P.1 

OAR Box 1110 

Prepped by Ryan Dugan 

Document Number: 

1) IV-A-1 

Docket Number: 

A-82-39 

Printed 4/14/2008 1:23:54 PM Sheet 1 of 156 
P.2 

EPA-600/2-77-172 

August 1977 Environmental Protection Technology Series 

HI-*'/ 

VENTURI SCRUBBER 

PERFORMANCE ^ODEL 

o' *«* > *** , 

Industrial Environmental Research Laboratory 

Office of Research and Development 

U.S. Environmental Protection Agency 

Research Triangle Park, North Carolina 27711 
_E^_ 

RESEARCH REPORTING SERIES 

Research reports of the Office of Research and Development, U.S. Environmental Protection Agency, have been grouped into nine series. These nine broad cc^ccisr. vore 

established to facilitate further development and application of enviro^r ??;'••.'.]

 v:;

 -

nology. Elimination of traditional grouping was consciously planned to fc'. ';•:-,• •>

 : •:: 

transfer and a maximum interface in related fields. The nine sen'?* ars: 

1. Environmental Health Effects Research 

2. Environmental Protection Technology 

3. Ecological Research 

4. Environmental Monitoring 

5. Socioeconomic Environmental Studies 

6. Scientific and Technical Assessment Reports (STAR) 

7. Interagency Energy-Environment Research and Development 

8. "Special" Reports 

9. Miscellaneous Reports 

This report has been assigned to the ENVIRONMENTAL PROTECTION TECHNOLOGY 

series. This series describes research performed to develop and demonstrate instrumentation, equipment, and methodology to repair or prevent environmental degradation from 

point and non-point sources of pollution. This work provides the nev/ or improved technology required for the control and treatment of pollution sources to meet environmental 

quality standards. 

REVIEW NOTICE 

Tnis report has been reviewed by the participating Federal Agencies, and approved for 

publication. Approval does not signify that the contents necessarily reflect the views and 

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constitute endorsement or recommendation for use. 

This document is available to the public through the National Technical Information 

Service, Springfield, Virginia 22161. 
P.4 

EPA-600/2-77-172 

. August 1977 

VENTURI SCRUBBER 

PERFORMANCE MODEL 

by 

Shui-Chow Yung, Seymour Calvert, and 

Harry F. Barbarika 

A.P.T., Inc. 

4901 Morena Boulevard, Suite 402 

San Diego, California 92117 

Contract No. 68-02-1328 

Task No. 13 

ROAP No. 21ADL-002 

Program Element No. 1AB012 

EPA Task Officer: Leslie E. Sparks 

Industrial Environmental Research Laboratory 

Office of Energy, Minerals, and Industry 

Research Triangle Park, N.C. 27711 

Prepared for 

U.S. ENVIRONMENTAL PROTECTION AGENCY 

Office of Research and Development 

Washington, D.C. 20460 
P.5 

ABSTRACT 

A review and evaluation of the available venturi scrubber 

design equations are presented. Calvert's differential equation 

for particle collection and Boll's differential equation for 

pressure drop are selected for numerical solution and the results 

presented graphically. 

The particle collection and pressure drop of venturi scrubbers can be approximated by the collection occurring in the venturi throat and by the drop acceleration loss respectively. Simplified equations were derived by applying Calvert's and Boll's 

equations to the venturi throat section. The new design equations are much simpler to use and compare well with available 

performance data. 

This report was submitted in partial fulfillment of Contract 

Number 68-02-1328, Task Number 13 by Air Pollution Technology, 

Inc. under the sponsorship of the U.S. Environmental Protection 

Agency. This report covers the period March 1, 1976 to May 30, 

1976, and work was completed as of June 30, 1976. 

ENVIRONMENTAL PROTECTION 

AGENCY 

APR 2 5 1988 

CENTRAL DOCKET 

SECTION 

n 
P.6 

CONTENTS 

Abstract 

Page 

ii 

Figures iv 

Tables ix 

Abbreviations and Symbols x 

Acknowledgement xv 

Introduction 

Summary and Conclusions 

Literature Search 

Comparison of Model with Experimental Data. 

Performance Model 

Comparing Model Predictions with Performance 

Data 

1 

4 

16 

41 

61 

114 

7. Design Analysis 128 

8. Entrainment Separator 161 

References ... . 191 

Appendix . 195 

in 
P.7 

FIGURES 

Number Page 

1-1 Venturi Scrubber Sy.stem 3 

3-1 Target Efficiency Results of Various 

Investigators 20 

3-2 Drag Coefficient of a Sphere 27 

4-1 Dimensions of OAP Venturi Scrubber . . 43 

4-2 Comparison of Predicted Pressure Drop 

with Experimental Data from Wen and 

Uchida 44 

4-3 Comparison of Predicted Pressure Drop 

with Experimental Data from Wen and 

Uchida 45 

4-4 Comparison between Behie and Beeckmans' 

Prediction and Experimental Data from 

Wen and Uchida 46 

4-5 Comparison of Predicted Pressure Drop by 

Modified Calvert's Equation with Data 

from Wen and Uchida 51 

4-6 Prototype Venturi Scrubber Used by Boll 52 

4 7 Comparison of Boll's Pressure Drop Data 

with Theory 53 

4-8 Dimension of Pease-Anthony Venturi 

Scrubber Used by Brink and Contant. . . 55 

4-9 Comparison of Brink and Contant Experimental Data with Theories 57 

4-10 Dimensions of the Ekman and Johnstone 

Venturi 58 

4-11 Comparison of Eleman and Johnstone's 

Pressure Drop Data with Theories .. . 59 

5-1 Chart for Obtaining ul for a Circular 

Duct 72 

iv 
P.8 

FIGURES (continued) ' • 

Number Page 

5-2 Chart for Obtaining u^ for a Rectangular 

Duct 73 

5-3 Chart for Obtaining p*, for a Circular Duct 74 

5-4 Chart for Obtaining p^ for a Rectangular 

Duct 75 

T-5 Chart for Obtaining Penetration for Circular Duct 76 

5-6 Chart for Obtaining Penetration for Circular Duct 7 7 

5-7 '.':•.art for Obtaining Penetration for Circu-

"ar Duct 78 

5-8 Chart for Obtaining Penetration for Circu-

" :r Duct 79 

5-9 Chart for Obtaining Penetration for Circular Duct 80 

5-10 Chart for Obtaining Penetration for Rectangular Duct 81 

5-11 Chart f«. r Obtaining Penetration for Rectangular Du-t 8 2 

5-12 Chart to Obtain Penetration for Rectangular 

Duct 83 

5-13 Chart to Obt in Penetration for Rectangular 

Duct 84 

5-14 Chart to Obtaii Penetration for Rectangular 

Duct 85 

5-15 Chart to Obtain Penetration for a Rectangular Duct 86 

5-16 Chart to Obtain Penetration for a Rectangular Duct 87 

5-17 Concept of a Hypothetical Section ... . 88 

v 
P.9 

FIGURES (continued) 

Number Page 

5-18 Chart for Obtaining LH for a Circular Duct 90 

5-19 Chart for Obtaining LH for a Rectangular 

Duct 91 

5-20 Ventrui Scrubber for Sample Calculation. . 93 

5-21 Predicted Grade Efficiency Curve 98 

5-22 Predicted Grade Efficiency Curve H O 

6-1 Experimental and Predicted Performance of 

AAF Kinpactor 32 Venturi Scrubber 116 

6-2 Experimental and Predicted Performance for 

AAF Kinpactor 32 Venturi Scrubber 117 

6-3 Predicted and Experimental Penetration for 

Venturi Scrubber Used by Brink and Contant 118 

6-4 Predicted and Measured Penetration for 

Chemico Venturi Scrubber 121 

6-5 Predicted and Experimental Grade Efficiency 

Curve for Chemico Venturi Scrubber ... . 122 

6-6 APS Electrostatic Scrubber 123 

6-7 Experimental and Predicted APS Venturi 

Scrubber Performance 124 

6-8 Predicted and Experimental Performance for 

Venturi Rod Scrubber 126 

7-1 Venturi Scrubber Integrated Penetration, 

"Pt" versus "dnrn/d ", with "K " as paraP Dil pg pg 

meter, "a =2.5" 134 

7-2 _Venturi Scrubber Integrated Penetration, 

Pt versus d rn/d , with k as parameter, 

a =5 . . .

P ^ ° . ?g. .. . ?g. .... . . . 155 

7-3 Venturi Scrubber Integrated Penetration, 

Pt versus d cn/d„n, with K as parameter, 

a=7.5 . . .P?°. ?g. .. . ?g. ... . . . . 136 

vi 
P.10 

FIGURES, .(-continued) 

Number E.^8^. 

7-4 "Pt" versus "B" with "K " as parameter, 

"a =2.5" ? g 138 

7-5 "Pt" versus "B" with "K " as parameter, 

g 

,a =5" ?g 139 

7-6 "Pt" versus "B" with "K " as parameter, 

"a =7.5" Pg 140 

/ d Cn/d versus "B" with "K " as parapaSO' pg pg ' 

meter 141 

7-8 Effect of Throat Length on Penetration . . . 142 

7-9 Iffect of Throat Length on Performance . . . 144 

7-10 "redicted Venturi Scrubber Performance, K rn 

versus B ? . 14 5 

7-11 Effect of Gas Velocity and Liquid to Gas 

Flow Rate Ratio on Performance Cut Diameter 147 

7-12 "B" vs "K c " for venturi throat of infinite 

length .

 pb V 148 

7-13 Predicted Venturi Performance, "d p a 5 o " versus Q T / Q'<J„f wit withh "u "u^G "" an andd " " P F"" a ass r Parameter. . 149 

7-14 Aerodynaaic Cut Diameter Versus Pressure 

Drop wit] Liquid to Gas Ratio as Parameter . 150 

7-15 Impaction parameter vs aerodynamic cut 

diameter fo~ a venturi design 154 

7-16 Pressure drop vs aerodynamic cut diameter 

for venturi design example 157 

7-17 Impaction parameter vs Q T / Q r for venturi 

design example 160 

8-1 Cyclone with tangential gas inlet 1^5 

8-2 Generalized flooding and pressure drop 

correlation for packed beds (Perry, 1963). . 174 

v n 
P.11 

. FIGURES (continued) 

Number EfLE? 

8-3 Theoretical and experimental collection 

efficiencies of rectangular aerosol jets. . \i(. 

8-4 Theoretical impaction efficiency as a func-

. tion of inertial parameter for different 

targets 177 

8-5 Friction factor, f, versus Reynolds number, Nn n for wire mesh entrainment se-

' Re , G 

parator with entrainment load 182 

8-6 Pressure drop due to presence of liquid in 

the knitted mesh with the crimps in the 

same direction 183 

8-7 Pressure drop due to presence of liquid in 

the knitted mesh with the crimps in the 

alternate direction 183 

8-8 Drag coefficient versus Reynolds number 

after Foust et al (1959) , with sphericity 

ty as the parameter 187 

8-9 Drag coefficients for flow past inclined 

flat plates (data from A. Fage § F.C. Johansen, (1927) 187 

v m 
P.12 

TABLES 

Number

 Pa§e 

2-1 Correlation for Particle Collection in 

Venturi Scrubber 5 

2-2 Correlations for Pressure Drop in Venturi 

Scrubber 8 

2-3 Entrainment Separator Design Equations . . 12 

"-I Empirical Equations for Average Liquid 

Drop Size and Their Applicable Ranges . . 25 

3-2 Correlations for Pressure Drop in Venturi 

Scrubber 37 

-i-l Wen and Uchida's Experimental Pressure 

Drop Data on O.A.P. Venturi Scrubber .. . 42 

4-2 Wen and Uchida's Experimental Data and 

Predictions by Boll and by Behie and 

Beeckmaws 48 

8-1 Bed Porosity, e, for Various Packing 

Materials 171 

8-2 Experimental Values of j, Channel Width 

as Fri11. tion of Packing Diameter 171 

8-3 Packin-- Factors "F", for Dumped Pieces 

(m2/m3, 172 

8-4 Packing Fictors "F" for Grids and Stacked 

Pieces (m2/m3) 173 

ix 
P.13 

2 

ABBREVIATIONS AND SYMBOLS 

Latin 

A = cross-sectional area, cm2 

A = cross-sectional area at the duct inlet, cm 

A = total projected area of baffles per row in 

the direction of inlet air flow, cm2 

A^ = ratio of exit to inlet duct cross-sectional 

area, dimensionless 

A = throat cross-sectional area, cm2 

a2 = specific area of mesh, cm2/cm3 

B = dimensionless liquid-to-gas flow-rate ratio 

parameter, dimensionless 

-i ^T M i ' u r ^ x L L ( bo 

CDo QG PG \uGo "do> 

B_ = dimensionless parameter 

4 B Dp 

^G^ d 

b = duct breadth, cm 

b = spacing between two consecutive baffles in 

same row, cm 

C = Cunningham slip factor, dimensionless 

CB = drag coefficient, dimensionless 

Cp = initial drag coefficient, dimensionless 

c = concentration of particles, g/cm3 

c = capillary number 

c, = number concentration of drops, #/cm3 

c. - concentration of particles in the main 

1

 r 

stream of gas, g/cm3 

D = diffusivity of particle, cm2/s 

d = cyclone diameter, cm 

d = collector or packing diameter, cm 

d, = liquid drop diameter, cm 

d = equivalent diameter, cm 

eq

 n 
P.M 

Abbreviations and Symbols (continued) 

d = mean drop diameter, cm 

m

 r 

d = nozzle diameter, mm 

n 

d = initial inlet or outlet duct diameter, cm 

o 

d = particle diameter, cm or ym 

P 

d = aerodynamic particle diameter, ymA 

d = cut diameter, ymA 

ps o ' 

dD r = required cut diameter, ymA 

d = venturi throat diameter, cm 

E = collection efficiency, fraction 

H, = eddy diffusivity of liquid drops, cm2/s 

E = eddy diffusivity of particles, cm2/s 

F = drop flux, g/cm2-s 

F = packing factor, m2 /m3 

F,, = foam density 

f = empirical constant, dimensionless 

f = friction factor, dimensionless 

f = average friction factor of the venturi 

throat, dimensionless 

f = average friction factor of the convergent 

section, dimensionless 

f-, = av ^rage friction factor of the divergent 

section, dimensionless 

g = coniersion factor 

H, = fractional liquid hold-up, fraction 

j = ratio i f channel width to packing 

diametei, dimensionless 

K = inertial parameter, dimensionless 

K . = inertial parameter at venturi throat, 

pt

 r ' 

dimensionless 

K = initial inertial parameter, dimensionless 

po ^ ' 

K = inertial parameter for mass median particle 

diameter, dimensionless 

k = Boltzman's constant 

xi 
P.15 

Abbreviations and Symbols (continued) 

dimensionless'length parameter 

3 £ CDo pG /uGo-UdoX°'5 

2 d d PL ^ uGo 

I = length, cm 

& = venturi throat length, cm 

£2 = thickness of mesh pad, cm 

M = liquid-to-gas mass flow-rate ratio, dimensionless 

mr = gas mass flow rate, g/s 

mT = liquid mass flow rate, g/s 

N = number of jet stages in the tube bank, i.e., 

(number of rows) - 1 

N = number of collection transfer units 

n = cyclone vortex component, dimensionless 

n = number of zigzag baffle rows 

P = drop flight path length, cm 

Pt(d ) = particle penetration for particles with 

diameter d , fraction 

P 

Pt = overall penetration, fraction 

p = local pressure, dyne/cm2 

p r = component of "p" associated with wall 

friction, dyne/cm2 

Q, = source strength, #/cm3 

Qr = gas volumetric flow rate, cm3/s 

QT = liquid volumetric flow rate, cm3/s 

R = radius (for circular duct) or half-width 

(for rectangular duct) at the start of a 

given duct, cm 

R, = washing factor for divergent section, dimensionless 

a 

R^ = washing factor for A^enturi throat, dimensionless 

S = dimensionless parameter characterizing slope 

of the given duct 

2 tan 3 dd PL ' " " °'5 

I

 ta n g ^ ^L / UGo \ 

3 R CDo PG \uGo-udo/ 

x u 
P.16 

FIGURES (continued) 

Number Page 

8-3 Theoretical and experimental collection 

efficiencies of rectangular aerosol jets. . 175 

8-4 Theoretical impaction efficiency as a function of inertial parameter for different 

targets 177 

8-5 Friction factor, f, versus Reynolds number, Nn r for wire mesh entrainment seRe, G 

parator with entrainment load 182 

8-6 Pressure drop due to presence of liquid in 

the knitted mesh with the crimps in the 

same direction 183 

8-7 Pressure drop due to presence of liquid in 

the knitted mesh with the crimps in the 

alternate direction 183 

8-8 Drag coefficient versus Reynolds number 

after Foust et al (1959) , with sphericity 

ty as the parameter 18 7 

8-9 Drag coefficients for flow past inclined 

flat plates (data from A. Fage $ F.C. Johansen, (1927) 187 

vm 
P.17 

Abbreviations and Symbols (continued) 

p = gas density,"g/cm3 ' -

G 

p = manometer fluid density, g/cm3 

p. = liquid density, g/cm3 

p = particle density, g/cm3 

6 = divergence angle or baffle angle, degrees 

61 = convergence angle, degrees 

62 = divergence angle, degrees 

n = single drop collection efficiency, fraction 

yG = gas viscosity, poise 

yr = liquid viscosity, poise 

v- - kinematic viscosity of gas,cm2/s 

ty = rate of deposition, g/s 

a = surface tension, dyne/cm 

AP = pressure drop, cm W.C. 

A P, = dry pressure drop, cm W.C. 

AT = temperature change, °K 

Superscript 

* = dimensionless parameter 

Dimensionless numbers 

N R , = drop Reynolds number based on diameter 

NR = initial drop Reynolds number 

No = particle Schmidt number 

N'Sh

 = particle Sherwood number 

xiv 
P.18 

ACKNOWLEDGEMENT 

A.P.T., Inc. wishes to express its appreciation for excellent 

technical coordination and for very helpful assistance in support 

of our technical effort to Dr. Leslie E. Sparks, EPA Project 

Officer. 

xv 
P.19 

CHAPTER 1 

INTRODUCTION 

Venturi scrubber is one type of gas atomized spray scrubber. 

It employs gradually converging, then diverging sections. The 

venturi throat is the section between the converging and diverging sections. Usually liquid enters the venturi upstream of 

the throat through nozzles. Alternately, the liquid may flow 

along the converging section walls until reaching the throat. 

At the throat, the liquid is shattered into drops by the high 

velocity gas. Sometimes the liquid is introduced as pre-atomized 

drops at or before the throat through a pressure nozzle. The 

venturi may have a round, square, or rectangular cross section. 

For the rectangular duct, the breadth of the duct is usually invariant and only duct width diverges or converges. 

Venturi scrubbers have been widely recognized as having a 

high collection efficiency for fine particles and have been 

successfully used for years to remove particles and mists from 

gas streams. Particle collection efficiency in a venturi 

scrubber generally increases with pressure drop. High pressure 

drop (100 cm W.C. or 40 in. W.C.) venturi scrubbers can efficiently collect submicron particles. 

The venturi scrubber has several distinct advantages when 

compared with other scrubber types. The scrubber construction 

is simple, thus the initial capital investment is low. Through 

adjusting pressure drop by varying liquid flow or gas velocity, 

it can be made to collect even submicron fume with good efficiency. Due to the absence of moving parts, it can be used for 

the collection of sticky particles. 

The venturi scrubber also has disadvantages: It requires 

high pressure drop for .the collection of submicron particles 

which results in a high operating cost, and its applicability 
for mass transfer problems is limited due to the co-current 

nature of the gas-liquid flow. To prevent possible water pollution problems, it also requires water treatment facilities. 

Figure 1-1 describes a commonly encountered venturi 

scrubber system. It consists of a venturi scrubber, an entrainment separator, liquid treatment facilities, and gas and 

liquid movers. 

The atomized liquid drops or liquid entrainment must be 

separated from the gas stream before the gas is emitted into 

the atmosphere. There are a number of devices which are commonly 

used as entrainment separators which are added either within the 

venturi cutlet duct or in another vessel. Zig-zag baffles, cyclone separators, and guide vanes causing rotation of the gas 

stream are frequently used for this purpose. 

In the present study, only the design of venturi scrubber 

itself and its entrainment separator will be reviewed and evaluated. 
Emission 

From 

Source 

Oi 

H

ntrainment f \ 

Separator V ) 

"0-

Pump 

Liquid 

Treatment 

Fan Stack 

Figure 1-1. Venturi scrubber system 

ho 
P.22 

CHAPTER 2 

SUMMARY AND CONCLUSIONS 

Venturi scrubbers are used extensively for the collection of small particles. The major impediment to their practical use is that they have high pressure drops which result in 

high operating cost. With a better understanding of the 

fundamentals of the operation of this type of scrubber, 

the pressure drop could be lowered without affecting 

particle collection. 

The objectives of the study reported here were to (1) 

review and evaluate all available venturi scrubber performance models and design models (2) recommend the best 

model and (3) prepare a design manual based on this model. 

LITERATURE SEARCH 

Particle Collection Efficiency. 

The particle collection efficiency of a venturi scrubber is influenced by many parameters, such as particle size 

and size distribution, gas velocity, liquid-to-gas ratio, 

etc. There are several mathematical models available for 

the prediction of particle collection efficiency in a venturi scrubber. All models are based on particle impaction 

on liquid drops. Table 2-1 summaries all models. 

Pressure Drop 

Pressure drop in a venturi consists of two parts, 

namely acceleration loss and wall-friction loss. Most of 

the losses are due to acceleration and these may 

be calculated from hydrodynamics. Wall-friction loss 

depends on scrubber geometry and usually is determined 

experimentally. Table 2=2 lists several available correlations for the prediction of pressure drop in a venturi 
TABLE 2-1-. CORRELATION FOR PARTICLE COLLECTION 

IN VENTURI SCRUBBER 

Investigator Correlation 

Ekman § Johnstone 

(19 51) 

Pt(dp) = exp 

3 n P s 

490,000 

Calvert (1968) dc _

 ur \ / 3 

c uG (uG-ur)A \4rd 

n dz 

Calvert (1970) Pt(d ) = exp 

2 QL UG PL dd 

55 QG PG 

F (Kpt, f) 

F(Kpt, f) = ^ 

Pt 

/K . f + 0.7 1

-« H-^ry 

0.49 

0.7 + Kpt f (Kpt

 £ + °'7) 

Morishima et al 

(1971) 

Pt(dp) = exp - (Rt + Rd) L 

R. 

3£ 

2l i/-*(•-*)« 

x 3£Q /--max ^ n \ 

2d, J " u

d X2"

 U d 

dX 

1 

Dropp ^ Akbrut 

(1972) 

Pt(d ) = exp 2 J Wld

c

 U d dz 

Boll (1973) Pt(dp) = exp 

0 c 

continued 
TABLE 2-1. (Continued) 

Investigator Correlation 

Behie § Beeckmans Pt(d )= exp 

(1973) L J pL

 d d U G Uc 

dz 

Taheri $ Sheih 

(1975) 

i£ = - u i£- + E 

at G az p 

3

2c + 92c 

—

 dd ( Vu d} c cd 

3cd 3cd 

3T~

 = " Ud 3Y~ + Ed 

3

2 c, a2 c, 

-A + d 

3y2 

3 ^

 + Qd 

where A 

c 

E = 

P 

F = 

f = 

Pt 

m. 

m L 

P 

Pt(d ) 

cross-sectional area, cm2 

concentration of particulates, g/cm3 

number concentration of drops, #/cm3 

drop diameter, cm 

eddy diffusivity of drops, cm2/s 

eddy diffusivity of particle, cm2/s 

drop flux, g/cm2-s 

empirical constant 

inertial parameter at venturi throat, 

dimensionless 

length, cm 

gas mass flow rate, g/s 

liquid mass flow, g/s 

drop flight path length, cm 

penetration for particles with diameter, 

d , fraction 

P 

source strength, #/cm 

continued 
P.25 

where Qr = volumetric'gas flow rate, cm3/s ' . 

Q, = volumetric liquid flow rate, cm3/s 

s = specific surface of drops, cm2/cm3 of gas 

t = time, s 

u, = drop velocity, cm/s 

ur = gas velocity, cm/s 

u = drop particle relative velocity cm/s 

x = rectangular coordinate, perpendicular 

to the direction'of flow 

X = dimensionless distance 

y = rectangular coordinate, perpendicular 

to the direction of flow 

z = rectangular coordinate, in the direction 

of flow 

PT = liquid density, g/cm 

n = single drop collection efficiency, fraction 
P.26 

TABLE 2-2. CORRELATIONS FOR PRESSURE DROP 

IN VENTURI SCRUBBER 

Investigator Correlation 

.tro^o v (1955 ) 3 ,,1- 0 8 

lGt 

0.6 

AP = AP , - 1.3 8 x 10

 3 ixC'l* I Qr

 \ 

^1 

' o s h i c a e t a 1 . 

;1960 j (1965 ) 

AP = 

p r u 

a + D k\ 

a r , 0 ^G ' 

m. „

 C

 n + 4 f . -

2 ta n Oi t c 

+

 C 1- 2 

o 

b = ( r - 1) 

4 £_ l_ 

~P d 

m t 

c.- i i C /-i 

^d'l jF " u' 

Km 

d 

o/ 

Geisek e (1968 ) AP 

&g Sc 

c 

raG AuG + mL Au L 

Am L ,. 

I IX.-m 1 _ +11 . 

"JI L j L 2 )] 

;1964 ) 

AP = 0. 3 (AT) _!?£ {_ • %) 

2

 «c " V 

ohat a e t al . 

•'.'1954) 

AP = 

- g, D 'J 

r — ^ 

o ta n 

01 5 tan 02J t ci^ l,l T U 

(continued) 
P.27 

TABLE 2-2. (Continued) 

Investigator Correlation 

•Volgin et al 

(1968) 

n °'2 6 

AP = 3.32 x IO"6 u,2 U ) ( ,t ) 

0 I.i* 3 

Calvert (1968) AP = 1.03 x IO"3 u 2 I ~ Gt\QG 

Gleason et al 

(1971) 

AP = 2.08 x IO"5 uG

2 (0.264 Q + 73.8) 

Boll (1973) Un- - u 2

 w _+. id u ,\ 

PG 2 gc gcJQ G\ dt / 

+ (M^D f f U G

 Uc dt + 

'C£ eq 

: g.y 

x: f u2 

dx 

eq 

Behie d- Beeckman (19 73) dp -J^-d)[2 CD

 PG C VU d} -4 -

dt 

Hesketh 

(1974) 

AP = 1.36 x IO"" uG^ PG At

0-133 

Q 

[0.56 + 935 ^ + 1.29 x 10 " ^ M .. , .„ „ ln~5 iV ' 

where A = throat cross-sectional area, cm2 

duct cross-sectional area, cm2 

liquid drop diameter, cm 

equivalent duct diameter, cm 

A 

eq (continued) 
P.28 

d = throat diameter, cm 

d = inlet or outlet duct diameter, cm 

o * 

f = friction factor, dimensionless 

f = average friction factor of the throat 

T - average friction factor of convergent 

section, dimensionless 

fj = average friction factor of the divergent 

section, dimensionless 

g6 = conversion factor 

c 

1 = throat length, cm 

M = liquid-to-gas mass ratio 

m„ = gas mass flow rate, g/s 

m = liquid mass flow rate, g/s 

Q„ = gas volumetric flow rate, cm3/s 

Q = liquid volumetric flow rate, cm3/s 

u„ = gas velocity, cm/s 

u„ = gas velocity at the throat, cm/s 

u, = liquid drop velocity, cm/s 

u = liquid velocity, cm/s 

t = time, s 

z = rectangular coordinate in the direction 

of flow, cm 

AP = pressure drop, cm W.C. 

