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Ind. Eng. Chem. Res. 1997, 36, 4308-4317
Modeling of Venturi Scrubber Performance Shekar Viswanathan† Ecotech Energy and Environmental Corporation, 148 Heath Meadow Place, Simi Valley, California 93065
The performance of the Brink and Contant industrial-size Venturi scrubber has been successfully simulated by means of a two-dimensional computer model. The two-phase, two-component, annular flow occurring in the unit was predicted using a Particle-In-Cell (PIC) numerical technique. Consideration of four different dust diameters, ranging from 0.5 to 10 µm, allowed evaluation of the Venturi grade efficiency curve. Liquid jet penetration and drop size distributions, incorporated as important parameters, were linked to significant liquid maldistribution in the Venturi throat. This study confirmed the observation that the drops are actually classified by inertial effects which enable bigger drops to penetrate further into the central core of the air stream and the smaller drops to stay closer to the duct walls. As a result, the smaller drops were not observed in the region occupied by the larger drops. This liquid maldistribution persisted throughout the scrubber and resulted in predictions of particulate collection efficiency that were lower than would be expected with the usual assumption of uniformly distributed drops of one size using one-dimensional models. Because this two-dimensional model can incorporate different liquid injection modes and drop size distributions, it provides considerable versatility for the simulation of cleaning processes in Venturi scrubbers. Introduction The Venturi scrubber is a simple, yet highly efficient, device for fine particulate removal from industrial exhaust gases. Cleaning is accomplished mainly by inertial impaction and interception, while various flux forces, such as diffusiophoresis, assist in the removal of submicron dust. It is a high-energy-impaction, atomizing system that is useful for controlling emissions of both particulate and gaseous pollutants. Its advantages include lower initial costs for comparable collection, low floor requirements, absence of internal moving parts, and capabilities to handle wet and corrosive gases. The large power requirements for operation represent its main drawback. Several attempts have been made in the past to theoretically calculate scrubber efficiency, but with moderate success. Visual observations and experimental work have indicated the existence of an annular twophase, two-component flow having a thin liquid layer on the walls and a high-velocity gas stream carrying the droplets in the core. Most of the efficiency models do not account for the presence of two-phase, twocomponent flow. The objective of this work was to develop a mathematical model that incorporates important parameters such as liquid jet penetration and drop size distribution which are linked to significant liquid maldistribution in the scrubber. The model developed in this work has been tested with the data collected by Brink and Contant (1958) on an industrial-size unit. Literature Review Many attempts to predict Venturi scrubber performance have been made since their first pilot-plant application to a Kraft recovery furnace in the mid-1940s. A chronological survey of Venturi scrubber particulate collection theories can be considered in terms of the usual engineering model development involving (1) correlation of experimental data to primary variables, † Present address: Department of Chemical Engineering, National University of Singapore, Singapore 119260, Singapore.
S0888-5885(97)00235-2 CCC: $14.00
(2) simple analytical models, and (3) detailed analyses requiring numerical solution. There are several important mathematical models available for the prediction of particle collection efficiency in a Venturi scrubber (Behie and Beeckmans, 1973; Boll, 1973; Calvert, 1970; Dropp and Akbrut, 1972; Ekman and Johnstone, 1951; Fathikalajahi et al., 1996; Morishima et al., 1972; Placek and Peters, 1981, 1982; Viswanathan et al., 1984; Yung et al., 1977). However, many of these models do not accurately predict the efficiency for a wide range of operating conditions. Ekman and Johnstone (1951) considered each single drop as a unit and followed the drop to determine particle collection during its entire flying path length. The total particle collection of the Venturi scrubber was the sum of the collection of all liquid drops. Calvert (1968, 1970), by performing a material balance on the dust over a differential scrubber volume, with the assumption of constant liquid holdup, obtained an equation for the prediction of Venturi scrubber performance. Later, Calvert et al. (1972) applied this equation to the Venturi throat to obtain a simplified expression for predicting particle penetration. This model used an empirical parameter, e, and assigned a value of 0.25 for hydrophobic dust, whereas a value of 0.5 was needed for hydrophilic dust. This model was found to be of limited use because of