by
CYCLONE DESIGN AND ANALYSIS Esco Engineering 179 Lansdowne Avenue, Kingsv ille, Ontario N9Y 3J2 Canada ph 5 19 7 33 3 12 2 fax 51 9 7 3 3 6 0 94 Contact: Neil Stone, Chief Engineer e-mail
[email protected] W ebsite www.mnsi.net/~pas/esco.htm
Revisions 26-Nov -98 18-Jan-99 3-Apr-99 2-Dec-99 13-Dec-99
Corrected error in cell D14 on efficiency sheets Added diagram Corrected cell O7, Efficiency 1 - thanks to Laercio Frare for pointing out this error Added metric option, NV sketch Corrected error in density calc (size! E9, Efficiency 1! and 2! E19)
Copyright 1997 by John Neil Stone. All rights reserved. May be redistributed free of charge, but may not be sold without the author's explicit permission. Provided "as is" without warranty of any kind.
HOW TO USE THIS SPREADSHEET NOTE: This spreadsheet is for the use of knowledgeable professionals, capable of evaluating the accuracy of the results. The author is not responsible for the use to which these results are put. 1 The 'Cyclone size' sheet calculates dimensions for for various standard cyclones. Enter the flow rate, design inlet velocity and gas density in the colored squares and the sheet will give dimensions for five standard cyclones - two high efficiency, and three low efficiency. The table also gives the predicted pressure drop, but be aware that this is a very uncertain calculation (see original references). See 'Diagram' sheet for nomenclature. On the 'Cyclone size' sheet you specify the units you want to use - metric or US Customary (Imperial) THIS UNITS SELECTION APPLIES TO ALL SHEETS 2 Two methods are provided for calculating cyclone efficiency. You can calculate both, and compare the results on the chart. Both sheets are set up with the same layout, layout, so data can be copied between sheets easily. 3 The efficiency calculation requires particle size data, cyclone dimensions, and physical property property data for the gas and the solids. The calculation assumes that the size distribution of the particles is log normally distributed. The sheet is set up so that you can enter either the mean and standard deviation of the log normal distribution, or the particle size data, from which these data are then calculated. 4 Procedure Procedure for efficiency efficiency calculations calculations:: a) Ente Enterr the the cycl cyclon one e dime dimens nsio ions ns in cell cells s D4 to D11. D11. If you you have have calc calcul ulat ated ed thes these e usin using g this this spreadsheet, the values in cells 13 to 20 for the selected cyclone design can be directly copied into D4 to D11. NOTE: Paste special the values - do not just copy the cells. b) Enter the gas property data in cells D18 to D21. c) Ente Enterr the the part partic icul ulat ate e dat data a in in cel cells ls D26 D26 to to D29 D29.. If you you ent enter er the the mea mean n and and stan standa dard rd devi deviat atio ion, n, and and select 'N' for cell D28, then the overall efficiency is immediately given in cell H15, and the inlet and outlet size distributions are given in cells O21 to O41 and R21 to R41. d) If you you want want to use use the the size size dist distri ribu buti tion on meth method od,, ent enter er 'Y' 'Y' in cel celll D28, D28, and and the then n the the ran range ge limi limits ts star starti ting ng in in cell N50 and the corresponding % in range starting in O50. If you want to use more than than nine ranges, you can extend these columns to as many rows as you want - just remember to copy the formulae in columns M and P through T into any rows that you add. After entering the size distribution distribution data, You have to run the regression tool. Choose the 'Tools' menu then 'Data Analysis' then 'Regression'. For the 'X' value pick all the values in column Q, starting in Q50; Q50; for the 'Y' values, pick all the values in column T, starting in T50. For the 'Output range' enter V48. You will get a message saying results will overwrite cells - pick OK. Once the regression is done, the results are available, as described in c) above. 5 The chart sheet graphs the penetration (col (col P = 1 - fractional efficiency) against particle size for the two efficiency calculation methods. CAUTION: The two efficiency sheets are not linked, so make sure they are both calculating from the same data if you want to compare the two efficiency calculations! 6 The spreadsheet is protected in order to prevent accidental overwriting of the formulae. formulae. However, there is no password needed to unprotect it, so you can freely adapt it to suit your purposes.
