Effect of Polydispersity of Droplets in the Prediction ... - ACS Publications

The effect of polydispersity of droplets on the liquid flux distribution in a Venturi scrubber is investigated using a 2-D model along the length of a...
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Environ. Sci. Technol. 2000, 34, 5007-5016

Effect of Polydispersity of Droplets in the Prediction of Flux Distribution in a Venturi Scrubber LIM DAW SHYAN AND SHEKAR VISWANATHAN* Department of Chemical and Environmental Engineering, National University of Singapore, 10, Kent Ridge Crescent, Singapore 119260

The effect of polydispersity of droplets on the liquid flux distribution in a Venturi scrubber is investigated using a 2-D model along the length of a Venturi scrubber. Two average drop-sizes (the Sauter mean diameter and the mass median diameter) and two drop-size distribution functions (the upper-limit distribution function and the universal root-normal distribution function) are used in the model to predict liquid flux distribution. It is found that the flux distribution is a strong function of the polydispersity of droplets. It is also found that the throat gas velocity has a greater effect on the polydispersity of droplets than L/G ratio. At low throat gas velocity, flux distributions, predicted by the model using drop-size distributions, match with experimental data for a wide range of L/G ratios. At high throat gas velocities, flux distributions, predicted using average drop-sizes, follow experimental results closely. An analysis of overall collection efficiency reveals that it is nearly independent of polydispersity of droplets at low liquidto-gas ratios and high gas velocities.

Introduction The Venturi scrubber is a high-energy impaction, atomizing system, which is effective in controlling emissions of both particulate and gaseous pollutants. The particulate collection efficiency of a Venturi scrubber is a complex function of many variables, which includes aerodynamic particle size, liquid-to-gas (L/G) ratio, liquid jet penetration, liquid dropsize distribution, throat coverage by liquid drops, film flow rates, and geometrical configuration of the scrubber. Several attempts have been made to theoretically optimize Venturi scrubbers (1-4). The principal limitation of all of these design approaches was the assumption that a single drop-size is used to represent the entire drop spectrum formed. Experiments conducted in scrubbers have revealed the existence of an annular two-phase, two-component flow with a thin liquid layer on the walls and a high velocity gas stream carrying a spectrum of droplets in the core (5-7). As a result, the earlier designs (1-4) generally over-predicted efficiencies at all L/G ratios. To accurately describe the physical phenomena that occur in a Venturi scrubber, a true representation of the flux distribution throughout the scrubber must be available as a function of both operating and design variables, and most importantly, the flux distribution must take into account drop-size distribution. Recently, a new design procedure to estimate maximum particle collection efficiency through the establishment of * Corresponding author phone: 858-638-0744; fax: 858-638-0745; e-mail: [email protected]. Current address: 4452 Via Amable San Diego 92122. 10.1021/es991150g CCC: $19.00 Published on Web 10/07/2000

 2000 American Chemical Society

liquid flux distribution as a function of operating and design variables has been proposed (9). In this recent work, a simplified 2-D model, that takes important factors, like nonuniform flux distribution and initial liquid momenta into consideration, was proposed. However, this model uses a single mean drop diameter as a representative for drop-size distribution, and on this basis, calculations are made for the liquid flux distribution and overall collection efficiency. It is known that the drop-size and the polydispersity of drops affect the efficiency of a Venturi scrubber (10). However, the effect of drop-size distributions on the liquid flux in a scrubber unit is still unknown. In this article, the effect of average drop-size and polydispersity on the liquid flux distribution and efficiency in a Venturi scrubber is investigated, and the results are compared with flux distribution measured experimentally in earlier works (11).

