Environ. sci. Technol. 1993, 27, 1842-1848
Performance Modeling of Single- Inlet Aerosol Sampling Cyclonest Murray E. Moore and Andrew R. McFarland' Department of Mechanical Engineering, Aerosol Technology Laboratory, Texas A&M University, College Station, Texas 77843
A technical basis has been developed which justifies using two nondimensional parameters: the ratio of the cutpoint particle diameter to the cyclone diameter, (Do,B/D,)and the flow Reynolds numbers, Ref. An improved method has also been developed for the design of single-inlet aerosol sampling cyclones using these parameters in a semiempirical functional relation. This allows predictions to be made of aerodynamic equivalent particle (AED) cutpoint diameter for a Stairmand cyclone which has had an alteration to its outlet tube diameter. The correlation coefficient for the functionid relationship is r2> 0.99. Using a particular cyclone, a designer can hold the airflow rate constant and then predict how the particle cutpoint will change as the outlet tube diameter is changed. Or, a designer can alter the system flow rate and keep the cutpoint the same by changing the outlet tube diameter. Three cyclone body diameters (38.10,57.15,and 88.90 mm) were used in experimental testing. Three outlet tube sizes (26.7, 42.9, and 68.3 mm) (inside diameter) were used in different combinations to vary the ratio of the outlet tube diameter to cyclone body diameter in the cyclone. Flow rates ranged from 16.3 to 124 L/min. The measured particle cutpoints ranged from 4.0 to 18.8 pm AED.
I. Introduction The EPA standard for sampling particulate matter from the ambient atmosphere is based upon an indicator that includes only those particles which pass through a fractionator with a cutpoint of 10 pm AED (aerodynamic equivalent diameter) (1). The justification for emphasis on particles with sizes less than 10 pm AED lies in the need to account for the deposition of these sizes in the thoracic region of the respiratory tract. In addition, aerosol fractionation is required for samplers which operate in the range of interest for industrial hygiene in the United States. That standard is for respirable particulate matter which is based on the use of a sampler with a 3.5-pm AED cutpoint (2). To achieve compliance with the standards, samplers are fitted with inertial impaction or cyclonic flow fractionation devices. For example, a 10-pm cutpoint sizeselective inlet was developed by McFarland et al. (3) for sampling at a rate of 1.13 m3/min from the ambient atmosphere. A cyclone sampler is an attractive concept for an airsampling device, as there are no moving parts associated with the cyclone, and provided it is cleaned periodically so there are no problems with excessive contaminant fouling of the walls which contact the airflow path, a cyclone will perform consistently. At the present time there are several models available for predicting the performance of air-sampling cyclones for a given set of criteria (e.g.,flow rate and cutpoint size); however, none reliably permits predictions of changes in cutpoint if changes are made to the outlet tube diameter.
These changes can be made to a cyclone with a modest modification to the cyclone geometry and with relatively low fabrication costs.
