Droplet Collision Modelling between Merging Immiscible Sprays in Direct Water Injection System

Transcription

1 ILASS Europe 00, r Annual Conference on Liqui Atomization an Spray Systems, Brno, Czech Republic, September 00 Droplet Collision Moelling beteen Merging Immiscible Sprays in Direct Water Injection System D. Tsuru, H. Tajima *, R. Ishibashi an S. Kaauchi * Interisciplinary Grauate School of Engineering Sciences Kyushu University Kasuga, Fukuoka JAPAN Engineering Mechanics Environment an Energy Department National Maritime Research Institute Mitaka, Tokyo JAPAN Abstract Droplet collision in a iesel spray has been stuie through the observations of a binary collision system ith to equivalent roplets of the same kin. Conventional CFD (Computational Flui Dynamics) coes also consier the coalescence an the separation of to same liqui roplets basically. Hoever, DWI (Direct Water Injection) system recently introuce to reuce NOx emission from marine iesels coul have consierable collisions beteen the roplets of the ifferent liqui, that is, beteen ater roplets an fuel roplets since it has a near co-axial nozzle layout an ater is normally injecte uner much loer pressure than fuel. In this stuy, a etaile collision moel for the immiscible roplets as nely evelope an implemente in a KIVA coe to simulate the merging process of the to sprays in a DWI system. Visualization of such spray merging using a stereo camera system ith to pulse N-YAG lasers emonstrate the valiity of the collision moel in general. Introuction Droplet collision in iesel sprays coul be an important phenomenon affecting the spray propagation an the roplet evaporation. Many researchers have been conucting visual investigations on ynamics of a colliing binary roplet system an classifying the collision outcomes on its Weber number an an alignment inex of the impact. In the DDM (Discrete Droplet Moel) in CFD fiels, hoever, the probability of a collision event has been a main issue in the Arbitrary Lagrangian Eulerian coorinate system, hich meiates beteen the finite volume cells fixe in a calculation omain an the roplets penetrating through them. Collision moelling for a iesel spray has been ealing ith inner-spray collisions beteen the roplets of the same kin an the collision event is regare as a siebar issue as far as iesel sprays are concerne. A fe attempts, hoever, have been recently introuce, hich utilize inter-spray collisions to promote the rop breakup or to promote the roplet entrainment of the liqui ifferent from iesel fuel. DWI system, for example, introuce to reuce NOx emission from meium-spee marine iesels coul have consierable collisions beteen to separately injecte sprays of fuel an ater. A DWI system of to-neele type injectors is surely the case since it has a near co-axial nozzle-hole layout an it usually injects ater uner the pressure much loer than the one for fuel injection. R. -H. Chen an C. -T. Chen [] shoe the collision beteen ater an fuel roplets as totally ifferent from the binary collision of ientical roplets. This coul explain hy conventional CFD coes have not been very successful in simulating such DWI spray propagation. In vie of this situation, the criteria of the collision outcomes beteen immiscible roplets shoul be theoretically erive an objectively examine to simulate the spray propagation of the DWI system. Moreover, its preiction results shoul be verifie by some actual observation of the to merging sprays in a DWI system. These are the main purposes of this stuy. Droplet collision theories an moeling In general, outcomes of the binary roplet collision are categorize by three non-imensional parameters, that is, Weber number: We, impact parameter: χ, an roplet iameter ratio:. The impact parameter is efine as a imensionless istance beteen the relative velocity vectors place on the centres of to roplets. The average iameter of the to roplets is use for its normalization. Collision moes can be expresse from frontal collision at χ0 to just grazing one at χ. In the case of immiscible roplet collision, We an shoul be reefine as shon in Nomenclature. The outcomes of roplet collision are categorize as bounce, coalescence, stretching separation, an reflexive separation as Qian et al [] shoe in Figure (a). Accoring to Chen et al. [], these categories are still vali in the outcomes of roplet collision beteen fuel an ater roplets, but the * Corresponing author: tasima@ence.kyushu-u.ac.jp

