a study on a lobed jet mixing ﬂow by using stereoscopic...

PHYSICS OF FLUIDS VOLUME 13, NUMBER 11 NOVEMBER 2001

A study on a lobed jet mixing flow by using stereoscopic particle imagevelocimetry technique

Hui Hu,a) Tetsuo Saga, Toshio Kobayashi, and Nobuyuki TaniguchiInstitute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

~Received 18 September 2000; accepted 31 July 2001!

In a continuing effort to study the mixing enhancement by large-scale streamwise vortices generatedby a lobed nozzle, a high-resolution stereoscopic particle image velocimetry~PIV! system was usedin the present study to conduct three-dimensional measurements of air jet flows exhausted from alobed nozzle and a conventional circular nozzle. The three-dimensional instantaneous andensemble-averaged velocity fields, instantaneous and ensemble-averaged streamwise vorticitydistributions and turbulent kinetic energy distributions were used to analyze the characteristics ofthe mixing process in the lobed jet flow compared with conventional circular jet flow. The existenceof large-scale streamwise vortices in the lobed jet mixing flow is revealed clearly from thestereoscopic PIV measurement results. The instantaneous streamwise vorticity distributions revealedthat the large-scale streamwise vortices generated by the corrugated trailing edge of the lobed nozzlebreak into smaller, but not weaker streamwise vortices gradually as they travel downstream. This isthe proposed reason why a lobed nozzle would enhance both large-scale mixing and small-scalemixing reported by other researchers. The overall effect of the lobed nozzle on the mixing processin the lobed jet mixing flow was evaluated by analyzing the ensemble-averaged streamwise vorticitydistributions. It was found that ensemble-averaged streamwise vortices in the lobed jet mixing flowgrew up and expanded radially over the first diameter of the test nozzle, then began to break downinto smaller and weaker vortices further downstream. The averaged turbulent kinetic energy profileindicated that most of the intensive mixing between the core jet flow and ambient flow, due to thespecial geometry of the lobed nozzle, occurred within the first two diameters of the lobed nozzle,which corresponds to the upstream region where the ensemble-averaged streamwise vortices breakdown. © 2001 American Institute of Physics.@DOI: 10.1063/1.1409537#

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INTRODUCTION

The physics of the mixing process is of considerainterest from both fundamental and practical points of vieIt has been widely suggested that the mixing process ismately connected with the transient of turbulence. In enneering flows, the mixing process governs the mixing ratecombustion chambers, jet noise level of airplanes andhicles, and the spread of pollutants at industrial sites. A ccal technical problem to be solved in many of these appltions is mixing enhancement of a jet flow with ambieflows. How quickly and how well a jet flow can be mixewith ambient flows will have a major influence on combution efficiency, heat release rate, pollutant formation,noise suppression and size reduction of such functionalvices.

The streamwise vortices generated in a jet flow, in adtion to the azimuthal~or ring type! vortices, have been founto mix fluid streams even more efficiently. As pointed outthe investigations of Zaman,1 both the azimuthal and streamwise vorticities are of equal importance to jet mixing proce

a!Author to whom correspondence should be addressed. Present adTurbulent Mixing and Unsteady Aerodynamics Laboratory, A22, ReseaComplex Engineering, Michigan State University, East Lansing, Micgan 48824; electronic mail: [email protected]

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and they are not independent of each other. The distortioazimuthal vortex structure may lead to streamwise vortiunder certain conditions. The streamwise vortices in jet ming flows can be generated by many methods. For examplobed nozzle used to generate large-scale streamwise vorin a jet flow has been considered to be a promising metfor jet mixing enhancement.

A lobed nozzle, which consists of a splitter plate wicorrugated trailing edge, has been given great attentionmany researchers in recent years. It has also been apwidely in turbofan engine exhausts and ejectors. Forample, for some commercial aero-engines, such as JT217C, CFM56-5C, and RB211-524G/H~which are widelyused on Boeing and Airbus airplanes!, lobed nozzles/mixershas been used to reduce take-off jet noise and specificconsumption~SFC!.2,3 In order to reduce the infrared radiation signals of military aircraft to improve their survivabilitylobed nozzles/mixers have also been used to enhancemixing process of the high temperature and high-speedplume from air-engine with ambient cold air.4,5 These mili-tary aircraft include the military helicopter ‘‘Tiger’’ developed by Germany and France, the American helicopRAH-66 ‘‘Comanche’’ and stealth Fighter F-117. More rcently, lobed nozzles have also emerged as an attractiveproach for enhancing mixing between fuel and air in co

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5 © 2001 American Institute of Physics

license or copyright, see http://ojps.aip.org/phf/phfcr.jsp

3426 Phys. Fluids, Vol. 13, No. 11, November 2001 Hu et al.

FIG. 1. The test nozzles.

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bustion chambers to improve the efficiency of combustand reduce the formation of pollutants.6

Most early studies of lobed nozzles/mixers were conctrated on optimizing the geometry design of lobed nozzmixers for bulk mixing enhancement. The findings of thostudies include that lobes with parallel sides can achihigher mixing performance compared with sinusoidal shalobes7 scalloping the lobes aids in mixing.8 The lobe penetra-tion in the fluid streams has the most significant effectmixing effectiveness as long as the flow does not separa9

Paterson10 is considered to be the first to research tfluid dynamical mechanism of the mixing process dowstream of a lobed nozzle/mixer. Based on the detailed psure and temperature data as well as three-dimensionalDoppler velocimetry~LDV ! measurement results of the vlocity field, Paterson10 found that the lobed nozzle could produce streamwise vortices with length scale on the ordethe nozzle radius. Horseshoe vortices with smaller scale walso found to exist at the lobe troughs. The contributionthese vortices to the overall mixing process was not clear,the secondary flows~streamwise vortices! were expected tobe dominant because of their much greater size.

