Performance of Upwind Schemes and Turbulence Models in Hypersonic Flows

Abstract

An evaluation of three upwind schemes and four turbulence models is presented in order to assess their respective separate and combined performance in complex hypersonic flows with large scale separation. The upwind schemes include Liou and Steffen’s advection upstream splitting method (AUSM) flux-vector splitting, its modification by Wada and Liou, called AUSMDV, and Roe’s flux-difference splitting. Turbulent effects were modeled utilizing Wilcox’s k‐ω model with two compressibility corrections by Coakley’s group, the widely popular Spalart‐Allmaras and supersonic transport (SST) models as well as an explicit algebraic Reynolds stress model (EARSM) by Wallin and Johansson. Using a powerful explicit/implicit finite volume computational-fluid-dynamics code, the upwind schemes are first tested on a complex double-wedge Euler flow configuration. A three-dimensional corner flow serves as a test case for a laminar Navier‐Stokes computation. Finally, AUSM schemes are used in combination with several turbulence models in a two-dimensional ramp flow and a three-dimensional crossing-shock interaction. Results are compared with either experiments or computations by other authors. The authors’ conclusions suggest that the AUSMDV is probably the most recommendable scheme for complex hypersonic flows. Regarding turbulence modeling, models with explicit compressibility corrections, in this case the k‐ω model, seem to deliver presently the comparatively best predictions in complex flows, particularly in case of separation.