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The formation and evolution of synthetic jetsBarton L. Smith a) and Ari GlezerWoodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405

Received 18 December 1997; accepted 6 May 1998

A nominally plane turbulent jet is synthesized by the interactions of a train of counter-rotatingvortex pairs that are formed at the edge of an orice by the time-periodic motion of a exible

diaphragm in a sealed cavity. Even though the jet is formed without net mass injection, thehydrodynamic impulse of the ejected uid and thus the momentum of the ensuing jet are nonzero.Successive vortex pairs are not subjected to pairing or other subharmonic interactions. Each vortexof the pair develops a spanwise instability and ultimately undergoes transition to turbulence, slowsdown, loses its coherence and becomes indistinguishable from the mean jet ow. The trajectories of vortex pairs at a given formation frequency scale with the length of the ejected uid slug regardlessof the magnitude of the formation impulse and, near the jet exit plane, their celerity decreasesmonotonically with streamwise distance while the local mean velocity of the ensuing jet increases.In the far eld, the synthetic jet is similar to conventional 2D jets in that cross-stream distributionsof the time-averaged velocity and the corresponding rms uctuations appear to collapse whenplotted in the usual similarity coordinates. However, compared to conventional 2D jets, thestreamwise decrease of the mean centerline velocity of the synthetic jet is somewhat higher( x 0.58 , and the streamwise increase of its width and volume ow rate is lower x0.88 and

x0.33 , respectively . This departure from conventional self-similarity is consistent with thestreamwise decrease in the jet’s momentum ux as a result of an adverse streamwise pressuregradient near its orice. © 1998 American Institute of Physics. S1070-6631 98 00909-X

I. INTRODUCTIONThe concept of synthesizing a turbulent shear ow by

controlled coalescence of its rudimentary coherent vorticalstructures e.g., turbulent spots in a transitional boundarylayer or vortex rings in a round jet was proposed by Coles inthe early seventies and was later tested in a at plate bound-ary layer experiment Savas and Coles 1 . While in the

boundary layer experiments of Savas and Coles, turbulentspots were triggered by hairpin vortices induced by the peri-odic protrusion of a spanwise array of small pins into theow, in the present work, synthetic jets are engendered bythe interaction of discrete vortical structures which areformed by time-periodic ejection of uid out of an orice atthe ow boundary. Unlike conventional continuous jets e.g.,Gutmark and Wygnanski, 2 2D jet or pulsed jets e.g., Brem-horst and Hollis, 3 axisymmetric jet a unique feature of syn-thetic jets is that they are formed from the working uid of the ow system in which they are deployed, and thus transferlinear momentum to the ow system without net mass injec-tion across the system boundary. Thus, the interaction of synthetic jets with an external ow near the ow boundarycan lead to the formation of closed recirculation ow regionsand consequently to an apparent modication of the owboundary Smith and Glezer, 4 Amitay, Honohan, Trautman,and Glezer 5 . This attribute enables synthetic jets to effectsignicant global modications of the base ow on scalesthat are one to two orders of magnitude larger than the char-acteristic length scales of the jets themselves.

It has been known for some time that streaming motionsin uids can be induced without mass addition by the trans-mission of sound often referred to as acoustic streaming orby oscillating the boundary of a quiescent medium. In a re-view of streaming motions induced by acoustic wavesLighthill 6 noted that acoustic streaming results from the dis-sipation of acoustic energy or the attenuation of the transmit-

ted sound. Such attenuation can occur either within the bodyof the uid i.e., away from solid surfaces at very high fre-quencies e.g., Meissner 7 , or due to viscous effects near asolid boundary Andres and Ingard 8 . Streaming motions as-sociated with oscillating solid boundaries have been the subject of a number of investigations, most notably time-harmonic oscillations of a cylinder normal to its axis e.g.,Stuart, 9 Davidson and Riley, 10 Riley and Wibrow 11 leadingto streaming velocities on the order of 1 cm/s in water at anominal frequency of 45 Hz.

Jet ows without net mass addition can be produced byan oscillatory ow having a zero time-averaged mean ve-locity through an orice, provided that the amplitude of os-cillations is large enough to induce ow separation at theorice and the time-periodic rollup of a train of vortices.Ingard and Labate 12 used standing waves in an acousticallydriven circular tube to induce an oscillating velocity eld inthe vicinity of an orice plate placed near a pressure nodeand observed the formation of jets from trains of vortex ringson both sides of the orice with no net mass ux. Morerecently, Lebedeva 13 created a round jet with velocities of upto 10 m/s, by transmitting high amplitude sound waves 150dB through an orice placed at the end of a tube. In a relateda Author to whom correspondence should be addressed.

PHYSICS OF FLUIDS VOLUME 10, NUMBER 9 SEPTEMBER 1998

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investigation, Mednikov and Novitskii 14 reported the forma-tion of a jet without net mass ux and average streamingvelocities of up to 17 m/s by inducing a low frequency 10–100 Hz oscillatory velocity eld with a mechanical piston.