II. Literature Review A model was developed by Lapple ( 4 )for predicting the fractionation characteristics as related to design and operational parameters of industrial cyclones. Because of a large difference in Reynolds numbers, the error introduced by utilizing industrial cyclone data for the design of sampling cyclones has proven to be unsatisfactory. There is frequently as great as a factor of 2 in the difference between the predicted cutpoint value and the experimentally determined value for a given flow rate. With respect to sampling cyclones,Beeckmans and Kim ( 5 )compared experimental data from a 152-mm diameter cyclone and a 76-mm diameter cyclone to the data of Lippmann and Chan ( 6 ) ,Blachman and Lippmann (7), and Lippmann and Kydonieus (8). Lippmann and his collaborators correlated cyclone efficiency on the basis of the Stokes number, Stk, which is defined as:
where C, = Cunningham's correction; pp = particle density; D, = aerodynamic particle diameter; Vi = inlet velocity; p = fluid dynamic viscosity; and D, = characteristic dimension of a cyclone (e.g., body diameter). When Beeckmans and Kim (5) compared their data with that of Lippmann and Chan (61, Blachman and Lippmann (9, and Lippmann and Kydonieus (8),they found that cyclone efficiency cannot be correlated only by the cyclone Stokes number, but rather it was necessary to analyze cyclone data in terms of the Stokes number and the cyclone Reynolds number, Re,, where the latter parameter is represented by:
where p = density of air. Beeckmans and Kim noted that the flow Reynolds numbers in industrial cyclones are frequently 3 X lo5 or higher. As a consequence, the theories for large industrial cyclones might not be valid for small air-sampling cyclones which operate with flow Reynolds numbers that are typically on the order of lo4. The investigative work of Chan and Lippmann (9) addressed the flow regimes in sampling cyclones. They developed a cyclone efficiency equation based on empirical data which gives efficiency in terms of flow rate and empirical constants. Their model is useful for predicting the performance of a cyclone previously tested at other flow rates; however, it is not applicable to cyclone design. Experimental data gathered from a 10-mmnylon cyclone by Blachman and Lippmann (7) were compared with the efficiency theories of Rosin et al. (IO),Lapple ( 4 ) , Barth * Author to whom correspondence should be addressed. t Aerosol Technology Laboratory Publication 5101/1Q/92/MEM. (II), Leith and Licht (12), and Beeckmans (13). Chan
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0 1993 American Chemical Society
and Lippmann found the fits were not adequate, and they presented an empirical model for collection efficiency, 7, as a function of the particle size and airflow rate. John and Reischl (14) also found the need for a correlation to model the performance of air-sampling cyclones. Test data using a 36.6-mm cyclone compared with the theories of Shepherd and Lapple (151, Sproull (16), Leith and Licht (12), Barth (11), Blachman and Lippmann (7),and Chan and Lippmann (9). None of these adequately fit John and Reischl's data, so they proposed the relationship: Do.5o= 52.5Q4." (3) where 00.50 = cutpoint aerodynamic particle diameter (pm), and Q = cyclone flow rate (Llmin). The John and Reischl model is not useful for predicting the performance of a cyclone with design parameters different than those of the unit they tested. The works of Chan and Lippmann (9) and John and Reischl(14) do not address the need for a comprehensive model for the design of sampling cyclones. However, their correlations only include calibration information for various unique cyclones. Saltzman and Hochstrasser (17) tested 15 different sampling cyclones and established a generalized relationship between the particle cutpoint size and the Reynolds number based on outlet tube parameters. However, the 15 cyclones are modifications of one particular cyclone, in that the cyclone body diameter (19.05 mm) was not changed for any of the 15 configurations. Three parameters were varied in order to produce the different cyclone geometries: cone length, outlet tube inside diameter, and outlet tube wall thickness. All the remaining dimensions were kept constant. Their range of aerosol diameters was limited to 2-4 pm and their flow rate was varied only from 10.0to 23.2L min-l. This forced their experimental results into a narrow range of Reynolds and Stokes numbers. Saltzman (18)fit the performance data from 30 different cyclones from a variety of studies using the same approach as Saltzman and Hochstrasser (17). One of his variables is the outlet tube Reynolds number, Reo,which is defined as Re, = [4dw1Q/D0 (4) where DO= cyclone outlet tube diameter, and Q = airflow rate. He used an empirical equation which relates the cutpoint particle to the cyclone diameter and outlet tube Reynolds number: where & = a dimensionless constant characterizing each cyclone, and n = an empirical constant. Burkholz (19) performed fractional efficiency and pressure drop coefficient measurements on 14 different cyclones. The cyclones differed both in size and geometrical design. He proposed that the fractional separation efficiency is a function of a dimensionless inertial separation parameter, @A. This number is a function of the Stokes number, Stk, the cyclone outlet tube Reynolds number, Re,, and a pressure drop coefficient, 5; namely: @A
= 312 Stk Re,"= el3
(6)
