An improved partially-averaged Navier-Stokes model for secondary flows

In the present study, the modified formulations of the partially-averaged Navier-Stokes (PANS) model were suggested for accurate prediction of the secondary flow by resolving the anisotropy of turbulence. The main characteristics of the modified PANS (mPANS) models were to resolve the wide range of turbulent length scale by decreasing fk value in the region where the anisotropic behavior of turbulence dominates. The information on the region, where there is highly anisotropic turbulence, was procured by using the budget analysis and the anisotropy invariant map. The level of how much fk should be reduced was determined by model factors, which were set to be able to resolve the secondary flow in a square duct and around a prolate spheroid. To identify the reliability of the model factors, the mPANS models were applied to the flow around the KRISO very large crude oil carrier at Froude number of 0.142. The mPANS models showed improved predictions of the hook-shape pattern of the streamwise component of velocity and secondary vortex on the propeller plane compared to the original PANS (oPANS) results by decreasing the modeled turbulent kinetic energy.