A THEORETICAL ANALYSIS OF THE ELECTROSTATIC FILTERS
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1 PUBLISHING HOUS PROCDINGS OF TH ROMANIAN ACADMY, Seies A, OF TH ROMANIAN ACADMY Volume 5, Numbe /4, pp.- A THORTICAL ANALYSIS OF TH LCTROSTATIC FILTRS Gleb DRAGAN* Romanian Acaem Calea Victoiei 5, 7 Bucaest, Romania -mail: bato@aca.o Te pape pesents a teoetical analsis of te electostatic filtes consieing te DC coona iscage between two conuctos, a geneal case being taken into consieation. Kewos: teoetical analsis, electostatic filtes.. INTRODUCTION neg epesents a polluting facto of te envionment. Te temoelectic powe plants ae among te most impotant stationa antopic souces fo te pollutant emission in te atmospee. Te combustion gases epesent one of te main polluting souces of te temoelectic powe plants. On appling te fossil fuels in te combustion pocess, in te boiles of te temoelectic powe plants tee take place impotant emissions of CO, SO, NO x in te ai as well as of suspension paticles. Since 9,5% fom te electic powe necessa in ou count is pouce in te temoelectic powe plants, te quantit of polluting gas emission is impotant. Fo tese easons, te application of te electostatic filtes sows a special inteest. Te pape eals wit te esults of te teoetical eseaces elate to te efficient application of te electostatic filtes.. THORTICAL ANALYSIS OF TH LCTROSTATIC FILTR PROCSS Fom te assembl of te analze teoetical poblems [ 4] we will efe to some aspects lagel elate to te electostatic filte functionalit... Detemination of te caacteistic of te coona iscage extenal aea fo biimensional fiels... DC Coona Discage fo Two Paallel Conuctos Te stu of te coona iscage in te case of two paallel conuctos is confonte wit ifficulties because of te electic fiel asmmet. Te calculation potesis suggeste b Deutsc [5] is not applicable in te case of two paallel conuctos. Consieing not onl te limit conitions but also te electic cage istibution aoun te conucto, in wic te coona iscage occus, fo vaious value of te applie voltage te coona iscage equation can be integate toug successive appoximations [,]. Fig. sows te computation iagam; one consie te known equation sstem: ε iv ρ () ϕ () *Membe of te Romanian Acaem
2 Gleb DRAGAN ρµ () i wee µ i is te mobilit of te cage caies. Te equation sstem () () leas to an equation wit patial eivatives fo te electic potential: in te conitions: as well as: ϕ ϕ iv( ϕ ϕ ) (4) (, β ) u( β ) (, β ) (,) ϕ(, ) ϕ(, ) ψ (5) (6) /6 β β β β- ξ Fig. liminating te volume ensit of te electic cage p fom te fist two equations () an () an taking into consieation elation () one obtains: ϕ ϕ ϕ ( ϕ) ϕ ϕ ϕ Afte a seies of a opeations te calculation elations ae obtaine: fo potential ϕ (, β ) u() ξ ( n ) ( n ) s s fo cage ensit 5ε ρ 4 u n () ξ ( n ) s s ( n ) ( n ) n fo te electic fiel intensit moule ( n ) ξ ( n ) β ξ ( n ) ξ ( n ) β ξ (7) (8) (9)
3 A Teoetical Analsis of te lectostatic Filtes s () ( ) ( n ) u ξ n s( n ) n ( n ) s( n ) s( n ) ( n ) ξ ( n ) ( n ) ξ ( n ) () u ξ n β ξ β ξ B means of te compute, one can etemine te electic cage epenence function te atio U U [ ]. U Te euce elations can be genealize, toug succesive appoximations, fo a seies of paallel an coplana conuctos, caacteistic of te electostatic filtes. n Fig. sows te epenence of te electostatic cage multiplication atio function te value if n ϕ ω t, fo vaious pecentage values of te atio 4 n/n U U U. / () % φ Fig... Calculation of te Caacteistics of te Coona Discage Aea fo Biimensional Fiels In te electostatic filtes tee is use te sstem of electoes: plate conucto seies o seies of conuctos between te plates. Te configuation fom te electofiltes of unit of te temoelectic powe station in Tuceni as been consiee as a moel of electoe configuation. plant in Tuceni as been consiee asa moel of electoe configuation. As elation ( 8 ) ( ) equie pefomant calculation means in te case of some complex configuations one as cosen te Deutsc Popkov calculation elation wic ae muc simple.
