Scientia Iranica B (2016) 23(1), 238{248

Sharif University of TechnologyScientia Iranica

Transactions B: Mechanical Engineeringwww.scientiairanica.com

Probing into the e�ects of fuel injection pressure andnozzle hole diameter on spray characteristics underultra-high injection pressures using advanced breakupmodel

M. Youse�farda, P. Ghadimia;� and S.M. Mirsalimb

a. Department of Marine Technology, Amirkabir University of Technology, Tehran, Iran.b. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran.

Received 27 June 2014; received in revised form 9 November 2014; accepted 13 April 2015

KEYWORDSDiesel spray;Ultra-high injectionpressure;Nozzle hole diameter;Penetration length;Breakup model;OpenFOAM.

Abstract. In this article, non-evaporating and non-reacting diesel spray is modeled underultra-high injection pressure using an Eulerian-Lagrangian scheme. This is accomplishedin order to probe into the e�ects of injection pressure, nozzle diameter, and ambientdensity on spray characteristics. An advanced hybrid breakup model that takes intoconsideration the transient processes during spray injection has been added to the opensource code, OpenFOAM. Reynolds-Average Navier-Stokes (RANS) equations are solvedusing the standard k� " turbulence model and the fuel droplet is tracked by a Lagrangianscheme. Published experimental data have been used for validation of spray characteristicsat 15 kg/m3 ambient density and injection pressures of 100, 200 and 300 MPa. Also, threenozzle diameters of 0.08, 0.12 and 0.16 mm have been implemented for investigating thee�ect of this parameter on spray formation. Computed spray shape, jet penetration, sprayvolume, equivalent ratio along the injector axis and Sauter Mean Diameter (SMD) illustrategood agreement with experimental data of a single hole nozzle and symmetric spray. Thee�ects of fuel injection pressure, nozzle hole diameter and ambient density on main sprayparameters are presented. It is concluded that the numerical model presented here is quitesuitable for accurately predicting diesel spray shapes under ultra-high injection pressures.© 2016 Sharif University of Technology. All rights reserved.

1. Introduction

Pollution and e�ciency in diesel engines are greatlyinuenced by the quality of atomization and the fuel-air mixture. Injection and chamber pressures aretwo of the most important parameters a�ecting fuelatomization. Moreover, the fuel injection pressureof Direct Injection (DI) engines has continued toincrease in recent years, and it has, therefore, becomenecessary to take an interest in modeling ultra-high

*. Corresponding author. Tel.: +98 21 64543117;Fax: +98 21 66412495E-mail address: pghadimi@aut.ac.ir (P. Ghadimi)

injection pressures (above 100 MPa). The mechanismof fuel atomization is extremely complicated, andthis multiphase ow consists of a large number ofphenomena, such as cavitation, breakup, evaporation,and reaction. Among these phenomena, the majorityof past numerical modeling has involved research intothe breakup of droplets during the injection process.Speci�cally, increasing the injection pressure leads tosome complicated breakup phenomena that should besimulated by an advanced model.

Recently, Computational Fluid Dynamics (CFD)has played a major role in engine development inautomotive and marine industries. Its application asan engine development tool can be dated back to

M. Youse�fard et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 238{248 239

the early 1980's with considerable development in thesecond part of the 1990s [1]. The Eulerian-Lagrangianscheme is a proper choice to conduct spray simulationin diesel engines. Moreover, in most literature relatedto spray simulation under Eulerian-Lagrangian formu-lation, the atomization process can be divided into twoprocedures; primary and secondary breakup. On theother hand, several theoretical studies, in particularthose based on surface instabilities, have been devel-oped. Liquid spray breakup can be caused by Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilitiesat the interface of two uids. KH instability is dueto high shear at the interface, while the RT breakuptheory is based on the stability of liquid-gas interfacesduring acceleration in the normal direction to theplane. Most commonly used breakup models are basedon KH and RT theories [2].

