Several other related questions arise during the design of the algorithm, such as the optimum number of points to be used in the holding time integrations, which are best answered by simple experiment with the program. Careful attention to these and the four points enumerated above will repay Ihe designer of such a program in terms of final efficiency and reliability in his algorithm.
AH, J k
K
Pi p.\ QO
Conclusions
This paper has sought to describe in sufficient detail the construction of an algorithm for the problem a t hand. A careful combination of direct dynamic programming iechniques, analytical criteria, and methods for monitoring and avoiding repetitive calculations has resulted in a program of high efficiency. Extension of these approaches to other more general problems should be feasible and easily made.
r
T U
XU
V X
0 Po
Acknowledgment
Nomenclature = specific heat of reactant stream, energy/(mole =--- ‘ H R ,
0
lr Z
1
literature Cited
The authors acknowledge with thanks free computer time made available by the Northwestern University Computing Center and a n NDEA Title IV fellowship (to MR) which made this work possible.
Cp H
heat of reaction, energy/(mole of product formed) moles dx, [(volume of catalyst) (time) ( 0 F.) -I = specific rate constant, moles/(time) (volume of catalyst) = equilibrium constant for reaction = profit from ith stage, dollars = total profit from a n N-stage system, dollars = volumetric flow rate of feed a t standard conditions, volume/ time moles = rate of production of product, (time) (volume of catalyst) = temperature, ’ F. = volume of process stream, dollars/(mole of desired product) = cost of reactor, dollars/(volume of catalyst) = catalyst volume, volume = mole fraction of product = nominal reactor holding time, time = molar density of feed a t standard conditions, moles/ volume =
’ F.)
(1) Aris, Rutherford, “Optimal Design of Chemical Reactors,” Academic Press, h’ew York, 1961. (2) Bellman, Richard, “Dynamic Programming,” Princeton University Press, Princeton, N.J., 1957. (3) Horn, Frederick, 2.Eleklrochem. 6 5 , 295-303 (1961). (4) Hougen, 0. A., Watson, K. M., Rogatz, R. A., “Chemical
Process Principles,” Part I, 2nd ed., Wiley, New York, 1958. (5) Moe, J. M.,Chem. Eng. Progr. 5 8 , 33-6 (1962). (6) Rafal, Marshall, M. S. thesis, Northwestern University, Evanston, lll., 1964.
F,
RECEIVED for review February 12, 1965 ACCEPTED November 15, 1965
G P
INLET-GAS HUMIDIFICATION SYSTEM FOR AN ELECTROSTATIC PRECIPITATOR S EN
-I
C H I
MASUDA
,
Department of Electrical Engineering, University of Tokyo, Tokyo, Japan
T0SH I 0 0N I SH I A ND H I R0S H I
SA IT0
,
Onoda Cement Manufacturing Go., Tokyo, Japan
A system for rapid evaporation of mist was developed for inlet-gas humidification in an electrostatic precipitator, which can evaporate a large quantity of water in a small spray chamber in the temperature range of 150” to 200” C. An improved type of multiple twin-fluid nozzles, developed for this purpose, can produce extremely uniform and small particles of mist in any amount, with the aid of an equal magnitude of high fluid resistances inserted into its water branches. Confinement of mist within the narrow space of a spray chamber was made possible by the mist thermal repulsion action of the wall surface kept a t elevated temperature. The mist lifetime measured in an actual spray chamber can b e explained by the theory, if a new type of mist average diameter is utilized.
EVERSE
ionization has long caused major trouble in electro-
R static precipitation, but it can be prevented by reducing
the electrical resistivity of dust within the precipitator below a critical value of about 2 X 1010 -v 1 X 1011 ohm-cm. with the aid of inlet-gas humidification (78). The inlet gas may most economically be humidified by water atomization within a spray chamber installed immediately ahead of the precipitator. However, the temperature of the inlet gas in most cases is in such a low range (about 150’ to 200’ C.) that mist usually evaporates very slowly. As a result, mud or slurry often builds up inside the spray chamber be-
cause of the poor evaporation of mist, which may sometimes make necessary shutdown of the whole process. Complete evaporation may be possible, if the size of the spray chamber can be greatly enlarged or the mist particle size can be reduced to any desired amount. The present practice is to atomize water within a very large spray chamber, often larger than the precipitator itself, with the use of single-fluid nozzles, featured by very low operating cost as well as large mist size. This may be the most simple and economical solution in the case of large inlet-gas volume, although it can be applied only where adequate space is available for the installation of such a VOL. 5
NO. 2 A P R I L 1 9 6 6
135
