Prediction of Hypersonic Laminar Boundary-Layer/Shock-Wave Interactions

Abstract

UMERICAL solution of the compressible timedependent Navier-Stokes equations is one method of obtaining the theoretical solution of the interaction of an oblique shock wave and a laminar boundary layer. MacCormack1 and MacCormack and Baldwin2 used the method of MacCormack 3 to generate solutions for low supersonic Mach numbers. The purpose of this Synoptic is to ascertain the validity of the MacCormack algorithm for laminar boundary-layer/shock-wave interactions in the hypersonic regime. Results of several numerical solutions were compared with experimental data from the von Karman Facility (VKF) Hypersonic Wind Tunnel (B) and the Langley Research Center (LRC) Mach 8 Variable Density Tunnel. Agreement between the numerical solution and the data was generally satisfactory, although the extent of separation was under predicted in interactions with large separated regions. When applied to hypersonic interactions having large separated and recirculating regions, the method gave marginal performance. Lack of spatial resolution in the longitudinal direction is the suspected cause of the discrepancies. Contents The MacCormack method, which is an explicit, split, twostep algorithm, was used to solve the laminar, compressible, time-dependent Navier-Stokes equations expressed in conservative form. The equations, together with the details of the algorithm, are given by MacCormack. 2 Because of the difficulty in maintaining laminar flow throughout hypersonic boundary-layer/shock-wave interactions for strong shock waves and moderate-to-high Reynolds numbers, the incident shock angles (Fig. 1 for schematic) in this study are limited to a maximum of 16 deg and the Reynolds numbers to a maximum of 106/ft. The computed pressure ratio at the wall, pw/pw, is compared with measured data of an AEDC-VKF Tunnel B experiment in Fig. I.4 Agreement is excellent particularly near the peak pressure location where the correct shape is generated, and in the midrange where the correct pressure gradient is obtained. No evidence of separation was obvious from the data, and no separated region was predicted by the program.