A MODEL TO PREDICT THE SYSTEM PERFORMANCE OF AN ELECTROSTATIC PRECIPITATOR FOR COLLECTING POLYDISPERSE PARTICLES

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A Model to Predict the System Performance of an

Electrostatic Precipitator for Collecting Polydisperse

Particles

Hsunling Bai a , Chungsying Lu b & Chung Liang Chang a a

Institute of Environmental Engineering, National Chiao-Tung University , Hsin-Chu , Taiwan

b

Department of Environmental Engineering , National Chung Hsing University , Taichung , Taiwan

Published online: 05 Mar 2012.

To cite this article: Hsunling Bai , Chungsying Lu & Chung Liang Chang (1995) A Model to Predict the System

Performance of an Electrostatic Precipitator for Collecting Polydisperse Particles, Journal of the Air & Waste Management Association, 45:11, 908-916, DOI: 10.1080/10473289.1995.10467423

To link to this article: http://dx.doi.org/10.1080/10473289.1995.10467423

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A Model to Predict the System Performance of an

Electrostatic Precipitator for Collecting Polydisperse Particles

Hsunling Bai

Institute of Environmental Engineering, National Chiao-Tung University, Hsin-Chu, Taiwan

Chungsying Lu

Department of Environmental Engineering, National Chung Hsing University, Taichung, Taiwan

Chung Liang Chang

Institute of Environmental Engineering, National Chiao-Tung University, Hsin-Chu, Taiwan

ABSTRACT

This paper presents a model for predicting the performance of an electrostatic precipitator (ESP) for collecting polydis-perse particles. The particle charge was obtained by modify-ing Cochet's charge equation; the particle size distribution was approximated by a lognormal function; and then the statistic method of moments was employed to obtain a set of the first three moment equations. The continuous evolu-tion of the particle size distribuevolu-tion in an ESP is easily taken into account by the first three moment equations. The per-formance of this model was validated by comparing its pre-dictions with the existing data available in the literature. Effects of the particle size distribution on the ESP perfor-mance were examined, and the results indicated that both overall mass and number efficiencies are lower for inlet par-ticles with a larger mass median diameter and a higher geo-metric standard deviation. The methodology introduced may be applied to develop design criteria and determine optimal operating conditions of an ESP for improving the collection efficiency of the submicron particles.

INTRODUCTION

Electrostatic precipitators (ESPs) are one of the most com-mon particulate control devices used to control fly ash emis-sions from utility boilers, incinerators, and many industrial

IMPLICATIONS

Since the passage of the Clean Air Act Amendments of 1990 in the United States, toxic substances in fine fly ash particles have been of concern around the world. The over-all mass efficiency traditionover-ally used for a particulate con-trol device is insufficient to clearly confirm that toxic substances collect on the fly ash particles. This paper pre-sents a model to predict the overall mass and number effi-ciencies of an ESP. By applying this model, the operation and design of an ESP can be improved, and the collection efficiency of submicron particles (and therefore the toxic substances in fine fly ash particles) can be increased.

processes. The first mathematic model of ESP performance is the famous Deutsch-Anderson equation,1

r] = 1 - exp ( fr*~) (1)

where rj is the collection efficiency, Ac is the collector sur-face area, Ve is the effective migration velocity of particles, and Q is the volumetric flow rate of gas through the unit. Although the Deutsch-Anderson equation is widely used in the design of ESPs, its assumptions of monodisperse par-ticles and constant effective migration velocity of parpar-ticles in the ESP restrict its ability to provide accurate predictions. A common industrial application of the Deutsch-Ander-son equation is to compute the grade efficiency over all par-ticle size spectrum, and then integrate the grade efficiency for obtaining the overall mass efficiency as given by2

J0>V|(dp)dpni(dp)d(dp)

Jo~djni(clp)d(dp) (2)

where -m, (dp) is the grade efficiency, dp is the particle diam-eter, and nj (dp) is the inlet particle size distribution func-tion. Feldman3 employed this approach and modified the Deutsch-Anderson equation by assuming a lognormal size distribution function. The grade efficiency appearing in his model is

2k. _)

d

(3)

where e() is the permittivity of free space, Eav is the average field strength, C is the Cunningham slip correction factor, u. is the fluid viscosity, A. is the mean free path of the gas, and K is the dielectric constant of the particle.

