Experimental study of the flow regimes resulting from the impactof an intermittent gasoline spray

M.R.O. Panao, A.L.N. Moreira

Abstract The present paper reports a complete set ofmeasurements made with a two-component phaseDoppler anemometer of the two-phase flow generated atthe impact of a transient gasoline spray onto a flatsurface. The spray is generated by a pintle injector andthe fuel used was gasoline. The measurements of dropletsize–velocity were processed to provide time fluxes ofnumber, mass, normal momentum, and energy of thepoly-dispersion of droplets ejected at impact, and ana-lyzed based on predictive tools available in the litera-ture. The results show that splash is the dominantmechanism by which secondary droplets are ejectedfrom the surface, either in the stagnation region or inthe core region of the spray. In the stagnation region, alarge fraction of each incident droplet adheres to thesurface and the axial incident momentum contributeswith a larger parcel than tangential momentum. As aresult, the normal velocity of ejected droplets is muchsmaller than that of the original incident droplets, whiletangential velocity is enhanced. The region near thestagnation point is immediately flooded upon impact ofthe leading front of the spray, forming a liquid film thatis forced to move radially outwards as droplets continueto impinge during the steady period. Spray/wall inter-action in the core region thus occurs in the presence ofa moving thin liquid film, which enhances transfer oftangential momentum. As a result, film spreading anddynamics as a result of impingement forces are crucialto accurate model spray/wall interaction. The outerregion of the spray is dominated by the vortical struc-ture induced by shear forces, which entrains smallresponsive secondary droplets to re-impinge. Further-more, prediction of the outcome of spray impactrequires a precise knowledge of the two-phase flow inthe presence of the target.

1IntroductionWhen a spray impacts on a solid surface, differentphenomena can occur depending on the kinetic energyand angle of impact of individual droplets, liquidproperties and nature of the surface. Droplets canadhere to the target surface and the resulting liquid filmwill deform periodically until all the energy at impact isdissipated, eventually causing radial instabilities that cangrow and disrupt to give rise to secondary smallerdroplets, which detach from the surface. Re-atomizationcan also occur as a result of other mechanisms such asrebound or film stripping. A basic picture of theimpingement process is usually constructed based onsingle droplet impingement, either on dry or wettedsurfaces (see Mundo et al. 1995, 1998; Yarin and Weiss1995; Cossali et al. 1997; Lee and Hanratty 1988; Stowand Hadfield 1981; Cossali et al. 1999; Rioboo et al.2000, 2001; and Sikalo et al. 2002). However, in a poly-disperse spray, different phenomena occur simulta-neously because of the impact of multiple droplet sizes,which interact in a complex manner and the spraycannot be described as a summation over the entiredroplet size range, as shown by Roisman et al. (1999)and Tropea and Roisman (2000). In addition, when thespray is intermittent and the interposed surface is cold,the dynamic behavior of the re-atomized droplets alsodepend on the transient formation of a liquid film, localtemporal variations of its height and velocity associatedwith multiple drop impact, interaction between crownsof splashing drops and tiny bubble formation, and sec-ondary airflows induced by momentum transfer betweenthe spray front and the surrounding air. These are theimportant phenomena determining features such asmixing and combustion in reciprocating and gas turbineengines, heat transfer rates in spray cooling systems, orthe quality of the surface in surface treatment applica-tions. A better knowledge of these mechanisms istherefore needed to improve the performance of prac-tical devices, but still depends on the availability ofdetailed experiments in laboratory configurations. Thisis the aim of the work reported here.

Only a few experiments are reported in the literature,which consider poly-dispersed sprays impinging ontosolid surfaces with or without a pre-existent liquid film(e.g. Brenn et al. 1995; Roisman et al. 1999; Tropea andRoisman 2000; Sivakumar and Tropea 2002; Hardalupaset al. 1992; and Panao and Moreira 2004). Hardalupaset al. (1992), for example, report measurements

Experiments in Fluids 37 (2004) 834–855

DOI 10.1007/s00348-004-0868-1

834

Received: 19 February 2004 / Accepted: 6 August 2004Published online: 2 October 2004� Springer-Verlag 2004

M.R.O. Panao, A.L.N. Moreira (&)Instituto Superior Tecnico,Department of Mechanical Engineering, Av. Rovisco Pais,1049-00 Lisbon, PortugalE-mail: moreira@dem.ist.utl.ptTel.: +351-21-8417875Fax: +351-21-8496156

performed with a single component phase Doppleranemometer (PDA) on a gasoline spray striking a flatdisc at several inclinations. Analysis includes timevariations of mean droplet size, velocity and net flux atthe impact region for different size classes. Primary andsecondary (or re-atomized) droplets were discriminatedbased on the direction of the velocity componentperpendicular to the surface. Analysis showed thatprimary droplets include droplets that after impact arere-entrained into the spray by the secondary airflowinduced by momentum transfer between the spray frontand the surrounding quiescent air. Despite the detailedinformation, the authors do not relate the secondarydroplets with the mechanisms from which they weregenerated. However, it is known that the transient nat-ure of the spray is an additional difficulty in such ananalysis (Mundo et al. 1998) and therefore further studyof the effect of unsteadiness in the outcome of multipledrop impact is required.

