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. An experimental investigation in a reduced scale model of a turbine runner, using modal analysis, was carried out. Several impact tests with the runner freely suspended in air and in water were done. The response was measured with accelerometers located in different positions of the runner. From the modal analysis, the natural frequencies, damping ratios, and mode-shapes were determined. The same mode-shapes obtained in air were obtained in water but with lower natural frequencies and higher damping ratios in water. The difference in the natural frequencies is shown to be dependant 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 nondimensional values, the reduction in the natural frequencies can be extrapolated to other Francis runners presenting similar geometrical characteristics. r

The highest vibration levels in large pump turbines are, in general, originated in the rotor stator interaction (RSI). This vibration has specific characteristics that can be clearly observed in the frequency domain: harmonics of the moving blade passing frequency and a particular relationship among their amplitudes. It is valuable for the design and condition monitoring to count on these characteristics. A CFD model is an appropriate tool to determine the force and its characteristics. However, it is time consuming and needs highly qualified human resources while usually these results are needed immediately and in situ. Then, it is useful to determine these characteristics in a simple, quick, and accurate method. At present, the most suitable method indicates a large amount of possible harmonics to appear, without indicating the relative importance of them. This paper carries out a theoretical analysis to predict and explain in a qualitative way these frequencies and amplitudes. The theoretical analysis incorporates the number of blades, the number of guide vanes, the RSI nonuniform fluid force, and the sequence of interaction. This analysis is compared with the method currently in use, and both methods are applied to a practical case. The theoretical analysis gives a resulting force over the pump turbine, which corresponds well to the measured behavior of a pump turbine in terms of its frequencies and the relationship between their amplitudes. A corrective action is proposed as a result of the analysis and after it is carried out in one of the units, the vibration levels are reduced. The vibration induced by the RSI is predicted considering the sequence of interaction and different amplitudes in the interactions between the same moving blade and different stationary blades, giving a different and original interpretation about the source of the vibration characteristics. A successful corrective action is proposed as a consequence of this new interpretation.

a b s t r a c tA failure investigation was conducted on a high-pressure machine with a large pump-turbine runner that was 2.9 m in diameter and had a maximum discharge rate of 32 m 3 /s.A part of the runner broke off during operation. This released a piece of the crown, which went through the machine, causing further damage. An analysis of the broken runner revealed a fatigue problem, so the dynamic/vibratory behavior of the runner during machine operation was investigated to determine the cause.First, the excitation forces acting on the runner during operation were studied. The main excitation in pump-turbines is generated by the interference between the rotating blades and the stationary vanes, known as a rotor-stator interaction (RSI), which produces large pressure pulsations. The amplitude of the pressure pulsations was measured in the prototype using pressure transducers.Second, the modal response of the runner structure was analyzed. A finite element (FEM) model of the runner was developed and the main natural frequencies and associated mode shapes were identified.A dynamic analysis was then performed to determine the runner response. A harmonic excitation simulating the pressure pulsation of the RSI was applied to the numerical model of the runner. The results showed a large stress concentration in the T-joint between the blade and crown where the crack originated. Finally, the possible causes of the damage are discussed.

In this paper, a numerical simulation to analyze the influence of the surrounding water in a turbine runner has been carried out using finite element method (FEM). First, the sensitivity of the FEM model on the element shape and mesh density has been analysed. Secondly, with the optimized FEM model, the modal behaviour with the runner vibrating in air and in water has been calculated. The added mass effect by comparing the natural frequencies and mode shapes in both cases has been determined.The numerical results obtained have been compared with experimental results available. The comparison shows a good agreement in the natural frequency values and in the mode shapes. The added mass effect due to the fluid structure interaction has been discussed in detail.Finally, the added mass effect on the submerged runner is quantified using a non-dimensional parameter so that the results can be extrapolated to runners with geometrical similarity.

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