Interaction of a Synthetic Jet with a Flat Plate Boundary Layer

Transcription

1 AIAA Intertion of Syntheti Jet with Flt Plte Bounry Lyer R. Mittl 1 P. Rmpunggoon Deprtment of Mehnil Engineering University of Flori Ginesville, Flori, 3611 H. S. Uykumr 3 Deprtment of Mehnil Engineering University of Iow Iow City, Iow, 54 ABSTRACT The intertion of moele syntheti jet with flt plte ounry lyer is investigte numerilly using n inompressile Nvier Stokes solver. The iphrgm is moele in relisti mnner s moving ounry in n effort to urtely ompute the flow insie the jet vity. The primry fous of the urrent stuy is on esriing the ynmis of the syntheti jet in the presene of externl rossflow. A systemti prmetri stuy hs een rrie out where the iphrgm mplitue, externl flow Reynols numer n slot imensions re vrie. The simultions llow us to extrt some interesting flow physis ssoite with the vortex ynmis of the jet n lso provie insight into the sling of the performne hrteristis of the jet with these prmeters. 1. INTRODUCTION The syntheti jet hs emerge s one of the most useful miro (or meso) fluii evies with the potentil pplition rnging from thrust vetoring of jet engines (Smith et l. 1997), mixing enhnement (Chen et l. 1999, Dvis et l. 1999) to tive ontrol of seprtion n turulene in ounry lyers (Smith & Glezer 1998, Crook et l. 1999). The utility of these evies in ontrolling seprtion hs for the most prt, een emonstrte in lortory setups only, n numer of issues nee to e resse in orer to trnsition this tehnology to prtil pplitions. First, the performne of syntheti jet tutor epens on numer of geometril, struturl n flow prmeter n there is little unerstning s to how this performne sles with these prmeters. Suh n unerstning woul e ritil element in the sizing, esign n eployment of these tutors. Seonly, lthough experiments hve shown tht for instne, syntheti jets n e use to ely seprtion (Amity et l. 1997), our unerstning of the physil mehnisms tht le to this effet is quite limite. Both of these issues n e resse y systemti prmeter stuy of syntheti jet. In the urrent stuy we hve use numeril simultions to perform etile prmetri 1 Assistnt Professor Grute Stuent 3 Assistnt Professor stuy of simplifie onfigurtion whih inlues two-imensionl syntheti jet interting with flt plte ounry lyer.. FLOW CONFIGURATION AND SIMULATION APPROACH Flow Configurtion Consier the two-imensionl syntheti jet evie in Figure 1, whih is tthe eneth flt plte on whih evelops lminr Blsius ounry lyer. The syntheti jet is rete t the slot y the osilltion of iphrgm tthe to the ottom of the jet vity n the iphrgm efletion is hrterize y the efletion mplitue (A) n ngulr frequeny ( ). The vity, whih is retngulr in shpe is efine y the vity with (W) n the vity height (H). A slot type exit is hosen for the jet n this orifie is hrterize y height (h) n with (). The exterior flow whih onsists of lminr Blsius ounry lyer is hrterize y freestrem veloity ( ) n ounry lyer thikness ( ). Finlly, the flui is hrterize y its kinemti visosity ( ) n ensity ( ). Aitionl prmeters nee to e onsiere in the sitution where ompressiility effets insie the vity eome signifint. However, from the point of view of evie effiieny, it might e vntgeous to operte in the inompressile flow regime n this n e esily omplishe y etuning the iphrgm frequeny from the ousti resonne frequeny of the vity. Therefore, with the unerlying ssumption tht tul evies will e esigne to operte in the inompressile flow regime, in the urrent stuy, we lso fous only on this regime. Jet Chrteriztion n Sling The flow emerging from the slot is in priniple funtion of ll the prmeters esrie in the prgrph ove. The exit flow whih is oth funtion of spe n time, n e hrterize through numer of ifferent prmeters. In mny previous stuies, prmeter onsiere key to hrterizing the jet in the presene of n exterior flow is the momentum *Copyright 001 The Amerin Institute of Aeronutis n Astronutis In. All rights reserve. 1