Much of the later work on lobed nozzle/mixer concetrated on discovering the underlying physics of the lobmixing process by using two-dimensional lobed mixwhich is essentially a corrugated plate. Werleet al.11 sug-gested that the large-scale streamwise vortex formationcess was an inviscid one. The mixing process in the lomixing flow was suggested to take place in three basic st~1! The vortices form,~2! intensify and then~3! rapidlybreak down into smaller turbulence. So the lobed mixer wthought to act as a fluid stirrer initially to mix the flow, untthe vortices break down to produce small scale mixing.

Eckerleet al.12 used a two-dimensional LDV system tstudy the mixing process downstream of a planar lobmixer at two velocity ratios of the two mixing streams. Threported that the breakdown of the large-scale streamwvortices and the accompanying increase in turbulent mixare important parts of the mixing process. They also fouthat the vortex breakdown occurs further upstream forvelocity ratio 2:1 case rather than for 1:1 case.


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Elliott et al.13 found that both the streamwise vorticeshed from lobed trailing edge and the increased initial intfacial area associated with the lobe geometry are also sigcant for increasing mixing compared to that occurring withconventional flat plate splitter. At velocity ratio close to 1.the increased mixing is due mainly to the increased conarea, whereas the streamwise vortices have a larger rolevelocity ratio of 2.0, and its importance rises as the velocratio increases.

The study by McCormicket al.14 revealed more detailsabout the flow patterns downstream of a planar lobed miBased on the pulsed-laser sheet flow visualization wsmoke and three-dimensional velocity measurements whot film anemometer~HFA!, they suggested that the interation of Kelvin–Helmholtz ~azimuthal! vortices with thestreamwise vortices produce the high levels of mixing. Tstreamwise vortices deform the Kelvin–Helmholtz~azi-muthal! vortices into pinch-off structures and increase tstirring effect in the mixing flow. These result in the creatioof intense small-scale turbulence and mixing.

Ukeiley et al.15,16and Glauseret al.17 measured a planalobed mixer flow field by using a rake of hot wires. Basedthe proper orthogonal decomposition~POD! analysis andpseudo-flow visualization~PFV! of the data from the hotwire rake, they suggested that the turbulence dominated ming in the lobed mixer flow field is due to the collapse of tpinch-off shear layer. The collapse of the shear layer oitself, which occurred 3 to 6 times of the lobe height dowstream, induced a burst of energy characterized by a reor pocket of high turbulence intensity.

In the paper of Belovich and Samimy,18 the results ofthose previous studies were summarized by stating thatmixing process in a lobed nozzle/mixer is controlled by thrprimary elements. The first is the streamwise vortices geated due to the lobed shape. The second is the increasinterfacial area between the two flows due to the spegeometry of lobed structures, and the third is the BrowRoshko-type structures occurring in any shear layer duethe Kelvin–Helmholtz instabilities.

Although many important results were obtained in thoprevious studies, much work is still needed in order to u


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3427Phys. Fluids, Vol. 13, No. 11, November 2001 A study on a lobed jet by using stereoscopic PIV

derstand the flow dynamics of the mixing enhancement uslobed nozzles. Previous studies have revealed the existof unsteady vortical and turbulent structures in lobed mixflows by qualitative flow visualization. However, quantittive information about the evolution of these unsteady vocal and turbulent structures is far more limited. The expemental techniques used in most previous studies were Pprobe, laser Doppler velocimetry~LDV ! or hot film an-emometer~HFA!. It is very hard to detail the unsteady votical and turbulent structures in lobed mixing flows instanneously and globally due to the limitation of theexperimental techniques.

With the rapid development of modern optical tecniques and digital image processing techniques, whole-fioptical diagnostic technique like particle image velocime~PIV! is assuming an ever-expanding role in the diagnoprobing of fluid mechanics. The advances of PIV techniqin recent decades have lead it to become a matured technfor whole-field measurements of fluid flow. In an earliwork of the authors,19 both planar laser induced fluorescen~LIF! and particle image velocimetry~PIV! techniques wereused to study lobed jet mixing flows in a water channel.using directly perceived LIF flow visualization images aquantitative velocity, vorticity, and turbulence intensity dtributions of PIV measurement results, the evolution andteraction characteristics of the various vortical and turbulstructures in the lobed jet mixing flows were discussed.

The PIV measurement results reported in the earwork of the authors19 was obtained by using a conventiontwo-dimensional PIV system in a water channel. It is w

FIG. 2. The air jet experimental rig.


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known that a conventional PIV system is only capablerecording the projection of velocity into the plane of the lassheet. That means the out-of-plane velocity componenlost while the in-plane components may be affected byunrecoverable error due to the perspective transformatio20

For the highly three-dimensional flow fields like lobed jmixing flows, the two-dimensional measurement results mnot be able to reveal their three-dimensional features scessfully. A high-resolution stereoscopic PIV system is usin the present study to measure the near flow field of a lojet mixing flow in order to reveal the three-dimensional fetures of the lobed jet mixing flow more clearly. The charateristics of the mixing process in a lobed jet mixing flocompared with a conventional circular jet flow will be dicussed based on the three-dimensional measurement reof the stereoscopic PIV system.

