Viscous Flowfield Solutions about a Finite Parabolic Body

Abstract

AHYBRID computational technique that splits the flowfield into inviscid and viscous regions is used to investigate the complete flowfield about axisymmetric parabolic blunt bodies in a supersonic stream. The solutions are carried out on the CDC CYBER-203 computer which, with its extensive memory, allows for the use of a large number of finite-differ ence mesh points, allowing resolution of important flowfield features. Contents Analysis of the supersonic flow about blunt bodies has in the past been restricted by limited computational resources to flow over the forebody. This has led to some computational difficulties when the sonic line has moved outside of the computational domain; and, has left unresolved, the effect of base flow on the total drag of a blunt body. We have extended the hybrid computational technique described in Ref. 1 to investigate the complete flowfield about axisymmetric parabolic blunt bodies in a supersonic stream. The solutions are carried out on the CDC CYBER-203 vector computer, which with its extensive memory, allows for the use of a large number of finite-differ ence mesh points, allowing resolution of important flowfield features. The physical coordinate system used in the description of the body and flowfield is the orthogonal parabolic system used in Ref. 2 and is formed by the intersection of curves belonging to two cofocal parabolas. The parametric equations for the Cartesian coordinates in this system are x=lA (£2 — 772) and y = £r\. As seen in Fig. 1, the axisymmetric body surface is formed by rotating the coordinate lines about the X axis. As described in Ref. 1, the flowfield is split into viscous and inviscird regions that are coupled along the line 77 = rjc, Fig. 1. The computational plane, in £ and 77, is rectangular with the physical boundaries corresponding to the simple rectangular boundaries of the computational plane. Coordinate stretching/compression is applied both in the forebody and afterbody regions to resolve important flowfield features. Because the shock-fitting technique of Ref. 1 is used, the flow near the shock is considered to be inviscid and is governed by the conservative, compressible, time-dependent Euler equations. The remaining flowfield is governed by the full compressible, laminar, time-dependent Navier-Stokes equations in conservative form. The governing equations are cast in the form