List of symbols

A Cross-sectional area m2

A a constant in the Mothes and Löffler model AR total inside surface area of the cylone m2

Aw inside area of the cyclone inlet region (MM) m2

AJ, Ab A3, constants in the Cunningham coom factor equation a acceleration vector; components: ai; size: a m s-2

a height of the cyclone inlet or of vane open area m a area m2

B boyancy force N B a constant in the Mothes and Löffler model b width of the cyclone inlet or of vane open area m c,c,,c2 constants vanes c a constant in the Mothes and Löffler model Ce Cunningham correction factor Co drag coefficient Cyso characteristic cyclone number of Rietema c solids loading of inlet gas to cyclone or swirl tube gm-3

Co mass fraction of dust in the incoming gas

Cok mass fraction of liquid in the incoming gas

CoL limiting loading (as mass fraction) in the MM cv volume concentration of particles co- c4 vol. conc. of particles of size x (Mothes-Löffler) D with subscript: diameter, without: body diameter m D a constant in the Mothes and Löffler model D particle diffusivity (Mothes-Löffler) m2 s-'

d distance m dv, du dimensions characterizing the design of vane packs m Eu Euler number, 11pl('lz pv2)

e rate of erosion kg m-2s-'

F(·), F'O cumulative undersize distribution function F force vector with components and absolute value F N Fr Froude number, (gD)!i

f friction factor

10 differential density distribution function m-'

G friction factor in Stairrnand equation = j12 g gravitational acceleration vector with abs. value g m s-2

H height, total height of cyclone, submergence m

314 List of symbols

Hi height of the inner vortex m

Hcyt* dim'less height in the Meissner and Löfflermodel

h height m

Uo transmitted, incident light intensity wm-2

I electrical current A

j volume flux of particles ms-1

K constant in Barth's pressure drop model K constant relating press. drop to impactpress (=Eu) K, constant in the Mothes and Löffler model k parameter in the Rosin-Rammler distribution m-n

k turbulent kinetic energy per unit mass Jkg-1

k exponent in empirical relations for c0 L

ks absolute wall roughness m L diameter of a cylindrically shaped particle m

Ln natural vortex length m I length m l' horizontal thickness of vane m M mass of solids kg M mass flow of solids kg s-1

MF mass fraction MW gas molecular weight kg kgmor1

m exponent in functional forms for GEC or PSD curve m mass kg

N number K constant in Barth's pressure drop model n exponent in the n-type tangential velocity model p perimeter m p pressure Pa q term appearing in Stairmand's pressure drop model

Q volumetric flow rate mJ s-1

R D/2 m R gas constant JK-1 kgmor1

Rex ratio of vortex core to vortex finder radii Re Reynolds number, (pvD)/ f.1 ReR 'cyclone body Reynolds number' (MM)

Ro,Rdc radii of spin fluid surface and detector in disc centr. m r radial coordinate m s length ofvortex finder within cyclone m s source term, rate of generation of tpper unit volume varies

SAA velocity ratio of Abrahamsen and Allen Stk Stokes number, (ilpx2v)/(18,uD) s height, width m s estimate of standard deviation vanes T runtime or time-to-failure s

List of symbols 315

T temperature oc

time (s) thickness m

V' particle velocity vector rel. to gas; components U ms·'

V particle velocity vector; components: U ms -I

V volume m3

V superficial gas velocity ms·'

V electrical voltage V V gas velocity vector; abs. value v; components: v; ms -I

Vjm Vx mean gas velocity in inlet and vortex finder, resp. ms·'

vew* wall velocity just after inlet (Meissner and Löffler) ms·'

w weight N We Weber number, (pv2D)/(j w width m X particle diameter m <x>sa 'Sauter mean' particle diameter m

Xjact empirical correction factor y an independent observation y distance from side wall m z axial coordinate m

Greek and other:

a,ß,ß',y proportionality constants varies a entrance constriction coefficient ß angle ß ratio of velocities in the Meissner and Löffler model .d· difference in g,. 'offset' distance for scroll design m

E angle between conical wall and cyclone axis

E rate ofturbulent energy dissipation per unit mass J kg·' s·'

r Gamma function

qJ conserved quantity varies

r specific weight (density relativetothat ofwater)

17 overall fractional separation efficiency

770 grade-efficiency A, mean free path m

J.1 viscosity kgm·' s·'

() tangential coordinate

p density (without subscript: gas density) kgm-3

t/J Coulomb potential of an electrical field cm·' (j standard deviation, or spread varies (j surface tension Nm·'