2 ILASS Europe 00 criteria iviing these outcomes greatly change as shon in the lines of I, II or III in Figure (b). For example, the criterion beteen coalescence an reflexive separation emerges at larger We an the coalescence region oes not exist over We 65 an so on. Most striking feature in the oil-ater collision system is that merge roplets ere observe to have concentric structure as a result of the coalescence an the reflexive separation. In these cases, iesel fuel spreas over the surface of a ater roplet an covers it completely an the consequent roplet ill consist of a ater core insie an a fuel shell outsie. The reflexive separation prouces to smaller such concentric roplets after temporal roplet coalescence. In the stretching separation, the resulting roplets after separation are thought to be a pair of a pure fuel roplet an a ater roplet. Moelling of the spray propagation in DWI systems shoul preict the above-mentione collision outcomes, momentum exchange, breakup behaviour, an evaporation process. Firstly, the former to ere theoretically erive keeping the compatibility ith the experimental results in Figure (b), but the etail of the elicitation process has to be spare here because of the limitation of space. Definitions an terminology coul be referre in the Nomenclature. It is orth mentioning that only criterion II is consiere in O Rourke collision moel, hich is stanar in KIVA coe, so that coalescence an stretching separation are the only outcomes that numerically happen an neglect of bounce moe sometimes allos abnormal roplet groth aroun spray tip. Moreover, the ifference beteen bounce an coalescence coul be crucial in the case of oil-ater collision since the latter generates aforementione concentric roplets. For simplicity, hoever, further collisions among such concentric spheres, pure oil roplets an pure ater roplets ere not consiere in this stuy. Impact parameter:χ - 0. Coalescence (a) (a) Oil roplets binary collision.0 Tetraecane (C 4 H 0 ) Bounce Stretching separation Coalescence (b) ater-ater 4Reflexive separation Weber number: We - Impact parameter:χ - (b) Oil-Water roplets binary collision III Weber number: We - I II Figure. Criteria among collision outcomes on the experiments by Qian et al [] (a) an Chen et al. [] (b) The criterion I etermines the critical conition of the bounce outcome. An approach similar to TAB moel as nely employe to preict the maximum eformation of an oil roplet, hich as essentially given as a solution of its ampe free oscillation after the impact. An oil roplet as alays assume to eform or stretch because of its smaller surface tension about one-thir of ater s. Critical Weber number as then obtaine on the conition that the elongate axis of the oil roplet equals the semiperimeter of the paire ater roplet, so that it can cover the ater roplet thoroughly. The effect of a gas film beteen the to colliing roplets is not consiere here. The elicitation for the criterion I results in the expression (). We crit_i c c C F χ π cdν π + exp r ω ω σ µ here, () ρ r ρ r The criterion II etermines the loer limit of the stretching separation, hich happens in the range of Weber number above We crit_i (, χ) an also in the range of χ large enough to make the collision more grazing rather than frontal. Accoring to the Chen s experiments, stretching separation in DWI system shoul be characterise by an oil column beteen the to roplets, hich extens from an oil roplet, briges the ater roplet temporally, an retracts into the oil rop again leaving tiny satellite roplets. This criterion has been normally erive from the energy balance beteen initial kinetic energy of the roplets an total surface energies of the to spherical roplets an of the column []. It is also the oil roplet that acts as a source of kinetic energy of stretching an the briging. Assuming to-thir of an oil roplet transforms to the briging column an the interfacial surface tension beteen oil shell an ater core can be calculate by Fokes equation, a folloing equation for

