INVESTIGATION OF EFFECT OF NOZZLE GEOMETRY ON SPRAY WITH A 3-D EULERIAN-LAGRANGIAN SPRAY MODEL COUPLED WITH THE NOZZLE CAVITATING FLOW

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1 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp INVESTIGATION OF EFFECT OF NOZZLE GEOMETRY ON SPRAY WITH A -D EULERIAN-LAGRANGIAN SPRAY MODEL COUPLED WITH THE NOZZLE CAVITATING FLOW Introuction by Genmiao GUO a, Zhixia HE b*, Qian WANG a, Zhaochen JIANG a, an Liang ZHANG a a School of Energy an Power Engineering, Jiangsu University, China b Institute for Energy Research, Jiangsu University, China Original scientific paper A -D Eulerian-Lagrangian spray moel couple with the nozzle cavitating flow was propose to simulate the atomization an seconary break-up. The nozzle flow an near-fiel spray were simulate with the volume of flui multiphase moel. At a certain ownstream location, where the spray is ilute, the Eulerian spray approach was switche to the conventional Lagrangian approach. This entire methoology was valiate through the experimental ata of liqui spray penetration uner non-evaporating chamber conitions. The numerical simulations base on multi-scheme were implemente by this moel to investigate the effects of nozzle geometry an configuration on the subsequent spray evelopment. Key wors: Diesel engine, nozzle, X-rays, cavitating flow, primary atomization, spray moel The tiny nozzle in the high-pressure common rail injection system, connecte to the fuel injection upstream an ownstream spray atomization, has become one of the most key components of avance iesel injection an combustion engineering. Ranz [1] has propose the Diesel engine nozzle spray atomization is associate with internal nozzle flow, an later numerous stuies have verifie the cavitation phenomenon will prouce inevitably uner the high injection pressure in the small orifice, which in turn influence the external spray break-up, air/fuel mixing processes, an emissions [2-4]. A number of scholars have carrie out experimental an/or numerical investigations on the cavitation characteristics in the iesel orifice. Bergwerk [5] foun that the ischarge coefficient of the orifice is mainly epenent on the cavitation number an inepenent on the Reynols number base on the experiments on simplifie single-orifice acrylic nozzles. Mulemane et al. [6] performe experimental an numerical investigations to stuy the influence of operating parameters an critical injector esign parameters on the ynamic performance of avance high-pressure electronically controlle iesel injection systems. The neele lift characteristics show that the measure injection rate is a strong function of the injection pressure an the nozzle iameter. Sou et al. [7] stuie the effects of nozzle geometries on cavitation in the orifice using 2-D nozzles with various geometries. The research * Corresponing author, zxhe@ujs.eu.cn

2 1240 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp confirme that the thickness of the cavitation zone increases with the contraction coefficient of the cross-sectional area at upstream of the nozzle to that of the nozzle. He et al. [8] analyze the effects of the neele lift, the inlet raius an the sac volume on the cavitating flow base on a testifie cavitation moel which was valiate by the experimental ata obtaine from the flow visualization experiment system. Numerical results clearly reveal the istribution of the cavitation zone. Margot et al. [9] conucte a comprehensive stuy on a -D flow insie iesel injector-like geometries uner a cavitation moel implemente in a CFD coe. Various numerical parameters were use to simulate cavitation uner realistic Diesel engine conitions an the results show that the cavitation moel was able to preict the onset of cavitation, which were verifie with experiments both on the injection rate an the occurrence of choke flow. However, ue to the complex interaction of vortices, cavitation an turbulence, the CFD moeling remains one of the best techniques to explore an unerstaning the multiphase flow. The precise nozzle geometrical parameters provie a reliable basis for the numerical simulation, but it is rather ifficult to obtain the internal accurate geometric structure by non-estructive traitional methos, which can be solve effectively by the use of synchrotron raiation technology. Lebas et al. [10] stuie the ense spray region by implemente a -D moel for atomization base on an Eulerian single-phase approach in a professional CFD coe via AVL FIRE, which has been prove that can improve the escription of the primary break-up. Hoyas et al. [11] capture many of the most important characteristics of the spray, such as the