the unknown quantitative relationship between e and system variables, including Venturi size. Morishima et al. (1972) used the same approach as that of Ekman and Johnstone (1951). They considered particle collection in the Venturi throat as well as in the divergent section. In their analysis, they showed that, as the range of the drop size distribution widens, the overall efficiency decreases. Dropp and Akbrut (1972) evaluated Venturi scrubber performance data collected at several power plants. They concluded that the earlier models will overpredict the collection efficiencies of larger dust particles if the gas velocity is substituted for the particle velocity. They modified Calvert’s differential equation to account for the particle velocity. Boll (1973) proposed a new model involving simultaneous differential equations of drop motion and particle © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 4309
impaction on drops. He took into account the particle collection occurring in the Venturi throat, as well as in the convergent and divergent sections of the unit. The model was found to overpredict the collection efficiency since it did not account for nonuniformity of drop sizes and the maldistribution of droplets. All of the previous investigators had assumed that the liquid drop distribution was uniform across the duct and that there was no turbulent mixing between drops and dust. Tillman (1971) investigated the effect of free stream turbulence on the collection efficiency in a Venturi scrubber in terms of an analytical approach. He modeled an idealized scrubber in which monodispersed dust was collected by a uniformly distributed monodispersed water spray. For such an intimately mixed system, free stream turbulence would not play any direct role in the collection process. In reality, the drop distribution across the throat is far from uniform, as has been shown by many investigators (Boll et al., 1974; Taheri and Hains, 1969; Viswanathan et al., 1984). Taheri and Sheih (1975) took turbulent mixing and liquid drop distribution across the throat into account and obtained two partial differential equations, for predicting the transport and diffusion of the dust and water drops. In all of the previously mentioned models, the liquid drops were assumed to be of one size determined by the Sauter mean diameter, calculated from the Nukiyama-Tanasawa correlation. Boll (1975) criticized the omission of initial liquid momentum as well as the inability to correctly predict the liquid distribution through the line source treatment used in Taheri and Sheih analysis. Goel and Hollands (1977) developed a generalized approach for predicting Venturi scrubber performance by considering the Venturi as a single duct and used the approach of Boll (1973). However, the assumption of uniform distribution of drops within the Venturi was a major limiting factor of this model. Yung et al. (1978) proposed an expression similar to that of Boll’s model by considering particle collection to occur only in the throat. Their model provided a better estimate of particulate penetration than that obtainable from the Boll approach. Licht and Radhakrishnan (1978) reported that the overall efficiency and grade efficiency are much more dependent on the actual drop size distribution than on the Sauter mean diameter. Vlahovic (1976) and subsequently Viswanathan (1983) considered modeling of Venturi scrubber performance as a boundary value problem, in which they solved for the transverse as well as the axial distribution of liquid drops for an assumed and measured jet penetration, respectively. They incorporated the drop size distribution as an important parameter which was obtained through the Ingebo and Foster correlations (1957). Placek and Peters (1981) developed a theoretical model that included such operating variables as scrubber geometry, throat gas velocity, liquid to gas ratio, and collector droplet and particle size distributions. Liquid to gas ratio, throat gas velocity, location of liquid injection, and length of throat were found to be important design considerations. They also analyzed the role of heat and mass transfer in determining scrubber performance (Placek and Peters, 1982). Elevated temperatures reduced particulate collection, whereas masstransfer effects increased the collection when condensation onto the drop occurred. Koehler et al. (1987) developed a comprehensive framework for estimating axial variation in gas-borne liquid flow rate by conducting experiments in a pilot-scale Venturi unit. This
