A Numerical Model of an Electrostatic Precipitator

Transcription

1 16 th Autralaian Fluid Mechanic Conference Crowne Plaza, Gold Coat, Autralia -7 December 7 A Numerical Model of an Electrotatic Preciitator Shah M E Haque 1*, M G Raul, M M K Khan, A V Deev 1, and N Subachandar 1 1 Proce Engineering & Light Metal (PELM) Centre, Faculty of Science, Engineering and Health Central Queenland Univerity Gladtone, Queenland 468 AUSTRALIA College of Engineering and the Built Environment Faculty of Science, Engineering and Health Central Queenland Univerity Rockhamton, Queenland 47 AUSTRALIA Abtract Thi aer reent a Comutatal Fluid Dynamic (CFD) model for a wire-late electrotatic reciitator (ESP). The turbulent ga flow and the article mot under electrotatic force are modelled uing the CFD code FLUENT. Numerical calculat for the ga flow are carried out by olving the ynold-averaged Navier-Stoke equat and turbulence i modelled uing the k- turbulence model. An addital ource term i added to the ga flow equat to cature the effect of electric field. Thi addital ource term i obtained by olving a couled ytem of the electric field and charge tranort equat. The article hae i imulated by uing Dicrete Phae Model (DPM). The reult of the imulat are reented howing the article trajectory inide the ESP under the influence of both aerodynamic and electrotatic force. The imulated reult have been validated by the etablihed data. The model develoed i ueful to gain inight into the article collect henomena that take lace inide an indutrial ESP. Introduct An accurate CFD model of an ESP lay an imortant role in erformance otimizat by redicting the flow field characteritic and article trajectorie inide the ESP. The latetye ESP of the local ower lant conit of a erie of arallel collect late, aced 4 mm aart, oriented along the direct of the flue ga flow. A number of thin dicharge electrode (DE) hang vertically between thee late. The reciitat roce involve charging article of the flue ga by alying high negative voltage to the dicharge electrode and driving the charged article toward the grounded collect electrode (CE) by the electric field roduced. The collected article are then removed from the collect electrode by raing roce. The negligible change of the electric field in the vertical direct jutifie a two-dimenal aroach of thi tudy. Due to the ymmetry between the late, only half of the ditance between the late i conidered for modeling uroe. There i a limited reearch found in the literature on ESP imulat. Lami et al. [1], Zhao et al. [], Park and Kim [3], Anagnotooulo and Bergele [4] imlified their imulat by modeling ingle wire configurat. Suda et al [5] included even wire in their ga flow field model but conidered only ingle wire egment for their ic wind analyi. Single wire model might not cature the wake of the wire roerly and it can not be aumed that the electric field or article mot are recurrent in the ga flow direct. Hence three wire have been taken into coniderat for thi tudy to develo a rereentative numerical model of ESP. Only few tudie [6, 7, 8] have been found in the literature where three wire have been conidered for modeling ESP. The reent tudy attemt to develo a detailed numerical aroach and a imulat rocedure to redict the mot of ga, and article inide an ESP channel. The imulated reult ha been verified with the available literature data. The twodimenal Navier Stoke equat have been ued to model the ga flow. The article mot i conidered by mean of Lagrangian aroach. Geometry Configurat An ESP channel of the local ower tat conit of a erie of dicharge electrode laced between two collecting electrode having 4 mm acing between them. Due to the ymmetry of the geometry only half of a channel i modeled in thi tudy a i hown in Figure 1. The Fluent Inc. geometry and meh generat oftware GAMBIT wa ued a a reroceor to create the geometry, dicretize the fluid domain into mall cell to form a volume meh or grid and et u the aroriate boundary condit. The comutatal meh which conit of 15 cell i hown in Figure. Figure 1. D geometry configurat Figure. Comutatal meh 15