There has been much research into the numericalmodeling of diesel spray that has focused on breakupand atomization phenomena. Spray penetration hasbeen investigated numerically by Wan and Peters [3].Som and Aggarwal [4] performed 3-D simulations withdetailed chemistry using a new advanced breakupmodel. Hosseinpour and Binesh [5] also used a CFDcode to investigate the e�ect of a breakup model onspray and mixture formation in a heavy-duty dieselengine. Som et al. [6] reported a computationalinvestigation of internal nozzle ow and cavitationcharacteristics in a diesel injector. Ishii et al. [7]presented a method that combines two types of sim-ulation, based on the particle method, for simulationof liquid-�lm breakup near the injector outlet, and adiscrete droplet model for the secondary-drop breakup.Desantes et al. [8] developed a model which is able topredict spray tip penetration and spray axis velocity.Recently, Turner et al. [9] proposed a breakup modelfor analyzing the evolution of transient fuel. Also,Yadollahi and Boroomand [10] used AVL FIRE soft-ware to perform an investigation into direct injection ofnatural gas into the cylinder of spark ignition internalcombustion engines. Mohammadebrahima et al. [11]simulated in-cylinder ow using ANSYS FLUENTsoftware. Ghasemi et al. [12] presented a numericalstudy on the spray-induced air motion in single andtwin ultra-high injection diesel sprays using ANSYSFLUENT software.

Ultra-high pressure injection has been the aim ofsome recent studies. Kato et al. [13] and Yokota etal. [14] experimentally examined the e�ects of injectionpressure ranging from 55 to 250 MPa. An experimentalresearch study was carried out by Benajes et al. [15]to analyze the inuence of di�erent ori�ce geometrieson the injection rate of a common-rail fuel injectionsystem. On the other hand, Kastengren et al. [16]experimentally studied the e�ects of nozzle geometryand injection duration on diesel spray.

Ultra-high injection pressure has also been stud-ied by Lee et al. [17], experimentally and numerically,up to 355 MPa. Tao and Bergstrand [18] investigatedthe e�ect of very high injection pressures on engineignition and combustion using three-dimensional nu-merical simulations. Wang et al. [19] presented adetailed experimental inspection of diesel and biodieselspray characteristics for high injection pressure up to300 MPa. The e�ect of ambient pressure on thepenetration of a diesel spray was investigated experi-mentally and theoretically by Roisman et al. [20]. Also,Zhu et al. [21] experimentally investigated the e�ects offuel injection pressure, ambient gas density and nozzlehole diameter on the surrounding gas ow of a singlediesel spray under ultra-high injection pressures.

Shervani-Tabar et al. [22] have also carried outa numerical simulation to study the e�ect of injectionpressure on spray penetration length.

Recently, open source codes have been utilizedas e�cient methods for modeling diesel spray by re-searchers like Gjesing et al. [23], Kassem et al. [24],Vuorinen et al. [25], Nowruzi et al. [26] and Youse�fardet al. [27,28], among others. KIVA and OpenFOAMsoftware are becoming popular as open source codes inthis �eld of interest. Accordingly, in the current study,non-evaporating spray characteristics of an ultra-highinjection pressure diesel spray are studied under injec-tion pressures up to 300M Pa by the OpenFOAM free-ware code. The SprayFoam solver has been applied toconsider the compressibility e�ect of air, and a modi�edbreakup model has been added to the default solver toachieve more accurate results at ultra-high injectionpressures. A Lagrangian particle tracking approachhas been employed using a new and advanced KH-RTbreakup model to accurately simulate direct injectionof fuel at very high pressures. Spray tip penetration,spray angle and spray volume have been computed andcompared against available experimental results.

Governing equations in two-phase ow are pre-sented �rst, and the current spray breakup modelis discussed in more depth. Subsequently, detailsof experimental data that are used to validate thecurrent model are presented. Later, computed resultsare analyzed and compared against experimental data.Finally, the advantages of the current scheme in simu-lating ultra-high injection pressure have been presentedin the conclusions.