2 AIAA oeffiient (Amity et l. 1998, Seifert et l. 1996) whih is the net momentum imprte y the jet over one yle normlize y the momentum flux of the externl flow. However, it is not ler tht this or ny other single prmeter woul e suffiient to hrterize the ynmis ssoite with the omplex jet. Thus, even the hoie of prmeters tht woul equtely hrterize the jet in the presene of externl rossflow is n open question. In the urrent stuy more generl pproh to hrterizing the jet ehvior, whih employs the suessive moments of the jet veloity profile, is vote. The n th moment of the jet is efine s C n [V J (x, )] n x (1) where V J is the jet veloity normlize y suitle veloity sle (freestrem veloity or invisi jet veloity). Our preliminry simultions inite tht the jet flow is signifintly ifferent in the ingestion n expulsion phses n hrterizing this ifferene is ritil to unerstning the physis of this flow. Thus, it is nturl to efine the moment seprtely for the ingestion n expulsion phses n these re enote y n respetively. This hierrhil hrteriztion in terms of the moments of the veloity profile is extremely useful sine it provies systemti frmework for the evelopment of sling lws. Furthermore, this type of hrteriztion is not simply for mthemtil onveniene sine numer of these moments hve iret physil signifine. For instne C 1 in C 1 ex orrespons to the jet mss flux (whih is ientilly equl to zero for syntheti jet) n C 1 ex is the men normlize jet veloity uring the expulsion phse. Furthermore, C ex C in n C 3 in C 3 ex orrespon to the normlize momentum n kineti energy fluxes of the jet. This lst quntity is lso mesure of the symmetry of the flow uring the expulsion n ingestion phses. Finlly for n, (C n ex) 1 n represents the normlize mximum jet exit veloity. With the jet hrteristi prmeters hosen in this mnner, the question now is to etermine their epenene on the flow n geometril prmeters of this onfigurtion. Using the Bukinghm Pi theorem, this funtionl epenene n e written in terms of non imensionl prmeters s: () where W/H : with to height rtio of vity A/H : iphrgm mplitue to vity height rtio /h : orifie with to height rtio /W : orifie with to vity with rtio : Stokes numer : ounry lyer thikness Reynols numer : rtio of ounry lyer thikness to slot with. It is worth noting tht the first five prmeters on the RHS of Eqution () epen only on the syntheti jet evie, wheres the lst two prmeters epen on the outer ounry lyer. The first ojetive of sling nlysis woul then e to etermine the funtionl epenene enote in Eqution (). From previous stuies, it is ler tht the moment oeffiients will epen on the jet n slot prmeters. However, it is not ler wht effet the exterior flow prmeters hve on the jet flow n the flow in the vity. This requires urte simultion of the flow insie the jet vity n this is one ojetive of the urrent stuy. In the pst, the iphrgm hs een moele y ssuming piston like motion (Rizzett et l. 1998) n this n le to signifintly ifferent flow insie the vity. In the urrent simultions, the iphrgm is moele in more relisti mnner s plte osillting in its funmentl moe. Thus the iphrgm hs its mximum efletion t the enter n zero efletion t the two ens. Clerly, the prmeter spe of this flow onfigurtion is enormous n iffiult to over in ny single investigtion. We therefore fous on the prmeters tht re expete to hve strong influene on the hrteristis of the jet. The prmeters to e vrie in the urrent stuy re the iphrgm mplitue (A/H), orifie with to height rtio (/h) n the ounry lyer thikness Reynols numer of the externl flow ( ). In ition to this, the Stokes numer n hve lso een vrie ut those results re not inlue in the urrent pper. These prmeters re hosen euse preliminry simultions inite signifint vrition in the jet with these prmeters n it ws therefore expete tht useful insight into the physis of this flow oul e gine y vrying these prmeters. The vlues of the other prmeters re fixe t W/H=5, /W=0.05, = n