Optimization of Synthetic Jet Actuators

Transcription

1 AIAA Optimiztion o Synthetic Jet Actutor Quentin Gll, Guiqin Wng, Melih Ppil, Mrk Sheplk nd Loui Cttet Univerity o Florid Gineville, FL 4 t Aeropce Science Meeting & Exhibit 6-9 Jnury 3 / Reno, NV For permiion to copy or republih, contct the Americn Intitute o Aeronutic nd Atronutic, 8 Alexnder Bell Drive, Suite 5, Reton, Virgini

2 Report Documenttion Pge Form Approved OMB No Public reporting burden or the collection o inormtion i etimted to verge hour per repone, including the time or reviewing intruction, erching exiting dt ource, gthering nd mintining the dt needed, nd completing nd reviewing the collection o inormtion. Send comment regrding thi burden etimte or ny other pect o thi collection o inormtion, including uggetion or reducing thi burden, to Whington Hedqurter Service, Directorte or Inormtion Opertion nd Report, 5 Jeeron Dvi Highwy, Suite 4, Arlington VA -43. Repondent hould be wre tht notwithtnding ny other proviion o lw, no peron hll be ubject to penlty or iling to comply with collection o inormtion i it doe not diply currently vlid OMB control number.. REPORT DATE JAN 3. REPORT TYPE 3. DATES COVERED --3 to TITLE AND SUBTITLE Optimiztion o Synthetic Jet Actutor 5. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Univerity o Florid,Deprtment o Electricl nd Computer Engineering,Gineville,FL,36 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES). SPONSOR/MONITOR S ACRONYM(S). DISTRIBUTION/AVAILABILITY STATEMENT Approved or public relee; ditribution unlimited 3. SUPPLEMENTARY NOTES The originl document contin color imge. 4. ABSTRACT 5. SUBJECT TERMS. SPONSOR/MONITOR S REPORT NUMBER(S) 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT. REPORT uncliied b. ABSTRACT uncliied c. THIS PAGE uncliied 8. NUMBER OF PAGES 9. NAME OF RESPONSIBLE PERSON Stndrd Form 98 (Rev. 8-98) Precribed by ANSI Std Z39-8

3 AIAA Optimiztion o Synthetic Jet Actutor Quentin Gll, Guiqin Wng, Melih Ppil, Mrk Sheplk, nd Loui Cttet Deprtment o Mechnicl nd Aeropce Engineering Univerity o Florid Gineville, Florid (35) , (35) (FAX), ctmn@me.ul.edu Abtrct Thi pper decribe the optimiztion o piezoelectric-driven ynthetic jet ctutor bed on Lumped Element Modeling (LEM). To impliy the problem, thi pper plit the optimiztion problem into two prt. Firt, contrined optimiztion o the cvity volume nd oriice dimenion o two beline ynthetic jet, ech with given piezoelectric diphrgm, i conducted uing two dierent objective unction. One eek to improve the centerline output velocity over brod requency rnge, nd the other mximize the centerline velocity t precribed reonnt requency o the device. Signiicnt improvement re chieved uing both objective unction or both ynthetic jet. Second, the two beline piezoelectric diphrgm hve been optimized uing two conigurtion. One ue the tndrd inner-dic piezocermic ptch bonded to metl him, while the other employ n outer piezocermic ring. In ech ce, the objective i to mximize the chievble volume diplcement o the diphrgm t the coercive electric ield trength o the piezocermic, while the nturl requency o the piezoelectric diphrgm i contrined to be greter thn or equl to the beline deign. Both conigurtion yield modet (~5%) improvement or one diphrgm nd igniicnt improvement or the other diphrgm (>5%). Nomenclture oriice rdiu (mm) c ir peed o ound (m/) C C cvity coutic complince = V (. m 4 /kg) ρ c Grdute Student, Student Member AIAA. Grdute Student. Pot Doctorl Reerch Aocite, Member AIAA. Aitnt Proeor, Member AIAA. Aitnt Proeor, Aocite Fellow, AIAA. Copyright 3 by the Univerity o Florid. Publihed by the Americn Intitute o Aeronutic nd Atronutic, Inc. with permiion. C diphrgm hort-circuit coutic complince = V P V c = (. m 4 /kg) C EF