Ind. Eng. Chem. Res. 1988,27,123-131 octane number of the stripper OHP. A balance must be made between the degree of separation and the octane requirement for the stripper OHP. 3. The hydrocarbon feed temperature of the TLPED operation was shown to be another sensitive operating variable. A 10 O F decrease in the feed temperature caused the separation factor to increase from 3.3 to 6.0. 4. The solvent-to-hydrocarbon feed ratio (S/F) is a major economic variable for TLPED. High S/F does not necessarily improve the separation factor. The experimental results showed that a decrease in S/F from 2.8 to 1.9 actually increased the separation factor from 3.0 to 4.6. A reduction in S/F will significantly lower capital and operating costs of the process. Acknowledgment We thank Phillips Petroleum Company for the oppor-
123
tunity to perform this work and for permission to publish the results. Literature Cited Cines, M. R. US. Patent 4053 369, 1977. Crow, P. Oil Gas. J. 1984, Sept 10, 73. Graves, C. W. “Octane Upgrading of the Catalytically Cracked Gasoline”, unpublished report, Phillips Petroleum Company, 1980. Halpern, L. B.; Noble, D. R. Chem. Eng. Prog. 1985, 81(10), 39. Lee, F. M.; Coombs, D. M. Ind. Eng. Chem. Res. 1987, 26(3), 564. Pierce, V. E.; Bansal, B. B. Annual Meeting of the American Institute of Chemical Engineers, Chicago, IL, Nov 1985; Preprint No. 3549-2a. Thompson, R. G. “Cost of Increasing Reformer Severity”, unpublished report, Phillips Petroleum Company, 1981. Received for review April 29, 1986 Revised manuscript received September 3, 1987 Accepted September 23, 1987
Ac Collection Efficiency of Precharged Particulate in Turbulent Flows Stephen
F. B a r t , James R. Melcher,* and R i c h a r d M. E h r l i c h t
Laboratory for Electromagnetic a n d Electronic Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
It is shown that turbulence can greatly improve the efficiency of a two-stage ac electrostatic particle precipitator. A numerical model is developed and experimental results are obtained for the collection efficiency as a function of frequency. T h e mixing due t o the turbulent gas flow is treated as a quasi-one-dimensional convective diffusion process with a position-dependent diffusion coefficient. The particle flux at the collection electrode is assumed proportional to the difference between the migration length (twice the peak electric migration velocity divided by the angular frequency) and a “laminar” sublayer thickness based on the dominance of the migration velocity over the turbulent fluctuating velocity. Particles of an aerosol of dioctyl phthalate (DOP) were unipolarly charged with a corona triode and convected (Reynolds numbers = 3000 and 9000) between parallel plates excited with a high voltage ac source a t frequencies between 2 and 500 Hz. The collection efficiency’s rate of decrease with increasing frequency was found t o be a strong function of the laminar sublayer thickness. T h e magnitude and frequency dependence of the collection efficiency were accurately predicted by the model. 1. Introduction One of the largest applications for electrostatic particle precipitators (ESPs) is the collection of fly ash from the combustion of coal for industrial and domestic energy production. Virtually all common ESP designs employ dc excitation for the charging and collection of the particulate. However, difficulties may arise when the coals used produce ash which is very highly resistive. Assumulating surface charges on the highly resistive collected layer can cause localized discharges called “back-corona”, which seriously degrade precipitator performance (White, 1974). Consider a precipitator energized with an ac sinusoidal excitation so that no time-average charge is deposited on the ash layer. Under such circumstances, the back-corona effect could be avoided (Bart, 1985; Ehrlich, 1984; Krug, 1969; Lau, 1969). The charging and precipitation processes in a singlestage ac ESP have been examined theoretically and experimentally elsewhere (Ehrlich and Melcher, 1987b; Ehrlich, 1984; Ehrlich and Melcher, 1987a; Krug, 1969; Lau, 1969). Of interest here is a two-stage precipitator in ‘Present address: Hewlett-Packard Labs, 1501 Page Mill Road, Palo Alto, CA 94304.