The evolution of a submerged synthetic round turbulentwater jet that is formed without an orice by an oscillatingdiaphragm ush-mounted on a at plate was recently inves-tigated by James, Jacobs, and Glezer. 15 The jet which wasproduced without net mass injection normal to and at thecenter of the diaphragm, was comprised entirely of radiallyentrained uid, and was formed only when a small cluster of cavitation bubbles appeared near the center of the diaphragmduring each oscillation cycle. The authors conjectured thatthe time-periodic formation of these bubbles displaces vor-ticity from the actuator’s boundary layer, and leads to theformation of vortical puffs in the parlance of Kovasznay,Fujita, and Lee 16 that coalesce to synthesize a turbulent jet.Laser Doppler velocity measurements showed that the timeaveraged jet is similar to a conventional turbulent round jetin that both its nominal diameter and the inverse of its cen-terline velocity increase linearly with the distance from theactuator.

In the present implementation, plane or round turbulent jets having nite streamwise momentum are synthesized nor-mal to an orice in a at plate by a train of vortex pairs orvortex rings . The vortices are formed at the edge of an ac-tuator orice without net mass injection by the motion of adiaphragm in a sealed cavity. Because the characteristic di-mensions of the jet scale with the characteristic dimension of the orice, it is possible to synthesize jets over a broad rangeof length scales microfabrication of synthetic jets having anominal orice dimensions of 150 m using standard siliconmicromachining techniques was reported by Coe, Allen,

Trautman, and Glezer17

and by Coe, Allen, Smith, andGlezer 18 . The present work focuses on the evolution of anominally two-dimensional aspect ratio 150 synthetic jet.The jet actuator and other experimental hardware are de-scribed in Sec. II. The formation and evolution of the two-dimensional vortex pairs that synthesize the jet are describedin Sec. III A, while the far-eld structure of the ensuing jet isdiscussed in Sec. III B.

II. EXPERIMENTAL METHODS AND PROCEDURE

In the work reported here, the synthetic jet is formed inair at a rectangular orice measuring 0.5 75 mm ush

mounted in a at plate measuring 30 38 cm as shown sche-matically in Figs. 1 a and 1 b . The exit plane of the jet isinstrumented with a linear array of 17 static pressure portsequally spaced along z/h 0 between y/h 6.3 and 39, andconnected to a Scannivalve pressure switch.

The jet is synthesized by the time-harmonic formationand subsequent interactions of a train of vortex pairs that areformed at the edge of the orice by the motion of a dia-phragm mounted in a sealed cavity. The circular diaphragmis driven at resonance nominally 1140 Hz by a centrallybonded piezoceramic disk. During the forward motion of thediaphragm, uid is ejected from the cavity. The ow sepa-rates at each of the sharp edges of the orice forming a

vortex sheet that rolls into a vortex pair and begins to moveaway from the orice under its own self-induced velocityAuerbach 19 . When the diaphragm begins to move away

from the orice, the vortex pair is already sufciently re-moved and is thus unaffected by the ambient uid that isdrawn into the cavity. Therefore, during each cycle the netmass ux out of the cavity is zero while the mass and hy-drodynamic impulse of each vortex pair are nonzero.

A schlieren image of the ensuing two-dimensional jet is

shown in Fig. 2. For the purpose of the schlieren visualiza-tion, the air inside the actuator’s cavity is slightly heatedusing a thin-lm surface heater that is internally mounted onone of the cavity walls. The schlieren view is in the x-y planeand extends approximately through x 70h. The motion isrecorded at standard video rate using a CCD camera havingan exposure time of 100 s. The image shows a vortex pairthat is formed near the orice, and a turbulent jet fartherdownstream. Although this image does not show the motionof the ambient air that is drawn towards the cavity along thesurface of the at plate, such motion is evident in a similarimage of the merging of two identical coowing synthetic jets operating side by side with their orices parallel length-

FIG. 1. Schematic diagrams of synthetic jet: a side view, b top view.

2282 Phys. Fluids, Vol. 10, No. 9, September 1998 B. L. Smith and A. Glezer




wise and 3 h apart as shown in Fig. 11 below. The schlierenimage in Fig. 11 a shows evidence of strong entrainmentalong the plate towards the jet orices which is manifestedby the rollup of 2D vortices at the left and right edges of theplate the edges of the plate are not shown in Fig. 2 .

As for axisymmetric vortex rings e.g., Didden 20 andGlezer 21 , each vortex pair may be characterized by two pri-mary dimensionless parameters based on a simple ‘‘slug’’model; i the dimensionless ‘‘stroke’’ length L0 / h( L0 0

u 0( t ) dt where u 0( t ) is the velocity at the exit planeof the orice and T /2 is the time of discharge or half theperiod of the diaphragm motion , and ii a Reynolds numberbased on the impulse per unit width i.e., the momentumassociated with the discharge per unit width Re I 0

I 0 / h( I 0 h 0

u 02( t ) dt , and are is the uid density and vis-

cosity, respectively . When these vortices are generatedtime-periodically to synthesize a jet, additional formation pa-rameters include the formation frequency and the duty cycle,both of which are xed in the present experiments. Underthese conditions and for a xed orice width , the formationparameters of the jet depend only on the amplitude of thediaphragm motion and cannot be varied independently. Inthe present experiments 5.3 L0 / h 25 and 1400 I 0 / h

30 000. The corresponding Reynolds number of the syn-thetic jet, Re U 0based on the orice width h and the average

orice velocity U 0 L0 / T varies between 104 and 489.Cross stream distributions of the streamwise and cross

stream velocity components are measured at a number of streamwise and spanwise stations 0 x/h 177 and 80 z/ h 80 using hot wire anemometry with 1 mm long, 5 mdiameter single- and X-conguration sensors. The single-sensor probe was used primarily in the near eld of the jetand the two sensor probe was used for x / h 10 where crossstream distributions of the mean streamwise velocity mea-sured with both probe types are virtually identical . The hotwire probes are traversed using a three-axis computer-

controlled traversing mechanism and are calibrated in an adjacent conventional laboratory jet. A laboratory computersystem equipped with a 12 bit 100 kHz A/D board is dedi-cated to experiment control and data acquisition.