penetration an the axial velocity, using 2-D simulations base on the Eulerian-Lagrangian spray atomization moel via STAR-CD. As can be seen in many commercial software an open source coes, the most efficient an wiely-applie approach is the Lagrangian-roplet-Eulerian-flui (LDEF) metho. Instea of solving the liqui phase as a partial-ifferential-equation base continuum, such as in the LDEF metho treats the liqui as iscrete particles. These particles are assume to be negligible in volume an are superimpose on the continuous gas phase as material points. At the nozzle exit, liqui fuel is injecte as iscrete blobs, an a linear stability base phenomenological moel is applie to account for the primary breakup [12]. In spite of its efficiency, the accuracy in the near-nozzle region is low, ue to the fact that the liqui fuel is actually a continuum as observe in both experiments an irect numerical simulation (DNS). As a result, the moel s connection to the nozzle flow is inherently weak, espite some efforts to moel the unresolve near-nozzle physics an to consier the effects of in-nozzle cavitation an turbulence on the primary breakup [1,14]. In this paper, the accurate -D geometric structure of the real nozzle was measure as a basis for numerical simulations. The volume of flui (VOF) metho was use to simulate the internal nozzle flow an the primary break-up near the outlet of the nozzle orifice, an then the traitional LDEF metho was set in the ilute spray region of the nozzle ownstream. An then, in orer to valiate this simulation moel, experimental ata compare to were performe. Finally, the effects of ifferent injector geometries on the spray angle, penetration, an particle size istribution uner ifferent injection pressures were investigate. Synchrotron raiation measurement of nozzle structure The synchrotron raiation facility (SRF) applie in this paper can provie a variety of synchrotron raiations from infrare light to har X-ray. During the measurements, 55 kev electrons penetrate the front of injector an exposure to scintillation crystal, an then the X-ray absorption image can be capture by the charge couple evice (CCD) camera in the front of injector. In the orifice measurement process, the injector seate on the sample rotation stage revolve

3 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp at the spee of 1.8 per secon. In this process, an X-ray absorption image were capture every 0.2 with 10 secons exposure time an 9 mm spatial resolution by the CCD camera. Much etaile information about the measurement was shown in tab. 1. The photon flux ensity of the SRF is phs s 1 mm 2 at 20 kev an the maximal beam size can arrive 48 mm (horizontal) 5 mm (vertical) at 20 kev, where the istance between the light an the sample is 0 m. Figure 1(a) shows the measurement results of eight orifices of the teste nozzle, an the tab. 2 gives more etaile information about the eight ifferent orifices. In orer to simplify the calculation, we just choose one orifice (e. g. the 4 th orifice) of the eight ifferent ones to stuy. Figure 1(b) shows the slice of the 4 th orifice of the eight ifferent orifices which are the basis of the consequent nozzle flow an spray simulation. The left part of the axis is the mirror image of the 4 th orifice which is at the right part of the axis. It is can be seen that both the inlet iameter (D in ) an the outlet iameter (D out ) of the 4 th orifice are about 18 μm, an the orifice length (L) is about 598 μm, while the orifice inlet top curvature raius (R a ) an the orifice inlet bottom curvature raius (R b ) are about 65 μm an μm, respectively. The spray angle (θ) between orifice axis an injector axis is Spray simulation couple with nozzle flow Table 1. Main parameters of the experiment Energy range 8~72.5 kev Energy resolution 10 Photon flux ensity phss 1 mm 2 Maximal beam size (a) mm (H) 5 mm (V) Moels of hyroynamic cavitation In this paper, VOF multiphase moel was employe to eal with the internal cavitating flow an the near-fiel ense spray. VOF moel is mainly base on transportation of the volume fraction, that is, a source term representing phase transition which is governe by the ifference between the local pressure an the vapor pressure. Accoring to the vapor fraction transport equation, cavitation is assume to occur ue to the bubble nuclei or micro bubbles in the liqui, which can grow or collapse with the changing of the surrouning conitions. Moreover, the growth an collapse of the bubbles are taken into account accoring to the Rayleigh s simplifie bubble ynamics equation [15]. The bubble istribution can be escribe by a single scalar fiel which is the vapor volume fraction α v, because it is assume that all vapor bubbles in the control volume have (b) μm R 65.2 μm R.1 μm Axis 18.1 μm μm μm Ori ce cone angle μm Figure 1. The slice of injector in ifferent irections; (a) the measurement results of eight orifices of the teste nozzle, an (b) the slice of the 4 th orifice of the eight ifferent orifices Table 2. Measurement results of eight ifferent orifices D in [μm] D out [μm] L [μm] R a [μm] R b [μm] θ [ ]

