Modeling of Dielectric Barrier Discharge Plasma Actuator with Atmospheric Air Chemistry

Transcription

1 37th AIAA Plasmadynamics and Lasrs Confrnc 5-8 Jun 6, San Francisco, California AIAA th AIAA Plasmadynamics and Lasrs Confrnc, 5-8 Jun 6, San Francisco, California Modling of Dilctric Barrir Discharg Plasma Actuator with Atmosphric Air Chmistry KP Singh *, Subrata Roy Datta V Gaitond Computational Plasma Dynamics Laboratory Mchanical Enginring, Kttring Univrsity Flint, MI 4854, USA Computational Scincs Branch Air Forc Rsarch Laboratory Wright Pat AFB, hio 45433, USA Surfac discharg in air has bn studid using chmistry of formation of diffrnt ion and nutral spcis of nitrogn and oxygn Continuity quations govrning dnsitis of lctrons, ions and nutral spcis of nitrogn and oxygn ar solvd with Poisson s quation to obtain spatial and tmporal profils of dnsitis, and voltag Rsults show that dnsity profils of chargd spcis ar narly opposit to ach othr about th lctrod st at positiv and ngativ paks of th cycl Dnsity profils of nitrogn atom N and oxygn atom ar similar to ach othr at th sam tmporal location in a cycl bcaus ths do not rspond to th lctric fild Also N and rspond to lctric fild in a similar mannr, hnc, thir dnsity profils ar similar to ach othr at sam tim instanc Thr is diffrnc in th lvl of ionization of diffrnt spcis du to diffrnc in rat cofficints Th motion of lctrons and ions in rspons to lctric fild rsults in charg sparation Th valu of sparatd spac charg shows footprints of lctron dposition downstram of th ovrlap rgion of th lctrods rsulting in formation of virtual ngativ lctrod Th lctrodynamic body forc pr unit volum has bn prdictd about th dilctric surfac for th twntith cycl A tim avragd forc, prdominantly downstram with a transvrs componnt towards th wall, acts on th plasma in forward dirction This rsults in a moving wav of plasma ovr dilctric surfac in th positiv x-dirction which can induc a control mchanism in th nighboring air flow Nomnclatur D Diffusion cofficint, cm /s xygn atom E Elctric fild, V/cm Positiv oxygn ion Elctron charg, statcoulomb - Ngativ oxygn ion ε Prmittivity, farad/m ω Applid frquncy, radians F Elctric forc dnsity, dyns/cm 3, µn/cm 3 P Prssur, Pa φ Potntial, V q Charg sparation, statcoulomb K Rat cofficints, cm 3 s -1 T Tim coordinat, s k B Boltzmann constant t Tmpratur, V L Elctrod lngth, cm V Vlocity, m/s λ D Elctron Dby lngth, cm X Spatial coordinat, cm M mass, kg µ Mobility, cm V -1 s -1 Subscript s: N Numbr dnsity, cm -3 α Spcis N Nitrogn molcul B Boltzmann N Nitrogn atom E Elctron, finit lmnt N Positiv nitrogn ion I Ion xygn molcul N Nutral * Post Doctoral Rsarch Associat of th CPDL, 17 Wst Third Avnu Associat Profssor of Mchanical Enginring, 17 Wst Third Avnu, and AIAA Associat Fllow Tchnical Ara Ladr, Air Vhicls Dirctorat/VAAC, 1 8 th St, and AIAA Associat Fllow 1 Amrican Institut of Aronautics and Astronautics Papr No Copyright 6 by By Authors Publishd by th Amrican Institut of Aronautics and Astronautics, Inc, with prmission

2 Rport Documntation Pag Form Approvd MB No Public rporting burdn for th collction of information is stimatd to avrag 1 hour pr rspons, including th tim for rviwing instructions, sarching xisting data sourcs, gathring and maintaining th data ndd, and complting and rviwing th collction of information Snd commnts rgarding this burdn stimat or any othr aspct of this collction of information, including suggstions for rducing this burdn, to Washington Hadquartrs Srvics, Dirctorat for Information prations and Rports, 115 Jffrson Davis Highway, Suit 14, Arlington VA -43 Rspondnts