Modeling diesel spray tip and tail penetrations after end-of-injection

Abstract

Zero-dimensional (0-D) modeling of spray development plays increasingly significant roles in the model-based optimization of parameter designs and control strategies in diesel engine systems. Partially premixed low temperature diesel combustion that has been deemed essential in simultaneous reductions in the nitrogen oxides (NOx) and soot emissions usually features ignition occurrence after the end of fuel injection (EOI). However, so far modeling of the spray development after the EOI is far from adequate. Particularly, a theoretical model for the spray tail penetration is still absent. The objective of this paper is therefore to develop the 0-D model for both diesel spray tip and tail penetrations. The model of spray tip penetration after the EOI is based on the existing models, and the model constant is further developed. The mathematical expression of spray tail penetration is newly deduced with the discrete control volume method. These models are validated against the experimental spray data with varied ambient densities, injection pressures and nozzle hole diameters using the high-speed shadowgraphy and the constant volume chamber. The calculated results by the models agree very well with the experimental ones. The spray tip penetration exhibits a t dependence at the initial stage of injection, a t1/2 dependence at the later stage, and a (t−ti)1/4 dependence after about two injection durations from the start of injection (SOI). While the spray tail penetration is independent of the fuel injection pressures, it exhibits a (t−ti)1/2 dependence. Since the spray tail penetration rate is rather slower than the spray tip, the spray development after the EOI shows a trend with remarkable length extension, causing the quick fuel-air over mixing. These results are believed to be valuable reference for researchers or engineers who are considering the model-based design and control strategy development for diesel engine systems.