piezocermic electricl ree cpcitnce (F) d eective coutic piezoelectric coeicient = VV c (m 3 /V) P= E mx mximum electric ield (V /m) requency (Hz) H D Helmholtz requency π M + M C (Hz) N Rd C = ( ) hort-circuit diphrgm reonnt requency = π M CC (Hz), ynthetic jet lowet nd highet reonnt requencie, repectively (Hz) K D nondimenionl oriice jet dump lo coeicient L oriice length (mm) M diphrgm coutic m (kg/m 4 ) R π V = ρ ( ) A wr rdr M N oriice coutic m (kg/m 4 ) = 4ρL 3π or Poieuille low M Rd oriice coutic rdition m = 8ρ 3π (kg/m 4 ) P dierentil preure on the diphrgm (N/m ) q electric chrge tored on the piezoelectric (C) Q c volume low rte through the cvity (m 3 /) Q out volume low rte through the oriice (m 3 /) Q volume low rte diplced by the diphrgm = Q c + Q out (m 3 /) R diphrgm coutic reitnce = ζ M C (kg/. m 4 ) R N vicou oriice coutic reitnce (kg/. m 4 ) 4 = 8νρL π or Poieuille low R O nonliner oriice coutic reitnce 4 =.5K D ρq out π (kg/. m 4 ) piezocermic rdiu (mm) R

4 R t p t u c him rdiu (mm) Lplce vrible = jω piezocermic thickne (mm) him thickne (mm) centerline oriice velocity (m/) V input c voltge (V) V mximum pplied voltge = t E (V) p mx c,mx V cvity volume (mm 3 ) w( r ) trnvere diplcement o the diphrgm (m) V volume diplced by the diphrgm φ R π rw r dr (m 3 ) electrocoutic turn rtio o the piezocermic = ( ) diphrgm = d C (P/ V) ν ir kinemtic vicoity (m /) ρ A re denity (kg/m ) ρ ir denity (kg/m 3 ) ω rdin requency = π (rd/) ζ empiricl diphrgm dmping coeicient Introduction Synthetic or zero-net m lux jet re commonly ued low-control ctutor in wide pectrum o ppliction including jet vectoring, eprtion control, 3,4 nd boundry lyer control. 5,6 The perormnce peciiction o ny ctutor re quntiied in term o n exhutive lit o prmeter uch bndwidth, control uthority, etc. Flowcontrol ppliction require known ctutor requency repone unction tht relte the input voltge to the output property o interet (e.g., mximum velocity, volumetric low rte, momentum lux, etc.). Clerly, the required perormnce metric re ppliction peciic, nd method re needed to chieve the optiml deign o thee device. Deign nd optimiztion tudie hve been conducted or piezoelectric cntilever-type low control ctutor, but the modeling iue re impler compred to ynthetic jet. 7 Speciiclly, the cvity nd oriice conigurtion o ynthetic jet igniicntly complicte the overll ytem dynmic. Recently, LEM h been combined with equivlent circuit repreenttion to etimte the nonliner dynmic repone o ynthetic jet unction o device dimenion nd mteril propertie. 8,9 Thee model hve provided good greement between predicted nd meured requency repone unction nd thu re uitble or ue deign tool. The purpoe o thi pper i to leverge LEM in the optimiztion o piezoelectric-driven ynthetic jet ctutor. The ollowing ection briely review the lumped element model nd correponding equivlent circuit o ynthetic jet rom Gll et l. 8 nd dicue the bic dynmic behvior. The reulting ytem model i then employed in n optimiztion cheme. For the current tudy, the optimiztion problem i decoupled into two prt. Firt, the piezoelectric diphrgm i ixed while the cvity volume nd oriice dimenion re vried. Second, the piezoelectric diphrgm i optimized while the other deign prmeter re ixed. Dicuion on the choen cot unction nd ccompnying contrint employed in the optimiztion nd the correponding reult re preented. Thi pper i concluded with dicuion o the reult nd uture work. Deign Problem nd Anlyi In thi ection, the lumped element model o piezoelectric-driven ynthetic jet i reviewed nd the bic dynmic behvior dicued. Lumped Element Model At low requencie, where the chrcteritic length cle o the governing phyicl phenomen re much lrger thn the lrget geometric dimenion, the governing prtil dierentil eqution o the