The work reported here contributes to this area. Theexperiment consists of a multi-point injector sprayinggasoline onto a flat disc located at 30 mm. The transientnature of the spray is associated with pressure fluctua-tions inside the fuel line (Zhao et al. 1996), whichgenerate periodic velocity fluctuations during the injec-tion period.

Moreover, in a spark ignition engine with multi-pointinjection, the fuel spray impacts onto the surface of theintake port and valves. In cold start conditions, thevaporization time is larger or, at least, of the same orderof magnitude as the time between successive injectionsand therefore a liquid film forms at the surface, whichaffects the outcome of droplet impact. The experimentsreported here were performed at ambient temperature toreproduce the phenomena occurring in cold start con-ditions.

Measurements were made with a two-component PDAsystem in the near-wall region and are reported to provideinformation to deepen the knowledge of the impingementmechanisms and their relation with the unsteadiness of theimpinging spray. Analysis is based on predictive toolsavailable in the literature, which are described in the fol-lowing sections.

2Experimental arrangement

2.1Experimental set up, measurement technique,and experimental procedureThe experimental setup consists of a pintle-type port fuelinjector (PFI) directed perpendicularly to an impingingdisc made of aluminum with a mean roughness of 0.4 lmand 36 mm in diameter. The injector pintle diameter is0.79 mm and is inserted in a cylindrical hole of 0.9 mmdiameter (D) to produce a hollow-cone spray with interiorand exterior angles of 8� and 19�, respectively. The fluidused is gasoline with a density of 749.6 kg/m3, a viscosityof 4.2612·10–4 kg/mÆs, a refractive index of 1.44, and asurface tension of 19.4 mN/m.

The opening and closing of the injector pintle is con-trolled by a transistor–transistor logic (TTL) pulse gen-erated by a NI5411 function generator computer board(National Instruments Corporation, Texas, USA) and theinjection pressure is manually controlled by a regulationvalve. The information on droplet size and velocity char-acteristics was obtained with a Dantec two-componentPDA system (Dantec Dynamics, Skovlunde, Denmark)synchronized with the injection system as shown in Fig. 1.Data were processed with the co-variance processorDantec 58N10. The optical parameters of the PDA system,as well as the main validation parameters in data pro-cessing are summarized in the Table 1. Each measurementcorresponds to more than 50,000 validated droplets toassure a minimum of 100 validated measurements withinthe time window considered for phase calculations. Thisresults in deviations from the cumulative size distributionbelow 13% (Tate 1982) and uncertainties less than 10% influx calculations (Saffman 1987). Droplet fluxes are cal-culated from droplet size and velocity measurements and,therefore, further errors may be induced as a result of thelack of the third velocity component, W (Roisman andTropea 2001). However, assuming that the transversevelocity component W is of the same order of magnitudeas the radial component V, these errors are estimated to besmaller than 5% for the experimental conditions reportedhere.

Fig. 1. Synchronization between the fuelinjection system and the PDA acquisitionsystem

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Gasoline is injected in a series of seven injections tosimulate conditions occurring in a multi-point injectionengine at cold start. A time delay of 10 s is set betweenseries to avoid the excess of fuel on the surface. For thecharacterization of the spray in the absence of the targetwall (referred to as the ‘‘free spray’’ from hereon) theinjection cycles were continuous. The start of injectioncorresponds to the instant when the injector receives theTTL pulse. However, because of the electromechanicalcommand of the pintle, a time delay is expected betweensignal arrival and the fuel discharge. This delay was esti-mated to be 1.6 ms at pintle opening and around 1.3 ms atclosing, independent of pressure. Nevertheless, the in-stants considered in the analysis refer to the TTL signalarrival at the Dantec covariance processor. The injectionpressure was set at 3 bar, the injection duration at 5 ms,the injection frequency at 10 Hz, and the average liquidvolume injected at this pressure was 12.5 mg/injection.

Measurements were made traversing the PDA controlvolume at a distance of 2 mm from the wall, which is theclosest distance at which the control volume could be lo-cated without blockage of the laser beams in the planeperpendicular to the wall. Measurements were made in acylindrical coordinate as shown in Fig. 2, where the radial(r) and axial coordinates (z) are normalized by thediameter of the nozzle of the injector (D = 0.9 mm).The origin of the radial coordinate is taken at the axis ofthe injector and the measurements were made at r/D2{)5,)1, )0.5, 0, 0.5, 1, 2, 3, 4, 5, 6, 8, 10, 12}/D. Figure 2 furtherillustrates the location of the reported measurement pointsin relation to the hollow-cone structure of the spray.