2. Governing equations

Mathematical models of uid ow and heat transferare generally developed according to conservation lawsof physics, such as the conservation of mass, Newton'ssecond law, and the �rst law of thermodynamics [29].Compressible ows can be expressed by Navier-Stokes(NS) equations describing the conservation of mass,

240 M. Youse�fard et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 238{248

momentum and energy. Navier-Stokes equations forconservative variables of a continuous �eld are asfollows [30]:

a) Equation of mass conservation:

@�@t

+@@xj

(�uj) = 0; (1)

where � denotes the uid density, xj is the jthcomponent of the Cartesian coordinates, and ujrepresents the jth component of the uid velocity.

b) Equation of momentum conservation:

@@t

(�ui)+@@xj

(�ujui)=� @P@xi +@@xj

��ij + �Rij

�;

(2)

where P � p+�gz is the modi�ed pressure variable,p is the pressure, g represents body force, and � =�ij denotes the stress tensor [31].

�ij = �p�ij + 2�Sij ;

Sij =12

�@ui@xj

+@uj@xi

�: (3)

Sij is the rate-of-strain tensor

�Rij = ��u0iu0j : (4)c) Equation of energy conservation:

@�E@t

+@(�Eui)@xj

= � @qj@xj

+ �giui+@@xj

(puj)

+@@xi

(�ijuj): (5)

Here, E denotes the total energy per unit volume,qj is the jth component of the heat ux vector,q. Favre time averaging is applied to the owvariables. The PISO algorithm [32] is used for thepressure-velocity coupling, and the standard k � "turbulence model [33] is applied in RANS modeling.

To capture the turbulence characteristics of the

ow, there are three important approaches for simu-lation of turbulent ows: Reynolds Average Navier-Stokes (RANS), Large-Eddy Simulations (LES) andDirect Numerical Simulation (DNS). Among these,RANS is still favorite in ow simulation due to itseconomy, robustness and reasonable accuracy in a widerange of turbulent ows. The standard k�", which is aclassical turbulence model within RANS and is basedon transport equations for turbulence kinetic energy(k) and its dissipation rate ("), has been adopted forthe current study.

The Lagrangian Particle Tracking (LPT) ap-proach is usually employed for spray simulation. In thecurrent simulation, the motion of particles is governedby Newton's equation of motion. It is assumed that theforce acting on a droplet due to a drag will be given as:

16�p�d3

dupdt

=12

(ug � up) jug � upj �gCD �d2

4; (6)

where up is the particle velocity, ug is the gas velocitythat is interpolated to the particle position from theadjacent cells, and CD is the droplet drag coe�cientde�ned by:

CD =

8>:24

Rep

�1 + 16Re

2=3p

�Rep < 1000

0:424 Rep � 1000(7)

The droplet Reynolds number is given by Rep =jug�upjdvg .

Several sub-models, such as droplet breakup andcollision, should be used in spray modeling. Asnoted before, the breakup process is described by theaerodynamic stripping of small droplets from the largerdroplets (Kelvin-Helmholtz instability) or the disinte-gration of large droplets into smaller ones due to thee�ect of normal stresses (Rayleigh-Taylor instability).The Kelvin-Helmholtz wave is driven by aerodynamicforces among gas liquid phases, whereas the Rayleigh-Taylor wave is the result of acceleration of shed dropletsejected into free-stream conditions. The current hybridmodel combines the e�ects of Kelvin-Helmholtz (KH)waves with Rayleigh-Taylor (RT) instabilities [34]. Inthe KHRT model, aerodynamic force on the drop

attens it into the shape of a liquid sheet, and thedecelerating sheet breaks into large-scale fragments bymeans of RT instability. KH waves with a much shorterwavelength originate at the edges of fragments andbreak up into micrometer-size drops.

