Review of Active Control of Flow-Induced Cavity Resonance

Transcription

1 AIAA Review of Ative Control of Flow-Indued Cavity Resonane Louis Cattafesta, a David Williams, b Clany Rowley, and Farrukh Alvi d a University of Florida, Gainesville, FL b Illinois Institute of Tehnology, Chiago, Ill Prineton University, Prineton, NJ d Florida A & M University and Florida State University, Tallahassee, FL 33 rd AIAA Fluid Dynamis Conferene June 23-26, 2003 Orlando, FL 0 For permission to opy or republish, ontat the Amerian Institute of Aeronautis and Astronautis 1801 Alexander Bell Drive, Suite 500, Reston, Virginia

2 Review of Ative Control of Flow-Indued Cavity Resonane Louis N. Cattafesta III, a David R. Williams, b Clarene W. Rowley, and Farrukh S. Alvi d a Mehanial & Aerospae Engineering, University of Florida, Gainesville, Florida b Fluid Dynamis Researh Center, Illinois Institute of Tehnology, Chiago, IL Mehanial & Aerospae Engineering, Prineton University, Prineton, NJ d Mehanial Engineering, Florida A & M University and Florida State University, Tallahassee, FL Abstrat A review of ative ontrol of flow-indued avity osillations is presented. This paper is motivated by two fators. First, the searh for solutions to the pratial problem of suppressing osillations aused by flow over open avities has generated signifiant interest in this area. Seond, avity osillation ontrol serves as a model problem in the growing multidisiplinary field of flow ontrol. As suh, we attempt to summarize reent ativities in this area, with emphasis on experimental implementation of open- and losed-loop ontrol approahes. In addition to desribing suesses, failures, and outstanding issues relevant to avity osillations, we highlight the harateristis of the various atuators, flow sensing and measurement, and ontrol methodologies employed to date in order to emphasize the hoies, hallenges, and potential of flow ontrol in this and other appliations. These instabilities grow to form large-sale vortial strutures that onvet downstream at a fration of the freestream speed before impinging near the trailing edge. The relevant dimensionless parameters are LD, LW and L θ, as well as the flow parameters prms q, Re θ, M, and shape fator * H = δ θ, where q is the freestream dynami pressure and δ * is the displaement thikness of the upstream boundary layer. Turbulent Boundary Layer δ y x Reeptivity Feedbak L λ Soure Charateristis 1 Introdution The omplex nature of avity resonane is Fig. 1: Shemati illustrating flow-indued avity illustrated in Fig. 1. A boundary layer of thikness resonane for an upstream turbulent boundary layer. δ and momentum thikness θ separates at the Cavity flows have been the subjet of numerous upstream edge of the avity of length L, depth D, studies sine the 1950 s. 1-3 Therefore, we annot and width W. The resulting shear layer develops based upon its initial onditions (imposed by the provide a omprehensive review of the subjet in this short paper. The interested reader is referred to upstream boundary layer and avity aousti field) several exellent reviews In partiular, the reent and the instability harateristis of the mean shearlayer review by Colonius 10 provides a summary of profile. The shear layer spans the length of the avity and ultimately reattahes near the trailing edge of the avity in an open avity flow. The reattahment region ats as the primary aousti soure. Aousti waves travel inside the avity (and numerial simulations and flow physis modeling, permitting us to largely ignore these relevant topis. Grazing flow over avities is pertinent to a wide range of real-world appliations, ranging from landing-gear and weapons bays in airraft to flow in outside for subsoni flow), towards the avity leading gas transport systems 11 and over sunroofs and edge. The inident aousti waves fore the shear windows in automobiles. 12 The flow-aousti layer, setting the initial amplitude and phase of the instability waves through a reeptivity proess. oupling inherent in avity resonane an produe a highly unsteady flowfield haraterized by strong disrete tones and a large bakground or broadband Assoiate Professor, Assoiate Fellow AIAA level. Professor, Assoiate Fellow AIAA In airraft bays, for example, dynami loads in exess of 160 db (re 20 µp a ) are not unommon. Assistant Professor Assoiate Professor, Senior Member AIAA Copyright 2003 by the authors. Published by the Amerian Institute of Aeronautis and Astronautis, In. with permission. Suh high dynami loads an lead to strutural fatigue of the avity and its ontents. In addition, the highly osillatory flowfield generated by avity flows D 1

3 an also adversely affet the safe departure and aurate delivery of munitions stored in the weapons bay. This problem has beome more aute with the reent emphasis on smart weapons that are lighter and more ompat. 13 The goal of this paper is to summarize reent ativities in ative ontrol of flow-indued resonane of open avities, with emphasis on experimental implementation of open- and losed-loop ontrol approahes. In addition to desribing suesses, failures, and outstanding issues relevant to avity osillations, we highlight the harateristis of the various atuators, flow sensing and measurement, and ontrol methodologies employed to date in order to emphasize the hoies, hallenges, and potential of flow ontrol. Due to spae onstraints (and perhaps ignorane), there are undoubtedly omissions. For this, we apologize. The paper is organized as follows. Setion 2 provides a brief overview of passive and open-loop suppression studies. While reent studies are emphasized, some lassial results will be reviewed to plae these new results in proper ontext. Setions 3, 4, and 5 desribe atuators, flow sensors and measurements systems, and losed-loop ontrol suppression and modeling/design approahes, respetively. Setion 6 provides a summary and offers our perspetive on outstanding issues and future diretions. 2 Suppression of Cavity Osillations Flow Control Classifiations Tehniques to suppress avity osillations an be lassified in several ways. In this paper, we hoose the lassifiation shown in Fig. 2 to be onsistent with terminology used in ative noise and vibration ontrol. Ative ontrol provides external energy (e.g., mehanial or eletrial) input to the flow, while passive ontrol tehniques do not. Passive ontrol of avity osillations has been suessfully implemented via geometri modifiations using, for example, rigid fixed fenes, spoilers, ramps, 14,15 and a passive bleed system. 16 Note that some passive flow ontrol devies extrat energy from the flow itself and have been alled ative. Pertinent examples inlude unpowered or passive resonane tubes 13,17 and ylinders or rods plaed in the boundary layer near the leading edge of the avity. 