EFFECTS OF CYCLONE DIAMETER ON PERFORMANCE OF 1D3D CYCLONES: CUTPOINT AND SLOPE W. B. Faulkner, M. D. Buser, D. P. Whitelock, B. W. Shaw
ABSTRACT. Cyclones are a commonly used air pollution abatement device for separating particulate matter (PM) from air streams in industrial processes. Several mathematical models have been proposed to predict the cutpoint of cyclones as cyclone diameter varies. The objective of this research was to determine the relationship between cyclone diameter, cutpoint, and slope of the fractional efficiency curve (FEC) based on empirical data. Tests were performed comparing cutpoints and FEC slopes of 15.24, 30.48, 60.96, and 91.44 cm (6, 12, 24, and 36 in.) diameter cyclones with poly‐disperse PM having an aerodynamic mass median diameter near 10 mm. The mass of PM collected by the cyclones and the mass and particle size distributions of PM that penetrated the cyclones were used to determine each cyclone's FEC, characterized by a cutpoint and slope. The cutpoints of cyclones showed no relationship to cyclone diameter, while the slope of the cyclone FECs increased as cyclone diameter increased. Statistically different collection efficiencies were observed among the 30.48, 60.96, and 91.44cm (12, 24, and 36 in.) diameter cyclones. None of the previously published mathematical models analyzed in this article accurately predicted cyclone cutpoint. Keywords. Abatement, Cutpoint, Cyclone, Particulate matter, PM, Similitude, Slope.
C
yclones are a commonly used air pollution abate‐ ment device for separating particulate matter (PM) from air streams in industrial processes. Cyclones are relatively inexpensive with low operational costs and maintenance requirements. Figure 1 shows the rela‐ tive dimensions of a 1D3D cyclone. The Ds in the 1D3D des‐ ignation refer to the diameter of the cyclone barrel, while the numbers preceding the Ds refer to the length of the barrel and cone sections, respectively. A 1D3D cyclone, for instance, has a barrel length equal to the barrel diameter and a cone length equal to three times the barrel diameter. The mechanics of cyclone operation are simple: an air stream containing PM enters a cyclone tangentially near the top of the cyclone and spirals downward. Inertial and centrif‐ ugal forces move the particulates outward to the wall of the cyclone where the PM slides down to the trash outlet at the bottom of the cone section and is removed (fig. 1).
Submitted for review in October 2007 as manuscript number SE 7214; approved for publication by the Structures & Environment Division of ASABE in November 2007. The authors are William Brock Faulkner, ASABE Member Engineer, Research Associate, Department of Biological and Agricultural Engineering, Texas A&M University, College Station, Texas; Michael D. Buser, ASABE Member Engineer, Agricultural Engineer, USDA‐ARS Cotton Production and Processing Research Unit, Lubbock, Texas; Derek P. Whitelock, ASABE Member Engineer, Agricultural Engineer, USDA‐ARS Southwestern Cotton Ginning Research Laboratory, Mesilla Park, New Mexico; and Bryan W. Shaw, ASABE Member Engineer, Associate Professor, Department of Biological and Agricultural Engineering, Texas A&M University, College Station, Texas. Corresponding author: William B. Faulkner, 2117 TAMU, College Station, TX 77843‐2117; phone: 979‐862‐7096; fax: 979‐845‐3932; e‐mail:
[email protected].
Cyclone collection efficiency varies with particle size, with larger particles being collected more efficiently than smaller particles. The performance of a cyclone is defined by its fractional efficiency curve (FEC), which indicates the effi‐ ciency with which a cyclone collects particles of a given size. An ideal FEC is characterized by a lognormal distribution de‐ fined by the cutpoint and slope of the FEC (eq. 1):
Figure 1. 1D3D cyclone configuration (Faulkner et al., 2007).
