Although the stability of Newtonian liquid jet has been investigated experimentally and theoretically, many problems has remained unsolved. Especially, the stability of liquid jets in immiscible liquid systems has been little studied. Furthermore, one has to point out that the stability of jets may be influenced by the turbulence in the nozzle and the velocity profile. This work presents the experimental result about the effect of the nozzle length on the breakup length of liquid jets in the air and in the immiscible liquid, as the beginning of a systematic investigation of the influence by these factors on the
breakup of jet. The dependence of the initial amplitude of surface disturbances on the nozzle geometry is presented for evaluating the effect of the nozzle length on the breakup length of laminar liquid jet in the air and in the
immiscible liquid

Kitamura, Yoshiro

Takahashi, Teruo

Okayama University Scientific Achievement Repository

MEMOIRS OF THE SCHOOL OF ENGINEERING, OKAYAMA UNIVERSITY, Vol. 4, No.1, SEPTEMBER 1969Effect of Nozzle Length on Breakup Length of Liquid JetTeruo TAKAHASHI and Yoshiro KITAMURADepartment of Industrial Chemistry(Received June 10, 1969)Although the stability of Newtonian liquid jet has been investigated exper-imentally ani theoretically, many problems has remained unsolved. Especially,the stability of liquid jets in immiscible liquid systems has been little studied.Furthermore, one has to point out that the stability of jets may be influenc-ed by the turbulence in the nozzle and the velocity profile. This work pre-sents the experimental result about the effect of the nozzle length on thebreakup length of liquid jets in the air and in the immiscible liquid, as thebeginning of a systematic investigation of the influence by these factors on thebreakup of jet. The dependence of the initial amplitude of surface disturb-ances on the nozzle geometry is presented for evaluating the effect of the noz-zle length on the breakup length of laminar liquid jet in the air and in theimmiscible liquid.§ 1. IntroductionIt is important in many industrial opera-tions to inject one liquid from a nozzle into theair and into another immiscible liquid. Atlow injection velocities uniform size drops areformed directly at the nozzle. At higher in-jection velocities a liquid jet issues from thenozzle and breaks into drops. Although the be-havior of the liquid jet has been investigatedexperimentally and theoretically, many prob-lems have remained unsolved. For example,the effect of the turbulence in the nozzle orthe extent of development of the velocity pro-file upon the behavior of liquid jets has beenlittle studied.Miesse4) reported that the turbulent breakuplength of liquid jets injected into the air wouldbe a function of the shape of orifice. Grantand Middleman2) found that the critical ve-locity of liquid jets injected into the air wasaffected by the nozzle length. Furthermore, thefirst auther7) found the effect of nozzle lengthon the breakup of liquid jet in the immiscibleliquid. However, there is as yet no literaturethat deals with fundamental studies, and manyproblems are to be solved. Especially, theeffect of the nozzle length on the breakup ofjet must be systematically investigated.In this work the breakup length of the lami-nar jet injected from various nozzles into theair and the im~iscible liquid was measured to57investigate experimentally the effect of the noz-zle length on the stability of liquid jet.§ 2. Experintental Apparatus andProcedure2-1 Liquid Jet in AirA schematic flow diagram of experiment isshown in Fig. 1. A gear pump ® circulatedFig.!. Experimental apparaLs for jet in liquid-airsystems.I. liquid reservoir 2. gear pump3. constant l:ead device 4. valve 5. nozzle6. xenon tute 7. camerathe liquid from a liquid reservoir CD through aconstant head device @, a valve @ and a noz-zle @, and back to the reservoir. A jet issueddownward into the air from a nozzle.Most of nozzles used in this experiment were58 T. TAKAHASHI and Y. KITAMURA (Vol. 4,constructed from drilled blass disks and lodsmounted to the vinylchroride pipe as shown inFig. 