Controlled Manipulation of Small- and Large- Scales in a Turbulent Shear Layer, Part I: Experimental Studies

Transcription

1 AIAA Controlle Mnipultion of Smll- n Lrge- Sles in Turulent Sher Lyer, Prt I: Experimentl Stuies Bojn Vuksinovi *, Dvison G. Lus, n Ari Glezer Wooruff Shool of Mehnil Engineering, Georgi Institute of Tehnology, Atlnt, GA The effets of fluii tution of smll- n lrge-sle strutures in single strem, plne sher lyer re investigte experimentlly. While smll-sle motions re effete y iret, high-frequeny tution (ompre to the nturl frequeny of the seline flow), lrge-sle oherent motions (t sles omprle to the ross strem with of the lyer) re inue iniretly y trnsients ssoite with onset n termintion of the tution. High-resolution PIV n hot wire mesurements show tht lrge vortil strutures re forme y rollup tht follows the trnsient isruption of vortiity flux in the upstrem ounry lyer. The high-frequeny tution ouples to the sher lyer vi the formtion of trin of vorties t the tution frequeny tht re vete long the high-spee ege of the lyer. Conomitnt exittion of oth smll n lrge sles les to enhne mixing through iret enhnement of the smll-sle motions n ugmente entrinment y the inue lrge-sles. As result, the turulent kineti energy (espeilly within the lrge sles) s well s the ross strem spreing of the lyer re signifintly enhne. In the sene of the trnsients tht le to the formtion of the lrge sle strutures, ontinuous high-frequeny tution results in enhne issiption n therey stiliztion of the se flow. θ ρ φ j C µ f AM f H k U i U i u i U U j Re St Nomenlture = ounry lyer momentum thikness = flui ensity = phse ngle = sher lyer with = tutor orifie with = tutor jet momentum oeffiient = mplitue-moultion frequeny = rossover frequeny = step height = turulent kineti energy = i-omponent of the veloity = i-omponent of the men veloity = flututing i-omponent of the veloity = free strem veloity = verge jet veloity = Reynols numer = Strouhl numer * Reserh Engineer, AIAA Memer. Grute Reserh Assistnt. Professor, AIAA Assoite Fellow. 1

2 T I. Introution HE present pper fouses on the role n oupling mehnisms of iret high-frequeny tution on plne turulent sher lyer. The intertion etween the sher lyer n tution is provie through the wll ounry lyer just upstrem from the seprtion point, s shown shemtilly in Figure 1. High-frequeny tution is impose y trin of ounter-rotting vortex pirs tht re ejete into the ounry lyer. Depening on the injetion frequeny n their U initil intertion region irultion, the initil intertion zone etween the highfrequeny vorties n the sher lyer n e vrie. sher lyer The impose vortiity n e ompletely ontine syntheti jet within the ounry lyer n rrie into the sher tutor lyer without impting the free strem, or the vorties n protrue through the ounry lyer n intert Figure 1. The single-strem sher lyer n with the initil sher lyer from the free strem. The vortiity mnipultion using iret highfrequeny tution. min ojetive of the present work is to gin etter unerstning of the role of suh tution in the short- n long-rnge omin of the sher lyer. An exmple of the signifint effet of the high frequeny tution on the reistriution of energy within the sher lyer is shown in Figure 2. Power spetr of the stremwise veloity flututions re plotte t n ritrry point in the sher lyer for the seline (unfore) n the sher lyer fore t frequeny nominlly n orer of mgnitue higher thn the nturlly-evolving frequeny of the seline flow. The spetrum of the unfore lyer exhiits strong pek t the nturl frequeny f n. As the tution is pplie, the orresponing spetrum shows severl istintions. First, it shows the fouse pek t the tution frequeny (~ 1f n ), ut there is lso ro rnge of high frequenies hving inrese energy (mrke s zone B). Simultneously with the inrese of energy t the high frequenies, there is erese of energy t lrge sles (mrke s A). Suh energy efiit seems to suppress formtion of the oherent strutures t the nturl frequeny n there is no pek t f n in the fore flow. Overll, there is rnge of lrge sles with lowere energy in the fore flow while t the sme time rnge of smll sles enhnes its energy, with the rossover frequeny f, s enote on the plot. The role of the oherent vortil strutures in the evolution of plne sher lyers hs een tritionlly investigte in two-strem flows (ting k to the pioneering works of Brown n Roshko 1 n Winnt n Brown 2 ) n reltively little work hs een evote to single-strem sher lyers. A single strem lyer forme y kwr step lower ws investigte y Wygnnski n Fieler 3. In orer to voi n extensive trnsition region these uthors inserte trip wire upstrem of the sher lyer n oserve funmentlly ifferent flow evelopment from previous stuies n inite the signifine of initil onitions for flow evelopment (the onnetion etween flow evelopment n the trip wire ws onfirme in lter experiments). Using the sme fility, Chmpgne, Po, n Wygnnski 4 ltere the initil onitions of the flow prouing ifferent results for the growth rte of the sher lyer from Wygnnski n Fieler 3 ut repliting the results of other experimenters. Hussin n Zmn 5 lso investigte single strem sher lyer in similr experimentl setup to hrterize the oherent strutures with the ition of n entrinment flow norml to the free strem ownstrem of the step. Morris n Foss 6 lso stuie n unfore single strem sher lyer in win tunnel with similr entrinment flow pprtus s tht of Hussin n Zmn 5 n fouse on the initil evelopment of the sher lyer onuting experiments where the Reynols numer ws n orer of mgnitue lrger thn in the present work. The erlier works on the seprting single strem sher lyer from kwr-fing step hve elt primrily with the issues of seprtion n retthment. In review rtile of flow seprtion n retthment ownstrem of kwr-fing step Eton n Johnson 7 lso ompre the single- n two-strem sher lyers n ite severl investigtions in whih the mesure growth rte of the two flows re omprle. Their ultimte onlusion is tht ps.1 1E-3 1E-4 1E A 1E f/f n Figure 2. Power spetr of the stremwise veloity showing the effet of iret high-frequeny tution: unfore (lue) with spetrl pek t the nturl frequeny f n, n fore (re) with spetrl pek t the tution frequeny [O(1f n )] f B