III. THE SYNTHETIC JET

The evolution of the synthetic jet can be divided into twodistinct domains which are described in Secs. III A and III B.Near the jet exit plane Sec. III A , the ow is dominated bythe time-periodic formation and advection of discrete vortexpairs which ultimately undergo transition to turbulence, slowdown and lose their coherence. The transition process is fol-lowed by the emergence of a fully-developed turbulent jetSec. III B which is similar in some respects to a conven-

tional 2D jet.

A. Near-eld formation and evolution

The formation of a synthetic jet at Re U 0383 and Re I 0

18,000 referred to below as the ‘‘nominal case’’ is shownin a sequence of digitized video schlieren images Fig. 3that are each taken phase-locked to the actuator driving sig-nal at 27 equal time intervals 33.8 s apart during theforcing period. The sequence begins with the forward motionof the actuator diaphragm ( t / T 0) which results in the ejec-tion of uid from the jet cavity. The coordinate system isshown for reference in the image corresponding to t/T

0.481 which is repeated on the bottom right hand side. Itshould be noted that while the images in Fig. 3 are phase-locked to the actuator’s driving signal, the video frame rate isa submultiple of the forcing frequency, and thus successiveimages do not show the same vortex pair.

The front end of the uid slug that is ejected out of the

orice and leads to the formation of the vortex pair is appar-ent on the left at time t / T 0.11. Some traces of the previousvortex pair are still discernible near x/h 11 and the emerg-ing turbulent jet is visible farther downstream. In subsequentimages (0.15 t / T 0.41), the new vortex pair continues itsrollup as it is advected downstream while the previous vortexpair becomes indistinguishable from the background owand, as discussed further below, it is no longer phase locked

to the excitation signal . The new vortex pair and the remain-der of the ejected uid behind it appear to be laminar afterthe rollup process is completed and while the vortex core isadvected through x/h 8.5 ( t / T 0.407).

The cores of the vortex pairs begin to exhibit small-

scale motions and undergo transition to turbulence aroundt / T 0.5 which, as shown in Fig. 8 below, is accompaniedby a reduction in their advection velocity. The transition pro-cess begins with the onset and rapid amplication of a span-wise instability of each primary vortex that leads to theformation of nominally spanwise-periodic counter-rotatingstreamwise vortex pairs that are wrapped around the cores of the primary vortices and ultimately lead to a cellular breakupof their cores as shown in the spanwise view in Fig. 4 . Theformation of these streamwise vortices and the small-scaletransition of the primary vortices is shown in a sequence of phase-locked smoke visualization images taken in the x-zplane y 0 using a laser sheet. In order to maintain smoke-

FIG. 2. Schlieren image of a rectangular synthetic jet. Re I 018124 (Re U 0

383), h 0.5 mm, f 1140 Hz.

2283Phys. Fluids, Vol. 10, No. 9, September 1998 B. L. Smith and A. Glezer




concentration that is adequate for spanwise visualization, the jet frequency was lowered to 360 Hz and, as a result, theadvection velocity of the vortex pairs is reduced to approxi-mately one tenth the advection velocity for the nominal case.

The images in Figs. 4 a –4 d show a spanwise section of the jet that is approximately 30 h wide about z 0 and arecaptured at t / T 0.5, 0.625, 0.75, and 0.875, respectively.

Figure 4 a shows a new spanwise vortex on the left and

FIG. 3. Phase-locked schlieren images of the synthetic jet in the cross stream (x-y) plane taken at 27 equal intervals during the actuator cycle. The forwardand backward motions of the diaphragm from the rest position begin at t / T 0 and t / T 0.5 respectively. Re I 0

18,124 (Re U 0383).





the previous vortex which is in the nal stages of the transi-tion process. The image clearly shows the formation of spanwise-regular rib-like secondary vortical structures aboutthe core of the primary vortex on the left with an average

spanwise spacing of 2.5 h. As the primary vortex is advecteddownstream Figs. 4 b , t / T 0.625 and 4 c , t / T 0.75 , thesecondary vortical structures intensify and shortly thereafterappear to lead to a cellular breakdown of the core of theprimary vortex Fig. 4 d , t / T 0.875 . As is evident fromthe image of the downstream primary vortex in Fig. 4 a , thecellular segments apparently continue to break down tosmaller and smaller scales until the primary vortex loses itsidentity e.g., on the right hand side of Fig. 4 d . Similarsecondary vortex tubes that are wrapped around the core of an isolated vortex ring appear during the nal stages of itstransition following an azimuthal instability of the vortexcore Didden 1977, 22 Schneider 1980 23 , and were also ob-served in a turbulent vortex ring Glezer, 21 Glezer and Coles1990 24 . The appearance of counter-rotating pairs of stream-wise vortices around the cores of the spanwise primaryvortices in plane shear layers e.g., Bernal and Roshko1986, 25 Nygaard and Glezer 1991 26 and wakes e.g., Rob-erts 1985, 27 Williamson 1991 28 marks the appearance of small scale motion within the cores of the primary vorticesand the onset of mixing transition.

