Numerical investigation of gas/liquid two-phase flow in nozzle holes considering the fuel compressibility

Abstract

In this paper, a numerical study on the fuel flow in a nozzle hole considering the fuel compressibility was performed. The results indicated that the discharge coefficient Cd in the nozzle hole for the compressible fuel was greater than that for the incompressible fuel. The critical cavitation number Kcrt was not affected by the fuel compressibility; rather, it only depended on the structural parameters and pressure difference of the nozzle hole. The Kcrt of compressible and incompressible fuel increased with the injection pressure. The difference between the Cd for compressible and incompressible fuel increased sharply in the initial short period before cavitation occurred. Subsequently, the difference decreased with an increase in the pressure difference. After cavitation occurred in the nozzle hole, the difference gradually decreased. Until the cavitation rapidly developed into supercavitation, the effect of the compressibility on the Cd in the nozzle hole became weak. For incompressible fuel, Cd decreased significantly in the single-phase flow of the fuel as the injection pressure increased. After cavitation occurred, the degree of the decrease in Cd caused by the increase in the injection pressure became insignificant. For compressible fuel, the injection pressure had little effect on Cd before cavitation occurred. However, the increase in the injection pressure reduced Cd after cavitation occurred. A fitting formula for Cd with respect to K1/2 under different injection pressures was obtained using an optimization algorithm. The good agreement between the calculation results and computational fluid dynamics simulation data confirmed the accuracy of the formula.