3 in the ner fiel retthing (single-strem) sher lyer is inee very similr to two-strem sher lyer in terms of the overll struture n turulene hrteristis. Similr to the trip wire use in Wygnnski n Fieler 3, Otugen 8 use pssive methos to lter flow evelopment suh s hnging the geometry (kwr-fing step expnsion rtio or rtio of step height to test setion height) whih when inrese le to erese in retthment length. Ative flow ontrol methos re ommon; Ngi, Reisenthel, n Kog 9, 1 use perioi osilltions of mehnil flp to ontrol retthment length. In numeril stuy, Kiktsis n Monkewitz 11 employe omintion of sution on the step fe n lowing ownstrem of the step to estilize the flow. They onlue tht their strtegy works well for more-esily simulte lminr flows ut unertinty is expresse onerning the pplition to the more relevnt se of turulent flow over the kwr-fing step. Chun n Sung 12 n Chun, Lee, n Sung 13 use n ousti speker to tute the flow n minimize the retthment length. This work proue inrese mixing in the ner fiel n enhne entrinment y ffeting the lrge strutures rete y the nturl frequeny of the lyer. As note ove, the present pper fouses on the role n oupling mehnisms of iret high-frequeny tution on plne turulent sher lyer where the intertion etween the sher lyer n syntheti jet tution is effete through the ounry lyer just upstrem of seprtion (Figure 1). Some of the spets of the intertions etween syntheti jets n the free strem were lrey isusse y Vuksinovi, Lus, n Glezer 14, n were 15, 16, 17 lso the sujet of other investigtions. Besies the effet of the pure high-frequeny tution, the effet of onomitnt exittion of the low- n high-frequeny motions is stuie with the emphsis on the iniret formtion of lrge oherent strutures tht rise in the flow s onsequene of the moulte tution signl. The experimentl setup n proeures re esrie in Setion II. Setions III hrterizes the seline (unfore) flow. The effets of high-frequeny tution using pure single-frequeny wveform re esrie in Setion IV, while the effets of the simultneous exitement of smll- n lrge-sles re presente in Setion V. Finlly, the trnsient ynmis of the lrge-struture formtion is further isusse in Setion VI. II. Experimentl Setup n Proeures The experiments re onute in low-spee, lose return win tunnel tht is speifilly esigne for highresolution PIV mesurements. Figure 3 shows sle shemti igrm of the ontrtion, test setion, n iffuser of the win tunnel. The test setion hs U U Figure 3. The win-tunnel test setion n the kwr-fing step flow onfigurtion on the upper surfe. y x trnsprent wlls on three sies n mesures m. The tunnel hs no sreens n is equippe with miniml numer of honeyom setions to voi PIV seeing lokge n umultion. Nonetheless, the mesure free strem turulene intensity is less thn.5% over the entire rnge of tunnel spees. The sher lyer is generte y the flow seprtion off the ege of kwr-fing step, thus representing nonil single-strem sher flow. The step spns the full with of the test setion n its height reltive to the wll of the test setion is H = 5.8 mm. Although the step is uilt in the upper wll of the test setion (Figure 3), the results re presente in flippe fiel of view. A six-moule syntheti jet tutor is integrte into the step surfe. The orifie of eh iniviullyontrolle moule mesures mm n the spnwise sping etween jent orifies is 1.9 mm (the tutors spn out 95% of the step). The tutor orifies re 8 mm (21 orifie withs) upstrem of the step ege n the jets issue norml to the step surfe. Figure 3 lso shows the lose-up shemtis of flow geometry. The operting frequeny of the tutors is within the rnge St H = for the teste free strem flow. Eh moule is lirte outsie of the test setion y mesuring ross strem veloity istriutions over the exit orifie using hot wire nemometry. A movle miniture pressure proe is use for ssessing the moule performne in-situ etween the runs. The input to the tutors is timehrmoni rrier signl n two operting frequenies re selete suh tht St H = 3.31 n 7.36 over rnge of jet momentum oeffiients. The jet momentum oeffiient C µ = ρu j 2 j /(ρu 2 H) is vrie etween n (the verge jet veloity U j is mesure 1 mm ownstrem from the orifie n j =.38 mm). Amplituemoulte foring ws omplishe using squre wve moultion t moultion frequeny f AM tht is n orer 3

4 of mgnitue lower thn the rrier (.18 < St AM < 1.1). The ounry lyer over the step surfe is trippe well upstrem of the ege (using 1 mm imeter trip wire) n the flow over the tutors is turulent. In the sene of tution, the ounry lyer thikness t the step ege is 4.7 mm, n the momentum thikness is θ =.35 mm with Reynols numer Re H 43, (se on the step height H n the free strem veloity U ) n Re θ 47 (se the momentum thikness t the step ege). The flow fiel within the omin.5 < <.5 n.5 < < 2.5 (in the vertil, x-y plne) is mesure using high-resolution prtile imge veloimetry (PIV) hving nominl imging resolution of 26.9 µm/pixel. The PIV mesurements re tken over eleven prtilly overlpping winows n the CCD mer n prt of the lsersheet optis re mounte on omputer-ontrolle trverse mehnisms. Mesurements of the intertion etween the high-frequeny vortex pirs n the ross flow were tken t finer resolution (6.5 µm/pixel). Spetrl nlysis of the flow ws otine from single-sensor hot-wire nemometry. III. The Bseline Flow Cross-strem istriutions of the ensemle-verge, 6 stremwise veloity omponent U t eight ownstrem lotions =.1,.2,.25,.5,.75, 1, 1.5, n 2 re 4 plotte in Figure 4. The men flow evolves slowly in the 2 ownstrem iretion, n the finite step height n presene of the wll ffet the veloity profiles s wek, reirulting flow is forme elow the low strem ege of -2 the sher lyer. As the ounry lyer evolves into the single-strem sher lyer, there is n symmetry in its -4 ross strem spreing owing to the entrinment on the low-spee (wll) sie, n s result, the sher lyer -6 spres more on this sie. Two glol prmeters tht hrterize the spreing of the sher lyer re shown in Figure 4, nmely the stremwise vrition of the ross 6 strem with n momentum thikness θ. The sher 5 lyer with is efine s the ifferene etween rossstrem elevtions where the lol men veloity is 95% 4 n 5% of U. These t show tht the stremwise growth rte of the lyer is mesure y /x ~.179 n 3 θ/x ~.32, whih re omprle to similr 18, 19 2 mesurements in two-strem sher lyers n the single-strem sher lyer 5, 6. 1 Next, the reeptivity to n mplifition of nturl isturnes re onsiere. For tht purpose, power spetr of the veloity flututions re mesure ross the sher lyer t eight stremwise lotions through = 1.4. Figure 5 shows ontour plots of the spetrl power t the frequenies f = 5, 1, 2, n 3 Hz. As expete, the omins of mximum mplifition move ownstrem with the erese in frequeny. For instne, motions t 3 n 2 Hz re the most mplifie roun sher lyer with n momentum thikness θ. =.4 n.6, respetively while the mximum mplifition of motions t lower frequenies pper to pek outsie of the mesurement omin. IV. Diret High-Frequeny Atution The effet of high-frequeny tution on the evolution of the sher lyer is emonstrte in Figure 6 for foring t St H = 7.36 n C µ = The full-fiel plot shows the men vortiity ontour with equiistnt men veloity profiles. The men flow oes not exhiit signifint eprture from the seline flow with slowly evolving veloity profiles in the ownstrem iretion. The only notle ifferene in the men flow is slight inrese in vortiity immeitely ownstrem from the jet orifie. In orer to isolte the high-frequeny strutures tht re impose in the flow through the ounry lyer, phse-loke veloity mesurements re tken within the /θ y/δ /x ~.179 U/U θ/x ~ θ/θ x/θ Figure 4. ) Cross strem istriutions of the stremwise veloity t =.1 ( ),.2 ( ),.25 ( ),.5 ( ),.75 ( ), 1 (+), 1.5 ( ), n 2 ( ). ) The orresponing stremwise vrition of the 4