18 These devies, desribed further in Setion 3, are sometimes referred to as ative beause they provide an osillatory input to the flow, but their effet annot be adjusted without either hanging the flow onditions or hanging the devie itself. Passive Control Flow Control Approahes Open-Loop Ative Control Quasi-stati Closed-Loop Fig. 2: Classifiation of flow ontrol. Dynami Ative ontrol is further divided into open- and losed-loop ontrol. As shown in Fig. 3, by its very definition, losed-loop ontrol implies a feedbak loop, in whih some flow quantity is diretly sensed or estimated and fed bak to modify the ontrol signal. 19 Open loop orresponds to the ase when there is no feedbak loop. A further lassifiation of losed-loop avity ontrol is that of quasi-stati vs. dynami feedbak ontrol. The quasi-stati ase orresponds to slow tuning of an open-loop ontrol approah and ours when the time sales of feedbak signal are large ompared to the time sales of the plant (i.e., flow). As disussed in Setion 5, this approah was suessfully used by Shaw and Northraft. 20 The usual dynami ompensation ase orresponds to the situation when these time sales are ommensurate. This an be implemented using an analog (see, for example, Williams et al. 21 ) or real-time digital ontrol systems. 22 In this ontext, real time refers to the situation in whih the ontrol signal is updated at the sampling rate of the data system. Referene Input r + Atuating (Error) Signal e = r b Primary Feedbak Signal Feedforward (Control) Elements g 1 Control Signal or Manipulated Variable Feedbak Elements Fig. 3: Components of a feedbak ontrol system. 19 u FORWARD PATH h FEEDBACK PATH Summary of Suppression Studies Disturbane Plant or Proess g 2 n Controlled Output Passive and Open-Loop Ative Control Table 1 in the Appendix provides a summary of seleted passive and open-loop avity suppression studies. Where possible, the avity dimensions and flow onditions are summarized. The methods and key results are also inluded. The investigations are listed in hronologial order for historial purposes. 2

4 Again, there are numerous other passive studies that have not been inluded beause of spae limitations and beause these are summarized in the other reviews ited earlier. Some key points are disussed here. Sarohia and Massier studied the effiay of steady mass injetion at the base or floor of two different axisymmetri avity models for both laminar and turbulent boundary layers. 23 While base injetion was effetive at suppressing avity tones, large mass flow rates were required - B = 5-15%. The mass flow rate parameter used by the authors is equivalent to that proposed later by Vakili and Gauthier 24 for retangular avities B ρ V A m w w inj = = ρeve Aavity ρeve Aavity. {1} Sarno and Franke studied stati and osillating fenes and also steady and pulsed injetion (at 0º or 45º with respet to the freestream diretion) at transoni speeds near the avity leading edge. 25 Blowing oeffiients B of up to 7% were used. While the stati fenes provided the best suppression, the bandwidth of the mehanial fenes were limited to < 220 Hz, while the pulsed injetion was < 80 Hz. These frequenies were at least an order of magnitude lower than the frequenies of the avity tones and thereby onstituted a quasi-stati or lowfrequeny foring. Nonetheless, they represented an important step in the evolution of ative ontrol of avity osillations. Vakili and Gauthier 24 obtained signifiant attenuation with steady normal mass injetion through variable-density porous plates upstream of the avity leading edge at Mah 1.8 using B ~ 4%. They attributed the attenuation to a thikening of the avity shear layer and a orresponding alteration of its instability harateristis. MGrath and Shaw subsequently studied mehanial osillations of hinged flaps at frequenies up to 35 Hz over a range of subsoni and supersoni Mah numbers. 18 The stati and osillatory defletions were on the order of the boundary layer thikness δ and were shown to be effetive despite their limited bandwidth. MGrath and Shaw were the first to study the effet of a ylinder plaed in the upstream subsoni boundary layer. Beause of the well-known shedding harateristis of a irular ylinder of diameter d, St = fd U 0.2, over a wide Reynolds number range, this devie was alled a high-frequeny tone generator (HFTG). The ylinder was apable of produing substantial redutions of both the avity tones and the broadband level. The authors disussed the potential mehanism of the atuator: the interation of the shed vorties with the shear layer instabilities. As will be disussed further below, however, there are other possible mehanisms, noted by other investigators, that may influene the suppression effetiveness of the ylinder. At the same time, Ahuja and his olleagues were investigating some other novel ontrol strategies. For example, Mendoza and Ahuja studied the effet of a steady wall jet via a Coanda surfae. 26 Although no mass flow measurements were obtained to doument the suppression harateristis, upstream boundary layer profiles showed an inrease in δ with blowing, thereby leading to the hypothesis that the suppression was due to a redued shear layer growth rate. Hsu and Ahuja 27 studied the effet of a trailingedge array of Helmholtz resonators (i.e., ommerial syringes) on avity noise and obtained some suppression at lower Mah numbers. At intermediate Mah numbers, the resonators redued the magnitude of the targeted tone, but new tones appeared at other frequenies a phenomenon that has been observed by many researhers. At high Mah numbers, no suppression was obtained, but the authors believed that the reason was likely due to the diffiulty in setting the small resonator volume aurately. This study is noteworthy for its attempt to ontrol avity osillations in the viinity of the aousti soure origin near the trailing edge impingement reason. In 1997, Cattafesta et al. studied the use of a sixelement piezoeletri flap array flush mounted at the leading edge of the avity. 28 The bandwidth of the atuators was large enough (300 Hz) to provide foring at frequenies omparable to that of the avity tones. Open-loop sinusoidal foring at a suffiient amplitude and appropriate detuned frequeny was apable of suppressing the avity tone. Shear layer veloity measurements indiated that the atuators seeded the shear layer with a disturbane that was large enough to prevent the growth of the natural avity disturbanes. In 1998, Shaw ontinued his study of leading edge HFTGs, low frequeny pulsed fluidi injetion, and osillating flaps. 29 While various diameter HFTGs mounted at a fixed height were shown to be effetive, the suppression improved as the diameter was inreased. However, the relative height of the ylinder in the boundary layer was not reported. Shaw also disusses two potential mehanisms of the HFTG: (1) high frequeny foring due to shedding, (2) redued shear layer growth rates due to boundary layer thikening. We have found that his pulsed blowing results were onsistent with prior results that B of a few perent were required to suppress the tones. However, no spetra were reported to assess the 3

