CFD On the development of large-scale structures of a jet normal.pdf

PHYSICS OF FLUIDS VOLUME 13, NUMBER 3 MARCH 2001

On the development of large-scale structures of a jet normalto a cross flow

T. T. Lim, T. H. New, and S. C. LuoDepartment of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent,Singapore 119260

~Received 25 February 2000; accepted 6 December 2000!

It is well known that vortex rings are the dominant flow structures in the near field of a free jet, andthis has led many researchers to believe that they also occur in a jet in cross flow~JICF!. Previousstudies have postulated that these vortex rings deform and fold as they convect downstream, whichculminates in the formation of vortex loops at both the upstream and the lee-side of the jet column.In this paper, we take a fresh look at the vortical structures of JICF in water by releasing dye atstrategic locations around the jet exit. The results show that there is no evidence of ring vortices inJICF, and the postulation that vortex loops are formed from the folding of the vortex rings does notreflect the actual flow behavior. The presence of a counter-rotating vortex pair~CVP! at the jet exitis found to inhibit the formation of the vortex rings. Instead, vortex loops are formed directly fromthe deformation of the cylindrical vortex sheet or jet column, without going through the vortex rings,in a process similar to the buoyant jet and wake structures studied by Perry and Lim@J. Fluid Mech.88, 451 ~1978!#. © 2001 American Institute of Physics.@DOI: 10.1063/1.1347960#

n

eica

inb

noeu

mvam

avp

llr-

pis

t t

te

am,w-fw,hee aith

ternaltest

thea

ro-n.

sedtrac-l inary

on

or.ingpeed

ofthe

entinve-

INTRODUCTION

The jet in cross flow~JICF! is relevant to a wide varietyof technological applications, including plume dispersiocontrol of missiles, chimney flow and V/STOL aerodynamics. In the past few decades, our knowledge of JICF has bincreasing steadily due to the combined efforts from physexperiments,1–19 numerical simulations,20–27 and theoreticalanalyses.28,29 For an overview of the recent developmentsthis area, the reader is referred to the review articleMargason.30

It has been recognized that when a jet is dischargedmal to a cross flow, there is a complex interaction betwethe jet and the cross flow, leading to the formation of fovortical structures. They are~a! the leading-edge or upstreavortices which form along the jet/cross flow interface abothe jet exit,~b! the horseshoe vortices which appear upstreof the jet exit,~c! the wake vortices which occur downstreaof the jet exit, and~d! the counter-rotating vortex pair~CVP!which appear in the far field. These vortical structures hbeen studied extensively by many researchers. For examKelso et al.,15 Sykeset al.,24 and Coelho and Hunt31 studiedthe vortex dynamics of the exiting jet; Moussaet al.,7 Fricand Roshko,14 Kelsoet al.,15 McMachonet al.32 and Eiff andKeffer33 investigated the wake vortex system; Krothapaet al.34 and Kelso and Smits35 examined the horseshoe votex system, and Kamotani and Greber,4 Moussa et al.,7

Scorer,36 and Fearn and Weston37 studied the CVP. Despitethe considerable progress made in these areas, many asof the flow field remain poorly understood. Among thosethe evolution of the jet shear layer vortices. In an attempinterpret the flow physics, Andreopoulos,9 Kelso et al.,15

Sykes et al.,24 and Lim et al.38 have used vortex rings tomodel the flow structures. They postulated that the vor

7701070-6631/2001/13(3)/770/6/$18.00

Downloaded 25 Jun 2008 to 216.54.44.227. Redistribution subject to AIP

,-enl

y

r-nr

em

ele,

i

ects

o

x

rings deform and stretch as they propagate downstreleading to the eventual formation of the loop vortices. Hoever, our recent studies~New et al.39! on a different aspect oJICF do not show any evidence of vortex rings in the floand that the loop vortices do not really originate from tvortex rings. This unexpected finding prompted us to makdetour from our original plan, and to pursue this study wthe aim of resolving the above anomaly.

EXPERIMENTAL SETUP

The experiments were conducted in a recirculating wachannel in the Fluid Mechanics Laboratory at the NatioUniversity of Singapore. The channel has a Plexiglassection that measures 0.4 m3 0.4 m, and is powered by avariable-speed ac motor driving a centrifugal pump onreturn leg of the flow circuit. The pump, together withbutterfly valve located downstream of the pump exit, pvides a wide range of cross flow velocities in the sectioBefore the flow entered the test section, it was pasthrough a honeycomb, three fine screens, and a 4:1 contion section. This was to ensure that the turbulence levethe cross flow was kept to a minimum, and the boundlayer on the test section floor remained laminar.