AP, = dry pressure drop, cm IV.C. 

AT = temperature change, °K 

p = gas density, g/cm3 

p = manometer fluid dnesity, g/cm3 

m

 J ' & 

0! - convergence angle, degree 

02 = divergence angle, degree 

C = coefficient on divergent loss of gas 

flow, dimensionless 

£ = head-loss ratio for throat, dimensionless 

Cj = head-loss ratio for divergent section, 

dimensionless 

10 
P.29 

scrubber. Correlations by Matrozov (1953), Volgin et al. 

(1968), Gleason et al (1971) and Hesketh (1974) are experimental correlations. All others are theoretical equations. 

Entrainment Separator 

The entrainment separator is an integral part of the 

scrubber system. Generally, any device that can be used to 

collect particles can also be employed to knock out entrainment. However, due to economical reasons, only a few find 

practical usage. Calvert, et al. (1975) have evaluated 

several suitable entrainment separators experimentally. 

Table 2-3 lists several comir.on entrainment separators and 

their design equations. 

CONCLUSIONS 

The principal objectives of this study were achieved. 

The following conclusions can be drawn. 

(1) Collection by atomized liquid drops is the principal collection phenomena in a venturi scrubber. Even 

though each investigator presented a different equation 

for the prediction of particle collection in a venturi 

scrubber, most of these equations can be reduced to the 

same basic model, i.e., 

r

z

 3 u Q, n 

-in Pt. ( V =_/ 2 U g ( ; G . V ^ dz (2-!) 

where Pt(d ) = penetration for particles with diameter d , 

fraction 

u = relative velocity between dust and drop, 

cm/s 

ur = gas velocity, cm/s 

dj = drop diameter, cm 

n = single drop collection efficiency, fraction 

Q = liquid volumetric flow rate, cm3/s 

z = length, cm 

11 
TABLE 2-3. ENTRAINMENT SEPARATOR DESIGN EQUATIONS 

Separator Type Investigator Design Equation 

Gravity Settler E = 

utb£ 

Sieve Plate Taheri {j Calvert 

(1968)' 

E = 1 - exp (-40 F2 K ) 

Mesh Bradie $ Dickson 

' (1969) 

E = 1 e x P C-f I a 2

£ 2 1) 

Packed Bed Jackson § Calvert 

(1966) 

Pt = 1 exp ^TT+

 j') (e - H ) a~

 K

p 

Tube Bank Calvert § Lundgren 

(1970) 

E = 1 (1 - n.) N 

Cyclone Leith 6 Licht 

(1971) 

ln Pt = - 2 

p, /2d, u^

 2 

5TTG\ dc (n+l)t 

2n+2 

0.3 

n = 1 r T i 

_2Mj 

(0.393 dc) 

~T75 

o.i i» 

Zig-zag Baffles Calvert et al 

(1974) 

n = 1 - exp 

ut c nwe 

57.3 un b tan 0 

b 

cont i nued 
P.31 

TABLE 2-5. (continued) 

Where a2 = specific area of mesh, cm2/cm3 

b = settler width or baffle spacing within row, cm 

d = cyclone diameter, cm 

d = packing diameter, cm 

F, = foam density 

H, = fractional liquid hold-up in the bed 

j = ratio of channel width to packing diameter 

K = inertial parameter, dimensionless - p F 

I = settler length, cm 

lz = thickness of mesh pad, cm 

N = number of jet stages in the tube bank 

= (number of rows) - 1 

n = cyclone vortex or number of zig-zag rows 

Qp = volumetric gas flow rate, cm3/s 

Pt(d,) = penetration for drops with diameter d,, 

fraction 

T = gas temperature, °K 

t = residence time, s 

u = gas velocity, cm/s 

u = drop terminal settling velocity, cm/s 

u = centrifugal gas velocity, cm/s 

u = tangential velocity of gas, cm/s 

w = width of baffle, cm 

6 = bed length, cm 

p, = drop density, g/cm3 

ur = gas viscosity, poise 

0 = angle of inclination of the baffle to 

the flow path, degree 

n = target efficiency of cylindrical wire, fraction 

n- = collection efficiency for a given drop dia3 meter in one stage of rectangular jet impingement, fraction 

z = packed bed porosity 

13 
P.32 

(2) A generalized method for applying equation 2-1 to 

predict particle collection in a venturi was developed. 

(3) Particle collection predicted by equation 2-1 

agrees satisfactorily with performance data. 

(4) Most of the particle collection occurs in 

the venturi throat. The solution to equation 2-1 for the 

venturi throat, using the inertial collection efficiency 

correlation proposed by Calvert (1970) and assuming a zero 

initial drop velocity is, 

In Pt (d ) 

L_P = 

B po( de) 

4 V^de)1'5 •^(l-uJJ 

0.5 

5.02 K0'

5 /l- u * + °-

po \ ude Ka-w. i 

V ' ^ 4 K p o + 4.2 - 5.02 K-(l + ^tan-(^f 

(2-2) 

where 

Uj_ = -— = dimensionless drop velocity de u Gt 

(2-3 ) 

u, = 2 de 

/L+jV . (h + S\ fL + 8) 

\-T-) \ 8 ) \ s ; 

0-5 

(2-4 ) 

^G/\ p G /

 CDo 

(2-5 ) 

C d_ p uG 

K = — n P N = inertial parameter based on 

po 9 Ur d, 

throat velocity, dimensionless (2-6) 

14 
P.33 

5 & t CDo PG 

2 dd pL 

= dimensionless throat length (2-7) 

and, C = Cunningham slip factor, dimensionless 

C,- = initial drag coefficient, dimensionless 

d = particle diameter, cm 

I - venturi throat length, cm 

u, = liquid drop velocity, cm/s 

ur,,. = gas velocity at the venturi throat, cm/s 

b L 

pp = gas density, g/cm3 

p. = liquid density, g/cm3 

p = particle density, g/cm3 

\ir = gas viscosity, poise 

b 

Equation 2-2 slightly underestimates the particle collection occurring in a venturi scrubber. For most industrial venturi scrubbers, particle collection can be predicted closely 

by neglecting the first term in the right hand side of equation 

(2-2). 

(5) Pressure drop predictions by the modified Calvert's 

equation and by Boll's equation agree with experimentl data. 

The modified Calvert's equation has the following form, 

AP = 1.03 x 10 u* u 2 \~) (2-8) 

where AP = pressure drop, cm W.C. 

Qr = gas flow rate, cm3/s 

(6) The use of a drag coefficient from the "Standard Curve" 

gives a better fit between model and experimental data than does 

Ingebo's correlation. 

15 
P.34 

CHAPTER 3 

LITERATURE SEARCH 

The literature survey and background information dis^ 

cussed in this chapter summarize what could be distilled from 

a survey of the background information and represent 

what was known at the onset of this study. 

COLLECTION MECHANISM 

The basic approach to the study of collection of small 

particles is through the evaluation of unit mechanisms that 

can occur in the control device. The "Scrubber Handbook", Calvert, et al. (1972), discusses five basic unit 

me ch an i s ms , n arne ly : 

(1) Collection by drops 

(2) Collection by cylinders 

(3) Collection of particles by bubbles 

(4) Deposition from a moving aerosol in pipes and ducts 

(5) Collection of particles by liquid jets. Of the 

five, collection by drops is the predominant mechanism 

occurring in the venturi scrubber. 

Particle collection by liquid drops may arise through 

several mechanisms or phenomena, such as inertial collection, 

interception, diffusion, electrostatic collection, and 

gravitational collection. All investigators have concluded 

that inertial impaction is the principal mechanism of particle collection in a venturi scrubber for particles larger 

than 0.5 ym in diameter. For particles smaller than 0.1 ym 

in diameter, diffusional collection prevails. 

Inertial Impaction 

A drop moving through a gas will sweep out a cylindrical volume equal to the product of drop cross sectional area, 

relative velocity between gas and drop and time. However, 

not all of the particles in this gas volume will necessarily 

impinge upon and be collected by the drop. 

16 
P.35 

- As the gas stream approaches the drop, the fluid .streamlines spread around it, while a particle suspended in the gas 

stream tends to move in a straight line due to its inertia. 

Therefore, as the gas flows around the drop, the particle keeps 

moving toward the drop. Due to the fluid drag some particles, 

especially the smaller ones, will be deflected from their path 

toward the drop and carried by the gas around the drop. 

The trajectory of the particle determines the target efficiency of the drop. Target efficiency is defined as the ratio 

of the number of particles striking the drop to the number which 

would strike it if the streamlines were not diverted by the drop, 

If the particles bounce rather than stick on impaction, this 

definition of efficiency is incorrect. Thus an assumption is 

always made that all the particles adhere on striking. 

Three factors determine the inertial impaction efficiency. 

The first is the velocity distribution of the gas flowing by 

the drop, which depends on the drop Reynolds number. The second factor is the trajectory of the particle. This depends 

on the mass of the particle, its air resistance, the size of 

the drop, and the flow rate of the gas stream. The third factor is the adhesion of the particles to the drop. Each of these 

factors is discussed below. 

The drop Reynolds "NR ," number is defined as, 

uo _^G dd 

v, 

NRed - -^ ^ »- « 

'G 

where "u " is the undisturbed upstream air velocity, with 

respect to the drop; "pr" amd "yr" are respectively the air 

density and viscosity, and "d," is the drop diameter. At high 

values of "Np,"(potential flow), the parting of the gas streamlines occurs close to the drop. Except near the drop surface, 

the flow pattern corresponds to that of an ideal gas. When the 

Reynolds number is low, flow is governed.by viscosity (viscous 

flow) and the effect of the disturbance created by the drop is 

17 
P.36 

noticed at relatively large distances upstream. The sud"den 

spreading of the streamlines at high Reynolds numbers enhances 

the influence of particle inertia and therefore causes a higher 

collection efficiency than at low "NR ,." 

If all field forces are ignored and if it is assumed that 

the particles obey Stokes' law, then the equations of particles 

motion can be derived by equating the particle inertia force to 

the air drag on the particle. The equations in dimensionless 

form are: 

Kp J - (aG - y (3-2) 

dv 

K —E. = (vr - vJ (3-3) 

P dt

 G P 

where: 

C p d2 u 

K = P P o (3_4) 

P 9 V G dc 

u = J- ; v = -E- (3-5); (3-6) 

P „U ' P o

 Uo 

UG , _ VG 

UG = ~ ; VG 

(3-7); (3-8) 

u u 

o o 

2 u t 

t = 2 _ (3-9) 

dd 

where K = inertial impaction parameter, dimensionless 

p = particle density, g/cm3 

d = particle diameter, cm 

P 

u = undistrubed upstream gas velocity with 

o 

respect to the drop, cm/s 

y„ = gas viscosity, poise 

d, = drop diameter, cm 

18 
P.37 

C = Cunningham correction factor 

t = time, sec 

u = particle velocity component in the X direction 

v = particle velocity component in the Y direction 

Up = gas velocity component in the X direction 

vf = gas velocity component in the Y direction 

The dimensionless inertial parameter, K , which characterized the motion of the particle, has a physical meaning. It is 

the ratio of the particle "stopping distance" to the radius of 

the collector. The particle stopping distance is that distance 

it would travel before coming to rest if injected into a still 

gas with velocity "u ", when all forces on the particle except the 

drag force are zero. 

The solutions to the equations of motion depend upon the 

velocity field assumed. Figure 3-1 shows theoretical and experimental target efficiencies for a single drop. As revealed 

by this figure, target efficiency depends on drop Reynolds number and inertial impaction parameter. 

Walton and Woolcock's (1960) experimental data agree quite 

well with Langmuir and Blodgett's (1946) and Heme and Fonda's 

(i960) theoretical calculations for potential flow0 That Walton 

and Woolcock's drop Reynolds numbers often fell substantially 

below the criterion for potential flow was apparently unimportant. For potential flow and for values of "K " greater than 

0.2, the experimental values of inertial collection efficiency 

for spheres can be approximated by the correlation (Calvert, 

1970): 

n 

P

 = (Kp +P O .7 ) t3"10) 

Diffusional Collection 

Small particles, in the sub-micron size range, are 

19 
1.0 

o 

o 

u 

rt 

4-1 

>-

U 

W 

I—I 

u 

f-H 

u. 

UJ 

Ew 

Di 

< 

El.Ranz ^ Wong (1952) experimental data 

700<NRe<5650 

2.Walton f, Woolcock (1960) experimental 

data, 65<NR <890 

3.Heme § Fonda (1960) theory for potential flow 

4.Langmuir $ Blodget (1946) theory 

5.Heme § Fonde, theory for viscous 

flow 

6.Calvert's approximation

 : 

0.5 

0.01 0.1 1.0 

INERTIAL PARAMETER, K 

10 100 

Figure 3-1. Target efficiency results of various investigators. 
P.39 

rarely collected by inertial impaction or interception 

because they follow the gas streamlines surrounding the 

collecting body, and their ratio of d /d is small. In a 

still gas, small particles move freely across gas streamlines due to random bombardment from gas molecules. Some 

of the particles hit the collector and are removed from 

the gas. 

If one estimates that the.aerosol concentration near 

the collector surface takes the form, Hidy and Brock (1970) 

r 

• c^i-jS ) (3-n) 

where "r " is the collector radius, "6" is the distance from 

c ' 

the collector center and "c " is the concentration of par1

 r 

tides in the main body of the gas stream, then the concentration gradient at the collector surface is: 

96 

c. 

5 = _ _i_ 

 r^ r c c 

(3-12) 

The rate of deposition, 4>(g/s

 i f cj is g/ cm3 ) , o n a 

spherical collector for a gas at rest is equal to: 

cf) = 4 TT D^ r c. (3-13) 

Y p c 1 

Particle diffusivities are several orders of magnitude 

smaller than diffusivities of gases, and are closer to the 

values obtained for diffusivities of solutes in liquids. 

The particle diffusivity may be calculated from an equation 

by Fuchs (1964) 

D = -—

k T Cj (3-14) 

P

 3 * ^G dp 

where D = diffusivity of particle, cm2/s 

k = Boltzmann constant = 1.38 x 10"16 erg/°K 

21 
P.40 

T = temperature, °K 

C = Cunningham correction factor, dimensionless 

Up = gas viscosity, poise 

d = particle diameter, cm 

P 

For an aerosol flowing past a spherical collector, the 

rate of diffusion increases and becomes a function of the 

Reynolds and the Schmidt numbers. The Schmidt number "N- " 

Sc 

is a dimensionless group indicating the ratio of convective 

and diffusive transf 

number is defined as 

and diffusive transfer rates (at constant ND ). The Schmidt 

Ke 

NSc = p^ " C3"15) 

For low diffusivities, leading to high Schmidt numbers 

(N„ = IO6) , and low Reynolds numbers (NR , < 3) Levich 

(1962) showed that: 

ty = 2 K Dp rd c. N Red " NSc>'3 (3-16) 

For large Reynolds numbers (600 - 2,600) and (Ngc= IO6, 

Akselrud (1953) showed that, 

ty = 1.6 TT Dp rd C i N Red - NS c^

3 (3-17) 

For Reynolds number = 100 - 700 and Schmidt number - IO3, 

Garner et al. (1958a and 1958b) showed that, 

ty - 1.9 TT Dp rd c. N Red - N S c ^ (3-18) 

Johnstone and Roberts (1949) presented an expression for 

estimation of single drop collection efficiency due to 

Brownian diffusion. Their expression is 

4 D N» 

P \ 

|

uG"Ud| dd 

n = ,—_

p j S h (3-19) 

22 
P.41 

where n = single drop collection efficiency, dimensionless 

D = particle diffusivity, cmz/s ' -

d, = drop diameter, cm 

Up = gas velocity, cm/s 

u, = drop velocity, cm/s 

N'cv, = particle transfer number analogous to the Nusselt 

number for heat transfer or the Sherwood 

number to mass transfer, dimensionless 

By using the semi-theoretical equation of Frossling for 

"N' " i e 

S h ' ' ' ' 

N'sh « 2 + 0,552 N R - N S c - (3-20) 

equation 5-19 becomes 

4 D 

n = 

uG_ud dd 

(2 + 0.552 N R - NSc3) (3-21) 

where N„ = Schmidt number defined by equation 3-15 

NR j = drop Reynolds number 

LIQUID DROP SIZE 

As mentioned earlier, the principal collection mechanism 

occurring in a A^enturi scrubber is the collection of particles 

by liquid drops. The collection efficiency of a drop depends 

on its size. Thus, in order to model the particle collection by a venturi scrubber, we must have some knowledge 

about the atomized liquid drop size. 

Hesketh et al. (1970), based on a study performed on a 

small venturi scrubber, claimed two types of atomization 

can occur. 

Cloud-Type Atomization 

This type of atomization can be achieved when nozzles 

larger than 1 mm i.D. are used and when gas velocity is 

above the critical gas velocity. The critical gas velocity is 

23 
defined by the following equation 

un, ... , (cm/s) G' critical 

0.5 

2 (mm2 ^D.)]+ 466'

3 t3"22> 

This type of atomization yields small drops and gives 

lower drop acceleration which results in better particle 

collection than drop type atomization. 

Drop-Type Atomization 

Several correlations are available for estimating the 

average liquid drop size in drop type atomization. These correlations are based on different mechanisms of atomization under 

various operating conditions. Each is applicable to a certain 

range of operation conditions and physical properties of fluids, 

such as viscosity, density, and surface tension. They are summarised in Table 3-1. 

Most of the data taken in pneumatic atomization are 

for liquid injection, either parallel or opposite to the 

gas flow and with a small apparatus. Venturi scrubbers 

are quite large in comparison and normally have the liquid 

injection across the gas flow. While it is questionable 

that these correlations would apply to a venturi scrubber, 

they have been so applied. 

The most widely quoted correlation is that of Nukiyama 

and Tanasawa, which gives the Sauter mean diameter, even 

though almost all investigators doubted its applicability 

to a full-size venturi scrubber. Boll (1973), after comparing the results of Nukiyama and Tanasawa with those of 

several subsequent investigators, stated that Nukiyama 

and Tanasawa correlation is subject to an uncertainty 

factor of two. 

In a later study, Boll et al. (1974) measured the 

atomized drop size in a full-scale venturi scrubber by means 

of a transmissometer. They showed that the N-T equation 

gives values of mean drop size that are accurate within 

about 50% for L/G's and throat velocities of commercial 

24 
TABLE 3-1 EMPIRICAL EQUATIONS FOR AVERAGE LIQUID DROP SIZE 

AND THEIR APPLICABLE RANGES 

Investigators Equations 

Applicable ranges 

u

G ,(cm/s) mG

7irL y L (poise . 

Nukiyama § Tanasawa 

(1938,1939,1940 ) d

d = 

5.85 

UG \ P

L / 

,8881 (o p L ) « r&r 101* -sonic 

velocity 

1.8 -15 0.1-0.4 6 

Mugele (1960) d, B 

ar

 = A (N R e ) 

d _ .,.. ,"/uL ur 

n 

Gretzinger § 

Marshall (1961) 

d = 0.26 

m 

mT 

m. 

N ReG 

(A,B,C are constants) 

O.lf 

10 -sonic 

velocity 

1.8 -15 

Kim $ Marshall 

(1971) 

d = 0.512 

m 

a

0-*1 yL 

0.3 2 

(u2 

G

 PG 

•) 0.5 7 A 0.3 6 0.1 6 

+ 1.89 

0.1 7 

m, 

m 

n 

10 -s on i c 

velocity 

1 -15 0.01-0.3 

0.5 "f 

7.5 x 10' 

sonic 

velocity 

0.06-40 

n = -1 for "fe 

mL < 3 

n = -0.5 for mG/mT >3 

0.01-0.5 

wh ere d, = Sauter mean drop diameter, cm 

d = mean drop diameter, cm 

m

 r ' 

p. = liquid density, g/cnr 

n 

u 

nozzle di arne ter, cm 

reiative.velocity , cm/s 

a = surface tension, dyne/cm 

Q = volumetric flow rate, cm /s 

G 

y. = liquid viscosity, poise 

m = mass flow rate of liquid, g/s 

L i 

m = mass flow rate of gas, g/s 

u 

A = flow area of atomizing air 

u = relative velocity between gas and liquid, 

cm/s 

CO 
P.44 

interest. For the particular venturi geometry they used, 

the N-T equation consistently over estimates mean drop diameter at high-gas velocities and under estimates it at 

low-gas velocities. They presented the following empirical 

equation to correlate their drop data. 

d = 6.75 x IO6 + 5.28 x IO12 ( QL

/ Q G ) ^12 (3-23) 

d u 1.6 0 2 

i 

where d, = Sauter mean drop diameter, ym 

QL/QG = liquid-to-gas ratio, m3/m3 

u. = gas velocity at liquid injection point, cm/sec 

DRAG COEFFICIENT 

The inertial impaction parameter, "K " is also a function of the relative velocity between particle and drop. The 

atomized liquid drops will be accelerated by the gas. The 

effect of acceleration on the drag coefficient has been studied 

by Hughes et al. (1952), Ingebo (1955), Torobin et al. (1960), 

Crowe (1961), and others. Hughes et al. state that as a 

general rule, acceleration drag exists and that it is higher 

than the drag for steady motion. Ingebo's results disagree 

with this statement. He obtained acceleration drag coefficients 

lower than those predicted by the standard curve, (see Figure 

3-2). According to Ingebo, the drag coefficients "CD" for 

drops can be correlated fairly well with the Reynolds number 

according to the following empirical expression: 

Cn = U— (3-24) 

f XT 0.8 if 

JNRed 

where C^ = drag coefficient 

N , = drop Reynolds number 

This expression is applicable for a Reynolds number range of 

6 to 800 and spheres with a diameter range of 20 to 120 

26 
P.45 

Nj^e -Reynolds Number 

Figur e 3-2 . DRAG COEFFICIENT OF A SPHERE . 

27 
P.46 

microns. Calvert (1968) used the Ingebo data and simplified 

the above equation to 

C = IA- for J 00 < ND , < 500 T3-25) 

^n w Red ^°

 i0J 

Red 

However, this expression is applicable for a Reynolds number range between 100 and 500. While this range is more 

narrow than the range of the original correlation, it is 

the range that is of interest for venturi scrubbers. Calvert 

stated that this correlation is also a fairly good approximation for the Reynolds number up to 1,000. 

The Ingebo correlation and the Standard curve have 

been used in the modeling of venturi scrubber by different 

investigators. Howeverj Boll (1973) concluded that in the 

case of a venturi, the Standard curve of the drag coefficient is the better choiee. He argued that Ingebo injected 

the particles or drops as a small concentrated stream into 

the center of a much larger duct. Thus, the high central 

concentration of slowly moving drops or particles would 

have much the same effect as a stationary porous body in 

the duct. Consequently, some of the gas must have flowed 

around the mass of drops rather than between them, reducing 

the actual gas velocity in the vicinity of the individual 

drops. This would have lowered the actual drop acceleration and reduced the apparent drag coefficient, accounting 

for the low C„ values. 

Dickinson and Marshall (1968) approximated the Standard 

curve by the followin-g correlation 

CD = °-22 + HT7'1 + °-15 NRed) C3"26) 

Red 

28 
P.47 

SCRUBBER COLLECTION EFFICIENCY 

Calvert (1968 , 1970) , by performing a material balance 

for dust over a differential scrubber volume with the assump 

tion of constant liquid holdup, obtained a differential 

equation for the prediction of venturi scrubber performance. 

This equation is 

dc . 3 K l "a " dz

 f3.271 

where c = dust concentration, g/cm3 

u = u -u, relative velocity between particle and 

r p d ' r 

liquid drop, cm/s 

n = single drop collection efficiency, fraction 

d, = drop diameter, cm 

uf = gas velocity, cm/s 

z = distance, cm 

H, = drop holdup or volume fraction of drops at 

any point 

_ \ 

udA 

QT = liquid flow rate, cm3/sec 

u, = drop velocity, cm/sec 

A = cross-section area, cm2 

By substituting the defining equation of "H," and "u " 

into equation 3-27, one obtains 

dc

 1 '5

l

u

p - ud|/ Q L \ , f. 9R , 

- — = 5 TC- h dz (d>-28) 

u

d

 dd \ V 

Another assumption in the derivation of this equation is 

that particle velocity is the same as gas velocity. 

Calvert -(1970) and Calvert et al. (1970) applied 

equation 3-28 to the venturi throat and obtained the 

29 
P.48 

following simplified equation for predicting particle 

penetration 

Pt(dp)= exp 

2 QL uGtpL dd 

55 QG yG F(K p t '

 f (3-29) 

where Pt(d„)= penetration of particle s with diameter d 

K

 V * p' 

fraction 

QT = liquid flow rate,' cm3/s 

QG = gas flow rate, cm3/s 

d, = average liquid drop diameter given by 

the empirical correlation of Nukiyama 

and Tanasawa, cm 

u = velocity of the gas in the throat, cm/s 

bt 

\.c gas viscosity, poise 

p, = liquid density, g/cm3 

K . = inertial parameter evaluated at the velocity 

pt ^ ' 

of the gas in the throat. "F(K f) " is a parameter defined by the following equation p t , 

F(Kp t , f) K 

pt L 

1.4 In 

0.49 

0 .7 + K 

K «. f + 0.7 Pt 

0.7 (3-30) 

r - (K «. f 

,t

 f P 1 

+ 0.7) 

"f" is an empirical parameter. For hydrophobic aerosols a 

value of 0.25 is suggested by Calvert for this parameter. 

For hydrophilie particle raaterials it is usually equal to 

0.5. 

Boll (1973) took into account the particle collection, 

occurring in tlie venturi throat as well as in the divergent 

and convergent section of tlie venturi, and presented the 

following integral equation for the calculation of particle 

penetration 

30 
P.49 

- f,\ P- pG\ lUG'Udl .t N

"i'-M-pr/-^—n d t c

 =^i

-

s

 \-pf/~5r~ n dt C3"

31) 

where N = number of collection units 

= - ln Pt(d ) 

P 

M = ratio of liquid-mass flow rate to gas-massflow rate 

PG = gas density, g/cm3 

p. = liquid density, g/cm3 

n = target efficiency, fraction 

t = time, s 

d, = liquid drop diameter given by Nukiyama 

and Tanasawa correlation, cm 

uG = gas velocity, cm/s 

u, = liquid drop velocity, cm/s 

" |Up-u,[" is the relative velocity between gas and drops. 