5 impat of blowing on the broadband. Interestingly, the tone amplitude ontinued to derease as the pulse frequeny of the injetor reahed its upper limit of 100 Hz. Furthermore, normal injetion was shown to be superior to tangential blowing. The osillatory flap in Shaw s experiment, varied from Hz, provided maximum suppression at 5 Hz and a monotoni improvement as the dynami defletion angle inreased to its upper limit, orresponding to a defletion of order δ. However, the inrease in δ for a full-sale airraft led Shaw to onlude that this approah (low frequeny, large amplitude, open-loop foring) was not feasible for a full-sale airraft. In 1999, three new approahes were reported. Fabris and Williams used unsteady bleed foring to produe a broadband atuator apable of produing a omplex input disturbane omprised of multiple frequeny omponents. 30 They demonstrated that the shear layer was most reeptive to horizontal foring via shear layer veloity measurements. Lamp and Chokani 31 used a rotary valve atuator to provide steady and/or osillatory blowing upstream of the avity leading edge at a partiular pulsing frequeny. Their atuator onfiguration emphasized three-dimensional effets and showed that osillatory blowing an redue tone amplitudes provided the foring frequeny is not a harmoni of the avity resonane. Raman et al. used novel miniature fluidi osillators to suppress avity osillations. 32 These devies were apable of produing up to 3 khz osillations with mass flow rates of less than 0.12% of the main jet flow and produed signifiant tonal redutions. However, the mass flow rate and frequeny of osillations are oupled (in a preditable fashion). Stanek reported on a series of larger-sale experiments in the UK over the past few years. 13,33,34 In the first experiment, 13 they investigated powered resonane tubes, protruding piezoerami driven wedges, a ylindrial rod, and passive resonane tubes vs. a onventional spoiler. An interesting result was that the powered resonane tubes (see ref. 17 and Setion 3) demonstrated signifiant tonal and broadband redution when B ~ 1.6%. The suess was termed a suessful demonstration of high frequeny foring (at a frequeny that is very large ompared to that of the avity tones). The authors hypothesized that the mehanism was an aelerated energy asade from the largest to the smallest turbulent sales. 35 A follow-on study 33 investigated powered and unpowered resonane tubes (in whih the resonator tubes were bloked to prevent high frequeny exitation), and mirojets vs. various other devies. While the powered resonane tubes were redesigned to redue their mass flow requirements, optimal suppression still required B ~ 0.6%. The unpowered resonane tubes onsistently provided the best suppression, indiating that the primary suppression mehanism of these devies may not be high frequeny foring but the steady blowing omponent. The results also introdued mirojet blowing and showed that vertial blowing is required for these devies to be suessful in this appliation. Furthermore, Stanek et al. 33 offered a new model for high frequeny foring. Simply stated, high frequeny foring alters the mean flow and, hene, its instability harateristis suh that the growth of large sale disturbanes is inhibited or prevented. This argument, while plausible, requires onfirmation in the form of experiments and validated simulations to determine the mean veloity profile and subsequent shear layer growth harateristis for various high frequeny devies. Most reently, Stanek et al. investigated various aspets of the ylindrial rod in rossflow. 34 They studied the vertial position of the rod H δ in the boundary layer, its relative size d δ, installation issues, and end onditions. They reommended an optimal loation as entered at the edge of the boundary layer and an optimal size of d δ = 23. They argued that their results onlusively demonstrate that the suppression is due to high frequeny rod shedding. Again, while the ylinder learly affets the mean flow and its stability harateristis, there are other important fators that annot be ignored, inluding experimental evidene presented by Ukeiley et al. 36 and the numerial simulations of Arunajatesan et al. 37 that the ylinder lifts the shear layer and auses the impingement region to be altered. If the shear layer impingement loation is altered, then the soure strength is presumably affeted. One other mehanism, not yet disussed in the literature, is the possibility of rod or wire resonane. A ylinder in rossflow an vary in omplexity from a resonating string in tension 38 to a pinned or lamped rod in tension or ompression (that an sustain bending) depending on its diameter, length, material and boundary ondition. 39 Sample alulations reveal fundamental resonane frequenies that an vary from several hundred Hz to several khz, depending on the mounting onfiguration. If the wire/rod resonates due to the broadband exitation of the turbulent boundary layer or flutuating pressure field, fluid/struture interation effets, whih have been ignored to date, may be signifiant. 4

6 There are a few other reent studies involving steady and/or pulsed blowing that have provided physial insight or have shown promising results. Bueno et al. 40 used an array of six fast-response (~3 ms) miniature jets mounted upstream of the leading edge to study the effets of normal injetion on a Mah 2 avity flow. They used instantaneous and ensemble-averaged pressure time histories and ross orrelations to study the effets of single short and long ylial pulses (50% duty yle), the latter with relatively low foring frequenies ompared to that of the tones (50 or 80 Hz). They ompared their pulsed results to steady blowing with B = 0.28%, 0.24%, 0.18%, and 0.16% at LD =5, 6, 8, and 9, respetively, and onluded that ontinuous mass injetion is more effetive for suppression than pulsed blowing. Ukeiley et al. 41 used an array of eight powered whistles mounted in the forward avity wall. These devies essentially produe a high frequeny tone superimposed on a steady jet. The jet is direted in the downstream diretion but has a slight vertial veloity omponent. The authors studied the novel use of different injetion gases (heated air, nitrogen, and helium) with and without the high frequeny whistle omponent. Their best results were obtained using steady helium blowing (no high frequeny omponent) with very low B = 0.09%. The suppression mehanism requires further study, but sample PIV images and ross orrelations of pressure