Alternating Field Electrofluidized Beds in the Collection of Submicron Aerosols Jeffrey C. Alexander and James R. Melcher’ Department of Electrical Engineering, MasSachusefts Institute of Technology, Cambridge, Massachusetts 02 139
A theoretical model for collection of an aerosol in an electrofluidized bed (EFB) with an alternating electric field of variable frequency in both the co-flow and cross-flow configurations is presented. The theory asymptotically predicts the EFB collection efficiency at low and high excitation frequencies. A cut-off frequency is predicted above which the effect of using an ac excitation will significantly reduce the collection efficiency relative to that with dc fields. Experimental data for co-flow and cross-flow EFB’s of sand and glass beads collecting 0.4 wm diameter dioctyl phthalate confirm the ac collection model. Effective operation at 60 Hz is demonstrated under practical conditions.
Basic studies by Zahedi and Melcher (1976) have demonstrated the effectiveness of electrofluidized beds (EFB’s) for the control of fine particulate matter. In such devices, a fluidized bed of typically millimeter sized particles is stressed by an imposed electric field that effectively polarizes the bed particles. They then act as collection sites for the previously charged fine particulate entrained in the fluidizing gas. Advantages of the EFB derive from the greatly reduced residence time for effective cleaning of the gas, realized by virtue of the bed’s large collection surface area per unit volume, and the ease of handling the bed particles for removal of collected particulate. One practical motivation for this study comes from the difficulty encountered when conventional electrostatic precipitators (ESP’s) are used to collect highly resistive ash from low sulfur coal combustion. Poor performance is linked to the dc energization necessary for conventional ESP operation. The collection of highly resistive ash results in the buildup of net charge and an attendant interference with the imposed precipitating field. Such effects are not expected in alternating field devices where the gas-entrained ash can be a mixture of positively and negatively charged particulate. The feasibility of the ac energized EFB, especially with 60-Hz excitation, is of primary interest here, but also demonstrated is the use of frequency parameterized alternating field precipitation as a diagnostic tool that gives insights concerning the basic mechanisms of particulate transport. The alteration of bed particle mechanics and associated corona discharge in EFB’s at relatively high field strengths reported by Katz and Sears (1969) and electromechanical phenomena without electrical breakdown described by Johnson and Melcher (1975) are purposely avoided in the work reported here. Sufficiently low field strengths are used that such effects are not evident in the state of fluidization. Probably because of a general lack of practical motivation, very little work has been done to date on ac precipitation. Wells and Gerke (1919) photographed charged particles convected through transverse ac fields in an attempt to measure particle mobilities, and demonstrated regular periodic particle trajectories. Klemperer (1951) and Lau (1969) have proposed ac ESP’s but each depends on an effective rectification process to produce a time average net force on the particles. The following section, concerned with ac precipitation in a simple E S P geometry, serves to present basic ideas and motivate the model presented in the subsequent section on bed particle collection. In these sections high and low frequency asymptotic expressions for electrically induced par-
ticulate collection rates for the model system and then for single bed particles are derived. With this particle-scale collection model incorporated into a general flow collection model for the bed as a whole, an expression for the EFB ac collection efficiency is then obtained. Finally, experiments are reported in which DOP is used as a particulate having an assured stable agglomeration once collected by a bed particle. Results are correlated and interpreted in the light of the basic collection model.
Alternating Field Precipitation The response of a charged particle to an electric field having the angular frequency w = 2rf is determined by the inertial and viscous retarding forces. For a submicron particle having radius a and mass density pp moving in a gas of effective viscosity qc, the viscous effects dominate inertial forces if
In the experiments reported here, a = 2 X m, pp = lo3 kg/m3, and vC = 2 X kg/m-s. Thus, the condition of eq 1 is maintained over the frequency range 0 < f < 5 kHz used in the experiments. For a particle having a mobility b entrained in a laminar flow with an applied transverse field Eo cos ut, the displacement y relative to the gas is essentially
bE0 y = -sin w
wt
Typically, b is of the order of (m/s)/(V/m) and Eo is less than 5 x IO5 V/m so that bEo is less than 5 cm/s. In the next section, each bed particle with a surrounding unit cell is pictured as a “microscopic” ESP. By way of motivating approximations used, it is helpful to consider the simpler ESP configuration of Figure 1. The length of the electrodes, L , plays the role of the length of the unit cell traversed by the particulate as it passes through the bed. The distance between electrodes, h , is similar in its role to the distance between bed particles. With the gas flow taken as uniform over the cross section (velocity U ) and particulate taken as entering uniformly, the collection efficiency is worked out in detail by Alexander (1975) and shown to be a function of the parameters (bEo/U)(L/h)and wL/U. This detailed and complete analysis helps to place in perspective the approximations now used. Typical gas velocities U are 1-3 m/s, while for the unit cell, L and h are comparable. Hence, the first of these parameters is generally much less than unity. In this limiting case, the Ind. Eng. Chem., Fundam., Vol.
