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ILASS-Americas 25th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 2013

Secondary Atomization Modelling of High Pressure Electrostatically ChargedDiesel Fuel Sprays

G. H. Amine-Eddine∗, J. S. Shrimpton, and A. Kourmatzis†

Energy Technology Research GroupUniversity of Southampton

Southampton, UK

AbstractElectrostatic atomization presents itself as a novel way to improve fuel spray characteristics and dynamicsprior to combustion. Pertinent to high pressure fuel injection systems typically employed within automotiveand marine sectors, potential improvements include the creation of finer spray droplets through thepromotion of secondary atomization, increased droplet dispersion due to electrostatic repulsion forces,and as a consequence, increased spray evaporation rates when subjected to elevated engine temperatures.These improvements are particularly advantageous for achieving combustion efficiency and reducing sootemissions. However, to evaluate the impact of electrostatic fuel atomization on the design, development,and optimization of high pressure fuel injection systems, there is the need for a cost-effective and reliableCFD methodology that can predict charged high pressure spray behaviour.

In this paper, a 2D Eulerian-Lagrangian code is used to evaluate a numerical methodology designedfor the simulation of high pressure electrostatically atomized Diesel fuel sprays. A secondary atomizationmodel, modified to include the effects of electrical charge on droplet deformation and breakup mechanisms,is examined through simulations and validated in relation to spatial statistics obtained from experimentalphase Doppler anemometry measurements.

Spray dispersion rates examined qualitatively during the transient initial injection period were ob-served to increase in charged sprays at the cost of decreased spray penetration rates. Droplet diameterPDFs sampled at centreline downstream locations within computed uncharged sprays, show a distinctevolution from a bi-modal, to uni-modal droplet size distribution as spray injection velocities increase. Forcomputed charged sprays, PDFs sampled at the same locations are all uni-modal, with a single peak fordroplet diameters present within the range 0.1-0.25D/dinj . Droplet axial velocity profiles from simulatedcharged sprays show reasonable agreement with corresponding experiments, with average percentage errorsbetween profiles ranging from 16.2% to 27.5%.

∗Corresponding Author: gae106@soton.ac.uk†Institutional Address: Clean Combustion Research

Group, Aerospace Mechanical and Mechatronic Engineering,The University of Sydney, NSW 2006, Australia

Introduction

Fuel spray behaviour, including the dynamicsof breakup, dispersion and penetration all have astrong influence on the performance, and efficiencyof combustion processes. High pressure fuel injec-tion systems typically employed within automotive,aerospace, and marine sectors, have existing capabil-ities in benefiting these combustion processes. How-ever, with rising costs of fuel and the tightening ofemissions legislation, comes an increasing demandfor engine manufacturers to seek technologies thathelp to reduce fuel consumption and harmful airpollutants in their newly developed engines. Onesolution, is the use of charged injection technology,which via the process of electrostatic atomization,presents itself as a novel way to improve fuel spraycharacteristics and dynamics prior to combustion.

When electrically insulating dielectric liquidsare subjected to charged injection at high hydrody-namic pressures, the increase in flow-rate allows forgreater levels of charge to be imparted to the spray.Recent experiments by Kourmatzis et al. [1] havereached spray specific charge levels of 6C/m3, at el-evated injection pressures ranging 15-35bar, whichcorresponds to injection velocities of 40-50m/s fora nozzle orifice of diameter 125µm. At these ele-vated injection conditions, spray processes such assecondary atomization start to dominate. This pro-cess is promoted further by the high levels of chargeon droplets, acting to decrease their stability andincrease their likelihood of breakup.

Despite these potential benefits, there yet ex-ists a reliable CFD methodology that can success-fully predict the behaviour of charged high pressuresprays. In this paper, we present a methodology thatachieves this aim.

