asymmetric forcing of a turbulent rectangular jet with a

PHYSICS OF FLUIDS VOLUME 13, NUMBER 5 MAY 2001

Asymmetric forcing of a turbulent rectangular jetwith a piezoelectric actuator

Stamatios Pothosa) and Ellen K. Longmireb)

Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis,Minnesota 55455

~Received 6 June 2000; accepted 25 January 2001!

A moving wall section attached to a piezoelectric actuator was used to perturb the airflow exiting afully developed turbulent channel. The Reynolds number based on the channel width and centerlinevelocity was 4240. The maximum velocity of the moving wall section was 9.5 cm/s~2.3% of themean centerline velocity!, and the maximum displacement was 120 microns, corresponding to 1.84wall units. The actuator frequency and displacement amplitude were tuned independently togenerate different effects on the flow, and both quantities were documented to provide preciseboundary conditions for numerical codes. Hot-wire measurements showed that actuation affectsboth the mean and rms velocity profiles downstream of the channel exit. In all cases, forcing yieldsmean profiles that are symmetric with respect to the centerline. However, forcing at low frequencies(St<0.30) causes faster decay of the centerline velocity, higher spreading rates in the far field, andasymmetric rms profiles compared with unforced flow. The maximum rms value crosses from theactuator side to the nonactuator side as the flow moves downstream. This behavior is thought to becaused by staggered but asymmetric vortical structures developing in the opposing shear layers.Forcing from St50.39 through 1.46 leads to altered but symmetric rms profiles and spectracompared with unforced flow. Forcing in the rangeSt,0.50 yields centerline rms values thatinitially are larger than, but further downstream smaller than in the unforced flow. ©2001American Institute of Physics.@DOI: 10.1063/1.1357817#

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I. INTRODUCTION

Over the last three decades, the amount of researccontrol of single-phase flows has been significant. Accordto Gad-el-Hak,1 the idea of flow control was originated bPrandtl ~1904!, who introduced boundary layer theory, eplained the physics of separation involved, and demonstrexperiments in which a boundary layer could be controllOver the last decades, we have experienced a wide variecontrol methods, both passive and active. Active conschemes refer to methods that add energy to the flow, wpassive methods do not. Active methods can be used inmittently and tuned in real time, while passive methods ually involve fixed alterations in geometry, and hence are liited to steady configurations.

Much effort has been devoted to investigating the flof rectangular jets. Examples of the numerous studiesincompressible jets include the work of Sforzaet al.,2 Tren-tacoste and Sforza,3 and Sfeir4,5 on jets from sharp-edgeorifices, Heskestad6 and Sfeir4,5 on jets exiting long rectangular channels, and Gutmark and Wygnanski7 and Kroth-apalli et al.8 on jets exiting contractions. These studishowed that jets exhibit a self-preserving region in thefield characterized by a quadratic decay of the mean cenline velocity, a linear growth of its spreading, and const

a!Research Assistant.b!Associate Professor. Author to whom correspondence should be addre

Telephone: 612-626-7853; Fax: 612-626-1558; electronic m
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values of centerline turbulence intensities when normaliby the local mean centerline velocity.

In the near field of rectangular jets, large-scale coherstructures have been detected and examined by a numbresearchers. Both symmetric and antisymmetric modes ostabilities have been identified in the initial region of thshear layer. The type of mode depended on the shape ojet exit velocity profile9 and the downstream location.10 An-tonia et al.11 and Thomas and Prakash12 found that the nearfield is dominated by large-scale, symmetric structures. Tsymmetric alignment of instabilities was associated with tohat shaped mean velocity profiles at the exit of the nozFurther downstream, in the fully developed region of thethe existence of antisymmetric structures has been descrby a number of researchers.11,13–15

In light of the many practical applications of rectanguljets, numerous attempts have been made to control mixand entrainment by manipulating the natural developmencoherent structures in the jet near field. Active contschemes have been used extensively to alter thestructure.1 Typically these schemes are open loop, andcontrol strategy is predetermined.

Examples of active control methods include acousticcitation, deflection of flexible walls or tabs, and oscillatioof rigid walls. Acoustic excitation, applied by Crow anChampagne16 to study the preferred frequency of a circuljet, has become a common manipulation technique. Inexperiments described below, acoustic speakers were immented to perturb the initial shear layer of rectangulared.

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1481Phys. Fluids, Vol. 13, No. 5, May 2001 Asymmetric forcing of a turbulent rectangular jet

plane jets. Hussain and Thompson17 studied the near field oa plane jet subjected to sinusoidal acoustic perturbatioThey found that the induced symmetric modes remaisymmetric as they propagated downstream. Also, ZamanHussain18 demonstrated that the turbulence intensities innear field of an acoustically forced plane jet were supprescompared with the values in the unforced case. ThomasGoldschmidt15 and Farrington and Claunch19,20 appliedacoustic forcing to increase spreading and mixing in plajets. The observed increases were attributed to larger vorstructures induced in the shear layers by the forcing. Rajapalan and Ko21 studied the near field of a plane jet subjectto excitation at two frequencies corresponding to the shlayer mode and the preferred mode. Most recently, Huand Hsiao22 used earphones on both sides of a plane jeacoustically excite the fundamental frequency in either symetric or antisymmetric modes. In all of the above forcistudies, the jets typically initiated downstream of a contrtion. Thus, the initial mean velocity profiles were top-hshaped with thin shear layers, and initial turbulence levelthe jet cores were small or negligible.

