A partially-averaged Navier–Stokes model for the simulation of turbulent swirling flow with vortex breakdown

This paper presents the development and validation of a new partially-averaged Navier–Stokes (PANS) model which can successfully predict turbulent swirling flow with vortex breakdown. The proposed PANS model uses an extended low Reynolds number k–ε model as the baseline model. Furthermore, a new formulation for the unresolved-to-total turbulent kinetic energy ratio fk is developed using partial integration of the complete turbulence energy spectrum. Therefore, the present formulation of fk is believed to be superior to the previously used constant or computed values. The newly developed PANS model is used in unsteady numerical simulations of two turbulent swirling flows containing vortex breakdown, namely swirling flow through an abrupt expansion and flow in a draft tube of a hydraulic turbine operating under partial load. The present PANS model accurately predicts time-averaged and root-mean-square (rms) velocities in the case of the abrupt expansion, while it is shown to be superior to the Delayed Detached Eddy Simulation (DDES) and Shear Stress Transport (SST) k–ω models. Predictions of the reattachment length using the present model shows at least 14% and 23% improvements compared to the DDES and the SST k–ω models respectively. Also, transient features of the flow, e.g. vortex rope formation and precession, is well captured in the case of the complex draft tube flow. The frequency of the vortex rope precession, which causes severe fluctuations and vibrations, is well predicted by only 7% deviations from the experimental data.