Experimental Spray Characteristics

In order to make reliable CFD predictions ofcharged high pressure sprays, we need to be certainabout the accuracy of numerical methodologies used.To achieve this, simulated CFD sprays are set-up toreflect the conditions present in selected experimen-tal sprays from the investigation presented by Kour-matzis et al. [1]. A summary detailing the operatingconditions of these experiments are listed in Table 1,along with liquid properties for the Diesel fuel usedlisted in Table 2.

The primary investigation of Kourmatzis etal.[1] was to assess the electrical and atomizationperformance of a plane-plane type, charge injectionatomizer illustrated in Figure 1, at pump pressuresranging from 15 to 35 bar. Such pressures corre-spond to injection velocities of up to 50m/s, and

Case Uinj m Qv Rej Wej(m/s) (kg/s) (C/m3)

1P 37 0.38 6 1943 57502P 40 0.41 6 2100 67203P 48 0.49 5.5 2520 9677

Table 1. Operating conditions for charged highpressure spray cases from experiments of Kourmatziset al. [1]. For all spray cases Diesel fuel was used,the orifice diameter was dinj = 125µm, and thesurrounding gas density throughout the spray was1.184kg/m3.

Property DieselDensity, (ρd) kgm−3 840

Dynamic Viscosity, (µd) kgm−1s−1 0.002Surface Tension, (σ) Nm−1 0.025Relative Permittivity, (εr) 2.0

Electrical Conductivity, (k) pSm−1 5.0

Table 2. Properties of Diesel fuel at 293K unlessotherwise stated.

due to these high injection velocities present, sprayspecific charges up to 6 C/m3, were successfully in-jected into the spray. Spay specific charges at such alevel had never been achieved previously, with impli-cations considered significant in terms of advancingelectrostatic atomization technology towards indus-trial application within existing high pressure spraysystems.

High Voltage Electrode

Earthed OrificeInter-Electrode Gap

Jet Plate

Figure 1. Schematic Diagram of Plane-PlaneCharge Injection Atomizer with Modelled PrimaryAtomization (Jet) Region.

The analysis provided by Kourmatzis et al.[1]did not cover effects of electrical charge on sec-ondary atomization performance. However, men-tion was made to the existence of secondary atom-ization through evidence shown in droplet diame-ter PDFs, that were obtained from PDA measure-

ments taken along the spray centreline. On thismatter, a bi-modal PDF was present at locationscloser to the nozzle exit orifice, for both cases 1Pand 2P of Table 1. With further downstream dis-placements, the bi-modal PDF peaks for case 1Premained relatively unchanged, whereas for case 2P,the peak density present at larger droplet diame-ters gradually diminished whilst the peak densitypresent at smaller droplet diameters increased. Forcase 3P, a uni-modal PDF was observed with a sin-gle peak present at small droplet diameters for allsampled downstream displacements. These obser-vations demonstrate how secondary atomization isan ongoing process, with characteristics unique tothe spatial and temporal development of the sprayplume.

Regions of Droplet Deformation and Sec-ondary Atomization

The non-dimensional parameters that charac-terise deformation and breakup processes of liquiddroplets, are the Weber and Ohnesorge numbers de-fined as,

We =ρgu

2relD0

Oh =µd√ρdσD0

Here the surface tension σ is responsible for thecohesiveness properties of the liquid droplets sur-face, and the dynamic viscosity µd responsible forthe dampening of unstable perturbations. An in-crease in viscosity essentially corresponds to a slow-ing down of the droplet deformation process. Thisallows time for drag forces to react, reducing rela-tive velocities and the potential for the droplet tobreakup. If the Weber number for a given dropletexceeds a critical Weber number Wecrit, only thenwill the droplet undergo breakup. According to thereview of Faeth [2], the critical Weber number maybe taken as Wecrit = 12 for Oh < 0.1, where the ef-fect of dynamic viscosity is negligible. For Oh > 0.1,the correlation reported by [3] may be used.

Wecrit = 12(1 + 1.077Oh1.62) (3)

Qualitatively, prior to the onset of secondary at-omization for We < Wecrit, the droplet experiencesa deformation that may be approximated as a thindisc-like shape normal to the flow direction.

