-------
T = temperature, °K
C1 = Cunningham correction factor, dimension! ess
y_ = gas viscosity, poise
d = particle diameter, cm
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 "Nc "
oC
is a dimensionless group indicating the ratio of convective
and diffusive transfer rates (at constant ND ). The Schmidt
KG
number is defined as
For low diffusivities , leading to high Schmidt numbers
(Ng - 106), and low Reynolds numbers (NR , < 3) Levich
(1962) showed that:
* = 2 TT Dp rd c. N^ Nsci/3 (3.16)
For large Reynolds numbers (600 - 2,600) and (Ngc ~ 106 ,
Akselrud (1953) showed that,
* - 1.6 w Dp rd c. NRed- N^ (3.17)
For Reynolds number = 100 - 700 and Schmidt number * 103,
Garner et al. (1958a and 1958b) showed that,
* = 1.9 TT Dp rd c. NRed^ NSc^ (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'
n = |ur-u,.d, (3-19)
I G d| d
22
-------
where n = single drop collection efficiency, dimensionless
Dp = particle diffusivity, cmz/s
d^ - drop diameter, cm
UG = gas velocity, cm/s
u^ = drop velocity, cm/s
N'g, = 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>
Sh ' »
N'sh = 2 + 0.552 N°'N"3 (3-20)
equation 3-19 becomes
n =
I G d
(2.0.552 NR-NSC-) (3-21)
where Nc = Schmidt number defined by equation 3-15
oC
N_ , = drop Reynolds number
LIQUID DROP SIZE
As mentioned earlier, the principal collection mechanism
occurring in a venturi 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 col-
lection 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
UG> critical (cm/s)
Q.5
47,205
d (mm
466-3 (3"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 cor-
relations 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 sum-
marised 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 com-
paring 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
ts)
en
AND THEIR APPLICABLE RANGES
Investigators
Nukiyama § Tanas aw a
(1938,1939,1940)
Mugele (1960)
Gretzinger §
Marshall (1961)
Kim § Marshall
(1971)
Equations
°- i° \" i PL fVM"
, _ O.OD / O \ , oppl 1 I 1
d UG K) ' V" o^ / K^
dd ,, ,B/W, u \C
-3 — = A/N 11 1 fA PL r Trr rnn^-tTnt'-l
d V Re / \ rt / v.'^>D>(-' «i<^ v-UJio 1.0.11 1.0 _/
r -, O.lt
1 mT 1
dm = 0.26 Ji NDor
m mr ReG
L b J
11 °-32
rt o-ti y T
d - 0 51°
"m " (UG pG)0'57 A°-36pL°'16
/mG \n
/ ^L\oa7 \mT/
+ 1 °nl I \ i* r
T -L . oy i - — - • i —
\pLa / u's*
n = -1 for nu
"£ <3
n = -0.5 for mr/mT >3
b L
Applicable ranges
un,(cm/s)
101* -sonic
velocity
101* -sonic
velocity
101* -sonic
velocity
7.5 x 10 3-
sonic
velocity
mG/mL
1.8 -15
1.8 -15
I -15
~_
0.06-40
yL(poiseJ
0.1-0.46
I
0.01-0.3
0.01-0.5
where d, = Sauter mean drop diameter, cm PL = liquid density, g/cm3
d = mean drop diameter, cm yT = liquid viscosity, poise
m ij
d^ = nozzle diameter, cm mi " mass flow rate of liquid, g/s
n Jj
UG = relative -velocity, cm/s mG = mass flow rate of gas, g/s
a = surface tension, dyne/cm A = flow area of atomizing air
Q = volumetric flow rate, cm3/s ur = relative velocity between gas and liquid,
-------
interest. For the particular venturi geometry they used,
the N-T equation consistently over estimates mean drop dia-
meter at high -gas velocities and under estimates it at
low-gas velocities. They presented the following empirical
equation to correlate their drop data.
A 6.75 x 106 * 5.28 x 1012 (QL/QG ), ™*2 ,-
d, = - {3
d 1.602
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 func-
tion 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:
CD '
Red
Where CD - drag coefficient
NRed = drop R®vnolds 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
-------
I io2
o
•H
o
u 10
BJ
O
C5
O
0.1
0.01
0.
Stokes Law
0.1
Ingebo (1956)
10
1CP10*10*107
N^e-Reynolds Number
Figure 3-2. DRAG COEFFICIENT OF A SPHERE .
27
-------
microns. Calvert (1968) used the Ingebo data and simplified
the above equation to
CD = T" £°r 10° < NRed < 50° (3-25)
D NRed
However, this expression is applicable for a Reynolds num-
ber 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 approxima-
tion 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. However, Boll (1973) concluded that in the
case of a venturi, the Standard curve of the drag coeffi-
cient is the better choise. 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 prorous 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 accelera-
tion and reduced the apparent drag coefficient, accounting
for the low C~ values .
Dickinson and Marshall (1968) approximated the Standard
curve by the following correlation
C3-26)
28
-------
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 holdupi, obtained a differential
equation for the prediction of venturi scrubber performance.
This equation is
dc . 3 Kl"d " dz ,, „,
C 2 ddUG ( }
where c = dust concentration, g/cm3
u = ut)~ud relative velocity between particle and
liquid drop, cm/s
r| = single drop collection efficiency, fraction
d, = drop diameter, cm
Up = gas velocity, cm/s
z = distance, cm
H, = drop holdup or volume fraction of drops at
any point
udA
Q = liquid flow rate, cm3/sec
L
ud = 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 . .
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
-------
following simplified equation for predicting particle
penetration
Pt(d )- exp
2 \ uGtpl cld p
55 CL y" M^pt'
(3-29)
where Pt(d )= penetration of particles with diameter d t
fraction
QT = liquid flow rate, cm3/s
i-j
QG = gas flow j-ate, cm3/s
= average liquid drop diameter given by
,
the empirical correlation of Nukiyama
and Tanas awa, cm
u = velocity of the gas in the throat, cm/s
bt
Vip gas viscosity, poise
p. = liquid density, g/cm3
L
K = inertial parameter evaluated at the velocity
of the gas in the throat.
"F(K f)" is a parameter defined by the following equation
PL ,
i r , .. /K f + 0.7 \
"^ [ l^TTT - )
(3-30)
• - - /
0.49
f + 0.
"f" is an empirical parameter. For hydrophobic aerosols a
value of 0.25 is suggested by Calvert .for this parameter.
For hydrophilic particle materials it, is usually equal to
0.5.
Boll (1973) took into account the particle collection,
occurring in the venturi throat as well as in the divergent
and convergent section of the venturi, and presented the
following integral equation for the calculation of particle
penetration
30
-------
C3-31}
where NC = number o£ collection units
= - In Pt(dp)
M = ratio of liquid-mass flow rate to gas-mass-
flow 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
" |ur-Uj|" is the relative velocity between gas and drops.
This velocity depends on the geometry of the venturi scrub-
ber. Boll assumed that the gas is incompressible. Thus,
the gas velocity at any location in the scrubber is given by
mG
UG " A~7 (3-32)
U
where nu = 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
0
pr (up - u.
/r, \J f, I Up 1*1 I
T 57 LV^i CD dt ('-")
where u,. = initial velocity of the drop, cm/s
di
Cn = drag coefficient
31
-------
Boll used the Standard curve for CD for solid spheres due to
Lapple and Shepherd (1940).
Boll's equation, i.e., equation 3-51 can be reduced
to Cal vert'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
(3-34)
where c = dust concentration , g/cm3
F = v-drop mass flux, g/cm2-s
PL = liquid density, g/cm3
n = target efficiency* fraction
u... = 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 Cal vert'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. How-
ever, 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 par-
ticles 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 parameter and lower ef-
ficiency. Dropp and Akbrut proposed the following equation
to predict venturi scrubber performance.
32
-------
Pt(d ) = exp
'.3A, i
T / CCT cT7 u
*r 11 tl
P' "J *G "d ud
o
dz
(3-35)
where Pt(d ) » penetration for particles with
diameter d , fraction
QL = liquid-flow rate, cm3/s
QQ = gas-flow rate, cm3/s
u = particle velocity, cm/s
u^ = drop velocity, cm/s
This equation has the same form as Galvert's differ-
ential 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(dJ = :exp - ,nnnnnn (3-36)
P'
490,000
where Pt(d ) = penetration for particles with diametet
d , fraction
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. (1972) used the same approach as Ekman
and Johnstone and considered the particle collection in the
33
-------
venturi throat and in the divergent section. They arrived
at the following equation
Pt(d) = exp I- (R. + R,) ^1 (3-37)
I (Rt
"R " and "R," are, respectively, the washing factor of gas
in the venturi throat and in the divergent section. Wash-
ing 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,
ur / u,\
1 - dx
max
where I. = venturi throat length, cm
C
X = dimensionless distance
x_
" *t
d, = drop diameter from Nukiyama and Tanas aw a
correlation, cm
n = target efficiency
0 = t ' cm
0 2 tan §L
2
d = venturi throat diameter
0 = 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
-------
throat is far from uniform (Taheri and Raines (1969),
Boll (1973)). Taheri and Sheih (1975) took turbulent mix-
ing and liquid drop distribution across the duct into
account and obtained the following equations for predict-
ing the transport and diffusion of the particles and water
drops.
—•— = - u ——
at G az
a2c
'd= - u
^+f5F]-Vldd CuG-ud) ccd
(3-40)
3c,
at "d az "d l"ay^
where c - particle concentration, g/cm3
Cj = number concentration of liquid drop, #/cm3
u,, = gas velocity, cm/s.
u, = drop velocity, cm/s
E = eddy diffusivity of particle, cmz/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 effi-
ciency. They found that as the range of size distribution
35
-------
widens, the impaction efficiency decreases.
PRESSURE DROP
Pressure drops for gas flowing through a venturi scrub-
ber 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 theo-
retical and experimental correlations, for the prediction
of pressure drop in a venturi scrubber. They are summa-
rized in Table 3-2.
Correlations by Matrozov, Yamanchi et al., Volgin et al.,
Gleason et al., and Hesketh are experimental correlations.
Matrozov1s correlation and Volgin1s correlation were
obtained mainly on small-size venturi scrubbers. Yama-
uchi'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 equa-
tion is similar to that of Geiseke's except Boll had
36
-------
TABLE 3-2. CORRELATIONS FOR PRESSURE DROP
IN VENTURI SCRUBBER
Investigator
Correlation
Matrozov .(1953) AP = AP, + 1.38 x 10"3 ui'°8 / QT
Cl V3t I Li
0.6 3
CM
\5c/
Yoshida et al.
(I960) (1965)
AP =
n —>
PG UGt
2 g.
4 £
S
4 £
d
Geiseke (1968) AP =
[
mr Aur + mT AyT
b b L ' 1
Am,
(uGl + UG2 - UL, - UL2)]
Yamauchi et al,
(1964)
AP = 0.3 (AT)"0-28
Tohata et al.