furthermore, ll results presente here orrespon to Stokes numer of 10. One prmeter foun useful in the normliztion of the jet veloity is the mximum invisi jet veloity ( ) whih, for the presrie iphrgm motion is given y V inv mx AW (3) Simultion Approh A previously evelope Crtesin gri solver (Uykumr et l. 1999, Ye et l. 1999, Uykumr et l. 000) is eing employe in these simultions. Detils of the solution proeure n e foun in these ppers. This solver llows simultion of unstey visous inompressile flows with omplex immerse moving ounries on Crtesin gris. Thus, the gri oes not nee to onform to the omplex moving ounries n this simplifies the griing of the flow omin. The solver employs seon orer urte entrl ifferene sheme for sptil isretiztion n mixe expliit impliit frtionl step sheme for time vnement. An effiient multigri lgorithm is use for the solving the pressure Poisson eqution. The key vntge of this solver for the urrent flow is tht the entire geometry of the syntheti jet inluing the osillting iphrgm is moele on the sttionry Crtesin mesh. Figure shows the typil mesh use in the urrent simultions. As the iphrgm moves over the unerlying Crtesin mesh, the

3 AIAA isretiztion in the ells ut y the soli ounry is moifie to ount for the presene of the soli ounry. In ition, suitle ounry onitions lso nee to e presrie for the externl flow. For the quiesent externl flow se, soft veloity ounry onition (orresponing to homogeneous Neumnn onition) is pplie on the north, est n west ounries. In the simultions with n externl ross flow, the Blsius ounry lyer profile is presrie on the west ounry n uniform freestrem veloity presrie on the north ounry whih is lote more thn 40 wy from the slot. On the est ounry, soft ounry onition is pplie whih llows vortex strutures to onvet out of the omin with miniml istortion n refletions. All simultions re run for few yles until stey stte is rehe. The simultions re then ontinue over t lest five yles eyon this stge n sttistis umulte over this time intervl. Thus, ll results presente here orrespon to the sttionry stte of the flow. 3. DISCUSSION OF RESULTS In this setion, we esrie the vortex ynmis oserve for some selete ses. For ese of omprison, ll ses isusse in the following setion, unless otherwise note, orrespon to A/H=0.1 n h/=1.0 Quiesent Externl Flow Cse 1 ( = 0) This se orrespons to quiesent externl flow whih hs een stuie extensively in the pst y other groups (Jmes et l. 1996, Krl et l. 1997, Rizzett et l. 1998). Figure 3 shows sequene of ontour plots of spnwise vortiity plots for this se. At the mximum expulsion stge (when the iphrgm is moving up with the mximum veloity), pir of ounter rotting vorties forms t the orifie. This vortex pir is remove from the surfe y its own inue veloity. As the iphrgm moves own, it entrins externl flui through the slot. However, sine the vorties hve lrey trvele wy from the orifie, they re not ffete y the motion of the entrine flui. Another pir of vorties generte insie the vity uring the ownstroke sets up omplex flow insie the vity. However, for this simultion, the flow insie the vity remins symmetri out the vertil enterline. There is lso lrge region of lmost stgnnt flui ner the two sie wlls of the vity. Currently it is not ler wht effet this stgnnt flui hs on the jet flow. However, it shoul e pointe out tht in these regions espeilly, the flow proue y piston like motion of the iphrgm woul e quite ifferent. Cse ( = 0, n A/H = 0.1 h/ =3) Comprison of this se with Cse 1 llows us to guge in limite mnner, the effet of the h/ prmeter. The sequene of vortiity ontour plots over one yle is shown in Figure 4. In generl it is foun tht for this prtiulr set of prmeters, the flow outsie n insie the jet vity is mrkely similr to tht for Cse 1. However, s will e isusse lter, there re some qulittive hnges in the jet veloity profile whih point towrs tren with inresing slot height. Cse 3 ( = 0, h/ =3 n A/H = 0.05). This