Simulation of transient cavitation processes in diesel injectors using KIVA with a Homogeneous Equilibrium Model

Transcription

1 Internation Mutidimension Engine Modeing User's Group Meeting, pri 9, 9 Detroit, MI imuation of transient cavitation processes in diese injectors using KIV with a Homogeneous Equiibrium Mode W. G. Lee * and R. D. Reitz Engine Research Center University of Wisconsin-Madison Madison, WI 5376 U bstract The high speed, transient cavitating fow distribution inside diese injector nozzes with consideration of the opening and cosing neede vve is ccuated using a generized equation of state (EO) to describe the fuid density, a homogeneous equiibrium mode (HEM) for phase change, and an arbitrary moving mesh to account for neede motion. The KIV-3V code was modified for the generized equation of state, and an isotherm acoustic speed formuation, reated to the void fraction in two phase fow, was used to account for the rate of fuid voume change due to pressure changes (dv/d). The neede vve motion was impemented by expoiting the piston motion feature ready avaiabe in the KIV code, using the arbitrary Lagrangian-Euerian (LE) approach. Cavitation zone formation and deveopment were simuated and compared in three-dimension re-sized nozze modes for both convention muti-hoe and group-hoe arrangements. The effects of geometric factors of the group-hoe nozze on the discharge coefficient, area contraction and density variation were investigated. The tempor evoution of cavitation during the opening and cosing of the neede vve was so studied. It is shown that pressure waves and transient fow effects brought about by the time-varying neede motion significanty affect the fow structure and cavitation processes. Introduction The combination of higher injection pressure and smer diameter nozzes has been usefu to reduce M and NOx emissions from diese engines. However, it has been reported that smer diameter nozzes can entrain too much air and give a shorter spray penetration, resuting in increased M, especiy under high-speed and high-oad conditions []. To overcome this drawback, the concept of using group-hoe nozzes has been proposed []. The idea is to arrange sm-sized hoes cosey spaced so as to reduce spray dropet size whie restricting air entrainment and maintaining the penetration ength. Even though the merit of the group-hoe nozze in a re combustion engine is sti under debate [3], there has been much research on the structure of the sprays from various configurations of group-hoe nozzes [4, 5, 6]. Recenty ark et. [7] numericy investigated the effect of group-hoe nozze ayout on diese engine combustion and emissions. In their research the injection conditions of the two sprays from a group-hoe injector were assumed to be identic. However, different fow structures may yied different rates of injection and cavitation inside the two hoes in a group-hoe injector due to the different ayouts of the nozze hoes. ince the discharge coefficient of a nozze orifice depends highy on the injector design and is not constant during the injection process, it is important to estabish a method to predict the transient rate of injection. Many attempts have been made, incuding visuization and simuation studies. However, transient cavitation inside the injector nozze passage increases the uncertainty in measurements and eads to difficuty in modeing. ever approaches have been proposed to simuate highy transient, cavitating fow. One of them is the singe-fuid approach so used in the present study. Based on the Homogeneous Equiibrium Mode of Wis [8], the method treats the two-phase mixture as one compressibe fuid. HEM was appied to simuate cavitation phenomena in - dimension nozze passage geometries by chmidt et. [9]. The HEM method was then successfuy impemented into the KIV code and was further deveoped as a code ced CVIF []. In their mode [9,], the pressure was ccuated directy from the equation of state of the mixture, and the fow was treated as aminar. Ning et. [] appied the HEM method in conjunction with the Euerian-Lagrangian pray tomization mode []. They proposed a new pressure equation that was derived from the continuity equation, and some modifications to the turbuence modes were so proposed. There are many other cavitation modes, such as the three-fuid approach of Grogger et. [3] and the cavitation bubbe-tracking mode of Gavaises et. [4]. However, a singe-fuid mode is reativey easy to * Corresponding author

