Cyclone Spreadsheet

04/07/2023 document.xls

CYCLONE DESIGN AND ANALYSISby Esco Engineering

179 Lansdowne Avenue,Kingsville, Ontario N9Y 3J2 Canada Revisionsph 519 733 3122 ### Corrected error in cell D14 on efficiency sheetsfax 519 733 6094 18-Jan-99 Added diagramContact: Neil Stone, Chief Engineer 3-Apr-99 Corrected cell O7, Efficiency 1 - thanks to Laercio Frare for pointing out this errore-mail [email protected] 2-Dec-99 Added metric option, NV sketchWebsite www.mnsi.net/~pas/esco.htm ### 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 various standard cyclones.Enter the flow rate, design inlet velocity and gas density in the colored squaresand the sheet will give dimensions for five standard cyclones - two high efficiency, andthree low efficiency. The table also gives the predicted pressure drop, but be aware that this is avery 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, andcompare the results on the chart. Both sheets are set up with the same layout, so data can be copied between sheets easily.

3 The efficiency calculation requires particle size data, cyclone dimensions, and physical propertydata for the gas and the solids. The calculation assumes that the size distribution of the particlesis log normally distributed. The sheet is set up so that you can enter either the mean and standarddeviation of the log normal distribution, or the particle size data, from which these data are then calculated.

4 Procedure for efficiency calculations:a) Enter the cyclone dimensions in cells D4 to D11. If you have calculated these using this

spreadsheet, the values in cells 13 to 20 for the selected cyclone design can be directly copied

b) Enter the gas property data in cells D18 to D21.c) Enter the particulate data in cells D26 to D29. If you enter the mean and standard deviation, and

select 'N' for cell D28, then the overall efficiency is immediately given in cell H15, and the inlet andoutlet size distributions are given in cells O21 to O41 and R21 to R41.

d) If you want to use the size distribution method, enter 'Y' in cell D28, and then the range limits starting in cell N50 and the corresponding % in range starting in O50. If you want to use more than nine ranges, youcan extend these columns to as many rows as you want - just remember to copy the formulaein columns M and P through T into any rows that you add.After entering the size distribution data, You have to run the regression tool. Choose the 'Tools' menuthen 'Data Analysis' then 'Regression'. For the 'X' value pick all the values in column Q, starting in Q50;for the 'Y' values, pick all the values in column T, starting in T50. For the 'Output range' enter V48. You willget 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 P = 1 - fractional efficiency) against particle size for the two efficiency

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.However, there is no password needed to unprotect it, so you can freely adapt it to suit your purposes.

into D4 to D11. NOTE: Paste special the values - do not just copy the cells.

calculation methods. CAUTION: The two efficiency sheets are not linked, so make sure they are both calculating

04/07/2023 document.xls

DEFINITION OF CYCLONE DIMENSIONS

D

b De

a Sh

H

NV = Neutral vaneExtension of innerside if inlet to centerlineof cyclone

B ELEVATION PLAN

Cyclone size

Page 3

CALCULATE DIMENSIONS FOR CYCLONE NOTES Sheet 1 is for sizingSheets 2/3 are for efficiency (alternates)Sheet 4 are charts of results of sheets 2/3

SPECIFY UNITS (U = US CUSTOMARY[IMPERIAL], M = METRIC) U This setting applies to the whole spreadsheetInput Working

Flow rate Q cfm 2000 2000 cfmDesign inlet vel vi fps 50 50 fpsGas density rg pcf 0.0740 0.074 pcfInlet area 0.67 sfPD parameter 0.56 in water

Dimensions Type of cycloneStairmand Swift Lapple Swift Peterson/Whitby

HE HE LE LE LE

Dia D ft 2.58 2.69 2.31 2.31 2.34Inlet ht a in 15.49 14.18 13.86 13.86 16.40Inlet width b in 6.20 6.77 6.93 6.93 5.85Outlet length S ft 1.29 1.34 1.44 1.39 1.37Outlet dia De in 15.49 12.89 13.86 13.86 14.07Cylinder ht h ft 3.87 3.76 4.62 4.04 3.13Overall ht H ft 10.33 10.48 9.24 8.66 7.43Dust outlet dia B in 11.62 12.89 6.93 11.09 14.07# vel hds Nh 5.14 4.87 4.49 4.69 4.77Press drop, no NV in water 2.85 2.70 2.49 2.60 2.65Press drop, with NV in water 1.34 1.27 1.17 1.22 1.24

Cyclone data from "New design approach boosts cyclone efficiency", W.H.Koch and W.Licht, Chem Eng Nov 7 1977, 80Pressure 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

Cyclone size

Page 4

Sheets 2/3 are for efficiency (alternates)Sheet 4 are charts of results of sheets 2/3

This setting applies to the whole spreadsheet

Copy one col of outlinedata (copy values only)to efficiency sheet.

