This article was downloaded by:[kaist Korea Advanced Inst Science & Technology] On: 24 March 2008 Access Details: [subscription number 731671394] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Aerosol Science and Technology Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713656376 A Two-Dimensional Model for Polydisperse Particles on the Effective Migration Rate of the Electrostatic Precipitator with Wider Plate-Spacing Joon-Ho Ko a ; Son-Ki Ihm a a DEPARTMENT OF CHEMICAL ENGINEERING, KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY, TAEJON, KOREA First Published on: 01 January 1997 To cite this Article: Ko, Joon-Ho and Ihm, Son-Ki (1997) 'A Two-Dimensional Model for Polydisperse Particles on the Effective Migration Rate of the Electrostatic Precipitator with Wider Plate-Spacing', Aerosol Science and Technology, 26:5, 398-402 To link to this article: DOI: 10.1080/02786829708965440 URL: http://dx.doi.org/10.1080/02786829708965440 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
Downloaded By: [KAIST Korea Advanced Inst Science & Technology] At: 12:04 24 March 2008 A TWO-,Dimensional Model for Polydisperse Particles on the Effective Migration Rate of the Electrostatic Precipitator with Wider Plate-Spacing Joon-No KO and Son-Ki Ihm* DEPARTMENT OF CHEMICAL ENGINEERING, KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY, INTRODUCTION In electrostatic precipitation (ESP), Deutsch equation is used to obtain the particle migration velocity from the known collecting area, the measured collection efficiency, and the volumetric flow rate for existing precipitator. This migration velocity is called the effective migration rate. Experimental and most industrial-scale tests over many years show that the effective migration rate increases with plate-spacing [McLean, 19881. These observations seems to contradict the Deutsch concept. Various hypotheses have been proposed for the explanation of the so-called non-deutschian phenomenon. The hypotheses for explaining the wider plate-spacing effect [Riehle and Loffler, 19921 can be classified as follows: Higher electrical field strength due to the space charge Back-diffusion of particles near the plate due to the turbulent mixing effect Loss mechanism such as non-idealities in commercial ESPs Although it is accepted that the electrical field, turbulence and particle back-diffusion 373-1 KUSONG-DONG, WSONG-GU, TAEJON 305-701, KOREA in the proximity of the collection plate decisively affect the collection behavior, the quantification of this influence is, even today, scarcely possible. The present work is aimed to investigate how these hypotheses are related to the wider plate-spacing effect. MODEL ANALYSIS Consider a simplified plate precipitator in Figure 1. The electrical field induces a motion of particle in transverse direction. It is usually assumed that the mean particle velocity in the longitudinal direction is identical with the mean gas velocity. Neglecting the effect of gravity and assuming a steady state, the two-dimensional transport equation of the size i particle in the range of diameter a and a + Aa can be obtained: where CPi is the number concentration of the size i particle, D is the turbulent diffusivity, u is the mean gas velocity, wi is the electrostatic velocity of the size i particle given by *Corresponding author. Aerosol Science and Technology 26398-402 (1997) O 1997 American Association for Aerosol Rcsearch Published by Elsevicr Science Inc.
Aerosol Science and Technology 265 May 1997 2D Model of Electrostatic Device 399 Downloaded By: [KAIST Korea Advanced Inst Science & Technology] At: 12:04 24 March 2008 FIGURE 1. Simplified representation of electrostatic precipitator. where Q, is a particle charge, E, is the electrical field near the particle, p is the fluid viscosity, and C,(A) is Cunningham correction factor with mean free path A of the gas molecule. Qp is assumed to have its maximal electrostatic charge based on Cochet's equation. Inlet and boundary conditions are given as follows: field becomes where Ye collection electrode 6HWo exp[4.5 1n2 a,] S,ao where n(a) is the inlet particle size distribution. The use of the moments gives the advantage of simplicity while providing the most important information for the process. The evolution of the moment of the distribution is obtained by multiplying both sides of Eq. (1) by a9 and integrating over all particle sizes. The log-normal function is used since many experimental results indicate that the particle size distributions are log-normal or, more frequently, particles are measured and characterized by using the parameters of a log-normal function. One-dimensional electrical field is here assumed along the transverse direction. Since the space charge in system is due to the charged particles, the local electrical In Eq. (5), a, is the number-specific median of distribution, In o is distribution width,
Downloaded By: [KAIST Korea Advanced Inst Science & Technology] At: 12:04 24 March 2008 400 J. -H. KO and S.