(1964)
AP =
PG UGt
Sc
£
[• •
92]
+ £
(continued)
37
-------
TABLE 3-2. (continued")
Investigator Correlation
Volgin et al. AP = 3.32 x 10
(1968)
/Q x°-26
u2 ( ^ (
V^/
Calvert (1968) AP = 1.03 x 10
Gleason et al. AP - 2.08 x 10"5 u2 (0.264 QT + 73.8)
(1971) bt L
Boll (1973) _ u 2 - 2
u^ r
§c^o G^^
1 u dx
eq 6Cx*0 "eq
2
Behie § Beeck- / 6F \fl r , . 2 T 1 -
mans (1973) dp = - (^djl^/p CD PG ^G'11^ "T" J dt
Hesketh AP = 1.36 x 10 "* u~i pr A"-133
(1974) Gt G t
r /QT\ /QT\2i
0.56 * 935U^ + 1.29 x 10"5 Ji
L \Q^/ \Qn/ J
where At = throat cross-sectional area, cm2
AQ = duct cross-sectional area, cm2
d^ = liquid drop diameter, cm
d = equivalent duct diameter, cm
(continued)
38
-------
where dt = throat diameter, cm
dQ = inlet of outlet duct diameter, cm
f = friction factor, dimensionless
ft = average friction factor of the throat,
dimensionless
c = average friction factor of convergent section
f^ - average friction factor of the divergent
section, dimensionless
g = conversion factor
&t = throat length, cm
M = liquid-to-gas mass ratio
nig = gas mass flow rate, g/s
m. = liquid mass flow rate, g/s
Q,, = gas volumetric flow rate, cm3/s
QL = liquid volumetric flow rate, cm3/s
UG = gas velocity, cm/s
uGt = ^as velocity at tne throat, cm/s
u, - liquid drop velocity, cm/s
u, = liquid velocity, cm/s
Li
t - time, s
6 = 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
pr = gas density, g/cm3
b
p = manometer fluid dnesity, g/cm
GI = convergence angle, degree
92 = divergence angle, degree
5 = coefficient on divergent loss of gas
flow, dimensionless
E, = head-loss ratio for throat, dimensionless
£, = head=loss ratio for divergent section,
a
dimensionless
39
-------
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 0.027 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
-------
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 perfor-
mance 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 ob-
tained under contolled conditions and for a well-defined
scrubber system will be utilized to test the performance
models.
COMPARISON OF PREDICTED PRESSURE DROP WITH EXPERIMENTAL
DATA
Data by Wen and Uchida
Wen and Uchida (1972) obtained pressure drop data on
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 the scrubber.
Figures 4-2 through 4-4 compare pressure drop predic-
tions 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
temperature once it is in contact with water (within 5 cm
from the water injection point). Thus, in calculating
the predicted pressure drop, the volumetric gas flow rate
was adjusted 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
by Volgin et al. and Hesketh ar6 always lower than data.
41
-------
TABLH4-1. 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
IS
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
43.3
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 /rain
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
I fc/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
r 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
-------
04
28.9cm
28.9 cm
Figure 4-1. Dimensions of OAP venturi scrubber.
-------
iiJLi'ir;4:.fJ-l:
[iff 0 Calvert's Prediction ^
r. j j- , -,.,
Hesketh's Prediction
0 10 20 30 40 50
EXPERIMENTAL PRESSURE DROP, cm 1ft.C.
Figure 4-2. Comparison of predicted pressure drop with
experimental data from Wen and Uchida.
44
-------
u
•s
E
u
o
Q
o;
s
co
CO
Q
W
O
36
32
28
20
16
Boll's equation
^iiiil^J,!::^,:.!.!; [jjlLiU.
;i Volgin's equation ;
U-r- ----t—---J—I ' i ' i I : : ', i , i ' - I-- Ll-l-li
.:, , j, . ., i i; r, ' . rr,,,
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
-------
36
12
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
-------
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 con-
tribution 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
AP = 1.0 x 10"3 u*e UG* /QL\ (4-1)
where AP = pressure, cm W.C.
Up. = gas velocity in the throat, cm/s
Q. = liquid flow rate, cm3/s
L
Q = gas flow rate, cm3/s
47
-------
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
22.9
21.6
21.3
23.4
31.5
25.9
21.8
Prediction, cm W.C.
Boll
19.2
19.9
18.9
22.7
20.4
27.5
19.1
19.8
88.7
16.8
16.8
20.4
24.9
17.4
16.&
21.9
20.3
17.2
16.7
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
-------
where u*g = correction factor, dimensionless
and
*
_ Ude ?
UGt "
1 - X2 + (X
" •- ** VJ TV D *••
X = Do PG
(4-2)
uGt = gas velocity in the throat, cm/s
ude = drop velocity at the exit of the throat,
cm/s
Si = 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
PL = liquid density, g/cm3
CL = drag coefficient at the liquid injection
point
"CD " is the drag coefficient obtained from Standard
durve for spheres. Drop Reynolds number is defined as
where ND , - drop Reynolds number
Re, d
u, = initial drop velocity, cm/s
v = kinematic viscosity of gas, cm2/s
The physical meaning of "u|e11 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 friction and pressure recovery in the diffuser
were neglected in the correction factor to Calvert's equa-
tion, 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 pres-
sure 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. ,
Number of velocity heads lost =
2*c ^
where AP = pressure drop predicted by theory, cm W.C.
gc = 980 cm/s2
PG = gas density, g/cm3
PL = water density, g/cm3
uGt = 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. Hes-
Keth's equation gives too low a pressure drop. Volgin's
equation gives a different slope.
50
-------
34
30
S
o
O
OS
o
m 20
CO
CO
w
OS
H
u
oS
OH
10
T,
Do
D
from standard curve
from Ingebo's correlation j i:•:
10
Figure 4-5,
20 30 34
EXPERIMENTAL PRESSURE DROP, cm W.C.
Comparison of predicted pressure drop by modified
Calvert's equation with data from Wen and Uchida.
51
-------
en
txj
Liquid
Inlet
Figure 4-6. Prototype venturi scrubber used by Boll
-------
H
en
o
Q
<
w
u
o
_!
W
o
OS
3C
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
j|il!l!i!!iii ilillilliliJl
' Calvert's
\' equation
nozzles -H
; Modified Calvert's !l!
i equation
; uGt=9150 cm/s
Hesketh's i
equation ]
Boll's equation
ill Caverage)
":
Modified Calvert?s
equation
u. =4050 cm/s
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
-------
The range of gas velocity in throat covered by Boll
was 45.8 m/s - 91.5 m/s (150 - 300 ft/s). The
line representing the predictions by Boll's equation
was an average curve for the predicted pressure drops.
Even though Boll's equation slightly under estimates pres-
sure 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 satis-
factory.
Predicted pressure drops by modified Calvert's equa-
tion 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 pres-
sure drops, lies within this area signifies that the modi-
fied 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
measured 15.2 x 86.4 cm (6 x 34 inches) with a straight
section 30.5 cm (12 inches) long. The angle of the con-
vergent 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 Pease-
Anthony 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
-------
en
Liquid Inlet
86.4 cm breadth
2.2°
Figure 4-8,
Dimension of Pease-Anthony venturi scrubber used by
Brink and Contant.
-------
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 Con-
tant'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 Johns tone Data
Ekman and Johnston (1951) ha^e 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 condlude that both
Boll's equation and the modified Calvert's equation are ade-
quate for the prediction of pressure drop in a venturi scrub-
ber. 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
-------
2.5
CO
o
2.0
O
ctf
a:
UH
O
§ 1.5
«v
ac
a.
f 90 spray jet
^ 45 spray jet
1.0
1.0. 1.2 1.4 1.6 1.8 2.0
LIQUID TO GAS RATIO, i/m3 of gas
Figure 4-9. Comparison of Brink and Contant experi-
mental data with theories.
57
-------
Liquid
Gas
00
Figure 4-10. Dimensions of the Ekman and Johnstone venturi.
-------
1.4
H
S 1
J
Q
<
W
x
>-
H
1.0
u
o
> °
H
<< .
O
05
^ 0
PH
O
6 --
o
2
E
<3
D-,
<
0.4
0.2
;Data for radial
[outward injection;;;
Data for radial
inward injection
0.2 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
-------
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.,
(uG-ur)A
n dz (4-4)
u = relative velocity between dust and drop, cm/s
where c = dust concentration
= relative velocity
Up = gas or dust velocity, cm/s
A = duct cross-sectional area, cm2
TJ = drop radius, cm
= single drop collection efficiency, fraction
QL = 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 perfor-
mance by comparing theoretical predictions with experimental
data. Thus, we will choose this equation as the particle col-
lection design equation for venturi scrubber.
No general solution for this equation was found in the,
literature. In order to calculate the particle collection ef-
ficiency, 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 deriva-
tion of the generalized method will be presented in the next
chapter.
60
-------
CHAPTER 5
PERFORMANCE MODEL
i
In this chapter, we will present the generalized method for
predicting venturi scrubber performance by using both Boll's
p'ressure 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 were developed by
Calvert (1968, 1970) and Boll (1974); rewritten here after
some rearrangement they are:
c UG (uG-ur)
A
du,
a
dz
G
3
4
3 PG
PG
PL
CD
(V
dd
(VU
Ud)2
ud
d)2
c.
mL
(5-2)
- (VmG)
dz " PGG dz " 4 p d u A " m
B.C. at z=0, C=CQ; ud=udo ; UG=UGO; p=pd
where A = duct cross-sectional area, cm2
c = dust concentration, g/cm3
CD = drag coefficient, dimensionless
dj1 = drop diameter, cm
d, = hydraulic diameter of the duct, cm
£, = friction factor, dimensionless
61
-------
m
G
gas mass flow rate, g/s
mr = liquid mass flow rate, g/s
LI
p = pressure
Q = liquid volumetric flow rate, cm3/s
LI
r _, = drop radius , cm
u, = drop velocity, cm/s
u~ = gas velocity, cm/s
u
u
relative velocity between gas and liquid drop,
cm/s
rectangular coordinate in the direction of flow
PL = liquid density, g/cm3
p,, = 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.
(3) 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:
mr
ur = _£- (5-4)
(j n A
PGA
where m^ = gas mass flow rate, g/s
A = duct cross-sectional area, cm2
PG = gas density, g/cm3
62
-------
Duct cross-sectional area depends on location .and can be
be determined from the following general formula:
A - AO ^ 1 + ^p-* 1 (5.5)
*
j = 1 for rectangular duct
j = 2 for circular duct
where AQ = cross-sectional area of the duct at the start of
a section, cm2
R = radius (for circular duct) or half width (for
rectangular duct) at the start of a given
section, cm
3 = 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) :
C-. = (constant) N"°*5
jj KB
where Cn = drag coefficient applying at z=0, dimensionless
Up = gas velocity at z=0, cm/s
u, = drop velocity at z = 0, cm/s
"Cr> " is determined from the "standard curve" using a Reynolds
Do
number calculated on the basis of the relative velocity
applying at the beginning of the duct, i.e.,
63
-------
. C5.7)
K6,O v
where NR = drop Reynolds number at the beginning of
XX t* 9 \J
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:
CDo ' °'22 + ~- l +0'15
Re , o
NRe,o)
'
(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:
- ~ = u I d IT1) n dz (5'9)
(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.
n - PL-)'
\K + 0.7/
C' p d 2 |uG-ud|
where K = £—£ (5-11)
P 9 UG dd
If one defines total pressure as:
PT - p.+ %p U2 (5-12)
64 .
