Modeling of diesel spray tip penetration during start-of-injection transients

Abstract

Multiple-injection strategy that has been applied widely in diesel engines usually features a short duration for each injection pulse. As a result, the shortened injection makes the needle opening and closing transients increasingly important for spray in an injection event. Owing to the needle movement, the spray development during the transient processes is complex and quite different from the spray at the quasi-steady state. However, so far modeling of the spray development during the transient processes is far from adequate. Particularly, a theoretical zero-dimensional (0-D) spray tip penetration model considering the needle opening and sac pressurization processes as well as ambient and injection conditions during the start-of-injection (SOI) transients is still absent. In this paper, considering the sac pressurization processes, the 0-D model of spray tip penetration during the SOI transients is derived. Then, the model is validated against the experimental spray data using a long-distance microscope together with an ultrahigh speed CMOS camera. The model and experimental results show that the spray tip penetration shows a t3/2 dependence at the initial stage of injection rather than the t dependence suggested by Hiroyasu’s model. Later, the spray tip penetration shows a t3/4 dependence owing to the spray breakup, and a t1/2 dependence with the completion of sac pressurization. The models and analysis are believed to provide new insights into the transient spray behaviors and valuable reference for engineers and researchers who are considering the model-based development of next-generation diesel engines.

Phenomenological models of the transient processes of diesel spray tip penetration

“…As discussed in the above paragraphs, the Hiroyasu model [3] can be used at the quasi-steady stage and the transition stage 2. Based on the relationship among sac pressure, needle lift and time after start of injection (aSOI), the authors of this paper proposed a theoretical model for S tip at the acceleration stage and the transition stage 1 [8]. Moreover, a theoretical model for S tip at the decelerating stage is developed by the present authors [7].…”

“…Moreover, a theoretical model for S tip at the decelerating stage is developed by the present authors [7]. Making the models in [3,[7][8] continuous at the turning points leads to 1) is suitable when t p is smaller than t b , while Equation ( 2) is suitable when t p is larger than t b . It can be seen that both sides of Equations ( 1) and ( 2) can satisfy the conservation of dimensions, which verifies the correctness of the models.…”

“…They confirmed that S tip has a t 1.5 dependence at the injection startup. Recently, the authors of this paper proposed a theoretical model for S tip during the SOI transients [8]. They reported that S tip is proportional to t 1.5 at the acceleration stage, t 0.75 or t 1 at the transition stage, and t 0.5 at the quasi-steady stage.…”

“…In the derivation processes of the above models, an idealized rectangular fuel injection rate profile was assumed [1][2][3][4][5][6], and the increase of sac pressure during the start-of-injection (SOI) transients and the termination of fuel momentum supply after the end-of-injection (EOI) were not considered. Recently, the above models were found to give an unacceptable prediction of S tip during the SOI transients and after the EOI [7,8]. These limitations seem to be acceptable when using a single long-pulsed fuel injection [1][2][3][4][5][6], where the SOI transients account for a relatively small proportion of the entire injection processes and the spray usually impinges upon the wall before the EOI.…”

“…This is because the existing studies about the SOI and EOI transients are independent of each other. One of the objectives of this paper is to summarize the present authors' previous work on the transient diesel spray [7,8] and further develop a model for the entire development processes of S tip . Another objective is to provide experimental data to verify the newly developed model.…”