Models of fuel spray penetration

Abstract

AbstrKt. A bricfreview of models of diescl fuel spray penetration, developed at !he University of Brighton. are presented. 11lcse refcr to the initial stagc of spray penetration and the two-phase flow stage. when the relative vclocity bet .... een droplcts and gas can be ignored. ll1e predictioos of the two-phase models 0(spray penetratioo arc compared with the ('e$ults of experimental studies. A rapid comprtSSion diesel spray rig. based at Brightoo University. and a high-pressure dimethyl ether spny chamber. based at Chungbuk National University. have been used. In both cases !he experimental results arc shown to be in agreement " 'ith !he predictioo of Iheomical models. Key " 'ord5: diesel fuel spray. dimethyl ether spray. t .... o .. phase flow, spray penetration. L INTRODUCTION A rigorous theory of spray penetration would be very complex as it would need to involve modelling of the fonnation of ligaments and their breakup. droplet breakup and evaporation. the entrainment of ai r and the effects of turbulence Ill. A self-consistent model of all these processes is still a major challenge. However. this modelling is not always essential for understanding the process and engineering applications. On many occasions it is far more important to establish a "hicrarchy" of the importance of various processes and to develop si mplified models suitable for practical applications. Somc resu lts in this direction were reported in 1 2 \. whcre sim ple ana lytical models. describing the initial stage of spray penetration and droplet breakup. were ' " derived. TIle reduction of the droplet size due to the breakup was considered. but an unrealistic assumption that droplet velocity remains constant, was used. The effects of ~uction of the droplet size during the penetration process due to effects of evaporatIon and breakup were ignored. "These will be taken into account in the present analysis. This model was further de\'eloped in (31. where effects of droplet evaporation. breakup and air entrainment on diesel fuel spray penetration were studied theoretically at the initial stage of spray penetration. when the influence of air entrainment is small (u p to 0.1-0.2 ms after the start of injection). Theoretical plots of spray penetration versus time were compared with experimental results. obtained using an optical si ngle cylinder rapid compression test rig based on a Ricardo ~teus engine. Three models of spray penetration were compared. In the first. neither breakup nor air entrainment were taken into account. The breakup processes (bag and stri pping) were taken into account in the second mode l, while in the third model both bag breakup and air entrainment processes were considered. It was found that the agree ment between the predictions of the third model with experimental measurements is better than that for the first two models. It was shown in (21 that for realistic diesel spray parameters the droplet break-up takes place almost immediately after the droplets leave the nozzle. This leads to a considerable shortening of the initial stage and a rapid conversion of the flow to the two-phase stage. This allows the analysis to be restricted to the two-phase flow approximation for th is type of spray, when the expressions for spray penetration are derived, based on the equations of conservation of mass an d momentum. The expressions for spray penetration derived in (2) gave more accurate predictions compared with those suggested earlier. This conclusion. hov.-·ever. was reac hed based on just two cases taken from the literature. and cannot be considered to be reliable. Further generalization of thi s model. taking into account the effect o f turbulence. was reponed in (4). "The focus of this paper will be on the two-phase models of spray penetration. ~se models ~ill be compared with the observed spray penetrations, using rather dIfferent expenmental setups at the University of Brighton f·-i] and Chungbuk National University of Korea (8.9). ."The t;vo-ph~ models for spray penetration, suggested in (21. are briefly reVieWed In Section 2. The experimental setups used are described in Section 3. Comparison between experimental and theoretical results is presented in Section 4. The main results of the paper are summarized in Section 5. 2. TWO-PHASE FLOW The analysis of the influence of the air jet on spray dynamics in the area beyond the vici nity of the nozzle appears to be a rather difficult task. At the same time, as t~e distance from the nozzle increases, the velocities of droplets approach the veloctty of the en trained air. As a result. the dynamics of both droplets and '"