quiesent flow se hs hlf the iphrgm mplitue of Cse n onsequently, hlf the nominl jet veloity. Figure 5 shows the ontour plot of vortiity t four ifferent stges in the yle. It is oserve tht s the iphrgm moves into the expulsion strokes, pir of vorties form n seprte from the jet lip. However, s the iphrgm moves into the ingestion stroke, these vorties re still in the ner viinity of the slot n the effet of the flow generte ner the jet lip uring this phse tens to iminish the strength of these vorties. Consequently the trin of strong, ompt vorties oserve in Cse 1 is not oserve here. Thus in orer to form trin of onveting vorties, the vortex pir must e well seprte from the jet lip t the initition of the ingestion stroke. Although, it seems ler tht this seprtion istne is epennt on the jet veloity s well s the inue veloity (n therefore strength) of the vortex pir, no simple riterion hs yet een estlishe for the formtion of the vortex trin. Jet with Externl Crossflow Cse 4 ( = 60) This is the first se with n externl rossflow. The ounry lyer thikness Reynols numer of the externl flow ( ) is 60 n Figure 6 shows sequene of vortiity ontour plots for this se. It is oserve tht s in the se of quiesent externl flow, vortex pir forms t the jet lip uring the expulsion stoke. However this vortex pir immeitely omes uner the influene of the rossflow n egins to onvet ownstrem. As the xis of the vortex pir rottes lokwise, the lokwise vortex (tht forme from the right lip of the slot) moves towr the wll n onsequently slows own. On the other hn the ounter-lokwise vortex, whih is expose to higher spee flow, onvets ownstrem rpily n pprohes the lokwise vortex forme in the previous yle. These two vorties now form pir whih moves vertilly ue to self-inution while ontinuously eing onvete ownstrem. It shoul e pointe out tht for this se. Thus even through the jet veloity is muh higher thn the rossflow veloity, the ynmis of the jet formtion is signifintly ffete y the rossflow. Cse 5 ( = 100). In this se, the ounry lyer Reynols numer is inrese to 100 with n ompnying inrese in the freestrem veloity suh tht. Figure 7 shows the sequene of vortiity ontour plots for this se n signifint ifferenes etween this se n the previous ses re oserve. First unlike the previous ses, the flow in the vity is highly non-symmetri out the vertil enterline. Furthermore the vortil struture forme insie the vity re stronger n onsequently the region of lmost stgnnt is smller. During expulsion, two sets of ounter rotting vorties re proue. However, ue to the lower reltive jet veloity, the vorties generte uring expulsion o not penetrte out into the freestrem. Furthermore, the ounterlokwise rotting vortex is nelle out y the ounry lyer, whih is omprise of lokwise vortiity. In ontrst, the lokwise vortex entrins flui from the ounry lyer n from the freestrem n grows in size s it onvets ownstrem. In ition, nother smller lokwise vortex is forme whih trils ehin the primry vortex. The entrinment 3

4 AIAA of high momentum freestrem flui into the ounry lyer y these vorties is n importnt feture sine it hs een hypothesize tht this mkes the resulting ounry lyer more resistnt to seprtion. Cse 6 ( = 600). This se orrespons to the highest Reynols numer exterior flow simulte n for this simultion,. Figure 8 shows the sequene of vortiity ontour plots for this se. With the higher exterior veloity, the ounter-lokwise vortiity is nelle quikly. Furthermore, the lokwise vorties re lso foun not to penetrte to the freestrem sie of the ounry lyer. Consequently, no iret entrinment of freestrem flui into the ounry lyer is oserve. However s in the previous se, the primry lokwise vortex is followe y smller lokwise vortex. The formtion of more thn one vortex per yle is initive of the presene of strong superhrmoni omponent in the jet. This hs implitions for seprtion ontrol sine it implies tht the jet is ple of proviing signifint perturtion t twie the