where (7) Here, Ap = pressure drop across the cyclone. The dimensionless inertial separation parameter was plotted against the fractional separation efficiency for the 14cyclones. In this manner, the experimental results could then be used in the design of new cyclone devices. The correlation showed a noticeable amount of scatter which Burkholz attributed to experimental error and to the influence that different cyclone geometries have on the slope of the separation efficiency curve. A model for aerosol sampling cyclones was also offered by DeOtte (20). The experimental data were at one flow rate condition for each of two cyclones. The model is not convenient for design purposes, as it requires detailed knowledge of the cyclone flow field. The work of Moore and McFarland (21) involved tests of four different sizes (38-, 57-, 89-,and 140-mm diameter) of Stairmand high-efficiency cyclones over four different flow rates for each cyclone. The range of flow rates extended from 9.4 to 1080LImin which resulted in cyclone flow Reynolds numbers from 2100 to 64 000. Experiments were conducted to determine separation efficiency for a range of monodisperse aerosol sizes from 3.0 to 17.4-pm aerodynamic diameter. Their data were fitted to a quadratic logarithmic function: 25200 Stk,, = ~ ~ ~ 2 . 7 2 - 0 . 1 In1 9Re, where Stk0.50= the Stokes number for the aerodynamic cutpoint diameter, and Re, = the Reynolds number based on the cyclone body diameter. As an example, if a cyclone is required that operates with a particular flow rate and aerodynamic cutpoint, this relation would provide the appropriate diameter for a Stairmand-design cyclone. The correlation of Moore and McFarland (21) was utilized in designing a sampling cyclone for URG Corp. (Carrboro, NC). An aerodynamic cutpoint of 2.5 pm was desired for a device that was to be operated at an airflow rate of 10.0 Llmin. The MooreMcFarland correlation predicted a diameter of 16.5 mm for a cyclone of Stairmand design. Subsequent testing of a manufactured prototype a t the University of Minnesota (22) verified the 2.5-pm cutpoint. While the results of Moore and McFarland (21) are applicable to cases where the cyclone geometry is fixed into predetermined ratios, there exist many different single-inlet cyclone designs that deviate from the standard Stairmand pattern. The influence of the size of cyclone outlet tube on collection efficiency was noticed by Kim and Lee (23), who tested nine cyclone geometries that were constructed of three different body diameters and four different outlet tube sizes. In general, they noted a reduction in outlet tube diameter would cause a decrease in the aerodynamic cutpoint diameter. Kim and Lee (23) provided a comparison of their results with the theories of Barth (11)and Leith and Licht (12). However, they used a particle counter to sample aerosol upstream and downstream of the tested cyclone in order to measure the collection efficiency. Particle deposition losses at the cyclone inlet, in the sampler lines and tubing elbows, along with the Environ. Sci. Technol., Voi. 27, No. 9, 1993
1843
irregularity of the flow in the cyclone outlet tube could have caused errors in the analysis.
The influence of fluid flow characteristics upon particle deposition is generally characterized through the use of a Reynolds number, where the reference velocity and characteristic length depend upon the particular flow situation. In our previous work, we had used a Reynolds number based upon the cyclone body diameter and the inlet velocity; however, when we attempted to correlate data from the present study using that version of the Reynolds number, the results were unsatisfactory. For flow in elbows,where the radius of curvature of the elbow is less than five times the diameter of the flow passage, the Dean number can be of consequence (24). The Dean number is a function of the Reynolds number based upon the tube diameter and the square root of the ratio of the radius of curvature of the bend to the tube diameter. When we attempted to correlate our current experimental data with the Dean number, we also obtained poor results. Much improvedresults are obtained when the correlation is based upon a Reynolds number which uses the inlet velocity, Vi, in that there is persistence of that velocity into the body of the cyclone. Inside of the cyclone, the channel width (R, - R,) is a natural characteristic length since the flow is radially constrained within that dimension. Using these characteristic parameters, a flow Reynolds number can be defined as:
Our correlation will employ this flow Reynolds number. Particle trajectories in swirling flows were studied by Dring and Suo (25). In their analysis, the tangential flow velocity and the tangential particle velocity were taken to be equal. The acceleration of a particle in cylindrical coordinates is
After consideringthe particle acceleration only in the radial direction, Dring and Suo (25) showed that
where f = r/rref;rref= a reference radius; CD = particle drag coefficient, which is a function of Rep, the particle Reynolds number; and P = ratio of fluid density to particle density. They defined the particle Reynolds number in terms of a Reynolds number based on the initial swirl radius, namely: (12)
where Re, is the swirl Reynolds number: Re, = P Woro ~
P
(13)
and W O= initial particle velocity, and ro = initial swirl radius. Environ. Sci. Technol., Vol. 27, No. 9, 1993
-' 1
----
INLET 7
INLET GAP 0 1 2 5 D
I l l . Theoretical Basis
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OUTLET TUBE
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CYCLONE
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CYLINDER HEIGHT
COhE LiElGhT
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Flgure 1. Geometrical scale ratios of a Stairmand hlgh efflclency cyclone.