The growth of KH instabilities on the liquidsurface at the interface of two phases that have di�erentdensities, causes \child" droplets to be stripped fromthe liquid core of the jet, which is approximated by\parent" droplets. Radius, rd, of the injected dropletis assumed to continuously decrease in size duringthe breakup process, as described by the followingequation:drddt

= �rd � rs�bu

; (8)

where �bu is the characteristic breakup time of thedroplet, and rs is the radius of stable droplets, givenby:

rs =

8>>>:�0� B0� � rd

min

(3�r2dUm=2)0:33

(3r2d�=4)0:33

!B0� > rd

(9)

M. Youse�fard et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 238{248 241

where B0 = 0:61 is the model constant, and � and

are wave-length and growth rate of the fastest growingwave on the surface of the liquid jet, respectively, givenby:

KH =r

��lr30

:0:34 + 0:38We1:5g

(1 + Oh)(1 + 1:4Ta0:6); (10)

�KH = 9:02r0:(1 + 0:45

pOh)(1 + 1:4Ta0:7)

(1 + 0:865We1:67g )0:6; (11)

where:

Oh =p

WelRel

; Ta = Ohp

Weg;

Weg =�gr0u2rel

�; Wel =

�lr0u2rel�

;

Rel =�lr0urel�l

; (12)

r0 is the droplet radius before breakup, urel = jud �uj is the relative velocity between the droplet andsurrounding gas, Oh is the Ohnesorge number, Ta is theTaylor number, Weg and Wel are the Weber numbersfor liquid and gas, respectively, and Rel is the Reynoldsnumber for liquid.

Also, the breakup time is given by:

�bu = 3:7626B1R�

; (13)

where B1 is an adjustable model constant which variesapproximately between

p3 and 60, depending upon the

injector type. A higher value of B1 leads to a reducedbreakup and increased penetration, while a smallervalue, on the other hand, results in an increased spraydisintegration, a faster fuel-air mixing, and reducedpenetration. The default value of B1 in the softwareis B1 = 40, and some higher values up to 60 have beensuggested. This model was modi�ed to incorporatetransient e�ects by Sazhin et al. [35]. The modi�edWAVE breakup model introduced new breakup time.The model constant in Eq. (13) has been modi�ed to:

Bmod1 = B1�1 + C1(a+)C2

�; (14)

where:

a+ = 2p

Re2rdU2inj

dUinjdt

; (15)

is the acceleration parameter, C1 and C2 are adjustablemodel constants, and Re2 is the gas Reynolds number.

RT instabilities appear when acceleration is nor-mal to the interface of two uids with di�erent den-sities. Similar to KH instabilities, the wavelengthand growth rate of the fastest growing wave can beobtained from linear stability analysis. The growthrate of the fastest growing wave and the correspondingwave length of the Rayleigh-Taylor model are given byBellman and Pennington [36], as in:

RT =

s2

3p

3�[a(�l � �g)]3=2

�l � �g ; (16)

�RT = C32�

s3�

a(�l � �g) : (17)

For the current numerical model, both instabilitymodels are utilized simultaneously and breakups aredetermined by the fastest growth rate of waves. In thisequation, a is the droplet acceleration given as:

a =38CD

�gu2rel�lr

: (18)

Figure 1 illustrates the schematic diagram of thebreakup mechanism in the KH and RT models.

The KHRT model is the most popular of allhybrid breakup models. It has been successfullyvalidated against experimental data and used by manyauthors in order to predict the disintegration processof high-pressure diesel sprays [1].

In the current study, the modi�ed WAVE breakupmodel that was introduced by Sazhin et al. [35]has been implemented, and a new advanced KHRTbreakup model is developed based on Eq. (14) tosimulate ultra-high pressure diesel injection. This mod-i�ed model has been added to the SprayFoam solverof the OpenFOAM freeware. The results producedby this new model have been compared against thedefault breakup model and validated by the availableexperimental data of Wang et al. [19].

Figure 1. Schematics of Kelvin-Helmholtz model (a), and Rayleigh-Taylor instability (b) [1].

242 M. Youse�fard et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 238{248

3. Computational model

A simple grading structured mesh has been used tosimulate a single-hole injector under a set of conditionsthat was experimentally presented by Wang et al. [19].The modi�ed SprayFoam solver has been utilized tosimulate high-pressure spray. The OpenFOAM 2.1.1version has been used in this study and run in parallelusing 16 processors. For validation of the current sim-ulations, the nozzle diameter is taken to be 0.16 mm.The injector opens and closes rapidly and thus has top-hat injection rate pro�les. Injection duration was setto be 1.5 ms. Ambient temperature was considered tobe 295 K and fuel density was set equal to 830 kg/m3.Three injection pressures of 100, 200, and 300 MPawere adopted.