2 IMEM 9 impement into existing codes and with some modifications, it can be combined with turbuence and spray modes. Therefore, the singe fuid mode based on HEM approach was seected in the present study to investigate the structure of the fow and cavitation inside both convention muti-hoe and group-hoe injectors. Numeric Methods In this study, the two-phase fow was assumed to be one homogeneous mixture of vapor and iquid, as with the Homogeneous Equiibrium Mode. The barotropic equation of state of Wis [8] was used. Under the assumption of constant temperature, the acoustic speed of the two-phase fow is expressed as: α α = [ α + ] + v ( α) () a vav where α is the void fraction, defined as: α = () v To derive the equation of state, the pressure was integrated directy from the equation: d = a d (3) resuting in [9]: = a v if v (4) where sat a + v og sat + a ( + α( )) v v v ( ( )) vav α vav = ( ) = v vav v av ( ) v if < < (5) v if (6) = (7) sat sat v av = v + v og (8) In this study a modified code based on the KIV-3V Reease code [5] was used. ince the standard KIV code uses the ide gas assumption for the equation of state, a generized impementation of the equation of state was needed. The method introduced by Trujio et. [6] was adopted: V C = V V + C ( ) V M V V = = = () a where a s is the isentropic speed of sound. Trujio et. [6] showed an appication of the eng-robinson equation with this method. In present study, the above equations of state (4)~(8) were impemented into the KIV code using the generized forms of Eqs. (9) and (). QOU scheme and expicit Euer scheme are used for convection fux and time marching. Computation meshes were generated for a muti-hoe nozze and for three group-hoe nozzes. ince the nozzes have 8 singe hoes or 8 groups of hoes in the circumferenti direction, the meshes were modeed as /8 sector meshes with periodic boundaries. The shapes of the computation domains are shown in Figure, and the important dimensions are shown in Tabe. The exit pressure was set as 5 bar, and the pressure difference between the inet and exit was set as 5 bar. The computation domains consist of 3 regions. The first is for a sac voume and the gap between the neede and the housing, the second is for the high pressure zone, and the third is for the nozze passage and orifice. When the neede is moving, the mesh in region is added to or removed by the snapping gorithm in the KIV code. The ocation of the neede is defined in Figure. t the start of the simuation, the pressure in regions and 3 was 5 bar, and the pressure in region was 55 bar. Resuts and Discussion The fows and cavitation phenomena inside the injectors were simuated for the 4 different nozze geometries. In Figure 3, the transient mass fuxes due to neede movement are shown as discharge coefficients (C d ) defined by: (9)

3 IMEM 9 where U b (= f C d u d = () U f / ) is the Bernoui veocity and f is the nomin density of the fue at 5 bar. b Cavitation deveopment during the neede vve opening event is shown in Figure 4. For cases, the discharge coefficients ready reached about 9 % of their maximum vues when the neede vves were opened to. mm. The maximum C d was about.6 for the inge Hoe Nozze (HN). For the Group Hoe Nozze # (), the fow rate passing the ower nozze hoe was decreased, mainy because the ower nozze is attached to the sac voume at an obique ange of about 4 degrees. This eads to fow separation at the nozze entrance and causes cavitation to occur at the entrance of the, as shown in Figure 4. If the ower nozze hoe is exacty perpendicuar to the nozze sac surface, as in GHN3, then the C d of the ower nozze passage is seen to increase, and is even sighty arger than that of the upper nozze. However, this kind of arrangement coud induce more entrainment of the surrounding air and acts as 6 hoes with different targeting points, which is not consistent with the concept of group-hoe nozzes. Cavitation in this nozze deveoped mainy in the, because the fow direction turns suddeny after foowing the sac voume surface. The other way to bance the mass fuxes of both hoes may be to ocate the two hoes coser, ike GHN. In this case the ower nozze is neary perpendicuar to the sac voume surface and the arrangement respects the concept of the group-hoe nozze, that favors production of sm MD and air entrainment equivent to the singe hoe nozze. However, with the coser hoe arrangement, the C d s of both nozzes were found to be smer than that of the HN, despite the fact that the fow rates are we banced. If the two hoes are ocated too cose together, the mass fuxes between the two hoes has to be divided, and the fux at the upper side of the is not sufficient. In addition, the fows entering neighboring hoes interact with each other, and this make the C d s fuctuate, as can be seen in Figure 3. When the ower side of the entrance of the attracts more mass fux, the upper side of the entrance of the suffers from a ack of entering fux, which eads to a rotating fow and resuting cavitation, as shown in Figure 4. Therefore, a desirabe arrangement of the group-hoe nozze may be to arrange sufficienty separated hoes, which are both norm to the w. possibe way to achieve this is a group-hoe nozze on a cone shaped sac voume, not a hemispheric one. When the neede vve coses, cavitation is augmented inside the nozze passages, as shown in Figure 5. Cavitation increases because the pressure drops inside the nozze passage as the entering mass fux at the passage entrance is rapidy decreased by bocking by the neede whie the exit mass fux is decreased reativey sowy due to inertia. Thus, the fow is stretched and its pressure drops. However, if the neede cosing speed is not fast enough, this phenomenon may not happen. t the end of the neede cosing event, the increased cavitation reaches the exit of the nozze and outward mass fux is maintained positive for a period of about.5 ms after the neede is fuy cosed at t=.65 ms. It is interesting to note that the cavitation ocation changed direction in the HN, and GHN3 nozzes during the injection due to the change of fow direction. When the neede ift is high, the mass fux is suppied uniformy (HN) or mainy upward (, GHN3). However, when the ift is ow, the fow passing through the sm gap between the neede and housing is injected toward the center of the sac voume and then turns back upward to the hoes. These fow detais change the cavitation inception point in the upper nozze hoes, as shown in Figure 6, and in the streamine patterns. The transient behaviors of veocity and density are shown in Figure 7. The veocity and density were averaged over the exit area and normized by the Bernoui veocity U b and the nomin density f, respectivey. vue of density ratio (/ f ) ess than unity means that vapor generated by cavitation reaches the exit. In the HN case, the cavitation vapor reached the exit intermittenty and fied most 4 % of the exit area when the neede vve coses. On the other hand, in the case, the cavitation vapor did not reach the exit in most of the injection period, except in the ate period of the neede vve cosing event at the. The veocity ratio U mean /U b is the same as C d when / f is unity, but it is arger than C d when cavitation reaches the exit. For exampe, in the HN case, at the time when the vve is fuy cosed (t=.65 ms), U mean /U b remains as high as. if cavitation is augmented, whereas the C d drops to.5. Figure 8 shows the veocity distribution at the exit of the injector nozzes at t=.34 ms, which represents the steady state injection period at the time just before the neede cosing event. The veocity distribution at the exit of the HN is more uniform than those of the s the GHNs, even though the nozzes are attached at the same position to the sac voumes. The veocity distribution at the exit of the s of and GHN3 are neary same, but it is different at the of the GHN, due to the interaction with the. Obviousy there is 3

