AIAA 2003-0634

Optimization of ControlledJets in Crossflow

S. Shapiro, J. King, A. Karagozian and R. M'CloskeyUCLALos Angeles, CA

41st AIAA Aerospace SciencesMeeting and Exhibit

6–9 January 2003Reno, Nevada

For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.

AIAA–2003–0634

OPTIMIZATION OF CONTROLLEDJETS IN CROSSFLOW

S. R. Shapiro ∗, J. M. King †, A. R. Karagozian ‡, and R. T. M’Closkey §

Department of Mechanical and Aerospace EngineeringUniversity of California, Los Angeles, CA 90095-1597 ¶

Abstract

This experimental study focused on the controlledacoustical excitation of a round gas jet injectedtransversely into crossflow. Use of an open loop,“feed forward” controller or compensator in theexperiments

1allowed for straightforward compar-

isons to be made among jet responses to differentconditions of acoustic excitation of jet fluid. It wasfound that, for a variety of excitation frequencies,optimal temporal pulse widths during square waveexcitation produced clear and distinctly rolled upvortical structures as well as increased jet penetra-tion into the crossflow. In many cases, applicationof forcing frequencies corresponding to subharmon-ics of the natural vortex rollup mode for the un-forced transverse jet also produced increased jet pen-etration coincident with deeply penetrating, distinctvortical structures in the jet. Yet in other instances,merely exciting at the “optimal” pulse width and alow excitation frequency (in comparison to the nat-ural rollup frequency) yielded the best jet penetra-tion and spread. These results on optimization wereinterpreted in terms of a universal time scale associ-ated with vortex ring formation and propagation.

Introduction

The canonical flowfield associated with the roundjet injected normally into crossflow is one that hasbeen extensively studied

2–7because of its widespread

∗Graduate Researcher†Graduate Researcher; presently, MTS, Northrop-

Grumman Corp.‡Professor; Associate Fellow, AIAA. Corresponding author

(ark@seas.ucla.edu).§Associate Professor¶Copyright (c) 2003 by S. Shapiro. Published by the Amer-

ican Institute of Aeronautics and Astronautics, Inc., with per-mission.

applications, particularly in air-breathing engines.One significant observation in these experiments hasbeen that of the dominance of a counter-rotatingvortex pair associated with the jet cross-section, par-ticularly in the farfield

4–7. Mean measurements of

the flowfield suggest that improved mixing in thetransverse jet (over that of a jet injected into a qui-escent fluid) may be due to enhanced entrainment ofthe crossflow into the injected fluid, resulting fromthe actions of the counter-rotating vortex pair.

Through temporal excitation of the transverse jetfluid, active control of vorticity generation and henceinjectant mixing processes may be accomplished.Recent experiments on pulsed or acoustically excitedtransverse jets

1, 5,8–11suggest that for certain excita-

tion conditions, increased jet penetration into thecrossflow, with associated increased mixing, may beachieved. Yet specific conditions yielding increasedpenetration vary rather widely among these differentsets of experiments, which were conducted in bothliquids

9,10and gases

1,5,8, 11. Some of these studies

focus on sinusoidal excitation5,8

and find some im-provement in transverse jet mixing at specific valuesof the Strouhal number based on mean jet veloc-ity and jet orifice diameter, Stj ≡ fDj/Uj. Otherstudies

1,9–11utilize square wave excitation, with the

ability to modify both excitation frequency f andthe duty cycle α of the waveform, the latter of whichis defined as the ratio of the on-time or pulse widthτ to the period of square wave excitation, T ≡ 1/f .Studies of fully modulated transverse jets by Johari,et al.

9, for example, suggest that optimal jet penetra-

tion and spread may occur for specific values of theStrouhal frequency and relatively low values of dutycycle, on the order α of 20%. Yet it is clear from thelimited forced transverse jet data available that the“optimal” forcing conditions, yielding a maximiza-

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tion of transverse jet penetration and spread, maywell be configuration- or apparatus-dependent.

