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Specifying Venturi Scrubber Throat Length forEffective Particle Capture at Minimum PressureLoss PenaltyHoward E. Hesketh a & Krishna Mohan aa Southern Illinois University, Carbondale, Illinois, USAVersion of record first published: 12 Mar 2012.

To cite this article: Howard E. Hesketh & Krishna Mohan (1983): Specifying Venturi Scrubber Throat Length forEffective Particle Capture at Minimum Pressure Loss Penalty, Journal of the Air Pollution Control Association, 33:9,854-857

To link to this article: http://dx.doi.org/10.1080/00022470.1983.10465662

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Specifying Venturi Scrubber Throat Lengthfor Effective Particle Capture atMinimum Pressure Loss Penalty

Howard E. Hesketh and Krishna MohanSouthern Illinois UniversityCarbondale, Illinois

A simplified equation for specifying the optimum minimum lengthfor commercial venturi scrubber throats is presented in this paper.This theoretical correlation is derived using an optimum velocity ratio(velocity of collector droplet at end of venturi throat to velocity of gasin throat) and is a function of throat gas velocity and liquid to gas ratio.This velocity ratio establishes the minimum throat length and is basedon available literature data. Predicted venturi scrubber particle col-lection for throats specified by this procedure compare favorably withreported commercial venturi collection efficiencies and with modeledventuri efficiencies over the practical range of venturi scrubber op-eration.

Venturi scrubbers are widely used for the control of particu-late air pollution emissions. Much of the commercial venturicollection data is either unavailable or in a form that is un-usable. One of the most comprehensive studies undertakento correlate venturi collection efficiency with design and op-erating parameters was assembled under an EPA contract byYung et al.1 This study includes the effects of converger,throat, and diverger on particle collection efficiency. However,the correlation procedures are very detailed and complex anda simplified approximation is needed.

Most of the particle collection in a venturi occurs by inertialimpaction in the throat and it occurs within a few inches fromwhere the liquid is atomized. Additionally, about another 5%occurs in the downstream diverger section. The bulk of col-lection which occurs at the throat is related to the velocity ofthe gas, the amount of liquid, and how long it takes to accel-erate the collector droplets. Therefore, the throat length ofa venturi will influence collection efficiency and is significant.To a limited degree, the longer the throat, the more efficientthe scrubber. However, the gas phase pressure loss also in-creases with throat length, so it is imperative for economicaloperation to optimize the length of the throat.

Previous studies

The EPA study by Calvert1 derived a relation for collectionefficiency as a function of throat length, as shown in Figure1. In this figure the terms used are:

d 2V *KP0 = ^ T (1)

R =(Qg)(Pg)CDo

_ 3 C D 0 X t p g2ddpd

where Kpo

B

CDO

L =

Pt =

dd =dp =Qi =Q g =p d =

Pg =Hg =X t =

impaction parameter at entrance of thethroat, dimensionlessa dimensionless parameter for thethroatdrag coefficient of droplet at point ofliquid injection, dimensionless.dimensionless throat length (wheredroplet initial axial velocity s 0)penetration, which is 1 minus fractionalefficiencyliquid drop diameter, fimparticle diameter, /xmliquid volumetric flow rategas volumetric flow rateliquid density, g/cm3gas density, g/cm3gas viscosity, g/(cm s)throat length

Copyright 1983-Air Pollution Control Association

Associated with the L term would be a factor to account fordiverger length if appropriate. Note from Figure 1 that effi-ciency (-In Pt/B) increases rapidly up to 2-3 dimensionlessthroat lengths and increases little beyond about 4 throatlengths.

Crowder et al.2 calculates minimum venturi throat lengthsrequired for atomized droplets to reach gas velocity for variousvelocities with liquid to gas ratio as a parameter, as shown inFigure 2. This shows that at any given velocity, the throatlength required to enable an atomized droplet to reach the gasvelocity increases as the liquid to gas ratio (L/G) increases.Reflected in these data is the fact that particle collection ef-

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0.01 1000.1 1.0 10Dimensionless throat length, L

Figure 1. Effect of venturi throat length on particle penetration.1

ficiency increases rapidly as throat length increases up toabout 8 in. and little increase is obtained as length is increasedbeyond about 12 in. However, this is influenced by liquid togas ratio.

