An Improve Monosze Droplet Generator for MD albraton Hao hen, Mn Xu, We Zeng, Mng Zhang, Gaomng Zhang, Yuyn Zhang Insttute of Automotve Engneerng, hangha Jao Tong Unversty, hangha, hna E-mal: mxu@sjtu.eu.cn Abstract Base on the Raylegh s nstablty theory of lqu jets, an mprove metho to generate monosze roplets s propose n ths paper. A lqu jet whch emts from a capllary tube wll break up nto monosze roplets wth unform spacng when mposng a constant frequency mechancal sturbance on t. Weber precte theoretcally that there s an mum frequency for the mechancal sturbance to generate the roplets wth unform sze an spacng for each ntal jet velocty, an the sze of the roplets epens manly on the nner ameter of the capllary tube through whch the lqu flows. In ths stuy, a monosze roplet generator wth an acoustc vbraton system was bult, an roplet szes rangng from 2µm to 1µm were generate by varyng the capllary tube ameter an the vbraton frequency. The results show that the roplet ameters measure agree very well to those calculate from Raylegh s equaton. The Weber s mum frequency was also verfe. By use of ths roplet generator, the laser sheet ropszng (LD), whch etermnes the auter mean ameter (MD) of a spray base on the rato of to Me sgnals, was calbrate. It has prove that ths mprove monosze roplet generator s a promsng tool for MD calbraton. Keywors: Monosze roplet generator, Lqu jet nstablty, Laser sheet ropszng, MD, pray 1. Introucton Measurng rop sze n a spray s mportant n many applcatons, such as fuel njectors, coolng systems, power generators an so on. The popular cal technque for measurng rop sze s Phase Doppler Anemometry, whch makes tme ensemble pont-wse measurements of roplet sze an velocty. Unfortunately, PDA also has rawbacks. For example, PDA fals to gve relable ata n an cally ense spray an eep roplet fel, because hghly ense roplet clous attenuate the probe beams an scatter lght sgnal. A complete spray characterzaton takes hours or ays for a spatal resoluton of typcally 1mm epenng on spray overall geometry. Laser sheet ropszng (LD) s a recently evelope planar magng base technque. A planar laser-nuce fluorescence (P) an Me-scatterng mages orgnate from a clou of roplets n a spray are taken smultaneously. The ntensty of P sgnal be gven by: 3 = wll = (1) n whch s the ameter of roplet, s the constant whch epens on the magng system an the property of the lqu. The ntensty of Me scatterng sgnal s gven by: 2 Me Me = = (2) The rato of ntensty measure n the mage to the ntensty measure n the Me mage s thus gven by: Me = = Me = 3 2 (3) ote the efnton of auter mean ameter (MD) s gven as MD = = = 3 2 ombnng Eq. (3) an (4) yels (4) MD = K (5) Me n whch K s gven by K = Me. Thus, MD can
be obtane from the rato of the sgnal to the Me scatterng sgnal, f the coeffcent K s known. In practce, K s usually etermne by calbraton wth known ameter of roplets. The laser sheet ropszng (LD) technque offers several avantages over the PDA technque. Frst of all, snce LD technque bases on an Me mages llumnate or excte by a pulse laser sheet, but PDA sgnal s orgnate from the nvual roplet crossng the tny probe volume at a pont nse the spray, LD tens to suffer less from sgnal attenuaton an mult-scatterng cause by the spray. Further, LD technque measures the value of /Me. The ntenstes of an Me are each affecte n a smlar manner by source of nterference, such as nonunformty of the laser sheet profle an the seconary scatterng by the spray between the object plane an camera. These nterferng effects to some egree cancel when the rato s taken. econly, LD s a snapshot of the spatal strbuton of spray roplet sze, not temporally ntegrate an ensemble value hence more sutable to transent automotve sprays. Fnally, LD s a much faster technque to obtan nformaton of MD strbuton n a spray than any pont-wse measurement technque. However, the LD technque nees MD calbraton whch s challengng. Jermy