In prior gas phase transverse jet experiments byour group

1, a dynamical compensator or “feedfor-

ward” controller is developed and utilized to be ableto accurately generate temporal waveforms at thejet exit plane. The compensator enables us to ex-amine in detail the excitation conditions (for squarewave excitation, forcing frequency f , duty cycle α,and/or pulse width τ) that lead to improved jet pen-etration via the generation of distinct, deeply pen-etrating vortical structures. For the single jet-to-crossflow velocity ratio examined in these studies,R ≡ Uj/U∞ = 2.58, optimal jet penetration andspread conditions are found to occur for square waveexcitation at subharmonics of the “natural” vortexrollup frequency of the jet, with specific pulse widthsof the order τ = 3 msec. At higher forcing frequen-cies (especially those well above the first subhar-monic, f = fn/2), the jet response was not muchdifferent from that of the unforced jet in crossflow.

The present experimental study sought to con-tinue an examination of the optimization of theacoustically excited jet in crossflow. The compen-sator allowed relatively accurate generation of de-sired temporal waveforms to be produced at the jetexit plane, and hence provided the ability to sys-tematically study conditions which could increase jetpenetration and spread and the relation of these con-ditions to the control of vorticity generation at thejet exit plane.

Experimental Facility and Methods

In the present experimental configuration, shownin Figure 1, a blow down wind tunnel created cross-flow velocities U∞ in the range 1.2 to 10.8 m/s. Thetunnel had a 12 x 12 cm test section, consisting ofa steel plated bottom with interchangeable walls ofceramic or quartz windows. There were three ad-ditional tunnel sections present downstream of thatshown in Figure 1. The jet orifice was located 9.51cm downstream of the end of the tunnel contrac-tion section. The mean jet exit velocity, Uj , rangedfrom 1.2 to 13 m/s and the jet orifice inner diam-eter, Dj , was 7.62 mm. The jet was formed by a16:1 contraction ratio nozzle connected to a circu-lar cylinder with a length of 14 cm. Upstream of thecircular cylinder was a small plenum in which a loud-speaker used for acoustical excitation of the jet was

mounted. The jet fluid was injected into the circularcylinder from a compressed cylinder of gaseous N2

whose mean flow rate was measured using a Tylanmass flowmeter.

For this experiment, a hot-wire anemometer cali-brated by a pitot probe was used to measure the tem-porally evolving velocities at the jet exit plane, andin addition, to characterize the natural vortex rollupfrequencies of the jet in crossflow. The former mea-surement was made by placing the hot wire at thecenter of the jet nozzle exit, flush with the injectionwall. The latter measurement was obtained in theupstream shear layer of the unforced jet in crossflow,whereby the signal analyzer acquired power spectra(in the range 40 - 1600 Hz) resulting from naturalvortex rollup via the Kelvin-Helmholtz instability.The hot-wire position for these spectra was variedwithin the upstream jet shear layer until clearly re-solved peaks, representing fundamental frequenciesfn and higher harmonics, were obtained. In gen-eral the position of the hot-wire varied from approx-imately 1 to 1.5 jet diameters above the upstreamedge of the jet exit.

Smoke visualization was used to observe jet be-havior here. Quartz windows adjacent to the jetinjection region and a 500 W light source above thetest section allowed this visualization, shown in Fig-ure 1. A heated seeder using a liquid parafin solu-tion was used for smoke generation. The nitrogeninjectant passed through the seeder, then throughan ice bath which allowed the injectant to enter thewind tunnel at temperatures equal to that of thecrossflow

12. To aid in the visualization of the jet,

the walls of the tunnel were sooted for increased res-olution. During smoke visualization, a camera (ini-tially a Nikon N2000 SLR and later a Nikon D100CCD) was positioned in front of the test section ofthe tunnel. The visualizations of the transverse jetwere recorded with long (1/15 sec) and short (1/2000sec) exposures.