approach was similar to that proposed earlier by Viswanathan et al. (1984). The limitation of this work is that the measurements were made in a small-scale Venturi which behaves quite differently compared to a large-scale pilot plant/normal industrial unit and hence may have some limitation for scale (Calvert et al., 1972; Viswanathan, 1983). In addition, the divergent angle of the diffuser used in this study is large (usually is around 7°) and is not likely to be encountered in practice, since large diffuser angles would cause excessive pressure losses due to flow recirculation in the regions adjacent to the diffuser walls. This effect is commonly known as stalling (Wade and Fowler, 1974; Azzopardi, 1992). Fathikalajahi et al. (1996) proposed a three-dimensional model that takes into account nonuniformity of drop distribution by considering liquid jet penetration developed by Viswanathan et al. (1983). Their model did not consider droplet distribution that occurs in typical scrubber conditions. Several details regarding the initial treatment of drops, such as initial drop velocity, have not been mentioned. Also, the initial position of the drops were determined by the maximum jet penetration length, which may be an overestimation of the actual conditions. In addition, based on liquid injection arrangements, a two-dimensional model would be sufficient to describe the drop distribution in the scrubber. However, their results agreed well with the experimental work. All other models proposed (Behie and Beeckmans, 1973; Hesketh, 1974; Leith and Cooper, 1980; Azzopardi and Govan, 1984; Haller et al., 1989) are minor modifications to the ones that are mentioned earlier. The important limitation of most of these onedimensional models was the assumption of the existence of only a homogeneous core with uniform flux across the scrubber and the absence of film flow on the wall. In order to describe accurately the physical phenomena occurring in a Venturi scrubber, a true representation of the liquid distribution throughout the scrubber must be available. The film on the containing walls do not participate in the collection process. This research work utilizes the reviewed literature in the development of an improved model for predicting Venturi scrubber performance. Theoretical Model The development of a Venturi scrubber performance model invariably starts from a presumed knowledge of drop size, liquid droplet distribution, and initial coverage of the throat by liquid drops. The importance of a realistic concentration distribution of liquid drops can be appreciated by recalling that the main collection process for particulate matter occurs in the Venturi throat, a region where large relative velocities exist between the drops and the dust with the drop concentration distribution is mostly nonuniform. The initial transverse momentum of injected liquid drops must be considered to be of prime importance because this variable determines the initial spread of liquid drops and Venturi throat coverage (Taheri and Hains, 1969; Boll, 1975; Viswanathan et al., 1983). Under normal operating conditions, it is valid to assume uniform inlet particulate matter distributions for modeling purposes. It is also valid to assume that the dust has momentum in the axial direction only, with movement along the lateral axis solely due to turbulent diffusion. The model developed during this program takes into account (1) jet penetration length, (2) non-
4310 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
Figure 1. Configuration of a Pease-Anthony Venturi scrubber.
uniformity of droplet size distribution, (3) maldistribution of liquid drops, (4) initial liquid momenta, (5) drop movement in the axial and lateral directions by both convective and diffusive mechanisms, (6) no drop to drop interactions, (7) uniform inlet distribution of dust particles, (8) nonuniformity of inlet dust size distribution, (9) dust motion in axial direction through convective and in the lateral direction through diffusive mechanisms, (10) no interaction between dust particles, and (11) particulate matter collection by droplets through inertial and interception mechanisms. Droplet Motion. The configuration of the Brink and Contant industrial scrubber chosen for simulation is shown in Figure 1. Only half of the flow cross section in the y-direction needs be considered because of symmetry. Since the separation distance between liquid injection orifices is very small, negligible variation in the drop concentration can be assumed for the zdirection to make the model two-dimensional. The problem of predicting the droplet distribution was treated as a transient process. The two-dimensional unsteady-state continuity equation for liquid drops has been described by the expression (Viswanathan, 1983)
∂Cd ∂ ∂ )[V C ] - [VdyCd] + ∂t ∂x dx d ∂y ∂Cd ∂Cd ∂ ∂ Ed + Ed + Qd (1) ∂x ∂x ∂y ∂y
[
] [
]
In eq 1, the time rate of change of drop concentration is equated to the sum of the changes in drop concentration due to bulk motion and the diffusion superimposed on the bulk flow plus the drop source strength. The diffusional terms can be modified by introducing turbulent flux velocities (Sklarew et al., 1972), as
VtdxCd ) -Ed
∂Cd ∂x
and
VtdyCd ) -Ed
∂Cd (2) ∂y
Substitution of eq 2 into eq 1 yields
∂Cd ∂ )[(Vdx + Vtdx)Cd] ∂t ∂x ∂ [(Vdy + Vtdy)Cd] + Qd (3) ∂y It becomes apparent from the revised form of the continuity equation that the liquid drops are being transported by the sum of the bulk and turbulent
Figure 2. Velocity vector diagram.