EXPERIMENTAL SETUP AND THE STEREOSCOPICPIV SYSTEM

Figure 1 shows the two test nozzles used in the presstudy; namely a baseline circular nozzle and a lobed nowith six lobes. The width of each lobe is 6 mm and theight of lobes is 15 mm (H515 mm). The inner and outepenetration angles of the lobed structures areu in522° anduout514°, respectively. The equivalent diameters of the tnozzles are designed to be the same, i.e.,D540 mm.

Figure 2 shows the air jet experimental rig used in tpresent study. A centrifugal compressor was used to supair jet flows. A cylindrical plenum chamber with honeycomwas used to settle the airflow. Through a convergent conntion ~contraction ratio is about 50:1!, the airflow is exhaustedfrom the test nozzles. The whole jet supply rig was instalon a two-dimensional translation mechanism, which canused to change the position of the test nozzles.

The velocity of the air jet exhausting from the test nozzcan be adjusted. In the present study, the core jet velo(U0) was set at about 20 m/s. The Reynolds number ofjet flow, based on the nozzle diameter (D) and the core jetvelocity is about 60 000.

The air jet flows were seeded with small DEHS~di-2-

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ethlhexyl-sebact! droplets generated by a seeding generaThe seeding generator is composed of an air compressoseveral modified Laskin nozzles.21 The diameter of theDEHS droplets used in the present study is about 1 to 5m m.The DEHS droplets out of the seeding generator werevided into two streams; one is used to seed the core jetand another for the ambient air seeding.

Figure 3 shows the schematic of the stereoscopicsystem used in the present study. The objective jet mixflows were illuminated by a double-pulsed Nd:YAG laser~New Wave 50 mJ/Pulse! with the laser sheet thickness beinabout 2 mm. The double-pulsed Nd:YAG laser set can supthe pulsed laser~pulsed illumination duration 6 ns! at thefrequency of 15 Hz. Two high-resolution~1 K by 1 K! cross-correlation CCD cameras~TSI PIVCAM10-30! were used todo stereoscopic PIV image recording. The two CCD camewere arranged in an angular displacement configurationmaximize the measurement window size. In order to hthe measurement field focused on the image planes perfetilt-axis mounts were installed between the camera bodand lenses, the lenses and camera bodies were adjustsatisfy the Scheimpflug condition.22 In the present study, thedistance between the illuminating laser sheet and image

FIG. 4. PLIF flow visualization results of the lobed jet mixing flow in watchanal (Re53000).


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cording plane of the CCD camera is about 650 mm, andangle between the view axis of the two cameras is aboutFor such arrangement, the size of the overlapped view oftwo image recording cameras for stereoscopic PIV measment is about 80 mm by 80 mm.

The CCD cameras and double-pulsed Nd:YAG laswere connected to a workstation~host computer! via a syn-chronizer ~TSI LaserPulse synchronizer!, which controlledthe timing of the laser sheet illumination and the CCD caera data acquisition. In the present study, the time intebetween the two pulsed illuminations was set as 30ms. Thehost computer is composed of two high-speed CPU~450mHz, Pentium III CPU!, colossal image memory and hardisk ~1 GB RAM, Hard Disk 100 GB!. It can acquire con-tinuous stereoscopic PIV image pairs up to 250 frames evtime at the framing frequency of 15 Hz.

Since the angular displacement method was used inpresent study to do stereoscopic image recording, the mnification factors between the image planes and object pare variable due to the perspective distortion. In orderdetermine the local magnification factors, anin situ calibra-tion procedure was conducted in the present study to obthe mapping functions between the image planes and obplane.

Following the work of Soloffet al.,23 the in situ calibra-tion procedure involved the acquisition of several imagesa calibration target plate, say a Cartesian grid of small dacross the thickness of the laser sheets. Then, these imwere used to determine the magnification matrices ofimage recording cameras. This method, which determithe mapping functions between the image planes and obplanes mathematically,24 therefore, takes into account thvarious distorting influences between test section andCCD arrays of the image recording cameras. With the mping functions determined by this method, the stereoscodisplacement fields obtained during the experimentreadily recombined into three-dimensional velocity vecfields.25

To accomplish thein situ calibration in the present studya target plate~100 mm by 100 mm! with 100 mm diameterdots spaced at interval of 2.5 mm was used. The front surof the target plate was aligned with the center of the lasheet and then calibration images were captured at threcations across the depth of the laser sheets. The spaceval between these locations was 0.5 mm for the presstudy.

The mapping function used in the present study wtaken to be a multidimensional polynomial, which is fourorder for the directions~X andY directions! paralleling thelaser sheet plane and second order for the direction~Z direc-tion! normal to the laser sheet plane. The coefficients ofmultidimensional polynomial were determined from the cabration images by using least-square method.26

The two-dimensional particle image displacementsevery image plane were calculated separately by using aerarchical Recursive–PIV~HR–PIV! software developed‘‘in-house.’’ The hierarchical recursive–PIV softwarebased on hierarchical recursive processes of conventispatial correlation operation with offsetting of the displac



FIG. 5. Stereoscopic PIV measurement results in theZ/D50.5 (Z/H51.33) cross plane of the lobed jet mixing flow.