Here we introduce the diameters D0, Dcro andDmin, corresponding to the initial spherical droplet

Flow Direction

Figure 2. Diagram of Deformed Droplet

diameter, the cross-stream diameter normal to theflow direction, and the minimum diameter parallelto the flow direction respectfully.

Zhao et al. [4] showed that at the onset or sec-ondary atomization, droplet deformation was relatedto the Weber number of the surrounding fluid suchthat,

)−1/2= 1 + 0.20We0.56(1− 0.48Oh0.49) (4)

For Oh > 0.1, the maximum deformation of thedroplet at a given Weber number decreases due toslowing of the rate of deformation, which subse-quently reduces the droplets relative velocity [4].In equation (4), (Dcro/D0)max represents the max-imum possible deformation which occurs at the on-set of secondary atomization. Considering the ef-fects of droplet deformation on drag characteristics,we utilise the correlation by Liu et al. [5], whichapproximates drag of a deformed droplet as a linearfunction of deformation.

CD = CD,Sphere(1 + 2.632y) (5)

Here y = 1 − (D0/Dcro)2

is the non-dimensionaldisplacement of the droplet equator, and CD,Sphere

the co-efficient of drag for a sphere.

CD,Sphere =24

6Re2/3

);Re ≤ 1000

=0.44 ;Re > 1000(6)

To take into account the time-varying proper-ties of droplet deformation, we assume that the ratio

Dcro/D0 varies according to a half normal distribu-tion with a mean of unity and a standard deviationequal to 1

3 (Dcro/D0)max.For We > Wecrit, different droplet breakup

regimes may be identified [6]. These breakupregimes are typically identified for Oh < 0.1 as fol-lows.

• Bag, 12 < We < 20

• Multi-mode, 20 < We < 80

• Stripping, 80 < We < 800

• Catastrophic, We > 800

Many authors have reported different rangesof Weber numbers classifying the aforementionedbreakup regimes. However, regardless is the factthat as droplet Weber numbers increase, differentbreakup mechanisms occur. The reader is referredto the comprehensive review of Guildenbecher et al.[7] for details regarding the characteristics of dropletbreakup within these regimes.

Time-scales of Secondary Atomization

Most secondary atomization processes occurover a finite period of time. Experimentallymeasured time-scales for these processes are typi-cally made non-dimensional using the characteris-tic droplet deformation time-scale derived by Rangerand Nicholls [8].

τ∗ =D0

(ρdρf

The duration for initial droplet deformation tiniis typically a constant 1.6τ∗ [9]. Beyond such a du-ration, the droplet is said to undergo breakup thatlasts for a finite period of time. Following a surveyon hydrodynamic fragmentation, Pilch and Erdman[10] devised a set of correlations that characterisedthe total breakup time of droplets, spanning a widerange of Weber numbers.

tbτ∗

= 6 (We− 12)−0.25

; 12 < We < 18

= 2.45 (We− 12)0.25

; 18 < We < 45

= 14.1 (We− 12)−0.25

; 45 < We < 351

= 0.766 (We− 12)0.25

; 351 < We < 2670

= 5.5 ;We > 2670(8)

For high pressure cases examined in this study,it is unlikely for uncharged spray droplets to exceed

Weber numbers greater than ≈ 45. However, forcharged spray droplets, the presence of charge wouldact to decrease the effective surface tension, result-ing in much higher Weber numbers than one wouldotherwise expect for an uncharged spray.