The recent work of Wiltse and Glezer23,24 on square jetsdiffers from the above control studies in that the jets emnated from a relatively long duct with constant cross sectiand the flow exiting the duct was turbulent. In these expments, piezoelectric actuators in the form of cantileveplates were located immediately downstream of the jetand oriented to generate streamwise velocity fluctuationsthe earlier experiments,23 actuators were placed on eachthe four sides and driven at their resonance frequency~ f r

5500620 Hz!. The excitation signal was subjected to amplitude modulation at relatively low frequencies~2–75 Hz!in order to introduce low-frequency disturbances. In laexperiments,24 Wiltse and Glezer applied resonant forcin~f r55092 Hz! on one side only to excite the small scalesthe dissipation range of the shear layer. Direct small-scexcitation resulted in enhanced energy transfer from the lato the small scales and in a substantial increase in the drate of turbulent kinetic energy.

In the present work, we attempt to use a moving wsection attached to a piezoelectric actuator to control the flexiting a fully developed, turbulent channel flow with a recangular cross section. In this case, the wall oscillates norto the flow direction. This forcing arrangement was chosfor several reasons. The ceramic actuator is both durabletunable. The amplitude and frequency can be tuned indedently with a high degree of accuracy in order to achievvariety of forcing conditions. The moving wall can eventally be implemented within an enclosed channel configution. Finally, the moving wall can be used to alter particmotion in particle-laden flows, which will be investigatedfuture experiments.

The fully turbulent initial condition~as opposed to amore quiescent one! was chosen in order to conform witindustrial flows. Furthermore, the initial flow conditions anthe forcing boundary conditions~which can be documenteto a high degree of accuracy! provide a case that can bcomputed numerically in order to test the accuracy of varinumerical models. In this paper, we attempt to docum


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how asymmetric disturbances propagate and evolve aand across the jet flow. In the following sections, we dscribe the experimental setup, the actuator performance,the effect of various excitation conditions on the timaveraged quantities and frequency context within the jet.

II. FACILITY AND EXPERIMENTAL TECHNIQUES

A. Channel flow facility

The flow facility is a blower-driven channel that habeen designed to generate a fully developed turbulent cotion near its exit. The channel body, which can be seenFig. 1, consists of three main sections: the flow conditionsection, the development section, and the actuator secThe entire assembly is mounted vertically on a Unistframe with the air jet issuing into ambient, laboratory contions. The air, which is driven by a frequency-controlled cetrifugal blower, travels through a flexible hose and a laminflow meter before it enters the top portion of the flow coditioning section. The air enters the channel through a sefour diametrically opposed ports at the upstream end. Aries of grids and coarse and fine honeycombs are locatethe flow conditioning section to eliminate swirl andachieve uniformity across the channel span. The flow is ssequently tripped by two wires placed along the span ofchannel at the entrance to the development section. Ovlong time period, low frequency fluctuations in the bulk florate are less than 0.5% of the mean.

FIG. 1. Air jet facility and actuator detail.


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1482 Phys. Fluids, Vol. 13, No. 5, May 2001 S. Pothos and E. K. Longmire

The length of the development section is 70w, wherewrepresents the channel width of 15.75 mm. The crosstional area is constant with an aspect ratio of 11.45.shown in Fig. 1, the development section consists of taluminum side walls and two glass end walls. The glwalls are pressed against the aluminum ones with spacThe lengths of the aluminum walls differ by 40 mm, whiccorresponds to the height of the moving wall section.

The moving wall consists of a rectangular plate attachto a piezoelectric actuator. A detail of the actuator sectcan be seen in Fig. 1. In the present configuration, the avated wall is located at the downstream end of the chanoriented to generate wall-normal motions. The actuatorPZT stack~Polytec-PI, model P-245.77! with a maximumdisplacement of 120 microns, a maximum operating voltaof 1000 volts and a resonant frequency of 2550 Hz. Tdisplacement is directly proportional to the operating voage. The actuator can sustain pulling forces up to 300compressive forces up to 2000 N, and minimal shearforces. The moving plate is made of aluminum and hamass of 96 grams.

A linear amplifier~Polytec-PI, model P-270.10! is usedto drive the piezoelectric translator. The maximum outpvoltage is 1000 volts with a negative polarity. The peak oput current is 500 mA. The peak value of current requiredsinusoidal operation of the translator can be calculated fthe equation:i P5p• f •C•Vi , wheref is the frequency,Vi isthe peak voltage of the input signal to the actuator, andC isthe capacitance of the translator. For the P-245.77 transused,C50.5 mF. Because the required input current is prportional to the product of frequency and peak input voltait scales directly with the peak velocity of the translator.