Literature Review Single Average Drop-Sizes. Several theoretical and experimental correlations have been established to estimate the mean size of liquid drops due to atomization in terms of Sauter mean diameter (12-15). Among these, the most widely quoted correlation is that of Nukiyama and Tanasawa’s (NT) developed using coaxial injection of liquid into gas stream. The N-T equation was based on data obtained by physical sampling techniques, which were probably liable to be nonrepresentative due to evaporation and target effects. Kim and Marshall (16) as well as Boll et al. (17) performed experiments similar to those of N-T but covered a wider range of important variables and employed an improved technique for measuring the drop-sizes. Kim and Marshall (16) reported a modified form for estimating the mean size by correlating with Gretzinger and Marshall’s (15) data and Wetzel’s (18) drop-size data that was obtained by venturi atomization. These data resulted in a mass median diameter for the representation of drop distribution in a venturi. Boll et al. (17) measured the Sauter mean size of drops using transmissometer in an experimental venturi scrubber operating with water injected perpendicularly into the gas stream. The correlation proposed by Boll et al. (17) for estimating the mean drop-size has a similar form compared to that of N-T equation. However, it was noted that the N-T equation underestimated the effect of gas velocity rather seriously, predicting drop-sizes about 48% too large at a throat velocity of 90 m/s and about 25% too low at a throat velocity of 30 m/s. It was also noted that the N-T equation is accurate only for the data at a throat velocity of about 45 m/s. This velocity is low in many Venturi scrubber applications. Boll et al.’s correlation seems to be more realistic than that of N-T, since they measured the drop-size in a venturi scrubber under practical ranges of operating conditions (19). Atkinson and Strauss (20), who studied the effect of surface tension on drop-size in a venturi scrubber, later confirmed that the Sauter mean drop diameter prediction of Boll et al.’s correlation agrees with their experimental data. They compared their calculated Sauter mean diameter with those predicted by N-T and Boll et al. They also found that Boll et al.’s equation gave a more accurate estimation of the Sauter mean diameter than N-T equation. Based on this discussion, the Sauter mean diameter (d32) used in this work is determined by Boll et al.’s (17) equation.

d32 )

42200 + 5776(L/G)1.932

(1)

1.602 VG,th

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Another drop-size, such as mass median diameter, can be used to represent the drop-size distribution in a venturi scrubber. The mass median diameter (dm) used in this work is based on the empirical relationship between the Sauter mean and mass median diameter presented by Kim and Marshall (16):

dm )

d32 0.83

(2)

Drop-Size Distributions. Several semiempirical equations, like log-normal distribution, Rosin-Rammler distribution, Weibull probability distribution, and Roller distribution, can be used to predict the size distribution of particles and aerosols. Nukiyama-Tanasawa (12), Kim and Marshall (16), Mugele and Evans (21), and Licht (22) described some correlations for the size distribution of sprays, which were produced by pneumatic atomization. Bayvel (10), Wessman (23), Leith et al. (24), and Teixeira (25) measured data on the size distribution of atomized drops in venturi scrubbers; however, they did not perform detailed analysis of the usefulness of the correlations measured. The empirical equation of size-distribution of sprays obtained from Nukiyama-Tanasawa’s experiments is shown below:

dn ) ax2 exp(-bxq) dx

(3)

Mugele and Evans (21) applied various size distribution functions, like Rosin-Rammler, N-T, and log-probability equations, to a variety of experimental data on sprays and dispersoids. They also proposed a new equation, the upperlimit equation, as a standard for describing drop-size distributions in sprays, as it provided a better fit to the available data than the other three equations mentioned. Kim and Marshall (16) proposed a generalized cumulative distribution of particle volume (or mass) by plotting the proportionality constant for a corresponding percentage diameter against a reduced diameter, x* ) (d/dm). The data were then fitted to a curve by a Pearl-Reed or logistic equation (1930), and the resulting correlation is

1.15 Φ′V ) - 0.150 1 + 6.67 exp(-2.18x*)

(4)

Licht (22) analyzed the data of Kim and Marshall (16) and proposed that a value u ) (d/dmax - d) should be log-normally distributed with respect to the volume fraction, Φ′V. They replaced d by the reduced diameter x* ) (d/dm), so that u ) (x*/x/max - x*) where x/max ) (dmax/dm). The maximum dimensionless drop-size, x/max was found out to be 2.97. The values of u were plotted against Φ′V on log-normal probability paper and that gave a good straight line, thus indicating a fit to the upper-limit distribution function. This model has a median value of u50 ) 0.52 and a geometric standard deviation of σg ) u84/u50 ) 2.94. This is the first drop-size distribution correlation used in this work. The cumulative volume fraction of drops less than size d (Φ′V1) is given as

Φ′V1 )

[

]

ln(u/0.52) 1 1 + erf 2 x2 ln 2.94

(5)

The second drop-size distribution used in this study is proposed by Simmons (26). Simmons presented the dropsize/volume-fraction distribution data for sprays from a large number of gas-turbine fuel nozzles including both pressure and air-atomizers, using a range of fuel viscosities and operating conditions. The data were obtained by both optical and molten wax-droplet methods. His study showed that a universal root-normal distribution correlation could be 5008

