Compressibility Considerations for k-w Turbulence Models in Hypersonic Boundary-Layer Applications

The ability of k-w models to predict compressible turbulent skin friction in hypersonic boundary layers is investigated. Although uncorrected two-equation models can agree well with correlations for hot-wall cases, they tend to perform progressively worse (particularly for cold walls) as the Mach number is increased in the hypersonic regime. Simple algebraic models such as Baldwin-Lomax perform better compared to experiments and correlations in these circumstances. Many of the compressibility corrections described in the literature are summarized here. These include corrections that have only a small influence f or k-w models or that apply only in specific circumstances. The most widely used general corrections were designed for use with jet or mixing-layer free-shear flows. A less-well-known dilatation-dissipation correction intended for boundary-layer flows is also tested and is shown to agree reasonably well with the Baldwin-Lomax model at cold-wall conditions. It exhibits a less dramatic influence than the free-shear type of correction. There is clearly a need for improved understanding and better overall physical modeling for turbulence models applied to hypersonic boundary-layer flows.