should b awar that notwithstanding any othr provision of law, no prson shall b subjct to a pnalty for failing to comply with a collction of information if it dos not display a currntly valid MB control numbr 1 REPRT DATE JUN 6 REPRT TYPE 3 DATES CVERED --6 to TITLE AND SUBTITLE Modling of Dilctric Barrir Discharg Plasma Actuator with Atmosphric Air Chmistry 5a CNTRACT NUMBER 5b GRANT NUMBER 5c PRGRAM ELEMENT NUMBER 6 AUTHR(S) 5d PRJECT NUMBER 5 TASK NUMBER 5f WRK UNIT NUMBER 7 PERFRMING RGANIZATIN NAME(S) AND ADDRESS(ES) Kttring Univrsity,Computational Plasma Dynamics Laboratory,Dpartmnt of Mchanical Enginring,Flint,MI, PERFRMING RGANIZATIN REPRT NUMBER 9 SPNSRING/MNITRING AGENCY NAME(S) AND ADDRESS(ES) 1 SPNSR/MNITR S ACRNYM(S) 1 DISTRIBUTIN/AVAILABILITY STATEMENT Approvd for public rlas; distribution unlimitd 13 SUPPLEMENTARY NTES 14 ABSTRACT 11 SPNSR/MNITR S REPRT NUMBER(S) 15 SUBJECT TERMS 16 SECURITY CLASSIFICATIN F: 17 LIMITATIN F ABSTRACT a REPRT unclassifid b ABSTRACT unclassifid c THIS PAGE unclassifid Sam as Rport (SAR) 18 NUMBER F PAGES 11 19a NAME F RESPNSIBLE PERSN Standard Form 98 (Rv 8-98) Prscribd by ANSI Std Z39-18

3 I Introduction LASMA actuators ar usful flow control dvics for various arodynamic applications Thy hav bn P dmonstratd for activ mitigation of prformanc dficincis undr off-dsign conditions 1-4 Ths actuators ar distinctiv for thir absnc of moving parts, rapid on-off dploymnt and attractiv slf-limiting charactristics Th intrst of this work is in dilctric barrir discharg (DBD) drivn plasma actuators oprating at atmosphric prssurs DBD is widly usd in applications for ozon production, surfac tching, dcontamination, plasma display panls, tc,3 Typically in an atmosphric DBD, a fw watts of powr is supplid by a 1-5 kilovolts rms with 5 Hz to 5 khz frquncis Th discharg is charactrizd as transint with a minut tim scal, svral ordrs of magnitud smallr than that for th bulk gas flow, thus allowing fast rspons of th fluid to th lctrical impuls Th plasma actuators typically oprat in air Whil succssful xprimnts 1-4 and simplifid numrical modling fforts 5-8 hav promptd a trmndous intrst in plasma actuators, basic first principls undrstanding for ths dvics ar yt to b xplord for air chmistry so that th oprational limits can b furthr allviatd Th applications of plasmas in hyprsonic flows for sustaind flight in low-prssur at uppr atmosphr and during atmosphric rntry ar known for physical complxity 9 Svr thrmal, chmical, and ionizational nonquilibrium conditions ar xprincd du to high vlocitis and high altituds during tranatmosphric missions Th xtrm nvironmntal conditions hav a major impact on th dsign and study of th vhicl arodynamics and thrmal loading Chmical kintic procsss in th plasma play an important rol in lctromagntic intrfrnc surrounding th craft Knowldg of chmical kintic procsss is crucial to mission plannrs Th computational study has to includ mass, momntum, and nrgy quations of th nutral spcis and charg particl spcis Th influnc of th charg particls on th flow fild nds to b includd and th lastic and inlastic collisional nrgy transfr mchanisms also nds to b takn into account for th high dgr of thrmal, chmical and ionizational nonquilibrium in th flow fild Th ractions includ momntum transfr, molcular ionization, xcitation, dissociation, dissociativ rcombination and scondary lctron mission 1 Th chmistry for ionizd air at atmosphric prssur is vn mor complicatd du th fastr spcis raction rats 1 Spcifically, barrir dischargs in air-lik N / mixturs consist of a multitud of micro and nanoscal dischargs Thortical modling of ths