iphrgm frequeny. It is lso oserve tht the ingestion of higher momentum flui energizes the flui insie the vity n onsequently, the size of e volume insie the vity ereses. This further unersores the two wys oupling etween the externl flow n internl flow. Jet Veloity Profiles The sptil n temporl vrition of the jet veloity etermines ll of the jet hrteristi n therefore insight n e gine through etile nlysis of the jet profile. Figure 9 shows the jet exit veloity profiles for quiesent externl flow ses s well s ses with n externl rossflow. All plots orrespon to the sme iphrgm mplitue of A/H = 0.1. The four ifferent lines in eh plot represent four ifferent stges in the yle (similr to the vortiity plots) n the veloity in these plots hs een normlize y. In Figure 9() re shown the jet veloity profiles for the quiesent externl flow ses. Soli n she lines orrespon to Cses 1 n respetively. In oth ses, the veloity profile is symmetri out the enterline of the jet. The first thing to note is the ifferene in the profile uring the expulsion n ingestion stges. The veloity exhiits more of jet like profile uring expulsion where the profile is more plug like uring ingestion. The normlize enterline veloity is out 1.4 t mximum expulsion n 1.0 t mximum ingestion. The profiles for the two ses re not signifintly ifferent. However, the more proli shpe t pek expulsion for the higher vlue of h/ oserve in Figure 9(), represents tren tht eomes more pprent t higher vlues of this prmeter. Figure 9() shows the jet exit veloity profile for the Cse 4 ( =60). Comprison with the profiles for the orresponing quiesent flow suggests mrke ifferene uring the expulsion phse. In prtiulr, oth t mximum volume n mximum expulsion, the jet profile is skewe to the right In ontrst, the jet profile is reltively unhnge uring the ingestion stroke. Figure 9() n () show the jet veloity profiles for Cses 5 n 6 with =100 n 600 respetively. In generl, the tren oserve for Cse 4 is lso foun to e present here. The jet is pushe to the right sie of the slot ue to the tion of the externl ross flow n this hs two onsequenes. First, inrese skewness of the jet to the right is oserve with inresing Reynols numer of the externl rossflow. Seon, the effetive re of the jet ereses n mss onservtion then emns n inrese in the jet veloity. The ifferene etween the =0 re =100 veloity profiles uring the ingestion phse is somewht less notiele. Prtiulrly t mximum ingestion, oth flows exhiit lmost plug like veloity profiles. However the tren towrs inrese skewness with Reynols numer is lso oserve in the ingestion phse. The veloity profiles for Cses 5 n 6 re quite similr, n in orer to explore this similrity, in Figure 10 we hve ompre the two sets of profiles where eh profile hs een normlize y its own pek expulsion veloity. The omprison inites tht the profile t the higher Reynols numer hs greter egree of skewness. Skewness in the veloity profile is ynmilly importnt sine it ffets the enstrophy flux of the jet n the strength of the vortex strutures expelle into the externl flow. Thus, it might e pproprite to inlue some mesure of skewness mong the importnt hrteristi fetures of the jet. Jet Moment Coeffiients Figure 11 shows the momentum oeffiient plotte versus A/H for Cses 1,, 5 n 6. In eh plot, the momentum oeffiient hs een normlize y the momentum oeffiient of the orresponing invisi jet. Sine our simultions inite tht the jet profile is mrkely ifferent uring the expulsion n ingestion strokes, the momentum oeffiient hs een ompute n plotte seprtely for these two phses. For the quiesent externl flow ses (Figures 11 () n ()), the normlize momentum oeffiient of the expulsion stoke is greter thn tht of the ingestion stoke whih is initive of the jet like veloity profile oserve uring expulsion. Furthermore, the vlues o not vry gretly with iphrgm mplitue n h/, initing tht for t lest the rnge of prmeters stuie here, the jet momentum flux sles in simple