Application of a two-equation turbulence mix model

A mass averaged k-epsilon model was derived by Leith using a moment expansion and appropriate closure models. Moving the mesh with the mass averaged velocity results in a Lagrangian model with constant mass in each zone. In this paper Leith's model is transformed into an open-quotes Almost Lagrangianclose quotes model by taking the mesh velocity to be the ensemble averaged fluid velocity. Here the mass in each zone may change with time. The resulting 1-D model is used to simulate the Smits and Muck supersonic wind tunnel experiment in which preexisting turbulence is amplified by a shock wave. From the model results we deduce a simplified k-var-epsilon model that is applicable to the Smits and Muck (S ampersand M) experiment. In the analytic solution for the simplified model we find the shock thickness to be increased by a factor of 105; behind the shock the turbulent energy decays as t-1