The schlieren images for t / T 0.444 in Fig. 3 suggestthat similar to a vortex ring Glezer 21 , the onset of small-scale transition appears to take place near the front stagna-tion point of the primary vortex where the strain rates arehigh. Based on the schlieren visualization, the transition pro-cess seems to proceed towards the rear of the vortex, andultimately progresses through the uid stem behind it. In Fig.3 for 0.67 t / T 1 the entire vortex pair appears to be tur-bulent and its celerity, or propagation velocity, is diminishedas it merges into the ensuing turbulent jet. An importantfeature of this sequence of images is that unlike vortex pairsthat form near the edges of the potential core of conventional

2D jets, consecutive vortex pairs in the present jet do notcoalesce or undergo pairing and as shown in Figs. 20 a and20 b below there are no subharmonic components in powerspectra of the streamwise velocity.

Time series of the streamwise velocity component aremeasured along the centerline of the jet y 0 using a singlesensor hot wire probe. The sensor is operated at low overheatratio 1.2 to minimize heat transfer to the jet orice, and themeasured velocity is corrected for changes in the room tem-perature. These data are taken phase-locked to the actuatorsignal 1,140 Hz, T 0.877 ms at 88 equal time intervals percycle i.e., 10 s apart for 1200 cycles. Figure 5 shows asequence of phase-averaged velocity traces u ( t / T ; x) / U 0

measured in the domains 0 x / h 5 at ve equally-spacedpositions, marked with closed symbols , and 5 x / h 25 atnine equally-spaced positions, marked with open symbolsfor the nominal case. Near the jet orice, the velocity tracesare rectied by the hot wire sensor when the velocity re-verses its direction at mid-cycle. Thus, for x / h 3.0, the ve-locity during the suction part of the cycle is inverted to re-ect the correct ow direction, and data are not plottedwhere the magnitude of the velocity is below the low end of the calibration range of the sensor i.e., within the gapsaround zero .

The phase-averaged centerline velocity near the exitplane of the orice reects the momentary uid ejection as

FIG. 4. Phase-locked smoke visualization images of the synthetic jet(f 360 Hz in the x-z plane taken at equal time intervals ( T /8).





well as the rollup and ultimately the advection of the vortexpair during the discharge period, and the ow toward theorice behind the advected vortex pair during the suctionperiod. At the center of the orice x/h 0 , the two halves of the velocity cycle are virtually identical and the time-averaged velocity and the net mass ux are indeed zero. Thelocal velocity extreme at t / T 0.08 and 0.58, mark the sym-metrical rollup and advection of a vortex pair at the upstreamand downstream sides of the orice during both the ejectionand suction parts of the cycle symmetric rollup on bothsides of a circular orice was also reported by Ingard andLabate 12 .

The rollup of the vortex pair proceeds as it is advecteddownstream and the velocity peak induced by its passage ata given streamwise position increases in magnitude, whilethe magnitude of the velocity minimum associated with thesuction decreases. These changes are accompanied by an in-crease in the mean time-averaged velocity. It appears thatat x/h 4, the vortex pair is fully formed and the suctioncycle no longer affects the phase-averaged velocity. Similarto the streamwise velocity measured along the axis of a vor-tex ring, 24 the centerline velocity reects the passage of thecores of a vortex pair where the peak corresponds to thecenter of the cores. As demonstrated in Fig. 5 (3.9 x / h

9.8), the magnitude of the induced velocity peak on thecenterline decreases monotonically as the vortex is advecteddownstream, ostensibly as a result of the transition to turbu-lence cf. Fig. 3 and loss of vorticity to the wake which arealso accompanied by reduction in phase coherence. Figure 5( x / h 3.0) also shows that in addition to the time-dependentvelocity induced by the passage of the vortex pair, the meanvelocity at a given streamwise position includes a time-invariant offset component uos( x) min( u(t / T ; x) ) as

marked in Fig. 5 which increases with downstream distance.The evolution of uos is discussed further in connection withFig. 9 below.

As the magnitude of the velocity that is induced by thepassage of the vortex pair diminishes farther downstream, itbecomes evident that the centerline velocity of the emergingsynthetic jet has a low-level time-periodic component at thefrequency of the actuator and its higher harmonics. Figures6 a –6 c show phase averaged time traces with the localtime-averaged velocity subtracted at x / h 15.7, 17.7, and19.7. While at x / h 15.7 Fig. 6 a , the velocity increaseassociated with the passage of the vortex pair is still detect-able during the rst half of the cycle, at x / h 19.7 Fig.