Stable Droplet Diameters following Sec-ondary Atomization

During breakup, the size of unstable droplets isassumed to vary continuously in time according toequation (9), reflecting the finite time required forthe breakup mechanisms to result in a stable dropletwith diameter Dstable.

dt= − (D0 −Dstable)

The stable droplet diameter Dstable is subsequentlyevaluated using the following correlations.For 12 < We < 18,

Dstable =D0.5

D320.32We2/3

(We− 12)1/4

]2/3σ

ρgu2rel(10)

for 18 < We < 45,

Dstable =D0.5

D320.32We2/3×[

2.45(We− 12)1/2 − 1.9

(We− 12)1/4

]2/3σ

ρgu2rel(11)

for 45 < We < 100,

Dstable =D0.5

D320.32We2/3

(We− 12)1/4

]2/3σ

ρgu2rel(12)

and for We > 100,

Dstable = Wecritσ

ρfu2rel

(1− V ∗c

)−2(13)

In equation (13), V ∗c is the velocity of the fragmentcloud post-breakup, and is calculated via,

V ∗c = urel

(ρfρd

)1/2 (B1τ

∗b +B2τ

where co-efficients B1 and B2 are chosen to fit exper-imental data [11], and their values taken typically as0.375 and 0.236 respectively1.

1It should be noted here that according to Pilch and Erd-man [10], co-efficients B1 and B2 differ depending on whether

Correlations defined by equations (10)-(12) werebased on improved estimates for average fragmentdroplet sizes produced in the bag and multi-modebreakup regimes [12]. Furthermore, we employ theuse of the relation D0.5/D32 = 1.2 which relatesthe mass median to the Sauter mean diameter ofthe droplet fragment cloud post breakup [13]. Wefound these improved correlations overcome the pit-falls in Dstable prediction for We < 100 originallynoted by Pilch and Erdman [10]. Figure 3 illus-trates the variation of Dstable/D0 as a function ofWe predicted by these improved correlations. Se-lected and most recent experimental observations onstable droplet diameters produced in the bag andmulti-mode breakup regimes are included in Figure3 for reference [4][14][15][16].

Dstable/D

Wert [12] & Pilch and Erdman [10]Chou and Faeth [14]Dai and Faeth [15]Zhao et al. [4]Kulkarni et al. [16]

Figure 3. Influence of We on Dstable/D0 predictedby correlations (10)-(13)

Accounting for Electrical Charge on Droplets

Charge Mobility During Breakup

An experimental study by Guildenbecher andSojka [17] noted that breakup is not only a functionof charge level, but also dependant on the rate ofcharge movement [18]. It was therefore assumed thatsimilar dependencies exist within the principles ofsecondary atomization. To account for this, all fluidsposses an electrical resistivity, resulting in a finiterate of charge movement characterised by the chargerelaxation time.

τQ =ε0εrk

Here εr is the relative permittivity of the liquid andk is the electrical conductivity of the liquid. Thischarge relaxation time can be made non-dimensionalusing (7), yielding the conductivity number k∗ [17].

incompressible or compressible flow is considered. For in-compressible flow, co-efficients are in fact taken as 0.375 and0.227, whereas for compressible flow these co-efficients aretaken as 0.75 and 0.348 respectively.

k∗ =ε0εrk

urelD0

(ρfρd

The conductivity number allows us to comparethe time-scale of charge movement throughout thedroplet to the characteristic breakup time of adroplet undergoing secondary atomization. There-fore, when k∗ � t∗b , the rate of charge movement ismuch faster than the rate of deformation such thatthe charge will re-distribute itself quickly throughoutthe droplet, by migrating and spreading uniformlyacross the droplet surface to achieve a distributionthat minimizes electrostatic stresses [17]. Alterna-tively, when k∗ � t∗b , the rate of charge movementis assumed to be frozen throughout the breakup pro-cess. Therefore, any droplet deformation whether itbe prior to, or during secondary atomization shouldresult in a faster breakup process. Guildenbecherand Sojka [17] examined this effect, but found no sig-nificant impact on either the initial breakup times,nor total breakup times of charged droplets undergo-ing secondary atomization. This is not to say a roledoes not exist, but rather the effect is hidden withinthe inevitable existing experimental uncertainty andthe dominant mechanisms of aerodynamic fragmen-tation. For high pressure sprays examined in thisstudy, k∗ ≈ O(10−5), which indicates that charge iseffectively frozen throughout breakup processes.

