Structure parameter modification of stress limiter in k - ω shear stress turbulence model for high-speed flows with shock-wave/turbulent boundary layer interaction

For some high-speed separated flows featured by shock-wave/turbulent boundary layer interaction (SWTBLI), the k-omega shear stress model (SST) tends to overestimate the size of the separation bubble while the baseline model (BSL) tends to underestimate. The constant value of the structure parameter in the stress limiter is one of the important reasons for the discrepancy of the SST model. Therefore, it is recommended that the structure parameter should be taken as the variable. In this work, we analyze the distribution of the interested turbulent variables and quantify the uncertainty of the results of the SST model near the onset of the SWTBLI. The constant structure parameter is modified by introducing the correlation, which is the function of the non-dimensional pressure gradient. The distribution of the correction factors shows that it essentially achieves a dynamic weighting of the BSL model and the SST model. Several flows over the flat plates with impinging shock wave, ramp, and cylinder-flare are simulated with different turbulent models. The results show that the correction factor effectively increases the structure parameter of the interaction region in the boundary layer and reduces the sensitivity of the SST model to the adverse pressure gradient. Correspondingly, the predicted separation location moves downstream. Compared with the results predicted by the SST model and BSL model, the pressure and skin friction coefficients at the wall predicted by the modified SST model overall agree better with the high-fidelity simulation or experimental data, which validates the proposed correction factor.