The axial velocity U corresponds to the velocity com-ponent perpendicular to the target surface and becomespositive when directed towards the target surface. Thetraverse velocity V corresponds to the velocity componentparallel to the wall and becomes positive in the positivedirection of the radial coordinate. Henceforth, primarydroplets refer to impinging droplets and therefore thosemoving toward the wall (positive U) while secondary

droplets refer to those moving away from the wall (nega-tive U).

3Data processingThe droplet size distribution is characterized by thearithmetic and the Sauter mean diameters (AMD and SMDrespectively), defined in Lefebvre (1989) as:

SMD ¼

PNsv

i¼1

d3i

PNsv

i¼1

d2i

; AMD ¼

PNsv

i¼1

di

Nsvð1Þ

where Nsv is the number of validated signal measurements.Deviations from the cumulative drop size distributiondepend on the sample size used to calculate the meandiameters and were estimated according to the analysis ofTate (1982): % deviation = 127.32ÆN)0.492, N being thesample size considered for the calculation of the meandiameter.

The PDA allows estimation of the local volume flux ofdroplets from direct measurements of droplet velocity andsize. However, despite each highly accurate validatedmeasurement of droplet velocity and size, the effectivecross-section of the measurement volume is both droplet-size and trajectory dependent, which may lead to mea-surements of the local flux being less accurate. In addition,the number of droplets detected and validated by theprocessor is sensitive to a number of parameters such aslow signal-to-noise ratio (SNR), obscuration of the trans-mitting laser beams or of the light dispersed by particlescrossing the control volume, the presence of multipledroplets in the detection volume, and other factors.

The software of the Dantec processor uses an algorithmto account for the effective cross-section of the measuringvolume. However, this software does not allow the calcu-lation of the volume fluxes from encoded measurements inthe application for rotary machines and, therefore,

Table 1. Optical parameters

Transmitting optics Value

Laser power 300 mWWavelengths 514.5 nm (green)

and 488 nm (blue)Beam diameter 1.35 mmBeam spacing 60 mmNominal measurementvolume diameter

243 lm

Focal length 500 mmReceiving optics ValueScattering angle 30� (first order

refraction mode)Receiver focal length 500 mmMasking device ClassicProcessor parameters ValueMaximum diameter 203 lmU bandwidth 36 MHzV bandwidth 12 MHzS/N validation 0 dBSpherical validation 10% Fig. 2. Relative location of the measurement points reported

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post-processing was required. For that we consider thealgorithm developed by Roisman and Tropea (2001):

_Q ¼ 1

Dt

XNsv

i¼1

qi � cos cið ÞAc dk; ckð Þ ð2Þ

ci ¼ a tanVi

Ui

� �

ð3Þ

where qi is the flux of droplets of size di, Dt is the mea-surement time, Nsv is the number of validated signals, dk

and ck are the diameter and direction of a certain size classand Ac is the reference area of each droplet crossing thedetection volume, which was determined for different sizeclasses with a 2 lm size bin. Accounting for the effect ofmultiple scattering, as in the original algorithm ofRoisman and Tropea (2001), would require knowledge ofthe transit time of non-validated droplets, which cannotnot be measured because it is not possible to discriminatebetween individual droplets in a non-validated signal.However, if each non-validated measurement is assumedto be associated with a single particle crossing the controlvolume, the effect is an underestimation of the flux around20%. Because the results reported here refer to the ratio offluxes between impinging and secondary droplets, the netinaccuracy induced by the unaccounted effect may be evensmaller.

Furthermore, the evaluation of higher order fluxes isimportant for the development and validation of physicalmodels to describe spray/wall interaction. Equation 2 isused for that purpose, where qi may be the number, mass,axial momentum or kinetic energy flux, as described inTropea and Roisman (2000) (see Table 2).

4Transition criteria for drop impact and correlationsfor deposition/splashThe outcome of droplet impingement is described by re-gimes, whose onset depends on the relative magnitude ofthe several forces acting upon the surface of the droplet,on the microscopic and macroscopic geometry of thetarget surface, and on the thermodynamic properties ofthe droplet–surface–surroundings system. Among thepossible mechanisms of droplet–wall interaction, the fol-lowing are considered by Bai et al. (2002) as illustrated inFig. 3:

– Stick: the droplet sticks to the wall in a nearly sphericalform;

– Rebound: the droplet bounces off the surface afterimpact;

– Spread: the droplet adheres to the surface and forms aliquid film on the wall, which spreads out periodicallyuntil all the energy is dissipated;

– Splash: as the liquid film spreads out, a crown is formedowing to the kinematic discontinuity (Yarin and Weiss1995) and lateral cusps emerge, which become unstableand eventually break up into smaller fragments.