which the charging and precipitation processes occur in different regions. The particles arrive at a migration region with essentially constant particle charge and migrate in an oscillatory electric field. The resulting particle motion is composed of the oscillatory migration superimposed on convection in a turbulent flow. A model for the way in which these particles cross through the boundary layer is used to predict the frequency dependence of the collection efficiency. The predictions are compared to efficiency data obtained from the second stage of a laboratory-scale precipitator. Two sinusoidal collection region potential differences (10 and 5.35 kV rms) are examined with both a turbulent air flow (mean velocity = 8 m/s; Reynolds number N 9000) and a transition flow (mean velocity = 2.8 m/s; Reynolds number N 3100) (Bart, 1985). The reader is referred t o White (1963, 1981), Melcher (1981),and Melcher et al. (1977) for details on the general theory of precipitator operation and to White (1974) and Masuda (1981) for a discussion of back-corona and its associated problems in dc ESPs. 1.1. Two-Stage Ac Electrostatic Precipitation. If the charging and collection regions of an ESP are separated, precharged particles will enter the corona-free (fixed particle charge) collection region and migrate in a collection electric field (transverse to the gas flow direction) with a 1988 American Chemical Society
124 Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988
velocity dictated by the balance of the electric force and Stoke’s drag force. It is assumed that the particles are small enough so that their inertia is unimportant and, apart from electrical migrations, stay entrained in the gas flow. It is also assumed that the volume particle charge density is small, so that particle self-precipitation times are large compared to the time a particle spends in the precipitation region. In the case of a zero time-average ac (sinusoidal) collection field, a particle in a stagnant fluid would traverse an oscillatory path whose maximum transverse displacement is given by
1,
= &T’2bE
2bE, dt = -
S ( n ) ( x , y , L )da
w
where b is the particle mobility, T l / f is the cycle time of the sinusoidal excitation, w = 2 r f is the radian frequency, E is the electric field, the subscript p indicates the peak value of a sinusoidal excitation, and t = 0 is chosen as the time when the electric field begins to point in the direction which will carry the particles toward the collection plate of interest. For typical parameter values ( b = lo-’ m2/ (V-s);E, = lo6 V/m; f i= 60 Hz), this length is on the order of 0.5 mm. Such a migration length is much smaller than typical (or even practically possible) ESP collection plate spacings. If there were no other source of transverse particle motion, as is the case with laminar gas flow, the collection efficiency would be very low (Alexander et al., 1981). In most practical precipitators, however, the flow is turbulent (Reynolds number, R, = lo4). This turbulence causes significant mixing, which could conceivably bring particles to within the distance 1, of a collection plate, where their migration would cause them to reach the collection plate. In order for this scheme to result in appreciable precipitation, the turbulence must be capable of bringing a large number of particles close to the collection plates in a time shorter than the particle’s residence time in the collection region. The turbulent velocity fluctuations of a duct flow decrease as the walls are approached, leaving a thin region near the wall of significantly reduced turbulence intensity. The thickness of the region over which electric migration dominates turbulent diffusion can be estimated by determining where the electric migration velocity is on the order of the velocity of the turbulent fluctuations close to the wall (Sonin, 1987): v’ms
- bErm,
(2)
Equation 2 can be solved for the thickness of this region, 6, by relating ,’v to the distance from the collection plate (see eq 20). Within 6, mass transport due to electrical migration dominates molecular diffusion as well as turbulent diffusion
bE >> D / 6
2. Ac Two-Stage Precipitation Model Consider a precipitator with a rectangular cross section, where z is the gas flow (longitudinal) direction and x is the transverse dimension, perpendicular to the energized collection plates (i.e., parallel to the applied electric field). The collection region of this precipitator has length L and height H and is assumed wide enough in the other transverse dimension, y , to be considered two-dimensional. The collection efficiency of the precipitator, 7,is defined as unity minus the ratio of particulate leaving the collection region to that entering
(3)
where D,the molecular diffusion coefficient, is approximately for 1-km-diameter particles (Leonard et al., 1980) and 6 is on the order of m (other typical values as previously mentioned). Clearly, to the extent that a “laminar” sublayer is a region where turbulent fluctuations cause negligible mass transport, particles must cross the region by electric migration alone. This requires the laminar sublayer thickness, 6, to be smaller than the distance 1, to obtain appreciable collection. To describe the process of collection, a simple boundary layer model is chosen, sufficiently complex to chsracterize the basic mass-transfer mechanism, yet simple enough to be consistent with the control of experimental conditions.