time histories suggest that the injetion alters the impingement region and disrupts the aousti feedbak loop. Their results also highlight the need to rigorously study isolated high frequeny foring effets. Most reently, Zhuang et al. 42 investigated the use of a vertially direted mirojet array mounted upstream of the avity leading edge. The mirojets had a 400 µm diameter and produed soni jets that interat with the upstream boundary layer. The authors show how, at Mah 2, an oblique shok is formed that deflets the shear layer and alters its trajetory and the resulting impingement region. Signifiant tonal and broadband suppression levels were ahieved with B = 0.14%. Higher levels of B produed no additional improvement. Colletively, the blowing results desribed above indiate that manually optimized steady blowing onfigurations with B 0.1% an be effetive suppression devies. At subsoni speeds the primary mehanisms appear to be an alteration of the shear layer stability harateristis and the shear layer impingement loation. While stability harateristis are also important at supersoni speeds, shok wave/boundary layer interations at the upstream avity edge and the ensuing shear layer trajetory alteration appear to be dominant fators. It is interesting that when all of the available blowing data is expressed using the blowing oeffiient definition of Vakili and Gauthier, 24 one finds that the evolution of steady blowing tehniques has redued effetive (not neessarily optimal) B from O(10%) by two orders of magnitude down to O(0.1%). Note that the definition of B aounts for the avity area but does not diretly inorporate the saling effets of the boundary layer thikness. This has important impliations for full-sale appliations and is addressed further in Setion 3. In omparison, low frequeny foring does not appear to be very attrative when the atuator bandwidth is insuffiient in omparison to the frequenies of the avity tones. This is disussed further in Setions 3 and 5. High frequeny exitation, whether it is passive or ative, appears promising for both tonal and broadband suppression. However, the responsible mehanisms require further study. There is ample evidene that high frequeny foring alters the mean flow. As a result, the shear layer stability harateristis are altered and, in some ases, the trajetory of the shear layer is modified. When the impingement loation is altered, the strength of the aousti soure is redued and the broadband noise level dereases. We will show in Setion 5 that, to date, losed-loop ontrol produes omparatively little hange in the mean flow properties and, as suh, has only been shown to be effetive for tonal ontrol. 3 Atuators In general atuators for avity tone ontrol are devies that at to disrupt the aousti resonane mehanism. Atuators may be a omponent of a losed-loop ontrol system or at independently in an open-loop or passive mode. One is normally interested in attenuating the narrow band Rossiter modes, but in some ases the broadband noise level is redued as well. 18 Examples of atuators, their strengths and weaknesses, and the issues assoiated with their appliation will be disussed in this setion. Passive Atuators Passive atuators attenuate tones by hanging the harateristis of the shear flow over the avity. Passive atuators require the fewest moving parts and tend to be the least expensive and least ompliated devies. However, they often do not work well at off-design onditions. 43 Passive atuators disrupt the resonane through one of at least three mehanisms: 5

7 1) the trajetory of the mean shear layer is hanged suh that the reattahment point is shifted downstream of the avity edge, 36,37,40 2) the stability harateristis are modified by the hange in the shear layer (veloity profiles or gas properties), 10,41 so that the resonant modes are not amplified, and 3) the spanwise oherene of the shear layer and orresponding Rossiter mode is disrupted. 37 Examples of passive atuators inlude leading edge ramps, 25 spoilers, 44 fenes, 36 steady gas injetion, 24 or ontouring of the trailing edge of the avity. 14 Spoilers and fenes are ommonly installed on prodution airraft to redue the resonant tones in weapons bays and deploy when the bay doors open. The fenes at to inrease the shear layer thikness, whih shifts the most unstable shear layer frequenies to lower values. Spoilers and ramps deflet the mean separation streamline higher into the flow so that reattahment ours downstream of the avity edge. This weakens the feedbak aousti wave and the resulting strength of the Rossiter mode. Similarly rods plaed in the upstream boundary layer will produe a mean wake (momentum defiit) that modifies the mean shear layer development. 34,36,37 Ukeiley et al. 36 studied both rods and variable height fenes, and found the effet of the devie on the mean gradient of the shear layer to be important in determining the level of attenuation. Ative Open-Loop Atuators Atuators that add energy to the flow are defined as ative ontrol devies. The term open loop emphasizes that a feedbak signal is not used to ontrol the atuator output. Examples inlude osillating eletromehanial 25,44,45 and piezoeletri flaps, 28,46,47,48 steady blowing, 25,40,49,50 and pulsed blowing, 20,29,51 voie-oil drivers, 52,53 powered resonane tubes, 13,17,54,55 and fluidi osillating jets. 32 All of these open-loop atuators have demonstrated ontrol of avity resonane at subsoni flow onditions, but only the powered resonane tube and the steady and pulsed jets have been suessful at supersoni freestream onditions. It is important to reognize that a mean omponent of foring is assoiated with most unsteady atuators. Even in the ase of atuators that have no net mass addition, suh as voie oils, and syntheti jets, there will be a net momentum flux assoiated with the seond-order streaming effet. 