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

The ability of k-! 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 theMach number is increased in the hypersonic regime. Simple algebraicmodels 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 for k-!models or that apply only in specific circumstances. Themost widely used general corrections were designed for usewith jet ormixing-layer free-shear flows. A less-wellknown dilatation–dissipation correction intended for boundary-layer flows is also tested and is shown to agree reasonablywell with the Baldwin–Lomaxmodel 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.