Acknowledgment We thank W. T. Edmondson, D. P. Larsen, and I. Ahlgren, respectively, for the use of unpublished data for Lake Washington, Shagawa Lake, and lakes Norrviken, Edssjon, and Oxundasjon. We also thank R. J. Allan for providing a preprint of his study of Canadian prairie lakes. We benefited from discussions with S. C. Chapra, B. R. Forsberg, E. Smeltzer, and E. B. Swain, and from the participants in the workshop on phosphorus-chlorophyll relationships (40).We also appreciate critical reviews of the manuscript by D. E. Canfield, D. P. Larsen, and K. H. Reckhow. Literature Cited (1) Dillon, P. J.; Rigler, F. H. J . Fish. Res. Board Can 1975, 32, 1519. (2) Vollenweider, R. A. Mem. Ist. Ital. Idrobiol. Dott. Marco de Marchi 1976,33,53. (3) Dillon, P. J.; Rigler, F. H. Limnol. Oceanogr. 1974,19,767. (4) Jones, J. R.; Bachmann, R. W. J Water Pollut. Control Fed. 1976, 48,2176. (5) Rast, W.; Lee, G. F. “Summary Analysis of the North American ( U S . Portion) OECD Eutrophication Project: Nutrient Loading-Lake Response Relationships and Trophic States Indices”; US. EPA, Corvallis Environmental Research Laboratory: Corvallis, OR, 1978; EPA-600/3-78-008. (6) Nicholls, K. H.; Dillon, P. J. Int. Reu. Gesamten Hydrobiol. 1978, 63, 141. (7) Kalff, J.; Knoechel, R. Annu. Rev. Ecol. Syst. 1978,9,475. ( 8 ) Carlson, R. E. Limnol. Oceanogr. 1977,22,361. (9) Lorenzen, M. W. “Effect of Phosphorus Control Options on Lake Water Quality”; U S . EPA: Washington, D.C., 1979; EPA-560/ 11-79-011. (10) Draper, N. R.; Smith, H. “Applied Regression Analysis”; Wiley, New York, 1966. (11) Meaard, R. 0. Limnol. Oceanoar. 1972,17,68. (12) Megard; R. 0. In “North American Project-A Study of U.S. Water Bodies”; Seyb, L., Randolph, K., Eds.; U.S. EPA, Corvallis Environmental Research Laboratorv: Corvallis. OR. 1977: EPA600/3-77-086; pp 91-116. (13) Lamoert. W.: Schober. U. Arch. Hydrobiol. 1978.82,364. (14) Lambert, W. Verh.-Int. Ver. Their. Angew. Limnol. 1978,20, 969. (15) Sakamoto, M. Arch. Hydrobiol. 1966,62,1. (16) Forsberg, C.; Ryding, S.-0.;Claesson, A.; Forsberg, A. Mitt.-Int. Ver. Theor. Angew. Limnol. 1978,21,352. (17) Steel, R. G. D.; Torrie, J. H. “Principles and Procedures of Statistics”: McGraw-Hill: New York. 1960. (18) Edmondson, W. T. Spec. Symp.-Am. Soc. Limnol. Oceanogr. 1972.1.172-88. (19) Larsen, D. P.; van Sickle, J.; Malueg, K. W.; Smith, P. D. Water Res. 1979,13,1259. (20) Welch. E. B. In “Lake Restoration. Proceedines of a National Conference, August 22-24, 1978, Minneapolis, M?nnesota”; U.S. EPA, EPA-440/5-79-001; Office of Water Planning and Standards, Washington, D.C., 1979, pp 133-9. I
,
(21) Funk, W. H.; Gibbons, H. L. In “Lake Restoration, Proceedings of a National Conference, August 22-24,1978, Minneapolis, Minnesota’’, U.S. EPA, EPA-440/5-79-001; Office of Water Planning and Standards, Washington, D.C., 1979, pp 141-51. (22) Cooke, G. D.; Kennedy, R. H. Verh.-Int. Ver. Theor. Angew. Limnol. 1978,20,486. (23) Brydges, T. D. Ciba Found. Symp. 1978,57,217-26. (24) Michalski, M. F. P.; Conroy, N. Proc.-Conf. Great Lakes Res. 1973,16, 934. (25) Holden, A. V.; Caines, L. A. Proc.-R. Sot. Edinburgh, Sect. B 1974, 74, 101. (26) Forsberg, C.; Ryding, S.