Maximum Rayleigh Limit Charge

Assuming an isolated, electrically conductingspherical droplet, the maximum charge held is de-fined by the droplets Rayleigh limit.

Qray = 4π√

0.5ε0σD30 (17)

In reality, this Rayleigh limit is rarely ever reached,due to the fact that either electrical or aerodynamicforces act to deform the droplet away from the per-fect electrical, and physical symmetry conditions as-sumed. This typically limits the maximum chargelevel to be ≈ 80% of the Rayleigh limit [19].

Charged Droplet Fission

Charged droplets that exceed their Rayleighlimit undergo a process known as Coulomb fission,whereby a stream of sibling droplets, each carry-ing with them a fraction of the parents mass andcharge, eject from the surface of the parent droplet[19][20][21]. For evaporating droplets whereby massis lost without any loss of charge from the surface,modelling the Coulomb fission process is essential toensure that total spray evaporation rates are pre-dicted as accurately as possible. Evaporation ratesare promoted in sprays by the increase in number

of small droplets, and the subsequent increase in to-tal spray surface area, relative to a spray containingthe same volume of liquid across larger droplet sizes.Although evaporation does not occur for high pres-sure sprays investigated in this study, we found thatapproximately 2% of droplets exceed their Rayleighlimits after aerodynamically induced secondary at-omization. We therefore include the modelling ofCoulomb fission processes, only for completeness ofthe numerical method.

Theoretical analysis performed on chargeddroplet fission processes have predominately reliedupon the minimization of Gibbs free energy tech-nique [22][23][24], using knowledge of parent dropletparameters, and assumptions relating to the forma-tion of a stream of ejected sibling droplets. To modelCoulomb fission, we utilise the relationship [25][26],

√ρdD3

ε0εr(18)

Here, fq = ∆Q/Qd and fm = ∆m/md denote thefractional charge and mass lost from the parent tosibling droplets. The empirical constant in equation(18) was calculated to be C ≈ 14.78. This value wasfound following numerical tests of equation (18) withinput parameters from known experimental obser-vations [19][20][21], predicting that parent dropletstypically lose between 10-18% of their charge, and1-2.3% of their mass [21]. Any number betweennp = 7-30 of sibling droplets may eject from theparent droplet during fission [27], each with a diam-eter ≈ 10% of their parents original droplet diame-ter prior to fission [21]. Assuming identical siblingdroplets and a uniform variation of ∆Q, ∆m, and npwithin experimentally observed ranges, one can sub-sequently calculate the size, and the charge held bysibling droplets produced during the fission process.

Effective surface tension

To account for electrically charged droplets, onemay equate a force balance between the surface ten-sion restorative forces of a spherical droplet, and thedisruptive forces of electrostatic charge. One maythen obtain an equation for the effective surface ten-sion,

σ∗ = σ − Q2d

8π2ε0D30

valid within the limits, as Qd → 0, σ∗ → σ, andQd → Qray, σ∗ → 0. Subsequently, equation (19)may be used in place of σ, appearing in (1) and(2), to yield corresponding electrostatic Wee− andOhe− numbers. Usage of σ∗, Wee−, and Ohe− is

then incorporated within the aforementioned defor-mation and secondary atomization models relatingto uncharged spray droplets.

Impact on Weber, Ohnessorge and BreakupTime-scales

An increase in surface charge density leads toincreased Wee− and Ohe− numbers. At elevatedOhe− numbers, Wecrit also increases. However, theobserved breakup modes for droplets that exceedWecrit within a given Weber number range remainsthe same [7]. With a predicted increase by Ohe−in the dampening of unstable perturbations, thereis yet a greater influence of droplet charge on Wee−numbers, subsequently promoting secondary atom-ization. This was validated during an experimentalstudy performed by Guildenbecher and Sojka [28],who showed that for highly conductive liquids, use ofequation (19) leads to an increased agreement withthe Pilch and Erdman [10] breakup correlations gov-erning total droplet break-up times.

