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Proceedings of the Combustion Institute 35 (2015) 1595–1602

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CombustionInstitute

Droplet/ligament modulation of localsmall-scale turbulence and scalar mixing

in a dense fuel spray

J. Shinjo a,b,⇑, J. Xia b, A. Umemura c

a Institute of Aeronautical Technology, Japan Aerospace Exploration Agency, 7-44-1 Jindaiji-higashimachi, Chofu,

Tokyo 182-8522, Japanb Mechanical Engineering Subject Area, School of Engineering and Design, Brunel University, Uxbridge, Middlesex

UB8 3PH, United Kingdomc Department of Aerospace Engineering, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8603, Japan

Available online 10 July 2014

Abstract

In this study, the modulation of turbulence and scalar mixing by finite-size droplets/ligaments in a densefuel spray is investigated using a DNS (Direct Numerical Simulation) dataset. Ejected from a spray nozzlewith a high speed, a liquid-fuel jet deforms and the fuel spray is atomized into many ligaments and drop-lets. During these processes, the gas flow becomes turbulent due to droplet/ligament dynamics. At the sametime, droplet evaporation and mixing with ambient air are affected by the small-scale gas turbulence. Anunderstanding of the mixing characteristics in the dense spray zone is important for modeling spray com-bustion. In a region where the droplet number density is relatively low, a universal feature of isotropic tur-bulence was found, although the alignments of strain eigenvectors with vorticity and the mixture fractiongradient are slightly modulated by the presence of droplets, which is a characteristic of particle-laden flows.In gas-phase regions close to droplet surfaces, where the dissipation rate of turbulent kinetic energy isstrongly increased, the alignments are more modulated, especially those of the scalar gradient with straineigenvectors. This can also be seen in the topology similarity among energy dissipation, enstrophy and sca-lar dissipation in the near field of droplet/ligament surfaces. For the first time, it is found that dropletswhose size is comparable to turbulence scales do affect the mixing characteristics in a realistic turbulentspray. This finding has shed new light upon the modeling of flow turbulence and scalar mixing in an evap-orating and atomizing fuel spray.� 2014 Published by Elsevier Inc. on behalf of The Combustion Institute. This is an open access articleunder the CC BY license (http://creativecommons.org/licenses/by/3.0/).

Keywords: DNS; Spray; Turbulence modulation; Scalar mixing; Small-scale structures

http://dx.doi.org/10.1016/j.proci.2014.06.0881540-7489/� 2014 Published by Elsevier Inc. on behalf of TheThis is an open access article under the CC BY license (http://

⇑ Corresponding author at: Mechanical EngineeringSubject Area, School of Engineering and Design, BrunelUniversity, Uxbridge, Middlesex UB8 3PH, UnitedKingdom. Fax: +44 1895 256 392.

E-mail address: Junji.Shinjo@brunel.ac.uk (J. Shinjo).

1. Introduction

Liquid-fuel atomization, evaporation, mixingand combustion closely interact with turbulencein spray combustion. The physics is very complex

Combustion Institute.creativecommons.org/licenses/by/3.0/).

1596 J. Shinjo et al. / Proceedings of the Combustion Institute 35 (2015) 1595–1602

since there is a wide range of temporal and spatialscales in an atomizing spray [1–6]. Droplets/liga-ments are generated by primary atomization inthe near-nozzle region, and the droplet size anddistribution subsequently impose a significantimpact on the downstream spray dynamics.

In the downstream dilute spray region, the tur-bulence scale is in general much larger than thedroplet scale. While in the dense spray region nearthe injection nozzle, the turbulence scale is compa-rable to the droplet scale. For combustion, mixingof fuel/oxidizer is critical. Scalar mixing isstrongly affected by small-scale turbulence struc-tures [7–23]. Therefore, when the droplet/ligamentsize is comparable to the turbulence scale, it isexpected that droplets/ligaments would changethe small-scale structures, hence mixing. Despiteits determining role in the entire spray combus-tion, droplet/ligament effects on turbulence andscalar mixing in a dense atomizing fuel spray havenot been fully understood yet and will be the mainobjective of the present study.

