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The dynamic response of an hydraulic machine is greatly affected by the water due to the added mass effect. However, the presence of cavitation can change the modal response of the coupled fluid-structure system because it modifies the properties of the surrounding fluid, i.e. the speed of sound and density. In this paper, a FEM-based acoustic-fluid model has been used to simulate the dynamic response of a NACA0009 hydrofoil with attached leading edge cavitation. The natural frequencies and the corresponding mode shapes have been compared for the hydrofoil in air, in still water and in cavitation conditions. The numerical predictions show a good agreement with the experimental results obtained in a high-speed cavitation tunnel. They confirm that different fluid conditions can modify the mode shapes in comparison with the modes in air. The nodal lines of the torsion and the second bending modes are slightly shifted with water and cavitation. Furthermore, the third mode of vibration under cavitation conditions appears as a combination of the torsion and the second bending shapes. The results indicate that such alterations are mainly induced by the value of the speed of sound inside the cavity.

International audience; The added mass effects on a NACA0009 hydrofoil under cavitation conditions determined in a cavitation tunnel have been numerically simulated using finite element method. Based on the validated model, the effects of averaged properties of the cavity considered as a two-phase mixture have been evaluated. the simulation results point out that the average properties of the cavity, considered as a mixture of vapor/water, have a significant effect on added mass coefficients and mode shapes. These effects appear to be more important for higher modes of vibration. For instance, the first torsion mode can evolve towards the second bending mode when reducing the cavity void ratio from 1 to 0.9.

A series of tests have been put into effect in a laboratory to improve the cavitation monitoring techniques. Simultaneous vibrations and dynamic pressures have been measured in a reduced scale Francis turbine model with different types of cavitation: weak and intermittent cavitation at the blade outlet, outlet cavitation combined with intermittent von Karman cavitation, strong bubble cavitation and pulsating inlet cavitation. The structure and the fluid-borne noise induced by cavitation have been analyzed in the time and the frequency domains. Initially, the low and high frequency signal contents have been compared for the various types of cavitation. Then, the main hydrodynamic frequencies that modulate in amplitude high frequency bands have been identified. From the analysis of the results several conclusions can be extracted concerning the most suitable sensor, position and signal processing for detection of each type of cavitation. Besides, a detailed analysis of the processed data permits to infer some of their particular hydrodynamic characteristics that can be extrapolated to the real case for reliable identification.

An experimental investigation has been carried out to quantify the effects of surrounding fluid on the modal behavior of a reduced scale pump-turbine impeller. The modal properties of the fluid-structure system have been obtained by Experimental Modal Analysis (EMA) with the impeller suspended in air and inside a water reservoir. The impeller has been excited with an instrumented hammer and the response has been measured by means of miniature accelerometers. The Frequency Response Functions (FRF’s) have been obtained from a large number of impacting positions in order to ensure the identification of the main mode shapes. As a result, the main modes of vibration have been well characterized both in air and in water in terms of natural frequency, damping ratio and mode shape. The first mode is the 2 Nodal Diameter (ND), the second one is the 0ND and the following ones are the 3ND coupled with the 1ND. The visual observation of the animated mode shapes and the level of the Modal Assurance Criterion (MAC) have permitted to correlate the homologous modes of vibration of the fluid-structure system in air and in water. From this comparison the added mass effect on the natural frequencies and the fluid effect on the damping ratios have been quantified for the most significant modes. With the surrounding water, the natural frequencies decrease in average by 10%. On the other hand, the damping ratios increase in average by 0.5%. In any case, the damping ratio appears to decrease with the frequency value of the mode.

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.