Search

We evaluate the partially-averaged Navier-Stokes (PANS) methodology of turbulence computations by including non-linear eddy viscosity based closures for both turbulent stresses and thermal flux. We extract the filtered PANS version of the Shih’s quadratic model (originally proposed for the Reynolds averaged Navier-Stokes (RANS) paradigm) for arriving at a PANS closure model for the turbulent stress tensor. The unclosed thermal flux process is modeled using the gradient diffusion hypothesis, wherein we sensitize the coefficient of diffusion to the presence of non-linear stresses in the formulation. The resulting methodology is evaluated by simulating flow past a heated square cylinder. Evaluations are performed in terms of both hydrodynamic variables and heat transfer characteristics. We find that the non-linear PANS methodology shows improved results in terms of hydrodynamic quantities (coefficient of drag, pressure, velocity profiles, and high-order statistics). While the predictions of the heat transfer rate on the front face of the cylinder are similar in the linear and the non-linear PANS methodologies, in the wake region and parts of the lateral wall where shear layer detachment takes place, the non-linear PANS methodology shows improved results.

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.