In turbulent single-phase flows [7–14], correla-tions between turbulence structures and scalarmixing have been investigated. Abe et al. [14] con-ducted a DNS study in a heated channel to inves-tigate scalar mixing. At the wall, small-scalestructures are dominant due to high strain rates,and are different from those of isotropic turbu-lence. The small-scale topologies of the vorticity,energy dissipation and scalar dissipation ratebecome strongly correlated near the wall. Awayfrom the wall, the correlations become weakerand the structures appear more similar to thoseof isotropic turbulence.

For turbulent multiphase flows, turbulencemodulation by liquid droplets or solid particleshas been of considerable interest [15–19]. In earlystudies [15–17], the particle size was much smallerthan the turbulence scale, i.e. point particles. Par-ticles, even at a low number density, modify thevorticity dynamics and turbulence production/dis-sipation rate by the drag force, and the turbulentmass and heat transport [15,16]. The alignmentsbetween the vorticity vector and strain eigenvec-tors are changed as a result of increased dissipationby the particles. Reacting flows laden with point-droplets were investigated by large-eddy simula-tion [17]. The turbulence modulation was inducedby droplets (and heat release) due to the change ofthe alignments between the strain eigenvectors andthe vorticity and also the scalar gradient. Theeffects of particles, whose size is comparable tothe Kolmogorov or Taylor scales, on turbulenceare also of interest recently [18,19]. The strain-rateeigenvalue modification was also observed forfinite-size particles. In the near field of particles,the increased dissipation rate of turbulent kineticenergy due to the non-slip particle interface canbe observed. In most of the studies above, theparticles were solid and spherical. In this study,

turbulent energy dissipation and heat/masstransport at the surface of deformable droplets/ligaments in a spray configuration are additionalphysical phenomena.

For simple configurations such as a singledroplet or a droplet array in a gas flow, theflow-droplet interaction has been investigatedextensively on turbulence, evaporation and com-bustion modes [20–23]. Although simple configu-rations are useful to improve our understanding,actual turbulent flow fields in a spray are morecomplicated. Since a dense liquid spray containsmany droplets and ligaments, whose size is com-parable to the turbulence scale, and the liquid–gas relative velocity is high, it is expected that tur-bulence modulation will occur. Formation ofwake and vortex shedding by droplets/ligamentswill change the production and dissipation ofthe gas-phase turbulence. This phenomenon canalter flow structures and fuel/oxidizer mixing,and thus impact the combustion characteristicsin the downstream dilute spray region. Therefore,it is important to investigate the turbulent mixingof the gas phase with finite-size droplets in a fuelspray to properly model spray dynamics andcombustion.

In this study, to elucidate the turbulent mixingcharacteristics in the dense spray region, the DNSdataset of the primary atomization of a liquid fueljet is utilized. Since the droplet distribution is non-uniform due to atomization [3,4], the turbulenceand mixing characteristics in regions with distinctdroplet number densities are investigated. To thebest of our knowledge, this is the first study onturbulence and scalar mixing in a dense fuel spray.

2. DNS of an evaporating and atomizing fuel spray[6]

The liquid fuel n-heptane is injected from around nozzle of diameter DN = 0.1 mm into hotquiescent air (900 K, 30 atm) at a high speed(100 m/s). The bulk liquid Weber numberðWe ¼ qlU

2l a=rÞ is 14,100 and the bulk liquid Rey-

nolds number (Re ¼ qlU la=ll) is 1477, wherea = DN/2, q denotes density, U the injection veloc-ity, r the surface tension coefficient, l viscosityand the subscript l denotes liquid. Slip velocitystill exists between the liquid and gas phases, withthe estimation of the Stokes number around 20(St ¼ qlD

232U s=18lgL; where D32 is the Sauter

mean droplet diameter, Us the slip velocity, Lthe characteristic flow length and the subscript gstands for gas) [6]. The droplet size isD32=g ¼ 4:3, where g is the Kolmogorov scale.

The governing equations for mass, velocity,temperature, interface shape and species massfractions of C7H16, O2, CO2, H2O, and N2 aresolved [6]. The global one-step reaction model byWestbrook is used [6]. The reaction heat release

J. Shinjo et al. / Proceedings of the Combustion Institute 35 (2015) 1595–1602 1597

is negligible in the dense spray region. (The tem-perature rise is below 1 K within the simulationperiod.) Therefore, both temperature and mixturefraction are nearly passive scalars, and the currentresults can be compared with those of Abe et al.[14] where the temperature is a passive scalar.The Lewis number is assumed to be unity. Theevaporation rate is formulated by the equilibriumvapor pressure model and given by the jump con-dition at the interface [24]. The mixture fraction zis z ¼ ðsY F � Y O þ Y O;0Þ=ðsY F ;0 þ Y O;0Þ with s ¼mOW O=mF W F . mi is the stoichiometric coefficientand Wi molecular weight. The subscript F denotesfuel, O oxidizer, and 0 the inlet condition for thefuel or oxidizer. z = 1 for the fuel stream andz = 0 for the air stream. The stoichiometric mix-ture fraction is zst = 0.062.