316 List of symbols

T

T

t q Q

1/f V <·>

II-II

Subscripts:

1,2 2 50 25,75 a air acc B b b body c c c eh comm cyc cyl es D d d dust e e eq F

f fact fin

particle relaxation time turbidity shear stress tensor with components r =b!R angular velocity Wadell's sphericity del operator mean

absolute value

s

Pa

-1 m

at points 1 and 2 in the system or two different solids loadings in the cyclone inlet region cut size reference to 0.25, 0.75 fractional efficiency, respectively annular in a clean (air only) cyclone due to acceleration into the cyclone inlet back bed bulk in the cyclone body captured ( or underflow) fraction cone, conical wall vortex core characteristic commercial cyclone cylindrical wall in the surface es drag dust outlet dipleg solids due to the dust overflow ( or emitted or lost) fraction extemal equivalent front feed factor final

in ini

Iid N m, mid m med 0

of p pr r reS req s s s s SC

SV

sepspace sl Stk str

t th tot uf V V

v, u, ov, iv, mid vol vt w wet X

z

()

ocs

flapper plate index or intemal inlet initial liquid top surface number geometric mean model median start or reference or gas-only overflow particle primary radial

List of symbols 317

radial gas velocity component in the surface es required stagnation secondary spiral submerged scroll surface-to-volume in the separation space due to solids loading when Stokes' law applies of a strand of solids tube terminal velocity throat total underflow volume vessel pertaining to vane pack geometry volume vortex tube wall wetted gas exit tube or vortex tinder axial tangential tangential velocity component in the surface es

318 List of symbols

Superscripts

0 angular or temperature degrees

* dimensionless parameters in the Equations of Motion

List of tradenames

- Mathematica - Wolfram Research, Inc. - MathGV - Greg VanMullem - Windows - Microsoft Corporation - MATLAB- The MathWorks, Inc. - Mathcad- MathSoft Engineering & Education, Inc. - FLUENT - Fluent Inc. - TEEPOL- Royal Dutch/Shell Group - Triekle Valve - Ducon Technologies Inc. - Calgon - Calgon Corporation - Hexmetal, Flexmetal, Hexmesh - Causeway Steel Products, Ltd. - CoorsTek - CoorsTek Incorporated - Porta-Test Revolution - Natco, Canada - G-Sep - K vaemer Group - Cyclo-Trell - Hamon Research-Cottrell - Teflon - DuPont

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Index

abrasive particles, 215 absolute roughness. See

roughness:absolute acceleration, 5, 12, 19, 23, 30, 92, 109

centripetal, 16, 23, 33, 94, 118, 119 gravitational, 30, 139 loss, 108, 109, 204,205

access ports, 39, 222 accessibility/inspection, 288 aeration, 199- 203, 208, 209 aerodynamic particle size, 25, 43 afterbuming, 23 I agglomeration, 48, 112, 138, 139, 149,

158, 161, 175, 185 aggregate, 226 airlock, 9, 10 analyzer, 185 anchoring, 225- 231 anemometer, fringe, 178 angular momentum, 12, 57, 169,221,243,

280 angular velocity, 16, 32, 186 anisotropy, 127 anti-creep skirts, 240, 244 ASM. See turbulence model:Algebraic

Stress Model attrition, 222 average, 45, 53, 100, 125, 179, 190,202,

219,227,233 drop size, 249- 255 gas velocity, 54, 58, 61, 62, 259, 260 overtime, 126,127,130,131 particle size, 28, 106, 107, 120,216,

221 axial velocity

and particle motion, 81 by CFD, 127- 129 distribution, 38 in in Iet. See inlet velocity in vortex finder, 58, 61 locus of zero, 68 mean, 45, 75, 138, 146 measurements of, 128 models for, 54, 61, 62, 64

axisymmetrical, 31

backmixing, 43, 80 backup,203,204,209- 213 bands, 178,227,228 barre!, 12, 40, 56, I 03, 118, 215, 228, 230,

279,281,287 Basset

integral, 20 term, 20, 148

Bemoulli equation, 17,19,63,291 trinomial, 18

bleed stream, 185 blow-down, 197,206 blowout, 266 boundary layer separation, 279, 294 boyancy,22,211,232 brownian motion, 22, 188 buffeting, 287 bulk rotation, 243, 244

calibration, 177, 188 carryover,242,266,268 carryunder, 266 Cartesian, 20, 50, 135 cascade impactor, 186, 190 Cast Basalt, 231 castable, 225 catalytic cracking, 8, 21, 223, 225, 305,