The jet nozzle comprised of a 14:1 circular contractichamber with an exit internal diameter (D) of 32.47 mm,and was mounted flushed with the main water channel floTo create the transverse jet, a gravity-feed technique utilizan overhead tank was used. Here, a small constant-spump was used to supply water from the tank downstreamthe test section to the overhead tank located 1.5 m abovetest section floor. The tank had an overflow compartmwhich allowed the overflow to be directed back to the mawater channel just upstream of the honeycomb. The jet

© 2001 American Institute of Physics

license or copyright; see http://pof.aip.org/pof/copyright.jsp

s

-

e--

re

771Phys. Fluids, Vol. 13, No. 3, March 2001 Large-scale structures of a jet normal to a cross flow

FIG. 1. A sequence of photographshowing how the folding of the cylin-drical shear layer~or vortex sheet!from the jet nozzle leads to the eventual formation of the counter-rotatingvortex pair, and the upstream and leside vortices indicated as A and B, respectively. In ~a!, the time has arbi-trarily been set to 0.00 s. It isimportant to note that although theflow structures look complicated, theoriginal fluid leaving the nozzle re-mains in its original cylindrical bound-ary. To avoid overcrowding of the fig-ure, the sign of circulation of theupstream and the lee-side vortices ashown only in~d! as semi-circular ar-rows.

clete

e-to

.n

suiorelinnti

ds

.dbtianaro

oke

rlya

d,y,nc

oodneuchedi-

altledn,of

the

jetthe

eetto

elsolin-

locity was controlled by a ball-valve located some distanupstream of the jet exit and was measured by using an etromagnetic flow meter. Another larger capacity flow mewas used to measure the cross flow velocity.

To visualize the flow, dye/alcohol mixture with a spcific gravity of approximately one was released slowly onthe inner surface of the jet nozzle, through a 1 mmwidecircumferential slit located 2.5D upstream of the nozzle exitIn some runs, fluorescein disodium dye was used in conjution of a 5 W argon ion laser.

RESULTS AND DISCUSSION

Since the aim of the present study is to resolve the isof the vortex structures in JICF, we pay particular attentto the generation of these vortices near the jet exit. Figushows a sequence of photographs illustrating how the cydrical shear layer issuing from the nozzle deformed arolled up into concentrated vortices. Here, the velocity ra(VR5Vj /V`) was approximately 4.6, and the Reynolnumber~Re5VjD/n) was about 1600, whereVj andV` arethe jet and the cross flow velocity, respectively,D is thenozzle diameter andn is the kinematic viscosity of waterThe scale of the pictures can be inferred through the cylindiameter (D) of 32.47 mm. These photographs were otained by releasing dye uniformly around the circumferenslit mentioned earlier. In all cases, the dye concentratiokept to a minimum so that the salient features of the flownot unduly obscured by the thickness of the dye. In manythe previous studies, a high concentration of dye or smmade the interpretation of the flow difficult, and in somcases led to misinterpretation of the flow field, particulaon the lee-side of the jet. In this study, since the dye wreleased at the location where the vorticity was generateis reasonable to assume that the dye marked the vorticitleast during the early stages of the flow development. He


ec-r

c-

en1-

do

er-lisefe

sitate,

the behavior of the dye sheet depicted in Fig. 1 gives a gindication of the behavior of the vortex sheet. However, oshould be cautioned that since dye generally diffuses mslower than vorticity, and over a long period of time, thregion occupied by the dye may no longer give a true incation of the region of vorticity~see Lim40!.

Inspection of Fig. 1 clearly shows that as the cylindricvortex sheet~or shear layer! emerged from the nozzle, iunderwent three distinct folding processes. One processto the formation of the CVP on the sides of the jet columand the other two resulted in the formation of two rowsvortices; one at the upstream side~identified as A, in Figs. 1and 2!, and the other at the lee-side of the jet~identified asB!. The latter two vortices are henceforth referred to as

FIG. 2. Sectional view of the vortex structures in the center plane of aissuing normal to a cross flow. The photograph is obtained by premixingjet fluid with the fluorescein dye, and then illuminated with a narrow shof laser light. Note that the vortices A and B correspond approximatelythose in Fig. 1~d!. The counter-rotating vortex pair is not visible in thphotograph because it is out of the illumination plane. This picture aclearly shows that the original fluid leaving the nozzle remains in the cydrical boundary.


