Collection of Airborne Dust by Water Sprays lung Cheng Pittsburgh Mining and Safety Research Center, U.S. Department of the Inferior, Bureau of Mines, 4800 Forbes Ave., Pittsburgh, Pa. 16215
A general theoretical equation was developed for the collection efficiency of airborne dust particles by spray drops. The model assumes an inertial impaction collection mechanism and is based upon mean interdrop length and mean interparticle area. Particular attention was given to the optimum drop size for collection with open and also confined sprays from a high-pressure nozzle. This general model was specifically adapted to the collection of dust particles in a horizontal tunnel by a solid-cone water spray by including the effects of duct size and spray configuration. The theoretical collection efficiencies agreed reasonably well with experimental data. The present results can be used to select a specific spray nozzle that will provide optimum collection efficiency for airborne dust based upon the available water flow rate and line pressure.
w a t e r spray is one of the chief methods employed to control airborne dust in industrial operations. The spray drop collides with the dust particle and the particle-drop agglomerate then sediments t o the floor or is otherwise collected. For uncharged dust particles greater than about 0.5 gm in diameter, it is generally accepted that inertial impaction is the major collection mechanism. The overall collection efficiency of the spray then is
Eo = 1 - exp (-37LQ/2DQ0)
(1)
where 7 is the fraction of impaction (target or capture efficiency) of a single drop with the particles in the dust cloud, L is a characteristic length for the total capture process, D is the mean drop diameter, and Q and Q, are the volume flow rates of the water and the air component of the dust cloud. Ekman and Johnstone (1951), and Johnstone, et al. (1954), verified the exponential relation between Eo and 7 in Equation 1. Stairmand (1950) and also Walton and Woolcock (1960) concluded that the optimum collection efficiency for drops falling a t gravitational terminal velocity is obtained with drops about 1000 pm in diameter and that the collection efficiency increases with increasing particle size. Such conclusions were largely confirmed by experiment for drops greater than about 500 pm in diameter, but the theoretical collection efficiency was too low for smaller drops (Ralton and Woolcock, 1960). Walton and Woolcock (1960) also considered a spray ejected from a high-pressure nozzle and noted that such a spray should have a high collection efficiency because the drops have a high initial velocity and a long traverse distance before air resistance slow them to their terminal velocity. They further concluded that the total collection efficiency by a given quantity of sprayed water should be largely independent of the drop size between 100 and 500 pm in diameter. Experimental data were not available to test these theoretical conclusions. In practice, the collection efficiency of the high-pressure spray w l l depend upon operating parameters such as line pressure, nozzle design (e.g., spray angle, water flow rate), and chamber geometry. At present, nozzles seemingly are selected without insight as to the dust collection efficiency of the nozzle, and even modest guidelines for nozzle selection should be of value.
This paper presents a theoretical analysis of the collection of airborne dust particles with spray drops ejected from a high-pressure nozzle. ,511open spray and also a spray confined in a duct are considered. The present results can be used t o select a specific spray nozzle that n-ill provide optimum dust collection efficiency based upon the available line pressure and water flow rate. This work is one part of the research program being conducted by the U.S. Bureau of Mines to develop advanced technology oriented toward the control of respirable dust in underground coal mines and thus the elimination of coal workers’ pneumoconiosis. Sprayed water is used in many mining operations to inhibit the formation of dust, to immobilize any dust and prevent it from becoming airborne, and to collect airborne dust. This study is concerned with the latter process. Open Spray
I n dealing n-ith interaction of two species of particle clouds, drops and dust, the concept of mean interdrop and interparticle spacing is useful for a general approach that provides an intuitive insight into the interaction betn-een the two species of clouds (Soo, 1969). The mean interdrop length, s, is given as (n/6 4)lI3D,where D is the mean diameter of the drop and 4 is the volume fraction of the spray. If Q is the volume of water to be atomized by a spray nozzle to fill a volume that has a differential length, 1, and a cross-sectional area, A, then 4 = Q/Al, and the mean interdrop length is ( ~ A 1 / 6 & ) l / ~ Then D. umber of drop layers, n, along the length, 1, can be written as