discharg procsss rquirs a tim-rsolution in th subnanoscond rang to dscrib disparat lctron and ion tim scals Also, small spatial dimnsions of barrir dischargs at ths prssurs rquir a spatial rsolution much finr than th submillimtr scal Thus, invstigation of th spatio-tmporal volution of such multiscal barrir discharg is quit a challnging but ncssary task to undrstand th govrning physics of discharg in air and in N / mixturs Barrir dischargs offr a good tchnical challng to proprly undrstand th flow and physical modls xygn and nitric oxid spcis in th air could significantly altr th discharg du to th prsnc of ngativ oxygn ions and nitric oxid spcis Th ngativ ions add momntum in th opposit dirction to th positiv ions and oxygn and nitric oxid hav diffrnt rcombination, dissociation, and xcitation bhavior In ordr to xplor th forc production diffrncs btwn nitrogn, oxygn and nitric oxid, computational study nds to b carrid out by including major spcis Th asymmtric surfac dilctric barrir discharg has bn usd in an xprimntal stup for airflow production clos to th dilctric surfac Effct of svral discharg paramtrs such as applid voltag wavform, distanc btwn lctrods, dilctric thicknss and prmittivity has bn xprimntally dtrmind for atmosphric prssurs Th tim-avragd flow vlocity spatial profils has found th wall jt vlocitis of up to 35 m/s at hights of 1 mm 4 In anothr ffort 11, th masurmnts of th instantanous flow vlocity inducd by surfac plasma actuators in air at atmosphric prssur hav bn conductd with two diffrnt typs of plasma actuators in ordr to dtrmin th stablishmnt tim of th inducd airflow A strong corrlation was found btwn th transint rgim of th discharg currnt and th ionic wind vlocity Th AC discharg was found to induc a pulsd airflow at a frquncy corrsponding to th high voltag wavform frquncy and th DC discharg airflow with important fluctuations 11 Th prformanc of plasma actuators has bn studid with wind tunnls, drag balancs, Pitot tubs, smok flow visualization, and fluid dynamic modling programs Th lctric powr transfrs th momntum to th nutral gas flow through ion-nutral collisions Th ffcts of actuator gomtry, matrials, th RF frquncy and RMS voltag hav bn studid both xprimntally 3 and numrically 1 Th first principls modling of th surfac DBD has bn rportd in rcnt litratur A two-dimnsional fluid modl of th surfac discharg showd th forc pr unit volum acting on th flow du to th momntum transfr from chargd particls to nutral molculs 13 Th forc in th DBD was found to b of th sam natur as th lctric wind in a corona discharg and localizd in th cathod shath rgion of th discharg xpanding along th dilctric surfac Th prsnt authors hav carrid out simulation study of th dilctric barrir plasma actuator 5 and its ffct on th mitigation of sparatd flows ovr flat plat 6,1 and NACA15 airfoil Thy hav shown that lctron dposition downstram of th ovrlap rgion of th lctrods rsults in formation of virtual ngativ lctrod Th forc du to th charg sparation is in th positiv stramwis dirction during most of th positiv part of th rf cycl and in ngativ-x dirction during most of th ngativ part of th cycl Th magnitud of th formr forc is highr that th lattr Thus, domain intgration of th forc on th charg sparation and tim avrag of th forc was found primarily Amrican Institut of Aronautics and Astronautics Papr No

