A comparison of hybrid RANS/LES models across the complete transition from URANS to DNS

Non-zonal hybrid RANS/LES models are derived from the mathematical invariance of the filtered Navier-Stokes equations such that a modified RANS closure may operate as a consistent LES model at higher resolutions than typical of a URANS. Despite this, however, very few individual or comparative studies have been conducted on hybrid models to determine how accurately and controllably each model transitions from URANS mode (model stresses, τ_ij, are independent of Δx) to LES mode (τ_ij ~ Δx²), to an effective DNS (τ_ij ≈ 0).  In this talk we will compare the performance of standard k-ε formulations of several hybrid models – including Partially-Averaged Navier-Stokes (PANS) and Very Large Eddy Simulation (VLES), among others – against the dynamic Smagorinksy model using initial conditions filtered from a pseudospectral DNS of incompressible decaying HIT on computational meshes ranging in size from a single-cell mesh (URANS) up to 512³ (DNS). We will compare each model against the DNS truth values of typical RANS and LES quantities of interest, as well as the grid-size dependence of the model stress, as we systematically vary both the simulation mesh size and “resolution parameter”, a tunable coefficient most models employ to hybridize the underlying k-ε model.