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ment estimated by the former iteration step and hierarchreduction of the interrogation window size and search dtance in the next iteration step.27 Multiple-correlation valida-tion technique28 and sub-pixel interpolation treatment29 arealso incorporated in the software. Compared with convtional cross-correlation based PIV image processing mods, the hierarchical recursive–PIV method has advantain the spurious vector suppression and spatial resolutionprovement of PIV result.

Finally, by using the mapping functions obtained by tin situ calibration procedure described previously andtwo-dimensional displacements in the two stereoscopicage planes, the three components of the velocity vectorthe illuminating laser sheet plane were reconstructed.

The position of the illuminating laser sheet and imarecording CCD cameras were fixed during the experimeThe distance changing between the exit of the test noz


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and the illuminating laser sheet was achieved by operathe two-dimensional translation mechanism~Fig. 2! tochange the position of the air jet experimental rig. Suchrangement can insure that all the stereoscopic PIV measments at different cross planes of the jet mixing flows aconducted while doing thein situ calibration procedure onlyonce.

In order to evaluate the measurement results ofpresent stereoscopic PIV system, a LDV system was usedo simultaneous measurement of the lobed jet mixing floThe stereoscopic PIV measurement results were compwith the LDV results. It was found that the difference btween the measurement results of the present stereoscPIV system and LDV data is less than 2%. Further detaabout the present stereoscopic PIV system, thein situ cali-bration procedure and the comparison of the stereoscPIV and LDV measurement results can be found in Ref.




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EXPERIMENTAL RESULTS AND DISCUSSIONS

The large-scale streamwise vortices generated bylobed nozzle and azimuthal Kelvin–Helmholtz vortices asuggested to pay important roles in the mixing processcore jet flow with ambient flow. Figure 4, taken form Re19, illustrates the evolutions and interactions of these voces qualitatively. The pictures are planar LIF flow visualiztion images of a lobed jet mixing flow exhausted from tsame lobed nozzle used in the present study. Downstreathe lobed nozzle trailing edge (Z/D50.25, Z/H50.67), theexistence of the streamwise vortices in the form of six pe‘‘mushrooms’’ at the lobe peaks can be seen clearly. Tazimuthal Kelvin–Helmholtz vortices rolled up earlier at tlobe troughs were found to be six ‘‘crescents’’ at this crosection. As the streamwise distance increased toZ/D50.5(Z/H51.33), the ‘‘mushrooms’’ at the lobe peak grew uwhich indicated the intensification of the streamwise vortic


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generated by the lobed nozzle. Further downstream cplane of Z/D50.75 (Z/H52.0), the streamwise vorticegenerated by the lobed nozzle in the form of ‘‘mushroomstructures continue intensification. Six new counter-rotatstreamwise vortex pairs can be found at lobe troughs, whare called horseshoe vortex structures by Paterson.10 In thecross plane ofZ/D51.0 (Z/H52.67), some small-scalevortical and turbulent structures were found to appear inflow. The interaction between the streamwise vortices aazimuthal Kelvin–Helmholtz vortices made adjacent ‘‘musrooms’’ merge with each other, which may indicate that tstreamwise vortices deform the azimuthal Kelvin–Helmhovortical tube into pinch-off structures as suggested by MCormick and Bennett.14 In Z/D51.5 (Z/H54.0) andZ/D52.0 (Z/H55.33) downstream cross-planes, the ‘‘musroom’’ shape structures almost disappeared and the flow fiwas filled with small-scale turbulent and vortical structure




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The stereoscopic PIV measurement results of the prestudy will give quantitative information about the evolutioand interaction of these vortices.

The velocity distributions in the lobed jet mixing flowand circular jet flow

Figures 5–8 shows the stereoscopic PIV measuremresults at four typical cross-planes of the lobed jet mixflow, which include instantaneous velocity fields aensemble-averaged velocity fields. In the present study,ensemble-averaged velocity fields were calculated usinginstantaneous stereoscopic PIV measurement results.projections of the three-dimensional velocity vector in tcross planes~X–Y plane views! were also given in the fig-ures in order to reveal the cross stream~streamwise vortices!in the lobed mixing flow more clearly.

In the Z/D50.5 (Z/H51.33) cross plane, the lobed jeflow was found to be in the same geometry as the lonozzle trailing edge. The ‘‘signature’’ of the lobe nozzlethe form of ‘‘six-lobe structure’’ can be seen clearly fro


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both the instantaneous and ensemble-averaged velocity fi~Fig. 5!. Seven high-speed peaks can be seen fromensemble-averaged velocity field, which represent thelobes and the central core. From theX–Y plane view of theensemble-averaged velocity field shown in Fig. 5~d!, a strongcross stream was found to exist in the lobe jet mixing floThe core jet flow expanded outward in the lobe regions aambient flow injected inward in the lobe trough regionBoth the core jet flow and ambient flow are generally folloing the inward and outward contours of the lobed nozzwhich results in the large-scale streamwise vortices seethe lobed jet mixing flow. The maximum cross streaensemble-averaged velocity in theX–Y plane is found to beabout 4.7 m/s at this cross plane. This value is found toalmost the same value asU0•sin(uout), whereU0 is the corejet velocity at nozzle exit anduout is the outer penetrationangle of the lobes.

