Contribution à l'étude de l'érosion de cavitation: mécanismes hydrodynamiques et prédiction

In the field of hydraulic power plant, the leading edge cavitation is often responsible of sever erosion which may cause a premature shutdown of energy production with costly consequences. This type of cavitation is characterized by an attached vapour cavity at the leading edge of the blades. Transient vapour vortices are generated and convected by the mean ow to the pressure recovery region where they collapse violently. The resulting water hammer pressure is responsible of material damage. In order to investigate the cavitation erosion problem, many theoretical and experi- mental research has been performed in hydrodynamics, mechanical science and metallurgy. We intend in the present work to describe the hydrodynamic attack and provide new mathematical model to characterize and predict the pressure impulses induced on solid surface by repeated collapses of transient cavities. First, the dynamics of a single vortex collapse is performed in the IMHEF Cavitation Vortex Generator. High speed visualization shows systematic rebound of such cavity after the collapse. This explosive rebound is due to the dissolved gas and leads to the generation of a strong shock waves which propagates in the liquid and the solid as well. Assuming Tait'equation for water, an estimation of the shock overpressure has been performed by image processing. Overpressure as high as 2 GPa has been thus measured. Furthermore, the maximum potential energy of the cavity and the uid corresponding to the maximum volume of the cavity stands as a good basis to characterize the collapse overpressure. Investigation of the shedding process by an attached cavity is carried out in the IMHEF High Speed Cavitation Tunnel on a 2D NACA009 blade. The hydrofoil is equipped with 30 piezo resistive pressure transducers. Beside the pressure acquisition, cavitation induced vibrations as well as the main cavity dimensions are synchronously acquired. Pressure spectra and cavitation patterns analysis leads us to consider the free and the forced regime of the main cavity. The forced regime occured when the von Karman vortices frequency matches the first natural frequency of the hydrofoil. In this case, the main cavity pulsation as well as the shedding process are modulated by the blade vibration fre- quency. In the free regime, the main cavity may be stable or unstable. Stable cavitation is characterized by small amplitude of the main cavity pulsation. In this case, the tran- sient cavities have a small size compared to the cavity length and the shedding process is highly instationnary. The unstable cavitation is characterized by large amplitude of main cavity pulsation. The shedding process is modulated by the main cavity pulsation witch is governed by a Strouhal like law. The Strouhal number depends on the incidence angle and stands between 0.2 and 0.32. The cavitation induced vibrations are found to be highly modulated by the main cavity pulsations. Envelope calculation of acceleration signals allows to identify the shedding frequency. This result is validated in a centrifugal pump model. In this case, vibration signal is found to be modulated by the blade passing frequency. Furthermore, we have shown that the use of two accelerometers allows a better cavitation detection through the coherence function corresponding to the acceleration envelopes in well chosen frequency band. Amplitude demodulation of vibration signals stands as a promising technique that may allow in short future the cavitation monitoring in hydraulic machines. Analysis of the previous results allows to build the model of Cavitation Erosion Power. This model is based on the assumption that the pressure aggressiveness of a single cavity is proportional to its potential energy. Furthermore, in the lake of direct measurements of the vapour volume of the transient cavities, the main cavity length is used to scale the dimension of the erosive cavities. The cavitation Erosion Power is related to the macroscopic parameters in a simple way. The validation of this model is performed in the case of isolated hydrofoil by assuming that the pressure uctuations downstream of the main cavity is characteristic of the cavitation aggressiveness. In hydraulic runners, the leading cavitation is often in the forced regime and the Strouhal law is no more available. In this case, the shedding frequency is unknown. In order to overcome this problem and calculate the cavitation erosion power, vibratory approach may be used to measure the shedding frequency.

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