Numerical simulation of flow past a square cylinder using Partially-Averaged Navier–Stokes model

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In this study, we carry out a two-stage partially averaged Navier–Stokes (PANS) simulation past a square cylinder to examine the effect of a grid system on the predicted results. The important focus in PANS is how the control parameter which is the ratio of unresolved-to-total turbulent kinetic energy is determined in the flow field. In this work, the parameter is evaluated by using an equation that we propose. The model equation utilizes the turbulent length scale, the Kolmogorov length scale and the cut-off grid length. We first perform RANS simulation to approximately evaluate the turbulent length scale and the Kolmogorov length scale. Then we construct five different grid systems based on these length scales and perform PANS simulation in which the length scales to determine control parameter are also updated as the simulation proceeds. Simulation results are compared with experimental data and the other LES and DES results. The comparison suggests that PANS approach is very effective in simulating separated turbulent flows in the sense that accurate predictions can be obtained by using a much coarser grid system than is required for LES. We then suggest the grid spacing requirements for a proper PANS simulation.