A compressibility correction to k-ω models for hypersonic wall-bounded flows

In this talk, we introduce a compressibility correction for k-ω models such that the effects of high Mach numbers and wall-cooling are explicitly taken into account. The compressibility correction is validated by a Direct Numerical Simulation database with and without pressure gradient for a range of Mach numbers between 2.5 and 14, and wall-to-recovery temperature ratios between 0.18 and 1. In the present approach, assuming a correspondence between compressible and incompressible eddy viscosity in the near-wall region, we demonstrate that the standard models fail to calculate accurate eddy viscosity profiles for hypersonic turbulent boundary layers with a cold wall. By only modifying the production and destruction terms of the ω-equation, the proposed correction collapses the eddy viscosity profiles on the incompressible eddy viscosity data. This results in significant improvements in velocity, temperature, skin friction, and wall heat transfer coefficient profiles. The present formulation is local and can easily be implemented for any k-ω models in existing codes.