It has been shown3 that in a typical venturi scrubber,scrubbing liquid injected into the throat is pneumaticallyatomized when it is moving at a velocity of about 15.3 ft/s. Thesame study observed that when stationary 100 jum glass par-ticles are introduced into a venturi throat they leave the dif-fuser of a conventional venturi at velocities equal to about halfthe initial throat gas velocities and twice the exit gas veloci-ties.

0 100 200 300 400 500 600Throat velocity, ft/sec

Figure 2. Minimum venturi contactor length vs. velocity.2

Procedures for This Evaluation

This study attempts to develop a meaningful and simplifiedrelationship for establishing minimum venturi scrubber throatlength as a function of throat velocity and liquid to gas ratioat particle collection efficiencies comparable to conventionaland accepted scrubber system data. The following assump-tions are used:

1. The gas is air at standard conditions.2. Flow is incompressible, one-dimensional, and iso-

thermal.3. Liquid drops are spread uniformly across the venturi

cross-section.

4. Collection drops are atomized water of uniform diam-eter, with a mean size as predicted by the simplifiedNukiyama and Tanasawa4 equation.

5. Liquid is injected at the throat of the venturi with noaxial velocity.

An evaluation of the data referenced above reveals that akey parameter in determining how long the throat should beis the ratio of droplet velocity at the exit of the throat (Vde)divided by the throat gas velocity (Vst)- This velocity ratio,Vfe/Vgu indicates the velocity difference between particlesin the gas and the mean collector droplet and is therefore di-rectly related to impaction parameter and collection effi-ciency. In addition, throat length increased pressure drop.From a practical point of view, velocity ratios >0.8 requirethroats which are too long (pressure drop too high) and ratios

than 0.5. The optimum velocity ratio of 0.5 is assumed in thispaper as the basis for venturi scrubber throat length design.The subsequent design data are then verified showing this isa good value.

Establishing Venturi Scrubber Throat Length

Using an optimum velocity ratio (Vde/Vgt) of 0.5 and theassumptions stated, a generalized equation for minimumthroat length is developed as follows. A range of liquid to gasratios and throat gas velocities typical to conventional in-

5 10 15 20 25 30Liquid to gas ratio L/G, gallons/1000 acf

Figure 4. Velocity ratio vs. liquid to gas ratio for typicalventuri scrubbers operating at 200 ft/s.

dustrial venturi scrubbers is used to obtain the Sauter meandiameter of the atomized droplets by the simplified Nuki-yama-Tamasawa4 equation assuming air and water:

29.6 (L/G) (4)gt

where Vst = gas throat velocity, cm/sdd = liquid drop diameter, jum

L/G = liquid to gas ratio, L/m3

Eq. 5 is integrated to obtain throat length, X t, at a velocity of0.5 for throat velocities from 66 to 300 ft/s and for liquid to gasratios from 7.5 to 30 gal/1000 acf. These are the ranges ofthroat gas velocities and liquid to gas ratios of greatest interestto industry. The results are given in Table II.

The data from Table II are plotted in Figure 5 and lines aredrawn to smooth the data. It is interesting to note that theselines intersect at 15.3 ft/s, which is the value observed byHesketh3 as the velocity at which liquid streams are atomizedin a venturi scrubber. Note that effectiveness of pneumaticatomization to form water droplets decreases below about 150ft/s, although relatively fair atomization still occurs at veloc-ities of about 80 ft/s. Below this velocity, atomization may notbe sufficient to produce adequate particle collection droplets.Below 15.3 ft/s essentially no droplets would be formed bypneumatic atomization.

10 15.3 30 60 100 300

Throat gas velocity Vg t , ft/sec600

Figure 5. Venturi scrubber throat length vs. throat gas velocity for the velocityratio of 0.5.

Table I. Sauter mean diameter of drops obtained by the Nukiyama-Tanasawaequation.

Liquid to gas ratiogal/1000 acf

7.512.52030

L/m3

10051675

268402

Mean droplet diameter,

66(2000)

280315380488

dd, in nm forgas velocities, VRt, ft/s (cm/s) of

120(3658)

167200267375

150(4572)

140175240348

200(6096)

112147212321

300(9199)

85119185294

These results are given in Table I.Fuch's5 solution to the unsteady state equation of motion

for accelerating particles in a constant velocity gas streamis:

(5)where subscripts f and i denote final and initial conditions andRed is droplet Reynolds number.