56 Streaming is the steady, seondary flow omponent resulting from the quadrati nonlinear interation of the unsteady flow omponents. Whether this effet is signifiant or not depends on the amplitude of the osillations. Atuators with a nonzero mass addition suh as pulsed jets, siren valves, powered resonane tubes, fluidis, and whistles will have first-order mean flow omponents with disturbane magnitudes that are omparable to or exeed the amplitude of the unsteady omponent. It is often a hallenge to the atuator designer to maintain, for example, veloity flutuation amplitudes at the same order of magnitude as the mean flow as the frequeny inreases. Beause these devies have a strong mean omponent, it is often diffiult to separate whih effet is responsible for the flow ontrol. As suggested by Stanek et al., 13 atuators an be further ategorized into low-frequeny exitation and high-frequeny exitation ( hifex ). Hifex orresponds to foring an order of magnitude larger than the frequenies of the resonant tones, while lowfrequeny exitation orresponds to frequenies that are the same order of magnitude or less. Sarno and Franke 25 proposed the onept of foring the shear layer at a frequeny different from the Rossiter mode as a way to suppress resonane. Beause their atuators were limited to frequenies an order of magnitude lower than the first Rossiter mode, the results did not provide onvining evidene that the low-frequeny foring approah ould be effetive. By using a piezoeletri flap, Cattafesta et al. 28 were the first to learly demonstrate that foring the shear layer to osillate at a frequeny different from the Rossiter modes would result in noise attenuation. Provided the exitation frequeny was not in a narrow band near a Rossiter mode, the piezoeletri flaps were able to attenuate the mode by exiting shear layer instabilities inommensurate with the Rossiter resonane mehanism. The effetiveness of this approah at higher Mah numbers remains an open question. Wider bandwidth open-loop atuators (voie-oil type) are being used by Debiasi and Samimy to further explore the low frequeny onept. 57 Atuation at frequenies an order-of-magnitude larger than the Rossiter modes an also lead to suppression of the avity tones via hifex. In partiular, the tehnique pioneered by MGrath and Shaw 18 and revisited by others has suppressed tones at supersoni flow onditions. One hifex hypothesis 13 argues that energy addition to the shear layer at length sales muh smaller than the oherent shear layer vorties will diretly inrease dissipation and aelerates the turbulent energy asade. An alternate hypothesis proposed by Stanek et al. 33 argues that hifex results in a deeleration of the turbulent energy asade. Note that hifex an be ahieved via ative ontrol (with powered whistles 41,58 and powered resonant tubes) or passive ontrol with rods mounted in the upstream boundary layer (due to passive high frequeny vortex shedding). A typial hifex 6

8 experiment will produe disturbanes in the range of 5 khz or higher in order to suppress tones in the 500 Hz range or lower. The physis of the hifex effet are diffiult to sort out beause all hifex atuators realized to date also have a substantial effet on the mean flow that an influene the shear layer development and the aousti soure. This effet using rods in rossflow has been demonstrated by Ukeiley et al. 36 and Arunajatesan et al. 37 Note that Rizzetta and Visbal 59 have shown, via large eddy simulations in a Mah 1.19 avity, that pure highfrequeny foring an suppress avity osillations. But suh a devie has yet to be realized. Irrespetive of the type used, ative open-loop atuators are attrative beause of their relative simpliity and ability to be ativated when needed. However, Shaw & Northraft 20 demonstrated the sensitivity of the ontrol effet to foring frequeny and hanging flow onditions. Open-loop atuators, like passive atuators, must be optimized for eah flow ondition. Furthermore, Cattafesta et al. 28 demonstrated with piezoeletri atuators that an order-of-magnitude higher power is required to drive the atuators ompared to losed-loop systems. Similar power penalties with other open-loop atuators are expeted. Ative Closed-Loop Atuators Atuators for losed-loop ontrol form part of a system that inludes at least one flow state sensor and a feedbak ontrol algorithm. This approah is the most expensive in terms of hardware and omplexity, but it offers the greatest adaptability to hanging flow onditions and potentially the lowest power onsumption. A summary of some atuators used in losed-loop avity ontrol experiments are listed in Table 2. Closed-loop atuators for ative ontrol of avity osillations also fall into two types. What we all a Type A atuator is a devie with suffiient bandwidth that is apable of produing, at any instant in time, a ontrol input onsisting of several frequenies, eah with their own amplitude and phase. This type of atuator has a time response ommensurate with the time sales of the avity flow dynamis so that it an be used in a dynami feedbak ompensation sheme. A Type B atuator is also a broadband devie but produes a ontrol signal of presribed amplitude and primarily one frequeny (and perhaps its harmonis) at any instant in time. The atuator frequeny an hange on a time sale that is large ompared to the time sales of the avity flow dynamis. Shaw and Northraft suessfully used this approah with a rotary valve, pulsed blowing atuator. 20 At any instant in time, the rotor spins at a partiular rotation rate (rpm) and the supply pressure has a ertain value. These an both be hanged via, for example, ontrol voltage to a d motor and servo valve, but the slow time response of this atuator preludes a rapid hange in the atuator output. The majority of losed-loop flow ontrol experiments summarized in Table 2 use Type A atuators. 28,53,60-65 Note that the bandwidth of the atuator must be large enough in order to suppress more than one Rossiter mode. The bandwidth of the atuator plays a ruial role through the area rule in determining the losed-loop system response. More details will be given in Setion 5, but an atuator with too narrow a bandwidth will leak energy into undesirable neighboring modes. 63 For this reason, it is important to know the atuator transfer funtion when designing a losed loop ontrol algorithm. Tehniques to aomplish this for piezoeletri flaps and syntheti jets are desribed, for example, in Ref. 46 and 66, respetively. Initially the losed-loop atuator must have enough power to produe a disturbane that exeeds the reeptivity-indued perturbation at the upstream end of the avity. After the system responds to the atuation, the atuator power requirements derease with the dereasing tone amplitudes. Cattafesta et al. 28 demonstrated the initial high amplitude piezoeletri atuator output redued by an order-ofmagnitude after ontrol was established. To date there has not been a demonstration of losed-loop ontrol (Type A) at supersoni speeds. Shaw and Northraft 20 demonstrated both open-loop and Type B losed-loop ontrol were apable of ontrolling the tones and reduing the broadband noise levels with pulsed-fluidi injetion at supersoni speeds. The hallenge assoiated with losed-loop ontrol is to ahieve similar noise redutions with an order of magnitude less input power by using Type A losed-loop ontrol. Atuators with large amplitudes, high bandwidth, and fast time response are required, whih raises the issue of atuator saling. Shaw 67 studied the mean mass flow rate requirements for a pulsed injetion system direted perpendiular to the freestream and determined that the steady momentum oeffiient C = mu q W saled two sets of data at Mah ( ) µ jet δ 0.95 with frequenies ranging from 100 Hz to 600 Hz and widely varying δ and q. Note that the area in the denominator of the saling parameter is the width of the avity multiplied by the boundary layer thikness at the leading edge of the avity. This saling parameter was used suessfully for weapons bay avity flow ontrol in the flight test of an F

