Improvement and assessment of the SST equation based on Karman scale and fileter method

A modified filter method of SST turbulence model based on Karman length scale correction has been proposed in this paper. With application of the sub-grid model in LES theory, a new DES method has been established, which could alleviate the restriction to flow fluctuation by the time averaging in RANS solver so that the multi-scale effect in separated flow could be simulated. Besides, the filter factor has been modified with the Karman scale to reduce the dissipation of Reynolds stress which would occur in the original DES cased by grid refinement. In the numerical study case of flat plate boundary layer, the velocity profile within the boundary layer would match well the result by RANS, compared to the low robustness and poor capability inside boundary layer of DES method with grid refinement, which shows that the Karman scale has guaranteed that the flow inside the boundary layer would be solved by RANS instead of LES. HGR-01 airfoil test case proves that BY-SST method can avoid the grid induced separation more robust than that of DES method.