It follows that the number of drops per layer is
A s2
- 6Q 1 rD3n
(3)
For the dust cloud, the mean interparticle area, a, perpendicular to the direction of the dust flow is Q,,”V& where Q, is the volume of the air and SOis the number of the dust particles in the differential length of the particle cloud. The fraction impaction, 7 , is the ratio of the cross-sectional area of the original airstream from xhich particles of a given Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
221
r Boundary . of .particle trajectory
Water droplet
Figure 1. Impaction of dust particles with a droplet
Figure 3. Axial spray in horizontal duct 2'5 2.0
The occurrence of interaction between drops and the air can be interpreted in terms of
1.5
where ud and u p are the velocities of the drop and the airstream, respectively, and, following So0 (1967), F is the time constant of momentum transfer between the drop and the air. For most practical situations, the local drop Reynolds u,)p/p] is greater than two, and F number N R [= ~ D(ud then is
I.o
.5
0 20
-
I
I 40
I I I I I I l l 60 80 100 200 400 600 DROPLET DIAMETER, D, in pm I 1 1 1 1 1
1
loo0
Figure 2. Optimum droplet diameter for open air sprays
size are impacted onto the drop to the projected area of the drop. If p is the diameter of the intersecting airstream (Figure l), the fraction impaction is pz/D2. The number of particles captured by the drop is @/4a or ?rqNoD1/4Qs. From Equation 3, the number of particles, NI, captured by the first layer of drops is (4) Complete mixing of dust particles occurring between the layers does not change the mean interparticle spacing. Therefore, the collection efficiency, E , for the length, 1, containing n layers can be written as (5) where Nn' is the number of uncaptured particles leaving a spray havi?g n layers of drops, n is given by Equation 2, and Q and Qs are the water and airflow rates. For given water and airflow rates, the collection efficiency of the spray thus varies with the local value of the parameter ql/D as in Equation 5. The fraction impaction, q , involves the equation of motion of the dust particle around the drop and has been the subject of many studies (e.g., Langmuir and Blodgett, 1944-45; Ranz and Wong, 1952; Walton and Woolcock, 1960; Soo, 1967). For example, values of 7 are given by So0 (1967) in terms of the inertia impaction parameter +b for different values of the parameter for non-Stokesian behavior, 9,where $ = ppud2/18pD, 9 = 9pzuD/ppp, p p is the material density of the dust particles, u is the relative velocity between the drop and dust particle, d is the particle diameter, p is the viscosity of the air with dust particles, D is the drop diameter, and p is the density of the air. For a given particle size, q thus is proportional to the relative velocity between the drop and particle and inversely proportional to the drop diameter. 222 Ind.
Eng. Chcm. Process Des. Develop., Vol. 12, No. 3, 1973
where C D is the drag coefficient and g d is the material density of the drop. Therefore, for N R greater ~ than two, a dimensionless ratio
(7) The drag coefficient is
c,
= 18 N R ~ ~ " = 0.44
2 2 NRe I :500 N R >~ 500
Equation 7 gives ql/D as a function of D, ud, us, and d. Using values of q in So0 (1967) and material density of coal particle 1.3 g/cm3, typical results are given in Figure 2 for the case of negligible air velocity. For a given quantity of sprayed water and dust cloud, Figure 2 shows that 200-pm-diameter drops have the maximum collection efficiency for 2-Fm-diameter particles for a wise variation in drop velocity. The optimum drop size is about 300 pm for 3-pm particles and about 150 pm for 1-pm particles. This dependence of collection efficiency on drop size for drops between 100 and 500 pm in diameter is contrary to what Walton and Woolcock (1960) concluded. However, it may be noted that the total effective swept volume per unit volume of sprayed liquid calculated by Walton and Woolcock (1960) also measures overall dust collection efficiency, and their values possess maxima which confirm the results shown in Figure 2. Equation 5 is the collection efficiency for each differential length, I , of a spray. The overall efficiency of the total spray is obtained by summing 1 as n approaches t o infinity as a limit. Denoting the effective length over which a spray drop encounters dust particles by L , and assuming ql/D has a mean value in the spray, we point out that the mean overall collection efficiency of the spray is identical to Equation 1. Coaxial Spray Confined in Horizontal Duct
Consider a solid-cone spray located coaxially in a horizontal circular duct and spraying into a countercurrent dust-laden airflow. In Figure 3, a-b-c'-d'-e-a represents the boundary
I
I
I
I
6
I
I
e-Experimental. Table I --'Optimum
E
u.
v)
3 0
7
I-
6
5.5.'