-------
Equation (5-3) can be written as:
dp
T
dz
•z Pp/^n\ ur~uj I UP~UJ I/mT\ (M+l) f 00U*
-i ^1^1 u dIG dl/L\ v ^KGG
= --—1 — 1 — ± (5.13)
4 pT \d,/ Uj \A/ 2d,
where M = m,/nu
L (j '
= liquid to gas mass flow rate ratio
The hydraulic diameter "d^" is given for a circular
duct by:
dh = 2 (R + z tan 6) (5-14)
and for a rectangular duct by:
d, o 2b (R + z tan g) (5_15)
n b + R + z tan g
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
Equations (5-2), (5-9) and (5-13) are the governing
equations for venturi scrubber performance. These equations
are now non-dimensionalized, using "Ug " as the characteristic
velocity scale, M^PGUG 2" as the characteristic pressure scale,
~ d, p, / ur \o.s
and - —5- -2- j ——) as the characteristic length scale
3 CDo PG \uGo"udo/ f°r "the equations below
(in the case of dh, RQ , and b, duct length "A" is used as
characteristic length scale), i.e.,
u * = - (5-16)
d u~
Go
65
-------
* =
U
Go
0.5
(5-17)
n* =
PT
(5-18)
By using these definitions, we obtain
u
u -u, =
Go
UGo ud
G d /I + z tan p \j UGQ
^ K. '
= u
Go
, tan 3 2 ad
*T iii • • .1—.- .• ^^— i
PL / UGO \
pG\UGo-Udo/
0.5
-jj
1
.-u
(5-19)
Let S =
Let 5
2 tan 6 dd PL / UGo
0.5
3R
CDo PG
(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:
= U
Go
- u
66
-------
Fi-om equation (5-10) we have:
K
n =
K
C'
9
C1
9
PP
WG
PP
UG
d 2
P
dd
d 2
P
dd
u - u j
^ G d
Vud
+ 0.7
(1
(1 + Sz*)'3
- u
d
po
(5-20)
C' p "
where K
Go
po 9 yr d,
r b d
By substituting equations (5-17), (5-19), and (5-20) into
equation (5-9), we have:
3
I
dc _ 1.5R
c d tan
S
rjjdz* (5-21)
Let B =
PG CDo
(11 \°-5
UGo \
UGo-Udo/
(5-22)
then we obtain
In Pt
B
Sz*)"3-u*
u* f|(l + Sz*)'3-^!* 0.7>
dz*
(5-23)
67
-------
where L = dimensionless duct length
3
CDO
2d,
a
*
pd
P
G
UGo
-udo"
«
0.5
i, = duct length, cm
Equation (5-23) 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:
dz*
dz*
= (1
u
-J - Ud|]
0.5
2 u*
a
. u8
0.5
us
+ CM + i) f (i + Sz*)"
djL
B.C. at z*=0, u*=uJQ, p*=0
d* = 2R* (1 + Sz*) Circular duct
,* 2 b* R*(l + Sz*) _ . ' , .
dr = ^ J Rectangular duct
n b* + R*(l + Sz*)
f = friction factor, dimensionless
b* = b/£ = dimensionless duct breadth,
R* = R/£ = dimensionless radius
(5-24)
(5-25)
(5-26)
68
-------
The first terra on the right hand side of equation (5-25)
represents the pressure change associated with the accelera-
tion 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
write:
* * *
PT = Pd + PW (5-27)-
where p* = total pressure, dyne/cm2
p^ = component of p* associated with liquid flow,
dyne/cm2
p* = wall friction component of p£, dyne/cm2
By this definition, we have:
~j
Sz*)~- u
*
o.s
dp£ ^ ^
dz* u*
a (5-28)
and
dpw = (M + 1) f (1 + Sz*)"2j
dz* d* L
n
(5-29)
with boundary conditions
at z* = 0, pj = 0, p* = 0 (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
-------
sci'ubber is,
AP,
CAP),
(5-31)
where AP» = overall pressure drop, dyne/cm2
(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 penetra-
tion for the venturi scrubber will be,
Pt(dp) - n Pt(dp)I
(5-32)
where Pt(d ) = overall penetration for particles with
diameter "d ", fraction
Pt(d ) = penetration of a section, fraction
p J i
SOLUTION
The analytical solution to equation (5-29) is,
p* = (M-M)f
ho
(5-33)
1 - A
where F = .
W I4CA0.5
-2
for circular duct
(5-34)
F = J- 11 + R*(Ar-l)(l+b*-*R*)'
w Ar2 [
for rectangular
duct
70
-------
and Ar = the ratio of exit to inlet cross-sectional area
= (1+SL)^
d£Q = dimensionless hydraulic diameter at duct
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 udo=0. These
figures along with equation (5-32) may also be used to deter-
*
mine penetration for u, ^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 "g", 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 ven-
turi divergent sections connected in series. The outlet of
the imaginary added on section is the inlet of the real sec-
tion. By equation (5-32) the particle penetration for the
real divergent section ABCD is equal to,
= FECD (5-35)
p. l J
FtFEBA
71
-------
3.0()
2.00
1.00 r
Oo75
0.50
0.25
-0.2I-0.1---0.05' -0.02--9.01
ffjchange of
'^scale
o.oi
0.1
1.0
10
100
Figure 5-1. Chart for obtaining u5 for a circular duct.
-------
3.00
2.00
1.00
0.75
0.50
0.25
0.01 0.1 1.0
(L + LH) F
Figure 5-2. Chart for obtaining u5 for a rectangular duct.
100
-------
6.0
ft.
-o.os:: -o.o2p -o'.oi
0.5.1- -0.2:7-0.1'
change
of scale
I. i^ii^ilP^i'llJ^iHiia'iiMJiMJitMiliirti im_ w*\ fniLJi' ii i o injit 'i i »Mii« lliillw iiiMiii^B T 0 Of
; i i jjii jiiMijff'iP "ii ™i"i ii^^ Lrr^^5^^^*iT'''"»iiP2M^^ __ __.. p
10
100
Figure 5-3. Chart for obtaining p*| for a circular duct.
-------
en
P.
]••• I-!-1 ft^
- , - j -- - - -g -. ... i - , -M. —L \—(.
, ^ rx i-\ ^i y^ /% -1 ! T
-o.osf -o.oz- --. i
change
of scale
iob^-R
0.01
1.0
10
100
Figure 5-4. Chart for obtaining pj| for a rectangular duct.
-------
0.0
o\
Circular duct:
0.01
0.1
100
Figure 5-5. Chart for obtaining penetration for circular duct.
-------
^Circular duct1-
0.01
100
LH)F
Figure 5-6. Chart for obtaining penetration for circular duct.
-------
.3
oo
•P
P-,
• . , I
Circular duct
•••••mil nmiMEi iiHHni minii inn nm MI in mnmniniiiiin iniiiin ininii inn mm m m
.01
.1
10
100
(L + LR)F
Figure 5-7. Chart for obtaining penetration for circular duct-
-------
•P
a,
rt
rt-n
Circular duct
0.1
.1
10
100
LH)F
Figure 5-8. Chart for obtaining penetration for circular duct.
-------
1.0
00
o
4-J
c
iH
s—s
ft.
100
(L + LR)F
Figure 5-9. Chart for obtaining penetration for circular duct.
-------
O.Q
•p
P-,
0.04
0.03
0.02
0.01
0. 01
Figure 5-10. Chart for obtaining penetration for rectangular duct.
100
-------
00
c-o
•P
CL,
fi
0.16
0.12
Rectangular, duct
0.08
0.04
o.i i.o 10
(L + LH)F
Figure 5-ll.Chart for obtaining penetration for rectangular duct.
100
-------
0.3
00
0.2
0.1
jIRectaneular duct
'
0.01
100
(L + LR)F
Figure 5-12. Chart to obtain penetration for rectangular duct.
-------
0.5
CO
TtRectangular duct
t- • ••••'* ™-, «-n-
0.2
0.1
0
0.01
0.1
(L
1.0
LR)F
100
Figure 5-13. Chart to obtain penetration for rectangular duct.
-------
1.0
00
Rectangular duct
0
0.01
100
Figure 5-14. Chart to obtain penetration for rectangular duct.
-------
oo
Rectangular duct
0.01
100
Figure 5-15. Chart to obtain penetration for rectangular duct
-------
CO
-J
2.4
2.2
2.0
1.8
1.6
1.4
Rectangular duct
V - 10
F = 1-SL
m
1.2
5 1.0
•M
OH
PH
0.8
0.6
0.4
0.2
0
0.01
0.1
10
1.0
(L+LH) F
Figure 5-16. Chart to obtain penetration for rectangular bed,
100
-------
Z = 0
Figure 5-17. Concept of a hypothetical section.
88
-------
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 "Ptcc~n" and
TELL)
"PtpEBA" 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 deter-
mined by integrating equation 5-2 with the following boundary
conditions:
at z = 0, ud = udo
z = _JIH, Ud = o
Figures 5-18 and 5-19 are the results of the integra-
tion for a circular duct and a rectangular duct respectively.
"Lij" is the dimensionless counterpart of "&LJ" and is defined
by,
LH =
In calculating "PtFECD" and "PtFEM", it is necessary
to use the gas and liquid parameters at the inlet of the
imaginary added on section, i.e., at z=-H^. From the geometry
of the duct, parameters at z=-&H 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) j/2 (5-37)
S' = S (1-SLH) "J/2 -1 (5-38)
u*' = u* (l-SLH)j (5-39)
89
-------
100
CM O
53-
u
do
Figure 5-18. Chart for obtaining LR for a circular duct. >
-------
100
10 +n-
1.0
0,1
•: o. o.o. o —-:"_
1.
50: 30 ' 20 ! 15 - i 10.0 .7.0^5.0!
0.25
1.0
1.25
1.5
u
do
Figure 5-19. Chart for obtaining L for a rectangular duct.
-------
and B' = B(1-SLH)"J/2 (5-40)
where prime (') refers to z= -Si^. Detailed derivation o£
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. We will predict its perfor-
mance for the following operating conditions:
QG = 800 Am3/min
Q.L/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
Nukiyama and Tanasawa is:
A, = —
1V
.
d Q
= 0.0107 cm
Drop Reynolds number
d, /ur -u, \
N = d \~Go do/
Re,o v
= 0-0107 C8060-0)
0.15
92
-------
VD
LIQUID
INLET
Breadth = 81.3 cm
Figure 5-20 . Venturi scrubber for sample calculation.
-------
From Standard curve, or from equation (5-8):
So ' °'22
Re , o
= 0.22 + — [l + (0.15)(575)°-6)
575 L J
- 0.545
L 1
2 dd \PL "Go
= 2.79
B =
/ u \0>5
L_ | Go )
Do \UGo"Udo/
\QG/\PG/ CDo \"Go "do
= 2.03
For venturi throat, S=0. Since u-, =0, we have L =0
and F=l.