16, No. 3, 1977
311
I&\\, Is‘\ V
h
0
,:
\, \ \
(3
,,
\
\ \ \ \
/:\
,
, -
4-
\
X
L
Figure 1. Model ESP configuration.
REFERENCE PLANE
Figure 3. Dense-phase particle collection sites showing unit cells and likely local flow orientations.
wt0.O
+
@
excursion, ymax,of a particle from the stream line it is on as it crosses the reference plane, is a function of the time t o when it crosses the reference plane.
+ U T \
+
bE0 (1 sin w t o ) ymax(t0)= w
ut.:=
XIAX
Figure 2. Particle excursions from streamline under transversely applied alternating field.
If this reference plane is established at the entrance of the system, all particulate entering a t time t o a t distances above the electrode less than ymax(to)will be collected. Using the assumed linear flow profile, this instantaneous flux of particles to be collected is
r(to)= nw*(ym,,(to)) residence time L/U is short compared to the time required for the particle to move the transverse distance h between collecting surfaces, even if the field were constant. With the understanding that (bEo/U)(L/h)is small, low- and highfrequency asymptotic efficiencies are now considered, wLIU > 1, respectively. Because the particles collected are confined to the neighborhood of the collecting surface, the gas velocity is approximated in this region as being tangential to the boundary and having a linear dependence on the perpendicular coordinate y as sketched in Figure 1.
a* v, = -; dY
9
2
SY 2
(3)
For plane Poiseuille flow, S is related to the mean gas velocity ( U ) by S = 6( U ) l h . In the low-frequency limit, particles are either collected or have passed through the length L before the field has changed appreciably. Hence, the collection rate is the average of a succession of collection rates with particle trajectories determined as though the field were constant. For constant applied field, Edc, the collection rate is determined (without regard for the gas velocity profile) by noting that all collected particles arrive at the electrode surface with the same number density n as they have a t the entrance. Hence, the particle density at the electrode surface is n , the particle flux density is nbEd,, and the rate of collection is simply nbEd,Lw. Actually, Edc is a slowly varying sinusoid, and the average collection rate is found by averaging the “dc” collection rate over the half period during which the field has the proper polarity for collection. Over the other half period similar collection occurs on the upper electrode. With Eo defined as the peak field, the total collection on both electrodes is 2nbEo r l o w w = -Lw (4) lr
The high-frequency asymptotic efficiency is obtained by realizing that any particle has the opportunity to experience several complete oscillations in a residence time. A particle is collected if its trajectory causes it to intercept one of the electrodes. A useful concept is illustrated in Figure 2, where a reference plane is established in the flow. The maximum downward 312
Ind. Eng. Chern., Fundarn., Vol. 16, No. 3, 1977
(5)
(6)
Upon time averaging, the combined collection rate of the lower and upper electrodes is (7) The two asymptotic collection rates, eq 4 and 7, can be extended as functions of w to intercept each other a t a defined cutoff frequency.
Within a numerical factor, this cutoff occurs a t a frequency such that the residence time of a particle entering on a streamline a distance bEo/w from the collection surface is equal to the excitation period 2nlw. The cutoff in collection occurs when the frequency becomes high enough to begin turning around particles (during their residence time) which would be collected at dc.
Bed Particle Scale Collection For the collection of submicron particulate, the EFB can be considered an assemblage of unit cells, each comprised of a bed particle and the adjacent gas. Because of the random geometric organization of the bed, which with fluidization is continually evolving, each cell tends to act as an independent low efficiency ESP, much as described in the previous section. The generally accepted bubbling model for fluidized beds implies that in the dense phase, the local flow velocities and fraction voids are essentially those of a bed a t minimum fluidization. Excess flow passes through the bed in the form of bubbles. Most of the particulate collection occurs in the dense phase of the bed, where minimum fluidization parameters are presumed. The effect of the bubbles on the overall bed performance can be treated through the macroscopic bed collection dynamics (Zahedi and Melcher, 1977). A t minimum fluidization, the dense-phase unit-cell distribution sketched in Figure 3 prevails so that the equivalent radius Ro of the unit cell is related to the fraction voids in the entire bed by (9)
I Or
I
I
i I
/
D
\
\
i
!
n
’
2;
/
I
6-
,
;COLLINEAR CONTRALINEAR
-L I6 32 48
00
E ,
IN UNITS OF
64
lo5 V/M
1 00
P =-$urn,rzSiN2e
F i g u r e 4. Co-flow E F B collection efficiency as a function of applied electric field for collinear and contralinear configurations. R = 0.5 mm, b = 1.2 X lo-’ (m/s)/(V/m), relative humidity = 90%. Packed: U = 0.5 m/s, lo = 2.5 cm. Fluidized: U = 1.5 m/s, lo = 2 X lo-* cm, and l f = 2.5 cm.