f

h

ter

n

772 Phys. Fluids, Vol. 13, No. 3, March 2001 Lim, New, and Luo

FIG. 3. Authors’ interpretation of thefinally developed vortex structures oJICF. ~a! The sketch shows how the‘‘arms’’ of both the upstream and thelee-side vortex loops are merged witthe counter-rotating vortex pair.~b!Cross sectional views of~a! taken atvarious streamwise distances. Notheir close resemblance with the lasecross sections of the jet depicted iFig. 5.

egb

einlenu

ss

en

dc

ng-stte

thV

arVtio

bgmndna2s

pre-

upstream vortices and the lee-side vortices, respectivThese vortices resemble a ‘‘daisy chain’’ of interlockinloops, which are similar to the buoyant jet structures oserved by Perry and Lim.41 What is interesting about thesloop vortices is that they were not produced by the bendor folding of the vortex rings, as some researchers wereto believe. In fact, there is no evidence of vortex rings in aof our studies. This observation has also been made by Yet al.27 in their large eddy simulation of a round jet in croflow.

To better understand how these loop vortices evolvvideo images of the flow field were replayed in slow motioThey show that as soon as the cylindrical vortex sheet~seealso Fig. 1! emerged from the nozzle, it immediately foldeup on its edges to form a CVP. This finding is consistenwith the experimental observation of Kelsoet al.,15 and thelarge-eddy simulation of Yuanet al.27 Furthermore, it wasfound that the CVP played a significant role in preventithe cylindrical vortex sheet, which contains ‘‘circular’’ vortex lines, from rolling up into vortex rings. This is in contrato the free jet, where the absence of CVP allows the vorsheet to roll up ‘‘axisymmetrically’’ into vortex rings. In thecase of JICF, the vortex sheet can roll up freely only atupstream and the lee-side of the jet column since the Csuppresses similar roll up at the two sides. This scengives rise to two rows of loop vortices separated by the Cat the sides. Close examination shows that this formaprocess is similar to the buoyant jet structures observedPerry and Lim,41 although the details are different. Durinthe folding of the vortex sheet, the fluid that originated frothe nozzle remained within the cylindrical boundary, athere was no indication of holes or openings in the origivortex sheet. This feature is clearly illustrated in Fig.where the jet fluid, which had been premixed with fluore


ly.

-

gd

yan

d,.

e

x

ePioPny

l,-

FIG. 4. Detailed sketches of the proposed model.~a! The sketch shows howthe vortex loops give rise to the resultant Section B-B.~b! Section E-E alongthe deflected jet centerline in the streamwise direction. This sketch resents the laser cross section of JICF depicted in Fig. 2.


t-

ed

e

-

e


FIG. 5. Laser cross sections of a jetaken with the laser plane perpendicular to the jet axis. The symbols de-notes the distance measured from thfloor and along the jet trajectory, anD is the nozzle diameter. In~b!, theside arms of the upstream loop havalready merged with the CVP whilethose of the lee-side loop are still distinct. The latter also merged with theCVP further downstream as can bseen in~c! and ~d!.

jeouinnc-

dymemahe

idb

ndeefaiceinitedo

ar

nm

notthe, a

nu-taingethe

lizeurew-

ave.’’e-iew

tentjet

in-f a

cein dye, was illuminated with a thin laser sheet in thecenter plane. Here, both the upstream and the lee-side vces can be clearly seen while the CVP is not visible becait was outside the laser plane. It is worth noting at this pothat although the sectional views such as the one showFig. 2 provide valuable information about the internal strutures of the flow field, one should be mindful that it is difficult to deduce three-dimensional flow structures from stuing the sectional view alone. For example, the ‘‘mushrooshape’’ vortices in Fig. 2 may lead one to misinterpret thas part of the same vortex rings, however, as the broad bpictures in Fig. 1 clearly show, they are actually part of ttwo separate vortex loops.