As may be noted from the right-hand side of eq 12, the work of Dring and Suo (25)suggests that cyclone separation performance can be described in terms of the Reynolds number and the particle diameter normalized to the radius of curvature of particle motion. As a consequence, we use the dimensionless parameter, Do.s~lD,,for our correlations of the cutpoint particle size.
IV. Experimental Procedures The experimental aspects of this study involved varying cyclone physical dimensions and determining the aerodynamic particle cutpoint diameter of these variously ratioed cyclonesfor different flow conditions. These data provided input to correlations based on dimensionalscaling and similarity. By constructing and testing cyclones of differing design, the parameters which dictate design and performance could be related through nondimensional numbers. The cyclone geometry was patterned after that of the Stairmand high-efficiency design (26) (Figure 1); however,the cyclone outlet tube diameter to cyclone body diameter ratio was varied (Figure 2). This meant that the cyclone body Reynolds number, Reo and the outlet tube Reynolds number, Re,, could be varied over a broad range with respect to each other. The outlet tubes used in this study were constructed from thin-walled aluminum tube stock. The inside diameter was used as the outlet tube dimension in this study. Inside diameters of 26.70, 42.90, and 68.3 mm corresponded to tube outside diameters of 28.40, 44.45, and 69.80 mm, respectively. Cyclone testing was carried out with the apparatus shown in Figure 3. During a test, an upstream filter sampler and the corresponding cyclone were alternately mounted at the plenum test chamber location. For each case, at least three replicates were run with both the upstream filter sampler and the cyclone. The upstream filter was used to characterize the particulate concentration entering the cyclone while the cyclone outlet filter sampled the aerosol particles which penetrated through the cyclone. In tests with both liquid and solid particles, a vibrating orifice aerosol generator (27) was used to produce the aerosol particles from a solution of oleic acid and ethanol tagged with sodium fluorescein. For selected tests, solutions of ammonia and sodium fluorescein were used to produce solid ammonium fluorescein particles. After aerosolization, the droplets were passed near a 10-mCi
38 1
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CONICAL SECTION
Flgure 4. Diagram of single-inlet cyclone indicating regions where particulate deposition was measured.
Glass fiber filters were used to collect the upstream and downstream aerosol samples. The filters were then placed in measured solutions of ethanol and distilled water. Fluorescein tracer was quantified fluorometrically with a Sequoia-Turner Model 450 fluorometer (Mountain View, CA). Relative fluorescein concentration in the aerosol samples was calculated from c = FLITQ (14) where F = numerical reading from fluorometer, L = liquid volume of the measured solution, T = testing time for each filter, and Q = filter flow rate during the sampling period. The cyclone collection efficiency, q,was determined from
Flgure 2. Schematic of outlet tube variation In a basic Stairmand cyclone geometry. Outlettube variationsaffect cyclone performance.
f:y[-
EXCESS AEROSOL DISCHARGE RESSURE 8AUGE
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Flgure 3. Apparatus for testing single-Inlet cyclones.