a a
Yn
5
DROP TRAJECTORY, cm
Figure 4. Theoretical trajectories of drops in a horizontal duct; exit velocity 4000 crn/sec and air velocity 50 cm/sec
of the fully developed spray cone and a is the spray half angle. Drops ejected from the nozzle collide with the duct walls, are decelerated by air resistance a t a rate depending upon their size and exit velocity, and fall to the floor of the duct by gravitation. We will assume that a water drop which collides with the wall will stick on the wall and no longer be effective for removal of dust. An effectiveness ratio of water flow rate, y, is introduced, where y is the ratio of the total mass of drops in the volume of the confined spray zone represented by a-b-c-d-e-a in Figure 3 t o that of the fully developed unconfined spray cone. When we modify Equation 1, the collection efficiency for the confined coaxial spray then is E o = l - e x p [ - - . o - - - -3] L r Q 2 DQa where L is the mean effective length of the spray in the duct. If pc and p f denote mass densities of the drop cloud in the confined zone and the full spray, then y is obtained by substituting values of geometrical volumes and 1 - r-3 cot a
- (1 - r-z)s'z
Pc -
(9) 1 - cos a Pf where r = S / R , S is the projection distance of the spray, and R is the duct radius. The mass distribution of drops in sprays produced by several commercial solid-cone nozzles was investigated by Pigford and Pyle (1951). Their results showed that the mass of water was uniformly distributed throughout the spray except a t the edges. If we ignore the edge effect, pc/pf = 1 for such a spray. Equation 9 then reduces to y =
3r
-
Y = 2ry1
2 cot a
- cos a)
(10)
The mean effective length, L , is taken as the distance between S and the point along the spray cone (Figure 3) where the upstream volume of the spray is equal to the adjacent downstream volume unoccupied by spray, or, in terms of a convenient dimensionless form
L R
=
r
- 23- c o t
a
I n practice, for a given duct radius, the line pressure and nozzle design (water flow rate, spray angle, mean drop size) can be varied t o optimize the dust collection in the duct. For a selected nozzle and line pressure, the spray angle, a , and mean drop diameter, D , can be obtained from the manufacturer. The value of r is obtained from the known duct radius and a calculated projection distance, 8. The exit velocity, U , of a plain atomizing nozzle is
+
4
3
2
I
0
5
15
IO
20
25
r
Figure 5. Relations between yL/R and r with various halfspray angles
where Ap is the total pressure drop across the nozzle, P d is the density of water, g is the gravitational acceleration, and C, is a velocity coefficient of discharge which equals approximately 0.9. Drop trajectories can be calculated by standard techniques (e.g., Giffen and Murdszen, 1953). Typical values are plotted in Figure 4 with the ordinates representing values of S for a given R. Drops having less than about 250 bm diameter will reverse their flow and then follow the airstream before they sediment to the floor of the duct if the duct radius is greater than 25 cm in this example. An approximate value of S can be obtained by S = ( U - ua)R/vr,where u t is the terminal velocity of the drop. The predicted value of the collection efficiency for this selected spray then can be calculated from Equation 8 using q from So0 (1967). Selection of the optimum spray requires repeating this sequence for various line pressures for the nozzle or for different nozzles and selecting the spray giving maximum collection efficiency. Assuming that q , D,and Q remain essentially unchanged in a set of nozzles, an approximate approach to maximizing collection efficiency is to select the nozzle having an a which maximizes y L . The value of y L depends upon T and a. Maximization of y L / R , from Equations 10 and 11 with respect t o y gives
r
=
2 cot a
(13)
Substituting r from Equation 13 back into the expression for y L / R gives
rL 1 = -
R
3
sin a COS
a(1
- COS
a)
(14)
Equation 14 gives the maximum value of y L / R for sprays with a different a . Figure 5 gives typical results. Values of y L / R for four experimental sprays used by Tomb, et al. (1972), are included in Figure 5. Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
223
Table 1. Performance of Solid-Cone Spray Orifice diameter = 0.118 cm (0.047 in.) Duct diameter = 45.72 cm (18 in.) Airflow rate = 8 . 3 5 X 104 cma/sec (177 cfm) Mean diameter of coal dust particles = 1.65 gm
Water flow. rate,Q, cm8/sec
Spray angle,
Data points
water pressure, psi
Estimated mean drop diameter,
2a
D,
deg
pn
Spray exit velocity,U, cm/sec
1 2 3 4
60 100 150 200
31 40 49 57
28 30 32 32
600 470 450 440
2580 3340 4100 4730
Feed
Effectiveness ratio, 7 ,%
Mean full length, 1, cm
31.4 32.1 26.2 24.3
191 176 193 203
Av impaction parameter, $, dimensionless
0.270 0.423 0.533 0.623
Impaction parameter for nonStokesian behavior, 0, dimensionless
