passive control of transonic cavity flow

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assive Control of Transonic Cavitylow

avid G. MacManus-mail: [email protected]

iane S. Doran

epartment of Aerospace Sciences,ranfield University,harley End,

edfordshire MK43 0AL, UK

pen cavities at transonic speeds can result in acoustic resonantow behavior with fluctuating pressure levels of sufficient intensityo cause significant damage to internal stores and surroundingtructures. Extensive research in this field has produced numerousavity flow control techniques, the more effective of which mayequire costly feedback control systems or entail other drawbacksuch as drag penalties or rapid performance degradation at off-esign condition. The current study focuses on the use of simpleeometric modifications of a rectangular planform cavity with theim of attenuating the aeroacoustic signature. Experiments wereerformed in an intermittent suck-down transonic wind tunnel bysing a typical open flow rectangular planform cavity, which wasodularly designed such that the leading and trailing edge geom-

tries could be modified by using a family of inserts. The currentork focused on a variety of recessed leading edge step arrange-ents. Configurations were tested at transonic Mach numbers

panning the range Mach 0.7–0.9, and unsteady pressure mea-urements were recorded at various stations within the cavity inrder to obtain acoustic spectra. The most effective configurationt Mach 0.9 was the leading edge step employing a step height totep length ratio of 0.4. This configuration achieved a tonal at-enuation of up to 18.6 dB and an overall sound pressure levelOASPL) reduction of approximately 7.5 dB. This is a significantevel of noise suppression in comparison with other passive con-rol methods. In addition, it offers the additional benefits of being

simple geometric feature, which does not rely on placing flowffectors into the high-speed grazing flow.DOI: 10.1115/1.2917427�

ntroductionThe high intensity resonant flow behavior inherent to the un-

teady aerodynamics encountered within cavity flows under high-peed conditions is renowned to cause significant damage to in-ernal stores and surrounding structures �1�. Indeed, for a typicalpen-cavity flow, the acoustic signature can achieve levels of over65 dB �2–5�. The resulting impact on internal stores of high-peed aircraft has led to extensive studies to attenuate the un-teady flow and the examination of a broad range of flow controltrategies �3,4,6–12�. These comprise both active and passive con-rol methods and have met with mixed success. Indeed, some ofhese methods �such as spoilers� have been adopted in service.owever, as there is an ever pressing drive for aircraft stealth and

nternalized stores, there remains an ongoing interest in furtheringhe understanding of open-cavity aerodynamics and potential ro-ust flow control technologies.

Contributed by the Fluids Engineering Division of ASME for publication in theOURNAL OF FLUIDS ENGINEERING. Manuscript received April 13, 2007; final manu-cript received March 26, 2008; published online May 19, 2008. Assoc. Editor:
hillip M. Ligrani.
ournal of Fluids Engineering Copyright © 20

om: http://fluidsengineering.asmedigitalcollection.asme.org/ on 09/05/201

The flow physics fundamentally depends on the cavity length todepth aspect ratio �l /d� and encompasses closed, transitional, andopen-cavity regimes �1,13,14�. The unsteady aerodynamics en-countered for open flows, in which the shear layer bridges thecavity, is characterized by the presence of internal acoustic modes.The associated frequency peaks can be readily observed by inves-tigating the acoustic spectra. The semi-empirical modified Ros-siter equation �Eq. �1�� is used to predict the acoustic mode fre-quencies within a rectangular open-cavity flow �14,15�:

St = fml

U�

=m − �

M��1 +� − 1

2M�

2�−0.5 +1

K�1�

where fm is the frequency of a given longitudinal acoustic mode,m is the mode number, and � and K are empirical constants. � isa function of the cavity length to depth ratio and is related to thephase between the vortices within the shear layer and the up-stream traveling pressure waves within the cavity. K is a functionof freestream Mach number and is defined as the relative speed ofthe propagation of the vortices within the shear layer to the veloc-ity of the freestream flow. Although this expression can be used topredict the modal frequencies, it does not predict the magnitude ofthe peaks. A variety of researchers have proposed models of theunderlying flow physics, which generate such aeroacoustic char-acteristics �2,11,14,16,17�. Most of these highlight the interactionof the pressure waves within the cavity and the vortical structureswithin the cavity shear layer coupled with an internal feedbackmechanism arising from the shear layer interaction with the cavitytrailing edge.