Gooch and Francis4 also incorporated a lognormal size dis-tribution function in their ESP model and reported that both the mass median diameter (MMD) and the geometric stan-dard deviation (o-,r) have profound effects on the overall mass

Bai, Lu, and Chang efficiency. The overall mass efficiency increases with

increas-ing MMD or decreasincreas-ing ag. Recently a study of the effect of the particle size distribution on the effective migration veloc-ity of particles was conducted by Riehle and Loftier.5 In their study, a lognormal inlet particle size distribution was assumed and they concluded that <rg has a significant influence on the effective migration velocity of particles in the ESP.

Although the polydisperse nature of particles can be ac-counted for by the integration of grade efficiency, it usually requires one to be familiar with numerical analysis, such as the Gauss-Hermite quadrature method.2 In addition, when more complicated mechanisms (such as fluid dynamics and the space charge effect, which may influence the particle transport behavior) are to be incorporated into the model, the integration method often requires a significant compu-tational effort.

Another widely employed ESP model accounting for the polydisperse nature of particles is the Matts-Ohnfeldt Model,6

ri=l-exp(-^k)* (4)

where k is an adjustable parameter which normally ranges from 0.4 to 0.6. Since this method employs a rough esti-mate of particle polydispersity, it is simpler than the inte-gration method used by Feldman3 and Gooch and Francis.4 Although the above models account for the effects of particle polydispersity, the continuous change of the par-ticle size distribution along the ESP may not be easily con-sidered. Furthermore, most ESP models predict the mass efficiency, with which the collection of submicron particles could not be actually evaluated. And it is known that con-centrations of many toxic substances are higher in fine fly ash particles than in coarse particles.7 Therefore the collec-tion efficiency, in terms of the particle number, would be more meaningful for the collection of submicron particles.

The goal of this study is to present a model considering the continuous evolution of lognormally distributed par-ticles in terms of the moments over the entire particle size spectrum for predicting the overall mass and number effi-ciencies of an ESP. The performance of this model is vali-dated by comparing its predictions with the existing data available in the literature. Effects of the specific collecting area (SCA) and the particle size distribution on the overall mass and number efficiencies of an ESP are investigated and quantitatively determined.

MODEL DEVELOPMENT

Basic Assumptions

The following major assumptions are made in developing the proposed model to study the performance of an ESP:

1. The system is in a steady-state operating condition. 2. Particle resistivity is not considered in this model. 3. Effects of gas leakage and rapping reentrainment are

neglected.

4. An average dust flow velocity is used which approxi-mates the actual velocity profile.

5. The size distribution is approximated by a lognor-mal function throughout the ESP.

6. The particle saturation charge is attained in a very short time, compared to the total residence time of particles.

Mass Balance Equation

The schematic diagram of a dust stream flowing through a plate-plate or wire-plate ESP is shown in Figure 1. The mass balance equation in terms of the particle size distribu-tion funcdistribu-tion, n(v), over a control volume of finite length, Ax, is given by

ApUav(n(v)lx - n(v)lx + AX) = VeAcn(v)lx (5)

where Ap is the precipitator cross sectional area (= h w); h is the height of the collecting plate; w is the space between two parallel plates; Uav is the average dust flow velocity; v is the particle volume; and x is the axial distance. The collec-tor surface area (Ac) is equal to 2hAx. The left-hand term of equation (5) accounts for the flow convection, while the right-hand term accounts for the external electrostatic force. On dividing both sides by Ax and taking the limit as Ax goes to zero, equation (5) becomes

d n ( v ) _ «Ven(v)

U JIY j — — ~ ~ — —£d I 01

Once the effective migration velocity of particles is determined, the evolution of the particle size distribution function, n(v), along an ESP can be solved using equation (6). The effective migration velocity of a particle of diameter dp is8

Ve =

where q is the particle charge and Ec is the electric field strength at the collector surface.