The piezoelectric translator can be operated in eitopen loop~uncontrolled! mode or closed loop~controlled!mode. In the open loop mode, the PZT ceramic exhibtime-dependent, long-term drift, hysteresis, and temperadependence. These effects contribute to uncertainties anrors in the absolute position of the translator. The closed lmode provides a means of minimizing these uncertaintiessensing and controlling the translator position. Strain gasensors attached to the stack are used to provide the cofeedback. Although, the feedback circuit limits the maximuvelocities achievable with the translator, its applicationnecessary to achieve repeatability and accuracy of the trlator position. Therefore, for the experiments described,translator was operated in the controlled mode.

B. Actuator measurements

A laser vibrometer system~LV ! was used to monitorboth the velocity and displacement of the moving plate unvarious control conditions. The system consists of an opthead~Polytec, model OFV-352! and an electronic signal processor or velocity decoder~Polytec, model OFV-2600!. Thesystem operates as follows: a He–Ne laser beam is projeonto the oscillating surface~target! using a variable focuslens system that also serves as a collecting lens. A portiothe backscattered light is converted by a photodetector toelectric signal that is eventually output as a velocity read


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based on the measured Doppler shift. The target displament is determined by integrating the velocity signal. Ovemeasurement range of 0 to660 m/s, the system is specifieto yield 60.1% accuracy with a repeatability of60.02%.

For the experiments described, the optical head wasented to reflect from the outer face of the moving plate.increase signal-to-noise ratio, a piece of reflective tapeattached to the plate. Velocity and displacement measments were made by holding the input frequency (f ) fixedand increasing the peak-to-peak voltage (Vp–p) input to theamplifier from low values up to a maximum near 10 volThis peak input corresponds to 1000 volts output to thetuator. For each set of inputs~f, Vp–p), the feedback loopwas optimized for a step response by tuning the differenand integral terms of the controller. After the optimizatioprocedure, the velocity and displacement of the moving pwere measured.

C. Velocity and spectral measurements

Air flow at the exit plane of the channel was qualifiewith a single hot-wire probe. Also, detailed velocity mesurements of the flow were obtained for a variety of contconditions. In all cases, a single sensor with diameter ofmicrons and a working length of 1.25 mm was employedcombination with a TSI IFA100 anemometer. The bridoutput voltage was conditioned by passing it throughoffset-and-gain configuration box and a low-pass filter. Tconditioned signal was sent to a Macintosh IIvx computequipped with a multifunction I/0 board~National Instru-ments, NB-MIO-16X!. All data were collected on 12 bit A/Dchannels using Labview programs. The hot wire was cbrated against mean velocities obtained with a pitot proattached to a manometer. During the calibration, the hot wand pitot probe were placed adjacent to each other atcenter of the channel exit plane. For each calibration,channel was run at nine speeds, and a calibration curvecomputed using King’s law. For time-averaged velocmeasurements and flow qualification, 2048 samples per pwere acquired at 50 Hz. These signals were filtered atkHz. Spectral analysis was performed in the jet core ashear layers in both forced and unforced flows. For thstudies, 35 files of 8192 points were acquired at a samprate of approximately 5.4 kHz. The signals were filtered2.6 kHz to prevent aliasing.

Uncertainties in single-sample velocity measuremeresulted mainly from flow unsteadiness and the flow calibtion, since the uncertainty due to the instrumentation acracy was assumed to be negligibly small. Uncertainty dueflow unsteadiness was60.5%, and uncertainty in the flowcalibration was60.55% for a single sample in the jet corand61.90% in the shear layer. Since velocity statistics wcalculated from a finite number of samples, the statisthemselves have inherent uncertainties. Absolute uncertain mean velocity values was60.04(u8/Ucl), whereu8 wasthe streamwise rms velocity, andUcl was the centerlinemean axial velocity. Absolute uncertainty in variance valuwas 60.06(u8/Ucl)

2. In the jet core, whereu8/Ucl'5%,the uncertainty in the mean was60.20%. In the shear layers


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where u8/Ucl'20%, the uncertainty in the mean wa60.80%. The total uncertainty due to all sources was t60.77% for the mean and66% for the variance in the jecore region and62.12% for the mean and66% for thevariance in the shear layers.

The probe holder was mounted on a horizontal travewith an accuracy of60.01 mm. The probe was fixed at eavertical position with an accuracy of60.16 mm.

D. Flow visualization

Flow visualization was performed to assist in the intpretation of hot-wire results. Instantaneous images weretained by illuminating smoke-seeded flow with a thin shfrom a Nd:YAG pulsed laser~Continuum Surelite I!. Thelaser operating frequency and pulse duration were 10 Hz5–6 ns, respectively. A fog generator~Rosco 1500! was usedto produce an aerosol of fine droplets~1–2 mm diameter!that were injected into the flow through the flow conditionisection of the channel. The light scattered perpendiculathe laser sheet was captured by a digital video camera~Sony,model DCR-TR7000, 30 frames per second!.

