Assessment of the shear stress transport dynamic l(2)-? delayed detached eddy simulation in Bachalo-Johnson flow with shock-induced separation

Driven by the need for simulating compressible flows, Germano identity-based [Z. Yin and P. A. Durbin, "An adaptive DES model that allows wall-resolved eddy simulation," Int. J. Heat Fluid Flow 62, 499-509 (2016)] and Vreman operator-based [Bader et al., "A hybrid model for turbulence and transition, with a locally varying coefficient," Flow, Turbul. Combust. 108, 935-954 (2022)] dynamic l 2 - ? delayed detached eddy simulation (DDES) formulations are constructed on the k - ? shear stress transport (SST) model. The Bachalo-Johnson transonic axisymmetric bump is simulated to assess the models' capability in handling the compressible boundary layers under pressure gradient and transonic shock-boundary layer interaction. The new dynamic l( 2) - ? DDES formulation based on k - ? SST overcomes the issues of freestream sensitivity and inaccurate compressible boundary layer profile observed in the original k - ? (88) based model. The new SST-based dynamic model using the Vreman operator to compute the model coefficient (Vreman-dynamic model) has superior performance against Germano identity-based model due to its capability of suppressing the subgrid viscosity during the initial development of a separating shear layer. The Vreman-dynamic model predicts a reattachment location similar to the zonal improved-DDES/direct numerical simulation approach by Spalart et al. ["Large-eddy and direct numerical simulations of the bachalo-johnson flow with shock-induced separation," Flow, Turbul. Combust. 99, 865-885 (2017)] on a much coarser mesh demonstrating its potential for application in industrial flows.