Application of the PANS turbulence model to calculate the flow in the Francis-99 model radial-axial hydroturbine

Swirling f lows are widespread in various fields of technology. At a high degree of swirling, the f low is complicated by the collapse of the vortex and the formation of large-scale unsteady structures. In hydropower engineering, the swirling f low instability is manifested by a precessing’s vortex bundle in the suction pipe. These non-stationary structures have a significant turbulent kinetic energy and are characterized by a sufficiently long lifetime, which causes serious difficulties in the numerical simulation of f lows in the duct of hydraulic turbines. The aim of this work is to construct a hybrid PANS turbulence model based on a second-order closure model. Using this model with different values of the resolution parameter, numerical calculations of the unsteady f low in the draft pipe in the partial load mode were performed. The proposed version of the PANS turbulence model makes it possible to reproduce well the characteristics of highly anisotropic f lows, while being less demanding on the grid resolution than the large eddy simulation method, and in the considered implementation does not contain an explicit dependence on the spatial grid spacing.