4 to b in th positiv-x and ngativ-y dirction In this papr, w study atmosphric air discharg using a mixtur of oxygn and nitrogn about an asymmtric dilctric barrir plasma actuator W solv th quations govrning dynamics of lctrons, ions and nutral nitrogn and oxygn spcis to obtain spatio-tmporal profils of lctron dnsity, ion dnsity, lctric potntial, and nutral gas dnsity W idntify rasons for diffrnc in profils of diffrnt spcis Th valu of sparatd spac charg and lctrodynamic body forc pr unit volum has also bn obtaind for th twntith rf cycl This papr is organizd as follows Sction II dscribs th problm statmnt along with th air chmistry Sction III prsnts th computational rsults and rlvant discussion Sction IV highlights th conclusions II Problm Statmnt Fig 1 shows schmatic of an asymmtric singl dilctric barrir plasma actuator It consists of two lctrods sparatd by a dilctric Th uppr lctrod is xposd to th air whil th lowr lctrod is placd undrnath th dilctric Th rgion simulatd is 6 cm long and 4 cm high Th lowr part of th domain consists of a 1 cm thick insulator with dilctric constant ε d = aε whil th uppr part is filld with air of ε f =155ε, whr ε is prmittivity of th fr spac W hav takn a =35 for Kapton polyimid and ngligibl rf lctrod thicknss Th thicknss of th lctrods is assumd to b infinitsimally small Th lngth L of both th lctrods is mm Th rf lctrod xtnds from x=8 cm to x=3 cm at y=1 cm, th groundd lctrod is from 3 cm to 34 cm at y=, with a cm gap btwn lctrods along th x-axis Th mbddd lctrod is groundd and a sinusoidal voltag φ = φ sin(πft) is applid to th xposd lctrod Th frquncy of xcitation is fixd at f =5 khz and xcitation potntial is φ = 1 volt air φ (t) Dilctric E(t) Plasma To Ground FIG 1 Schmatic of asymmtric singl dilctric barrir plasma actuators oprating in air Th quations govrning chmistry of discharg ar as follows 1 Th mtastabl spcis along with N 4 and 4 ar nglctd du to thir fast rcombination rats Also, N is not includd to rduc th numrical complxity in th first principls modl at this stag (1) Nitrogn modl Ionization N N, (1) Dissociation N N, () (c) Dissociativ rcombination N N, (3) () xygn modl Ionization, (4) Dissociation, (5) (c) Dissociativ attachmnt, (6) (d) Rcombination (7) () Dissociativ rcombination, (8) Th drift-diffusion form of continuity and Poisson s quations for th lctrons, ions and nutrals ar as follows: n ( nv ) = k1 nnn k 3nn ( k5 k7) n N n k9nn, (9) t 3 Amrican Institut of Aronautics and Astronautics Papr No

5 nn ( nn v N ) = knnn, t (1) nn ( nn v = N ) k 1nnN k nnn k 3nn N t (11) n N ( n v ) = k1nnn k N 3nn N N t (1) n ( n v = ) ( k 4 k5 k6 ) n n k7n n k 8nn t (13) n ( n v ) = (k5 k6 ) nn k 7n n t (14) n ( n v ) = k 6nn k 7n n t (15) n ( n v ) = k4nn k 7n n k 8nn t (16) ε φ = 4π( n n n n ), (17) n with momntum flux sgn ( ) n v = n µ φd n, and lctric fild E = φ α α α α α α Abov, k 1 k 8 ar various rat cofficints rlatd to Equations (1) through (8) obtaind from Kossyi t al 1 Elctron tmpratur apparing in ths rat cofficints is calculatd from E = k T / n / n, which is obtaind assuming initial Boltzmann distribution, n xp( φ / kbt) In Eqns (9)-(17) n α and v α ar dnsity and vlocitis of spcis α Th mobilitis µ α and diffusion rats Dα ar takn from Ellis t al 17 Th bulk dnsity of th air is takn to b gm/cm 3 Atmosphric ratio of 36 is takn for nitrogn to oxygn gas molculs Th slf-consistnt formulation is solvd using a Galrkin variational formulation basd finit-lmnt mthod 18 to obtain lctron, ion and nutral spcis dnsitis of nitrogn and oxygn, and th lctric potntial Initial and boundary conditions ar as follows Th all initial particl concntrations, xcpt thos of th lctrons, nitrogn and oxygn molculs, ar takn to b zro Initial lctron dnsity is takn 1 3 /cm 3 Initial rf potntial is also zro All nutral particl concntrations ar takn zro at th boundaris of th dilctric and normal componnts of flux ar zro at