On the Correction of k-ω SST Turbulence Model to Three-Dimensional Shock Separated Flow

Conventional eddy-viscosity turbulence models always overpredict the separation in three-dimensional shock separated flow due to inadequate Reynolds stress prediction. Grid and scheme convergence studies also give unreasonable tendency since the flow mechanism is not properly revealed from turbulence modeling perspective. Two corrections for this defect are proposed based on k-ω SST model. One directly aims at modifying the Bradshaw assumption, which was derived from observation of two-dimensional attached flow but will prevent the increasing of eddy viscosity in three-dimensional shock separated cases. The other one constructs a correction term to the dissipation term of specific dissipation rate equation by the production and dissipation of turbulent kinetic energy, which exists apparent imbalance in non-equilibrium flow. A switching function is also designed to control this correction term by a special ratio of “modeling” length scale and “required” length scale for the log layer. Two corrections are validated by the ONERA M6 wing at α = 6.06°, and the results shows better agreement with the experiment than that of the Reynolds-stress model. Grid convergence study, Reynolds stress analysis and verifications on other angles of attack are also conducted to show the validity and applicability of the proposed correction approaches.