3 ILASS Europe 00 the critical Weber number as finally reache ith interaction volume parameter φ an φ meaning ho much volume of each roplet is truly effective in the relevant collision. The equation () belo remains general expression although it shoul be concretely classifie into one by one accoring to the roplet size ratio an impact parameter χ. This criterion as set to be superior to the criterion III for the reflexive separation accoring to the aforementione experimental results []. We We crit_iii crit_ii µ ρ ρ σ ρ 6 φ h h + [ σ ( σ + σ cosθ )] - ρ ( ) ρ + + ( ) ρ ρ χ φ + φ α We 4 b b 5 b b α We ρ The criterion III efines the minimum kinetic energy to evelop the roplet coalescence into reflexive separation. This criterion has been most ifficult one to formulate because of uncertainness in estimating the energy losses uring eformation process that shoul result in re-breakup of the temporally coalesce rop. Ieas of Qian an La [] to ientify such loses ere basically continue to be use in this stuy. Unlike the above to criteria, hoever, it is a ater roplet that ecies hether the eformation reaches critical point or not since its ater core is harer to breakup than its thin oil shell. After proper transformations by setting ater properties to representative ones, the folloing equation () as erive. Accoring to the experimental observation of Chen et al. [] in the case of the hea on collision of the fuel an ater roplets, 0.75 an as taken to be appropriate for c III _ an c III _ respectively. here, σ + + 6c III_ σ ρ ρ ρ ρ + ρ ( We ) α 4 π ± π + 64 We 6 c III_ ρ σ 4c ( χ )( c ) _ III III_ + c III_ () Bol lines in Figure (a) sho the ne three criteria on χ-we iagram. Their valiities ere examine by comparison ith the experimental results of Chen et al shon as the thin lines in the figure. Although some isagreement coul be pointe out in the range of large impact parameters, here collisions selom happen in the near-coaxial DWI layout, the equations for the critical Weber numbers give exact values on hea-on collision case (χ 0) an proper preiction tenencies against χ. () Impact parameter:χ - (a) Valiation ith experimental results.0 / Bounce I Coalescence III Stretching separation Reflexive separation Weber number: We - II Impact parameter:χ - (b) Effects of roplet size ratio on criteria I II III Weber number: We - Figure. Theoretical criteria iviing outcomes of immiscible binary roplet collision in DWI system

4 ILASS Europe 00 Figure (b) shos the effects of roplet size ratio on the critical Weber numbers. The original efinition of / is usable only in oil-ater collision system. The effects are remarkable to say the least an ifferent from one criterion to the other. An oil roplet larger than a ater roplet, for example, makes the coalescence easier to happen an makes stretching separation harer, hich is ell ithin the expectation in the oil-ater collision system. It shoul be note that the O Rourke moel oes inclue in its critical Weber number expression, but it only shos subtle epenency on unlike the present collision moel. All in all, the elicitation of the critical Weber numbers in this stuy seems successful to etermine the collision outcomes an its implementation into CFD coes coul have great influence over the DWI spray simulation. Next, the momentum (an the temperature) of the resulting roplets after the immiscible roplet collision shoul be ientifie in orer to continue tracing their behaviour, hich is essential to the spray simulation. In the bounce moe, there is no substantial ifference from O Rourke moel consiering to colliing roplets of the same liqui in calculating the after-collision momentum. Momentums of both roplets are as follos. u col_ u col_ u temp col [ mu + mu m ( u u )]( χ χcrit ) ( m + m )( χ ) crit [ mu + mu + m ( u u )]( χ χcrit ) ( m + m )( χ ) crit In the stretching separation, the momentums of oil an ater roplets oul remain unchange since the groth an the break of the oil-brige affects only internally in the colliing system an the rotation of the temporally brige roplets inuce by grazing contact coul be negligible in the case of the DWI configuration. In the coalescence moe, the properties of a coalesce