Mode split prediction for a rotating disk coupled with a flexible stator through water*

High-head turbine runners are subject to multiple sources of excitations. Coupled with the added mass of water, rotation induces a mode split in natural frequencies of runners, where co-rotative and counter-rotative waves travel at different relative speeds through the runner. Disks, by displaying a similar behavior, are used as a simpler model. Mode split is characterized for a rotating disk in water but, in high-head turbines, the runner and the flexible upper cover are coupled through the axial gap fluid. In this project, we develop an analytical model of coupled stationary and rotating disks to analyze the effect of their interaction on the mode split. First, we apply the potential flow theory, considering water as irrotationnal, incompressible, and inviscid. We assume the same mode shapes in water as in air for the disks. 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. We finally couple the two obtained fluid flows through the structural equations of motion. The derived model displays less than 3% error with experimental data for large axial gaps and a thick rotor.