[American Institute of Aeronautics and Astronautics 15th AIAA Computational Fluid Dynamics...

(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

AM A A A01-31337

AIAA 2001-3031

BIFURCATION AND CONNECTIVITY IN A SYNTHETICJET VORTEX TRAIN

Anwar Ahmed and Zafar Bangash

Aerospace Engineering DepartmentAuburn University, AL 36849

31st AIAA Fluid DynamicsConference & Exhibit

11-14 June 2001 / Anaheim, CA

For permission to copy or republish, contact the copyright owner named on the first page. For AlAA-held copy-right, write to AIAA, Permissions Department, 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344.


BIFURCATION AND CONNECTIVITY IN A SYNTHETIC JET VORTEX TRAIN

Anwar Ahmed1 and Zafar Bangash2

Aerospace Engineering DepartmentAuburn University, AL 36849

AbstractReported are the results of flow visualization, PIV and hotfilm measurements in the flow field of synthetic jetsemanating from an orifice connected to a round cavity.Vortex train was observed to bifurcate into elliptical lobeswith the additional fluid continuously ejecting through athin layer between them. Streamwise vortex filaments fromthe successive ring vortices remained connected to theamalgamated vortices of opposite sign within the cavity.Due to axial compression the azimuthal instability of thevortices in the cavity amplified resulting in a "continuous"stream of filaments from the orifice. Flow within thecavity was dominated by counter rotating foci structuresthat were periodically fed by the vorticity within the flow.The rotation of foci induced a slow swirling motion thatwas observed even outside the cavity. The direction ofswirl often reversed after one or the other of the two focigained strength and swelled. Piston velocity and amplitudeof oscillations had a strong influence on the jetcharacteristics such as the maximum velocity, trajectory,spread rate and blooming. With increasing frequency ofoscillations the location of jet blooming moved upstreamtowards the orifice and finally resulted in fully"turbulent" bifurcated jets. Interactions between the jetand adjacent recirculating regions resulted in 90° bloomingand trifurcation in certain cases.

NomenclatureA Amplitude of oscillations - mmb Jet width (based on 1 /2)D Diameter of nozzle/orificef Frequency of oscillationsfr Reduced frequency -fA/VpRe Reynolds number tyD/vU0 Jet velocity at the nozzle exit - mm/sUmax Maximum/centerline velocity of jet - mm/sVp Piston velocity - mm/sx Streamwise distance measured from exity Cross-stream/redial distance measured from

center of exitv Kinematic viscosity of water

1 Associate Professor, Associate Fellow AIAAGraduate Research Assistant, Student Member AIAA

Copyright ® 200 Iby the American Institute of Aeronauticsand Astronautics, Inc. All rights reserved

I. IntroductionAcoustic streaming due to periodic boundary layers inquiescent surrounding finds its origin in the mathematicaltreatment of acoustic phenomenon observed in Kundt'sdust tube by Lord Rayleigh1. Schlichting2 in 1932 appliedhis theory to the flow generated by an oscillating cylinderand observed that the streamlines from the outer fluidwere directed towards the body in the plane of oscillationand away in the direction of motion. Similar streamlinespattern can be envisioned through heuristic argument byenforcing continuity equation at a point on the oscillatingsurface where a fluid element has been displaced. Classicaltreatment of acoustic streaming is considered in detail by