Spray Discretisation

The CFD code used to simulate our chargedhigh pressure sprays was originally developed aspart of theoretical, computational and experimen-tal studies on mechanisms governing electrostatic at-omization of hydrocarbon oils [29]. The code waslater extended during a previously published CFDstudy evaluating a numerical methodology suitablefor simulating low pressure electrostatically atom-ized dielectric liquid sprays [30], where specific de-tails regarding the numerical methods may be found.

In this section, we present only details relevantto the specification of initial discrete phase condi-tions.

Initial Conditions of the Discrete Phase

Due to the large injection velocities presentwithin high pressure sprays, there is an inherent dif-ficulty faced by experimentalists in measuring meanjet breakup lengths. Based on previous work regard-ing charged low pressure sprays [30], we can justifythe use of equations (20), (21), and (22) below tospecify jet breakup lengths for all our charged highpressure sprays.

lj = Uinjτj (20)

τj =ε0εrκQv

κ = Aµ−1d (22)

Here A is taken as a constant equal to 4 × 10−11

[30]. These equations were found to be far more re-

liable in predicting finite mean jet breakup lengthsthan classical models governing laminar and turbu-lent jets. These classical models failed in their pre-dictive capabilities when their jet Weber and Ohnes-sorge numbers were modified to account for electricalcharge using an effective surface tension derived fora round cylindrical jet [1].

The initial velocity of droplets is specified byboth mean and fluctuating components of the in-jection conditions, assumed at the atomizer orificeplane.

Ud,t=0 = Uinj + U ′ ×RANG (23)

Vd,t=0 = Vinj + V ′ × |RANG| (24)

Here RANG, is a random number taken from aGaussian distribution with zero mean and unit vari-ance. We assume that the initial axial velocity ofdroplets is equal to the bulk mean injection veloc-ity Uinj , plus a fluctuating component where U ′ wastaken to be equal to 40% of Uinj . Furthermore, weassume droplets have a mean radial velocity compo-nent Vinj = 0, with a fluctuating radial componentV ′ determined via the half-spray cone angle θ/2◦.For charged sprays, the half spray cone angle is adifficult quantity to measure experimentally, mainlydue to the fact that charged droplets tend to fol-low parabolic paths. However, if we assume that allspray droplets originate at, or near the centreline ofthe liquid jet, we may utilise the following correla-tions to determine the half-spray cone angle [31][32].

tan(θ/2) =4π

(ρfρd

)0.5 √3

A is taken as a constant dependant on the nozzledesign, or approximated using,

A = 3.0 + 0.28

These correlations were chosen for their suitabilityacross most modern Diesel injectors.

The next part of the injection procedure requiresspecification of the initial droplet size distribution.Due to the presence of secondary atomization, it isunreliable to use measured PDFs obtained from ex-perimental PDA data. This is because measuredPDFs are functions of transient secondary atomiza-tion processes, exhibiting themselves as spatially de-pendent characteristics within the spray plume. Ini-tial PDFs are therefore assumed to take the form of

a normal distribution, chosen such that the mean di-ameter equals the orifice diameter, with a standarddeviation equal to 1

3dinj . This yields a normallydistributed diameter PDF, with diameters spanningthe range ≈ 0-2dinj , aimed to reflect the theorywhereby diameters of droplets produced from thelargest unstable wavelength on a liquid jet, are equalto 1.89dinj [33][34].

For initial specification of droplet charges, weuse the modelled Q-D method as employed in previ-ous computational studies [35][30].

Qd,k+1=

Here the constant m is taken as 1.8 [36]. This allowsthe total charge injected during any time intervalQ∆t, to be expressed in terms of a conserved in-jected current Q(t) such that,

Q∆t =

Kp∑k=1

Nd,kQd,k = Qd,1

Kp∑k=1

where Kp is the total number of parcels injectedduring the time interval, and Nd the number ofreal droplets contained within each injected parcel.Charge is then defined conservatively without explic-itly constraining it to obey any limits. Furthermore,we include a variation in charge based on typical val-ues determined from experiments, for the standarddeviation of charge levels across different diameterclasses. From experiments of Rigit and Shrimpton[37], standard deviations of charge levels are approx-imately 10% of droplet Rayleigh limits.