line source of Kr-85to neutralize the mean electrical charge on the particles. The aerosol was then passed into the plenum chamber, where it was separated into two streams: the main flow, which was drawn into the sampling device, and the excess aerosol, which was drawn into a cleanup filter by a hi-volume blower. The flow rate of air through the cleanup filter was adjusted so that there was a slightly negative pressure in the plenum chamber. A vacuum pump was used to draw air through the test device and then through a rotameter. Both solid and liquid particles were sized using a light microscope. The solid particles were collected on a membrane filter, and the diameters were determined by direct sizing. However, the liquid oleic acid particles were impacted onto a glass slide that had been treated with an oil-phobic fluorocarbon compound. The gravitational distortion of the liquid particle was taken into account by the oleic acid flattening coefficient of Olan-Figueroa et al. (28).
~
(15) where u MCd = downstream aerosol concentration, and cu = upstream aerosol concentration. Figure 4 shows the regions in a cyclone where the local particle deposition was measured in selected tests. A total of five different pieces of the cycloneconstituted the scope of the regional deposition analysis: the inside of the cyclone outlet tube, the outer surface of the outlet tube portion which is inside the cyclone itself (including the top cap portion), the straight cylindrical section of the cyclone, the conical section of the cyclone, and the bottom cap of the cyclone.
V. Results and Analysis An example of the data collected in this study is presented in Figure 5, where the efficiency is given as a function of aerodynamic diameter for a range of flow rates (45.9, 79.3, 103.0, and 124.0 L min-l). The cyclone used in these tests had a body diameter of 88.9 mm and outlet tube diameter of 26.7 mm. For a particular flow condition, an aerosol particle moving in a curved airstream will move across flow streamlines because of the particle centrifugal force. A larger particle will have a greater centrifugal force, causing greater deposition on the internal cyclone walls, increasing cyclone collection efficiency. An increase in cyclone airflowrate causes an overall increase in air velocity and centrifugal effects within the cyclone, thereby decreasing the aerodynamic particle cutpoint diameter. A summary of the cutpoints, Do.60, from tests with different cyclone geometric parameters and flow rates is given in Table I. In the first section of the table, the results Envlron. Sci. Technol., Vol. 27, No. 9, 1993
1845
L
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l
w
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0 CI 0 0 A A A A
A A A A
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*
124.0 L\min
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D.L42.9 rnrn. CONE REGION, D.=42.9 mm. EFFICIENCY, D.=42.9 mrn. BOTTOM CAP, D.=26.7 mm. CONE REGION, D p 2 6 . 7 mm. EFFICIENCY, D.=26.7 mm.
o o o olBOTTOM CA;,
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AERODYNAMIC PARTICLE DIAMETER, D,, p m
Flgure 5. Efficiencyversus particle diameter for an 88.9-mm diameter cyclone with a 26.7-mm outlet tube.
Table 1. Aerodynamic Particle Cutpoint Data Results8 cyclone cyclone configuration body flow rate Reynolds D, = 38.10 mm D, = 57.15 mm D,= 88.90mm (Lmin-1) number Do = 26.70mm Do = 26.70mm Do = 26.70mm 16.3 27.5 45.9 79.3
842 1420 2370 4100
11.6pm 7.8pm
15.3 pm 10.4pm 6.7 pm 4.0 pm
10.5pm 7.8 pm
cyclone cyclone configuration body flow rate Reynolds D, = 88.90mm D, = 88.90mm D,= 88.90 mm (Lmin-1) number Do = 26.70 mm Do = 42.90mm Do = 68.30mm 79.3 103 124
7730 10040 12090
7.8 pm 6.1 pm 5.3 pm
9.4pm 7.7pm 6.5pm
18.8 pm 14.1 pm 12.2pm
For different cases, the outlet tube Reynolds numbers were held constant, while respectively varying the cyclone body diameter and outlet tube diameter.