roplet coul be simply calculate thorough eighe averaging as follos. u mu + mu m + m m T ( u u ) + m ( u u ) 0 m m C T, col (6) mc + mc In reflexive separation the energy issipation shoul be consiere in course of re-breakup of a temporally coalesce rop. It may be noteorthy that to ientical concentric roplets generate in the present collision moel, but they acquire ifferent velocities from each other to reflect the initial momentum ifference of the oil an ater roplets. Great amount of the kinetic energy is consume through the large eformation proucing the to concentric spheres. An energy issipation factor ϕ as set to as high as 0.5 accoring to the theoretical analysis of Jiang et al [4]. The results are as follos. + m m C T, u ϕ, ϕ (7) u col_ temp + u u u col_ temp + u Finally, the breakup an the evaporation process in DWI system can be iscusse. Again, it is the coalesce ater-in-oil concentric roplet that matters in these processes. As for a popular seconary breakup moel in marine iesel simulations, a hybri moel of KT (Kelvin-Helmholtz) breakup moel an RT (Rayleigh-Taylor) breakup moel as continuously aopte to the coalesce roplet ith a ifferent application manner. The coalesce rop behaves as an oil roplet in KH breakup moe because surface properties of the relevant roplet have ominant effects there, hile it behaves as a ater roplet because RT breakup supposely requires large rop eformation. The effects of roplet size ratio ere isregare in the breakup calculation. The evaporation process of a concentric spheres starts at the equilibrium temperature (6) immeiately reache after the coalescence. The concentric sphere evaporates from its fuel surface assuming the ater core keeps the same temperature, hich means the concentric ater in-oil roplet evaporates as an oil roplet of an expane surface area. After the fuel layer is completely vaporize, the roplet continues to evaporate (an also to breakup) as a pure ater roplet, so that phenomena like micro-explosion of the concentric roplet ere not consiere. Experimental setups an calculation methos Visual constant volume combustion chamber (VCVCC) an DWI injectors Figure epicts an outline of the apparatus for DWI spray visualization insie a visual constant-volume combustion chamber (VCVCC). The vessel is optically accessible via three quartz inos an injectors for ater an fuel injection are mounte on its top li. To of the inos are oppose to each other on the cham- (4) (5)

5 ILASS Europe 00 ber s sieall an cover the DWI spray propagation from nozzle exits to a point at 50 mm onar. DWI sprays injecte in the plane parallel to the both inos an the longituinal centre axis of the vessel. Both injectors have the variations of their inclination from the centre axis an the merging angles (MA) forme beteen the fuel spray an the ater spray are set to 0 MA (parallel), 5 MA, 0 MA accoring to the combination of these injectors. Experimental conitions about the DWI system are summarize in Table. ater injector fuel injector VCVCC half mirror mirror camera # (for irect photo) laser light sheet light-sheet optics ban pass filter camera # (for ater etection) N-YAG laser Figure. Schematic illustration of experimental apparatus Table. In-cyliner conitions of VCVCC an Fuel/Water injection conitions In-chamber conitions Injection conitions Chamber iameter 50 mm Injecte liqui Fuel (JIS No.Gas oil) Water Chamber hight 70 mm Inj. pressure 80 MPa 8 MPa Chamber volume ~9000 cm Inj. perio ms 6 ms Infill gas Nitrogen Inj. ireciton 0,.5, 7.5 0, -.5 Pressure.5 MPa Merging angle 0 MA, 5 MA, 0 MA Temperature 98 K Hole istance 6.0 mm Hole iameter φ 0. mm Optical apparatus an visualization metho As shon in Figure, a stereo PIV system ith a ouble pulse N-YAG laser as converte into a DWI spray observation evice in this stuy. Main specifications of the PIV system are summarize in Table.To cameras of stereogram photographing are both aligne in the normal irection to the spray propagating plane an share the same spray image through a half mirror. The length of the light path is carefully equalize to make it easier to compare an superimpose the images from the to cameras. A light sheet from laser sheet optics after the N-YAG laser is incient through