outr boundaris of plasma Normal componnts of lctric fild ar takn zro on all th outr boundaris of th domain (dilctric as wll as plasma domain) No lctron and ion currnt flow insid th dilctric is considrd Elctric fild normal to th dilctric surfac is discontinuous by th sparatd charg B III Rsults and Discussion As w switch on th rf voltag, discharg in th air occurs Diffrnt ion and nutral spcis ar formd through ionization, dissociation and dissociativ attachmnt tc Rcombination also occurs Full chmistry of diffrnt spcis formation and rcombination is dscribd by Equations (1) to (8) Figur shows lctron dnsity n as a function of normalizd timωt for =15 and y/ λ D = Stady stat is rachd within a fw cycls, thraftr; thr is a small loss in th dnsitis as dscribd in Figur a Initial lctron dnsity is takn 1 3 /cm 3 Th lctrons ar rplld from th ara of groundd lctrod and ar attractd towards rf lctrod during positiv part of th cycl Rvrs happns during ngativ part of th cycl, hnc, dnsity profils ar opposit of ach othr in Figur b-c in th contxt of location of lctrods Spatial and tmporal dnsity profil of lctrons is govrnd by continuity Equation (1) coupld with othr quations Elctron dnsity grows to a lvl 1 11 /cm 3 Elctrons rspond to lctric fild vry fast du to low mass and high mobility Thr is dposition of lctrons on th dilctric surfac ovr groundd lctrod during ngativ part of th cycl Dilctric surfac bhavs as a ngativ lctrod aftr ngativ pak of th rf voltag till th nd of th cycl 4 Amrican Institut of Aronautics and Astronautics Papr No

6 n / π 1π π 3π 4π ωt E11 16E11 938E1 817E1 696E1 5E1 455E1 334E1 13E1 9E (c) FIG Evolution of lctron dnsity n as a function of normalizd tim ωt for =15 and y/ λ D =, at positiv pak of th th cyclωt = 38 5π, and (c) at ngativ pak of th cycl ωt = 39 5π Initial dnsity of th nitrogn atoms was takn zro Th nitrogn atoms ar producd through dissociation Chmistry of nitrogn atom formation is givn by Equation () and its dnsity is govrnd by continuity Equation (1) coupld with othr quations Dnsity of nitrogn atoms grows to th sam lvl as that of lctrons, i, 1 11 /cm 3 Figur 3 shows distribution of nitrogn atom dnsity at positiv and ngativ paks of th twntith cycl Sinc nitrogn atom do not hav any charg, no lctric forc works on ths atoms E11 111E11 97E1 83E1 69E1 551E1 411E1 7E1 13E1-14E E11 13E11 919E1 84E1 689E1 574E1 459E1 345E1 3E1 115E E11 15E11 931E1 815E1 699E1 58E1 466E1 349E1 33E1 116E1 FIG 3 Distribution of nitrogn atoms N at positiv pak of th cycl ωt = 38 5π, and at ngativ pak of th cyclωt = 39 5π 5 Amrican Institut of Aronautics and Astronautics Papr No

7 Initial dnsity of th nitrogn ions of nitrogn molculs Chmistry of nitrogn ions N was takn zro Th nitrogn ions N ar producd through ionization N formation is givn by Equation (1) and its dnsity is govrnd by continuity Equation (1) coupld with othr quations Dnsity of nitrogn ions N grows to th sam lvl as that of lctrons, i, 1 11 /cm 3 Figur 4 shows distribution of nitrogn ions dnsity n at positiv and ngativ paks of th N twntith cycl Th nitrogn ions N ar rplld from th ara of rf lctrod and ar attractd towards groundd lctrod during positiv part of th cycl Rvrs happns during ngativ part of th cycl, hnc, dnsity profils ar opposit of ach othr in Figur 4 Sinc positiv ions rspond to lctric fild in an opposit mannr, dnsity profils ar opposit to that of dnsity profil of lctrons in th contxt of location lctrods Th ions ar much havir than that of lctrons; mobility of ions is low, th ions rmain clos to th wall than lctrons E11 159E11 141E11 14E11 16E11 88E1 76E1 59E1 353E1 176E1 E FIG 4 Distribution of