Models for predicting which regime occurs areempirical and make use of dimensionless numberscharacterizing the relative magnitude of the forces actingupon the droplet. Estimations of these dimensionlessnumbers are, in turn, obtained by scaling the forces(surface tension, shear, and gravity) with physical prop-erties of the liquid (density, viscosity, and surface ten-sion), and considering all lengths and velocitiesproportional to the diameter and velocity at the instantof impact, respectively. Examples are the Reynoldsnumber (Re = Ud/m), Weber number (We = qU2d/r),Ohnesorge number (Oh = We0.5/Re) and Laplace number(La = Re2/We). Re is proportional to the ratio betweeninertial and viscous forces, We to the ratio betweeninertia and surface tension forces, Oh to theratio between capillary and viscous forces, and La to theratio between surface tension and viscous forces. Existingmodels do not consider the influence of the nature of thetarget surface as described by Moita and Moreira (2002)but more recently they include the influence of apre-existing liquid film. Table 3 summarizes the maincriteria for transition regimes found in the literature,where d is the ratio between the film thickness and theinitial drop diameter (hf/di).

Despite the criteria in Table 3 being formulateddifferently, they can be all formulated in terms of aparameter K, which assumes a critical value Kc at eachtransition. In general, this value can be expressed in termsof the Ohnesorge and Reynolds numbers as in Mundoet al. (1995), except for the criteria of Yarin and Weiss(1995). Thus, all transition criteria can be represented in aplot of Oh versus Re, as depicted in Fig. 4.

The transition between spread and splash is representedas a region instead of a solid line because this mechanismbehaves differently when the surface is either dry or wet.

Table 2. Different expression for the arbitrary quantity qi

qi Expression

Number flux qi=1Mass flux qi ¼ qpd3

i

6

Moment fluxin the axial direction

qi ¼ qpd3i uxi

6

Kinetic energy flux qi ¼ qp12 d3

i u2xi þ 2u2

yi

� �

Fig. 3. Outcome of single drop impacting on a solid surface

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When the surface is wet, the dissipation of kinetic energyduring the deformation is increased (Marengo 1996) and,therefore, Kc is larger. The model of Bai et al. (2002) as-sumes that a wet surface behaves as a rough wall.

The criteria proposed by Wang et al. (2002) wereobtained from systematic experiments made with singledroplets impinging onto wetted surfaces with several filmthickness and the transition spread–splash was expressedby a critical Weber number Wec. The authors identifiedfour regions: Wec has a minimum value for d £ 0.1; itincreases monotonically for 0.1 < d £ 1; it decreases for1 < d £ 3; and it reaches a constant value for d > 3. Thelines in Fig. 4 show that the criteria of Wang et al. (2002)extends the occurrence of splash for lower values of Ohand Re.

Figure 4 will be later used in the analysis of theexperimental results to predict the behavior of droplets atimpact. However, care is taken to compare the presentexperimental conditions with those for which the modelswere developed. This is done based on visualization of theflow in the vicinity of the wall, as reported in Panao andMoreira (2004).

Visualization of the spray confirmed the formation of aliquid film on the target surface with an average thicknessaround 200 lm. Transient impact of the spray onto theliquid film gives rise to waves with crests below 500 lm.Therefore, for the measurements reported here, the PDAmeasurement volume was not disturbed. Considering thatthe drop size distribution at impact extends from 10 to160 lm, as measured with the PDA system, the dimen-

Table 3. Transition criteria obtained from single drop impact

Authors Experimental conditions Model

60<d0<150 lm12<U0<18 m/s

Mundo et al. (1995, 1998) 4�<a<65� (imping. angle) K=OhÆRe1.25

1<l<2.9 (10)3 kg/m/s) K=57.7 (deposition to splash)22<r<72 mN/m70<d0<340 lmU0 £ 30 m/s Splashing at �=rm1/2f3/2 (q U0

4))1>1Yarin and Weiss (1995) Ra�1 or 16 lm (average roughness) When � £ 18)4

hf={min: 20, max: 50} lm(liquid film thickness)

and f is the impact frequency

0 £ d £ 0.3Cossali et al. (1997) 0.0022 £ Oh £ 0.141 KL=(Oh)0.4 We)L=2,100+5,880d1.44

Ra=0.14 lm Valid for 0.1<d=hf/D0<1 and Oh>7·10)3

Bai et al. (2002) DryAdhesion(stick/spread) fi splash wetted Wec�2,630ÆLa)0.183

Stick fi rebound Wec�2Rebound fi spread Wec�20Spread fi splash Wec�1,320ÆLa)0.183

for d £ 0.1, Wec=450Wang et al. (2002)a Spread to splash for 0.1<d £ 1, Wec=1,375.7d+340

for d>1,Wec=1,043.8+232.6d)1)1,094.4d)2+1,576.4d)3

aThe curves were obtained empirically by the authors by fitting the experimental results of Wang et al.

Fig. 4. Transition regimesaccording to several models ofdrop impact

838

sionless film thickness d varies between 1.25 and 20. Thisvalue is above the maximum limit at which the correlationof Cossali et al. (1997) for thin liquid films is valid(0.1 < d < 1). Therefore, the splashing threshold proposedby Wang et al. (2002) seems to be more appropriate todescribe the flow studied here.