Electrode plate (or wires)

Gas flow

Collector plate

Figure 1 . Schematic diagram of a dust stream flowing through a plate-plate or wire-plate electrostatic precipitator.

Particle Charge Equation

The particle charge (q) is a function of particle size, and can be described by Cochet's charge equation9

K+2 (8)

where \4 is the ionic mean free path and E,. is the local elec-tric field strength. Although Cochet's equation is simple com-pared to other particle charge theories, it is not an integrable form. Therefore Cochet's equation is brought into an inte-grable form by the following procedures.

Fine particle charge. For fine particles much smaller than the

ionic mean free path (Vdp» 1)> t n e second term in the bracket of equation (8) can be ignored. The particle charge equation is thus simplified as

(9)

A further simplification can be made by approximating (l+2X,/dp)2 to (2ydp),z given by

(10)

Coarse particle charge. For coarse particles much larger than the

ionic mean free path (Vdp» 1)/ the value of 2A,/dp for the first and second terms in the bracket of equation (8) can be ne-glected. The particle charge equation is thus simplified as

K - 1

qc= ( l + 2 K_2 ) 7 r e0EMd2 p

(11)

Total particle charge. Both equations (10) and (11) have

maxi-mum departures from Cochet's equation as values of 2\j/dp approach unity. However, departures are found to be mini-mum if these two equations are additive. Hence the particle charge in terms of particle volume (v) over the entire par-ticle size spectrum is a combination of the two equations and is expressed as

where

and

(13)

(14) A comparison of the particle charges using the modified form of Cochet's equation and the original form of Cochet's equation is shown in Figure 2. The approximation is quite close to the charges predicted by Cochet's equation, with

10 10 o 10 10 10 10 "' 1

Particle Diameter, micron

10

Figure 2 . The particle charges predicted by the modified Cochet's equation and by Cochet's equation.

some differences for fine particles. The agreement would be better if equation (9) was used instead for fine particle charge. However, equation (10) is employed in the following study for computational simplicity.

Cunningham slip correction factor. Similarly, the Cunningham

slip correction factor can also be brought into an integrable form by using the approximation proposed by Bai and Biswas:10

c = C* + 3 . 3 1 4 —

dP (15)

where C = 0.56 for X/dp>l and C* = 1 for \/dp£ 1.

Effective migration velocity. The electric field strength at the

collector surface (£<) and the local electric field strength (EJ can be assumed to equal the average field strength (Eav) in a single-stage ESP.2 Substituting equations (12) and (15) into equation (7), the effective migration velocity of a particle is written as v = where and 3.314XEa 317(1 ) (16) (17) (18)

Method of moments. The use of moments has the advantage

of simplicity in evaluating the continuous evolution of poly-disperse particles. However, a close set of moment equa-tions can not be obtained unless the shape of the size distribution is represented by a specific function. For this

Bai, Lu, and Chang purpose, a lognormal function is used, since most ESP

models characterize the particle size distribution by a lognormal function. The jth moment of a particle size distribution is11

and

M =

(19) while the size distribution function, n(v), for lognormally distributed particles is defined as8

n(v) = N

ln<r

_181nV.

(20)

where N is the total particle number concentration, vg is the geometric mean particle volume, and ag is the geo-metric standard deviation. Values of vg and <rg can be ex-pressed in terms of the first three moments of the distribution as12

v =•

_M

rl/2 (21)

(22)

where Mo is the zeroth moment which represents the total particle number concentration (= N); Mx is the first volume moment which denotes the total particle volume; M2 is the second volume moment which indicates the amount of light scattered due to the particles' exit from the ESP. Thus, the first three moments of the distribution are sufficient to de-scribe the behavior of the size distribution of lognormally preserving particles and the jth moment of the distribution can be written in terms of Mo, vg, and <rg as12

(23)

Model equations. Substituting equation (16) into equation

(6), multiplying both sides by v i dv, and integrating over the entire particle size spectrum, the continuous evolution of the first three moments of the distribution along the ESP are given by (24) - dx w w (25) (26) 3 e xP( 2 1 n a (27) ve2=qxq/ (28) i 2 'exp (6.51n a) (29) The associated initial conditions of equations (24) - (26) are:

at x = 0, Mo=Ni, M1=N1vglexp(4.51n2ffgi),

M2=Nivgi2exp(181n2agi) (30)

where subscript "i" represents the inlet condition.