This velocity depends on the geometry of the venturi scrubber. Boll assumed that the gas is incompressible. Thus, 

the gas velocity at any location in the scrubber is given by 

mp 

UG = 3Tp^ (3

-

32^ 

where mp = gas mass flow rate, g/s 

A = cross-sectional area of the scrubber, cm2 

The drop velocity is equal to the time integral of drop 

acceleration 

ud = udi + f(^r)dt 

0 

• "di *fi ~ ^37 ^

 c °d t C3"33) 

O L u 

where u,. = initial velocity of the drop, cm/s 

CD = drag coefficient 

31 
P.50 

Boll used the Standard curve for CD for solid spheres due to 

Lapple and Shepherd (1940). 

Boll's equation, i.e., equation 3-31 can be reduced 

to Calvert's differential equation. Thus, these two 

equations are essentially the same. 

Behie and Beeckmans (1973) also gave a differential 

equation for aerosol capture in the venturi scrubber. Their 

equation is 

-a (.» o - \ \«$X iz (3"

34) 

where c = dust concentration , g/cm3 

F = drop mass flux , g/cm2-s 

PL

 = liquid density, g/cm3 

n = target efficiency , fraction 

ur = gas velocity , cm/s 

b 

u, = drop velocity , cm/s 

d, = drop diameter , cm 

z = the distance from the origin in the direction 

of gas flow , cm 

This equation is equivalent to Calvert's differential 

equation for particle collection in a venturi scrubber. 

Calvert, Boll and Behie and Beeckmans all assumed that 

the particle velocity is the same as gas velocity. However, Dropp and Akbrut (1972) , after evaluation of venturi 

performance data taken from several power plants, concluded 

that the model will over-predict the efficiency of a venturi 

scrubber for big particles if gas velocity is substituted 

for particle velocity. This is because while the fine particles move at practically the same velocity as the gas, the 

velocity of large particles differs markedly from the gas 

velocity. Big particles move at a lower velocity than the gas 

which results in a lower impaction param-eter and lower efficiency. Dropp and Akbrut proposed the following equation 

to predict venturi scrubber performance. 

32 
P.51 

Pt(dp) = exp|-;[3f A n ^c 

I

2

J ^* d

 ud dz (3-35) 

where Pt(d ) = penetration for particles with 

diameter d , fraction 

P 

QT = liquid-flow rate, cm3/s 

Qr = gas-flow rate, cm3/s 

u = particle velocity, cm/s 

u, = drop velocity, cm/s 

This equation has the same form as Calvert's differential equation except particle velocity is used in Dropp 

and Akbrut's equation. 

Calvert derived his equation by considering particle 

collection by all liquid drops existing in a unit volume. 

Ekman and Johnstone (1951) employed another approach to 

arrive at an equation for the calculation of particle 

collection in a venturi scrubber. They looked upon a 

single liquid drop as a unit and followed the drop to 

determine its particle collection for its entire flying 

path length. Total particle collection of the venturi 

scrubber is then the sum of the collection of all liquid 

drops. Ekman and Johnstone's equation is, 

Pt(d ) = exp 3 n Ps 

490,000 (3-36) 

where Pt(d ) = penetration for particles with diameter 

d , fraction 

P 

n = single drop impaction efficiency, fraction 

P = length of effective path of liquid drop, cm 

s = specific surface of drops formed in 

scrubber, cm2/cm3 

Morishima et al. (19 72) used the same approach as Ekman 

and Johnstone and considered the particle collection in the 

33 
P.52 

venturi throat and in the divergent section. They arrived 

at the following equation 

Pt(d) = exp ["- (Rt + Rd) Q^l (3-37) 

"R " and "RJ" are, respectively, the washing factor of gas 

in the venturi throat and in the divergent section. Washing factor is defined as the volume of gas swept clean by 

a liquid drop per unit volume of liquid drop. For venturi 

throat and divergent section, the defining equations for 

these two washing factors are, 

where £ = venturi throat length, cm 

X = dimensionless distance 

x 

~

 £t 

d, = drop diameter from Nukiyama and Tanasawa 

correlation, cm 

n = target efficiency 

d^ 

_ t , cm 

£ Q " 2 tan

 9-

2 

d = venturi throat diameter 

O = divergence angle 

All investigators cited earlier had assumed that the 

liquid drop distribution is uniform across the duct and 

there is no turbulent mixing between drops and particles. 

In reality, the drop concentration across the venturi 

34 
P.53 

throat is far from uniform (Taheri and Haines (1969) , 

Boll (1973)). Taheri and Sheih (1975) took turbulent mixing and liquid drop distribution across the duct into 

account and obtained the following equations for predicting the transport and diffusion of the particles and water 

drops. 

i£ = 

3t 

3c 

u, 

— + E 3z j 

3c 

3

2c + 32c 

3T2

3y' " 

o t 

U d 3z 

+ E 

3y2 

TT n 

—

 dd (U

G-Ud^

 C Cd 

3

2 c 

3x< 

(3-40) 

(3-41) 

where c = particle concentration, g/cm3 

c, = number concentration of liquid drop, #/cm3 

Up = gas velocity, cm/s 

u., = drop velocity, cm/s 

E = eddy diffusivity of particle, cm2/s 

E, = eddy diffusivity of drop, cm2/s 

x = rectangular coordinate, perpendicular to 

direction of the flow, cm 

y = rectangular coordiante, perpendicular to 

the flow, cm 

z = rectangular coordiante, in the direction 

of flow, cm 

Q, = source strength of drops, #/cm3 

In all the above mentioned performance models, the liquid 

drops were assumed to have one size, namely the Sauter mean 

diameter calculated from Nukiyama and Tanasawa's empirical 

correlation. In reality, the liquid drop size varies widely 

Morishima et al. (1967) performed a mathematical analysis 

to determine the influence of liquid drop size distribution 

on the particle impaction and diffusion collection efficiency. They found that as the range of size distribution 

35 
P.54 

widens, the impaction efficiency decreases. 

PRESSURE DROP 

Pressure drops for gas flowing through a venturi scrubber consists of the friction loss along the wall of the 

scrubber and the acceleration of liquid drops. Friction 

loss depends largely upon the geometry of the scrubber. 

Acceleration losses, which are frequently predominant in 

the venturi scrubber pressure drop, are fairly insensitive 

to scrubber geometry and in most cases can be predicted 

theoretically. 

There are several correlations available, both theoretical and experimental correlations, for the prediction 

of pressure drop in a venturi scrubber. They are summarized in Table 3-2. 

Correlations by Matrozov, Yamauchi et al., Volgin et al 

Gleason et al., and Hesketh are experimental correlations. 

Matrozov's correlation and Volgin's correlation were 

obtained mainly on small-size venturi scrubbers. Yamauchi 's correlation was based on experimental data taken 

from a venturi scrubber with high temperature gas flow 

(100°C - 900°C). Hesketh's correlation is an experimental 

correlation he obtained after he had evaluated data 

obtained from many fixed throat venturi scrubbers. 

Equations proposed by Yoshida et al., Calvert, Tohata 

et al., Boll and Behie and Beeckmans are theoretical 

correlations. Calvert derived his equation by use of 

Newton's law to obtain the force required to change the 

momentum of liquid at a given rate. Wall friction and 

momentum recovery by the gas in the divergent section 

were neglected in the derivation. All other theoretical 

equations were derived from the equations of motion and 

momentum balance. Geiseke's equation also accounts for 

the mass transfer between liquid and gas. Boll's equation is similar to that of Geiseke's except Boll had 

36 
P.55 

TABLE 3-2 

Investigator 

CORRELATIONS FOR PRESSURE DROP 

IN VENTURI SCRUBBER 

Correlation 

Matrozov (1953) AP = APd + 1.38 x IO"3 u£{8 / QL 

0-6 3 

Yoshida et al. 

(1960) (1965) 

AP = 

a = 

PG UGt 

TT, a + b/^L 

2 tan 0i + 4 f 't / dt 

t T: + n1"

2

 ar 

t o 

b = u t - D 

4 ft l t 

m 

3 7 ^ tSd-^rf1- a*) 

t

 Km \ o / 

Geiseke (1968) AP = 

76 

52 Se 

c 

[mG AuG + mL AuL 

A m L 1 

— (U

Gl

 + U G2 " u

Ll -

 UL2)J 

Yamauchi et al 

(1964) 

AP = 0.3 (AT)"0-

28 -J 

PG UGt /x + -L 

S, QG" 

Tohata et al. 

(1964) 

AP = 

PG UGt 

'C 

f 

A \2 

TV J 2 g 

[5 tan Oi ' 5 tan 02 •]'

 f* 4 Sr 

(continued) 

37 
P.56 

TABLE 3-2. (continued) 

Investigator Correlation 

Volgin et al 

(1968) 

AP = 3.32 x IO"5 uG

2 ^ ) C*t) 

0.2 6 

0 1.4 3 

Calvert (1968) AP= 1.03 x IO"' ^( ^ 

Gleason et al 

(1971) 

AP = 2.08 x 10"5 uG

2 (0.264 QL + 73.8) 

Boll (1973) 2 2 

u

rt ~

 ur 

•Ap _ b l b 

P7 " 2 §r 

•uN^)* 

M + l) f 

2 g I 

f u2 ud 

2 Q I d 

"-•6 eq 

2 g c / 

$i f u2 

dx 

eq 

Behie § Beeckmans (19 73) dp 

6F 

*

d

d

 p d ) ! 

IT d d

2

 ^ 

CD PG (u cr u

d

) 2

 —r ~ 

dt 

Hesketh 

(1974) 

AP = 1.36 x 10~" uG

2 pG At0-133 

0.56 + 9 3 5!o^/

 + 1'

29 X 10 \0^ 

where A. = throat cross-sectional area, cm2 

duct cross-sectional area, cm2 

liquid drop diameter, cm 

equivalent duct diameter, cm 

A = 

o 

d j = 

eq (continued) 

38 
P.57 

where d = throat diameter, cm 

d = inlet or outlet duct diameter, cm 

o ' 

f = friction factor, dimensionless 

f = average friction factor of the throat, 

di men sionless 

c = average friction factor of convergent section 

f, = average friction factor of the divergent 

section, dimensionless 

g = conversion factor 

" c 

I = throat length, cm 

M = liquid-to-gas mass ratio 

nip = gas mass flow rate, g/s 

m - liquid mass flow rate, g/s 

Qr = cas volumetric flow rate, cm3/s 

0. = liquid volumetric flow rate, cm3/s 

Up = gas velocity, cm/s 

u„ = gas velocity at the throat, cm/s 

u, = liquid drop velocity, cm/s 

u. = liquid velocity, cm/s 

t = time, s 

5 = rectangular coordinate in the direction 

of flow, cm 

AP - pressure drop, cm W.C. 

AP, = dry pressure drop, cm W.C. 

AT = temperature change, °K 

p = gas density, g/cm3 

p = manometer fluid dnesity, g/cm3 

Gr -- convergence angle, degree 

S'2 = divergence angle, degree 

x, = coefficient on divergent loss of gas 

flow, dimensionless 

£. = head-loss ratio for throat, dimensionless 

£, = head-loss ratio for divergent section, 

dimensionless 

39 
P.58 

neglected the mass transfer between phases. Equations by 

Tohata et al., Yoshida et al., and Boll contain terms 

attributed to wall friction. While Tohata et al. and 

Yoshida et al. had used different values for the friction 

factors in the covergent throat and divergent section, 

Boll suggested a single value for all sections. A value 

of 0.02 7 was suggested by Boll for the friction factor "f" 

because it gives a slightly better fit in the shape of the 

pressure drop curves he obtained, experimentally. 

40 
P.59 

CHAPTER 4 

COMPARISON OF MODEL WITH EXPERIMENTAL DATA 

There are numerous venturi scrubber performance data 

reported in literature. However, most of these data were 

found to be of a limited value for the testing of performance models. This is because, some important information, 

such as scrubber geometry, water injection method, particle 

size distribution, etc. was generally not given. In the 

following sections, only those data which have been obtained under contolled conditions and for a well-defined 

scrubber system will be utilized to test the performance 

models. 

COMPARISON OF PIlEDICTED PRESSURE DROP WITH EXPERIMENTAL 

DATA 

Data by Wen and Uchida 

Wen and Ucnida (1972) obtained pressure drop data 0:1 

a pilot scale O.A.P. venturi scrubber. Their pressure drop 

data are shown in Table 4-1. Figure 4-1 shows the dimensions 

of che scrubber. 

Figures 4-2 through 4-4 compare pressure drop predictions by various models with Wen and Uchida's data. For 

the O.A.P. scrubber, the water injection nozzle is at the 

start of the convergent section. According to Wen and 

Uchida, the gas cools down quickly to scrubber outlet 

t.?i:;perature once it is in contact with water (within 5 cm 

frcvd the water injection point). Thus, in calculating 

the xaxxC .ctc-d pressure drop, the volumetric gas flow rate 

was -didi L..-. ted for this temperature drop plus the volume 

increase due to vaporized water. 

As can be seen from Figures 4-2 to 4-4, Calvert's equation 

consistently over estimates the.pressure drop. Predictions 

bv Volgin et al. and Hesketh are always lower than data. 

41 
P.60 

TABLE 4-1 . WEN AND UCHIDA'S EXPERIMENTAL PRESSURE DROP 

DATA ON O.A.P . VENTURI SCRUBBER 

Run 

No. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

• 

Gas Temp. °c 

Inlet 

154.4 

160 

160 

157.2 

148.9 

154.4 

135 

154.4 

160 

148.9 

148.9 

148.9 

148.9 

121.1 

148.9 

148.9 

148.9 

121.1 

148.9 

„,, 

Outlet 

46.1 

43.3 

46.1 

43.3 

37.8 

43.3 

4 3.3 

43.3 

46.1 

46.1 

46.1 

37.8 

43.3 

43.3 

46.1 

46.1 

37.8 

35 

40.6 

' 

Inlet gas 

Flow rate 

Am3/min 

29.4 

30.8 

29 

34.8 

34.2 

28.5 

28.6 

30.3 

29.8 

25.5 

25.5 

31.2 

25.5 

25.5 

25.5 

25.5 

31.2 

25.5 

25.5 

• 

Liquid 

Flow rate 

£/min 

37.9 

37.9 

37.9 

37.9 

37.9 

56.8 

37.9 

37.9 

56.8 

37.9 

37.9 

37.9 

56.8 

37.9 

37.9 

56.8 

37.9 

37.9 

37.9 

Pressure 

Drop 

cm W.C. 

22.2 

21.8 

19.8 

30.5 

29 

22.9 

21.6 

21.3 

24.1 

21.8 

19.8 

29 

22.9 

21.6 

21.3 

23.4 

31.5 

25.9 

21.8 

42 
2 8. 9 cm 

OJ 

Figure 4-1. Dimensions of OAP venturi scrubber. 
P.62 

Q Calvert's Prediction 

i^Hesketh's Prediction 

10 20 30 40 

EXPERIMENTAL PRESSURE DROP, cm W.C, 

50 60 

Figure 4-2. Comparison of predicted pressure drop with 

experimental data from \^en and Uchida. 

44 
P.63 

36 

c_> 

o 

~ 2 8 

: — i 

00 

"nr. 

'_> 

A Boll's equation 

Q Volgin's equation 

16 20 24 28 32 36 

EXPERIMENTAL PRESSURE DROP, cm W.C. 

Figure 4-3. Comparison of predicted pressure drop with 

experimental data from Wen and Uchida. 

45 
P.64 

3 6 

2

 32 

u 

I 28 

LOOO 

^ 24 

< 

cc 

20 

16 

i ? 

12 16 20 24 28 32 

EXPERIMENTAL PRESSURE DROP, cm W.C 

36 

Figure 4-4. Comparison between Behie and Beeckmans' prediction 

and experimental data from Wen and Uchida. 

46 
P.65 

Predictions by Boll and by Behie and Beeckmans are slightly 

better, but still have .a tendency to under estimate 

pressure drop. 

The only difference between models by Boll and by 

Behie and Beeckmans is that Behie and Beeckmans neglected 

wall-friction loss. In a venturi scrubber, most of the 

pressure drop is due to acceleration of liquid drops. 

Table 4-2 proves this statement'. Table 4-2 lists'Wen and 

Uchida'a data along with predictions by Boll's equation 

and by Behie and Beeckman's equation. Behie and Beeckmans' 

equation always predicts a lower pressure drop than Boll's 

equation. The difference between the predictions by these 

two equations is equal to the wall friction. The last 

column in Table 4-2 shows the values of wall friction for 

all runs. For this particular scrubber geometry, the contribution of wall friction is less than ten per cent of 

the total loss. 

Calvert's equation is based on the assumptions that 

all liquid drops accelerate to the gas velocity in the 

throat and that none of the drop momentum is converted to 

pressure in the diffuser. It is possible that in some 

scrubbers, liquid drops do not have sufficient residence 

time to accelerate to the gas velocity in the throat. In 

order to take this fact into account, a correction factor 

was developed and added to Calvert's equation. The new 

equation now reads 

2 /Q 

*deUGt'-Ll C4"

1) 

where AP = pressure, cm W.C. 

Up = gas velocity in the throat, cm/s 

Q. = liquid flow rate, cm3/s 

Qp = gas flow rate, cm3/s 

47 
P.66 

TABLE 4-2. WEN AND UCHIDA*S EXPERIMENTAL DATA 

AND PREDICTIONS BY BOLL AND BY 

BEHIE AND BEECKMANS 

Run 

No. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

Experimental 

AP, cm W.C. 

22.2 

21.8 

19.8 

30.5 

29 

22.9 

21.6 

21.3 

24.1 

21.8 

19.8 

29 

2 2.9 

21.6 

21.3 

23.4 

3 1 ^ 

25.9 

21.8 

Pre 

Boll 

19.2 

19.9 

18.9 

22.7 

20.4 

27.5 

19.1 

19.8 

28.7 

16.8 

16.8 

20.4 

24.9 

17.4 

16.8 

21.9 

20.3 

17.2 

16.7 

diction, cm W.C. 

Behie (., Beeckmans 

17.4 

18 

17.1 

20.4 

18.1 

25.3 

17.4 

17.9 

26.4 

15.3 

15.3 

18.4 

23 

15.9 

15.3 

20.4 

18.3 

15.7 

15.2 

Wall Friction 

cm W.C. 

1.8 " 

1.9 

1.8 

2.3 

2.3 

2.2 

1.7 

1.9 

2.3 

1.5 

1.5 

2 

1.9 

1.5 

1.5 

1.5 

2 

1.5 

1.5 

48 
P.67 

wTi wnere U j f e = correction, factor, dimensionless 

ana 

u 

JJ 

de 

de u Gt 

1 - X?+ (X14- X 2 )

0 - (4-2) 

3 £ C,,. p_ 

X = D° G + ! 

1 6 dd PL 

Up = gas velocity in the throat, cm/s 

u, = drop velocity at the exit of the throat, 

cm/s 

I = throat length or distance between liquid 

injection point and the exit of throat, cm 

d^ = drop diameter from Nukiyama and Tanasawa 

correlation, cm 

PG = gas density, g/cm3 

p, - liquid density, g/cm; 

Cn = drag coefficient at the liquid injection 

point 

"C^ " iv. the drag coefficient obtained from Standard 

Do

 to 

curve fo r si:; ;;res, Drop Reynolds number is defined as 

N 

_

 d d ( UGt ' Udo) 

Re . d (4-3 ) 

where N., , = drop Reynolds number 

ke , d. 

u, = initi.1 drop velocity, cm/s 

v = kinematic viscosity of gas, cm'/s 

The physical meaning of "l ]5e" is the fraction of gas 

velocity to which the liquid drops have accelerated. If 

liquid drops are accelerated to gas throat velocity, "u ^ 

is equal to 1 and equation 4-1 reduces to Calvert's 

equation. Pressure drop prediction by equation 4-1 is 

49 
lower than Wen and Uchida's data as shown in Figure 4-5. 

Wall frictior and pressure recovery in the diffuser 

were neglected in the correction factor to Calvert's equation, however, Boll's predictions are no better than the 

modified Calvert's equation. 

Predictions based on the "standard" drag coefficient 

are better than those based on Ingebo's correlation, as 

shown in Figure 4-5. Because Ingebo's drag coefficients 

are low, drop velocity and pressure drop predictions are 

low. 

Boll's Data 

Boll (1973) derived an equation to predict the pressure drop in a venturi scrubber. He obtained some pressure 

drop data on a proto type venturi scrubber to confirm his 

equation. The cross-sectional dimensions of the venturi 

scrubber throat was 35.6 cm x 30.5 cm (14 x 12 inches). 

The throat length was 30.5 cm (12 in.). The convergence 

and divergence angles were 25° and 7°, respectively. 

Figure 4-6 is a sketch of the venturi scrubber used by Boll 

Figure 4-7 shows the comparison between Boll's data 

and theories by various investigators. The pressure drop 

was expressed in terms of the number of throat velocity 

heads, i.e., 

-AP Number of velocity heads lost = 

i Pr 2 

2§c PL 

where AP = pressure drop predicted by theory, cm W.C 

2 g = 9 80 cm/s 

pp = gas density, g/cm3 

, 3 p. = water density, g/cm' 

Up = gas velocity in the throat, cm/s 

As can be seen, Calvert's equation predicts too high a 

pressure drop for liquid-to-gas ratio above 0.7 £/m3. HesKeth's equation gives too low a pressure drop. Volgin's 

equation gives a different slope. 

50 
P.69 

34 

30 _ 

u 

u 

o 

a. 

Q 

w 20 

cc 

; = > u. 

LC 

PC 

Q 

w 

t-m 

u 

r—1 

Q 

w 

CC 

10 

—i 1 1 1 1 1 1 1 r 

/\ Cn from standard curve 

_£Y ^n from Ingebo's correlation 

c

 J ••:••!:-:•-! :-!- ---A " 

.... A' 

10 

Figure 4-5 

J 4 1 I I I ' ' ' i 

20 30 

EXPERIMENTAL PRESSURE DROP, cm W.C. 

34 

Comparison of predicted pressure drop by modified 

Calvert's equation with data from Wen and Uchida. 

51 
Liquid 

Inlet 

On 

tNj 

Figure 4-6. Prototype venturi scrubber used by Boll 
P.71 

2.0 

1.8 ~ 

00 

o 

-J 

o 

< 

>-1 

E-> 

1.6 

1-1 1.4 

> 

< 1.2 

o 

X 

Eo 

o 

< 

a, 

< 

1.0 

0.8 

0.6 

0.4 

di:'d"l :x,\ccj 

/"•V -i 7 7 ,~ 

.:! Irrdr' • ; • :.::: ! ^i-- : :;.:h; li:.! :! 

~~„_i„ _ !• : ! : baive i L » 

-T: j W . . i : i.,.::-.j:;equati 

£J\1.9 1 cm nozzles 

"Tn~:rj:::":" "~ 

'..' ' 

• I • • i • ; 

• . i ! ' : " . 

i.d. •

 : :

 :|.:"d.:': 

d i; [ ::'d Modl f i(=rl PaliPrtl c ::.;: / 

ii; :i - • 

.......... . , .. . . 

•:. ' * 

• 

•'••: i : d'i'....' i 

— . . . . j ' . , , 

— : • • . ! * : . 

-.7--,—:-

:.-:::.::!' ': 

'•'•••'••• i • • 

. .:. :.|:. e ^ 

':-•'•'•]•.:•.ylT 

y V 

—:-• : •:• : -

HL^J::.^i...j:.:.L.:l::Li.:„ 

:\IV,:::.\::\: .":'. ! :.. j. d d .. 

• • :!'•: . 

. ••:• : . 

:i::;;::'; — i_~._... 

':•: \". ']'• . ' : 

rr-r r r; Q wl 

: ! 

"

:

"-": • r ~ L 

^••w-cc^'x^m 

•—:-:-.-

\lrX.X. .. 

-:--:-!::-

•'-it/]' j / 

~-y-- \ff~j 

i \/&' :'/:.. 

... ... /¥ 

/'•'•'•' / -• -

squation 

uGt=9150 cm/s > 

.idf.jl.di^LdL: :~-jyZ 

• • •'! xJ^' " / 

•• • •yjj^l:.: .\". r. 

::::i'::'::l::::ii:-: 

••:• : . • 

' v * 

C-CC-/\-

r-ffi 

c/r/x 

Cftf-

... | . . . . 

•r.'rr, :dr 

' :'/{'•'•''• 

. . • :•!.. « 

d/V y 

---:|':-H 

: :_di:_:. 

j_. r i.::: 

'/\xx 

r.-Cj/tr 

St' i^' 

'ii^fr 

c.c.yCC-x 

YrfX''-

:: y:. : 

f/\v\- :..!.••: 

V |...: 

Sfci 

ddjdd 

'!..• ; 

'••SC'. Modifie d Calvert ? s 

S c : e- n n a t n n n 

•••- f 

.;•• : u 

d

:

i;i:i 

~«.-^050 cm/s 

Gt 

iii- - - ' ^ • — 

.•> * 

:::r:.: 

. . . 1 . 

dd|d d 

•••:|.: . 

.- :!:::. 

on

 N 

I A \ 

-Xx/CXrCXr.C—CC.-CC/hrr 

... . ^ ^ •• • ;jXd 

\- y -J i - -f.j ¥ - -

,yrX/ty$C^-

... i ^ ^ 

//y^:\rX}XX\y ]• 

f - •••• i (•-•; • -~ y 

' '.Wi *""* 

^i**!*-

7 

..... . 

y;:..:^p|^.,.:u._j 

.:•• l::-J/^o„-1,^4-1 . I „ ...- " 

... . . .^^- - -

diii>^prn 

h—:-:-::-•] r—'?-• -

ncsK C LII a .. . 

equation C^xl 

- . . * 

:.:..-...;:-... .:.f- -

Boll' s ^ n n a 1* *5 « « - i" 

(average) 

::::|::.' 

. ..; . 

ddiddjddid d 

.' . ri:. .: 

;^i:;;iii;;:i;:;;

|;^!;:..|--i- C '.x 

::::r.-:_ 

• - i • - • 

::::;•: . 

::•:!.•: . 

: ::i::::|d:.i i:.i.--i: •:• ' • • 

...:::::!.::•!::.. 

:•.• ( d"..j' : 

:--::i:;::i::..:-..-

.:•.!•:••! : .• : 

: : . : : • • i • : 

:...: . ..:.::L.::.._|— - • -

::::!..:.|:::.;.. . :' :. .. . i. r. 

.::.!::..!:.•. : .. : 

•m$w. 

: 

II • - ! ••:: -

0.2 0.4 0.6 0.8 1.0 1.2 1.4 

LIQUID TO GAS RATIO, 1/m3 of gas 

1.6 

Figure 4-7. Comparison of Boll's pressure drop data with theory 

53 
P.72 

The range of gas velocity in throat covered by Boll 

was *5.8 m/s - 91.5 m/s (150 - 300 ft/s). The 

line representing the predictions by Boll's equation 

was ^n average curve for the predicted pressure drops. 

Ever, though Boll's equation slightly under estimates pressure drop at low values of liquid-to-gas ratio and slightly 

over estimates at high liquid-to-gas ratio, the agreement 

between his data and equation is considered to be satisfactory. 