-0.; Forsberg, A.; Claesson, A. Verh.Int. Ver. Theor. Angew. Limnol. 1978,20,825. (27) (a) Ahlgren, I. Verh.-Int. Ver. Theor. Angew. Limnol. 1978, 20,846. (b) Ahlgren, I. Arch. Hydrobiol. 1980,89, 17. (28) Shapiro, J. In “Hypertrophic Ecosystems”; S.I.L. Workshop on Hypertrophic Ecosystems held at Vaxjo, Sweden, Sept 10-14,1979; Barica, J.; Mur; L. R. Ed.; W. Junk, The Hagne; pp 105-116. (29) Lee, G. F.; Rast, W.; Jones, R. A. Environ. Sei. Technol. 1978, 12,900. (30) Edmondson, W. T., University of Washington, Seattle, WA, personal communication, 1980. (31) Larsen, D. P., USEPA, Corvallis, OR, personal communication, 1980. (32) (a) Cooke, G. D.; Waller, D. W.; McComas, M. R.; Heath, R. T. In “North American Project-A Study of U. S.Water Bodies”; Seyb, L., Randolph, K., Eds.; U.S. EPA, Corvallis Environmental Research Laboratory: Corvallis, OR, 1977; EPA-600/3-77-086; pp 91-116. (b) Cooke, G. D., Kent State University, Kent, OH, personal communication, 1980. (33) (a) Oglesby, R. T. In “Eutrophication: Causes, Consequences, Correctives”; National Academy af Sciences: Washington, D.C., 1969; pp 483-93. (b) Oglesby, R. T., Cornel1 University, Ithaca, NY, personal communication, 1980. (34) Dillon, P. J.;Nicholls, K. H.; Robinson, G. W. Verh.-Int. Ver. Theor. Angew. Limnol. 1978,20,263. (35) Bindloss, M. E. Proc. R. SOC.Edinburgh, Sect. B 1974, 74, 157. (36) Ryding, S.-0.;Forsberg, C. Ambio 1976,5, 151. (37) Megard, R. 0. In “Proceedings of a Symposium on Surface Water Impoundments, June 2-5, 1980, Minneapolis, Minnesota”, ASCE, in press. (38) Forsberg, B. R.; Shapiro, J. In “Proceedings of an International Symposium on Inland Waters and Lake Restoration, September 8-12, 1980, Portland, Maine”, USEPA, in press. (39) HrblEek, J.; Desortova, B.; Popovsky, J. Int.-Ver. Theor. Angew. Limnol. Verh. 1978,20,1624. (40) Lorenzen, M. W. “Workshop on Phosphorus-Chlorophyll Relationships, Draft Final Report”; Tetra Tech, Inc.: Bellevue, WA, Oct 1980. (41) Smith, V. H.; Shapiro, J. In “Proceedings of an International Symposium on Inland Waters and Lake Restoration, September 8-12,1980, Portland, Maine”, USEPA, in press. (42) Smith, V. H., submitted to Limnol. Oceanogr.
Received for review May 19,1980. Accepted November 24,1980. This work was supported by National Science Foundation Grant DEB77-15069 and by NIH Research Service Award T32GM07323.
Particle Collection in Cyclones at High Temperature and High Pressure R. Parker,* R. Jain, and S. Calvert Air Pollution Technology, Incorporated, 4901 Morena Boulevard, Suite 402, San Diego, California 921 17
D. Drehmel and J. Abbott Particulate Technology Branch, Industrial Environmental Research Laboratory, U S . Environmental Protection Agency, Research Triangle Park, North Carolina 2771 1
Introduction In recent years there has been a renewed interest in the performance of cyclone dust collectors a t high temperature and high pressure. This interest is related to the need for reliable sampling and particulate control equipment for advanced coal conversion and combustion processes. Applications at temperatures up to 1200 “C and pressures up to 5000 kPa are being considered.