large spray chamber. The rather high investment cost of a large spray chamber may be more than offset in this case by the extremely low operating cost of single-fluid nozzles. O n the other hand, in many cases no such space is available and yet the inlet gas must be humidified to improve the collection efficiency of a precipitator. I n such cases, it becomes necessary to atomize water in a very small spray chamber, without mud buildup or slurry formation. However, this has been extremely difficult to achieve because of the lack of data concerning the speed of mist evaporation within the industrial spray chamber and also lack of nozzles capable of producing a large quantity of extremely fine and uniform mist particles. The present paper reports a practical inlet-gas humidification system especially suited to such cases (72),based on a new type of multiple hvin-fluid nozzle developed for this purpose
produce air jets only, or air may enter into water pipes QeCaUSe of the fluctuations of air and water pressurc!S. O n e practical solution is to insert higl1 fluid resistances of equal magnitude into the water branche s connecting nozzles -f .-a"e+.."+ "...*-..* to the common water pipe, on the analogy "~ cyII~III source in an electric circuit (73). Figure 1 shows a structure of multiple twin-fluid nozzles developed on this principle, where the high fluid resistances are orifices of equal size fixed a t the entrances of the mixing chamben. termed "halancing orifices." The fluid resistances to be inserted should be a t least one order of magnitude higher than those in wazer p a n s Irom me inlet of the common water pipe iD the mixing chambers of the nozzles, so that the fluid resistam:es of water paths are concentrated a t the inserted high fluid ncsistances of equal magnitude,
-
~Y1ll.I..l
.,
much larger flow rate. The role of the balancing orifice for air shown in Figure 1 is to check water entry into air pipes occurring a t a reduced air-feeding rate rather than to equalize air-feeding rates. I n the field test of this multiple-nozzle set, noticeable mud buildup occurred on its whole surface, owing to the collision of swirling mist caused by vortex in its doivnstream. But this trouble could be solved by extending the nozzle head outside of the vortex zone, as shown in Figure 1. Jet openings of the nozzle head are shaped in the form of slits to produce a fanlike mist pattern suitable for rapid evaporation. Figure 2 is a photograph of this type of multiple-nozzle set, Lvhich met all requirements for the present purpose. Figure 3 shows the flow characteristics of a single-nozzle unit, where P, and P, are the gage pressures of water and air a t the nozzle inlets, respectively, and y is a ratio
(1)
7 = Qa/Qzo
where
was utilized, with a suitable mixing ratio. About 1000 particles in five photographs were used to obtain a particle size distribution for each set of Pa and P,. T h e distributions obtained were approximately log-normal as exemplified in Figure 5, consistent with the results of Gretzinger and Marshall (2). T h e distribution function therefore is (5)
where
2, = geometric mean diameter, microns geometric standard deviation
uu =
and is determined by two parameters, and uu. These two parameters were solely determined by y, defined by Equation 1, independent of both Pa and P,, as is indicated in Figure 6, inconsistent with the results of Nukiyama and Tanasawa (76, 77). They obtained the following experimental formula of Sauter's mean with a type of twin-fluid nozzle, based on the data measured within the range of y = Q a / Q 1 = 1000 to 10,000.
qa = air-feeding rate into a single-nozzle unit, normal
4..
=
cubic meters per hour water-ferding rate into a single-nozzle unit, normal cubic meters per hour
where density of liquid, grams per cc. surface tension of liquid, dynes per cm. ,u = \iscosity of liquid, dyne sec. per sq. cm. Qa = volume flow rate of air Q1 = volume flow rate of liquid u = relative velocity between air and liquid, meters per second
p
Mist Particle Size Distribution
u
Mist particle size distribution, one of the most important factors in the present research, was measured by a microscopic method \\ithin \vide ranges of Pa and P,. T h e value of Pa \\as varied from 1 to 4.5 kg. per sq. cm , \vhereas that of P,, \vas changed from 1.1 to 5.5 kg. per sq. cm. independently. hlist was sampled a t a point on the nozzle axis 50 cm. away from its jet opening, with the use of a sampling device of shutter type as sho\in in Figure 4. Mist particles were caught upon the oil film coated on a glass plate during the exposure time, and were photographed with a photomicroscope. Then their diameters n e r e measured from the enlarged photographs. T h e surface tension, viscosity, and density of oil were adjusted in such a way that the sampled mist became completely embedded in the oil film in the form of spherical particles (75, 77). For this purpose, a mixture of lubricating oil and kerosine
= =
Relations similar to Equation 3 should hold also for the present case and parameters d, as well as uo determining the particle size distribution will become functions of not only y but also Pa and P,. both of which will determine the relative velocity, 2'. I n the present research, however, the measurement was carried out within a smaller range of y, from 50 to to 250, to make it possible to neglect the first term of Equation 3
99 59
59 90
I (kg/crn2) 0
55 00
-
~2 Pa 3
L
a X
1 4
I45
95C0
50 00 8000 70 00
50 00 30 00 20 00 I000
w
I 0 CL
kw
2 1 LE
0
20
50
N3ZZLE
2
4
IO
20
40
100
PARTICLE DIAMETER d , p
Figure 5.