Predicted pressure drops by modified Calvert's equation for throat velocities of 40.5 m/s and 91.5 m/s 

are also shown in Figure 4-7. Since Boll operated his 

venturi scrubber in this throat velocity range, the area 

bounded by these two theoretical lines represents the 

range of expected pressure drops. The fact that Boll's 

theoretical curve, which is the average of predicted pressure drops, lies within this area signifies that the modified Calvert's equation and the more complicated Boll's 

equation predict pressure drop in equal accuracy. 

Brink and Contant's Data 

Brink and Contant (1958) perform a thorough study on 

an industrial-scale Pease-Anthony venturi scrubber. The 

scrubber had a rectangular cross section. Its throat 

r.easured 15.2 x 86.4 cm (6 x 34 inches) with a straight 

section 30.5 cm (12 inches) long. The angle of the convergent section was 25°; the divergent section had an angle 

of 2.2° for 152 cm (5 ft) following the vneturi throat and 

then an angle of 15°. Figure 4-8 is a sketch of the PeaseAnthony venturi scrubber. 

Brink and Contant's pressure drop data are compared 

with theories by various investigators in Figure 4-9. 

Again, Calvert's equation consistently over predicts the 

pressure drop and Hesketh's equation consistently under 

estimates the pressure drop. Both Boll's equation and 

54 
Liqui d Inle t 

on 

on 

Figure 4-8. Dimension of Pease-Anthony venturi scrubber used by 

Brink and Contant. 
P.74 

the modified Calvert's equation compare favorably with 

experimental observations. As can be seen from Figure 4-9, 

Boll's equation is in better agreement with Brink and Contant's data for 90 spray jets and the modified Calvert's 

equation is in better agreement with 45 spray jet data. 

Overall, the modified Calvert's equation predicts slightly 

better than Boll's equation for this particular scrubber 

geometry. 

Ekman and Johnstone Data 

Ekman and Johnston (1951) have measured pressure drop 

across a laboratory-scale venturi scrubber. Figure 4-10 

shows the venturi scrubber used by Ekman and Johnstone. 

The venturi throat was 3 cm (1-3/16") in diameter and 3.8 

cm long. The convergent and divergent angles were 25° and 

7°, respectively. Water was introduced in three ways: 

from a single 32 mm jet injected downstream along the axis 

of the throat radially outward from a brass pipe 32 mm in 

inside diameter with four 18.5 mm holes, and radially 

inward from a single 32 mm jet at the entrance of the throat 

Ekman and Johnstone recorded a higher pressure drop for 

radial inward injection. 

Figure 4-11 compares Ekman and Johnstone's experimental 

data with theoretical predictions . As can be seen, only 

Boll's equation and the modified Calvert's equation are in 

agreement with data. 

Conclusions 

Based on this evaluation, we can conclude that both 

Boll's equation and the modified Calvert's equation are adequate for the prediction of pressure drop in a venturi scrubber. Since the modified Calvert's equation is simpler, we 

will choose it as the venturi scrubber design equation. 

However, the method for applying Boll's equation to predict 

pressure drop will also be given. 

56 
P.75 

2.5 

ioo 

o 

Q 

< 

UJ 

X 

>-> 

i — i 

U 

o 

ou 

> 

< 

O 

CC 

X 

H 

O 

X 

< 

a, 

< 

2.0 

1.5 

1.0 

1.0 1.2 1.4 1.6 1.8 2.0 

LIQUID TO GAS RATIO, l/m3 of gas 

Figure 4-9. Comparison of Brink and Contant experi 

mental data with theories. 

57 
Liqui d 

Gas 

on 

Oo 

Figure 4-10. Dimensions of the Ekman and Johnstone venturi. 
P.77 

] .4 

0.4 0.6 0.8 1.0 

LIQUID TO GAS RATIO, £/m3 

1.2 1.4 1.6 

Figure 4-11. Comparison of Eleman and Johnstone's pressure 

drop data with theories. 

59 
P.78 

PARTICLE COLLECTION 

Most authors (except Taheri and Sheih) cited in the last 

chapter use the same basic model for the prediction of particle 

collection in a venturi scrubber, i.e., 

dc

 ur 

" '^ K ^ K n d z (4"

4) 

where c = dust concentration 

u = relative velocity between dust and drop, cm/s 

Up = gas or dust velocity, cm/s 

A = duct cross-sectional area, cm2 

r, = drop radius, cm 

= single drop collection efficiency, fraction 

Q, = liquid volumetric flow rate, cm3/s 

z - axial distance, cm 

Boll (1973) and Behie and Beeckmans (1973) had demonstrated 

the success of this equation in predicting venturi scrubber performance by comparing theoretical predictions with experimental 

data. Thus, we will choose this equation as the particle collection design equation for venturi scrubber. 

No general solution for this equation was found in the 

literature. In order to calculate the particle collection efficiency, one must integrate this equation numerically, taking 

into account the scrubber geometry. It is inconvenient to use this 

equation to predict venturi scrubber performance. 

A generalized method for predicting venturi scrubber 

performance by equation (4-4) was developed in this study. 

This method is similar to that used by Hollands and Goel (1975) 

to obtain pressure drop in venturi scrubber. Detailed derivation of the generalized method will be presented in the next 

chapter. 

60 
P.79 

CHAPTER 5 

PERFORMANCE MODEL 

In this chapter, we will present the generalized method for 

predicting venturi scrubber performance by using both Boll's 

pressure drop equation and Calvert's modified pressure drop 

equation combined with Calvert's differential equation for 

particle collection. The method was developed by Hollands and 

Goel (1975). However, they only covered Boll's pressure drop 

equation. Their method was extended to Calvert's differential 

equation for particle collection. 

MATHEMATICAL MODELING 

The basic equations governing the particle collection 

and pressure drop in a venturi scrubber ivere developed by 

Calvert (1968, 1970) and Boll (1974); rewritten here after 

some rearrangement they are: 

A u Q, 

dc r X L 

c uG (uG-ur)A \4rd 

n dz (5_!) 

dud 3 pG 

^

2

 cD 

dz 4 pL dd ud 

dp

 du G 3 PG C D (UG"Ud)2 m L (V m

G )

 fp GU G rc „ 

— = prur - — — — — - (5-3) 

dz " <-> dz 4 p. d, u, A mr 2d, 

PL d d G h 

B.C. at z = 0, c-=c^; u, = u, • ur=ur : p=p„ ' o d do G Go o 

where A = duct cross-sectional area, cm2 

c = dust concentration, g/cm3 

Cp = drag coefficient, dimensionless 

dd = drop diameter, cm 

d, = hydraulic diameter of the duct, cm 

f = friction factor, dimensionless 

61 
P.80 

nip = gas mass flow rate, g/s 

m. = liquid mass flow rate, g/s 

p = pressure 

Q = liquid volumetric flow rate, cm3/s 

r , = drop radius, cm 

u, = drop velocity, cm/s 

u„ = gas velocity, cm/s 

u = relative velocity between gas and liquid drop, 

cm/s 

z = rectangular coordinate in the direction of flow 

p, = liquid density, g/cm3 

pp = gas density, g/cm3 

n = single drop collection efficiency, dimensionless 

Several assumptions were made in the derivation of these 

equations. They are: 

(1) The flow is one-dimensional, incompressible and 

isothermal. 

(2) Liquid drops are uniformly spread across the duct 

and the drop diameter is invariant with axial 

distance. 

(5) Drops are of uniform diameter. 

We will introduce several additional assumptions: 

(4) There is no wall loss of liquid drops. 

(5) At any cross section of the scrubber, liquid 

fraction is small. Therefore, at any location, the 

gas velocity can be calculated by the following 

equation: 

m 

u 

G p GA 

where mp = gas mass flow rate, g/s 

A = duct cross-sectional area, cm2 

pr = gas density, g/cm3 

62 

£- (5-4) 
P.81 

Duct cross-sectional area depends on location and can be 

be determined from the following general formula: 

j = 1 for rectangular duct 

j = 2 for circular duct 

where A = cross - sectional area of the duct at the start of 

o 

a section, cm2 

R = radius (for circular duct) or half width (for 

rectangular duct) at the start of a given 

section, cm 

8 = half angle of divergence or convergence, degree 

"3" is positive when duct is diverging and is negative when 

duct is converging. 

Equation (5-5) assumes that for rectangular duct, duct 

breadth remains unchanged; only duct width is converging or 

diverging. 

(6) The drag coefficient is governed by the following 

relationship as suggested by Hollands and Goel 

(1975) . 

CD = (constant) N~°-5 

where C~ = drag coefficient applying at z=0, dimensionless 

u„ = gas velocity at z=0, cm/s Go

 & J 

u, = drop velocity at z=0, cm/s do

 K ' ' 

"Cn " is determined from the "standard curve" using a Reynolds 

number calculated on the basis of the relative velocity 

applying at the beginning of the duct, i.e., 

63 
P.82 

u„ -u , j d, 

v = ' Go dol d 

Re,o v (b"

7

J 

where NR = drop Reynolds number at the beginning of 

the duct, dimensionless 

d, = drop diameter, cm 

VQ= kinematic viscosity of gas, cm2/s 

The equation for the standard curve, due to Dickinson 

and Marshall (1968) , is : 

Cn = 0.22 + 24 (l +0.15 N°"6 \ (5-8) 

Do N \ Re,o)

 v J 

Re.o

 v ' 

(7) Liquid drop diameter is that predicted by Nukiyama 

and Tanasawa correlation. 

(8) Particles are flowing at the same velocity as gas, 

then Equation (5-1) can be reduced to: 

dc

 1'5 lUG-Udl/V\ . 

- — = — hi dz (5-9) 

ud dd \%l 

(9) Particle collection is primarily due to inertial 

impaction. We will use the simplified equation 

by Calvert (1970) to estimate the single drop 

target efficiency. 

/ K \ 2 

'

 P ' (5-10 ) 

K +0.7 / 

P 

C ' p d 2 I u r - u , I 

wher e K -

 P P ' G d ' (5-11) 

P 9 UG d d 

If one define s tota l pressur e as: 

PT = p + ,-iPG u

2

G (5-12) 

64 
Equation (5-3) can be written as 

P.83 

dp T 3

 P G / C D \ U G " U

d l U G " Udl/ m L \

 (M+1 ) f P G V 

dz 4 p L \ d d A 2d, 

(5-13) 

where M = mT/m„ 

L L> 

= liqui d to gas mass flow rat e rati o 

The hydrauli c diameter "d, " is given for a circula r 

duct by: 

d, = 2 (R + z tan 8) (5-14) 

and for a rectangular duct by: 

d =

 2 b (R + z ta n g ) 

h b + R + z tan £ 

where R = radius (for circular duct) and half-width 

(for rectangular duct) at the start of a 

given section, cm 

b = duct breadth for a rectangular duct, cm 

(5-15) 

Equations (f-2), (5-9) and (5-13) are the governing 

equations for venturi scrubber performance. These equations 

are now non-dimensionalized, using "un " as the characteristic 

'

 & Go 

velocity scale, "%pru

 2 " as the characteristic pressure scale, 

ana 

dd pd u Go 

r.S 

as the characteristic length scale 

^ ^Do

 PG \Go~Udc/ f°r the equations below 

(in the case of d, , RQ, and b, duct length "£" is used as 

characteristic length scale), i.-e., 

u 

u 

u Go 

(5-16) 

65 
P.84 

* = i

1

^ 

3 CDo PG 

*Go 

Go do 

0.5 (5-17) 

DP* 

T 1 2 

-2 P r Up 

G Go 

( 5 - 1 S) 

By using these definitions, we obtain 

u„-u , = 

'Go Up u, 

Go d 'G "d (1 + z tan 3 \j " ur I R / Go 

*Go u 1 * Go tan B I t± \ 

R 3 Cn„ Pp lur -u. Do G \ Go do 

o.s 

* 

J d (5-19) 

Let S = 2 tan 3 dd

 PL u Go 

0-5 

3R Cn^ Pr- \tlp -U, 

Do "u \ Go do 

(5-19b) 

"S" is the dimensionless parameter characterizing the slope of 

a given duct and it has the following characteristics 

S < o for convergent section 

S = o for venturi throat 

S > o for divergent section. 

By substituting equation (5-19b) into equation (5-19), we have: 

ur-u, = Up Li d Go 

(1 + Sz*)"3 '- u* 

66 
From equatio n (5-10 ) we have : 

P.85 

K + 0. 7 

P , P d ' 

^1 P P 

9

 "G

 d d 

( 1 + Sz*) ^ 

" C ^ d~2" 

P ,P 

9

 *G d d 

•

 U d i 

V

U

d 

Up-u.1+0. 7 

-.2 

( 1 + Sz* ) - 1 

u 

0. 7 

K 

po 

(5-20) 

wher e K 

p o 

C

'

 p p d p2 UGo 

9

 ^G

 d d 

By substitutin g equation s (5-17) , (5-19) , and (5-20 ) int o 

equatio n (5-9) , we have : 

I .

 3 

dc _ 1.5R / Q L \ S |(1 + Sz*)" J

^ -Ud l L\ S 

c dr1 ta n B I QG / u^f 

|( 

-i I 0 71^ *

 (5 "2 1 ) 

1 + Sz*) -

1

-u*| + p l 'd' ic 

po 

J

d 1 * r--

Go 

QL 

Le t B = — 

^G

 PG rDo \ U Go- u

d o 

0.5 

(5-22) 

the n we obtai n 

In Pt 1 + Sz*)~ 3

-u* | dl 

Sz*) ~

]

 -u 

d z : 

+ 0. 7 

K 

P°. 

(5-25) 

67 
P.86 

where L = dimensionless duct length 

5 CDo

 l pG 

2 d d pd 

Up u, Go- do 

u Go 

0,5 

I = duct length, cm 

Equation (5-25) is the general equation to predict, particle 

collection by inertial impaction in a venturi scrubber. 

By following the same procedures as the derivation of 

equation (5-23), the following equations are obtained for 

drop velocity and pressure drop: 

0.5 

du* 

d 

dz* 

(1 + Sz*)"J Ud 1(1 + Sz*)" "I 

? ii* 

(5-24) 

dp* = M 

dz* 

(1 + Sz*)'' J - u> (1 + Sz*) n -

 u; 

0.5 

+ (M + 1) f (1 + Sz*)"2j 

d* L h 

(5-25) 

.C. at z* = 0, .u*=u* , p* = 0 

' d do ' • *i 

d* = 2R* (1 + Sz*) Circular duct 

[A = 2 b* R*(l + Sz*) 

h b* + R*(l + Sz*) 

Rectangular duct 

(5-26) 

f = friction factor, dimensionless 

i* = b/l - dimensionless duct breadth, 

!.* = \\r>\ =• dimensi onless radius 

68 
P.87 

The first term on the right hand side of equation (5-25) 

represents the pressure change associated with the acceleration of liquid drops; the second term is the wall friction 

loss. From this equation, it seems that the contributions 

of the liquid acceleration loss and the wall friction loss 

to the total pressure loss are additive. Therefore, one may 

wr ite: 

PT

 = Pd + P (5-27) 

where PT 

Pd 

* = 

W 

total pressure, dyne/cm2 

component of p*, associated with liquid flow, 

dyne/cm2 

wall friction component of p£, dyne/cm2 

By this definition, we have: 

dz* 

M(l + Sz*) J (1 + Sz*) u- (1 + Sz*) -3 

and 

d p w = (M + 1) f (1 + Sz*) 

dz* d* L 

h 

2j 

U S 0.5 

(5-28) 

(5-29) 

with boundary conditions 

at z* = 0, p* = 0, p* = 0 

w 

(5-30) 

Equations (5-23), (5-24), (5-28), and (5-29) are the final 

forms of the governing equations. 

For each section of the venturi scrubber, its pressure 

drop and particle penetration can be calculated from equations 

(5-23), (5-24), (5-28), and (5-29). Since pressure drops 

are additive, the overall pressure drop for the venturi 

69 
scrubber is, 

P.88 

AP, £ (AP ; (5-31) 

where AP = overall pressure drop, dyne/cm 

(AP). = pressure drop of a section of the venturi 

scrubber, dyne/cm2 

The venturi scrubber is a scrubber with a convergent 

section, a throat section, and a divergent section connected 

in series. Particles that are collected in one section cannot 

be collected in another section. Therefore, if the particle 

penetration for each section is known, the overall penetration for the venturi scrubber will be, 

Pt(d ) = n 

P i 

Pt(dp) (5-32) 

where Pt(d ) 

P 

Pt(1d ) 

 P 

overall penetration for particles with 

diameter "d ", fraction 

penetration of a section, fraction 

SOLUTION 

The analytical solution to equation (5-29) is, 

>* = (M+l)f F 

w 

ho 

w 

(5-33) 

wlie r e F 

A -2 

4 (A

 0>5

 -1 ) 

v

 r J 

for circula r duct (5-34) 

1 + 

R*(Ar-l)(l+b*+R*) 

2(b* + R*) 

for rectangular 

duct 

70 
P.89 

and A = the ratio of exit to inlet cross-sectional area 

r 

= (1+SL)J 

d,* = dimensionless hydraulic diameter at duct ho

 ; 

inlet, cm 

f = friction factor, dimensionless 

A value of f=0.027 was suggested by Boll because it 

seemed to give a slightly better fit in the shape of the 

pressure drop curves than other values of "f". 

Equations (5-23), (5-24), and (5-28) are solved by 

numerical integration on a digital computer. Figures 5-1 

through 5-16 show the results of a numerical integration for 

* 

the range of L, S, and K „ of interest and for u, =0. These ° po do 

figures along with equation (5-32) may also be used to determine penetration for u, 5^0. The method is discussed in the 

following paragraphs. 

The drop velocity at the beginning of the divergent 

section differs from zero. We will use the divergent section 

to illustrate the method of applying Figures 5-1 through 5-16 

to determine the particle collection efficiency of a section 

where at its inlet the liquid drop velocity is not zero. 

Refer to Figure 5-17 in order to find the penetration 

of the divergent section ABCD, we project it in the upstream 

direction with the same divergence angle "6", i.e., add an 

imaginery section FEBA to the upstream of ABCD as depicted 

in Figure 5-17 by the dashed lines. The result is two venturi divergent sections connected in series. The outlet of 

the imaginary added on section is the inlet of the real section. By equation (5-32) the particle penetration for the 

real divergent section ABCD is equal to, 

Pt 

^ABCD p

 l b

 •ii)J 

FEBA 

71 
P.90 

zd?n 

72 
3.00 

<^> 

PL, 

2.00 

1.00 

0.75 

0.50 

0.25 

si -u 1 0 -5 

i f rT

r_T 7r n 7T 

-1'! -0.5" -0.2 i -0.1 -0.05 -0.02 . -0.01 

0.01 

(L + LH) F 

Figure 5-2. Chart for obtaining u^ for a rectangular duct. 
'•••Wi. 

6.0 

3-

PL, 

*xi 

P. 

4.0 

2.0 

1.5 

1.0 

0.5 

T—rp-rrjifrri i—| Mf . rrq 1 | i <|iii y.1—71—if 1 in n 

S=-20 ' 1 -10 I i -5. 0 -2. 0 -1.0 ! -0. 5 -0. 2 -0.1.-0.0 5 -0.0 2 -0.0 1 

change 

of scal e 

0 

0.01 

*S 

0.1 1.0 10 100 

(L+LH)F 

Figure 5-3. Chart for obtaining p* for a circular duct. 
6.0 

SF-°' 5 = -2 0 '•• ' ; - 1 0 

. . TH! r ___ T p T _—j— j j j wjjr 

0 . 5 I! ? 

I ' I"! 

•0. 1 ! -0.0 5 -0.0 2 -0.0 1 ; 

4 . 0 -

change 

of scal e 

2.0 

F-1-SL H ; 

1.5 

-^1 

On 

CM 

U H 

* T 3 

CX 

1.0 -

0.5 

01 

J I IIIIII I I i n i liti i i i i u iii i i i i i m 

o.i 1.0 10 100 

(L + LH)F 

Figure 5-4. Chart for obtaining p*. for a rectangular duct. 
0.0 

-J 

am 

4-> 

C-r 

C 

PL, 

0.0'— 

0.0 

— 0.02 

0.01 

0.01 100 

L + L 

- ) 

Figure 5-5. Chart for obtaining penetration for circular duct. 
CQ 

PL, 

16 

12 — 

08 

04 

pfwuiawi g*mixr<r. 

i .;..J::lil:..t....;...J....i.. 

Ci rcuJar duct 

. .. ..........t„. 

0.01 0.1 10 

(L + LH)F 

Figure 5-6. Chart for obtaining penetration for circular duct. 

100 
.3 

oo 

eq 

a, 

c 

P-, 

I 

.2 

. . . I . I ,. .1. 

Circular duct 

u

nTr~rnrTT~TrT- J . 

.01 

(L + LH)F 

Figure 5-7. Chart for obtaining penetration for circular duct 
U3 

pa 

4-> 

a, 

PL, 

.2 

:.cc\c\ 

Circula i • duc t 

. . . ,.- d i r\ :.;... . 

:• p° : ir: 

~ F=1-SL,,.: \J 

. . . j . . . . 

1 

• • • • i • • 

. . . . i . . . 

i 

-•••>- -

:::'!::: 

• • • • j :••• 

... . I... . 

... . i... . 

... . |.... 

1 

• ' • ' \ • • ' • 

: '/j:::' 

Lr; 

| i 

._.!.... 

....!... 

• • • ' • i 

....i .-

...,i.. . 

....j... . 

—(. _ 

_J_ 

... L. 

i 

...p.. 

.. L... 

1 

....... 

j.... 

.... 

• ' • 1 

— 

.... 

.... 

— 

- • 

... 

...j . .. 

-+-• 

J . . . 

r 

: 

. . . i... . 

"... . 

L... 

riffd" 

. . i . 

....j... . 

T 

. 

i 

• • 

^c 

,..)...:.... 

1 

::|::r. z 

,...i 

i?.* 

— 

.... 

3 

... }.... 

" ~ 

J|F* : . . 

-• 

L.UL 

i 

! • • • 

• i&Pfs'^ 

:.•::: Li 

.. :... 

.. i .. 

^^•"'^"T 

..... . . . ; 

•-- • :^_ 

— -

i 

—j... . 

'.'.'J,** 

^rc. j — 

i 

1 — 

- •• j--- -

y... 

„ i . . 

1 

)-•• ' 

....;... 

... r . 

...J... 

.-J — 

i ......... 

._..!.... 

.i.... ... 

XI 

. ..J. ... ... 

I— o-v -'•-

— 0.0.U 

" !"' ' ' '" 

4 0.0 2 

r III , 

...... 

1.0 5 J 

hap. I. ; 

^h 

...|.^e» ^ 

0 . 2 

" i i 

~±.:r ::: iso. 5 

.. .i.... 

..„j.„ 

....... 

i, 

i 

T 

— i — 

...L... 

y: \- l-h 

-..? o 

2.0 

r 

0 . i. 

10 

20 

50 

4 

i-r 

' 

:::::.: 

. . J 

i 

. . ;. 

• • 

i ^ 

-* • • - • j - • •• 

:::;:,':,, : 

i... . 

• 

"H "I 

... j...:. . 

•;•;;; " 

CTC. 

.. .i... . 

. .j.. . 

• - - .- i • - - • 

— 4 — 

- - •;•;; ; 

:•••• ! 

1 

,1 N • 

....... 

... L. 

....L... 

....j... . 

T' 

—H 

...,|.... 

] 

i *t 

—i— 

-i-j 

...!.... 

1 

...j... . 

...!.... 

........ 

...i... 

i 

i 

...i... 

"V" 

••+-

...:.... 

.... 

— 

— 

— 

-

:±fc 

•-

_ 

u 

— -*- m 

-.::.'. 

m 

i. . 

i'i;,ir 

0. 1 10 10 0. 

(L + Ln )F 

Figure 5-8. Cliart for obtaining penetration for circular duct 
1.0 

oo 

o 

m 

4-> 

ft 

PP 

(L + LI()F 

Figure 5-9. Chart for obtaining penetration for circular duct. 
0.0 

cn 

4-> 

ft 

ft 

r^rnrrnTi T^TTTTITO 

0.04 

0.03 

0.02 

0.0 1 _ 

0.0 1 

Figure 5-10. Chart for obtaining penetration for rectangular duct. 

100 
00 

to 

CQ 

ft 

ft 

i 

0.16 

0.12 

0.08 

0.04 

0 

j-^rmTn pn' 

Rectangular duct 

0.01 

jTfn TT T" i—rrrrrrT 

• i i ] i-ii 

(L + LH)F 

F'igure 5-11.Chart for obtaining penetration for rectangular duct 

I lit ! 

100 
0 . 3 

0 0 

PQ 

OL, 

f--1 

0. 2 

0 . 1 

r^T^rTTTTrr~~nr—rnrrTrrn T"~'prnTTTw

 •{ . i r'l j I n 

i i i • i M i j J III I iiii i i IIIII I 

0.01 0.1 1.0 10 100 

(L

 + LH)F 

Figure 5-]2. Chart to obtain penetration for rectangular duct 
oo 

OQ 

4-> 

D H 

I 

0.4 

0. 3 

0.2 

0. 1 

0 

•HMBH^U . w '.iujuun.am^mm^. 

! _ iii i 

Rectangula r duct j 

K = J . 0 

po 

I in 

i IIIIIII I i iiiiiii i j i i m m J I MMM 

0.0 1 0 . 1 1.0 10 100 

(1. • lj,)F 

Figure 5-13. Chart to obtain penetration for rectangular duct 
1.0 

oo 

CQ 

+J 

% 

0.8 

0.6 

0.4 -

0. 2 

0 

0.01 0.1 1.0 10 

Figure 5-14. Chart to obtain penetration for rectangular duct 

I I l.l Mi ' 

100 
oo 

2.0 

1.8 

1.6 -

1.4 

« 1.2 

Dw 

1.0 

^ 0. 8 

0 . 6 

0 . 4 

0.2 

0 

i—rnrrTTTT 

RcctanguJa r duc t 

--3-"""TTM7'*"s"T"*"l"T' 1 ! I ili l 

0.01 

L. > ' i i i I i Ji.~^--JL^i~.JjJLJjJjLjL 

o.i i.o 

(L+LH) F 

10 100 

Figure 5-15. Chart to obtain penetration for rectangular duct 
PQ 

2.4 

2.2 

2.0 -

1.8 -

1.6 -

1.4 

1.2 

OO D H 

c 

rH 

U H 

1.0 

0 . 8 

0 . 6 

0.4 -

0. 2 

0.01 0.1 1 .0 

(L+Ij,j F 

10 100 

Figure 5-16. Chart to obtain penetration for rectangular bed, 
P.6 

F U rl 

,:

 ^ ud 

G 

u , = 0 

£,, •* 

.

u G = UGo 

.U ,

= u, d do 

Figure 5-1.7. Concept of a hypothetical section 
P.7 

If we adjust the length of the imaginary section in 

such a way so that the liquid drop velocity at the inlet of 

the imaginary divergent section is zero, then "Ptpprn" and 

"PtppBA" can be obtained from Figure 5-3 through 5-16 and 

penetration for the real section can be calculated from 

equation 5 - 35. . 