9 For the purposes of Type A flow ontrol atuation with piezoeletri flaps or with zero-net-mass atuators like the syntheti jet, the momentum oeffiient will need to inlude the flutuating omponent of veloity. Experiments at IIT with pulsed-blowing jets for separation ontrol on airfoils have shown that an osillatory momentum oeffiient is the orret saling parameter, and we expet a 2 = ρ u A q Wδ, to similar parameter, ( ) µ jet rms jet = 2 apply to the avity as well. Sine q 0.5γ p M, the dynami pressure will inrease by a fator of nine as the Mah number goes from 0.5 to 1.5. This implies that the atuator rms veloity flutuation level will need to inrease by a fator of 3 to be effetive at supersoni onditions. Finally, we note the reported disrepany for the optimal injetion angle. As summarized in Table 1, Shaw 29 has found vertial injetion is superior for pulsed blowing at low frequenies, while Williams et al. 21 and Kegerise et al. 65 find horizontal injetion is superior for Type A syntheti jet atuators. Stanek et al. 33 have found that steady mirojets have only been effetive in vertial injetion onfigurations. The reason for this observed disrepany is unlear. 4 Sensors and Flow Measurements Sine the aim of most avity ontrol experiments is to redue the pressure flutuations, unsteady pressure sensors are ommonly used in laboratory ontrol appliations. Lou et al. 69 used mirophones to measure (and ontrol) the flow indued pressure osillations in an impinging jet. By far the most ommon sensors used to examine these flows are miniature, high frequeny response transduers, suh as those made by Kulite, Endevo, PCB, and mirophones, suh as from Brüel & Kjær. These transduers are usually flush-mounted on one of the avity surfaes, generally the floor and/or the leading and trailing surfaes. Alternatively, they are plaed in the flowfield or tunnel walls near the avity to measure the aousti field. The small size, linearity (output voltage linearly proportional to input pressure), their flat-frequeny response over a large frequeny range, and their high dynami range (ratio of maximum-to-minimum detetable pressure) make them an exellent tool for haraterizing the avity dynamis. Suh transduers have been used to examine subsoni, 70 supersoni, 42 and hypersoni 71 avity flows. They have been used in small sale, laboratory failities and in larger ommerial testing failities. 33,69 In order to better understand the global flow behavior, one must look beyond the surfae pressure or aousti field. The dynamis of avity flows have been examined using a number of other diagnosti tools. For example, relatively low Mah number avity flows have also been examined using onstanttemperature hot wire anemometry. Shear layer profiles (mean and flutuating) and, in some ases, instability growth rates have been obtained. Examples an be found in Mendoza and Ahuja, 26 Hsu and Ahuja, 27 Cattafesta et al., 28 Garg and Cattafesta, 72 Kegerise, 73 and Williams et al. at IIT. 21,30,62,70,74 Hot wire anemometry beomes inreasingly problemati in high speed flows due to wire breakage and ompressibility effets. 75 Consequently other tehniques have been used. Vakili et al. 76 used a multi-hole probe to obtain upstream boundary layer profiles as a funtion of mass injetion. Kegerise et al. 73,77 and Garg and Cattafesta 72 haraterized the spatio-temporal behavior of high-speed, subsoni, avity flows using a ombination of flutuating pressure measurements and phase-onditioned measurements of the density field inside the avity using a non-intrusive shlieren instrument. The quantitative shlieren tehnique (and hot wires) were used to study nonlinear mode interations and mode swithing. 78,21 Zhuang et al. 42 also used a ombination of shlieren and shadowgraph methods along with unsteady surfae pressure measurements to study supersoni avity flows. Suh data provide invaluable information regarding the spatio-temporal nature of the events that dominate the avity dynamis and an provide insight of nonlinear interations and model swithing. Similarly, Forestier et al. 79 have studied transoni (Mah 0.8) flow over deep avities ( LD ~ 0.4) using high-speed shlieren photography to visually examine the periodi omponent of the avity shear layer osillations. In addition, they obtained phaseloked laser Doppler veloimetry measurements to examine the evolution of periodi and spatially oherent strutures (or vorties) extrated from the veloity-field data. Murray and Elliott 80 have used shlieren photography and planar laser imaging of supersoni avity flows (1.8 to 3.5) to study the harateristis of avity shear layer strutures. Some investigators have used partile image veloimetry with varying degrees of suess to study high speed avity flows. 41,42,81 Most of the diffiulties are assoiated with proper seeding of the avity flow. Zhuang et al. 42 have obtained veloity and vortiity-fields in a supersoni flow and have examined the effets of mirojet ontrol. With regards to safe separation of stores from military airraft, 82 one wishes to predit the trajetory, based on a simple measurement, suh as the flutuating pressures inside the avity. To aomplish this, orrelations between the measurements made inside the avity to store separation harateristis are required. Suh a database an be reated through aptive trajetory 8

10 tests where fores and moments on the store are measured simultaneously with the unsteady pressures inside the avity. Another approah is the use of sensors, suh as aelerometers, gyros, and inlinometers, whih measure the pertinent store trajetory parameters. Stores embedded with suh sensors ombined with telemetry data systems an then be used to obtain orrelate simultaneous store trajetory and the pressure signals. 