nitrogn ions N dnsity at positiv pak of th cyclωt = 38 5π, and at ngativ pak of th cyclωt = 39 5π Initial dnsity of th oxygn atoms was takn zro Th oxygn atoms ar producd through dissociation of oxygn molculs Chmistry of oxygn atoms formation is govrnd by Equation (5) and its dnsity is govrnd by continuity Equation (14) coupld with othr quations Figur 5 shows dnsity profil of oxygn atom at positiv pak of th cycl ωt = 38 5π, and at ngativ pak of th cyclωt = 39 5π Dnsity of oxygn atoms is highr than that of nitrogn atoms du to diffrnc in rat cofficints rlatd to formation of nitrogn and oxygn atoms Dnsity profils of both nitrogn and oxygn atoms ar similar bcaus both ar nutral atoms and do not rspond to lctric fild E11 18E11 16E11 14E11 1E11 1E11 8E1 61E1 41E E11 418E11 371E11 3E11 79E11 3E11 186E11 139E11 98E1 464E E11 4E11 373E11 37E11 8E11 33E11 187E11 14E11 934E1 467E1 FIG 5 Distribution of oxygn atom dnsity at positiv pak of th cyclωt = 38 5π, and at ngativ pak of th cyclωt = 39 5π 6 Amrican Institut of Aronautics and Astronautics Papr No

8 Initial dnsity of th oxygn ions was takn zro Th oxygn ions ar producd through dissociativ attachmnt of oxygn molculs with lctrons govrnd by Equation (6) Its dnsity is govrnd by continuity Equation (15) coupld with othr quations Dnsity of oxygn ions grows to a lvl of slightly lss than that of dnsity of nitrogn ions N Figur 6 shows distribution of dnsity of oxygn ions at positiv and ngativ paks of th twntith cycl Th oxygn ions ar rplld from th ara of groundd lctrod and ar attractd towards rf lctrod during positiv part of th cycl Rvrs happns during ngativ part of th cycl, hnc, dnsity profils ar opposit of ach othr in Figur 6 Th oxygn ions ar much havir than that of lctrons and mobility is low; rspons is dlayd Th ions rmain clos to th wall than lctrons E1 496E1 441E1 386E1 33E1 E1 E1 165E1 11E1 551E E1 495E1 44E1 385E1 33E1 E1 E1 165E1 11E1 55E9 FIG 6 Distribution of ngativ oxygn ion pak of th cyclωt = 39 5π at positiv pak of th cyclωt = 38 5π, and at ngativ Initial dnsity of th oxygn ions was takn zro Th oxygn ions ar producd through ionization of oxygn molculs Chmistry of oxygn ions formation is givn by Equation (4) and its dnsity is govrnd by continuity Equation (16) coupld with othr quations Dnsity of oxygn ions i /cm 3 Figur 7 shows distribution of oxygn ions dnsity twntith cycl Th N and grows to th sam lvl as that of at positiv and ngativ paks of th rspond to lctric fild in a similar mannr, hnc, thir dnsity profils ar similar to ach othr at sam tim instanc Th diffrnc btwn dnsity lvls of nitrogn and oxygn is bcaus of ratio of ths gass in atmosphric air E1 415E1 369E1 33E1 77E1 31E1 185E1 138E1 93E9 461E FIG 7 Distribution of positiv oxygn ion at positiv pak of th cycl ωt = 38 5π, and at ngativ pak of th cyclωt = 39 5π Amrican Institut of Aronautics and Astronautics Papr No E1 47E1 417E1 365E1 313E1 61E1 9E1 157E1 14E1 5E9

9 Chargd particls mov in rspons to th lctric fild as dscribd abov This giv ris to charg sparation q = ( n n n n ) Dnsity profil of charg sparation is shown in Figur 8 It rsmbls that of N dnsity profils of positiv nitrogn and oxygn ions Lvl of charg sparation matchs dnsity of and lctrons bcaus dnsitis of othr charg spcis slf-gnratd lctric fild through Poisson s Equation N ions and is small in comparison Charg sparation givs ris to a E11 136E11 119E11 11E11 841E1 668E1 495E1 33E1 15E1-6E E11 158E11 138E11 117E11 97E1 767E1 564E1 361E1 158E1-45E9 FIG 8 Distribution of charg sparation q = ( n n n n ) at positiv pak of th cycl ωt = 38 5π, and at ngativ pak of th cyclωt = 39 5π N Figur 