6 c , the velocity distributions during each of the two halvesof the cycle are virtually identical. As shown in Fig. 21 be-low, although the magnitude of the spectral component at theactuator frequency decreases with downstream distance, it isnevertheless detectable throughout the present domain of measurements ( x / h 180). That the phase of this spectralcomponent relative to the actuator motion does not changeappreciably with downstream distance suggests that it is in-duced by the oscillating pressure eld which is associatedwith the pumping of the jet uid in and out of the cavity.

The time t p corresponding to the passage of the phase-averaged velocity peak on the jet centerline during the pas-sage of the vortex pair at a given measurement station allows





streamwise dependence is shown in Fig. 9 a for differentimpulse levels. It is remarkable that except for the lowest

I 0 regardless of the impulse, u os of all vortex pairs initiallyincreases along the same curve before it reaches a maximumvalue which depends on and increases with the initial im-pulse. Past the maximum, for a given impulse level, uos be-gins to decrease with streamwise distance ostensibly as aresult of the cross stream spreading of the jet. Finally, for x / h 20, u os is equal to U cl , which, as is shown in Fig. 13,decreases like x 0.58 . The same data are plotted in dimen-sionless form in Fig. 9 b which shows a reasonable collapsewith the possible exception of the vortex pair that is formedat the lowest impulse level. The streamwise dependence of the celerity, offset velocity and the mean velocity for thenominal case is shown in Fig. 10. It is interesting to note that

when the vortex pair undergoes transition to turbulencearound x / h 7, the streamwise rate of decay of the centerlinevelocity and the celerity increases substantially. The celerityand the offset velocity change again at x / h 10 and ulti-mately merge with the mean velocity at x / h 20.

While for the orice geometry presented here, the vortexpairs are advected along the centerline of the jet, this trajec-tory and consequently the direction of the ensuing jet can beeasily altered. Lee and Reynolds 29 demonstrated that smallchanges in the azimuthal formation of successive vortexrings in a circular jet can lead to changes in their trajectoriesand consequently to substantial changes in the far eld struc-ture of the jet which the authors refer to as ‘‘bifurcation’’ or‘‘blooming’’ . In order to demonstrate the role of the vortexdynamics in the formation of the synthetic jet, the formationprocess is modied by placing two synthetic jets in closeproximity. Each of the jets is essentially similar to the single jet described above and they are placed side by side in a atplate so that they are parallel along the long dimension of their orices and 3 h apart. The resultant jet can be effectivelymanipulated by modifying the formation and evolution of thevortex pairs of each jet by varying the amplitudes or therelative phase of the driving waveforms. In particular, phasevariation between the driving signals effectively changes therelative timing of the rollup of the adjacent vortex pairs andthus leads to strong vortex interactions that alter the trajec-tories of the vortex pairs and the direction of the ensuing jet.Figure 11 shows a schlieren image of the jets and demon-strates the effect of phase variation between two driving sig-nals having the same frequency and amplitude. When thetwo jets are in phase Fig. 11 a , the inner vortices of eachvortex pair cancel each other, resulting in a single, largersynthetic jet. As mentioned in Sec. II above, Fig. 11 a also

shows evidence of the strong entrainment ow along theplate towards the jet orices which is manifested by the rol-lup of 2D vortices at the left and right edges of the plate.When one of the jets is leading in phase, the interactionbetween the adjacent vortex pairs which is also affected bythe suction ow alters their ultimate trajectories and themerged jet is vectored towards the leading jet. When the jeton the right is leading in phase by 60°, the merged jet isvectored to the right. When the phase angle is 150° Fig.11 c , the merged jet becomes almost attached to the exitplane.

B. The mean ow

Cross stream distributions of the time-averaged stream-wise U and cross stream V velocity components alongwith the corresponding rms velocity uctuations u ,v , andu v of the nominal case are plotted in Figs. 12 a –12 e inthe usual similarity coordinates of conventional 2D jets thecross stream coordinate is normalized with the local jet widthb ( x) based on U cl /2 . These data are measured at a 11streamwise stations between x / h 9.8 and 78.7 and, at leastwithin this streamwise domain, collapse reasonably well de-spite the fact that the jet is formed by time-harmonic motion.The mean cross stream velocity component Fig. 12 b isnominally antisymmetric about the jet centerline and its nor-

FIG. 8. Variation of vortex pair celerity U c ( x, t ) with time symbols as inFig. 7 .





malized magnitude is similar to the cross section velocity of corresponding conventional jets. 30 The normalized distribu-tions of the rms velocity uctuations u Fig. 12 c , v Fig.12 d and of u v Fig. 12 d are also very similar to andhave approximately the same magnitudes as correspondingdistributions in conventional jets. 2,30,31,32

The cross stream distribution of u Fig. 12 c exhibitstwo distinct peaks on both sides of the centerline where u

0.25 U cl which coincide with the peaks of the cross streamvelocity components. In conventional jets, u and v typi-cally increase rapidly downstream of the potential core andtheir cross stream peaks are normally between 0.2 U cl and0.3U cl where the ow becomes fully developed 2,30,32 and in-crease with decreasing Reynolds number based on the jetheight .32 In contrast to conventional plane jets which be-come fully developed at x / h 40 e.g., Gutmark andWygnanski 2 , the mean ow of the synthetic jet appears tobecome fully developed considerably closer to the jet exitplane ( x / h 10).