The fuel properties of kerosene, which are basedon experimental data of Wang et al., are presented inTable 1.

In general, theoretical studies have assumed thatthe injection rate shape is perfectly rectangular. How-ever, in real cases, this is not completely true, sincethe mass ow rate curve is inuenced by the dynamicbehavior of the injector that depends on injection pres-sure and back pressure. Some authors have describedthe mass ow rate in the stabilized zone as:

_m0 = CDiA0q

2�(pinj � pb); (19)which has been previously introduced by Payri etal. [37]. Here, _m0 is the mass ow rate, CD is thedischarge coe�cient, A0 is the nozzle ori�ce surface atthe outlet, � is the uid density, pinj is the injectionpressure, and pb is the chamber pressure during theinjection time. Figure 2 shows the fuel mass ow ratevs. time at the injection pressure of 300 MPa.

Table 1. Fuel properties [19].

Density (kg/m3) 830Kinematic viscosity (mm2/s) 3.36Surface tension (mN/m) 25.5Nozzle diameter (�m) 160Injection duration (ms) 1.5Ambient gas temperature (K) 295

Figure 2. Injector mass ow rate for Pinj = 300 MPa.

3.1. Numerical uncertainty analysisA constant volume chamber of size (50�50�100 mm3)has been used, and, based on a grid independencystudy, 1:2 � 106 cells were applied to the considereddomain. Also, numerical uncertainty has been es-timated by applying the Celik [38] method. Threedi�erent grid sizes are selected and the obtained spraypenetration is compared as the main key parameterof the current study. Based on the error estimationpresented by Celik [38], the procedure of determiningnumerical uncertainty is described as follows:

1. Representative grid size, h, is de�ned as:

h =

"1N

NXi=1

(�Vi)

#1=3; (20)

where �Vi is volume of the ith cell, and N is thetotal number of cells.

2. Three di�erent sets of grids are selected and thefollowing equations are solved numerically to �ndthe apparent order, p:

p =1

ln(r21)j ln j"32="21j+ q(p)j;

q(p) = ln�rp21 � srp32 � s

�;

s = 1:sign("32="21); (21)

where r21 = h2=h1, r32 = h3=h2 (h1 < h2 < h3),"21 = �2 � �1 and "32 = �3 � �2.

3. Approximate relative error is de�ned as:

e21a =�����1 � �2�1 ���� : (22)

4. The convergence index is de�ned as:

GCI21�ne =1:25e21arp21 � 1 : (23)

This index is considered as numerical uncertainty.Spray penetration at various time steps, error,

and the convergence index of these simulations(Pinj = 300 MPa) are presented in Table 1. Ac-cording to Table 2, numerical uncertainty for spraypenetration in a �ner-grid solution is approximately9.8, 3.1 and 2 percent for times 0.4, 0.6, and 0.8 msafter the start of injection.

4. Results and discussion

Spray tip penetration and spray angle are two of themost described spray characteristics in the literature.Penetration length is de�ned as the distance between

M. Youse�fard et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 238{248 243

Table 2. Calculation of discretization error at three timesteps.

t = 0:4 ms(ASOI)

t = 0:6 ms(ASOI)

t = 0:8 ms(ASOI)

N1 5� 105 5� 105 5� 105N2 1:5� 106 1:5� 106 1:5� 106N3 3:5� 106 3:5� 106 3:5� 106��1 52 65 75�2 55 69 78�3 56 70 78.5

GCI21�ne 0.098 0.03079 0.02002�� is spray penetration (mm) for pinj = 300 MPa.

Figure 3. Comparison of the numerical results undervarious injection pressures (for each pressure: left (Exp.),right (Num.)) at t = 0:7 ms and �amb = 15 kg/m3 againstthe experimental jet penetration shapes [19].

the nozzle and the farthest axial location of the sprayboundary. Also, spray angle is measured based on theradial distance at the axial location of 40 mm.