Equations (24) - (26), along with the initial conditions, constitute a set of coupled ordinary differential equations (ODEs) that describe the continuous evolution of the first three moments of the distribution along the ESP. These ODEs are then solved by an IMSL stiff ODE solver, DIVPAG.13

Once the first three moments of the distribution are solved, the number efficiency of an ESP can be obtained from the evolution of Mo while the mass efficiency of an ESP can be obtained from the evolution of M^ The values of V^ and Vel are related to the number and mass average ef-fective migration velocities, respectively. It must be noted that particles of different sizes are being collected by the ESP at different rates. This produces continuous changes in N, vg, and crg, and thus results in variations of V^, Vel, and Ve2 along the ESP.

If other mechanisms are considered, they can be incor-porated into equations (24) - (26). However, if only particle polydispersity is of concern, the calculation procedure can be simplified by assuming no variations of V^, Vel, and Ve2 over a spatial step size (Ax). Therefore equations (24) - (26) are integrated to obtain a form similar to the Deutsch-Ander-son equation, given by

(31)

(32)

(33)

av

where superscript "m" denotes the calculation steps, and xm is equal to m«Ax.

The computation effort required using equations (31) -(33) is much simpler than that using equations (24) - (26). It can be done on a calculator or using spreadsheet software. By starting with the inlet vg and ag, the inlet values of Ve0, Vel, and Ve2 are obtained from equations (27) -(29). And using the values of V^, Vel, Ve2 and equation (30), the first three moment equations (31) - (33) are solved to obtain the new values of vg and ag at the next spatial step. The proce-dure is repeated step-by-step to determine the first three moments of the distribution at any location in an ESP.

Space Charge Effect

Derivation of the above equations was based on ignoring the space charge effect. The space charge effect, which en-hances the electric field strength, may be important if the inlet particle number concentration is high. The electric field strength at the collector surface for a plate-plate ESP which considers the space charge can be derived from the Gauss law14

E = + E ₍₃₄₎

where qv is the space charge density (= q N). Therefore as particles are continuously collected, the values of qv and Ec vary along the ESP.

When equations (12), (15), and (34) are substituted into equation (7), the effective migration velocity of a particle, considering the space charge effect, is written as

+2q1q2q4+2qiq2q3v3 +q'2q4v3 +cf2q3v)N +(qiq6 3 + q2q6+ q2qsv3 where and WC* q 6 3.314X.W / n \ T 12iT|xe0 6 (35) (36) (37)

By substituting equation (35) into equation (6), multiply-ing both sides by vi dv, and integratmultiply-ing over the entire par-ticle size range, equations (24) - (26) are also derived. The only difference between considering and neglecting the space charge effect is in the formulations of the three par-ticle migration velocities, given by

2 - - 2 2 - - - 2, : V^sfq^v 3exp (2 In <j)+qlqsv 3 exp3(0.5In

- 2 2 -+2q1q2q5vg3exp (0.5 In ffgHq&v,3 e xI -2 2 -~ 2 - 2 +q1q4vg"%xp (2 In o p + q ^ v ^ e x p (0.5 In a p +q2q4+q2q3vg3 exp (0.5 In CT (38) nV^+q^vexp (4.5 ln2ag)]Mo 1

+2qiq2qsvglf exp (3-5 lnVp+q^v^exp (8 lnVj+q^q^ exp (13.5 lnV)]M0

i e x p (-4 l n ^ + q ^ v f ^exp (-2.5 inV) 4q2q4+q2q3VgJ exp (3.5 InV) (39)

g K ^ V

"

-

2

-+2qiq2q5vg3exp (6-5 In " g H ^ ^ g3 ^ P (1 4

-1 2 - - 2 I 2

• H j ^ v 3exp (-10 In o-g)+qiq3vg 3exp (-5.5 In ffg)+q2q4+q2q3vg3 exp (6.5 In a )

