Computation of internal high-speed separated flow with modified B-L and J-K models

The existence of shock-turbulent boundary layer interactions lead to very complicated flow phenomena and pose a challenge for numerical simulation. In this paper, two turbulence models, The Baldwin-Lomax (B-L) model and the Johnson-King (J-K) model, which were originally developed for simple external flow simulation, are modified to model complex high-speed internal separated flows. The full Navier-Stokes solver used in this paper is based on a cell-centered finite volume method and multistepping time marching scheme. Both implicit residual smoothing and local time stepping techniques are incorporated to accelerate the convergence rate. To ensure the numerical stability with the present explicit scheme, a point-implicit treatment to the source term in the ordinary differential equation (ODE) of the J-K model has been developed and has proved to be very effective in modeling such a complex flow. An arc-bump channel flow case has been studied. Comparisons of computed results with experimental data show that the present solver, with the modified turbulence models, predicts the shock and the flow separation very well. The J-K model is found to predict the size of the separation bubble with a higher accuracy.