The length of the imaginary section "£,,", can be determined by integrating equation 5-2 with the following boundary 

conditions: 

at z = 0, uj = u do 

z = -£H, ud = 0 

Figures 5-18 and 5-19 are the results of the integration for a circular duct and a rectangular duct respectively. 

"LH" is the dimensionless counterpart of '*£„" and is defined 

by, 

£H 

L 

In calculating "Ptpp~n" and "P1: PFBA"' ^•t *s necessar y 

to use the gas and liquid parameters at the inlet of the 

imaginary added on section, i.e., at z = -P,„. From the geometry 

of the duct, parameters at z = -ly, are related to the known 

parameters at z=0, i.e., at the inlet of the real duct, by 

the following equations, 

L' = (L + LH) (1-SLH) -

l/2 (5-57) 

S' = S (l.-SLH) ~J/2 _1 (5-38) 

u* ' = u* (l-SLH)

j • (5-39) 

89 
100 

o 

CM O 

1.0 

0. 1 

0. 75 1.0 1. 25 .1 .5 

'do 

Figur e 5-18 . Cliart for obtainin g I, for a circula r duel 
P.9 

U 

-a 

rc 

rH 

3 

oo 

C 

oi 

u 

o 

o 

oa 

c 

•r-i 

c 

• H 

ro 

+-> 

O 

i-H 

o 

rro 

U 

LO 

o 

* 11 t -M t • I I 

OPW / H "j 3 * 

91 
P.10 

and B'"= B(1-SLH)"J/2 '""(5-40) 

where prime ('•) refers to z= -£,,. Detailed derivation of 

these equations is given in Appendix A. 

SAMPLE CALCULATION 

To illustrate the application of these figures to predict 

the performance of a venturi scrubber, we will calculate the 

pressure drop and particulate collection for the venturi 

scrubber shown in Figure 5-20. IVe will predict its performance for the following operating conditions: 

QG = 800 Am3/min 

QL/QG = 1.33 £/m3 

Gas temperature = 20°C 

Particle Collection 

Convergent Section - Water is injected at the start of the 

throat. Therefore, there is no particle collection in the 

convergent section. 

Throat Section - The water is assumed to be injected with 

no axial momentum so that "u, " is equal to zero. The 

gas velocity at the inlet of the throat is calculated to 

be 8,060 cm/sec. Thus, the drop diameter according to 

Nukivama and Tanasawa is: 

50 /QL d, = — + 91.8 — d UG K 

= 0-010 7 cm 

Drop Reynolds number 

_

 dd]Vu

do| 

1.5 

N Re, o 

0.0107 (8060-0) = 57 5 

0.15 

92 
LIQUID 

INLET 

Breadth = 81.3 cm 

Figure 5-20. Venturi scrubber for sample calculation, 
P.12 

From Standard curve, or from equation (5-8): 

JDo 

= 0.22 + 

0.22 + 

24 

N Re ,o 

24 

(1 + 0.15 N°- 6

v ) Re,o^ 

575 

1 + (0.15)(575 ) 0.6 

= 0.545 

1 IC - /p„\/U „ "Uj 

3 t Do / rG w Go do 

0.5 

2 d

d w< 'Co 

= 2.79 

'\\(pl u Go 

V

XG/ \ 0/ Do \ Go do> 

= 2.03 

For venturi throat, S=0. Since u, =0, we have L,J j = 0 

H 

and F=l 

K 

uGo d p a = (8060) (IQ- 8

)

 (d p a } 

po 9 uG dd (9) (1. 8 x IO""4) (0.0107) 

= 4.65 d2 

pa 

or d = (0.21 5 K \ °'5 ymA 

p a \ po 

Read "-F In Pt/B" from Figures 5-10 to 5-16 for L=2.79 and 

S=0 for various "K ", we obtain the following: 

po ' 6 

94 
P.13 

V 

0.2 

0.5 

0.7 

1 

2 

5 

10 

d „ , ymA 

pa ' 

0.21 

0.33 

0.39 

0.46 

0.66 

1.04 

1.5 

-F ln Pt/B 

0.044 

0.176 

0.272 

0.41 

0.77 

1.3 

1.7 

Pt(vd ) 

 pa' 

0.91 

0.7 

0.58 

0.44 

0.21 

0.071 

0.032 

Divergent Section - At the exit of the venturi throat, the 

drop velocity is: 

u* F2 = 0.78 (Figure 5-2) 

i.e.,ud = (0.78) (8060) = 6287 cm/s 

u* = 0.7 8 

At the start of the divergent section, gas and drop velocities 

are the same as at the throat exit. Therefore, at the beginning of the divergent section: 

un = 8060 cm/s Go 

and u, = 6287 cm/s do 

Drop Reynolds number is 

dd (UGo"Ud)_ (0.0107) (8060 - 6287) 

'Re ,o 0.15 

= 126 

From Standard curve or by equation (5-8) 

95 
P.M 

Cn = 0.9 3 Do 

S 2_ ta n 

3 R 

d

d

 PL 

0.5 

u Go 

Cn P„ \u r -u . Do G x Go do 

= 0.17 7 

3 z S o ^G / U Go' Ud o 

2 d d PL ' UGo 

0.5 

12.5 

l\'e need "L,_/' which can be found by using Figure 5-19, 

u 

* •-

= 2.0 

Therefore , LH = 2. 0 (0.78) 2 = 1.2 

L + LH = 13. 7 

F = 1 - SLH = 1 - 0.17 7 (1.2 ) =0.7 1 

Thus, (L + L? ])F 

LHF 

and SF" 0-

5 

po 

10. 8 

0.9 5 

0 . 2 

u r d 2 

Go pa 

9 UG d d 

4.6 5 d 2 

pa 

o r 

pa 

(0.21 5 K ) °'5

v umA 

 po 

*.i%i°^ > Q-/\p r S / C,, \u „ -u , G ' G' Do \ Go do 

u 

0.5 

Go 

= 2.5 4 

96 
P.15 

Read "-F In Pt/B" from Figures 5-10 to 5-14 at SF-°-5=0.2 and 

(L + LtI) F=10 . 8 and 0.95-for various K , we obtain: II po' 

K 

PO 

0.2 

0.5 

0.7 

1.0 

2.0 

5.0 

10 

d ,ymA 

p a' 

0.21 

0 . 35 

0.39 

0.46 

0.66 

1.04 

1.5 

(-F ln Pt/B) . 

0.037 

0.148 

0.233 

0.35 

0.68 

1.25 

1.75 

Pt(d ) 

P

a L+LH 

0.89 

0.62 

0.47 

0.32 

0.11 

0.018 

0.0035 

(-F ln Pt/B) 

LH 

0.035 

0.142 

0.213 

0.315 

0.57 

0.93 

1.15 

Pt(d ) 1 

pa Lj. 

0.89 

0.63 

0.50 

0.36 

0.16 

0.05 

0.025 

The penetration for the whole venturi scrubber is calculated with the help of equation (5-32), i.e., 

* 

Pt(vd ) . «. Pt(d ) T T pa ; throat ^ pa'L + L 

Pt(d J = ^ pa' Pt(vd ) T pa' L H 

H 

dpa,ymA 1 0.21 

! Pt 1 0.91 

0.33 

0.69 

0.39 

0.55 

0.46 

0.39 

0.66 

0.14 

1.04 

0.025 

1.5 

0.0045 

Figure 5-21 shows the result of this calculation. For 

this particular scrubber geometry and operating conditions, 

the particle collection in the divergent section contributes 

little to the overall scrubber collection efficiency as shown 

in the figure. 

Pressure Drop 

We will use both the modified Calvert's equation and Boll's 

equation to predict the pressure drop of the sample venturi 

scrubber. 

97 
P.16 

1.0 

% 

< 

~ 0.1 

Wr 

u 

< 

a. 

0.01 

0.1 

I J I J llJIJJ 

VENTURI THROAT 

ONLY 

* - IIIIII I J I I llll l 

1.0 

PARTICLE DIAMETER, ymA 

10 

Figure 5-21. Predicted grade efficiency curve. 

98 
P.17 

Modified Calvert's Equation - Modified Calvert's equation is: 

AP = 1.03 x IO- 3 u* u 2 [ — ) 

d G t

 \Q G / 

For the present example, ur =8060 cm/s 

bt 

and { — 1 = 1.33 x 10'3 K-

\ Q G / 

Therefore, drop diameter by Nukiyama and Tanasawa: 

d UG V 

= 0.010 7 cm 

Drop Reynolds number 

N _

 d d (UGo"udo) 

Re,o v 

0.0107 (8060-0) _ rnr 

0 .1.5 

From Standard curve, or from equation (5-8): 

CD o - 0.545 

3 £t S o PG A -

and x = + 1 16 dd pL 

= 1.35 

* - ? ud " 2 1 - x2 - (x1* + x2 )

0 -5 

= 0.80 

99 
P.18 

Therefore, pressure drop is: 

AP = (1.03xl0"3)(0.80)(8060)2(1.33xl0"3) 

= 71.5 ci W.C. 

Boll's Equation - The procedure to calculate the pressure drop 

using Boll's equation is to calculate wall friction loss and 

acceleration loss separately. The sum of the two losses is 

the total pressure drop. 

(1) Convergent section 

A. Wall friction 

= (M + 1)F F 1 w d * w 

ho 

f = 0.027 

w A 2 

r 

1 + 

and A r = 

R*(Ar-l)(l+b*+R*) 

2(b* + R*) 

exit cross-sectional area 

inlet cross-sectional area 

At the convergent section inlet 

Go 

M 

I 

b 

R 

= 

= 

= 

-

= 

2 500 cm/ 

0 

6 2 cm 

81.3 cm 

(0.5) (65 

2b(R + I 

• 4) = 

tan 

-- 32 

6) 

.7 cm 

h° b + R + £ tan 6 

(2)(81.3) 32.7 + (62) tan 20' 

81.3 + 32.7 + (62) tan 20° 

= 6 5.8 cm 

(5-15) 

100 
P.19 

By the definition of dimensionless parameters, we have 

R* = 

ho 

A = 

81.3 

62 

32.7 

62 

65.8 

62 

1.31 

0.527 

1.06 

(81.3)(20.3) 

(81.3) (65.4) 

= 0.31 

Therefore , 

F 

w 

1 1 + 0.527(0.31-1)(1+1.31+0.527) 

(0.31)2 2(1.31+0.527) 

= 7.48 

> * = 

w 

AP 

wc

 PG "G

° 

- (0.027H7.48) = Q i g 

1.06 

Ap 

w 

(0.19)(1.2xl0~3)(2500)2 

(2)(980) 

= 0.7 3 cm W.C. 

B. Acceleration loss 

There is no water in this section, therefore acceleration 

loss is zero, i.e., 

Ap, = 0 

Total pressure drop in convergent section 

Ap = Ap + Ap , = 0.73 cm W.C, 

101 
P.20 

2) Throat section 

A. Wall loss 

At the throat inlet 

and 

Go 

b 

R 

6 

ho 

M 

= 

= 

= 

= 

= 

_ 

8060 cm/. 

81 

(0 

0 

18 

^L 

3 cm 

5) (20 

1 cm 

!id = 

sec 

• 3) = 

1 .33 : 

10 

vcl.0 • 

2 

- 3 

cm 

= 

QP P, 1.2x10 - 3 

I* =

 18 '1 

ho 30.5 

0.593 

Ar = 1 

Fw = 1 

Therefore, 

and 

> * = 

w 

AP = 

(1.1 + 1) (0.027) 

0.593 

0.0956 

(0.0956)(1.2xlQ-3)(8060)2 

(2)(980) 

3.8 cm W.C. 

B. Acceleration loss 

From Nukiyama and Tanasawa correlation, ue have 

d, = 0.0107 cm d 

u, = 0 do 

Drop Reynolds number 

dd(UGo~udo) _ (0.0107) (8060-0) 

N Re ,o 0.15 

575 

102 
P.21 

From equation (5-8): 

24 C D Q = 0.22 + ^£1 (1 + (0.15)(575)0-

6) 

0.545 

2 d. 

3

 £ ^Do /^G\/UGo"Udo 

0.5 

U Go 

= 2.79 

For venturi throat, 6=0, S=0, F=l. 

From Figure 5-4, we obtain: 

M = 1.6 

Since p 

AP, 

* -

for (L+LH)F = 2.79 

, Ave have 

AP, 

2g

 PG U

5 Go 

c 

1.6M

 PG UGo 

2g F2 

sc 

= (1.6)(1.1)(1.2xlQ-3)(8060)2 

(2)(980) 

= 70 cm W.C. 

Therefore, total pressure drop in venturi throat 

Ap = /dp + Ap, = 2.79 + 70 

w 

= 7 2.79 cm W.C, 

103 
P.22 

(5) Divergent Section 

A. Wall loss 

At divergent section inlet 

'Go 

b 

R 

M 

I 

8050 cm/s 

81.3 cm/s 

(0.5)(20.3) 

7.5° 

1.1 

171 cm 

= 10.2 cm 

. = 2b (R + I tan B) 

ho b + R + I tan 6 

(2)(81.3) [10.2 + (171) tan 7.5° 

81.3 + 10.2 + (171) tan 7.5° 

df ho 

46.7 cm 

d ho 46.7 

171 

= 0.273 

(81.5)(65.4) 

(81.3)(20.3) 

3.22 

R 10.2 

b 

171 

81.: 

171 

0.06 

= 0.475 

and 

. 222 1 + 

0.06(5.22-1) (1+0.06 + 0.475) 

2(0.475+0.06) 

0.115 

w 

= (1.1

 + D (0.027) (0 .115) = Q _0 2 5 

0.273 

104 
P.23^ 

APw Since pf. = — , we have 

Ii~

 PG u

to Go 

c 

A = (0.025)(1.2xl0'3) (8060)2 

? w (2)(980) 

= 0.99 cm W.C. . 

B. Acceleration loss 

In the divergent section, liquid drop diameter is the same 

as in the throat, i.e., dj=0.0107 cm. At the divergent section inlet, drop velocity is equal to the velocity at the 

throat exit. From Figure 5-2, we obtain: 

u^F2 = 0.78 for (L+LH)F = 2.79 and SF-°S= 0 

.*. u, = (0.78) (8060) do ^ ' v 

= 6 287 cm/s 

u = 8060 cm/s 

Go 

Drop Reynolds number 

dd(UGo"udo) 

NRe,o 

(0.0107) (8060-6287) = U6 

0.15 

Using equation 5-8, we obtain Cn =0.93 

s = 2 tan 6 dd

 PL./ UGo 

Do 

0.5 

3 R Cp. Pr \u_ -u. Do G \ Go do 

= 0.177 

105 
P.24 

L = 

C.. p „ / u „ -u, £ „ Do

 KG / Go do 

0.5 

d d PL u,. Go 

= 12.5 

From Figure 5-19, we obtain: 

L H 2.0 

u

: 

Therefore , LH = 2. 0 (0.78) 2 = 1.2 

L + LH = 13. 7 

F = 1 - SLH = 1 - 0.17 7 (1.2 ) = 0.7 ! 

Thus, (L + L{ I)F =10. . 

LHF =0.9 5 

a n d SF" 0-

5

 = (0 .177 ) (0-788 ) " °'5 = 0.19 9 

From Figure 5-4, we obtain 

'p* F2^ 

y M 

= 1.0 

L + LT 

'pa F " 

v M I 

= i.i 

JH 

(n) L + L H 

= ri.o)(i.i) 

CO . 788)2 

= 1.77 

106 
P.25 

(p*\ =

 (1,1 ) (1,1 ) = 1.95 

^

 d>L (0.788)2 

H 

(PS) L - (P3)LtLu - (P3) = -0.179 

H

 LH 

Ap* 

Since p*; = , we have 

d 1 .. . 2 

2g G Go 

6c 

Ap* = (0.179)(1.2xl0-3)(8060)2 

d (2) (980) 

= - 7.1 cm W.C. 

Negative pressure drop is equivalent to pressure recovery by 

the gas. Total pressure drop in the divergent section is 

then equal to: 

Ap = 0.99 - 7.1 = -6.11 cm W.C. 

The pressure drop for the whole venturi scrubber is equal 

to the sum of convergent, throat and divergent section loss. 

Ap (overall) = 0.73 + 72.79 - 6.11 

= 6 7.4 cm W.C. 

The difference in predictions by the modified Calvert's 

equation and by Boll's equation is 4.1 cm W.C. However, the 

modified Calvert's equation is simpler to use as proven by 

this calculation example. 

PARTICLE COLLECTION IN THE VENTURI THROAT 

For a venturi scrubber, most of the particle collection 

action occurs in the throat section where the relative velocity between particles and drops is highest. Thus, it would 

be desirable to obtain an expression for particle collection 

in a venturi throat. 

107 
P.26 

For particle collection in a venturi throat, equation 

(5-23) reduces to: 

^ Pt(dp) 

B 

1 - u' 

u' 

0.7 

K 

po 

dz* (5-41) 

Equation (5-24) for liquid drop velocity becomes: 

d u 5 

dz* 

(^a)1-

2U* 

a 

(5-42) 

We will solve these two equations for the special case 

u5 =0, i.e., initial liquid drop velocity is zero. By 

rearranging equation (5-42), we have: 

dz * = 

2u* ^

ud du* (i.»3)" d 

By substituting equation (5-45) into (5-41), we obtain: 

1

j^i$_\.l['i c-»tr 

1 - ud* + 0.7\ d F

p

~ 

o 

(5-43) 

(5-44) 

The closed form solutions to equations (5-44) and (5-42) are: 

1* Pt (

d

p ) l 

B K.. . /1-u * + 0.7 

po d K 

po 

4

 Soi1^)1'

5 + 4

-

2

(

1

-

u J)°' 5 

5.02 K0' 

P 

K 

po 

v po / 

I-TTTTJ 4 K

Po

 + 4 ' 

po 

2 - 5.02 Ku'

b

 1 + rr 

p o \ K 

r0.5 / -. . 0 

po/

 J 

(5- 4 5) 

108 
P.27 

and u * = = 2 Cx* - x2) (5-46) 

where x = 

5 lt So PG 

16 dd pL 

+ 1 = £ (L + 8) (5-47) 

po 

dpa UGt 

9 ^G dd 

(5-48) 

(5-49) 

I = venturi throat length, cm 

Cn = drag coefficient for drops at the venturi throat 

inlet, dimensionless 

"C^ " is a function of drop Reynolds number and is obtained 

from "Standard Curve." 

Drop Reynolds number is defined as: 

N 

dd UGt 

Re,d (5-50) 

v 

For an infinite length venturi throat, u| approaches unity 

and equation (5-45) reduces to: 

Pt (d )= exp 

4 K +4.2-5.02K 0 -

5 

B P° E2. \ po/ V 0.7 c5_51 

K n + 0.7 

po 

(5-51) 

Equations (5-45) and (5-51) were used to predict the 

particle collection for the venturi scrubber mentioned in 

the last section. Figure (5-22) shows the calculation results 

along with the grade efficiency curve obtained in the last 

section. As can be seen, there is little difference between 

the three curves. For this particular scrubber geometry, we 

can assume that the venturi throat is of infinite length and 

its particle .collection is that predicted by equation (5-51). 

109 
P.28 

1.0 

< 

0 . 1 

-J 

0.01 

0.1 

.U^fe4aM:.-f;!*:y ! I »J,l Iij, 

- - *t- t - - > ' i i I I iii i 

i.o 

PARTICLE DIAMETER, ymA 

10 

Figure 5-22. Predicted grade efficiency curve. 

110 
P.29 

PARTICLE COLLECTION BY .DIFFUSION 

In all previous developments, particle collection by 

impaction is assumed to be the only collection phenomenon 

occurring in a venturi scrubber. This assumption is true 

for particles with diameters larger than 0.5 micron. 

Particles smaller than 0.1 ym in diameter are rarelycollected by inertial impaction, because they follow the gas 

streamlines surrounding the liquid drops. For particles in 

this size range, diffusional collection is usually the predominant collection phenomenon. In the following sections, 

we will derive an expression for the prediction of particle 

collection by diffusion in a venturi scrubber. 

Again, we will use Calvert's differential equation as 

our starting equation. His equation is: 

d£ 

d 

l.slV^di 

Ud dd 

Nw n dz (5-52) 

where c 

UG 

u , 

Qr 

particle concentration, g/cm3 

gas velocity, cm/s 

drop velocity, cm/s 

liquid flow rate, cm3/s 

gas flow rate, cm3/s 

single drop collection efficiency, dimensionless 

According to Johnstone and Roberts (194 9), single drop 

diffusional collection efficiency is given by the following 

equation: 

4 D " /vr 

.-, = 2_ 2 + 0.552 (ND

0-5) -^ 

hrudidd [ ( Re >P 

(5-5 

where D 

N 

P 

Re 

'X rm 

particle diffusivity, cm2/s 

drop Reynolds number, dimensionless 

kinematic viscosity of gas, cm2/s 

111 
By using the same dimensionless parameters defined 

earlier (equations (5-16), (5-17), (5-20) and (5-22) we have 

4 D 

n = 

2 + 0.552 u 

Go 

'Go 'udo 

0.5 i^rM 

N Re,o \^CC (1 + Sz*)^ - u* 

d Go 

(l + Sz*)~J - u* 

(5-54) 

and - ^ 

c 

where B 

4 B D 

P 1 

uGo dd ud 

(Q,,\P^ 

(l+Sz*)~J - u* 0.5 

0.5 

U Go 

C^ \Qr/p_ \u,~ -u , Do \XG/ G x Go do 

u 

0.552 

4 B D 

Go 

0.5 

uGo"udo, 

let B 

D 

Go d 

N 0.5 / C \ 

Re,o I D 

dz; (5-55 

(5-56) 

(5-57) 

(5-58) 

we have 

dc D 

/ + E (1+Sz*)"3 - uj 

0.5 

dz: 

(5-59) 

Upon integration, we obtain: 

L A 

InPt,, - I 2dz* 

Pc*o 

u

5 

Cl+Sz*JJ - u*10*

5 dz; (5-60) 

Equation (5-60) is the final equation describing the particle collection by diffusion in a venturi scrubber. Plots 

similar to Figures 5-1 through 5-10 can be constructed. 

112 
P.31 

For venturi throat (S=0) and for the special case that 

initial drop velocity is zero (u*j =0) , the analytical solution to equation (5-60) is: 

InPt 

BD 

(dp)=8+2E ln(l-uj) 8 

V ^ (5-61 ) 

113 
P.32 

CHAPTER 6 

COMPARING MODEL PREDICTIONS WITH PERFORMANCE DATA 

There are numerous venturi scrubber performance data 

scattered in literature. However,' most of these data 

are of little use in model comparison because either 

scrubber geometry information or particle information, e.g. size distribution and loading are not available 

In the following sections, only those data with well defined scrubber geometry and particle parameters will be 

compared with the mathematical model. 

Data by Calvert, et al 

Calvert, et al (1975) measured the performance of 

an American Air Filter Kinpactor 32 venturi scrubber. 

The scrubber is used to control the emission from an 

asphalt aggregates dryer. 

The scrubber operating conditions during the test 

were as follows: 

1. Gas flow rates were as shown in the tabulation 

below. 

Gas Parameters 

Temperature 

Pressure during 

pi tot runs 

Actual m3/min 

ACFM 

DS m3/min 

DSCFM 

Vol % H20 vapor 

Inlet Duct 

149°C 

+73.5 cm W.C. 

799 

28,200 

429 

16,300 

21 

Out 

Scrubber 

Outlet Duct 

57°C 

+ 0.5 cm \i X. 

_ 

-

13 

et 

Ch imney 

49°C 

+0.02 cm W.C. 

670 

2 5,700 

500 

19,000 

11.8 ! 

114 
P.33 

2. Water flow rate to the venturi scrubber was reported by the plant as approximately 1.06 m3/min 

(280 GPM). Water temperatures were 32°C (90°F) 

and 63°C (145°F) for the inlet and outlet streams, 

respectively. 

The performance predicted by equation 5-25 is compared 

with experimental measurements in Figure 6-1. The prediction 

agrees with the average of the measurements. 

Predictions by Calvert's equation for venturi scrubber 

are shown in Figure 6-2. As can be seen, the experimental 

results lie between predictions for f = 0.25 and 0.5. A "f" 

value of f = 0.4 will give better fit between Calvert's 

model and data than other values of "f". 

Brink and Contant's Data 

Brink and Contant (1958) obtained performance data 

on a Pease-Anthony venturi scrubber installed in a phosphoric acid plant. The dimensions of the scrubber are 

shown in Figure 4- 8. Brink and Contant gave a grade efficiency curve for the following scrubber operating conditions: 

1) Throat velocity of gas: 66.4 m/sec (218 ft/sec). 

2) Liquid flow rate: 757 £/min (200 GPM). 

Figure 6-3 shows the model predictions for (1) particle collection occurring in the venturi throat, (2) 

combined particle collection in venturi throat and divergent section, (3) particle collection occurring in the 

venturi throat and the throat is of infinite length. 

The particle diameters given by Brink and Contant 

are actual size. However, aerodynamic particle diameter 

is used in the mathematical model. Aerodynamic particle 

diameter is related to actual diameter by the following 

express ion: 

115 
P.34 

1. Q r T 1— t 1 M i i I 

< 

< 

0.1 

dJ 

0.01 

Experimental data 

Predicted by 

Equation 5-23 

and by infinite 

throat model 

ll » » I I » I I . \ i MP 

o. 1 1.0 

PARTICLE DIAMETER, ymA 

10 

i^ure 6-1. Experimental and predicted performance 

of AAF Kinpactor 32 Venturi scrub ber. 

116 
P.35 

1,0 

o 

l—l 

rO.l 

H 

W 

CJ 

< 

0.01 

0.1 1,0 10 

PARTICLE DIAMETER, ymA 

Figure 6-2. Experimental and predicted performance 

for AAF Kinpactor 32 venturi scrubber. 

117 
P.36 

1.0 

c2 

2 

C 

< 

H 

W 

Z 

UJ 

C 

tu 

J 

CJ 

l—l 

CK 

< 

0.1 

Predicted for 

venturi throat 

with infinite 

throat length 

0.01 

T — I » I ! \X 

Brink § Contant 

data 

Predicted for 

venturi throat 

only 

Predicted 

overall 

J I llll l 

0.1 1.0 

PARTICLE DIAMETER, ymA 

10 

Fi gure 6-5 Predicted and experimental penetration 

for venturi scrubber used by Brink 

and Contant. 

118 
P.37 

d = d / p C'\0'

5 (6-1) 

pa p \ Mp / v J 

where: 

d = aerodynamic particle diameter, ymA 

pa

 J r ' 

d = actual particle diameter, ym 

p = particle density, g/cm3 

C' = Cunningham slip factor, dimensionless 

Aerodynamic diameter was transformed to actual diameter based on equation 6-1. A particle density of 2.6 

(for MgP205) was assumed in the calculation. 