In order to examine the capability of the cur-rent model in predicting spray characteristics underultra-high-pressure conditions, the produced resultsare compared against experimental measurements fornon-evaporating and non-reacting sprays. Figure 3presents a set of spray images and numerical resultsat t = 0:7 ms for various injection pressures. Thespray shape is compared against experimental resultsof Wang et al. [19]. As observed in this �gure, sprayshape, droplet penetration and radial dispersion arein good agreement with the experimentally capturedimages of considered cases.

Spray tip penetration, as a function of time, isperhaps the most common quantity to study in the�eld of diesel spray research, since the tip positioncan be easily detected from spray shadowgraph images.Figure 4 shows the e�ect of the breakup model onthe spray shape for the injection pressure and ambientdensity of 100 MPa and 15 kg/m3 at t = 1:0 ms afterthe start of injection. It is quite evident that themodi�ed KHRT model presents more acceptable sprayshape and penetration.

Figure 5 illustrates a comparison of the currentspray tip penetration against the experimental mea-surements of Wang et al. [19] for various injection

Figure 4. Comparison of spray shapes of di�erentbreakup models with experimental data [19]: (a)Pilch-Erdman; (b) default KHRT; (c) modi�ed KHRT;and (d) experiments.

Figure 5. Comparison of spray jet penetration length ofcurrent simulation with Wang et al. �ndings [19].

pressures under ambient density of 15 kg/m3. It canbe observed in this �gure that the numerical jet fuelpenetration distance agrees well with the experimentaldata. Root Mean Square Errors (RMSE) are 1.72,1.73 and 2.21 for injection pressures of 100, 200and 300 MPa, respectively. It is quite evident thatincreasing injection pressure leads to higher valuesof jet penetration. Also, prediction of penetrationat initial times after the start of injection seems tobe more accurate. The spray tip penetration clearlyincreases when the injection pressure increases from100 to 200 MPa. This increase seems to be verymoderate, from 200 to 300 MPa.

The e�ects of ambient density on spray tip pen-etration have been presented in Figure 6. Higherspray penetrations have been achieved under high spraydensity. On the other hand, increasing the nozzle holediameter leads to higher fuel mass ow rate and, thus,higher spray penetration, as shown in Figure 7.

Average spray angles for each injection pressure

244 M. Youse�fard et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 238{248

Figure 6. E�ects of ambient density on spray tippenetration.

Figure 7. E�ects of nozzle hole diameter on spray tippenetration.

Figure 8. Comparison of the average spray angle undervarious injection pressures (d = 0:16 mm).

for two di�erent ambient densities and 0.16 mm nozzlediameter are presented in Figure 8. From this �gure,one may conclude that the spray angle is not sensitiveto injection pressure. Injection pressure appears tohave little inuence on diesel spray angle and remainsnearly constant during the whole injection. On theother hand, ambient condition is an e�ective parameteron spray angle. The e�ects of nozzle diameter on sprayangle are shown in Figure 9. As evident in this �gure,increasing the nozzle hole diameter leads to highervalues of spray angle.

To further understand the spray morphology,spray volume is estimated and presented in Figure 10.Spray volume can be described by the relation [39].

Figure 9. E�ects of nozzle hole diameter on averagespray angle under various injection pressures(�amb = 15 kg/m3).

V (t) =13�S3(t) tan2

��2

� �1 + 2 tan

� �2

���1 + tan

� �2

��3 : (24)Comparison of the numerical results of spray volumeunder di�erent pressures (100, 200, and 300 MPa)with the experimental data in Figure 10 indicates goodagreement. Similar to the case of spray penetration,RMSE values are below 3 for the spray volume. Basedon the experimental data presented by Wang et al. [19],to eliminate the inuence of injection timing on sprayarea, the spray area is plotted versus the spray tippenetration.