5 Closed-Loop Control Methodologies The studies desribed in Setion 2 suppressed avity noise using open-loop tehniques. Here, we disuss several studies using losed-loop ontrol, whih inorporates some type of feedbak from a sensor plaed in the flow. One way to use this feedbak is to tune an inherently open-loop approah, for instane by slowly modulating the frequeny of open-loop foring to ahieve the best suppression. A different way uses dynami feedbak at the timesale of the unsteadiness, and an have even more benefiial effets, as very low-power ontrol is possible. Open-loop ontrol annot alter the dynamis of a system (e.g., stabilize an instability) exept by exiting nonlinearities (e.g., by modifying the mean flow). This implies a large power requirement, either as power expliitly supplied to an atuator, or as a drag penalty. By ontrast, losed-loop ontrol an linearly stabilize a system (i.e., with infinitesimal atuation), and furthermore it an redue the amplifiation of external disturbanes, suh as boundary layer turbulene or external aousti waves. In addition, adaptive tehniques may be used to tune the ontroller s behavior in real time. Quasi-Stati Controllers The first losed-loop strategies were modifiations of open-loop strategies. We ategorize these strategies as quasi-stati, beause in these approahes, the time sales by whih feedbak ats are muh slower than the time sales of the flow. In perhaps the first known losed-loop avity ontrol experiments, Gharib 83 used periodially-fored strip heaters to exite Tollmien-Shlihting waves in the boundary layer upstream of a avity. By feeding bak a veloity measurement from a downstream loation in the avity, and phase-loking the sinusoidal foring to this measurement, they obtained a 40% redution in veloity flutuations. Shaw and Northraft 20 also used feedbak to modulate a sinusoidal foring funtion. They measured the sound pressure level (SPL) in a bandpass-filtered pressure signal and then used an iterative searh algorithm to adjust the frequeny and amplitude of a pulsed jet atuator and ahieved a signifiant suppression of the tones, along with some suppression of broadband noise. Debiasi and Samimy 57 are also pursuing an adaptive learning approah, in whih open-loop foring is applied at a partiular frequeny, and this frequeny is automatially adjusted by a learning algorithm to obtain the best suppression. Dynami Controllers As desribed in Setion 2, the lass of losed-loop ontrol we all dynami ontrollers use feedbak at the timesale of the unsteady motion of the fluid. This is type of ontrol is most amenable to tehniques from lassial and modern ontrol theory, and has some distint advantages over modulated open-loop tehniques, as disussed at the beginning of this setion. Nearly all of the dynami losed-loop avity ontrol studies to date have used linear ontrol tehniques. While this might seem restritive, it is atually reasonable to expet that linear ontrollers would perform well. The reasons for this are twofold. First, reent experiments have indiated that in some regimes, purely linear mehanisms an desribe even finite-amplitude osillations of the avity. 63 Seond, even in regimes in whih nonlinearities play a role in the naturally osillating avity, one hopes that in the ontrolled avity, osillations will be small, and thus linear models will remain valid. Models Most linear ontrol approahes rely on an aurate model of the system to be ontrolled. In this setting, the avity flow is viewed as an input-output system, where the input is, for instane, the voltage signal supplied to the atuator, and the output is a sensor measurement. There may be multiple sensors, or even multiple atuators, in whih ase the input and/or output are vetors. Many different modeling tehniques have been used in reent years, either based on flow physis or empirially identified diretly from an experiment, and we desribe some of these tehniques below. System Identifiation Several studies have determined a model for the avity flow empirially, using some form of frequeny response experiment. The general approah is to fore the atuator at a range of frequenies, measure the response from the sensor, and then either determine an empirial transfer funtion from spetra, or use an adaptive algorithm to tune oeffiients in a filter suh that the output from the filter mathes the data as losely as possible. In the first ase, the model takes the form of frequenyresponse data, whih may be expressed as a urve on a Bode or Nyquist plot. In the seond ase, the model takes the form of a rational transfer funtion, 9

11 either disrete-time or ontinuous-time, whose oeffiients are known. Many tools for ontrol design (e.g., LQR/LQG, to be disussed later) depend on suh a model, but for lassial tehniques suh as loopshaping, a urve on a Bode plot is suffiient. The first approah was used by Mongeau et al., 60,61 in whih they determined open-loop transfer funtions for low-speed flow past a Helmholtz resonator at several different flow veloities. A similar approah was used by Rowley et al., 53 who obtained an empirial transfer funtion for a ompressible avity flow. An important differene in this work was that a manually-tuned ontroller was used to stabilize the osillations prior to performing the frequeny response experiment. The frequenyresponse experiment was performed on the stabilized system, and then the effet of the known ontroller was inverted out. The reason for this is that a frequeny response experiment makes sense only for stable linear systems. If the system is unstable, with the amplitude of osillation limited by nonlinearities, then it is not lear how to interpret the results of the frequeny response experiment. Several system-identifiation tehniques have been used to determine models in the form of rational transfer funtions, or state-spae representations. Most of these involved frequeny response experiments on the unontrolled avity, and as mentioned above, if the linearized system is indeed unstable, and the osillations are self-sustained then the meaning of suh experiments is not lear. Kestens and Nioud 84 used a filtered-x least mean square (LMS) algorithm to determine a model for a 2D Navier-Stokes simulation of a fored avity flow. The model was determined with no flow, so effets suh as shear-layer onvetion and amplifiation would not be aptured by suh a system identifiation. Cattafesta et al. 28 performed a frequeny-response experiment on the osillating avity, using a leastsquares method to identify the parameters in a disrete-time transfer funtion, and then an eigensystem realization algorithm to onvert this to state-spae form. Cabell et al. 64 used a similar approah and obtained models of very high order ( states). In these experiments, low oherene was observed between input and measured signals in the system identifiation experiment, so long time reords (10 seonds) were olleted. Controllers designed from these models yielded reasonably good suppression, and models predited general trends observed in the experiments. Cattafesta et al. 22 also used an adaptive algorithm whih ould be used either offline, or with a feedbak ontroller in plae, in whih ase it also served as an adaptive ontroller, tuning ontroller oeffiients to minimize the output. Suh losed-loop system identifiation avoids the problem of doing a frequeny response experiment on an unstable system, mentioned earlier. Kegerise et al. 65 and Pillarisetti and Cattafesta 85 have used various adaptive algorithms to tune oeffiients in linear and nonlinear disrete-time models for the avity. Kegerise et al. ompared finite