Modeling And Simulation Of Transitional Taylor-Green Vortex Flow With Partially Averaged Navier-Stokes Equations

The partially averaged Navier-Stokes (PANS) equations model is used to predict the transitional Taylor-Green vortex (TGV) flow at Reynolds number 3000. A form of the closure is proposed in which the PANS procedure is applied to a variant of the Besnard-Harlow-Rauenzahn turbulence model. The TGV is a benchmark case for transitional flows in which the onset of turbulence is driven by vortex-stretching and -reconnection mechanisms. Since these physical phenomena are observed in numerous flows of variable density (e.g., oceanography and material mixing), this study constitutes the first step toward extending the PANS method to such a class of problems. We start by deriving the governing equations of the model and analyze the selection of the parameters controlling its physical resolution, f(epsilon) and f(k), through a priori testing. Afterward, we conduct PANS computations at different constant physical resolutions to evaluate the model's accuracy and cost predicting the TGV flow. This is performed through simple verification and validation exercises, and the physical and modeling interpretation of the numerical predictions. The results confirm that PANS can efficiently (accuracy vs cost) predict the present flow problem. Yet, this is closely dependent on the physical resolution of the model. Whereas high-physical-resolution (f(k) < 0.50) computations are in good agreement with the reference direct numerical simulation (DNS) studies, low-physical-resolution (f(k) >= 0.50) simulations lead to large discrepancies with the reference data. The physical and modeling interpretation of the results demonstrates that the origin of these distinct behaviors lies in the model's ability to resolve the phenomena driving the onset of turbulence not amenable to modeling by the closure. The comparison of the computations' cost indicates that high-physical-resolution PANS achieves the accuracy of DNS (f(k) = 0.00) at a fraction of the cost. We observe a cost reduction of one order of magnitude at the current Re, which is expected to grow with Re.