Mist particle size distribution
200
00
PARAMETER
200
,
5CO
I
Figure 6. Effect of nozzle parameter on geometric mean diameter and geometric standard deviation VOL. 5
NO. 2
APRIL 1966
137
expressing the effect of the relative velocity (6). I t would therefore not be surprising that d, as well as u, becomes independent of Pa and P, in the present case. The relation between y and Sauter’s mean d, obtained from Figure 6 with the use of Formula 4 (5)
d,
=
exp(1n 2,
+ 2.5 (In u , ) * }
(4)
is plotted in Figure 7 , which leads to the experimental formula
2,
=
4.81 X 102/y0.5,microns
(5)
Here, 2, is proportional to l/yO.S, while in Equation 3 it is proportional to l/ylJ, which may be attributable to the difference in the type of nozzle used. Lewis et al. also reported that Equation 3 does not always hold in the twin-fluid atomization
(6). Mist Thermal Repulsion Phenomena
The wetting of a metal surface a t elevated temperature was studied, since it not only causes mud buildup inside a spray chamber but is also one of the factors determining the effective mist lifetime itself. In the surface temperature range of 100’ to 200’ C., there are three stages in the wetted state of the surface-dry, semiwet, and wet. When mist particle size 2, its colliding angle to the surface, 0, and its colliding velocity, V , are small and the surface temperature, t s , is high, water spots can hardly be observed over the surface and it is kept materially dry. With the increase of 2,0, and V , or the decrease oft,, water spots begin to appear on the surface, but they evaporate instantly and the surface is kept in a semiwet state. I n the dry and semiwet states, the major portion of the mist does not come into contact with the surface and flows parallel to it, usually keeping about 0.3 to 3 cm. away, where a mistless zone is formed (Figure 8). This effect is caused by the repulsive force of vapor flow produced by the evaporation of large drops colliding onto the surface, which are few in number and therefore have only a limited wetting effect. This phenomenon was termed “mist thermal repulsion of the first kind.” With the further increase of 2, 0, and V , or the further decrease of ts, the number of drops coming onto the surface against the vapor flow increases, and finally the whole area becomes wet, covered by a continuous water film. When t, was raised above 200’ C., the colliding mist was reflected elastically without making a spot on the surface because of the vapor cushion produced a t the point of contact duz to the higher temperature. This phenomenon was termed “mist thermal repulsion of the second kind.” These phenomena play very important roles in the confinement of mist within a spray chamber ( 7 4 ) .
exit-gas duct leading from the waste heat boiler of a dryprocess cement rotary kiln to its electrostatic precipitator. Table I shows the major parameters ip this test spray chamber. At its upstream end, two bypass ducts and a shut damper were installed, to make observations inside the duct possible a t any desired instant, even during plant operation, by bypassing the gas into two other precipitators. Five manholes and 12 test holes were also installed on the upper wall of the duct, and a set of the multiple twin-fluid nozzles described was inserted a t the upstream end, as shown in Figure 9. After atomizing for a constant period of time, the inside of the duct was inspected through the manholes. So far as mist was atomized parallel to the wall in the direction of gas flow with y 2 20 and h 2 30 cm., the inner surface of the wall (except the bottom) was kept a t most in a slightly semiwet state and suffered only a small amount of dry and flakelike mud buildup, which could be easily removed by a mechanical shock. The buildup speed of such a mud layer was about 2 to 5 mm. per hour when y = 20 and h = 30 cm. The mud buildup onto the bottom surface was much more pronounced, but it became negligible when y 2 140 a t h’ = 55 cm. The speed of buildup onto the bottom surface was about 5 mm. per hour when y = 140 and h’ = 55 cm. In contrast, any obstacles inserted into the mist-surviving zone or “wet zone” with a large angle to the direction of gas flow suffered a noticeable mud buildup, owing to the collision of mist. The tip of the nozzle head also suffered a slight amount of mud buildup, which could, however, be easily removed by a mechanical shock. 2OOr
I (kg/crn*i
0
2
A
3
X
14 (45
v
I
Pa
, OCI
I
80
IC‘
Mist Confinement in Spray Chamber
50
100
200
300
N O Z Z L E PARAMETER, 8
The possibility of confining atomized mist within a limited space with the aid of mist thermal repulsion phenomena was studied in a field test. T h e test was carried out in the horizontal portion of an
Table 1. Parameters in Test Spray Chamber D = 2 . 3 meters Q , = 7.53 X l o 4 normal cu. meters/ hour = 8.18 meters/sec. 1, = 190” C. L , = 1 1 . 0 meters H g = 14.1 g./normal cu. meter T = 1 . 3 sec.
Figure 7. Effect of nozzle parameter on Sauter’s mean diameter
MISTLE
vg
A
138
= 15.5%
l&EC PROCESS DESIGN AND DEVELOPMENT
Figure 8.
Phenomena of mist thermal repulsion
I t \\as therefoie concluded that mist could be confined in a narroiv space of spray chamber without any trouble, so far 7 s it was atomized parallel to the chamber \Val1 in the direction of gas flo~vand the temperature of wall \vas kept high enough for the effective action of mist thermal repulsion. Suitable hammeling devices for knud removal should be installed a t the chamber Lvall as !\ell as a t the nozzle set.
