Implementation of Radiation, Ablation, and Free Energy Minimization in Hypersonic Simulations

Aj–Ej = curve fit constants for Kj T to define equilibrium relation for nonbase species j ~ ci;abl = elemental mass fraction of element i in ablation products Dj = effective diffusion coefficient for species j, LrefV1 F = transformation matrix from species continuity to elemental continuity equations Fi;j = element of F defined in Eq. (1) f = species flux vector frad = fraction of divergence of radiative flux introduced into flow solver, Eq. (19) Gj;k = coefficient of ln k in partial equilibrium relation for nonbase species j [Eq. (10)] Hn = enthalpy of species n, J=kmole Kj T = equilibrium constant for reaction j, Eq. (11) Lref = reference length used to nondimensionalize distance, m ~ Mi = molecular weight of element i, kg=kmole Mj = molecular weight of species j, kg=kmole _ m = blowing rate of ablation products per unit area, 1V1 Ne = number of elements Nexchange = frequency for updating ghost cells Nrad = frequency for updating divergence of radiative flux in interior Ns = number of species pn = partial pressure of species n, atm p = pressure, 1V 2 1 q = vector of dependent variables, species densities, 1 q = heating rate,W=m R = universal gas constant, 8314.3, J=K kmole R = modified gas constant Sn = entropy of species n, J=K kmole T = temperature, K t = time, Lref=V1 _ w = vector of chemical source terms, 1V1=Lref x, y = distance in Cartesian coordinates, Lref u, v = velocities in x and y directions, respectively, V1 ~ Vi = diffusion velocity of element i, V1 Vj = diffusion velocity of species j, V1 V1 = reference velocity in the freestream, m=s Z = 10; 000=T used in Eq. (11) i;j = number of atoms of element i in species j m;j = stoichiometric coefficient of reactant m in nonbase species relation j n;j = stoichiometric coefficient of product n in nonbase species relation j F j = change in free energy in Eqs. (7) and (8), J=kmole = surface emissivity " = damping coefficient on surface temperature updates ~ i = density of element i, 1 j = density of species j, 1 1 = reference density in the freestream, kg=m 3 = Stefan-Boltzmann constant, 5:66961 10 8 W= m K j = mole fraction of species j

[1]  Christopher O. Johnston,et al.  Nonequilibrium Stagnation-Line Radiative Heating for Fire II , 2008 .

[2]  Cheatwood F. McNeil,et al.  User''s Manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) , 1996 .

[3]  W. I. Scallion,et al.  Flight parameters and vehicle performance for Project Fire Flight II, launched May 22, 1965 , 1966 .

[4]  Alireza Mazaheri,et al.  A Study of Ablation-Flowfield Coupling Relevant to the Orion Heatshield , 2012 .

[5]  Frank S. Milos,et al.  Ablation and Thermal Response Program for Spacecraft Heatshield Analysis , 1999 .

[6]  Kam-Pui Lee,et al.  Viscous-shock-layer solutions with coupled radiation and ablation injection for earth entry , 1990 .

[7]  Christopher O. Johnston,et al.  Nonequilibrium Shock-Layer Radiative Heating for Earth and Titan Entry , 2006 .

[8]  W. K. Anderson,et al.  An implicit upwind algorithm for computing turbulent flows on unstructured grids , 1994 .

[9]  Akihiro Sasoh,et al.  Numerical Simulation of Galileo Probe Entry Flowfield with Radiation and Ablation , 2005 .

[10]  C. Johnston.  A Comparison of EAST Shock-Tube Radiation Measurements with a New Air Radiation Model , 2008 .

[11]  P. Gnoffo,et al.  Multi-Component Diffusion With Application to Computational Aerothermodynamics , 1998 .

[12]  Peter A. Gnoffo,et al.  The Influence of Ablation on Radiative Heating for Earth Entry , 2009 .

[13]  Alireza Mazaheri,et al.  A Study of Ablation-Flowfield Coupling Relevant to Orion Heatshield , 2009 .

[14]  Chul Park,et al.  Stagnation-Point Radiation for Apollo 4 , 2004 .

[15]  Kazuhisa Fujita,et al.  Impact of Ablation Gas Kinetics on Hyperbolic Entry Radiative Heating , 2006 .

[16]  James N. Moss,et al.  Radiative Viscous-Shock-Layer Solutions with Coupled Ablation Injection , 1976 .

[17]  L. B. Garrett,et al.  An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing , 1972 .

[18]  Kam-Pui Lee,et al.  Viscous shock-layer solutions with coupled radiation and ablation for earth entry , 1992 .