The loudspeaker for the acoustically excited jetwas driven by an amplifier which was controlled bythe dynamic compensator, used to generate desiredsquare waveforms at the jet exit. The original de-sired input to the compensator was delivered by afunction generator (initially analog and later digi-tal). An overview of the compensator is provided inthe next section.

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Feedforward Controller or Compensator

As described in M’Closkey, et al.1, the jet actuator

in the present study was comprised of the amplifier,loud speaker, jet plenum, and nozzle. The actuatorwas such that its nonlinear dynamics altered the (de-sired) temporal input waveform from the signal gen-erator so that the output waveform measured at thejet exit by the hot wire was distorted. The frequencydependence of the amplitude and phase of the out-put signal required development and implementa-tion of a dynamic compensator, or offline “feedfor-ward” controller. The compensator was developedvia a mathematical inversion of a linear model rep-resenting the frequency response for the jet actua-tion system. When the inversion, or compensator,was applied to the jet forcing, there resulted a moreprecisely prescribed temporally varying jet exit ve-locity whose RMS amplitude of perturbation couldbe made independent of the forcing frequency.

The effect of the compensator on the actual wave-form output at the jet exit (with the mean sub-tracted) is shown by the example in Figure 2. Re-sults are shown for the uncompensated and com-pensated jet response (in m/s), in which the RMSamplitude of the velocity perturbations was matchedbetween the two. The compensator was seen to haverelatively little effect on sine waveform excitation ofthe jet (see M’Closkey, et al.

1for details), but the

compensator had a significant effect on square wave-form excitation. The compensator forced the wave-form to more closely resemble a square wave withessentially the desired duty cycle. Higher frequency“ringing” in the waveform did occur in specific ex-citation cases, seen, for example, in Figure 2. Whilethe elimination of this ringing is the subject of ongo-ing studies

13, as long as the temporal waveform had

a sharp upsweep for the delivery of sharp pulses ofvorticity, the ringing appeared to have little effecton transverse jet behavior.

Smoke visualization revealed that jet compensa-tion made a significant difference when square waveexcitation of the jet was desired, especially at specificfrequencies and specific values of the pulse width τ .Figures 3b and 3c show smoke images for jet evolu-tion without and with compensation, respectively, atthe same frequency and input duty cycle. Figure 3ashows the unforced jet in crossflow for comparison.Figures 3b and 3c demonstrate that, with a better

delineated square wave due to compensation, deeply-penetrating and rather distinct vortex rings could beintroduced into the flowfield at the frequency of ex-citation, resulting in significant increases in jet pene-tration and spread. The “offline control” allowed bythe dynamic compensator also permitted a compar-ison of the effects of different excitation frequenciesand duty cycles on jet behavior, and this is whatallowed the present set of experiments to be con-ducted. Further details on the compensator may befound in M’Closkey, et al.

1and King

12.

Results

The present experiments considered the optimiza-tion of four distinct cases of the jet in crossflow. Thefour cases, numbered 1-4 and defined by their meanjet velocity Uj and crossflow velocity U∞, are shownTable 1. Also shown in Table 1 are important pa-rameters to be discussed in detail below. The fourcases corresponded to two distinct jet-to-crossflowvelocity ratios and four different jet velocities; Case1 was explored to a limited extent in M’Closkey, etal.

1.

Case Uj U∞ R U′j,rms fn (Hz)

1 3.1 1.2 2.58 1.7 220

2 4.8 1.2 4.0 2.0 454

3 6.2 2.4 2.58 2.5 600

4 8.0 2.0 4.0 2.6 870

Table 1. Operating conditions for the present jet in

crossflow experiments; velocities Uj , U∞, and U′j,rms

are given in m/s.