Moreover, the presence of a liquid film prior to dropletimpact may cause bubble formation and entrapment asshown in Fig. 5, which also affects the outcome of dropletimpact. In this context, liquid films may behave as shallowor deep, depending on the magnitude of the crown radiusrelatively to the thickness of the liquid film. Macklin andMetaxas (1976) addressed the limits between deep andshallow splash based on droplets impacting onto liquidlayers with dimensionless thickness 0.2 < d < 25 and forimpact drop energies Ed between 200 and 1,000 erg.

Ed ¼Es

12Weþ Boþ 12ð Þ ð4Þ

where Es is the droplet surface tension energy (Es = pÆd2Ær)and Bo is the Bond number defined as the ratio betweengavitational and surface tension forces (Bo = qÆcÆd2/r).

The authors report that the ratio between film thicknessand crown radius varies with the impact energy, but al-ways increases with d. For example, a droplet with impactenergy equal to 200 erg has deep liquid splashing ford > 2.5 and shallow splashing for d < 1.0. The onset ofsplash occurs at smaller values of d, as the initial dropenergy decreases for both deep and shallow splash. Thismeans that deep liquid splashing may occur for small dvalues if the initial drop energy is also small (<200 erg).

In the present work, the initial drop energy was eval-uated for each droplet and all values were below 5 erg,suggesting that deep liquid splashing is more likely tooccur than shallow liquid splashing. This would explainthe bubble entrapment observed in the visualization,which is characteristic of this mechanism of splashing asreferred by Weiss and Yarin (1999), who report encapsu-lation of tiny bubbles within the film caused by jettingfrom drop impact.

5Results and discussionThe experimental results are presented and discussed inthis section under two headings: the first considers thetime average spray. Measurements in the free spray (FS)

are compared with those at corresponding coordinates inthe spray impacting onto the disc (SI) so the effects of thetarget surface on the fluid-dynamic behavior of the poly-dispersion can be evaluated. In the second subsection, thetransient nature of the spray is accounted for in predictingthe outcome of impinging drops. The analysis includes thefluxes of number, mass, axial momentum, and kineticenergy of impact droplets within the period of injection,and emphasizes the performance of existing physicalmodels to describe droplet/wall interaction in non-sta-tionary poly-dispersions.

5.1Time average characteristics of the free sprayand of the spray impacting onto the discFigure 6 shows the probability distributions of diameter,axial, and transverse velocity as measured by the PDA atfour radial locations, r/D = 0, 2.2, 5.6 and 11.1 without andwith interposition of the target. It is worth mentioning atthis point that the relative number used in the PDFs doesnot allow comparison of the absolute number of dropletsmeasured in both cases. However, measurement of abso-lute values (e.g., droplets per injection) is strongly sensi-tive to the validation ratio, which decreases drastically inthe region of large concentration of droplets with randomtrajectories in the vicinity of the wall. Therefore, all rea-soning has to be based on probability distributions. In thiscase, the accuracy is assured by the independence of thePDF on the size of the sample.

A peak around zero velocity is observed in the freespray in both velocity components, which becomes shar-per in the impinging spray, as in Hardalupas et al. (1992),who argued that it was the result of re-atomization at thewall. Although this may also be in part true for the presentflow, the fact that the peak also exists in the absence of thedisc, suggests it is due to the airflow induced betweeninjection cycles. This peak sharpens in the presence of thedisc as a result of the entrainment of small droplets by thevortical structure induced by the wall.

Interposition of the surface spreads the size distribu-tion towards larger diameters. It may be speculated thatthe secondary airflow induced by shear forces exerted bythe spray front upon the surrounding air may havechanged when the surface is interposed, thus deviating thetrajectory of smaller responsive droplets from their origi-nal path. This would explain the observed variation in theshape of the size distribution around the centerline. Themajor effect of the impinging surface on the velocity dis-tribution is observed in the axial component, for whichdroplets with a negative value appear as the result of there-atomization of the primary droplet upon impact,namely at r/D = 11.1.

The effects of impact on the fluid-dynamic character-istics of the spray issuing from the injector may also bequantified in the joint probability density functions (JPDF)of size-axial velocity, as shown in Fig. 7. Gray levels in theplots represent the probability of a droplet with size di tocross the measuring location with an instantaneousvelocity Ui.

The joint distributions have a bimodal shape in the freespray: at r/D = 0 one peak corresponds to large droplets

Fig. 5. Bubble formation on the liquid film839

Fig. 6. Histograms of droplet size, axial and transverse velocity components for radial locations at r/D = 0, 2.2, 5.6 and 11.1 for: a freespray; b impinging spray

840

Fig. 7. Joint PDF of droplet size and axial velocity for FS and SID

841

(center at around 40 lm) moving with large axial velocity(center at around 17 m/s); another peak corresponds tosmall droplets (�17 lm) moving with almost null axialvelocity (�2.5 m/s). One may recall that Fig. 7 includes alldroplets crossing the measurement volume during theentire period of injection. Therefore, the first peak corre-sponds to droplets flying downwards directly from thenozzle of the injector during most of the injection, whilethe second peak corresponds to small droplets entrainedinto the ring vortex induced by shear stresses at the edgeof the spray and which remained suspended at the end ofinjection. As the measuring volume is traversed outwardsit changes its relative location within the spray core, aswell as within the ring vortex. The location at r/D = 11.1corresponds to a point outside the spray as shown inFig. 2.