1 A. ^ (\Westervelt, Nyborg , Andres and Ingrad ' . An excellentreview article by Lighthill summarizes this phenomenonas due to the dissipation of acoustic energy. Earlyexperimental results are credited to Schlichting , Andrade ,and Ingrad and Labate .Acoustic streaming in an unbounded domain such as acylinder oscillating in quiescent environment results insecondary flows surrounding the bodies themselves. Inconfined domains with finite openings such as tubes orcavities a flow with directional characteristics results as aconsequence of acoustic streaming. The resulting flowimparts finite momentum to its surrounding at a zero netmass flux and because of its synthetic character is referredto as "synthetic jet."The underlying mechanism for the formation of jet is thetrain of ring vortices that form at the edge of theaperture/orifice and their subsequent convection due toself induction10'11. With increasing frequency of oscillationsthese vortices form closer and the resulting stream appeareither as a laminar or a turbulent jet depending on theinitial momentum and axial pressure gradient.Following the detailed work of Ingard12 on the design ofacoustic resonators in the early fifties, new generation ofdevices with acoustic drivers have gained notoriety onceagain for fluid dynamics applications due to theirsimplicity and small sizes.A need for effective flow control as well as enhancementof mixing between different species is paramount invarious fields of engineering as outlined by Gad-el Hakin his recent book. The reincarnation of an over a centuryold phenomenon as synthetic jet has therefore become apanacea for flow control. Micro and/or macro applicationsof synthetic jets or zero mass flux devices vary fromcontrol of separated flow on an airfoil operating in the highalpha regime to efficient combustion .The present set of experiments were focused on the study


acoustic streaming at a fundamental level with an emphasison the understanding of the connectivity between thevortex train and the source cavity from where thesevortices emerge, and overall mechanism of entrainment.

n. Experimental SetupTests were conducted in the Vortex Dynamics Laboratoryof Aerospace Engineering Department. Piston drivensynthetic jets were produced with water as a workingmedium in a clear acrylic tank with internal dimensions of24cm x 24cm x 60cm(L). A 76 mm long transparentcylindrical cavity of 25 mm bore was machined from solidacrylic rod to accommodate nozzle plugs of three orificesizes of 3mm, 6mm and 12mm. A Teflon piston wasconnected to a heavy duty linear drive motor by a 3mmOD stainless tube which was also used to supplyfluorescent dye and seeding particles to the cavity. Asawtooth waveform from a Wavetec 182A functiongenerator and amplified by MB Dynamics SS250VCFpower amplifier was used as an input signal to ensure rapidresponse at low frequency bandwidth used in thisinvestigation. A position sensor attached to the linearmotor was used to monitor the amplitude of oscillations inreal time (Figure 1.) The output voltage of the positionsensor was calibrated with the help of a high speedcamera and motion analysis software to monitor pistontravel and velocity. The piston was capable of moving ±30 mm in the cylinder and its mean position within thecavity was maintained at a fixed axial location by adjustingthe DC offset voltage of the function generator. Due to themechanical limitations the frequency response of the linearmotor remained below 300Hz and therefore maximumdisplacement (amplitude) of the piston was controlled foreach forcing frequency to maintain a constant value of 0.5for the reduced frequency fr. Piston velocity was restrictedto 30mm/sec at the highest frequency of oscillations(lOOHz) to completely eliminate the accumulation ofcavitation bubbles in the cavity after they formed on bothsides of the nozzle exit.

A. Flow VisualizationA variety of flow visualization techniques were used todetermine the nature of synthesis in the flow field of thejet. These techniques included laser induced fluorescenceof Sodium Fluoresceine and Rhodamine dyes with 5WArgon ion laser and a laser fiber light sheet generator,illumination of seeded particles with a synchronizedOxford Lasers HS1000 IR laser operating at 810nmwavelength, and a Red Lake Imaging Motion ScopePCI2000 high speed camera capable of 2000 frames persecond. Data was captured at 250 frames per second andplayed back at 10 frames per second. Output fromcomputer was stored on video tapes with the help of a JVCBR-S622DXU professional video recorder. Results wereinterpreted from frame by frame analysis of high speedimages that were later printed on a Sony video printer.