As can be seen, the experimental data have a higher 

penetration than predicted. This discrepancy probably is 

caused by non-uniform licjuid^drop distribution as mentioned. 

by Boll (1973). For this particular venturi scrubber, the 

prediction based on infinite throat length assumption is 

close to the prediction for the actual scrubber. 

Data by Calvert et al 

Calvert et al (1974) measured the performance of a 

Chemico venturi scrubber operating on the flue gas from 

a coal fired utility boiler. The scrubber might more 

accurately be described as a variable annular orifice 

type because .its throat is formed by a movable "plumb 

bob" concentrically mounted in a conical "dental bowl." 

The scrubber operating conditions during the test 

period were as follows: 

1. Ga'3 flow rates were as shown in the tabulation 

below and on the following page: 

Duct Inlet Outlet 

Temperature 163 . 0°C(325°F) 54 . 0°C(130°F) 

Pressure during pitot run 60.0 cm Hg 60.0 cm Hg 

A m3/min 13,400 12,700 

ACFM 4.75x10s 4.5xl05 

DN m3/min 6,300 7,150 

119 
P.38 

Duct Inlet Outlet 

DSCFM 2.4x105 2.7x105 

% H20 vapor (vol.) 6.0% 15.0% 

The flow measured by the outlet velocity traverse 

is judged to be more reliable because the velocity distribution was much more regular than at the inlet. Based 

on 7,120 DNm3/min (2.7x105DSCFM), the inlet flow rate 

would be 15,300 Am3/min (5.4x105ACFM), which is %% higher 

than the design flow rate of 14,200 Am3/min (5xl05ACFM). 

2. Slurry flow rate to the scrubber was reported by 

the plant as approximately 24.6 m3/min (6,500 GPM). 

Since the throat length and divergent angle for this 

scrubber were unknown, we will assume that it is equivalent to the venturi throat of infinite length. The throat 

velocity of the gas was calculated to be 42 m/sec and the 

liquid to gas ratio was 1.75 £/m3. Figure 6-4 shows the 

model prediction along with experimental data. The agreement between the two is reasonably well. Figure 6-5 compares data with predictions by Calvert's equation for 

venturi scrubber. A value of 0.5 for the empirical constant 

will make the model agree with data. 

Data by Calvert et al 

Calvert et al (1976) reported the performance test 

conducted on an APS electrostatic scrubber. When 

the charge inside the scrubber is turned off, the electrostatic scrubber becomes a venturi scrubber. The dimensions 

of the scrubber are shown in Figure 6-6. The measured performance of the scrubber is shown in Figure 6-7 along with 

predictions by equation 5-23 and by Calvert's equation for 

f = 0.25 and f = 0.5. The scrubber operating condition was: 

1. QL/QG = 1-4 l/m* 

2. Qr = 21 Am3/min 

120 
P.39 

1 .0 

5 0.1 

CU 

c 

0.01 

T 1 1 I I M » 

Predicted 

Experimental ' 

data i 

I Ilillll l J I » i i i i r 

o.i 1.0 

PARTICLE DIAMETER, ymA 

10 

Figure 6-4. Predicted and measured penetration for 

Chemico venturi scrubber. 

12.1 
P.40 

1 .0 ! i j-.r_.rgsL 

< 

o 

Calvert's 

equation, f 

-0.1 

2 

UJ 

u 

t-H 

H 

PS 

< 

0.01 

0.1 

I Ll . I 

1.0 

PARTICLE DIAMETER, ymA 

10 

Figure 6-5 Predicted and experimental grade efficiency 

curve for Chemico venturi scrubber. 

122 
t-o 

CAI 

-eLO 

LIQUID INLET 

-I-T-J. + — 

k 30.5" 

cm 

\ 

A \ 

. 

\ ) 

t 

-ehO 

• e 

o u 

r

1 

_JL 

15.2fp 36.8 cm—^ 

cm 

Figure 6-6 - APS Electrostatic Scrubber 
P.42 

1.0 

o 

CJ 

< 

« 0. 1 

0.01 

TTT 

Experimenta l 

Data 

I I I I llll l 

for infinit e throat 

length 

I I I IM I 

o.i 1.0 

PARTICLE DIAMETER, ymA 

10 

Figure 6-7. Experimental and predicted APS venturi 

scrubber performance. 

124 
P.43 

As can be seen, in small particle regions, neither 

model agrees with experimental data. The models predict 

too high a penetration. Between the two models, equation 

5-23 gives a better prediction than Calvert's equation. 

Data by Calvert et al 

Calvert et al (1974) obtained performance data on 

an Environeering Venturi-rod scrubber (Model A33 HydroFilter) . This device consists primarily of several parallel rods which are positioned in a duct with some space 

between the rods so that gas can flow between them. Water 

is introduced upstream from the rod bed and is atomized by 

the gas stream as it flows between the rods. Strictly 

speaking, this scrubber is not a venturi scrubber but is 

one type of gas atomized spray scrubber. 

The scrubber was installed to control the emission 

from an iron melting cupola. The scrubber operating conditions during the performance test runs were: 

1. QL/QG = 2.4 l/m3 

2 . Gas velocity in the space betweed rods was calculated to be 196 m/s 

This scrubber operates like a rectangular free jet. 

Since we do not know the expansion angle of the jet and 

the total jet length, we will assume that the scrubber 

operates like a venturi throat with throat length equal 

to five times and ten times the jet width. Figure 6-8 

shows the calculation results along with experimental 

data. The experimental data lie in the area bounded by 

the curves for throat length equal to five times and ten 

times jet width. 

CONCLUSIONS 

Based on these comparisons, the following conclusions 

can be drawn: 

1. If the venturi scrubber geometry is well defined, 

then the model prediction agrees with experimental data. 

125 
P.44 

1.0 

O.l 

CJ 

< 

DS 

P-, 

< 

QX. 

t-m 

UJ 

UJ 

a, 

UJ 

u 

ax. 

< 

Cu 

0.0 1 .. 

0.001 

I I I | | l M 1—T 

Predic 

.infini 

.length 

Predi 

length 

times 

J » IIIM I i. J L 

o. i 0.5 1.0 

PARTICLE DIAMETER, ymA 

5.0 

Figure 6-8 Predicted and experimental performance 

for venturi rod scrubber. 

126 
P.45 

2. liquation 5-25 gives better predictions than Calvert's model. Another advantage of equation 5-23 is that 

it contains no empirical constants. However, Calvert's 

model is simpler to use than equation 5-23. 

3. If the venturi scrubber throat length is long 

enough (dimensionless throat length, "L", larger than 2), 

then the scrubber performance can be approximated by the 

particle collection occurring in a straight tube of infinite length. 

127 
P.46 

CHAPTER 7 

DESIGN ANALYSIS 

In this chapter, we will discuss the factors that 

affect the performance of a venturi scrubber, design 

techniques, and the optimization of the venturi scrubber 

design. Several factors have an influence on the performance and the design of a venturi scrubber. Some 

of these factors are: 

1. Throat length of the scrubber 

2. Throat velocity and liquid-to-gas ratio 

3. The size distribution of the particles to be 

collected. 

Effect of Inlet Particle Size Distribution on Performance 

The overall (integrated) penetration, Pt", of any device 

on a dust of any size distribution will be 

W 

w = w- fvt (dp)dw t7"

1) 

o 

where Pt = overall penetration, fraction 

Pt Id \ = penetration of particles with diameter d 

W = total weight of particle, g 

dw = particle weight corresponding to the interval 

d '(d) of particle "size, g 

The number and weight size distribution data for most 

industrial particulate emissions follow the log normal law. 

Hence, the two well established parameters of the log normal law 

law adequately describe the size distributions of particulate 

matter. These parameters are the geometric mean weight diameter, "d ", and the geometric standard deviation, "° g " • 

The log-normal particle distribution density is: 

128 
P.47 

dw 

wc d(m dp) 

= f id 

?)

 =(2Trf-ln a 

exp 

ln d - ln d \2 

P E£ 

(2)°-5m 

g 

(7-2) 

By combining equations 7-1 and 7-2, we have 

Ft -ftt (d ) f (d ) d (lndp) 

• / 

Pt (d

p)/~F

 6XP 

1 P/(2TT) ln a 

ln d - ln d \2 

P ' P M 

, ,0.5 

(2) in g 

d(ln dj 

(7-3) 

For convenience we will use the following transformations. Let: 

x = 

ln d - ln d 

E R£ 

(2)°'5ln a 

g 

dx = 

(2)0'

5 

d/ln d\ 

ln a

 X P/ 

(7-4) 

(7-5) 

Equation 7-7 in terms of x will be come 

Pt 

=

 xhC Pt exp (-x 2

) dx (7-6) 

By substituting the expression for Pt (equation 5-23) 

into the above equation and performing the required integration, we can obtain the overall penetration for the whole 

particle population. This integration is tedious. Thus, 

the following simplification is made: 

129 
P.48 

Based on the conclusion of the last chapter, the performance of a venturi scrubber can be approximated by the 

particle collection occurring in a straight tube of infinite length if the dimensionless throat length is larger 

than 2. Since most industrial venturi scrubbers have 

dimensionless throat length between 2 and 3, we will use 

the infinite throat length model to represent the performance of the venturi scrubber.. The penetration for the 

venturi scrubber is then given by equation 5-46, i.e., 

Pt(dp) exp 

4K + 4.2 

po 

5.02 K0^ 

po 

1 + 0.7 tan 5-

0.7 

KTM + °-7 

po 

(7-7) 

where Pt(d ) 

P 

= penetration for particles with diameter 

d , fraction 

B = dimensionless liquid-to-gas ratio 

parameter 

K 

po 

c G /\P G / C D Q 

= inertial parameter 

= d2 

u Gt 

u 

ud 

C 

Gt 

Vr = 

P _P 

9

 »G d d 

particle diameter, cm 

liquid drop diameter, cm 

Cunningham slip factor, dimensionless 

gas throat velocity, cm/s 

particle density, g/cm3 

liquid density, g/cm3 

gas density, g/cm3 

gas viscosity, poise 

130 
P.49 

The diameter for which collection efficiency is 50?. is 

designated cut. diameter "d , i.e., 

pa5o 

Pt = 0.5 when d = d 

p pas o 

In terms of cut diameter, equation 7-7 becomes 

ln(0.5)=-B 

4 Kr,<n + "4-2 - 5.02 K°"5

 ( 1 + p^—\ tan" 1. 

P P5 ° ' K

P 5 o / S 

K + 0.7 

p5 0 

p5 0 

0.7 

(7-8) 

where "K " is the inertial parameter for d 

Pso

 r

 pa50 

and is defined as 

ur. d 2 

K =

 G} P^° 

Pso 9 yG dd (7-9) 

By rearrangin g equatio n 7-8 , we obtai n 

B = 

ln (0.5 ) (K + 0.7) 

v J pso _ 

4K + 4.2 - 5.02 K c n ( 1 + %^—\ tan" 1 

ps o ps o I K / 

IK 

Jj£LL_ 

10.7 (7-10) 

By substituting equation 7-10 into equation 7-8, we have 

l n (0.5 ) (K + 0.7) 

Pt( d ) = exp P5 0 

( K + 0.7) ^ po

 J 

4K + 4.2 - 5.02 K0'

5

 (1 + v po ps o \ K 

° - 7W > < 

££ 

22. 

0.7 

4Kp5fl + 4.2-5.0 2 K- Q (1 + ^ 0.7 

i5 0 

TT 

t a n 

5 0 

10. 7 

(7-11) 

131 
P.50 

From equation 7-4, 

d = d exp 

pa pg 

0 . 5 

(21 xln a, 

By using this expression, we get for the inertial parameter, 

2(2)0-

5xln a v - i 

u _ d 2 u _ d_

 2 

K = „

G t Pa = Gt pg ext 

po " 9 uG dd \ \~*d (7-12) 

= b K 

Pg 

wh 

0 . 5 

ere b = exp (2(2) ' xln o 

K = Pg Gt 

pg 9^" ^ (7-12a) 

Since 

K / d \2 

Ps o _ f pa5p \ 

pg v pg / 

let Y =

 u p a5 0 

Pg 

then K = Y2 K 

Pso pg 

(7-13) 

By substituting equations 7-12 and 7-13 into equation 7-11 and 

after rearranging, we get, 

Pt(dp) = exp 

0.693 (Y2 K + 0.7) 

Pg 

(b Kp g + 0.7) 

4 b Kp g + 4.2 - 5.02 Cb K p g ) - (1 + ft^-jtan *1 

"" 

0.7 bK 

_E& 

0.7 

4 Y Kpg + 4"2 " Pg 

5.02 Y K°'i [l + J;,7 Itan"1-

Y^K 

Pg 

Y

2K C£A 

0.7 

(7-14) 

132 
P.51 

By substituting equation 7-14 into equation 7-6, we have 

Pt 

a 

TrO.sJ 

0.693 (Y2 K + 0.7) 

exP < "x2 + (b K +0.7) 

Pg 

4 b K + 4.2 - 5.02 (b K ) 0 5 1 

Pg Pg' 

n \ ib K 

Kpg/ ^ °'7 

4 Y2 K + 4.2 

Pg 

5 . 0 2 Y K- (1 + ^ 7 

Pg 

tan 7 

(7-15) 

dx 

Equation 7-15 is the final equation relating the 

overall penetration "Pt" to inlet particle size distribution (d , a ) and to the inertial parameter for the mean 

v pg' g

J v 

particle diameter "K ". 

Pg 

Figures 7-1 through 7-3 are plots of "Pt" versus 

(d /d ) with "K " as parameter for various "a " values. *• paso' pg' pg * g 

These plots are exact solutions of equation 7-15, accounting 

for log-normal particle size distribution as given by 

equation 7-2. 

The overall penetration can also be determined by knowing the size distribution and liquid-to-gas mass flow rate 

ratio. By substituting equation (7-12) into equation (7-7), 

we obtain, 

Pt(d ) = exp -B 

4 b K +4.2 

Pg 

b Kpg + 0.7 

5.02 (b Kpg)-((l+^tan" 1 + „ ^ 

\ Pg/ 

W p g + 0.7 

(7-16) 

133 
P.52 

1.0 

2 

O 

W 

UJ 

&, 

< 

Cri 

UJ 

> 

o 

0.05 r 4 

0.02 

Figure 7-1 Venturi scrubber integrated penetration, 

"Ft" versus "dp50 /dp g ", with "Kpg ' as 

parameter, "o =2.5" F g 

134 
P.53 

< 

UJ 

•z. 

UJ 

1.0 

0. 

0.2 

0 . 1 

0.05 

0.02 

0. 01 

0.005 

0.002 

0. 001 1 i I I I M i 1 IMUI , 

0.01 i)!l ' l)A'"l'.U 2.0 0.02 0.05 0.1 

d /d 

Pso/ pg 

Figure 7-2. Venturi scrubber integrate d penetration , Pt 

versus d ,d , with K as parameter, ^=5 . 

135 
P.54 

2 

O 

t-H 

H 

< 

UJ 

UJ 

PM 

> 

o 

1.0 

0. 5^JU:lisf 

Q.2 

Q.1 

Q.Q5 

0.02 

0-0 1 

0.005 

0.00 5 0.0 1 0.0 2 Q.Q5 Q. l 0.2 0.5 1.0 2.0 

P 5 0 

/ • 

Pg 

Figur e 7-3 . Venturi scrubber integrated penetration, 

Pt versus d__ /d„„, with K as parameter, 

sr o 

o =7.5 . 

g 

Pso/ dp g ' 

136 
P.55 

Equation 7-6 now becomes 

4 b K 

P t -

 1 

TT 0 5 

exp -x2 

B Pg 

+ 4.2 

b K 

Pg 

+ 0 

5.0 

K p S + °'7 V b w J °- 7 J dx 

(7-17) 

Pg ^ Pg' 

Figures 7-4 through 7-7 are the solutions for equation 7-17. 

Throat Length of the Scrubber 

For a venturi scrubber, most of the particle collection occurs in the venturi throat. From the results of the 

last chapter, for a well-designed scrubber there is only 

a slight difference between the grade efficiency curves of the 

venturi throat and the whole venturi. Thus, in the following design analysis, we will assume that particle collection only occurs in the venturi throat. This approach will 

give us a conservative design. 

For particle collection in a venturi scrubber, the 

collection efficiency is predicted by equations (7-45 to 7-47) 

Figure 7-8 shows the graphical form of this equation. 

This figure applies both to the circular duct and the rectangular duct. 

Under a specific operating condition, the performance 

of the venturi scrubber depends on the throat length as 

revealed by Figure 7-8. The longer the throat, the more 

efficient the scrubber. This dependence is more profound 

for larger particles, i.e., larger K . Thus, in designing a venturi scrubber, we should use a long throat. However, we should not use a longer throat than necessary 

because the pressure drop will increase with increasing 

throat length. The final choice of throat length should 

be a compromise of the two. A close inspection of Figure 7-8 reveals that a dimensionless throat length of 

2 to 3 would be sufficient. Further increase in the 

137 
P.56 

o 

I — I 

E-

< 

OX. 

E-< 

CM 

< 

UJ 

> 

o 

0.5 

0.1 -

0.05 " 

0.01 -

0.05 -

0.001 

0.5 

Figure 7-4 'Pt" versus 

'a =2.5". 

g 

•B" with "K 

Pg 

as parameter, 

138 
P.57 

1.0 

0.01 

0.5 

:i"ure 7-5. "Pt" versus "B" with "K " as parameter, 

"a = 5" 

'g * " 

139 
P.58 

2 

O 

< 

< 

Qi 

UJ 

> 

O 

a, 

1.0 

0.1 

0.05 

0.01 5000 

0.5 

Figure 7-6. "Pt" versus "B" with "X 

"a„ = 7.5".

 ] 

as parameter, 

140 
P.59 

0.5 

o 

LO 

rt 

X3 Cnh3 

oo 

0.1 

0.0 5 

0.01 

0.5 

1000 

1500 

2000 

Figur e 7-7 pa50 

Pg 

versu s "B" with "K " as paramete r 

141 
2.0 

CQ 

a. 

1.0 

0.8 

0.6 

0.4 

0 . 2 

0 

0.0 1 

1 ) 1 1 IT 

i i i ! 

M !• 

- ' i i 

i i ! 

•! !--i - -l 

M l ! 

; i ' ' 

I | ! • i4-h-lI I M IliJLJ ' i i i i ii ^ 

100 

Figure 7-8. F.ffect of throat length on penetration. 
dimensionless throat length will increase pressure drop 

with little gain in scrubber performance (Figure 7-9). 

It is possible to predict the performance cut diameter, "d " from Figure 7-8 if the scrubber operating 

condition is known. Figure 7-10 is a simplified plot of 

Figure 7-8. For an industrial-size venturi scrubber, "B" 

is usually larger than 1. As can be seen from Figure 7-10, 

the performance "K " is almost constant for dimensionless 

Pso 

throat length, "L", larger than 2, and "K " becomes a 

function of "B" or liquid-to-gas mass flow-rate ratio. 

For a venturi scrubber with dimensionless throat 

length between 2 and 3, the correction factor "u, " in 

the modified Calvert's pressure drop equation is approximately equal to 0.8. therefore, the expected pressure 

drop is 

AP (cm W.C.) = 8.24 x 10"4uG (|^) l^ \ (7-18) 

Throat Velocity and Liquid-to-Gas Ratio 

The principal collection mechanism occurring in a venturi scrubber is the collection, by drops. It is a known 

fact that the target efficiency of a drop increases by 

decreasing the diameter and increasing the relative velocity between the gas and the drop. However, smaller drops 

accelerate faster than do bigger drops with the results that 

the relative velocity goes to zero earlier in the case of 

smaller drops. Consequently, there exists an optimum drop 

diameter for particle collection. Since atomized liquid 

drop diameter is a function of gas velocity and liquid-togas flow ratio, therefore, there exists an optimum combination of throat gas velocity and liquid-to-gas ratio. 

Figure 7-11 shows the theoretical effect of throat gas 

velocity and liquid-to-gas flow rate ratio on the performance cut diameter of the venturi scrubber. Properties 

14 3 
-1^ 

0.01 

500 1000 

Figure 7-9. Effect of throat length on performance. 
.00 

50 

10 

5 — 

0.5 

0. I 

0.05 500 1000 

Pso (kib 

9

 "G ^d 

Figure 7-10. Predicted Venturi scrubber performance K 5 0 vs. B. 
P.64 

of air and water at room temperature were used to construct this figure. For other liquid/gas combinations . 

and conditions, one should construct different plots. 

Optimum liquid drop diameter can easily be obtained 

from Figure 7-11. For instance, if the gas throat velocity 

is known, then the optimum drop diameter will be that 

which gives the smallest aerodynamic cut diameter. 

If the scrubber required .performance cut diameter 

is known, optimum throat velocity and gas -to-1iquid ratio 

can be determined from Figure 7-11. Figure 7-12 shows the 

relationship between "B" and "K ". This curve was 

calculated from equation (7-8) and is applicable to all 

scrubber operating conditions. From this graph, we can 

calculate the anticipated cut diameter and pressure drop 

for various throat velocity and liquid-to-gas ratio com 

binations. Figure 7-13 shows such a calculation for airwater system at 25°C. Figure 7-14 is the cut diameter 

pressure drop relationship with water flow rate as parameter 

for this system. 

Design Procedure 

The information presented in this chapter allows one to 

design a venturi scrubber to meet a required "PT". The 

general method does not use Figures 7-13 and 7-14 .since they 

represent the specific case of an air-water system at 25°C. 

. If the conditions are close to those for these two figures 

then the procedure is simplified. 

The general procedure is as follows: 

1) Determine required cut diameters: First find the 

aerodynamic geometric mass mean diameter of the incoming 

dust at thc temperature expected in the venturi. Then, 

construct a plot of K vs d or r (required) by, 

pg pa J o 

a) Obtaining several K - B pairs using Figures 

7-4 to 7-6 (depending on o p ) . 

b) Knowing d , obtain d 50 for each of the K -

B pairs using Figure 7-7. 

146 
P.65 

5,000 

1,000 

a, o 

ax. 

r~m 

5 ioo 

cy 

—i 

10 

T 1 I I llll l T 1 1 1 IM I 

! I f M fl l t I M M 

o.i 1 .0 

AERODYNAMIC CUT DIAMETER, umA 

10 

Figure 7-11 Effect of gas velocity and liquid to gas flow 

rate ratio on performance cut diameter. 

147 
P.66 

10 

I o 

—II C3 

°- ' °: 1.0 

J I ID 

o Ic 

" 0.5 

05 

0 . 1 

T—n—I I IM M 

0.1 

J I MM M 

I I J ! J M J 

I I I llll l 

p50 

0.5 2 1.0 

=

 d p50 C ' p p uGt 

10 

9 yG d d 

Figur e 7-12. "B"' vs "K '' fo r venturi throa t of infinit e 

length .

 p M 

148 
P.67 

< 

£ 

P. 

Di 

UJ 

i — i 

Q 

E -

r> 

u 

u 

o 

o 

Oi 

UJ 

< 

1.0 

0.5 

0.1 

0.2 

Figure 7-13, 

0.6 1.0 3.0 

QL/QG, £/m3 

Predicted venturi performance, "d. 

QL/QG with "uG " and "AP" as parameter. 

pa5o 

6.0 

vs 

149 
5 . 0 T ! 1 »||l l ! ! « \ ! U H ! » U M U 

tn 

O 

< 

Qi 

H 

UJ 

< 

l-H 

Q 

CJ 

U 

>-

Q 

O 

CX. 

1.0 

0 . 5 

0 . 1 J I lllll l J_ J I I I I I M J I IM M 

1 .0 10 100 

PRESSURE DROP, cm W.C. 

1 ,000 

Figure 7-14 Aerodynamic cut diameter versus pressure drop with liquid to gas 

ratio as parameter. 
P.69 

2) Determine performance cut diameters: First determine viscosities, densities, and Nukiyama-Tanasawa coefficients for the 

venturi conditions. Then construct a number of performance 

curves corresponding to different QT / Qr ratios as follows: 

L Li 

a)1 Select a "u~ " Go 

b) Drop diameter, d,, from Nukiyama-Tanasawa relation 

(Table 3-2) 

c) NR from equation (5-7)(assuming u, =0) 

d) Cr, from equation (5-8) 

J

 Do 

e) Parameter B from equation (5-22) (assuming u, =0) 

f) K from Figure 7-12 

' P5 0

 b 

g) d from equation (7-9) 

bJ

 paso

 M K J

 • 

h) K from equation (7-13) 

' pg

 M K 

i) AP from equation (7-18) 

Repeat steps (a) through (i) for several velocities. Plot performance K vs d curves on the same plot as the requirement 

pg paso

 y ^ 

curve from Step (1). Plot AP vs d on a separate graph. 

3) Determine required pressure drops: The intersections of 

the requirement and performance curves determine the proper 

design points. The corresponding pressure drops required can then 

be found from the plot of AP vs d nr . The required pressure 

r pas o l r 

drops will correspond to a certain QT / Q~ ratios so.that the fan 

costs versus the water and pumping costs can be compared to allow 

selection of the optimum design. 

4) Determine throat cross-sectional area: Using the selected optimum combination of AP and Qi/Qp proceed as follows, 

a) From the design K solve equation 7-12a for u„ as 

a function of d ,. 

b) Substitute this equation for d, into the NukiyamaTanasawa relation and solve for u~ . 

c) Divide the volume flow rate by u~ to get the throat 

cross-sectional area. 

151 
P.70 

5) Determine throat length: Using the design velocity, 

perform steps (2a-d) and then, solve equation (5-47) for I 

based on the desired L (2 to 3). 

6) Determine convergence, divergence angles: These have 

little effect on particle collection but they do have some effects on pressure drop. Of the two, divergence angle is more 

important. Divergence angle should be designed such that, 

a) Boundary layer separation does not occur 

b) Momentum recovery occurs in the divergent section 

The general procedure would be facilitated by use of a programmable calculator or a digital computer. As a check, or if 

the conditions are close to those of an air-water system at 

25°C. Figures (7-11) and (7-14) can be used in an almost purely 

graphical procedure. 

The graphical procedure is as follows (air-water at 25°C), 

1) Determine required cut diameter: Same as general procedure . 

and equation (7-12a) to calculate the performance d „c„ vs 

n v j r

 pa s o 

2) Determine performance cut diameter: Use Figure 7-11 

quation (7-12a) to calculate th 

K curves for various QT/Q~ ratios. 

pg

 X L 'X G 

3) Determine required pressure drops: Same as general 

procedure except use Figure 7-14 to find required pressure drop 

Steps (4-8) same as general procedure. 

152 
P.71 

Venturi Design Example 

The problem of designing a venturi scrubber to control 

dust from a typical asphalt plant dryer is illustrated. 

The dust has a log-normal distribution of diameters 

described by a geometric standard deviation, o =5.0 and 

a geometric mass mean particle diameter, d = 18 um 

(physical). The particle density is 2.6 g/cm3. The flue gas 

flow rate is 567 Am3/min with a gas temperature of 116°C. 

The uncontrolled emission rate is 2,310 kg/hr. 