5/26/2012
98245565.xls.ms_office
DEFINITION OF CYCLONE DIMENSIONS
D
b
De
a
S h
H
NV =
B
ELEVATION
Neutral vane Extension of inner side if inlet to centerline of cyclone PLAN
DEFINITION OF CYCLONE DIMENSIONS
D
b
De
a
S h
H
NV =
ELEVATION
B
Neutral vane Extension of inner side if inlet to centerline of cyclone PLAN
5 /26 /20 12
98245565.xls.ms_office
Cyclone size
NOTES
CALCULATE DIMENSIONS FOR CYCLONE
SPECIFY UNITS (U = US CUSTOMARY[IMPERIAL], M = METRIC) Input Flow rate Q cfm 2000 Design inlet vel vi fps 50 Gas density rg pcf 0.0740 Inlet area PD parameter
U Working 2000 cfm 50 fps 0.074 pcf 0.67 sf 0.56 in water
Dimensions
Dia Inlet ht Inlet width
D a b
ft in in
Sheet 1 is for Sheets 2/3 ar Sheet 4 are c
Stairmand HE
Swift HE
2.58 15.49 6.20
2.69 14.18 6.77
Type of cyclone Lapple Swift LE LE 2.31 13.86 6.93
2.31 13.86 6.93
Cyclone size
NOTES
CALCULATE DIMENSIONS FOR CYCLONE
SPECIFY UNITS (U = US CUSTOMARY[IMPERIAL], M = METRIC) Input Flow rate Q cfm 2000 Design inlet vel vi fps 50 Gas density rg pcf 0.0740 Inlet area PD parameter
U Working 2000 cfm 50 fps 0.074 pcf 0.67 sf 0.56 in water
Dimensions
Dia Inlet ht Inlet width Outlet length Outlet dia Cylinder ht Overall ht Dust outlet dia # vel hds Press drop, no NV Press drop, with NV
D a b S De h H B Nh
ft in in ft in ft ft in in water in water
Sheet 1 is for Sheets 2/3 ar Sheet 4 are c
Stairmand HE
Swift HE
2.58 15.49 6.20 1.29 15.49 3.87 10.33 11.62 5.14 2.85 1.34
2.69 14.18 6.77 1.34 12.89 3.76 10.48 12.89 4.87 2.70 1.27
Type of cyclone Lapple Swift LE LE 2.31 13.86 6.93 1.44 13.86 4.62 9.24 6.93 4.49 2.49 1.17
2.31 13.86 6.93 1.39 13.86 4.04 8.66 11.09 4.69 2.60 1.22
Cyclone data from "New design approach boosts cyclone efficiency", W.H.Koch and W.Licht, Chem Eng No Pressure drop vel head correlation from "A better way to calculate cyclone pressure drop" J. Casal and J.M.
Page 3
Cyclone size
sizing for efficiency (alternates) arts of results of sheets 2/3 This setting applies to the whole spreadsheet
Peterson/Whitby LE 2.34 16.40 5.85 1.37 14.07 3.13 7.43 14.07 4.77 2.65 1.24
Copy one col of outline data (copy values only) to efficiency sheet.
7 1977, 80 artinez-Benet, Chem Eng, Jan 24, 1983, 99
Page 4
Efficiency 1
CALCULATE EFFICIENCY FOR CYCLONE (method 1) CALCULATIONS ARE IN US CUSTOMARY [IMPERIAL] UNITS Geometry Input Working Dia D ft 2.58 2.58 Inlet ht a in 15.49 15.49 Inlet width b in 6.20 6.20 Outlet length S ft 1.29 1.29 Oulet dia De in 15.49 15.49 Cylinder ht h ft 3.87 3.87 Overall ht H ft 10.33 10.33 Dust outlet dia B in 11.62 11.62 Natural length L ft 6.40 6.40 # vel hds Nh 5.14 Press drop, no NV in water 2.85 Press drop, with NV in water 1.34 Gas data Flow rate Density Viscosity Temperature Salt. temp fact Salt dens. fact Particle data Log mean dia Log SD Use distribution? (Y/N) Specific gravity
Q rg u T fT fp
dp sd
acfm pcf cP °F
2000 0.0740 0.010 60 1.00 1.00
2000.00 0.0740 0.010 60 1 1
Limits/warni
Overall efficie
33.3333333 cfs 0.076 air @ 1 atm, s 0.00000672 lb/f-s
Value used 12 11.905565 3 3.1077764
µm µm y
0.8
If yes, run regression - adj 49.92 pcf
References Efficiency from "New design approach boosts cyclone efficiency", W.H.Koch and W.Licht, Chem Eng Nov 7 1977, 80 Pressure drop vel head correlation from "A better way to calculate cyclone pressure drop" J.Casal and J.M. Martinez-Benet, Chem Eng, Jan 24, 1983, 99