Liquid–gas interfaces are captured by the level-set method and surface tension is formulated bythe CSF (Continuum Surface Force) method.The advection term is solved by the CIP (CubicInterpolated Pseudo-particle) method. The com-putational domain size is 5.5 � 4.5 � 4.5 in DN.The grid system is fixed on the jet head, which is20DN away from the injection nozzle [6]. The gridresolution is 0.35 lm, and the total number of gridpoints is 2.2 billion. Grid resolution tests havebeen done in our previous research on primaryatomization and spray evaporation [3–6]. Forcold-flow cases [3], where finer resolution is gener-ally needed to capture smaller vortex structuresdue to a lower gas kinematic viscosity (thus ahigher Reynolds number), the current resolutionwas sufficient. Additionally, several evaporatingdroplet cases at similar droplet Reynolds numbershave been tested to obtain satisfactory results ofevaporation at droplet/ligament surface [6].

3. Results and discussion

Hereafter, an upper-case letter denotes themean of a variable and a lower-case letter its fluc-tuation. For example, uinst ¼ �uþ u ¼ U þ u,where inst stands for “instantaneous” and thebar denotes a mean value. In the present study,the time period for averaging to obtain a meanvalue is Dt ¼ 1:5, which is non-dimensionalizedby DN/Ul. x,y,z are also denoted by the subscripts1,2,3, respectively, and the velocity componentsare u,v,w or u1,u2,u3. @a=@xi is abbreviated as a;i.The Einstein notation applies in aibi, i.e.aibi ¼ a1b1 þ a2b2 þ a3b3.

3.1. Overall flow field

Figure 1a shows the instantaneous shape of theliquid fuel jet head and gas-phase eddies visual-ized by the second invariant of the velocity gradi-ent tensor (Q-value) [4,6]. At this time, the liquidjet head is 20DN away from the nozzle. It is

deformed like an umbrella due to the impact onthe ambient air. At the head edge, the gas flowseparates and large-scale vortex shedding occurs.A large recirculation zone is formed behind thejet head, where a significant amount of droplets/ligaments is detached from the liquid head edgeand fine eddies are generated [6]. Jets or shear lay-ers develop self-similarly in both the near-nozzleand downstream regions [25,26]. For the sprayshown in Fig. 1, the recirculation zone developsself-similarly [4]. This is confirmed by thestreamwise velocity profiles in the recirculationzone and the size development of the recirculationzone during the calculation time period (notshown).

Figure 2 shows the mean strain rateSij ¼ ð1=2ÞðU i;j þ U j;iÞ in the recirculation zone,which is covered by the dashed rectangle inFig. 1b. High shear is observed at the spray-jethead edge in the solid circle, where the gas flowseparates and vortex shedding occurs. Muchlower shear is observed on the periphery of therecirculation zone in the dashed ellipse, and thelowest near the liquid core in the dotted ellipse.It is expected that the flow field becomes closerto isotropic turbulence when the mean shear islow.

At t ¼ 0, the gas-phase flow is quiescent. Allthe gas kinetic energy is supplied from the injectedliquid [3]. Part of the energy is initially used toform the umbrella-like jet head, and the residualis supplied to the gas flow through high-shearregions to form the recirculation zone behind thejet head, which is a large-scale energy-containingregion of the gas flow. The gas-phase kineticenergy is about 7% of the total energy of theinjected liquid at the time of Fig. 1 [3]. At thisstage, most of the energy is being transferred tothe gas through the atomized droplets and liga-ments. The turbulent Reynolds number is defined

as Rek ¼ u0k=m where k ¼ u2=u2;1

� �1=2

is the Taylor

microscale in the axial direction, u0 the root-mean-square (rms) of the axial velocity fluctuation and mthe kinematic viscosity. It is almost the same (Rek

� 60) during the current simulation period.

