On the shock wave boundary layer interaction in slightly-rarefied gas

TL;DR

This study derives three-temperature NSF equations from gas kinetic theory to better simulate shock wave boundary layer interactions in slightly-rarefied gases, successfully matching experimental data and addressing previous discrepancies.

Contribution

It introduces a systematic analysis of temperature-jump boundary conditions and heat conductivities, improving the accuracy of SWBLI simulations in hypersonic flow regimes.

Findings

NSF equations with proper heat conductivities match experimental heat flux data

Simulation accurately predicts separation bubbles and reattachment points

Addresses discrepancies between numerical and experimental results in hypersonic flows

Abstract

The shock wave and boundary layer interaction (SWBLI) plays an important role in the design of hypersonic vehicles. However, discrepancies between the numerical results of high-temperature gas dynamics and experiment data have not been fully addressed. It is believed that the rarefaction effects are important in SWBLI, but the systematic analysis of the temperature-jump boundary conditions and the role of translational/rotational/vibrational heat conductivities are lacking. In this paper, we derive the three-temperature Navier-Stokes-Fourier (NSF) equations from the gas kinetic theory, with special attention paid to the components of heat conductivity. With proper temperature-jump boundary conditions, we simulate the SWBLI in the double cone experiment. Our numerical results show that, when the three heat conductivities are properly recovered, the NSF equations can capture the position and peak value of the surface heat flux, in both low- and high-enthalpy inflow conditions. Moreover, the separation bubble induced by the separated shock and the reattachment point induced by impact between transmitted shock and boundary layer are found to agree with the experimental measurement.