The obtained results show that spray volumehas been a�ected by spray angle and penetration.Therefore, injection pressure has little e�ect on sprayvolume and it is expected that increasing the ambientdensity and nozzle diameter leads to higher sprayvolumes. Figure 11 illustrate the e�ects of ambientdensity on spray volume.

The total amount of air entrained up to any axiallocation in a fuel jet relative to the amount of injectedfuel is estimated using formula [39]:

��(x) =2(A=F )stp

1 + 16(x=x+)2 � 1 ; (25)

where �� is the averaged cross-sectional equivalenceratio at any axial location of x. (A=F )st is thestoichiometric air/fuel ratio (14.69 for diesel fuel [19]),and x+ is the characteristic length scale for the fuel jet,as in:

x+ =r�f�a

pCad0

a tan(�=2); (26)

where Ca is the ori�ce area contraction coe�cient,which is assumed to be 0.95 in this study [37], anda is constant, with a value of 0.75.

Figure 12 illustrates the averaged cross-sectionalequivalence ratio at any axial location. It is evidentthat increasing the ambient density leads to lowerequivalent ratio.

M. Youse�fard et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 238{248 245

Figure 10. Comparison of the numerical andexperimental results of spray volume in terms of spray jetpenetration length at (a) 100 MPa, (b) 200 MPa, and (c)300 MPa.

Further insight into the breakup process canbe gained by examining the droplet size predictions.Sauter Mean Diameter (SMD) is de�ned as the diame-ter of a sphere that has the same volume/surface arearatio as the entire spray. The SMD correlation has beenpresented by Ejim et al. [40] as in:

SMD = 6156v0:385�0:737�0:737f �0:06a �P

�0:54; (27)

where v and � are viscosity and surface tension, and�P is the di�erence between injection and ambientpressures. The e�ect of injection pressure on SMD forvarious injection pressures is presented in Figure 13.

At the start of injection, SMD is close to thenozzle size and then sharply reduces, as a result of thebreakup process. As shown in Figure 10, higher sprayinjection leads to smaller droplet size. SMD valuesmatch the analytic data under high injection pressure.

Figure 11. E�ects of ambient density on spray volumefor Pinj = 100 MPa and d = 0:16 mm.

Figure 12. Equivalence ratio along the injector axis(Pinj = 100 MPa, d = 0:16 mm).

Figure 13. E�ect of injection pressure on SMD(Pinj = 100 MPa, d = 0:16 mm).

Based on the numerical results of spray penetra-tion, spray angle and spray volume, and their favorableagreement with existing experimental data, for whichmaximum RMSE is below 3, one may suggest thatthe proposed solver and the applied sub-models aresuitable tools for accurate simulation of ultra-highpressure diesel spray.

5. Conclusions

A numerical investigation has been performed, basedon three dimensional CFD simulations, for validationof the atomization model of a single hole nozzleand symmetric diesel spray under ultra-high pressures

246 M. Youse�fard et al./Scientia Iranica, Transactions B: Mechanical Engineering 23 (2016) 238{248

and non-evaporating and non-reacting conditions. ALagrangian particle tracking scheme has been imple-mented for the liquid droplet modeling, and the RANSmethod has been used to simulate the gas �eld. TheSpraydFoam solver of the OpenFOAM open sourcecode has been modi�ed to consider the transient e�ectsof ultra-high injection pressures, based on a validscheme. A comprehensive study of the e�ects ofdi�erent parameters, such as fuel injection pressure,ambient gas density, and nozzle hole diameter, on spraycharacteristics has been conducted. The new modi�edbreakup model presented more accurate results in thecase of ultra-high injection pressures. Based on theacquired results, it is concluded that fuel pressure,ambient density and nozzle diameter have the greateste�ect on spray penetration length. The spray tip pen-etration clearly increases when the injection pressureincreases from 100 to 200 MPa. This increase seemsto be very moderate, from 200 to 300 MPa. Higherspray penetrations have been achieved under high spraydensity. Increasing the nozzle hole diameter leads tohigher fuel mass ow rate and higher spray penetration.Injection pressure appears to have little inuence ondiesel spray angle and remains nearly constant duringthe whole injection. On the other hand, ambientcondition is seen to be an e�ective parameter on thespray angle.