velocities which, for convenience, can be called the “total equivalent transport velocity”. Hence eq 3 can be written as
∂Cd ∂ ∂ )[VeqdxCd] [V C ] + Qd ∂t ∂x ∂y eqdy d
(4)
By introducing the concepts of “turbulent flux velocity” and total equivalent transport velocity, the original problem of turbulent droplet transport is transformed to a description of advective changes of fluid density (i.e., Cd ) Ff ) fluid density) in a compressible fluid moving in a fictitious velocity field (Veqdx, Veqdy) of total equivalent transport velocities. Liquid Droplet Velocity. The velocities of a liquid droplet in the x- and y-directions can be determined from a force balance. Each droplet in the Venturi scrubber is subjected to both gravitational and drag forces with the drag force acting in the direction of the relative velocity. For a typical droplet shown in Figure 2 whose instantaneous velocity V B d can be resolved into the x- and y-components Vdx and Vdy, Newton’s law gives
a) m db
∑FB ) FBdrag + FBgravitational
or
V Br π 1 m db + mdb a ) Dd2CD FG|V B r|2 g (5) 4 2 |V B r|
Substitution of md ) (π/6)Dd3Fd in eq 5 gives
b a)
V Br 3 CDFG +b g |V B |2 4 DdFd r |V B r|
(6)
A new drag function, CDN ) CDNRE ) CDFGV B rDd/µG, was introduced in eq 6 to preserve the proper sign of b a and to avoid a potential problem associated with CD f ∞, when NRE f 0 (Boll, 1973). Equation 6 then can be modified as b a ) kDV Br + b g, where kD ) (3/4)(CDN/Dd2)(µG/Fd). Drag Coefficient. The variation of the droplet drag coefficient, CD, with drop Reynolds number can be obtained from either the standard drag curve or the Ingebo approach. The standard drag curve is believed to be the better choice because reviews have shown that the lower values of drag coefficients determined by Ingebo were due to turbulence effects rather than acceleration effects. It is also possible that Ingebo’s method of water injection provided lower acceleration
Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 4311
rates because of actual reductions in effective air velocity. In this work, linear approximations were made to the standard drag curve over the range 0 e NRE e 1200 with an error of less than 1%. Drop Size and Drop Size Distribution. The high dependence of the overall particulate collection efficiency on drop size and on the heterodisperse nature of the drop size distribution (Licht and Radhakrishnan, 1978; Placek and Peters, 1981) emphasizes the importance of proper selection of drop size and drop size distribution during model development. The conventional use of the Nukiyama-Tanasawa correlation (1938) to predict drop size leads to an underestimation of the drop diameter by 25% for a gas throat velocity of 33 m/s and an overestimation by 48% for a gas throat velocity of 99 m/s (Boll et al., 1974). Studies of liquid jet breakup by high velocity gas streams carried out by Ingebo and Foster (1957) provided the empirical correlation for the mean-volume diameter D30 in the form of
D30 ) 3.9(NWe/NRe)0.25 d0
(7)
The maximum drop diameter, Dmax, in a spray was correlated according to
Dmax ) 22.3(NWe/NRe)0.29 d0
sequently, they vary according to their position in the system (Himmelblau and Bischoff, 1968). It is generally accepted that the dimensionless group (Ef/Vf)Deq reaches a constant value for higher Reynolds numbers characteristic of flow in pipes and ducts (Baldwin and Walsh, 1961). In this particular work, this value was taken as 0.01 based on theoretical fit of the concentration distribution of droplets to the experimental value (Viswanathan et al., 1984). The eddy diffusivity of a drop is smaller than that of the gas stream and is a function of the drop size and density. Large drops, because of their inertia, cannot follow the random motion of eddies as easily as gases can. As a result, their eddy diffusivity has been studied by Longwell and Weiss (1953). These researches have assumed that the velocity fluctuations in turbulent flow are sinusoidal and that Stokes’ law applies to the drag on drops. Their correlations, Ed/Ef ) b2/(ω2 + b2) and Ep/Ef ) b2/(ω2 + b2), have been used in the current model. Particle Motion. The two-dimensional, steadystate, continuity equation describing the transport of particulate matter, neglecting longitudinal diffusion, has the form (Viswanathan, 1983)
0 ) -VG
∂Cp
∂ +
∂x
[ ] Ep
∂Cp
∂y m* n* πη F ij i Ddj2(VG - Vdxj)CpCdj (10) i)1 j)1 4
∂y
∑∑
(8)
Using eqs 7 and 8, Ingebo and Foster derived an expression for drop size distribution by modifying the Nukiyama-Tanasawa expression to yield