III. RESULTS

A. Actuator performance

The overall performance of the actuator can be sumrized by the two graphs shown in Fig. 2. In both graphs,solid lines are linear fits to the individual data points plotteFigure 2~a! shows the variation in the maximum displacment (dmax) of the moving plate in terms of the input frequency and peak-to-peak voltage. In the low frequency ra(35, f ,110 Hz!, curves associated with individual frequecies coincide. The maximum displacement of 120mm can beachieved when 9.5,Vp–p,10 volts. As the frequency is increased (200, f ,400 Hz!, a dramatic decrease in the maxmum displacement takes place. This occurs because omaximum current limitation on the linear amplifier. Becauof this limitation, the maximum input voltage has to be lowered, resulting in a narrower range of possible displaceme

In Fig. 2~b!, the variation of the maximum velocity(nmax) of the moving plate is presented as a function of inpfrequency and amplitude. For low frequencies (f <110 Hz!,input frequency and amplitude increase directly with increing velocity. At higher frequencies (200, f ,400 Hz!, theamplitude of the input voltage becomes more and morestricted, so that the maximum achievable velocity peakseventually decreases. One can observe that the maximvalue of nmax is limited to about 95 mm/s~see f 5200 HzandVp–p57.5 volts!.

B. Flow conditions

An (x,y,z) coordinate system is employed to descrithe results~see Fig. 1!. The x-axis originates at the channeexit and points downstream. The normal ory-axis, originatesat the channel center and points toward the moving plThe z-axis runs along the span of the channel havingorigin at the channel center. When the plate is not actuaits inner face is aligned withy/w50.5. In all of the experi-


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ments, the mean velocity of the unforced flow at the cenof the channel exit wasUunf(0,0)54.14 m/s, the turbulencelevel was 5%, and the Reynolds number~Re! based on thisvelocity and the channel width (w) was Re54240. Themaximum displacement of the moving plate (dmax5120mm!corresponds toy151.84 (y15y•u1/n; u15shear veloc-ity!. Qualification measurements showed that the meanrms velocities were uniform in thez direction to within 1%over 60% of the channel span. The measurements descbelow were all taken at the mid-span of the channel.

In addition to unforced flow, a range of forcing condtions was investigated. The three cases investigated in mdetail are characterized in Table I. Cases I and II are choto be within the low frequency range, where spectral m

FIG. 2. Actuator performance based on the voltage input to amplifie

TABLE I. Characteristic parameters of the forcing cases.

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I 65 9.5 115.2 47.0 4.14 0.25II 110 9.5 114.8 79.5 4.14 0.42III 385 4.0 31.9 80.1 4.14 1.46


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surements reveal strong energy content in the flow. Casis chosen to be in the high frequency range where the enwithin the flow is an order of magnitude smaller than in tother two cases. The maximum displacement of the platchosen to be the same for cases I and II, while the maximvelocity of the plate in case II is twice that of case I. Tmaximum velocity in cases II and III is the same. The lacolumn of Table I corresponds to the Strouhal number (St)based on the frequency of the input signal, the chanwidth, and the mean, centerline velocity of the unforced fl@St5 f •w/Uunf(0,0)#.

C. Flow visualization

The upper sequence of photos in Fig. 3 shows instaneous smoke-marked images of the unforced jet taken inx–y plane. The field of view, which extends tox/w56.5,includes the silhouette of the channel exit with the movwall section on the upper left side. In both images~a! and~b!, the left and right shear layers appear to spread almlinearly with downstream distance. The linear spreadingmore obvious when one superposes several instantanimages of the unforced flow. In image~a!, small-scale struc-tures occupy the near field of the jet. In image~b!, largeeddies with length scale;w appear in the area close to thjet exit (1.0,x/w,3.0) while smaller eddies or structureexist further downstream. It is difficult to comment owhether or not these large-scale structures are assocwith symmetric or antisymmetric modes of instabilitieHowever, since most of the eddies appear distorted andwell defined, one can conclude that the turbulent initial codition prevents any individual instability from dominatinthe overall flow structure.

The lower set of photos in Fig. 3 shows instantaneoimages of the forced jet. The conditions are similar to tholisted for case I. Forcing is applied atSt50.27, and thecorresponding maximum displacement is 115.8mm. ThisStrouhal number is near the low end of the range wherepreferred mode is typically observed in round jets. In ima~c!, both large- and small-scale structures appear in thefield of the jet, and the overall flow resembles the unforccase in image~b!. Image~d! clearly shows the existence olarge, antisymmetric structures fromx51.5w to 4.5w. In im-age ~e!, large symmetric structures occur. Therefore, bsymmetric and antisymmetric modes of instabilities existthe initial shear layers, and it appears that forcing increatheir probability of occurrence. At the same time, structuassociated with a wide range of frequencies persist owinthe turbulent initial condition.

