We propose a novel approach to evaluate the relaxation time of vapor bubble growth in the context of the flash boiling of a superheated liquid. In alternative to the empirical correlation derived from superheated water experiments almost fifty years ago, the new model describes the thermally-dominated growth of vapor bubbles in terms that are dependent on the local Jakob number (the ratio of sensible heat to latent heat during phase change) and the number density of vapor bubbles. The model is tested by plugging the resulting relaxation time into the Homogenous Relaxation Model (HRM). Flash-boiling simulations carried out with HRM are compared with n-pentane (C5H12) injection and boil-off experiments conducted with a real-size, axial-hole, transparent gasoline injector discharging into a constant-pressure vessel. The long-distance microscopy images from the experiments, processed to derive the projected liquid volume (PLV) of the spray, provide a unique set of time-resolved validation data for direct fuel injection simulations. At conditions ranging from flaring to mild and minimal flash boiling, we show that switching to the new relaxation time improves the agreement with the measured PLV profiles with respect to the standard empirical model. Particularly at flaring conditions, the predicted increase in gas cooling caused by rapid vapor production is shown to be more consistent with the observed boil-off.
Gas ingested into the sac of a fuel injector after the injector needle valve closes is known to have crucial impacts on initial spray formation and plume growth in a following injection cycle. Yet little research has been attempted to understand the fate sac gases during pressure expansion and compression typical of an engine. This study investigated cavitation and bubble processes in the sac including the effect of chamber pressure decrease and increase consistent with an engine cycle. A single axial-hole transparent nozzle based on the Engine Combustion Network (ECN) Spray D nozzle geometry was mounted in a vessel filled with nitrogen, and the nitrogen gas pressure was cycled after the end of injection. Interior nozzle phenomena were visualized by high-speed longdistance microscopy with a nanosecond pulsed LED back-illumination. Experimental results showed that the volume of gas in the sac after the needle closes depends upon the vessel gas pressure. Higher back pressure results in less cavitation and a smaller volume of non-condensable gas in the sac. But a pressure decrease mimicking the expansion stroke causes the gas within the sac to expand significantly, proportional to the pressure decrease, while also evacuating liquid in front of the bubble. The volume of the gas in the sac increases during the expansion cycle due both to isothermal expansion as well as desorption of inherent dissolved gas in the fuel. During the compression cycle, the volume of bubbles decreases and additional non-condensable ambient gas is ingested into the sac. As the liquid fuel is nearly incompressible, the volume of both liquid and gas essentially remains constant during compression.
Numerical simulations of internal nozzle flow that include transient needle valve motion offer the potential to better predict spray penetration, mixing and liquid breakup. For example, the level of gas initially inside the sac and holes, as well as the rate of needle movement, influence the initial fuel delivery rate and spray development, thereby affecting ignition position and combustion. In this study, needle movement and gas exchange inside operating transparent fuel injectors are imaged at high speed, and CFD simulations with fine resolution (2-micrometers) in the needle-seat area are performed to understand the impact of needle movement and initial gas in the sac on ramp-up in rate of injection. The injector bodies and sac geometries are replicas of the Engine Combustion Network Spray A and Spray D injectors. Imaging shows that gas is ingested into the injector at the beginning of needle movement, an unexpected results given the high injection pressure above the needle valve. Finite element analysis simulations accounting for the elastic properties of the metal seat and needle are performed to explain this result. As forces on the needle and seat are relieved at the beginning of injection, the sac volume enlarges while contact between sealing surfaces remains. Needle and nozzle wall measurements confirm that the needle tip may move roughly 5-10 micrometers before the passage opens at the needle seat to allow flow and pressurization of the sac. Measured needle movement from an experiment (optical or X-ray) must be corrected to achieve a different "needle gap" profile for simulations with no elasticity. This elasticity-corrected profile should be used for CFD simulations, otherwise, early and incorrect spray development will be predicted. Simulations with the corrected needle-lift profile and gas initially within the sac show that the mass flow rate at the start of injection includes cycling in flow rate caused primarily by sac pressure fluctuations, which are recommended for future Lagrangian CFD simulations.