Research on strength of electric field of the electrostatic precipitator with longitudinal transverse collecting plates

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1 valabl nln Jurnal f Chmcal and Pharmacutcal Rsarch, 0, 6(6): Rsarch rtcl ISSN : CODEN(US) : JCPRC5 Rsarch n strngth f lctrc fld f th lctrstatc rctatr wth lngtudnal transvrs cllctng lats Chn Zu-yun,, Jn B, and Wu Chang-fu, Faculty f Rsurc and Envrnmntal Engnrng, Jangx Unvrsty f Scnc and Tchnlgy, Ganzhu, Chna Jangx Ky Labratry f nng & tallurgy Envrnmntal Pllutn Cntrl, Ganzhu, Chna BSTRCT Th lctrstatc rctatr wth lngtudnal transvrs cllctng lats had bttr charactrstcs. Th thrtcal crrlatn fr th calculatn vltag, whch was rducd by sac lctrc charg n th ESP wth lngtudnal transvrs cllctng lats, was dducd n ths ar. Nt nly th lctrc tntal, but als th calculatn frmula f strngth f lctrstatc fld,wr stablshd n th bass f mag charg mthds. Th masur rsults f bth th lctrc currnt dnsty f cllctng lat, and th avrag strngth f lctrc fld f cllctng lat, wr cnsstnt wth ndvdual lctrc fld ntnsty dstrbutn. Ths ndcatd that th nfrnc curs was crdblty. Kywrds: Elctrstatc rctatr (EPS), strngth f lctrc fld, mag charg mthds, lctrc tntal INTRODUCTION Th lctrstatc rctatr wth lngtudnal transvrs cllctng lats had xcllnt faturs and ts cllctng mchansm was mr cmlx. Th lctrstatc rctatr (ESP) wth lngtudnal transvrs cllctng lats, whs th lat currnt dnsty and gas vlcty dstrbutn wr mr unfrm than ths f th cnvntn wr-lat ESP, and cllctng ffcncy was hghr than th lattr n th sam cndtn. Basd n th xrmnt and thry, th lctrstatc rctatr wth lngtudnal transvrs cllctng lats lwrd stl and shrtnd vlum []. But th strngth f lctrc fld was n f th man factrs whch affctd th lctrstatc rctatr rfrmanc. It was mr dffcult t drv th calculatn frmula f strngth f lctrc fld. Th mag charg mthd was usd t rsnt a calculatn mthd f lctrc tntal and th strngth f lctrc fld was gnratd at ths ar. Whn th strngth f lctrc fld n th lctrstatc rctatr was masurd, th xrmntal rsults wr cnsstncy wth th thrtcal analyss; th study was nrch th ty f lctrstatc rctatrs and dvld th thry f lctrstatc cllctn.. Calculatn frmula f tntal and strngth f lctrc fld n th lctrstatc rctatr wth lngtudnal transvrs cllctng lats Th lctrstatc rctatr wth lngtudnal transvrs cllctng lats had a scal structur, that was t say, n a dust cllctn unt, th lngtudnal transvrs cllctng lats wr cmsd f a hrzntal sctn f a squar cubd and th * ty rckl f crna wr wr lacd n th cntr axs f th cubd []. Th lctrc fluxln wr gnratd by bth th * ty rckl f crna wr and th lngtudnal transvrs cllctng lats n th vrtcal drctn dstrbutn, as n Fg.. In th thrtcal analyss f lctrc fld, nt nly th mact f sac charg, but als th mact n sac lctrstatc fld was cnsdrd. Namly, sac lctrc fld f lctrstatc rctatr culd b cmsd f th surstn f th dynamc lctrc fld and lctrstatc fld. 388