The streamwise variation of the mean velocity andrms velocity uctuations along the jet centerline for

9.8 x / h 177 are shown in Fig. 13. For x / h 80, U cl de-creases like x 0.58 and u decreases like x 0.5 , while forconventional 2D fully developed turbulent jets, both U cl andu decrease like x 0.5 . Note also, that for x / h 80, the rate of streamwise decay of the centerline velocity diminishes to x 0.25 ostensibly due to three-dimensional effects associatedwith the streamwise decrease in the aspect ratio of the jetcross section in the y-z plane cf. Fig. 19 below . It is inter-esting to note that u appears to be unaffected by thesechanges and continues to decrease like x 0.5 . Figure 13 alsoshows that for 10 x / h 80, the jet width b( x) based onU cl /2 in the cross stream plane z 0 increases like x0.88

while in conventional 2D jets, b x. The streamwise rate of increase of the jet width at x / h 30 is 0.194 and is almosttwice the corresponding streamwise increase in the width of conventional 2D jets at Reynolds numbers on the order of 104 which varies between 0.09 to 0.12 .2,30,33 Note also thatthe linear t b1.136 x yields a virtual origin for the nominalcase of x0 4 h which is comparable to what was mea-sured by Gutmark and Wygnanski 2 ( 2.5h ) and Krothapalli

FIG. 9. Offset velocity u os . a Dimensional variables, b normalized variables: Re I 04,967 , 9,072 , 12,552 , 18,124 , 20,761 , 22,282

, 27,025 , 29,654 .





et al. 30 ( 2 h ) in conventional 2D jets. Gutmark and Ho 34

suggested that the disparity in streamwise spreading rates of 2D jets in earlier investigations could be attributed to thespontaneous emergence of different instability modes of the jet shear layers. Thus, because the synthetic jet is formed bya train of 2D vortex pairs which do not interact or pair it isexpected that at least near the exit plane, the cross streamspreading of the synthetic jet would be limited.

As noted in Sec. II, when the motion of the diaphram is

time-harmonic and for a xed orice width , the formationparameters of the jet depend only on the amplitude of theactuator signal, and cannot be varied independently. Figures8 and 9 b demonstrate that the celerity and offset velocity of the vortex pairs, respectively, scale with the average oricevelocity and thus with the amplitude of the actuator signal.The effect of the amplitude on the global properties of theensuing jet is demonstrated by considering the dependenceof the centerline velocity normalized by U 0 , Fig. 14 on x / h . These data show that the existence of three distinctstreamwise domains corresponding to the formation of thevortex pairs, their laminar advection and transition to turbu-lence, and nally the emergence of the turbulent jet. In the

rst domain x / h 2, the jet centerline velocity increases rap-idly to a level which scales with the average orice velocitywhich depends on the formation amplitude . In the second

domain, the streamwise rate of increase of the centerline ve-locity is much smaller although not zero . Farther down-stream nominally x / h 10 the centerline velocity begins todecay with streamwise distance within the third domain . Asnoted in Sec. III A, the streamwise decay of the centerlinevelocity begins at t / T 0.5, and thus the corresponding

streamwise locations increase linearly with the formationamplitude or the slug length L0 . Note that all the datawithin the third domain ultimately collapse onto a singlecurve given by x0.58 cf. Fig. 13 which is also shown forreference.

The streamwise variation of integral quantities such asthe jet volume ow rate and its streamwise momentum uxare assessed using a least squares t of the hyperbolic cosinefunction U f U cl cosh 2( y) where is a parameter of thet to cross stream distributions of the streamwise velocity.The quality of the t at x / h 20 is demonstrated in Fig. 15.Similarity arguments for conventional 2D turbulent jetssuggest that the volume ow rate per unit width i.e.,

FIG. 10. Mean centerline velocity , celerity and offset velocity for the nominal case Re I 0

18,124 ( Re U 0383).

FIG. 11. Schlieren images of the interaction between two adjacent synthetic jets: 0° a , 60° b , and 150° c .





Q Udy increases like x0.5 . However, Fig. 16 showsthat, at least within the domain of the present measurements,the normalized volume ow rate Q / Q 0 where Q 0 U 0hincreases only like x0.33 . Nevertheless, despite the lowerstreamwise increase in volume ow rate compared to con-ventional jets, the net entrained volume ow rate of the syn-thetic jet within the domain x / h 10 is 4 Q 0 which, as sug-gested by ow visualization e.g., Figs. 11 a –11 c resultsfrom strong entrainment along the at plate towards the jetorice. Substantial entrainment is also maintained fartherdownstream and the net entrained volume ow rate withinthe domain 10 x / h 80 is also 4 Q 0 . The normalized vol-

ume ow rate in a conventional 2D jet computed from ve-locity measurements of Heskestad 33 at Re h 3.4 • 104 is alsoplotted for comparison in Fig. 16 open symbols and showsthat although Q x0.5 for x / h 60, it is considerably smallerthan the volume ow rate of the synthetic jet indicatinglower entrainment in the near eld.

