EPA-600/2-76-066
March 1976
Environmental Protection Technology Series
EVALUATION OF TURBULENT AGGLOMERATION
FOR FINE PARTICLE CONTROL
Industrial Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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EPA-600/2-76-066
March 1976
EVALUATION OF
TURBULENT AGGLOMERATION
FOR FINE PARTICLE CONTROL
by
K.P. Ananth and L.J. Shannon
Midwest Research Institute
425 Volker Boulevard
Kansas City, Missouri 64110
Contract No. 68-02-1324, Task 26
ROAP No. 21ADL-029
Program Element No. 1AB012
EPA Task Officer: B.C. Drehmel
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
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CONTENTS
Summary 1
Introduction 2
Theoretical Aspects of Turbulent Agglomeration 2
Experimental Studies of Turbulent Agglomeration 7
Conclusions 9
References 10
iii
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SUMMARY
Fine particle control with conventional control devices will be much
simplified if the particles can be made to form agglomerates. Agglomera-
tion can be achieved as a result of different forces acting on the parti-
cles. This task was undertaken to evaluate the potential of turbulent
agglomeration in fine particle control.
Both theoretical and limited experimental work indicate that the in-
fluence of turbulence on particle agglomeration is strongly dependent upon
particle size, decreasing with decreasing particle size. Theoretical mod-
els suggest that turbulence does not significantly enhance the agglomera-
tion constants for particles less than 0.2 um in diameter, but can in-
crease the agglomeration constant of 0.5-um particles by about a factor
of 10 and 1-um particles by a factor of 100. In view of the fact that
particles in the 0.1 to 0.5 um size range are the most difficult to col-
lect by conventional systems and one is most interested in achieving ag-
glomeration in this size range, the preceding facts are discouraging.
Fostering turbulence in a stream to enhance particle agglomeration with
the intent of improving control of fine particles does not appear useful.
If turbulence occurs naturally and does not act to the detriment of the
main control system, then one could attempt to make use of the existing
turbulence to achieve some agglomeration.
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INTRODUCTION
Particle agglomeration can be enhanced by the turbulent motion of
a flowing medium. The collisons of particles in turbulent flow are
linked to the fact that particles are not fully entrained by turbulent
eddies as a consequence of the significant differences in density be-
tween the medium and the aerosol particles. In addition, differences
in inertial forces which are caused by differences in particle size also
lead to collision between particles. These mechanisms are discussed in
the next section. Experimental studies on turbulent agglomeration are
also reviewed in a separate section.
THEORETICAL ASPECTS OF TURBULENT AGGLOMERATION
Turbulence can affect agglomeration by two different mechanisms.
Suppose particles are suspended in a turbulent medium whose character-
istic length scale of small eddies is larger than a characteristic par-
ticle size ri . In the first case, since spatial nonhomogeneities are
brought about by the turbulent flow, different velocities of neighboring
particles must appear, causing collisions by a mechanism analogous to
the mechanism of laminar shearing flow. In addition, each particle has
a relative motion differing from that of the turbulent air because its
inertia will not be the same as an equivalent mass of air. Since the
inertia of particles depends on their size, the first mechanism can give
rise to collision between both equally and unequally sized particles,
while the second mechanism results only in encounters between unequally
sized particles.
Theoretical studies on the agglomeration of aerosols in turbulent
flow have been conducted by Levich,.!/ East and Marshall,ji' Tunitsky,^/
Obukhov and Yaglom,_t' Beal,^' and Saffman and Turner.^' LevichZ' and
Saffman and Turner both have made estimates of the agglomeration rate
caused by the two mechanisms mentioned above. Their results apply to
cases where the particle radii are smaller by an order of magnitude than
the size of the smallest eddies. That is, these theories estimate the
effect of turbulent motion on the scales determined largely by the vis-
cosity of the fluid, and the dissipation rate of turbulent energy.
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Although Levich used the concept of a turbulent diffusivity with
Smoluchowski's method to obtain his results, Saffman and Turner applied
a technique similar to kinetic theory, using probability theory to reach
essentially the same conclusions.
Levich derived the following equations for the coagulation rate!/
(1)
where (3 = coagulation constant,
y = kinematic viscosity,
e = rate of dissipation of turbulent energy per gram of medium
/ y3 \ 1/4
, and
\ € /
\0 = microscale of turbulence.
The ratio of the constants of turbulent and thermal agglomeration for
this case is
(2)
where K-i is a constant of the order 0.1 to 0.5. For particles 1 um
in radius r^ /D « 0.1. Hence, it follows that for the agglomeration
of such particles to be accelerated noticeably by turbulence vf/V must
be about 100 and X0 about 0.1 cm. This in turn requires a very high
velocity. Under these conditions, the effect of turbulent agglomeration
is negligible for particles of radius 0.1 um while for particles of 10
um it is very large.
