Fluid-Structure Coupling Effects on the Dynamic Response of Pump-Turbine Guide Vanes

Hydraulic pump-turbines are subject to a high periodic excitation due to the Rotor-Stator Interaction, RSI. Basically, the RSI is caused by the impeller blade passage in the wake of the guide vanes in generating mode, or upstream from the guide vanes in pumping mode. Therefore, the structural parts, notably the guide vanes, suffer from high cycle fatigue strength. The dynamic behavior of the guide vanes is influenced by the surrounding flow. Additional inertia and dissipation strongly affect the structural vibrations; the added mass and the hydrodynamic damping being of the same order of magnitude as the structural mass and damping. In addition, should the entire guide vane cascade be considered, the neighboring guide vanes are influencing each other through the fluid medium. Their eigenfrequencies as well as the vibration amplitudes close to resonance may, thus, be strongly modified. A poor assessment of their dynamic behavior during the design stage may lead to premature failures due to RSI in the early stage of commissioning. So far, researchers have studied the RSI phenomenon, but have not established an analytical description. They have also investigated the added mass, especially the one acting on vibrating runner blades. However, few studies are related to the hydrodynamic damping in hydraulic machines. Moreover, to the author's knowledge, researchers have not yet considered neither the influence of the guide vane vibrations on the pressure fluctuations arising from the RSI nor the coupling between the guide vanes. Therefore, the present experimental work considers the response of the guide vanes in a pump-turbine reduced scale model to the RSI excitation. The pump-turbine is operated at the Best Efficiency operating Point, BEP, in turbine mode. The guide vane cascade consists of a complex mechanical system featuring many degrees of freedom. The study aims to show that the cascade may be viewed as a 2nd order mechanical system. The impulse response of immersed guide vanes is enabled with the use of a spark plug flush mounted in the bottom ring in a guide vane channel. This type of measurements is successfully undertaken in water, model at rest, and model in operation. Keeping the operating conditions of the BEP constant, the impeller rotation frequency is then swept and the guide vanes are therefore excited by the RSI over a wide frequency range. The combination of zb impeller blades with zo guide vanes makes apparent many different rotating diametrical pressure modes. The guide vanes respond up to the RSI 5th harmonic, but are mostly excited at the frequencies corresponding to the RSI fundamental f = zbn and the 2nd harmonic f = 2zbn. The amplitude of the fluctuating bending displacement and torsion angle of the guide vanes is strongly varying across the impeller frequency range. The ranges of the 1st and the 5th RSI harmonic frequency contain the frequency of the 1st bending eigenmode and the 1st torsion eigenmode, respectively. The pressure fluctuations close to the vibrating guide vanes are strongly varying and may even decrease by 50% at resonance. Therefore, a transfer of energy between the vibrating structure and the flow pressure should occur. The influence of an adjacent guide vane on the vibrations of a guide vane is found to vary significantly between its position on the pressure side and suction side of the latter. Regarding the guide vane bending vibrations, the hydrodynamic force acting on a guide vane induced by its neighboring guide vane on the pressure side is up to 10 times higher than the force induced by its suction side neighbor. As for the guide vane torsion vibrations, the hydrodynamic torque acting on a guide vane induced by its neighboring guide vane on the pressure side is up to 5 times higher than the force induced by its suction side neighbor. The hydrodynamic damping coefficient and the added mass corresponding to the vibrations of the adjacent guide vanes are successfully identified and an influence matrix is built. These two terms are shown to depend strongly on the relative amplitude of their vibrations, the absolute flow velocity and the phase shift between their vibration signals. Taking into account the periodicity condition, the influence matrix is built in order to predict the dynamics of the entire guide vane cascade. Four and six different eigenmodes are investigated for the case of bending and torsion motions, respectively. The eigenvalue real part of each bending eigenmode remains positive on the investigated impeller frequency range, that is the mechanical system is stable. On the other hand, the eigenvalue real part of the torsion eigenmode which is the most likely to be excited by the RSI becomes negative. This means that the mechanical system is unstable and premature failures of the guide vanes are expected. Finally, two different ways to prevent damage to the guide vanes excited at the RSI 5th harmonic frequency are proposed. On the one hand, it is shown that by increasing the structural damping constant by a factor 2, the mechanical system becomes stable. On the other hand, the modification of the shape of the cascade eigenmode is achieved by mistuning the cascade, such that its shape does no longer match the shape of the RSI pressure mode. This way, even if the mechanical system remains unstable, the risk of damaging the guide vanes is reduced.

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