Study on the Behavior of Droplet in Air-Water Separator

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1 Study on the Behvio of Doplet in Ai-Wte Septo Hideki Sugit*, Tkehi Nkzw*, Lu Jio-Long* 3, Xu To* *: Kobe Univeity, Fculty of Mitime Science, -- Fukeminmi, Highind,Kobe 8- JAPAN, E-mil Phone *: Wold Mitime Univeity, Chi of Mitime Technology, PO Box S- Mlmo, SWEDEN, E-mil Phone *3: Pe-Gdute School of Mitime Science nd Technology(Mte Coue), Kobe Univeity of Mecntile Mine. *: Gdute School of Science nd Technology(Docto Coue), Kobe Univeity. ABSTACT The i-wte epto in thi tudy i bed on the pinciple of the electottic pecipitto with the poitive nd negtive pole, which h been widely utilized to collect the dut contined in flue g exhuted fom the indutil plnt uch col fied powe ttion. Thi mechnim of eption i tht the Coulomb foce opeting between the both pole collect the wte doplet chged negtive ion by coon dichge on the ufce of poitive pole. The cylindicl epto by the Coulomb foce ued hee conit of tinle tube of 7.mm nd length of mm poitive pole, nd tinle wie of.mm negtive pole. The expeiment wee cied out t m/ without doplet nd.m/ with nd without doplet in men i velocity, nd t to 7,V in DC high voltge. And, the theoeticl nlye lo wee done uing the dt unde the me expeimentl condition. Conequently, the behvio of doplet flowing in the epto nd exiting between two electode i mde cle to detemine the bic eqution of motion fo doplet nd the ditibution of dielectic contnt. And, the theoeticl length to collect wholly in the epto by the Coulomb foce cn be etimted nd thi length gee with the length obtined by the expeiment.. Intoduction The i-wte eption technology emove fine doplet contined in tem flow to ue the tbility nd economic efficiency, i.e., the high qulity nd high efficiency of the powe ouce indipenble fo the moden ociety uch tem powe plnt. In thi tudy, in the i-wte epto hving the cylindicl collecting pole which i opeted by the Coulomb foce, the behvio of doplet w obeved expeimentlly, the theoeticl nlyi w pefomed bout the poce in which the fine doplet wee collected, nd theoeticl eqution on the tck of motion of doplet nd the geometicl dimenion of the epto wee obtined by uing viou type of influence fcto unde ctul opeting condition pmete to obtin bic dt fo the commeciliztion of the i-wte epto opeted by the Coulomb foce. Pinciple on Collection of Ai-Wte Septo Opeted by Coulomb Foce The pinciple on the eption of doplet collected by the electic field in the cylindicl tube co ection i hown in Fig.. When high DC voltge exceeding citicl vlue i pplied co the collecting pole nd the wie dichge pole, loclized dielectic bekdown occu, nd coon dichge i poduced to cue ionic tmophee. The negtive ion e jetted on the doplet, nd the doplet e pulled to the collecting pole ince they e chged nd eceive the Coulomb foce by the chge mount nd the field intenity ). dichge pole electic field collecting pole epted doplet chged doplet unchged doplet DC high voltge eth Fig. Mechnim of eption negtive ion poitive ion Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