308 cavitation, 243, 265, 273 centrifugal force, 16, 19, 23, 33, 37, 40, 77,

78,87, 105,117,157,186,227,245, 263

ceramic, 6 filter, 3 lining, 39,222,225,229- 231

CFD, 37, 40, 53, 67, 68, 70, 83, 88, 89, 123- 125, 127- 129, 131 , 132, 286

choke,243 classification, I 05, I 07, 116, 118, 121 ,

253,254 duty, 43 in inlet, 108, 121, 122, 157, 158 in vortex core, 107,254 of centrifugal separators, II, 13

326

closing tilt, 196 coalescence, 5, 239, 265 coking,9, 128,226 communicate, 207,267, 307 compaction, 197, 20 I , 209 computational fluid dynamics. See CFD computational grid, 123, 124 concentration

effect on erosion, 217, 222 effect on pressure drop, 238 for conservation equations, 124, 134 in cyclone, 94, 95, 175 in inlet, 94, 159, 162, 172, 174,299,

300 in overflow, 300 in overhead, 2 in sizing equipment, 186, 188 Iimit loading. See Iimit Ioad measurement of, 182-185 of droplets, 249, 253

condensables, 183 condensation, 48, 183 cone, 12,91,92,287,289

and vortex end, 168, 170, 220 design of, 282, 283, 285 erosion in, 168, 199, 215, 217-22 1,

223,292 erosion protection of, 230 flow in, 69, 118, 209, 227, 228 pressure in, 130, 207 surface area of, 103, 118 vortex stabi1izing, 169

conservation, 30, 51 , 126, 134,297 conservative force fie1d, 139 constriction, 56, 73, 91, 98, 118, 252,293 constriction coefficient, 98, 118, 293 control-surface, 54 coordinate system, 16, 23, 31, 49 core model, 61-66 Coulter Counter, 188 counter-weighted flapper valve, 196 counting technique, 189 critical deposition velocity, 215, 232, 235 critical size, 188 cross plate, 285 cross-talk, 168, 205 cross-triangulation, 180 cumulative undersize distribution, 27, 28,

34,44,46 definition, 27

Cunningham correction, 22, 25, 234 current, electrical analogue, 188, 206, 207 cut size, 6, 43, 44, 68, 158, 159, 168, 186-

190, 198,234-238,280,287

definition, 43 in demisting cyc1ones, 239- 254 in multicyclone arrangements, 299-312 mode1s for, 77-123 scaling rules for, 137- 155

cyclone length, 74, 86-89, 128, 145, 146, 163, 168,291,292

cyclone train, 186, 190 cylinder-on-cone, 7, 9, 12-14, 37, 53, 68-

71, 76,90,98,99, 168,217,277, 292, 293,296

decoupled, 242 deflector p1ate, 266 defluidized bed, 201 defoaming, 15,263-275 degas,265 demisting, I , 8, 9, 23,239, 245,268 demisting cyclones, 38, 58, 168,239-262,

296 density, 24, 29, 109, 211, 225, 231, 255,

300 air, 73, 110, 113, 115 bulk, 102, 110,113,115,202,204,210 difference, 139 dust, 121 fluid, 17- 20,30,33 gas, 72, 78, 81, 82, 100, 104, 138, 153,

234,236,238,249,250,255, 260, 261,266

liquid, 249, 250, 253, 255, 272, 274 offeed solids, 107 particle, 2, 15, 19, 21, 22, 24, 25, 27,

29,41-43, 110, 113, 115, 138, 175, 186,188- 190,221,253

powder, 87, 90, 149 ratio, 141, 148 solids, 84, 107, 159,212 strand, 102, 110, 113

density distribution, 26, 27, 34, 35, 42 definition, 25, 26

deposits, 5, 39, 58, 128, 240, 268 designs, frequently used, 277 destabilized, 169 destabilized vortex, 169 deviatoric, 30, 31 diameter, 12, 24- 29, 34, 40-43, 65, 170,

180, 183, 196,216,225,230,233,240, 242,244, 245,249,255,289, 295,301 aerodynamic, 25 cone,219,220,282,287 critica1, 84 cut. See cut size droplet, 250, 255, 256

dynamically equivalent, 24, 190 mean, 250 median, 250 ofcyclone, 7, 55, 84, 139, 144, 148,

