The effects of Maxwellian accommodation coefficient and free-stream Knudsen number on rarefied hypersonic cavity flows

Abstract

A comprehensive numerical calculation has been conducted to investigate a rarefied hypersonic flow past a three-dimensional (3-D) cavity with a length-to-depth ratio of 4 using the direct simulation Monte Carlo (DSMC) method. In this calculation, the representative atmospheric environment at altitudes of 70 km, 75 km, 80 km and 90 km is considered and Maxwell model was employed to simulate the gas-surface interaction (GSI). A comprehensive understanding of the effects of Maxwellian accommodation coefficient and free-stream Knudsen number on flow-field characteristics is obtained and the sensitivity of aerodynamic surface quantities i.e. the pressure, shear stress, and heat flux, to the accommodation coefficient and free-stream Knudsen number is assessed in depth based on the flow-field patterns from a point of view of gas kinetic theory. The results emphasise the sensitivity of flow-field characteristics inside the cavity and aerodynamic surface quantities on the cavity surfaces to the accommodation coefficient and free-stream Knudsen number. As the GSI changes from diffuse into specular reflection, the two vortices inside the cavity move closer to each other and merge into one, leading to a representative open cavity. The peak values for pressure on and heat flux to some surfaces of the cavity in the case of near specular reflection are much larger than that in the diffuse-reflection case. As free-stream Knudsen number rises, the ability of external stream to enter the cavity is lowered, causing that the flow pattern inside the cavity develops from a closed flow with two vortices generated into an open flow with only one vortex produced and the peak-density point changes from the lower-right corner to the exit of the cavity. In addition, the increase in free-stream Knudsen number also results in more non-uniform distributions of aerodynamic surface quantities along the aft wall, with most of the pressure and heat loads exerted on the top the aft wall for the case of a largest free-stream Knudsen number considered here.