Figure 11 shows the relation between y and r . 7 is determined by y independent of a1 within the range of ZL tested and a t the inlet-gas temperature oft, = 190' C. From the curve in Figure 11, the following experimental formula was obtained T
=
x 102/y3/2,seconds
8.31
Mist lifetime in Spray Chamber
Atomized mist confined in a spray chamber ought to end its evaporation lvithin a straight portion of the chamber, or mud may build up a t its bend. Mist lifetime within a spray chamber therefore is one of the most important factors in its design. T h e relation betxveen mist lifetime and y was measured in the test duct described. During the atomization, twelve pipes lvere inserted simultaneously into the duct through the test holes as sho\vn in Figure 9 > and, after 1 minute, were pulled out all a t once. l ' h e shape and the length, L,, of the wet zone in the duct could be clearly detected by the mud buildup onto these probe pipes (Figure 9 ) . Figure 10 illustrates various grades of mud buildup onto the probe pipes, corresponding to the varying concentrations of surviving mist a t the points inserted. From a practical point of view, the tip of the wet zone was assumed to lie bet\veen two points, one corresponding to 6 and the other to c in Figure 10, bebveen which mist \vould lose its \vetting effect to the obstacles inserted normal to the direction of gas flow. The value of L, \vas measured for the various values of y and lvater-atomizing rate, E , expressed in grams per normal cubic meter: grams of ivater atomized per 1 normal cu. meter of the inlet gas. The value of y was varied from 50 to 700, \chile the value of zu was varied from 3.7 to 16.9 grams per normal cu. meter independently, by changing the number of nozzles from 6 to 14. The temperature of the atomized \vater !vas about 22' C. throughout the measurement. \Vhen the atomized mist is very small: the relative velocity of the mist and its ambient gas falls instantly to materially zero because of the predominant viscous friction. Therefore, the value of mist lifetime was estimated by
L,/vQ, seconds
7
(6)
where FQ= average gas velocity Lvithin the test duct, meters per second. TEST PROBES M,ST ,PATTERNTTEsT 3UCT
. /
NOZZLE SET
(7)
Thus, it may be possible to estimate the necessary length of the spray chamber under similar conditions by
L,
=
P P , ~meters .
(8)
where p is a safety factor. Theoretical Interpretation of Mist lifetime
The theoretical lifetime of a single mist particle suspended in a stationary atmosphere is given by Marshall (7) as:
(9)
ro = ad:, seconds
where CY
=
{ bi/8kj(ta
-
t,) 1 X
3.6
X
10-9, seconds per sq. micron
(10)
do = initial diameter of mist, microns X = latent heat of liquid a t t s ' C., kcal.;kg. p 1 = density of liquid, kg./cu. meter t, = ambient gas temperature, ' C. t , = mist surface temperature N wet bulb temperature,
' c.
k,
=
thermal conductivity of gas film around mist particle, kcal./meter hr. ' C.
Equation 9 is assumed to hold below a Reynolds number of 20. I n the present case of inlet-gas humidification, t, and t, will change in the course of the mist evaporation process, according to the inlet-gas temperature, t,, water temperature, t,, and water-atomizing rate, LL. I n the estimation of CY, it is therefore necessary to use the average values for t, as well as t , and those corresponding to such average values for A and k , in Equation 10. Figure 12 shoivs the relation between CY and u, as well as t, calculated for the inlet gas of the test chamber described. The change of oi with the increase of ZL from 3.7 to 16.9 grams per normal cu. meter a t t, = 190' C.,
TEST HOLES
I I I
n
'i,
c
i 3' ML36JlL3UP (wet)
Figure 9. zone
M U ~ B U I L D U P( s e m i - w e l l
Probe method for measurement of wet
5t
1
L 31 w z
u1 z N 0
a WET DJST
1
02
b SEMI-WET
C D R Y DUST
d D R Y DUST
Ir e
N O DUST
DUST
Figure 10.
Mud buildup on test probes
j:
c a
O3
50
100 150200XiO 500 NOZZLE
PARAMETER
c 07 3 w
?
