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 . 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.
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This work was sponsored by the Air Force Office of Scientific Research under Grant FA9550-04-1-0341 and by the Department of Defense National Security Science & Engineering Faculty Fellowship. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AFOSR or the US Government.