Tunitsky assumed that agglomeration occurs in turbulent flow due to
the relative fluctuation velocity at right angles to the lines of centers
of the particles.—' Using this approach Tunitsky develops an equation
similar to Levich1s.
r3n (3)
P o
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Beal has extended Levich's analysis to include the effect of Brownian mo-
tion and has studied in more detail the case where the sink particle is
larger than the turbulent microscale (r > X ) and has derived the fol-
lowing equation for the collision rate per unit area of sink particle,:!/
1/3
(4)
where Bi = constant, <-' 1/4.
For this case the ratio of constants of turbulent and thermal agglomera-
tion is
Figures 1 and 2 present some of the results of Seal's theoretical calcu-
lations. As shown in Figure 1, the "exact" solution of the diffusion equa-
tion is asymptotic to the solutions based on either Brownian motion or
turbulent diffusion alone and does not differ very much from a simple sum
of these solutions. Figure 2 presents the normalized coagulation constant,
K , as a function of particle diameter.
Beal's analysis has several limitations. Only the steady-state solu-
tion of the diffusion equation was obtained, only interactions among par-
ticles of equal size were considered, and all particles were assumed to
stick together on impact. The last assumption is the most tenuous.
Inspection of Eqs. (1), (3), and (4) indicates that the key parameters
influencing turbulent agglomeration are particle size (r ) , particle con-
centration (n ) , rate of dissipation of turbulent energy (e) , and vis-
cosity (Y) . Since the agglomeration rate varies directly with particle
size, turbulent agglomeration will decrease in effectiveness as the par-
ticle size decreases—a discouraging result with regard to its utilization
to collect fine particles. A decrease in the agglomeration rate with de-
crease in particle size could be compensated for by increasing the dissi-
pation of energy or increasing the particle concentration. The former
would require increasing the turbulence of the stream while the latter
would undoubtedly involve seeding of the aerosol. However, in view of the
fact that the agglomeration rate is a direct function of particle size,
seeded particles may very well agglomerate with themselves and be of no
use in promoting the agglomeration of fine particles. The extent to which
the viscosity of the gas stream can be varied in an industrial application
is limited, and gas viscosity is not a meaningful variable to use to modify
the agglomeration rate.
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I I \ I I I 1111 I I I I 11 llj
Fluid Air
Pipe DiameterrlO CM
Temperature :20° C
u = 3000 CM/Sec
€0=2.7x 10"
DYNE-CM-Sec"
"EXACT" Solution
Simple Sum
Turbulent
Diffusion
Only
e0=2.7x 10
u= 100
€ =103
Brownian
Diffusion Only
I I II I I till I I I I II I
5 10° 2 5 10'
PARTICLE DIAMETER,/im
Figure 1. Particle agglomeration flux for various particle
diameters and fluid velocities.
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I I I I I I 11
I I I I I IIII
Fluid = Air
Temperature = 20° C
Pipe Diameter = 10 CM
Particle Density = l.OGM/CC
u = 3000 CM/Sec
10'
10'
PARTICLE DIAMETER./im
Figure 2. Coagulation constants for various particle
diameters and fluid velocities.
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Experimental work on turbulent agglomeration is meager and difficult
to interpret. Pertinent work is discussed in the next section.
EXPERIMENTAL STUDIES OF TURBULENT AGGLOMERATION
Experimental study of the rate of agglomeration in the presence of
turbulence is difficult because turbulence also accelerates the deposi-
tion of particles on walls. The rate of deposition increases with par-
ticle size so that the assessment of the course of agglomeration is com-
plicated.
Langstroth and Gillespie made extensive experimental studies on ag-
glomeration in strongly turbulent air.^' They used a chamber with a
volume of about 1 m^ in which ammonium chloride smoke coagulated in static
and in moving air with different degrees of turbulence. The air movement
was produced by an oscillating agitator consisting of two perforated
plates. Particle number and mass concentration were measured at inter-
vals of 30 min over a period of 5.5 hr. Two constants were assumed in
order to separate the effects of coagulation and of precipitation of the
aerosol particles on the chamber walls. It is difficult to apply the
results of these experiments to other chamber dimensions, particle sizes,
and turbulent flows. The method used to stir up the air also introduces
an uncertainty because the motion produced does not resemble any of the
kinds of turbulence usually encountered in flow systems.
Experiments by Yoder and Silverman are the only results that appear
to be subject to any rigorous analysis.—' These investigators performed
experiments to obtain data on the deposition and agglomeration of parti-
cles in turbulent air flow. In their experimental design, deposition
and agglomeration were occurring simultaneously, and their basic problem
was to separate the two effects. They did this by measuring both the
total number concentration and the fraction of particles which had ag-
glomerated at the inlet and outlet of their test section. By applying
certain theoretical concepts, they could then infer the separate effects
of both deposition and agglomeration from the measured parameters. They
did not, however, make any direct observation of either phenomenon.