4 Gleb DRAGAN 4 Making use of te isognal epesentation wit te co-oinates an fo te plate conucto seies configuation one obtains te elations: - fo ( ) () - fo < < ( ) actg ctg () - fo ( ) k ρ () - fo < < ( ) ρ actg ctg k (4) wee: ( ) ( ) x s x s, (5) ( ) ( ) x s s x actg, c, k ε. (6) Fig. sows te electical fiel istibution in te plate conucto seies sstem wit x /, 7,5 cm, cm,,75 cm Ison 5.
5 5 A Teoetical Analsis of te lectostatic Filtes 5 5 [KV/CM] X,5 [MM] X 6 [MM] X [MM] X 5 X Fig. Y [CM]... Calculation of te Coona Discage Cuent Voltage Caacteistic Ug te seies evelopment meto caies out te poblem solving. Tis meto is base on te isogonal epesentation of te initial space on te ing, as well as on te epesentation of te seies sape file potential: ϕ (,) f () fn ()n (7) n wee an ae pola cooinates in te ing plane f n (); n,,, ae unknown functions of te a. Te equation of te unipola coona iscage in te ing plane takes te fom: ϕ (K ϕ) ϕ (K ϕ) K( ϕ) (8) On substituting te sei evelopment (7) in te equation 98), te poblem euces itself to te integation of te obtaine iffeential eqaution sstem function of te unknown quantities f n (). One can pove tat te value of te cuent given b te coona iscage I epens onl on te appoximation function f () i i I - e µqu I ( ) (9) wee μ I is te ionic mobilit, a of te coona iscage conucto, I ( ) te opeato wic is epenent on function f n () (te calculations sow tat onl I ( ) is of inteest), I te coona cage initial intensit, q te electic cage coesponing to i. Te appoximation function f () is eteminate fom te zeo appoximation equation as well as fom te expession fo te isogonal tansfomation coefficient K( φ). Afte a seies of tansfomations one obtains te zeo appoximation equation wic takes te fom: I f I I f k (9) Taking into consieation equations (8) an () one obtains:
6 Gleb DRAGAN 6 - C C f - Hence, b eteminating te opeato I ( ) wen b means of elation (9) tee esults: U I C µε i () In oe to fin C one must put own te limit conitions fo te zeo appoximation function f ( ). Afte some tansfomations fo te plane electoe sstem te quantit C esults fom elation () ( - C (7-4 )( ) () Te poblems concening te C () cuve appoximation ( wee is a paamete epening on te electical fiel intensit I ) fo vaious electoe sstems ae solve b ug te meto of V.Levitov an S.I. Riaboi [4] an b appling to te seies evelopment solution. 4. CONCLUSIONS Te teoetical analsis gives te possibilit to analse te influence of iffeent paametes efeing to te functionalit of te electostatic filtes. Te electostatic multiplication atio B/ epens on te fequenc an on ωt, wile te epenence of te atio (U-U )/U is not so impotant. Te electic fiel istibution on te plate conucto sstem epens on te atio /, consequentl on te constuctive caacteistics of te filtes. RFRNCS. DRAGAN, G., Contibution à l étue e l effet e couonne bipolaie e couant continu, Rev. Roum. Sci. Tecn. lectotecn. t neg., tom 4, n., DIGA, SILVIA MARIA, Contibutions to te analsis of te electofilte tecnical pefomance incease, Doctoal Dissetation (scientific cooinato G. Dagan), UPB, DRAGAN, G., Su l effet couonne e couant continu ans le case eux conucteus paalleles, Rev. Roum. Sci. Tecn. lectotecn. t neg., tom 5, n., LVITOV, V.I., RIABOI, S.I., Te voltage-cuent caacteistic of te unipola coona iscage fo te conucto-plane electoe sstem (in ussian), lektoenegetika, Izatelstvo AN SSSR, no. 7, DUTSCH, W., Ann. e Psik, 6, 588, 9. Receive Mac, 4
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