Figure 6 shows the stereoscopic PIV measurementsults in theZ/D51.0 (Z/H52.67) cross plane of the lobejet mixing flow. The instantaneous velocity field was foun




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to become more turbulent than that in theZ/D50.5 (Z/H51.33) cross plane. However, the ‘‘signature’’ of the lobnozzle can still be identified from the instantaneous velocfield. The core jet flow was found to diffuse to the ambieflow substantially, and the size of the high-speed regionthe center of the jet flow became smaller compared within theZ/D50.5 (Z/H51.33) cross plane given in the Fig. 5The maximum value of the ensemble-averaged cross-strvelocity in theX–Y plane is found to decrease to 4.3 mSince the present lobed jet mixing flow is a free jet, tvector plot of the cross stream flow@Fig. 6~d!# shows that thecenter of the streamwise vortices have spread outwardthey travel downstream. The same phenomena werefound in the LDV measurement results of Bleovich aSamimy.18

As the downstream distance increases toZ/D52.0(Z/H55.33) ~Fig. 7!, the lobed jet mixing was found tobecome much more turbulent. The ‘‘six-lobe structures’’the core jet flow are nearly indistinguishable in the instan


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neous velocity field. Although seven humps still canfound in the ensemble-averaged velocity field, which repsent the high speed flow from the nozzle core and six lobthey have become much more rounded than that in thestream cross planes. The cross stream velocity vector shon Fig. 7~d! also indicated that the magnitudes of the crostream velocity have decreased quite a lot compared wthose in upstream cross planes. The size of the high-spregion in the center of the jet flow and six lobes were fouto decrease substantially due the intensive mixing of the cjet flow with ambient flow.

When the downstream distance increases toZ/D53.0(Z/H58.0) ~Fig. 8!, the lobed jet mixing flow became sturbulent that the ‘‘six-lobe structure’’ of the core jet flowcan not be identified in the instantaneous velocity field. Tflow field is almost fully filled with many small-scale vortices. The ensemble-averaged velocity distribution ashowed that the distinct hump representing the high-spcore jet flow has dissipated so seriously that the iso-velo


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contours of the high-speed core jet flow have become smconcentric circles in the center of the jet flow. The ensembaveraged cross stream velocity in this cross plane is so wthat it almost cannot be identified from the velocity vecplot.

Figure 9 shows the decay of the maximum value ofensemble-averaged cross-stream velocity normalized byvalue of U0•sin(uout) with increasing downstream distancIt can be seen that the maximum velocity of the ensemaveraged cross stream velocity decayed very quickly witthe first two diameters due to intensive mixing of the coreflow with ambient flow, then the decay rate became mmoderate further downstream. In the downstream cross pof Z/D52.0 (Z/H55.33), the maximum value of thensemble-averaged cross stream velocity became less20% of the value at the exit of the lobed nozzle.

Figure 10 shows the ensemble-averaged velocity fiein the circular jet flow at the same four cross planes as thshown in Figs. 5–8 for the lobed jet mixing flow. From thfigures it can be seen that the ensemble-averaged veldistribution of the circular jet was found to be a round humas it is expected. As the downstream distance increaseshump expands radially due to the growth of the shear labetween the core jet flow and ambient flow.

The streamwise vorticity distributions in the lobed jetmixing flow

The above velocity vector plots show the existence overy strong cross stream~streamwise vortices! in the lobedjet mixing flow. The core jet flow expands outward along tlobes and ambient flow injects inward in the lobe trougwhich results in the generation of large-scale streamwisetices with the vortex size on the order of the lobe heightpair of counter-rotating streamwise vortices in the lobedmixing flow can be generated for each lobe. In order to stuthe evolution characteristics of these streamwise vortquantitatively, the streamwise vorticity distributions in seeral cross planes of the lobed jet mixing flow were calculabased on the velocity data obtained by the stereoscopicmeasurement. The normalized instantaneous streamwise

FIG. 9. Decay of the normalized maximum velocity of the ensembaveraged cross stream in the lobed mixing flow.


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ticity (Ãz) and ensemble-averaged streamwise vortic(Ãz) were calculated based on the following equations:

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Figure 11~a! shows the instantaneous streamwise vority distribution in theZ/D50.5 (Z/H51.33) cross plane. Asindicated in the above velocity vector plots, six pairscounter-rotating streamwise vortices were found to be geated in the lobed jet flow downstream of the six lobes. Tsize of these streamwise vortices is found to be equivalenthe height of the lobes. Compared with the instantanestreamwise vorticity field, the ensemble-averaged strewise vorticity was found to be smoother. The maximuvalue of the ensemble-averaged streamwise vorticity, whis about 4.0, is found to be a bit smaller than that ofinstantaneous counterpart, which is about 4.5.

In the Z/D51.0 (Z/H52.67) cross plane, the six pairof the large-scale streamwise vortices shown in Fig. 11~a!were found to deform seriously. Some of the streamwise vtices were even found to break into smaller [email protected]~a!#. The adjunct streamwise vortices were found to mewith each other to form a vortex ring in the lobe troughwhich is quite similar to the planar LIF flow visualizatioimages shown in Fig. 4~d!. The maximum value of the in-stantaneous streamwise vorticity in this cross plane wfound to be almost at the same level as the value inZ/D50.5 (Z/H51.33) cross plane. From the ensembaveraged streamwise vorticity distributions shown in F12~b!, the six pairs of large-scale streamwise vortices wfound to grow and expand radially. The strength of theensemble-averaged streamwise vortices were found tocrease with the maximum value of the ensemble-averastreamwise vorticity being about the half of that at theZ/D50.5 (Z/H51.33) cross plane.