5 Figure 5. Amplifition of spetrl omponents of the stremwise veloity flututions in the seline (unfore) sher lyer: f = 3 Hz (), 2 Hz (), 1 Hz (), n 5 Hz (). Contour levels: 1E-3 2E-2. frme region for the sme flow onitions. The mesurements re phse-loke to the high-frequeny tution signl t (ritrry) phse φ = 14. The vortiity onentrtions re shown in the top plot of Figure 6. These mesurements lerly show vortex trin long the upper ounry of the sher lyer whih retins its phse oherene up to pproximtely =.5 n therefore signifint oupling etween these vorties n the sher lyer is expete frther ownstrem. As mentione erlier in onnetion with Figure 1, the irultion of these vorties n e mnipulte n the initil intertion zone etween the jets n the sher lyer ltere. Furthermore, sine the vortex trin is forme entirely out of lokwise vorties, it is instrutive to ssess the ynmis of the vortex pir from the point of its injetion into the flow. For tht purpose, mximum flow fiel resolution is use to yiel fiel of view tht spns pproximtely sixteen orifie withs with vetor fiel resolution of j /4. These PIV mesurements re tken phse-loke with the tution signl in phse inrements of φ = 2 uner the sme flow onitions s in Figure 6. Vortiity onentrtions t every seon phse re shown in Figure 7. The initil formtion of the vortex pir is shown in figure 7 (φ = 1 ). The vorties re not visile t the eginning of the yle ue to the inherent ely etween input signl n the motion of the piezoeletri isks. It is pprent in this erly stge of the syntheti jet yle tht the struture with lokwise (CW) vortiity is ominnt ue to the presene of ross flow [note the signifint spreing of CW vortiity while the ounterlokwise (CCW) remins onentrte in smll region t the orifie]. As the jet yle ontinues (Figure 7, φ = 14 ) the CCW struture whih is lso wekene y the CW vortiity in the ounry lyer is move over n is wrppe roun Figure 6. The men vortiity fiel with ross strem veloity istriutions the fore sher lyer (St H = 7.36, C µ = ) n zoome-in phse-loke imge of the vortiity ner the step ege. Vortiity ζ z (s -1 ) ontour levels: the CW struture. The jet yle proees through the next two phses, φ = 18 n 22 (Figures 7 n 7, respetively) where the CW struture eomes lrger n more onentrte n the CCW struture ontinues to wrp roun the CW struture nerly surrouning it (exept ner the wll) y φ = 22. The expulsion yle onlues fter hlf of the entire yle (etween φ = 26 n 3, Figures 7e n 7f, respetively). At this point, the CCW vortex egins to form more oherent struture tht is signifintly less onentrte thn the orresponing CW struture n the two strutures move ownstrem (the CW vortex is vete slower in the wll region). During the remining prt of the yle, the CCW struture issiptes muh fster thn the CW vortex n exits the mesurement omin fter pproximtely one full yle ( φ = 36, Figure 7). At the sme time, the CW struture is vete own to x = 8 j n egins to lose oherene when the next vortex pir is istintly visile t the origin. Therefore, it is expete tht the CW vortex hs ominnt impt on the seprting flow off the step just ownstrem from the mesure omin (t x 21 j ). 5