dynmic ytem cn be lumped into et o coupled ordinry dierentil eqution. The reulting lumped-prmeter ytem cn then be repreented n equivlent electricl circuit poeing idelized dicrete circuit element nd conjugte power vrible or the equivlent voltge nd current. Thi pproch provide imple method to etimte the non-liner dynmic repone o ynthetic jet ctutor or deign nd optimiztion purpoe. A cro-ectionl chemtic nd correponding equivlent circuit repreenttion or typicl piezoelectric-driven ynthetic jet re hown in Figure. The detil o the circuit prmeter etimtion technique, umption, nd limittion re given by Gll et l. 8 The tructure o the equivlent circuit i explined ollow. A hrmonic voltge V c i pplied cro the piezocermic to crete n eective coutic preure tht drive the diphrgm into motion. Thi repreent converion rom electricl energy to coutic energy nd i repreented by n idel trnormer poeing turn rtioφ. The motion o the diphrgm (i.e., volume velocity, Q ) cn tore potentil energy vi compreibility eect in the cvity ( Q c ) nd/or cn tore kinetic energy vi ocilltory low through the oriice ( Q out ). Phyiclly, thi i repreented volume velocity divider, Q = Qc + Qout.

5 There re everl impliying umption employed in the current model. Firt, the ynthetic jet i umed to exhut into emi-ininite quiecent ir medium. In prctice, thee device interct with boundry lyer tht gretly lter the jet-exit velocity proile nd thu the totl oriice impednce. The correponding dierence in the requency repone unction o ynthetic jet ctutor exhuting into quiecent medium veru one exhuting into boundry lyer men tht the bench-top clibrtion o thee device i inuicient to ccurtely etimte the volume velocity or momentum lux exhuted into cro low or given excittion voltge. Second, compreibility eect in the oriice, but not in the cvity, re neglected. The incorportion o thee eect into the lumped element model i n ongoing reerch re both in the low control ctutor community well the engine ncelle coutic liner community. 3 Equivlent Circuit Model Beore conducting orml optimiztion, the bic dynmic eture o the ytem re reviewed. The requency repone unction o the volume low rte through the oriice per pplied voltge or the equivlent circuit hown in Figure i our-pole, ingle-zero dynmic ytem, 8 where 3 4 c ( ) = 4 3 ( ) Qout d V , {} 4 3 ( ) ( ), ( ) ( ) ( ) M ( RO + RN ), nd + ( MRd + MN ) R ( ). = C RO + RN + R + CC RO + RN = C MRd + MN + M + C M + M + C C R R + R C Rd N C O N = C C C = C C M M + M C Rd N, {} To irt order, the coeicient in Eq. {} re contnt determined vi imple lgebric expreion unction o geometry nd mteril propertie. Thi model include one empiricl contnt, R, tht repreent the tructurl dmping o the piezoelectric compoite. In generl, ome o the coeicient exhibit requency nd mplitude dependence (i.e., due to nonliner eect). Speciiclly, R i non-liner oriice reitnce O tht i proportionl to the volume velocity, Qout ( ). For dc voltge ( = ), the volume velocity i zero. At low requencie ( ), the volume velocity i proportionl to jω dv c. At high requencie ( ), Qout d V C C M M + M, {3} ( ) 3 c C N Rd nd the output ttenute t 6 db/decde. The our-pole ytem in Eq. {} poee two reonnt requencie, nd >, tht re relted to the hort-circuit piezoelectric diphrgm nturl requency D, D =, {4} π M C nd the Helmholtz reontor requency H, H by the equlity = π M M C ( + ) N Rd C, {5} = D H. {6} From Eq. {6}, it i obviou tht the cvity volume nd the oriice dimenion, well the piezoelectric-diphrgm chrcteritic determine the dynmic repone o the ynthetic jet. Model Veriiction Gll et l. 8 hve experimentlly vlidted the lumped element model or two dierent prototypicl ynthetic jet ctutor uing phe-locked Ler- Doppler Velocimetry. For illutrtion purpoe, thee reult re briely reviewed. The dimenion