Low-Frequency Collection Consider first the low-frequency asymptotic collection rate of a unit cell. For a dc applied field, this rate is (Zahedi and Melcher, 1976) rdc
= 3sR2cbEdcn
~
F i g u r e 5. Unit cell flow model.
number is somewhat greater than unity, the volume rate of flow is now related to the velocity profile immediately adjacent to the particle by using the low Reynolds number approximation. Then, a unit cell model (Happel, 1958) represents the flow around the particle as having no velocity at the particle surface and uniform flow with no shear stress at the unit cell radius Ro defined in eq 9. Within the unit cell, the gas velocity is related to the stream function Q by
(10)
where theoretical considerations indicate that c is approximately unity for somewhat conducting particles (such as sand or glass a t relative humidities in excess of 40%) and is t / ( c 2 4 (where t is the particle permittivity) if the bed particles are highly insulating. Co-flow experiments at relatively high states of fluidization and relative humidity show that c is in the range 0.8 < c < 1.1.A somewhat wider range occurs when the bed is a t low fluidization (Zahedi and Melcher, 1976). These experiments indicate little difference between co-flow collection rates with field and flow in the same direction (collinear) and in opposite directions (contralinear). More recent experiments carefully examining the effect of reversing the dc field in a co-flow shallow bed are represented by the data of Figure 4.The collinear collection rates are discernably higher than contralinear rates, but the difference represents a refinement beyond the predictive capacity that is the objective of the present study. It is reasonable to consider the asymptotic low-frequency collection rate as related to the dc collection rate in the same way as for the ESP in the previous section. With the understanding that (bEo/U) wc. The cut-off frequency wc, defined as the frequency a t which the low- and high-frequency asymptotes are equal, is given by eq g or h of Table I. The high-frequency collection rates depend on the parameter (1/u)(we/wm) which is a measure of the relative importance of electrical and mechanical effects. When mechanical effects dominate, w , / ~ , > 1, r depends only on o = w / w e , wc becomes W, and is identical in form with that of the model ESP. The same rationalization of the cutoff frequency applies; namely, particulates which would be collected with dc applied fields are turned around by the temporal variation of the ac field before being collected. Overall Bed Efficiency It is difficult to measure single particle collection rates, especially in a fluidized bed. Overall bed collection efficiencies, however, are relatively easy to measure. Zahedi and Melcher (1976,1977) have studied overall EFB collection with reference to several models. The simplest model for bed collection assumes uniform bed particle density and plug flow. Collection efficiency, 7, is then expressible in terms of the single particle collection rate r, the unfluidized bed height lo, the superficial gas velocity U , and the bed particle radius R 7=1
[
“-1
- exp - 8 n U R 3
For co-flow beds, where the electrode screens serve to effect the conditions assumed for the theory, eq 20 is well verified. It is inadequate in describing cross-flow collection where bubbles serve to pass gas through the bed providing little contact with bed particles. Gas which passes through the dense phase of the bed is cleaned like that in a plug flow bed. It would be possible to insert the theoretical collection rates directly into these overall bed collection theories. These models are subject to their own errors and attempts to account for differing bed properties (superficial velocities, particle radii, degrees of fluidization, size of bubbles, etc.) would obscure the issues of interest here. However, for small values of 7 and r all the bed collection models reduce to the same linear dependence of 7 on r
similar principles. It is assumed that the measured Vdc and Vnf can be correlated respectively to the theoretical r d c and rnf in Table I. Linearity of with r then implies
FAN
Vdc -=
- Vnf
__ AC CHARGER
= I U . J I
FLOW METER
AMBIENT AIR
GENERATOR CHARGER
Figure 7. EFB experimental facility.
CO- FLOW
CROSS- FLOW
Figure 8. Cross-flow and co-flow fluidized bed electrode configurations.
