Bubbly flow model for the dynamic characteristics of cavitating pumps

Abstract

This paper is concerned with understanding the dynamic behaviour of cavitating hydraulic machines during unsteady or transient operation. The linear transfer matrices which relate the small fluctuating pressures and mass flow rates at inlet and discharge are functions not only of the frequency but also of the mean operating state of the machine, especially the degree of cavitation. The recent experimental transfer matrices obtained by Ng & Brennen (1978) for some axial flow pumps revealed some dynamic characteristics which were unaccounted for by any existing theoretical analysis; their visual observations suggested that the bubbly cavitating flow in the blade passages could be responsible for these effects.A theoretical model of the dynamic response of this bubbly blade-passage flow is described in the present paper. Void-fraction fluctuations in this flow result not only from pressure fluctuations but also because the fluctuating angle of attack causes fluctuations in the rate of production of bubbles near the leading edge. The latter causes kinematic waves which interact through the boundary conditions with the dynamic waves caused by pressure fluctuation. The resulting theoretical transfer functions which result are in good qualitative agreement with the experiments; with appropriate choices of two parameters (the practical values of which are difficult to assess) good quantitative agreement is also obtained. The theoretical model also provides one possible explanation of the observation that the pump changes from an essentially passive dynamic element in the absence of cavitation to a progressively more active element as the extent of cavitation increases.