149,169,186,223, 228,231,236, 245, 246,263,267,280, 289,302, 310- 312

of dipleg, 200, 20 I , 211 of dust exit, 7, 199,200 of friction surface, 57 ofinlet, 143, 252 of innervortex,68,287 ofthe surface es, 54 ofvane assembly, 295,297 ofvortex finder, 7, 54, 82, 115, 139,

169,242,278,280,287,289,301 , 310

particle, 5, 19, 24, 43, 105, 116, 156, 186, 199, 217, 256

Stokesian, 25, 139 surface equivalent, 24 surface/volume, 24 volume equivalent, 24, 139, 189

diffuser, 53, 61 ,266, 289 dimensional analysis, 137-142, 147, 148 dimensional ratios, 98, 311 dimensionally consistent, 137 dimensionless group, 137, 140, 147, 148 dimensionless number, 46, 139, 141, 153 dipleg, 194-213, 215, 220, 225, 285 disc centrifuge, 157, 186, 187, 190 dispersing agent, 185 dispersion, 22, 23, 43, 48, 77, 86, 132, 138,

161, 184, 185, 187, 190 dissipation, 18, 51-53, 126 distribution function, 27, 28, 120, 138 dollar plate, 196, 197, 201 Doppler burst, 178 double vortex, 7 doub1e-b1ock va1ves, 210 drag, 19- 23, 39, 40, 45, 52, 59, 77, 87,

102- 105, 161 , 162, 170,227,232,234 coefficient, 20, 105 Stokes,20-23,25,40, 77, 78,85, 104,

105, 119, 123, 132, 148, 188,233, 234

drainpipes, 242 droplet, 5, 239- 262, 297 droplet distribution, 251 dumping, ofhopper, 210 dust hopper, 200, 220 dust outlet, 6, 38, 91, 94, 95, 113, 180,

278,284,285

327

dynamic pressure, 17, 18, 45, 51- 53, 60, 61,63,88, 177,179,291

dynamically equiva1ent, 25, 29, 186, 187, 189, 190

eddy viscosity, 129 effective density, 262 effective viscosity, 22 electrica1 analog, 206, 207 electrical charge, 185 e1ectrica1 sensing zone, 188-190 e1ectrofi1ter, 2, 4 electro-po1ished, 6 electrostatic, 2, 4, 112, 140, 312 emission, I , 2, 155, 299,308,309 entrainment, 198-200, 265, 273, 284 entry, 7, 9, 13, 37, 43, 45, 107, 11 7, 164,

290,292 envelope density, 29 equation of continuity, 30, 135 equation ofmotion, 19, 20, 123, 132, 137,

138, 141 , 147, 148 equilibrium orbit, 68, 77, 78, 83, 85, 90,

97,245 equivalent sphere, 24 erosion, 2, 30, 140, 166, 168, 198, 199,

2 10,2 13,215-232,240,250, 279, 285, 292,3 12

erosion peak, 218, 220, 22 1 erosion protection, 6, 52, 101, 107, 130,

221-232 erosion ring, 218 error,20,28, 48,64, 144, 176, 177,181,

183- 186, 190-192,233,236, 297 error propagation, 191 Euler number, 45, 63, 66, 141 , 146, 260,

301 Eu1erian, 30, 123, 131, 133 exit scroll, 289

failure, 5, 216, 217, 231, 242 FCC, 21, 149 FCCU, 8- 10, 52, 128,225- 228, 231, 305,

308 feed, 12, 117, 183, 222, 239, 256, 266,

267,274, 279,301,302,304 air-on1y, 67 captured fraction of, 41-44, 103, 106,

253 chemically aggressive, 5 density, 43 dirty, 265 droplet size, 248, 252, 253 fin~21, 86,112,254

328

flow rate, 181,231,247,252,267 foam, 265, 266 fraction, 41 , 184 gas, 140 liquid, 239, 241,252 particle size, 41--4 7, 90, 91, 97, I 07-

117,120,138,152,157,158,181, 184, 192, 300

properties, I, 87, 138, 309 to secondary cyclone, 300

feeder, 193 film, 240, 243, 253 filtration, 2, 3 fines, 28, 112, 161,221, 222 flapper plate, 194-213 flapper valve, 194- 213 flooding, 200, 202, 204 flow disturbances, 40, 145, 179, 249 flow meter, 18, 279 flow pattem, 7, 13, 17, 20,37--40, 46,49-

59,67- 71,82, 123- 131, 140, 147, 162, 176,178,198,232, 246, 249,286, 290

flow regime, 201,202 flow-through cyclone, 13, 37,245,247 fluctuating velocity, 178 fluidized bed, 109, 194, 196, 197-213,