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FIGURE 1. Schematic diagram of the Venturi scrubber used. established for all the fuel nozzles that he had studied when the drop-size is normalized to the mass median diameter. He also showed that the ratio of (d32/dm) has an average value of 0.83, as supported earlier by Kim and Marshall (16). This distribution can also be expressed as a normal cumulative distribution fraction of drops less than size d (ΦV2′). The standard normal variant, u, is expressed as u ) ((xd/dm µ)/σ) where the mean, µ ) 1, and the standard deviation, σ ) 0.238, are given by Simmons (26). In this study, the following drop-sizes and drop-size correlation are tested for their applicability: (1) Sauter mean diameter predicted by Boll et al. (17), eq 1; (2) mass median diameter predicted by Kim and Marshall (16), eq 2; (3) upperlimit function proposed by Licht (22), eq 5; and (4) universal root-normal distribution by Simmons (26).

Model In a recent work (9), a simplified model, which considered factors such as jet penetration length, mal-distribution of liquid drops, initial liquid momenta, and drop movement in the axial direction by convection and in the lateral direction solely due to convective diffusion was proposed for a scrubber system as shown in Figure 1. The model assumes constant film flow and no drop-to-drop interactions. Only one-half of a scrubber is considered for simulation, assuming the system is symmetric. Since, in all practical applications, the distance between the liquid injection orifices is very small, negligible variation in the drop concentration can be assumed in the z-direction making the model 2-D (27). This makes the entire system axis-symmetric with respect to the physical area to be considered in the simulation. (See extract in Figure 1 to identify the x- and y-direction in the 2-D model.) The droplet motion in this model is predicted as a steadystate process. The 2-D steady-state continuity equation for liquid drops can be written as

( )

∂Cd ∂ ∂ (V C ) ) E + Qd - Qf ∂x dx d ∂y d ∂y

(6)

In eq 6, the change in concentration due to bulk motion is equated to the change due to convection diffusion plus the drop source strength minus the amount of liquid flowing as film on the walls. The fraction of liquid flowing on the walls is averaged over the entire scrubber and is obtained from the following correlation (28).

F)

89.379

( ) L Ro G do

1.007

(7)

(VGth)0.888

The drop velocity in the axial (x) direction (Vdx) can be determined from a force balance on the drops, as shown below (28).

dVdx 3 (VG - Vdx) ) CDNµG 2 dx 4 DF V

(8)

d d dx

The term CDN is the modified drag coefficient, calculated as CDN ) CD × NRe. The value of CD is calculated using eq 9, proposed by Fathikalajahi et al. (29).

CD )

25.8 N0.81 Re

(9)

The eddy diffusivity of the drop, Ed can be calculated using the concept that velocity fluctuations in turbulent flow are sinusoidal and Stokes’ Law applies to the drag on drops.

Ed b2 ) 2 EG ω + b2

(10)

where

b)

18µG FLD2d

(11)

Viswanathan (27) proposed that (EG/VGDeq) ) 0.01 after performing extensive numerical experiments. The value of frequency of air fluctuation, ω, is 300 rad/s (27).

Numerical Procedure Since the system is axisymmetric, the total volume chosen for simulation accounts for one nozzle (z-direction), the entire length of the scrubber (x-direction), and one-half of the width of the scrubber (y-direction). The extract in Figure 1 shows the front view of the throat section of the Venturi scrubber used in this simulation. The physical space is divided into cells of a fixed Eulerian grid, and the Lagrangian mass particles carry the fluid from cell to cell by the sum of bulk and turbulent velocities. To evaluate the movements of each mass particle, the bulk velocities, eddy diffusivity, gas stream drag, and initial liquid momenta are calculated. The initial position of the liquid drops (jet penetration) is very important, as it affects the distribution of the liquid flux significantly. The initial position of the liquid drops is assumed to correspond to the point of jet atomization (11) as calculated from

FjVj l* ) 0.1145 do FGVG,th

(12)