2-a. Longer- nozzles were constructedfrom copper tubes and from hypodermic tubesof stainless steel as shown in Fig. 2-b. These(a) ( b )nozzles were examined under a microscope.The dimensions of them are given in Table 1.The nozzles were coated with the paraffine toprevent from being wetted with the liquid.The glycerine aqueous solution and the wa-ter were used in this experiment. The physicalproperties of them are given in Table II.Fig. 2.Table I Nozzle DimensionsDiam-I NozzleDiam-Nozzle eter LIDo eter LIDocm I cmI1-1* 0.050 12.0 5-9 0.200 15.12-1* 0.090 22.2 5-10* 0.215 17.23-1 0.105 0.69 6-1 0.259 0.613-2 0.112 I. 74 6-2 0.252 0.763-3 0.114 2.68 6-3 0.253 1.963-4 0.108 6.42 6-4 0.253 3.913-5 0.103 9.29 6-5 0.256 7.023-6 0.100 15.3 6-6 0.260 7.643-7 0.100 20.3 6-7 0.254 12.44-1 0.162 0.44 6-8* 0.254: 20.34-2 0.157 1.26 6-9* 0.254 25.14-3 0.162 1.82 7-1 0.300 0.524-4I0.156 3.10 7-2 0.303 0.834-5 0.157 6.96 7-3 0.307 1.474--6 I 0.157 9.52 7-4 0.3H 2.084-7 0.160 13.7 7-5 0.305 7.564--8 0.164118.3 7-6 0.318 10.44-9* 0.157 22.6 7-7 0.310 15.85-1 0.203 0.35 8-1 0.405 0.79I5-2 0.204: 0.95 8-2 0.405 1.485-3 0.208 1.45 8-3 0.408 1.955-4 0.217 1.80 8-4 0.402 3.925-5 0.217 3.69 8-5 0.403 6.965-6 0.210 .7.15 8--6 0.410 9.745--7 0.210 9.93 , 87 0.413 14.5I5 8* t 0.215 I 14.4III----------Asterisk (*) indicates tutesTable II Physical properties of experimental systems"s;t~~ ISub- Density Viscosity Surface Workingtension tcmper-No. stance g/cm3 c.p. dynlcm ature°CGIY'''-I ;I ine aq. 1.110 3.68 67.9 30(approx.45wt%)The average injection velocity of the dis-persed liquid was measured by timed volumeof effluent liquid. The breakup length wasobserved by a stroboscope with a xenon tubeand measured from negative films exposuredby high speed flash.2-2 Liquid Jet in Irmuiscible LiquidFigs. 3-a and 3-b show schematic flow dia.grams of experiment for denser liquid jets andlighter liquid jets in the immiscible liquid,respectively. The dispersed liquid pumpedup to a constant head device ® flowed trougha temperature regulator @) and through a nee-dle valve @, and issued into the continuousliquid from a nozzle @. The liquid dispersedinto the continuous liquid was discharged froma test section ® through an overflow tube @.The test section was a rectangular column (5 x10 x 50 em), whose front was made of glass.The experimental apparatuses were set in anair bath @ for the purpose of maintainingboth phases at a constant temperature.The nozzles shown in Table I were used inthis experiment. Table III shows physicalproperties for experimental systems, and allliquid pairs were mutually saturated prior tothe experiment. The average injection veloc-ity of dispersed liquid was measured by timedvolume of discharged liquid from the overflowtube. The breakup length of jets was meas-ured from negative films exposured by the highspeed flash.1969) Breakup Longth of Liquid Jet 59( b )@l0=1(j)IIIFig. 3. Experimental apparatus for jet in liquid-liquid systems.(a) Dispersion of denser liquid. (b) Dispersion of lighter liquid.I. liquid reservoir 2. pump 8. constant head device 4. temperature regulator5. needle valve 6. nozzle 7. test section 8. outlet pipe 9. air-out pipe10. overflow tube 11. heater 12. xenon tuce 13. camera 14. air cathTable III Fhysical properties of experimental systems26.5°C30Workingtemperature41.042.6tensionInterfacialdyn/cm1.2401.059Viscosityg/cm3 c. p.1.0270.778DensityContinuous phaseSubstanceII KeroseneIGlycerineaq.~._---------I Disper~phas~System I~--- -,1 Density I ViscosityNo. Substance II I g/cm3 c. p.