+ u W
LL
IO00
8
Figure 1 1. Effect of nozzle parameter on wet-zone length and effective mist lifetime VOL. 5
NO. 2
APRIL 1966
139
corresponding to the present experiment, is only lo%, which may be within the experimental error, while T~ is proportional to d,2. Hence, the effective mist lifetime measured in the present experiment was a function of only 7, a determining factor of mist particle size distribution, and was nearly independent of w , as shown in Figure 11. Figure 12 also indicates that T will not be so dependent on t o . T h e mist cloud atomized into a spray chamber consists of various sizes of drops corresponding to irs distribution function, and each drop will have its own lifetime according to its particle size. However, if such distribution function follows Equation 2, the theoretical over-all mist lifetime will become infinitely large. The effective lifetime, T, shown in Figure 11 should therefore be considered as a kind of average lifetime, after which the mist cloud would materially lose its wetting effect to the obstacles within a spray chamber. Now, it is assumed that the lifetime of each drop within the mist cloud follows Equation 9, since the relative velocity between mist and its ambient gas will instantly fall to approximately zero and the Reynolds number will be kept below 20 during a substantial period of its lifetime. Then, the lifetime of ith particles having diameter d, will be T~
= ad?,
r = adz, seconds
From Equations 12 and 13, we obtain the effective mean diameter
d
1 / ~ n , d i 5 / ~ n i microns d~,
=
d
=
expjln dg
= ~ ~ x n , d , ~ / ~ n seconds ,d,~,
+ 4 (In
d
=
2.96
x
(15 )
go)*]
1O3/y3I4,microns
(16)
Figure 14 shows the relation between T and d replotted from Figures 11 and 13, where the curve represents Equation 13 with-a = 0.95 x l o F 4second per sq. micron, the average value of 0 90 x second per sq. micron corresponding to
/
1
tg = I90 deg C t w = 2 2 deg C W = 3.7-16.9 g/normat
m3
i/" X '8
X
,/bX
(1 2)
/
YA
where ni = number of particles having a diameter between di and di Adz. Here, we define the effective mean diameter, 2, of mist by the relation
+
.b ( 3
PO
4 ( 4 5
8
v
T H E O R E T I C A L CURVE
z=aa2 S ec
a = 0 9 5 x 1:0 .
I
I
I
I
I l l ,
I
ATOMIZING
EFFECTIVE MEAN DIAMETER
R A T E w, g/normaLm3
/p2
I
'
I GO
IO W
a,
,u
Figure 14. Relation between effective mean diameter of mist and effective lifetime
Figure 12. Effects of gas temperature and atomizing rate on evaporation COefficient
0' (0
r; W
2 F
E
_1
-r $J
w
2
L
J
EXPERIMENT)L, 7=7.49xIO ds
:,[
THEORETICAL 7 = O 9 5 * l O 4 as2
LL iw L
0.I 40 5060 80 100 NOZZLE
200 300
PARAMETER, I
Figure 13. Effects of nozzle parameter on effective mean diameter 140
I&EC PROCESS D E S I G N A N D DEVELOPMENT
d
The relation between y and d calculated by Equation 15 is replotted in Figure 13, which gives the experimental formula
I t is also assumed that the effective mist lifetime, r , is the mean lifetime of its constituent drops, weighted by their volume. Then T will become T
(14)
I n the case of log-normal distribution given by Equation 2, becomes
(11)
seconds
(13)
I0 SAUTER'S
M E A N DIAMER a s ,
p
Figure 15. Relation between Sauter's mean diameter of mist and effective lifetime
X second per sq. micron corresponding to w = 16.9 grams per normal cu. meter. A good coincidence between the experimental points and the theoretical curve may provide a basis for taking the effective mean diameter of Equation 14 in the calculation of effective mist lifetime within a spray chamber. On the other hand, the relation between T and Sauter's mean d, replotted from Figures 7 and 11 is shown in Figure 15, which gives the experimental formula w = 3.7 grams per normal cu. meter and 1.00
T
=
7.46
x
d?, seconds
(17)
The effective mist lifetime, T, varies with the cube of Sauter's mean in the present experiment. We consider now the meaning of the effective mist lifetime in more detail. We again assume Equation 9 for the lifetime of each drop within a mist cloud, and Equation 2 for its distribution function. Then, since the drop diameter after 0 seconds becomes (7) d' = (d2 - O/a)l/z,microns
(1 8 )
the ratio of the weight of the surviving mist after a time, 0, to its initial weight becomes
R
=
lm
(d2 - ~ / L u ) X~ /fm ~ X d (In d)/
Lrn
(exp c)
- 0/a)3i2 x
exp (-y2/2)
d y / ~ ' G expi3 In
d,
X d(ln d)
x
+ 4.5 (In ug)2)
where f(d) =
a
=
=
c
=
{ l n ( 0 / ~ ~ ) /2 In d,}/ln uI d, 2 y In up
2 In
+
Hence, R becomes a function of y and CY, since d, and uo are functions of y . Equation 20 was calculated for various values of and O/CY, with the aid of an electronic digital computer and the use of data in Figure 6, and is described in Figure 16. If CY is known, it is possible from Figure 16 to obtain the relation between y and the effective mist lifetime, 0, during which the residual rate of mist reaches a fixed value of R. A , B, and C in Figure 17 represent such relations corresponding to R = 0.001, 0.01, and 0.1, respectively, with CY = 0.95 X lop4second per sq. micron. Experimental points are also plotted in Figure 17. Curve C corresponding to R = 0.1 coincides with the experimental points. However, the value of R = 0.1 is evidently too large for the mist cloud to lose its wetting effect. This conflict may be explained by a slight upward deviation of the plots from the log-normal line in Figure 5, always appearing a t large values of d. I t can easily be shown that such deviations will move the curves in Figure 17 down to a noticeable extent but will reduce the value of d in Equation 14 only a little. Atomizing Rate
f(d)
=
b
log-normal distribution function of Equation 2 ln(0/a)/2
1
I n the design of a n inlet-gas humidification system, it is necessary to estimate the minimum value of the specific atomization rate, w,, required to improve the collection efficiency. The performance of an electrostatic precipitator under normal conditions is dependent upon its charging current and satisfactory results may usually be obtained when the average current density, 5, over the surface of the collecting electrode is about 0.2 ma. per sq. meter (3, 4 ) . However, once reverse ionization occurs, the performance becomes anomalous (78). When the electrical resistivity, P d , of dust exceeds the limit of about 2 x 1O1O to 1 x loll ohm-cm., excessive sparking starts to take place within the precipitator, which makes it impossible to operate the precipitator without lowering the charging voltage. As a result, the value of i will have to be largely decreased and the collection efficiency will be decreased to a great extent. When P d is further increased beyond the limit to 1 X l O I 3 ohm-cm., the excessive sparking of about 1 x may disappear, but the charging current will grow abnormally
260\
o l -:!
