| Summary: | To predict the resonance characteristics of hydraulic machinery, it is necessary to accurately calculate the natural modes of the runners in the operating environment. However, in the existing research, the boundary conditions of the numerical modal analysis of the runner were not unified. In this paper, numerical modal analysis of a prototype Francis pump turbine runner was carried out using the acoustic–structure coupling method. The results of three different constraints were compared. The influence of the energy loss on the chamber wall on the natural modes of the runner was studied by the absorption boundary. The results show that the constraint condition (especially the rotating shaft) has significant impacts on the torsional mode, the radial mode, the 1 nodal-diameter mode, and the 0 nodal-circle mode, and the maximum differences in the natural frequencies under different conditions are 69.3%, 56.4%, 35.1%, and 9.4%, respectively. The change of the natural frequencies is closely related to the modal shapes. On the other hand, the energy loss on the wall mainly affects the nodal-circle modes, and the influence on other modes is negligible. The results can provide references for the design and resonance characteristics analysis of hydraulic machinery runners.
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