As the forcing frequency is increased (St.0.27), thesize of the associated structures and the spacing betwthem decrease. No obvious changes in the jet structure wobservable from the flow visualization~although the velocitymeasurements below show do exhibit changes!. For lowerfrequencies (0.14,St,0.27), instantaneous images yieflow patterns similar to the ones observed forSt50.27.


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D. Velocity measurements

The sequence of plots in Fig. 4 shows both forced aunforced mean and rms velocity profiles taken in thex–yplane at three streamwise locations (x/w51,4,10). BothmeanU( i , j ) and rmsu8( i , j ) velocities@wherei denotes thedownstream location (x/w) and j denotes the cross-strealocation (y/w)], are normalized with respect to the locmean centerline velocity of the unforced caseUunf( i ,0).

In Fig. 4~a!, the mean profile of the unforced casex/w51 is symmetric with respect to the centerline, andshape is typical of those found in fully developed turbulechannel flows. The side-wall boundary-layers measured(x/w,y/w)5(0,60.5) were found to be turbulent, and thvelocity profile atx/w50 is similar to the one shown. Symmetry persists further downstream, and the jet spreadsincreasing streamwise distance@see Figs. 4~b! and 4~c!, re-spectively#. Note that the (y/w) scale in these plots changewith downstream location. The mean velocity profiles wefound to be geometrically similar forx/w>8 when plottedagainst the parametery0.55y/d0.5, whered0.5 is the jet widthcorresponding to one half of the mean centerline velocThe self-similar velocity profiles agree well with those mesured by Heskestad6 and Sfeir.5 In the present study, geomeric similarity first occurred at an earlier axial location thathose reported in previous studies (x/w;30). The earlieroccurrence of geometric similarity in the present flow canexplained by the higher turbulence intensity and thicker itial shear layers when compared with jets exiting contrtions.

In Figs. 4~a!, 4~b!, and 4~c!, the mean velocity profiles oall three forcing cases are symmetric with respect to the cterline. At x/w51, the forced profiles lie on top of the unforced one except forSt50.42, where the velocity is largein the outer region of both shear layers. Atx/w54, lowervalues of velocity with respect to the unforced onesfound close to the centerline for bothSt50.25 and St50.42, while no difference is observed betweenSt51.46and the unforced case. Further downstream, atx/w510, theprofile corresponding with the lowest forcing frequen~St50.25) is broader, and the velocity decay is larger thanthe other cases. Atx/w510, the profile ofSt51.46 is notplotted because no differences in mean velocity betweencase and the natural jet were found forx/w>6. In general,one can conclude that although the shape of the mean veity profiles is not altered substantially, asymmetric excitatiaffects the downstream evolution of the centerline veloci

The different forcing cases did alter the rms profilesseen in Figs. 4~d!, 4~e!, and 4~f!. At x/w51, the unforcedcase yields a symmetric profile with a low turbulence levof 5% in the core surrounded by higher levels of 19% in tshear layers. The difference in core and shear layer tulence levels decreases with downstream distance@see Figs.4~e! and 4~f!#. At x/w510, the difference in turbulence levels has decreased to 4%. Therefore, at further downstrlocations the mixing initiated at the jet boundaries has pmeated the entire flow field. The unforced rms profiles wsymmetric at all measurement locations.

In the following paragraphs, the three forcing cases



FIG. 3. Instantaneous images of unforced flow@images~a! and ~b!# and flow forced atSt50.27 @images~c!,~d!, and~e!#.

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discussed. First, we consider the lowest forcing frequenSt50.25. At x/w51, the rms profile is asymmetric withrespect to the centerline, and turbulence intensities arehanced compared with the unforced ones. The enhanceis most obvious within the range 0,y/w,0.5. A peak rmsvalue of 0.21 is found aty/w50.45. Atx/w54, increases inturbulence intensity have spread across the jet whichbecome more asymmetric. Specifically, the region of lowrms velocity has shifted off center, and the shear layer onactuator side is broader as well as more energetic. The prms value of 0.21 is located aty/w50.5. At x/w510, theprofile is also asymmetric, but the peak rms value of 0.24shifted to the opposite side of the jet (y/w520.8). Theactuator-side shear layer at this location has a shapeintensity similar to the unforced one. From this seriesplots, it appears that the disturbances caused by the forpropagate from one shear layer to the other. Additional pfiles reveal that the rms value in the flow crosses fromforcing side to the unforced side betweenx/w57 and 8.Within the range 0,x/w,10, no suppression of turbulencintensities compared with the unforced values was detecFurther downstream, however, suppression occurs atcross-stream locations.