B. Flow Field MeasurementsFlow field measurements were made with the help of aDantec MT Inc. PIV-2000 FlowMap system with a Ik x1.3k CCD/PLIF camera and 50mJ dual pulsed YAG lasers.Data consisted of measurements that were phase locked atpiston upstroke and downstroke, and unlocked conditionsas well. An average of 20 images was used to calculate themean velocities using standard cross-correlationtechniques. Power spectra of the jet and flow with in thecavity was measured with the TSI Inc. IFA 300anemometer and a film probe. Measurements were made ata sampling frequency of 1000 Hz. Time histories of 2 to 4seconds were obtained and power spectra was computedusing signals processing routines of Matlab software.

HI. Results and DiscussionTable I shows the test matrix for frequencies, pistonvelocities, their corresponding amplitudes, exit velocitiesand Reynolds numbers.The term nozzle and orifice are interchangeably used as anapproximation however it may be noted that the"openings" tested had finite converging angle. Based onthe thickness of the nozzle lip jets produced in the presentset of experiments were within the acoustic streamingregime outlined by Ingrad12.

A* Flow VisualizationJet characteristics were dominated by the amplitude of thepiston displacement, velocity and its proximity to the exitaperture. Ingrad and Labate have classified acousticstreaming into four regions that depend on the thicknessand diameter of the orifice. These regions were alsoobserved during the present experiments however onlyresults of regions three and four are relevant to theformation of jet and are discussed in detail. The globalfeatures of the flow can be described for the entire range offrequencies to consist of formation and convection of ringvortices during the upstroke of the piston followed byformation of ring vortex at the lip of the nozzle inside thecavity during downstroke. It is the downstroke andformation of counter vortex during which period the jetformed outside exhibits two lobes instead of a singlevortex when viewed from the direction of motion. As themotion of the piston continues, a recirculation region setsup within the cavity and consists of a sheet of closelypacked vortices. A clear distinction can be drawn betweenentrainment of dye free fluid from the surrounding and thedyed fluid in the cavity (Figure 2a.) Inside the cavity thecircumferential compression of vortices leads to theirbreakup that results in the formation of counter rotatingfoci. During the transients of changing frequency oramplitude the number of foci increased from two to fourhowever as the flow settled to new forcing conditions onlytwo dominant foci were visible to which the lobes in theouter jet remained anchored (Figure 2b.) Amongst the twofoci, one always appeared to entrain more and induced


rotational motion on the entire flow field. The direction ofrotation switched sign when the opposite focus dominated.The overall period of this rotational oscillation wasmeasured to vary between four to fifteen seconds and isattributed to inherent nonlinear acoustic impedance . It isinteresting to note that during the formation of ring vortexoutside the nozzle, flow was marked by the dye in theboundary layer of the nozzle inner wall however flow fromthe cavity always appeared to eject along a thin layerdistinctively marking the boundary between the two lobes.Unlike traditional ring vortices in conventional jets thatmaintain a coherent physical appearance for fairly largedistances the cross-sectional view of the jet at sevendiameters do not show any toroidal structure (Figure 2c.)The four arms visible in the same figure reduced to two forhigher frequencies (40Hz and greater). This feature of theflow will be discussed later.A closeup view of 12mm diameter nozzle is shown inFigure 3a. During the downstroke, vortex at the exit makesa sweeping motion inwards which is followed by theejection of a vortex during upstroke. Repetition of thisprocess results in necking of the jet. The recirculationregion inside the cavity is also visible in Figure 3a for a5Hz oscillation. As the frequency is increased, herringbonepattern of flattened vortex lobes become visible and bothedges of the nozzle act like periodic sources (FigureSb)This pattern persists for the remaining frequencies exceptthat the large recirculating flow becomes random and twovortical structures appear to position themselves on theinside and outside of the of the exit and resembles Region3 flow of Ingrad and Labate9. A view of flow inside thecavity reveals formation of cellular structures continuouslyfed by the fluid entrained from outside (Figure 3c.) At sixdiameters downstream the cross-sectional view of the jetcuts across strong streamwise vortices (Figure 3d).A sequence of photographs in Figure 4. show a side viewof a jet from 3mm nozzle for Vp = 2mm/sec. At lOHzvortex lobes are clearly visible. Since the entire jet has arotational component superimposed on it due to foci in thecavity, the jet appears to wander out of the plane ofsymmetry. As the frequency was increased the vortex lobesrolled outward in an incoherent manner and separated(Figure 4d.) The distinctive line between the lobes alongwhich the flow is fed from the cavity remains clearlyvisible. Another feature of this flow is the reversed flowalong the outer edges of the jet and formation of rollerssimilar to those observed in the shear layers. This reverseflow is clearly visible in Figures 4f-4i. Large amplitudeinstability of the jet in Figure 4f and Figure 4g is due to anout of plane interaction between the two lobes dividing theflow. At yet higher frequency a thin jet was formed whosefeatures are still under investigation (Figure 4j.)As the piston velocity was increased from 2mm/sec to6mm/sec, jet started to bloom. Oblique blooming of jethave been observed and reported for high speed jets1