As the vortex loops convected downstream, their s‘‘arms’’ were swept downstream by the cross flow and susequently paired up with the CVP@see Fig. 1~d!#. Duringmerging, the ‘‘side arms’’ were stretched by the CVP, athis resulted in realignment of the vorticity with that of thCVP. Although not shown in the photographs, we suspthat the mutual interaction between the loop vorticesdownstream was partly responsible for causing the vortto undergo instability and became turbulent, leaving behonly the CVP with fine scale motion superimposed onFigure 3 shows our interpretation of the finally developflow structure. Note how the CVP is initiated at the sidesthe cylindrical vortex sheet and how the vortex loops


trti-setin-

--

nd

e-

ctrsd.

fe

formed from the folding of the vortex sheet. The ‘‘break’’ ithe figure indicates that section D-D is taken far away fronozzle exit. For clarity, the fine-scale structures areshown in the figure. In fact, the best way to understandfinal structure is to make a model using wire gauze tubetechnique used successfully by Perry and Lim41 to illustratehow buoyant wake and jet structures are formed. By contiing to wrap the sides of the wire gauze tube, one can obthe CVP. Similarly, by continuing to fold the upstream edand the lee-side of the wire gauze tube, one can obtaintwo rows of vortex loops as shown in Fig. 3~a!. Indeed, awire gauze model was built and used as an aid to visuaand construct the 3D view of the proposed model. Fig4~a! shows the 3D view of the proposed jet structures, shoing how the upstream and lee side vortex loops may hinteracted to produce Section B-B via their side ‘‘armsAnd Fig. 4~b! shows the cross section E-E along the dflected jet centerline, showing the same cross sectional vin Fig. 2.

To demonstrate that the proposed model is consiswith the experiment, laser cross sections of the actualstructures normal to the jet axis~see Fig. 5! are comparedwith the corresponding cross sections of the model@see Fig.3~b!#, and the agreement between them is good. It is ofterest to note that in a recent large-eddy simulation oround jet in crossflow by Yuanet al.,27 it was found that the


ee

.d

774 Phys. Fluids, Vol. 13, No. 3, March 2001 Lim, New, and Luo

FIG. 6. Photographs showing thwake structures from the nozzle at thvelocity ratio of 1.~a! Side view.~b!Plan view taken at a different instanceNote that the vortex loops are pointedownstream~see New, Ref. 43!.

ctic

i

out

Thciteuawtthfosictchao

3sigsero

eistes

entioet.aom

hnavisnoa

esex

dis-esasrch-ntal

aleesro-

ty38.

,’’

a

,’’

ss

cter-

cterans.

he

a

h.

jets

a

near field of the jet consists of three different vortical strutures, namely spanwise rollers, hanging vortices, and verstreaks. These structures are presented in terms of thesurface of vorticity, as shown in Fig. 5~a! of their paper.While it is clear that their spanwise rollers correspond toupstream and lee-side vortices, it is not so clear as to howhanging vortices and the vertical streaks are formed.uncertainty arises because their isosurface of the vortiplot does not give a clear picture of how the three vorstructures are interconnected. But the comment by Yet al.27 that the hanging vortices undergo vortex breakdosimilar to that reported by Kelsoet al.15 leads us to suspecthat the hanging vortices are likely to be the side arms ofupstream vortex loops before it merges with the CVP. Asthe vertical streaks, we believe that they are the side armboth the upstream and lee-side vortex loop vortices, whhave been stretched by the CVP during merging. The streing causes the vorticity of the side arms to realign with tof the CVP. Overall, our observation agrees well with thatYuan et al.27

An important feature of the model depicted in Figs.and 4 is that the upstream loops can exist without the lee-loops. This is in contrast to the model using vortex rinwhich suggests that for every upstream vortex loop, thmust be a corresponding one on the lee-side. However, four experimental results and the results of Kelsoet al.,15

single-sided vortex loops are known to exist in JICF whthe velocity ratio is low, typically less than one. Thisclearly shown in Fig. 6. Here, one can see that the vorloops are pointed downstream rather than upstream acommonly observed in high velocity ratio cases. The oritation of the vortex loops suggests that, at low velocity rathe ‘‘jet structures’’ have transformed into wake structur~see Perry and Lim41!. Under this condition, the buoyanwake model of Perry and Lim41 is equally applicable hereOther examples in nature where single-sided loopsknown to occur include the smoke structures issuing frfactory chimney in cross flow, and a cigarette smoke inslight draft ~see Perry and Lim41!. However, one should beaware that, for these two cases, the buoyancy of thesmoke does play an important role in determining the fistructures of the flow. Nevertheless, these examples profurther support to our model that the large-scale structureJICF consists essentially of loop vortices, which arecaused by the folding of the vortex rings. We believe th


-also-

rhee

tyxn

n

erofhh-tf

de,rem

n

xis-,s

re

a

otl

deoftt

vortex rings will not form ‘‘naturally’’ in JICF unless theyare deliberately fired into a cross flow~see Sykeset al.,24

Chang and Vakili,42 and Lim et al.38!, or when the velocityratio is close to infinity~i.e., a free jet!. Far away from theseconditions, the cross flow will cause the circular vortex linsurrounding the cylindrical vortex sheet to tilt, and the vortsheet to roll up into loop vortices.

