Abstract: When operating at the off-design condition, the pressure pulsations within a hydraulic machine may contain multiple frequency components. In time domain analysis of the flow, the unsteady characteristics of the lower-amplitude subharmonic frequency components are often overshadowed by the time-domain evolution of the dominant frequency component. Based on the ideas of the modal parameter extraction methods in structural dynamics, this paper describes a new method for extracting frequency-domain modal information from the flow field, using the natural excitation technique. Modal parameters at different frequencies are obtained through complex response functions, and relevant codes are developed to apply this method to analysis of the unsteady flow fields in a mixed-flow water turbine. We examine the simulation results of the turbine operating at low flow rates, characterize the vibration modes of draft tube vortices, and reveal the relationship between the generation of higher-order frequency components in the draft tube and the rotational perturbation source in the bladeless section. Meanwhile, we give an analysis of the impeller excitation modes caused by rotor-stator interference and other factors. The modal results has been verified with theoretical predictions. Thus, our frequency-domain modal analysis method helps reveal information such as the sources and propagation of pressure pulsations at different frequencies.

Key words: hydraulic machinery, pressure oscillation, mode, complex response function, Francis turbine