20
40 60
80
IO0 I20
( e / a ) ' : ,u
I40 I60
21
Figure 16. Theoretical mist residual rate during evaporation
NOZZLE
?ARAMETER d
Figure 17. Relation between nozzle parameter and theoretical effective mist lifetime VOL. 5
NO.
2
APRIL
1 9 6 6 141
CRITICAL FOR REVERSE LINE 10NZAT,ON C
STEAM HUMIDIFICATION CURVE
R
I ci3
IdZ
lo-'
IO
RELATIVE HUMIDITY OF AMB,ENT G A S
Figure 18. Effects of temperature and relative humidity on apparent conductivity of cement rotary kiln dust
I N L E T - GAS
TMPERATURE
ig,
OC
Figure 19. Humidification chart for exit gas from a waste heat boiler of a dry-process cement rotary kiln
large, with a further decrease of the collection efficiency. Therefore, w m should be so selected that either pd comes down to about 1 X 10l1 ohm-cm. or the abnormally lower or higher value of i caused by the reverse ionization goes back to the normal value of i = 0.2 ma. per sq. meter. The value of a', may be affected by a number of factorsnot only by the dust, temperature, and moisture content of inlet gas, but also by various unknown factors met in practice, such as a minute quantity of SO3 contained in the gas (7, 79)and can be estimated only by a field test. However, a rough estimation from laboratory data might be of some value. For this purpose, wm evaluated from the laboratory data of pd measured in terms of temperature and humidity was compared to wm obtained by a field test for the precipitator of a dry-process cement rotary kiln where this research was carried out. Figure 18 shows the effects of temperature and humidity on the apparent conductivity, Ud, of dust sampled in such a precipitator (9, 70). Figure 19 is the humidification chart for its inlet gas, where curve C represents the critical line for reverse ionization from Figure 18, on which Pd becomes just equal to 1 x 10" ohm-cm. T h e operating point, first a t P, moves toward R with the increase of atomizing rate LU,and in the neighborhood of point R reverse ionization will stop. Hence, the value of w, will be w m = w,
-
w p = 39.9 grams per normal cu. meter
(21)
O n the other hand, the value of wm estimated by the field atomizing test was 12.3 grams per normal cu. meter, with which it became possible to increase ?-at the third stage of the collecting chamber-from 0.0067 ma. per sq. meter under conditions of excessive sparking up to the normal value of 0.21, with a n increase in collection efficiency from 91 to over 99% (8,77). 142
l&EC PROCESS D E S I G N A N D DEVELOPMENT
Table II. Design Data Q , = 2 . 2 X 105 normal cu. w = 12 g./normal cu. meter meters /hour Q w = 2.64 tons/hour t u = 180" C . Pa = 6 kg./sq. cm. L e = 6 meters P, = 7 . 1 kg./sq. cm. Vu = 2.93 meters/sec. q, = 11 . 7 normal cu. meters/ T = 2.05 sec. hour 0 = 4 q, = 0.09 tons/hour L , = 1.25 meters Q e = 5 . 8 5 normal cu. meters/ T = 0 . 5 sec. min. y = 130 N = 30 = 78 microns W , = 12 kw. hr./ton Pi = 32 kw.
