Multigrid computation of high-speed turbulent flows in ducts

Abstract

The existence of shock/turbulent-boundary-layer interaction leads to very complicated flow phenomena and poses a challenge for numerical simulation. In this study, three different turbulence models, the Baldwin-Lomax (B-L) model, the Johnson-King (J-K) model and a two-layer k-e/k-1 model, are incorporated and modified to model internal compressible flows with multiple walls. A more advanced Reynolds stress model, the so-called algebraic stress model (ASM) which was originally developed for incompressible flow simulations, is also discussed and formulations for two-dimensional (2D) and three-dimensional (3D) compressible flows are derived in details for future implementation to the present solver. The numerical method used is based on an explicit five-stage Runge-Kutta time-stepping scheme. Multigrid technique and implicit residual smoothing strategy are employed to ensure a high computing efficiency and convergent rate. Different grids of various refinement are tested in the computation and the grids used have been proved to be sufficiently refined.