however blooming was observed to occur at 90 degrees and

some cases in the direction opposite to the flow. This isattributed to the interaction between the jet and therecirculating eddies around it. The blooming became veryregular at higher frequencies and finally resulted in acompletely bifurcated jet at lOOHz (Figure 5d.) Bloomingwas also observed for piston velocity of lOmm/sec. Ateven higher piston velocities the emerging jet becamecompletely turbulent (not shown.) Figure 6 shows thestreamwise location measured from flow visualizationrecords where blooming was first observed for the range offrequencies tested. Also presented in the same figure arethe blooming locations for constant amplitude oscillations.Since the reduced frequency fr was constant, a fixedamplitude at high frequency implied lower piston velocity.Thus the curve indicates that the blooming occurred fartheraway from the exit for lower piston velocities even athigher frequencies.The important aspects of the flow visualization resultsbased on detailed observations are summarized in a cartoonin Figure 7. As the piston begins its downstroke, flow ismomentarily reversed and the vortex filaments on the ringvortex from pervious upstroke undergo axial stretching thatincreases the vorticity within the filaments and hence theinduced velocities. Azimuthal bending waves of a ringvortex and their amplification due to rotation of vortex

18 19filament has been reported elsewhere ' and isconsidered to play an important role in the formation oflobes. In the cavity the radius of curvature of rolled upsheet of vorticity continues to decrease during the upstrokeand bends toward the "straight" vortex filaments. Thehigher concentration of vorticity eventually realigns theflow in the filaments into symmetric foci shown in Figure2b. The next cycle begins with the distorted ring vortex orlobe bifurcated in the middle. Throughout the jet fluidfrom the cavity gets pumped along the vortex filaments.Some aspects of this flow are similar to cut-and-connectprocess described by Hussain and Hussain20.One additional feature of the flow was its excursion fromthe plane of symmetry. This is also observed in the resultsof Thurston and Martin16 and is attributed to loss ofmomentum, adverse streamwise pressure gradient as wellas asymmetry at in the initial conditions due rotation offlow in the cavity.

B. Mean Velocities1. Constant Piston Velocity. An average of twenty sets ofcross-correlated images of phase locked PIV measurementsare presented in Figure 8 for two piston velocities. Asingular point was always observed near the exit andbetween the successive set of vortices. Jet statisticspresented in the remaining figures were calculated frommean PIV measurements.In presenting the velocity data maximum velocity insteadof conventional centerline velocity is used due to the out ofplane excursion of the jet. The amount of shift or thetrajectory of mean location of U,, is plotted in Figure 9


for two piston velocities. It may be noted that the jetappears to maintain its direction for higher frequencies.For higher range of piston velocities (Vp J>_30mm/sec) jetwas visibly more centered.Mean velocity distribution in the jet collapsed well and isplotted for x/D=10 in Figure 10. Streamwise decay ofUmax normalized by exit velocity U0 is plotted in Figure11. For this range of x/D the data is similar to acousticstreaming data of Lebedeva21. After the initial overshootumax begins to decay linearly with the distance x, thoughat a higher rate compared to conventional jet. This isattributed to the large scale mixing, recirculation androtation of the jet. Data of Figure 11 is plotted in Figure12 with UQJ^ normalized by piston velocity Vp A bettercollapse of data suggest that the U, scales weli with thedriver variables. Jet width b plotted in Figure 13 exhibitshigher growth rate compared to conventional trends pastthe potential cone of three to six diameters. A rapid decayof jet past thirty diameters indicate departure of jet fromthe plane of symmetry.