Next we consider the normalized rms profiles forSt50.42. In this case, the average kinetic energy of the actor is approximately four times that for case I~ St50.25). Atx/w51, the rms profile is asymmetric with respect to tcenterline, and turbulence intensities are enhanced acroscore region. The rms values are comparable with those


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St50.25 except at the peak locations. The maximum rvalues~0.18 in both shear layers! are smaller than those observed for unforced flow andSt50.25. Further downstreamat x/w54, intensities are increased only within20.35,y/w,0.35, and the increases are smaller than thoseserved whenSt50.25. At x/w54 and x/w510, the rmsprofiles appear symmetric. In fact, symmetric profiles wefound for all x/w.2. Hence, asymmetric disturbances iduced at this frequency appear to permeate the entire flowx/w52, and no evidence of a disturbance crossover isserved. Atx/w510, the rms values are smaller than in tunforced case over the entire jet width. Therefore, turbulereduction or suppression forSt50.42 occurs sooner than foSt50.25.

The third forcing case (St51.46) is similar to the sec-ond (St50.42) in that the average kinetic energy associawith the actuator was equivalent. Nevertheless, the higfrequency and smaller displacement corresponding withthird case was much less effective at altering the rms flpattern. In all locations examined, no significant differencin rms velocity were found when comparingSt51.46 withunforced flow.

In Fig. 5, the centerline evolution of the mean velocdecay, characterized by the parameter@U( i ,0)/Uunf(0,0)#22,is shown for both forced and unforced conditions. In tself-similar region of the unforced case (x/w.8), this pa-rameter varies linearly with the downstream location, asbeen well documented in the existing literature. Forx/w<3, the four cases appear identical, suggesting that ex


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FIG. 4. Normalized unforced andforced mean and rms velocity profileat three downstream locations (x/w51, 4, and 10!.

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tion does not affect the velocity decay in this region. Furthdownstream (x/w.3), forcing at St50.25 reveals largervalues of decay. As the forcing frequency increases, hever, the centerline velocity decay tends to approachobserved in the unforced case.

The phenomena of turbulence enhancement and supsion are considered further in Fig. 6, where the streamwevolution of the normalized, centerline rms value is showThe magnitude of the unforced rms value increases dostream of the jet exit and begins to level off nearx/w510where it reaches a value of about 0.20. Heskestad6 and Sfeir5

reported values of 0.25 in the self-similar region of their jeForcing atSt50.25, causes strong enhancement of thevalues for 1,x/w,10, while suppression occurs forx/w.11. The enhancement is maximized in the near field ofjet (2,x/w,5), while suppression appears to increase wdownstream distance beyondx/w511. Please note that de


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spite persisting asymmetry in the rms profiles ofSt50.42,the local centerline values are close to the minimum valmeasured, and the centerline evolution of rms values caused to trace the evolution of both enhancement and suppsion. For St50.42, enhancement takes place within trange 1,x/w,5, while suppression occurs forx/w.6. Theamount of turbulence suppression seems to be constan8,x/w,13 before it begins decreasing atx/w513.

The initial streamwise location of the turbulence supression is plotted as a function of frequency in Fig. 7.dmax'115 mm and within the forcing range of 0.2,St,0.5, suppression occurs at earlier downstream locatwith increasing frequency. A linear curve fit to the log–loplot indicates that the streamwise location and the forcfrequency are related by a power law. For the case plotthe linear fit corresponds tox/w;St21.085.


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E. Spectral measurements

Normalized power spectra of the axial velocity wemeasured for both unforced and forced cases in the rax/w51210. Power spectra measured along the centerand the actuator-side shear layer are plotted in Figs. 8 arespectively.

The sequence of plots on the left-hand side of Figcorresponds to the natural jet. Atx/w51, the normalizedplot of the power spectral density function (Euu) is broad-band and shows no distinct peak at any frequency. Thisclearly indicates the presence of turbulent flow conditioAt x/w52 and 3, a hump between 60 and 120 Hz is oserved. The corresponding Strouhal numbers vary from 0to 0.42. This range of Strouhal number is typical of what omight expect for large symmetric structures developacross the jet span as was observed in Fig. 3~b! for 1.5,x/w,3.5 and has been observed by many researcheround jets with less turbulent initial conditions. Atx/w53,the hump contains peaks atSt'0.26 and 0.37. Wiltse andGlezer23 mentioned the existence of a similar hump in tnear field of their square jet. The power spectrum of thunforced jet atx/De51 (De was the equivalent diameter othe duct cross section! revealed a hump centered atf 535Hz, corresponding to a Strouhal numberStDe

50.38. At

FIG. 5. Evolution of the mean velocity decay along the flow centerlin

FIG. 6. Streamwise evolution of the normalized centerline rms value


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x/w54, the hump in our rectangular jet has practically dappeared. Additional plots show that, further downstreaenergy shifts toward the highest frequencies plotted, imping that energy is transferred from lower to higher frequecies as larger structures break down. Smaller structudownstream of larger ones are seen clearly in Fig. 3~b!.