2 3. Expeimentl wok The expeimentl pptu hown in Fig. i compoed of the i compeo, the boote pump, the egulto, the two-fluid tomizing nozzle, the tightening ection, the cylindicl i-wte epto, nd the meuement ection of the PDPA device (phe Dopple pticle nlyze). Fit the i peuized by the i compeo i combined with the wte peuized by the boote pump to fom fine doplet, nd they e pyed fom the two-fluid tomizing nozzle of.9 x -3 m in dimete. The py flow, i tightened while ping the hoizontl duct, pe the wie meh demite intlled to emove the doplet of lge pticle ize befoehnd, nd ente the cylindicl i-wte epto. The doplet in the py flow e collected in the epto bed on the pinciple mentioned befoe. Alo, the i leving the i-wte epto nd the doplet not collected e dichged though the meuement ection. The vege i flow velocity in the duct w vied by the fn intlled in font of the two-fluid tomizing nozzle. The high DC upply unit ued in thi expeimentl pptu i obtined by ectifying powe upply with bidge ectifying cicuit which incopote high-peed, hevy inultion ectifying diode of AC V, Hz. The tnfome in the cicuit i opeted on V/3, V, nd the powe voltge cn be djuted within to V (coeponding mx. pplied voltge i 7, V). velocity mete peo DC upply unit fn egulto mmete dichge pole collecting pole dichge pole nozzle PDPA i-wte ep electic wte ytem i yt boote pump Fig. Expeimentl pptu Figue 3 how the tuctul dwing of the cylindicl i-wte epto. Figue how the eltion between the pplied voltge nd cuent nd the obeved eult of the collected tte obtined unde the condition when the doplet e not pyed t flow velocity of zeo nd m/ nd when the doplet e pyed t flow velocity of m/ by uing the i-wte epto of 7. x -3 m in inne dimete nd x -3 m in length. When the pplied voltge i inceed, up to point in the figue, cuent hdly flow co the electode unde ny condition nd, theefoe, coon dichge i not yet poduced. When the pplied voltge exceed point, unde two condition in which py i not pefomed, the cuent tt to flow co the electode, nd then incee lightly (ymbol nd in the figue). Thi i pobbly becue fine pticle uch dut floting in the cylindicl tube e chged. Since the numbe of uch fine pticle i extemely le, the cuent vlue poduced i lo loweed. On the othe hnd, when doplet e pyed, up to point, lmot ll doplet p though the cylindicl tube without moving in the dil diection. Accodingly, the cuent will not flow. When the pplied voltge exceed point, coon dichge occu, nd the doplet e pulled to the collecting pole by the tong Coulomb foce. By the movement of lge numbe of chged doplet, the cuent i poduced co the electode (ymbol in the figue). A voltge coeponding to point i the citicl voltge. Between nd, the cuent vlue incee teeply the pplied voltge incee, i.e., the numbe of the doplet moving in the dil diection incee teeply. Between nd, the cuent i genelly kept contnt. Duing tht peiod, the movement Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

3 of the doplet in the dil diection i tbilized nd, even if the pplied voltge i inceed to 7, V mx., the numbe of the doplet collected i not chnged. Nmely, it men tht, beyond point, ll doplet included in the i flow e collected. x v = ; not pyed v = m/ ; pyed v =m/ ; not pyed pimy voltge(v) DC high voltge - flnge cylic tube cente pole wie denity ditibution of doplet S S cuent (A) 8 mit decee cle not collected tt of intbility of econdy voltge collected (incee) v = ; not pyed contnt v = m/ ; not pyed pplied voltge (v) iflow with doplet Fig.3 Stuctul dwing of epto Fig. eltion between pplied voltge nd cuent. Theoeticl Anlyi. Nomencltue :Appoch poition of doplet (m) E :Actul field intenity (N/C) E c :Field intenity occuing in citicl tte (N/C) E :Mximum vlue of field intenity in cylindicl tube co ection (N/C) mx E* :Field intenity in doplet-fee tte (N/C) E :Avege field intenity in doplet-fee tte (N/C) F :Coulomb foce (N) f :Fictionl foce between geou phe nd doplet (N) f = f f z f :Fictionl foce in dil diection of cylindicl tube (N) f z :Fictionl foce in flow diection of i flow (N) g :Gvittionl cceletion (m/ ) L :Theoeticl length of cylindicl tube (m) m :M of doplet (kg) q :Actul chge mount of doplet (C) q :Stuted chge mount of doplet (C) Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

4 :diu of cylindicl tube (m) :Ditnce in dil diection (m) :diu of cente electode wie (m) :diu of doplet (m) t :Motion time of the doplet in cylindicl tube () V :Applied voltge co electode (V) V c :Citicl voltge (V) ν :Avege velocity of the doplet in z-diection (m/) z :Ditnce in flow diection (m) : Actul eltive dielectic contnt in cylindicl tube co ection : Avege eltive dielectic contnt in cylindicl tube co :Dielectic contnt in vcuum : eltive dielectic contnt of pue wte vpo (, tm) : eltive dielectic contnt of dy i (, tm) : eltive dielectic contnt of wte (t tempetue of ) : Coefficient of vicoity (kg/(m )) : Denity of doplet (When expeimentl tempetue i T, i ppox. 98 kg/m 3 = ). Aumption () The field on the outide of the cylindicl tube doe not ffect the chge of doplet. () The denity of doplet i unifomly ditibuted t the inlet of the epto. (3) The vicou fictionl foce nd gvity cting between doplet nd i flow e vey mll comped with the Coulomb foce cting on the doplet nd, theefoe, cn be neglected. Fo exmple, fo the doplet hving n pplied voltge of 8, V, flow velocity of m/, nd dimete of 3 x - m, the toke vicoity eitnce foce i ppox. / of the Coulomb foce, nd cn be neglected. () The flow i ttiony nd, theefoe, colliion between the doplet cn be neglected. () The doplet collected to the inne wll of the cylindicl tube pemnently emin on the ufce. () The doplet dheed to the collecting pole do not ffect the chge tte..3 Citicl voltge, field intenity, chge mount, nd eltive dielectic contnt Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

