Comparison of CFD and theoretical post-shock gradients in hypersonic flow

In the recent work of Prof. Hans Hornung, expressions for the gradients of flow properties immediately behind a curved shock wave were obtained for a reacting gas [1]. In this paper, I use the expressions derived by Hornung to compare with inviscid computational fluid dynamics simulations of a Mach 8 flow over a cylinder. A finite-rate vibrational relaxation model is used to simplify the comparisons with theory. The shape of the bow shock wave is extracted from the CFD results, fitted with a polynomial, and then used to compute the post-shock gradients of the main flow variables. It is found that in general the CFD results are in very good agreement with the theory for both perfect gas and vibrationally relaxing flows. There are some notable differences, mostly centered on the location of the change in sign of the post-shock density gradient; this quantity is found to be highly sensitive to the relaxation rate of the gas. The theoretical post-shock gradients provide a rigorous test of CFD and suggest possible experiments that would be a very sensitive test of the models of finite-rate vibrational and chemical processes.