The flux distribution at any axial point is obtained by applying a central difference formula on eq 6 and solving it by tridiagonal matrix method. Values of the drop concentration for each cell are then calculated by solving this matrix using Gaussian elimination and back substitution. In this study, all design parameters such as size of Venturi unit, number of nozzles and nozzle arrangement are kept constant, only the effect of operating conditions, like throat gas velocity and L/G ratio, are being investigated. Three throat gas velocities (45.7, 61.0, and 76.2 m/s) and five L/G ratios (0.4, 0.93, 1.2, 1.47, and 1.79 m3 liquid/1000 m3 gas) are used in the simulation. There are two sets of simulation performed in this work. One set uses two different single-average drop diameters to

represent the droplet spectrum formed in the scrubber, while the other uses two different drop-size distribution functions to represent the droplets. The ranges of drop-sizes calculated from the drop-size distribution functions are divided into eight equal intervals for the simulations. Since it has been established (9) that the uniformity in flux distribution determines the performance of Venturi scrubber, the effects of drop-size distribution and polydispersity of drops on the liquid flux distribution in a venturi scrubber are analyzed by comparing the results of simulations with experimental data (11).

Results and Discussions Effect of Operating Conditions on Polydispersity of Droplets. Figure 2a,b shows the effects of throat gas velocities and L/G ratios on the polydispersity of drops calculated using eq 5. The data from these figures show that the effect of throat gas velocities on the polydispersity of drops is much higher than the effect of L/G ratios. With a decrease in the throat gas velocity from 76.2 m/s to 45.7 m/s at a constant L/G ratio of 1.2 m3 liquid/1000 m3 gas, the maximum drop-size increases by 130% from 170 µm to 390 µm, and the median diameter increases by 125% from 60 µm to 135 µm. However, with an increase in the L/G ratio from 0.4 m3 liquid/1000 m3 gas to 1.79 m3 liquid/1000 m3 gas at a constant throat gas velocity of 76.2 m/s, the maximum drop-size only increases by 50% from 140 µm to 210 µm and the median diameter by 37% from 51 µm to 70 µm. Based on the spread of the distribution (P90 - P10) calculated, it can be found that a decrease in the throat gas velocity from 76.2 m/s to 45.7 m/s at a constant L/G ratio of 1.2 m3 liquid/1000 m3 gas, the spread of the distribution increases by 124% from 98 µm to 220 µm. However, with an increase in the L/G ratio from 0.4 m3 liquid/1000 m3 gas to 1.79 m3 liquid/1000 m3 gas at a constant throat gas velocity of 76.2 m/s, the spread of the distribution only increases by 37% from 84 µm to 115 µm. This analysis was consistent for all liquid-to-gas ratios and gas velocities analyzed. This is clear evidence that the gas throat velocity has a greater effect on the polydispersity of the drop-size distribution than the L/G ratio in the typical operating range of Venturi scrubber. These results contradict with the results of Bayvel (10), who claimed that the polydispersity of drop-size distribution is only a function of throat gas velocity and not L/G ratio. These findings may be due to the low L/G ratio (0.1-0.8 l liquid/m3 gas) that Bayvel chose in his work and as a result the majority of the drop-sizes formed were below 80 µm. Based on the findings from this work, it is expected that the effects of L/G ratio operated by Bayvel would not have produced significant variation in drop-sizes. These findings need detailed experimental verification. Effect of Operating Conditions on Liquid Flux Distribution. Figure 3a illustrates the effect of throat gas velocity on liquid flux distribution. Higher throat gas velocities give a uniformly distributed liquid flux, when all conditions such as L/G ratio, nozzle diameter, and Venturi geometry remain the same. Increase in gas velocity for a constant liquid loading essentially increases the liquid rate. Therefore, there is no change in jet penetration as the liquid injection velocity increases or decreases proportionally with the throat gas velocity. Higher gas velocities tend to break up the injected liquid jet (higher turbulence) into a larger number of fine droplets than the coarser ones formed at lower gas velocities. As a result narrow drop-size distribution would be produced, thereby reducing the polydispersity. Finer droplets also tend to distribute more laterally than coarser droplets in the venturi scrubber resulting in a more uniform flux distribution and better throat coverage. As it was seen in Figure 2b, the change in the L/G ratios, while all operating conditions remain constant, does not VOL. 34, NO. 23, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 2. (a) Comparison of the drop-size distribution at different operating conditions. The upper-limit distribution (distribution 1) is used in this comparison. L/G ) 1.2 m3 liquid/1000 m3 air, VG,th varies from 45.7 m/s to 76.2 m/s. (b) Comparison of the drop-size distribution at different operating conditions. The upper-limit distribution (distribution 1) is used in this comparison. VG,th ) 76.2 m/s, L/G varies from 0.4 to 1.79 m3/1000 m3. affect the polydispersity of the drop-size distribution greatly. Its effect on the uniformity of liquid flux distribution at the end of the venturi throat is not as clear-cut as varying throat gas velocity. It can be seen from Figure 3b that there is an optimum L/G ratio (VG,th ) 76.2 m/s, L/G ) 1.2 m3 liquid/ 1000 m3 gas) at which the droplets are uniformly distributed (uniform flux distribution is observed). Ananthanarayanan and Viswanathan (9) also arrived at this conclusion. Increasing L/G ratio at a constant throat gas velocity affects the jet penetration due to changes in initial liquid momenta. The 5010