2. Constant Piston Amplitude* Tests were also conductedto determine the effect of fixed piston travel on the jetcharacteristics. Since the reduced frequency for the entireseries of tests was kept at a constant value of 0.5, pistonvelocity was accordingly increased with increasingfrequency. Thus, for lOOHz operation a piston velocity of30mm/s was obtained (Refer to Table I.) Figure 14confirms the fact that even at low amplitudes, higher pistonvelocities are likely to produce jets comparable toconventional jets. At a fixed mean location of the piston inthe cavity changes in frequency and hence Vp resulted inflow similar to Region 1 and 2 of Ingard and Labate9 i.e.without any substantial jet flow. However jet did formwhen piston was moved closer to the exit. This signifiesthe influence of cavity depth on acoustic streaming.

3. Power Spectrum. Power spectrum measured with a hotfilm probe positioned in the middle of the jet at x/D = 10is presented in Figure 15 for two frequencies and pistonvelocities. Mid position of the probe was intended toexplore the spectral contents close to the layer of fluidbetween the two lobes of the bifurcated jet. As mentionedin the flow visualization section, it is within this layerthrough which the fluid from the cavity periodically butsteadily flows out.A cutoff frequency of 500Hz was used for entire range ofmeasurements. Higher PSD levels were always associatedwith higher piston velocities. For piston oscillation at20Hz forcing frequency and its harmonics are clearlyvisible for Vp = 20mm/sec. The spectra for Vp =lOmm/sec in the same figure does not register anyharmonic interaction on the contrary. This trend iscompletely reversed at lOOHz oscillation and harmonics arevisible for Vp = lOmm/sec and not for Vp = 20mm/sec.This can be explained with reference to the flow

visualization results. At low piston velocity and lowfrequency the only dominant frequency on the mid layeris the forcing frequency itself. The observed transversestreaks on the thin layer between the lobes did not exhibitany distortion and/or interaction with the outer flow. Athigher piston velocities the mixing of outer shear layer andtransport of fluid to and from the central region increaseunsteadiness of the central layer and therefore theturbulence content. This is manifested in the form ofhigher PSD levels. Same argument is presented to describethe spectra in Figure 15b i.e. higher turbulence levelssuperimposed on the basic flow.A 12mm diameter nozzle was used to investigate theswirl/rotation of flow inside the cavity. Hot film probe waspositioned well inside opening at x/D=-0.5. Pistonvelocity was increased to obtain flow pattern of Figure 2b.A time history of four seconds was recorded and only datafor one second is shown in Figure 16a. Unlike the timehistories obtained from the jet outside, a low frequencyfluctuating component can be seen carrying the lOOHzfrequency components. This is the slow rotational motionthat is superimposed on the entire flow and as explainedearlier is due to the strengthening of Streamwise vorticityin the jet and is firmly anchored in the cavity. First peak ataround 3Hz in the power spectrum corresponds to thisparticular motion. Also visible are the harmonics of thefundamental frequency. Power spectra in Figure 16b ispresented in log-linear scale only to highlight the lowerfrequencies.

