Asymptotic solution of the two-dimensional equations for a thin viscous rarefied shock layer on a cold surface

Abstract

Hypersonic rarefied flow past blunt bodies is studied in the continuum-free-molecular transition regime. On the basis of an asymptotic analysis three rarefied gas flow patterns are established depending on the relation between the relevant parameters of the problem. In the first regime corresponding to a cold surface asymptotic solutions of the equations of a thin viscous shock layer are derived at low Reynolds numbers in the axisymmetric and plane cases. Simple analytical expressions for the pressure and the heat transfer and friction coefficients are obtained as functions of the freestream parameters and the body geometry. With decrease in the Reynolds number the coefficients approach the values corresponding to free-molecular flow. In this regime a similarity parameter for the hypersonic rarefied flow past bodies is determined. The asymptotic solutions are compared with numerical solutions and the results of direct statistical simulation by the Monte Carlo method.

The applicability of continuum models in the transitional regime of hypersonic flow over blunt bodies

“…The regimes of hypersonic rarefied gas flow over the bodies were considered for the neighbourhood of the stagnation line 1 and for the windward part of axisymmetric and plane bodies. 8 In the case of two-dimensional flows we can distinguish three flow regimes when Re = o(1):…”

“…In this paper, we use both the numerical method 6,7 and the asymptotic method 8,9 of investigation. By comparing the asymptotic and numerical solutions of full and thin various shock layer equations with the results of calculations obtained in the literature by the Direct Simulation Monte Carlo method, carried out for the continuum and transitional flow regimes, and also with the solutions in the freemolecule flow regime, it is shown that it is possible to use the continuum models to predict the heat flux and the skin friction on smooth blunt bodies for all hypersonic flow regimes, and that these methods are much more economic in computing costs than kinetic methods and Direct Simulation Monte Carlo methods.…”