for constant outlet tube Reynolds numbers show that the cutpoint decreases as the cyclone body diameter is decreased. In these tests, the cyclone flow rate, Q, and the outlet tube diameter, DO,were held constant while the cyclone body diameter was varied. A smaller inside diameter of a sampling cyclone forces the airflow into a tighter spiral than in a larger diameter cyclone. This tighter, smaller spiral allows imparting of sufficient centrifugal force to cause deposition of smaller aerosol particles. A larger diameter cyclone, however, has straighter streamlines, allowing less particle deposition by centrifugal separation. In the last section of Table I, the results of tests for constant cyclone body Reynolds numbers show that the cutpoint decreasesas the outlet tube diameter is decreased. In these tests, the cyclone flow rate, Q, and the cyclone body diameter, D,, were held constant while the outlet tube diameter was varied. A smaller diameter cyclone outlet tube squeezes and forces the vortex spiral into a smaller cross section flow area, increasing the fluid velocities in the inner and outer vorticies. The combination of these increased velocities and tighter spirals in the 1846 Environ. Scl. Technol., Vol. 27, No. 9, 1993
cyclone causes increased deposition of smaller diameter aerosol particles. As a part of this study, it was desirable to investigate the patterns of deposition of different size aerosol particles in the cyclone device (Figure 6). For tests of the 88.90mm cyclone at a flow rate of 103.0 L/min, the reduction of the outlet tube from 42.90 to 26.70 mm i.d. caused an increase in total cyclone efficiency (Figure 6). The amount of aerosol deposited in the cone region and on the bottom cap increased dramatically when the outlet tube diameter was decreased. The variation of outlet tube diameter under the constraint of a constant cyclone Reynolds number, Rec, produced a change in the aerodynamic particle cutpoint diameter. The explanation for this lies in the manner of particulate deposition in the cyclone device. The patterns of deposition on the inner walls gave an indication of the effect that the outlet tube has on cyclone performance. The data for (1)the inner surface of the outlet tube, (2) the outer surface of the outlet tube and top cap, and (3) the cylindrical body section were omitted for sake of clarity. All of these results, except for two values, are less than 5 % )while the remaining two values are less than 10%. Figure 7a shows the experimental data plotted in the who suggest manner of Saltzman and Hochstrasser a relation between the outlet tube Reynolds number, Reo, and the nondimensionalizedaerodynamicparticle cutpoint diameter, D0.50/Dc. When their model is represented as
(In,
ln(Do,50/Dc)= In a + b In Reo (16) a linear regression of our data to their model gives In a = -2.536 f 0.110, b = -0.829 f 0.047, and rz = 0.957. The correlation coefficient r2 = 0.957 will be shown to be rather low compared with r2 values for another model. A goal of this present work is to develop a design correlation that will provide a better fit to the data than the correlation of Saltzman and Hochstrasser (17). The results of the present study were formulated nondimensionally in terms of the cyclone flow Reynolds number, Ref, and the ratio of the cutpoint diameter to the
l
-
lxlo-'
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Table 11. Comparison Correlations Based on Flow Reynolds Number, &, and Outlet Tube Reynolds Number, Re,a
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correlation typeb experimental data set
Ref vs Do.soID,
Moore-McFarland Saltzman John and Reischl Kim and Lee
r2 = 0.994 r2 = 0.984 r2 = 0.996 r2 = 0.926
Re, vs DQ.M)IDC r2 = 0.957 r2 = 0.976 r2 = 0.996 r2 = 0.394
0 Experimental data from other researchers show that the flow Reynolds number approach produces the better correlation coefficient. b Correlation coefficient, r2, results.
the data from different researchers are correlated using the outlet tube Reynolds number (eq 16) and the flow Reynolds number (eq 17). In all cases, the correlation coefficient, r2,using the flow Reynolds number is better than or equal to the correlation coefficient result from using the outlet tube Reynolds number. The experimental data of Kim and Lee (23)show a poor correlation coefficient of 0.394 with the outlet tube Reynolds number, Reo, but a much better correlation, r2 = 0.926, if the flow Reynolds number, Ref, is used. Because John and Reischl(14) did not vary the outlet tube diameter, the correlation coefficient, r2, is the same for both cases.