6 y/ j 12 e f g h i x/ j 15 Figure 7. Phse-loke vortiity onentrtions showing the intertion of the jet vortex pir with the ross flow. The tution frequeny is f = 2 Hz n the jet orifie ( j = 381 µm) is lote t x = y =. The phse ngles reltive to the riving frequeny re φ = 1 (), 14 (), 18 (), 22 (), 26 (e), 3 (f), 34 (g), 2 (h), n 6 (i). Vortiity ontour levels re the sme s in Fig.6. The work of Vuksinovi, Lus, n Glezer 14 showe tht the verge turulent kineti energy k eomes lower in the high-frequeny fore thn in the seline sher lyer in spite of signifint lol inrese immeitely ownstrem from the jet injetion. To further investigte the trnsfer of energy in the fore flow, spetrl nlysis is onute se on the hot wire mesurements of the stremwise veloity flututions. The mesurements re tken t eight ross setions of the sher lyer etween =.1 n Four ifferent foring onitions re nlyze t C µ 1-3 = 4, 26, 51, n 69 for St H = As isusse in onnetion with Figure 2, the rossover frequeny f is efine s the frequeny up to whih the energy ontent of the lrge sles is lowere s onsequene of the high-frequeny foring n ove whih the energy of the smll sles is enhne in the fore flow (reltive to the unfore flow). For this reson the spetrl results in Figure 8 re shown s ontour plots of the rossover frequeny f. An inrese in the mgnitue of f [up to 1 khz (St = 37), represente y inresingly intense lue] implies n inrese of rnge of sles with erese energy in the fore flow. Similrly, eresing f [own to 1 Hz (St =.37), represente y inresingly intense re] inites inresing rnge of sles with inrese energy. The enter of the rnge, nmely the rossover frequeny t 5 khz (St = 18.4) is shown in white. The results of Vuksinovi et l. 14 inite tht the region of high k inue y the vete vortil trin termintes ownstrem of =.1 for C µ = ue to the iret intertion etween the high-frequeny vorties n sher lyer through the onoming ounry lyer. The vorties o not protrue through the ounry lyer, re rrie iretly into the seprtion region, n s onsequene, the verge mesure of k eomes lower thn in the unfore flow immeitely fter this short intertion region The present spetrl results re shown in Figure 8. It is seen tht initil suppression of energy ross the lrge sles spres lmost uniformly ross the sher lyer n tht rnge of ffete sles rpily inreses towr the smll sles. In other wors, n initil nrrow-n inrese in energy of the smll sles is rpily issipte with ownstrem istne n the energy over ll sles is lrey suppresse ownstrem of =.2.3. Therefore, the overll effet of the high-frequeny foring n e esrie s hving stilizing impt in terms of the overll suppression of the flututions. The erlier work of Vuksinovi et l. 14 showe tht even s C µ inreses, there is stremwise lotion t whih n verge mesure of the turulent kineti energy k in the fore flow is ultimtely lower thn in the unfore flow n tht this lotion moves ownstrem with C µ. The ontour plots of f in Figure 8 suggest tht the trnsfer of energy mong the sles is signifintly ltere with the inrese in C µ. Alrey t C µ = (Figure 8), n initil shrp inrese of the rnge of sles with lower energy is visile Figure 8. Contour of the rossover frequeny f for the fore sher lyer (St H = 7.36): C µ 1 3 = 4 (), 26 (), 51 (), n 69 (). Contour levels: 1E 1E4.

7 in the enter of the sher lyer ut oth the high- n low-spee eges show overll inrese in k. The high-spee ege of high k is inue y the vetion of the tutor jet vorties, while the low spee ege is inue y the inrese spreing of the sher lyer. As the foring vorties issipte ownstrem, k in the upper rnh eomes lower ross ll sles. In the lower rnh, the issiption of energy in the smller sles ours frther ownstrem n full reution over ll sles is not etete in the mesurement omin. Figures 8 n show no sustntil roening of the low-energy spetrl ns within the sher lyer. The strongest erese in energy ours within the enter of the sher lyer n spres slowly towrs its eges. The inrese energy ue to the extene intertion region fees the energy of the smll sles, while inrese spreing towrs the low spee sie inreses the energy ontent ross ll sles. It ppers tht the most signifint reution of turulent kineti energy ours if the high-frequeny ontrol is ontine within the wll ounry lyer. Otherwise, there is reistriution of energy ross the sles, whih tens to erese the energy over ro n of sles within the ore of the sher lyer, ut inrese the energy t the smll sles ner its eges. Therefore, it n e rgue tht the energy tht is fe into the sher lyer t smll sles through the intertion region enhnes sptil trnsfer of energy from lrge sles in the ulk of the sher lyer to the engulfe flui t the low-spee sie. Finlly, the impt of lower foring frequeny on energy reistriution within the sher lyer is investigte. For tht purpose, the flow is fore t St H = 3.31 while C µ = The orresponing ontour plot of f is shown in Figure 9. As expete, the energy tht is fe into the sher lyer t lrger sles issiptes over longer ownstrem istne n s onsequene, the trnsition to the omin where the energy is iminishe over ll sles is pushe frther ownstrem. Otherwise, the energy lne ross the sher lyer is similr to tht t higher St H. Four profiles of the rossover frequeny f for the two Strouhl numers re lso plotte in Figure 9 for =.2,.6, 1, n The stremwise inrese in the mgnitue of the rossover frequeny is seen in oth ses n it is interesting tht the profiles on ner the low-spee ege re very similr initing similr energy trnsfer to the entrine flui. V. Conomitnt High- n Low-Frequeny Atution Although the high-frequeny tutors operte t the frequenies tht re n orer of mgnitue higher thn the nturlly-evolving frequenies in the flow, they n e lso use to mnipulte frequenies tht re omprle to f [Hz] Figure 9. Contours of the rossover frequeny f for the fore sher lyer (St H = 3.31, C µ = ) n ross strem istriutions of f (---) t =.2 ( ),.6 ( ), 1 ( ), n 1.38 ( ) long with the orresponing istriutions for St H = 7.36 n C µ = (, soli symols). Contour levels re the sme s in Fig Figure 1. Contours of the turulent kineti energy k with ross strem istriutions of the men veloity for the seline flow () n the fore flow St AM =.184 (),.364 (), n.736 (). TKE k (m 2 /s 2 ) ontour levels:

8 g m h n i o j p e k q f l r Figure 11. Phse-loke vortiity onentrtions for StAM =.184 (-f),.364 (g-l), n.736 (m-r) for moultion phse ngle φ = 2 (, g, m), 8 (, h, n), 14 (, i, o), 2 (, j, p), 26 (e, k, q), n 32 (f, l, r). Vortiity ontour levels re the sme s in Fig.6. the nturl frequenies. Lrge-sle motions re introue y low-frequeny mplitue-moultion of the highfrequeny signl. Wiltse n Glezer2 first emonstrte experimentlly tht the spetrl siens of the time hrmoni, high-frequeny tution wveform tht re introue through mplitue moultion inue oherent motions t the moultion frequeny. This pproh s lrge-sle motions to the iretly inue smll-sle motions in the flow n hs een use in other flow ontrol pplitions to the sher flows21, 22. In the present experiments this pproh is pplie to tution t StH = 7.36 n Cµ = using 5% uty yle squre-wve mplitue moultion t moultion frequenies: StAM =.184,.364, n.736. As result, the nominl high-frequeny tution is tive only uring the first hlf of the moultion perio. In the presene of moultion, the jet veloity is juste so tht it is unhnge. Sptil istriutions of turulent kineti energy k mesure within the full-fiel PIV omin (-.5 < < 2.5) re shown in Figures 1- (the seline flow is shown for referene in Figure 1). These onentrtions inite signifint enhnement in the ross strem spreing of the fore sher lyer tht is ompnie y sustntil inrese in k. However, the zones of mximum enhnement of k re iretly relte to the time sle of StAM. Sine the hrteristi formtion time of the lrge struture t the moultion frequeny inreses with the erese in StAM, the pek k moves ownstrem n is 8

