Improved scale-resolved predictions of flow and heat transfer past a bluff body using partially averaged Navier–Stokes and a high-order eddy viscosity closure

The partially averaged Navier–Stokes (PANS) methodology has emerged as a viable bridging method of turbulence computations. Partially averaged Navier–Stokes methodology allows the user to implicitly choose the filter cut-off seamlessly in the inertial sub-range of motion. In past, most PANS simulations have been performed using the linear eddy viscosity closure for the unclosed turbulent stresses. Recently, evaluation of the advantages of higher order eddy viscosity closures with the PANS methodology has also been initiated. With our motivation to make further progress in this direction, this study presents an evaluation of PANS methodology wherein the turbulent stresses are modelled involving closures up to the cubic products of the resolved strain-rate and the rotation-rate tensors. After appropriately adapting a popular Reynolds-averaged Navier Stokes cubic closure for the PANS paradigm, an extensive evaluation of the method is performed in the flow past a heated sphere at a Reynolds number of 10,000. Time-averaged PANS predictions of surface-related as well as wake-related quantities are compared against available experimental, direct numerical simulation as well as large eddy simulation results. Indeed, very significant improvements are demonstrated by the PANS methodology in conjunction with the cubic eddy viscosity closure when compared to the corresponding predictions of the PANS methodology using a linear or even a quadratic eddy viscosity closure. This study demonstrates the promising augmentative ability of the higher eddy-viscosity to the PANS framework in performing improved simulations of the separated flows.