an. Greenhalgh [1] calbrate the calbraton constant K by a PDA system. Gal an Farruga [2] use a roplet generator (TI moel 345) to prouce roplets to calbrate MD. For a pulse multple-sburse spray consstng of a large number of roplets n temporally varyng roplet sze strbuton, the roplet sze measurement s very fferent between the two methos. PDA measures temporal statstcs of the spray rop sze strbuton at a sngle pont nse the spray, whle LD measures spatally average MD strbuton at a moment. Therefore, t s not esrable to correlate the two measurement results an to calbrate each other. In the present work, an mprove monosze roplet generator, whch can prouce the roplets of known sze, s propose an bult for MD calbraton of a LD system. 2. Theores relate to monosze roplet generator The roplet generator, whch s use for MD calbraton, s base on the theory of the nstablty of lqu jets stue by Raylegh [3], known as Raylegh jet breakup. Raylegh jet breakup results from the growth of axsymmetc oscllatons of the jet surface, nuce by surface tenson. Drop ameters excee the jet ameter n ths breakup regme. Raylegh showe that all sturbances on a nonvscous lqu jet wth wavelengths greater than ts crcumference wll grow. Further more, Raylegh s results show that one class of sturbance wll grow fastest an eventually control the breakup. A more general theory for sntegraton at low jet veloctes was evelope by Weber [4], who extene Raylegh s analyss to nclue vscous lqus. Hs research showe that there was a mnmum ntal wavelength of the sturbance for the roplets formaton. If the wavelength of the ntal sturbance s less than mnmum wavelength mn, the surface tenson tens to amp out the sturbance. If the wavelength s greater than mn, the surface tenson tens to ncrease the sturbance, whch eventually leas to sntegraton of the jet. There s a partcular wavelength most favorable for rop formaton. For nonvscous lqus, mn, whch s = π D, = 2πD = 4.44D (6) For vscous lqus, mn = π D, 3μ L 1/2 = 2 πd(1 + ) (7) ρσ L D where D s the lqu jet ameter, μ L, ρl an σ are the ynamc vscosty, ensty an surface tenson of the lqu, respectvely. These equatons suggest that the mnmum wavelength s the same for both vscous an nonvscous lqus, whch s also consstent wth Raylegh s analyss. From Eq. (7), the mum wavelength can be calculate. The jet velocty v coul be obtane from the constant fee rate of lqu fee system. Therefore, an mum frequency whch s most esrable for the proucton of unform sze roplets wth unform
spacng between roplets s obtane: 2. Expermental apparatus f = v/ (8) After break up, a cylner of length becomes a sphercal rop, so that π 2 4 ( / 2) 3 1.145 3 2 D = π = D (9) 4 3 where equals to the spacng between ajacent roplets, an D s the nner ameter of the capllary. From ths equaton, the ameter of the roplets generate by the generator can be calculate. chneer an Henrcks [5] expermentally etermne that unform roplets can be prouce by varyng wthn the followng lmts: 3.5D< < 7D (1) The n Eqs. (6) an (7) s n ths lmts an t s the mum wavelength for unform roplets generate. Lnbla an chneer [6] erve that a mnmum lqu velocty s requre to form a lqu jet from a capllary tube: vmn = 8 σ / ρld (11) Base on the above theory an fnngs, a monosze roplets generator was bult an teste n ths work. Monosze roplet generator The expermental apparatus s shown schematcally n Fg.1. The lqu jet flows out from the tp of a glass capllary tube, whch s seamlessly connecte to a stanless-steel capllary tube. nce the glass capllary tube s smoother than stanless-steel capllary tube, the glass capllary tube s use as the ext of the lqu jet. The lqu jet nstablty s excte by a small louspeaker. The vbraton strength an frequency from the louspeaker was ajuste by a functon generator. The louspeaker s vbraton s transferre to the stanless-steel capllary tube by a stanless-steel wre that s glue solly on the stanless-steel capllary tube. The nner ameter of the stanless-steel capllary tube s 1mm. Three glass capllary tubes were use n ths stuy, wth the nner ameter of 5, 2 an 1µm, respectvely. The lqu fee system conssts of a syrnge pump whch forces the lqu through the capllary tubes at a constant rate. A snusoal sgnal from a functon generator was exerte on the louspeaker. The frequency can be contnuously vare. A D camera s use to photograph the roplets for further analyss. Water s use as the testng flu. Fgure 1 chematc of monosze roplet generator