CONCLUSION

We have shown that the large-scale structures of jetcharging normally into a cross flow consist of loop vorticwhich are not caused by the folding of the ring vorticeshave been previously thought otherwise by many reseaers. Our proposed model is consistent with the experimeobservations and the large-eddy simulation of Yuanet al.27 Itprovides a more realistic representation of the large-scmotion of JICF for all velocity ratios higher than 1. For caswhere the velocity ratio is lower than one, the model pposed by Perry and Lim41 for the buoyant coflowing wakesgives a good representation.

ACKNOWLEDGMENT

The authors would like to thank the National Universiof Singapore for the support of this project under RP 9506

1J. F. Keffer and W. D. Baines, ‘‘The round turbulent jet in a crosswindJ. Fluid Mech.15, 481 ~1963!.

2B. D. Pratte and M. Baines, ‘‘Profiles of the round turbulent jet incrossflow’’ J. Hydraul. Div., Am. Soc. Civ. Eng.92, 53 ~1967!.

3N. A. Durando, ‘‘Vortices induced in a jet by a subsonic crossflowAIAA J. 9, 325 ~1971!.

4Y. Kamotani and I. Greber, ‘‘Experiments on a turbulent jet in a croflow,’’ AIAA J. 10, 1425~1972!.

5P. Chassaing, J. George, A. Claria, and F. Sananes, ‘‘Physical charaistics of subsonic jets in a cross stream,’’ J. Fluid Mech.62, 41 ~1974!.

6G. Bergeles, A. D. Gosman, and B. E. Launder, ‘‘The near-field charaof a jet discharged through a wall at 90 degrees to a main stream,’’ TrASME: J. Heat Trans.98, 373 ~1976!.

7Z. M. Moussa, J. W. Trischka, and S. Eskinazi, ‘‘The near field in tmixing of a round jet with a cross-stream,’’ J. Fluid Mech.80, 49 ~1977!.

8D. Crabb, D. F. G. Durao, and J. H. Whitelaw, ‘‘A round jet normal tocrossflow,’’ J. Fluids Eng.103, 142 ~1981!.

9J. Andreopoulos, ‘‘On the structure of jets in a crossflow,’’ J. Fluid Mec157, 163 ~1985!.

10N. Rajarantnam and T. Gangadharaiah, ‘‘Vortex structure of circularin crossflow,’’ J. Wind Eng. and Industrial Aero12, 155 ~1983!.

11J. Andreopoulos and W. Rodi, ‘‘Experimental investigation of jets incross flow,’’ J. Fluid Mech.138, 93 ~1984!.


ns

rse

d

ss

&

et

at-ta

e-

th

J.

in

ics

s-

p.

f a

ng.

-

of

m

of

m

omjet,’’

ss

sics

sgs,

nd

’

,


12J. E. Broadwell and R. E. Briedenthal, ‘‘Structure and mixing of a traverse jet in incompressible flow,’’ J. Fluid Mech.148, 405 ~1984!.

13J. W. Wu, A. D. Vakili, and F. M. Yu, ‘‘Investigation of the interactingflow of nonsymmetric jets in crossflow,’’ AIAA J.26, 940 ~1988!.

14T. F. Fric and A. Roshko, ‘‘Vortical structure in the wake of a transvejet,’’ J. Fluid Mech.217, 1 ~1994!.

15R. M. Kelso, T. T. Lim, and A. E. Perry, ‘‘An experimental study of rounjet in cross flow,’’ J. Fluid Mech.306, 111 ~1996!.

16B. A. Haven and M. Kurosaka, ‘‘Kidney and anti-kidney vortices in croflow jets,’’ J. Fluid Mech.352, 27 ~1997!.

17L.-E. Brizzi, E. Foucault, and J.-L. Bousgarbie`s, ‘‘Vortices organization inthe near field of a jet issuing normally into a crossflow,’’ J. Flow Vis.Image Processing5, 17 ~1998!.

18S. H. Smith and M. G. Mungal, ‘‘Mixing, structure and scaling of the jin cross flow,’’ J. Fluid Mech.357, 83 ~1998!.

19J. N. Blanchard, Y. Brunet, and A. Merlen, ‘‘Influence of a counter roting vortex pair on the stability of a jet in a cross flow: An experimenstudy by flow visualizations,’’ Exp. Fluids26, 63 ~1999!.