Cyclone data from "New design approach boosts cyclone efficiency", W.H.Koch and W.Licht, Chem Eng Nov 7 1977, 80Pressure 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

Efficiency 1

Page 5

CALCULATE EFFICIENCY FOR CYCLONE (method 1)CALCULATIONS ARE IN US CUSTOMARY [IMPERIAL] UNITSGeometry Input Working Limits/warningsDia D ft 2.58 2.58Inlet ht a in 15.49 15.49Inlet width b in 6.20 6.20Outlet length S ft 1.29 1.29Oulet dia De in 15.49 15.49Cylinder ht h ft 3.87 3.87Overall ht H ft 10.33 10.33Dust outlet dia B in 11.62 11.62Natural length L ft 6.40 6.40# vel hds Nh 5.14Press drop, no NV in water 2.85Press drop, with NV in water 1.34 Overall efficiency

Gas dataFlow rate Q acfm 2000 2000.00 33.33333 cfsDensity rg pcf 0.0740 0.0740 0.076 air @ 1 atm, spec'd tempViscosity u cP 0.010 0.010 6.72E-06 lb/f-sTemperature T °F 60 60Salt. temp fact fT 1.00 1Salt dens. fact fp 1.00 1

Particle data Value usedLog mean dia dp µm 12 11.905565Log SD sd µm 3 3.1077764Use distribution? (Y/N) y If yes, run regression - adjust input ranges (cols Q,T) to suit dataSpecific gravity 0.8 49.92 pcf

ReferencesEfficiency from "New design approach boosts cyclone efficiency",

W.H.Koch and W.Licht, Chem Eng Nov 7 1977, 80Pressure 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 constants2.5155170.8028530.0103281.4327880.1892690.001308

Efficiency 1

Page 6

Calculated data

Log SD 1.133907Inlet velocity fps 50Ratio inlet/salt vel 2.155166Corrected L ft 6.397135Core dia ft 1.628202Eff vol cf 26.49728Inlet vol cf 2.534862Cycl const Kc 0.916939G 733.5509Vortex exp n+1 1.648398

84.2 %

Efficiency calcsDia, um

air @ 1 atm, spec'd temp Min Max Inlet mass fraction

0 0.4 0.00200.4 0.6 0.00280.6 1.2 0.01681.2 1.8 0.02601.8 2.4 0.03092.4 3 0.0330

3 3.6 0.0336If yes, run regression - adjust input ranges (cols Q,T) to suit data 3.6 4.2 0.0333

4.2 4.8 0.03244.8 7 0.1080

7 10 0.119710 13 0.092613 16 0.072416 22 0.105222 28 0.069828 34 0.048634 40 0.035140 49 0.037249 64 0.038464 79 0.022079 94 0.0136

0.9736Overall efficiency

Distribution dataSize, um Cum %

Min Max0 2 6

Efficiency 1

Page 7

2 3 113 5 225 10 44

10 20 6720 30 8030 40 8540 50 9050 100 97

Efficiency 1

Page 8

Int calcsDistribution Relax time Penetration

Penetration Outlet amt Outlet mass fl fh tl th plfraction

0.8752 0.0017 0.0111 0 0.009991 0 7.11E-07 10.7215 0.0020 0.0129 0.009991 0.018218 7.11E-07 1.6E-06 0.7503670.6321 0.0106 0.0672 0.018218 0.037832 1.6E-06 6.4E-06 0.6926140.5304 0.0138 0.0871 0.037832 0.048784 6.4E-06 1.44E-05 0.5716280.4579 0.0141 0.0893 0.048784 0.054068 1.44E-05 2.56E-05 0.489080.4020 0.0133 0.0839 0.054068 0.056018 2.56E-05 4E-05 0.4267290.3568 0.0120 0.0758 0.056018 0.05603 4E-05 5.76E-05 0.3771710.3195 0.0106 0.0672 0.05603 0.054921 5.76E-05 7.84E-05 0.3365220.2879 0.0093 0.0590 0.054921 0.053178 7.84E-05 0.000102 0.3024460.2346 0.0254 0.1602 0.053178 0.04504 0.000102 0.000218 0.2734170.1640 0.0196 0.1241 0.04504 0.034769 0.000218 0.000444 0.1958750.1126 0.0104 0.0659 0.034769 0.026983 0.000444 0.000751 0.1321120.0805 0.0058 0.0368 0.026983 0.021255 0.000751 0.001137 0.093170.0530 0.0056 0.0352 0.021255 0.013811 0.001137 0.00215 0.067750.0305 0.0021 0.0135 0.013811 0.009455 0.00215 0.003483 0.0381740.0185 0.0009 0.0057 0.009455 0.006743 0.003483 0.005136 0.0228210.0117 0.0004 0.0026 0.006743 0.004969 0.005136 0.007108 0.0142270.0071 0.0003 0.0017 0.004969 0.003297 0.007108 0.010667 0.0091570.0034 0.0001 0.0008 0.003297 0.00183 0.010667 0.018197 0.0049510.0014 0.0000 0.0002 0.00183 0.001106 0.018197 0.027727 0.0019470.0006 0.0000 0.0001 0.001106 0.000711 0.027727 0.039256 0.000832