Only very limited experimental data have been reported, and these are insufficient for evaluating the effects of temperature and pressure on the mechanisms responsible for particle deposition in cyclones. An understanding of these fundamental mechanisms is essential to evaluate and develop design models for high-temperature and high-pressure cyclones.
0013-936X/81/0915-0415$01.25/0 @ 1981 American Chemical Society
Volume 15,Number
4, April 1981
451
An experimental study of cyclone efficiency and pressure drop was conducted a t temperatures up to 700 "C and pressures up to 25 atm. The cyclone efficiency was found to decrease a t high temperature and increase a t high pressure for a constant inlet velocity. Available theoretical models could not predict the observed effects of high temperature and high pressure on collection efficiency. Pressure-drop models predict the effects of temperature and pressure fairly well. Collec-
tion-efficiency data correlated well against Reynolds number and the square root of Stokes' number. This correlation accurately accounted for the effects of both temperature and pressure. These data are for a 2-in. diameter cyclone a t relatively low velocities ( 0 2
W
RUN
T . OC
P.kPl
49-09
495
518
0
50-02
602
518
C
60-01
6q2
51e
A
\
6o
- - -
'1 Y Y W
-
7
0
1
2
3
4
5
8
7
8
PARTICLE AERODYNAMIC
0
10
1 1
12
13
I4
15
DIAMETER, pmA
Figure 5. Combined effects of high temperature and pressure.
----
THEORY
lo OATA
PARTICLE AERODYNAMIC DIAMETER. pmA
Flgure 6. Comparison with model of Leith and Licht (7).
0 2
Y
PARTICLE AERODYNAMIC
DIAMETER. pmA
Figure 7. Comparison with model of Sproull (8).
Volume 15, Number 4, April 1981
455
Table II. Experimental and Theoretical Cut Diameters exptl
exptl
run no.
dp50
dpeo
48-01 48-02 48-03 48-04 48-05 48-06 48-07 49-01 49-02 49-03 49-04 49-05 49-06 49-07 49-08 49-09 50-01 50-02 50-03 55-02 55-03 55-04 55-05 55-06 55-07
3.5 4.2 5.3 6.3 13.2 10.0 18.8 8.8 4.8 2.2 2.1 1 .o 1.2 1.6 1.4 6.9 8.4 7.6 19.4
6.3 6.6 10.0 10.5 23.1 17.9 24.6 16.6 9.8 4.7 5.0 4.1 3.4 3.5 2.7 13.0 15.2 18.3 a 2.3 2.6 1.9 1.7 1.6 2.3 1.7 2.5 2.4 2.4 2.8 2.6
a a
a a a
a
55-08
a
55-09 55-10 55-11 55-12 55-13
a a a a a
a
Rosin ( 10)
Daviea (11)
dcrit
dcrlt
4.79 4.75 5.48 5.63 6.73 6.43 6.75 5.98 5.79 5.60 5.66 5.68 4.77 4.75 4.82 6.72 6.69 6.67 6.95 4.87 4.90 3.36 3.35 3.38 3.39 3.37 3.35 4.83 4.91 4.87 4.86
9.44 9.37 10.79 11.06 13.19 12.60 13.22 11.73 11.41 11.10 11.22 11.26 9.45 9.42 9.55 13.26 13.21 13.16 13.56 9.67 9.73 6.67 6.65 6.71 6.73 6.69 6.65 9.58 9.74 9.65 9.65
aerodynamic cut diameters, pmA Strauss Stairmand Earth (14) dcrit dp50 dp50