4.9 4.7 5.5 6.1
Distance of prolaction,
Feed water 6 0 psip
cm
Final axial velocity, cm/sec
252 233 247 257
380 305 297 294
S,
V
z
w
-V
IV
w
A A
8
Av impaction fraction,
Overall collection efficiency, colcd,
%
4, %
vt
28 42 48 52
15 30 37 45
Overall collection efficiency, measured (Tomb et alJ,
401
100 psip
YMeasured by Tomb et al
1
Equation
20
in So0 (1967)
0
:I
Measured by
20
Equation in So0 11967)
I
U
1,111111111111 0 I
2
3
4
5
6
0
1
2
3
4
5
6
PARTICLE SIZE, m ,,
4, %
21 28 41 43
Figure 6. Collection efficiency vs. particle size Three repeated measurements for each particle aize ronge a r e indicated
Results
Tomb, et al., have reported experimental data on the dust collection efficiency in a horizontal duct of a solid-cone nozzle a t four different feed water pressures with known water flow rates and spray angles. Table I compares the overall experimental collection efficiency with theoretical values predicted by Equation 8 using (a) estimated drop sizes [The standard deviation of the mean volume diameter distribution curves (supplied by the manufacturer) was determined from the ratio of 84.1% size to 50% size. A mean drop diameter was found from the relationship of the standard deviation t o the ratio of mean volume diameter t o mean count diameter (Brinker and Hatch, 1954).], (b) S from Figure 4 or from computed trajectories and then L from Equation 11, (c) 7 from Figure 5.7 in So0 (1967), using the estimated drop size and a mean drop velocity equal to the arithmetic mean of the initial and final drop velocities (from the table), and (d) 7 from Equation 10. The agreement is very satisfactory, although the present use of the mean velocity is a first-order approximation. Figure 6 compares the experimental collection efficiencies for different particle sizes with the predicted values and again indicates satisfactory agreement. The disparaties for small particles a t 60 psi and large particles a t 200 psi are unexplained, but perhaps are due to incorrect estimates of mean drop size. On the basis of the present analysis, the above experimental work did not use nozzles which optimized dust collection. Nozzles with maximum -yL were obtained from Figure 5 for a water flow rate of 126.2 cm3/sec (2 gal/min) for the air velocity and duct diameter given in the table. Results are plotted in Figure 7, together with experimental points from the table and the optimum points from Figure 5, for maximum collection efficiency. The experimental data are adjusted t o this water flow rate Q. The collection efficiency for the ad224
it
Feed water
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
0
A
s
O p t i m u m collactlon rfficiansias 01 various 0 R n d a points ot bs 1 ~ 6 . cmYsrc 2 with various 6,Toblc I Eaparimantol points correctrd for 91126.2 C m h W
= Optimum
* Eaparimantol points s
100
G z Y
O
eo
0
LL LL W
60
40
20
>
0
0
IO00
2000 3000 4000 5000 EXIT VELOCITY OF SPRAY, cm/8rc
Figure 7. Optimum droplet diameters
collection efficiencies for
6000
various
justed data is smaller than the optimum collection efficiency predicted here. This adjusted collection efficiency would have been increased by changing the drop diameter (solid line) and the spray angle (dashed line). Air flow rates for mine conditions usually are considerably greater than used above. Nevertheless, high dust collection efficiencies should be achievable. For example, with a water flow rate of 252 cma/sec (4 gal/min) and a nozzle giving 500-pm diameter drops with an exit velocity of 5000 cm/sec and an 18-degree spray angle (a = go), the predicted collection efficiency is 75% for 5-pm-diameter particles and 30%
for 1-pm particles in a 45.7-cm diameter (18-in.) horizontal duct with an airflow of 472 cm*/sec (1000 cfm). Discussion
The collection efficiency of a spray is directly proportional to the fraction impaction of the particles by drops, the water flow rate, and the total length of the spray and is inversely proportional to the air flow rate and the mean diameter of drops. For dust particles of a given size, maximum collection efficiency requires small drops as shown in Equation 1. However, increased efficiency with smaller drops is largely offset by the decreased distance of projection and the rapid decrease in relative velocity between drops and dust particles due to the air resistance. Therefore, the highest practicable water pressure should be used t o the given small high-velocity drops. An additional consideration of drop size in spray operations is that a larger drop may retain its size with less evaporation and retain its velocity with less momentum loss through impaction with dust particles. Thus, the theoretical disadvantage of large drops may further be offset to some extent on this account. These aspects were not included here. Equation 1 is in a general and more tractable form than the expression given by Walton and Woolcock (1960) formulated