4 1242 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp the same raius an a homogenous istribution. Also, assuming that only exists a single liqui phase, an the bubbles will occupy the corresponing control volume when the cavitation take place. Equation (1) is a escription for the relationship between the vapor volume fraction α v an the average vapor bubble raius R: Nbub πr nv 0 l πr n0 πr Vv α v = = = = (1) V 4 4 tot Vl + Vv V + nv π R 1+ n πr l 0 l 0 where V v an V l are the volume occupie by the vapor phase an liqui phase, respectively, an V tot the total cells volume, N bub the number of vapor bubbles in the control volume, an n 0 the number ensity of bubbles per volume of liqui. The vapor volume fraction α v in the control volume will change with the convective transport an bubbles growth or collapse. The eq. (2) escribing the transport of α v base on the assumption that the vapor ensity is much smaller than that of the liqui ensity: 4 n πr V v v R V 0 4 αv + αv( s)α = t 4 π 1 t V S V + n0 πr (2) The right sie of eq. (2) is the cavitation bubble growth rate of the moel, which can be obtaine by the observation on the Lagrangian of a clou of bubbles an the conventional bubble ynamic observation of a single bubble in an infinite stagnant liqui, respectively. This analysis results is the extene Rayleigh-Plesset equation: R 2 2 psat p 2σ µ l = t 2 ρl ρl ρl R R R t R R t where, P sat is the saturation pressure corresponing to the temperature at the bubble surface, P the pressure of the surrouning liqui, ρ l an µ l are the liqui ensity an viscosity, respectively, an σ the surface tension coefficient. The precise geometry structure of the 4 th orifice of the nozzle obtaine by synchrotron Ori ce Flow inlet Sac volume Ori ce outlet Constant volume Figure 2. The mesh of injector use (the 4 th orifice) for nozzle flow simulation () raiation measurement was use to simulate the nozzle flow. Figure 2 was the structure an the mesh use for nozzle flow simulation, an the total gri number chosen was base on the gri inepenence tests. All simulations were mae with the stanar k-ε turbulence moel with stanar wall functions. The solver applie was base on the pressure correction an the algorithm applie was SIMPLEC. What the iscretization of the k-ε turbulence moel equations use was the upwin ifferencing scheme an the cavitation moel use was base on the Rayleigh equation an associate with the rate of change of the bubble raius epene on the local pressure, where the ensity of liqui an vapor were constant an there is no slip between the bubbles an the liqui.

5 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp Eulerian-Lagrangian spray moel The near-fiel ense spray is simulate with the VOF multiphase moel the same as the flow in the orifice. The atomization of iesel sprays is moele as a turbulent mixing process of the liqui fuel with the ambient gas. At a certain ownstream location, where the spray is ilute, this Eulerian spray approach was switche to conventional Lagrangian approach which thought the roplet parcels as the control liqui volumes in the computational omain of spray an coul epicte the mutual effects between roplets an gas, evaporation an break-up an so on. Figure is the iagram for the Eulerian-Lagrangian couple spray moel, which gives the thought of this spray moel clearly. The conventional Lagrangian spray was simulate by STAR-CD. Theoretical stuies provie a criterion for the onset of break-up an an estimate of the stable roplet iameter (D, stable ) an the characteristic time scale τ b of the break-up process, simultaneously. The break-up rate of the spray can be calculate by eq. (4): D t D = D τ b, stable where D is the instantaneous roplet iameter. Instability of the spray is etermine by a critical value of the Weber number (We) an the roplet Reynols number (Re), eqs. (5) an (6): We (4) 2 ρ u u D = (5) 2σ ρµ µ D Re µ The criterion for the onset of this Stripping break-up regime: = (6) We Re (7) C s 1 The characteristic time scale for this Stripping break-up regime: C τ b = 2 ρ D s2 ρ u u Here, the empirical coefficient C s1 is 0.5 an, C s2 is in the range from Switch metho of the Eulerian- Lagrangian moel Zone of cavitation an turbulence ow VOF multiphase approach Switch position DROICO.f subroutine The calculation ata of injector flow (cavitation an turbulence) elivere to ownstream conventional Lagrangian spray simulation by the mean of subroutine in STAR-CD, Nozzle ow Figure. Zones ivision of couple spray moel Zone of primary atomization VOF multiphase approach Zone of seconary break-up conventional Lagrangian approach (8)