Statistical correlation constants 2.515517 0.802853 0.010328 1.432788 0.189269 0.001308
Page 5
Efficiency 1
Page 6
Efficiency 1
Calculated data gs
cy
Log SD Inlet velocity Ratio inlet/salt vel Corrected L Core dia Eff vol Inlet vol Cycl const G Vortex exp
84.2 % Efficiency calcs Dia, u Min
pec'd temp
0 0.4 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 7 10 13 16 22 28 34 40 49 64 79
st input ranges (cols Q,T) to suit data
Distribution data Size, u Min 0 2 3
Page 7
Efficiency 1
5 10 20 30 40 50
Page 8
Efficiency 1
1.13390749 50 2.15516647 6.39713542 1.62820227 26.4972831 2.53486167 0.91693868 733.550942 1.64839814
fps ft ft cf cf Kc n+1
Int calcs Distribution Max 0.4 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 7 10 13 16 22 28 34 40 49 64 79 94
m
Inlet mass frn Penetration Outlet amt Outlet mass fraction fraction 0.0020 0.8752 0.0017 0.0111 0.0028 0.7215 0.0020 0.0129 0.0168 0.6321 0.0106 0.0672 0.0260 0.5304 0.0138 0.0871 0.0309 0.4579 0.0141 0.0893 0.0330 0.4020 0.0133 0.0839 0.0336 0.3568 0.0120 0.0758 0.0333 0.3195 0.0106 0.0672 0.0324 0.2879 0.0093 0.0590 0.1080 0.2346 0.0254 0.1602 0.1197 0.1640 0.0196 0.1241 0.0926 0.1126 0.0104 0.0659 0.0724 0.0805 0.0058 0.0368 0.1052 0.0530 0.0056 0.0352 0.0698 0.0305 0.0021 0.0135 0.0486 0.0185 0.0009 0.0057 0.0351 0.0117 0.0004 0.0026 0.0372 0.0071 0.0003 0.0017 0.0384 0.0034 0.0001 0.0008 0.0220 0.0014 0.0000 0.0002 0.0136 0.0006 0.0000 0.0001 0.9736 0.1582 1.0000 Overall efficiency 84.2 %
Cum %
% in range
Max 2 3 5
6 11 22
fl
fh
0 0.00999118 0.01821771 0.03783188 0.04878351 0.05406752 0.05601818 0.05602999 0.05492097 0.05317768 0.04503989 0.03476918 0.02698254 0.02125479 0.01381122 0.00945487 0.00674347 0.00496863 0.00329665 0.00182986 0.00110627
0.00999118 0.01821771 0.03783188 0.04878351 0.05406752 0.05601818 0.05602999 0.05492097 0.05317768 0.04503989 0.03476918 0.02698254 0.02125479 0.01381122 0.00945487 0.00674347 0.00496863 0.00329665 0.00182986 0.00110627 0.00071142
ln dia max 6 5 11
0.69314718 1.09861229 1.60943791
2.37209221 2.10108301 1.74018834
Page 9
1.55509667 -1.55509667 1.2266687 -1.2266687 0.77197049 -0.77197049
Efficiency 1
10 20 30 40 50 100
44 67 80 85 90 97
22 23 13 5 5 7
2.30258509 2.99573227 3.40119738 3.68887945 3.91202301 4.60517019
1.2813903 1.48906858 1.79412258 1.94788089 2.14596603 2.6482288
Page 10
0.15065203 -0.15065203 0.4394801 0.4394801 0.84145672 0.84145672 1.03643149 1.03643149 1.28172876 1.28172876 1.88121279 1.88121279
Efficiency 1
Relax time tl 0 7.1083E-07 1.5994E-06 6.3975E-06 1.4394E-05 2.559E-05 3.9984E-05 5.7577E-05 7.8369E-05 0.00010236 0.00021769 0.00044427 0.00075082 0.00113733 0.00215027 0.00348308 0.00513576 0.00710832 0.01066692 0.01819729 0.02772688
Penetration th
7.1083E-07 1.5994E-06 6.3975E-06 1.4394E-05 2.559E-05 3.9984E-05 5.7577E-05 7.8369E-05 0.00010236 0.00021769 0.00044427 0.00075082 0.00113733 0.00215027 0.00348308 0.00513576 0.00710832 0.01066692 0.01819729 0.02772688 0.03925568
pl
ph
1 0.75036692 0.69261439 0.57162791 0.48908028 0.42672888 0.37717142 0.33652189 0.30244582 0.27341703 0.19587466 0.13211175 0.09317044 0.06775047 0.03817372 0.02282072 0.01422714 0.00915695 0.00495123 0.00194656 0.0008316