Based on a local Air Pollution Control District rule 

for the amount of weight processed, the emission should 

not exceed 25 kg/hr. The required efficiency is then: 

(2,310-25)/2,310 x 100 = 98.9%. Thus, the design should 

meet an efficiency requirement of 99%. 

Step 1. Specifying the required cut diameters: First, 

the aerodynamic geometric mean diameter must be found. 

For air at 116°C the Cunningham slip correction factor 

for 18 ym particles is C* = 1.013. Thus, 

d =1 8 (1.01.3 x 2.6)0-

5

 = 29.2 ymA 

pga 

Next, a plot of the required cut diameters (d 50 ) for an 

overall penetration of 0.01 is made by using Figures 7-5 

and 7-7. The points which are shown in Figure 7-15 as circles are listed below: 

B 

4.3 

2.8 

2.2 

1.6 

1.4 

K 

1,000 

1,500 

2,000 

5,000 

10,000 

d 

pas o 

ymA 0 

0 

0 

0 

0 

64 

58 

55 

41 

30 

Step 2. Specifying the performance cut diameters: 

First the flow parameters must be found. For air at 116°C 

and water at 25°C, 

153 
P.72 

10,000 

5,000 

a 

1,000 

500 

0.2 0.4 0.6 

dpaS0, ^mA 

0.8 1.0 1.2 

Figure 7-15 Impaction parameter vs aerodynamic cut 

diameter for a venturi design. 

154 
P.73 

Gas Viscosity, yG =_ 2.23 x 10 ^ g/cm-sec 

Gas density, p G = 0.907 kg/m3 

Gas kinematic viscosity, v„ = 0.246 cm2 /sec 

Liquid density, pT = 997 kg/m3 

so, 

PL 

— = 1,09 9 

P„ 

d^(cm) = J1L .- + 87 ( J*-) 

d

 u G o (cm/sec )

 0/ \ Q r

/ 

1.5 

and the Nukiyama and Tanasawa equation for drop size reduces 

to , 

Si 

*Go

 L,""l/ J'~y

-J \ Qr 

Other design equations to be used are, 

and 

u Go d d 

N R eo = —^ " (5-7) 

C °0 = °*22 + ^ U + °'15 N^o) (5"8) 

1

 Q L P L 

L Do W G P G 

K = 0.2087 + ^ 6 + M8 

ps 0 B B2 

0.5 * B < 5 

(Based on Figure 7-12) 

v»-(9>Cdd)"

 xl0< (PmA) (7"9) 

K pg

 = KP- fc,) 

AP » 8.24 x 10 '. u ... A ^ 

Solution of these equations for various ^L and

 u Go can be 

greatly facilitated by use of a programmable calculator. 

155 
P.74 

The solution to the design equations are plotted on Figure 

7-15 and 7-16 for Q,/Qr ratios of 0.001, 0.0015, and 0.002. 

L Li 

Step 3. Determine the required pressure drops: 

The intersections of the performance lines with the requirement line in Figure 7-15 determine the cut diameters (both 

required and performance). These cut diameters are represented on Fig. 7-16 as triangles. The required pressure 

drops corresponding to these cut diameters are then, 

^L

 dpaso AP 

Qr ymA cm I.C. 

0.001 0.42 67 

0.0015 0.57 40 

0.002 0.675 32 

Based on the flue-gas rate of 567 Am3/min these QT/Qr 

ratios represent water requirements of 0.57 m3/min (150 

gal/min) 0.87 m3/min (225 gal/min) and 1.13 m3/min (300 

gal/min), respectively. Based on pump and water costs 

versus fan costs the designer can select the optimum 

design. 

Step 4. Determine throat cross-sectional area. In 

order to carry out the calculation illustration we will 

assume that Q,/Qr = 0.002 and d^0.n = 0.675 ymA is the 

optimum. From Figure 7-15 the required K = 980. 

K 

Pg 

uGt 

d

 2 u,-. 

= P§

 G t = 980 

9 ^G dd 

9(980) (yG) (dd) 9(980) (2.25 x 10"1*)dd 

d

2 (29.2 x 10'1*)2 

pa

 v J 

= 2.3 x IO5 dd 

156 
100 

u 

u 

CL, 

< 

50 

10 

1.2 

Figure 7-16. Pressure drop vs aerodynamic cut diameter 

for venturi design example. 
P.76 

From the "Nukiyama-Tanasawa correlation for'the present example, 

(

Q V'5 

— 1 = — +' 7.7S x IP "3 

J

 UGt 

Sub stituting into the expression for

 ,:ur." we have 

ur. = 2.3 x 10 

Li t 

50 

L

uGt 

+ 7.78 x IO'3 

ur. = 5,300 cm/sec 

bt 

Throat cross - sectional area 

567 x IO6 

(60)(5300) 

Step 5. Determine throat length: 

1,783 cnr 

d, = -^ - + 7.78 x 10" 3= 0.0172 cm 

a

 5300 

M =

 UGt dd PG = (5300)(0.0172)(9.07 x 10~") = __n 

'^Re ' " .iT •*/u 

yG 2.23x10 

C D Q = 0.62 

Therefore, throat len gth - (i)(^mi)( 1 \ CL: 

\3/ \ 0.62 /\9.0 7 x IO"14 / 

= 20.3L cm 

If design L = 2, then throat length = 40.6 cm 

Suppose the gas temperature was 25°C, then the 

previously constructed performance curves (Figures 7-11 

and 7-13) could be used. 

158 
P.77 

Step (1) : 

At 25°C C = 1.009 for d = 18 ym so, d =18 

P pga 

(1.009 x 2.6)

 12

 = 29.2 ymA. Since this is the same d 

. Pga 

as before, the K - d requirement pairs are the ' pg paso

 n r 

same. 

Step (2): 

Using Figure 7-11 and the equation for K , Figure 

IT O 

7-17 is generated. The shaded triangles represent the 

design points where the performance and required K 's 

match. Thus the results, using Figure 7-14 are 

l/m3 

1.03 

1.1 

1.55 

1.85 

2.8 

d pas o 

ymA 

0.30 

0.41 

0.55 

0.58 

0.64 

AP 

cm W.C. 

140 

74 

44 

40 

44 

These results are close to what we obtained using the general procedure and a higher temperature gas. 

159 
P.78 

20,000 

10,000 -

5,000 -

P. 

2,000 

1,000 

500 X 

1 I 

A Design Points 

Gas Temperature = 25°C 

d„__ = 29.2 ymA 

1 2 

QL/QG, £/m; 

0.55 

0.58 

0.64 

Figure 7-17 Impaction parameter vs Q,/Qr for 

venturi design example. 

160 
P.79 

CHAPTER 8 

ENTRAINMENT SEPARATOR 

All scrubber systems include an entrainment separator, 

either as an integral part of the scrubber configuration 

or as a separate, clearly identifiable device. There are 

a number of devices which are commonly used as entrainment separators. Zigzag baffles, knitted mesh, packed beds, 

cyclone separators, and guide vanes causing rotation of the 

gas stream are frequently used for this purpose. Calvert 

et al (1975) had performed a detailed study of entrainment 

separators. The following is an abstract of their study. 

ENTRAINED LIQUID INFORMATION 

In order to design a proper entrainment separator, or 

to predict the collection efficiency of an entrainment separator, certain entrainment liquid information is needed. 

This includes: 

1. Entrainment drop and size distribution. 

2. Quantity or inlet loading. 

An extremely important factor in choosing and designing an entrainment separator is drop size distribution. 

Different entrainment separators are limited to certain 

drop diameters, below which their efficiency falls off 

sharply. The size of the drops depends upon the way they 

were formed. 

Entrainment rate and size distribution data for gas 

atomized spray scrubbers such as Venturis have not been 

reported. Estimates can be made, as discussed below, but 

they are very rough because of uncertainties in predicting 

the characteristics of the initial atomization and the drop 

separation occurring within the venturi diffuser and similar 

flow elements. 

161 
P.80 

Drop diameter can be predicted by means of the correlation by Nukiyama and Tanasawa (1938-40). For air 

and water at standard conditions thc N+T correlation for 

Sauter mean diameter is: 

ds(cm) =

 5fl-° + 92.0 | — | (8-1) 

u (cm/sec) 

where: d = Sauter (volume-surface) mean diameter of 

s 

drops, cm 

ur - air velocity relative to drops, cm/s 

Li ' 

Q,, = water flow rate, m/3 s 

Qr = air flow rate, m3/s 

Li 

According to Steinmeyer in Perry (1973), the Sauter 

mean diameter is typically 701 to 90% of the mass median 

diameter. If the drop size distribution is log normal, 

this implies that the geometric standard deviation, "a " 

is about 1.6 for 90% and 2.3 for 701. 

To illustrate the application of the above to the 

prediction of entrainment characteristics for a venturi 

scrubber, we can consider the case of a throat air velocity 

of 100 m/sec and water to air ratio of 1 £/m3(10 "3 m

3 / m3 ). 

The gas pressure drop would be about 80 cm W.C. and the 

Sauter mean diameter computed from equation (8-1) is 79 ym. 

From the typical ratios of mass median to Sauter diameter, 

we would expect the mass median drop diameter to range from 

88 to 113 ym, with "o " from 1.6 to 2.3, respectively. 

One would therefore predict that the cumulative entrainment concentration would be related to drop diameter within 

the range ol high and low values tabulated on the following 

page. 

162 
P.81 

Drop diameter, ym 4 5 10 15 20 

High concentration, 

cm3/m3 0.035 0.11 2 8 20 

Low concentration, 

cm3/m3 - - 0.0025 0.06 0.6 

If the entrainment contained 10% solids by weight, 

the residual particle concentrations after evaporation 

would be such that if one wanted to limit the particle 

loading due to entrainment to 0.01 g/m3(0.0044 gr/ft3) 

the separation of all entrainment larger than 5 ym diameter 

for the high estimate and 16 ym diameter for the low would 

be required. Since particle loadings of this magnitude can 

be significant for plume opacity, the example shows the 

efficiency with which entrainment must be. controlled and 

the necessity for good data on entrainment size distribution and concentration. 

DESIGN EQUATIONS FOR ENTRAINMENT SEPARATORS 

The design and operation of most entrainment separators are governed by three factors: 

1. Pressure drop 

2. Collection efficiency 

3. Reentrainment velocity and reentrainment rate 

Knowledge of the pressure drop through a separation 

system is important in calculating the energy loss incurred 

and in selecting the proper pumps and other auxiliary 

equipment to overcome that energy loss. 

Collection efficiency or overall collection efficiency 

is defined as the fractional collection of the droplets by 

the separator, i.e. 

, effluent concentration 

n = 1 -

influent concentration 

16 5 
P.82 

When the gas velocity in the entrainment separator 

is high, some separated droplets in the separator will be 

reentrained in the gas stream. Because of this reentrainment, the observed collection efficiency of the separator 

is less than the primary collection efficiency which is 

defined as the efficiency an entrainment separator would 

have if reentrainment were not present. 

Reentrainment velocity is the gas velocity at which 

drops are first observed to become reentrained in the gas. 

The onset of reentrainment will vary for different kinds 

of entrainment separators and different operating conditions. Reentrainment velocity determines the maximum allowable gas velocity in the separator. Reentrainment rate 

and drop size distribution are needed for the prediction 

of emissions from the system. 

Once design equations predicting the primary efficiency, pressure drop, and reentrainment are available; the 

operating characteristics of the entrainment separator 

can be established. 

Six different kinds of entrainment separators will 

be discussed in this section: cyclone, packed bed, zigzag 

baffles, tube bank, mesh, and sieve plate. 

Cyclone 

The cyclone is the most commonly used entrainment separa 

tor for venturi scrubbers. Commercially available cyclones 

in standard designs for entrainment separators have a maximum capacity of up to' 141 m3/sec (300,000 CFM) of gas. Efficiencies of about 95% are claimed for 5 ym diameter drops 

in a wel1-designed cyclone. Some manufacturers use a bundle of small cyclones (multicyc1 ones), which can efficiently 

collect drops as small as 2 ym in diameter. However, this 

arrangement reduces the capacity of thc device. 

164 
P.83 

Primary Efficiency - Leith and Licht (1971) derived an 

equation to predict primary collection efficiency in conical bottom cyclones as pictured in Figure 8-1. With slight 

modification it can be applied to cylindrical cyclones. 

The equation for predicting primary collection efficiency is : 

•

 2 i 1 

PA 

In Pt = 2 

2d , u t d tg 

9 p G 

(n+l)t 

2n + 2 

(8-2) 

where: 

n = 1 -

r 

T 

283 

*- -> 

• 3 

0.1 H 

,-0.393 dc) 

2.5 

(8-3) 

Pt 

"d 

u tg 

t 

penetration, fraction 

drop density, g/cm3 

gas viscosity, poise 

drop diameter, cm 

tangential velocity, cm/sec 

mean residence time of the gas in the cyclone, 

sec 

cyclone diameter, cm 

The mean residence time of the gas stream in the 

cyclone is: 

V 

Qr 

(8-4) 

wnere: 

V effective volume of the cyclone, cm3 

volumetric gas flow rate, cm3/sec 

= uGA 

165 
P.84 

Figure 8-1. Cyclone with tangential gas inlet 

66 
P.85 

inlet area, cm2 

u G = inlet gas velocity, cm/sec 

The effective volume of the cyclone, "V " is defined 

as the volume of the cyclone minus the volume occupied 

by the exit duct and exit gas core. The diameter of the 

exit gas core can be assumed equal to the diameter of 

the exit duct. Leith and Licht (1971) gave the following 

equations for the determination of effective volume of a 

conical bottom cyclone. 

V = V + 1/2 V, 

e i 2 (8-5) 

where 

V = annular shaped colume above exit duct inlet 

to mid-level of entrance duct 

\ (S - |) (d2 - d') 4

 v 2J K

 c e

J (8-6) 

V = volume of cyclone below exit duct inlet 

2 

to the natural length of the cyclone 

*

d c *(L+S-hs ) d^ / + d2 

— S . (h -S) + ^—L_|i+5 _

 + £_ 

4

 s 12 \ d,. d* 

\ c c 

^ d2 L 

e (8-7) 

wh ere: 

d = d -(d -b ) 

c c e ' 

S + L-h 

s 

h-h 

(8-8) 

and L = natural length of the cyclone 

167 
2 1/>/3 3 

2.3d. 

ab. 

(8-9) 

a, b, d , d , S, h, h are cyclone dimensions defined 

in Figure 8-1. 

Pressure Drop -Shcphard and Lapplc (1940) derived an equation 

for a cyclone with inlet vanes for pressure drop as a function 

of inlet gas velocity and the cyclone inlet and outlet 

dimensions: 

2 

AP = 0.000513 pr — 

G \ab> 

7.5 ab 

d

2

 t 

e 

(8-10) 

where : 

AP = pressure drop, cm W.C. 

PG = gas density, g/cm3 

Qr = gas volumetric flow rate, cm3/sec 

a = cyclone inlet height, cm 

b = cyclone inlet width, cm 

d = cyclone exit pipe diameter, cm 

Equation (8-1!)) can be modified by writing it as a function 

of the geometric average of the gas velocity at the cyclone 

inlet and outlet: 

AP - 0.000513pGv^ye (8-11) 

Shepard and Lapple also developed an equation for a cyclone 

without inlet vanes: 

2 

' fyA [16ab\ 

AP = 0.000 51 3 p. 

ah. d

2 

e 

(8-12) 

168 
P.87 

Packed Bed 

Packed beds of standard design with a capacity of 

up to 65 m3/sec (140,000 CFM) are available. They can 

remove drops as small as 3 ym in diameter at 80-90% 

efficiency. Superficial gas velocities range from 75 

to 240 cm/sec, and pressure drop is generally low, 0.05-

0.1 cm W.C. per cm of bed length. 

Cross flow beds are claimed to have high drainage 

efficiency and therefore are less prone to plugging. Upstream washing is recommended to avoid plugging if solids 

are present in the drops to be removed. 

Packing in different materials, shapes and sizes is 

available. Various rings are claimed to have high collection efficiency and low pressure drop. 

Packed beds are often used for mass transfer because 

of theix high interfacial area. Thus they are sometimes 

employed when simultaneous mass transfer and entrainment 

separation are desired. 

Primary Efficiency - Jackson and Calvert (1966) and Calvert 

(1968) have developed a theoretical relationship between 

particle collection efficiency and packed bed operating 

parameters: 

Pt = 1 exp . 2 2(j+r) (e-H,) 

i-K (8-13) 

d

 dd UG 

9 ^G dc 

wnerc: 

'd 

r 

A 

ratio of channel width to packing diameter 

fractional liquid hold-up in the bed 

bed porosity , fraction (Table 8-1) 

bed length, cm 

169 
d, = packing diameter, cm 

ur = superficial gas velocity, cm/sec 

d, = drop diameter, cm 

The experimental data of Jackson (1964) were analyzed 

to determine appropriate values of "j " to use in equation 

(8-13) with all quantities in the equation known except "j" , 

which was calculated. The results are given in Table 8-2 

which lists "j " values for various types and sizes of packing material. For the manufactured packing materials, "j " 

i.s fairly constant at about 0.16-0.19. The very low value 

of 0.03 for coke may be due to the small passages within 

the coke itself, which make each large piece of coke function effectively as a number of smaller pieces. 

Pressure Drop - Perry (1963) gives a generalized pressure 

drop and flooding correlation plot which appears as Figure 

p2pm 0.2 

8-2, where a dimensional group of function [_L , 

PGPLg 

0 2 

(centipoise) , is plotted against a dimensionless group 

L /PG\^2 

of function — j — 1 , where "G" and "L" refer to the gas 

G \P L/ 

and liquid mass fluxes respectively. "V" is the ratio 

of water density to entrained- liquid density. Values for 

the packing factor, "F", for dumped pieces, stacked pieces 

and grids are given in Tables 8-3 and 8-4. If "F" is not 

known, —3 may be used instead. 

Tube Bank 

Tube banks made of streamlined struts have been used 

as entrainment separators but no experience with round 

tubes has been reported. Particle collection efficiency 

and pressure drop for round tube banks have been studied 

and the characteristics appeared promising for entrainment 

separation application. i 

170 
P.89 

TABLE 8-1 

BED POROSITY, e, FOR VARIOUS PACKING MATERIALS 

Name 

Size 

(cm) 

1.27 

1.9 

2.54 

5.8 

5.1 

Stoneware 

Raschig 

Rings 

0.57* 

0.67 

0.68 

0.68 

0.75 

Carbon 

Raschig 

Rings 

0.71* 

0.75 

0.67 

_ _ 

Steel 

Raschig 

Rings 

(1/16" 

thick) 

0.92 

0.92 

Stoneware 

Berl 

Saddles 

0.65 

0.69 

0.70 

- -

Stoneware 

Intalox 

Saddles 

0.70 

0.81 

Steel 

Pall 

Rings 

0.93 

0.94 

*Treyball (1955) All other data from Perry (1963) 

TABLE 8-2 

EXPERIMENTAL VALUES OF 

j, CHANNEL WIDTH AS FRACTION OF PACKING DIAMETER 

Size (cm) 

1 2 7 

2. 54 

5.8 

7.6 - 12.7 

Type of Packing ' 

Berl Saddles, marbles, Raschig Rings, 

Intalox Saddles 

Berl Saddles, Raschig Rings, 

Pall Rings 

Berl Saddles, Raschig Rings 

Pall Rings 

Coke 

3 

0.192 

0.190 

0.165 

0.03 

Adapted from Jackson (1964) and Calvert (1968) 

171. 
P.90 

Tabic f-5. PACKING FACTORS, "F" , FOR DUMPED PIECES (m2/m3'l 

Rasch ig r inj;s , 

ceramic 

. ld cm wall 

. 5 2 cm wal 1 

. 6 5 cm wal 1 

.95 cm wall 

Rasch i g r i ngs , 

carbon 

.16 cm wall 

.52 cm wall 

.65 cm wall 

.7 9 cm wall 

Raschig rings, 

metal 

.OS cm wal1 

.16 cm wal.1 

Less ing rings , 

porcelain 

.52 cm wall 

.65 cm wall 

Lessing rings, 

metal 

.08 cm wall 

.16 cm wall 

[0.64 J 

5,250 

5,250 

2,300 

Nominal size of 

[0.95J [1.27] [1.59J 

3,2 80 

1,540 

1,280 980 560 

1,34 0 9 50 

(1,060) 

packing, cm 

[1.9] (2.5) 

5 I 0 

920 525 

510 580 

720 450 

(800) 

(630) 

(472) 

I-.2] 

360 

(587) 

[3.8) 

-150 

4 30 

272 

(295) 

[5] 

210 

210 

1S7 

(3601 

(200) 

[8] 

121 

U S 

105 

[10] 

98 

Table 6-3. PACKING FACTORS, "F", FOR DUMPED PIECES (m2/m3) (continued) 

Nominal size of packing, cm 

[0.64] [0.95] [1.27] [1.59] [1.9] [2.5] [3.2] [3.8] [5] [S] [10] 

Part it ion ri ngs 

Pall rings, 

plastic 

Pall rings, 

metal 

Berl saddles 2,950 

51( 

230 

790 

171 

158 

560 360 

475 522 

10S 

200 

intalox saddles, 2,380 1,080 660 

ceram i c 

intalox saddles, 

plast i . 

Super-i ntalox, 

ceramic 

Tellerettes 

?ntheses denote a value of a / c 3 , rather than empirical )'•. 

10 5 8 2 

9 2 66 

213 148 

171 131 

69 

100 

130 

262 190 

172 
P.91 

able 8-4. PACKING FACTORS,"F" FOR GRIDS AND STACKED PIECES 

(m2/m3). 

Nominal size of packing, cm 

2.5 3 10 13 14 15 

Wood grid 

Metal grid 

Grid tiles 

Checker brick, 

£=0.55 

Raschig rings, 

ceramic 

.63 cm wall 

.95 cm wall 

Raschig rings, 

metal 

Partition rings, 

diameter 

7.6 cm length 

10.2 cm length 

15.2 cm length 

Partition rings, 

square set 

7.6 cm length 

10.2 cm length 

15.2 cm length 

20 

8.2 

11 8.2 

95 

5.9 

16 

36 

21 

(1,200) 

(690) 

4.9 

12.8 

(725) 

(705) 

(460) 

(450) 

118 

135 

(410) 

(375) 

(275) 

(260) 

Parentheses denote a value of a/c:3, rather than empirical r . 

173 
P.92 

OH 

<D 

o 

tu 

o 

bo 

- 3 

Q. 

0.5 

0.2 

0 . 1 

0.0 5 

0.0 2 

1

 0.0 1 

0.005 

0 .002 

0.001 

0.0 1 0.02 

L 

x = — 

G 

IPrA V

2 

\

p

L / 

(dimensionless) 

Figure 8-2 Generalized flooding and pressure drop 

correlation for packed beds (Perry, J965) 

174 
P.93 

Primary Efficiency - Calvert and Lundgren (1970) found that 

the collection efficiency for closely packed rods is given 

by the equation for rectangular jet impaction. The collection efficiency of each stage of impaction can be found in 

Figure 8-3. Each rav: of tubes except the first represents 

one stage of impaction. "6" is used as a parameter in 

Figure 8-3 and is defined by: 

2 £/b (8-14) 

where : 

b = jet orifice width 

I = distance between orifice and impingement plane 

"K ", the inertia parameter, is defined with drop radius, 

"r ", rather than diameter. 

P 

Efficiency for the bank of tubes is given by: 

E = 1 (1-Oj) N (8-15) 

where 

r . 

' ] 

N 

collection efficiency for a given particle 

diameter in one stage of rectangular jet impingement 

number of stages in the tube bank 

(number of rows) -1 

If the tubes are widely spaced, the target efficiency, 

"'"", can be calculated from Figure 8-4. In this case the 

efficiency for the entire tube bank is: 

l - d-n^) n (8-16) 

175 
P.94 

1.0 

< 

IS 

>r 

U 

z 

^0.5 

tu 

O 

I—I 

H 

U 

(JJ 

-J 

o 

u 

(K ) 

P 

0 

0.5 

2p C u *p o 

1.0 

V* 

9 y 

1 .5 

G 2 

Figure 8-3 - Theoretical and experimental 

collection efficiencies of 

rectangular aerosol jets. 

176 
P.95 

U 

UJ 

tU 

—c Rectangular half body 

_ _ (ribbon with wake) 

Probable curve for 

recessed trap 

o.i 10 100 

C p , d\ u 

INERTIAL PARAMETER, K = S—3—G_ 

P 9p G dc 

Figure 8-4 _ Theoretical impaction efficiency as 

a function of inertial parameter 

for different targets. 

17 
where: 

a' = cross-sectional area of all the tubes in one row 

A = total flow area 

n = number of rows 

Pressure Drop - Pressure drop for gas flow normal to banks 

of round tubes can be predicted by means of Grimison's correlations (Perry, 1973). As an approximation, Lapple (Perry, 

1973) suggests that 0.72 velocity heads are lost per row of 

tubes in arrangements of the kind commonly used in heat exchangers. Calvert and Lundgren (1970) found that for closely 

spaced tube banks Lapple's approximation agreed satisfactorily 

with experimentally determined pressure drops. 

Houghton and Radford (1939) studied streamline strut 

banks and found that for a center-to-center spacing of 2 

strut widths (i.e. open space = strut width) the pressure 

drop was about 0.16 velocity heads per row. This can be 

expressed as: 

AP = 0.16 N pG (5.3 x IO--*) (u£)2 cm W.C. (8-16 a) 

where: 

ui is the actual gas velocity 

Mesh 

Knitted mesh of varying density and voidage is widely 

used for entrainment separators. There are basically three 

different kinds of mesh: (1) Layers with crimp in the same 

direction - each layer is actually a nested double layer. 

(2) Layers with crimp in alternate directions - this results 

in an increase in voidage, reduced sheltering, a decrease 

in pressure drop per unit length and an increase in target 

efficiency per layer. (3) Spirally wound layers - the pres178 
P.97 

sure drop is lower by about 2/3 than in layers with crimp 

in the same direction, but the creeping of fluids, which 

contributes to reentrainment, is expected to be higher. 

Standard mesh 10-15 cm thick having a density of 

about 0.15 g/cm3 is used to remove drops larger than 5 ym 

in diameter. Gas velocities range from 0.3 to 5 m/sec and 

liquid flow rate is limited by the drainage capacity of the 

mesh to 2.5 x 10 "3 g/sec cm2 of mesh. A lower density mesh 

made of standard wires is used when 10-20% higher fiow rates 

are desired. 

Often two mesh type separators in series are used to 

remove drops in the 1-5 ym diameter range. The first inesh, 

normally made of fine wires, coalesces the small drops, and 

the second mesh, made of standard wires, removes them. The 

first mesh is operated beyond the flooding velocity and the 

second under flooding velocity. A major disadvantage with 

this arrangement is a pressure drop which may reach 25 cm 

W.C. 

Some manufacturers use two or three stages of mesh, 

the first being coarser and the final being finer, to remove 

large and small drops successively. 

A mesh type separator has the advantage that it can 

be made to fit vessels of any shape. Any materials which 

can be drawn into the shape of a wire can be used for fabrication. However, mesh separators are limited in application because they plug easily. This can be avoided by 

upstream washing, which will decrease removal efficiency and 

increase pressure drop. 