6 1244 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp which containe 1 return values. Figure 4 shows the etail information of these parameters. The velocity (magnitue an irection) an ensity of the upstream Euler flow were mae as the initial conitions of the ownstream applying the conventional Lagrangian approach. It was assume that DRD: Droplet iameter [m] 1 UD,VD, WD: Droplet velocity [ms ] XD,YD, ZD: Droplet initial position coorinate [m] the spray zones, where the istance to orifice outlet is longer than 2 mm, were ilute spray zone. The simulation cells of switch location cross-section, whose liqui volume of fraction was bigger than 0.5, were chosen as the fuel injector cells. The positions of these cells were consiere as the position of the roplet parcels injecte an the velocities of these cells were consiere as the initial velocities (magnitue an irection) of roplets. So this moel coul simulate the spray angle an it was not neee to give previously. The initial roplet size was etermine by the fuel liqui volume of fraction. The iameters of fuel roplets were proportional to the volume of fraction value of fuel liqui. It was assume that the initial size was the orifice iameter multiply by corresponing scale factor [16]. Valiation of Eulerian-Lagrangian spray moel IDRT: Droplet type RNDP: Droplet number of each parcel DENDR: Droplet ensity [kgm ] TD: Droplet temperature [K] Traitional spray moel means simulating the spray irectly without couple the nozzle flow, Eulerian-Lagrangian couple spray moel on STAR-CD that is the moel applie in this paper, an couple spray moel on FIRE [17] were simulate base on the 4 th nozzle. From fig. 5, it can be easily foun that the simulation ata of couple spray were much closer to Penetration [mm] Local coorinate system ICSRGP: DDe ne local coorinate of injection velocity OMEGRP: Angular velocity [ras per s] VOF smaller than the transition criterion Figure 4. The etail information of return values Experiment Traitional spray STAR-CD coupling spray FIRE coupling spray Crank angle [ ] Figire 5. Tip penetrations of traitional spray, couple spray an experiment ata the experimental ata [17] than traitional spray moel, which verifie the accuracy of the couple spray moe. Meanwhile, the ata obtaine from the couple spray moel on FIRE is consistent with that got from the Eulerian-Lagrangian couple spray moel on STAR-CD, which justifying the subprogram compile couple the cavitating flow to spray moel was feasible in some egree, an the calculation precision of moel propose in this paper can meet the current mainstream commercial software. What obtaine from the two kin of couple spray moe further verifie the accuracy of the Eulerian-Lagrangian couple spray moel. Though the preicte results of the couple spray moe were higher than the experimental, results obtaine from spray simulations which couple with internal cavitating flow were superior to that traitional spray moel which i not consier the influence of internal cavitating flow. For the slight unavoiable ifferences between preicte an experimental results, the errors in the measurement of spray penetration istance an simplification of the bounary conitions in spray simulation were regare as the ominant causes.

7 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp Base on the verification above, numerical simulation was conucte with the Eulerian -Lagrangian couple spray moel on STAR- -CD. The conitions were same as the experiment by Verhoeven et al. [18], that is, the injection pressure is 50 MPa, an the back pressure is 2 MPa. As shown in fig. 6 is the istribution of the spray roplet iameter obtaine by ifferent methos, though the Eulerian-Lagrangian couple spray moel on STAR-CD simulations result was less than the traitional spray moel, the spray penetration was much closer to the experiment, especially the spray near the outlet of the orifice because of consiering the flow insie the nozzle. Effects of ifferent injector geometries on the spray characteristics Accoring to the stuy [8], the injector geometries have important effects on the spray. In this paper, using the above verifie couple spray moel, the multi-scheme numerical simulations were carrie out for the ifferent nozzle geometry parameters, such as the ratio of nozzle orifice length