301,306,308 foam, 15,261,263- 274 foam-breaking, 15,263,263- 274 force balance, 77, 105, 186 forced vortex, 15, 16, 32 fouling, 6, 13, 168, 198, 239, 279 fractional efficiency, 43, 46, 159 frameofreference, 30, 123,131 free vortex, 15, 21 9 free-vortex, 62 friction factor, 71, 73, 76, 80, 101, 140,

144, 163, 228,238,259, 274 chart, I 01 effect ofliquid on, 58 effect of so Iids on, 58, 71 , 76, I 02 gas phase, 58, 100- 102,253 Moody,258,261 total, 60, 67, I 02, 236, 252

froth, 261 , 263 Froude number, I 02, 141

Gamma function, 35 gas distribution, 5, 256,258,261, 267,

302, 304, 307 gaskets, 39, 106, 222 Gaussian distribution, 27 G-E curve, 152 GEC, 42, 79, 80, 158, 161

geometric mean radius, I 00 geometric similarity, 67, 147 geometrically similar, 66, 98, 137- 149,

301 grade-efficiency, 43, 44, 145, 161

calculating from size data, 46--48 definition, 42 from experiment, 184- 190, 192 from models, 77- 84, 90, 92, 93 , 95,

I 05, 120, 253, 309 from scaling, 137, 138, 146, 149, 150,

152 shape of curve, 42, 43, 54, 83, 85, 86,

93 , 121,132,152,155- 165,300 gravitational field, 19, 22, 139, 158 gravity, 37,232

analogy to centrifugal force, 16, 23 , 119, 157

effect on cyclone separation, 38 effect on flow field, 142, 147 separator, 264 separators, 23 9 settling in, 6, 21, 25, 157, 187,239

grooves, 227, 228

hardfaced, 39 hatches, 39, 199, 222 header, 222,224, 267,304 helical roof, 278 helix, 40 hooks, in data, I II hopper, 3, 70, 168, 169, 199,200,227,

282,285- 287, 302,304,307 crossflow, 30, 168, 175, 205- 207, 261 ,

301 erosion in, 215, 224 reentrainment from, 43 , 284, 285 venting, 30, 207- 210

hot-wire anemometer, 37, 176, 179 hydrocyclone, 15,20, 266 hydrostatic pressure, 33, 272

ideal rectifier, 53, 179 ideal vortex, 18,32, 55 imbalance, 206, 207, 259- 261 impaction plate, 186 incompressible, 30, 135 industrial-scale, 142 inertial forces, 250 in-leakage, 194, 197 inlet area, 149,278,296 inlet chute, 205, 207, 226, 291 inlet configurations, II, 12, 98, 267

axial, 12- 14,279

circular, II, 12, 82, 143, 252, 278 full scroll, 56 pipe-type, II, 12,278 rectangular, 12, 279 scroll, 12,40,57,228,246,248,279-

281 slot, 7, 9- 14, 56, 57, 66, 68, 70-74, 76,

82, 90, 98, 164,246,279,280 tangential, 7, 12, 14, 38, 45, 53, 55, 71,

108, 128, 129, 143, 155, 156, 161-164,2 17, 277- 279, 292,293

vaned, 12, 156, 245, 247, 289, 293-298 wrap-around, 12, 14, 56, 57

inlet design, 7, 278 inlet distributor, 264, 301, 304,305 inlet duct, 176,209,222, 256- 261,271 ,

287,304-306 inlet floor, 287 inlet hom, 225, 306 inlet pipe, 65, 112, 209, 222, 260, 301,

302,306 inlet target zone, 215,217, 223,224,279 inlet velocity recommended, 292 inline, 244 innerfeed, 108, 117, 119, 120 inner vortex

cut size, 100, 103, 104, 107, 158,253, 254

definition, 38 flow in, 100 particles reporting to, I 08, 117, 120,

158, 171 separation in, I 03, I 07 spin velocity, 87, 100, 198 stability of, 199 tail end of, 220

instability, 130,220, 228 inter-bracing, 231 , 306 interference pattem, I 78 interstitial, 29 irrigated, 58 irrigation, 6 ISO 9096, 183 isokinetic, 48, 182, 183, 185 isosurface, 129, 130

