A dynamic delayed detached-eddy simulation model for turbulent flows

The current study developed a new dynamic delayed detached-eddy simulation (dynamic DDES) model based on the k-ω SST model and the well-established dynamic k-equation subgrid-scale model. Instead of using a constant model coefficient CDES in traditional DES formulations, the present model employs two coefficients Ck and Ce, which are computed dynamically by taking into account the spatial and temporal variations of the flow field at the grid and test filter levels. A modification on shielding function fd is proposed, with a spatial uniformization operator imposed on the velocity gradient to obtain a smooth and monotonous hybrid interface. A damping function φd is introduced based on the local grid resolution and flow condition to damp the Reynolds-averaged Navier-Stokes (RANS) region and achieve wall-modeled LES (WMLES) mode dynamically. The test of the model in developed channel flow shows the log-layer mismatch (LLM) problem is significantly improved with respect to the dynamic LES model and original DDES model. The use of the spatial uniformization operator and the damping function convincingly demonstrates the improvement in prediction of separated flows, with the model coefficients dynamically computed. The LES region is maximized at the limit of grid resolution and more turbulent vortical structures are resolved. The test in the ribbed channel flow shows the present model has considerably better performance in prediction of the mean and turbulence velocity in the strong shear layer and the recirculation bubble. In addition, the simulation of impinging jet shows the model exhibits rapid switching from the RANS to LES under the flow instabilities when the inflow does not include turbulence content.