In order to accurately characterize the behaviorof the jet in crossflow, the natural vortex rollup fre-quencies for the unforced transverse jet, fn, werequantified from power spectra measured by the hotwire in the upstream shear layer of the transverse jetwithout acoustic excitation. Plots of two of the thefour cases’ power spectra, for example, are shown inFigures 4ab. The distinct peaks in the power spec-tra occurred when the hot-wire was placed in the re-gion observed in smoke images to contain rolled upnearfield vortices, such as those seen in the upstreamregion near the jet orifice in Figure 3a. The quan-tified natural frequencies in fact coincided closelywith those that could be measured from smoke pho-tographs. Clearly defined higher harmonics of the

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vortex rollup frequency were also observed. Themeasured natural frequencies fn for each case ex-plored are shown in Table 1.

Using the compensator, square wave excitationwas examined in detail in the experiments sincesine wave excitation was observed in our priorexperiments

1not to have a significant effect in in-

creasing jet penetration and spread. The root meansquare of the net (mean-subtracted) jet perturbationvelocity, U

′j,rms, was matched for a wide variety of

excitation frequencies and duty cycles α (or tempo-ral pulse widths τ). This matching effectively deliv-ered a scaled perturbation impulse to the jet fluid(impulse being proportional to the square of the av-erage perturbation velocity) among different excita-tion conditions. It was found that there existed acritical or minimum excitation level U

′j,rms that was

required in order for the jet to respond in any sig-nificant way to the excitation. The matched U

′j,rms

value was thus always chosen to lie above this criti-cal level in order to adequately compare the effectsof different frequencies, duty cycles, and hence pulsewidths of acoustical excitation on transverse jet be-havior. Yet in all cases the perturbation velocitieswere chosen to be small enough so that the jets werenever “fully modulated”, and hence the velocity atthe jet exit never became negative. The chosen val-ues of U

′j,rms for each set of excitation experiments

are listed in Table 1.

In Figure 5, sample waveforms for selected exci-tation cases of the transverse jet show the originalinput waveforms from the function generator and thecompensated measured waveform at the center of thejet exit orifice measured by the hot wire. For eachexperimental case, two plots are shown in each ofFigures 5a-d to illustrate the matching of the RMS ofthe velocity perturbation, U

′j,rms, and pulse width,

τ , for two different frequencies f and duty cycles α.For example, the solid waveforms in the two plotsshown in Figure 5b display two different excitationconditions for Case 2 (where Uj = 4.8 m/s and U∞= 1.2 m/s). The plot on the left has an input squarewave frequency of 151.3 Hz and pulse width of 2.3msec, and the plot on the right has f = 113.5 Hz andτ = 2.3 msec, while the value of U

′j,rms was matched

at 2.0 m/s for each condition. By studying the jetresponse to these alternative cases (and many otherswith other matched quantities), one could then de-

termine which specific excitation conditions resultedin improved jet penetration and spread and in theformation of distinct vortical structures.

Smoke visualizations for all of the four experimen-tal cases yielded very consistent results. One notableresult was the appearance of an optimal pulse width,τ , for a fixed forcing frequency, which resulted inthe generation of distinct, deeply penetrating vor-tical structures. For example, Figure 6 shows, forsquare wave excitation at a fixed frequency, thatwhen the duty cycle (or pulse width) was increased,the jet penetration reached a maximum at a spe-cific value of α and then decreased for higher valuesof α. The maximum in the penetration appearedto occur under conditions where the jet formed themost distinct vortical structures at the nozzle exitplane. It is noted, however, that while the produc-tion of deeply penetrating vortical structures andtransverse jets was achieved at rather specific valuesof excitation pulse width τ , these conditions oftenproduced strongly bifurcated jets, which may notnecessarily have produced improved injectant mix-ing with crossflow as compared with excited jets atother values of τ .

The above observation was made for every exper-imental set of conditions examined here; in fact, foreach experimental condition examined (Cases 1-4 inTable 1), there was in general one value of τ whichresulted in the greatest jet penetration, for a varietyof forcing frequencies. These values of “optimal” τ

are shown in Table 2.

Case τopt (msec)

1 3.0

2 2.5

3 1.7

4 1.6

Table 2. Values of pulse width τ which maximize jet

penetration for the different experimental cases explored.

