Modeling and Simulation of Transitional Taylor-Green Vortex Flow with PANS

A new PANS model is used to predict the transitional Taylor-Green vortex flow at initial Reynolds number $3000$. This problem 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 (eg, 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, fe and fk, through apriori 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<0.5) computations are in good agreement with the reference DNS studies, low-physical resolution (fk>=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 capture the instabilities and coherent structures driving the onset of turbulence. The comparison of the computations' cost indicates that high-physical resolution PANS achieves the accuracy of DNS (fk=0.0) 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. These results clearly indicate the potential of PANS to predict transitional flows efficiently.