The aim of the present study has been to generatea model for accurately predicting spray shapes andproperties, especially at ultra-high injection pressures.High injection pressure breaks droplets into smallersizes, thus slightly reducing spray penetration. As a re-sult, a higher dispersion rate is predicted. Meanwhile,increasing injection pressure leads to small droplets anda decrease in Sauter Mean Diameter (SMD). Goodagreement has been achieved between the proposednumerical model and the experimental measurementsreported in the literature. The maximum value of theRoot Mean Square Error (RMSE) is determined tobe below 3 for the spray penetration and volume. Inconclusion, it is also found that the proposed Eulerian-Lagrangian scheme, using RANS formulation for thecontinuous �eld, and the new advanced compositebreakup model are appropriate for simulation of a veryhigh direct injection pressure.

Nomenclature

Ao Nozzle ori�ce surface (m2)B0 Breakup constantB1 Breakup constantCD Drag constantCDi Discharge coe�cientE Total energy per unit volumeg Body force per unit of mass

Lb Breakup length (m)Oh Ohnesorge number_mo Mass ow rate (kg.s�1)p Pressure (Pa)pb Chamber pressure (Pa)pinj Injection pressure (Pa)Pr Prandtl numberq Heat ux vectorr0 Droplet radius before breakup (m)rc Radius of child droplets (m)Rep Particle Reynolds numberRel Liquid Reynolds numberSij Rate-of-strain tensorTa Taylor numberu Fluid velocity (m.s�1)up Particle velocity (m.s�1)ug Gas velocity (m.s�1)Um Jet velocity (m.s�1)Weg Gas Weber numberWel Liquid Weber number

Greek letters

�KH Kelvin-Helmholtz wavelength (m)

KH Kelvin-Helmholtz growth rate (s�1)�RT Rayleigh-Taylor wavelength (m)

RT Rayleigh-Taylor growth rate (s�1)� Dynamic viscosity (kg.m�1.s�1)v Kinematic viscosity (m2.s�1)� Density (kg.m�3)�p Particle density (kg.m�3)�bu Breakup time (s)�ij Stress tensor (kg.m�1.s�2)�KH Kelvin-Helmholtz breakup time (s)

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Biographies

Mahdi Youse�fard received his BS degree in NavalEngineering from the Persian Gulf University, Bushehr,Iran, in 2003, and an MS degree in Naval Architecu-ral Engineering from Sharif University of Technology,Tehran, Iran, in 2005. He is currently a PhD de-gree candidate in the Marine Technology Faculty ofAmirkabir University of Technology (AUT), Tehran,Iran. His research interests include CFD modelingof high pressure diesel injection. He has published�ve scienti�c papers in the �eld of computational uiddynamics of one and two-phase ows.

Parviz Ghadimi received his PhD degree in Mechan-ical Engineering, in 1994, from Duke University, USA.He served one year as Research Assistant Professor inM.E. and six years as a Visiting Assistant Professor inthe Mathematics Department at Duke. He is currentlyAssociate Professor of Hydromechanics in the Depart-ment of Marine Technology at Amirkabir Universityof Technology, Tehran, Iran. His main research inter-ests include hydrodynamics, hydroacoustics, thermo-hydrodynamics, and CFD, and he has authored severalscienti�c papers in these �elds. He has also authoredtwo textbooks in Farsi; Applied Computational FluidDynamics and Engineering Mathematics.

Seyyed Mostafa Mirsalim received his BS and MSdegrees in Mechanical Engineering from the Universityof Poitiers France, in 1967 and 1969, respectively. Hereceived his certi�cate in Thermodynamics and FluidMechanic, in 1970, from the same university. Heis currently Assistant Professor in the Department.of Mechanical Engineering at Amirkabir Universityof Technology, Tehran, Iran. He has published twoFarsi language reference books on Internal CombustionEngines and Gas Engines and published and presentedover �fty scienti�c articles in international journals andat di�erent national and international conferences.