nd propertie o the device re given in Tble nd Tble. The mplitude o the piezoelectric excittion voltge w 5 V in ll ce. The comprion between the ull nonliner model prediction nd the experiment re hown in Figure nd Figure 3. In both igure, the centerline velocity mgnitude i plotted unction o requency. For the lumped element model prediction, the centerline velocity w etimted by modeling the low in the oriice low in circulr duct driven by n ocilltory preure grdient. The irt ce (I, Figure ) clerly illutrte the two reonnt requencie o the coupled ocilltor. The econd ce (II, Figure 3) correpond to ytem poeing ingle dominnt pek. The lower pek t 35 Hz i hevily dmped in thi ce due to the requency dependent nonliner oriice reitnce term R O. In both ce, there i uicient greement between prediction nd experiment to jutiy the employment o LEM deign nd optimiztion tool. It i importnt to note 3

6 tht the underlying umption ued to derive ech lumped element limit the pplicble requency rnge o the correponding element rom dc to ome upper limiting requency (ee, or exmple, Roi ). Tble : Piezocermic diphrgm detil. Ce Shim (Br) I II Eltic Modulu (P) Poion Rtio.34 Denity (kg/m 3 ) 87 Thickne (mm).. Dimeter (mm) Piezocermic (PZT-5A) Eltic Modulu (P) 6.3 Poion Rtio.33 Denity (kg/m 3 ) 77 Thickne (mm).. Dimeter (mm). 5. Rel. Dielectric Contnt 75 d (m/v) C (F) EF Tble : Synthetic jet detil. Ce Cvity: I II Volume V (m 3 ) Oriice: Rdiu (mm).85.4 Length L (mm) Optimiztion o Synthetic Jet The lumped element model preented in the previou ection i powerul deign tool tht enble the multi-energy domin dynmic modeling o ynthetic jet ctutor. In thi ection, the model i ued vehicle to enble optimiztion. For implicity nd phyicl inight, the optimiztion problem i decoupled into two prt. Firt, the piezoelectric diphrgm i held contnt, nd the cvity volume nd oriice dimenion re vried. Two dierent cot-unction nd et o contrint re explored or thi problem. Next, the piezoelectric diphrgm i optimized nd vriou concept or the driver conigurtion re preented long with their ocited reult. In ll ce, the optimiztion problem w olved vi MATLAB optimiztion toolbox. Oriice/Cvity Optimiztion For given piezoelectric compoite diphrgm, the device behvior i governed by the cvity volume V, the oriice rdiu, nd oriice length L. For exmple, Figure 4-Figure 6 illutrte the eect o vrying V,, nd L on the centerline velocity output o the nominl ynthetic jet ctutor hown in Figure (Ce I). Increing the cvity volume reult in lrger coutic complince, C C, nd thu lower irt reonnce, V, nd lo decree the overll brodbnd mplitude, while lightly reducing the econd reonnt requency reltive to the nominl ce (Figure 4). Increing the oriice rdiu decree totl coutic m, MN + MRd, reulting in higher irt reonnce nd correpondingly higher econd reonnce (Figure 5). Converely, increing the oriice length incree the totl coutic m, MN + MRd, nd thu reduce the irt reonnce, much in the me mnner vrying the cvity volume (Figure 6). It i cler tht vrying thee three geometric vrible cn igniicntly ect the requency repone unction. Dierent low control ppliction will require dierent requency repone peciiction in term o bndwidth nd the output phyicl quntity o interet. For exmple, certin ppliction my require igniicnt ctution uthority in term o momentum lux over nrrow requency rnge, while nother my require lt, brodbnd repone poeing precribed minimum centerline velocity. Thi emphize the importnce o clerly peciying deign objective. In ddition to chooing deign objective, the optimiztion problem require the peciiction o vriou contrint. Thee contrint cn be brodly cliied into three ctegorie: perormnce contrint, deign vrible contrint, nd model contrint. Perormnce contrint my conit o peciying the deired loction o the