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jet penetration length increases as the L/G ratio increases due to the increase of initial liquid momenta. The initial position of liquid jet breakup moves from the wall of the throat to the center of the throat as L/G ratio increases. At lower L/G ratio, the initial position for jet breakup is very close to the wall of the throat, and therefore the droplets that are formed closer to the wall of the scrubber cannot be distributed across the throat efficiently. At high L/G ratio, the drop-size distribution is highly dispersed, as coarser droplets are being produced at the middle of the throat. As

FIGURE 3. (a) Comparison of the flux distribution at throat end calculated from the Flux Distribution model using the upper-limited distribution (distribution 1). L/G ) 1.2 m3 liquid/1000 m3 gas, VG,th varies from 45.7 m/s to 76.2 m/s. (b) Comparison of the flux distribution at throat end calculated from the Flux Distribution model using the upper-limited distribution (distribution 1). VG,th ) 76.2 m/s, L/G varies from 0.4 to 1.79 m3/1000 m3. coarser droplets have less efficient lateral distribution, they tend to remain at the center throughout the throat. This is why there is a high flux concentration at the center of the throat and the flux distribution is the least uniform at high L/G ratio. Effect of Polydispersity on Liquid Flux Distribution. Figures 4 and 5 illustrate the comparison of our simulated results of the flux distribution across the cross section of the throat with the experimental data. Every diagram consists of four simulated results assuming different drop-size distribution, namely the mass mean diameter (dm), Sauter mean diameter (d32), the upper-limit distribution (distribution 1), and the root-normal distribution (distribution 2) along with the experimental data (11). Figure 4 compares the flux distribution at the end of the throat for L/G ratio of 0.4 m3 liquid/1000 m3 gas at a throat gas velocity 45.7 m/s. Figure 5 compares the flux distribution at the end of the throat for the same L/G ratio at throat gas velocity of 76.2 m/s. “Goodness-of-fit” tests, namely the sum of the square of

residuals (SSR) test and the Chi-square test (χ2), were done to check how well experimental data fitted with the simulated results. An interesting observation can be made from these two sets of results from Figures 4 and 5. From Figure 4 (VG,th ) 45.7m/s, L/G ) 0.4 m3/1000 m3), it can be seen that the experimental flux data agree very well with the simulated results for the upper-limit distribution (distribution 1) (SSR ) 0.6708, χ2 ) 2.3404). For other L/G ratios (L/G ) 0.9 to 1.79 m3/1000 m3), the experimental data fit reasonably with the upper limit distribution (distribution 1) and the root-normal distribution (distribution 2) curves. However, some of the quality of matching is not as good as the one found in Figure 4. For the other L/G ratios, the SSR values of the upper limit distribution (distribution 1) range from 1.7583 to 5.6074, while the χ2 values range from 0.0492 to 8.4823. The flux distributions calculated assuming polydispersed drop-sizes (distribution 1 and distribution 2) fit the trend of the experimental data better than calculations assuming monodispersed dropVOL. 34, NO. 23, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Comparison of flux distribution at the end of throat using various drop-size modelss upper-limit distribution (distribution 1), root-normal distribution (distribution 2), mass median diameter (dm), Sauter mean diameter (d32), and experimental data (experimental) at throat gas velocity at 45.7 m/s, L/G ) 0.4 m3 liquid/1000 m3 air.