The invariance of the time-averaged momentum ux perunit width, i.e., J (U 2 u 2) dy in a conventional 2D jet, is tacitly connected with the assumption that the staticpressure within the jet is also streamwise invariant. Thestrong ow induced towards the actuator during the suctioncycle indicates that the mean static pressure near the exit

FIG. 12. Cross-stream distributions of U / U cl a , V / U cl b , u u / U cl2 c , v v / U cl

2 d , and u v / U cl2 e , at x / h 9.8 , 11.8 , 13.8 , 15.7 , 19.7

, 23.6 , 27.6 , 31.5 , 35.4 , 39.4 , and 78.7 . ReU 0383.





plane is lower than the ambient pressure. This is evident inmeasurements of the static pressure on the exit plane along z 0 at different Reynolds numbers. The static pressure portsare equally spaced (2.3 h apart , and unfortunately, owing tostructural constraints, it is not possible to achieve better reso-lution near the jet orice. The resulting pressure coefcientnormalized by U 0

2 in Fig. 17 shows that the mean staticpressure near the jet orice is lower than the ambient pres-sure and is consistent with the steady suction of ambientuid towards the jet orice as is evident in Fig. 11 above.Figure 17 also shows for reference a line segment whichrepresents the radial decrease of the static pressure in theow eld of a 2D potential sink i.e., p r 2 . These mea-surements suggest the existence of an adverse streamwise

pressure gradient near the jet orice and consequently astreamwise decrease in the momentum ux of the synthetic jet. The streamwise variation of the momentum ux per unitwidth normalized by the average momentum ux of theejected uid is shown in Fig. 18. The closed symbols corre-spond to integration of the tted hyperbolic cosine proleswhich near the jet exit plane yields a value near unity ,

while the open symbols are based on integral limits of half the centerline velocity i.e., b y b . The data set repre-

sented by open symbols is effectively based on measuredvelocity rather than the tted curve and is included for

FIG. 13. Streamwise variation of: U , u , and b . ReU 0383.

FIG. 14. Variation of centerline velocity U cl( x, t ) with axial distance sym-bols as in Fig. 7 .

FIG. 15. Least-squares t of a cross stream distribution of the mean stream-wise velocity at x / h 20 to a hyperbolic cosine function.

FIG. 16. Streamwise variation of the volume ow rate. The straight linesegment denotes Q x0.5 for self-similar 2D jet .





reference. For a conventional self-similar ow, both curvesshould be streamwise invariant. However, the momentumux of the synthetic jet decreases monotonically withstreamwise distance. The decrease is further complicated bythe spanwise nonuniformities in the jet cross section and thestreamwise decrease in its aspect ratio as shown in Fig. 19. Asingle measurement taken at x/h 78.7, suggests that farenough downstream ( x / h 100), the momentum ux as-

ymptotes to a constant value around 0.55.

As noted by Kotsovinos and Angelidis, 35 the streamwisevariation of the time-averaged momentum ux in plane oraxisymmetric jets depends critically on the pressure eld,and on the geometry of the jet. Based on data published byother investigators since 1957, these authors assert that inconventional jets emanating normal to a plane surface themomentum ux decreases with downstream distance. Varia-tion in the streamwise rate of decrease among the differentdata sets results in momentum ux levels at x / h 80 that are

between 75% and 85% of the level at the exit plane at x / h 0 .The streamwise variation of the jet cross section in the

y-z plane can be assessed from contours of the mean stream-wise velocity at x / h 19.7, 39.4, and 78.7 shown in Figs.19 a –19 c , respectively contours start at 1 m/s and thecontour increment is 0.5 m/s . These plots indicate that theaspect ratio of the jet cross section based on contour level of 1 m/s decreases from approximately 6 at x / h 19.7 to 3 at x / h 78.7. While near the exit plane x / h 19.6, Fig. 19 athe jet appears to be reasonably spanwise-uniform, fartherdownstream, x / h 39.4, Fig. 19 b the cross-stream widthof the jet near its spanwise edges is larger than at the mid

span. At z / h 55, the streamwise velocity has local spanwise maximas, and the normalized momentum ux in these x-y planes is 1.16 compared to 0.58 at z / h 0 which may beassociated with the streamwise decrease in the jet aspect ra-tio. At x / h 78.7, the centerline velocity is relatively low2.8 m/s and the cross section of the jet appears to be

slightly rotated about its centerline. Similar saddle-like dis-tributions of the streamwise velocity was also observed inconventional high aspect ratio rectangular jets. 30,36

Additional insight into the evolution of the synthetic jetmay be gained from spectra of the streamwise velocity.Power spectra of the jet centerline velocity measured at x / h 5.9, 9.8, 19.7, 98.4, and 177.2, are shown in Figs.

FIG. 17. Distributions of the pressure coefcient at the exit plane:Re U 0

270 , 383 , 424 , and 489 .

FIG. 18. Streamwise variation of the jet momentum ux based on tted coshyperbolic distribution, and on the velocity data for b y b .ReU 0

383.

FIG. 19. Contour maps of the streamwise velocity in the y- z planes x / h19.7 a , 39.4 b , and 78.7 c . The rst contour is 1 m/s and contour

increment is 0.5 m/s. Re U 0383.