reonnt requencie, the ltne tolernce o the gin ctor o the requency repone unction, etc. Deign vrible contrint my be needed due to phyicl limittion bed on mnucturbility, pckging conidertion, mteril ilure, etc. A tted t the end o the previou ection, there re limit to the pplicbility o ech lumped element unction o requency. Thereore, ter n optiml olution i chieved, the vlidity o the umption in the model mut be evluted, or the optimiztion problem mut be contrined by the limittion o the model. The ltter pproch w choen or thi tudy. For exmple, the lumped element or the piezoelectric compoite re limited to requencie below the econd nturl requency o the compoite diphrgm. The ize o the cvity i limited uch tht the impednce o the cvity cn be pproximted by complince. 8 Another limittion pper or the oriice pect rtio, L. Bed on experimentl reult or everl ce, Gll 9 ound tht 4

7 reonble greement w chieved between the lumped element model nd meured dynmic repone when the oriice pect rtio pproximtely exceeded unity. For the preent optimiztion tudy, the gol i to improve the perormnce o the nominl deign preented in Figure (Ce I) nd Figure 3 (Ce II). The objective unction, contrint, nd deign vrible re ummrized in Tble 3. Speciiclly, Ce I i optimized uing one cot unction, while Ce II i optimized uing two dierent cot unction. The irt cot unction employed mximize the integrted centerline velocity over the entire lim requency rnge, u ( ) d where the upper limit o integrtion i 3 Hz nd 5 Hz or Ce I nd II, repectively. The motivtion or uch n objective unction i to incree the brodbnd repone o the ctutor. The contrint on the oriice rdiu re motivted by device mnucturbility nd low perturbtion concern, while the minimum oriice length contrint i driven by the requirement tht the oriice plte be rigid. The volume rnge i dictted by ize limittion. In ddition, contrint re impoed on the oriice pect rtio nd by ixing the piezoelectric drive voltge. Figure 7 how the reulting optimized requency repone unction compred to the nominl repone or Ce I. The requency repone unction increed over the entire requency rnge by decreing V,, nd L. In ddition, the irt reonnt pek i hevily dmped in the optimized repone. The reult uing imilr pproch or Ce II re hown in Figure 8. Agin, the requency repone unction increed over nerly the entire requency rnge by decreing V,, nd L. In ddition, the lt portion o the repone unction i increed nd the econd reonnt pek i moved to higher requency. Thi ctutor deign i ueul or ppliction tht require lt brodbnd repone. The econd cot unction employed mximize the centerline velocity t the econd reonnt requency o the ytem, u ( ). From prcticl tndpoint, thi optimiztion i ueul or ppliction requiring high ctution uthority over nrrow requency rnge. The contrint on the oriice nd cvity geometry, well the pect rtio nd drive voltge re imilr to thoe outlined bove. A new equlity contrint, however, i plced on the loction o the econd reonnt requency. The reult o thi optimiztion or Ce II re hown in Figure 9. The econd reonnt pek i increed deired (by ~ 35%). In ddition, the brodbnd repone, epecilly t the lower requencie, i increed with repect to the nominl ce. While the optimiztion tudie in thi ection indicte the promie o improved perormnce, dditionl gin cn likely be chieved by optimizing the piezoelectric compoite diphrgm. Thi i decribed in the next ection. Tble 3: Summry o optimiztion problem or ynthetic jet ctutor. Objective Contrint Vrible lim Upper/Lower bound on u ( ) d vrible: L Ce I: V.5.5 L 5 V 47, 64 Ce II:.5.38 L 78 V, 7 Oriice pect rtio L Fixed input voltge V = 5 V c u( ) Upper/Lower bound on vrible: Ce II:.5.38 L 78 V, 7 Nturl requency = 8 Hz Oriice pect rtio L Fixed input voltge V = 5 V c Piezoelectric Compoite Optimiztion