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2008 American Society of Agricultural and Biological Engineers ISSN 0001-2351
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FEC(d p , d 50 , slope) = ⎡− (ln d p − ln d 50 ) 2 ⎤ exp⎪ ⎥ 2 d p ln(slope) 2π ⎪⎣ 2[ln(slope)] ⎥⎦ 1
(1)
where FEC(dp , d50, slope)= collection efficiency of particle with diameter dp d50 = cyclone cutpoint, which is the particle size corresponding to 50% collection efficiency slope = slope of the FEC. Overall cyclone collection efficiency is calculated ac‐ cording to equation 2: mtrash η= × 100% (2) mtrash + m filter where h = overall collection efficiency of the cyclone (%) mtrash = mass of PM collected in the trash bin of the cyclone (g) mfilter = mass of PM that penetrated the cyclone and was collected on filters downstream (g). The slope of the FEC indicates the sharpness of cut of the cyclone and is calculated according to equation 3: d 84.1 d15.9
slope =
(3)
where d84.1 and d15.9 are particle diameters corresponding to 84.1% and 15.9% collection efficiencies, respectively. An example FEC is shown in figure 2. Several mathematical models have been proposed to predict variations in cutpoint with changes in cyclone barrel diameter. The Lapple (1951) model predicts cyclone cutpoint using equation 4: d pc =
9μW 2πN eVi (ρ p − ρ g )
where dpc = cyclone cutpoint (mm) m = gas viscosity (kg/m‐s) W = width of inlet duct (m) Ne = number of turns of the air stream in the cyclone Vi = gas inlet velocity (m/s) ρp = particle density (kg/m3) ρg = gas density (kg/m3). The Barth (1956) model is based on force balance on particles within the cyclone and was corrected by Wang et al. (2003) to more closely match empirical data. Barth (1956) proposed that cyclone cutpoint may be predicted according to equation 5: d pc =
9μQ πρ p Z oVi 2
(5)
where Q = volume flow rate through the cyclone (m3/s) Zo = vortex length, also known as cyclone effective length (m). Based on experimental data, Wang et al. (2003) added a “cutpoint factor” (K) multiplier to the Barth (1956) model (eq. 6): d pc = K
9μQ πρ p Z oVin2
(6)
The equation for K is dependent on cyclone geometry and the particle size distribution (PSD) of the PM entering the cyclone. For a 1D3D cyclone, Wang et al. (2003) determined that K was calculated according to equation 7: K = 5.3 + 0.02( MMD ) − 2.4(GSD )
(7)
where MMD= mass median diameter of PM entering the cyclone (mm) GSD = geometric standard deviation of the PM PSD.
(4)
100
Cyclone Collection Efficiency (%)
90 80 70 60 50 40 30 20 10 0
d 15.9
d50
d 84.1
Particle Size (logarithmic scale)
Figure 2. Fractional efficiency curve.
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TRANSACTIONS OF THE ASABE
Table 1. Cyclone collection efficiencies from Faulkner et al. (2007). Collection Efficiency (%) Cyclone Diameter,
The MMD of an aerosol is the diameter at which 50% of the mass is comprised of particles smaller than the MMD and 50% by particles larger than the MMD. The model proposed by Pant et al. (2002) was developed empirically for “miniature” cyclones and was based on a 90% cutpoint diameter (eq. 8), but the limits of the model were not defined by the authors: ⎛D ⎞ d 90 = D(Re )− 0.4941 (0.015 . )⎢ e ⎟ ⎝ D⎠ ⎛ B⎞ ×⎢ ⎟ ⎝D⎠
− 0.578
⎛S⎞ ⎢ ⎟ ⎝ D⎠
− 0.086
⎛ Lc ⎞ ⎢ ⎟ ⎝D⎠
cm (in.) 15.24 (6) 30.48 (12) 60.96 (24) 91.44 (36) [a]
0.197
− 0.052
(8)
where d90 = 90% cutpoint (m) D = cyclone diameter (m) Re = Reynolds number De = cyclone gas outlet diameter (m) B = cyclone trash outlet diameter (m) S = length of intrusion of gas outlet into the cyclone (m) Lc = cyclone cone length (m). Assuming a constant slope, changes in d90 predicted by the Pant et al. (2002) model would mirror changes in d50. No literature was found characterizing the relationship between cyclone FEC slope and barrel diameter. Using lognormal distributions to describe PM PSD and cyclone FEC and assuming constant FEC slope, the collection efficiency of a cyclone increases as cutpoint decreases. Collection efficiency may increase or decrease with increasing FEC slope, depending on the PSD of the PM and the cyclone cutpoint. If the MMD of the PM is sufficiently smaller (around 0.5 mm smaller) than the cutpoint of the cyclone, then increases in the slope of the FEC will lead to increases in collection efficiency. If the MMD of the PM is greater than or equal to the cyclone cutpoint, then increases in the slope of the FEC will lead to decreases in collection efficiency. Faulkner et al. (2007) reported that the collection efficiency of 1D3D cyclones decreased nonlinearly as cyclone barrel diameter increased from 30.48 to 91.44 cm (12
Average [a]
Std. Dev.