5 ), 3) () Bic eqution of motion fo doplet A doplet floting in the i flow cue vicou fictionl foce between the doplet nd the i flow, i.e., toke vicoity eitnce ). The vecto diection of the fictionl foce e diectionlly oppoed to the moving diection of the doplet. Whee the flow diection of the i flow nd the fictionl foce of the cylindicl tube in the dil diection e f z nd f, epectively, thei epective cl eqution e follow. f = πµ z f = πµ dz dt d dt Then, the eqution of motion fo the doplet i follow. d z m = f mg = z dt (fo flow in z-diection t peed of ν ) d z m = F f dt (eultnt foce of Coulomb foce nd fictionl foce in dil - diection) Subtituting the eqution of f z nd f into the bove two eqution, bed on the umption (3) bove, the bic eqution of motion fo the doplet cn be expeed follow(fig. ). dz πµ = mg...() dt d m = F f dt = qe πµ qe...() d dt inne ufce of epto cente pole wie Fig Motion of doplet by Coulomb foce ) () Citicl voltge V c The condition in which coon dichge occu i follow. E mx > E c... (3) E c = 3. x V/m (fo i) Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

6 The citicl voltge Vc t which the coon dichge occu i follow. V c > V =E c ln( )... () ' (3) Field intenity The field intenity (in doplet-fee tte) E* in the cylindicl tube co ection i follow. V E* =... () ln ' The ctul field intenity E in the dielectic envionment i follow. E * V E = =... () ln ' () Chge mount of the doplet In genel, in conidetion of the chge time, the ctul chge mount q of doplet i conideed to be 7% of the tuted lod mount q ). Accodingly, q cn be expeed follow. q = 7. π 3 V ln... (7) ' () eltive dielectic contnt The eltive dielectic contnt in the cylindicl tube co ection i elted lgely to the denity ditibution of doplet. Though it meuement i genelly difficult, it i n impotnt fcto lgely ffecting the behvio of the doplet. Fo the theoeticl nlyi of the eltive dielectic contnt, thee type of the ditibution of eltive dielectic contnt in the cylindicl tube co ection wee umed, which e the pbolic ditibution, line ditibution, nd elliptic ditibution. The eon why the eltive dielectic contnt in the cylindicl tube co ection fom thee ditibution e follow. ) Accoding to the pinciple of eption in the cylindicl epto, doplet e moved dilly to the neet inne wll of the cylindicl tube by the Coulomb foce. ) The mgnitude of the Coulomb foce moving the doplet i detemined bed on the field intenity nd the chge mount of the doplet, i.e., on the pplied voltge nd the poition of the doplet. 3) The numbe of the doplet ne the cente electode wie i few, nd to the conty, ne the inne wll of the cylindicl tube. Alo, the numbe of the doplet, i.e., the denity of the doplet i genelly popotionl to the eltive dielectic contnt. Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

7 ) The doplet ne the cente electode wie eceive the Coulomb foce nd pidly pulled to the inne wll of the cylindicl tube. A eult, the eltive dielectic contnt i bought into doplet-fee tte vlue. On the othe hnd, the doplet e collected contntly ne the inne wll of the cylindicl tube, thin wte lye i fomed, nd the eltive dielectic contnt i bought into n only wte tte vlue. The ditibution of thee eltive dielectic contnt e hown in Fig.. Ech ditibution cn lo be expeed by Eq. (8), (9), nd (). eltive dielectic contct dichge pole line ditibution pbolic ditibution elliptic ditibution collecting pole Fig. Thee type ditibution of eltive dielectic contnt () Pbolic ditibution ' ( ) = ( )... (8) ' (b) Line ditibution ( ) = ' (c) Elliptic ditibution '... (9) ( ) = ( )... () One of the fcto ffecting the eltive dielectic contnt of wte i the tempetue of the wte ). The eqution () nd (7) indicte tht the effect of tempetue on the chge of the doplet i elted only to the eltive dielectic contnt of the wte. Ntully, vition in the eltive dielectic contnt of wte ffect the field intenity nd the chge mount of the doplet nd lo the behvio of Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