(40)

RESULTS AND DISCUSSION

Model Verification

Except for the purpose of comparison with experimental data available in the literature, predictions were made based on the parameter values listed in Table 1. The stability of numerical solutions predicted by equations (24) - (26) and (31) - (33) as a function of spatial step sizes (Ax) was first investigated by comparing the overall mass efficiency of an ESP. Trails with varying Ax from 0.1 to 106 m, which corre-spond to ASCA of 0.5 to 5 x 106 s m1, were conducted and the results were that nearly identical solutions were observed for Ax < 0.01 m. Therefore Ax of 0.01 m was used in the following predictions.

The overall mass efficiency of an ESP predicted by the present model was then compared with the efficiency pre-dicted by Feldman's model.3 Figure 3 shows the compari-son results as a function of SCA. The inlet MMD and crg were selected as 2 \im and 2, respectively. The difference between the two models is that the present model predicted the overall mass efficiency in terms of the evolution of the first volume moment (Ma), while the Feldman's model cal-culated the grade efficiency of each particle size and then integrated it over all particle size regimes. Figure 3 shows that a reasonable agreement was obtained between the two models.

The differences in predicting the overall mass efficiency using Cochet's equation and the modified form of Cochet's

Table 1 . Parameters used in the study of an ESP performance.

Unit mass loading particle density ^-av

u

Bai, Lu, and Chang

100

This work

Feldman's model (with modified Coehet's equation) — — Feldman's model (with Coehet's equation)

40 60 SCA, sec m"1

80 100

Figure 3. The overall mass efficiencies predicted by the present model and by the Feldman's model using the modified Coehet's equation and Coehet's equation.

1.0 O.B 0.2 SCA= 0 s m" , - SCA-= 5 a m " » ,^ SCA-10 s erf V \ SCA-20 s m" 0.0 0.1 1 10 Particle diameter, Mm 100

Figure 4. The evolution of the particle size distribution obtained by computing the grade efficiency of each size. The inlet particle MMD and Og were 15 ^im and 2.2.

equation were evaluated and the results are also shown in Figure 3. Since Coehet's equation is not an integrable form, it can not be used in the present model. Therefore a com-parison of the two charge equations was made using Feldman's model. As Figure 3 shows, these two charge equa-tions yield close results in the overall mass efficiency. The maximum deviations between these two charge equations are less than 1% for the overall mass efficiency, and about 10% for the grade efficiency as the value of 2A.j/dp equals 1. The lognormal conservation of the particle size distribu-tion in an ESP was then investigated. Figure 4 shows the evolution of the particle size distribution along an ESP. The inlet particle MMD and ag are 15 \im and 2.2, respectively. As can be seen, when starting with a lognormal inlet par-ticle size distribution (SCA = 0), the distribution shifts con-tinuously to the finer particles as SCA becomes larger. But the size distribution can still be approximated well by a

8.0

& 1.5

m E

• • • • • Wigger's expeerimental data Predicted with space charge Predicted without space charge

10 15 20 SCA, sec m"'

25 30

Figure 5. Comparison of the effective migration velocities predicted by the present model with the experimental data documented by Wiggers.15

lognormal function. This is observed from the Gaussian shape of the distribution when it is plotted on a logarithmic scale, and may be attributed to the fact that both very large and very fine particles are collected efficiently by field charg-ing and diffusion chargcharg-ing, respectively. As a result, the par-ticle size distribution remains a lognormal function along an ESP, without a significant deviation.

Space Charge Effect

Figure 5 shows a comparison of the effective migration ve-locities predicted by the present model with the experimen-tal data documented by Wiggers.15 His experimental conditions are summarized as: the ESP was 3 meters in length and the average electric field strength was 6.4 ± 0.6 kV cm1. The variation in SCA was controlled by variable plate spac-ing. A quartz dust with inlet MMD and ag of around 8.5 fim and 2.5 was employed. The dielectric constant was assumed to be 10 for the quartz dust. Predictions were made both considering and neglecting the space charge effect. As can be seen in Figure 5 for small SCAs, the model predictions which considered the space charge effect resulted in better agreement than those that neglected the space charge ef-fect. On the other hand, for large SCAs the space charge effect is not significant, and both compare well with Wiggers' experimental data.

