Numerical Solution of the Navier-Stokes Equations for a Three-Dimensional Corner

Abstract

A three-dimensional, time dependent Navier-Stokes code employing MacCormack's finite-difference scheme has been developed. Successful comparisons were performed for analytic solutions first to validate the numerical procedure. The strong inviscid-viscous interacting flow field for a three-dimensional compression corner at a Mach number of 12.5 and a Reynolds number of 1.21 x 10 was then computed and compared with experiment. The computed result nearly duplicated the experimental observations, including wall pressure, heat transfer, oil flow streamline pattern, and impact pressure flowfield survey. The numerical result not only verified the experimental finding of an extensive penetrating inviscid stream (inviscid finger) in the corner region as the source of the extremely high local rate of heat transfer, but also revealed an embedded crossflow supersonic region in the viscous vortex. The present result tends to substantiate the separation criterion established by the limiting line theory, in which the separation line is defined as an envelope of limiting streamlines. This investigation demonstrated that numerical methods may be used to determine the general features of complex threedimensional flows.