2 Chn Zu-yun t al J. Chm. Pharm. Rs., 0, 6(6): Th analyss f lctrc fld was dvdd nt tw sts. Frstly, th lctrc tntal and th strngth f lctrc fld wr gnratd by th sac charg at any nt n an lctrc fld. Scndly, th tntal lctrstatc fld was calculatd by mag charg mthd. Thn th tw knds f lctrc fld wr surmsd as th frmula f th lctrc fld strngth f th lctrstatc rctatr wth lngtudnal transvrs cllctng lats.. Calculatn f th sac charg Sac vltag and currnt charactrstcs btwn th lctrds f th lctrstatc rctatr had a sgnfcant mact, whn a lt f dust ntrd th ESP. Hgh-sd mvmnt f gas ns wr surrundd by th mvmnt f dust arund, whch rducd th vlcty f th charg carrrs. Th sac chargs causd by th dust and by th gas n wr as th sam, and thy must b takn nt accunt, bcaus thy had had an mact n th strngth f lctrstatc fld and th strngth f lctrc fld gnratd by th charg nar th cllctng lat. If th fr lctrn was cnsdrd, th lat currnt dnsty was gnratd by th charg transfr f ns and chargd dust. Its rlatnsh was as fllws: J T = E ρ b E ρ b = E ρ b () a a a T Whr: J T Ttal currnt dnsty btwn th lats,/m ; E a vrag strngth f lctrc fld btwn th lats,v/m; ρ Charg dnsty f ns,c/m 3 ; b In mblty,m /v.s; ρ Charg dnsty f chargd dust,c/ m 3 ; b Chargd dust mblty,m /v.s; ρ T Ttal sac charg dnsty,c/ m 3 ; b Effctv mblty f ns and chargd dust,m /v.s. Thn, th ffctv mblty f ns and chargd dust was btand by frmula (), whch was as fllws: b = ( ρ b ρ b ) / ρ T Bsds,th frmula was dducd by frmula () as fllws: J ρ J T = E a ρ ρ b ρ (E a ρ ρ b ρ E a ρ b )=J ρ (J ρ J ) () Whr:J ρ Currnt dnsty gnratd by th chargd dust,/m ; jⅰ Currnt dnsty gnratd by th n,/m Currnt dnsty f th dust transmssn was accuntd fr nly a small fractn f th ttal currnt dnsty (j >> J ρ ),and th nc charg mblty was avrag f 00 tms that f dust mblty 's,b =00b ρ, s t was asy t gt as fllws: b =b [J T (00J ρ J T )] (3) By frmula (3) th b was btand,whch rflctd th mact f sac charg, n th fact t was t mak th mvmnt f ns and dust ths tw knds f charg carrd n th lctrc fld wth an avrag ffctv mblty t b rflctd.. lngtudnal cllctng lats,. transvrs cllctng lats, 3. crna wr,. flw drctn, 5. lctrc fluxln. Fg. Dstrbutn f lctrc fluxln whch was gnratd by th * ty rckl f crna wr and th lngtudnal 389

3 . Sathsh Kumar t al J. Chm. Pharm. Rs., 0, 6(6): transvrs cllctng lats. Elctrc tntal gnratd by th sac charg Bcaus th chargd dust unfrmly was dstrbutd wthn a dust cllctn unt f th lctrstatc rctatr wth lngtudnal transvrs cllctng lats, th lctrc tntal was nly gnratd by th sac charg. s t was shwn n Fg.,n th x axs, f th dstanc btwn th nt f O and n nt was, and th strngth f th nt n th lctrstatc flds was E, s th frmula was btand by th Gauss Thrm as fllws: de/dx=ρ T /ε 0 () By frmula (), t was gttn as fllws: ρ T =J T /E a b (5) Fg. Elctrc tntal gnratd by th sac charg Th avrag strngth f lctrc fld E a was rlacd arxmatly by th fld strngth E f th f Fg. n frmula (5). Th J T whch was lctrc currnt dnsty f cllctng lats was substtutd by lctrc currnt dnsty (6), whch was arxmatly qual t frmula as fllws: J J T ρ T = = (6) Eb Eb Basd n th frmula (6), th frmula was ntgral as fllws: J x E = C ε b (7) Th strngth f lctrstatc flds was mad as a bundary cndtn n X = b (b was half f th dstanc btwn th sam lats). Bcaus a lt f thrtcal and xrmntal study had shwn that n th cas f th sac charg dnsty was nt larg, th strngth f lctrstatc flds nar th lats was arxmatly qual t a cnstant. In th X = b, thr was th arxmat frmula [3] : E J b πε b = (8) Whr: E Strngth f lctrc fld (v/m); J vrag currnt dnsts n cllctng lats(/m ); ε Dlctrc cffcnt f ar, n nrmal tmratur, ε c/v m; b Inc mblty,dry ar,ngatv crna,b =. 0 - m /v s. 390