= "Go pa = (8060) (1Q-8)
po 9 UG dd (9) (1.8 x 10-"*) (0.0107)
or dpa = (0.215 Kpo)°'5 umA
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:
94
-------
V
0.2
0.5
0.7
1
2
5
10
dpa' ^mA
0.21
0.33
0.39
0.46
0.66
1.04
1.5
-F In Pt/B
0.044
0.176
0.272
0.41
0.77
1.3
1.7
Pt(d )
v paj
0.91
0.7
0.58
0.44
0.21
0.071
0.032
D i ve r gen t S e c t i on - 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
ujj = 0.78
At the start of the divergent section, gas and drop velocities
are the same as at the throat exit. Therefore, at the begin-
ning of the divergent section:
Go
= 8060 cm/s
and u, = 6287 cm/s
do
Drop Reynolds number is
dd (UGo""d)= (0.0107) (8060 - 6287)
N
Re,o
v
0.15
= 126
From Standard curve or by equation (5-8):
95
-------
So
0.5
c _ 2 tan 3 d
'"s:
PL / UGo \'
P \u-u/
= 0.177
/- _ ,., ,, , 0.5
L = I I
2 dd
!G /uGo"udo\
PT. \ uno /
= 12.5
We need "L^" which can be found by using Figure 5-19,
L
-
U
Therefore, LR = 2.0 (0.78)2 = 1.2
L + Lu = 13.7
n
F = 1 - SLH = 1 - 0.177 (1.2) = 0.788
Thus, (L+LH)F =10.8
LHF = 0.95
and SF-°-5 = 0.2
ur d 2
K = Go Pa = 4.65 d 2
PO 9 u, dd P*
or dpa = (0.215 Kpo)°-5 ymA
/QT\/PT\ ^ I ur ^
-, L\(-k\ JL GO
"VV\PG; CDO iuGo-U(
= 2.54
96
-------
Read "-F In Pt/B" from Figures 5-10 to 5-14 at SI'-0*5 =0.2 and
(L+LH)F=10.8 and 0.95 for various K , we obtain:
n po'
KPO
0.2
0.5
0.7
1.0
2.0
5.0
10
dpa,ymA
0.21
0.33
0.39
0.46
0.66
1.04
1.5
(-F In Pt/B)
L+LH
0.037
0.148
0.233
0.35
0.68
1.25
1.75
Pt(d )
Pa L+LH
0.89
0.62
0.47
0.32
0.11
0.018
0.0035
(-F In Pt/B)T
LH
0.035
0.142
0.213
0.315
0.57
0.93
1.15
Pt(d J
pa LH
0.89
0.63
0.50
0.36
0.16
0.05
0.025
The penetration for the whole venturi scrubber is calcu-
lated with the help of equation (5-32), i.e.,
throat
IT,
dpa,vimA
Pt
0.21
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
-------
o
I—I
H
U
2
O
H
W
w
VENTURI THROAT
0.01
0.1
1.0
PARTICLE DIAMETER, ymA
Figure 5-21. Predicted grade efficiency curve.
98
-------
Modified Calvert's Equation - Modified Calvert's equation is;
AP = 1.03 x ID
" 3
For the present example, ufi =8060 cm/s
and ~ = 1.33 x lO"3
\Q/
Therefore, drop diameter by Nukiyama and Tanasawa:
d, = ^ + 91.s(^i)
d UG V
= 0.0107 cm
; Drop Reynolds number
. dd (UGo"Udo)
Re,o v
t
0.0107 (8060-0) = 5?5
0.15
From Standard curve, or from equation (5-8):
(:„_ = 0.545
5 £t So PG , .
and x = ... ; - + -1-
16 dd PL
= 1.35
u* = 21 - x2 4 (x1* * x2)0-5
d L
= 0.80
99
-------
Therefore, pressure drop is:
AP = (1.03xlO-3)(0.80)(8060)2(1.33xlO-3)
= 71.5 cm 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.
Convergent section
A. Wall friction
p* = CM + 1)F F , f = 0>027
*w d* w '
- i
- —s- 1
ho
R*(Ar-l)(l+b*+R*)
A* L 2fb*+R*) J
exit cross-sectional area
and Ar =
inlet cross-sectional area
At the convergent section inlet:
u,, = 2500 cm/s -.'
bO
M = 0
£ = 62 cm
b = 81.3 cm
R = (0.5)(65.4) = 32.7 cm
d = 2b(R + & tan 3) fg ,,,
ho b + R + H tan 0 l )
(2H81.3) 32.7 + (62) tan 20°
81.3 + 32.7 + (62) tan 20°
= 65.8 cm
106
-------
By
the definition of dimensionless parameters, we have:
b* = 1L1 = 1.31
62
R* = f = 0.527
ho-~ = l-°6
A - C81.3H20.5)
r (81.3)(65.4)
Therefore,
F = 1 l + 0.527(0.31-1)(1+1.51+0.527)
w (0.31)2 2(1.31+0.527)
= 7.48
p* = Ap = (0.027)(7.48) Q lg
w l p u_2 1.06
•->• ' G Go
'. A = (Q.19)(1.2xlQ-3)(2500)2
' ' Pw (2)(980)
= 0.73 cm W.C.
B. Acceleration loss
There is no water in this section, therefore acceleration
loss is zero, i.e.,
Apd - 0
Total pressure drop in convergent section:
Ap = Ap + Ap, = 0.73 cm W.C.
101
!
-------
(2) Throat section
A. Wall loss
At the throat inlet:
un = 8060 cm/sec
bO
b = 81.3 cm
R = (0.5)(20.3) = 10.2 cm
3 = 0
dho = 18.1 cm
and M = — — = •••••'•""•"— =1.1
Or p- 1.2xlO-3
b b
• = n
u*
Ar = I
Fw ' !
Therefore,
p. = Ci.i * 1KO.Q27) = 0>Q956
w- 0.593
and AP = C0.0956).(1.2xlQ-3)(8060)2
(2) (980)
= 3.8 cm W.C.
B. Acceleration loss
From Nukiyama and Tanasawa correlation, we have:
dd = 0.0107 cm
udo = °
Drop Reynolds number
N = dd(UGo"Udo) = (0.0107)(8060-0) =
Re>° v 0.15
102
-------
From equation (5-8) :
CDo - 0.22 * J± (l + (0.15H575)0-6)
= 0.545
L -
JDo /pG\/uGo"udo^
2 dd \PL UGo
= 2.79
For venturi throat, 3=0, S=0, F=l.
From Figure 5-4, we obtain:
—{— = 1.6 for (L + LH)F = 2.79
Apd
Since p^ = , we have
77" PG UGo
1-6M PG UGo
= (1.6)(l.l)(1.2xlO"3)(8060)2
(2) (980)
= 70 cm W.C.
Therefore, total pressure drop in venturi throat
Ap = Apw + Ap^ = 2.79 + 70
72.79 cm W.C.
103
-------
(3) Divergent Section
A. Wall loss
At divergent section inlet:
u
Go
b
R
6
M
I
8050 cm/s
81.3 cm/s
(0.5K20.3)
7.5°
1.1
171 cm
2b (R + I tan B)
b + R + £ tan 8
= 10.2 cm
(2)(81.5) [10.2 + (171) tan 7.5°
81.3 + 10.2 + (171) tan 7.5°
dho
= 46.7 cm
= dho = 46.7
I 171
= 0.273
A_ =
(81.5)(65.4)
(81.3)(20.3)
3.22
D in?
R* = £ = iiL_i = o.06
a m
b* = b = ii^l = 0.475
£ 171
and Fw =
3.222
0.115
1 +
0.06(5.22-1)(1+0.06+0.475)
2(0.475+0.06)
,* =
W
.1 + 1)(0.027) (0.115)
0.273
104
-------
Since p = — - - , we have
PG UGo
Ap = CO'025)(1.2xlQ-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., d,=0.0107 cm. At the divergent sec-
tion inlet, drop velocity is equal to the velocity at the
throat exit. From Figure 5-2, we obtain:
u|F* = 0.78 for (L+LH)F = 2.79 and SF-05= 0
•'' udo = (°'78) C8060)
= 6287 cm/s
u = 8060 cm/s
Go
Drop Reynolds number
_ dd(UGo-Udo)
NRe,o
v
(0.0107)(8060-6287) =
0.15
Using equation 5-8, we obtain C=0.93
1 tan g dd ^L / UGo
3 R CDo PG \UGO-U
= 0.177
105
Do
0.5
-------
T _ 3 „ CDo PG
]_, — -—
« dd PL \ UGo /
= 12.5
From Figure 5-19, we obtain:
LH
"f~
Therefore, LH = 2.0 (0.78)2 = 1.2
L + LH = 13.7
F = 1 - SLR = 1 - 0.177 (1.2) = 0.788
Thus, (L+LR)F =10.8
LHF = 0.95
ri
and SF-°-5 = (0.177) (0-788) "°"5 = 0.199
From Figure 5-4, we obtain
2 =1.0
M
H
LH
L+LH (0.788)2
..77
106
-------
(0.788)
J+LH
APd
Since p* = , we have
1 p u 2
?tr G GO
Ap* = (0.179)(1.2xlQ-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
= 67.4 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 velo-
!
city between particles and drops is highest. Thus, it would
be desirable to obtain an expression for particle collection
in a venturi throat.
107
-------
For particle collection in a venturi throat, equation
(5-23) reduces to:
Equation (5-24) for liquid drop velocity become-s:
-TT- = o <5-42)
dz* 2u*
d
We will solve these two equations for the special case
U*, =0, i.e., initial liquid drop velocity is zero. By
rearranging equation (5-42), we have:
2u*
dz* = d
-. - • •; , E
h_u*\i.5 d
By substituting equation (5-43) into (5-41), we obtain:
Pt
0
The closed form solutions to equations (5-44) and (5-42) are:
in
E'
ito/l-»J* "ilX
\ o/
0.5
po
- 5 02 K°'5 //l-u*\+ - '1 po
5'U^ 1 Ud) KpQ
\ tan't1/' "^
jtan V 0.7
KPO
(* I
rr "" J I
no/
- 5-02
po-
C5-45)
108
-------
and u* - 2 1 - x2 + (xk - x2)
2, 0.5
(5-46)
CL
K _ dpa uGt f ^
Kpo - 911717 C5-48)
b 0.
f5-49)
*• '
&t = venturi throat length, cm
CDQ = drag coefficient for drops at the venturi throat
inlet, dimensionless
"CDo" is a function of drop Reynolds number and is obtained
from "Standard Curve."
Drop Reynolds number is defined as:
dj ur.
NRe,d - ~^ (5-5»5
For an infinite length venturi throat, u| approaches unity
and equation (5-45) reduces to:
Pt(d )- exp - B
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
-------
1.0
H
U
2
O
H
W
2:
w
0.01
VENTURI THROATS
VENTURI THROAT
iINFINITE LENGTH
0.1 -rt^
0.1
1.0
PARTICLE DIAMETER, ymA
10
Figure 5-22. Predicted grade efficiency curve.
