Simulations and Measurements of Pressure Oscillations Caused by Vortex Ropes

Pressure oscillations caused by vortex rope were measured in the draft tube of a prototype Francis turbine. The three-dimensional, unsteady Reynolds-averaged Navier-Stokes equations with the RNG $κ−ϵ$ turbulence model were solved to model the flow within the entire flow path of the prototype hydraulic unit including the guide vanes, the runner, and the draft tube. The model was able to predict the pressure fluctuations that occur when operating at 67–83% of the optimum opening. The calculated frequencies and amplitudes of the oscillation show reasonable agreement with the experiment data. However, the results at 50% opening were not satisfactory. Pressure oscillations on the runner blades were found to be related to the precession of vortex ropes which caused pressure on the blades to fluctuate with frequencies of $−fn+fd$ (⁠$fn$ is the rotational frequency and $fd$ is vortex procession frequency). The peak-to-peak amplitudes of the pressure oscillations on the blades at the lower load conditions (67% opening) were higher than at higher load conditions (83% opening). Fluctuations on the suction side tended to be stronger than on the pressure side.