Modifying the diffusional term in eq 10 by introducing turbulent flux velocity similar to eq 2, yields
dR ) dD30
VG
[
]
D305 D30 106(NWe/NRe)0.24 exp -22.3(NWe/NRe)0.04 6 Dmax Dmax (9) Equation 9 utilizes a limiting maximum drop size distribution as a function of liquid to gas ratio and gas velocity at the point of atomization for any nozzle diameter. In this work, the drop size spectrum was divided into four equal volume fractions for which four representative diameters were defined. These representative drop sizes are specified only at the point of atomization as indicated by Ingebo and Foster (1957). Drops with a Weber number exceeding 12-13 are unstable and have a tendency to break up (Wallis, 1969; Parker and Cheong, 1973). A characteristic series of photographs from the Ingebo and Foster study suggest that the drops are actually classified by inertial effects which enable bigger drops to penetrate further into the central core of the air stream while the smaller drops stay closer to the duct walls. In addition, no smaller drops were observed in the region occupied by larger drops. This behavior suggests that larger drops disintegrate into smaller but still relatively larger droplets. In order to enable the model to account for this phenomenon, drops whose Weber numbers became greater than 12 were allowed to disintegrate into a smaller size of the next lower class. Eddy Diffusivity. Values of eddy diffusivity are usually estimated from empirical correlations. Their magnitudes depend on the flow situation and are functions of the degree of turbulence or mixing. Con-
∂Cp
∂ )
∂x
∂y
[VtpyCp] m* n* πη F ij i
∑ ∑ i)1 j)1
4
Ddj2(VG - Vdxj)CpCdj (11)
This steady-state equation is similar to eq 3 obtained for droplet motion, except that the source term in eq 3 has been replaced by a dust removal term. Determination of Single Drop Collection Efficiency. The principal collection mechanism in a Venturi scrubber is usually inertial impaction. It has been identified that the flow fields around collector droplets generated during typical Venturi scrubber operations are not strictly potential or viscous in nature (Placek and Peters, 1981; Viswanathan, 1983). They depend on throat length, throat gas velocity, and location of liquid injection. Since many of the Venturi scrubber performance models assume the flow fields to be entirely potential and the single drop collection efficiency for a given Stokes number is higher for potential flow, they overestimate overall particulate matter collection efficiencies. In this work, an improved single droplet collection efficiency model developed by taking into account both inertial impaction and interception mechanisms was used (Viswanathan, 1997). Based on this approach, potential flow efficiencies were correlated by the relationship
ηpol1/2 ) 1 - exp(-AKB) 1 + NR where
(12)
4312 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
A ) 1.15(1 + NR)2.2
and
B)
0.46 (1 + NR)1.6
For Stokes flow, the efficiencies were calculated from
ηstk1/2 ) 1 + NR
1 0.15 ln(K) + 1.75 1+ K - 0.68
(13)
The collection efficiencies for the intermediate flow region were calculated from the relationship
ηint ) ηpotφ + ηstk(1 - φ)
(14)
in which the value of φ was obtained from φ ) tanh(0.175K0.234NRe,c0.406). Determination of the Overall Collection Efficiency. The overall collection efficiency at any axial location can be calculated by determining the concentration of particulate matter at that location by an integration process. The overall collection efficiency is given by
ηov ) 1 -
∫Cp(x,y) dy ∫Cp(0,y) dy
(15)
Numerical Procedure. The numerical computation used in this work is based on one of a family of ParticleIn-Cell (PIC) techniques (Evans and Harlow, 1957) with K-theory approximation (Sklarew et al., 1972). For convenience this procedure is normally called the “PICK” method. In this approach, the spatial distribution of fluid is represented by means of a large number of Lagrangian mass particles (i.e., ones of constant mass of fluid that are simply advected in the fictitious field of total equivalent transport velocity). The physical space is divided into cells of a fixed Eulerian grid and the Lagrangian mass particles carry fluid from cell to cell as they are moved by the fictitious field. The Lagrangian mass particles are referred to as “particles” in gas dynamic calculations; however, they are termed here as “mass points” to avoid confusion with the dust particles. In order to evaluate the movements of each mass point, the turbulent flux velocities, gas stream drag, and initial liquid momentum were calculated as explained in the earlier sections. The initial position and velocity chosen for the liquid drops are very important because they affect the concentration significantly. In this work, the initial position of the liquid drops is assumed to correspond to the point of jet atomization as (Viswanathan, 1983)