0.1582 1.0000Overall efficiency 84.2 %

% in ln dia max SUMMARY OUTPUTrange

6 0.693147 2.372092 1.555097 -1.555097 Regression Statistics

Efficiency 1

Page 9

5 1.098612 2.101083 1.226669 -1.226669 Multiple R 0.99987411 1.609438 1.740188 0.77197 -0.77197 R Square 0.99974922 2.302585 1.28139 0.150652 -0.150652 Adjusted R 0.99971323 2.995732 1.489069 0.43948 0.43948 Standard E 0.02289413 3.401197 1.794123 0.841457 0.841457 Observatio 9

5 3.688879 1.947881 1.036431 1.0364315 3.912023 2.145966 1.281729 1.281729 ANOVA7 4.60517 2.648229 1.881213 1.881213 df SS

Regression 1 14.59118Residual 7 0.003669Total 8 14.59485

CoefficientsStandard ErrorIntercept 2.477006 0.007748X Variable 1.133907 0.006796

Efficiency 1

Page 10

Penetrationph

0.7503670.6926140.571628

0.489080.4267290.3771710.3365220.3024460.2734170.1958750.132112

0.093170.06775

0.0381740.0228210.0142270.0091570.0049510.0019470.0008320.000378

Efficiency 1

Page 11

MS F Significance F14.59118 27837.76 7.33E-140.000524

t Stat P-value Lower 95%Upper 95%Lower 95.000%Upper 95.000%319.6806 7.74E-16 2.458684 2.495328 2.458684 2.495328166.8465 7.33E-14 1.117837 1.149978 1.117837 1.149978

Efficiency 2

Page 12

CALCULATE EFFICIENCY FOR CYCLONE (method 2)CALCULATIONS ARE IN US CUSTOMARY [IMPERIAL] UNITSGeometry Input Working Limits/warningsDia D ft 3.33 3.33Inlet ht a in 20.00 20.00Inlet width b in 8.00 8.00Outlet length S ft 1.67 1.67Oulet dia De in 20.00 20.00Cylinder ht h ft 5.00 5.00Overall ht H ft 13.33 13.33Dust outlet dia B in 15.00 15.00Natural length L ft 8.26 8.26# vel hds Nh 5.14Press drop, no NV in water 1.03Press drop, with NV in water 0.48 Overall efficiency

Gas dataFlow rate Q acfm 2000 2000.00 33.33333 cfsDensity rg pcf 0.0740 0.0740 0.076 air @ 1 atm, spec'd tempViscosity u cP 0.010 0.010 6.72E-06 lb/f-sTemperature T °F 60 60Salt. temp fact fT 1.00 1Salt dens. fact fp 1.00 1

Particle data Value usedLog mean dia dp um 24 11.905565Log SD sd um 3 3.1077764Use distribution? (Y/N) y If yes, run regression - adjust input ranges (cols Q,T) to suit dataSpecific gravity 5 312 pcfRe-entrainment coeff alpha 0 default = 0 (see original paper for definition)

ReferencesEfficiency from "A new collection theory of cyclone separators",

L.Enliang & W Yingmin, AIChEJ Vol 35, #4 April 1989, 666Pressure 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 constants2.5155170.8028530.0103281.4327880.1892690.001308

Efficiency 2

Page 13

Calculated data

Log SD 1.133907Inlet velocity fps 30Ratio inlet/salt vel 0.969756Vortex exp 1-n 0.205812theta 37.41762rw 1.666667rn 0.833333uw 46.44141Dr 0.100623