IV. ConclusionsAcoustic streaming phenomenon was revisited tounderstand the dynamics of vorticity under periodic cross-stream and axial strains and its implications. Based ondetailed flow visualization and spectral measurementsfollowing conclusions are drawn for synthetic jets:Periodic forcing bifurcates a ring vortex. The bifurcatedvortices form continuous loops and are anchored to theircounterparts at the source (cavity). A synthetic jet is aclosely packed train of bifurcated vortices and appear aslobes. Legs of the vortex loop (parts that are aligned withthe direction of flow) entrains and merges with similar signvortex filaments (a feature of ring vortex), swell, intensifyand form only two dominant counter-rotating legs that areclearly visible as stable foci in the cavity. As the jet flowmoves downstream the distance between the Streamwisevortices increase that makes the vortex loops elliptical.Farther downstream, these loops become more flattenedand lose coherence. At this point the jet diffuses rapidly inthe dividing plane. Since either of the two foci candominate, acoustic streaming from axisymmetric orificewill be asymmetric - the level of asymmetry largely dependon the initial momentum of the jet that depends on thepiston velocity, amplitude and depth of the cavity. Theasymmetry of the flow is responsible for the out of planewandering of the jet. There is a rotational component


superimposed on the flow due to die foci in the cavity andcan be controlled if the exit velocity is high enough (orflow through very small openings) to split the streamwisevortices near the exit. Vortex re-connection under thosecircumstances will produce stable loops. The rotationalcomponent due to foci switches direction depending on thestrength of a particular focus. High exit velocity results inblooming and a completely bifurcated jet - further increasein velocity results in fully turbulent jet.

AcknowledgmentPart of this work was funded through a grant from AuburnUniversity College of Engineering Infrastructure Program.

ReferencesLRayleigh, L., "Theory of Sound," 1896, DoverPublications, New York, second edition, 1945

Schlichting, H., "Boundary Layer Theory," McGraw-Hill, New York, 7th edition, 19783'Westervelt, P. J., "The theory of steady rotational flowgenerated by a sound field," J. Acoustical Soc. OfAmerica, Vol. 25, 1953, pp. 60-674"Nyborg, W. L., "Acoustic streaming equations; laws ofrotational motion for fluid elements," /. Acoustical Soc.Of America, Vol. 25, 1953, pp. 938-944'Anders, J. M., and Ingard, U., "Acoustic streaming at

low Reynolds numbers," J. Acoustical Soc. Of America,Vol. 25, No. 5, 1953, pp. 932-938'Anders, J. M., and Ingard, U., "Acoustic streaming at

high Reynolds numbers," J. Acoustical Soc. Of America,Vol. 25, No. 5, 1953, pp. 928-932

Lighthill, J., "Acoustic streaming," /. Sound andVibrations, Vol. 61. No. 3, 1978, pp 391-418Andrade, E. N., "On the circulations caused by

vibrations of air in a tube," Proc. Roy. Soc. A, Vol. 134,1931, pp. 445-470Ingard, U., andLabate, S., "Acoustic circulation effects

and nonlinear impedance of orifices," /. Acoustical Soc. OfAmerica, Vol. 22, No. 2, 1950, pp. 211-218

2.

7.

8.

9.

' James, R. D., Jacobs, J. W., and Glezer, A., "A roundturbulent jet produced by an oscillating diaphragm,"Physics of Fluids, Vol. 8., No. 9, 1996, pp. 2484 - 2495u" Smith, B. L., and Glezer, A., "The formation andevolution of synthetic jets," Physics of Fluids, Vol. 10,No. 9, 1998, pp. 2281-2297

'Ingard, U., "On the theory and design of acousticresonators," J. Acoustical Soc. Of America, Vol. 25, No.6, 1953, pp. 1037-1060'Gad-El-Hak, M., "Flow Control," Cambridge

University Press, I8t edition, 2000.14* Hsiao, F. B., Liu, C. F., and Shyu, J. Y., "Control ofwall-separated flow by internal acoustic excitation," AIAAJournal, Vol. 28, NO. 8., 1990, pp. 1440 - 1446

