Prediction of shock / turbulent boundary layer separated flows using the Navier-Stokes equations

[摘要] Progress made in computational method in fluid mechanics will allow the increasing use of numerical solutions of the compressible Navier-Stokes equations to determine flows of increasing complexity. Much attention is now given in computational aerodynamics to viscous-inviscid interaction phenomena which are frequently encountered in real flows. This present work concentrates on numerically solving complete, compressible Reynolds-averaged Navier-Stokes equations for a turbulent interaction problem. The original MacCormack's implicit method has been developed and improved in the present research work to enable it to be used for calculations using complex multi-equation turbulent models and to increase its ability to control nonlinear instability. These extensions retain second order accuracy and the block bidiagonal form of the original MacCormack's implicit scheme (1981) which constitute its main advantage. The computed results and validation of them through comparison with experiments, as follows, showed that these developments are feasible. The scheme developed was mainly tested on the calculations for an interaction between an incident shock wave and a laminar boundary layer on a flat plate and an isothermal wall supersonic turbulent flow over a ramp set at various angles. The computed results for the laminar interaction problem provided very good agreement with experimental data. For turbulent interacting problems, three different turbulence models, the original Cebeci-Smith (C-S) model, the C-S model with a relaxation modification and the K-e model are investigated as was the influence of Reynolds number on the flow. The results have been compared with experimental data obtained by Princeton University. These comparisons showed that the solution strongly depends on the turbulence model. Generally, all the models can predict the overall pressure rise, but fail to predict the flow field near to and downstream of the reattachment point. Comparatively, the K-e model gives the best results.

[发布机构] University:University of Glasgow

[关键词] Mechanical engineering, Fluid mechanics, Computational physics