For given cvity/oriice conigurtion, the repone o the ynthetic jet i directly proportionl to the eective coutic piezoelectric coeicient, d, hown in Eq. {}. The repone i lo governed by the nturl requency o the diphrgm, D, which i unction o the coutic m,, nd hort-circuit coutic complince, C L V M, o the piezoelectric diphrgm. Thee lumped element re ll dictted by the geometry nd mteril propertie o the diphrgm. Beore conducting orml optimiztion o the piezoelectric compoite diphrgm, the bic modeling concept re reviewed. Top-view nd cro-ectionl chemtic o two xiymmetric piezoelectric compoite plte conigurtion exmined in thi tudy re hown in Figure -Figure 3. The irt type (Figure nd Figure ) conit 5

8 o n inner circulr dic, poeing piezocermic mteril o thickne t p nd rdiu R bonded to him mteril o rdiu R nd thickne t. The econd type (Figure nd Figure 3) conit o n nnulr ring poeing piezocermic mteril o rdil extent R R bonded to him mteril o rdiu R. In generl, the ctutor i ubjected to n pplied voltge V c cro the piezocermic thickne. Thi loding crete both trnvere wr ( ) nd rdil ur ( ) diplcement. Idelly, piezoelectric ctutor i liner, conervtive, reciprocl trnducer. The piezoelectric compoite deorm in repone to both n pplied c voltge nd dierentil preure. The lumped piezoelectric coupling eqution or the trnduction model re 4 V C d P =, {7} q d C EF V c where V i the volume diplced by the plte due to the ppliction o dierentil preure P nd/or voltge V c, q i the chrge tored on the piezoelectric electrode, C EF i the electricl ree cpcitnce o the piezoelectric mteril, C i the hort-circuit coutic complince o the plte, nd d i the eective coutic piezoelectric coeicient. The coutic m M i determined by equting the lumped kinetic energy o the vibrting diphrgm expreed in coutic conjugte power vrible to the totl kinetic energy. The determintion o the lumped element prmeter or thi two-port model require the olution o the trnvere ttic delection ield unction o preure nd voltge loding. For thi tudy, liner lminted plte theory i ued to olve or the trnvere ttic delection, nd n optimiztion cheme i then implemented uing thi two-port model. The detil o the compoite plte model re preented in Prd et l. 4 The mteril propertie re E, ν, E p, nd ν p, where the ubcript nd p denote the him nd piezoelectric, repectively, while E, ν, nd d 3 re the eltic modulu, Poion rtio, nd piezoelectric contnt, repectively. In thi tudy, the mteril propertie re contnt nd re lited in Tble. The optimiztion objective unction mximize the chievble diplced volume per pplied voltge, d = V V P= c,mx, compred to the nominl vlue or Ce I nd II. The motivtion behind thi objective unction i tht the trength o piezoelectric-driven ynthetic jet i directly proportionl to thi quntity. Note tht V i the c,mx mximum voltge tht cn be pplied to the piezoelectric without depolriztion nd i etimted ( ) Vc,mx = tp E mx tp 3 V mil, {8} where E mx i the coercive electric ield pplied through the thickne t p o the piezocermic. Next, contrint re deined. Reonble lower nd upper bound re deined or the geometric vrible t, t p nd R, while R i ixed in thi tudy. The reonnt requency o the compoite diphrgm ply n importnt role in the deign proce. Without contrint, the optimiztion reult in very complint diphrgm tht cn chieve lrge volume diplcement but h low nturl requency. Since bndwidth i oten n importnt quntity, lower bound i plced on the reonnt requency o the diphrgm. The gol here i to improve the perormnce o the diphrgm compred to the exiting deign in Tble. Thu, the undmentl requencie o the nominl deign ued in Ce I nd II re choen the lower bound. Optimiztion o both the inner-dic nd outerring conigurtion were thu perormed or Ce I nd II uing the MATLAB optimiztion toolbox. The reult re