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

Abstract

A general conservative numerical model for the 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 conservative homogeneous two-phase barotropic flow model of a pure liquid, its vapor, and a gas, both dissolved and undissolved. A physically consistent sound speed equation was set in a closed analytical form of wide application. 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 relation derived from the energy equation. Nevertheless, in the cavitating regions, an isothermal flow was retained consistently with negligible macroscopic thermal effects due to vaporization or condensation, because of the tiny amounts of liquid involved. A novel implicit, conservative, one-step, symmetrical, and trapezoidal scheme of second-order accuracy was employed to solve the partial differential equations governing the pipe flow. 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 relevant to model assessment because, at part loads, it presented cavitating flow conditions that can be considered as severe, at least for a diesel injection system. The predicted time histories of pressure at two pipe locations and of injector needle lift were compared to experimental results, substantiating the validity and robustness of the developed conservative model in simulating acoustic cavitation inception and desinence with great accuracy degree. Cavitation transients and the flow discontinuities induced by them were numerically predicted and analyzed.