The plots on the right-hand side of Fig. 8 correspondthe forced case ofSt50.40. The conditions are very similato those listed for case II. Strong peaks at the forcing fquency occur for 1<x/w<5. The peak at the forcing frequency is strongest atx/w52 and decreases monotonicalwith streamwise distance. Whenx/w<3, peaks are alsopresent at twice the forcing frequency. These harmonmost likely result from out of phase fundamental~or anti-symmetric! structures developing on opposite sides of tcore and extending across the centerline. Also, a peak athalf of the forcing frequency appears forx/w52 – 3. Thispeak, which is broader than the fundamental peak and stgest atx/w53, indicates possibly the presence of pairstructures. Outside of the locations of the strong peaks,normalized energy in the forced spectra is suppressed cpared with the unforced flow. In addition, the broad-humcharacteristic of the unforced flow does not appear. Figurthus demonstrates that forcing at this frequency has altethe structure in the jet core significantly.

The spectral evolution along the actuator-side shlayer is examined in Fig. 9 for both unforced and forcconditions. All measurements were obtained at the spanwlocation where the rms value was a maximum. In the nfield of the natural jet (1,x/w,4), highly energetic fluidexists at low frequencies~20–150 Hz!. For St50.40, strongpeaks at the forcing frequency are observed within the sarange. Atx/w51, additional harmonics are present. Theare thought to be caused by harmonics within the movwall. ~Such harmonics were observed also in laser vibromter measurements of the wall displacement.! Note that theseharmonic disturbances die out quickly. Atx/w52, only aweak peak at twice the forcing frequency can be observe

At x/w51, a distinct hump that covers a frequen

FIG. 7. Initial streamwise location of turbulence suppression fordmax

>115 mm.


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FIG. 8. Normalized power spectradensity functions along the centerlinfor unforced flow ~left! and flowforced atSt50.40 ~right!.

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range from 80 to 140 Hz is observed in the forced flow. Tpresence of this hump suggests that the forcing enhastructures not only at the forcing frequency, but also ovefairly broad frequency range surrounding it. Atx/w52 and3, the hump narrows and shifts toward lower frequencwhile at x/w54, the hump has disappeared. Further dowstream (x/w>5), significant differences between unforceand forced spectra were not detected.

Separate measurements~not shown! revealed spectraalong the opposing shear layer that were identical tospectra on the actuator side. This reinforces our observathat asymmetric forcing withSt>0.40 generates disturbances felt equally by points located on either side ofcenterline forx/w.1.

Next we consider spectra forSt50.25~case I!. Measure-ments along the centerline~not shown! revealed that thespectral evolution is similar to that described forSt50.40.


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Strong peaks at the forcing frequency are observed withe range 1<x/w<6, while peaks at twice the forcing frequency are detected forx/w<4. The peaks persist slightlylonger than whenSt50.40 indicating that the larger structures formed at the lower frequency remain coherent ovelonger distance. Again, the persistence of the harmonic palong the centerline is consistent with the presence of sgered antisymmetric vortices as observed in Fig. 3~d!. It isworth mentioning that no peak appears at one-half offorcing frequency on the centerline for this case.

Figure 10 reveals the asymmetry in the spectra aloboth shear layers forSt50.25. As before, these spectra wemeasured at spanwise locations where the maximumvalues were detected. On the actuator side, strong peathe forcing frequency are observed fromx/w51 to 4, whilepeaks at additional harmonics occurred also forx/w51 and2. At x/w52, a distinct hump covers the range of 50–1


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FIG. 9. Normalized power spectradensity functions along the actuatorside shear layer for unforced flow~left! and flow forced at St50.40~right!.

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Hz. The hump subsequently narrows and decreasestrength, disappearing byx/w54. On the opposing wall sidestrong peaks at the forcing frequency are detected ovgreater streamwise distance (1<x/w<6), and peaks atwice the forcing frequency are found atx/w52 and 3. Thepresence of the harmonic peaks can be explained by antismetric structures generated on the actuator side that areall the way across the jet. Relatively broad peaks at halfforcing frequency, indicating the presence of paired strtures, are observed atx/w55 and 6. Further downstream(x/w>8), the wall-side spectra appear similar to thesethe actuator side of the jet.

The existence of strong peaks on the wall side at strewise locations where the corresponding spectra inactuator-side shear layer are featureless is consistent witrms velocity behavior shown in Fig. 4. The spectra show tthe large structures forming at the forcing frequency per


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over longer distances in the wall-side shear layer. Therefalthough higher rms values are initially closer to the actuadue to the immediate formation of structures there, furtdownstream, the peak rms switches to the unforced side@seeagain Fig. 3~d!#.

Forcing atSt51.46~case III! results in spectra with narrow peaks at the forcing frequency. Outside of these pethe shapes of the forced spectra are similar to the unforones. The values of the peaks measured on the centerlinein the shear layers are smaller than those forSt50.40, lead-ing to the conclusion that high frequency disturbancesdissipated more quickly than those at lower frequencies. Tbehavior was demonstrated also by Wiltse and Glezer.23 Intheir jet, the high frequency component of the carrier waform was barely noticeable even atx/De51. Conversely,low frequency disturbances (0.10,StDe

,0.80) introduced


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FIG. 10. Normalized power spectradensity functions along the actuatorside shear layer~left! and the wall-sideshear layer~right! for St50.25.