Such a discrepancy in w, may be explained by the reduction of pd due to SO3 contained in the industrial flue, or by the increase of the flash over voltage starting from a positive corona in the reverse ionization due to the increase of the gas humidity. Design Data
The first inlet-gas humidification system of the present type was installed for the precipitator of a dry-process cement rotary kiln, where it had been impossible to obtain a good collection efficiency because of excessive sparking and no space was available for the installation of a large spray chamber Figure 20 shows the construction of the spray chamber, for which the inlet chambers, ABEC, of the precipitator were utilized. Thirty nozzles were divided into three sets of multiple nozzles according to the gas flow rates of the respective ducts, and these nozzle sets were installed a t the tops of the chambers. Table I1 shows some of the design data, and Figure 21 is a photograph of this system. The length of the
observed that Z as well as 17 could be much more improved by the further increase of w. Figure 22 shows another application of the present system for the rapid cooling of exit gas from the cyclon-type heat exchanger of the Humbolt suspension preheater for a dryprocess cement rotary kiln. I t atomizes water within the vertical outlet duct from the cyclons and cools its exit gas from 350’ to 190’ C., in order to make it possible to utilize the ordinary precipitator for its cleaning. The duct has a n inner diameter of 2 meters and an effective length of 30 meters available for atomization, where the average gas velocity was 15 meters per second. Thus 6.4 tons per hour of water corresponding to zw = 100 grams per normal cu. meter was atomized by 64 nozzles installed a t the point of atomizing station indicated in the photograph, and could be successfully evaporated \vithout trouble. All the operations, including start and stop, are controlled automatically by the controllers located in the kiln control room, and the rate of water feeding is controlled in such a way that the gas temperature after cooling is kept constant. In the design of the present system, if we choose the larger value of y in order to reduce the size of the spray chamber, the operating cost of the atomizing system may increase to the higher value; the cost of the power consumption of the air compressor represents the major portion. Figure 23 sho\vs the relation between y and the total power consumption, TV, of the air compressor plus the water pump necessary to atomize 1 ton of water for the present type of twin-fluid nozzle. I t was calculated on the assumption that the motor efficiency, compression efficiency, and mechanical efficiency of air compressor are 0.85, 0.80. and 0.85, respectively, and the motor efficiency and pump efficiency of the water pump are 0.85 and 0.65. TV, is proportional to y and can be reduced by decrease of Pa, which is, hoivever. limited by the fluctuation of Pa and P,. On the other hand, if we choose the smaller value of y, it becomes necessary to increase the size of the spray chamber, rvhich may increase the investment cost and raise the interest, depreciation, taxes, etc. As a result, the over-all annual cost will come to the minimum a t a certain value of 7 , as is exemplified by Figure 24. I n the case of large gas volume, the over-all annual cost will become considerably higher for the present type system, even designed with the optimal value of 7, than for the system using a single-fluid nozzle. For the case when gas of about 150,000 cu. meters per hour a t 350’ C. has to be humidified with the water atomization of 6 tons per hour a t 20’ C. and cooled to 135’ C., for instance, the operating cost of the present type system amounts to 881,000 yens per year a t y = 30 and Pa = 2 kg. per sq. cm., and 1,581,000 yens per year a t y = 30 and Pa = 5 kg. per sq. cm., whereas that of the system using a single-fluid nozzle amounts to only 504,000 yens per year when the mist evaporation time is taken as 6 seconds, under present Japanese economic conditions. In the case of smaller gas volume, the present type becomes more economical than the system using single-fluid nozzles. I t may therefore be concluded that the present type of system is suited for cases where no large space is available or the inlet-gas flow rate is comparatively small.
2C
15
10
I
5
1
I
0
50 NOZZLE
100
I50
250
200
‘t
PARAMETER
Figure 23. Specific power consumption for atomization
Q g = I x IO5 n o r m a l
m3/ h r
t g = 180 deg C
Pa = 5 kglcrn‘
Conclusions
The rapid and complete evaporation of atomized water mist within a narrow spray chamber a t comparatively low temperature is possible, based on newly developed “orifice balanced multiple twin-fluid nozzles” capable of producing a large 144
I & E C PROCESS D E S I G N A N D DEVELOPMENT
H / D=4
L .o
I
I
20
I
40
60
I
I
L
80
100
N O Z Z L E PARAMETER,
Figure 24. Relation between nozzle parameter and overall annual cost for inlet-gas humidification
quantity of extremely fine and uniform mist, the mist confinement effect of the spray chamber wall a t elevated temperature, owing to the mist thermal repulsion phenomena, and data on the mist lifetime within an actual spray chamber. Such data can be well interpreted theoretically with the use of a new type of mean diameter of mist particles. O n the basis of these results, a practical inlet-gas humidification system for a n electrostatic precipitator was developed, suited to the cases where no space is available for the installation of a large spray chamber or the inlet-gas flow rate is small. T h e system could also be utilized for rapid cooling of dusty flue gas.