for spray curtains. Additional work to verify the present theoretical analysis relating drop size to dust collection would be t o conduct detailed collection-efficiency tests in open and ducted systems with optimum and nonoptimum drops shown in Figures 2 and 5, respectively. At present we are investigating dust collection efficiency in open systems in underground coal mines using spray nozzles which give optimum and nonoptimum drops and which were selected on the basis of manufacturer’s data. With hollow cone sprays, the drops are localized a t the edge of the spray cone and the condition that p c / p f = 1 is no longer fulfilled. If we follow the same approach t o the full cone sprays, an approximate treatment of a hollow cone spray requires determining the average densities of the drop cloud in the confined zone and the full spray. The collection efficiency for multiple nozzles confined coaxially in a duct is given by E, = 1 - (1 - Eo)”, where E, is the overall collection efficiency of the multiple nozzle system, EOis the collection efficiency of a single nozzle, and m is the number of stages of that system. For cases of periodic spraying, the dust penetration can be computed from a given curve which plots instantaneous efficiencies against periodic time. Acknowledgment
The author gratefully acknowledges the help rendered by W. G. Courtney through technical discussions and suggestions. Thanks are also extended to D. N. H. Chi for assistance in computations with computer. Nomenclature
A
cross-sectional area mean interparticle area C D = drag coefficient C, = velocity coefficient of discharge D = mean diameter of drop d = diameter of dust particles E = collection efficiency E,,, = overall collection efficiency of a multiple nozzle system EO = overall collection efficiency F = time constant of momentum transfer
a
=
=
= gravitational acceleration = characteristic length or mean effective length 1 = differential length m = number of stages for multiple nozzles N O = number of particles in a particle layer which con-
g
L
fronts the drop cloud = number of particles captured by the first layer of drops N,’ = number of particles uncaptured with n layers of drops N R ~= local drop Reynolds number n = number of drop layers Qe = volume of air Q = volume of water Qe = air flow rate 4 = water flow rate R = duct radius 8 = distance of projection s = mean interdrop length u = spray exit velocity u = relative velocity between a drop and dust particles ‘&j = velocity of a drop ug = velocity of the carrier gas vc = terminal velocity of a drop N1
GREEKLETTERS a = half-spray angle, in Figure 3 B = diameter of the area, in Figure 1 effectiveness ratio of water consumption Y = fraction impaction 9 = p = viscosity of the air with dust particles Pc = mass density of drop cloud in the confined zone P f = mass density of drop cloud in the full cone p = material density of the air Pd = density of water PP = material density of dust particles 9 = impaction parameter for non-Stokesian behavior 6 = volume fraction of drop cloud i c . = inertia parameter for impaction Ap = total pressure drop literature Cited
Brinker, P., Hatch, T., “Industrial Dust,” 2nd ed., p 194, McGraw-Hill, New York, N.Y., 1954. Ekman, F. O., Johnstone, H. F., “Collection of Aerosols in a Venturi Scrubber,” Ind;lEng. Chem., 43, 1358 (1951). Giffen, E., Murdseen, A., The Atomization of Liquid Fuels,” pp 10-14, Wiley, New York, N.Y., 1953. Johnstone, H. F. Feild, R. B., Tassler, M. C., “Gas Absorption and Aerosol Collection in a Venturi Atomizer,” Ind. Eng. Chem., 46, 1601 (1954).
Langmuir, I., Blodgett, K. B. “Mathematical Investigation of Water Droplet Trajectories,’” General Electric R&D Center, Schenectady, N.Y., R;yt. No. RL-225, 1944-45. Pigford, R. L., Pyle, C., Performance Characteristics of SprayType Absorption Equipment,” Znd. Eng. Chem., 43, 1649 ,,ne,, (IYJI 1.
Ranz, W. E., Wong, J. B., “Impaction of Dust and Smoke Particles,l’l’Znd. Eng. Chem., 44, 1371 (1952). 800,8. L., Fluid Dynamics of Multiphase Systems,’’ Sect. 5.2, Blaisdell, Waltham, Mass., 1967. Soo, S. L., “Heat Transfer Processes of Particulate Suspensions” in Advanced Heat Transfer, pp 415-37, B. T. Chao and J. C. Chato, Eds., Un,iy. of Ill. Press, Urbana, Ill., 1969. Stairmand, C. J., Dust Collection by Impingement and Diffusion,” Trans. Inst. Chem. Engr., 28, 130 (1950).rl Tomb, T. F., Emmerling, J. E., Kellner, R. H., Experimental Investigation on the Collection of Airborne Coal Dust by Water Spray in a Horizontal Duct,” presented a t Am. Ind. Calif., May, 1972. Hyg. Conference held at Sen -cisco, Walton, W. H., Woolcock, A., The Suppression of Airborne Dust by Water Spray,” Aerodynamic Capture of Particles, 129-53, E. G. Richardson, Ed., Pergamon Press, New %rk, N.Y., 1960. RECEIVED for review September 5, 1972 ACCEPTED January 8, 1973 Ind. Eng. Chern. Process Des. Develop., Vol. 12, No. 3, 1973
225