-3-1-~t~--10.996 I 0.864----~:_o_-~-;_~4 I Kerosene I 0.780 I 1.037----'-----'---_---.:...._--~-§ 3. Experimental Results andDiscussions3-1 Breakup PatternThe breakup pattern of the liquid jet issuedfrom the nozzle was observed as same as thatof previous works1,2l. The liquid simply dripsout of the nozzle at very low injection veloci-ties and forms a laminar jet beyond the jettingvelocity, and at higher injection velocities aturbulent jet issues from the nozzle.Fig. 4 shows a series of photographs of thewater jet injected into the air from the nozzle5~8, the breakup length of which is plottedin Fig. 8. When the injection velocity increasesover the jetting velocity, the liquid formsa laminar jet whose breakup length increaseswith the velocities and becomes the maximumat the critical velocity. At the region past thecritical velocity the breakup length decreasesteeply with the injection velocities. In thisregion the liquid forms a transient jet. Photo.a shows dripping at the nozzle. A typicallaminar jet is presented in photo. b. The lami-nar jet is seen to break only by symmetricaldisturbances. Photo. c shows the jet nearly atthe critical velocity, the breakup of whichseems to be as same as that shown in b. In thenext instant, however, the jet breakes at theupper point shown by an arrow because of theinitiation of surface disturbances which havelarger amplitude, so, the breakup point fluctu-ates in widder range than at the lower veloc-ities. Photos. d and e show the breakup atthe region immediately past the critical veloci-ty. In this region, the jet becomes unstableand has a tendency to break into segments.The reason of such a phenomena may be con-sidered that the initial amplitude of disturb-ance fluctuates in very wide range. Photos. fand g show the turbulent jet, and the breakuplength increases with the injection velocityagain. The turbulent jet seems to break bysinuous disturbances or waves.60 T. TAKAHASHI and Y. KITAMURA (Vol. 4:a b c d e f 9~.! .:III -WI Fig. 4. Photographs of0 () I water jet from nozzleI 5-8.(;,"(a) 1I0=4.59cm/sec0 \ (b) 1I0=57.4cm/sec0 (e) 1I0=91.gem/see0 0 ~ (d) 1I0=106.gem/see(' b (e) 110= 109.4cm/see"(f) 110 = 220. Iem/sec~ (g) 1I0=441.8em/seeII ,..,~ .... ,.. ("'A ('\h . k lJ m n.;.J~ JJV ...0 ~. -.J~ ..... _J\)...;f. wi;;; •..".J J -"1Fig. 5. Phot0.sraphs of water jet in kerosene from nozzle 4-7.(h) 1I0=1O.4em/see (i) 1I0=33.1em/see (j) 1I0=47.gem,see (k) 1I0=47.gem/see(I) 1I0=56.3em'see (m) 1I0=77.6em/see (n) 1I0=143.8em,"see1969) Breakllp Longtll of Liqllid Jet 61o p q r 5 tFig. 6. phot0.sraphs of kerosene jet in glycerine aqueous solution from nozzle 5 -9.(0) 1I0=22.2cm, ec (p) 1I0=25.9cm/scc (q) lIo=40.5cml ec(r) lIo=53.Ocm sec (s) lIo=65.5cm/sec (t) 1l0=74.5cm/secFig. 7. Breakup curves for jets in some systems.Fig. 7 shows breakup curves for four sy -tems, which are obtained by plotting breakuplengthes against injection velocitie. Thebreakup length of laminar jets in both of the airand the immiscible liquid increases being pro-potional to injection velocities, and decreaseswith injection velocities when it exceed thecritical velocity. At higher injection velocities,liquid jets in the air issue as turbulent jetswhose breakup length increases with velocities,while the liquid injected into the immiscibleliquid forms a spray, and the breakup lengthdecrea es with \·elocities. On the other hand,extrapolating lines of laminar breakup data20 nozzle system3002!'J. 4-9• 4-7• 4-7o 4-Eu- IOI----+-/__Fig. 5 shows a series of photographs of thewater jet injected in to the kerosene from thenozzle 4-7, and also photographs of the ker-osene jet in the glycerine aqueous solution arepresented in Fig. 6. Photos. hand 0 showdripping, Photos. i and q how the laminar jetwhich is disrupted by ymmetric disturbancesas same as liquid jet in the air. Laminar jetsseem to break into uniform ize drop. Photos.j, k and r show the breakup nearly at the criti-cal velocity. The jets in this region are veryunstable, as is evident from the fact that j andk are exposured at the same velocity. Turbu-len t jet are shown in Photos. I, m, and t.At very high velocitie the disper ed liquidform sprays as shown in Photo. n. It is evi-dent from the above observation that the flowpattern of the denser liquid injected into theimmi cible liquid are the same as that for thelighter liquid injected into the immiscible liq-uid; and that the liquid drips out of the noz-zle and forms laminar jets, turbulent jets andsprays as the injection velocity increases.The flow pattern and the breakup patternof lig uid jets in the air are analogou to thoseof liquid jets in the immiscible liquid exceptat very high velocitie as described above.62 T. TAKAHASHI and Y. KITAMURA (Vol. 4,6-7 12.4• 6 - 3 0.96151---t---l--I-;;t~6t':_~4Lt"3~.c9i17~16 - 5 7.0221---+--M m"-----+--t--E~41----+--Fig. II. Effect of nozzle length on heakup lengthof kerosene jet in glycerine aqueous solution.61----+---+-[00 40UoFig. 