V
colliding velocity of mist cloud average gas velocity, metersjsecond ze, specific water-atomizing rate, grams/normal cu. meter W a specific power consumption for atomization, kw.-hr./ ton w, = minimum specific water-atomization rate, grams/ normal cu. meter
Vg
GREEKLETTERS a:
p u,
pci ud
7 T
Ac knowledgmenl
T,
T h e authors thank Yamada for helpful discussions and guidance, and Matsunobu and Asami for their kind help. They also thank R. F. Heinrich and D. 0. Heinrich for helpful discussions. Nomenclature
= excess air ratio of inlet gas, % In ( O / C Y ) / ~ b = (In (O/a:)/2 - In d,)/ln uo c = 2 In (7, 2 2 In U, D = diameter of test spray chamber, meters d , d, = mist diameter, microns 2, = geometric mean diameter, microns 2 = effective mean diameter, microns (7, = Sauter‘s mean diameter, microns f(d) = log normal distribution function of Equation 2 H , h = height of spray chamber H, = inlet-gas humidity, gramsinorma1 cu. meter k , = thermal conductivity of gas film around mist particle, kcal./meter hr. C. Le = effective length of spray chamber, meters L , = wet-zone length in spray chamber, meters ‘V = number of nozzles d, Adt n, = number of mist particles within d, Pa = gage pressure of air a t nozzle inlet, kg./sq. cm. P,‘ = gage pressure of water a t nozzle inlet, kg./sq. cm. P , = total power for atomization, kw. qa = rate of air feed to single-nozzle unit, normal cu. meters/ hour qlL = rate of water feed to single-nozzle unit, cu. metersjhour Qa = total air-feed rate. cu. meters/min. Qw = total water-feed rate, tonsjhour Q, = inlet-gas flow rate, normal cu. metersjhour R = mist residual rate T = gas travel time in L,, seconds t o = inlet-gas temperature, O C. t8 = surface temperature, O C. u - relative velocity betbteen air and liquid, meters/second A a
=
+
-
+
= = = =
y 0 X
= = = = = = = = = = =
theoretical evaporation coefficient, secondsjsq. micron safety factor for spray chamber geometric standard deviation apparent resistivity of dust, ohm-cm. apparent conductivity of dust, mhojcm. collection efficiency of precipitator, % effective mist lifetime, seconds theoretical mist lifetime, seconds nozzle parameter = qa/qu colliding angle to surface latent heat of liquid, kcal./kg.
literature Cited (1) Busby, H. T., Darby, K., J . Inst. Fuel 36, 184 (May 1963). (2) Gretzinger, J., Marshall, \V. R., Jr., A . I. Ch. E. J . 7, No. 2, 312 (1961). (3) Heinrich, D. O., Stauh 23, H. 2 , 83 (1963). (4) Heinrich, R. F., Anderson, J. R., “Chemical Engineering Practice,” Vol. 3, p. 505, Butterworths, London, 1957. (5) Irani, R. R., Callis, C. F., “Particle Size. Measurement, Interpretation and Application,” pp. 39-55, LViley, Sew York, 1963. (6) Lewis. H. C., Edwards. D. G., Goglia, M. J., Rice, R. I., Smith. L. IV,, Ind. Eng. Chem. 40, 67 (1948). (7) Marshall, \V. R., Jr., Chem. Eng. Progr. 46, No. 10, 501 (1950). (8) Masuda, S., Bull. Dept. Elect. Eng. UnzL. Tokyo 11, 1 (1963)
English ).
(9f Muasud;, S., Electrotech. J . Japan 7, No. 3, 108 (1962) (English). (10) Masuda, S., J . Inst. Elect. En,c. Japan 80, No. 867, 1790 (1960) (Japanese). (11) Ihid., 81, No. 873, 968 (1961) (Japanese). (12) Masuda. S.. Japan. Patent 38-3.640 (April 18, 1963). ’ 435,866 (Dec. 24, 1.964); French Patknt 1,343,702 (SOY. 25, 1963) ; Swiss Patent 378,293 (June 15, 1964). (13) Masuda. S., U. S. Patent 3,137,446 (June 16, 1964) ; French Patent 1,347,022 (Nov. 18, 1963) ; Swiss Patent 389,521 (March 15, 1965). (14) Masuda, S., Saito, H., Asatni, I., Inst. Elect. Engrs. of Japan, Tokyo-Branch Conference Paper, No. 301 (October 1964)
(Japanese).
(15) n‘ukiyaina, S.. Tanasawa, Y . , Trans. Soc. Mech. Engrs. Japan 4, No. 14, 128 (1938) (Japanese). (16) Ihid., 5 , No. 18, 136 (1939) (Japanese). (17) Sukiyama, S., Tanasawa, Y . , h d . . 4-6, Reports 1 to 6 (1938-40), translated by Hooc for Defence Reskarch Board, Dept. of Satl. Defence, Canada, 10~M-9-47 (393), H.Q. 2-0264-1 11950). (18) Sprbull, \V. T., Nakada, Y . , Ind. Eng. Chem. 43, 1350 (1951). (19) Il’hite, H. J., Roberts, L. M., Hedberg, C. LV., Mech. E n g . 72, 873 (1950).
RECEIVED for review August 18, 1964 ACCEPTED October 27, 1965
VOL. 5
NO. 2
APRIL
1966
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