The appearance of specific values of an “optimal”pulse width τ occurred in fact for acoustical forcingat both subharmonic and non-subharmonic frequen-cies of the natural vortex rollup mode. For someexperimental conditions, e.g., Case 1, the maximumjet penetration occurred for cases where τopt was em-ployed and in addition a subharmonic forcing fre-quency of the natural rollup mode was applied. In

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Figure 7a, for example, smoke images for Case 1 indi-cate that when the pulse width was fixed at approx-imately τopt = 3 msec, the deepest penetration andmost distinct vortical structures occurred when theapplied frequency corresponded to a subharmonic offn = 220 Hz, i.e., 44, 55, 73.5, and 110 Hz. At othernon-subharmonic frequencies, e.g., 85 and 125 Hz,fairly distinct vortical structures were formed, butthey and the jet in general did not penetrate intothe crossflow as well as for subharmonic forcing. Forrelatively high forcing frequencies, well above fn/2(e.g., 147 Hz as shown), there was little response ofthe jet to forcing, despite the fact that the RMS ofthe velocity perturbation, U

′j,rms, was matched at

1.7 m/s for all images in Figure 7a.

When the natural rollup frequency was relativelyhigh, however, e.g., fn = 870 Hz for experimen-tal Case 4, both subharmonic and non-subharmonicforcing produced good penetration of the jet andvortical structures. In Figure 7b, for example, aslong as the pulse width was matched at τopt =1.6 msec, subharmonic as well as non-subharmonicforcing frequencies produced uniformly good jet re-sponse. Yet the excitation conditions producingthese deeply penetrating jets always required verylow forcing frequencies, that is, those well below halfof the natural vortex rollup frequency. Further, inFigure 7b, one finds that since different frequencieswith a fixed pulse width could produce deep jet pen-etration, one could optimize penetration with differ-ent values of duty cycle α, and thus different distri-butions of high and low momentum fluid. Hence inthe “sweep” of frequencies exhibited in Figure 7b,one can have very different levels of mixing and in-jectant distribution, despite very similar jet pene-tration and overall spread. It should be noted, how-ever, that these observations in Figure 7b may haveresulted from simply applying a sufficiently large jetperturbation velocity (U

′j,rms). Large enough per-

turbations to the jet fluid could have caused the in-put forcing frequency dominate in the influence ofjet behavior, rather than that of a subharmonic fre-quency via multiple vortex merging

14.

To further examine the issue of optimizing jet pen-etration via distinct vortex formation, the conceptof the universal time scale associated with coher-ent vortex ring formation, proposed by Gharib, etal.

15, was explored. These researchers find that a

piston-generated vortex ring attains a maximum cir-culation and is disconnected from its trailing jet atcritical values of the ratio of piston stroke to diame-ter (L/D), corresponding to a “universal time scaleof vortex formation”. These critical values for dis-tinct vortex ring formation and propagation appearin the range 3.6 ≤ L/D ≤ 4.5. While the presentexperiments involved the acoustically pulsed, contin-uous jet, rather than piston-driven starting vortexrings, the observation of a critical time scale for dis-tinct ring formation (τopt) suggests a similar physicalmechanism for enhanced penetration.

One could consider an analog to the stroke lengthL (for piston-generated vortex rings) in the presentexperiments to be the product of the peak-to-peakvelocity perturbation, ∆Uj and the pulse width τ .The vortex tube diameter D was considered to beequivalent to the transverse jet diameter Dj . Thusin order to examine the concept of the “optimal”L/D ratio, the present experiments had to be con-ducted by matching ∆Uj among different excitationconditions and seeing if there were critical values ofτ that created optimal vortex formation and deeplypenetrating jets. Figure 8 displays, for experimen-tal Case 1 and for three different forcing frequencieswith matched values of ∆Uj , smoke images wherethe duty cycle α (and hence pulse width τ) was sweptfrom low to high values. Interestingly, for each forc-ing frequency, there were two distinct values of pulsewidth that produced the deepest penetrating jets.At 55 Hz, for example (Figure 8a), as duty cycle wasincreased from 10%, the jet and vortex ring penetra-tion reached a peak at α = 15% (or τ = 2.7 msec),then decreased, then increased again to reach a peakat α = 30% (or τ = 5.4 msec), then the penetrationdropped off again at higher duty cycles. Similar ob-servations of two “optimal” time scales were madefor other forcing frequencies, whether subharmonicor non-subharmonic.