J-bend, 194, 196, 197, 201

knock-out,2, 5,6,239

Lagrangian, 30, 123, 131- 133, 148 Iaser diffraction particle analyzer, 186 Iaser scattering, 188, 189, 190 Laser-Doppler Anemometry, 37, 67, 178

law ofthe wall, 261 layer loss, 240, 242, 245

329

LDA, 37, 67- 70, 127, 128, 178-1 80,286 leakage flow, 104 LES. See Large Eddy Simulation light scatter, 178, 180 lightly-loaded, 103, 140, !52, 196,212,

292 Iight-ports, 39 Iimit Ioad, 102,103,108, 11 7, 11 8, 158 Iiner, 6, 52, 101, 107, 169, 170,221- 232,

312 lip flow, 54 lip-leakage, 40, 54, 70 liquid creep, 240, 252 liquid distribution, 272, 301 liquid loading, 239, 240, 243, 252, 254,

260,301 liquid pool, 243,244,247, 266,267 log-normal distribution, 34, 35, 309 loss fraction, 120, 152 loss free, 17, 57 loss-free, 17, 32, 38, 55 louvres, 290

macroscopic, 52 maldistribution, 48, 175, 206, 259, 260,

267,301 manometer effect, 212 mass distribution, 27, 189 mass loading, 55, 98, 238

effect on erosion, 217 effect on separation, 38, 97, 102, 103,

107, 112- 122, 155, 252- 254,299, 300

effect on wall friction, 76, 253 mean, 126, 190, 191

displacement, 188 droplet size, 250, 251 , 255 flow pattem, 41 , 123, 126, 286 gas velocity, 45, 46, 70, 75, 100, 126,

132, 138, 146, 178,250 particle movement, 23 particle size, 28, 33- 35,90, 138, 159,

216 pressure, 53, 63 vane diameter, 295

mean free path, 22, 233, 234, 236 mechanical energy, 18, 51 , 109, 179,291 mechanical energy balance, 109,291 median, 28, 34, 35, 107, 120, !56, 158,

25 1 mesh, 225,226,229,263 micro-dispersion, 265

330

mixing baffie, 183 mode,28,34,35, 137 model, 30, 40, 92, 97, 98, 123, 137, 157,

164,174,199,277,307, 319 distribution, 27, 28, 33 , 34, 35, 46 for erosion, 219,220 for flow pattem, 46, 49-59, 67- 71, 74,

76, 77,85,86, 126 for natural vortex length, 169 for pressure drop, 46,49-67, 71 - 76,

82, 85, 88- 90,92, 103, 108, 109, 144, 163,164, 173, 174,180,204, 260,280,292

for separation, 44, 46, 49, 53, 68, 77-122, 146, 156-163, 165, 166, 171, 172,231,245, 309

laboratory, 66, 67, 137- 153, 155, 165, 168

turbulence, 127 Moh's hardness, 231 molecular viscosity, 126 moment-of-momentum, 15, 17, 32, 50, 51 ,

57,59, 74, 75,87, 163 momentum balance, 50, 135 monodisperse, 184 monosized, 184 multiclone, 246, 247

natural end, 82, 130, 220 natural tuming length, 85, 86, 89, 155, 165 natural tuming point, 30, 145, 166 Navier-Stokes, 18, 30, 33, 50, 123- 128,

134, 135, 147 Newtonian viscosity, 32, 147 no flow-through condition, 70 non-spherical, 25 , 189, 190 normal distribution, 34 number distribution, 26, 189

definition, 25 numerical diffusion, 128

off-line, 176,184--190 once-through cyclone, 37 on-line, 176, 181,182- 190, 192 optical detection, 187, 188 orifice, 188, 194,210, 249,296 overall efficiency

and emission, 120 effect ofloading on, 122, 155, 156,

171 , 299 experimental determination of, 175,

184, 185 in separation models, 102, 113, 245 relation to cut size, 41 , 43, 44, 93, 310

required for given duty, 309 overflow

entrainment into, 198, 200, 205, 262 in parallel cyclones, 301, 302, 304 in series-connected cyclones, 300, 309 mass flow solids in, 41, 42, 181- 183,

192 particle size, 106, 181 , 184, 300 piping, 209, 222 plenum, 13, 206, 224,305 pressure/pressure drop, 109,204, 206,

212, 272,273

packed bed, 202 parallel

cyclones, 168,176,205, 206, 222,224, 256,258,267,299,300-312

swirl tubes, 271,299, 300-303 path length, 187 pattem angle, 282, 283 Phase Doppler Anemometry, 180 photosedimentometer, 186 pipe bends, 216 pipelines, 250, 251 pitot tube, 18 pitot-tube, 177, 183 plastic, 215, 222, 225 plenum, 13, 168,206, 207, 224,231 , 246,