2.54 2.53 2.92 3.01 3.61 3.45 3.62 3.20 3.08 2.95 2.98 2.99 2.52 2.50 2.54 3.57 3.55 3.54 3.76 2.56 2.58 1.77 1.76 1.78 1.78 1.77 1.76 2.54 2.58 2.56 2.55
2.25 2.23 2.58 2.67 3.20 3.06 3.21 2.84 2.72 2.60 2.63 2.63 2.22 2.21 2.23 3.15 3.14 3.12 3.34 2.25 2.27 1.55 1.55 1.57 1.57 1.56 1.55 2.23 2.27 2.25 2.25
4.70 4.66 5.38 5.53 6.60 6.31 6.62 5.87 5.68 5.50 5.56 5.57 4.68 4.66 4.73 6.60 6.57 6.54 6.83 4.78 4.81 3.30 3.29 3.32 3.33 3.31 3.29 4.74 4.82 4.77 4.77
Lapple (75) dp50
SprOUll (8) dpSO
4.307 4.31 4.97 5.1 1 6.10 5.83 6.12 5.42 5.24 5.07 5.12 5.14 4.32 4.30 4.36 6.09 6.06 6.04 6.31 4.41 4.44 3.04 3.03 3.06 3.07 3.05 3.03 4.37 4.44 4.40 4.40
1.28 4.77
LelthlLICht (7) ‘$50
1.28 1.45 1.63 2.13 2.13 2.29 1.65 1.52 1.46 1.53 1.53 1.24 1.23 1.22 2.35 2.27 2.27 2.51 1.32 1.35 0.91 0.91 0.91 0.91 0.91 0.91 1.37 1.37 1.31 1.34
5.85
6.03 7.29 6.98 7.46 6.36 6.22 6.09 6.16 6.65 5.18 5.17 5.17 7.28 7.28 7.20 7.44 5.46 5.46 3.72 3.72 3.72 3.72 3.72 3.72 5.31 5.31 5.39 5.39
No data
100 0 varies with ( N ~ ~ ~ N s t kwhere ’ . ~ ) b, is an empirical constant. We have used this empirical approach successfully in correlating our data. The best correlation was obtained by basing Nstk on the hydraulic diameter of the cyclone inlet and N R ~ 30 0 A EXXON on the overall cyclone diameter. We used a value of the ex20 0 ponent b = 1.0 in our correlation. The Stokes number that we 0 used is given in eq 3 NStk = C’dpg2PpU~/(gPGdH) (3) where dp, is the mass median diameter of the test aerosol. Our data are plotted in Figure 8 in the form of 50% aerodynamic cut diameter vs. the correlation parameter, 0 0 N ~ a s t k ’ .The ~ . high-temperature and high-pressure data fall OO on the same curve as the room-temperature and low-pressure O O data. We also have plotted data from the Exxon Miniplant tertiary cyclone. The Exxon data agree well with our correlation. 0.3 Figure 9 compares our data correlation with the data of Smith et al. ( 3 ) .Their data show a similar functionality between cut diameter and “N~astkO.~”; however, the curves are I I 1 1111111 I I I I I 1111 displaced below our data, especially for the smaller cyclones. 0.1 1 O1 103 1 o4 Apparently the cyclone size is an additional important parameter for small cyclones. The high-pressure data of Knowlton and Bachovchin ( 4 ) do not extend low enough to give 50%cut diameters. We have Flgure 8. Data correlation with 50% cut diameters. plotted their data in terms of 90%cut diameters for compar-
DATA
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Environmental Science & Technology
I
1
1
llld
106
Table 111. Comparison of Experimental and Theoretical Pressure Drop theoretical predictions ( A P ) , cm water
run no.
