Assessment of the shear stress transport dynamic ℓ2−ω delayed detached eddy simulation in Bachalo–Johnson flow with shock-induced separation

Abstract

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 ℓ2−ω delayed detached eddy simulation (DDES) formulations are constructed on the k−ω 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 ℓ2−ω DDES formulation based on k−ω SST overcomes the issues of freestream sensitivity and inaccurate compressible boundary layer profile observed in the original k−ω (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.