< t
VI. Summary and Conclusions
1 e**** Presenl Study I
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FLOW REYNOLDS NUMBER, Re,
Flgure 7. (a) Plot of the aerodynamic particle cutpoint data of the present study. The outlet tube Reynolds number format of Saltzman and Hochstrasser ( 77) Is used. (b) Plot of the aerodynamic particle cutpoint data of the present study. The flow Reynolds number format is used.
cyclone diameter, (Do.~olD,).A plot of the experimental results of this study giving Do.50/Dcas a function of Ref is presented in Figure 7b. The justification for using Ref lies in looking at the airflow geometry in a cyclone as a curved channel, with a characteristic channel diameter of (R, - R,,). It should be noticed that the cyclone inlet velocity is included in this formulation. When the data in Figure 7b are fitted to the following function: (17) ln(D,,dD,) = In a + b In Re, a linear regression of the data gives In a = -2.933 f 0.042, b = -0.81719 f 0.017, and r2 = 0.994. The correlation coefficient of r2 = 0.994 is a better result than if the outlet tube Reynolds number is used as the correlating parameter. A comparison of the two models for predicting the cutpoint of sampling cyclones is given in Table 11,where
Tests were conducted with single-inlet samplingcyclones over a broad range of conditions. Cyclone body diameters varied from 38.10 to 88.90 mm, while outlet tube diameters varied from 26.7 to 68.3 mm (inside diameter). Cyclone flow rates ranged from 16.3 to 124 L min-l, and the measured particle cutpoints varied from a minimum of 4.0 pm AED to a maximum of 18.8pm AED. A functional relationship has been provided to facilitate design through permitting calculation of the cyclone size for a given flow rate, cutpoint diameter, and ratio of body diameter to outlet tube diameter. For the designer who desires to build a new single-inlet cyclonic sampling system, it is recommended that the standard Stairmand (26) high-efficiency cyclone design be used. The existing database for this device is much larger than for any other geometry. However, if the system designer desires to modify an existing system, the work presented here allows that to be done. For example, many aerosol sampling systems have a specified flow rate. If a designer seeks to change the particle cutpoint diameter of a cyclone with a particular body diameter but maintain the same airflow rate, the cyclone outlet tube diameter can be changed with minimum cost in regard to materials, design time, and labor. The correlation given as eq 17 allows the system designer to accomplish this.
Acknowledgments The authors wish to express appreciation to several individuals for their technical assistance: namely, C. A. Ortiz, B. Gamble, and Dr. G. L. Morrison. Funding for this study was provided by the U.S. Environmental Protection Agency under Grant R-811315-01. The opinions, conclusions, and suggestions that are presented are those of the authors and do not necessarily represent the policies of the U S . Environmental Protection Agency. Nomenclature C, = Cunningham's slip correction factor c = aerosol concentration Environ. Sci. Technol., Vol. 27, No. g, 1993 1847