4 IMEM 9 much discrepancy between the veocity distributions of the s and those of the s. The discrepancy undoubtedy infuences the atomization process and shoud be refected in next-generation spray modes. Concusions In this study, it has been shown that the current singe-phased, HEM approach can be appied to investigate cavitation processes inside injector nozzes. Differences in the rate-of-injection for each hoe can be predicted, as we as the detaied veocity distribution and vapor fraction at the nozze exit. The resuts show that pressure waves and transient fow effects can ead to fow osciation between cosey spaced fow passages that can promote cavitation and presumaby atomization of the resuting spray so. The present modeing method can be utiized to optimize nozze shapes and hoe arrangements to prevent or encourage cavitation. The resuts can be so used as an input condition for spray mode improvement. Nomencature a speed of sound pressure V Lagrangian voume of a ce α void fraction of mixture density ubscripts v vapor s isentropic iquid uperscripts C corrected predicted sat saturated cknowedgement The authors thank Cummins Engine Company for supporting this work. References. Bergstrand,. and Denbrantt, I., E --,.. Zhang, Y., Nishida, K., Nomura,. and Ito, K., E 3--35, Dohe, U., Krüger, M., Naber, D., tein, J. O. and Gauthier, Y., 7th Vienna Motor ymposium, pri Tokuda, H., Itoh,., Kinugawa, M. and hirabe, N. 6th Vienna Motor ymposium, pri Nishida, K., Nomura,., and Matsumoto, Y., ICL 6, aper No. ICL6-7, awowski,., Kneer, R., Lippert,. M. and arrish,. E., E 8--98, ark,. W. and Reitz, R. D., ME J. Eng. Gas Turbines and ower 3: 385 (8) 8. Wis, G. B., One-dimension two-phase fow, McGraw-Hi, chmidt, D.., Rutand, C. J. and Corradini, M. L., Trans. E, 6(3), pp , (997). Habchi, C., Dumont, N. and imonin, O., tomization and prays, vo. 8, pp. 9 6, (8). Ning, W., Reitz, R.D., Diwakar, R., Lippert,.M., E , 8.. Bokkee, G., Barbeau B. and Borghi, R., E 3--5, Grogger, H. and ajbegovic,., ME Fuids Engineering Division ummer Meeting, June -5, Gavaises, M., apouias, D., ndriotis,., Giannadakis, E., and Theodorakakos,., E 7--46, msden,.., KIV-3V, Reease, Improvements to Kiva-3V, L-UR-99-95, Los amos, NM, Trujio, M.F., Torres, D.J. and O Rourke,.J., Internation Journ of Engine Research, Vo.5, No.3, (4) Tabe. Important dimensions of the injectors Nozze type HN GHN GHN3 # nozze hoes in a /8 sector Hoe diameter (mm) Distance between hoe axes (mm) ~.95 Incuded ange of hoe (deg) Incuded ange of hoe B (deg)

5 IMEM 9 inet pressure 5.9 ms.354 ms HN B neede ift (µm) 5 5 opening speed =.65 m/s cosing speed =.7 m/s.65 ms 3 exit pressure GHN B GHN3 B..4.6 Figure. Computation geometries considered in the present study HN muti-hoe Figure. Neede ift motion GHN GHN3 Figure 3. Discharge coefficients during injection processes in various injectors. Figure 4. Cavitation deveopment during nozze opening event. 5

6 IMEM 9 Figure 5. Cavitation augmentation during nozze cosing event. Figure 6. Change in streamine patterns during the nozze cosing event av / f.8.6 inge-hoe.4 density veocity. Cd Umean / UB, Cd av / f density veocity. Cd Umean / UB, Cd.8.6 av / f.4 density veocity. Cd Figure 7. Transient changes in density and veocity during neede cosing events Umean / UB, Cd upper inge Hoe Nozze ower GHN GHN3 Figure 8. Exampe of exit veocity distributions at t=.34 ms 6