Besides the six pairs of large-scale streamwise vorticorresponding to the six lobes, six pairs of smaller aweaker streamwise vortices can also be identified fromensemble-averaged streamwise vorticity distributions, whare at the six-lobe troughs. These smaller and weaker strewise vortices at lobe troughs are the horseshoe vortex sttures noted by Paterson,10 which had also been visualizeclearly in Fig. 4. McCormick and Bennett14 also proved theexistence of such horseshoe vortex structures in a plalobed mixing flow.

As the downstream distance increased toZ/D52.0(Z/H55.33), the six pairs of large-scale streamwise vorticcould no longer be easily identified from the instantaneostreamwise vorticity field shown in Fig. 13~a!. Instead oflarge-scale streamwise vortices, many smaller streamwvortices were found in the instantaneous streamwise vorti

-



FIG. 10. The ensemble-averaged velocity fields in the circular jet flow.

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distributions. The large-scale streamwise vortices obserin the upstream cross planes have been broken downmany smaller streamwise vortices. However, it shouldmentioned that the maximum value of the instantanestreamwise vorticity is found to be at the same level as thin the upstream cross planes.

From the ensemble-averaged streamwise vorticity disbution shown in Fig. 13~b!, it can be seen that the large-scastreamwise vortices revealed in the ensemble-averastreamwise vorticity distributions of upstream cross plawere found to break down into many smaller vortices. Tstrength of these streamwise vortices decayed substantand the maximum value of the ensemble-averaged strewise vorticity was found to be just about one-fifth of thatthe Z/D50.5 (Z/H51.33) cross plane.


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As the downstream distance increased toZ/D53.0(Z/H58.0) ~Fig. 14!, so many small-scale streamwise votices were found to appear in the lobed jet mixing flow ththey almost fully filled the measurement window. The mamum vorticity value of these smaller instantaneous streawise vortices was found to be still at the same level of thoin upstream cross planes. However, from the ensemaveraged streamwise vorticty distribution in this cross plait can be seen that the size and strength of the ensemaveraged steamwise vortices decreased substantially.‘‘signature’’ of the lobed geometry of the nozzle almost canot be identified from the ensemble-averaged streamwvorticity distribution.

From the above instantaneous streamwise distributiin different downstream cross planes, it can be seen tha



FIG. 11. The streamwise vorticity distributions atZ/D50.5 (Z/H51.33) cross plane of the lobed jet mixing flow.

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the downstream distance increases, the size of the instaneous streamwise vortices in the lobed jet mixing flow dcreases. This indicates the large-scale streamwise vortgenerated by the lobed nozzle broke into smaller vorticethey travel downstream. However, the maximum vorticvalues of the smaller vortices were found to be almost atsame level as their parent streamwise vortices. These resuggested that the dissipation of the large-scale streamvortices generated by the corrugated trailing edge oflobed nozzle did not happen abruptly, but rather appearebe a gradual process. The large streamwise vortices wfound to break down into many smaller, but not weakstreamwise vortices as the downstream distance increaThus, besides the mixing enhancement at large scale, mi


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at a finer scale could also be achieved in the lobed jet mixflow. The result, therefore, agrees well with those obtainby Belovichet al.31

The ensemble-averaged streamwise vorticity distributcan be used to indicate the overall effect of the specialometry of the lobed nozzle on the mixing processes inlobed jet mixing flows. The cross stream generated byspecial geometry of the lobed nozzle results in the generaof large-scale ensemble-averaged streamwise vortices inlobed jet mixing flow. The large-scale ensemble-averagstreamwise vortices revealed in the ensemble-averastreamwise vorticity distributions were found to grow up aexpand radically within the first diameter, which may corrspond to the streamwise vortex formation and intensificat





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steps suggested by Werleet al.11 and Eckerleet al.12 ~TheirLDV measurement results only reveal the ensembaveraged streamwise vortices in a planar lobed mixing flo!In the downstream cross planes ofZ/D52.0 ~Fig. 13! andZ/D53.0 ~Fig. 14!, the large-scale ensemble-averagstreamwise vortices were found to break down into smavortices. The strength of the ensemble-averaged streamvorticity was also found to decay rapidly as the downstredistance increases. Figure 15 gives the decay of the mmum value of the ensemble-averaged streamwise vorticitthe lobed jet flow quantitatively. From the figure, it canseen that over the first diameter of the test nozzle,ensemble-averaged streamwise vorticity decayed veryidly. In the downstream region of theZ/D51.0 (Z/H52.67) cross plane, the large-scale ensemble-avera


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streamwise vortices were found to break down into masmaller vortices, then the decay rate of the ensemaveraged streamwise vorticity slows down. In the dowstream cross plane ofZ/D53.0 (Z/H58.0), the ensembleaveraged streamwise vorticity dissipated so seriously thatstrength of the streamwise vortices became about one-tof that at the lobed nozzle exit. This may also indicate tthe overall effect of the special geometry of the lobed nozon the jet flow mixing has almost disappeared at this dowstream location. It should be noted that the profiles shownFig. 9 and in Fig. 15 are very similar. This may be explainby that since the streamwise vorticity is computed by takthe gradient of the cross-stream velocity components, thfore, the decay of ensemble-averaged streamwise vort



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shown in Fig. 15 is quite similar to the decay of the mamum cross-stream velocity shown in Fig. 9.