3.2. Unsteady flow dynamics around droplets andligaments

Before presenting turbulence statistics,unsteady mixing dynamics around droplet wakeregions is investigated due to its close relation toturbulence generation and small-scale turbulentscalar mixing. Fig. 3 shows an example of vortexshedding in the recirculation edge region wherethe local droplet number density is high(�3 � 1014 m�3). The gas phase flows from thelower-right region to the upper left, as indicatedby the streamlines in Fig. 3c. Figure 3a shows a3D view of liquid structures superimposed on a

Air entrainment

Vortex

L L

R

2 1

Stagnation flow region

l

Vinner

Vouter

Vsheet

p =p =pouter sheet inner

Recirculation region

R’

(a) (b)

Fig. 1. Overall liquid structures and gas-phase eddies.

Fig. 2. Mean strain rate S (s�1). The instantaneousliquid shape is shown for reference.

1598 J. Shinjo et al. / Proceedings of the Combustion Institute 35 (2015) 1595–1602

plane view of the fuel mass fraction YF. The redarrow indicates a front ligament in the gas flow.

Fig. 3. Unsteady flow dynamics around droplets/ligaments. Atvapor/air mixing starts; at a later time t ¼ þ0:42, evaporation b(a) Liquid structures and YF at t ¼ þ0:32, (b) YF at t ¼ þ0:42

Several droplets and ligaments exist behind thisligament. Figure 3b and c present YF at a latertime when mixing is more developed. The Rey-nolds number of the front ligament is 230, whichis larger than the critical Reynolds number forthe Karman vortex shedding over a cylinder in auniform flow (Rec �50 [27,28]). Therefore, theKarman vortex shedding occurs as seen inFig. 3. The observed Strouhal number is 0.23.The kinematics of fuel gas pockets is stronglyaffected by these vortices. Evaporated fuel gaspockets from each droplet/ligament can easilyinteract with each other and form a larger clusterof fuel vapor in a short time. Here, the local inter-droplet distance L is L=D32 6 5. Qualitatively, thisclustering phenomenon is similarly observed fordroplet arrays with a small inter-droplet distance[22].

In a region where the local droplet numberdensity is smaller (the far left side in Fig. 1), the

an earlier time t ¼ þ0:32, evaporation is strong and fuel-ecomes weaker, and fuel vapor and air are better mixed., (c) streamlines and YF at t ¼ þ0:42.

J. Shinjo et al. / Proceedings of the Combustion Institute 35 (2015) 1595–1602 1599

droplet Reynolds number is lower (Red < 30). Onthe other hand, the velocity fluctuation of the gasflow is typically much larger. Here, vortex shed-ding from each droplet is also observed becausethe incoming velocity-fluctuation is large (u0/U �0.3). Even for low Red, the Karman vortex shed-ding occurs when the gas-flow velocity-fluctuationis large [27,28]. The inter-droplet distance isL=D32 P 8. Each fuel gas pocket is affected bythese vortices, but is typically isolated (notshown).

The above unsteady vortex shedding is thesource of turbulence generation. The vortices areconvected away from the mean wake region.Thus, the gas flow is turbulent even in the recircu-lation zone where the droplet number density islow (shown later). In the high number-densityregion, the mutual interaction among wakesmakes the wake survival slightly longer. In bothregions, vortex shedding by droplets/ligamentsalters the local flow structures and mixing at thedroplet scale, and thus at the turbulence scale. Arough estimation of the droplet evaporation Dam-kohler number Dav using the classical formulation[23] is Dav �O(0.01–0.1), which suggests a slightincrease in evaporation due to turbulent eddiesaround droplets in the dense spray region [6]. Inthe downstream dilute spray region where thedroplet Stokes number reduces, the wake charac-teristics are different and therefore the turbulenceand mixing characteristics are differentaccordingly.

3.3. Turbulence structures and mixingcharacteristics

The turbulent production terms for xixi andz;iz;i are xixjsij and �z;iz;jsij, respectively, wheresij ¼ ð1=2Þðui;j þ uj;iÞ is the fluctuating strain ten-sor. The alignments between the vorticity xi; thescalar gradient z;i and the principal rate of sij are

(a)Fig. 4. PDFs of the alignment angles between the principal stshear and droplet number density are low. (a) Vorticity (b) sc

important to determine the variation of the turbu-lent production terms [7–14]. Since sij is symmet-ric, the eigenvalues a, b, c are real and satisfya P b P c ða P 0 P cÞ and aþ bþ c ¼ 0.Hereafter, the eigenvectors are denoted as a, b, cfor the eigenvalues of a, b, c, respectively.