FIGURE 5. Comparison of flux distribution at the end of throat using various drop-size modelssupper-limit distribution (distribution 1), root-normal distribution (distribution 2), mass median diameter (dm), Sauter mean diameter (d32) and experimental data (experimental) at throat gas velocity at 76.2 m/s, L/G ) 0.4 m3 liquid/1000 m3 air. sizes (dm and d32). As mentioned earlier, at low throat gas velocity (45.7 m/s), a highly dispersed drop-size distribution is formed. This could be the reason flux distributions that were calculated from the two drop-size distributions were able to describe the experimental data more closely than the one calculated from a single mass median diameter. It appears that a single average drop-size is unable to describe the entire drop-size distribution at low gas velocities. From Figure 5 (VG,th ) 76.2 m/s, L/G ) 0.4 m3/1000 m3), it is quite evident that the experimental flux data agree reasonably well with the simulated results using the mass median diameter (dm). An opposite trend is observed in Figure 5 as compared to Figure 4. The flux distribution calculated from the mass median diameter (dm) gives a closer match to the experimental data than flux distributions calculated from the two drop-size distributions in Figure 5. This is evident from the “goodness-of-fit” analysis where lower values of SSR (0.1945) and χ2 (0.0329) were obtained. Similarly, for other L/G ratios (L/G ) 0.9 to 1.79 m3/1000 m3), the 5012

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experimental data fit reasonably with mass median diameter (dm). However, the quality of matching is not as good as the one found in Figure 5. For the other L/G ratios, the SSR values of the mass median diameter (dm) range from 0.205 to 3.2544, while the χ2 values range from 0.0368 to 1.5112. At high throat gas velocity, the drop-size distribution predicted is much narrower than the one at low velocity and hence a single average drop-size (for example, mass median diameter, dm) could describe the entire distribution. The above observation from Figures 4 and 5 is dependent only on the throat gas velocity and independent of the L/G ratio. At high throat gas velocity, flux distribution predicted using drop-size distribution tends to be more uniform than the ones found by experiments. At low throat gas velocity, use of drop-size distribution produced flux contours that matched well with the experimental results. However, the use of single drop-sizes in the model at low throat gas velocity yielded flux distributions that did not match with experimental values. Since the drop-size distribution becomes

FIGURE 6. (a) Iso-flux plot along the throat of the Venturi scrubber at a throat gas velocity of 76.2 m/s. Liquid flux was calculated from model using the upper-limit drop-size distribution (distribution 1). L/G ) 0.4 m3 liquid/1000 m3 air. (b) Iso-flux plot along the throat of the Venturi scrubber at a throat gas velocity of 76.2 m/s. Liquid flux was calculated from model using the upper-limit drop-size distribution (distribution 1). L/G ) 1.2 m3 liquid/1000 m3 air. (c) Iso-flux plot along the throat of the Venturi scrubber at a throat gas velocity of 76.2 m/s. Liquid flux was calculated from model using the upper-limit drop-size distribution (distribution 1). L/G ) 1.79 m3 liquid/1000 m3 air. VOL. 34, NO. 23, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 7. (a) Dependence of overall collection efficiency on throat gas velocity at different values of L/G ratio for a particle radius of 0.5 micron. Bayvel’s calculation. Solid linesstaking into account the polydispersity of drops. Dashed linessignoring the polydispersity of drops. (b) Dependence of overall collection efficiency on throat gas velocity at different values of L/G ratio for a particle radius of 0.5 micron. Present work. Solid linesstaking into account the polydispersity of drops. Dashed linessignoring the polydispersity of drops. narrower with the increase in throat gas velocity, the droplets in the scrubber become more uniform and hence can be represented by a single mean drop-size like the mass median diameter. The flux distribution changes along the length of the throat as the gas stream accelerates the drops. Figures 6 depict flux distribution along the throat length as contours of constant normalized flux. As seen earlier, the optimum operating condition that produced a near-uniform flux distribution also produced near-uniform throat coverage along the entire throat (Figure 6b). For gas throat velocity of 45.7 m/s, the flux distributions show a less than uniform coverage throughout the throat. Condition of VG,th ) 45.7 m/s, L/G ) 0.4 m3/ 1000 m3 produced higher flux closer to the wall of the throat while condition of VG,th ) 45.7 m/s, L/G ) 1.79 m3/1000 m3 produced higher flux closer to the center of the throat. From this analysis, it became clear that there are regions in the throat, where the flux is zero or minimal. With an increase of L/G ratio at constant gas velocity and scrubber geometry, the flux distribution changes significantly. This analysis also shows that the higher flux values at the beginning of the throat tend to distribute into lower flux values toward the end of the throat, thereby producing a relatively better coverage further downstream of the throat. Increases in liquid rate indiscriminately at constant gas velocity can result in mal-distribution of droplets (Figure 6c). Haller et al. (4) and Ananthanarayanan and Viswanathan (9) reported similar observations from their experimental studies on a pilot-scale Venturi scrubber and computer simulation, respectively. Comparisons of Bayvel’s Results with Present Work. Bayvel (10) developed a light scattering device for measuring drop-sizes and its distribution along the length of a Venturi scrubber for various throat gas velocities (50-120 m/s) and 5014