9 entere out = 2 for St AM =.364 (Figure 1), out = 1 for St AM =.736 (Figure 1), n it is outsie the mesurement omin for the lowest St AM (Figure 1). Although there is unnt experimentl eviene of iniret exittion of the lrge-sle strutures vi f 1 e g Figure 12. Contours of the turulent kineti energy k for t St = 3.31 n St AM =.364 (), n orresponing phse-loke vortiity onentrtions for moultion phse ngles φ = 2 (), 8 (), 14 (), 2 (e), 26 (f), n 32 (g). Vortiity ontour levels re the sme s in 2 mplitue moultion of the high-frequeny tution wveform, the physil mehnisms of their formtion hs not een investigte in etil. The erlier work of Vuksinovi, Lus, n Glezer 14 showe tht the lrge oherent strutures re forme y the trnsient motions ner the flow seprtion n tht they re ssoite with the onset n termintion of the moultion uty yle. The ynmis of the lrge oherent struture formtion is further investigte here for the three moultion ses of Figure 1 (St AM =.184,.364, n.736). The PIV mesurements re tken phse-loke to the moultion perio with phse inrement φ = 2 n the fiel of view is omprise of two prtilly overlpping winows tht re entere out the step ege. Figure 11 shows six phse-verge vortiity mps t phse inrements of 6 reltive to the moultion wveform for the three moultion frequenies (the 5% uty yle squre-wve moultion egins t φ = ). These imges show the formtion of lrge CW vortil struture ownstrem of the step. Although the initil rollup of this vortex ppers to e inepenent of St AM, there is ler ifferene in its ynmis fterwrs. The lowest St AM llows for the longest formtion time of the lrge struture n simultneously with its formtion, trin of highfrequeny CW vorties is vete long the high-spee ege of the sher lyer. At φ = 8 (Figure 11) eight Fig.6 n TKE-levels re sme s in Fig. 1. high-frequeny vortex pirs re injete into the free strem, while the lrge struture grows long the lower oun of the sher lyer (mrke y the she irle). By the en of the hlf of the moultion yle (φ = 18 ) the lrge vortex still grows n strts to move out of the fiel of view. Following the en of the tution (Figure 11), the upstrem ounry lyer reovers n the onset of sher lyer temporrily returns to the unfore stte (Figures 11e n 11f). The full intertion etween the smll-sle vorties tht re forme y the tution n the lrge vortil struture is more pronoune t St AM =.364 (Figures 11g-l). Following the termintion of the tution (Figure 11j), the high frequeny vortex trin prtilly oleses with the lrge vortex while the remining high-frequeny vorties re vete ownstrem n my form the ri region etween two onseutive lrge strutures. The growth of the lrge vortex epens on the moultion perio n for St AM =.736 (Figures 11m-r) it is onsierly Figure 13. Contours of the spetrl omponent t the moultion frequeny f AM. St = 7.36 n St AM =.184 (),.364 (), n.736 (), n St = 3.31 n St AM =.364 (). Contour levels: 1E-3 1E. 9

10 Figure 14. Contours of the spetrl omponent f AM /2 for St = 7.36 n St AM =.184 (),.364 (), n.736 (), n St = 3.31 n St AM =.364 (). Contour levels: 1E-3 4E-2. smller n its intertion with the high-frequeny vortex trin strts lrey t =.2 (Figures 11q n 11r). By the time tht next moultion perio strts, lrge struture from the previous perio still interts with the vortex trin within the fiel of view (mrke with full irle). These t show tht the trnsients ssoite with the onset n termintion of the moultion yles re the primry trigger for the formtion of the lrge vortil strutures t the moultion frequeny n inite tht the lrge vortex formtion is primrily ffete y the moultion yle n is lmost inepenent of hnges in the ext rrier (high) frequeny. To hek this, the rrier frequeny ws hnge to St H = 3.31 while the moultion frequeny is kept t St AM =.364 (similr to St H = 7.36, Figures 11g-l). Figure 12 inlues ontours of k (Figure 12, f. Figure 1) n phse-loke vortiity onentrtions tht orrespon to the phses of Figures 11g-l (Figure 12-g). Both the time- n phse-verge fiels re strikingly similr. For exmple, oth fiels exhiit mximum k out = 2. Although there re some ifferene in the etils of the flow fiel (e.g., t the lower St H, the high-frequeny vorties re somewht lrger in size n only four high-frequeny tution yles re omplete uring the tive hlf of the moultion perio, Figure 12e), the ynmis of the lrge vortex is unhnge. As the first CW vortex isrupts the ounry lyer, the lrge vortex egins to form off the step ege (Figure 12) n its susequent growth is similr to St H = 7.36 (note the similrity etween Figures 11k n 12f n Figures 11l n 12g) Figure 15. Contours of the spetrl omponent 2f AM for St = 7.36 n St AM =.184 (),.364 (), n.736 (), n St = 3.31 n St AM =.364 (). Contour levels: 1E-3 1E-1. Further insight into the ynmis of intertion etween the high-frequeny vorties n the single lrge vortex is gine from spetrl nlysis of time-tre of the stremwise veloity. The mesurements re tken for St H = 7.36 with St AM =.184,.364, n.736, n St H = 3.31 with St AM =.36. The sptil mplifition of the veloity flutution t the moultion frequeny is onsiere s the lrge vortex is forme t f AM. Figure 13 shows sptil istriutions of the mgnitue of the spetrl omponents t f AM for the four ses. Eh plot shows two rnhes of mplifie f AM. The lower, more ominnt rnh orrespons to the trjetory of the lrge vortex while the upper rnh orrespons to the high-frequeny vortex trin. As implie from the phse-loke mesurements, these two regions egin to merge fter the ompletion of the tive hlf of the moultion yle. Following the merging, the motions ssoite with f AM re ttenute s mnifeste y the ey of the mgnitue of spetrl energy. Figure 1

