Flow Similarity in the Rotor–Stator Interaction Affected Region in Prototype and Model Francis Pump-Turbines in Generating Mode

Similarities of the flow in the rotor–stator interaction (RSI) affected region (stay vanes, guide vanes, and runner domain) in prototype and model Francis pump-turbines are analyzed using numerical simulations with special attention on the influence of Reynolds number. The ratios of characteristic length and velocity between the prototype and the model are 10.97 and 2.54; thus, the Reynolds numbers differ by about 28 times. Detailed flow analysis argues for higher partial load condition, Q = 0.8Q_d, and severe partial load condition, Q = 0.45Q_d. The flows in the distributor (spiral casing, stay vanes, and guide vanes domain) are well-behaved for both conditions with no separation, presenting high level of similarity in both space and time domain. The flows in the runners are well-behaved at higher partial load, Q = 0.8Q_d, and present good flow similarity and weak Reynolds number effects between the model and the prototype. At severe partial load, Q = 0.45Q_d, flow separation develops on the blade pressure sides and partially blocks the runner passages, showing prominent flow discrepancy and stronger Reynolds number effects between the two turbines. For the prototype flow of high Reynolds number, viscous effects have a minor role and less momentum is lost in the boundary layer. Therefore, the flow deceleration is less severe and the emergence of separation is restrained, presenting spatially delayed separation and a less disorganized flow pattern in the prototype. Validated by the model tests and on-site measurements, pressure fluctuations recorded in the vaneless space show that the relative fluctuation amplitudes in the model are slightly higher than those in the prototype. Resorting to dimensionless analytical equations and simulation results, the deviation in pressure fluctuations is found out to be influenced by Reynolds number effects. The research provides an improved understanding of Reynolds number effects on the flow discrepancy and pressure fluctuation difference in the RSI-affected region, which will facilitate better estimations of performance from scale model to prototype.