Measurements of the same lobed nozzle at lower Rnolds numbers ~water jet! using a conventional two

FIG. 15. The decay of the maximum value of the ensemble-averastreamwise vorticity in the lobed jet mixing flow.


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dimensional PIV system19 is also given in Fig. 15. From thecomparison of the maximum ensemble-averaged streamvorticity decay profiles at two Reynolds number levels, it cbe seen that the ensemble-averaged streamwise vorticihigher Reynolds numbers decayed more rapidly. This incates that the location where the large-scale ensemaveraged streamwise vortices break down into smaller voces is expected to move upstream for the higher Reynnumber case.

The distribution of the turbulent kinetic energy

The mixing process between the core jet flow and ament flow can be represented directly and quantitatively frthe distribution of the turbulent kinetic energy distributionThe turbulent kinetic energy distributions of the lobedmixing flow in four selected cross planes are shown in F16. The turbulent kinetic energy values shown in theseures are calculated by using the following equation:

d

FIG. 16. The turbulent kinetic energy distributions in the lobed jet mixing flow.



FIG. 17. The turbulent kinetic energy distributions in the circular jet flow.

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K~x,y,z!51

2U02 ~rms~u8!!21~rms~v8!!21~rms~w8!2!

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where N5400 is the number of the instantaneous sterscopic PIV measurement frames used for the ensemaveraged parameter calculation.ut , v t , and wt are the in-stantaneous velocity components inx, y, and z direction,while U, V, andW are the ensemble-averaged velocity coponents.

In theZ/D50.5 (Z/H51.33) cross plane, the contour othe turbulent kinetic energy distribution was found to exhithe lobed nozzle ‘‘signature,’’ which indicates that mixing


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the core jet flow with ambient flow is conducted mainlythe interface of the two streams. A low turbulent kinetic eergy region was found in the center, which correspondsthe unmixed high-speed core in the center of the jet flowshould also be noted that the regions with higher turbulkinetic energy values are found to concentrate at the ltroughs instead of lobe peaks. This may be caused byearlier rolling-up of the azimuthal Kelvin–Helmholtz vortces at the lobed troughs, which has been reported and valized in the earlier work of the authors19 by using planarlaser induced fluorescence~LIF! technique.

In the Z/D51.0 (Z/D52.67) cross plane, the mixingarea between the core jet flow and ambient flow was founincrease and the mixing region was found to expand outwand inward. The unmixed core jet flow in the center of theflow decreased. The contour of the turbulent kinetic enedistribution was found to form ‘‘mushrooms structures’’ inthe downstream projections of the lobed peaks, which m


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be caused by the pinch-off effect of the streamwise vortion the azimuthal Kelvin–Helmholtz vortices suggestedMcCormick and Bennett.14 The similar ‘‘mushrooms structures’’ in the lobed jet flow has also been reported by Belich et al.31 in their passive scalar measurement results.

As the downstream distance increased toZ/D52.0(Z/H55.33), the mixing region between the core jet floand ambient flow increased substantially, which almost filthe investigation window fully. The adjacent ‘‘mushroostructures’’ merged with each other. At theZ/D53.0 (Z/H58.0) cross plane, the contour of the turbulent kineticergy were found to be circular, which is quite similar to thin the far field of a circular jet flow.

Figure 17 shows the turbulent kinetic energy distribtions in the same cross planes for the circular jet flow. Atexit of the circular jet flow, the contour of the turbulent knetic energy distribution was found to be a thin ‘‘ring struture’’ as it is expected. As the downstream distancecreased, the ‘‘ring structure’’ was found to expand inwaand outward, which corresponds to the growth of the shlayer between the core jet flow and ambient flow. Compawith the turbulent kinetic energy distribution in the lobedmixing flow at the same downstream locations, it can be sthat the area of the mixing region in the lobed jet mixiflow will be much bigger than that in the circular jet.

In order to compare the mixing effectiveness in the lobjet mixing flow and circular jet flow more clearly and quatitatively, averaged turbulent kinetic energy~ATKE! of thejet mixing flows~Fig. 18! at each measured cross plane wecalculated by using the following equation:

ATKE5*rW~x,y,z!K~x,y,z!dx dy

*rW~x,y,z!dx dy, ~4!

wherer is density of the air jet flows,W is the ensemble-averaged velocity in theZ-direction andK is the turbulentkinetic energy value of the stereoscopic PIV measuremresult at each measurement cross plane.

For the lobed jet mixing flow, it can be seen that taveraged turbulent kinetic energy profile grew very rapiwithin first diameter of the test nozzle, then decrease tmore moderate rate in the downstream region ofZ/D.1.0

FIG. 18. The averaged turbulent kinetic energy profile in the lobedmixing flow and the circular jet flow.