11 13 shows tht the merging of the lrge vortex n the vortex trin egins t pproximtely = 1.3. In the se of StAM =.364 (Figure 13), the merging ours roun =.6, whih orrespons to the ynmis in Figure g g-l. The existene of two rnhes is rely visile in Figure 13 euse the intertion strts lrey t =.25, s is evient from Figure 11m-r. Finlly, the similrity of Figures 13 n 13 h -.25 StAM ut ifferent StH) (sme -.25 emonstrtes gin the ominnt role of the moultion frequeny in the evolution of the single vortex. As the energy t the moultion frequeny i ereses following the merging, it is expete tht energy t the suhrmoni of the moultion frequeny woul egin to inrese ue to the piring of the lrge vorties. Contours of the spetrl energy j t fam/2 re shown in Figures 14 -, orresponing to Figures 13-. The grul stremwise inrese in the energy of the suhrmoni motions is lerly visile in ll plots exept StAM =.736 where the suhrmoni is e k not istint. Note tht for StAM =.364, the suhrmoni motions eome signifint for > 1 regrless of StH. Sine the high-frequeny vorties olese n merge with the lrge f l vorties, it is expete tht the energy t integer multiples of the rrier frequeny woul pek in the merging omin. Figure 16. Phse-loke vortiity onentrtions (-f) n the Regrless of the tul fam, the merging orresponing mgnifie veloity fiel (g-l) for the flow fore t of the vorties shoul e mrke y the StAM =.364 n 5% uty yle t moultion phse ngles φ = 6 inrese in the energy omponent t 2fAM. (, g), 8 (, h), 1 (, i), 12 (, j), 16 (e, k), n 24 (f, l). Figure 15 shows sptil istriution of Vortiity ontour levels re the sme s in Fig.6. the energy t the first hrmoni of the moultion frequeny. Eh of the plots exhiits strong initil pek t 2fAM immeitely ownstrem of the step s the hrmoni of the fam is inherently inue y the tution (long with other higher hrmonis). Downstrem of this omin, the energy t the hrmoni ereses ut inreses gin further ownstrem within the merging omins. Thus, the seon pek t 2fAM is seen roun =.7 for StAM =.364 (oth StH, Figures 15 n 15), while it is roun =.5 for StAM =.736 (Figure 15). As expete, the seon pek t 2fAM is not present in the fiel of view for StAM =.184 (Figure 15) sine the merging ours outsie of the fiel of view (Figure 13). VI. Trnsient Dynmis The formtion ynmis of the lrge vorties is further lrifie y minimizing their intertions with the smllsle vorties. This is omplishe y single-yle moultion of the high-frequeny wveform. For the se of StH = 7.36 n StAM =.364 the moultion uty yle is tken to e 5%. Uner this foring onition, only single pir of ounter-rotting vorties is forme y the tutor uring eh moultion yle. The ynmis of the lrge vortex is ssesse using phse-loke PIV mesurements (s esrie in Figure 11). The mesure vortiity fiel is shown in Figure 16-f with the emphsis on erly stge of formtion. Zoome-in views of the orresponing veloity fiels re shown in Figures 16g-l. At φ = 6 (Figures 16 n 16g), the smll-sle CW vortex hs just 11

12 Figure 17. Dt quisition timing for f AM = 1 Hz (.5 % uty yle), phse loke with the moultion input t φ psse the step ege n this trnsient pssge of the CW vortex isrupts the ounry lyer vortiity n results in lrge-sle rollup. The rollup of the new vortex entrins nerly stgnnt flui from the region unerneth the step s it grows (Figures 16 n 16h). By φ = 12 (Figures 16 n 16j), the smll CW vortex egins to merge with the lrge vortex tht ws rete y the trnsient of the previous = 18, 36, 54, 72. moultion yle. At out 2/3 of the moultion perio (Figures 16f n 16l), the lrge vortex grows sustntilly with its enter vete to =.5. The previous exmple shows tht single smll-sle vortex pir is suffiient for exittion of single lrge oherent struture. When suh tution is pplie t the low-frequeny perioi rte, it effetively reners the ontrol of sher lyer to sequene of qusi-trnsient events rther thn ontinuous foring t low frequenies. A shemti for the timing of the t quisition for the 1 Hz trnsient se is shown in Figure 17. The uty yle is erese suh.25 e Figure 18. Phse-loke vortiity onentrtions ( < < 1.5) for St H = 7.36, f AM = 1 Hz (.5% uty yle), t phses φ = 1.8 (), 3.6 (), 7.2 (), 1.8 (), 14.4 (e), 18 (f), 21.6 (g), 25.2 (h), 28.8 (i), n 36 (j). Vortiity ontour levels re the sme s in Fig.6..5 f g h i j tht single high frequeny yle is proue t the eginning of the moultion yle or.5% for f AM = 1 Hz (St AM =.364, Figures 18 n 19). Figure 18 shows prtil fiel t ( < < 1.5,.25 < <.25) of ten phse-verge imges over the initil progression of the lrge struture rete y the single vortex pir in the sher lyer. The effet of the tution is first etete in Figure 18 n is evient y the next phse φ = 7.2 (Figure 18) whih ours fter four perios of the high frequeny tution. The rek in the lyer whih forms in front of the vortil struture n preees it in the ownstrem flow is first visile t φ = 14.4, Figure 18e (t eight perios) roun =.35 n is more istinguishle t the rest of the phses in Figure 18. The finl view in figure 18 shows the progression of the struture t φ = 36 (figure 18j) whih ours fter ten perios of the 2 Hz tution. Figure 19 shows full fiel view of the sme foring sheme s (Figure 18) with phses in inrements of ten perios so tht Figure 19. Phse-loke vortiity onentrtions (-.5 < < 2.5) t St H = 7.36 with f AM = 1 Hz (.5% uty yle), t the phses φ = 18 (), 36 (), 54 (), n 72 (). Vortiity ontour levels re the sme s in Fig.6. 12