Figure 9 shows a quantification of the observed“optimal” L/D = ∆Ujτ/Dj values, e.g., as observedin the starred conditions shown in Figures 8abc. Theobservation of two distinct critical τ values resultedin two critical values of L/D, the first lying in therange 1.8 – 2.2 and the second in a range coinci-dent with that suggested by Gharib, et al.

15, 3.5–4.7.

There was no obvious difference in jet behavior, fora fixed forcing frequency, between the two different

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L/D conditions. Yet clearly, the time scales asso-ciated with the generic jet in crossflow should alsoinfluence time and length scales leading to optimizedformation of distinct vortical structures.

Discussion and Conclusions

The present experiments on the acousticallyforced jet in crossflow suggested clear sets of ex-citation conditions that produced deeply penetrat-ing jets, with corresponding formation of distinct,deeply penetrating vortical structures. When theRMS of the velocity perturbation was matchedamong different excitation conditions, single valuesof pulse width and a wide variety of frequencies (sub-harmonic as well as non-subharmonic) were observedto generate deeply penetrating vortical structuresand improved levels of jet penetration. As long asthe forcing frequency was relatively “low” (in com-parison to the natural vortex rollup frequency ofthe unforced transverse jet, fn), jet penetration andspread could be optimized through application of theappropriate pulse width, τopt.

It should be noted, however, that a maximum injet penetration may not necessarily translate intoan optimally mixed jet in crossflow, as strongly bi-furcated jets may have a lesser degree of quantifiedinjectant mixedness than that of a jet with a moreuniform spatial distribution of injectant. This sug-gests that acoustical forcing at very low frequencies,e.g., as shown in Figure 7b, may have benefits forenhanced mixing in that specific subharmonic fre-quencies are not required to achieve deep jet pen-etration, and thus the duty cycle can be increasedto produce a better-mixed jet in crossflow. It is fur-ther noted that the issue of optimal frequencies toachieve maximum jet penetration requires more ex-tensive examination, in the sense that large enoughperturbation velocities can force strong vortex rollupirrespective of the relation of the forcing frequencyto the natural frequency.

Finally, it is noted that the present experimentalresults were consistent with the ideas of Gharib, etal.

15in terms of a critical stroke ratio L/D associated

with optimal vortex ring formation. It is interestingto note that a second critical L/D ratio, roughly halfof that predicted by Gharib, et al., also producesdeeply penetrating vortical structures and improvedjet penetration. This issue will be explored further in

the context of time scales associated with the genericjet in crossflow and their relation to periodic vortexring formation.

Acknowledgments

The authors wish to acknowledge the helpful as-sistance provided by UCLA undergraduate studentresearchers Robert Lobbia, Lydia Trevino, MarcusGeorge, and Rebekah Tanimoto in the course ofthese experiments. The authors also wish to ac-knowledge the extensive contributions made in vari-ous stages of this study by Professor Luca Cortelezziof McGill University. The research reported herewas supported by the National Science Foundationunder grant CTS-0200999 and by NASA DrydenFlight Research Center under grant NCC4-153.

References

[1] M’Closkey, R.T., King, J.M., Cortelezzi, L. andKaragozian, A. R., “The actively controlled jet incrossflow,” J. Fluid Mech., 452, 325–335, 2002.

[2] Broadwell, J. E. and Breidenthal, R. E., “Struc-ture and mixing of a transverse jet in incompress-ible flow,” J. Fluid Mech., 148, 405–412, 1984.