10. Effect of nozzle length on breakup lengthof water jet in kerosene.E10 ....L::=:..f--"!.6-=.-r8~2r-0"""'"3:!....IJI---I--/~DU20 r----r---rr=""r"'=='i""""''''''''''''''"i1nozzle LI Dosystem - 3 1--t-'-'7'-==:-t7--=:::'-:-f1o 6-1 0.61Fig. 8 shows one of experimental results a-bout the effect of the nozzle length for water jetsin the air, and Fig. 9 shows that for glycerineaqueous jets in the air. Figs. 10 and II shownozzle LIDo300 5 - 1 0.35b. 5 - 2 0.95 system - 2• 5 - 4 1.800 5 - 6 7.15... 5 - 8 14.4e 5 -10 17.220oL..._...L-._...J.."";"--L__.I-_...L-._.....L........lo 100 200 300Uo (em / sec)Fig. 8. Effect of nozzle length on breakup len3thof water jet.,....Eufor liquid jets in the air pass through an ori-gin, but those for jets in the immiscible liquiddo not through an origin. It may be supposedas the reason of this phenomena that the sur-face velocity of liquid-liquid jets is lower thanthe average injection velocity.3-2 Effect of Nozzle LengthFrom the observation of the breakup lengthof the liquid jets injected into the air and intothe immiscible liquid from the nozzles present-ed in Table I, it is evident that the behaviorof the liquid jets in both systems are influencednot only by the nozzle diameter but by thenozzle length.nozzlet; 5- 2 system - 1• 5-340 @ 5-4E ... 5-5u 0 5-730 e 5-82010100 200 300Uo (em/sec)Fig. 9. Effect of nozzle length on breakup lengthof glycerine aqueous solution jet.the experimental results for liquid jets in theimmiscible liquid. The behavior of liquid jetsin all systems is apparently influenced by thenozzle length. The same effect is observed forother nozzles of different diameter. The resultsfrom the above observation are as follows; thelaminar breakup length of the liquid jet inboth of the air and the immiscible liquid in-creases with the nozzle length, and approachesto a constant value for each diameter whenthe ratio of nozzle length to the nozzle diame-ter exceeds a critical ratio. The critical ratiois about 15 for the water jet in the air, about10 for the glycerine aqueous solution jet in theair and about 10 for both jets of the denserand lighter liquid in the immiscible liquid,within the limits of this experiment. (eL Figs.12 and 13. )1969) Breakup Longth of Liquid Jet 63_ system - 1 I I I I I I I - Do emI I... ~6...-err-~~ • 0.05c.c_e-e -•0.09-~~I I I • O. 1 1system - 2 0 O. 1 6O. 21~~ e._~o-~ 0 0.250- ef-~/\ .~e 6- O. 31"If 0.40-120108,....6I~-020eu-c:-10860.2 0.4 0.6 2L I Do4 6( - ) 10 20 40Fig. 12. Variation of initial amplitude of disturbances for liquid-air systems with nozzle length.3-3 Initial AlUplitudeof Surface Disturbances10whereIt is known that thebreakup of liquid jet canbe reasonably explained bythe following model3, 8) •Small disturbances are in-itiated on the jet surface asa result of pressure fluctua-tions or turbulences in thenozzle, when the liquid jetissues from the nozzle exit.All disturbances with awavelength greater thanthe jet circumference in-crease exponentially withthe time and destroy the jetinto drops.Fig. 12 shows the valueof In (ao/6o) for the liquidjet in the air, and Fig. 13 shows that for theliquid jet in the immiscible liquid. In thesefigures, In (ao/do) are plotted against the ratioof nozzle length to the nozzle diameter.The values of In (ao/ao) in these figures arecalculated from following equations.For the noncylindricalliquid jet in the air6).Fig. 13. Variation of initial amplitude of disturbances forimmiscible liquid-liquid systems with nozzle length.40r.=?'0===;--r-I'I--rI-r-TI-r---r----,oem 4• 0.11 system -20U-~~:t----+---+--+-+---J-o 0.16 ~[I e-~o-e 0.2 1 0 0 0 I e A10 6. 0.31 - A A -1-----+----1...... 11~A TT~6~t>e-:3<_ ~a~~o':£ 20 0.-- Do em 20o eO ~eC:'" 0 • O. 11_0.----- 0 I 0 O. 1610 e eO. 21system- 3 0 0 256 ~~~_~:L-....L-~I~I~~==#.