110
-------
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 jam in diameter are rarely
collected by inertial impaction because they follow the gas
streamlines surrounding the liquid drops. For particles in
this size range, diffusional collection is usually the pre-
dominant 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 Cal vert's differential equation as
our starting equation. His equation is:
C5-S2)
d d
where c = particle concentration, g/cm3
UG = gas velocity, cm/s
u, = drop velocity, cm/s
Q = liquid flow rate, cm3/s
W
Qf = gas flow rate, cm3/s
n = single drop collection efficiency, dimensionless
According to Johnstone and Roberts (1949), single drop
didjfusional collection efficiency is given by the following
equation:
4 D
n =
hrudldd
2 + 0.552
(5-53)
where D = particle diffusivity, cm2/s
ND = drop Reynolds number, dimensionless
2 /
vn = kinematic viscosity of gas, cm /s
b
111
-------
By using the same dimensionless parameters defined
earlier (equations (5-16), (5-17), (5-20) and (5-22) we have:
u
n =
dd UGo
3 - u*|
- u
(5-54)
and -
dc
4 B D
_2
uGo dd ud
0.5
U
where B = — — —
Go
CDo\VpG\UGo-Udo
u
= 0.552
4 B D
Go
0.5
- u*°'5 dz*
d
N °-5 —
NRe,o U
\ p
let BD =
uGo dd
(5-55)
(5-56)
(5-57)
(5-58)
we have:
B r
_ dc = J> 2 + E (l+Sz*)~J - u*
c u*[ <
Upon integration, we obtain:
0.5
dz*
- u
°-5
dz*
(5-59)
(5-60)
Equation (5-60) is the final equation describing the par-
ticle collection by diffusion in a venturi scrubber. Plots
similar to Figures 5-1 through 5-10 can be constructed.
112
-------
For venturi throat (S=0) and for the special case that
initial drop velocity is zero (u^ =0), the analytical solu-
tion to equation (5-60) is:
113
-------
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 informa-
tion, e.g. size distribution and loading are not available
In the following sections, only those data with well de-
fined 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
pitot runs
Actual m3/min
ACFM
DS m3/min
DSCFM
Vol I H20 vapor
Inlet Duct
149°C
+73.5 cm W.C.
799
28,200
429
16,300
21
Outlet
Scrubber
Outlet Duct
57°C
+0.5 cm W.C.
-
;
-
13
Chimney
49°C
+0.02 cm W.C.
670
23,700
500
19,000
11.8
114
-------
2. Water flow rate to the venturi scrubber was re-
ported by the plant as approximately 1.06 m3/min
(28,0 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 5-23 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 scrubbfer
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 phos-
phoric acid plant. The dimensions of the scrubber are
shown in Figure 4- 8. Brink and Contant gave a grade effi-
ciency 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) par-
ticle collection occurring in the venturi throat, (2)
combined particle collection in venturi throat and di-
vergent 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
expression:
115
-------
l.Q
2
O
2:
O
PH
u
a,
0.1
0.01
Experimental data?
Predicted by
! throat model
iiiniiiiiniiifliitr
0.1
Figure 6-1
1.0
PARTICLE DIAMETER, pmA
Experimental and predicted performance
of AAF Kinpactor 32 Venturi scrubber.
116
-------
1,0
o
I—I
H
U
o
M
H
w
PM
w
nJ
U
I—I
H
rt
<
PU
0.1
0.01
Calvert's model
f » 0.25
Calvert's model
£ = 0.5
t. Experimental Data
PARTICLE DIAMETER, ymA
Figure 6-2. Experimental and predicted performance
for AAF Kinpactor 32 Venturi scrubber.
117
-------
1.0
E-
U
o
I—I
H
W
PH
W
H^
U
t—I
H
0(5
0.1 j
0.01
venturi throat
with infinite
throat length
venturi throat
0.1
1.0
10
PARTICLE DIAMETER, ymA
Figure 6-3. Predicted and experimental penetration
for venturi scrubber used by Brink
and Contant.
118
-------
where:
d = aerodynamic particle diameter, ymA
d = actual particle diameter, urn
p = particle density, g/cm3
C' = Cunningham slip factor, dimensionless
Aerodynamic diameter was transformed to actual dia-
meter 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 liquid 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. Gas 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 4.75xl05 4.5xl05
DN m3/min 6,300 7,150
119
-------
Duct Inlet Outlet
DSCFM 2.4x105 2.7x10s
I H20 vapor (vol.) 6.01 15.0%
The flow measured by the outlet velocity traverse
is judged to be more reliable because the velocity dis-
tribution was much more regular than at the inlet. Based
on 7,120 DNm3/min (2.7xl05DSCFM), the inlet flow rate
would be 15,300 Am3/min (5.4xl05ACFM), which is 8% 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 equiva-
lent 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 agree- ,
ment between the two is reasonably well. Figure 6-5 com-
pares 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 electro-
static scrubber becomes a venturi scrubber. The dimensions
of the scrubber are shown in Figure 6-6. The measured per-
formance 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 £/m3
2. QG = 21 Am3/min
120
-------
o
I—I
H
u
o
I—I
H
H
W
W
PL,
W
U
PL,
Experimental
1 data
0.01
1.0
PARTICLE DIAMETER,
Figure 6-4. Predicted and measured penetration for
Chemico venturi scrubber.
121
-------
1.0
H
U
o
I—I
H
w
PL,
W
J
u
0.01
Calvert's
-! equation, £=0.5
Calvert's
equation, £=0.4
Experimental
data
0.1
1.0
PARTICLE DIAMETER, ymA
10
Figure 6-5. Predicted and experimental grade efficiency
curve for Chemico venturi scrubber.
122
-------
LIQUID INLET
t
"* 6
CM
1
cm cm
tsj
Figure 6-6 - APS Electrostatic Scrubber
-------
1.0
E-
U
O
w
gO.l
w
•J
U
ss
o.oi
p Calvert's
model, £-0.25M
if Predicted by
r| equation 5-23
I | Experimental a
i Data
Calvert's
; model, £=0.5 :
Model for in-
finite throat
length
Illtlliiiiiiiiiiiiiiimttiniiiiii
o.i
1.0
PARTICLE DIAMETER, ymA
10
Figure 6-7. Experimental and predicted APS venturi
scrubber performance.
124
-------
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 Hydro-
Filter) . This device consists primarily of several par-
allel 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 con-
ditions during the performance test runs were:
1. QL/QG = 2.4 £/m3
2. Gas velocity in the space betweed rods was cal-
culated 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
-------
1.0
o 0.1
U
O
I—I
H
H
W
2
w
W
U
b o.oi
0.001
\l-Prediction for throat :|ii
length equal to five fi
:*JHr times rod spacing r-
^Prediction for
[infinite throat
length
; •; T rr.r .r: i
^Prediction for throat
length equal to ten
• times rod spacing
0.1
0.5 1.0
PARTICLE DIAMETER, ymA
5.0
Figure 6-8. Predicted and experimental performance
for venturi rod scrubber.
126
-------
2. liquation 5-23 gives better predictions than Cal-
vert'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 in-
finite length.
127
-------
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 per-
formance and the design of a ventari 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, Ft", of any device
on a dust of any size distribution will be
= r;/*
W
P
pt (ddw
where FT = overall penetration, fraction
Pt /d \ = penetration of particles with diameter d
W = total weight of particle, g
\n*
dw = particle weight corresponding to the interval
d Id j 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 dia-
meter, "d ", and the geometric standard deviation, "a " .
pg &
The log-normal particle distribution density is:
128
-------
dw
d(ln dp)
f (dp) '
1
(2irh.n
-------
Based on the conclusion of the last chapter, the per-
formance of a venturi scrubber can be approximated by the
particle collection occurring in a straight tube of infi-
nite 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 perfor-
mance of the venturi scrubber. The penetration for the
venturi scrubber is then given by equation 5-46, i.e.,
4K + 4.2 - 5.02
Pt(dJ = exp "
;-o (i * F) t«->S
vpo
(7-7)
where Pt(d ) = penetration for particles with diameter
d , fraction
B = flimensionless liquid-to-gas ratio
parameter
• •• ^^ i
«W _
K = inertial parameter
= d* p C' ur.
P p bt
9 ^G dd
d = particle diameter, cm
d, = liquid drop diameter, cm
C' = Cunningham slip factor, dimensionless
ufit = gas throat velocity, cm/s
p = particle density, g/cm3
PL = liquid density, g/cm3
PG = gas density, g/cm3
Ur = gas viscosity, poise
130
-------
The diameter for which collection efficiency is 501 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
4-2 - 5-02
K
p5o
where "K " is the inertial parameter for d
Pso r
(7-8)
and is defined as
K
uu. d 2
pso
(7-9)
By rearranging equation 7-8, we obtain
B = -
in (0.5) (Kpso * 0.7)
4K + 4.2 - 5.02 K _0
pso P°u
l * -) tan
pso/
(7-10)
By substituting equation 7-10 into equation 7-8, we have
In (0.5) (K^n + 0.7)
Pt(d ) • exp
-0.5
(7-11)
131
-------
From equation 7-4,
d = d exp (2) xln a
pa Pg r '
0.5
g
By using this expression, we get for the inertial parameter,
K
po
= b K
where b = exp ( 2(2)°'sxln a )
uGt dpa _ UGt
9 UG
^d
Pg exp
2(2)°'5xln a
5 UG
d
(7-12)
K
P8
Since
Pso _ [
V" \
let Y = dpa50
Pg
(7-12a)
(7-13)
By substituting equations 7-12 and 7-13 into equation 7-11 and
after rearranging, we get,
Pt(d )
= exp
0.693 (Y2 K + 0.7)
Kpg + 0.7)
- 5.02
tan
4 Y2 K n + 4.2 - 5.02 Y K0'5
PS PS
(l +
(7-14)
132
-------
By substituting equation 7-14 into equation 7-6, we have
Pt =
00
oo
4 b Kpg *
y2 -f
Cb KPg
4.2 - 5.02 (b K
v Pg
A 7 _ c; n? Y K"0-5
4.Z b.02 Y Kpg
K +0.7)
+ 0.7)
I0-5 (l + °'7 Uan-Jb V
\ Kpg/ ^ °'^
11 + °*7 It-in"1 J Pg
\ Y2Kna/ ^ 0.7
dx
(7-15)
Equation 7-15 is the final equation relating the
overall penetration "Pt" to inlet particle size distribu-
tion (d , a ) and to the inertial parameter for the mean
particle diameter "K ''•
ir o -,., .
Figures 7-1 through 7-3 are plots of "Pt" versus
(d /d ) with "K " as parameter for various "0 " values.
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 know-
ing the size distribution and liquid-to-gas mass flow rate
ratio. By substituting equation (7-12) into equation (.7-7),
we obtain,
Pt(dp) = exp
5.02
-B
4 b
b K
pg
0.7
0.7
(7-16)
133
-------
1.0
0.5
0.2
l£ o.i
z
o
0.05
H
P4
2
£ 0.02
J
1-1
i o.oi
§
0.005
0.002
0.001
0.02 0.05 0.1 0.2
Figure 7-1.
