Partially Averaged Navier-Stokes Method for Turbulence: Fixed Point Analysis and Comparison With Unsteady Partially Averaged Navier-Stokes

Hybrid/bridging models that combine the advantages of Reynolds averaged Navier Stokes (RANS) method and large-eddy simulations are being increasingly used for simulating turbulent flows with large-scale unsteadiness. The objective is to obtain accurate estimates of important large-scale fluctuations at a reasonable cost. In order to be effective, these bridging methods must posses the correct “energetics”: that is, the right balance between production $(P)$ and dissipation $(ε)$⁠. If the model production-to-dissipation ratio $(P∕ε)$ is inconsistent with turbulence physics at that cutoff, the computations will be unsuccessful. In this paper, we perform fixed-point analyses of two bridging models—partially-averaged Navier Stokes (PANS) and unsteady RANS (URANS)—to examine the behavior of production-to-dissipation ratio. It is shown that the URANS-$(P∕ε)$ ratio is too high rendering it incapable of resolving much of the fluctuations. On the other hand, the PANS-$(P∕ε)$ ratio allows the model to vary smoothly from RANS to DNS depending upon the values of its resolution control parameters.