A Comprehensive Thermodynamic Approach to Acoustic Cavitation Simulation in High-Pressure Injection Systems by a Conservative Homogeneous Barotropic-Flow Model

Abstract

A general conservative numerical model for simulation of transmission-line unsteady fluid-dynamics has been developed and applied to high-pressure injection systems. A comprehensive thermodynamic approach for modeling acoustic cavitation, i.e. cavitation induced by wave propagation, was proposed on the basis of a homogeneous barotropic mixture model of a pure liquid in equilibrium with its vapor and a gas, both dissolved and undissolved. For the pure liquid flow simulation outside the cavitation regions, or in the absence of these, temperature variations due to compressibility effects were taken into account, for the first time in injection system simulation, through a thermodynamic state equation which was derived from energy considerations. Nevertheless, in the cavitation regions, an isothermal flow was retained which is consistent with negligible thermal effects due to vaporization because of the tiny amounts of liquid involved. A novel implicit, conservative, one step, symmetrical and trapezoidal scheme of the second-order accuracy was applied to solve the hyperbolic partial differential equations governing the pipe flows. It can also be enhanced at a high-resolution level. The numerical model was applied to wave propagation and cavitation simulation in a high-pressure injection system of the pump-line-nozzle type for light and medium duty vehicles. The system was of relevance to the model assessment because it presented severely cavitating flow conditions. The predicted pressure time histories at two pipe locations and injector needle lift were compared to experimental results, substantiating the validity and robustness of the developed conservative model in simulating cavitation inception and desinence with great degree of accuracy. Cavitation transients and the flow discontinuities induced by them were numerically analyzed and discussed.