Modal Response of Hydraulic Turbine Runners

The mechanical design of hydraulic turbines is conditioned by the dynamic response of the runner that is usually estimated by a computational model. Nevertheless, the runner has complex boundary conditions that are difficult to include in the computational model. One of these boundary conditions is the water in which the runner is submerged. The effect of the added mass and damping of water can modify considerably the natural frequencies of the runner. In order to analyze this effect on a Francis turbine runner, an experimental and a numerical investigation in a reduced scale model was carried out. The experimental investigations was based on modal analysis. Several impact tests with the runner in air and in water were done. The response was measured with accelerometers located in different positions of the runner. Special attention was taken to determine the most suitable positions of measurements and impacts. From the modal analysis, the natural frequencies, damping ratios, and mode shapes were determined. The simulation of the same runner was also carried out using a FEM method. First, some tests including a sensitivity analysis wee done to check the accuracy of the numerical results. Second, the runner was simulated and the frequencies and mode shapes were calculated both in air and in water like in the experiment. The simulation was compared with the experimental results to determine its accuracy especially regarding the added mass effects. Similar mode shapes and frequency reduction ratios were obtained so the simulation gave rather good results. In the paper, the frequencies, damping and mode shapes obtained in air and in water both from experiment and simulation are indicated. The same mode shapes obtained in air were obtained in water bit with lower natural frequencies and higher damping ratios. The difference in the natural frequencies is shown to be dependent basically on the added mass effect of the water and not on its added damping. This difference also depends on the geometry of the mode presenting different values for different mode shapes. Using non-dimensional values, the reduction in the natural frequencies can be extrapolated to other Francis runners presenting similar geometrical characteristics.