impulse-response (FIR) and infinite impulse response (IIR) filters and found that IIR filters were neessary to apture the dynamis well, as one expets sine FIR filters annot represent resonanes or instabilities. Physis-Based Models The system identifiation proedures desribed above treat the avity as a blak box, and models are obtained by observing the response to foring. In this setion, we review models based solely on the physis of the flow. Of ourse, the models in the previous setion will also ontain flow physis, but the models in this setion are obtained exlusively by studying the flow physis. The advantage of this approah is that it an give insight into the mehanisms of avity osillations that might not be apparent otherwise. In addition, one may obtain saling laws whih determine how the models vary as a parameter suh as Mah number or avity length is varied. POD/Galerkin Models. The governing equations for fluids are the Navier-Stokes equations, so in a sense a very aurate model of avity flows is already known. However, tools for ontrol analysis and design do not apply to nonlinear partial differential equations. So in order to use these tehniques, it is desirable to approximate the Navier- Stokes equations by a finite-dimensional system. An inreasingly popular method for obtaining suh lowdimensional models is the method of Proper Orthogonal Deomposition (POD) and Galerkin projetion. In this method, data from simulations or experiments is used to determine a finite-dimensional subspae whih ontains the most important features of the flow (based on energy). The Navier- Stokes equations are then projeted onto this subspae to obtain a low-dimensional model. For a thorough review of this method, see Holmes et al. 86 POD/Galerkin models for 2D flow past a avity were omputed by Rowley, 87,88 and POD modes were also omputed by Ukeiley. 89 The standard method for inompressible flows was modified for ompressible flows, in whih the thermodynami variables beome important. It was found that vetor-valued POD modes worked better than salarvalued POD modes, but to use vetor-valued modes, one must hoose an inner produt that appropriately weights the thermodynami (e.g. density) and 10

12 kinemati variables (e.g. veloity). See Rowley 90 for a thorough desription of the method for ompressible flows. While these models apture the open-loop dynamis well, inluding all nonlinearities, it is diffiult to inlude the effets of atuation, and we are not aware of any studies whih have inluded atuation in POD models of the avity flow. Rossiter-Type Models. In ontrast to POD models, in whih the full Navier-Stokes equations are simplified, another approah is to model different omponents of the Rossiter mehanism, and onnet these together, building more omplex models from simple models of the individual omponents. Cain et al. 91 used a nonlinear model for shear layer amplifiation, oupled with models for aousti sattering and reeptivity, to predit amplitudes of avity osillations. Their proedure was iterative, and provided an estimate for steady-state amplitude, but was not time-aurate. Nonetheless, it represented a signifiant improvement over the Rossiter model 3 and the improved Tam and Blok model 92. Rowley et al. 53 used purely linear models for the various omponents, inluding shear-layer amplifiation, and obtained time-aurate models in the form of transfer funtions. The model suggested an alternative mehanism for avity osillations: while the onventional view is that the osillations are self-sustained, an alternative view is that the avity ould at as a lightly damped osillator that amplifies noise at resonant frequenies. In this ase, the osillations are not self-sustaining. The linear models obtained in this paper explained some peaksplitting effets observed in experiments, and implied some fundamental performane limits, disussed later. Clearly, the models desribed above provide physial insight but are not suffiiently aurate to design a ontrol system. Reently, Kershen and Tumin 93 desribed a theoretial model of avity resonane that shows great promise for physis-based avity ontrol design. The model ombines a propagation model based on a finite-thikness shear layer with sattering models for the leading and trailing edge regions of the avity using an exat Wiener-Hopf tehnique. The model predits the avity resonane frequenies without any empirial onstants and also provides the temporal growth rate of eah mode. Control Algorithms Here, we fous on dynami ontrol algorithms, in whih the feedbak is at the timesale of the unsteadiness. The simplest ontrol strategies do not require a model, and the parameters of the ontroller are tuned manually. Williams et al. 21 used suh a strategy, in whih a pressure signal was bandpass filtered about the frequeny of a avity tone, and a phase shifter was manually tuned until the osillations were suppressed. Several bandpass filters were used in parallel to ahieve suppression of multiple modes, and a similar approah was used by Kegerise et al. 65 to suppress multiple modes. While manual tuning an work reasonably well, often new tones are produed; furthermore, tuning the parameters is usually diffiult, espeially when multiple modes were present. More preditable design methodologies are available if one has a model of the system. For instane, Mongeau et al. 60,61 used a lassial loopshaping tehnique to design a ontrol law for the flow past a Helmholtz resonator. Given a plant model P s, then with a ontroller given by gain L( s) P( s) C( s) ( ) C( s ), one may design the loop = suh that the losed-loop system has some desired properties (suh as good disturbane rejetion over a ertain frequeny range). One then determines C( s ) by inverting the plant: C( s) = L( s) P( s). If the plant model has righthalf-plane zeros or poles, then in order to avoid righthalf plane (RHP) pole-zero anellation, one must plae ertain restritions on L s, whih an be ( ) umbersome (see Doyle, Franis, and Tannenbaum 94 for more details). Modern ontrol tools provide systemati ways of designing ontrollers, given an adequate model. 95 Cattafesta et al. 28 used two suh methods, poleplaement and LQG, to suppress the osillations with an order of magnitude less input power than openloop tehniques. Cabell et al. 64 also used an LQG regulator, with a frequeny-dependent weighting on the ontrol effort. For both pole-plaement and LQG, one begins with a model of the system in statespae form where u k x = k 1 Ax + + k Buk y = Cx + Du, k k k {2} is the input (atuator voltage) at time t = k t, and is the orresponding output (sensor k y k measurement). Here x k is the state vetor, and A, BC,, and D are matries of appropriate dimension. If one hooses a feedbak law uk = Kx k, {3} where K is a matrix of gains, then the losed-loop system beomes 11