Venturi scrubber integrated penetration,
"Ft" versus "dp50/dpg", with "Kpg ' as
parameter,
"v2-5"
134
-------
o
I—I
H
H
a,
o
0.002
0.001
0.01 0.02
0.05 0.1 DTT
dpso/ pg
Figure 7-2. Venturi scrubber integrated penetration, Pt
versus dp50/dpg» with Kpg as Parameter> ag=5'
135
-------
1.0
2
O
2
W
W
>
O
Q.Q5
0.02
0.01
0.005
0.005 0.01 0.02
Q.I 0.2
0.5 1.0 2.0
Pso
Figure 7-3. Venturi scrubber integrated penetration,
Pt versus d /d , with K as parameter,
-t / r o to
a =7.5.
g
136
-------
Equation 7-6 now becomes
Pt =
5.02 (bK
•7 V bJW LCU1 ^-077:1 (7-17)
Figures 7-4 through 7-7 are the solutions for equa-
tion 7-17.
Throat Length of the Scrubber
For a venturi scrubber, most of the particle collec-
tion 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 follow-
ing design analysis, we will assume that particle collec-
tion 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 rec-
tangular 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 design-
ing a venturi scrubber, we should use a long throat. How-
ever, 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 Fig-
ure 7-8 reveals that a dimensionless throat length of
2 to 3 would be sufficient. Further increase in the
137
-------
1.0
0.5
100
0.001
Figure 7-4. "Pt" versus "B" with "K " as parameter,
"a = 2.5". pg
138
-------
1.0
0.5
O
I—t
E-
W
2
W
(X
O
0.05
500
0.01
B
Figure 7-5. "Pt" versus "B" with "K " as parameter,
rr =
°
139
-------
1.0
o
h- 1
H
<
&
E-i
W
2
W
P-,
w
o
Oi
0.1
0.05
0.01
1000
2000
5000
B
Figure 7-6. "Ft" versus "B" with "K " as parameter,
• I = 7 CTI Pg
ag '-* •
140
-------
;s|1000
1500
2000
0.01
Figure 7-7. Pa5° versus "B" with "K " as parameter,
141
-------
2.0
t .„
1.0
...ji i....
- change of
100
Figure 7-8. Effect 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 diam-
eter, "dpso" 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
throat length, "L", larger than 2, and "K " becomes a
... ps o
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
de
the modified Calvert's pressure drop equation is approxi-
mately equal to 0.8. therefore, the expected pressure
drop is
AE (cm W.C.) = 8.24 x lO'^fup (£HL_j|( ,-L\ (7-18)
L b v sec/J \QG/
Throat Velocity and Liquid-to-Gas Ratio
The principal collection mechanism occurring in a ven-
turi 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 velo-
city 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-to-
gas flow ratio, therefore, there exists an optimum combina-
tion 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 perfor-
mance cut diameter of the venturi scrubber. Properties
143
-------
rt 0.05
0.01
100
500 1000
K
po
Figure 7-9. Effect of throat length on performance.
-------
42.
en
100
50
10
0.5
0.1
0.05
50 100
500 1000
K
PS o
U
G
Figure 7-10. Predicted Venturi scrubber performance K 5o vs. B.
-------
of air and water at room temperature were used to con-
struct 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-liquid ratio
can be determined from Figure 7-11. Figure 7-12 shows the
relationship between "B" and "K so". 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 air- '<
water 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 "FT". 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 the temperature expected in the venturi. Then,
construct a plot of 1C vs d^Qcn (required) by,
Pg pd.3 0
a) Obtaining several K - B pairs using Figures
7-4 to 7-6 (depending on a ).
o
b) Knowing d , obtain d 50 for each of the K
B pairs using Figure 7-7.
146
-------
5,000
1,000
w
PL,
O
OS
a
;=>
ex
100
10
0.1
1.0
AERODYNAMIC CUT DIAMETER, ymA
10
Figure 7-11. Effect of gas velocity and liquid to gas flow
rate ratio on performance cut diameter.
147
-------
10
o- ex
1.0
0.5 —
0.1
0.1
K
0.5 2 1.0
= dp50 C> Pp uGt
10
p50
9 ^G dd
Figure 7-12. "B" vs "K , " for venturi throat of infinite
length.
p50
148
-------
2.0
H
W
ID
U
CJ
2:
>•<
o
o
0.1
0.2
Figure 7-13
0.6
1.0
3.0
6.0
QL/QG' £/m3
Predicted venturi performance, "d
QL/QG with "UG" and "AP" as parameter.
pa so
vs.
149
-------
5.0
C/l
o
w
H
w
CJ
U
t— (
S
Q
O
OS
1.0
0.5 fc
0.1
.-.:.-!- - ..: i-_-:i:_;-^=3;L:.T---ri-:.r--i~.-r3.---.;:L-J._l
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.
-------
2) Determine performance cut diameters: First determine vis-
cosities, densities, and Nukiyama-Tanasawa coefficients for the
venturi conditions. Then construct a number of performance
curves corresponding to different QL/QG ratios as follows:
a) Select a "ur "
bO
b) Drop diameter, d^, from Nukiyama-Tanasawa relation
(Table 3-2)
c) NReQ from equation (5-7)(assuming udo=0)
d) CDQ from equation (5-8)
e) Parameter B from equation (5-22) (assuming udo=0)
f) K from Figure 7-12
g) dpa50 from equation (7-9)
h) K from equation (7-13)
i) AP from equation (7-18)
Repeat steps (a) through (i) for several velocities. Plot per-
formance K vs d curves on the same plot as the requirement
curve from Step (1) . Plot AP vs d a_„ on a separate graph.
'pa s o
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^oc . The required pressure
TJ £15 0
drops will correspond to a certain QL/QG 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 selec-
ted optimum combination of AP and QL/QG proceed as follows,
a) From the design K solve equation 7-12a for UG^ as
a function of d,.
b) Substitute this equation for dd into the Nukiyama-
Tanasawa relation and solve for UG^.
c) Divide the volume flow rate by ufit to get the throat
cross-sectional area.
151
-------
5) Determine throat length: Using the design velocity,
perform steps (2a-d) and then, solve equation (5-47) for &.
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 ef-
fects 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 pro-
grammable 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 pro-
cedure.
2) Determine performance cut diameter: Use Figure 7-11
and equation (7-12a) to calculate the performance d 50 vs
K curves for various Qj/Qn ratios.
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
-------
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, a =5.0 and
a geometric mass mean particle diameter, d = 18 urn
PS
(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 urn particles is C1 = 1.013. Thus,
d a = 18 (1.013 x 2.6)°'5 = 29.2 umA
Next, a plot of the required cut diameters (dpaS9) 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 cir-
cles are listed below: j
pas o
B K pmA
4.3 17000 0.64
2.8 1,500 0.58
2.2 2,000 0.55
1.6 5,000 0.41
1.4 10,000 0.30
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
-------
10,000
5,000
bO
1,000
500
!.J I- « : I I' t ! I. I : .:!"{...
I .j r/l-i i -!-J I i I I- r T-. ! i* i UUp-j
i j i f.i i • ; LLkLL:
Requirement
Pt«0.01 -----
Performance
icurves
;;T^ = o.ooir-
0.002 — r--—-
0.2
0.4
0.6
paSO,
0.8
1.0
1.2
Figure 7-15. Impaction parameter vs aerodynamic cut
diameter for a venturi design.
-------
Gas Viscosity, u^ - 2.23 x ID"1* g/cm-sec
Gas density, pfi = 0.907 kg/m3
Gas kinematic viscosity, v~ = 0.246 cmVsec
Liquid density, PL = 997 kg/m3
so,
p
~ " 1,099
and the Nukiyama and Tanasawa equation for drop size reduces
to,
50 . M/QL\"
uGQ cmsec)
Other design equations to be used are,
M
W
Reo VG
CDo = 0.22 + ^- (1 H- 0.15 NJJ0) (5-8)
Keo
i QT PT
~ 0 . 48
pso ~ - — —
0.5 * B $5
(Based on Figure 7-12)
paso I 10-8U
C7-9)
Go
and
AP = 8.24 x 10'* u*
Solution of these equations for various ^L and uGo can be
greatly facilitated by use of a programmable calculator
155
-------
The solution to the design equations are plotted on Figures
7-15 and 7-16 for QL/QG ratios of 0.001, 0.0015, and 0.002.
1
Step 3. Determine the required pressure drops:
The intersections of the performance lines with the require-
ment line in Figure 7-15 determine the cut diameters (both
required and performance). These cut diabeters are repre-
sented on Fig. J-16 as triangles. The required pressure
drops corresponding to these cut diameter^ are then,
"L
<£
0.001
0.0015
0.002
pas o
ymA'
0.42
0.57
0.675
AP
cm W.C.
67
40
32
Based on the flue-gas rate of 567 Am3/min these QT /Qr
L o
ratios represent water requirements of 0.57 m3/min (150
gal/min) 0.87 m3/min (225 gal/min) and 1.13 m3/mdn (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 QL/QG = 0.002 and d 0 = 0.675 ymA is the
optimum. From Figure 7-15 the required K = 980.
tr O
~~ 98°
y yr a-,
U Q.
9(980) (VG)(dd) 9(980) (2.23 x 10-")dd
u
(29.2 x 10'1*)
ut A 2 f in i .-- i rt-
-------
100
e
u
50
10
A Design Points
0.2
1.2
"paSO,
Figure 7-16. Pressure drop vs aerodynamic cut diameter
for venturi design example.
157
-------
From the Nukiyama-Tanasawa correlation for the pre-
sent example,
Gt * G Gt
Substituting into the expression for "uGt" we have,
ur+ = 2.3 x 10SU9- + 7.78 x 10'
G kt
UG = 5,300 cm/sec
Throat cross-sectional area = 567 x 10— = 1,783 cm3
(60)(5300)
Step 5. Determine throat length:
5300
+ 7.78 x 10' = 0.0172 cm
= UGt dd PG = (5300)(Q.0172)(9.07 x
yG
2.23 x 10
CDo = 0.62
Therefore, throat length = /i\/°-0172W 1 \ (L)
\3/\ 0.62 /\9.07 x 10-" /
= 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
-------
Step (1);
At -25°C C' - 1.009 for d = 18 vim so. d =18
p ' pga
(1.009 x 2.6)12 - 29.2 ymA. Since this is the same d
as before, the K - d requirement pairs are the
same.
Step (2):
Using Figure 7-11 and the equation for K , Figure
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
*!§•
1.03
1.1
1.55
1.85
2.8
pa so
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 gen-
eral procedure and a higher temperature gas.
159
-------
20,000
10,000
5,000
bO
2,000
1,000
500
A Design Points
Gas Temperature = 25 C L
dpga = 29.2 ymA j
0.55
0.58
0.64
Figure 7-17. Impaction parameter vs QT/Qr for
venturi design example.
