Reacting Shock Layers with Slip and Catalytic Boundary Conditions

Abstract

The influence of wall slip and catalytic atom-recombination on the flowfield and wall heat flux are calculated for high-altitude flight and arcjet-flow conditions. Boundary equations, which include velocity slip, temperature jump, and wall catalytic atom-recombination, are coupled to the viscous reacting multicomponent NavierStokes equation. These equations are solved using a time-dependent finite difference technique applied to spheres in an arcjet flow (Reynolds number of 550) and a high-altitude flight case representative of the space shuttle orbiter (Reynolds number of 450). The results indicate that catalysis strongly influences the temperature jump, but not the velocity slip. Slip increases the atom fraction and temperature at both the wall and in the flowfield. Likewise, the shock stand-off distance, the wall heat flux, and friction coefficient are increased over the nonslip cases. The reacting gas calculations confirm the chemically frozen nature of the shock layer in arcjet flows. design the reusable space shuttle orbiter for highaltitude, low Reynolds number, atmospheric entry necessitates a more comprehensive treatment and understanding of the interaction between a high enthalpy gas flow and a relatively cold surface. At low densities the continuum model of the gas breaks down in regions of large gradients such as those near a cold body. Corrections to the equations for the boundary conditions are then required for the flow. These influences are reflected in the calculations of surface heat-transfer rate and chemical composition of the flow near the wall. The aim of this paper is to quantify how these low density phenomena interact, how they influence interpretation of test data obtained on thermal protection systems, and how they alter the predictions of heating rates and performance of the space shuttle orbiter thermal protection system (TPS) during its long high-altitude entry. The approach taken here is to obtain finite difference solutions to the reacting Navier-Stokes equations for the flow around spheres in both space shuttle flight and arcjet environments. The wall boundary conditions for these solutions are obtained from slip and jump relations for a nonequilibrium multicomponent gas mixture. They include the effects of catalytic atom recombination. From the solutions one can assess the effects. of the boundary conditions on the flow properties, the heat flux, etc. At low densities, the continuum-flow equations are no longer adequate close to the wall because the mean free path becomes long compared to characteristi c lengths associated with significant changes in macroscopic-flow parameters. The flow in a region next to the wall having a thickness on the order of a mean free path (the Knudsen layer) cannot be described by the Navier-Stokes description (Kogan1). To determine the flow properties within the Knudsen layer requires the direct solution of the Boltzmann equation matched to the solutions for the outer flow (Navier-Stokes equation) and the wall boundary condition. This is most conveniently done through the use of a slip model in which slip and jump properties are used for the boundary conditions for the Navier-Stokes equations.