Simulation of dynamic loads on Francis blades at partial load

The pressure oscillations on Francis blades were analyzed numerically for partial loads by solving the 3-D Reynolds-averaged Navier-Stokes (RANS) equations with the RNG k-e turbulence model. The calculational domain included the guide vanes, the runner, and the draft tube. The results show that with the runner rotating relative to the draft tube, a vortex rope appears in the draft tube at partial load that causes pressure fluctuations inside the runner with a frequency of -f_n+f_d. This frequency is usually dominant. Other frequencies such as the guide vane blade passing frequency, the rotational frequency and it's higher order harmonics can also be observed at some points near the inlet. The peak-to-peak amplitudes on the blades tend to be higher at 66% of the optimum opening than at 80% of the optimum opening. The pressure fluctuations on the suction side tend to be stronger than on the pressure side.