13 Figure 2. Phse-loke vortiity onentrtions t St H = 7.36 f AM = 1 Hz (5% uty yle), t the phses φ = (), 9 (), n 18 (). Vortiity ontour levels re the sme s in Fig.6. the finl phse φ = 72 ours fter forty perios of the 2 Hz tution. The rupt tution retes isontinuity in the vortiity fiel of the sher lyer n new CW vortex is inue. This isontinuity is lote t =.4 in Figure 19 n eomes more visile t = 1.2 y φ = 36 (Figure 19). Figure 19 orrespons to the prtil fiel plot (Figure 18f) n the full fiel plot of Figure 19 oinies with Figure 18j. By the finl phse fter forty tution yles (φ = 72, Figure 19) the struture rehes = 2 n the vortiity istriution (.6 < < 1) ppers very similr to the unfore flow. Sine the oherent strutures in sher lyer move nominlly t the verge veloity of the two strems, the veloity of the strutures here is expete to e pproximtely U /2, whih mens tht the vortex in Figure 19 woul e expete to move pproximtely = etween eh of the phses. However, it is seen tht it tully elertes s it is vete without rehing U /2 spee in the mesurement omin. When single pulse is forme using 1 Hz mplitue moultion with 5% uty yle (Figure 2), the shorter moultion perio ompresses the stremwise wvelength s shown in Figures 2 n 2 where the strutures from the two previous yles re visile in the mesurement omin. At φ = 9 (Figure 2) there re three istinguishle vorties inluing the struture tht is forme uring the urrent yle. For φ = 18 (Figure 2) the t orrespons to ten 2 Hz perios fter the eginning of the yle s in Figure 19. Ignoring the ownstrem ifferenes, the t in Figures 18 n 19 pper similr in the rnge -.6 < <.4. Although the moultion perio ereses, there is enough time to llow the sher lyer vortex to evolve to omprle size s for f AM = 1 Hz. The time inrement etween the phses in Figure 19 re five yles of the 2 Hz tution initing tht the struture is expete to move pproximtely = 1/3 etween eh phse, wheres it is gin seen tht it tully elertes uring this time. Figure 21 illustrtes the reltive timing shemes for vrious moultion ses, ll with single tution vortex pir inititing eh moultion yle. The sttus of the flow fter ten high frequeny tution perios is shown in Figure 22 for f AM = 1 Hz, 1 Hz, n 2 Hz. In ll three ses the newly forme struture ppers t Figure 21. Dt quisition timing for f AM = 1 Hz,.5% uty yle, f AM = 1 Hz, 5% uty yle, n f AM = 2 Hz, 1% uty yle. =.3. For f AM = 1 Hz in Figure 22 (whih orrespons to Figures 18f n 19) the t is quire fter 1/2 of the moultion yle n only the single struture is visile. When f AM = 1 Hz, Figure 22 (whih orrespons to Figure 2) shows phse loke t t the hlf-point of the yle n the struture forme in the previous yle remins in the fiel of view t = 1.3. Finlly, f AM = 2 Hz is quire (fter ten 2 Hz perios) t the en of the moultion yle (φ = 36, see Figure 21) n the shorter intervls llow vorties from three onseutive yles to remin visile in figure 22. It is interesting to note tht the lrge sle struture (lote t =.3) fter ten perios remins similr size for the three moultion frequenies in Figure 22 unlike the 5% uty yle ses, whih le to ifferent size strutures t ifferent moultion frequenies (see Figure 11). The t in Figure 23 re quire fter twenty 2 Hz tution perios (1 ms) n re isplye for f AM = 1 Hz, 5 Hz, n 1 Hz with shemti of the timing shown in Figure 21. The t for f AM = 1 Hz is quire t φ = 36 (1% of the moultion yle), the 5 Hz t t φ = 18, n the 1 Hz se t φ = 36. For the three 13

14 Figure 22. Phse verge (uring 1 highfrequeny tution perios) vortiity onentrtions t St H = 7.36 with: f AM = 1 Hz n.5% uty yle (), f AM = 1 Hz n 5% uty yle (), n f AM = 2 Hz n 1% uty yle (). Vortiity ontour levels re the sme s in Fig.6. ses, the lrge struture hs evolve to =.8 n in ll ses it is equl size. For f AM = 1 Hz (Figure 23) the struture from the previous moultion yle is ownstrem of the urrent struture (see isussion of Figure 19). It is interesting to note tht the vortiity plots (Figure 23i) for the three moultion frequenies re similr while the kineti energy hnges. For f AM = 1 Hz this struture from the previous moultion yle [whih n e seen in the vortiity istriution (Figure 23i-) t = 1.9] is responsile for signifint inrese in the turulent kineti energy in Figure 23f ompre to 1 Hz n 5 Hz moultion in Figures 23 n 23e. The reson for inrese in the kineti energy for 5 Hz moultion (Figure 23e) ompre to 1 Hz moultion (Figure 23) is ssumely ue to intertion with n feek from the wll t = whih retes reverse flow. It is speulte tht for free sher lyer with no wll intertion there woul e no isernle ifferene in the turulent kineti energy for the 1 Hz n 5 Hz moultion. This is supporte y the virtully ientil vortiity fiels for the 1 Hz n 5 Hz moultion (Figures 23 n 23) e VII. Conlusions The onomitnt smll- n lrge-sle tution of plne sher lyers is investigte experimentlly in singlestrem sher lyer. The effets of the tution re hrterize sptilly n spetrlly y high-resolution PIV n hot wire mesurements, respetively. The mnipultion of the smll-sle motions is iretly inue y the highfrequeny tution nominlly t frequenies tht re n orer of mgnitue higher thn the nturl frequenies of the flow. While ontinuous, uninterrupte high-frequeny tution suppresses the formtion of lrge oherent strutures, lrge-sle motions (t sles omprle to the nturlly-evolving vorties) re inue iniretly y trnsient strtups of the high-frequeny tution. It is shown tht these lrge strutures re forme y roll-up of 14 f 1 2 Figure 23. Phse verge (uring 2 high-frequeny tution perios) vortiity (-) n turulent kineti energy (-f) onentrtions t St H = 7.36 with: f AM = 1 Hz n.5% uty yle (), f AM = 5 Hz n 2.5% uty yle (), n f AM = 1 Hz n 5% uty yle (). Vortiity ontour levels re the sme s in Fig.6 n TKE levels re the sme s in Fig.1.

