Modelling approaches to acoustic cavitation in transmission pipelines

A general treatment of acoustic cavitation was presented, including both fluid dynamics instabilities that can occur at cavitation inception as well as non-equilibrium thermal and mechanical effects during bubble dynamics. Different approaches to cavitation modelling were considered and compared. A novel barotropic cavitation model has been developed, based on the partial differential equations governing the mass-conservation and momentum balance. The fluid has been taken as a homogenous mixture of a pure liquid, its vapor and a quantity of gas, both dissolved and undissolved. The analytical expression for the vapor source term driving cavitation has been carried out by means of the energy conservation equation and a general formula for the sound speed in homogeneous bubbly flows has been derived. A recently developed conservative, implicit, high-resolution, second-order accurate numerical scheme was applied to solve the equations governing the pipe flow. The resultant computational algorithm was assessed through comparison with experimental data referring to a system made up of a pipe connecting two constant-pressure reservoirs of water. The model predictions were examined and discussed in order to underline the most interesting fluid-dynamic phenomena, such as the dynamics of shock waves arising at cavitation collapse. The influence of the frequency-dependent friction on the simulation of the pressure wave dynamics in the presence of cavitation was also analyzed and discussed.