All experimental beds were operated approximately in this linear regime by design. Experimental deviations from linearity are estimated to be less than 10%. Assuming such a dependence, the results of Table I can be applied to the overall efficiencies with (7) Vdc
- v n f -- ( r )- r n f
- Bnf
rdc
- rnf
rdc
- rnf- 3nR2bCEdc
(23) nRSam2 All quantities on the left of eq 23 are measured, while all on the right except a, are experimentally specified. Thus, eq 23 can be solved for a,. The assumption of linearity between r and 17 introduces some error into the analysis. This error is estimated to be less than 10%.Any model for overall bed collection would do well to predict experimental results to a greater accuracy, especially for bubbling beds. Further, the linear approximation permits a rapid direct correlation of theory for a wide range of bed types. Under such light this assumption appears well justified. Vnf
(22)
T o verify the collection rate theory then, Vdc and Vnf must be determined for each bed tested and used to normalize (7). The effective particulate radius a, is found exploiting
rnf
Experimental Procedures and Results The experimental facility is shown schematically in Figure 7. A modified version of the Sinclair-La Mer generator produces an aerosol of DOP (dioctyl phthalate) droplets of radii (0.2 wm) uniform enough to be measured by higher order Tyndall spectra. Droplets are charged by ion impact to mobilities of 1.2 X (m/s)/(V/m) as measured by a small laminar flow ESP. The use of a liquid aerosol assures adhesion to the bed particles. To eliminate the effects of space charge on collection and collected aerosol on the state of fluidization, low DOP loadings are imposed. At low relative humidities, bed particles acquire charge frictionally. For basic studies, the associated “micro-field” collection of charged aerosol is undesirable. Such effects are eliminated when the fluidizing air is a t relative humidities greater than about 90%, because water absorbed on the bed particle surfaces increases their conductivity and allows frictionally generated charge to leak off (Zahedi and Melcher, 1976a). Packed ( U < Umf),forced packed ( U > Umf,with retaining screens to prevent fluidization), incipiently fluidized ( U U,f), and fluidized (U > U,f) beds of laboratory quality glass beads (radii of 0.25 and 0.5 mm) and sand (mean radius 0.4 mm) are tested in th’e co-flow and cross-flow electrode geometries, Figure 8. Power supplies provide peak voltages up to 15 kV over the frequency range 30-5000 Hz. Electrical resistance of the beds is very high, so the loading is capacitive. Collection efficiencies are determined from aerosol concentrations measured below and above the bed. After passage through a charge neutralizer, gas samples are analyzed by a
-
Table 11. EFB Operating Conditions
A
1.0 0.5 1.0
V
0.5
0.5 0.5 0.25 0.25
0
0.5
0.4
4.0
1.0
x o +
0.5 0.5 0.5
0.5 0.5 0.5
2.0
0.5 0.375
0
2.0
0.5
4.0
1.5
0
2.0
0.5
2.5
0.5
0 0
4.0 4.0 4.0 4.0
1.25 1.25
4.0 2.0
1.0
1.0
1.0
Cross-Flow Fluidized Glass Beads 0.4 6.9 0.165 0.4 6.9 0.18 9.7 0.19 0.4 0.4 9.7 0.125 Cross-Flow Fluidized Sand 0.5 0.5 4.0 0.16 Cross-Flow Packed Glass Beads 0.5 0.20 0.375 7.2 0.375 0.375 5.4 0.35 1.0 0.375 14.0 0.11 Co-Flow Fluidized Glass Beads 0.63 0.4 6.9 0.13 Co-Flow Packed Glass Beads 0.5 0.375 7.2 0.32 0.63 0.63 0.44 0.44
0.385 0.24 0.47 0.325
8.4 7.9 4.9 3.4
0.325
2419 1709 4053 2865
2690 2038 4475 3159
1.04 0.79 1.07 1.10
13.0
2061 2320
0.99
0.39 0.4 0.22
6.4 9.6 4.5
1747 1976 1514 1840 2809 3162
0.95 0.73 0.96
0.33
15.0
3431 3769
1.08
0.52
23.0
3493 4047
0.87
Ind. Eng. Chem., Fundam., Vol. 16, No. 3, 1977
315
i 2t
-_
’-‘=_p_0
5
1
u
2
5
1
Figure 9. Normalized EFB collection efficiency as a function of normalized frequency for cross-flow experiments with low- and high-frequency theoretical asymptotes. Solid lines, cross-flowtheory; dashed lines, co-flow theory. Rightmost curves w,/w, = 1, leftmost curves w,/w, = 0.75.
7
I
Figure 10. Normalized EFB collection efficiency as a function of normalized frequency for co-flow experiments with low- and highfrequency theoretical asymptotes. Solid lines, cross-flow theory; dashed lines, co-flow theory. Rightmost curves w,/w, = 1, leftmost curves w,/w, = 0.75. Thermo-Systems, Inc., mass monitor. In such a device, aerosol particles are precipitated onto a quartz crystal. The resulting shift in resonant frequency of the crystal is a measure of the deposited mass. For normalization purposes, qnf and ?& (with E d c = 2Eo/*) are measured for each bed tested. The effective mechanical radius is then determined as prescribed by eq 23. For similar beds, the effective mechanical radii are found to be comparable. Experimental considerations restricted w,/w, to be approximately 1. That is, we/w, >> 1 leads to bed collection efficiencies in the region of nonlinear dependence on single particle collection rate, while we/wm