mnner with the invisi jet veloity. The ses with the externl rossflow however show mrkely ifferent ehvior. While the momentum oeffiient of the ingestion stroke is oserve to symptotilly pproh unity with inresing iphrgm mplitue for oth ses, the momentum oeffiient of the expulsion stroke is oserve to inrese ontinuously with this prmeter. This lerly illustrtes the vntge of seprtely nlyzing the two phses of the jet yle. It is lso interesting to note tht for the highest Reynols numer, the momentum oeffiient of the expulsion stroke seems to sturte t high iphrgm mplitue where s similr ehvior is not oserve for =100. 4

5 AIAA Virtul Aero Shping Effet Finlly, in Figure 1 we hve plotte the stremlines orresponing to the men flow. As mentione erlier, some previous stuies (Amity et l. 1997, Chtlynne et l. 001) hve hypothesize tht the syntheti jet is ple of ltering the effetive shpe of the oy y forming men reirultion zone in the externl flow tht is signifintly lrger thn the size of the jet. To our knowlege, no iret support for this hypothesis hs een provie in experiments or simultions. The urrent simultions provie us with n esy mens of exploring this issue. In Figure 1 we ompre the men stremline pttern for three ses orresponing to =60, 100 n 600 with A/H = 0.1. From Figure 1, we see tht the high reltive veloity jet retes reltively lrge system of reirultion ules on the surfe of the flt plte with length tht is roughly 10. On the other hn, for the lower veloity jets (Figure 1 n 1), no reirultion zones re forme n the stremlines re just slightly perture only in the very ner viinity of jet exit. Thus, the syntheti jet is inee ple of forming lrge men reirultion zones. However this pility epens on the rtio of the jet to externl flow veloity. For =60, wheres for =100 n 600, this rtio is equl to 0.67 n 0.3 respetively. Thus, lrge men reirultion ule forms only if the jet veloity is signifintly higher thn the externl rossflow veloity. Reent simultions inite tht the prmeter lso hs signifint influene on the size of the reirultion ule ut these results will e presente elsewhere. 4. CONCLUSIONS Numeril simultions hve een use to stuy the intertion of syntheti jet with flt plt ounry lyer in simplifie, two-imensionl onfigurtion. The iphrgm is moele in relisti mnner s moving ounry in n effort to ompute the internl vity flow urtely. The simultions show tht the presene of the rossflow results in signifintly ifferent flow s eviene y the ynmis of the vortex strutures proue y the jet n the jet veloity profiles. A systemti frmework hs een put forth for hrterizing the jet in terms of the moments of the jet profiles. In ition to the moments, the simultions lso inite tht skewness might e n importnt hrteristi of the jet profile. Seprte nlysis of the ingestion n expulsion strokes is lso foun to e useful sine it revels istintly ifferent jet ehvior uring these two phses for ses where there is n externl rossflow. Finlly, the so lle virtul ero shping effet of the syntheti jet is investigte. It is foun tht lrge men reirultion ules re forme in the externl ounry lyer only if the jet veloity is signifintly higher thn the rossflow veloity. 5. ACKNOWLEDGEMENTS This work is supporte prtilly y NASA Grnt NAG monitore y Susn Gorton. Computer time hs een provie y strtup grnt from NCSA t the University of Illinois t Urn-Chmpign. We woul lso like to knowlege extensive isussions with Professors L.N. Cttfest n R.W. Mei uring the ourse of this work. 6. REFERENCES 1 Amity, M., Honohn, A., Trutmn, M., Glezer, A. (1997). Moifition of the Aeroynmi Chrteristi of Bluff Boies Using Fluii Atutors. AIAA Amity, M., Smith, B. L., Glezer, A. (1998). Aeroynmi Flow Control Using Syntheti Jet Tehnology. AIAA Chtlynne, E., Rumigny, N., Amity, M. n Glezer, A. (001). Virtul Aero Shping of Clrk Y Airfoil Using Syntheti Jet tutors. AIAA Chen, Y., Ling, S., Aung, K., Glezer, A., Jgo, J. (1999). Enhne Mixing in Simulte Comustor Using