Turbulent flows past hill and curved ducts exist in many engineering applications. Simulations of the turbulent flow arc carried out based on a newly developed technique, the Partially-Averaged Navier-Stokes （PANS） model, including separation, recirculation, reattachment, turbulent vortex mechanism. The focus is on how to accurately predict typical separating, reattaching and secondary motion at a reasonable computational expense. The effect of the parameter, the unresolved-to-total ratio of kinetic energy （ fk ）, is examined with a given unresolved-to-total ratio of dissipation （ fE ） for the hill flow with a much coarser grid system than required by the LES. An optimal value of fk can be obtained to predict the separation and reattachment locations and for more accurate simulation of the resolved turbulence. In addition, the turbulent secondary motions are captured by a smaller fi as compared with the RANS method with the same grid.
The pressure fluctuation caused by unsteady flow in runner is one of the main reasons of vibration for a large Francis hydraulic turbine. It directly affects the steady operation of the hydraulic turbine unit. The existing research of the pressure fluctuation in hydraulic turbine mainly focuses on the unsteady flow in draft tube. Accurate distribution of pressure fluctuations inside a runner is not very clear. In this paper, the numerical method for predicting the pressure fluctuations in runner is investigated and the numerical simulation is performed for a large Francis hydraulic turbine. It is proved that the combination of shear-stress transport（SST） k-o） turbulence model and pressure-implicit with splitting of operators（PISO） algorithm could give more reliable prediction of pressure fluctuations in runner. The frequencies of pressure fluctuations in runner are affected by the flow in guide vane and the flow in draft tube The first dominant frequency is significantly determined by the flow in draft tube, especially at part load condition. This frequency is approximately equal to one-third of the runner rotating frequency. The evident second dominant frequency is exactly equal to the guide vane passing frequency. The peak-to-peak amplitudes of pressure fluctuations in runner at small guide vane open angle are larger than that at large open angle at the same operating head. The amplitudes at points on blade pressure surface are generally greater than that on suction surface. The research results could be used to direct the hydraulic design and operation stability improvement of a large Francis hydraulic turbine.
