Comparisons between low Reynolds number two-equation models for computation of a shockwave-turbulent-boundary layer interaction

Abstract

A comparative study is made on the performance of several low Reynolds number k-epsilon models and the k-omega model in predicting the shockwave-turbulent-boundary layer interaction over a supersonic compression ramp of 16 degrees, 20 degrees and 24 degrees at a Mach numbers of 2.85, 2.79 and 2.84, respectively. The model equations are numerically solved by a higher order upwind scheme with the 3rd order MUSCL type TVD. The computational results reveal that all of the low Reynolds number k-epsilon models, particularly those employing y+ in their damping functions give erroneously large skin friction in the redeveloping region. It is also interesting to note that the k-epsilon models, when adjusted and based on DNS data, do not perform better, as expected, than the conventional low Reynolds number k-epsilon models. The k-omega model which does not adopt a low Reynolds number modification, brings about reasonably accurate skin friction, but with a later onset of pressure rise. By recasting the omega equation into the general form of the epsilon equation, it is inferred that the turbulent cross diffusion term between k and epsilon is critical to guarantee better performance of the k-omega model for the skin friction prediction in the redeveloping region. Finally, an asymptotic analysis of a fully developed incompressible channel flow, with the k-epsilon and the k-omega models, reveals that the cross diffusion mechanism inherent in the k-omega model contributes to the better performance of the k-omega model.