Abstract
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.
Highlights
Modes under Different Constraints theThe runner include the vibrationsurface, modes dominated fixed constraints were set on the shaft-connecting bolt centerline, and the by b top of the short shaft, respectively, and the modes of the runner in channels were calculated by the acoustic–structure coupling method
The first five modes are typical nodal diameter (ND) and nodal circle (NC) modes; the sixth is the torsional mode; the seventh is the radial vibration mode; the eighth and tenth order modes are dominated by blade vibration; and the ninth is an 0NC-counter phase (CP) mode
The constraint condition determines the local stiffness of the structure; it has a significant impact on the modes of the runner
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Hübner et al [7] took the modal shapes of the structure in air as the initial displacement condition of the twoway fluid–structure coupling simulation, analyzed the frequency reduction coefficient of each mode of the structure in water, and obtained the wet modes of the structure The defect of this method is that only one mode can be obtained in each calculation. Rodriguez et al [13] measured the modes of an underwater circular plate using the acoustic–structure coupling method and compared it with the experimental data, which further proved that this method can accurately predict the natural frequencies of underwater structures considering the influence of rigid walls. The smaller the thickness, the more significant the influence He et al [15] studied the effect of the clearance on the dynamic characteristics of a pump turbine runner using the acoustic–structure coupling method. The purpose is to investigate the influence of the constraints and the boundary conditions of the wall on the prediction of the natural modes of the runner
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