302, 304 pneumatic conveying, 157, 158,215, 217,

230 point of failure, 216 Prandtl, 177, 183 pre-separation, 280 pressure distribution, 17, 33 pressure drop, 37, 50, 82, 84, 179, 239,

267 across filters, 2, 3 across parallel cyclones, 301, 312 across wet scubbers, 5 and CFD, 123 and underflow configuration, 200, 204,

207,210, 212, 272- 274,285 compared to other separators, 6 effect ofbody length on, 87- 89,291,

292 effect ofloading on, 80, 155, 163- 165,

173, 174 effect ofvortex length on, 155 in pipes with gas and liquid, 243 in vaned swirl tubes, 294, 296 interpretation of, 45, 49, 51 - 53 , 55 measurement of, 176, 179, 180, 183 optimal range, 221 , 292

related to efficiency, 82 scaling rules for, 137, 141, 142, 144--

147, 149- 153 pressure-recovery, 289, 290 probe inlet, 183 profile plot, 70, 128, 129 prototype, 137-153 puffing,205 pull through, 222 pull-through, 9, 10,248 pycnometry, 29

raceways, 240 radial velocity, 23, 31, 32, 38, 40, 54, 70,

87,95,176, 290 distribution, 70

radioactive particles, 180 Rankine vortex, I 7, 3 8 real time, 184, 185 recirculation, 198, 240 rectification, 179 rectifier, 179 rectifying, 51, 53, 61, 179,290 re-entrainment, 94, 95, 285 refractory, 39, 52, 58, 71, 79, 101, 140,

170,221-232 relative humidity, 138 relative roughness, 58. See

roughness:re1ative relaxation time, 21 residence time, 21, 94 residual swirl, 179 resistance, electical analogue, 207 reverse-flow, 7, 13, 14, 37, 45,242, 244,

247,296 Reynolds number

cyclone, 58, 66, 100, 101 , 140-142, 147,148, 169,228

particle, 20, 21, 25, 104, 119 similarity, 142, 147, 148 vortex finder, 58, 65

Reynolds stress, 126, 127 ring, 12, 166, 168 rolled,2,39,225 roof ring, 263 roof skimmers, 240 roofline, 12 Rosin-Rammler distribution, 28, 35, 82,

120 Rosin-Rammler-Intelmann, 82, 83 rotary lock, 193, 199, 200, 207 rotational velocity, I 00, 118 rough-cut, 45, 140, 196,299

331

roughness,40,43,51,58, 71,80,97, 110, 113, 115,139,140, 145, 163, 164, 169, 221 absolute, I 0 I, 228, 231 additional due to liquid, 58, 243 additional due to solids, 59, 164, 169,

198 ofliner, 169,227,228,231 relative, 58, 67, 100, 101, 102, 140,

228 round-to-rectangular, II, 12 RSM. See turbulence model:Reynolds

Stress Model

saltation, 97, 102, 107, 117- 121,253,254 salt-out, 117, 292 sample point, 176, 183 sampling, 48, 143, 176, 180- 190,278 sampling tube, 185 Sauter-mean, 250, 255 saw-toothed liquid anti-creep ring, 240 scaling, 37, 66, 137-150, 153, 164,165 screw conveying, 193 scroll, 55,215,246,248,278-282,290,

291,306 circular, 280, 281

scrubber,2,5,6, 248,249, 268,3 12 seal, 193, 195, 196, 199,204,205,209,

222, 260, 267. See also underflow sealing

seams, 39, 222, 231 secondary flows, 38-40, 216, 228 segregation, 260 series

cyclones, 107, 176, 186,290, 299-300, 302,305,307

impactor stages, 186 mean values, 191 observations, 190

shape body, II, 13, 14, 98 cyclone, 8 disc centrifuge output curve, 187 hopper, 98 lining, 231 of distribution curve, 26, 33, 35, 80 particle, 2, 15, 138, 175, 186, 188, 190 vanes, 293-295 vortex finder, 287

sharpness, 43, 79, 168, 222 shea~5,31 , 32,50,249

sheet meta!, 223 short-circuit, 54, I 00, 220, 240, 287 sieve, 27, 43, 79, 103, 106, 152

332

sight ports, 222 sight-glasses, 39, 195 similarity, 66, 67, 141, 142, 144, 145, 147,