4 . Sathsh Kumar t al J. Chm. Pharm. Rs., 0, 6(6): Fg. 3 Imag charg grus gnratd by th charg smulatn Th cnstant C was dtrmnd by (8). J b C = ( ) (9) πε b π Basd n frmula (9) and (7), th strngth f lctrc fld was btand as fllws: E J b = [ x b( )] (0) ε b π ccrdng t th dfntn f th lctrc tntal, th frmula was btand as fllws: = U U Edx () Basd n frmula (0), frmula () was ntgratd as fllws U = U 3 J ε b [ x b( )] π 3/ () Th bundary cndtns wr as fllws: whn x = b U = 0, by th abv quatn frmula () was gttn as fllws: J b 3/ U 0 = ( ) (3) 3 ε b π Th tntal fr sac charg n th lctrc fld at any nt was as fllws: J b 3/ J 3/ U = ( ) [ x b( )] () 3 ε b π 3 ε b π.3 Frmula f lctrc tntal f lctrstatc fld and frmula f strngth f lctrc fld n rckl crna wr In th lctrstatc rctatr wth lngtudnal transvrs cllctng lats, bcaus th hrzntal slttd lar lats ga was vry small, t was nglgbl. Th * ty rckl f crna wr and th lngtudnal transvrs cllctng lats rducd unfrm lctrc fld n th vrtcal drctn, and th lctrc fuxln dstrbutn was shwn n Fg.. S th calculatn f lctrc fld dstrbutn f th * ty rckl f crna wr was smlfd t mak tw-dmnsnal rblm. s th structur f th * ty rckl f crna wr was cmlx, and th tntal f th lctrstatc fld was dffcult t drv th analytcal frmula. Th tntal was calculatd by mthd f charg smulatn bas n lctrc fluxln dstrbutn f lctrstatc rctatr wth lngtudnal transvrs 39

5 . Sathsh Kumar t al J. Chm. Pharm. Rs., 0, 6(6): cllctng lats. Elctrmagntc fld thry [,5] ndcatd that sm knds f aralll flds r axs- symmtrcal flds whch had artcular symmtrcal structur culd us th mag charg mthd t b slvd. Outsd th fld, a gru f chargs was assumd artfcally t rlac ths cntnuus dstrbutd ns n th surfac f actual lctrds. Th mag charg mthd was a knd f scal mthd t slv th lctrstatc fld bundary valu rblms, and ts thrtcal fundatns wr unqunss thrm and surstn rncl f th lctrstatc fld. Ths mthd s charactrstc f slvng rblms lay n nt t slv th Pssn quatn that satsfd th lctrc tntal, but t us assumd chargs t rlac th nducd ns n th surfac f cnductr and nflunc lctrc tntal. Insd th lctrstatc rctatr wth lngtudnal transvrs cllctng lats, crna wr was ut n th cntr f th lngtudnal transvrs cllctng lats, and th cllctng lat cnncts th grund, frmng fur zr-tntal surfacs f an unt, s t culd b mad smulatd chargs nsd th crna lctrd t rduc nnumrabl mag charg grus crrsnd t zr-tntal, as t was shwn n Fg.3. Th lctrc tntal f th nfnt ln charg at anywhr n sac was btand bas n th charg smulatn wth th nfnt ln by th Gauss thrm as fllws: ϕ Edl = = ln πε r r (5) whr: Charg lngr dnsty; r Pnt O s lctrc tntal was zr(th nt was dstant frm th wr); r Dstanc btwn th nt and th wr. Varatn f th mag charg f th charg smulatn(x,y )n th X, Y crdnats wr as fllws: x x x n = nb x n = (n ) b x n 3 = (n ) b x n = (n ) b x n = nb y n = (n ) b y n 3 = (n ) b y n = (n ) b y (6) (7) (8) x (9) y (0) y () y () y (3) Bcaus th lngtudnal transvrs cllctng lats was as a symmtrc, lctrc tntal f nfnt ln charg and ts mag charg gru at P(x, was calculatd aftr ratdly magng rflctn as fllws: = P ) 3),n ),n ) V( x, ln πε (, ) (, ) (, ) (, 3 ) n = 0 D n n D n n D n n D n n ) ) ) 3) ) 3) ) ) () Whr:,n)was th dstanc btwn th frst f (x n,y n )charg smulatn mag nt and th nt P(x,,thrs smlar, dcdd by th fllwng frmula:,n)=[(-nbx -x) ((n)b-y - ] (5),n)=[(-nbx -x) (-nby - ] (6),n3)=[(-nbx -x) ((n)by ] (7),n)=[(-nbx -x) ((n)by - ] (8),n)=[((n)b-x -x) (-nby - ] (9) 39