Critically, mass is conserved throughout the in-jection process by adjusting the number of realdroplets contained within each injected parcel. Sim-ilarly, charge is conserved by adjusting the relativedroplet charge levels across all injected parcels.

Results

Statistics were post-processed from simulatedCFD sprays in a similar manner to statistics pro-cessed from experimental PDA measurements. Sam-ple control volumes from CFD and experimentalmeasurements were taken at the same downstreamand radial locations away from the atomizer orifice.This allows for an accurate assessment of model per-formance and the CFD procedures employed.

Figures 4 and 5 show the initial spray develop-ment for the uncharged and charged, case 3P highpressure sprays respectively. Results show how thecharged spray penetrates less downstream over the5ms interval than the uncharged spray. Due to

the presence of Lorentz forces acting on chargeddroplets, there is an increase in radial dispersion,more so than what is typically observed for un-charged sprays. In agreement with theory suggestingthat the presence of charge on droplets increases thetendency for droplets to breakup, results show evi-dence of an increased abundance of small (D/dinj <1) droplets within the charged spray. In relationto findings of previous researchers, Kayhani et al.[38] stated that atomization to rapid leads to inad-equate spray penetration. Furthermore, Kwack etal. [39] who performed experiments examining elec-trostatic dispersion of Diesel fuel jets at high backpressures, observed a rapid breakup of the spray jetwithout any presence of large droplets within thespray core. Our results agree well with these previ-ous findings, giving confidence in the methods usedto model secondary atomization within charged highpressure sprays.

Figure 6 compares droplet diameter PDFs ob-tained from computed sprays, with available PDFsobtained from experimental spray measurements.With regards to uncharged computed sprays, a dis-tinct evolution from a bi-modal to uni-modal dropletsize distribution is observed with increasing sprayinjection velocity, relative to fixed downstream sam-ple locations. For charged computed sprays, dropletsize distributions are predominantly uni-modal, witha single peak for droplet diameters occurring inthe range 0.1-0.25D/dinj . Furthermore, the tailsin these distributions in the direction of increas-ing droplet diameters tend to show reduced prob-abilities as spray injection velocities increase. Com-parison of PDFs between computed and experimen-tal charged sprays only show reasonable agreementfor case 3P. For case 1P, computed results show auni-modal PDF, whereas the experimental PDF re-mains bi-modal. A similar behaviour is observedfor case 2P, the only difference being an increase insmaller droplet probability within the bi-modal ex-perimental PDF. These discrepancies are most likelycaused by weaknesses in the modelling of dispersionfor charged high pressure sprays.

Figure 7 shows mean axial velocity profiles ofcharged droplets compared between spray simula-tions and experiments. Profiles computed for highpressure sprays all show reasonable agreements withexperiments, with the exception being case 3P wherethe computed profile exceeds the experimental pro-file near the spray centreline by nearly a factor of 3.To explain this behaviour, one can observe in Figure7 that as spray injection velocities increase, the meanvelocity of droplets sampled at the spray centrelinedecreases. An increase in spray injection velocity

therefore leads to greater dispersion which adds a ra-dial component to droplet velocities. Our computedprofiles do not show evidence of this behaviour. In-stead, there is a tendency for computed profiles toexceed experimental profiles near the spray centre-line. Nevertheless, for increasing r/dinj , the com-puted profiles show reasonable consistency in theiragreement with experimental profiles.

Figure 7 also includes an experimental mean ax-ial velocity profile for a 34m/s low pressure spray,originally presented as spray (ii) by Shrimpton andYule [40], and its computed corresponding profiletaken from a recently published CFD study [30].Comparing case 1P to spray (ii) up to r/dinj =100, experimental profiles show reasonable agree-ment with each another. Furthermore, the com-puted profile for case 1P agrees well with its ownexperiment, and that of spray (ii). This gives usconfidence that the method used to model secondaryatomization within charged high pressure sprays, ac-counts reasonably well for charged spray behaviourexisting in sprays where secondary atomization isnot a dominant process.