Beal utilized the data of Yoder and Silverman for a comparison with
his theoretical predictions of particle agglomeration. Figure 3 presents
this comparison. The agreement is reasonably good for the 0.8-um parti-
cles, but poor for the 0.26-jun particles. No adequate explanation of the
difference in magnitude between the observed and predicted values of the
coagulation constant was offered by Beal. A general discussion of the
difficulties encountered in the experimental determination of turbulent
agglomeration coefficients is presented by Fuchs.—'
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0.26/im f Yoder and
D O.SOum I Silverman's Data O
5 104 2 5
REYNOLDS NUMBER
Figure 3. Comparison of theoretical predictions with Yoder and
Silverman's agglomeration data.
8
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CONCLUSIONS
Both theoretical and experimental work indicate that the influence
of turbulence on particle agglomeration is strongly dependent upon par-
ticle size, decreasing with decreasing particle size. Theoretical models
suggest that turbulence does not significantly enhance the coagulation
constants for particles less than 0.2-um in diameter, but can increase
the coagulation constant of 0.5-um particles by about a factor of 10 and
1-um particles by a factor of 100 (see Figures 1 and 2). In view of the
fact that particles in the 0.1 to 0.5 urn size range are the most diffi-
cult to collect by conventional systems and one is most interested in
achieving agglomeration in this size range, the above observation is
discouraging.
Considerations of energy expenditures required to achieve turbulent
agglomeration also dampen enthusiasm for utilizing turbulent agglomeration
in industrial applications. The energy expended to achieve the increases
in the coagulation constant cited above is of the order of 10' dyne-cm-
sec~Vg or 0.001 hp/g. The preceding energy expenditure is equivalent to
about 40 hp/1,000 ft^ of gas. This is an extremely high energy consump-
tion and, therefore, turbulent agglomeration is not very attractive if an
external source is required to provide the turbulence. Even if energy
levels of that magnitude were expended, it would take approximately 1 min
to increase the size of a 0.5-pm particle to 2 to 3 urn.
The preceding discussion indicates that fostering turbulence in a
stream to enhance particle agglomeration is not very useful. If turbu-
lence occurs naturally and does not act to the detriment of the main con-
trol system (e.g., turbulence often degrades ESP performance); then one
could attempt to make use of the existing turbulence to achieve some ag-
glomeration.
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REFERENCES
1. Levich, W., Dokl. Akad. Nauk., SSSR, 9£, 809 (1954a).
2. East, T. W. R., and J. S. Marshall, Quart. J. Royal Met. Soc., 8£,
26 (1954).
3. Tunitsky, N. N., Zh. Fiz. Khim.. £0, 1136 (1946).
4. Obukhov, A., and A. Yaglom, Prikl. Mat. Mekh., JL5_, 1 (1956).
5. Beal, S. K., "Turbulent Agglomeration of Suspensions," Aerosol Sci.,
J3, 113-125 (1972).
6. Saffman, P., and J. Turner, J. of Fluid Mech., 1, 16 (1956).
7. Levich, V. G., Physiocochemical Hydrodynamics, Prentice-Hall (1962).
8. Langstroth, G., and T. Gillespie, Can. J. of Res., 25JB, 455 (1947).
9. Yoder, J. D., and L. Silverman, "Influence of Turbulence on Aerosol
Agglomeration and Deposition in a Pipe," Paper No. 67-33, 60th
Annual Air Pollution Control Association Meeting, Cleveland, Ohio,
June 13, 1967.
10. Fuchs, N. A., The Mechanics of Aerosols, Pergamon Press, New York
(1964).
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TECHNICAL REPORT DATA
(Please read luantctions on :!ic reverse he/on' completing)
1. REPORT NO.
EPA-600/2-76-066
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Evaluation of Turbulent Agglomeration for Fine
Particle Control
5. REPORT DATE
March 1976
6. PERFORMING ORGANIZATION CODE
7. AUTHORiS)
8. PERFORMING ORGANIZATION REPORT NO.
K. P. Ananth and L. J. Shannon
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Midwest Research Institute
425 Volker Boulevard
Kansas City, Missouri 64110
10. PROGRAM ELEMENT NO.
1AB012; ROAP 21ADL-029
11. CONTRACT/GRANT NO.
68-02-1324, Task 26
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Task Final: 9-12/74
14. SPONSORING AGENCY CODE
EPA-ORD
i5. SUPPLEMENTARY NOTES pr0ject officer for this report is D.C.Drehmel, Mail Drop 61,
Ext 2925.
16. ABSTRACT
The report gives results of an evaluation of the potential of turbulent agglomeration
in enhancing fine particulate control. Available information on theoretical and
experimental aspects of turbulent agglomeration indicates that this is not a very
viable approach for improving fine particle control.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Air Pollution
Agglomeration
Turbulence
Dust
Evaluation
b.lDENTIFIERS/OPF.N ENDED TERMS
Air Pollution Control
Stationary Sources
Turbulent Agglomeration
Fine Particles
c. COSATI Reid/Group
13B
20D
11G
14A
13. DISTRIBUTION STATEMENT
19. SECURH Y CLASS (This Re
21. NO. O? PAGES
14
Unlimited
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20. SECURITY CLASS (Thispapc)
Unclassified
EPA Form 22£0-l (S-73)
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