/m 2 -s * Aerospace Engineer. t Aerospace Engineer. Senior Member AIAA. P = pressure, N/m 2 q c = conductive heat flux, W/m 2 qn = radiative heat flux, W/m 2 R = universal gas constant, J/kmol-K s = surface recession, m s = surface recession rate, m/s T = temperature, K u = velocity, m/s x = y -s, moving coordinate, m y = stationary coordinate, m Z* = coefficient in Eq.(9), defined in Ref. 14 a = surface absorptance e = surface emissivity F = volume fraction of resin K = optical thickness K D = optical thickness for path of length D A, = blowing reduction parameter 9 = time, s p = total density, kg/m 3 a = Stefan-Boltzmann constant, W/m 2 -K 4 a s = scattering coefficient, m" 1 I = mass fraction of virgin material, defined in Eq.(5) T = decomposition reaction order in Eq.(8) subscripts c = char e = boundary-layer edge g = pyrolysis gas i = density component (A, B, and C) j = surface species v = virgin w = wall

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