2 Numerical Model Numerical calculat for the ga flow are carried out by olving the ynold-averaged Navier-Stoke equat. An addital ource term i added to the ga flow equat to cature the effect of electric field. The article hae i imulated by uing Dicrete Phae Model (DPM). Ga Phae The air inide the ESP i treated a incomreible Newtonian fluid due to the mall reure dro acro the ESP. The flow can be decribed by the Conervat of ma equat [9] + ( V ) t (1) and the Momentum equat known a Navier-Stoke equat [9] µ V V + V + S () i the fluid denity (kg/m 3 ), µ i the dynamic vicoity (kg/m/) of the fluid, i the fluid reure (Pa) and V i the fluid velocity (m/). S i the ource term, which exree the momentum force (N/m ) on the ga flow due to the electric field and can be exreed a [6] S E i the charge denity (C/m 3 ) and E i the electric field intenity (V/m). Electrotatic Field A high negative voltage i alied to the DE to generate the electrotatic field between the DE and the grounded CE. The electric field intenity E inide the ESP can decribed by the Gau law equat [1]. E E φ (5) Combining Equat (3) and (4) give the well known Poion equat which i defined a φ E i the electric field intenity (V/m), φ i the electric otential (Volt) and i the ermittivity of the free ace. Under tatary condit, the electrical flux denity i divergence-free and can be written a [11].. J J i the denity of ic current. Auming diffu i of negligible imortance comared to conduct [1, 11]), J can be exreed a J b E (8) (3) (4) (6) (7) b i the mobility. Combining Equat (7) and (8) give the following exre.( b φ) (9) With the boundary condit of Table 1 and an aroriate olut method, two tranort variable φ and can be numerically calculated. Particle Trajectory FLUENT redict the trajectory of a dicrete hae article (or drolet or bubble) by integrating the force balance on the article, which i written in a Lagrangian reference frame. Thi force balance equate the article inertia with the force acting on the article, and can be written a [1]), du dt reectively. g ( ) F ( u u ) + + F, i i D i, i i (1) dx i u ; i x, y dt (11) u and, i denote article denity and velocity F i correond to external force exerted on the article that, in the reent tudy, are the electrotatic force: Eiq Fi m E i i the electric field intenitie (V/m), (1) q and m denote the electric charge (C) and ma (kg) of the article reectively. F ( u u ) D i, i Here, i the drag force er unit article ma, where F D 3µ CD 4 d (13) u i i the fluid hae velocity (m/), µ i the molecular vicoity of the fluid (N.m/), i the fluid denity (kg/m 3 ) and u, i, d and denote the velocity (m/), diameter (m) and denity (kg/m 3 ) of the article reectively. i the relative ynold number, which i defined a The drag coefficient equat [13]: C D d u u µ, i i (14) C D can be calculated from the following 4 3 (1 1 b b + b ) + b + 4 (15) 151

3 b ex( φ φ ) 1 b φ b φ+ φ φ b ex( ) + φ φ + φ 3 ex( ) The hae factor,φ, i defined a φ S (16) (17) i the urface area of a here having the ame volume a the article, and S i the actual urface area of the article. The ynold number i comuted with the diameter of a here having the ame volume. Particle Charge The charge, q, which i acquired by a herical dielectric article with radiu rand relative ermittivity r exoed to an flux in a field E can be calculated in the Lagrangian framework by the following Pauthenier equat [14, 15]): 1 t [1+ ( )]4π + 1 ( + τ ) r q r E r t (18) r i the relative ermittivity of the ga, t i the reident time of the article and τ i the charging time contant which can be defined by the following exre τ 4E J (19) Comutatal Procedure The finite volume method have been ued to dicretize the artial differential equat of the model uing the imlec method for reure velocity couling and the econd order uwind cheme to interolate the variable on the urface of the control volume. The egregated olut algorithm wa elected to olve the governing equat equentially (i.e., egregated from one another). Standard wall funct, which are a collect of emi-emirical formula and funct, were alied to bridge the vicoity-affected reg between the wall and the fully-turbulent reg. The wall funct aroach i a oular and ractical ot for the near-wall treatment for indutrial flow imulat [1]. The electric otential on the dicharge electrode urface i contant and equal to the corona onet value, wherea at the grounded collecting late, it value i zero. At corona electrode electric otential Φ 7 kv. The charge denity at the dicharge electrode can be aroximately calculated by [15]: ( E E ) d () E i the field trength in the cell adjacent to the emitting electrode, d i the ditance between the cell and the electrode urface. The corona onet field E along the corona-emitting urface i aumed contant, which can be obtained according to Peek law [16]: E E X δ C C δ r 6 o Peek ( 1+ / ) (1) E Peek i the current threhold value for an electrode of radiu r and C 1 1 V/m and C.31 V/ m in air of relative denity δ with reect to the normal temerature and reure condit. By olving Poion equat and the charge denity equat alternatively and udating the boundary condit for, the convergent olut for electric field and ace charge denity can be obtained. The oerating ga wa ambient air while the article were aumed to be ah with denity equal to 6 kg/m 3. The article of diameter equal to. µm were injected from the inlet urface with.1 kg/ ma flow rate. Turbulent intenity at the inlet wa 5%. Boundary condit ued to olve thi roblem are ummarized in Table 1. Table 1. Boundary condit alied to the ESP model Ga Electric velocity otential Inlet Outlet Collecting electrode Dicharge electrode ux uy 1. m/. m/ Ma conervat φ φ No li φ No li Ion charge denity Particle mot u x u y 1. m/. m/ Ecae Ecae Tra φ 7kV Peek law flect ult and Dicu The numerical redict i comared with the reult of Choi and Fletcher [6] who develoed their model conidering 1 mm wire-late ditance rather than mm ditance. The redicted electric otential ditribut along a line from the wire to the late of thi tudy yield a good agreement with their data u to a certain ditance and then reache zero otential at the collect electrode a hown in Figure 3. A tated earlier the model of thi tudy ha been develoed according to the ecificat of the ESP ued at a local ower tat. It i felt that the literature data [6] would have been the ame a our redicted electric otential ditribut data if their geometry had ued mm wire-late ditance. Figure 4, 5 and 6 how the characteritic contour of the flow field. A exected, flow earat occurred after the dicharge electrode which i hown in Figure 5. Figure 7 how the contour of the electric otential where the otential field form an ellitical reg around the dicharge wire. Figure 8 how the contour of charge denity where an initial value of 1-7 C/m 3 i ued on the urface of the dicharge electrode [15]. It i found from Figure 9 that article tart to deviate from their traight ath toward the collecting late a they aroach to the wire. A a reult the DPM concentrat i higher near the collect wall which i hown in Figure 1. DPM concentrat ditribut at the exit of the ESP are lotted in Figure 11 with and without coniderat of the electrotatic field. The article concentrat near the collect wall i oberved to be 14% higher in the reence of electrotatic field. 15