Previous control technologies have delivered attenuation ofboth tonal peaks and broadband noise �3,4,14� although some ofthe most successful methods require complex flow modulationmethods �9�. The aim of the current work is to assess the effect ofnovel modest geometric changes, which have the objective of dis-rupting the interaction of cavity internal and shear layer flow andthe fundamental internal feedback mechanism. To this end, a va-riety of simple leading edge step configurations for a rectangularopen cavity have been examined in this work.

Experimental Method

Facility and Instrumentation. The experimental work wasconducted by using an intermittent suck-down transonic wind tun-nel with working section dimensions of 63.5 mm wide and60 mm high. The tunnel is connected to a vacuum tank, and theworking section Mach number is controlled by using a down-stream throat. The inlet air at atmospheric temperature and pres-sure is drawn through an alumina bed in order to dry the flow andthe stabilised run time was typically 30 s. The cavity was builtinto the fixed working section upper liner. The lower liner con-tained slanted perforations providing 13% porosity leading to aventilated lower cavity. The lower liner was inclined by 2 deg tocounteract the boundary layer growth in the working section andto deliver a nominally pressure gradient. The static pressure gra-dient ��p / P0� in the working section was measured for the rangeof Mach numbers and was found to have a favorable pressuregradient of 0.5% in the worst case across the region of interest.

The operating Mach number was calibrated for a referencefilled cavity configuration and determined from the working sec-tion total and static pressures. These pressures were measured byusing a Druck PDCR22 15 PSI differential transducer, which wassampled at 300 Hz for 5 s to obtain an average reading. An arrayof up to six pressure transducers �Kulite XCS-190-15A 15 PSIabsolute� was used to obtain the unsteady data, which wassampled at 20 kHz to obtain 216 samples by using a 16 bit DAQcard. The Kulites are positioned on the cavity forward and rearfaces and along the cavity floor centerline. The unsteady pressuresignal is divided into 31 blocks of 4096 samples with a 50%
overlap. Each block is windowed by using the Hanning function,
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nd the resultant signal is analyzed by using a fast Fourier trans-orm with a power correction to counteract the windowing. The 31ata blocks are then averaged to create an ensemble average forhe entire signal. This provides a frequency resolution of 4.88 Hz.

The reference turbulent boundary layer was measured by usingflat-head Pitot probe �1.07 mm�0.37 mm� in the tunnel work-

ng section without the cavity present. Boundary layer traversesere taken at a location that corresponds to a position of 36 mmehind the cavity leading edge. The measurements are summa-ized in Table 1 for which the average stagnation pressure andemperature in the settling chamber were 9.89�104 Pa and98 K, respectively.

Experimental Accuracy. The Mach number is calculated fromhe total to static pressure ratio, and on average for the reportedominal Mach number, it is estimated to be within �0.01. Thensteady pressure data were acquired by using the Kulite sensor,hich the manufacturer quotes as having a natural frequency of

pproximately 200 kHz with valid data being obtainable from atatic calibration at up to 20% of the resonant natural frequency,.e., 40 kHz. The quoted typical transducer combined linearity,ysteresis, and repeatability error is �0.1% full-scale output. Inddition, the static calibration standard was estimated to have anncertainty of �0.13%. Based on these bias errors and a statisticalnalysis of the measurements, the OASPL is estimated to have anncertainty of �0.4 dB, and the typical mode peaks have a SPLncertainty of �2.5 dB. The total uncertainty on the boundaryayer traverse positioning was 0.11 mm.

Model Configurations. The cavity is of a modular constructionnabling modification of the leading and trailing edge geometriesy using a family of inserts. The datum rectangular cavity dimen-ions comprise length �l� 100 mm, width �w� 25 mm, and depthd� 20 mm. For the Mach number range under consideration0.7�M �0.9�, the flow field was therefore classified as an open-avity flow �1�. The inserts comprise leading edge steps employ-ng step height �h� to cavity depth �d� ratios of 0.3, 0.145, and 0.1or a fixed step length �s� of 15 mm. A schematic of the steponfiguration is illustrated in Fig. 1.