Syntheti Jet Atutors. AIAA Crook, A., Sri, A. M., Woo, N. J. (1999). The Development n Implementtion of Syntheti Jets for the Control of Seprte Flow. AIAA Dvis, S. A., Glezer, A. (1999). Mixing Control of Fuel Jets Using Syntheti Jet Tehnology : Veloity Fiel Mesurement. AIAA Jmes, R. D., Jos, J. W., Glezer, A. (1996). A Roun Turulent Jet Proue y n Osillting Diphrgm. Phys. Fluis. Vol. 8, No Krl, L. D., Donovn, J. F., Cin, A. B., Cry, A. W. (1997). Numeril Simultion of Syntheti Jet Atutors. AIAA Rizzett, D. P., Visl, M. R., Stnek, M. J. (1998). Numeril Investigtion of Syntheti Jet Flowfiels. AIAA Seifert, A., Bhr, T., Wygnnski, I. (1998). Applition of Ative Seprtion Control to Smll Unmnne Air Vehile. Journl of Airrft. Vol. 36, No.. 11 Seifert, A., Dri, A., Wygnnski, I. (1996). Dely of Airfoil Stll y Perioi Exittion. Journl of Airrft. Vol. 33, No Smith, B.L., Glezer A. (1997). Vetoring n Smll sle Motions Effete in free Sher Flows Using Syntheti Jet Atutors. AIAA Smith, D., Amity, M., Kiens, V., Prekh, D., Glezer, A. (1998). Moifition of Lifting Boy Aeroynmis Using Syntheti Jet Atutors. AIAA Uykumr, H. S., Mittl R., n Shyy, W. (1999). Soli Liqui Phse Front Computtions in the Shrp Interfe Limit on Fixe Gris. J. Comput. Phys. Vol. 18, pp Uykumr, H. S., Mittl R.,n Rmpunggoon, P. (000) Simultion of Soli Flui Intertion On Crtesin Gris. Pro. of 000 ASME Winter Annul Meeting. 16 Ye, T., Mittl, R., Uykumr, H. S., Shyy, W., (1999). An urte Crtesin gri metho for visous inompressile flows with omplex immerse ounries. J. Comp. Phys. Vol. 156, pp

6 AIAA () Figure 1. () Shemti igrm of syntheti jet tutor with the retngulr hmer n slot. () The onfigurtion of --D syntheti jet use in the urrent stuy. () Figure. A fixe non--uniform Crtesin gri use in the syntheti jet lultion. Every thir gri point is shown. 6

7 AIAA Figure 3. Plot of vortiity ontour t four ifferent stges forquiesent externl flow, h/=1 n A/H = 0.1. () Mximum expulsion () Minimum volume. () Mximum ingestion n () Mximum volume. Figure 4. Plot of vortiity ontour t four ifferent stges for quiesent externl flow, h/=3 n A/H = 0.1. () mximum expulsion () minimum volume () mximum ingestion n () mximum volume. 7

8 AIAA Figure 5. Plot of vortiity ontour t four ifferent stges for quiesent externl flow, h/=3 n A/H = () mximum expulsion () minimum volume () mximum ingestion n () mximum volume. Figure 6. Plot of vortiity ontour t four ifferent stges for Re =60, h/=1 n A/H = 0.1. ()mximum expulsion ()minimum volume () mximum ingestion n () mximum volume. 8

9 AIAA Figure 7. Plot of vortiity ontour t four ifferent stges for Re =100, h/=1 n A/H = 0.1. () mximum expulsion () minimum volume () mximum ingestion n () mximum volume. Figure 8. Plot of vortiity ontour t four ifferent stges for Re =600, h/=1 n A/H = 0.1. ()mximum expulsion () minimum volume () mximum ingestion n () mximum volume. 9

10 AIAA mximum expulsion 1.5 mximum expulsion v / V inv mx minimum volume mximum volume v / V inv mx minimum volume mximum volume mximum ingestion -1.5 mximum ingestion x / x / mximum expulsion 1.5 mximum expulsion v / V inv mx mximum volume minimum volume v / V inv mx mximum volume minimum volume -1 mximum ingestion -1 mximum ingestion x / x / Figure 9. The veloity profile t the orifie exit. () quiesent externl flow with h/ =1 shown s soli lines n h/ = 3 shown s otte line. (), () n () re for Re δ =60, 100 n 600 respetively with h/ =1. Four ifferent lines show four ifferent stges. Figure 10. The veloity profile t the orifie exit normllize y its mximum vlue for Re δ =100 n 600 with iphrgm mplitue A/H= 0.1. Re δ =100 se re shown with otte line n Re δ =600 se re shown with soli lines. 10

11 AIAA Figure 11. Momentum oeffiient of the jet exit veloity profiles for () Re = 0, h/=1 () Re = 0, h/=3 () Re = 100, h/=1 () Re = 600, h/=1. Figure 1. The men stremline plot of the verge veloity for the () Re =60 () Re =100 () Re =600 n A/H=0.1 11