·======.J0.4 06 2 4 6 10 20 40L/Do(-)The critical velocities from the laminar tothe transient jet in the air have a tendency todecrease with the nozzle length as shown inFigs. 8 and 9, but on the contrary, those fromthe laminar to the turbulent jet in the im-miscible liquid are independent of it. While thedependence of the critical velocity upon thenozzle length has found in the previous work2),the quantitative correlation between them hasnot yet been clear.Although the behavior of the liquid jets inboth of the air and the immiscible liquid areinfluenced by the nozzle length, the breakuppattern for the longer nozzle are hardly dis-tinguished from that for the thinner orifice.64 T. TAKAHASHI and Y. KITAMURAFor the liquid jet in the immiscible liquid5),and1a= T''; (g2.D~.PD) j (u~'O'),r= 3'!lDN PD·Do·O'1x= {(2.g.ljun+1(S.the dripping, the laminar jet and the turbu-lent jet.2) The laminar breakup length increaseswith the nozzle length and approaches to somesaturation values beyond the critical ratio ofthe nozzle length to the nozzle diameter. Thecritical ratio is about 15 for the water jet inthe air, about 10 for the glycerine aqueoussolution jet in the air and about 10 for bothjets of the denser and lighter lquid in the im-mis.cible liquid. It is considered that the initialamplitude of the surface disturbance is affect-ed by the nozzle length.N oIllenclatureThe value of In (ao/ao) increases with the noz-zle length and reaches to a constant valuebeyond the critical ratio of the nozzle lengthto the diameter, as shown in Figs. 12 and 13.In other words, the initial amplitude of dis-turbances ao decreases with the nozzle lengthapproaching some saturation values.The experimental results described abovecan be well explained by the following con-sideration. The effect of the nozzle length onthe laminar breakup length may be due to thedependence of the initial amplitude of surfacedisturbances upon it. The turbulences or thepressure fluctuations generated at the nozzleentrance dissipate into smaller and smaller onepassing through the nozzle. As disturbanceson the jet surface are initiated as a results ofthe turbulence at the nozzle exit, the initialamplitude of disturbances at the exit of thelonger nozzles becomes smaller than that forthe thinner orifice. In other words, In (ao/ao)increases with nozzle length to approach somesaturation values. Therefore, the laminarbreakup length is consequently affected by thenozzle length.§ 4. ConclusionsThe behavior of liquid jet in the air and inthe immiscible liquid was investigated experi-mentally, and following results were obtained.1) The breakup pattern of liquid jets in bothsystems are analogous to one another. As theinjection velocities of dispersed liquid becomegreater, the flow pattern of liquid jet showsao radius of nozzle [em]Do diameter of nozzle [em]g gravitational acceleration [cm/sec2]I breakup length of jet [em]L nozzle length [em]uo average injection velocity [em/sec]UJ jetting velocity [em/sec]lio initial amplitude of disturbance [em]p density of liquid [g/cm3]11 interfacial tension [dyn/cm]p. viscosity of liquid [g/cm·sec]SubscriptsC continupus phaseD dispersed phaseReferencesI) K. FUJINAWA, T. MARUYAMA and Y. NAKAIKE:Kagaku K6gaku, 21, (1957) 1942) R. P. GRANT, and S. MIDDLEMAN: A.1. Ch. E.journal, 12, (1966) 6693) Lord RAYLEIGH: Proc. London Math. Soc., 10,(1878) 7; "Theory of Sound Vol 2", 351, Dover(1945)4) C. C. MIESSE: Ind. Eng. Chern., 47, (1955) 16905) T. TAKAHASHI and Y. KITAMURA: Preprint of 1stAutumn Meeting of the Society of Chemical En-gineering, japan, Osaka, Oct. (1967)6) T. TAKAHASHI and Y. KITAMURA: Preprint of33th Annual Meeting of the Society of ChemicalEngineering, japan, Kyoto, Apr. (1968)7) T. TAKAHASHI and L. KOBASHI: Preprint of 30thAnual Meeting of the Society of Chemical Engi-neering, japan, Osaka, Apr. (1965)8) C. WEBER: Z. Angew. Math. Mech. 11. (1931)136

Effect of Nozzle Length on Breakup Length of Liquid Jet

Abstract

Similar works

Full text

Available Versions

Okayama University Scientific Achievement Repository

Okayama University Digital Information Repository