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50.174, strong low frequency peaks could be foundto x/De54).

Based on additional spectra measured atx/w51 andy0.5561 within the range 0.13,St,0.46, the following re-marks can be made. Forcing within the range 0.13,St,0.38 yields spectra with stronger peaks on the actuatorthan on the opposing side. As the forcing frequencycreases~while the amplitude is held constant!, the differencein magnitude between the peaks decreases until it reazero nearSt50.38. ForSt.0.39, asymmetric disturbanceare felt equally by points located in either shear layer.

For St50.40, then, the strong and wide hump observat x/w51 ~see Fig. 9! occurs in both shear layers. As thforcing frequency decreases (St50.39→0.29), the humpson both sides become narrower and weaker. The hump


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the opposing side weakens faster. Eventually, atSt50.25,no hump surrounding the forcing frequency remains in eitshear layer atx/w51 ~refer to Fig. 10!. The spectral resultsthus demonstrate that forcing at an intermediate freque(0.39,St,0.46) almost immediately excites structures ova band of frequencies surrounding it. Forcing at a lower fquency (St50.25), also excites a localized frequency banbut this does not occur untilx/w52. Forcing at a higherfrequency (St.0.60), however, enhances structures onlythe forcing frequency or its harmonics.

IV. SUMMARY AND CONCLUDING REMARKS

The experiments discussed have demonstrated an acontrol method for manipulating turbulent flow exitingchannel. The control scheme consists of a rectangular pattached to a piezoelectric actuator that is oriented to ge


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ate wall normal motions. The actuator allows the wall veloity and displacement to be controlled and tuned indepdently. In the experiments described, the maximachievable velocity was 2.3% of the mean centerline veloat the channel exit. The maximum displacement of the ming plate corresponded to 1.84 wall units.

Three forcing cases as well as an unforced case wexamined in detail. Both the actuator displacement andlocity were characterized to high accuracy providing precinitial conditions for numerical codes. Hot-wire measurments show that forcing can affect both the mean andvelocities. Compared with the unforced jet, forcing at lofrequencies (St<0.30) causes faster decay of the mean cterline velocity as well as higher spreading rates in thefield. Although mean velocity profiles are symmetric wirespect to the centerline, rms profiles are asymmetric. Ftuation levels are increased with respect to the unforcedin the near field of the jet, while further downstream a coparative reduction in turbulence takes place. The most sing feature of the low frequency forcing case is the propation of the maximum rms value from the actuator-side shlayer to the opposite one with increasing streamwisetance. This behavior is attributed to the existence of lfrequency staggered structures that maintain their coherfurther downstream on the unforced side of the jet.

Forcing at intermediate frequencies (0.39,St,0.60)yields mean velocity profiles similar to the unforced onThus, this forcing has a minimal effect on both the mecenterline velocity decay and the jet spreading rate. Unthe lower frequency case, the time-averaged rms veloprofiles and spectral behavior are symmetric with respecthe centerline already byx/w51. These higher frequencperturbations, therefore, propagate quickly across thewidth so that the resulting flow modification is equivalentboth sides. Spectra reveal evidence of staggered vorstructures occurring in the jet nearfield. Again, rms fluctution levels are increased with respect to the unforced casthe near field, while a turbulence reduction occurs furtdownstream. This crossover from turbulence enhancemereduction, also found in the low frequency range, dependsboth the forcing frequency and the maximum displacemof the moving plate. Earlier studies by Zaman and Hussa18

demonstrated immediate turbulence suppression over a rof forcing frequencies in forced round and rectangular jeTheir initial conditions, however, were significantly differefrom those in the present study. In their case, the flow issfrom a contraction with thin laminar boundary layers, athe initial core turbulence level was only 0.25%. In fawhen their boundary layers were tripped, no suppressionobserved.

Finally, forcing at an even higher frequency~e.g., St51.46) reveals no change in time-averaged flow statiscompared with the unforced flow. Both the mean and rvelocity profiles are similar to the natural ones. Although taverage kinetic energy of the actuator was equivalent tocase studied at an intermediate frequency, the flow was


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receptive to the excitations, and the disturbances wquickly attenuated. The high frequency case comes closethe flow of Wiltse and Glezer24 which was forced at substantially higher frequency and amplitude.~The actuator tip ve-locity was approximately 66% of the mean exit velocity!.The large forcing amplitude resulted in a crossover from tbulence enhancement to reduction close to the jet(x/De;1).

ACKNOWLEDGMENTS

This work was funded by grants from the ACS Petrleum Research Fund~32524-AC9! and the National ScienceFoundation~CTS 945-7014!.

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asymmetric forcing of a turbulent rectangular jet with a

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