Unsteady bubbly cavitating nozzle flows

Abstract

Unsteady quasi-one-dimensional and two-dimensional cavitating nozzle flows are considered using a homogeneous bubbly flow model. For quasi-one-dimensional nozzle flows, the system of model equations is reduced to two evolution equations for the flow speed and bubble radius and the initial and boundary value problems for the evolution equations are formulated. Results obtained for quasi-onedimensional nozzle flows capture the measured pressure losses due to cavitation, but they turn out to be insufficient in describing the twodimensional structures. For this reason, model equations for unsteady two-dimensional bubbly cavitating nozzle flows are considered and, by suitable decoupling, they are reduced to evolution equations for the bubble radius and for the velocity field, the latter being determined by an integro-partial differential system for the unsteady acceleration. This integropartial differential system constitutes the fundamental equations for the evolution of the dilation and vorticity in twodimensional cavitating nozzle flows. The initial and boundary value problem of the evolution equations are then discussed and a method to integrate the equations is introduced. Due to a lack of an algorithm to compute two-dimensional bubbly cavitating flows presently, the numerical simulation of 2D cavitating nozzle flows is obtained by the CFD-Tool CATUM, which is based on an equilibrium phase transition model. Results obtained for a typical cavitation cycle show instantaneous high pressure pulses at instances of cloud collapses.