20 a –20 e , respectively each of the curves in Figs. 20 b –20 e are successively displaced by seven decades, and thepower spectrum at x / h 5.9 is replotted for reference using ashaded curve . Near the jet exit plane Fig. 20 a , the spec-trum is dominated by the formation frequency of the vortexpairs and its higher harmonics although hot-wire rectica-tion of velocity traces within this domain clearly contributesto the spectral contents at the higher harmonics , while thespectral distribution below the fundamental frequency is vir-tually featureless. The harmonics of the formation frequencyare rapidly attenuated with downstream distance and by x / h 9.8, only four harmonics are present. Concomitantly,there is also a signicant increase in the magnitude of thespectral band below the formation frequency which is indica-tive of the decay of the vortex pairs and the development of the jet ow. However, with the exception of a weak band of spectral components centered around 10 Hz, which disap-pears by x / h 98, the spectral band below the formationfrequency remains featureless throughout the present domainof measurements and shows no evidence of subharmonics of the formation frequency.

A striking feature of the velocity spectra in Figs. 20 b –20 e is the rapid streamwise attenuation of virtually all spec-tral components indicating strong dissipation within the syn-thetic jet and a reduction in the total turbulent kinetic energy.The spectral decay is initially more prominent at frequenciesthat are above the formation frequency of the jet Figs. 20 aand 20 b while, as noted above, there is a concomitantincrease in the magnitude of the spectral band below theformation frequency. Thus, it is conjectured that followingthe time-harmonic formation of discrete vortex pairs, energyis transferred from these primary ‘‘large scale’’ eddies,which coalesce to form the jet, to the mean ow and also

cascades down to smaller scales at which dissipation ulti-mately takes place. Farther downstream Figs. 20 c –20 e ,the low frequency components of the jet are continuouslyattenuated and by x / h 177 Fig. 20 e , the nominal mag-nitude of the band f 100 Hz is comparable to the corre-sponding band near the jet exit plane suggesting energytransfer to the smaller scale. At the same time, the ‘‘roll-over’’ frequency at which the low-frequency end of thespectrum begins to undergo a change in slope , moves to-wards lower frequencies in Fig. 20 c , the roll-over fre-quency is below the formation frequency . The spectral dis-tributions in Figs. 20 c –20 e also include a relativelynarrow frequency band having a slope of approximately

53 suggesting the existence of an inertial subrange which is

limited by the low Reynolds number of the ow. It is note-worthy that because the characteristic local centerline ve-locity decreases with downstream distance, the spectral peak at the formation frequency actually shifts towards higherwave numbers where the dissipation ultimately takes placee.g., Fig. 20 e .

As mentioned in Sec. III A above, a notable feature of the synthetic jet is the absence of pairing interactions be-tween the vortex pairs that form the jet and consequently theabsence of subharmonic frequencies in spectra of the stream-wise velocity component in Fig. 20. The phase-lockedschlieren images in Fig. 3 indicate that the primary vortex

pairs undergo transition and breakdown to smaller eddiesand that the jet is ultimately formed by the coalescence of clusters of such smaller eddies. The breakdown of the span-wise vortex pair is alluded to by an abrupt and rapid decrease

FIG. 20. Power spectra of the centerline velocity each curve is successivelydisplaced 7 decades : x / h 5.9 a , 9.8 b , 19.7 c , 98.4 d , 177.2 e .ReU 0

383.





around x / h 10 in the magnitude of the spectral compo-nent at the forcing frequency, a f o Fig. 21 . This change isalso apparent in the gray-scale raster plot of the auto corre-lation function ( , x) of the centerline velocity shown inFig. 22. For a xed large x, ( ) 0 ( (0, x) 1) and de-cays monotonically to zero for large as in other fully de-veloped turbulent ows. However, as a result of the coherentvortex motion near the exit plane, the auto correlation is

nominally time-harmonic with a zero cycle average negativegrayscale values are marked with contours . As x increases,

becomes gradually non-negative and although uctuations atthe forcing frequency are still apparent, their amplitude is

considerably diminished indicating loss of coherence of thevortical structures. The streamwise domain where becomesnon-negative, coincides with the abrupt decrease in the am-plitude of the spectral peak of the formation frequency Fig.21 .

Finally, the spanwise correlation function R11 is mea-sured along the z axis at a number of streamwise stationsusing two single-element hot wire probes z apart one of the sensors is located on the jet centerline . A contour plot of R11 ( x, z) Fig. 23 shows that for x / h 6, the jet is nearlyspanwise-uniform the highest contour level is 0.8 but thatas a result of the transition process, R11 decreases rapidlywith streamwise distance and at x / h 12 the spanwise coher-

FIG. 21. Streamwise variation of the magnitude of the spectral componentat the forcing frequency. Re U 0 383.

FIG. 22. Gray-scale raster plot of the autocorrelation function of the stream-wise velocity ( x, ). Negative levels are marked with contours contourincrement 0.1 . ReU 0

383.

FIG. 23. Contour map of the spanwise correlation function of the stream-wise velocity component R 11( x, z). The lowest and highest contour levelsare 0.8 and 0.15, respectively, and the contour increment is 0.05.ReU 0

383.





ACKNOWLEDGMENTS

This work has been supported by AFOSR Grant No.F49620-96-1-0194, monitored by Dr. J. M. McMichael andDr. M. Glauser.

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