Evaluation of Partially Averaged Navier-Stokes Method in Simulating Flow Past a Sphere

In recent past partially averaged Navier-Stokes equation (PANS) has been proposed as a scale-resolving bridging method for turbulence computations. Despite the geometric simplicity of the involved boundary conditions, the flow past a sphere is ripe with various complex flow phenomena, which make it an excellent test bed to evaluate various computational fluid dynamics modelling methodologies − both in terms of numerical schemes as well as turbulence models. Specifically, in this work we evaluate PANS in conjugation with the standard k-ε model in terms of (i) influence of filter parameters, (ii) sensitivity to free stream viscosity ratio and (iii) choice of numerical schemes at supercritical Reynolds number of 1.14x106. Careful evaluations are made by comparing PANS results against available experimental data as well available detached eddy simulation (DES) and large eddy simulation (LES) results. Our study finds that indeed − as purported by the PANS theory − a reduction in the value of the first filter parameter (fk) successfully captures the complex vortical structures that exist past a sphere, shows far superior performance than unsteady Reynolds-averaged Navier-Stokes (URANS) simulations and somewhat improved performance even over some of the LES studies reported in literature. Our study shows that in terms of most of the quantities of interest, PANS performance is almost at par with that of DES.