Lastly, the average percentage errors betweencomputed and experimental mean velocity profileswere calculated to be 19.5%, 16.2%, and 27.5% forspray cases 1P, 2P, and 3P respectively.

Conclusions

A numerical methodology is presented, suitablefor predicting characteristics of high pressure elec-trostatically charged Diesel fuel sprays. Most im-portantly, the methodology is reliable at predictingsecondary atomization processes for both unchargedand charged sprays.

Qualitative examination between selected un-charged and charged high pressure sprays show howradial dispersion in charged sprays is increased sig-nificantly over uncharged sprays. This increase incharged spray radial dispersion comes with the costof decreased spray penetration rates.

For uncharged computed sprays, sampleddroplet diameter PDFs measured between casesshow a distinctive evolution from a bi-modal to uni-modal droplet size distribution as spray injection ve-locity is increased. For charged sprays, droplet di-ameter PDFs are predominantly uni-modal, with asingle peak in droplet diameters present within therange 0.1-0.25D/dinj .

For the fastest charged high pressure spray, thedroplet diameter PDFs between computed and ex-perimental sprays show excellent agreement. Fur-thermore, droplet axial velocity profiles from com-puted charged high pressure sprays show reasonable

agreement with corresponding experimental sprayprofiles, with average percentage errors ranging from16.2% to 27.5%.

The results from this investigation highlight thesuitability of the CFD methodology presented, forsimulating high pressure electrostatically chargedfuel sprays, at elevated injection conditions typicallyemployed within automotive and marine sectors.

Further work aims to apply this CFD method-ology within the context of a large marine Dieselengine application.

Acknowledgement

This work was supported by an ESPRC Doc-toral Training Centre grant EP/G03690X/1

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0 0.060

D/dinj

Figure 4. Initial spray development and penetration of the uncharged 3P high pressure spray. Timesnapshots of spray droplets taken at a)3ms, b)4ms, c)5ms after start of injection

0 0.060

D/dinj

Figure 5. Initial spray development and penetration of the charged 3P high pressure spray. Time snapshotsof spray droplets taken at a)3ms, b)4ms, c)5ms after start of injection

0 0.5 1 1.50

0.1Uncharged

bability

0 0.5 1 1.50

0.1Charged

0 0.5 1 1.50

bability

0 0.5 1 1.50

D/dinj

bability

0 0.5 1 1.50

D/dinj

(b)-ii

(c)-ii

(a)-ii(a)-i

Figure 6. Histogram PDF measurements obtained from post-processed CFD simulation data for uncharged(i) and charged (ii) high pressure sprays; a) Case 1P, b) Case 2P, and c) Case 3P. Overlaid profiles correspondto experimental spray PDFs. PDFs were sampled along the spray axis downstream from the atomizer at17cm for Case 1P, 15cm for Case 3P, and at 12.5cm and 17.5cm for the uncharged and charged Case 2Prespectively.

0 50 100 150 200 2500

r/dinj

Case 1P Expt. 37 m/s, (z/dinj = 1200)Case 1P Sim. 37 m/s, (z/dinj = 1200)Case 2P Expt. 40 m/s, (z/dinj = 1360)Case 2P Sim. 40 m/s, (z/dinj = 1360)Case 3P Expt. 48 m/s, (z/dinj = 1400)Case 3P Sim. 48 m/s, (z/dinj = 1400)Spray (ii) Expt. 34 m/s, (z/dinj = 600)Spray (ii) Sim. 34 m/s, (z/dinj = 600)

Figure 7. Mean droplet axial velocity profiles for charged high pressure cases 1P, 2P, and 3P, as well asspray (ii) from Shrimpton and Yule [40].

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