COMPARISONS BETWEEN LOW-REYNOLDS-NUMBER 2-EQUATION MODELS FOR COMPUTATION OF A SHOCKWAVE-TURBULENT-BOUNDARY LAYER INTERACTION

A comparative study is made on the performance of several low Reynolds number k-epsilon models and the k-omega model in predicting the shock wave-turbulent-boundary layer interaction over a supersonic compressio n 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 T VD. The computational results reveal that all of the low Reynolds numb er k-epsilon models, particularly those employing y+ in their damping functions give erroneously large skin friction in the redeveloping reg ion. It is also interesting to note that the k-epsilon models, when ad justed and based on DNS data, do not perform better, as expected, than the conventional low Reynolds number k-epsilon models. The k-omega mo del which does not adopt a low Reynolds number modification, brings ab out reasonably accurate skin friction, but with a later onset of press ure rise. By recasting the omega equation into the general form of the epsilon equation, it is inferred that the turbulent cross diffusion t erm between k and epsilon is critical to guarantee better performance of the k-omega model for the skin friction prediction in the redevelop ing region. Finally, an asymptotic analysis of a fully developed incom pressible channel flow, with the k-epsilon and the k-omega models, rev eals that the cross diffusion mechanism inherent in the k-omega model contributes to the better performance of the k-omega model.