Theoretical and experimental study of the inlet and outlet cavitation in a model of a Francis turbine

In order to study the inlet and outlet cavitation in a Francis turbine (nq = 48) a numerical model of the bubble dynamics is established. By using the pressure and velocity distribution obtained by a 3-D potential flow analysis of the turbine, the Rayleigh-Plesset equation is integrated for a wide range of head and bubble sizes and for two typical turbine operating points, where inlet and outlet cavitation respectively are observed. The numerical simulations agree very well with the main cavitation features observed in the turbine runner. The minimum explosive bubble radius is found to be an inverse function of the test head, as predicted by the equilibrium free nucleus stability theory, unless this theory overestimates the size of the minimum active nuclei, mainly in outlet cavitation. Hence, these results, in addition to a measured water nuclei radii histogram, can explain fairly well both the influence of water nuclei content in outlet cavitation and the inlet cavitation independence of this content for usual test heads. The test head is then found to influence the maximum explosive bubble sizes by an H^(-1/2) law