Abstract
A compressibility correction for models is proposed, and it explicitly takes the effects of high Mach numbers and wall-cooling into account. The correction is validated by a recent set of direct numerical simulation databases with and without pressure gradient. The proposed compressibility correction is based on the correspondence between eddy viscosity in compressible and incompressible turbulence, which shows that the standard models estimate incorrect values of eddy viscosity in the near-wall region of a hypersonic turbulent boundary layer with a cold wall. For a range of Mach numbers between 2.5 and 14, and wall-to-recovery temperature ratios between 0.18 and 1, the correction collapses the eddy viscosity profiles on the incompressible data and predicts significantly improved velocity, temperature, skin friction, and wall heat transfer coefficient profiles. The present approach is independent of the eddy viscosity definition and Reynolds stress model, and it can be implemented easily in any model by modifying the closure coefficients of the production and destruction in the equation. Furthermore, the formulation is completely local and is disabled as the effects of compressibility disappear.
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