160
-------
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 entrain-
ment separators. Zigzag baffles, knitted mesh, packed beds,
cyclone separators, and guide vanes causing rotation of thei j
I
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 se-
parator, 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 design-
ing 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
-------
Drop diameter can be predicted by means of the cor-
relation by Nukiyama and Tanasawa (1938-40). For air
and water at standard conditions the N+T correlation for
Sauter mean diameter is:
d fern) = bU-U + 92.0 I— (8-1)
u (cm/sec)
b
where: d = Sauter (volume-surface) mean diameter of
drops, cm
Up = air velocity relative to drops, cm/s
Q = water flow rate, m3/s
Q = air flow rate, m3/s
According to Steinmeyer in Perry (1973), the Sauter
mean diameter is typically 70% to 90% of the mass median
diameter. If the drop size distribution is log normal,
this implies that the geometric standard deviation, "cr "
is about 1.6 for 90% and 2.3 for 70%.
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 -3m3/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 "cr " from 1.6 to 2.3, respectively.
o
One would therefore predict that the cumulative entrain-
ment concentration would be related to drop diameter within
the range of high and low values tabulated on the following
page.
162
-------
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 urn 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 distribu-
tion and concentration.
DESIGN EQUATIONS FOR ENTRAINMENT SEPARATORS
The design and operation of most entrainment sepa-
rators 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
163
-------
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 reentrain-
ment, 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 condi-
tions. Reentrainment velocity determines the maximum allow-
able 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 effi-
ciency, 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 maxi- .
mum capacity of up to 141 m3/sec (300,000 CFM) of gas. Effi-
ciencies of about 95% are claimed for 5 ym diameter drops
in a well-designed cyclone. Some manufacturers use a bun-
dle of small cyclones (multicyclones), which can efficiently
collect drops as small as 2 ym in diameter. However, this
arrangement reduces the capacity of the device.
164
-------
Primary Efficiency - Leith and Licht (1971) derived an
equation to predict primary collection efficiency in coni-
cal bottom cyclones as pictured in Figure 8-1. With slight
modification it can be applied to cylindrical cyclones.
The equation for predicting primary collection effi-
ciency is:
In Pt = - 2
2da V
2n+2
(8-2)
where:
n = 1 -
0-3
FT]
2831
o.i n -
,0.393 d_)
1 - v
2.5
u
Pt =
pd =
\A* 1 **~
d
tg "
(8-3)
d_ =
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
t =
(8-4)
where:
V = effective volume of the cyclone, cm3
e
Q = volumetric gas flow rate, cm3/sec
165
-------
Figure 8-1. Cyclone with tangential gas inlet,
166
-------
A = inlet area, cm2
UG = inlet gas velocity, cm/sec
The effective volume of the cyclone, "V " is defined
c
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.
Ve = V + 1/2 V2 (8-5)
where:
V = annular shaped cdlume above exit duct inlet
to mid-level of entrance duct
V = volume of cyclone below exit duct inlet
2
to the natural length of the cyclone
v = — £- (h -S)
2 4 S 12
(8-7)
4
where:
• i_* * -i_j 11. •
(8-8)
and L = natural length of the cyclone
d = d -(d -bJ
167
-------
(8-9)
a, b, d , d , S, h, h_ are cyclone dimensions defined
G G S
in Figure 8-1.
Pressure Drop-Shephard and Lapple (1940) derived an equation
for a cyclone with inlet vanes for pressure drop as a function
of inlet gas velocity and the cycione inlet and outlet
dimensions:
2
AP = 0.000513 pr (—) ( 7>5 ab| (8-10)
G \ab/ \ d2 /
where:
AP = pressure drop, cm W.C.
PG = gas density, g/cm3
QG = gas volumetric flow rate, cm3/sec
a = cyclone inlet height, cm
b = cyclone inlet width, cm
d = cyclone exit pipe diameter,
6
cm
Equation (8-]D) 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£ve (8-11)
Shepard and Lapple also developed an equation for a cyclone
without inlet vanes:
2
AP = 0.000513pn l^ \\±^±\ (8_i2)
ab/ ' d2 /
G
168
-------
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 pm in diameter at 80-901
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. Up-
stream 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 col-
lection efficiency and low pressure drop.
Packed beds are often used for mass transfer because
of their 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
(e-Hd)
(8-13)
A j ur
m d d a
P 9 "6 dc
where:
j = ratio of channel width to packing diameter
H, = fractional liquid hold-up in the bed
e = bed porosity , fraction (Table 8-1)
A = 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 pack-
ing material. For the manufactured packing materials, "j"
is 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 func-
tion 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 o.2
8-2, where a dimensional group of function nL ,
PGPL§
(centipoise) ' , is plotted against a dimensionless group
L /PG\V'2
of function — I— J , where "G" and "L" refer to the gas
G \PL/
and liquid mass fluxes respectively. "Y" 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
r*
known, —3 may be used instead.
c.
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.
170
-------
TABLE 8-1
BED POROSITY, e, FOR VARIOUS PACKING MATERIALS
Size
(cm)
1.27
1.9
2.54
3.8
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
4
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)
1.27
2.54
3.8
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
j
0.192
0.190
0.165
0.03
Adapted from Jackson (1964) and Calvert (1968)
171
-------
Tablefi-3. PACKING FACTORS, "F", FOR DUMPED PIECES (m2/m )
Nominal size of packing, cm
[0.64] [0.95] [1.27] [1.59] [1.9] [2.5] [3.2] [3.8] [5] [8] [10]
Raschig rings,
ceramic
.16 cm wall 5,250 3,280
. 32 cm wall
.63 cm wall
.95 cm wall
Raschig rings,
carbon
.16 cm wall
.32 cm wall
.63 cm wall
. 79 cm wall
5,250
1,340
Raschig rings,
metal
.08 cm wall 2,300 1,280 980 560
.16 cm wall 1,340 950
Lessing rings,
porcelain
.32 cm wall
.63 cm wall
Lessing rings,
metal
.08 cm wall
.16 cm wall
(1,060)
510
430 210
121 98
920 525
430 210
118
510 380
720 450 360 272 187 105
(800)
(360)
(630)
(472) (387) (295) (200)
Table #-3.. PACKING FACTORS, "F", FOR DUMPED PIECES (mVm3) (continued)
Nominal size of packing, cm
[0.64] [0.95]
Partition ring's
Pall rings,
plastic
Pall rings,
metal
Berl saddles 2,950
Intalox saddles, 2,380 1,080
ceramic
Intalox saddles,
plastic
Super-Intalox,
ceramic
Tellerettes
[1.27] [1.59] [1.9] [2.5] [3.2] [3.8]
318 171 105
230 158 92
790 560 360 213
660 475 322 171
108
200
[5] [8] [10]
262 190
82
66
148
131 72
69 52
100
150
Parentheses denote a value of a/e3, rather than empirical F.
172
-------
Table 8-4. PACKING FACTORS,"?" FOR GRIDS AND STACKED PIECES
(m2/m3).
Nominal size of packing, cm
2.5 3.8 5 8 10 13 14 15
Wood grid 20 11 8.2 5.9 4.9
^letal grid 8.2
Grid tiles 118
Checker brick,
e=0.55 ' 135
Raschig rings,
ceramic
.63 cm wall 95 16
.95 cm wall 36 12.8
Raschig rings, 21
metal
Partition rings,
diameter
7.6 cm length (1,200) (725)
.10.2 cm length (705) (410)
15.2 cm length (375)
Partition rings,
square set
7.6 cm length (690) (460)
10.2 cm length (450) (275)
15.2 cm length . (26°)
Parentheses denote a value of a/e3, rather than empirical F.
173
-------
a,
•
u
c
0.5
0.2
0.1
0.05
cT1 0.02
u
Q.
" 0.01
0.005
0.002
0.001
:S\
Pressure drop
rm w r «of /Pressure Drop,\
cm W.C. per in W.C. per Ff|
cm packing \£t< packing htl
ht.
1
0.01 0.02
0.05 0.1 0.2 0.5
L /PG] 1/2
x = — —I
G IPLJ
(dimensionless)
10
Figure 8-2. Generalized flooding and pressure drop
correlation for packed beds (Perry, 1963) .
174
-------
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 collec-
tion efficiency of each stage of impaction can be found in
Figure 8-3. Each row of tubes except the first represents
one stage of impaction. "B" is used as a parameter in
Figure 8-3 and is defined by:
3 = 2 Jl/b (8-14)
where :
b = jet orifice width
£ = distance between orifice and impingement plane
"K " , the inertia parameter, is defined with drop radius,
"r ", rather than diameter.
Efficiency for the bank of tubes is given by:
E = 1 - (l-Tij)N (8-15)
where :
n .- = collection efficiency for a given particle
diameter in one stage of rectangular jet im-
.pingement
N = number of stages in the tube bank
= (number of rows) -1
If the tubes are widely spaced, the target efficiency,
"n", can be calculated from Figure 8-4. In this case the
efficiency for the entire tube bank is:
E - i - (i-n-V (8
175
-------
:er Chow
Exp.
LS Theory
0.5
1.0
1.5
V*
2p C
r*-|-i
u
Figure 8-3 - Theoretical and experimental
collection efficiencies of
rectangular aerosol jets.
176
-------
w
tu
UH
w
1.0
0.8
0.6
0.4
0.2
0
^ I Rectangular half body
Cylinder
(ribbon with woks)
Ribbon normal
to (lav
Ellipsoid of
revolution lot
thick
^•^ Ellipsoid
C~j of revolu-
'^"^ tion. ZO*
NACA 650,004 -at
zero angle of
attack 4t thick
low-drag symmet-
rical airfoil
Joukowski 15* thick sym-
metrical airfoil at zero
angle of attack
0.1
10
100
d U
INfiRTIAI PARAMETER, K * ——^—£—
P " 14- r1 ®,
Figure 8-4 - Theoretical impaction efficiency as
a function of inertial parameter
for different targets.
177
-------
where:
a1 = 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 cor-
relations (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 ex-
changers. 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 10 '") (u£)2 cm W.C. (8-16a)
where:
Up 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 pres-
178
-------
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 flow rates
are desired.
Often two mesh type separators in series are used to
remove drops in the 1-5 ym diameter range. The first mesh,
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 fab-
rication. However, mesh separators are limited in appli-
cation because they plug easily. This can be avoided by
upstream washing, which will decrease removal efficiency and
increase pressure drop.
Primary Efficiency-Eradie and Dickson (1969) present the fol-
lowing expression for primary efficiency in mesh separators:
179
-------
E = 1-exp ( - | ? a2*2 ") (8-17)
where:
a~ = specific area of mesh, surface area of wires
per unit volume of mesh pad, cm2/cm3
JU = 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)
a = (8-18)
L ac
\
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 = APdry + APL (8-19)
where:
AP, = pressure drop in absence of liquid, cm W.C.
APL = 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
180
-------
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:
APdry - - a (8-20)
7 e
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 dif-
ferent styles. Values of "APT " obtained by York and Poppele
Li
are presented in Figures 8-6 and 8-7, with liquid velocity
I1T II
as the parameter. Liquid velocity is defined as — x— where
"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. p, and PG
2. Liquid viscosity
3. 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).