91.4 %

Efficiency calcsDia, um

air @ 1 atm, spec'd temp Min Max Inlet mass Penetration Outlet amtfraction

0 0.4 0.0020 0.9998 0.00200.4 0.6 0.0028 0.9987 0.00280.6 1.2 0.0168 0.9814 0.01651.2 1.8 0.0260 0.9000 0.02341.8 2.4 0.0309 0.7003 0.02162.4 3 0.0330 0.4072 0.0134

3 3.6 0.0336 0.1523 0.0051If yes, run regression - adjust input ranges (cols Q,T) to suit data 3.6 4.2 0.0333 0.0303 0.0010

4.2 4.8 0.0324 0.0024 0.00014.8 7 0.1080 0.0001 0.0000

7 10 0.1197 0.0000 0.000010 13 0.0926 0.0000 0.000013 16 0.0724 0.0000 0.000016 22 0.1052 0.0000 0.000022 28 0.0698 0.0000 0.000028 34 0.0486 0.0000 0.000034 40 0.0351 0.0000 0.000040 49 0.0372 0.0000 0.000049 64 0.0384 0.0000 0.000064 79 0.0220 0.0000 0.000079 94 0.0136 0.0000 0.0000

0.9736 0.0860Overall efficiency 91.4

Distribution dataSize, um Cum % % in ln dia max

Min Max range0 2 6 6 0.693147

Efficiency 2

Page 14

2 3 11 5 1.0986123 5 22 11 1.6094385 10 44 22 2.302585

10 20 67 23 2.99573220 30 80 13 3.40119730 40 85 5 3.68887940 50 90 5 3.91202350 100 97 7 4.60517

Efficiency 2

Page 15

Int calcsDistribution Penetration

Outlet mass fl fh kh wh lh pl phfraction

0.0232 0 0.009991 0.000309 0.00574 1.17E-05 1 0.999560.0328 0.009991 0.018218 0.000695 0.012914 5.95E-05 0.99956 0.9977770.1919 0.018218 0.037832 0.002781 0.051658 0.000952 0.997777 0.9650150.2720 0.037832 0.048784 0.006258 0.11623 0.004818 0.965015 0.8350330.2513 0.048784 0.054068 0.011126 0.206631 0.015228 0.835033 0.5656470.1564 0.054068 0.056018 0.017384 0.32286 0.037177 0.565647 0.2488070.0596 0.056018 0.05603 0.025033 0.464919 0.07709 0.248807 0.0558810.0117 0.05603 0.054921 0.034072 0.632806 0.142819 0.055881 0.0047770.0009 0.054921 0.053178 0.044503 0.826522 0.243644 0.004777 0.000110.0001 0.053178 0.04504 0.094646 1.757795 1.102002 0.00011 1.24E-180.0000 0.04504 0.034769 0.193155 3.587337 4.589762 1.24E-18 2.6E-750.0000 0.034769 0.026983 0.326431 6.062599 13.10882 2.6E-75 9.5E-2140.0000 0.026983 0.021255 0.494476 9.183582 30.07946 9.5E-214 00.0000 0.021255 0.013811 0.934868 17.36271 107.5179 0 00.0000 0.013811 0.009455 1.514332 28.12472 282.1125 0 00.0000 0.009455 0.006743 2.232867 41.46961 613.3464 0 00.0000 0.006743 0.004969 3.090474 57.39739 1174.979 0 00.0000 0.004969 0.003297 4.637643 86.13196 2645.906 0 00.0000 0.003297 0.00183 7.911613 146.9373 7700.343 0 00.0000 0.00183 0.001106 12.05478 223.8857 17877.16 0 00.0000 0.001106 0.000711 17.06714 316.9771 35834.52 0 01.0000

%

SUMMARY OUTPUT

2.372092 1.555097 -1.555097 Regression Statistics

Efficiency 2

Page 16

2.101083 1.226669 -1.226669 Multiple R 0.9998741.740188 0.77197 -0.77197 R Square 0.999749

1.28139 0.150652 -0.150652 Adjusted R 0.9997131.489069 0.43948 0.43948 Standard E 0.0228941.794123 0.841457 0.841457 Observatio 91.947881 1.036431 1.0364312.145966 1.281729 1.281729 ANOVA2.648229 1.881213 1.881213 df SS MS F

Regression 1 14.59118 14.59118 27837.76Residual 7 0.003669 0.000524Total 8 14.59485

CoefficientsStandard Error t Stat P-valueIntercept 2.477006 0.007748 319.6806 7.74E-16X Variable 1.133907 0.006796 166.8465 7.33E-14

Efficiency 2

Page 17

Significance F7.33E-14

Lower 95%Upper 95%Lower 95.000%Upper 95.000%2.458684 2.495328 2.458684 2.4953281.117837 1.149978 1.117837 1.149978

charts

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