Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations—Flow Past a Square Cylinder

The partially averaged Navier–Stokes (PANS) approach is a bridging closure model intended for any level of resolution between the Reynolds averaged Navier–Stokes (RANS) method and direct numerical simulations. In this paper, the proposed closure model is validated in the flow past a square cylinder. The desired ratio of the modeled-to-resolved scales in the PANS closure is achieved by appropriately specifying two bridging parameters: the ratios of unresolved-to-total kinetic energy $(fk)$ dissipation $(fε)$⁠. PANS calculations of different bridging parameter values are performed and the results are compared with experimental data and large-eddy simulations. The Strouhal number$(St)$⁠, mean/root-mean-square (RMS) drag coefficient $(CD)$⁠, RMS lift coefficient $(CL)$⁠, mean velocity profiles, and various turbulent stresses are investigated. The results gradually improve from the RANS level of accuracy to a close agreement with the experimental results with decreasing value of the bridging parameter $fk$⁠. Overall, the results indicate that the PANS method clearly satisfies the basic tenets of a bridging model: (i) provides a meaningful turbulence closure at any modeled-to-resolved scale ratio and (ii) yields improved accuracy with increasing resolution (decreasing modeled-to-resolved ratio).