Figure 4 shows the probability density func-tions (PDFs) of the cosine of the angle of thealignment between the eigenvectors and xi or z;iin an area far away from the major liquid struc-tures (encircled by the dashed line in Fig. 2).cos h ¼ �1 means strong alignment andcos h ¼ 0 no alignment. The mean shear normal-ized by the Kolmogorov velocity and length scalesis S� < 0:1, thus the mean strain effect is not dom-inant here. The circles and triangles in Fig. 4 arefrom the literature for isotropic turbulence [10],isotropic turbulence with a mean scalar gradient[11] and a turbulent channel flow with wall heattransfer [14]. Known as a universal feature of iso-tropic turbulence, xi and z;i align with the inter-mediate (b) and compressive (c) strain rates,respectively [10,11]. In [14], this trend was alsoobserved in the far-wall region out of the bound-ary layer. The current results show the same trend.Turbulent eddy generation is strongly correlatedwith wake formation due to droplets/ligaments.When the eddies are convected to the centralregion of the recirculation zone where the dropletnumber density is low, the flow there exhibits sim-ilar characteristics to gas-phase isotropic turbu-lence. The PDF of the normalized intermediate

eigenvalue b� ¼ffiffiffi6p

b=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 þ b2 þ c2

pis plotted in

Fig. 5. It shows that b� is mostly positive and thusextensional. This was also observed in [11,12,17].The vorticity can have both sheet-like and tube-like structures [9]. When a vortex sheet wrapsup, a tube-like structure is formed. By the align-ment with b�, it will be stretched and becomelonger along its axis with increased rotationalmotion [14,17] (see the sketch in Fig. 4a). This

(b)rain rates and (a) xi, (b) z;i in a region where the meanalar gradient.

Fig. 5. PDF of the normalized intermediate eigenvalueb�.

1600 J. Shinjo et al. / Proceedings of the Combustion Institute 35 (2015) 1595–1602

sheet-to-tube process indicates a process of energycascade from large scales to small scales [9,17].The alignment of z;i with the compressive strainrate c means that z;i is sheet-like (see the sketchin Fig. 4b). The z;i sheets will wrap tube-like struc-tures of vorticity [9]. Therefore, it has been shownthat turbulence structures similar to those incanonical turbulent flows [7–14] also develop inthe dense fuel spray in a region away from themajor liquid structures.

In Fig. 4, some discrepancies between the sta-tistics of the dense fuel spray and those of isotro-pic turbulence can be observed. The alignment ofxi with b is reduced, while that with c is increased.For z;i, the alignment with c is reduced, while thatwith b is increased. (Reduced alignment can beindicated by reduced PDF near cos h ¼ �1 andincreased PDF near cos h ¼ 0; similarly forincreased alignment.) The same modulation issimilarly observed in flows laden with point parti-cles/droplets [15–17] and with finite-size particles[18,19]. Particles increase the local velocity gradi-ents, thus the strain rate sij and energy dissipatione ¼ 2msijsij [15–20]. Even if the particle numberdensity is low, the strain rate eigenvalues areincreased (sijsij ¼ a2 þ b2 þ c2) and the alignmentsare affected. Figure 6 shows an instantaneoussnapshot of the energy dissipation rate, in whichdroplets are edged by black lines. The existenceof droplets increases the local dissipation.

In near-droplet regions (L/D32 < 1/4), thealignments are changed by stronger local dissipa-tion due to droplets/ligaments boundary layer for-mation. As shown in Fig. 7, xi still aligns with theintermediate (b) strain rate. However, the align-ments of z;i with the compressive (c) and exten-sional (a) strain rates switch to an orientationangle of about 45� (cos h ¼ �0:7). Both trendsof the alignment of xi and z;i with the principalstrain rates are the same as those in the near-wallregion of channel flow turbulence (Fig. 4 of [14]).

This implies that the droplet surface acts like awall, makes the local flow non-isotropic andchanges the local mixing characteristics.