ummrized in Tble 4 or the innerdic conigurtion. The optimum deign lightly improve (by ~6%) the volume diplcement chieved or the nominl Ce I, while 5% improvement i chieved compre to the nominl Ce II. It hould be noted tht the lower requency bound on D i lwy ctive in the optimized deign, indicting tht direct comprion o d between the originl nd optimized deign i jutiied. Tble 4: Optimiztion reult o piezoelectric diphrgm with n inner-dic conigurtion. I II Originl Optimum Originl Optimum R (mm) R (mm) t (mm) t (mm) p D (Hz) d (x - ) (m 3 /V) The optimiztion reult re ummrized in Tble 5 or the outer-ring conigurtion. The 6

9 perormnce improvement i 3% nd 46% compred to the nominl Ce I nd II deign, repectively. The perormnce improvement i le thn the innerdic conigurtion. However, the outer-ring conigurtion i le pt to led wire ilure thn the inner-dic ce due to the reduced motion ner the clmp (ee Figure 3). Tble 5: Optimiztion reult o piezoelectric diphrgm with n outer-ring conigurtion. I II R (mm) R (mm) 7..9 t (mm).3.95 t (mm) p D (Hz) 4 63 d (x - ) (m 3 /V) Other conigurtion re poible nd will be tudied in uture work. For exmple, oppoitelypolrized inner- nd outer-ring cn be combined in both unimorph nd bimorph deign. Concluion nd Future Work The optimiztion o piezoelectric-driven ynthetic jet ctutor bed on LEM h been crried out. It h been hown tht LEM i vible tool to optimlly deign thee device or cndidte ppliction. To impliy the problem, the current tudy h plit the optimiztion problem into two prt by eprtely optimizing the () cvity volume nd oriice dimenion nd () the piezoelectric diphrgm. A contrined optimiztion o the cvity volume nd oriice dimenion o two beline ynthetic jet, ech with given piezoelectric diphrgm, h been conducted uing two dierent objective unction. One unction eek to improve the centerline output velocity, which i repreenttive meure o the device output, over brod requency rnge o interet. The other objective unction ocue on mximizing the centerline velocity t precribed reonnt requency o the device. Signiicnt improvement hve been chieved or ll ce. In ddition, two cndidte piezoelectric diphrgm conigurtion hve been optimized. One ue the tndrd inner-dic piezocermic ptch bonded to metl him, while the other ue n outer piezocermic ring. In ech ce, the objective i to mximize the chievble volume diplcement o the diphrgm, correponding to the coercive electric ield trength o the piezocermic. The nturl requency o the piezoelectric diphrgm w contrined to be greter thn or equl to tht o the beline deign. Both method yield modet (~5%) improvement or one diphrgm nd igniicnt improvement or the other diphrgm (>5%). The inner-dic conigurtion yield lightly better perormnce, but i likely to be more uceptible to led-wire brekge. In uture work, experiment will be conducted to conirm the optimiztion reult preented here. Other piezocermic diphrgm conigurtion will be tudied. In ddition, coupled contrined optimiztion will be crried out tht eek to optimize the device perormnce by imultneouly vrying the piezoelectric diphrgm dimenion, cvity volume, nd oriice dimenion. Alo, nother optimiztion problem o ynthetic jet will be invetigted. The current tudy i limited to improving n exiting beline deign. Perhp the more intereting ce i the optiml deign ynthei problem. In thi problem, the deigner eek to chieve deired requency repone unction. Due to the nonliner nture o the ytem, the deign objective cn be pproximted by liner trner unction tht i vlid t prticulr driving voltge. A key chllenge here i tht the end uer mut be ble to trnlte deirble ctutor chrcteritic into quntittive deign gol. Acknowledgment The uthor grteully cknowledge grnt upport rom NASA Lngley (monitored by S. Gorton) nd AFOSR (monitored by