a bottom ino of the chamber an it illuminates the spray propagating plane from unerneath. To istinguish ater roplets from the image of the to merging sprays, a fluorescent ye Rhoamine 590 is ae into injecte ater up to 00 ppm in mass concentration an its fluorescence aroun 590 nm is filtere by a lo-pass filter before camera #, hich cuts off the light of avelength of 550 nm or shorter. This enables ater roplets to be capture only by camera # an the ifference from the irect image of camera # gives the image of the fuel roplets. Numerical analysis metho The novel collision moel for the immiscible roplet collision is implemente in KIVA coe. Other than the relevant collision moel (an partially the moifie evaporation moel), rather stanar or proven sub moels 5

6 ILASS Europe 00 Table. Optical specifications for DWI spray observation Laser: NEW WAVE, Research Solo PIV 0XT Camera: PCO600-PIV Type Double pulse, N-YAG Type CCD ith Peltier evice Wavelength 5 nm Pixel size µm Pulse Energy 0 mj Image resolution Max Pulse With 6 ns Clour resolution 4 bits black an hite Cyclic Frequency 5 Hz Embee Memory 5 MB~ Dye for ater etection Rhoamine 590, 00 ppm Recoring Spee 0 fps are intentionally selecte in orer to evaluate the effects of the collision behaviours more objectively. The submoels are summarize in Table. Although O Rourke moel are knon to overestimate the collision probability because of its heavy mesh epenency an to give impact parameters ranomly, hich oes not seem proper in DWI cases, it is regare as a one ell time-teste an ell fitte to Discrete Droplet Moel (DDM) concept. In the DWI configuration, the spray formation is thought to be asymmetric because to incline sprays are interacting ith ifferent injection pressures. Therefore, a rectangular soli of 00 mm in height, 50 mm in ith an in epth is chosen for a computational omain as shon in Figure 4. In orer to reuce the gri epenency in the region here to sprays interact, refinement is provie in the central 0 mm square of the upper 0 mm region, here the injectors are locate, resulting in,000 cells in total. The maximum number of injecte parcels in DDM is set to 4,000 for fuel an ater sprays uring moest 5 ms of the total calculation perio. For comparison, the simulation of fuel-ater interacting spray as conucte ith an ithout the present collision moel. In case of the conventional collision moel, the outcome from the collision beteen fuel an ater roplets is restricte to result in the bounce moe. Table. Major sub moels aopte in KIVA Phenomenon Primary breakup Seconary breakup Collision an Coalescence Evaporation Turbulence Blob metho KH-RT moel Sub moel Moel of O Rourke (ater, fuel) Present moel (ater, fuel) Moel of Amsen (ater, fuel) + To-step evap. of coaxial rops of ater (inner) an fuel (outer) RNG k-ε moel ater injector fuel injector observing irection Figure 4. Computational omain an gri layout 6

7 ILASS Europe 00 Results an iscussions Visualization of DWI sprays in VCVCC Figure 5 shos an example of the DWI spray propagation observe in the VCVCC ith 0 MA at.0 ms after start of injection (ASOI). The left mile image (b) from the camera # shos ater roplets insie the merging sprays an the right mile image (c) from the camera # shos a irect photo of the to merging sprays taken at the same time ith (b). For comparison, a single ater spray case at far left (a) an a single fuel spray case at far right () are ae at both ens. In separating the ater spray image from the DWI sprays, the aperture of the # camera as narroe so as to extinguish the reflection of the ye fluorescence from the root of the fuel spray (see broken arros) because any luminosity from there can be regare as misinformation ith confience. In the parallel injection case in Figure 5, both ater roplets an fuel roplets insie the merge spray kept their penetrations same as the single spray cases, but faint an narro raiance as seen extening along ith a centre line beteen the sprays an reaching to the fuel spray tip (see an arro in (b)). The spreaing of the DWI spray in (c) is virtually superposition of the single spray s spreaing. Hoever, situations change rastically ith 0 MA at.0 ms ASOI as emonstrate in Figure 6. The merge spray has about 7 % longer penetration than the corresponing fuel spray as previously mentione by the authors [5]. Although the sprays of the DWI system seems iene especially to the ater spray (left) sie, main boy of the merge spray as approximately a vector synthesis of the to sprays an this oul explaine the slight inclination of the merging 0 mm 0 mm 0 mm 0 mm (a) (b) (c) () Figure 5. Visualize sprays in VCVCC (merging angle: 0 MA, timing:.0 ms ASOI) 0 mm 0 mm 0 mm 0 mm (a) (b) (c) () Figure 6. Visualize sprays in VCVCC (merging angle: 0 MA, timing:.0 ms ASOI) 7