Figures 6 and 7 further show that the interposition ofthe disc alters the behavior of the spray: around the cen-terline (r/D < 3.3), droplets issuing from the nozzle of theinjector have a larger mean axial velocity than in the freespray, suggesting that the wall induced an average decreaseof the nominal angle of the spray. Small droplets with verysmall axial velocities are now associated with secondarydroplets generated at the wall owing to splash or/and re-bound. Some of them are entrained by the vortex formedat the wall and re-impinge with small positive velocity, asreported in Panao and Moreira (2004) and schematicallydepicted in Fig. 8.

The above analysis shows that the interposition of thedisc gives rise to re-atomization of impinging droplets butalso alters the structure of the primary spray issuing fromthe nozzle. Together with Fig. 8, it further shows that asignificant part of secondary droplets generated at the wallare entrained by large-scale structures and re-impinge,which also alters the distribution of primary droplets.Therefore, the outcome of droplets after impact cannot beaccurately predicted based on the characteristics of thespray, but requires precise knowledge of the flow structureinduced by the target. The relative magnitude between thetwo effects may vary during the period of injection because

of the transient nature of the spray. This is addressed inthe following section.

5.2The transient behavior of free spray and of the sprayimpacting onto the discThe transient behavior is first characterized based on thetemporal variations of the AMD and SMD. These areshown in Fig. 9 for the FS and SI cases at r/D = 0 and r/D = 5.6, respectively. Primary droplets of the impactingspray are represented with downward facing symbols,while secondary droplets are represented with upwardfacing symbols. The results show three periods duringinjection: (i) a short period corresponding to the leadingfront of the spray, which lasts up to 4 ms ASOI (after startof injection). It is associated with the sudden expansion ofthe liquid after pintle opening and is characterized by asudden decrease of the size of primary droplets and asimultaneous increase of the size of secondary droplets;(ii) a second period, which is associated with a steadybehavior of droplet size lasting up to 7 ms ASOI; (iii) a lastperiod corresponding to the tail of the spray, which isassociated with pintle closing and which lasts up to dis-appearance of all droplets. Henceforth, these three periodsare identified in the figures as I, II and III, respectively.

Closer examination of Fig. 9 shows that during thesteady period of injection (5 ms < t < 7 ms), the inter-position of the disc increases the AMD of primary drop-lets, but decreases the SMD. This result first suggests thatthe disc diverts small droplets from the axis of the spray toouter locations. Second, if one recalls that the differencebetween the SMD and AMD increases with the poly-dis-persion of a spray, that result also suggests that theinterposition of the disc decreases the poly-dispersion ofthe spray at the axis. After the end of injection (EOI),t > 9 ms, only suspended droplets are still crossing thedetection volume until the start of a new injection.

The effect of the target on the transient behavior ofimpact and the resulting outcome is further analyzedbased on the joint distributions of [U, d] and [U, V] shownin Figs. 10 and 11 for the free spray and for the impactspray, respectively. The distributions are depicted alongthe impact region and for the three periods during injec-tion, namely within time windows of 0.5 ms centered att = 3.25, 5.75, 8.25 and 10.75 ms ASOI. The arrows in thescatter diagram of [U,V] depicted in Fig. 11a identify thedirection of droplet trajectories. The results for the freespray (Fig. 10) show the expected features of a pulsedspray issuing into quiescent surroundings.

In general, the distributions for the impact spray(Fig. 11) show a large populated group of droplets with alarge positive axial velocity component, which may beidentified with primary droplets moving towards the disc.Another group with negative axial velocity identifiesdroplets moving away from the surface because ofre-atomization, splash or rebound. In addition, a lesspopulated group is always seen from the earliest stage ofinjection, which contains droplets with nearly zero axialand radial velocities. These may be associated with drop-lets re-impacting after having bounced from the wall, as

Fig. 8. Visualization of the wall vortice with schematic of dropletentrainment and re-impingement

842

Fig. 9. Temporal evolution of droplets mean diameter at r/D2{0, 2.2, 4.4, 5.6}

843

844

also observed by Li et al. (1994) in a stagnation flow. Thisgroup increases during injection.

Closer examination shows that the structure of sprayimpact can be divided into three regions: (i) the centralregion around the stagnation point (r/D < 2.2); (ii) the coreregion of high droplet concentration (2.2 < r/D < 5.6)where interaction between droplets may be dominant; and(iii) the outer region (r/D > 5.6) where the two-phase flowis dominated by convective effects induced by the sec-ondary air motion.

