Performance of delayed functions in DDES for supersonic base flow

The DDES is a widely used approach among RANS/LES hybrid methods. It introduces the delayed function to ensure full RANS mode in the near-wall region, and has been proven to be quite efficient for separated flows. Up to date, various different delayed functions have been developed. However, the understanding to the performance and characteristics of different delayed functions still remains not comprehensive, especially lacking investigation on supersonic flows. The research focuses on the different delayed functions in the DDES methods by employing the supersonic base flow as the validation case. Through systematic comparisons with the experimental data and detailed analyses, the distributions and shielding behavior of different delayed functions together with resolving capabilities of different models are investigated. Studies show that there exist discrepancies in the shielding behavior and resolving capabilities between different delayed functions. Besides, DDES-F₁ behaves appropriately in this supersonic separated flow and reproduces the experimental data very well, providing sufficient protection without impairing the model's numerical accuracy.