FjVj l* ) 0.06 d0 FGVG,th
(16)
The constant 0.06 was obtained using a trial and error procedure by matching the measured and predicted liquid flux distributions in a pilot-plant scrubber (Viswanathan et al., 1984). The amount of liquid introduced through the portion of the nozzle for each time increment was calculated from a material balance on the feed liquid. Equation 9 provided the relative amounts of liquid for each drop size interval. The mean drop diameters and liquid fractions for each interval were then used to determine the number of drops for each class. Because of the very large number of drops
involved, it was necessary to reduce computer memory requirements by renaming the concept of liquid mass points in which each mass point represents specific numbers of drops of a given mean drop diameter. The number of liquid mass points introduced and the time interval chosen for simulation affect the accuracy of solution and also the computational memory required. An upper limit of the time interval, ∆t, had to be established to avoid large inaccuracies and instabilities in the numerical solution. Experience showed that the number of mass points that could be introduced during one time interval (∆t ) 1/10000 s) should not be greater than 50 nor less than 10. The drop instabilities mentioned earlier were taken into account by calculation of Weber numbers for each mass point by assuming that each mass point containing drops of a specific size, after disintegration, would move to the next lower size, thereby balancing the total mass of liquid. Any liquid mass point reaching the wall was assumed to contribute to the film flow and hence was removed from further transport calculations. Also, any liquid mass point crossing the X-axis was taken into account by assuming that an equal size liquid mass point crossed from the other side of the Venturi slice with the same magnitude but opposite sign for the Y-directional velocity. This simulation was continued until the concentration of liquid mass points in the two arbitrarily chosen columns of cells (in the Y-direction) did not differ by more than a mass point per cell after one time increment. After achieving the steady state, particulate matter was introduced as a one-cell-thick lateral front of uniformly distributed dust particles moving with the same velocity as the gas stream. Due to the different cleaning efficiencies encountered in each cell, the lateral diffusion of the dust in the scrubber was very intense. This problem was solved by using an arithmetic mean of the central difference formula. Further details of the numerical procedure used are given elsewhere (Viswanathan, 1983). After the concentrations of dust in each cell of a column had been determined, the cleaning process was allowed to occur. From the concentrations, the overall cleaning efficiency at any axial location was calculated according to eq 15. Results and Discussion The results of this investigation are discussed in terms of lateral dust concentrations along the scrubber axis, dust diameter, throat gas velocity, and liquid to gas ratio. Four different dust diameters (10, 1, 0.75, and 0.5 µm) were taken into account in order to obtain a grade efficiency curve for the Venturi scrubber. Lateral Dust Concentrations along the Scrubber Axis. Figure 3 illustrates changes in dust concentration profiles at several locations along the scrubber length for a dust diameter of 1 µm. This plot shows the extent of collection between various axial locations in terms of the penetration of dust, P (P ) 1 - ηov), as a function of lateral position. Effect of the Dust Diameter on Lateral Dust Concentrations. Figure 4 shows lateral concentrations of the four diameters at the same longitudinal position. This illustration provides an appreciation of how the dust diameter affects the penetration through the same spatial distribution of liquid drops. It must be emphasized that the data presented in these plots correspond to the specific liquid injection arrangement used by Brink and Contant and that changes in the
Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 4313
Figure 3. Penetration of 1 µm dust at different longitudinal locations along the Venturi scrubber.