Apparatus for MD calbraton Fgure 2 chematc of expermental setup for MD calbraton Fgure 2 shows the expermental apparatus for MD calbraton. The MD calbraton system conssts of a monosze roplet generator, a D camera magng system an a laser system. The laser beam s generate by an : YAG laser (Ltron, Pulse Wth: 4ns, Max. Power: 38mj at 266nm). A sheet c s use to transform the laser beam nto a 1mm thck laser sheet, whch s employe to llumnate the roplets generate by the monosze roplet generator. The focal length of cylnrcal lens n the sheet c s 2mm. An mage oubler s use to combne the sgnals of an Me on the camera D chp smultaneously. An mage ntensfer (IRO) was use to ntensfy the mages of an Me. The approprate an Me flters (center wavelength of flter for : 378nm, for Me: 266nm; full-wth at half-maxmum of the flter for : 14nm, for Me: 12nm) are mounte on the two ports of the oubler respectvely to separate the an Me sgnals. an Me mages of monosze roplets were recore smultaneously as the sample mages for MD calbraton. The test fuel n MD measurement was ethanol. The opant was qunne an the concentraton was 1mg/L. 3. Results an Dscusson Performance of monosze roplet generator 15Hz 16Hz 17Hz 18Hz 19Hz 2Hz Fgure 3 Droplets generate by the capllary tube D=2µm at varous vbraton frequences Measurements of the roplet sze an spacng were performe by usng Image Pro Plus software. Droplets generate by the capllary tube wth nner ameter 2µm excte at varous frequences are shown n Fg.
3. The velocty of the lqu jet s 172mm/s, whch s greater than the mnmum velocty calculate by Eq. (11). Accorng Eq. (7), the mum wavelength for water to break up s 899µm. Therefore, the mum vbraton frequency for water to sntegrate s estmate as 1913Hz from Eq. (8). The measure an calculate roplet ameters at fferent frequences are shown n Fg. 4. The sol curve shows the results calculate usng Eq. (9). Each measure roplet ameter n the fgure s obtane by averagng at least 15 roplet ameters n the regon where they are evenly space along the stream. An the error bars n Fg. 4 represent the stanar evaton of the measure ameters. From Fg. 4, t can be seen that for the frequency 19Hz, whch s close to the mum frequency, the error between the calculate an the measure roplet ameter s just 3.8µm. For other frequences, the error ncreases to a sgnfcantly large value as21~3µm. Fgure 5 Droplet ameters at varous frequences for 1µm capllary tube Fgure 6 Droplet ameters at varous frequences for 5µm capllary tube Fgure 4 Droplet ameters at varous frequences for the 2µm capllary tube The mum frequences for the 1µm an 5µm capllary tubes can be seen n Fg. 5 an Fg. 6 respectvely. Fg. 7 shows the mages of roplets generate at the mum frequences. Ths approves Weber s theory that all the roplets generate at the respectve mum vbraton frequency have the most unform an stable values of ameter an spacng between roplets. An also the fference between the calculate ameter an measure one s mnmal at the mum frequency. 5µm capllary 2µm capllary 1µm capllary Fgure 7 Droplets generate at the mum frequences