to iameter (L/D), orifice entrance curvature raius (R) an the ifferent nozzle configurations like the stanar (STD) type, valve covere orifice (VCO) type, an the improve (IMPROVED) type, to analyze the effects of the nozzle geometries on the subsequent spray. Effects of the L/D an r on the spray characteristics Figure 6. The istribution of the spray roplet iameter obtaine by traitional spray, experiment an couple spray; (a) traitional spray (b) experiment, an (c) STAR-CD couple spray The nozzle configuration was the STD type, an the pressure at the inlet was 50 MPa an the back pressure was 0.5 MPa. When stuying the effect of the ifferent (L/D) on the spray characteristics, the orifice entrance curvature raius (R) is 0, an the orifice iameter (D ) is mm. The simulation results for ifferent ratios of nozzle orifice length to iameter (L/D) = 2,, an 4 ( were shown in fig. 7. The spray tip penetration is increase with the ratio of length to iameter increase, an the sauter mean iameter (SMD) woul increase. SMD [ μ m] LD / = 2 LD / = LD / = LD / = LD / = 4 LD / = Crank angle [ ] Crank angle [ ] Figure 7. Spray tip penetration an SMD for L / D = 2,, an 4 SMD [ μ m]

8 1246 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp As for investigating the effect of the orifice entrance curvature raius (R) on the spray characteristics, the ratio of orifice length to iameter (L/D) was 4. Figure 8 showe the simulation results for the three ifferent kins of orifice entrance curvature raius, that is R = 0, R = mm, an R = mm. It presente that if the entrance curvature raius ecrease, the spray tip penetration an the SMD were ecrease rapily. It coul fin that both at R = an R = mm the spray tip penetration an the SMD were nearly similar, but ha a large istinction compare to the conition of R = 0. It coul be suppose that the existence of entrance curvature raius may reuce the cavitation insie the orifice. Penetration [m] RD / = 0 2 RD / = RD / = RD / = RD / = RD / = Crank angle [ ] Crank angle [ ] Figure 8. Spray tip penetration an SMD for R = 0, , an mm Effect of the types of sac volume on the spray characteristics The main ifference of the STD, VCO, an IMPROVED type nozzle is the relative location of the orifice an the neele valve seat, so there are ifferent sac volume, as shown in fig. 9. The orifice of STD type is uner the neele valve seat with a large sac volume, an the orifice of VCO type nozzle is above the neele valve seat nearly without sac volume, an STD Sac volume VCO SMD [ μ m] also the orifice of IMPROVED type is above the neele valve seat, but it has a sac volume a bit smaller than the STD type. For these three ifferent moels, they ha the same bounary conitions an orifice geometry. Injection pressure was 50 MPa an the back pressure was 0.5 MPa. The calculation results were shown in fig. 10. At the early stage of the injection, the tip penetration of the three ifferent types were similar, while at the en stage of injection, the VCO nozzle ha the longest penetration an the smallest value of SMD. Consiering of nozzle cavitating flow comprehensively, from the aspect of spray tip penetration an SMD, IMPROVED nozzle coul acquire better spray characteristics. Summary an conclusions IMPROVED Figure 9. Three types of nozzle with ifferent sac volume y In this paper, a -D high-precision structure moel of nozzle geometry was obtain use the X-ray phase contrast imaging measurement, which was helpful to establish the CFD moel of nozzle more exactly.

9 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp Penetration [m] SMD [ μ m] STD IMPROVED VCO y The moel propose in this paper aopte the VOF metho to simulate the internal nozzle flow an the near-fiel ense spray, then use the original position of the traitional LDEF metho for the nozzle ownstream. The velocity (magnitue an irection) an ensity of the upstream Euler flow were mae as the initial conitions of the ownstream applying the conventional Lagrangian approach. Comparing the visual spray experiment ata an numerical results, it was verifie that the spray moel couple with cavitating flow in nozzles was more accurate than the traitional spray moel wiely use nowaays. y The multi-scheme numerical simulations inicate that the nozzle structure has an important effect on the spray characteristics. The spray tip penetration is increase with the ratio of length to iameter increase, an the SMD woul increase. The existence of entrance curvature raius may reuce the cavitation insie the orifice, an causing a larger value of the tip penetration an the SMD. Consiering of nozzle cavitating flow comprehensively, from the aspect of spray tip penetration an SMD, IMPROVED