Effects of the Uncertainty of Wall Distance on the Simulation of Turbulence/Transition Phenomena

The uncertainty of the turbulence/transition model is a problem with relatively high attention in the CFD area. Wall distance is an important physical parameter in turbulence/transition modeling, and its accuracy has a large effect on numerical simulation results. As most CFD solvers use the solving strategy to calculate the nearest distance to the wall based on mesh topology, this makes wall distance one important source of the uncertainty of the simulation results. To investigate the role of wall distance in turbulence/transition simulations, we have conducted simulations for various aerodynamic shapes, such as the plate with zero pressure gradient (ZPG), RAE2822 supercritical airfoil and ONERA M6 transonic wing. Further, the prediction abilities on turbulence/transition and shock wave phenomena of several physical models, including SA, SST and Wilcox-k-ω turbulence models as well as the γ-Reθt-SST transition model, are analyzed with different degrees of mesh orthogonality. The results imply that the numerical solution of wall distance in the boundary layer has a relatively large error when the mesh orthogonality is bad, having a large effect on the accuracy of the turbulence/transition model. In detail, the Wilcox-k-ω turbulence model is unaffected by mesh orthogonality; under the condition of mesh non-orthogonality, the SA model leads to a substantially larger friction drag and change in the location of shock wave; the SST model also leads to a larger friction drag under the condition of mesh non-orthogonality, whose effect is much less than that for SA model; and the γ-Reθt-SST model leads to a substantial upstream shift of transition location.