99.49 a 99.17 a 97.84 b 94.52 c
0.19 0.20 0.28 0.56
Values followed by the same letter are not statistically different (α = 0.05) as determined by Tukey's HSD.
to 36 in.) when collecting poly‐disperse PM having an MMD near 10 mm (table1). The objective of this research was to characterize the changes in cyclone cutpoint and FEC slope that drive the differences in collection efficiency between cyclones of varying diameter.
MATERIALS AND METHODS The cutpoints and slopes of four 1D3D cyclones of 15.24, 30.48, 60.96, and 91.44 cm (6, 12, 24, and 36 in.) diameter were evaluated using microalumina with an MMD of 10.3mm aerodynamic equivalent diameter (AED) and GSD of 1.40. Details of the cyclone testing system (fig. 3) and experimental design are described by Faulkner et al. (2007). In order to minimize the effects of startup and stopping on the tests, a test period of 30 min was used for the 15.24, 30.48, and 60.96 cm (6, 12, and 24 in.) diameter cyclones. Due to rapid increases in system static pressure as filters became loaded, the duration of tests for the 91.44 cm (36 in.) diameter cyclone was limited to only a few minutes, and tests were terminated when the cyclone inlet velocity fell to 853.2m/min (2800 fpm), which is the low end of the Texas A&M Cyclone Design (TCD) recommended inlet velocity range (Wang et al., 2002). PM that penetrated each cyclone was deposited on 16filters downstream of the cyclone, while the PM collected by each cyclone was deposited in a sealed container at the trash exit. The mass of PM entering the cyclone was
Four filter housings with four filters each
Out
Dust feeder
Figure 3. Cyclone testing system.
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determined by adding the mass collected in the sealed containers at the trash exit of the cyclone to the mass of PM collected on the filters. Prior to weighing, filters were conditioned for a minimum of 48 h in an environmental chamber at 21.1°C (70°F) and 35% relative humidity. The filters were weighed to the nearest 10m g before and after the tests using a Mettler Toledo model AG‐285 balance (Columbus, Ohio) to determine the mass of PM that penetrated the cyclones. For quality control purposes, each filter weight was an average of three balance readings. If the standard deviation of the three readings exceeded 50 m g, the filter was re‐weighed. Tests were conducted in a randomized complete block design with replication as the blocking factor. Five replications were conducted. The PM that penetrated the cyclones was more heavily deposited on eight of the 16 filters, particularly for the 15.24 and 30.48 cm (6 and 12 in.) diameter cyclones, likely due to preferential flow paths as a result of elbows and flow splitters in the system. The PSD of PM that penetrated the cyclone during any one run was determined by weighting the PSD of PM on each of the eight heaviest loaded filters by the mass of PM deposited on each filter. The total mass that penetrated the cyclone was determined by summing the change in mass of all 16 filters during any one run. Using a Beckman Coulter Counter Multisizer 3 (Beckman Coulter, Miami, Fla.), the PSD of PM entering the cyclone and that deposited on each filter was determined using the method described by Faulkner and Shaw (2006). The mass of PM deposited on the filters in each size range measured by the Beckman Coulter Counter Multisizer 3 was determined using equation 9: m filt ,i = mtotal × f i
m filt , i min , i
(10)
where hi = cyclone efficiency of collection of particles in the ith size range min,i = mass of PM entering the cyclone in the ith size range. The lognormal distribution that best fit the measured collection efficiency data was determined by simultaneously minimizing equations 11 and 12 to solve for d50 and slope and inserting the determined values into equation 1: ∞
∫ [(f
J=
)(1 − FEC(d p , d50 , slope) )
in ( d p )
o
]
− f filter (d p ) dd p
290
min ∞
∫ [(f
−
0
)(1 − FEC(d p , d50 , slope))]ddp
in ( d p )
(12)
where fin (dp ) = mass fraction of particles entering the cyclone of size dp ffilter (dp )= mass fraction of particles deposited on the filters of size dp min = mass of PM entering the cyclone. The log‐normality of the distribution of collection efficiencies for each cyclone test was examined using a chi‐ square test (a = 0.05) with the null hypothesis that the distributions were not log‐normal. The smallest 0.1% of particles by mass were excluded from the analysis because the extreme variability in the measured collection efficiencies of these particles. Analysis of variance tests were conducted on the cutpoints and slopes of all treatments using SPSS (SPSS, Inc., Chicago, Ill.). A two‐tailed post hoc Tukey's HSD procedure was used with the null hypothesis (a = 0.05) that the cutpoints for each treatment were equal, and a second test was conducted with the null hypothesis (a = 0.05) that the slopes of the FECs for each treatment were equal. Empirically determined cyclone cutpoints were then compared to mathematical models proposed by Lapple (1951), Barth (1956) (as subsequently corrected by Wang et al. (2003), Pant et al. (2002), and the energy dissipation model derived by Faulkner et al. (2007).
