Mode split prediction for rotating disks with flexible stator coupling

Abstract

High-head turbine runners are subject to multiple sources of excitation. Coupled with the added mass of water, rotation induces a mode split in the natural frequencies of runners, where co-rotating and counter-rotating waves travel through the runner at different relative speeds. Disks, by displaying a similar behavior, can be used as a geometrically simpler model. Mode split is characterized for a rotating disk in dense fluid but, in high-head turbines, the runner and the compliant confinement are coupled through the axial gap fluid. In this article, we develop an analytical model of coupled stationary and rotating disks to analyze the effect of their interaction on the mode split phenomenon. First, we apply the potential flow theory, considering the fluid as irrotational, inviscid and incompressible. We assume that the modeshapes of the disk in a dense fluid are similar to their shapes in vacuum. We then derive the potential flows that respect the no-penetration boundary conditions. One after the other, each disk is considered flexible while the other one is rigid. By applying the superposition principle, we then couple the two obtained fluid flows through the structural equations of motion. A finite-element vibro-acoustic modal analysis was developed to verify the analytical model and propose a fast numerical tool for hydraulic turbine design. Analytical results show that rotation induces a split of the coupled rotor–stator frequencies as for a lone rotor, while the ratio of their amplitudes varies slightly. A change in the relative thickness of the rotor and stator affects their individual frequencies in vacuum, and in turn their coupling by the fluid, with a potential shift in dominance.