MD calbraton The monosze roplet generator was use to calbrate MD after the roplet ameter beng verfe. In ths work, constant K n Eq. (5) for MD measurement was etermne for ethanol fuel. For ths purpose a set of calbraton mages were recore. A number of an Me mages were average respectvely for the calbraton. nce the roplets generate from the capllary tube of 5µm are too large for MD calbraton, t was remove n ths step. Fg. 8 shows one group of an Me mages of roplets prouce by the capllary tube of 2µm. It ncates that both the ameter of the roplets an the spacng between roplets were unform. Fg. 9 shows the constant K as a functon of number, whch s the number of the average mages. 1µm capllary 2µm capllary Me Fgure 8 an Me mages of roplets prouce by capllary tube of 2µm for calbraton It can be seen that calbraton constant K becomes a constant as ncreases. The calbraton constant K obtane from 1µm an 2µm capllary tubes are 15.32, 16.95, respectvely. The epenence of the K on roplet sze s so small as to be consere as a constant. Therefore, the average value of K for 1µm an 2µm capllary tubes, 16.13, can be use for the MD calbraton. The calbraton constant K obtane from 1µm an 2µm capllary tubes are fferent by 1%. If the average K s use for roplet ameter calbraton, base on Eq. (12), the possble measurement error s about 7.12%. K K n δ = 1 = ( K K ) K average average (12) Fgure 9 albraton constant K obtane for the roplets generate by 1µm an 2µm capllary tubes 4. pray MD strbuton The calbraton constant K was use to calbrate the spray of an eght-hole rect-njecton njector. Wth the same laser magng system for MD calbraton, 2 mages were recore for both the an Me scatterng sgnals. nce eght plumes of the spray are symmetry, one plume of the spray was mage. Fg. 1 shows the mage an the Me scatterng mage of the spray, whch were taken smultaneously. ear the ext of the njector, the sgnal s not well efne snce ths regon contans fuel lgament, where the relatonshp shown n Eqs. (1) (2) o not hol. Therefore, the mages shown n Fg. 1 were just the regon from 3mm to 8mm ownstream the fuel njector tp. Fgure 11 shows the LD mage obtane from the rato of mean mage an mean Me scatterng mage. The spray contans roplets n the sze range 5-2µm.
calbraton. The agreement between the calculate ameter base on theory an measure ameter by photography was analyze. An the MD calbraton constant K was obtane from the planar /Me sgnals of the roplets generate. The calbraton constant K was use to calbrate the spray of an eght-hole DI njector. The conclusons are as followe: (1) The experments verfe the Weber s precton that there exsts an mum frequency of the sturbance to generate roplets wth a unform sze an spacng for each ntal jet velocty. (2) Droplets generate at ths mum frequency have the smallest screpancy n ameter to that calculate from the theoretcal equatons. (3) The calbraton constant K for ethanol MD calbraton was obtane as a value of 16.13 whch s almost nepenent of roplet ameter, ncatng that the monosze roplet generator s sutable for MD calbraton of LD technque. 6. Acknowlegement Fgure 1 an Me scatterng mages from an eght-hole njector The research was carre out at atonal Engneerng Laboratory for Automotve Electronc ontrol Technology an sponsore by General Motors ompany. The authors thank all the members of the team for the support an useful scussons. 7. References Fgure 11 LD mage of one plume of spray from an eght-hole DI njector 5. onclusons A monosze roplet generator, whch was capable of generatng monosze roplets wth unform spacng between roplets, was bult an nvestgate for MD 1. M.. Jermy, D.A. Greenhalgh, Planar ropszng by elastc an fluorescence scatterng n sprays too ense for phase Doppler measurement, Appl. Phys. B 71, 73 71 (2) 2. P.Le Gal,. Farruga, Laser heet Dropszng of ense sprays, Optcs & Laser Technology 31 (1999) 75-83 3. Lor Raylegh, the Instablty of Jets, Proc. Lonon Math. oc. 1, 4-12 (1878) 4. Weber, Dsntegraton of Lqu Jets, Z. Angew. Math. Mech., Vol. 11, 1931, 136-159 5. J.M.chneer an.d.henrcks, ource of Unform-ze Lqu Droplets, Rev. c Instrum., Vol. 35, 1349 (1964) 6..R.Lnbla an J.M.chneer, Proucton of unform-sze lqu roplets, J. c. Inst. Vol. 42, 635 (1965)