Do.50 = aerodynamic particle cutpoint diameter D, = aerodynamic particle diameter D, = characteristic dimension of a cyclone; body diameter Do = outlet tube diameter of cyclone D, = particle diameter f = r/ro = nondimensional radial coordinate F = numerical reading from fluorometer Kd = dimensionless constant L = liquid volume of solution p = fluid pressure Q = cyclone flow rate r = radial distance in cylindrical coordinate system r2 = correlation coefficient ro = initial swirl radius rref= reference radius of curvature Re, = cyclone body Reynolds number, Rec = PUiDJF Ref = flow Reynolds number, Ref = PUi(Rc - Ro)/p Re, = outlet Reynolds number, Re, = 4pQ/npDo Re, = swirl Reynolds number, Re, = p Worolp Stk0.50= Stokes number for cutpoint particle diameter T = testing time for each filter Vi = inlet velocity Wo = particle and fluid velocity at r = ro Greek P, = ratio of fluid density to particle density V * = nondimensional gradient operator ( = dimensionless pressure drop coefficient TJ = cyclone collection efficiency p = fluid dynamic viscosity p = density of air p , = particle density 0 = cylindrical coordinate in angular direction \ k =~dimensionless factor characterizing cycloneperformance Subscripts
c = cyclone d = downstream location f = flow o = outlet tube p = particle u = upstream location Literature Cited (1) U S . Environmental Protection Agency. Ambient Air
QualityStandards for Particulate Matter; Final Rules. Fed. Regist. 1987,52, 24634-24750. (2) Threshold Limits Committee. Threshold Limit Values of
Air-Borne Contaminants for 1968; American Conference
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of Governmental Industrial Hygienists: Cincinnati, OH, 1968. (3) McFarland, A. R.; Ortiz, C. A,; Bertch, R. W., Jr. J. Air Pollut. Control Assoc. 1984, 34, 544-547. (4) Lapple, C. E. Chem. Eng. 1951,58, 144-151. (5) Beeckmans,J. M.; Kim, C. J. Can. J.Chem. Eng. 1977,55, 640-664. (6) Lippmann, M.; Chan, T. L. Am. Ind. Hyg. Assoc. J. 1974, 35, 189. (7) Blachman, M. W.; Lippmann, M. Am. Ind. Hyg. Assoc. J. 1974,35, 311-326. (8) Lippmann,M.; Kydonieus,A. Am. Ind. Hyg. Assoc. J. 1970, 31, 730-738. (9) Chan, T.; Lippmann, M. Enuiron. Sci. Technol. 1977, 11 (4), 377-382. (10) Rosin, P.; Rammler, E.; Intelman, W. Z. Ver. Dtsch. Ing. 1932, 76, 433-437. (11) Barth, W. Brennst.-Waerme-Kraft 1956,8 (l), 1-9. (12) Leith, D.; Licht, W. AZChE Symp. Ser. 1972,68,196-206. (13) Beeckmans, J. M. J. Aerosol Sci. 1973,4, 329-336. (14) John, W.; Reischl, G. J.Air Pollut. Control Assoc. 1980,30 (8), 872-876. (15) Shepherd, C. B.; Lapple, C. E. Ind. Eng. Chem. 1939, 31, 972-984. (16) Sproull, W. T. Air Pollution and Its Control; Exposition Press: New York, 1970. (17) Saltzman, B. E.; Hochstrasser, H. M. Environ. Sci. Technol. 1983, 17 (7), 418-424. (18) Saltzman, B. E. Am. Ind. Hyg. Assoc. J . 1984,45 (lo),671680. (19) Burkholz, A. Ger. Chem. Eng. 1985,8, 351-358. (20) DeOtte, R. E. Aerosol Sci. Technol. 1990, 12 (4), 10551066. (21) Moore, M. E.; McFarland, A. R. Am. Ind. Hyg. Assoc. J . 1990, 51 (3), 151-159. (22) Particle Technology Laboratory; University of Minnesota: Minneapolis, MN, June 1990. (23) Kim, J. C.; Lee, K. W. Aerosol Sci. Technol. 1990, 12 (4), 1003-1015. (24) Pui, D. Y. H.; Romay-Novas, F.; Liu, B. Y. H. Aerosol Sci. Technol. 1987, 7, 301-315. (25) Dring, R. P.; Suo, M. J. Energy 1978, 2 (4),232-237. (26) Stairmand, C. J. J. Inst. Fuel 1956, 29, 58-76. (27) Berglund, R. N.; Liu, B. Y. H. Enuiron. Sci. Technol. 1973, 7, 147. (28) Olan-Figueroa,E.; McFarland, A. R.; Ortiz, C. A. Am. Ind. Hyg. ASSOC. J . 1982, 43, 395-399.
Received for review November 9, 1992. Revised manuscript received May 19, 1993. Accepted May 27, 1993.