(9)
where mfilt,i = mass of PM deposited on the filters in the ith size range mtotal = total mass deposited on the filters = mass fraction of particles on the filters in the ith fi size range. The efficiency of collection for each size range was determined according to equation 10: ηi = 1 −
m filter
K=
(11)
RESULTS AND DISCUSSION EXPERIMENTAL EVALUATION For all trials, the chi‐square analysis indicated that a log‐ normal distribution described by a cutpoint and slope was appropriate to characterize the performance of the cyclones. The average FECs (averaged over the five replications) for the cyclone sizes tested were plotted against each other (fig.4). The cutpoints and slopes for each treatment are given in table 2. No significant differences were detected in cutpoint among any of the cyclones tested. The average cutpoint (over all cyclones tested) was 3.8 ±0.2 mm AED. No significant difference was detected between the FEC slopes of the two smallest cyclone sizes: 15.24 and 30.48 cm (6 and 12 in.). Significant differences (a < 0.05) in FEC slope were detected between the 60.96 cm (24 in.) cyclone and all other cyclones as well as the 91.44 cm (36 in.) cyclone and all other cyclones. The slope of the FEC increased as cyclone barrel diameter increased. These results indicate that changes in the FEC slope, rather than changes in cyclone cutpoint, drove differences in overall collection efficiency observed by Faulkner et al. (2007). Had cyclone cutpoint increased with barrel diameter, one could conclude that collection efficiency decreases with increasing cyclone size. However, because changes in FEC slope drove differences in collection efficiency, the effect on collection efficiency is dependent on the MMD of the aerosol being collected. If the MMD of the PM is substantially lower than the cutpoint of the cyclone, then increases in slope will
TRANSACTIONS OF THE ASABE
100
Cyclone Collection Efficiency (%)
90 80 70 60 50 40 30 20 10 0 1
3
2
4
5
6
7
8 9 10
20
Particle Size ( m) 15.24 cm (6 in.)
30.48 cm (12 in.)
60.96 cm (24 in.)
91.44 cm (36 in.)
Figure 4. Average fractional efficiency curves for cyclones based on five replicates. Table 2. Cyclone cutpoints and fractional efficiency curve slopes with 95% confidence intervals.[a] Cyclone Diameter, d50[b] cm (in.) (μm) Slope 3.4 ±0.2 a 3.9 ±0.4 a 4.0 ±0.6 a 3.9 ±0.4 a
15.24 (6) 30.48 (12) 60.96 (24) 91.44 (36)
Results from the 91.44 cm (36 in.) cyclone should be interpreted cautiously, as the durations of these tests were shorter than those for all other cyclones, magnifying any effects from startup and termination of the tests. Further examination of the performance of larger cyclones is needed. Given the high leverage value of the results of the 91.44 cm (36 in.) cyclone when performing regression analysis and the magnified startup and termination effects, the results of these tests should not be extrapolated to estimate the performance of larger cyclones.
1.47 ±0.11 a 1.47 ±0.17 a 1.79 ±0.14 b 2.29 ±0.10 c
[a]
Values in a column followed by the same letter are not statistically different (α = 0.05) as determined by Tukey's HSD. [b] Cutpoint values are given in aerodynamic equivalent diameter.
lead to increases in collection efficiency. If the MMD of the PM is larger than the cutpoint of the cyclone, then increases in slope will lead to decreases in collection efficiency. The marginal change in collection efficiency with changes in cyclone barrel diameter will depend on the cutpoint of the cyclone and the MMD of the PM being collected.
