Alternative Numerical Techniques to Approximate the Electric Field of the Electrostatic Precipitators

Size: px

Start display at page:

Download "Alternative Numerical Techniques to Approximate the Electric Field of the Electrostatic Precipitators"

Jonah Fitzgerald
5 years ago
Views:

1 Matematcal Models Egeerg ad Computer Scece Alteratve Numercal Tecques to Approxmate te Electrc Feld of te Electrostatc Precptators IOANA-GABRIELA SIRBU Departmet of Electrcal, Power Systems ad Aerospace Egeerg Uversty of Craova 07 Decebal Boulevard, Craova ROMANIA ttp:// Abstract: - Ts paper proposes to sow ow dfferet umercal metods ca be used to estmate te electrc feld dstrbuto of a electrostatc precptator. Te prcple of eac metod ad te equatos uderlyg eac approac, wt cocrete mplemetato for ts applcato, are brefly preseted. Te results obtaed troug ter mplemetato computer programs are te explaed ad compared. Fally some coclusos are draw, wc glgts te advatages of certa metods. Key-Words: - Electrostatc precptator, electrc feld, doma metods, boudary elemet metod Itroducto Te developmet of te computg equpmet ad of ter performace as allowed, over tme, tat muc of te desg ad optmzato stages of te equpmet or of te stallato to go from laboratory ad test bec te vrtual evromet. I order to facltate certa operatos t became approprate to develop some software pacages, specalzed for te study of some partcular or more complex aspects of tese structures. I ts cotext some programs for te electromagetc ad termal felds modelg of te equpmet ave bee developed, ad also for te mecacal stress aalyss of some compoets, for te smulato of te electrcal ad electroc crcuts or of te electrcal etwors, ad so o, programs tat ca operate depedetly or eve correlated eac oter (te so-called coupled problems ) []-[4]. Over te tme for te electromagetc feld modelg several umercal tecques for solvg te problems were developed, wc, cosderg te approac, ca be dvded to [5]: doma metods, tat aalyze te feld te etre computatoal doma (wc s dscretzed to cells or fte elemets) based o te mposed boudary codtos ad source terms [6], ad boudary metods, tat dscretse completely te boudary of te doma, usg approxmato fuctos tat satsfy te problem equatos sde te doma. Te frst category cludes may wellow metods suc as fte dfferece metod (FDM), fte elemet metod (FEM), fte volume metod (FM), etc.. I te secod category te boudary elemet metod (BEM) s cluded. To ote tat eac of tese metods meets a seres of versos to mae tem to be appled more easly specfc problems. Also tey mgt be coupled so-called ybrd metods [7]. Ts paper ams to aalyze comparatvely bot doma metods ad boudary metods. Te study s appled for te determato of te electrc feld sde a electrostatc precptator [8]-[0]. Te modelg results, obtaed usg bot commercal softwares (e.g. QucFeld or FEMM) ad our ow programs created MATLAB, glgt te facltes of eac tecque ad te dffereces betwee te results obtaed usg eac metod separately. We vestgated bot data accuracy ad computato tme requred for solvg te problem. 2 Electrc Feld Modelg te Electrostatc Precptators Te electrostatc precptator s a electrcal stallato servg a dustral plat tat uses postve or egatve coroa peomeo for cargg electrcally te dust partcles (resulted from combusto) tat cross t. Te collectg camber of te electrostatc precptator cludes a seres of equdstat emssve electrodes placed te mddle plae betwee two parallel plates (collectg electrodes). Due to ts symmetry oly a quarter of te electrostatc precptator cael eeds to be modeled (Fg.). ISBN:

2 Matematcal Models Egeerg ad Computer Scece y 0 x L Fg. Computatoal doma of te electrostatc precptator I te electrostatc precptator tat wll be aalyzed te ed effect wll be eglected ad a stable coroa wll be cosdered. Also, because te effects of te arflow o electrcal potetal ad carge desty become otceable oly at g crossflow veloctes [2], tey wll be eglected, too []. Te parameters of te electrostatc precptator correspod to a exstg stallato from Turce Romaa [0], []: te dstace betwee te emssve electrodes s 2 L 0.3 m ; te dstace betwee te emssve ad collectg electrode s H 0.2 m ; te radus of te emssve electrode s 2 r.5 0 m (sody electrode). Te emssve electrode potetal s 0. Te collectg electrode as te potetal 0 (Fg.). Oe cosders a mea value of space carge desty ρ of C/m Fte Dfferece Metod Te fte dfferece metod uses a dfferetal formulato of te feld problem, wose equatos are [6]: curle 0 dvd ρ () D E + P were E s te electrc feld stregt, D s te electrc flux desty, ρ s te electrc carge desty te volume, s te permttvty of te gas ad P p s te permaet polarzato (ere P p 0 ). Usg as termedate uow te electrc potetal, E grad, te system () s reduced to te equato: p, H dv( grad ) ρ. (2) By dscretzg te equato (2) usg fte dffereces aroud a teror ode, (, ), for a uform mes bot o te x-axs drecto (of step ) ad o te y-axs drecto (of step ) [6], ad cosderg a costat permttvty all over te doma, we obta: +,, + (3) + + ρ. Te equatos of type (3), wrtte for eac ode sde te doma (wt some features for egborg border odes) ad arraged to glgt te coeffcets of eac uow,, lead to obta a system of algebrac equatos tat ca be solved umercally. 2.2 Fte olume Metod Te fte volume metod uses a tegral formulato of te feld problem terms of a approprate potetal [6], [2]. Te equatos of te problem are expressed as: curle 0 D ds q D E + P p were s te boudary surface of te doma ad qd s te electrc carge of te doma. Neglectg te permaet polarzato, for a costat ad usg as termedate uow te electrc potetal, relato (4) wrtte for a fte volume s [6]: D, Sγ (4) grad d r ρ dx dy. (5) γ (-,) ( +) () (+,) ( -) Fg.2 Dscretzato aroud a er pot of te mes [] γ ISBN:

Matematcal Models Egeerg ad Computer Scece γ s te boudary cotour of te fte volume, ad Sγ s ts surface (Fg.2).

, + (6) By comparg te relato (6) wt (3) oe otes tat tey are smlar. Terefore, for ts applcato, te two metods ca be aalyzed smultaeously, usg te same computer program.

To solve te system of algebrac equatos we used te Tomas algortm [2]. I Fg.3 te dstrbuto of te electrc potetal te aalyzed doma s preseted, obtaed usg te program mplemeted MATLAB.

I Galer s verso te equatos of te fte elemet metod are [6]: were φ, D D φ grad( φ ρ dω + ) grad S D φ ( φ ) dω g ds, (8) φ are te sape fuctos assocated wt te problem doma, ad g( r) correspods to te

3 Matematcal Models Egeerg ad Computer Scece γ s te boudary cotour of te fte volume, ad Sγ s ts surface (Fg.2). By dscretzg te equato (5) o a fte volume surroudg a teror ode, (, ), for a uform mes bot o te x-axs drecto (of step ) ad o te y-axs drecto (of step ) [6], [], oe obtas (Fg.2): +, + + ρ., + (6) By comparg te relato (6) wt (3) oe otes tat tey are smlar. Terefore, for ts applcato, te two metods ca be aalyzed smultaeously, usg te same computer program. Te relato (6), adapted for eac ode of te mes, as bee troduced to a program created MATLAB as: a + a+, +, + a,, + (7) + a +, + + a b, were: 2 ( / + ) a, / ; a +, a, / ; a + a / ; b ρ. To solve te system of algebrac equatos we used te Tomas algortm [2]. I Fg.3 te dstrbuto of te electrc potetal te aalyzed doma s preseted, obtaed usg te program mplemeted MATLAB. polyomally o parts of te doma (o fte elemets). Te tal equatos of te problem tae te same form (). I Galer s verso te equatos of te fte elemet metod are [6]: were φ, D D φ grad( φ ρ dω + ) grad S D φ ( φ ) dω g ds, (8) φ are te sape fuctos assocated wt te problem doma, ad g( r) correspods to te Neuma boudary codto. Te result s a system of algebrac equatos for uow odal varables (electrc potetals). Ts metod s well developed ad optmzed may software programs specfc to te electromagetc feld modelg, avalable o te maret (QucFeld, ANSYS, FEMM, etc.), so te creato of a ew program becomes useless. I te preset study we used as softwares QucFeld Professoal ad FEMM. Tus we could get bot te electrc potetal dstrbuto te etre doma of aalyss, ad te dstrbuto of te electrc feld stregt (Fg.4). It s easly observed te electrc feld cocetrato ear te emssve electrode. S D Fg.4 Dstrbuto of te electrc feld stregt E te aalyzed doma, obtaed usg FEMM Fg.3 Dstrbuto of te electrc potetal te computatoal doma, obtaed usg fte volume metod 2.3 Fte Elemet Metod Te fte elemet metod uses a tegrodfferetal formulato of te feld problem [3], [4]. Here te uow fuctos are approxmated 2.4 Boudary Elemet Metod I ts case oe starts also from a equato of type (2) [5], [6] wc, for a permttvty costat all over te doma, taes te form of a Posso type equato: ρ /. (9) It ca be sow tat for a boudary ode, usg te wegted resdual metod [5], ISBN:

4 Matematcal Models Egeerg ad Computer Scece ρ + dω g g d + d + g g d + d, (0) were o te porto of te boudary correspods to te Drclet codto, ad g g o te porto 2 of te boudary correspods to te Neuma codto. correspods to te wegtg fucto ad g. Te costat taes te value for te teral odes ad 0.5 for te boudary odes [5]. Troug dscretzato, for a boudary ode te relato (0) taes te form: ρ dω + g d + 2 g d, tat ca be brougt to te form B + H G g. (2) Te tegral terms H ad G ca be calculated by umercal tegrato (e.g. usg Gauss quadrature rule) [5],[7]. Based o tese relatos a program MATLAB was developed tat calculates te electrc feld produced sde te electrostatc precptator usg te boudary elemet metod. Some results are sow Fg.5 ad Fg.6. () Fg.6 arato of te electrc feld stregt betwee te emssve electrode ad te collectg electrode By comparg te results obtaed usg eac of tese metods oe observed tat smlar results bot qualtatvely ad quattatvely were aceved. Moreover tey are accordace wt te umercal ad expermetal results obtaed by oter experts [], [7], [0], [3]. To more torougly exame te devatos of te results, a comparatve study of tem s ecessary. 3 Comparatve Aalyss of te Results I order to empasze te dffereces betwee te results obtaed usg eac metod descrbed above a comparatve study was carred out. It amed to establs te order of magtude of te recorded devatos ad also to estmate te tme requred to perform te calculatos ad dsplay te results. Fg.5 arato of te electrc potetal o te boudary of te doma (startg from te lower rgt corer of Fg., couterclocwse drecto) Fg.7 arato of te electrc potetal alog te 0x axs (Fg.) - drecto of te gas flow ISBN:

5 Matematcal Models Egeerg ad Computer Scece Table Maxmum Error Calculato for te Electrc Potetal Potetal [] Absolute Relatve value [] value [%] o drecto y o drecto x o drecto x L Fg.8 arato of te electrc potetal betwee te emssve electrode ad te collectg electrode Fg.9 arato of te electrc potetal alog te le x L, 0y drecto (Fg.) Some of te obtaed results were preseted grapcally Fgs.7-9. Tey were focused maly o te aalyss of electrc potetal varatos, gve tat ts s te ma varable used te electrc feld modelg ad t s used afterwards to calculate oter feld quattes ( E, D ). For a suggestve aalyss t was amed as te umber of pots correspodg to te boudary to be, eac case (eac metod), te same (400 odes, 00 odes o eac sde). However, at te fte elemet metod (FEM) ts umber was ger to obta a g precso of te results (3343 odes te etre doma). Fg.7 sows te varato of te electrc potetal o te emssve electrodes drecto. It was foud tat te values obtaed usg FEM are average values betwee tose obtaed by te oter two metods (FM-FDM ad BEM). I ts case te gest recorded error (reported to FEM) was about 0% (Table ). Fg.8 sows te varato of electrc potetal betwee te emssve electrode ad te collectg electrode. I ts case t s foud also tat te values of te FEM are averages betwee tose obtaed by te oter two metods. Te maxmum relatve error tat was recorded ts case was about 0%. Fg.9 depcts te electrc potetal varato alog te le x L. I ts case te maxmum relatve error was below 5% (Table ). Reduced dffereces betwee results could be aceved by creasg te umber of odes ( te mes or o te boudary respectvely) ad by mposg a eve smaller error te umercal solvg. I Table 2 te worg tme tat s ecessary to obta te results s specfed. Table 2 Computg Tme Necessary for Eac of te Numercal Metod Metod FM, FDM BEM FEM Tme [s] Te relatvely g value of tme for FM-FDM s obtaed due to te use of a program MATLAB tat was ot optmzed. Ts program (tat s based o te Tomas algortm) uses a teratve process ad requres te acevemet of te covergece; te smaller te mposed error, te greater te computg tme. Accuracy s, owever, satsfactory. Te boudary elemet metod, usg a small umber of pots, requres less data ad a substatally reduced worg tme. Ts s te reaso wy ts metod as gaed groud te last years, fdg applcablty umerous teccal problems, cludg te couplg wt oter umercal tecques. Te lower tme requred to solve te problem usg FEM s due to te developmet ad optmzato of te commercal softwares tat use ts metod, bot terms of doma dscretzato ad solvg te systems of algebrac equatos. I cocluso, eac umercal metod ca be used successfully solvg te problem of te electrc feld sde te electrostatc precptator. ISBN:

6 Matematcal Models Egeerg ad Computer Scece Te results are comparable. Te dffereces coosg te metod cosst te facltes te obtag ad te mplemetato of te dscretzed equatos (at FM ad FDM), te tme ad computatoal effort decreasg (at BEM) or te easy use of some already developed programs (at FEM). 4 Cocluso Ts wor amed to compare some umercal metods ow for te modelg of te electromagetc feld, wt applcato to te electrc feld calculato of a electrostatc precptator. To smplfy te aalyss some smplfyg ypoteses were cosdered (costat permttvty, costat carge desty, arflow eglectg, etc.). Te study glgted te possblty of usg alteratve metods for modelg te electromagetc feld, eac metod avg ts advatages. Ay of tem ca be mplemeted ow computer programs tat ca be vable alteratves to commercal software, especally for some specfc applcatos. Refereces: [] S.M.E. Haque, M.G. Rasul, M.M.K. Ka, A.. Deev, N. Subascadar, A Numercal Model of a Electrostatc Precptator, Proceedgs of 6t Australasa Flud Mecacs Coferece, Crowe Plaza, Gold Coast, Australa, 2-7 December 2007, pp [2] P. Zamaa, G. Amad ad F. G. Fa, Couplg Effects of te Flow ad Electrc Felds Electrostatc Precptators, J. Appl. Pys, ol. 96, No. 2, 2004, pp [3] P. Cooperma, A Teory of Space-Carge- Lmted Currets wt Applcato to Electrcal Precptato, AIEE Tras., ol. 79, pp , 960. [4] L. Zao, E. Dela Cruz, K. Adama, A. A. Berez, J. S. Cag, A Numercal Model of a Wre-Plate Electrostatc Precptator uder Electroydrodyamc Flow Codtos, Proceedgs of te 0t Iteratoal Coferece o Electrostatc Precptator, Jue 2006, Cars, Queeslad, Australa. [5] C. A. Brebba, Te Boudary Elemet Metod for Egeers, Ed. Petec Press, Lodo: Plymout, 980. [6] A. Tomescu, I.B.L. Tomescu, F.M.G. Tomescu, Numercal Modelg of Electromagetc Feld ( Romaa), MatrxRom, Bucarest, [7] G. Kallo ad D. Stoc, Computato of Electrcal Codtos Isde Wre-Duct Electrostatc Precptators usg a Combed Fte-Elemet, Fte-Dfferece Tecque, J. Appl. Pys., ol. 59,No.6, 986, pp [8] K.R. Parer, Electrcal Operato of Electrostatc Precptators, IEE Power & Eergy seres, No.4, Lodo, [9] F. Beux, A. Iollo, M.. Salvett A. Soldat Curret-Desty Approxmato for Effcet Computato of te Electrostatc Feld Wre Plate Precptators, IEEE Tras. Id. Appl., ol.38, No.3, 2002, pp [0] S. M. Dgă, Electrostatc Dedustg Istallatos ( Romaa), Ed. Uverstara, Craova, 200. [] I. G. Sîrbu, S. M. Dgă, Al. St. Mtro O te Electrc Feld Smulato te Electrostatc Precptators, Proceedgs of te t Iteratoal Coferece o Appled ad Teoretcal Electrcty - ICATE 202, October 202, Craova, Romaa, pp [2] I. Popa, Modélsato umérque du trasfert termque. Métode des volumes fs, Ed. Uverstara, Craova, [3] B. Beamar, E. Favre, A. Doot ad M. O. Rgo., Fte Elemet Soluto for Iozed Felds DC Electrostatc Precptator, Proceedgs of te COMSOL Users Coferece, October 23-24, 2007, Greoble, Frace, pp.-4. [4] N. Oussala, Z. Zebboud, Fte-Elemet Aalyss of Postve ad Negatve Coroa Dscarge Wre-to-Plae System, Europea Pyscs Joural - Appled Pyscs, ol. 34, 2006, pp [5] K. Adama, Smulato of Coroa Wre- Duct Electrostatc Precptator by Meas of te Boudary Elemet Metod, IEEE Tras. Id. Applc., ol. 30, 994, pp [6] H. Igaras S. Saa T. Naamura, T. Moraga, ad T. Homa, A Boudary Elemet Aalyss of Space Carge Feld a Coroa Devce, IEEE Tras. Mag., ol. 29, 993, pp [7] H. Fscaller, K. Tö Numercal Itegrato - A Itroducto for te Boudary Elemet Metod, Graz Uversty of Tecology, ISBN:

Selection of Thermal Insulation Thickness of Cold Store Enclosures

Selection of Thermal Insulation Thickness of Cold Store Enclosures ISSN -77 (Paper ISSN -87 (Ole Vol.4, No.5, 3 Selecto of Termal Isulato Tckess of old Store Eclosures Jead Al-Radaede * Bassam Al-goul Muamad Freat 3. Al-uso Uversty ollege, Al-Balqa Appled Uversty, P.O