’
- S ( n ) ( x , y , O )da
(4)
where ( n )(x,y,O) and ( n )(x,y,L) are the time-average entrance and exit particle concentrations. (It is assumed that the system has been in operation for a time sufficient to establish a steady state.) 2.1. Bulk Equation. Application of the law of conservation of mass to the particle concentration yields (note that 7 is a vector position) an(?,t)/at = -V-[u’(r‘,t)n(r‘,t)+ G,(t)n(F,t) - DVn(r‘,t)] (5) where G is a uniform particle migration velocity and 17is the gas flow velocity. Since the flow is turbulent, the ensemble-averaged version of eq 5 is required. Our attention is restricted to steady, incompressible, turbulent duct flow with a twodimensional, fully developed, mean velocity profile, but not necessarily a fully developed concentration profile. The electric migration is assumed to be transversely (x) directed and driven by a zero time-average ac electric field. The typical assumption that the contribution of the turbulence to the transverse mass transport, u,’n’, can be expressed by an eddy or turbulent diffusivity (Lin et al., 1953; Friedlander, 1977), yields
u,‘n’= -D,(x) aii/ax
(6)
where I? is the local ensemble-averaged concentration. Measurements indicate that for micrometer-sized particles in turbulent air streams, transport due to molecular diffusion can be neglected in the core flow ( D 1: >
T, E
L/U,
(7)
where U, and Do are characteristic core flow values of the mean velocity and turbulent diffusivity, respectively (Ehrlich and Melcher, 1987~).Combining these assumptions with the ensemble-averaged form of eq 5 yields a quasi-one-dimensional bulk equation
where U ( x )is the mean flow velocity profile. Equation 8 is completed by specifying the turbulent diffusivity profile, D,(x), and the average velocity profile, U ( x ) . Considerable work has been done on developing semiempirical relations for these profiles in turbulent pipe flow (Schlichting, 1979; Monin and Yaglom, 1971). How-
Ind. Eng. Chem. Res., Vol. 27, No. 1, 1988 125 ever, the ESP literature typically uses constant values or piecewise linear approximations (Leonard, 1982; Feldman et al., 1976; Robinson, 1968). To identify the simplest approach consistent with experimental accuracy, the results of the numerical integration of eq 8 (to be described) were examined using a constant turbulent diffusivity, one that was piecewise linear (see eq 9), and the semiempirical relation of Reichardt (1951). These profiles were made consistent with the boundary conditions of section 2.2 by forcing D, to be zero inside the laminar sublayer and to be a constant value in the core flow. The examination was performed for the case V,,, = 10 kV; Uo= 8 m/s. The model predictions from all three diffusivity profiles were equivalent to within the average error in the efficiency data measurement (the greatest deviation occurred for frequencies in the range 30-100 Hz).As a consequence, the piecewise linear model was chosen as the simplest model that retained some connection with the physical behavior of D,. The diffusivity function is approximated as being uniform and finite in the core gas flow, dropping off linearly within a turbulent boundary layer, A, and equal to zero inside the laminar sublayer, 6 (Abedian and Sonin, 1982) D,(x) =
1.:
[Do!(A - 6 ) ] ( H / 2- 6
F X)
I
H / 2 > 1x1 > H / 2 - 6 H / 2 - 6 > *X > H / 2 - A (9) H I 2 - A > 1x1
where Do is the core turbulent diffusivity magnitude. The origin of the x coordinate is located midway between the collection electrodes, which are separated by a distance H. It is assumed that A C H / 2 and 6 6). At high frequencies where this restriction may not be satisfied, the turbulent diffusion precipitation mechanism is no longer applicable because the turbulence is assumed to be zero in the laminar sublayer. Under these circumstances, a lower bound approximation of the efficiency can be obtained by considering only those particles that enter the collection region at a position and excitation phase such that they will migrate to the collection electrode within one cycle. The reader is again referred to Alexander et al. (1981) for a straightforward derivation of the efficiency relation valid for this approximation, which is given by 2bE, 1, (16)
v=wH=H
Note that 71.IT must hold for this relation to be valid. 2.5. Numerical Implementation. The numerical integration of eq 14 (with D,(x) given by eq 9 and a uniform flow velocity profile) was carried out by using a standard predictor-corrector integration algorithm, with a RungeKutta start-up routine (Acton, 1970). A linearly interpolated “shooting” routine was used to satisfy the transverse boundary conditions (eq 10 and 12). The value of a which satisfied the boundary conditions was then used in eq 15 to calculate the collection efficiency. Apart from comparing the ac two-stage precipitation model predictions to experimental results, several checks were made to assure that the numerical results reduced to expected analytical results. In the limit where the core flow diffusivity goes to zero, the solution should approach that predicted by a purely laminar model, where the efficiency is given by the ratio of average excursion to the overall collection region height, H:
bE,
+
e-alL
_.
ZbE,
25
H