[3] Fric, T. F. and Roshko, A., “Vortical structurein the wake of a transverse jet,” J. Fluid Mech.,279, 1–47, 1994.

[4] Kamotani, Y., and Greber, I., Experiments on aturbulent jet in a cross flow,” AIAA J., 10, 1425–1429, 1972.

[5] Kelso, R. M., Lim, T. T., and Perry, A. E., Anexperimental study of round jets in cross-flow,”J. Fluid Mech., 306, 111–144, 1996.

[6] Smith, S. H. and Mungal, M. G., “Mixing, struc-ture and scaling of the jet in crossflow.” J. FluidMech., 357, 83–122, 1998.

[7] Cortelezzi, L. and Karagozian, A. R., “On theformation of the counter-rotating vortex pair intransverse jets,” J. Fluid Mech., 446, 347–373,2001.

[8] Vermeulen, P. J., Grabinski, P., and Ramesh,V., “Mixing of an acoustically excited air jet with

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a confined hot crossflow,” J. Engr. for Gas Tur-bines and Power, ASME Transactions, 114, 46–54, 1992.

[9] Johari, H., Pacheco-Tougas, M., and Hermanson,J.C., “Penetration and mixing of fully modulatedturbulent jets in crossflow,” AIAA J., 37(7), 842–850, 1999.

[10] Eroglu, A. and Breidenthal, R.E., “Structure,penetration, and mixing of pulsed jets in cross-flow,” AIAA J., 39(3), 417–423, 2001.

[11] Schuller, T., King, J., Majamaki, A.,Karagozian, A. R., and Cortelezzi, L., “An exper-imental study of acoustically controlled gas jetsin crossflow,” Bull. Amer. Phys. Soc., 44(8), 111,1999.

[12] King, J. M., “The actively controlled jet incrossflow”, M.S. thesis, Department of Mechan-ical and Aerospace Engineering, UCLA, 2002.

[13] Lobbia, R., Shapiro, S., M’Closkey, R. T., andKaragozian, A. R., “Feedback Compensation forReal-Time Control of Transverse Jet Injection”,Bull. Amer. Phys. Soc., 47(8), 2002.

[14] Ho, C.-M. and Huerre, P., “Perturbed FreeShear Layers”, Annual Reviews of Fluid Mechan-ics, Vol. 16, pp. 365-424, 1984.

[15] Gharib, M., Rambod, E., and Shariff, K., “Auniversal time scale for vortex ring formation,”J. Fluid Mech., 360, 121-140, 1998.

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spectrum analyzer

generatorsmoke

light sourcebell−mouth screens honeycomb

exhaust

amplifier compensator

gas cylinder

pressureregulator

quartz window

subwoofer

16:1 jet nozzle

quartz windows

9:1 contraction section

pulsed jet

crossflow

Fig. 1: Experimental setup for the acoustically controlled jet in crossflow.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05−2

−1

0

1

2

3

4

Vel

ocity

(m

/s)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05−0.1

−0.05

0

0.05

0.1

0.15

0.2

Vol

tage

(V

)

Time (s)

Fig. 2: Comparison of the input waveform to the jet actuator (dash-dotted line), in volts, with the measuredvelocity perturbations (i.e., with the mean subtracted) at the jet exit, in m/s. Results, taken from M’Closkey,et al.

1, are for velocity perturbations without compensation (solid lines) and with compensation (dashed

lines). Here U ′j,rms, the RMS of the velocity perturbations, was matched at 1.7 m/s between compensated

and uncompensated signals. Conditions here correspond to experimental Case 1 (Uj = 3.1 m/s and U∞ =1.2 m/s), with square wave input at 73.5 Hz and α = 22%.

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(a) (b) (c)

Fig. 3: Smoke visualization of the jet in crossflow for experimental Case 1. Results shown are for: (a) the“unforced” jet (in the absence of any acoustic excitation), (b) “uncompensated” square wave excitation at110 Hz and a duty cycle of 31%, and (c) “compensated” square wave excitation at 110 Hz and a duty cycleof 31%. For cases b and c, the RMS amplitude of the velocity perturbations, U′

j, was matched at 1.7 m/s.Images shown are for photographs taken with a short exposure time, taken from M’Closkey, et al.