nozzle coul acquire better spray characteristics. The simulation results supply the theoretical founation for the optimization esign of the injector. Acknowlegment STD IMPROVED VCO Crank angle [ ] Crank angle [ ] Figure 10. Spray tip penetration an SMD of three ifferent types of nozzle This work was supporte by the National Natural Science Founation of China (No , No ), Six Talent Peaks Project of Jiangsu Province (201-JNHB-017) Nomenclature C s1, C s2 empirical coefficient D iameter of orifice, [m] D roplet iameter, [m] L length of orifice, [m] L/D length to iameter of orifice l liqui phase N bub number of vapor bubbles P sat saturation pressure, [Pa] P surrouning pressure, [Pa] R average vapor bubble raius r curvature raius, [m] R a, R b orifice inlet top an bottom curvature raius, [m] Re Reynols number S total turbulence energy source Τ b characteristic time scale u average velocity u instantaneous velocity V volume, [m ] V tot total cells volume v fuel vapor phase We Weber number Greek symbols α volume fraction θ spray angle, [ ] μ ynamic viscosity, [Pa s] μ l liqui viscosity ρ ensity, [kgm ] σ surface tension coefficient, [Nm 1 ]

10 1248 THERMAL SCIENCE: Year 2018, Vol. 22, No., pp τ b characteristic time scale, [s] Acronyms CCD charge couple evice CFD computational flui ynamics DNS irect numerical simulation IMPROVED improve LDEF Lagrangian-roplet-eulerian-flui SMD sauter mean iameter, [m] SRF synchrotron raiation facility STD stanar VOF volume of flui Subscript instantaneus roplet iameter in upstream location of a nozzle l liqui out nozzle hole outlet s turbulence energy source term v vapor References [1] Ranz, W. E., Some Experiments on Orifice Sprays, Canaian Journal of Chemical Engineering, 6 (1958), Aug., pp [2] Molina, S., et al., A Computational Investigation on the Influence of the Use of Elliptical Orifices on the Inner Nozzle Flow an Cavitation Development in Diesel Injector Nozzles, Energy Convers Manage, 79 (2014), Mar., pp [] Monhan, B., et al., Development of an Accurate Cavitation Couple Spray Moel for Diesel Engine Simulation, Energy Convers Manage, 77 (2014), Jan., pp [4] Shinjo, J., Umemura, A., Detaile Simulation of Primary Atomization Mechanisms in Diesel Jet Spray, International Journal of Multiphase Flow, 6 (2010), 2, pp [5] Bergwerk, W., Flow Pattern in Diesel Nozzle Spray Orifices, Proceeings, Institution of Mechanical Engineers, 17 (1959), June, pp [6] Mulemane, A, et al., Moeling Dynamic Behavior of Diesel Fuel Injection Systems, SAE technical paper, , 2004 [7] Sou, A., et al., Effects of Nozzle Geometry on Cavitation in Nozzles of Pressure Atomizers, Journal of Flui Science an Technology, (2008), 5, pp [8] He, Z. X., et al., Effect of Nozzle Geometrical an Dynamic Factors on Cavitating an Turbulent Flow in a Diesel Multi-Orifice Injector Nozzle, International Journal of Thermal Sciences, 70 (201), Aug., pp [9] Margot, X., et al., Numerical Moelling of Cavitation: Valiation an Parametric Stuies, Engineering Applications of Computational Flui Mechanics, 6 (2012), 1, pp [10] Lebas, R., et al., Coupling Vaporization Moel with the Eulerian-Lagrangian Spray Atomization (ELSA) Moel in Diesel Engine Conitions, SAE technical paper, , 2005 [11] Hoyas, S., et al., Application an Evaluation of the Eulerian-Lagrangian Spray Atomization (ELSA) Moel on CFD Diesel Spray Simulations, SAE technical paper, , 2011 [12] Vallet, A., et al., Development of a Eulerian Moel for Atomization of a Liqui Jet, Atomization an Sprays, 11 (2001), 6, pp [1] Shi, J., et al., Complex Physics Moelling of Diesel Injector Nozzle Flow an Spray Supporte by New Experiments, THIESEL, Valencia, Spain, 2014 [14] Som, S., Aggarwal, S. K., Assessment of Atomization Mechanisms in Diesel Engine Simulations, Atomization an Sprays, 19 (2009), pp [15] Martynov, S., Numerical Simulation of Cavitation Process in Diesel Fuel Injectors, Ph. D. thesis, University of Brighton, Brighton, UK, 2005 [16] Reitz, R. D., Diwakar, R., Structure of High-Pressure Fuel Spray, SAE technical paper, , 1987 [17] Liu, J. Y., Stuy on Spray Simulation Couple with Nozzle Cavitating Flow in High-Pressure Common Rail Injection System, M. Sc. thesis (in Chinese), University of Jiangsu, Jiangsu, China, 2012 [18] Verhoeven, D., et al., Macroscopic an Ignition Characteristics of High-Pressure Sprays of Single-Component Fuels, SAE technical paper, , 1998 Paper submitte: September 4, 2016 Paper revise: October 26, 2016 Paper accepte: October 27, Society of Thermal Engineers of Serbia Publishe by the Vinča Institute of Nuclear Sciences, Belgrae, Serbia. This is an open access article istribute uner the CC BY-NC-ND 4.0 terms an conitions