Specific heat effects in two-dimensional shock refractions

Abstract

Compressible mixtures in supersonic flows are subject to significant temperature changes via shock waves and expansions, which affect several properties of the flow. Besides the widely studied variable transport effects such as temperature-dependent viscosity and conductivity, vibrational and rotational molecular energy storage is also modified through the variation of the heat capacity \(c_p\) and heat capacity ratio \(\gamma \), especially in hypersonic flows. Changes in the composition of the mixture may also modify its value through the species mass fraction \(Y_\alpha \), thereby affecting the compression capacity of the flow. Canonical configurations are studied here to explore their sharply conditioned mechanical equilibrium under variations of these thermal models. In particular, effects of \(c_p(T,Y_\alpha )\) and \(\gamma (T,Y_\alpha )\) on the stability of shock-impinged supersonic shear and mixing layers are addressed, on condition that a shock wave is refracted. It is found that the limits defining regular structures are affected (usually broadened out) by the dependence of heat capacities with temperature. Theoretical and high-fidelity numerical simulations exhibit a good agreement in the prediction of regular shock reflections and their post-shock aerothermal properties.