Asymptotic solutions of the two-dimensional equations for a thin viscous shock layer in a rarefied gas

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

“…9 The analytic solutions were obtained for the heat-transfer coefficient c H , the skin friction coefficient c f and the pressure coefficient on the wall p w for the three flow regimes in In the case of regimes II and III the solution also depends on the dimensionless surface temperature T w . For regime II we have (5.2) For regime III the solution is given by the first two equalities of (5.2) with ≡ 1 and = (ReT 1− w ␤) 1/2 .…”

“…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.…”

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

“…11 The analytical solutions for the heat transfer coefficient C H , the skin friction coefficient C f and the pressure coefficient on the wall C p in the case of axisymmetric (v = 1) and plane (v = 0) problems have the form (3.1) Solution (3.1) is a simple analytical relation between the coefficients C H , C f and C p and the free stream parameters Re, , Pr, and the geometrical parameters ␣, r w and R of the body surface. This solution gives the correct free molecular limits with a unique accommodation coefficient 9 for the heat transfer, skin friction and pressure cofficients when Re→0.…”