injection conditions would result in different drop distributions and consequently different dust penetrations. Model Validation. The results of these model comparisons are presented along with predictions from the other two models given in Figure 5 as functions of particle size. This model provides good agreement with experimental data, whereas the models of Boll (1973) and Yung et al. (1978) overestimate Venturi scrubber performance. The higher efficiencies predicted by earlier models can be related to their lack of accounting for nonuniform drop sizes and maldistribution of liquid droplets across the flow area. In addition, they assumed zero film flow rates on walls. Liquid flowing as a film is involved negligibly in the dust removal process. Figure 5 suggests that the Yung et al. model provides a better estimate of particulate penetration than that obtainable from the Boll approach. This improvement occurs simply because they assumed that particle collection occurred only in the throat. However, it can be shown theoretically, using the model of Yung et al., that a significant relative velocity still exists beyond the throat section to provide some measure of particle collection in the diffuser. When this contribution is acknowledged, the Yung et al. predictions do not differ significantly from those obtained by Boll. The expected variations in the overall collection efficiencies along the scrubber axis are shown in Figure 6. There is a systematic increase in the collection efficiency, along the axis of the scrubber, that extends into the diffuser for each particle size. According to Figure 6, most of the collection occurs in the Venturi throat and the initial portion of the diffuser (designated as zone one) where high relative velocities between
liquid drops and particulate matter exist. The influence of jet penetration is important here. Too high a penetration lowers the collection efficiency as shown by Vlahovic (1976). This effect is further amplified by larger drops penetrating deep into the scrubber as shown both experimentally and theoretically (Boll et al., 1974; Vlahovic, 1976; Viswanathan, 1983). Both jet penetration and liquid drop sizes can be controlled by using an appropriate type of liquid injection system and optimum throat gas velocity. This potential control makes the liquid injection system and throat gas velocity, two major design variables. Since the particulate matter and liquid drop residence times are extremely short in the throat, collection due to flux-force mechanisms would be negligible. By the time liquid drops reach the beginning of the diffuser (designated as the second zone), they are accelerated to the gas velocity. Consequently, the relative velocities between dust particles and liquid drops are essentially zero. As a result, the predicted collection efficiencies due to inertial impaction and interception are very low for all sizes in this zone. The third zone corresponds to that portion of the diffuser where drop velocities are higher than the gas velocity. Since the gas and the entrained liquid experience very little interaction under these flow conditions, the liquid droplet velocity remains essentially unchanged while passing through this portion of the diffuser. On the other hand, the gas velocity decreases in order to satisfy continuity requirements. Consequently, there is an increased relative velocity between drops and dust particles that leads to higher collection efficiencies. The section of the 15° angle diffuser designated as the fourth zone produces high relative velocities that are respon-
4314 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
Figure 4. Dust penetration for four different dust sizes at x ) 377 mm.
sible for significant particulate collection. In this region, any dust present where the higher droplet concentrations exist would be almost completely captured. This particular diffuser design is unusual and is not likely to be encountered in practice, since diffuser angles of 15° would cause excessive pressure losses due to flow recirculation in the regions adjacent to the diffuser walls. This effect is commonly known as stalling (Wade and Fowler, 1974). In the last section, minimal collection occurs since the relative velocities have been reduced close to zero. Effect of Throat Gas Velocity. Table 1 illustrates the effect of throat gas velocity on collection efficiency for a constant liquid to gas ratio (L/G) and site characteristics. Increasing the throat gas velocity at constant L/G ratio increases particulate matter collection for all sizes. Although the liquid rate must be changed correspondingly with increasing throat gas velocities to
maintain a fixed L/G ratio, flux measurements in the pilot-plant-scale Venturi have demonstrated similar patterns of drop concentration distributions for different throat gas velocities (Viswanathan et al., 1984). However, an increase in throat gas velocity reduces the droplet diameters and also leads to the formation of more droplets for a given volume of liquid. Consequently, it is reasonable to expect an increase in the collection efficiency with increasing throat gas velocities. This observation was different from that of Fathikalajahi et al. (1996), who observed that the throat gas velocity had no effects on droplet distribution when L/G is constant. Effect of Liquid to Gas Ratio. Figure 7 shows that, for a throat gas velocity of 61.0 m/s, there is a limiting value beyond which increases in the liquid ratio will not increase the collection efficiency for any particle size. This behavior is consistent with higher droplet concen-
Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 4315
Figure 7. Dependence of the overall collection efficiency on liquid to gas ratio.