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liquid-to-gas ratios (0.1-0.8 l-liquid/m3-gas). His work indicated that replacement of the polydispersive distribution of drops by monosize drops is not always possible and therefore it is necessary to use experimental drop-size distribution data collected in the Venturi throat to compute dust collection efficiency. Bayvel also did a simulation similar to this present work. However, unlike this work, he used a different set of operating conditions, and he also assumed a uniformly distributed liquid flux in the scrubber. In this work, Bayvel’s operating conditions are used with the model presented here to calculated the collection efficiency. The comparison of the results is shown in Figure 7a,b. Figure 7a shows the results of the overall collection efficiency from Bayvel’s calculation as a function of the throat gas velocity at different values of L/G ratio for particle radius of 0.5 µm. It is clear from Figure 7a that there are discrepancies between the results obtained using monodispersed and polydispersed drop-sizes. Furthermore, it can be seen that the effect of polydispersity of drops produces only slight increase in collection efficiency with increasing throat gas velocity. However, when monodispersity of drops is assumed, there appears a tremendous improvement in the collection efficiency with increasing throat gas velocity. It can also be seen that assumption of monodispersity results in lower collection efficiencies compared to the results assuming polydispersity. However, in Figure 7b (present work), it can be seen that the results of the present calculation predict lower collection efficiencies for all throat gas velocities and L/G ratios compared to Figure 7a. It can also be seen that there is not much difference between the values of collection efficiency obtained using the monodispersed drops (dm) and the polydispersed drops (Root-Normal Distribution Function).

FIGURE 8. (a) Flux distribution at throat end for a throat gas velocity of 100 m/s at different values of L/G ratio (0.1-0.8 l/m3). Using mass median diameter (dm) (b) Flux distribution at throat end for a throat gas velocity of 100 m/s at different values of L/G ratio (0.1-0.8 l/m3). Using root-normal drop distribution (distribution 2).

As mentioned before, the reason for this discrepancy between Bayvel’s work and the present work may be due to Bayvel’s assumption that the droplets are distributed uniformly across the scrubber cross-section. It is important to note that in the present work, nonuniform liquid flux distribution that occurs in the scrubber is predicted prior to the calculation of the collection efficiency. This observation can be explained by examining the flux distribution at throat end. Figures 8a,b show an example of the liquid flux distribution at throat end for a throat gas velocity of 100 m/s at all L/G ratios. It can be seen that the flux distribution of the single mass median diameter, dm, (Figure 8a) is very similar to the one of the root-normal drop distribution (Figure 8b) in terms of the shape and the values of local-flux-touniform-flux ratio. This can be due to the low L/G ratios (0.1-0.8 l-liquid/m3-gas) and relatively high throat gas velocities (50-120 m/s) that are used in this set of calculations. This can also be seen from Figure 5. At high throat gas velocity and low L/G ratio (76.2 m/s and 0.4 l-liquid/m3-gas), the four calculated flux distributions at throat end are quite similar in terms of the shape and the values of local-flux-to-uniformflux ratio. Since the collection efficiency of Venturi scrubber is a strong function of throat coverage by droplets, similar flux distributions will result in collection efficiencies that are closer to each other.

Deq

equivalent diameter, Deq ) 4(cross-sectionalarea-of-flow/wetted-perimeter)

D32

Sauter mean diameter, µm

dm

mass median diameter, µm

dmax

maximum drop diameter in spray ) 2.97 dm

do

orifice diameter, mm

Ed

drop eddy diffusivity, m2/s

F

fraction of liquid flowing as film on wall

l*

jet penetration length at which the droplets form, m

L/G

liquid-to-gas ratio

n

no. of particles with diameter between zero and x (eq 3)

NRe

Reynolds number

P10

The 10th percentile of the drop-size distribution

P90

The 90th percentile of the drop-size distribution

Qd

liquid drop source strength, no./m3‚s

Qf

amount of liquid flowing as film on the wall, no./m3‚s

Ro

half length of Venturi throat in the y-direction, mm

Nomenclature A, b, q

experimental quantities (eq 3)

u

(d/dmax - d) ) (x*/x/max - x*)