-K Ihm Aerosol Science and Technology 265 May 1997 E, is the applied field, W, is the mass concentration of the particles,.zr is dielectric constant, and S, is specific gravity of the particle. a, and In a, also denote the mass median and the distribution width in the inlet section. The dimensionless parameters are defined as follows where M, represents the qth moment. The d~mensionless migration velocity is also represented by where conditions in Eq. (3) are rearranged by the use of the moments. The exact solution is extremely difficult to obtain due to the nonlinear nature of the problem. The method of lines as a numerical method is used to solve the present model (Riggs, 1988). RESULTS AND DISCUSSION Figure 2 represents the effective migration rate as a function of specific collecting area (SCA = L/uH) for different levels of turbulent mixing in the case of a, = 5 Fm and In a, = 1.0. The values of parameters used for simulation are given in Table 1. In the figure, y, denotes the electrical disturbance parameter. y, = 2 means the electrical field at the collection plate is twice the applied field in the inlet section due to the particulate space charge. R represents the degree of turbulent mixing. So-called the electrical Peclet number Pe has been used as a measure of the relative strengths of electrostatic force and diffusion on particle transport. R is related to Pe as follows: Substituting Eqs. (4) and (7) into Eq. (I), the moment equations become as follows: dma d - + -(AIM; +A2M; +A3ML, dz' dy 1 d2mh +A,MI,) = - - R dyr2 ' dm; d - + 7(AlM; +A2M; +A3Mh dz' dy (8) 1 d2m; +A4ML1) = -T, (9) R dy dm; d - + -(AIM; +A2Mi +A3M; dz' dy The values of Pe in typical ESP conditions are 0-5. Since u/w > 3, the selected value R (0, 10, and 50) is in the proper range. 1 d2m; 0.0 I +A4Mi) = -- (10) 0 10 20 30 R dyt2 ' SCA [mlsec~' The set Eqs' (8)-(10) is a form of partial FIGURE 2. Effective migration rate as a function of differential equations (PDE~) with inlet and SCA for differentlevels of turbulent mixing (a, = 5 pm, boundary conditions. Initial and boundary In u,, = 1.0). I I I
Aerosol Science and Technology 265 May 1997 2D Model of Electrostatic Device 401 Downloaded By: [KAIST Korea Advanced Inst Science & Technology] At: 12:04 24 March 2008 TABLE 1. Parameters of the Present Model. Dielectric constant cr = 5 Specific gravity of dust S, = 2270 kg/m3 Fluid viscosity p = 2.4 x 10W5 kg/m. sec Electrical field strength E, = 3 kv/cm Average gas velocity Plate spacing Precipitator length L When the inlet dust concentration is very dilute, the electrical field is almost independent of the particulate space charge (yo = 0). The effective migration rates are higher than that for perfect turbulent mixing (i.e., R = 0) in the wider range of the SCA. For small values of SCA ( - O), larger particles tend to collect on the collection plate at a faster rate. It may lead to a higher effective migration rate. As the SCA increases, the size distribution of the remainder particles in the ESPs is shifted to be in the range of the particle sizes (0.2-0.5 Frn), which renders the minimum mobility. Accordingly it is expected for poor turbulent mixing (i.e., large R) that the effective migration rate does not decrease monotonously but shows an increase over some range of SCA. The fact for polydisperse particles that larger particles in the interior region move more quickly toward to the collection plate and have more chance to participate in precipitation than smaller particles can not be taken as benefit for the case of uniform size distribution (Leonard et al., 1980) or perfect turbulent mixing of R = 0 (Bai et al., 1995). For a higher space charge density, however, the electrical field strength around the discharge electrode is lower while the strength at the collection plate is higher. It can be seen that the separation efficiency is very high since a higher electrical field accelerates the migration of the charged particles toward the collection plate. The effect of the turbulent mixing on the effective migration rate seems to be surpassed by the strong effect of space charge. Figure 3 shows the effective migration rate as a function of design parameter for design parameter, uhil [mlsec] FIGURE 3. Effective migration rate as a function of the design parameter compared with Wiggers' 1982 experimental results. different plate-spacing in the case of a, = 8.5 pm, In a, =. 1.0. The scattering phenomena of Wiggers' experimental data (Riehle and Loffler, 1992) along the design parameter (uh/l) can be well explained by the present work. It is suggested that the scattering of the experimental data seems to be due to both the turbulent mixing effect and the space charge effect. CONCLUSIONS A two-dimensional model for polydisperse particles in an electrostatic precipitator has been proposed for explaining the effects not only from the particle size distribution but also from the turbulent mixing and particulate space charge. It was demonstrated that the model could explain one of typical non-deutschian phenomena, i.e., the wider plate-spacing effect. The effective migration rate seems to be a function of the levels of the turbulent mixing and the space charge as well as of the particle size distribution. In case of relatively lower space charge density, the turbulent mixing seems to enhance the effective migration rate in some region of SCA. In the present model for polydisperse particles, the levels of the turbulent mixing could be an important parameter to predict the collection
Downloaded By: [KAIST Korea Advanced Inst Science & Technology] At: 12:04 24 March 2008 402 J.-H. KO and S. -K Ihm efficiency. As the particulate space charge becomes higher, however, the influence of the turbulent mixing on the effective migration rate becomes less. References Bai, H., Lu, C., and Chang, C-L. (1995). A Model to Predict the System Performance of an Electrostatic Prccipitator for Collecting Polydisperse Particles, J. Air Waste Manage. Assoc. 45:908-916. Leonard, G. L., Mitchner, M., and Self, S. A. Aerosol Science and Technology 26:5 May 1997 (1980). Particle Transport in Electrostatic Precipitators, Atmos. Enuiron. 14:1289-1299. McLean, K. J. (1988). Electrostatic Precipitators, IEE Proceedings 135:347-361. Riehle, C., and Loffler, F. (1992). The Effective Migration Rate in Electrostatic Precipitators, Aerosol Sci. Technol. 16:l-14. Riggs, J. B. (1988). An Introduction to Numerical Methods for Chemical Engineers, Texas Tech University Press, p. 209. Received February 26, 1996; revised December 12, 1996.