The step configurations were designed primarily to disrupthear flow and internal cavity flow interaction at the leading edget which the shear layer is most susceptible to disturbances �6�.uch disruption would minimize oscillatory shear layer excite-ent and hence disrupt the internal cavity oscillation feedbackechanism at the cavity trailing edge generated by oscillatory

Table 1 Working section boundary layer characteristics

Machnumber �99 �mm� �* �mm� �mm� H Re�

*

0.90 3.28 0.76 0.44 1.72 13,5000.86 3.35 0.75 0.44 1.71 12,500

ig. 1 Schematic of cavity streamwise cross section illustrat-ng leading edge step cavity configuration and instrumentation
ositions
64501-2 / Vol. 130, JUNE 2008


impingement of the shear layer on the cavity trailing edge.The leading edge step configurations were designed based on

the reattachment length characteristics for a backward facing step�1,18,19�. The designs are arranged to span the regime where, fora simple backward facing step, the flow would reattach onto thedownstream face. Associated literature reports that for an isolatedbackward facing step, the reattachment line occurs at a down-stream distance of approximately x /h of 6–9 �18,19�. However,this is dependent on Reynolds number, Mach number, and theapproaching boundary layer characteristics �1�. Clearly, the pro-posed geometry is different for the cavity flow due to the forwardpropagating reflected pressure waves and the recirculating flow,which is characteristic of the datum cavity configuration. Never-theless, these simple reattachment guidelines are used as a refer-ence point for the leading edge steps. It is postulated that thedepth to length ratio �h /s� of the step needs to be sufficiently largeto avoid a simple reattachment on the step face to facilitate adisruption in the feedback mechanism. Based on these simpleguidelines, a set of three step sizes was tested; h /s=0.4, in whichthe shear flow is not expected to reattach to the step face, andh /s=0.193 and 0.133, in which the shear flow may reattach on thestep face according to a loose application of the backward facingstep research mentioned above.

Results and Discussion

Datum Cavity. The SPL spectra obtained for the datum rect-angular cavity configuration �l /d=5� show reasonable agreementwith the estimated Rossiter frequencies based on �=0.32 and K=0.67 �Fig. 2�. The level of difference is similar to that reportedby previous researchers under similar conditions �20�. As ob-served in previous research �2,3,5,21�, the second mode has thehighest SPL level of approximately 162 dB and in this case, thefirst three modes are clearly visible. Although the higher tones arenot discernible, it is expected that the observed unsteady flowcharacteristics are sufficient to diagnose any notable effect of thegeometric changes on the flow field. The minor resonance ob-served at 1200 Hz is not predicted by the Rossiter equation �Eq.�1�� and is currently unexplained although it is not observed for areference working section study with no cavity present. The tun-nel background noise signature was measured without the cavitypresent and the SPL spectrum at Mach 0.9 is also shown in Fig. 2.The background SPL across the spectrum is typically approxi-mately 110 dB with two very narrow peaks at about 2600 Hz and5500 Hz. These are not observed in the cavity case and Fig. 2clearly highlights the relative effect of the cavity on the pressuresignature. Similar levels of background noise were also found atMach 0.7 and 0.86.

Effect of Leading Edge Steps. The two leading edge step con-figurations �h /s=0.4 and 0.193�, distinguished by their expected

Fig. 2 SPL spectra for datum rectangular cavity „l /d=5, w /d=1.25… measured on the rear wall at Mach 0.9

shear layer step face reattachment characteristics, produce intrigu-

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ngly different sound pressure level attenuation characteristics.he largest leading edge step �h /s=0.4, h /d=0.3� has a signifi-ant effect on the unsteady aerodynamics with a notable attenua-ion of both the modal peaks and the broadband sound pressureevel. This is most apparent at Mach 0.90 where all three observedones are strongly attenuated by the step �Fig. 3�. Superposition ofhe recorded spectra with those of the datum rectangular cavityllustrates the significant attenuation of sound pressure levels �Fig.�. Indeed, the SPL peak for the second mode is reduced by 20 dBelative to the datum cavity, which, along with a reduction inroadband noise, results in an OASPL reduction of 7.6 dB. This issignificant level of noise attenuation achieved through a minor

eometric modification. There are two pressure sensors on thisace placed on either side of the centerline �z /w= �0.22�—inhese reported cases, there are no significant differences betweenhe pair of pressure sensors. The step also has the effect of de-reasing the frequency, and the fundamental first peak is reducedy approximately 19%. By considering the change in the maxi-um l /d when the step is included, the � term in the Rossiter

quation is increased as well as the characteristic length in thetrouhal number. Relative to the datum cavity, both of these ef-ects reduce the expected fundamental frequency by 19%, whichs in agreement with the measured reduction.

