Assessment of Gas-Surface Interaction Models for Computation of Rarefied Hypersonic Flow

Abstract

Among the few classes of computational approaches for examining rarefied gas dynamics, the most widely used technique for spatial scales relevant to suborbital spaceflight is the direct simulation Monte Carlo method. One area in which the direct simulation Monte Carlo method can be improved is the numerical modeling of the interactions between gas molecules and solid surfaces. Gas-surface interactions are not well understood for rarefied hypersonic conditions, although various models have been developed. The goal of this study is the assessment of gas-surface interaction models in use with the direct simulation Monte Carlo method. Assessment is made of the two most common gas-surface interaction models in use with direct simulation Monte Carlo: the Maxwell model and the Cercignani, Lampis, and Lord model. The assessment is performed by simulations of flat-plate wind-tunnel tests. Boundary-layer profiles are compared with existing wind-tunnel data. At about 90% accommodation, both models match the wind-tunnel profiles. Parametric studies demonstrate differences between the model predictions of scattering distributions, boundary-layer profiles, and surface-property distributions. The two models offer similar performance for computing flat-plate aerodynamics.= total enthalpy I 0 = modified Bessel function of the first kind and zeroth order K = scattering kernel Kn = global Knudsen number Kn DGL = density-gradient-length local Knudsen number m = mass of one molecule n = number density n = local normal unit vector of the solid surface P, P max = probability, maximum probability p = pressure q 1 = dynamic pressure, 0:5 1 V 2 1 R G = particular gas constant R u = universal gas constant St = Stanton number, (heat flux at the solid surface divided by q 1 V 1 ) T = temperature T = characteristic temperature of intermolecular potential T VHS = reference temperature for the variable-hard-sphere collision model t = local resultant tangent unit vector of the solid surface [t 1 t 2 =jt 1 t 2 j, t 1 and t 2 are orthonormal] V = magnitude of velocity jVj V = mass velocity, bulk velocity, or mean molecular velocity W p = reference particle weight, n=n simulation particles x, y = computational domain coordinates relative to the flat-plate leading edge Z rot;1 = maximum rotational collision number = energy accommodation coefficient VSS = deflection angle exponent of variable-soft-sphere collision model = Dirac delta function diameter = reference collision cross-sectional diameter = number of internal energy degrees of freedom vib = characteristic temperature of vibration = mean free path = absolute viscosity = absolute molecular velocity, V 0 0 = random molecular velocity = mass density = momentum accommodation coefficient = flux ! = viscosity index for the variable-hard-sphere collision model Subscripts E int = internal energy e = at the edge of the boundary layer i = incident M = Maxwell mp = most probable n = relative to surface normal vector Q = physical property r = reflected rot = rotational internal energy mode t = relative t...

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