MATHEMATICAL MODELS All models except the energy dissipation model predicted an increase in cutpoint as cyclone diameter increased (fig. 5). The predicted cutpoints of 1D3D cyclones increased according to equation 13: d 50 = ax b
(13)
10
Cyclone Cutpoint ( m)
8
6
4
2
0 10
25
40 55 70 1D3D Cyclone Diameter (cm)
85
Lapple
Pant
Measured
Barth
Energy dissipation
100
Figure 5. 1D3D cyclone cutpoint models and average measured cutpoints.
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Model
Table 3. Constant values for equation 13 predicted by mathematical models. a b
Lapple (1951) Barth (1956)[a] Pant et al. (2002) Energy dissipation (Faulkner et al., 2007) Measured [a]
0.441 0.730 0.624 4.300 2.855
0.488 0.496 0.576 0.000 0.076
R2 0.999 1.000 0.999 1.000 0.674
As corrected by Wang et al. (2003).
where d50 = cyclone cutpoint (mm) x = cyclone diameter (cm) a and b = curve‐fit coefficients. The values of a and b for each model are shown in table3. All R2 values are equal to 1.00. Of the aforementioned mathematical models, only the energy dissipation model predicted no change in cyclone cutpoint with changes in cyclone barrel diameter, indicating that this model may be the most appropriate model for determining cyclone cutpoint. Additional research should be conducted to determine whether the cutpoint is affected by the PSD of the PM. If so, the energy dissipation model (Faulkner et al., 2007) may be further refined. The Pant et al. (2002) model and Barth (1956) model as corrected by Wang et al. (2003) predicted the largest increase in cutpoint with increasing cyclone barrel diameter. These models may not match observed cutpoints of the larger cyclones tested in this study due to the relatively small barrel diameter of cyclones used to establish these relationships. Additional work should be done to determine the nature of the relationship between cyclone barrel diameter and the FEC slope.
CONCLUSIONS The cutpoints and slopes of 15.24, 30.48, 60.96, and 91.44cm (6, 12, 24, and 36 in.) diameter 1D3D cyclones operated with similar inlet velocities were compared using PM with an MMD of 10.3mm AED to maximize differences
292
in cyclone collection efficiency due to differences in cyclone barrel diameter. The cutpoint of the tested cyclones showed no relationship to barrel diameter, while the slope of the FEC increased with increasing barrel diameter with statistically significant (a = 0.05) differences found among the 30.48, 60.96, and 91.44 cm (12, 24, and 36 in.) diameter cyclones. Given the high leverage value of the results of the 91.44 cm (36 in.) cyclone when performing regression analysis and the magnified startup and termination effects, the results of these tests should not be extrapolated to estimate the performance of larger cyclones. None of the previously published mathematical models analyzed in this study accurately predicted the cutpoint of the 1D3D cyclones. To accurately predict the performance of air pollution abatement systems that use cyclone separators, a proper understanding of the relationship between cyclone diameter and abatement efficiency is needed. This work begins to characterize the driving forces behind observed differences in cyclone collection efficiency, allowing for more precise design of air pollution abatement devices in the future.
REFERENCES Barth, W. 1956. Design and layout of the cyclone separator on the basis of new investigations. Brenn. Warme Kraft 8: 1‐9. Faulkner, W. B., and B. W. Shaw. 2006. Efficiency and pressure drop of cyclones across a range of inlet velocities. Applied Eng. in Agric. 22(1): 155‐161. Faulkner, W. B., M. D. Buser, D. P. Whitelock, and B. W. Shaw. 2007. Effects of cyclone diameter on performance of 1D3D cyclones: collection efficiency. Trans. ASABE 50(3): 1053‐1059. Lapple, C. E. 1951. Processes use many collector types. Chem. Eng. 58(5). Pant, K., C. T. Crowe, and P. Irving. 2002. On the design of miniature cyclones for the collection of bioaerosols. Powder Tech. 125(2‐3): 260‐265. Wang, L., M. D. Buser, C. B. Parnell, and B. W. Shaw. 2002. Effect of air density on cyclone performance and system design. ASAE Paper No. 024216. St. Joseph, Mich.: ASAE. Wang, L., C. B. Parnell, B. W. Shaw, and R. E. Lacey. 2003. Analysis of cyclone collection efficiency. ASAE Paper No. 034114. St. Joseph, Mich.: ASAE.
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