1.

102

103

−150

−140

−130

−120

−110

−100

−90

−80

−70

−60

−50

Hz

dB

Uj=3.1 m/s, U∞=1.2 m/s, f = 220 Hz

(a)

102

103

−150

−140

−130

−120

−110

−100

−90

−80

−70

−60

−50

Hz

dB

Uj=6.2 m/s, U∞=2.4 m/s, f = 600 Hz

(b)

Fig. 4: Power spectra (amplitude of the hot wire voltage, measured in dB, as a function of frequency) forexperimental Cases 1 (a) and 3 (b) in the absence of acoustic excitation. The plots reveal natural vortexrollup frequencies and higher harmonics.

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(a)

(b)

(c)

(d)

Fig. 5: Compensated waveforms measured at the center of the jet exit plane (solid) for the four differentexperimental cases, compared with input waveforms (dashed). “Matched” U

′j,rms values (indicated in Table

1) and closely matched pulse widths τ were used for each set of waveforms. (a) Case 1; left: f = 110 Hz,τ = 3.1 msec; right: f = 73.5 Hz, τ = 2.9 msec; (b) Case 2; left: f = 151.3 Hz, τ = 2.3 msec; right: f =113.5 Hz, τ = 2.3 msec; (c) Case 3; left: f = 100 Hz, τ = 1.5 msec; right: f = 85.7 Hz, τ = 1.5 msec; and(d) Case 4; left: f = 145 Hz, τ = 1.6 msec; right: f = 110 Hz, τ = 1.6 msec.

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Fig. 6: Smoke visualization for experimental Case 1 with forcing frequency f = 110 Hz and for duty cyclesα ranging from 10% to 50%. The upper images display long exposure photos and the lower images displayshort exposure photos. The maximum jet penetration was observed to occur at a duty cycle of about 30%,corresponding to a temporal pulse width of τ = 3 msec.

(a)

(b)

Fig. 7: (a) Experimental Case 1, with a fixed input pulse width τopt = 3.0 msec and jet perturbation levelU

′j,rms = 1.7 m/s, for forcing frequency f swept between 44 Hz and 147 Hz. (b) Experimental Case 4, with

a fixed input pulse width τopt = 1.6 msec and jet perturbation level U′j,rms = 2.6 m/s, for forcing frequency

swept between 87 Hz and 130 Hz. Subharmonic forcing is denoted by (s).

11American Institute of Aeronautics and Astronautics

AIAA–2003–0634

(a)

(b)

(c)

Fig. 8: Smoke visualization at short exposure times for acoustically forced transverse jets, for experimentalCase 1, with peak-to-peak ∆Uj fixed at 5.3 m/s. Results are shown for forcing frequencies of (a) 55 Hz, (b)73.5 Hz, and (c) 85 Hz, with a sweep in duty cycle α from from 10–50%. Conditions with (*) denote thoseproducing a maximum jet penetration.

Forcing Frequency (Hz)

L/D

40 50 60 70 80 90 100 110 1200

1

2

3

4

5

Subharmonic: Most Distinct Vortical Structures

Subharmonic: Greatest Penetration into Crossflow

Non-subharmonic: Most Distinct Vortical Structures

Non-subharmonic: Greatest Penetration into Crossflow

Universal timescale zone, 3.6-4.5

Uj = 3.1 m/s, U = 1.2 m/s, U pk-pk = 5.3 m/s∞ ∆

Fig. 9: The measured experimental L/D ratio for experimental Case 1, with peak-to-peak ∆Uj = 5.3 m/s,as a function of forcing frequency. The universal time scale regime for L/D, suggested by Gharib et al.

15, is

shown for comparison.

12American Institute of Aeronautics and Astronautics