8 ILASS Europe 00 DWI sprays. Most striking feature of the cases of a significant merging angle is that the to merging sprays blene into each other an ater roplets invae to the tip of the merge spray, so that to images in the mile look virtually the same instea of the root of the fuel spray in (c). Figure 7 shos the effects of the merging angle on the ater roplet istributions an the merge spray profile at.0 ms ASOI. Water roplets are coloure re for the ientification. With 5 MA, the situations are basically the same as the 0 case, but the penetration is the longest among three cases an the spray profile looks slimmer than the others. In the parallel case, larger ots are ientifie as fuel roplets aroun the spray tip or the ege of the ligaments evolving in the sie of the spray hea. In contrast, almost all of the larger ots are ientifie as ater roplets ith 5 or 0 MA an such ater rops seem to generate from an intersecting area of the ater spray an the fuel spray an seem to cover the spray contour. All in all, the nozzle-hole layout of DWI systems must have a critical influence on the ater istribution over the sprays an on their NOx reuction effects. Moreover, CFD simulations shoul reprouce these complicate propagation process observe in the DWI system in orer to preict their NOx reuction effects an to optimise the system. 00 mm 00 mm (0 MA) (5 MA) (0 MA) Figure 7. Comparison of DWI spray propagations ith ifferent merging angles (ater roplets coloure re, timing:.0 ms ASOI) Numerical analysis of DWI spray Figure 8 emonstrates the effects of the present collision moel on the DWI spray propagation. Its preiction results are compare ith the ones of conventional O Rourke collision moel. The merging angles are obtaine from the same geometry of the ater an the fuel injectors attache on the VCVCC, so that the 0 MA case has an asymmetric injector configuration also in the numerical analysis. Conventional moel in the figure implies the stanar collision moel of O Rourke as consistently applie to all the collision cases beteen roplets (ater-ater, fuel-fuel) of the same kin an immiscible roplets (ater-fuel). It is note again that the collision moel of O Rourke only consiers a bounce an a coalescence of roplets of the same liqui. In this stuy, a colliing pair of immiscible roplets alays results in the bouncing moe regarless of their impact energy or impact parameter. With Present moel, the collision outcomes beteen a ater roplet an a fuel roplet are categorize in etail an concentric roplets of ater covere by fuel coul generate in course of spray propagation. Hoever, the calculation process of the collision probability or the collision outcomes of the roplets of the same kin remains the same ith the stanar collision moel. As might be expecte, simulation results of both moels are virtually the same before the intersection of the sprays. After merging of the sprays in DWI systems starts, hoever, the present collision moel clearly gives more similar propagation process to the visualize one an the effects of merging angles of the sprays are reasonably reprouce in the present moel. For example, the spray profile at 5 MA is narroer in ith an sharper in the spray tip than at 0 MA as observe in Figure 7, hile the profile given by the stanar moel shos much smaller change against the merging angles an it is fuel roplets that cover the surface of a merge spray in the stanar moel instea of concentric roplets in the present moel. At 0 MA, concentric roplets are forme just after the intersection of the sprays an larger amount of energy issipation thorough the reflexive separation coul be a key to explain hy the concentric roplets stagnates in upper part of the spray, hich might coincie ith large roplets of strong raiance from the ater roplets observe in the photo images. 8