48-01 48-02 48-03 48-04 48-05 48-06 48-07 49-01 49-02 49-03 49-04 49-05 49-06 49-07 49-08 49-09 50-01 50-02 50-03 55-02 55-03 55-04 55-05 55-06 55-07 55-08
55-09 55-10 55-11 55-12 55-13 a
temp, O C
22 20 130 209 375 332 410 155 22 20 20 20 20 20 20 495 512 502 693 30 40 22 21 29 30 25 22 42 49 45 41
press., kPa
192 190 200 192 192 192 192 141 157 516 931 1310 516 931 1220 516 516 516 205 1560 1540 2030 2030 2030 2520 2530 2520 2520 2030 2510 2030
measd press. drop (AP),cm water
SheDherd/ La'pple
First
Alexander
Stalrmand
( 16)
(17)
( 18)
(19)
0.64 0.64 0.46 0.30 0.19 0.20 0.15 0.23 0.20 0.76 2.29 4.57 2.41 6.35 9.91 0.51 0.51 0.51 0.25 5.59 4.19
0.89 0.89 0.63 0.59 9.32 0.39 0.33 0.33 0.34 1.23 2.11 2.91 2.34 4.26 5.26 0.87 0.89 0.90 0.35 6.50 6.4 36.8 37.2 36.3 44.9 45.5 46.3 11.1 8.5 10.8 8.7
0.81 0.81 0.57 0.52 0.29 0.35 0.30 0.30 0.31 1.11 1.91 2.64 2.12 3.86 4.77 0.79
0.64 0.65 0.41 0.36 0.18 0.22 0.18 0.21 0.25 0.89 1.53 2.11 1.69 3.08 3.80 0.46 0.46 0.47 0.17 4.6 4.5 26.5 26.9 25.9 31.9 32.6 33.3 7.8 5.9 7.6 6.1
a a
19.1 37.5 39.6 35.6 7.62 6.35 8.13 8.00
0.80
0.81 0.32 5.9 5.8
33.4 33.8 32.9 40.5 41.2 41.9 10.0 7.7 9.8 7.9
Earth ( 14)
0.84 0.86 0.60 0.56 0.31 0.37 0.31 0.32 0.32 1.16 2.00 2.76 2.22 4.04 4.99 0.82 0.84 0.85 0.33 6.9 6.0 35.0 35.3 34.4 42.4 43.1 43.9 10.5
0.66 0.66 0.47 0.43 0.24 0.28 0.24 0.24 0.25 0.90 1.55 2.14 1.72 3.13 3.87 0.64 0.65 0.66 0.26 4.8 4.7 27.1 27.4 26.7 32.9 33.5 34.0 8.2 6.2 7.9 6.4
8.0
10.2 8.2
No data.
ison with our data in Figure 10. Their data fall a t higher N R ~ s ~ ~than O . we ' considered and show somewhat higher cut diameters. Discussion and Conclusions. The effects of temperature and pressure are surprising when compared to conventional cyclone performance models. The data correlation with NR.&Stk0'j accounts for the observed temperature and pressure effects for our tests. This correlation also agrees with the Exxon Miniplant data where a larger cyclone (15 cm) was operated a t much higher velocity (36 m/s). Apparently the Reynolds number, and hence the flow pattern in the cyclone, is very important in determining particle deposition. The Knowlton and Bachovchin data show no effect of pressure on collection efficiency. Their data are at higher values of N R 3 S t k 0 ' 5 than we considered. Their cut diameters also are somewhat larger than ours. It may be that the gas flow is stabilized by the curved flow in the cyclone. It has been observed that the transition from ~ high as -15 000 in laminar to turbulent flow occurs at N R as flow through helical coils rather than at 2100 as in straight pipes. If we compare two cases in which the mean acceleration force on the particle is the same (i.e., same angular velocity of the gas streams), the particle deposition rate will be lower for turbulent flow than for laminar because the particle concentration gradient is decreased by the turbulent mixing.
1W
1
I
I I I l l
1
I
I
I
I I I l l
I
1
I I
I
I
I l l
30 20
10
0'
19 4.0
3.0
g
2.0
s0 19 ::
1.0
0.6 0.4 0.3 0 1 I
0.1
I
1
z
I
I
8
4
I l l 1 1
z
I
6
a 4 6
I,,
10s
102
\.
N,*
0.d
,
1
1
z
I
a
I
I , ,
4 6
10'
IO*
DIMENSIONLESS
Figure 9. Comparison with data of Smith et al. (3). Volume 15,Number 4,April 1981
457
100
I
1 I Ill11
I
I
I I I I I I I
I
I
I
1 1 1 1 1 ’ 1
I
I
I I ill1
I
1
1
1
1
1
j
60
t
0 O0&
8
6.n
0
0 0 O%=!j
B 1.0
0.6
----
----
pri -
-
0.1
KWWLTON DATA
I
1 I I I I I I
1
1
I I I
IIII
( N,)
I
( N,,)
I
0.6
I I I Ill1
I
I
1
I I Ill1
I
I
I I
IIlL
, DIMENSIONLESS
Figure 10. Data correlation with 90% cut diameters.