181
-------
1.0
0.5
0.1
0.05
0.01
I I I ' I 11
Satsangee data (1948)
and Shuring data (1946)
JZrimps in alternated direction
Crimps in same direction
- Layered mesh—r***
: Spiral-wound mesh
i i
i i i
ni
10
100
1,000
N
Re,G
i i
10,000
VJ
Figure 8--5. Friction Factor, £, versus Reynolds
number, NR G for wire mesh entrainment
separator ' with entrainment load.
182
-------
00
10
1.0
e
o
0.01
'I I I I I I I
I I
J i
56 7 8 9 10 11 12 13
cm/s
Fig. 8-6. Pressure drop due to
presence of liquid in
the knitted mesh with
the crimps in the same
direction .
10
1.0
e
o
0.1
0.01
I I
V
3 4 S 6 7 S 9 10 11 12
UG [ PG/(PL'PG) > cm/S
Fig.8-7 . Pressure drop due to
presence of liquid in
the knitted mesh with
the crimps in the alter
nate 'direction.
-------
un =30.5
G max
°'5
where "a," varies with operating conditions and mesh de-
sign. 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 de-
vices 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 sepa-
ration 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 baf-
fle section is:
= 1 - exp
57.3 ur b tane
b
u. nw6
r (8-22)
where:
n = primary collection efficiency, fraction
utc = drop terminal centrifugal velocity, in the
normal direction, cm/sec
UG = superficial gas velocity, cm/sec
n = number of bends or rows
6 = angle of inclination of the baffle to the flow
path, degrees
184
-------
w = width of baffle, cm
b = spacing between two consecutive baffles in
same row, cm
The drop terminal centrifugal velocity can be deter-
mined by performing a force balance on the drop. The result
is :
0.5
U,
(8-23)
where:
da = drop diameter, cm
p, = drop density, g/cm3
a = acceleration due to centrifugal force, cm/sec2
CD = drag coefficient
PG = gas density, g/cm3 „
If the drop Reynolds number is low (NRg D< 0.1),
Stokes1 law applies. For this condition, the drag co-
efficient is given by:
C = — ^- (8-24)
NRe,D
where ND n = drop Reynolds number
Ke , u
dd utc PG
By combining equations 8-23 and 8-24, we obtain:
d5 pj a
„ = d d _ (8-25)
utc 18 U V
185
-------
The acceleration due to centrifugal force is defined by
the following equation:
2 2
2 (ur) 2 ur sin 6
a = 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 indi-
vidual drop is neglected.
Pressure Drop-Determination of the pressure drop is based on
the drag coefficient, "fD", for a single plate held at an
angle "9" to the flow as presented in Figure 8-9 (Page
and Johanson, 1927) . Neglecting the effect of neighbor-
ing plates, pressure drop may be expressed as:
, 2
AP = E 1.02 x ID'3 f p -£ Ji (8-27)
i=l " b 2 At
where:
AP = pressure drop, cm W.C.
A = total projected area of baffles per- row in the
direction of inlet air flow, cm3
At = duct cross-sectional area, cm2
The summation is made over the number of rows of
baffles.
186
-------
10,000
1 ,000
H
O
H
fe4
k.
^
O
OS
100 -
ifi=0.125
ip= 0. 2 2 0
i)'=0.6nD
=0. 806
0.001 0.01 0.1 1 10 100 1000 10,000 10s 106
Reynolds nuisher N.
Re.D
dd utc pr,
u,
l:igure 8~8- Drag coefficient versus Reynolds number after
Foust et al (1959), with sphericity ip as
the parameter.
1 .2
-0.8
W
u-
PJ
o0.4
LJ
C3
I r i i i r i r
i i
Plate Inclined to Flow
„ 7"
Angle of
Incidence
j I
I i I I
20
40
60
80
ANGLE OF INCIDENCE, degrees
Figure 8'^. Drag coefficients for flow past inclined
flat plates (data from A. Page Si F.C.
Johansen, (1927).
187
-------
The actual gas velocity, "UG", in the baffle section
should be used in Equation (8-27). The actual gas velocity
is related to superficial velocity by:
ul = ur/cos 9 (8-28)
b b
Note that the angle of incidence for the second and sub-
sequent rows of baffles will be twice the angle of inci-
dence 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 col-
lection efficiency:
E = 1-exp (-40 F* K ) (8-29)
* P
where 0.30 < F. < 0.65,
x>
p jdjV,
Kp • -±±± (8-30)
P 9"Gdh
where:
F^ = foam density, ratio of clear liquid height
to total foam height
v = velocity of gas through hole, cm/sec
188
-------
d, = hole diameter, cm
.Pressure Drop - Perry (1963) has suggested that the
pressure drop in sieve plates can be calculated accor-
ding to :
AP=h+h+hj+h rs
w ow dp r I8
where :
hw = weir height = 4-9 cm, assume 5 cm, if unknown
h QT
ow = head over the weir = 0.143 F — —
W W-j
i Pr vh
hAn = dr7 Plate head loss = - -- - ^i
dP c2 PL 2g
tiJ J1 "f" f^ Y*
h = residual pressure drop = 0.013
PL
c2
= 1.14
0.4 (1.25 - £h) + (1 - £h)2j
(8-32)
where:
F = column wall curvature correction factor = 1.1
w
Q, = liquid flow rate, here in m3/hr
Li
w1 = weir length, m
f, = fraction of the perforated open area in the
plate
Bubble-cap Trays - Equations used to predict primary col-
lection efficiency and pressure drop of sieve plates can
also be applied to bubble-cap trays.
DESIGN PROCEDURES
The general steps in designing an entrainment separa-
tor are as follows:
189
-------
1. Based on process condition and separator con-
figuration, construct the grade efficiency
curve for the separation. Equations for pri-
mary 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 effi-
ciency .
2. Compute the collection efficiency for the whole
population of the drops. This can be done either
graphically or mathematically. For graphical
solution, plot Ft- versus fraction smaller than
d, - (where Pt. is penetration for drop size d-, -) .
The area under the curve is the overall pene-
tration. 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 sep-
arator configurations. The final configuration can then
be selected after optimization analysis.
190
-------
REFERENCES
Akselrud, G., Zh. Fiz. Khim. £7, 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 Indus-
trial 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 "Scrub-
ber Handbook" . A.P.T., Inc. Riverside, California.
NTIS No. PB-213-016. August 1972.
Calvert, S. and D. Lundgren. Particle Collection in
Closed Packed 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. Yunfe, and J. Leung, "Entrainment Separator
for Scrubbers - Final Report", EPA-650/2-74-1196, NTIS
No. PB-248-050.
191
-------
Carpenter, C.L. 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, 14,
541-552, 1968.
Dropp, L.T. and A.J. Akbrut, "Working Processes and
Calculation of the Efficiency of an Ash Trap with a Ven-
turi Tube", Tepoloenergetika, No. 7, 63-68, 1972.
Ekman, P.O. and H.F. Johnstons, "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, £, 114, 1958.
Garner, F. and R. Keey, Chem. Eng. Sci., 9_, 119, 1958.
Gieseki, J.A., Ph.D. Dissertation, University of Wash-
ington, 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 Venturi-
type Contactor for Removal of S02 by the Limestone Wet-
scrubbing 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
Herne, 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
-------
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
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hng. Chem. Fundam. 14, pp 16-22, 1975
Houghton, J.G. and W.H. Radford. Trans. A. Inst. of ChE,
•3o> HrZ/j JL y ,5 y
Hughes, R.R., Chem. Engr. Prog. 48, 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,
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Levich, V., "Physiochemical Hydrodynamics", Prentice-
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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 Con-
sideration given to Droplet Size Distribution" Kagaku
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Morishima, N., T. Yoshida, Y. Kosoka, and Y. Nonaka
"An Examination of Venturi Scrubber Design" Funtai
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Tohata, H., T. Nakoda, and I. Sekiguchi, "Pressure Losses
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142, 1960.
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Particles", ed. E.G. Richardson, Pergamon Press, Oxford,
129-153, 1960.
Wen, C.Y. 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, 27, 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, 24, 20-:
20-27, 1960. —
Yoshida, T., N. Morishima, M. Suzuki, and N. Hukutome, "
"Pressure Loss for the Acceleration of Atomized Droplets",
Kagaku Kogaku, 2£, 308-315, 1965
194
-------
APPENDIX A. DERIVATION OF SCALING FACTOR
In solving equation 5-23 we assumed ul = 0. In order
to find Pt(d ) for other values of u| , we make use of the
following artifice. Imagine the given duct to be projected
in the upstream direction until a distance !„ is reached
rl
such that at z = -lu, the liquid velocity is zero. That is,
the distance IH is that length of a hypothetical duct having
zero initial liquid velocity with established liquid velocity
u
do
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
and A1 = A
o o
tan
tan 3 \ j
(A-l)
(A-2)
From continuity of gas flow, we have
"GO*
m,
A'
o
m.
= ur I 1 -
Go I
lu tan 3
n
(A-3)
From the definition of C, we have
Do
DQ
U
Go
|uGo-udo|
10.5
f ' =
LDo
u
u~
Go
Go
-udo
0-5
JDo
u
Go
0.5
IH tan 6 1
~o J
J/2
(A-4)
195
-------
Using equations A-l through A-4 and the definitions
of the various dimensionless parameters, the following
relations are obtained:
/ W \
L' = (L + LH)(l - S LH) (A-5)
S' = S (l - S LH)":)/2"1 (A-6)
ud' = "d1 - S LH CA-7)
B, _/QL
"
G
196
= B (l - S LH)"j/2 ••• (A-8)
which give the desired scaling factors.
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
^£4^600/2-77-172
2.
3. RECIPIENT'S ACCESSION-NO.
-c AND SUBTITLE
• nturi Scrubber Performance Model
5. REPORT DATE
August 1977
6. PERFORMING ORGANIZATION CODE
Shui-Chow Yung, Seymour Calvert, and
Harry F.
J. PERFORMING ORGANIZATION REPORT NO.
3. PERFORMING ORGANIZATION NAME AND ADDRESS
A. P.T. , Inc.
j 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
\ ^.SPONSORING AGENCY NAME AND ADDRESS ~~
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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
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IERL-RTP task officer for
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E< Sparks Mail
ABSTRACT
report gives results of a review and evaluation of available venturi
-..rubber 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
'. Fonturi 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
I new design equations are much simpler to use and compare favorably with available
j performance data.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
; Air Pollution
tScrubbers
• Venturi Tubes
l Design
j Performance
Mathematical Models
Dust
Flue Gases
Entrainment
Separators
Air Pollution Control
Stationary Sources
Particulate
Venturi Scrubbers
13B
07A
14B
12A
11G
21B
07D
!13. DISTRIBUTION STATEMENT
: Unlimited
19. SECURITY CLASS (ThisReport)'
Unclassified
21. NO. OF PAGES
212
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Fo-m 2220-1 (9-73)
197
-------