The Dickinson and Marshall equation6 is used to obtain thedrag coefficient, CT>:

94CD = 0.22 + - p - (1 + 0.15 Red0-6)Red (6)

The generalized equation for minimum venturi scrubberthroat length is derived from Figure 5:X t = 328.582 ygt[o.O2343(L/G) - 0.8657] eXp[-0.063(L/G)] (7)

where X t = throat length, inchesL/G = liquid to gas ratio, gal/1000 acfVgt = throat gas velocity, ft/s

Validation of Findings

The theoretical, generalized Eq. 7 for minimum venturithroat length can be compared for particle collection efficiency

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Table II.of 0.5.

Integrated values of throat length at the velocity ratio

Liquid gas ratiogal/1000 acf

7.5 '12.52030

66

11.514.118.624.2

Throat length, Xt, in inches forthroat velocities in ft/s of

120

7.239.18

13.2220.73

150

6.28.4

12.5320.55

200

5.227.14

11.2219.94

300

45.83

11.1120.2

using reported data and procedures. An estimated efficiencyfor standard venturi scrubbers designed using Eq. 7 for thethroat lengths plus conventional diverger sections can becalculated using the procedures of Yung.1 This is done for

1.0

0.1

0.01

1

1

1

Illl II

\

0.01

Leisegangventuri 8

i

1 1

1 1

1 1

This study

\ \ Schifftner^Heske th empirical ^ -

i U

\ Calvert cut\ diameter 7

0.0010 10 20 30 40

Venturi AP, inches H2OFigure 6. Comparison of predicted venturi scrubberefficiencies on 1-/xm particles for various designs.

l-fim particles and the results for this study are plotted asFigure 6. Also in Figure 6 are shown predicted efficiencies forl-/tm particles estimated by the Cut Diameter Theory,7 by thecommercial Leisegang Venturi,8 and by the compilation ofindustrial scrubber data.9

In the range of pressure drops from 5 to 25 in. water gauge,data from this study agree well for 1-jwn particles with themajority of available venturi scrubber data. Conventionalventuri scrubbers usually do not operate at efficiencies ofgreater than 90% on l-/n particles, so it can be concluded thatmost of the data agree. The accuracy of the reported Leisegangscrubber data is unknown.

Summary and Conclusions

The velocity ratio is a key parameter in venturi scrubberperformance. An optimum velocity ratio of 0.5 is used basedon measured values of particle collection efficiency andpressure drop data. This optimum velocity ratio is used todevelop a mathematical correlation between throat length,gas throat velocity, and liquid to gas ratio. The equation forminimum venturi scrubber throat length (Eq. 7) is used topredict venturi throat lengths as a function of throat velocitiesand liquid to gas ratios. Predicted particle collection effi-ciences in venturi scrubbers designed with these throat lengthsare compared to empirical venturi data for l-/im size particles;within the ranges of typical venturi operation, the correlationis good.

References

1. S. C. Yung, S. Calvert, H. F. Barbarika, "Venturi Scrubber Per-formance Model," EPA-600/2-77-172, U.S. Environmental Pro-tection Agency, August 1977.

2. J. W. Crowder, K. E. Noll, W. T. Davis, "Modeling of venturiscrubber efficiency, " Atmos. Environ. 16: 2009 (1982).

3. H. E. Hesketh, "Atomization and cloud behavior in venturiscrubbing," JAPCA. 23: 600 (1973).

4. S. Nukiyama, Y. Tanasawa, "An experiment on the atomizatonof liquid by means of an air stream," Trans. Soc. Mech. Eng.(Japan) 4: 86 (1938).

5. N. A. Fuchs, The Mechanics of Aerosols, C. N. Davies, ed., Per-gamon Press, Elmsford, NY, 1964.

6. D. R. Dickinson, W. R. Marshall, AIChE J. 14: 541 (1968).7. S. Calvert, "How to choose a particulate scrubber," Chem. Eng.

84: 54 (1977).8. "Scrubber trims wastewater discharge," Chem. Eng. 89: 53

(1982).9. K. C. Schifftner, H. E. Hesketh, Wet Scrubbers, Ann Arbor Science

Publishers, Inc., Ann Arbor, MI 1982.

Howard E. Hesketh, P.E. is a Professor of Air PollutionControl Engineering at Southern Illinois University, Car-bondale, IL 62901, and Chairman of APCA's EducationCouncil. Krishna Mohan holds an M.S. in Engineering fromthe Department of Thermal and Environmental Engineeringat Southern Illinois University. This technical paper wassubmitted for editorial review on February 7, 1983; the re-vised manuscript was received June 20,1983.

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