Primary Efficiency-Bradic and Dickson (1969) present the following expression for primary efficiency in mesh separators: 

179 
C = 3-exp ( - | ^ a2£2 n) (8-17) 

where: 

a2 = specific area of mesh, surface area of wires 

per unit volume of mesh pad, cm2/cm3 

l y

 = thickness of mesh pad in the direction of gas flow, 

cm 

n = collection efficiency of cylindrical wire 

The collection efficiency of cylindrical wire "n" 

can be obtained from Figure 8-4. The factor of 2/3 in the 

exponential was introduced by Carpenter and Othmer (1955) 

to correct for the fact that all the wires in the knitted 

mesh are not perpendicular to the flow. That factor is 

the ratio of the projected area of wires perpendicular 

to the flow to the cross-sectional area of wires along 

the wire length. 

4(l-e) 

a2 = - r — (8-18) 

c 

Pressure Drop - York and Poppele (1963) have suggested 

that the total pressure drop in the knitted mesh is the 

sum of the pressure drop in the dry knitted mesh and the 

pressure drop due to the presence of liquid: 

AP = APd ry + APL (8-19) 

where : 

AP, - pressure drop in absence of liquid, cm W.C. 

AP, = pressure drop due to presence of liquid, 

cm W.C. 

York and Poppele considered the mesh to be equivalent 

to numerous small circular channels and used the D'Arcy 

formula for pressure drop in a pipe to correlate the dry 

I 

180 
P.99 

pressure drop through the mesh. York and Poppele's data 

for knitted mesh with crimps in alternated and in same 

direction are plotted in Figure 8-5. Their data are close 

to those obtained by Stasangee (1948) and Shuring (1946). 

Similar curves obtained by Bradie and Dickson (1969) for 

spiral-wound and layered mesh are also plotted in Figure 

8-5. Figure 8-5 should be used in determining dry pressure 

drop, which is calculated from the expression: 

AP 

f £2 a2 pG u^ 

dry 

(8-20) 

The unit of "AP, " is in dynes/cm2. It can be converted 

to cm W.C. by dividing it by 981. 

Pressure drop data due to presence of liquid are not 

available for all operating conditions or for mesh of different styles. Values of "APT" obtained by York and Poppele 

are presented in Figures 8-6 and 8-7, with liquid velocity 

as the parameter. Liquid velocity is defined as where 

"X 

"L" is the volumetric flow rate of liquid and "A" is the 

cross-sectional of the mesh in liquid flow direction. The 

specifications of the knitted mesh used are shown in the two 

figures. 

Maximum Allowable Gas Velocity - Several factors govern 

•the allowable gas velocity through wire mesh for a given 

set of conditions: 

1. pT and p r 

L in 

2 . Liquid viscosity 

5. Specific surface 

4. Liquid entrainment loading 

5. Suspended solid content 

Application of the Souders- Brown equation for the 

calculation of allowable vapor velocity for wire mesh mist 

eliminator based on gas and liquid densities has been 

suggested by York (1954). 

18.1 
P.100 

1 .0 

0.5 

0 . 1 

0.0 5 

0.0 1 

f I I I I'MI 

Satsangee data (1948) 

Spiral-wound mesh 

1 IIIIIII I 

10 100 

1 i i i i i" f 

1,000 10,000 

N Re,G PG uG/a2 yG 

Figure 8-5. Friction Factor, f, versus Reynolds 

number, NR r for wire mesh entrainment 

separator ' with entrainment load. 

182 
P.1 

rm—r 111 i 

HIIII I I lll l I I • I • l m lll l 

•3* M UID

 <q d V 

(•0 

K*) 

O 

o 

SH 

0) 

c x: +-> 

O -r-l +-» t- l 

-a s 

QJ - H QJ 

3 3 X. JC 

-3 O* tn +-< 

•rH QJ 

O ~ - H 

a> 

oo 

vO 

^ 

C3 

Q. 

i 

J 

Q. 

*—-* \ 

O 

a 

n3 

<D 

SH 

3 

i/i 

IT; 

QJ 

SH 

DO QJ U. 

•*-> CH 

0> -P E 

U -i-l -H 

C C SH 

OJ M 'J 

Ifl 

QJ Oi QJ 

U JZ mC 

a,+-> +J 

( j 

<D 

SH 

• H 

T3 

D 

•P 

(Tt 

c 

o 

3 

00 

QO 

•r-l 

U H 

r M I I 11111 M i i (IIIM I 

-

' • 

hO 

O l 

CO 

\0 

LO 

to 

E 

•J 

<^ 

a 

c; 

c HC E 

O - H -M « 

+J - H 10 

TJ S 

QJ - H QJ 

3 3 -C X 

t j a - i/i 4J 

• H QJ 

•cur-t E G 

O -H 

h*+IT I 

T) O ID Ifl 

a 

QJ QJ +-> E o 

3 

t/> QJ J 4 ' J 

tr, t/) 

QJ QJ Q) O 

4-> -a 

J -f. 

3-.M mn

 4l j v 

oo 

183 
P.2 

ur =30.5 a-l G max :> 

0-5 

(8-21) 

where "a " varies with operating conditions and mesh design. For most cases, a- = 0.35. 

Zigzag Baffles 

Baffles can efficiently separate drops greater than 

10 ym in diameter, while some of the better designed devices can separate drop diameters of 5-8 ym. Common gas 

velocities are 2.0-3.5 m/sec, and the pressure drop for 

a 6-pass separator is about 2-2.5 cm W.C. 

The most common baffle shape is zigzag with 3 to 6 

passes. These can be fabricated from a continuous wavy 

plate or each pass is separated, in which case the separation distance is normally smaller than the width of the 

baffles. Cross-flow baffles are claimed to have higher 

drainage capacity than countercurrent flow baffles. 

Primary Collection Efficiency - A model to predict primary 

efficiency was developed, based on turbulent mixing. The 

primary collection efficiency of a continuous zigzag baffle section is: 

n = l exp 

u. nw8 tc 

57.3 ur b tan( 

(8-22) 

where 

tc 

4G 

n 

primary collection efficiency, fraction 

drop terminal centrifugal velocity, in the 

normal direction, cm/sec 

superficial gas velocity, cm/sec 

number of bends or rows 

angle of inclination of the baffle to the flow 

path, degrees 

184 
P.3 

w = width of baffle, cm 

b = spacing between two consecutive baffles in 

same row, cm 

The drop terminal centrifugal velocity can be determined by performing a force balance on the drop. The result 

is : 

0.5 

tc 

4

 d dP da 

3 C D P G 

(8-23) 

where 

dd = 

pd = 

a = 

CD = 

drop diameter, cm 

drop density, g/cm3 

acceleration due to centrifugal force, cm/sec2 

drag coefficient 

gas density, g/cm3 

If the drop Reynolds number is low (N„ n < 0.1), 

Ke, u 

Stokes' law applies. For this condition, the drag coefficient is given by: 

C 24 

D N 

(8-24) 

Re,D 

;here NR ~ = drop Reynolds number 

dd utc PG 

By combining equations 8-23 and 8-24, we obtain: 

u tc 

'd

 pd a 

18 yr 

(8-25) 

185 
P.4 

The acceleration due to centrifugal force is defined by 

the following equation: 

t

 2 2 

2 (ur) 2 ur sin 6 

a = G _ = G (g_2 6) 

w cot 0 w cos3 9 

where: 

ul = actual velocity between baffles, cm/sec 

Up = superficial gas velocity, cm/sec 

If NR y. >0.1, another appropriate drag coefficient 

should be used in equation 8-23. Foust, et al. (1959) 

gave a plot of drag coefficient as a function of Reynolds 

number in Figure 8-8, which can be used to determine "u ". 

The effect of surrounding drops on the motion of any individual drop is neglected. 

Pressure Drop-Determination of the pressure drop is based on 

the drag coefficient,

 ;'fn", for a single plate held at an 

angle "8" to the flow as presented in Figure 8-9 (Fage 

and Johanson, 1927). Neglecting the effect of neighboring plates, pressure drop may be expressed as: 

n up A 

AP = E 1.02 x 10"3 fn p r — -AS- (8-27) 

1 U \3 J A. 1 = 1 L t 

where: 

Z\P = pressure drop, cm W.C. 

A = total projected area of baffles per- row in the 

direction of inlet air flow, cm? 

A = duct cross - sectional area, cm2 

The summation is made over the number of rows of 

baffles . 

186 
P.5 

I d ,0.'.)') 

1 ,'•")') 

Q 

CJ 

fci 

O 

i— 

fc, 

fci 

O 

a; 

ion 

10 -

-

_ 

-

-

-

-

-

V M > 1 1 IIII I 1 1 1 

^V^S V 

N/^SivX 

^\^$N^v 

\^>^> ^ 

N^$>^r """ 

X. ^SNs^^',N,,,,N,,,,,,,,,»-^_ 

^ \ . ^ „^^

 _ 

\sJ

N

\^-~ 

^ v ^^"^--^ ^ -_ 

: = 0 . 1 J .-» 

.- o . 7.' o 

= n. min 

• =0 . SOc, 

_ = \ . ooo 

-

-

_ 

-

-

-

" 

. 

0 . 1 

O.O'l l o.O l 1 M 1 0 0 100 0 | 0 (iiiii 10 

Revn o Ids 'iii:**Scr Re ,M 

<! .1 1 d tc (, 

figur e B'8- Drag coefficien t versu s Revnold s nirr.lter afte r 

Fcns t et al (1959) , uit h sphericit y C* as 

t he parameter . 

i r T r 

0 .8 

Plate I nc 1 ined to ]-" 1 ou 

J I J I 

Angle of 

1 11 c. i d c i i c c 

4 0 SO 

AN (7 Li. 01 INCIDLNC!:, degree s 

;u.re 8 ' *"'.

 !)rag •coefficients for flou past inclined 

flat plate s (data from A. Page j P . 7. . 

Johanseii, (1927 ) . 

187 
P.6 

The actual gas velocity, "Up", in the baffle section 

should be used in Equation (8-27). The actual gas velocity 

is related to superficial velocity by: 

u^ = uG/cos 6 (8-28) 

Note that the angle of incidence for the second and subsequent rows of baffles will be twice the angle of incidence for the baffles in the first row. 

Tray Towers 

Tray towers are vertical channels in which the 

liquid and gas are contacted in stepwise fashion on 

trays or plates. The liquid enters at the top and flows 

downward by gravity. On the way, it flows across each 

tray and through a downspout to the tray below. The gas 

passes through openings in the tray, then bubbles through 

the liquid to form a froth, disengages from the froth, 

and passes onto the next tray above. There are various 

tray geometries. The sieve tray and bubble cap are the 

two most common types. 

Sieve Plates - Primary efficiency - Taheri and Calvert 

(1968) derived an equation for sieve plate primary collection efficiency: 

E = 1-exp (-40 F2 Kp) (8-29) 

where 0.30 < F£ < 0.65, 

k" = -AA± (8-30) 

9^Gdh 

where: 

¥r = foam density, ratio of clear liquid height 

to total foam height 

v, = velocity of gas through hole, cm/sec 

188 
P.7 

d, = hole diameter, cm 

Pressure Drop - Perry (1963) has suggested that the 

pressure drop in sieve plates can be calculated according to : 

AP = h+ h + h, + h 

w ow dp r (8-31) 

where : 

h 

w 

weir height. = 4-9 cm, assume 5 cm, if unknown 

QT 

ow = head ove r th e weir = 0.143 F 

w w. 

1

 PG Vh 

ldP 

dry plate head loss = — — -~ 

c

2 pL 2 

= residual pressure drop = 0.013 water 

— = 1.14 0.4 (1.25 - fh) + (1 - f h )

2 (8-32) 

where: 

F 

w 

Q L 

wcolumn wall curvature correction factor = 1.1 

liquid flow rate, here in m3/hr 

weir length, m 

fraction of the perforated open area in the 

plate 

Rubble-cap Trays - Equations used to predict primary collection efficiency and pressure drop of sieve plates can 

also be applied to bubble-cap trays. 

DESIGN PROCEDURES 

The general steps in designing an entrainment separator are as follows: 

189 
P.8 

1. Based on process condition and separator configuration, construct the grade efficiency 

curve for the separation. Equations for primary efficiency can be used for this purpose. 

In case the gas velocity is higher than the 

reentrainment onset velocity, reentrainment 

should be subtracted from the primary efficiency . 

2. Compute the collection efficiency for tlie whole 

population of the drops. This can be done eith.er 

graphically or mathematically. For graphical 

solution, plot Pt. versus fraction smaller than 

d, • (where Pt• is penetration for drop size d , •) . di 1 * J di-' 

The area under the curve is the overall penetration. Outlet loading is equal to inlet 

loading times overall penetration. 

3. Compute expected pressure drop. 

In the process of designing an entrainment separator, 

the steps should be repeated for different proposed separator configurations. The final configuration can then 

be selected after optimization analysis. 

190 
P.9 

REFERENCES 

Akselrud, G., Zh. Fiz. Khim. 2]_, 1445, 1953. 

Behie, S.W. and J.M. Beeckmans. "On the Efficiency of 

a Venturi Scrubber", Canadian Journal of Chemical 

Engineering, _51, 430, 1973. 

Boll, R.H., "Particle Collection and.Pressure Drop in 

Venturi Scrubber", Ind. Eng. Chem. Fundam. Vol. 12, 

No. 1, pp 40-50, 1973 

Boll, R.H., L.R. Flais, P.W. Maurer, and W.L. Thompson, 

"Mean Drop Size in A Full Scale Venturi Scrubber via 

Transmissometer", EPA-A.P.T. Fine Particle Scrubber 

Symposium, San Diego, May 28-30, 1974. 

Bradie, J.K. and A.N. Dickson. Removal of Entrained 

Liquid Droplets by Wire Mesh Demisters. Paper 24 in 

Fluid Mechanics and Measurements in Two-Phase Flow Systems 

(A joint symposium of the Inst, of Mech. Engr. and the 

Yorkshire Branch of the Inst, of Chem. Engr.) 24-25, 

London= September 1969. 

Brink, J.A. and C.E. Contant, "Experiments on an Industrial Venturi Scrubber", Ind. Eng. Chem. 50., 1157, 1958. 

Calvert, S. "Source Control by Liquid Scrubbing" 

Chapter 46 in Air Pollution, Arthur Stern ed., 1968. 

Calvert, S. "Venturi and Ohter Atomizing Scrubbers 

Efficiency and Pressure Drop" A.I.Ch.E. Journal, Vol. 16, 

No. 3, pp 392-396, 1970. 

Calvert, S. Engineering Design of Fine Particle Scrubbers 

APCA Journal, 2£, 929-934, 1974. 

Calvert, S., J.Goldshmid, D. Leith, and D. Mehta "Scrubber Handbook". A.P.T., Inc. Riverside, California. 

NTIS No. PB-213-016. August 1972. 

Calvert, S. and D. Lundgren. Particle Collection in 

Closed PacYed Arrays. Presented at AIHA. 1970. 

Calvert, S., N.C. Jhaveri, and S. Yung, "Fine Particle 

Scrubber Performance Tests" EPA-650/2-74-093, NTIS 

No. PB-240-325. 

Calvert, S., S. Yung, and J. Leung, "Entrainment Separator 

for Scrubbers - Final Report", EPA-650/2-74-1196, NTIS 

No. PB-248-050. 

191 
P.10 

Carpenter, CL. and D.F. Othmer. Investigation of Wire 

Mesh as an Entrainment Separator. AIChE Journal, p 549, 

1955. 

Crowe, C.T., Ph.D. thesis, University of Michigan, 

Ann Arbor, Michigan, 1961. 

Dickinson, D.R. and W.R. Marshall, AIChE Journal, L4, 

541-552, 1968. 

Dropp, L.T. and A.J. Akbrut, "Working Processes and 

Calculation of the Efficiency of an Ash Trap with a Venturi Tube", Tepoloenergetika, No. 7, 63-68, 1972. 

Ekman, F.O. and H.F. Johnstone, "Collection of Aerosols 

in a Venturi Scrubber" Ind. Engr. Chem. Vol. 43, No. 6, 

pp 1358-1363, 1951. 

Fuchs, N.A. The Mechanics of Aerosols. The Macmillan 

Company. 1964. 

Garner, F. and R. Suckling, AIChE Journal, 4_, 114, 1958. 

Garner, F. and R. Keey, Chem. Eng. Sci., 9., 119, 1958. 

Gieseki, J.A., Ph.D. Dissertation, University of Washington, Seattle, Washington, 1963. 

Gleason, R.J. and J.D. McKenna, paper presented at the 

69th National Meeting of AIChE, Cincinnati, Ohio, 1971. 

Final report of Pilot Scale Investigation of a Venturitype Contactor for Removal of S02 by the Limestone Wetscrubbing Process, Cottrell Environmental Systems, Inc., 

1971. 

Gretzinger, J. and W.R. Marshall, Jr., AIChE Journal, 1 

312, 1961. 

Guntheroth, H., Fortschr. Ber. VDI Z. Ser. 3 No. 13, 1966 

Heme, H. Internal Journal of Air Pollution, Vol. 3, 

No. 1-3, 26-34, 1960. 

Hesketh, J.E. "Atomization and Cloud Behavior in Wet 

Scrubbers", US-USSR Symposium on Control of Fine 

Particulate Emission, Jan. 15-18, 1974. 

Hesketh, J.E., A.J. Engel, and S. Calvert, "Atomization 

A New Type for Better Gas Scrubbing", Atmospheric 

Environment, Vol. 4, pp 639-650, 1970. 

192 
P.11 

Hidy, G.M. and J.R. Brock, "The Dynamics of Aerocolloidal 

Systems", Pergamon Press, New York, 1970. 

Hollands, K.G.T. and K.C. Goel, "A General Method for 

Predicting Pressure Loss in Venturi Scrubber", Ind. 

Eng. Chem. Fundam. 14-, pp 16-22, 1975 

Houghton, J.G. and W.H. Radford. Trans. A. Inst, of ChE, 

35., 427, 1939 

Hughes, R.R., Chem. Engr. Prog. 4_8, 497, 1952. 

Ingebo, R.D. NACA TN3762, September, 1955. 

Jackson, S. and S. Calvert. AIChE Journal, 12, 1075, 

1966.

 — 

Johnstone, H.F. and M.H. Roberts, Ind. Eng. Chem., 41, 

2417, 1949. 

Kim, D.Y. and W.R. Marshall, Jr., AIChE Journal, 1]_, 

575, 1971. 

Langmuir, I. and K.B. Blodgett, Army Air Forces Technical 

Report 5418, 1946. 

Leith, D. and W. Licht. The Collection Efficiency of 

Cyclone Type Particle Collectors - A New Theoretical 

Approach. Paper presented at San Francisco meeting of 

AIChE. December 1971. 

Levich, V., "Physiochemical Hydrodynamics", PrenticeHall, Englewood Cliffs, New Jersey, 1962. 

Matrozov, V.I., 0. Soobscheniya, Nauchno-Tekhnicheskikh 

Rabotakh NIVIF, Nos. 6/7, 152, 1953. 

Morishima, N., T. Yoshida "Dust Collection on Atomized 

Droplets Calculation of Collection Efficiency with Consideration given to Droplet Size Distribution" Kagaku 

Kogaku, pp 1114-1119, 1967. 

Morishima, N., T. Yoshida, Y. Kosoka, and Y. Nonaka 

"An Examination of Venturi Scrubber Design" Funtai 

Kogaku Kenkyu Kaishi (J. Res. Assoc. Powder Technol.) 

Vol. 9, No. 6, pp 357-362, 1972. 

Mugele, R.A., AIChE Journal, 6_, 3, 1960. 

Nukiyama, S. and Y. Tanasawa, Trans. Soc. Mech. Engrs. 

(Japan), 4 (14), 86, 1938; 4 (15), 138, 1938; 5. (18), 

68, 1939; 6 (22), II-7, 1940. 

193 
P.12 

Perry, J.H. Chemical Engineering Handbook. 4th Edition. 

McGraw-Hill. New York. 1963 

Perry, J.H. Chemical Engineering Handbook. 5th Edition. 

McGraw-Hill. New York. 1963. 

Satsangee, P.D. Master's Thesis. Polytechnic Institute 

of Brooklyn, 1948. 

Schurig, W.F. D.Ch.E. Dissertation. Polytechnic 

Institute of Brooklyn. 1946. 

Shepherd, CB. and C.E. Lapple. IEC Chem. 31, 1246, 1940. 

Taheri, M. and CM. Sheih, AIChE Journal, 12, 153-157, 

1975. 

Tohata, H., T. Nakoda, and I. Sekiguchi, "Pressure Losses 

on Venturi-Mixers", Kagaku Kogaku, ^_8, 64, 1964. 

Torobin, L.B., W.H. Gauvin, Canad. J. of Chem. Eng. 38, 

142, 1960. 

Volgiii, B.P., T.F. Efimova, and M.S.Gofman, Int'l. Chem. 

Eng., £, 113, 1968. 

Walton, W.H. and A. Woolcock, in "Aerodynamic Capture of 

Particles", ed. E.G. Richardson, Pergamon Press, Oxford, 

129-153, 1960. 

Wen, CY. and S. Uchida, "Simulation of S02 Absorption 

in a Venturi Scrubber by Alkaline Solution", Proceedings 

of Second International Lime/Limestone Wet-Scrubbing 

Symposium, New Orleans, Louisiana, 1972. 

Yamauchi, J., T. Wada, and H. Kamei, "Pressure Drop Across 

the Venturi Scrubbers, "Kagaku Kogaku, 2_7, 974, 1963. 

York, O.H. Performance of Wire Mesh Demisters. Chem. 

Engr. Prog. Vol. 50, No. 8, 421, 1954. 

York, O.H. and E.W. Poppelle. CEP. 59^, 45, 1963 

Yoshida, T., N. Morishima, and M. Hayashi, "Pressure Loss 

in Gas Flow Through Venturi Tubes", Kagaku Kogaku, 2_4, 20-27 

20-27, 1960. 

Yoshida, T., N. Morishima, M. Suzuki, and N. Hukutome, " 

"Pressure Loss for the Acceleration of Atomized Droplets", 

Kagaku Kogaku, 29_, 308-315, 1965 

194 
P.13 

APPENDIX A. DERIVATION OF SCALING FACTOR 

In solvin g equatio n 5-23 we assumed u*$ = 0. In orde r 

do 

to find Pt(d ) for other values of ul , we make use of the 

p do 

following artifice. Imagine the given duct to be projected 

in the upstream direction until a distance 1„ is reached 

such that at z = -1H , the liquid velocity is zero. That is, 

the distance 1„ is that length of a hypothetical duct having 

zero initial liquid velocity with established liquid velocity 

u, at its exit. In this Appendix, we will distinguish 

quantities referring to the hypothetical duct from those 

referring to the given duct by using a prime (') with the 

former. Then from the geometry of the duct, we get 

r' = r - L tan B 

o o H 

and ' A1 = A 1 

o o \ 

1H tan B \ j 

(A-l) 

(A-2) 

From continuity of gas flow, we have 

= uGo l1

 ' 

1„ tan 6 \ "J 

(A-3) 

From the definition of C~ , we have 

Do' 

CL = C ' Do

 uDo 

bO 

|

u Go- u

d o | 

0.5 

Do u 

Do 

—I T0.5 

Go 

Go do 

= C Do 

Go do 

u Go 

0.5 

1„ ta n 8 J / 2 

(A-4) 

195 
P.M 

Using equations A-l through A-4 and the definitions 

of the various dimensionless parameters, the following 

relations are obtained: 

L' = (L + LR) (l - S LH) (A-5) 

S' = S (l - S LJJ)'^2 '

1 (A-6) 

ud' = u d( x " s LH) (A

-

y

) 

Wl pG

 CDi \^ W 

=WW i 

VQjtaG / / /„ -„ 7<>.5 

r / u G 0 -

u

d 0 r /. htan A i/2 

= B ( l - S L H ) " j / 2 (A-8) 

which give the desired scalin g factors. 

196 
P.15 

TECHNICAL REPORT DATA 

(Please read Instructions on the reverse before completing) 

1. REPORT NO. 

EPA-600/2-77-172 

3. RECIPIENT'S ACCESSION NO. 

4. TITLE AND SUBTITLE 

Venturi Scrubber Performance Model 

5. REPORT DATE 

August 1977 

6. PERFORMING ORGANIZATION CODE 

7. AUTHORIS) 

Shui-Chow Yung, Seymour Calvert, and 

Harry F. Barbarika 

8. PERFORMING ORGANIZATION REPORT NO. 

9. PERFORMING ORGANIZATION NAME AND ADDRESS 

A. P.T. , Inc. 

4901 Morena Boulevard, Suite 402 

San Diego. California 92117 

10. PROGRAM ELEMENT NO. 

1AB012; ROAP 21ADL-002 

11. CONTRACT/GRANT NO. 

68-02-1328, Task 13 

12. SPONSORING AGENCY NAME AND ADDRESS 

EPA, Office of Research and Development 

Industrial Environmental Research Laboratory 

Research Triangle Park, NC 27711 

13. TYPE OF REPORT AND PERIOD COVERED 

Task Final; 3-6/76 

14. SPONSORING AGENCY CODE 

EPA/600/13 

is. SUPPLEMENTARY NOTES IERL-RTP task officer for this report is Leslie E. Sparks, Mail 

Drop 61, 919/541-2925. 

ie. ABSTRACT r£^e re p 0 r t gi v e s results of a review and evaluation of available venturi 

scrubber design equations. Calvert's differential equation for particle collection and 

Boll's differential equation for pressure drop were selected for numerical solution, 

and the results are presented graphically. Particle collection and pressure drop of 

venturi scrubbers can be approximated by the collection occurring in the venturi 

throat and by the drop acceleration loss, respectively. Simplified equations were 

derived by applying Calvert's and Boll's equations to the venturi throat section. The 

new design equations are much simpler to use and compare favorably with available 

performance data. 

-.7. KEY WORDS AND DOCUMENT ANALYSIS 

3 DESCRIPTORS 

Air Pollution 

Scrubbers 

Venturi Tubes 

Design 

Performance 

Mathematical Models 

1?. DISTRIBUTION STATEMENT 

Unlimited 

Dust 

Flue Gases 

Entrainment 

Separators 

b.IDENTIFIERS/OPEN ENDED TERMS 

Air Pollution Control 

Stationary Sources 

Particulate 

Venturi Scrubbers 

19. SECURITY CLASS (This Report.-

Unclassified 

20. SECURITY CLASS (This page J 

Unclassified 

C. COSATI 

13B 

07A 

14B 

12A 

21. NO. OF 

212 

22. PRICE 

Field/Grou'ti 

11G 

2 IB 

07D 

-'AGES 

EPA Form 2220-1 (9-73) 197 
CO 

Q_ 

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Office of Research and Development 

Technical Information Staff 

Cincinnati, Ohio 45268 

POS r AGL AMU r EES PAID 

U S ENVIRONMENTAL PROTECTION AGENCY 

LPA-33S 

Spw.iul Fouith-Class Rale 

Book 

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