Figure 5. Comparison of model predictions with experimental data of Brink and Contant.
decreases with increasing liquid to gas ratios (Viswanathan et al., 1984), thereby enhancing the collection of particulate matter to compensate for reductions resulting from increased drop sizes. Conclusion and Recommendation
Figure 6. Variation of the overall collection efficiencies along the scrubber axis for different dust sizes. Table 1. Effect of Throat Gas Velocity on Particle Collection Efficiency Vj (m/s)
VG,th (m/s)
Dp (µm)
ηov (%)
4.2 4.2 4.2 5.6 5.6 5.6 7.0 7.0 7.0
45.7 45.7 45.7 61.0 61.0 61.0 76.2 76.2 76.2
10 1.0 0.5 10 1.0 0.5 10 1.0 0.5
96.87 93.70 69.23 98.97 96.30 74.52 99.99 98.52 88.66
trations but creation of larger drops as a result of increasing liquid to gas ratios. These effects combine to increase the collection efficiency to a maximum level beyond which no further improvement can occur. The fraction of injected liquid flowing as a film on the wall
The newly developed two-dimensional efficiency model provides considerable versatility for modeling Venturi scrubbers. The model incorporates two important parameters, jet penetration and drop size distribution, which are physically well-defined and can be correlated with other variables such as gas velocity, nozzle diameter, liquid injection velocity, and scrubber geometry. Steady-state droplet distributions were predicted employing a Particle-In-Cell technique which accounted for initial liquid momenta, drag forces, and turbulent diffusion. Validation of this model carried out with the Brink and Contant data (1958) showed better agreement than that obtainable from the one-dimensional representation utilizing a single drop size with uniform distribution over the flow area. Although increasing the gas velocity did not alter throat coverage significantly, the model shows that particulate collection efficiency improves because of the formation of increased numbers of smaller droplets and increased turbulence, which in turn promotes the capture of fine particulate matter through interception, and the capture of large particles through inertial impaction (Placek and Peters, 1981). It is necessary to develop grade efficiency curves along with spatial drop distributions on the same Venturi for a wide range of operating conditions so that the applicability of this model could be verified. Acknowledgment The author thanks the anonymous reviewers who made valuable comments regarding this paper. Nomenclature b a ) instantaneous drop acceleration, m/s2 b ) 18µG/FdDd2 C ) concentration, number/m3 Csc ) Stokes-Cunningham correction factor CD ) standard drag coefficient CDN ) modified drag coefficient, CDN ) CDNRe
4316 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 D ) diameter, m d0 ) orifice diameter, mm D32 ) Sauter mean drop diameter, µm e ) empirical constant E ) eddy diffusivity, m2/s F ) drop mass flux, kg/(m2 s) Fi ) mass fraction of particulate matter belonging to the ith class G ) gas flow rate, m3/min b g ) acceleration due to gravity, m/s2 gc ) gravitational conversion constant, (kg m)/(N s2) K ) Stokes number, 2CscFpU0rp2/9µrc L ) liquid flow rate, m3/min l* ) jet penetration length at which the droplets form, mm m* ) number of selected mean diameters describing the particulate matter size range n* ) number of selected mean diameters describing the liquid drop size range NR ) interception parameter, rp/rc NRe ) Reynolds number NWe ) Weber number Qd ) liquid drop source strength, number/(m3 s) r ) radius, m R ) volume fraction of drops having diameter greater than D30 R0 ) half the Venturi throat, mm s ) specific surface of drops, m2/m3 of gas V ) velocity, m/s W0 ) width of Venturi throat perpendicular to water injection, mm x, y, z ) rectangular coordinates, m Greek Symbols β ) half the angle of divergence, deg F ) density, kg/m3 η ) collection efficiency ηij ) collection efficiency of particulate matter belonging to the ith class by droplets belonging to the jth class φ ) interpolation function defined by eq 14 ∆ ) increment µ ) fluid viscosity, kg/(m s) ω ) frequency of air fluctuations, rad/s Subscripts c ) collector d ) drop e ) equivalent f ) fluid G ) gas int ) intermediate j ) jet or liquid L ) liquid max ) maximum 0 ) orifice ov ) overall p ) particle/dust pot ) potential r ) relative stk ) Stokes T ) total t ) turbulent th ) throat x, y, z ) rectangular coordinates
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Received for review March 21, 1997 Revised manuscript received June 16, 1997 Accepted June 17, 1997X IE970235S X Abstract published in Advance ACS Abstracts, August 15, 1997.
