Reynolds and Mach Number Dependence of Hypersonic Blunt Body Laminar Near Wakes

Abstract

Laminar separation on the aftbody of an adiabatic circular cylinder was numerically investigated over a range of freestream Mach and Reynolds numbers using the free open-source program OpenFOAM. Simulations were performed assuming laminar, continuum, thermally perfect flow of nitrogen gas. Simulation predictions have been compared to various empirical correlations in the literature. Empirical formulations were presented for the pressure minimum location, separation location, and separation length on the cylinder aftbody. The effects of both Mach and Reynolds numbers on the separation location were examined by correcting for the change in viscosity across the shock wave. This was accounted for explicitly in the presented empirical formulations by deriving an expression for the viscosity change across the shock. A free-interaction theory was used to examine the wall-pressure distribution due to lip-shock formation on the aftbody. Over a range of Mach and Reynolds numbers, it was found that the profile of a free-interaction parameter was predictable and nearly Reynolds number and Mach number independent. This free-interaction parameter was a correlation between the properties at the onset of the interaction and the ensuing pressure rise. This provided a means to predict the lip-shock formation, provided the boundary-layer properties at the pressure minimum were known.