0.75036692 0.69261439 0.57162791 0.48908028 0.42672888 0.37717142 0.33652189 0.30244582 0.27341703 0.19587466 0.13211175 0.09317044 0.06775047 0.03817372 0.02282072 0.01422714 0.00915695 0.00495123 0.00194656 0.0008316 0.00037786
SUMMARY OUTPUT Regression Statistics Multiple R 0.9998743 R Square 0.99974861
Page 11
Efficiency 1
Adjusted R S 0.99971269 Standard Erro 0.02289434 Observations 9 ANOVA df Regression Residual Total
Intercept X Variable 1
SS 14.5911821 0.00366906 14.5948511
MS 14.5911821 0.00052415
F Significance F 27837.7574 7.3319E-14
Coefficients tandard Erro 2.47700595 0.00774838 1.13390749 0.00679611
t Stat 319.680571 166.846509
P-value Lower 95% Upper 95% 7.7387E-16 2.45868396 2.49532794 7.3319E-14 1.11783725 1.14997772
1 7 8
Page 12
Efficiency 1
Page 13
Efficiency 1
ower 95.000 pper 95.000% 2.45868396 2.49532794 1.11783725 1.14997772
Page 14
Efficiency 2
CALCULATE EFFICIENCY FOR CYCLONE (method 2) CALCULATIONS ARE IN US CUSTOMARY [IMPERIAL] UNITS Geometry Input Working Dia D ft 3.33 3.33 Inlet ht a in 20.00 20.00 Inlet width b in 8.00 8.00 Outlet length S ft 1.67 1.67 Oulet dia De in 20.00 20.00 Cylinder ht h ft 5.00 5.00 Overall ht H ft 13.33 13.33 Dust outlet dia B in 15.00 15.00 Natural length L ft 8.26 8.26 # vel hds Nh 5.14 Press drop, no NV in water 1.03 Press drop, with NV in water 0.48 Gas data Flow rate Density Viscosity Temperature Salt. temp fact Salt dens. fact
Q rg u T fT fp
Particle data Log mean dia dp Log SD sd Use distribution? (Y/N) Specific gravity Re-entrainment coeff alpha
acfm pcf cP °F
2000 0.0740 0.010 60 1.00 1.00
2000.00 0.0740 0.010 60 1 1
Limits/warni
Overall efficie
33.3333333 cfs 0.076 air @ 1 atm, s 0.00000672 lb/f-s
Value used 24 11.905565 3 3.1077764
um um y
If yes, run regression - adj 5 312 pcf 0 default = 0 (see original paper for defini
References Efficiency from "A new collection theory of cyclone separators", L.Enliang & W Yingmin, AIChEJ Vol 35, #4 April 1989, 666 Pressure drop vel head correlation from "A better way to calculate cyclone pressure drop" J.Casal and J.M. Martinez-Benet, Chem Eng, Jan 24, 1983, 99
Statistical correlation constants 2.515517 0.802853 0.010328 1.432788 0.189269 0.001308
Page 15
Efficiency 2
Page 16
Efficiency 2
Calculated data gs
cy
Log SD Inlet velocity fps Ratio inlet/salt vel Vortex exp 1-n theta rw rn uw Dr
91.4 % Efficiency calcs Dia, um Min
pec'd temp
Max
0 0.4 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 7 10 13 16 22 28 34 40 49 64 79
st input ranges (cols Q,T) to suit data ion)
Distribution data Size, um Min 0 2 3
Page 17
0.4 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 7 10 13 16 22 28 34 40 49 64 79 94
Max 2 3 5
Efficiency 2
5 10 20 30 40 50
Page 18
10 20 30 40 50 100
Efficiency 2
1.13390749 30 0.96975611 0.20581206 37.4176238 1.66666667 0.83333333 46.4414091 0.10062305