Dr. J. Schmieur). Reerence. Smith, B. L. nd Glezer, A., The Formtion nd Evolution o Synthetic Jet, Phyic o Fluid, Vol., No. 9, pp. 8-97, Smith, B.L. nd Glezer, A., Vectoring nd Smll-Scle Motion Eected in Free Sher Flow Uing Synthetic Jet Actutor, AIAA pper 97-3, Crook, A., Sdri, A. M., nd Wood, N. J., The Development nd Implementtion o Synthetic Jet or the Control o Seprted Flow, AIAA Pper , July Amity, M., Kiben, V., Prekh, D., nd Glezer, A., The Dynmic o Flow Rettchment Over Thick Airoil Controlled by Synthetic Jet Actutor, AIAA pper 99-, Rthninghm, R. nd Breuer, K. S., Coupled Fluid-Structurl Chrcteritic o Actutor or Flow Control, AIAA Journl, Vol. 35, No. 5, pp , My Lee, C.Y., nd Goldtein, D.B., DNS o Microjet or Turbulent Boundry Lyer Control, AIAA pper -3,. 7

10 7. Cttet, L., Grg, S., nd Shukl, D., Development o Piezoelectric Actutor or Active Flow Control, AIAA Journl, Vol. 39, No. 8, pp , Augut. 8. Gll, Q., Holmn, R., Nihid, T., Crroll, B., Sheplk, M., nd Cttet, L., Lumped Element Modeling o Piezoelectric-Driven Synthetic Jet Actutor, AIAA Journl, Vol. 4, No, Jnury Gll, Q., Lumped Element Modeling o Piezoelectric-Driven Synthetic Jet Actutor or Active Flow Control, M.S. Thei, Deprtment o Mechnicl nd Aeropce Engineering, Univerity o Florid, Gineville, FL,.. Roi, M., Acoutic nd Electrocoutic, Artech Houe, Norwood, MA, pp , Senturi, S. D., Microytem Deign, Kluwer Acdemic Publiher,.. Mittl, R., Rmpuggoon, P., Udykumr, H. S., Interction o Synthetic Jet with Flt Plte Boundry Lyer, AIAA Pper -773, June. 3. Motigner, R. E., nd Krt, R. E., Deign nd Perormnce o Duct Acoutic Tretment, in Aerocoutic o Flight Vehicle: Theory nd Prctice, Volume : Noie Control, edited by Hubbrd, H. H., Acouticl Society o Americ, New York, Prd, S., Horowitz, S., Gll, Q., Snkr, B., Cttet, L., nd Sheplk, M., Two-Port Electrocoutic Model o n Axiymmetric Piezoelectric Compoite Plte, AIAA Pper - 365, 43 rd AIAA/ASME/ASCE/AHS Structure, Structurl Dynmic, nd Mteril Conerence, April. V c electrocoutic coupling i :φ I I-i Q V c electricl domin C eb Cvity (V ) Oriice Piezocermic Compoite Diphrgm C P R L M Q c coutic/luidic domin R N C C M N R O Q out M Rd Figure : Schemtic repreenttion nd equivlent circuit model o piezoelectric-driven ynthetic jet. center velocity [m/] Exp. LEM Figure : Comprion between the lumped element model nd experiment or Ce I. 8 8

11 7 6 Exp. LEM 45 4 nominl ce + % oriice rdiu 6% oriice rdiu 35 center velocity [m/] Center velocity [m/] Figure 3: Comprion between the lumped element model nd experiment or Ce II nominl ce + % cvity volume 6% cvity volume Figure 6: Lumped element model prediction or vrying oriice length (Ce I) originl: =.85 mm, L=.65 mm, V =.5x 6 m 3 optimized: =.3 mm, L=.5 mm, V =.5x 6 m 3 Center velocity [m/] Center velocity [m/] Figure 4: Lumped element model prediction or vrying cvity volume (Ce I) nominl ce + % oriice length 6% oriice length Figure 7: Optimiztion o Ce I, mximizing the overll output. 6 4 originl: =.4 mm, L=.84 mm, V =5x 6 m 3 optimized: =.6 mm, L=.38 mm, V =.3x 6 m 3 Center velocity [m/] Center velocity [m/] Figure 5: Lumped element model prediction or vrying oriice rdiu (Ce I). 5 5 Figure 8: Optimiztion o Ce II, mximizing the overll output. 9

12 originl: =.4 mm, L=.84 mm, V =5x 6 m 3 optimized: =. mm, L=.38 mm, V =4.83x 6 m 3 9 Center velocity [m/] piezocermic him Figure : Top view o the outer-ring compoite piezoelectric diphrgm conigurtion. Figure 9: Optimiztion o Ce II, mximizing the econd pek. V c + - t p t R R him piezocermic Figure : Top view o the inner-dic piezoelectric compoite diphrgm conigurtion. Figure 3: Cro-ection o the outer-ring piezoelectric compoite diphrgm conigurtion. V c t p t R R Figure : Cro-ection o the inner-dic piezoelectric compoite diphrgm conigurtion.