15 isrupte vortiity in the ounry lyer t the point of seprtion, whih entrins nerly stgnnt flui n therey signifintly impts the sher lyer spreing on the low spee sie. As ws shown in erlier work, the trin of high-frequeny vortex pirs tht issues into the ounry lyer just upstrem of seprtion results in suppression of turulent kineti energy y enhne issiption. Due to the ross flow (n ounry lyer) ynmis, the CCW vortex in eh pir is lrgely suppresse n elerte roun its CW ounterprt n rehes the sher lyer first. However, the mjor effet of the high-frequeny tution on the evolution of the sher lyer ours vi intertions etween the CW vortex trin long the high-spee ege. The trin of high-frequeny vorties iretly enhnes energy t the smll sles over n intertion region whose stremwise extent epens on the momentum oeffiient of the tution while suppressing the energy of the lrge sle motions. Spetrl nlysis shows tht if the intertion region etween the high-frequeny vorties n sher lyer is onfine to the upstrem ounry lyer, turulent kineti energy is suppresse through most of the with of the sher lyer exept in nrrow omin long its low-spee ege. However, if the tution level is suffiiently high so tht the vortex trin protrues through the ounry lyer n therefore interts with the high-spee ege of the sher lyer, the suppression of turulent kineti energy is onfine to the enter of the sher lyer with two higher energy omins long the high- n low-spee sies. In tht se, the suppression of the turulent kineti energy spres towrs the high-spee ege ut is lwys oune y the high entrinment zone on the low spee sie. When the high-frequeny tution is perioilly strte n stoppe, eh trnsient onset results in the formtion of lrge oherent struture long with trin of smll-sle vorties. As they egin to intert, the fster vete high-frequeny vorties olese either exlusively with the lrge struture forme uring the sme moultion perio or lso with the lrge struture forme uring the previous moultion perio. It is shown tht the sher lyer n simultneously enefit from enhne mixing through iretly-inue the smll-sle motions n enhne entrinment vi lrge-sle strutures uring onomitnt exittion of oth smll n lrge sles. As result, the turulent kineti energy is signifintly enhne n sher lyer spres fster. Sine the formtion of lrge oherent struture epens only on the trnsient isruption of the ounry lyer vortiity, it is shown tht trin of lrge oherent strutures n e sustine simply y perioi pulsing of the sher lyer t the esire rte using single high-frequeny tution yle. Aknowlegments The present work hs een supporte in prt y Air Fore Reserh Lortory n the Boeing Compny. Referenes 1 Brown, G. L. n Roshko, A., On ensity effets n lrge struture in turulent mixing lyers, J. Flui Meh., Vol. 64, 1974, pp Winnt, C. D. n Brown, F. K., Vortex piring, the mehnism of turulent mixing lyer growth t moerte Reynols numer, J. Flui Meh., Vol. 63, 1974, pp Wygnnski, I. n Fieler, H. E., The two-imensionl mixing region, J. Flui Meh., Vol. 41, 197, pp Chmpgne, F. H., Po, Y. H., n Wygnnski, I. J., On the two-imensionl mixing region, J. Flui Meh., Vol. 74, 1976, pp Hussin, A. K. M. F. n Zmn, K. B. M. Q., An experimentl stuy of orgnize motions in the turulent plne mixing lyer, J. Flui Meh., Vol. 159, 1985, pp , 6 Morris, S. C. n Foss, J. F., Turulent ounry lyer to single-strem sher lyer: the trnsition region, J. Flui Meh., Vol. 494, 23, pp Eton, J. K. n Johnson, J. P., A Review of Reserh on Susoni Turulent Flow Retthment, AIAA Journl, Vol. 19, 1981, pp Otugen, M. V., Expnsion rtio effets on the seprte sher lyer n retthment ownstrem of kwr-fing step, Exp. Fluis, Vol. 1, 1991, pp Ngi, H. M., Reisenthel, P. H., n Kog, D. J., On the ynmil sling of fore unstey seprte flows, AIAA Pper , Reisenthel, P. H., Ngi, H. M., n Kog, D. J., Control of seprte flows using fore unsteiness, AIAA Pper , Kiktsis, L. n Monkewitz, P. A., Glol estiliztion of flow over kwr-fing step, Phys. Fluis, Vol. 15, 23, pp Chun, K. B. n Sung, H. J., Control of turulent seprte flow over kwr-fing step y lol foring, Exp. Fluis, Vol. 21, 1996, pp Chun, K. B., Lee, I., n Sung, H. J., Effet of spnwise-vrying lol foring on turulent seprte flow over kwr-fing step, Exp. Fluis, Vol. 26, 1999, pp

16 . 14 Vuksinovi, B., Lus, D. G., n Glezer, A., Diret mnipultion of smll-sle motions in plne sher lyer, AIAA Pper , Mittl, R., Rmpunggoon, P., n Uykumr, H. S., Intertion of Syntheti Jet with Flt Plte Bounry Lyer, AIAA Pper , Prk, S.-H., Lee, I., n Sung, H. J., Effet of lol foring on turulent ounry lyer, Exp. Fluis, Vol. 31, 21, pp Cui, J., Agrwl, R. K., n Cry, A. W., Numeril Simultion of the Intertion of Syntheti Jet with Turulent Bounry Lyer, AIAA Pper , Roerts, F.A. n Roshko, A., Effets of Perioi Foring on Mixing in Turulent Sher Lyers n Wkes, AIAA Pper 85-57, Oster, D. n Wygnnski, I., The Fore Mixing Lyer Between Prllel Strems, J. Flui Meh., Vol. 123, 1982, pp Wiltse, J.M. n Glezer, A., Mnipultion of free sher flows using piezoeletri tutors, J. Flui Meh., Vol. 249, 1993, pp Dvis, S.A. n Glezer, A., The Mnipultion of Lrge- n Smll-Sles in Coxil Jets Using Syntheti Jet Atutors, AIAA Pper 2-43, Smith, B.L. n Glezer, A. Jet Vetoring using Syntheti Jets, J. Flui Meh., Vol. 458, 22, pp Ho, C-M. n Hung, L-S., Suhrmonis n Vortex Merging in Mixing Lyers, J. Flui Meh., Vol. 119, 1982, pp