Effect of the Speed Factor on the Amplitude of the Blade Passing Frequency in the Vaneless Space of a Pump Turbine in Turbine Mode

An exponential expression describing the relationship between the amplitude of the blade passing frequency in the vaneless space of a pump turbine operating in the turbine mode and the speed factor is proposed based on statistical analysis. This mathematical relationship was discovered through signal processing of the data recorded during the emergency load rejection process of a prototype pump turbine. Subsequently, based on the pumped-storage test rig at Wuhan University, an experimental investigation was conducted to verify this mathematical relationship. The results indicated that, under the optimal guide vane opening of the model pump turbine, the goodness of fit of this mathematical relationship was quite high. As for the Francis pump turbine, the speed factor corresponds to the Strouhal number. Therefore, for this correlation, the underlying physical mechanism is the influence of the Strouhal number. This relation could inform the design and operation of pump turbines to control the intensity of pressure pulsations in the vaneless space. In addition, based on this mathematical relationship, the intensity of the rotor–stator interaction for different pump turbines can be compared quantitively.