Temperature variations in the simulation of high-pressure injection-system transient flows under cavitation

Temperature variations and their effects on the simulation of unsteady pipe flows, in the presence of pressure-wave induced cavitation, were investigated with reference to high-pressure fuel injection systems. The thermal effects due to the compressibility of the liquid and to the thermodynamic process in the cavitating flow mixture were analyzed. To that end, the energy conservation equation was applied, in addition to the mass-continuity and momentum-balance equations, along with the constitutive state equation of the fluid. In particular, for the liquid, the physical properties (i.e., bulk modulus of elasticity, density, isothermal speed of sound, thermal expansivity, kinematic viscosity, specific heat at constant pressure) were implemented as functions of pressure and temperature in a closed analytical form matching carefully determined experimental data. Consistent with virtually negligible combined effects of heat transfer and viscous power losses involved in the flow process, the equation of energy was reduced to a state relation among the fluid thermodynamic properties, leading to a barotropic flow model. A comparison between isentropic and isothermal evolutions in the pure liquid regions was carried out for evaluating the influence of the temperature variation simulation on the macroscopic results given by local pressure time-histories. Besides, for cavitation analysis, different thermodynamic transformations of the vapor–liquid mixture were considered and compared. A recently developed conservative numerical model of general application, based on a barotropic flow model, was applied and further assessed through the comparison of prediction and measurement results on injection-system performance. A conventional pump-line-nozzle system was considered for this purpose, being relevant to model evaluation for its pressure-wave dynamics and also because it was subject to severely cavitating flow conditions at part loads. Predicted time-histories of injector-needle lift and pressure at two pipe locations were compared to experimental results. This substantiated the validity and robustness of the conservative model taking temperature variation effects into account, in the simulation of high-pressure injection-system transient flows with great degree of accuracy, even in the presence of cavitation induced discontinuities. The thermal effects due to the temperature variations in the liquid fuel and in the cavitating mixture were analyzed and discussed.