Effect of Step Height. For the smallest step size of h /s0.133 �h /s=0.1�, in which the shear flow may be expected to

eattach on the step face, the attenuation is less prodigious al-hough there is still a 9.2 dB peak reduction in the largest tonePL and a 3.1 dB reduction in the OASPL �Fig. 4�d��. However,

he interaction of this smaller step with the flow field results in aurious SPL signature in which there is an additional SPL peakositioned at 4115 Hz. This does not exactly equate to a Rossiterone and is not observed in the datum cavity �Fig. 4�a�� or back-round noise �Fig. 2�. For this configuration, it is expected that therimary shear flow reattaches to the step face, which is confirmedy oil flow visualization studies. In addition, for a slightly largertep h /s=0.193 �h /d=0.145�, the strongest second mode is al-ost completely attenuated although there are now a series ofinor peaks between 1600 Hz and 2200 Hz. Furthermore, the

hird mode is unaffected, and the additional fourth SPL peak islso observed �Fig. 4�c��. Overall, the OASPL is reduced by.7 dB. The achieved mode peak attenuation mostly increasesith increasing step size although there is a significant improve-ent in performance for the largest step �Table 2�. In addition, the

evel of attenuation varies slightly along the length of the cavitylthough the relative ordinal performance of the steps remainsnchanged �Fig. 5�.

Oil flow visualization studies indicate that the smaller stepsh /d=0.1,0.145� do not significantly alter the flow field in com-

ig. 3 Comparison of sound pressure level spectra obtainedor the datum rectangular cavity and the leading edge steph /s=0.4, h /d=0.3… configuration at Mach

arison with the datum rectangular cavity. The visualizations in-

ournal of Fluids Engineering


dicate that the attenuation achieved by the largest step �h /d=0.30� may be related to a large recirculation bubble, which sitson top of the step. It is postulated that this separation bubbleresults in the outward deflection of the approaching boundarylayer. It is known from previous flow control studies that an out-ward deflection of the shear layer can result in acoustic attenua-tion �22�.

Effect of Mach Number. Although the large leading edge step�h /s=0.4, h /d=0.3�, has a very notable impact on the unsteadyflow characteristics at Mach 0.9, additional results at lower tran-sonic speeds show that this attenuation mechanism is sensitive toMach number. This is a little unexpected considering that the fun-damental flow field associated with a backward facing step in

Fig. 4 Sound pressure level spectra for the datum rectangularcavity „a… and each of the leading edge step configurations „b…–„d… recorded at the cavity rear face for Mach 0.9

Table 2 Sound pressure level attenuation „dB… relative to thedatum cavity at Mach 0.90

Configuration

Mode

1 2 3

Step 1, h /d=0.30 10.5 20.0 15.8Step 2, h /d=0.15 3.1 17.1 2.2Step 3, h /d=0.10 4.8 9.2 0.4

Fig. 5 OASPL attenuation relative to the datum cavity at Mach
0.90 for Steps 1–3
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ransonic flow is primarily Mach number insensitive over theange tested �18,19�. Nevertheless, the effectiveness of the step isurtailed at lower Mach numbers. Overall, the largest step still hasn impact on the SPL signature at the lower transonic Mach num-ers but the peak attenuation is modest and the OASPL is onlyeduced by approximately 1.4 dB at Mach 0.86 �Fig. 6�. However,t Mach 0.70, the OASPL attenuation improves to approximately.6 dB. Furthermore, at Mach 0.86, an additional peak occurs atpproximately 2500 Hz when the step is included along with aeduction in the second tone frequency from approximately00 Hz to 1800 Hz.

onclusionsThe datum rectangular cavity configuration exhibited the ex-

ected flow features with OASPLs of up to 174 dB recorded onhe back wall at Mach 0.9. Results obtained for OASPL distribu-ions along the cavity centerline and SPL spectra are consistentith results obtained in previous research.The most effective geometric cavity modification was found to

e the largest leading edge step �h /d=0.3, h /s=0.4� at Mach 0.9,hich delivered up to a 20 dB attenuation in tone peaks togetherith a reduction in the broadband noise, which delivers anASPL reduction of up to 7.6 dB. Leading edge step configura-

ion performance was, however, found to be Mach number depen-ent with the greatest attenuation observed at Mach 0.9. Oil flowisualizations indicate that the most effective of the leading edgetep configurations �h /d=0.30� may have a large recirculationubble sitting on top of the step face, which results in a beneficial,utward deflection of the separated shear layer.