8 the doplet. The eltionhip between the eltive dielectic contnt nd the tempetue i hown in Fig. 7. The figue indicte tht the eltive dielectic contnt of wte i ppox. 8 t the oom tempetue of unde the tmopheic peue, nd ppox. t the tempetue of unde the tution peue. eltive dielectic contnt t.mp Tempetue Fig.7 eltion between eltive dielectic contnt nd tempetue A hown in Fig. 8, the ufce tenion of the doplet decee the tempetue incee, i.e., enegy inide the doplet i ctivted. We conide tht, ince the eltive dielectic contnt lo decee the tempetue incee, the doplet tend to be chged. Anothe fcto ffecting the eltive dielectic contnt of wte i peue ). Figue 9 how the eltion between the eltive dielectic contnt of wte t ech tempetue nd the peue. The figue indicte tht, unde the me tempetue condition, the eltive dielectic contnt of wte i ufce tenion not lmot ffected by the peue. uppe limit of eo lowe limit of eo meued vlue tempetue Fig.8 eltion between ufce tenion nd tempetue of doplet. eltive dielectic contnt nd ditibution of field intenity eltive dielectic contnt Peue Fig.9 eltion between eltive dielectic contnt nd tempetue of dople They wee clculted uing the following expeimentl equiement. Though the citicl voltge w 7,8 V bed on Eq. (), voltge of 8, V w dopted in the following clcultion. A cn be Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

9 een fom Fig., the citicl voltge w ppox., V in the expeiment. The diffeence between the expeimentl vlue nd the clculted vlue i conideed to occu due to the dielectic contnt of the cylindicl tube mteil, i.e., the enegy lo of the cylindicl tube the electode 7), 8). A citicl voltge of 8, V w pplied to the cylindicl tube, nd the eltive dielectic contnt in the cylindicl tube co ection nd the ditibution of the field intenity gint the eltive dielectic contnt wee clculted uing Eq. () nd Eq. (8), (9), nd (). The eult e hown in Fig.,, nd.. Motion tck of the doplet To implify the eqution, uing Eq. () nd (7), the contnt wee et follow. k = ' ( ) ln 9π V k = ln m ' ρ 3 = k k 3V 3 ( ) () In the ce tht the eltive dielectic contnt how pbolic ditibution: The eqution of motion fo the doplet obtined by uing the Eq. (), (), (7), nd (8), [ ] m z = v d C k k When the contnt e et follow, A = ' ( A' )... () A A C 3 7 ( ) 9 8 ' ( ) 7 ' ' ' ( ' ) = The integted potion in the eqution i, l A 3 A ( ) d = ( A' ) ( ' ) ' ( ' ) ' ( ' ) 7 Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

10 :pbolic ditibution :line ditibution Field intenity 3... denity ditibution of doplet field intenity E(ctul) E(vcum) eltive dielectic contnt Field intenity 3... denity ditibution of doplet field intenit E(ctul) E(vcum) (mm) eltive dielectic contnt Fig. eltive dielectic contnt nd field intenity in tube co ection () Fig. eltive dielectic contnt nd field intenity in tube co ection() Field intenity 3... :elliptic ditibution denity ditibution of doplet field intenit E(ctul) E(vcum) eltive dielectic contnt (mm) Fig. eltive dielectic contnt nd field intenity in tube co ection(3) Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

11 nd the eqution of motion i follow. v ln ' z = 3V ρ ( ) A ( ) ( A' ) 9 ( ) A ( ) 3 3 ' 9 33A ' 73 7 ( ' ) ( ' ) ( ' ) ( ' ) ( ' ) ]] 7 A '... () Figue 3 how the tck of the motion of the doplet clculted uing Eq. (). Alo, the clcultion eqution fo the theoeticl length (mximum length fo collecting the doplet) of the cylindicl tube i follow. cente pole wie diection of flow :pboic ditibution Doplet dimete =3m Velocity= m/ voltge=8 V =8. mm '=. mm Lo=88 mm (mm) Length of tube Fig.3 Motion tck of doplet() L = z = = v ln ' 3V ρ ( ) 3 Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

