Acoustic Cavitation Thermodynamic Modeling in Transmission Pipelines by an Implicit Conservative High-resolution Numerical Algorithm

A general treatment of acoustic cavitation for the case of one-dimensional pipe flows is presented, including both fluid dynamics instabilities, which can occur at cavitation inception, and non-equilibrium effects during bubble dynamics. Different approaches to cavitation modelling are also 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 analytical expression for the vapour 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 used. A newly developed high-resolution, conservative, implicit, second-order accurate numerical scheme was applied to solve the Euler's hyperbolic equations governing the pipe flow. It gave reduced oscillation problems at the discontinuities that were induced by cavitation. The resultant computational model was assessed through its application to a literature test-case, which involved a pipe connecting two constant-pressure reservoirs, water being the working fluid. The prediction outcomes were discussed so as 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 model on the simulation of the pressure wave dynamics in the presence of cavitation was also analysed.