Cd

drop concentration, no./m3

Vdx

drop velocity in the x-direction, m/s2

CDN

modified drag coefficient, CDN ) CD*NRe

VG,th

throat velocity of the gas, m/s

Dd

drop diameter, m (eq 8)

Vj

jet velocity, m/s

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(VG-Vdx)

relative velocity of drop with respect to gas, m/s

x

diameter of drops, m (eq 3)

x*

reduced diameter ) (d/dm)

Greek Letters (∆v/∆x)

gradient of cumulative volume frequency curve of drop-size distribution (Figure 2)

Φ V′

cumulative volume fraction less than size d (eq 4)

ΦV1′

cumulative volume fraction less than size d (distribution 1)

ΦV2′

cumulative volume fraction less than size d (distribution 2)

µG

viscosity of gas, kg/m‚s

F

density, kg/m3

σ

standard arithmetic deviation

σg

standard geometric deviation

ω

frequency of air fluctuations, rad/s

Subscripts d

drop

f

film

G

gas

j

jet

th

throat

x

x-direction

Literature Cited (1) Goel, K. C.; Hollands, K. G. T. Atmos. Environ. 1977, 11, 837. (2) Leith, D.; Cooper, D. W. Atmos. Environ. 1980, 14, 657.

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(3) Cooper, D. W.; Leith, D. Aerosol Sci. Technol. 1984, 3, 63. (4) Haller, H.; Muschelknautz, E.; Schultz, T. Chem. Eng. Technol. 1989, 12, 188. (5) Guntheroth, H. Progress Reports, VDI Publication; 1966; Ser. 3, No. 13. (6) Boll, R. H. Ind. Eng. Chem. Fundam. 1973, 12, 40. (7) Viswanathan, S.; Gnyp, A. W.; St. Pierre, C. C. Ind. Eng. Chem. Fundam. 1984, 23, 303. (8) Koehler, J. L. M.; Feldman, H. A.; Leith, D. Aerosol. Sci. Technol. 1987, 7, 15. (9) Ananthanarayanan, N. V.; Viswanathan, S. AIChE J. 1998, 44, 2549. (10) Bayvel, L. P. Trans. 1ChemE 1982, 60, 31. (11) Viswanathan, S.; Gnyp, A. W.; St. Pierre, C. C. Can. J. Chem. Eng. 1983, 61, 504. (12) Nukiyama, S.; Tanasawa, Y. Trans. Soc. Mech. Eng. (Japan); 4-6 Rept., 1-6 (1938-1940); Translated by E. Hope, Defense Research Board, Department of National Defense: Canada, March 18, 1950. (13) Lewis, H. C., et al., Ind. Eng. Chem. 1948, 40, 67. (14) Hrubecky, H. F. J. Appl. Phys. 1958, 29, 572. (15) Gretzinger, J.; Marshall, W. R., Jr. AIChE J. 1961, 7, 312. (16) Kim, K. Y.; Marshall, W. R., Jr. AIChE J. 1971, 17, 575. (17) Boll, R. H., et al. J. Air Pol. Ccon. Assoc. 1974, 24, 934. (18) Wetzel, H., Ph.D. Thesis, University Wisconsin, Madison, 1951. (19) Chongvisal, V., Ph.D. Thesis, University of Cincinnati, 1979. (20) Atkinson, D. S. F.; Strauss, W. J. Air Pol. Con. Assoc. 1978, 28, 1114. (21) Mugele, R. A.; Evans, H. D. Ind. Eng. Chem. 1951, 43, 1317. (22) Licht, W. AIChE J. 1974, 20, 595. (23) Wessman, E. D. Ph.D. Thesis, University of Waterloo, 1981. (24) Leith, D.; Martin, K. P.; Copper, D. W. Filtration Separation 1985, May/June, 191-195. (25) Teixeira, J. C. F., Ph.D. Thesis, University of Birmingham, 1988. (26) Simmons, H. C. J. Eng. Power 1977, 99, 309. (27) Viswanathan, S. Ind. Eng. Chem. Res. 1997b, 36, 4308. (28) Viswanathan, S.; Gnyp, A. W.; St. Pierre, C. C. Particulate Sci. Technol. 1997a, 15, 65. (29) Fathikalajahi, J.; Talaie, M. R.; Taheri, M. J. Air Waste Mgmt. Assoc. 1995, 45, 181.

Received for review October 1, 1999. Revised manuscript received July 10, 2000. Accepted August 28, 2000. ES991150G