12 A 9 7 ( A' ) A 33A ' A ' (3) A eult of the clcultion pefomed with thi condition, it could be undetood tht, in ode to obtin % collection efficiency, t let.9 m i equied fo the theoeticl length of the cylindicl tube. () In the ce of tht the eltive dielectic contnt how line ditibution: The eqution of motion fo the doplet obtined by uing Eq. (), (), (7), nd (9), m z [ d C ] = v kk = v m k k α αβ β ( ) ( ) ( ) 3 v ln ' = 3V ρ ( ) 3 α αβ β ( ) ( ) ( ) When the contnt e et follow, α = β = ' ' 3 =... () C α = αβ β 3 The clcultion eqution fo the theoeticl length of the cylindicl tube i, L = z = = v m k k α αβ β 3 v ln ' ρ( ) α αβ β =... () 3V 3 3 Figue how the tck of the motion of doplet clculted uing Eq.(). A eult of the clcultion pefomed with thi condition, it could be undetood tht, in ode to obtin % collection Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

13 efficiency, t let.7 m i equied fo the theoeticl length of the cylindicl tube. (3) In the ce tht the eltive dielectic contnt how n elliptic ditibution: The eqution of motion fo the doplet obtined by uing Eq. (), (), (7), nd (), [ ] = 3 C d k k m v z... () The integted potion in the eqution i, ( ) = d d l = 3 ( ) ( ) 3 8 cin When the contnt e et follow, C 3 3 = ( ) ( ) 3 cin 8 The clcultion eqution fo the theoeticl length of the cylindicl tube i, theefoe, z mx L = = ( ) ( ) ( ) C V ' ln v = π ρ... (7) Figue how the tck of the motion of the doplet clculted uing Eq. (). A eult of the clcultion pefomed unde thi condition, it could be undetood tht, in ode to obtin % collection efficiency, t let.7 m i equied fo the theoeticl length of the cylindicl tube. Appox. % collection efficiency could be obtined in the expeiment uing the cylindicl epto with length of.3 m in poximity to.7 m. Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

14 cente pole wie diection of flow :line ditibution Doplet =3m dimete Velocity= m/ voltge=8 V =8. mm '=. mm Lo=88 mm (mm) Length of tube cente pole wie diection of flow :elliptic ditibution Doplet =3m dimete Velocity= m/ voltge=8 V =8. mm '=. mm Lo=88 mm (mm) Length of tube Fig. Motion tck of doplet() Fig.Motion tck of doplet(3). Concluion () A poce in which doplet e collected by the Coulomb foce in the cylindicl tube could be mde cle by thi expeiment. Alo, it could be undetood tht, between nd in the Fig., the pplied voltge i oughly in popotion to the cuent, nd the doplet collection ditnce decee the pplied voltge incee, which i cle lo fom Eq. (), (), nd (). () Fo commeciliztion, the effect of the electode mteil with diffeent dielectic contnt nd the collecting wte film on the inne wll of the cylindicl tube mut be tken into ccount. (3) A hown by ditnce between nd in Fig., doplet e completely collected in the wide nge of the dimete of the doplet by the cylindicl i-wte epto opeted by the Coulomb foce. () It cn be undetood tht the eult of the eltive dielectic contnt nlyzed on the umption tht the eltive dielectic contnt how n elliptic ditibution well mtch the eult of the expeiment on collection ditnce. efeence ) H.Aiok, Mte thee, Kobe Univ.M.M., 998. ) T.Xu, Mte thee, Kobe Univ.M.M.,. 3) H.Sugit,T.Nkzw,T.Xu nd T.Okw, Poceeding of the th ISME Tokyo, Oct., 7-8. ) K.Iinoy, The Pecipitto, Sept.93, The Nikkn Kogyo Shimbun Ltd ) The Intitute of Electottic Jpn, Hndbook of Electottic, My 98, Ohmh,Ltd. ) STEAM TABLES, The Jpn Society of Mechnicl Enginee, Nov ) H.Sugit,T.Nkzw,T.Okw nd T.Xu, eview of Kobe Univ.M.M.,Pt,July, ) T.Okw, Mte thee, Kobe Univ.M.M.,. Tnlted fom Jounl of the JIME Vol.38,No. C 3(Oiginl Jpnee)

defined on a domain can be expanded into the Taylor series around a point a except a singular point. Also, f( z)

defined on a domain can be expanded into the Taylor series around a point a except a singular point. Also, f( z) 08 Tylo eie nd Mcluin eie A holomophic function f( z) defined on domin cn be expnded into the Tylo eie ound point except ingul point. Alo, f( z) cn be expnded into the Mcluin eie in the open dik with diu