6 . Sathsh Kumar t al J. Chm. Pharm. Rs., 0, 6(6): ,n)=[((n)b-x -x) ((n)b-y - ] (30),n)=[((n)b-x -x) ((n)by - ] (3),n3)=[((n)b-x -x) ((n)by ] (3) 3,n)=[((n)bx x) (-nby - ] (33) 3,n)=[((n)bx x) ((n)b-y - ] (3) 3,n)=[((n)bx x) ((n)by - ] (35) 3,n3)=[((n)bx x) ((n)by ] (36),n)=[((n)bx -x) ((n)b-y - ] (37),n)=[((n)bx -x) (-nby - ] (38),n3)=[((n)bx -x) ((n)by ] (39),n)=[((n)bx -x) ((n)by - ] (0) If th numbr f smulatn ln charg was, thn th lctrc tntal at (x, was as fllws: P ) 3),n ),n ) V = V = ln (, ) (, ) (, ) (, 3) = = πεο n= 0 D n n D n n D n n D n n ) ) ) 3) ) 3) ) ) () ccrdng t E=- V, lt () sk artal drvatv and was addd a ngatv sgn n x, y rsctvly,thn th cmnnt valu f th fld strngth f lctrstatc fld n th X, Y drctn wr gttn as fllws: E x V = x () P x nb x x nb x Ex = ( = πε n= 0 D (n, n ) D (n, n ) x nb x x nb x x(n ) b x x(n ) b x x(n ) b x x(n ) b x x (n ) b x D (n, n ) D (n, n 3) D (n, n ) D (n, n ) D (n, n 3) D (n, n ) D (n 3, n ) x (n ) b x x (n ) b x x (n ) b x x (n ) b x x (n ) b x x (n ) b x x (n ) b x D (n ) D (n 3) D (n ) D (n ) D (n ) D (n ) D (n 3) Smlarly E y V = y (3) E P x, = πε n= 0 y nb y y (n ) b y y (n ) b y y (n ) b y y nb y y (n ) b y D (n,n ) D (n,n 3) D (n,n ) D (n,n ) D (n ) D (n 3) y (n ) b y y nb y y (n ) b y y (n ) b y y (n ) b y ) D (n ) D (n ) D (n ) D (n ) D (n 3) Th ttal lctrstatc fld strngth was as fllws: y nb y y (n b) y ( y (n ) b y y (n ) b y y (n ) b y D (n ) D (n, ) D (n ) D (n 3) D (n,n ) y ( = n E(x =[E x (x E y (x ] () Bcaus th nt tntal f th crna wr surfac was qual t th ald vltag, and vrywhr thy wr qual, thn by () th ald vltag was calculatd as fllws: P ) 3),n ) V = ln = πεο n= 0 ) ),n ),n ) ) ) ) 3),n 3) ) 3) ) ) =V (5) 393

7 . Sathsh Kumar t al J. Chm. Pharm. Rs., 0, 6(6): whr:v ld vltag. Frm quatn (5), th charg smulatn f a nt P was rrtnal t th mrssd-vltag V 0. T dtrmn P, Ordrd V = kv, multly vltag V 0 by P was btand th charg smulatn f vry th lad vltag. Th N nts wr takn n th * ty f rckl crna wr, and lst f N mult-lnar quatn f P, smultanus quatns wr stablshd. If th charg smulatn amunt f P was dtrmnd, th lctrc tntal sz f any nt wthn th lctrc fld was calculatd by frmula ().. Frmula fr fld strngth gnratd by th * ty rckl f crna wr and th sac charg n th gas By (0) and (5), th frmula fr fld strngth was gnratd by th * ty rckl f crna wr and th sac charg n th gas as fllws:! E = { E( x, J b { [ x b( )]} } ε b π (6) Whr:E! th fld strngth whch was gnratd by th * ty rckl f crna wr and th sac charg n th gas. asurd rsults f currnt dnsty and avrag lctrc fld strngth f lat. Dtrmnatn mthd fr lat lctrc currnt dnsty Usd slt dtctn mthd t dtrmn th lat currnt dnsty, currnt mtr was qud wth calbratn fr /mm galvanmtr [6], and th transfr swtch was mad th masurd rgn accss t galvanmtr, whl th n masurd rgn f lat lctrc currnt wr accssd t grund.. Dtrmnatn rsults f th lctrd currnt dnsty Th dtrmnatn f currnt dnsty wr dtrmnd n th cndtn that th wrkng vltag f cllctng lat was 50kv, th lngth f th * ty rckl f crna wr was 90mm, th dstanc f lats was 00mm, and n-lad. Th masurd rsults f currnt dnsty and avrag lctrc fld strngth fr lat f ths lctrstatc rctatr and cnvntnal lctrstatc rctatr wr shw n tabl. In th tabl,th avrag currnt dnsty f lngtudnal transvrs cllctng lats was 0.566m/m, whch s bttr than th cnvntnal lctrstatc rctatr that was 0.55 m/m ; Th unfrmty f currnt