9 shows charg sparation q = ( n n n n ) along th surfac of dilctric at y / λ N D = and y / λ D =4 Charg sparation is highst in th ara of lctrods whr discharg activity occurs Charg sparation is highst at voltag paks of th cycl bcaus of high lctric fild Low lctric fild is associatd with ωt = 39π and 4π for y / λd =4, hnc, charg sparation is low at ths points W can also s that pak of charg sparation movs towards highr valu of y / λd at positiv pak of th cycl A small ngativ charg dposition is also noticd Ths solutions ar basic and nds to incorporat th ffct of nitrous oxid and mtastabl spcis q/ ωt= 385π 39π 395π 4π X/L q/ ωt= π 39π 395π 4π Figur 9 Charg sparation q as a function of normalizd distanc for ωt = 38 5π, 39 π, 395π and 4 π at y / λd = and y / λd =4 Elctric fild E xrts a forc X/L F = ( n n n n ) E on th charg sparation Figur 1 shows vctors N of forc distribution in th domain at positiv and ngativ paks of th twntith cycl Th forc is dirctd towards positiv-x dirction at positiv pak of th cycl and towards ngativ-x dirction at ngativ pak of th cycl It is also dirctd towards wall at both th points of th cycl Th forc follows dirction of th lctric fild 8 Amrican Institut of Aronautics and Astronautics Papr No

10 FIG 1 Vctors of forc in th domain at positiv pak of th cycl ωt = 38 5π, and at ngativ pak of th cyclωt = 39 5π Figur 11 shows tim avrag of th forc during twntith cycl Th tim avrag of th forc is mostly dirctd towards ngativ y-dirction with orintation towards positiv x dirction Th forc lins ar concntratd ovr th xposd and groundd lctrods Th lctrons rspond to th lctric fild vry quickly du to high mobility Th lctrons gt dpositd at th surfac of th dilctric abov groundd lctrod during ngativ part of th cycl and th dilctric surfac bcoms ngativly chargd It bhavs as virtual ngativ lctrod aftr ngativ pak of th cycl till th nd of cycl Th pak magnitud of th forc is locatd downstram of th rf lctrod FIG 11 Vctors of tim avrag of forc distribution in th domain during a full cycl x and y ar in cm Th x-componnt of th forc F x = qex is shown in Figur 1 along th surfac of dilctric at y / λd = and y / λ D =4 Magnitud of forc is larg at th paks of th cycl Most of th forc is concntratd in th rgion of lctrods Th forc is positiv at positiv pak of th cycl and ngativ at ngativ pak Th y-componnt of th forc is mostly ngativ as shown in Figur 13 W can s again that forc is highst at th paks of th cycl and concntratd in th rgion of lctrods At positiv pak of cycl, pak of th forc is at highr valu of Ths rsults can b xplaind by considring dirction and magnitud of th lctric fild Dirction of lctric fild is from rf lctrod to groundd lctrod at positiv pak of th cycl and vic vrsa Magnitud of lctric fild is highst at th paks of cycl Elctric fild dcrass with distanc from lctrods, hnc, forc also dcrass 5 9 Amrican Institut of Aronautics and Astronautics Papr No

11 F x / ωt= 385π 39π 395π 4π X/L F x / ωt= 385π 39π 395π 4π X/L Figur 1 x-componnt of th forc F x as a function of normalizd distanc for ωt = 38 5π, 39 π, 395π and 4 π at y / λd = and y / λd =4 5 1 F y / ωt= 385π 39π 395π 4π F y / ωt= 385π 39π 395π 4π X/L X/L Figur 13 y-componnt of th forc F y as a function of normalizd distanc for ωt = 38 5π, 39 π, 395π and 4 π at y / λd = and y / λd =4 IV Conclusions Air discharg has bn studid using an asymmtric dilctric barrir plasma actuator A slf-consistnt plasma actuator modl is mployd to study surfac discharg of air Chmistry of formation of diffrnt ion and nutral spcis of nitrogn and oxygn has bn takn into account Spcis with vry high rcombination rats and nitrous oxid hav bn