Figure 6 shows the overall mass efficiency as a func-tion of inlet particle MMD when the space charge effect is considered and when it is neglected. The SCA was 40 s m-1 and the inlet o-g was 2. As can be seen, the space charge effect was significant for inlet particle MMDs in the range of around 0.03 to 1 |im. However, for the typical range of particle MMDs (2-20 |j.m) encountered in many industrial combustion pro-cesses,16 the space charge effect may be neglected.

Particle Size Distribution Effect

Evolution of the size distribution. Figures 7a and 7b show the

evolutions of o-0 and MMD as a function of SCA for inlet

M Efficiency , Overal l Mas s 96 90 85 -0.01 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1 / / inlet / i MMD, Mm

With space charge Without space charge

10 100

Figure 6 . The predicted overall mass efficiencies as a function of inlet particle MMD with considering and neglecting the space charge effect. The SCA was 40 s rrr1 and the inlet ag was 2.

particles with different o-gs. The inlet particle was 2 jxm and the space charge effect was considered. As can be seen, both ag and MMD drop quickly as particles enter an ESP, and then the rates of change for <rg and MMD slow down. This is be-cause both very large and very fine particles are captured almost immediately after entering an ESP. The remaining particles whose sizes fall in the range of around 0 . 1 - 1 (xm require more time to be captured.

Overall mass efficiency. The overall mass efficiencies as a

func-tion of inlet particle MMD with different sgs are shown in Figure 8a. The SCA was 10 s m1 and the space charge effect was considered. If the inlet particle MMD is large (e.g., lSjim), the ESP tends to have a higher overall mass efficiency for inlet particles with a narrow spread (e.g. sg = 1.0) than for those with a wide spread (e.g., sg = 2.2). This is because inlet particles with a large MMD but a narrow spread (which in-cludes most particles in the dust stream) are very large and can be collected efficiently. On the other hand, the trend is opposite for a small inlet particle MMD (e.g., 1 \xm). How-ever, as will be shown later in Figure 8c, this observation is valid only for a small SCA or at the early stage of an ESP.

Figure 8b shows the overall mass efficiencies as a func-tion of SCA for inlet particles with different <rgs. The inlet particle MMD was 15 um. As the figure shows, the overall mass efficiency decreases with increasing particle polydis-persity at all SCAs.

Figure 8c shows the overall mass efficiencies as a func-tion of SCA for inlet particles with different o-gs. The inlet particle MMD was 1 um. At SCAs less than 30 s m1, the overall mass efficiency increases with increasing particle poly-dispersity. However, the opposite trend is observed at SCAs larger than 34 s m1. This is because inlet particles with a wide spread (e.g., crg = 2.2) tend to lose coarse particles to the collector surface at a fast rate, which may lead to a high overall mass efficiency at the early stage of an ESP. But as the SCA increases, the uncollected particles are in the size range

%.% -o 1.6

i

Figure 7 a . The evolution of ag as a function of SCA for inlet particle

MMD of 2 um with different as.

3 0 2.5 2.0

I

i,.

Figure 7b. The evolution of particle MMD as a function of SCA for inlet particle MMD of 2 |xm with different <xgs.

of charging difficulty (0.2 - 2 um). Therefore, the particle collection rate slows down, and the overall mass efficiency may become lower than for those with a narrow spread. And as Figures 8b and 8c show, it is expected that inlet par-ticles with a narrow spread eventually have a high overall mass efficiency at large SCAs, no matter whether the inlet particle MMD is large or small.