4 Figure 3. Comarion with the ublihed data Figure 6. Contour of turbulence intenity (%) Figure 4. Contour of ga velocity magnitude (m/) Figure 7. Contour of electric otential (Volt) Figure 5. Velocity vector of ga flow (m/) Figure 8. Contour of charge denity (C/m 3 ) 153

5 alied to any geometrical and electrical configurat and can be ueful in identifying ot for imroving erformance of the indutrial electrotatic reciitator. Figure 9. Particle reidence time () Figure 1. Contour of DPM concentrat (kg/m 3 ) Figure 11. DPM concentrat ditribut at exit Concluding mark A two dimenal numerical analyi for the ESP i reented. alizable k- model for turbulence condit inide the ESP i alied. The electrotatic field i olved through writing and comiling a number of ubroutine and linking them with the tandard ver of FLUNET 6. oftware. The DPM model i ued to calculate the article dynamic. Numerically redicted electric otential inide the ESP i comared with the literature data. The redict i found in reaonable agreement with the literature data. The comutatal rocedure develoed can be ference [1] Lami, E., Mattachini, F., Gallimberti, I., Turri, R. and Tromboni, U., A numerical rocedure for comuting the voltage-current characteritic in electrotatic reciitator configurat, Journal of Electrotatic, 34, 1995, [] Zhao, L., Cruz, E. Dela., Adamiak, K., Berezin, A. A., Chang, J.S. (6). A numerical model of a wire-late electrotatic reciitator under electrohydrodynamic flow condit, The 1 th Internatal conference on electrotatic reciitator, Autralia. 6. [3] Park, Seok. Joo & Kim, Sang. Soo., Effect of electrohydrodynamic flow and turbulent diffu on collect efficiency of an electrotatic reciitator with cavity wall, Aerool Science and Technology, 37, 3, [4] Anagnotooulo, J. & Bergele, J., Corona dicharge imulat in wire-duct electrotatic reciitator, Journal of Electrotatic 54,, [5] Suda, J. M., Ivancy, T., Ki, I. and Berta, I., Comlex analyi of ic wind in ESP modeling, The 1 th Internatal conference on electrotatic reciitator, Autralia. 6. [6] Choi, B.S., and Fletcher, C.A.J, Turbulent article dier in an electrotatic reciitator, Alied mathematical modeling,, 1998, [7] Nika, K.S.P., Varono, A.A. and Bergele, G.C., Numerical imulat of the flow and the collect mechanim inide a laboratory cale electrotatic reciitator, Journal of electrotatic, 63, 5, [8] Egli, Walter., Kogelchatz, Ulrich., Gerteien, Edgar. A. and Gruber, Ralf., 3D comutat of corona, induced econdary flow and article mot in technical ESP configurat, Journal of electrotatic, 4&41, 1997, [9] Munon, B.R., Young, D.F., Okiihi, T.H., Fundamental of fluid mechanic, 4 th ed., John Wiley & Son Inc., NY,. [1] Kallio, Gregory A. and Stock, David E., Comutat of electrical condit inide wire-duct electrotatic reciitator uing a combined finite-element, finitediffernece technique, Journal of Alied Phyic, 59 (6), 1986, [11] Poner, Marc., Sonnenchin, Rainer. and Meyer, Jorg., Electric field couled with ace charge. Part : comutat, Journal of electrotatic, 63, 5, [1] Fluent Inc. (5). Fluent 6. Uer Guide. [13] Haider, A. and Leveniel, O., Drag coefficient and terminal velocity of herical and nonherical article. Powder Technology, 58, 1989, [14] Bottner, C.U. and Sommerfeld, M. (1). Euler/Lagrange calculat of article mot in turbulent flow couled with an electric field. Proceeding of ECCOMAS Comutatal Fluid Dynamic Conference, 1. [15] Ye, Q. and Domnick, J., On the imulat of ace charge in electrotatic owder coating with a corona ray gun, Powder technology, , 3, 5 6. [16] Peek, F.W., Determinat Phenomena in High Voltage Engineering, McGraw-Hill, New York, 199,