Assessment of the k-ε turbulence model for compressible flows using direct simulation data

We evaluate the k-ε turbulence model using direct numerical simulation (DNS) data of a Mach 4 boundary layer. We find that the low Reynolds number damping functions for the Reynolds stress must be corrected by the density ratio to match the DNS data. We present the budget of the k equation and assess the modeling of the various source terms. The models for all the source terms, except for the production and dilatational dissipation terms, are found to be adequate. Finally, we present the solenoidal dissipation rate equation and compute its budget using the boundary layer data. We compare this equation with the dissipation rate equation in an incompressible flow to show the equivalence between the two equations. This is the basis for modeling the solenoidal dissipation equation. However, an additional term in the equation due to variation of fluid viscosity needs to be modeled.