Overall number efficiency. Figure 9a shows the overall

num-ber efficiencies as a function of inlet particle MMD with different sgs. The SCA was 10 s m1 and the space charge effect was considered. It is seen that variations of the overall number efficiency with respect to particle polydispersity are similar to those shown in Figure 8a for very large and very small inlet particle MMDs. On the other hand, for particles whose inlet MMD is in the range of charging difficulty (0.2 - 2 um), variations of the overall number efficiency with respect to particle polydispersity are quite different from those of the overall mass efficiency. For example, for inlet particles with an sg of 2.2 the minimum overall mass and number efficiencies occur at the same inlet MMD of around

Bai, Lu, and Chang 2 um. But the minimum overall mass efficiency (-90%) is

higher than that of monodisperse particles (-82%) while the minimum overall number efficiency (-70%) is lower than that of monodisperse particles (-82%).

Figure 8 a . The predicted overall mass efficiencies as a function of inlet particle MMD for different a s . The SCA was 10 s rrr1.

M o a o rai l

1

11/

-://

Figure 8b. The predicted overall mass efficiencies as a function of SCA for inlet particles with different o-gs. The inlet particle MMD

was 15 ^im. 100 BO • / • ' : '. ii • ij \ \ '/, '! / ' / / / /

1

Figure 8 c . The predicted overall mass efficiencies as a function of SCA for inlet particles with different <rgs. The inlet particle MMD was

Figures 9b and 9c show the overall number efficiencies as a function of SCA for inlet particle MMDs of 15 um and 1 um, respectively. As can be seen in Figure 9b, the overall number efficiency decreases with increasing particle

Figure 9 a . The predicted overall number efficiencies as a function of inlet particle MMD with different o- s. The SCA was 10 s nrr1.

w a ffi c UJ 0) qiu r z = i n n BO 60 40 "I 1 - 1 ' / • 1 ! ' - II '• II -11 - u -1 0 f 10 20 SCA, sec U - 1.0 rj - 1.8 rj = 2.2 30 40

Figure 9 b . The predicted overall number efficiencies as a function of SCA for inlet particles with different (Tgs. The inlet particle MMD

was 15 um. 100

100

Figure 9 c . The predicted overall number efficiencies as a function of SCA for inlet particles with different aQs. The inlet particle MMD

was 1 jim.

polydispersity for inlet particle MMD of 15 |xm at all SCAs. This observation is similar to variations of the overall mass efficiency shown in Figure 8b. On the other hand, as indi-cated in Figure 9c for inlet particle MMD of 1 (im, there is no clear trend for variations of the overall number efficiency with respect to the particle polydispersity.

CONCLUSIONS

This study demonstrated the use of moments in terms of a lognormal size distribution function to predict the overall mass and number efficiencies of an ESP. Two sets of equa-tions which result in analogous soluequa-tions were presented. The first set of equations (equations [24] -[26]) must be done using numerical analysis, while the second set of equations (equations [31] - [33]) can easily be done even with a calcu-lator. Equations (31) - (33) are practical for a primary design of an ESP while equations (24) - (26) can be employed and extended if more complicated mechanisms are to be incor-porated into the model. Both formulations of the effective migration velocities of considering and neglecting the space charge effect were also presented.

The performance of the present model was validated by comparing its predicted overall mass efficiencies as well as effective migration velocities with previous studies in the literature. The effects of the particle size distribution of MMD and ag on the overall mass and number efficiencies were

then investigated and quantitatively determined.

The advantages of the present model lie in the fact that it predicts the overall mass and number efficiencies of poly-disperse particles without having to compute the grade effi-ciency of each particle size. In addition, the total particle surface available (represented by M2/3) for deposition of heavy

metal vapors as well as the stack opacity (represented by M2) which leads to the visibility problem can also be readily calculated using the present model.

ACKNOWLEDGMENTS

Support from the National Science Council, Republic of China, through grant number NSC 84-221 l-E-009-002 is gratefully acknowledged.