nglctd for simplicity Continuity quations govrning dnsitis of lctrons, ions and nutral spcis of nitrogn and oxygn ar solvd with Poisson s quation using a two-dimnsional finit lmnt basd formulation of plasma to obtain spatial and tmporal profils of dnsitis, and voltag Poisson s quation govrns lctric fild gnratd du to charg sparation Computd rsults show that for this simplistic modl oppositly chargd spcis mov in opposit dirctions du to applid drivr rf potntial Rspons of lctrons to lctric fild is vry fast as compard to ions du to small mass and high mobility of lctrons Dnsity profils of diffrnt spcis ar narly opposit to ach othr at positiv and ngativ paks of th cycl Dnsity profils of nitrogn atom N and oxygn atom ar similar bcaus ths do not mov du to lctric fild Dnsity profils of N and ar similar to ach othr at any spcific tim instanc bcaus thy rspond to lctric fild in a similar mannr Thr is, howvr, diffrnc in lvl of ionization of diffrnt spcis du to diffrnc in rat cofficints Th motion of lctrons and ions rsults in charg sparation Elctron dposition downstram of th ovrlap rgion of th lctrods during ngativ part of th cycl rsults in formation of virtual ngativ lctrod Th valu of charg sparation q = ( n n n n ), and th lctrodynamic forc pr volum F = ( n n n n ) E hav bn obtaind nar th dilctric surfac for N twntith cycl Tim avrag of th x-forc is positiv and y-forc is ngativ ovr th domain, thrfor, thr is an 1 Amrican Institut of Aronautics and Astronautics Papr No N

12 avrag nt forc on th plasma in positiv x and ngativ-y dirction This will rsult in a moving wav of plasma ovr th dilctric surfac in positiv x-dirction which can find application in flow control A dtail air chmistry modl with Poisson-Navir-Stoks quations is also undr dvlopmnt for xploration of th ffct of a plasma actuator oprating in air using ralistic gomtry and lctrod configurations In this modl, an in-dpth study involving mor spcis lik N will b incorporatd to invstigat th ffct of surfac air discharg and its coupling with th nutral gas flow Acknowldgmnts Th work is partially supportd by Air Forc Rsarch Laboratory contracts and th AFSR grant with Tchnical Monitors Dr John Schmissur and Lt Col Rhtt Jffris Th authors acknowldg many thoughtful discussions about air chmistry with Mr Eswar Josyula Rfrncs 1 KW Van Trurn, t al J Turbomachinry 14, 1 () JP Bons, R Sondrgard and RB Rivir, J Turbomachinry 13, 198 (1) 3 J R Roth and X Dai, 6, AIAA J Pons, E Morau and G Touchard J Phys D: Appl Phys 38, S Roy, Appl Phys Ltt 86, 115 (); S Roy, KP Singh and D Gaitond, Appl Phys Ltt 88, 1151 (6) 6 KP Singh and S Roy, J Appl Phys 98, 8333 () 7 Y B Suzn, P G Huang, J D Jacob and D E Ashpis,, AIAA--4633, Jun 8 Gabril I Font and W Lowll Morgan,, AIAA--463, Jun 9 E Josyula and WF Baily, Journal of spaccrafts and Rockts, 4, 845 (3) 1 I A Kossyi, A Yu Kostinsky, AA Matvyv and VP Silakov, Plasma Sourcs Sci Tchol, 1, 7 (199) 11 M Fort, L Lgr, J Pons, E Morau and G Touchard J Elctrostatics 63, S Roy, KP Singh, H Kumar, DV Gaitond and MR Visbal, 6, AIAA-6-374, January 13 J P Bouf and L C Pitchford, J Appl Phys () 14 DV Gaitond, MR Visbal and Subrata Roy, AIAA--53, 36th AIAA Plasmadynamics and lasr cofranc, Jun, Toronto, Canada 15 M Visbal, D Gaitond, and S Roy, 6 AIAA-6-33, Jun 16 DV Gaitond, MR Visbal and S Roy, 6, FEDSM , ASME Joint US - Europan Fluids Enginring Summr Mting 17 HW Ellis, RY Pai, EW McDanil, EA Mason, and LA Vihland, Atomic Data Nucl Data Tabls, 17, 177, S Roy, t al, Phys Plasmas, 1, 78 (3); S Roy and D Gaitond, Phys Plasmas, 13, 353 (6) 11 Amrican Institut of Aronautics and Astronautics Papr No