Both the flow characteristics and the effect of high pressure on them need to be studied if we are to develop a rational design basis. Furthermore, our data are only for one cyclone geometry and are limited to relatively low velocities. More data at higher values of NReNStk0’5 would be useful. Also variations in cyclone dimensions and geometries should be investigated to determine how they affect this empirical correlation. Nomenclature
+
Cunningham slip correction factor = 1 N~,[1.257 0.4 exp(-l.l/N~,)], dimensionless cyclone diameter, cm critical diameter larger than which 100% of the particles are collected, cm hydraulic diameter of cyclone inlet = 2ab/(a b ) for rectangular inlet, cm particle diameter, pm aerodynamic particle diameter, pmA 5 pm (g/cm3)1’2 mass median diameter of test aerosol, cm particle diameter at which 50%of the particles are collected, pmA particle diameter at which 90% of the particles are collected, pmA Knudsen number = 2X/dp, dimensionless Reynolds number, dimensionless Stokes number, dimensionless absolute gas pressure, kPa gas temperature, “C cyclone inlet velocity, cm/s mean free path of gas molecules, pm gas density, g/cm3
+
+
458
Environmental Science & Technology
PP PG
= particle density, g/cm3 = gas viscosity, g/(cm S)
L i t e r a t u r e Cited (1) Parent, J. D. Trans. Am. Znst. Chem. Eng. 1946,42,989. (2) Yellott, J. I.; Broadley, P. R. Ind. Eng. Chem. 1955, 47, 94452. (3) Smith. W. B.: Wilson. R. R.: Harris. D. B. Enuiron. Sci. Technol. 1979,13,1387-92. ’ (4) Knowlton, T. M.; Bachovchin, D. M. Coal Process. Technol. 1978, 4. (5) Ernst, M.; Hoke, R. C.; Siminski, V. J.; McCain, J. D.; Parker, R.; Drehmel, D. C. “Evaluation of a Cyclonic Type Dust Collector for High Temperature High Pressure Particulate Control,” presented a t the 2nd Symposium on the Transfer and Utilization of Particulate Control Technology, Denver, CO, July 1979. (6) Lawless, P. A. “Analysis of Cascade Impactor Data for Calculating Particle Penetration”; EPA-600/7-78-189 (NTIS No. PB 288649). (7) Leith, D.; Licht, W. “The Collection Efficiency of Cyclone Type Particle Collectors-A New Theoretical Approach”; AZChE Symp. Ser. 1972. (8) Sproull, W. T. “Air Pollution and Its Control”; Exposition Press: New York, 1970. (9) Beechmans, 3. M. In “Aerosol Measurement”; Lundgren, D., Ed.; University a t Florida Press: Gainesville, FL, 1979. (10) Rosin, P. 2. Ver. Dtsch. Ing. 1932,76,443-37. (11) Davies, C. N. Proc. Phys. SOC.,London 1945,57,18. (12) Strauss, W. “Industrial Gas Cleaning”; Pergamon Press: New York, 1966. (13) Stairmand, C. J. Trans. Znst. Chem. Eng. 1951,29,356-83. (14) Barth, W. Brennst.-Waerme-Kraft 1956,8,1-9. (15) Lapple, C. E. Chem. Eng. (N.Y.)1951,58,141-4. (16) Shepherd, C.*B.; Lapple, C. E. Ind. Eng. Chem. 1940, 32, 1246-8. (17) First, M. W. Doctoral Thesis, Harvard University, Cambridge, MA, 1950. (18) Alexander, R. M. Proc. Australas. Znst. Min. Met. Metall. 1949, NOS.152-3,203-28. (19) Stairmand, C. J. Engineering 1949,16B, 409-11.
Received for review June 2,1980. Accepted December 1,1980.