" Center, K., Anderson, K., Mahalingam, S., andHertzberg, J., " Simulation of reacting vortex structureswithin a confined domain," AIAA Paper No. 96-0709.16* Thurston, G. B., and Martin, C. E. Jr., "Periodic fluidflow through circular orifices," J. Acoustical Soc. OfAmerica, Vol. 25, No. 1, 1953, pp. 26-3117' Lee, M., and Reynolds, W. C., "Bifurcating andblooming jets," Stanford Report No. TF-22, 198518'Windall, S. E., Bliss, B. D., and Tsai, C. Y., "Theinstability of short waves on a vortex ring," /. Fluid Mech.Vol. 66, part 1, 1974, pp. 35-47

"Saffman, P. G., "The number of waves on unstablevortex ring," /. Fluid Mech. Vol. 84, part 4, 1978, pp.625-63920' Hussain, F., and Hussain, H. S., "Elliptic jets. Part 1.Characteristics of unexcited and excited jets," J. FluidMech. Vol. 208, 1989, pp. 257-32021'Lebedeva, I. V., "Experimental study of acousticstreaming in the vicinity of orifices," Sov. Phys. Acoust.Vol 24, No. 4, 1980, pp. 331-333

Table I

fHz20406080100

Vp= 10 mm/secUo

mm/sec32113809197

Re

90319225257273

Amm0.250.1250.100.070.05

Vp = 20 mm/secUo

mm/sec273348312282772

Re

7719838817962180

Amm0.50.250.170.1250.1

A = 0.15 mmUo

mm/sec87231559379549

Re

245652157810701550

VPmm/sec612182430


Figure 1. Schematic of the experimental setup

Figure 2. Flow visualization of 3mm nozzle: (a) plane ofsymmetry, (b) head-on view of foci and swirling motion inthe cavity at x/D = -0.75, and (c) cross-section of the jetatx/D=7.

Figure 3. Flow visualization of 12mm nozzle flow: (a) and(b) plane of symmetry for 5Hz and lOHz, transverse planesat (c) x/D=-0.5 and (d) x/D=6.


Figure 4. Flow visualization of flow regimes at different forcing frequencies for a 3mm nozzle at Vp = 2mm/s

(c)2001 American Institute (j & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.3U -

24

| 0 1B '>12 '

8

O Vp =0 A Vp-

D Vp =O Amp

0

o on oo A a D0 A

A nA "-10 0 A A

0 0o 4 — • — - ———————— •

4 mm/sec8 mm/sec10 mm/sec= 0.15 mm

O

DA A

, 9-«

Figure 5. Flow visualization of flow regimes at differentforcing frequencies for a 3mm nozzle at Vp = 6 mm/s

10 20 30 40 50 60 70 80 90 100Frequency

Figure 6. Location of jet blooming

ring vortex

pinching

bifurcation

closeup of bsfurciring vortex

vortex filament/connectivity to fociInside cavity

recirculation

Figure 7. Cartoon of the vortex pinching, bifurcation andconnectivity in a synthetic jet vortex train.


? 6

S 5

4

3

2

1

0

5.0 "

Q 25

> 0.0

-2.5 •

-5.0

— •• - : • • * : • ::: :::: - ————— - •:: :::: ::: ::: :::: ::: ::: :::::::" ——— - ;;:

-::::::::::::::!!;--:===:: :::::::::::::::::::::::::: IZ^X

i... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... ..... .

•p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 5 10 15x(mm)

Figure 8. Phase locked PIV results of a synthetic je

vp= 10 mm/seca

A

O 2 0 H z D RA 40 Hz °D 60 HzO 80 HzV 100 Hz

0 6 12 18 24 30

E 6

i 54

3

2

10

t for different pistor

5.0 •

Q 2'5

CO

>? 0.0

-2.5

-5.0 •

• " - ' - • • • . ,.'"l-^1^**"""'* "^r^f^*"" ' '" ' ,"-, '" —

frv . . . . . . . . ... . . . . ... ... .... ... ... ... .... . . , , , . .... ...... .... ... . . .... . .

