Wall-Normal-Free Reynolds-Stress Closure for Three-Dimensional Compressible Separated Flows

Abstract

A near-wall Reynolds-stress closure that is independent of the distance from the wall and of the normal to the walldirection isdevelopedandvalidated.Particularattention wasgiven intheapplicabilityofthemodeltocomplex three-dimensional e ows with shock waves and boundary-layer separation. In the separated e ow region, measurements andmodelcomputations indicatethatthe e atnessparameter Aoftheanisotropy tensor aij approaches unity. Therefore, controlofseparation isachieved in themodel through theparticularfunctional dependenceoftherapid pressure‐strain isotropization of production model coefe cienton A. Echo termsaretreated by replacing geometric normalsanddistancesbyfunctionsofthegradientsofturbulencelengthscaleandanisotropytensorinvariants.The modelisinitiallycomparedwithmeasurementsforcompressiblee at-plateboundary-layere ows.Itisthenvalidated by comparison with experimental data in a two-dimensional compression corner oblique shock-wave/boundarylayer interaction at Mach 3. Finally the model is applied to the computation of the three-dimensional interaction of a Mach 1.5‐1.8 strong shock wave with the boundary layers of a rectangular channel e tted with a swept bump on the lower wall, and results are compared with measurements. One important advantage of the proposed model is its robustness in complex three-dimensional e ows. A detailed discussion of therange of validity of the model and possible improvements is presented.