To see this further, topologies of energy dissi-pation e, enstrophy xixi and scalar dissipationDz;iz;i are investigated. D is the mass diffusioncoefficient. Figure 8 shows instantaneous snap-shots. The positive Q-value is superimposed usingsolid lines to identify vortex structures. Ligamentsand droplets exist mostly in the lower right regionand there are few liquid structures in the centralregion. For isotropic turbulence, the energy dissi-pation and enstrophy are alike because �e ¼ mxixi.The structures of e and xixi are similar in the cen-tral region, as shown in Fig. 8a and b. As indi-cated by the red arrows, the structures of e, xixi

and Dz;iz;i wrap a vortex (indicated by the bluearrow) with some phase-angle difference. This ischaracteristic to isotropic turbulence. Meanwhile,near the liquid surface in the lower right region,all the structures become similar. This wassimilarly observed in [14]. The physical reason isthat the strong velocity and scalar gradients nearthe surface lead to xixi � ð@u=@xnÞ2 andDz;iz;i � Dð@z=@xnÞ2 where xn is the wall normaldirection.

The quantified topology correlations in the far-and near-surface regions are shown in Fig. 9 usingjoint PDFs. The joint PDFs are obtained by onerealization data of Fig. 8. The axes represent thevalues normalized by the mean of samples in eachregion. In the far-surface region, the correlationsare weak between the scalar dissipation and ens-trophy (Fig. 9b) and between the scalar dissipa-tion and energy dissipation (Fig. 9c). Meanwhilein the near-surface region, the corresponding cor-relations (Fig. 9e and Fig. 9f) are relativelystronger.

The PDF shapes in both regions are similar tothose in [13,14]. The no-slip droplet surfaces formlayers of velocity, temperature and scalar gradi-ents, hence changing the local flow topology.Since the mixing time scale is linked to the scalardissipation rate, the mixing characteristics nearthe surfaces are also changed. It is expected thatif the Reynolds, Prandtl and Schmidt numbersare similar to the present study, this effect is gen-eric in multiphase turbulent flows where the wallmodulation exists.

4. Concluding remarks

The turbulence and mixing characteristics in adense fuel spray, which is critical to combustion,have been investigated using DNS data. Inthe dense spray zone, turbulence is generated bythe atomization dynamics, meanwhile droplets/ligaments modulate the small-scale turbulence

Fig. 6. Increased energy dissipation (m2 s�3) arounddroplets.

J. Shinjo et al. / Proceedings of the Combustion Institute 35 (2015) 1595–1602 1601

characteristics, hence mixing. In most of the gas-phase regions except for near-surface regions, thealignments of the vorticity and scalar gradient with

Fig. 8. Close-up view of the instantaneous flow field. (a) Energydissipation Dz;iz;i (s�1).

(a)Fig. 7. PDFs of the alignment angles between the principal sVorticity (b) scalar gradient.

the principal strain rate eigenvectors show similartrends to those of isotropic turbulence. This indi-cates the turbulent energy cascade from large scalesto small scales. The observed small discrepancies ofthe alignments between the dense fuel spray andisotropic turbulence are due to the increased gas-phase energy dissipation by the existence of drop-lets, which is a characteristic of particle-laden tur-bulent flows. In regions close to droplets, thealignments are different due to increased localenergy dissipation by droplets, which affects thelocal small-scale fuel/air mixing. The effects offinite-size droplets, namely wake formation, vortexshedding and near-wall gradients generation, onturbulence and mixing in a realistic dense fuel sprayhave been investigated for the first time. Animproved understanding of the droplet/ligamenteffects on turbulence and scalar mixing in the densespray region is essential to properly model spraydynamics and combustion, and these effects shouldbe taken into account in such a model.

dissipation e (m2 s�3); (b) enstrophy xixi (s�2); (c) scalar

(b)train rates and (a) xi, (b) z;i in near-droplet regions. (a)

Fig. 9. Joint PDFs in (a–c) the far-surface region and (d–f) the near-surface region.

1602 J. Shinjo et al. / Proceedings of the Combustion Institute 35 (2015) 1595–1602

Acknowledgments

The first author is grateful to Dr. H. Abe fordiscussions. Financial support from the Engineer-ing and Physical Sciences Research Council(EPSRC) of the United Kingdom under the GrantNo. EP/L000199/1 is gratefully acknowledged.

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