In the vicinity of the spray axis (r/D = 0 and r/D = 2.2)the scatter diagrams of [U,V] are mostly symmetrical,denoting that droplets impact mostly perpendicularly tothe surface. Secondary droplets move away from the sur-face with random trajectories, which are expected to beassociated with the mechanism of splash. The mechanismsof droplet–wall interaction and the resulting outcome maybe predicted based on the Oh–Re transition models de-scribed before. The Oh and Re numbers were computed intime bins of 500 ls for all droplets crossing the PDA probevolume with downward velocity and the results plotted inFig. 12a–e without and with impact for the leading front ofthe spray (t = 4 ms ASOI); the steady state (t =7 ms ASOI)and the tail of the spray (t = 10 ms ASOI). Because thesample size was kept the same in both experiments, plotsfor the impacting spray include less measurement pointsthan the corresponding plots for the free spray. The dif-ference is the number of secondary droplets.

Fig. 10. (Contd.)

Fig. 10a–e. a Scatter diagrams along time for the free spray atr/D = 0. b Scatter diagrams along time for the free sprayat r/D = 2.2. c Scatter diagrams along time for the free spray atr/D = 4.4. d Scatter diagrams along time for the free spray at r/D = 5.6. e Scatter diagrams along time for the free spray atr/D = 11.1

b

845

846

Accordingly for the transition models considered here,the figures show that splash is expected to be the dominantmechanism by which secondary droplets are ejected in thestagnation region. The scatter diagrams of [U,V] show thatsecondary droplets at the spray axis were ejected within acone with an average half angle around 45� and, therefore,much smaller than considered by Bai and Gosman (1995)for droplet splash onto a dry surface. Discrepancies maybe attributed to the liquid film formed during injection,which alters the mechanism of splash from break-up of the

expanding lamella at early stages, to break-up of the crownwall at later stages, as reported by Wang et al. (2002).However, the average measured angle of the ejecteddroplets is still smaller than reported by Mundo et al.(1998) for splash promoted by disintegration of a corona,even at a smooth surface. In their experiments, the angle ofthe ejected droplets was observed to vary with the incidentangle according to aEJECTED = 0.3 aINC+61�.

The scatter diagrams of [U,V] at the stagnation region(r/D = 0 and r/D = 2.2) further shows that droplets are onaverage ejected with transverse velocities far exceedingthose of primary droplets, but with smaller normalvelocities. Similar observations have been reported byMundo et al. (1998), who argued that the normalmomentum of the incident droplets is partially transferredinto tangential momentum. In the present work, the sameresult is attributed to the fact that each incident dropletthat gives rise to splash, breaks up at the surface and leaves

Fig. 11. (Contd.)

Fig. 11. a Scatter diagrams along time for the impacting spray atr/D=0. b Scatter diagrams along time for the impacting spray at r/D=2.2. c Scatter diagrams along time for the impacting spray atr/D=4.4. d Scatter diagrams along time for the impacting sprayat r/D=5.6. e Scatter diagrams along time for the impacting sprayat r/D=11.1

b

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there a fraction of its mass at the same time that part of itsmomentum is transferred to the liquid film. A compre-hensive explanation may be given based on simple argu-

ments considering conservation of mass and momentum,as follows. Mass conservation equation for an impingingdroplet can be written as:

Fig. 12. a Prediction of the outcome of spray impact during time tASOI at r/D = 0. b Prediction of the outcome of spray impactduring time t ASOI at r/D = 2.2. c Prediction of the outcome ofspray impact during time t ASOI at r/D = 4.4. d Prediction of the

outcome of spray impact during time t ASOI at r/D = 5.6.e Prediction of the outcome of spray impact during time t ASOI atr/D = 11.1

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M ¼XNSPL

i¼1

mi þmLF ð5Þ

where M is the mass of the impacting droplet, mi is themass of each of the NSPL droplets and mLF is the contri-bution to the formation of the liquid film. This may beexpressed as a fraction aM of the impacting droplet, i.e.,

mLF = aMM. Conservation of transverse momentum iswritten as:

MV ¼XNSPL

i¼1

miVi þ qVLF ð6Þ

where Vi is the transverse velocity of each secondarydroplet and qV

LF is the parcel of momentum lost within the

Fig. 12. (Contd.)

849

liquid film, which may also be expressed as a fraction aqV

of the impacting momentum, qVLF ¼ aqV MV . Equations 5

and 6 together with the assumption that all secondarydroplets have the same size and transverse velocity, giverise to the conclusion that for Vi to be larger than V it isrequired that aqV < aM. For a value of aqV = 0.3, as con-sidered by Grover and Assanis (2001), Vi is larger than V ifmore than 30% of the mass of each impacting droplet

adheres to the surface. This value is within the correlationfollowed by Bai and Gosman (1995). Similarly, consideringthat aqV is the fraction of normal momentum lost at theimpact, for Ui < U is necessary that aqV > aM, i.e., for thegiven example, aqV > 0.3.

