Mean flow compressibility effects in transonic turbulence modeling

The mean flow compressibility effects greatly influence the behavior of turbulent flows, as long as the flow is compressible. The fact is even though Favre average has taken into account the variation of the density, less accurate CFD results are always obtained when the flow is compressible. Thus, many compressibility corrections are made for high Mach number flows. As for the transonic turbulence flow, the mean flow compressibility effects are not mentioned. In this paper, it is demonstrated that the mean flow compressibility effects are not ignorable in transonic flows on some flow features. The mean flow compressibility effects are taken into account by introducing a characteristic turbulence length scale. The key is a new definition of vorticity by the curl of momentum. A compressible von Kármán length scale is introduced to obtain a new turbulence model CKDO (Compressible Kinetic Dependent Only) for complex compressible flows on the basis of the KDO. The only two empirical coefficients in the KDO model are not changed, which were calibrated by a slice of the incompressible flat plate boundary layer flow. Numerical simulations of transonic flows around RAE2822 airfoil, axisymmetric bump pipe and ONERA-M6 wing show that compressibility is non-negligible, and the new length scale definition can improve the prediction accuracies of aerodynamic features, such as the onset locations of shock waves, skin friction and pressure coefficients.