Int calcs Distribution Inlet mass frn Penetration Outlet amt Outlet mass fraction fraction 0.0020 0.9998 0.0020 0.0232 0.0028 0.9987 0.0028 0.0328 0.0168 0.9814 0.0165 0.1919 0.0260 0.9000 0.0234 0.2720 0.0309 0.7003 0.0216 0.2513 0.0330 0.4072 0.0134 0.1564 0.0336 0.1523 0.0051 0.0596 0.0333 0.0303 0.0010 0.0117 0.0324 0.0024 0.0001 0.0009 0.1080 0.0001 0.0000 0.0001 0.1197 0.0000 0.0000 0.0000 0.0926 0.0000 0.0000 0.0000 0.0724 0.0000 0.0000 0.0000 0.1052 0.0000 0.0000 0.0000 0.0698 0.0000 0.0000 0.0000 0.0486 0.0000 0.0000 0.0000 0.0351 0.0000 0.0000 0.0000 0.0372 0.0000 0.0000 0.0000 0.0384 0.0000 0.0000 0.0000 0.0220 0.0000 0.0000 0.0000 0.0136 0.0000 0.0000 0.0000 0.9736 0.0860 1.0000 Overall efficiency 91.4 %
Cum %
% in range 6 11 22
fl
fh
kh
0 0.00999118 0.01821771 0.03783188 0.04878351 0.05406752 0.05601818 0.05602999 0.05492097 0.05317768 0.04503989 0.03476918 0.02698254 0.02125479 0.01381122 0.00945487 0.00674347 0.00496863 0.00329665 0.00182986 0.00110627
0.00999118 0.01821771 0.03783188 0.04878351 0.05406752 0.05601818 0.05602999 0.05492097 0.05317768 0.04503989 0.03476918 0.02698254 0.02125479 0.01381122 0.00945487 0.00674347 0.00496863 0.00329665 0.00182986 0.00110627 0.00071142
0.00030905 0.00069536 0.00278143 0.00625821 0.01112571 0.01738392 0.02503284 0.03407248 0.04450283 0.09464577 0.19315462 0.32643131 0.49447584 0.93486838 1.51433225 2.23286745 3.09047398 4.63764252 7.9116134 12.0547801 17.0671426
ln dia max 6 5 11
0.69314718 1.09861229 1.60943791
SUMMARY O 2.37209221 2.10108301 1.74018834
1.55509667 -1.55509667 1.2266687 -1.2266687 0.77197049 -0.77197049
Page 19
Regressio Multiple R R Square
Efficiency 2
44 67 80 85 90 97
22 23 13 5 5 7
2.30258509 2.99573227 3.40119738 3.68887945 3.91202301 4.60517019
1.2813903 1.48906858 1.79412258 1.94788089 2.14596603 2.6482288
0.15065203 -0.15065203 0.4394801 0.4394801 0.84145672 0.84145672 1.03643149 1.03643149 1.28172876 1.28172876 1.88121279 1.88121279
Adjusted R S Standard Erro Observations ANOVA Regression Residual Total
Intercept X Variable 1
Page 20
Efficiency 2
Penetration wh 0.00573974 0.01291441 0.05165765 0.11622971 0.2066306 0.32286031 0.46491884 0.6328062 0.82652239 1.757795 3.58733674 6.06259909 9.18358206 17.3627098 28.1247201 41.4696127 57.3973879 86.1319552 146.937313 223.885686 316.977074
lh 1.175E-05 5.9483E-05 0.00095173 0.00481815 0.01522773 0.03717707 0.07709038 0.14281944 0.24364366 1.10200185 4.58976197 13.1088192 30.079464 107.517928 282.112473 613.346415 1174.97906 2645.90644 7700.34279 17877.16 35834.5188
pl
ph
1 0.99956045 0.99777675 0.96501504 0.8350333 0.5656468 0.24880702 0.05588056 0.0047769 0.00010983 1.2364E-18 2.601E-75 9.51E-214 0 0 0 0 0 0 0 0
0.99956045 0.99777675 0.96501504 0.8350333 0.5656468 0.24880702 0.05588056 0.0047769 0.00010983 1.2364E-18 2.601E-75 9.51E-214 0 0 0 0 0 0 0 0 0
UTPUT Statistics 0.9998743 0.99974861
Page 21
Efficiency 2
0.99971269 0.02289434 9
df
SS 14.5911821 0.00366906 14.5948511
MS 14.5911821 0.00052415
F Significance F 27837.7574 7.3319E-14
Coefficients tandard Erro 2.47700595 0.00774838 1.13390749 0.00679611
t Stat 319.680571 166.846509
P-value Lower 95% Upper 95% ower 95.000 7.7387E-16 2.45868396 2.49532794 2.45868396 7.3319E-14 1.11783725 1.14997772 1.11783725
1 7 8
Page 22
Efficiency 2
Page 23
Efficiency 2
pper 95.000% 2.49532794 1.14997772
Page 24
charts
EFFICIENCY Koch and Licht
Enliang
1.2000
1.0000
0.8000 n o i t a r t e n e P
0.6000
0.4000
0.2000
0.0000 0
5
10
15 Particle dia um
Page 25
charts
20
25
30
Page 26