NOMENCLATURE Aj. = Collector surface area Ap = Cross sectional area of ESP C = C u n n i n g h a m slip correction factor dp = Particle diameter

Eav = Average electric field strength

Ec = Electric field strength at t h e collector surface

E^ = Local electric field strength h = Height of collecting plate

Mj = j t h m o m e n t of particle size distribution MMD = Mass m e d i a n diameter

n = Particle size distribution function N = Particle n u m b e r concentration

Q = Volumetric flow rate of gas t h r o u g h t h e u n i t q = Particle charge

qv = Space charge density

SCA = Specific collecting area

Uav = Average dust flow velocity t h r o u g h t h e u n i t

Ve = Effective migration velocity of particles

v = Particle v o l u m e

vg = Geometric average particle v o l u m e

x = Axial distance

w = Space between two parallel plates Greek Symbols r\ = Collection efficiency K = Dielectric c o n s t a n t of particles ix = Flow viscosity X = M e a n free p a t h of t h e gas \ , = M e a n free p a t h of t h e i o n eo = Permittivity of free space

CT. = Geometric standard deviation Subscript = Inlet condition

REFERENCES

1. White, H.J. Industrial Electrostatic Predpitator; Addison-Wesley: Reading, MA, 1963.

2. Benitez, J. Process Engineering and Design for Air Pollution Control; PTR Prentice Hall: Rahway, NJ, 1993.

3. Feldman, P.L. "Effects of particle size distribution on the performance of electrostatic precipitators," Paper No. 75-02-3, in Proceedings of 68th Air

Pollution Control Association Conference; Air Pollution Control

Associa-tion: Pittsburgh, PA, 1975.

4. Gooch, J.P.; Francis, N.L. "A theoretically based mathematical model for calculation of electrostatic predpitator performance," /. Air Poll. Cont.

Assoc. 197 S, 25,108-113.

5. Riehle, C ; Loftier, F. "The effective migration rate in electrostatic pre-cipitators, " Aerosol Sd. Technol. 1992,16,1-14.

6. Matts, S.; Ohnfeldt, P. "Efficient gas cleaning with SF electrostatic pre-dpitator," Flakt, 1-12. Cited in Lawless, P.A.; Sparks, L.E. "A review of mathematical models for ESPs and comparison of their successes," in

Proceedings of Second International Conference on Electrostatic Precipitation,

Kyoto, Japan, 1984, 513-522.

7. Davison, R.L.; Natusch, D.F.S.; Wallace, J.R.; Evans, Jr., C.A. "Trace ele-ments in fly ash - dependence of concentration on particle size," Environ.

Sd. Technol. 1974,8,1107.

8. Flagan, R.C.; Seinfeld, J.H. Fundamentals of Air Pollution Engineering; Prentice Hall: Rahway, NJ, 1988.

9. Licht, W. Air Pollution Control Engineering, Marcel Dekker: New York, NY 1988.

10. Bai, H.; Biswas, P. "Deposition of lognormally distributed aerosols ac-counting for simultaneous diffusion, thermophoresis and coagulation," /. Aerosol Sd. 1990,21, 629-640.

11. Friedlander, S.K. Smoke, Dust and Haze; John Wiley & Sons: New York, NY, 1977.

12. Lee, K.W.; Chen, H.; Gieseke, J.A."Log-normally preserving size distri-bution for Brownian coagulation in the free molecule regime," Aerosol

Sd. Technol. 1984,3, 53-62.

13. IMSL Contents Document. International Mathematics And Statistics li-braries, Houston 2, Version 1.0,1987.

14. Crawford, M. Air Pollution Control Theory; McGraw-Hill: New York, NY, 1976.

15. Wiggers, H. Dissertation. Universitat Essen. Fortschr. Ber. VDI-Z. Reihe 3, Nr. 67,1982. Cited in Reference 5.

16. Buonicore, A.J.; Davis, W.T. Air Pollution Engineering Manual; Van Nostrand Reinhold: New York, NY, 1992

About the Authors

H. Bai, Ph.D. (corresponding author) is an associate professor in the Institute of Environmental Engineer-ing, National Chiao-Tung University, 75, Po-Ai St., Hsin-Chu, Taiwan. C. Lu, Ph.D. is an associate professor in the Department of Environmental Engineering, National Chung Hsing University, Taichung, Taiwan. C.L. Chang is currently a graduate student working on his doctor-ate degree in the Institute of Environmental Engineer-ing, National Chiao-Tung University, Taiwan.