The effect of surface curvature on the boundary conditions in the viscous shock layer model for hypersonic rarefied gas flow

Abstract

The supersonic and hypersonic flow of a rarefied gas over blunt bodies is investigated within the framework of asymptotically correct models of a viscous shock layer (VSL) and a thin viscous shock layer (TVSL). In the case of the VSL model, terms associated with its curvature, which are important at low Reynolds numbers, are taken into account in the shock boundary conditions. Conditions are proposed for the slip velocity and the temperature jump on the body surface taking account of its curvature. A numerical simulation of hypersonic flow problems is performed within the sramerort of the continuum VSL and TVSL models over a wide range of Reynolds numbers using an implicit iterative-marching method having a high accuracy of approximation. It is shown, by comparing of the numerical and asymptotic solutions with the kinetic and free molecules solutions and also with the solutions obtained by the direct simulation monte Carlo method, that taking into account the terms in the VSL model associated with the shock curvatures and the streamlinked surface considerably affects the prediction of the heat transfer and skin friction at low Reynolds numbers and extends the domain of applicability of this model. The importance of the asymptotic correctness of the continuum models used in the transient flow regime is demonstrated.