9 ILASS Europe 00 As for the spray penetration, the present moel also gives better preiction of penetration length as ell as changing tenency against the merging angles. The present moel succees to preict the inversion of the penetration from 5 MA to0 MA. But it shoul be pointe out that both moels can preict the acceleration of the ater spray cause by the spray merging an the present moel gave unreasonable acceleration of the ater spray at 0 MA. In that case, the ater spray even overtakes the fuel spray at.0 ms ASOI, hich coul imply that the energy or momentum balance is not precisely approve in the present collision moel. By comparison, the spray initiation as not necessarily reprouce in both moels. This as partially from a synchronization error beteen the laser pulse an the mechanics in the DWI system an it is thought the influence of the error becomes relatively smaller in later photo timings. 50 mm Conventional moel Droplet type ater fuel concentric Present moel 50 mm 0 MA 5 MA Time after start of injection ms 50 mm 0 MA Time after start of injection ms Conventional moel Droplet type ater fuel concentric Present moel Spray penetration mm Time after start of injection ms Time after start of injection ms MA Present Conventional Experiment Figure 8. Effects of collision moel on DWI spray propagations ith ifferent merging angles Conclusions Novel iesel roplet collision moel as evelope to simulate NOx reuction effects of Direct Water Injection (DWI) system an to optimise such a sophisticate injection system. This collision moel inclues etaile categorization of the outcomes from the immiscible roplet collision. Through valiation by spray visualization using a stereo camera set an ye fluorescence to istinguish ater roplets, folloing conclusions ere erive. Theoretical three criteria iviing collision outcomes of ater an fuel roplets ere successfully erive an valiate by the measurements by Chen et al. Effects of roplet iameter ratio as also evaluate. 9

10 ILASS Europe 00 Ne collision moel reprouce the merging spray behaviour of a DWI system visualize in a constant volume chamber much better than the stanar collision moel in KIVA coe. Angles beteen the spray propagating axes have a critical influence not only on spray penetration length but also on ater istribution over the sprays. This means nozzle-hole layout in DWI system coul be most important in entraining ater effectively into fuel spray an in achieving rastic NOx reuction. Although further improvements in preicting roplet velocities after a collision is necessary, preiction an optimization of NOx reuction effects of DWI shoul be place in the next target of the stuy. Nomenclature c moel constant [-] χ impact parameter [-] C specific heat [J kg - K - ] roplet size ratio [-] iameter [m] φ interaction volume parameter [-] E energy [J] ϕ energy issipation factor [-] h height [m] µ viscosity [Pa s] m mass [kg] θ impact angle [ra] u velocity [m s - ] ρ ensity [kg m - ] We Weber number in DWI [-] σ surface tension [N m - ] We Weber number in ater base [-] ω angular velocity [ra s - ] X impact offset istance [m] Subscripts 0 initial properties F external force term, if for reflexive separation D amping force term b brige in stretching separation crit critical property iesel fuel: oil rel relative component ater temp temporal component C conservation force term col collision result References References shoul be inicate in the text by full size numbers enclose ithin square brackets. Use ifferent formats for journals [], books [], symposium proceeings [], internal reports [4], an eb pages [5] as illustrate in the examples belo. [] Chen, R.-H., Chen, C.-T., Experiments in Fluis, 4:45-46 (006). [] Qian, J., La, C.K., J. Flui Mechanics, :59-80 (997). [] Ashgriz, N., Poo, J. Y., J. Flui Mechanics, :8-04 (990). [4] Jiang, Y. J., Umemura, A., La, C. K., J. Flui Mechanics, 4:7-90 (99). [5] Tsuru, D., Kaauchi, S., Okazaki, K., Tajima, H., th Triennial International Annual Conference on Liqui Atomization an Spray Systems, Vail, Colorao USA, July 009, Paper 0, pp.-0. 0