) 5 10 15x(mm)

L velocities: (a)Vp = lOmm/s, (b)Vp = 20mm/s

Vp = 20 mm/sec

D

o g g g a g o o ° xD O

O 20 Hz 'A 40 HzD 60 HzO 80 HzV 100 Hz

0 6 12 18 24 30x/D x/D

1.0

0.8

% 0.6E§ 0.4

0.2

0.0

-0.2 •<

Figure 9. Mean location of maximu

Vp = 10 mm/secO 20 Hz ^jom a

A 40 Hz jr^D 60 Hz C&y A X/D = 10O 80 Hz ^ JITV 100 Hz ^J

S° °vn— n

%0

^^^^ i***5 - 2 - 1 0 1 2 2

im axial velocity in

1.2 -

1.0 '

0.8

c§ 0.6 'E§ 0.4

0.2 -

0.0

-0.2\

the plane of symmetry

Vp = 20 mm/secO 20 Hz yf& *A 40 Hz D o vmD 60 Hz A® XZlO 80 Hz ^V 100 Hz ^

ti a

r^ &vrS* ^

3 - 2 - 1 0 1 2

y/b y/b

Figure 10. Mean velocity distribution in a synthetic jet

(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

1.0 -Jo

Vp= 10 mm/sec

a

oAaoV

20 Hz40 Hz60 Hz80 Hz100 Hz

0.1

VA

x/D

' ' ' i

10.0

1.0 1o1(D

Vp = 20 mm/sec

b

a

oA

20 Hz40 Hz

D 60 HzoV

80 Hz100 Hz

0.1 1.0 x/D 10.0

Figure 11. Decay of centerline axial velocity U^ for two piston velocities

102

7543

10°

OADOV

oo20 Hz40 Hz60 Hz80 Hz100 Hz

O

Vp = 10 mm/sec

O

6 7 8

101 "I7543

10°

O 20 HzA 40 HzD 60 HzO 80 HzV 100 Hz

Vp = 20 mm/sec

x/D6 7 8 9<|Q1

x/D

Figure 12. Data of figure 11 normalized by piston velocity

1.0 -Q_Q

0.1

0.1

Vp= 10 mm/secOADOV

20 Hz40 Hz60 Hz80 Hz100 Hz

1 ri1.0 x/D

D

10.0

1.0 -Q-Q

0.10.1

Vp = 20 mm/secO 20 HzA 40 HzD 60 HzO 80 HzV 100 Hz

O

1.0 x/D 10.0

Figure 13. Streamwise variation of jet width b


7543

2 -

10°

Amplitude = 0.15 mm

O 20 HzA 40 HzD 60 HzO 80 HzV 100 Hz

1.0 -

0.1

O 20 Hz Amplitude = 0.15 mmA 40 HzD 60 HzO 80 HzV 100 Hz

4 5 6 7 8 9101 0.1 10.0

x/D

Figure 14. Effect of fixed amplitude of oscillation on the U, and b

1.0e3 • 1.0e2

1.0eO

1.0e-2

1.0e-4

f=100Hz, x = 10DVp = 20 mm/sec

-J0Q 2 3 4 5 6 7 ^ 0 1 2 3 4 567 ^g2 2 3 4

Frequency2 3 4 567 -JQ1 2 3 4 5 6 7 ^ 2 2 3 4

Frequency

Figure 15. Jet power spectrum for two forcing frequencies: (a) 20Hz and (b) lOOHz. (Arbitrary vertical scale)

o<D

O)(02,

0.0 0.2 0.4 0.6 0.8 1.0t

i

0

I

100

f=100HzVp = 30 mm/sec

= -0.5D

200 300Frequency

400r

500

Figure 16. Time history and power spectra of flow inside the cavity with 12mm nozzle. (Arbitrary vertical scale)

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