dnsty fr lngtudnal transvrs cllctng lats was 0.367, whch was largr than th cnvntnal lctrstatc rctatr that was 0.9. Th avrag lctrc fld strngth f th lat fr lngtudnal transvrs cllctng lats was.73kv/cm, whch was largr than th cnvntnal lctrstatc rctatr that was.5kv/cm. Tst rsults shwd that lngtudnal grv sha matchd th *-ty rckl f crna wr changng th dstrbutn f lctrc fld, lmnatng th l ln brdrln, lmnatng th "zr" currnt ara n th cllctng lat, and frmng a rasnabl unfrm dstrbutn f wr ln, as n tabl. ccrdng t th Sgmnd [7] saturatd currnt dnsty calculatn f was s=ε0μv /H 3 (H was wr lngth), lctrd currnt dnsty was nvrsly rrtnal f th cubc f th wr wr lngth, n thr wrds, undr th sam vltag, a nt lctrd currnt dnsty manly dnds n th dstanc frm th crna ara. That was th smlar xrssn f frmula(5), f thy culd mak as much wr wr lngth qual, thn th lat currnt dnsts wr qual, th mst unfrm dstrbutn at ths tm, qual t th avrag lctrc fld ntnsty n th surfac f th lat, fld strngth was als largst, t mrv cllctn ffcncy. Tabl Th masurd rsults f currnt dnsty and avrag lctrc fld strngth f lat Tys Elctrstatc Prctatr wth Lngtudnal Transvrs cllctng Plats Currnt dnsty (m/m ) Lngtudnal Cllctng Plats 38mm Th wdth f th 38mm transvrs lat 70mm Unfrmty f currnt dnstyδ vrag lctrc fld strngthfplat(kv/cm) Cnvntnal ESP 0.55 m/m CONCLUSION ()Sac charg n th lctrc fld at any nt n th tntal was as fllws: 39

8 . Sathsh Kumar t al J. Chm. Pharm. Rs., 0, 6(6): J / b 3/ J / U = ( ) ( ) ( ) ( ) 3 3 x b ε b π ε b π ()Th calculatn frmula f th lctrc tntal gnratd by lctrstatc fld was as fllws: P ) 3) V = ln = πεο n= 0 ) ),n ),n ) ) ) ) 3),n ),n 3) ) 3) ) ) (3)Th lctrstatc fld strngth f an arbtrary nt wthn fld rgn was as fllws: E(x,=[E x (x,e y (x,] / ()Th frmula fr fld strngth whch was gnratd by th * ty rckl f crna wr and th sac charg n th gas was as fllws:! J b E = { E( x, { [ x b( )]} } ε b π (5)Th avrag currnt dnsty f lngtudnal transvrs cllctng lats was 0.566m/m,whch was bttr than th cnvntnal lctrstatc rctatr that was 0.55 m/m ;Th unfrmty f currnt dnsty fr lngtudnal transvrs cllctng lats was 0.367, whch was largr than th cnvntnal lctrstatc rctatr that was 0.9. Th avrag strngth f lctrc fld f lat fr lngtudnal transvrs cllctng lats was.73kv/cm, whch was largr than th cnvntnal lctrstatc rctatr that was.5kv/cm. (6)Tst rsults shwd that lngtudnal grv sha matchd th * ty rckl f crna wr changng th dstrbutn f lctrc fld, lmnatng th l ln brdrln, lmnatng th "zr" currnt ara n th cllctng lat, and frmng a rasnabl unfrm dstrbutn f wr ln. cknwldgmnt Th wrk s Fundd by Jangx Prvncal Dartmnt f Educatn n Chna (GJJ,GJJ090);Fundd by th Natural Scnc Fundatn f Jangx n Chna (009GZC0035). 3 / REFERENCES [] Chn Zu-yun,Wu Chang-fu,Ln Da-jan, Tang n Kang. Envrnmntal Scnc and Tchnlgy, 003,5: [] Chn Zu-yun, Yang Shng-qang, Wu Zhang-fu. tal n, 006():69-7. [3] H.J.Wht, Etc. Wang Chng-han, Translatn. Industral Elctrstatc Prctatr []. Bjng, tallurgcal Industry Prss, 98. [] Quan Z-sng. Elctrmagntc Fld Thry[]. Chngdu, Chngdu Tlcmmuncatns Engnrng Unvrsty Prss.987.: [5] Ln Zh-yuan,Yang Quan-rang,Sh Yu-jun. Engnrng Fundamntals f lctrmagntc fld[]. Bjng, Hghr Educatn Prss,983.6:5-56 [6] Chn Zu-yun,Yang Shng-Qang,Wu Chang-fu. Jurnal f Safty and Envrnmnt, 006(3): [7] L Za-sh. Elctrstatc Prctatr [].Bjng: tallurgcal Industry Prss,