Stagnation region solutions of the full viscous shock-layer equations

Abstract

T re-entry problem continues to provide motivation for study of low Reynolds number, high Mach number blunt-body flows. This flow regime is one in which the viscous effects influence a significant portion of the total shock-layer thickness, thereby violating the classical boundary-layer approximations and requiring the use of a more comprehensive set of governing equations. The viscous shock-layer equations' represent an intermediate level of approximation between the boundary-layer and Navier-Stokes equations. Although some evidence exists that the viscous shock-layer model will suffice for re-entry-type flow problems,' there has, as yet, not been a critical assessment of the range of validity of these equations. This situation is due to the difficulties involved in solution of these equations. Although the thin-shock-layer version of these equations has been solved by numerous authors 5>6 only a few' have addressed the full set of equations, with none conducting an assessment of the range of validity of these equations. This is performed in the present paper through comparison with experimental stagnation point data for spherical nose shapes. Numerical solutions of the viscous shock-layer equations are obtained by combining an implicit finite-difference scheme with a relaxation technique for determining the bow shock shape. The effects of thin layer approximations, wall slip, and shock slip boundary conditions are included in the analysis to establish their relative importance.