Therefore, the argument here is that a large fraction ofeach incident droplet adheres to the surface and that theaxial incident momentum contributes with a larger parcel

Fig. 12. (Contd.)

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for the liquid film than tangential momentum. The scatterdiagrams show that the number of secondary dropletsdetected in the vicinity of the spray axis (r/D = 0 andr/D = 2.2) becomes an increasing fraction of the incidentdroplets as the injection proceeds. This can be quantifiedby the ratio of the number flux of secondary to primary

droplets crossing the measurement point, as shown inFig. 13. The figure also includes the ratio of mass, normalmomentum and energy fluxes, as defined by Eqs. 2 and 3and Table 2. The results in the vicinity of the spray axissuggest that a large fraction of the incident mass adheresto the surface during the steady period of fuel injection

Fig. 12. (Contd.)

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and even larger fractions of normal momentum and en-ergy are transferred to the wall film.

The above described behavior of the impact observed inthe vicinity of the spray axis is altered in the core region,as droplets at outward locations impact obliquely with

increasing angles. There, secondary droplets detectedduring the initial stage left the surface with random tra-jectories but all secondary droplets detected at later peri-ods move outwards with positive radial velocity. Thisresult suggests that a different mechanism of momentum

Fig. 12. (Contd.)

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Fig. 13. a Ratios of number, mass, axial moment, and kinetic energy between each flux after impact and each flux before impact ()r/D=0; n)r/D=2.2; d)r/D=3.3). b Ratios of number, mass, axial moment, and kinetic energy between the each flux after impact andeach flux before impact (N)r/D=4.4; .)r/D=5.6;

N

)r/D=11.1)

853

transfer may occur at outward locations, which provides asource of tangential momentum for secondary droplets. Infact, impingement at those locations occurs onto a movingliquid film, instead of onto a dry surface or quasi steadyfilm. The region near the stagnation point is immediatelyflooded upon impact of the leading front of the spray,forming a liquid film which is forced to move radiallyoutwards as droplets continue to impinge during thesteady period. The magnitude of the radial velocity of thefilm then depends on the amount of liquid supplied at thecentral region and on the efficiency of momentum trans-ferred by the incident droplets. Both have been shown tobe large in the experiments reported here. Experimentalevidence of the effect of moving films on the angle ofejected droplets was only reported by Roisman and Tropea(2002), but it was taken into account by Stanton andRutland (1996) and of Lee et al. (2001), who reported in-creased performance of their models to predict momen-tum transfer.

Figure 11 also showed that the axial velocity of incidentdroplets in the core of the spray increases with dropletdiameter. The axial velocity of secondary droplets at theearliest stage of injection is not correlated with size but, asthe injection proceeds, the velocity of secondary dropletsincreases with size. Therefore, momentum and kineticenergy of secondary droplets is also expected to increaseas shown in Fig. 13 for the steady period of injection.

Away from the centerline (at r/D = 11.1), the two-phaseflow is dominated by droplets with very small velocities,which are entrained by the three-dimensional vorticalstructure induced at the wall. The more responsive drop-lets ejected in the core region are entrained by the airmotion and re-impinge onto the surface with smallReynolds and Ohnesorge numbers, thus expecting tospread onto the surface (see Fig. 12).

It is worth mentioning at this point that prediction ofthe impact outcome based on the characteristics of the freespray at the same coordinate (Fig. 12) would have over-estimated the role of the spreading mechanism. Therefore,accurate prediction of the behavior of impacting dropletsrequires a precise knowledge of the two-phase flow in thepresence of the target.

6Summary and conclusionsDetailed PDA measurements were reported of the two-phase flow generated at the impact of a transient gasolinespray onto a flat surface at ambient temperature. Themeasurements were made in the near-wall region and wereprocessed in order to provide information to deepen theknowledge of the impingement mechanisms and theirrelation with the unsteadiness of an impinging spray. Theanalysis accounts for the fluxes of number, mass, normalmomentum and energy of the poly-dispersion of dropletsejected at impact and it is based on predictive toolsavailable in the literature.

The results show that splash is the dominant mecha-nism by which secondary droplets are ejected from thesurface, either in the stagnation region or in the core re-gion of the spray. A large fraction of droplets within thestagnation region adheres to the surface. A large fraction

of their normal momentum is fed onto the film for crownformation, while transfer of tangential momentumcontributes to increase the tangential velocity of ejecteddroplets.

Impact of droplets in the stagnation region forces radialspreading of the thin film formed at the wall, which in turninteracts with droplets impinging at outer regions in theform of tangential momentum. Incorporation of spreadand dynamics of the liquid film is crucial to enhance theperformance of spray/wall interaction models.

The outer region of the spray is dominated by thevortical structure induced by shear forces at the sprayedge, which entrains small responsive secondary dropletsto re-impinge. Accurate prediction of the behavior ofimpacting droplets there requires a precise knowledge ofthe two-phase flow in the presence of the target.

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