20S. V. Patankar, D. K. Basu, and S. A. Alpay, ‘‘Prediction of the thredimensional velocity field of a deflected turbulent jet,’’ J. Fluid Eng.99,758 ~1977!.

21A. R. Karagozian, ‘‘An analytical model for the vorticity associated wia transverse jet,’’ AIAA J.24, 429 ~1986!.

22D. J. Needham, N. Riley, and J. H. B. Smith, ‘‘A jet in cross-flow,’’Fluid Mech.188, 159 ~1988!.

23D. J. Needham, N. Riley, C. C. Lytton, and J. H. B. Smith, ‘‘A jetcross-flow. Part 2,’’ J. Fluid Mech.211, 515 ~1990!.

24R. I. Sykes, W. S. Lewellen, and S. F. Parker, ‘‘On the vorticity dynamof a turbulent jet in a crossflow,’’ J. Fluid Mech.168, 393 ~1986!.

25R. W. Claus and S. P. Vanka, ‘‘Multigrid calculations of a jet in crosflow,’’ J. Propul. Power8, 425 ~1992!.

26M. Rudman, ‘‘Simulation of the near field of a jet in a cross flow,’’ ExTherm. Fluid Sci.12, 134 ~1996!.

27L. L. Yuan, R. L. Street, and J. H. Ferziger, ‘‘Large-eddy simulations oround jet in crossflow,’’ J. Fluid Mech.379, 71 ~1999!.

28R. H. Nunn, ‘‘Vorticity growth and decay in the jet in crossflow,’’ AIAAJ. 23, 473 ~1985!.


-

l

29J. H. W. Lee, L. Li, and V. Cheung, ‘‘Semianalytical self-similar solutioof bent-over jet in cross-flow,’’ J. Eng. Mech. Div., Am. Soc. Civ. En125, 733 ~1999!.

30R. J. Margason, ‘‘Fifty years of jet in cross flow research,’’ AGARD-CP534, 1-1–141~1993!.

31S. L. V. Coelho and J. C. R. Hunt, ‘‘The dynamics of the near fieldstrong jets in crossflows,’’ J. Fluid Mech.200, 95 ~1989!.

32H. M. McMahon, D. D. Hester, and J. G. Palfrey, ‘‘Vortex shedding froa turbulent jet in a cross-wind,’’ J. Fluid Mech.48, 73 ~1971!.

33O. S. Eiff and J. F. Keffer, ‘‘On the structures in the near-wake regionan elevated turbulent jet in a crossflow,’’ J. Fluid Mech.333, 161 ~1997!.

34A. Krothapali, L. Lourenco, and J. M. Buchlin, ‘‘Separated flow upstreaof a jet in a crossflow,’’ AIAA J.28, 414 ~1990!.

35R. M. Kelso and A. J. Smits, ‘‘Horseshoe vortex systems resulting frthe interaction between a laminar boundary layer and a transversePhys. Fluids7, 153 ~1995!.

36R. S. Scorer,Natural Aerodynamics~Pergamon, New York, 1958!.37R. Fearn and R. P. Weston, ‘‘Vorticity associated with a jet in a cro

flow,’’ AIAA J. 12, 1666~1974!.38T. T. Lim, R. M. Kelso, and A. E. Perry, ‘‘A visual study of vortex ring

fired transversely into a cross-flow,’’ 13th Australasian Fluid MechanConference, Monash University, Australia, Vol. 2, pp. 961–964~1998!.

39T. H. New, T. T. Lim, and S. C. Luo, ‘‘On the effects of velocity profileon the topological structures of a jet in cross flow,’’ TSFP-1 Proceedinpp. 647–652~1999!.

40T. T. Lim, ‘‘Dye and smoke visualization’’ inFlow Visualization: Tech-niques and Examples,edited by A. J. Smits and T. T. Lim~ImperialCollege Press, London, 2000!, pp. 43–69.

41A. E. Perry and T. T. Lim, ‘‘Coherent structures in coflowing jets awakes,’’ J. Fluid Mech.88, 451 ~1978!.

42Y. K. Chang and A. D. Vakili, ‘‘Dynamics of vortex rings in cross-flow,’Phys. Fluids7, 1583~1995!.

43T. H. New, ‘‘A topological study of a jet in cross flow,’’ B. Eng thesisNational University of Singapore~1998!.


CFD On the development of large-scale structures of a jet normal.pdf

Documents

Transcript of CFD On the development of large-scale structures of a jet normal.pdf