omenclatured cavity depth, Fig. 1f frequencyh step depth, Fig. 1H boundary layer shape factorK empirical constant, Eq. �1�l cavity length, Fig. 1

ig. 6 Sound pressure level spectra obtained for the datumectangular cavity and leading edge step „h /s=0.4, h /d=0.3…onfigurations at Mach 0.9, 0.86, and 0.7; measurements on theavity rear face

M mach number

64501-4 / Vol. 130, JUNE 2008


m mode numberP0 total pressure

Re�* Reynolds number based on boundary layer

displacement thicknesss step length, Fig. 1

St Strouhal numberU streamwise velocityw cavity width� empirical constant, Eq. �1�

�99 boundary layer thickness where U=0.99Ue�* boudary layer displacement thickness

�*��0��1− ��U /�eUe��dy

boundary layer momentum thickness��0

��U /�eUe��1− ��U /�eUe��dy� ratio of specific heats

Subscripts� freestream conditions

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Mass-Injection,” J. Aircr., 31�1�, pp. 169–174.�4� McGrath, S., and Shaw, L., 1996, “Active Control of Shallow Cavity Acoustic

Resonance,” AIAA Paper No. 96-1949.�5� Cattafesta, L., Williams, D., Rowley, C., and Alvi, F., 2003, “Review of Active

Control of Flow-Induced Cavity Resonance,” AIAA Paper No. 2003-3567.�6� Ukeiley, L., Ponton, M., Seiner, J., and Jansen, B., 2003, “Suppression of

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�10� Smith, B., Welterten, T., Maines, B., Shaw, L., Stanek, M., and Grove, J.,2002, “Weapons Bay Acoustic Suppression From Rod Spoilers,” AIAA PaperNo. 2002-0662.

�11� Rockwell, D., and Naudascher, E., 1978, “Review—Self-Sustaining Oscilla-tions of Flow Past Cavities,” ASME J. Fluids Eng., 100�2�, pp. 152–165.

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�13� Charwat, A., Roos, J., Dewey, C., and Hiltz, J., 1961, “An Investigation ofSeparated Flows—Part II Flow in the Cavity and Heat Transfer,” J. Aerosp.Sci., 28�6�, pp. 457–470.

�14� Rossiter, J., 1964, “Wind-Tunnel Experiments on the Flow Over RectangularCavities at Subsonic and Transonic Speeds,” RAE Technical Report No.64037.

�15� Heller, H., Holmes, D., and Covert, E., 1971, “Flow Induced Pressure Oscil-lations in Shallow Cavities,” J. Sound Vib., 18�4�, pp. 545–553.

�16� Bilanin, A., and Covert, E., 1973, “Estimation of Possible Excitation Frequen-cies for Shallow Rectangular Cavities,” AIAA J., 11�3�, pp. 347–351.

�17� Heller, H., and Bliss, D., 1975, “The Physical Mechanism of Flow-InducedPressure Fluctuations in Cavities and Concepts for Their Suppression,” AIAAPaper No. 75-491.

�18� Plentovich, E., Stallings, R., and Tracy, M., 1993, “Experimental Cavity Pres-sure Measurements at Subsonic and Transonic Speeds,” NASA Technical Pa-per No. 3358.

�19� Zhang, J., Morishita, E., Okunuki, T., and Itoh, H., 2001, “Experimental andComputational Investigation of Supersonic Cavity Flows,” AIAA Paper No.87–0166.

�20� Tracy, M., and Plentovich, E., 1997, “Cavity Unsteady-Pressure Measurementsat Subsonic and Transonic Speeds,” NASA Technical Paper No. 3669.

�21� Komerath, N., Ahuja, K., and Chambers, F., 1987, “Prediction and Measure-ment of Flow Over Cavities—A Survey,” AIAA Paper No. 87-0166.

�22� Ukeiley, L., Ponton, M., Seiner, J., and Jansen, B., 2003, “Suppression ofPressure Loads in Resonating Cavities Through Blowing,” AIAA Paper No.
2002-0661.
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passive control of transonic cavity flow

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