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(Z/H.2.67). The ATKE growth rate reached the peak vaat Z/D52.0 (Z/H55.33), then began to decrease. Thisbecause that within the first one diameter of the test noz(Z/H,2.67), due to the stirring effect of the large-scastreamwise vortices revealed in the ensemble-averastreamwise vorticity distributions, the core jet flow and abient flow mixed intensively. In the downstream regionZ/D.1.0 (Z/H.2.67), the large-scale streamwise vorticgenerated by the lobed nozzle were found to break downsmaller vortices, i.e., the stirring effect of the ensembaveraged streamwise vortices weakened. So, the growthof the averaged turbulent kinetic energy was found tocrease, and reach its peak at theZ/D52.0 (Z/H55.33)cross plane. The ensemble-averaged streamwise vorticitybecome so weak that it almost cannot affect the mixing pcess in the downstream region ofZ/D.2.0 (Z/H.5.33).Most of the turbulent kinetic energy in the lobed jet mixinflow dissipated in the intensive mixing upstream, so the

t

FIG. 19. Reconstructed three-dimensional flow fields of the lobed jet mixflow in the near region (Z/D,3.0).


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eraged turbulent kinetic energy begins to decrease furdownstream. It also indicates that most of the enhancemof mixing caused by the lobe nozzle occurs within the fitwo diameters. The mixing between the core jet flow aambient flow beyond the first two diameters occurs bysame gradient-type mechanism as that for a conventionacular jet. This result is also found to agree with the findinof McCormick and Bennett14 and Glauseret al.17 in a planarlobed mixing flow, who suggested that the maximum effetiveness region for a lobed mixer is about the first six loheights.

For the circular jet flow, the averaged turbulent kineenergy is found to grow linearly in the investigated regi(Z/D,4.0). The linear growth behavior is consistent wclassical thin-layer approximations assuming simple edviscosity turbulent transport.32 At the exit of the nozzle, theaveraged turbulent kinetic energy in lobed jet mixing flowfound to be much greater than that in the circular jet floThis is believed to be caused by the mixing enhancemassociated with the increased initial interfacial area oflobe geometry as suggested by Elliottet al.13

As mentioned above, the enhancement of mixing cauby the special geometry of the lobes is almost negligiafter the first two diameters, and the mixing between the cjet flow and ambient flow will occur by the same gradientype mechanism as that of a conventional circular jet floDue to the intensive mixing upstream, the velocity of tcore jet flow decays very quickly. A weaker shear lay~lower velocity ratio! is expected in the further downstrearegion ~Z/D.3.0 andZ/H.8.0! of the lobed jet mixingflow compared with circular jet flow. Therefore, in the futher downstream region~Z/D.3.0,Z/H.8.0!, the averagedturbulent kinetic energy of lobed jet mixing flow was founto be smaller than the circular jet flow. McCormick anBennett14 reported similar results in the far field of a planlobed mixer flow field.

Reconstructed three-dimensional flow field

Based on the stereoscopic PIV measurement results across planes of the lobed jet mixing flow, the thredimensional flow field at the near field (Z/D,3.0) of thelobed jet mixing flow was reconstructed. Figure 19~a! showsthe three-dimensional ensemble-averaged velocity vecThe velocity iso-surfaces reconstructed from the thrdimensional measurement results are shown in Fig. 19~b!.The velocity magnitudes of these iso-surfaces are 4 m/m/s, 12 m/s, and 16 m/s, respectively. From the reconstruthree-dimensional velocity vectors and velocity iso-surfacthe three-dimensional features of the lobed jet mixing flcan be seen clearly.

CONCLUSIONS

In the present study, the flow field in the first four diameters of a lobed jet mixing flow and a conventional circujet flow were measured by using a high-resolution sterscopic PIV system. The characteristics of the mixing procin the lobed jet mixing flow were compared with the convetional circular jet flow. The existence of large-scale strea


ernttdeir-s

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-

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wise vortices in the lobed jet mixing flow is revealed cleafrom stereoscopic PIV measurements. From the instaneous streamwise vorticity distributions of the lobed jet ming flow, it can be seen that the large-scale streamwisetices generated by the corrugated trailing edge of the lonozzle break into smaller, but not weaker streamwise voces gradually as they travel downstream. This is proposethe reason that a lobed nozzle can enhance both the lascale mixing and small-scale mixing in flow field as reportin previous studies. The overall effect of the lobed nozzlemixing process in the lobed jet flow was evaluated by alyzing the ensemble-averaged streamwise vorticity distritions. The ensemble-averaged streamwise vortices inlobed jet flow were found to expand radially within the firdiameter downstream, then break down into smaller aweaker vortices in the following region, as has been calledthe formation, intensification, and breakdown processesother researchers. The strength of the ensemble-averstreamwise vorticity was found to decay very rapidly ovthe first diameter of the lobed nozzle, then decay at a mmoderate rate further downstream. The turbulent kineticergy distributions also indicated that most of the intensmixing between the core jet flow and ambient flow occurrover the first two diameters of the lobed jet flow~first sixlobe heights!. In the downstream cross plane of three nozdiameters, contours of turbulent kinetic energy distributiare quite similar to those in a circular jet flow at far fielThese may indicate the mixing enhancement caused byspecial geometry of the lobed nozzle is almost finished athe first two diameters downstream of the lobed nozzle~firstsix lobe heights!. The mixing between the core jet flow anambient flow further downstream of the lobed jet mixinflow will occur by the same gradient-type mechanism as tfor a circular jet flow.

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a study on a lobed jet mixing ﬂow by using stereoscopic...

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