Evaluation of Variable Parameter Partially Averaged Navier-Stokes Method with Non-Linear Eddy Viscosity Closure

We have recently augmented the partially averaged Navier-Stokes (PANS) methodology employing higher order eddy viscosity closures (both quadratic and cubic closures). Our evaluations of the augmented PANS methodology in flows past bluff bodies with heat transfer has yielded significant improvements in prediction of both hydrodynamic and heat-transfer statistics. However, so far, all these studies have used the sequential two stage PANS approach, wherein, an initial Reynolds-averaged Navier-Stokes (RANS) simulation is required to compute the appropriate value of filter control parameters. Besides the requirement of this preceding RANS simulation, the entire computational grid is simulated with static, pre-chosen value of the filter control parameters. Alternatively, the dynamic version of PANS attempts to use variable control parameters which are adaptive to the local physics of a flow field. However, so far, this version of PANS has been tested with conventional linear eddy viscosity closure only. In this work, we attempt to combine the advantages of dynamic PANS with quadratic and cubic eddy viscosity closures and extensively evaluate the performance of the resulting methodology. A detailed analysis will be presented on the interaction of the variable filter parameter and the evolution of non-linear turbulent stress field in the highly separated and three-dimensional flow past a sphere.