151,216 size distribution, 15, 25, 28, 29, 33, !59

density. See density distribution drop,241-252,254,256,257 feed,43,90- 93,97, 107,108,110,114,

115, 117, 138, 184, 300, 309, 310 in cyclone body, 180 'innerfeed', 107,108,117,119,120 measurement of, 183-190 models for, 28, 33, 34, 35 number. See number distribution overflow, 300, 309 overhead, 111,112,155- 157,309, 310 surface. See surface distribution underflow, 181 , 182 volume. See volume distribution

size distribution, 48 skeletal density, 29 slip, 20, 22, 85, 109,201 , 234-236 slip correction factor, 234, 235 slits, 240, 290 slope, 43, 79, 80, 84, 85, 105, 106, 111,

113, 115, 116, 120,253 slot, 244, 296

inlet. See inlet:slot slumping, 226 smoothness, 226, 227 smooth-walled, 55, 58, 67, 71, 80, 284 solid-body rotation, 15- 17, 32, 38, 53, 55,

61, 127 solids distribution, 202,301,307 so1ids loading

and inlet design, 279 effect on dipleg flow, 199 effect on erosion, 216, 217, 220, 222,

231,279,301 effect on pressure drop, 52, 60, 67, 71-

73,80,87, 108,109, 141 , 142, 155, 163, 164, 165,173- 175

effect on separation, 6, 30, 43, 66, 80, 84, 87,88,90,105- 122, 138-140, 145, 149, 155- 165, 170-172, 175, 184, 187

effect on swirl intensity, 55, 56, 71, 118, 147

effect on vortex length, 169 effect on wall friction, 58, 102, 163

solubility, 185 solubilization, 144 specific erosion, 175, 216 spent cat distributor, 306

sphericity, 138, 139, 186 spin fluid, 186, 187 spin velocity, 12, 52, 57, 65, 100, 280, 285 sp1ash, 196, 266 spray nozzles, 231, 240, 248 spread

in size distribution, 28, 33, 34, 90, 138 in velocity fluctuations, 132

s-shaped, 42, 43, 54, 79, 105, 116, 152, 158

stabilizing plate, 169, 252 stagnating, 232 stair-step, 79, I 06, 152 standard deviation, 191 , 192 starvalve, 193, 194 static, 179 static charge, 149 static pressure, 16-18, 51, 65, 82, 179, 266

difference between parallel cyclones, 256- 260

in bottom of cyclone, 204 in cyclone, 39 in cyc1one body, 51 , 52, 227, 247 in dipleg, 196, 197, 20 I in inlet, 52, 88 in vortex finder, 53, 179 loss, 52,59-61,63, 109,207 measurement of, 45, 179 recovery, 51, 53, 289,291

sticky, 6, 198 stilling plate, 243, 244 Stokes, 1

density, 29 diameter. See diameter:Stokesian drag 1aw. See drag:Stokes number, 141, 143, 147 velocity, 21

Stokesian scaling, 143 straight-through cyclone, 12, 13, 247 strand, 102, 139, 163,201,228

density. See density:strand streaming, 187 streamlines, 18, 129, 130,215 stress, 30-32, 126, 127, 287 stress tensor, 30, 31, 126 submerged seal, 196 submergence, 197,202,204,210-213,

272- 275 submicron, 21 , 22 surface distribution, 250 surface tension, 185,239,249,250,265 surge capacity, 239 swirl tube

definition, 12- 14, 247

design, 70, 277, 292- 297 flow pattem, 53, 67, 68, 69, 70, 76 pressure drop, 45 , 53 , 164 separation, 83, 90, 145, 162, 163, 168

swirl tubes in parallel. See parallel :swirl tubes

swirl vanes, 12, 14, 162, 166,279, 297 design, 292- 295, 297 in gas-liquid cyclones, 240, 244 pressure loss in, 45

swiss roll, 40 systems approach, 200

tangential velocity, 15, 23, 33, 38, 53, 61 and particle motion, 24 and pressure drop, 51, 52, 62, 63 by CFD, 127- 129, 133 definition, 16 distribution, 18 from swirl vanes, 294, 296 in 'ideal' vortex flows, 15, 17, 32 in the near-wall region, 39, 227 measurements of, 68, 69 models for, 55- 59, 71 , 74, 75, 81, 92,

103, 118, 252 tensor, 31 terminal velocity, 19, 21 , 23- 25 , 81, 104,

139, 201,234 thermal cycling, 231 thermowells, 39 third-stage, 140,212, 221 , 225,290, 303 time-of-flight, 77, 78, 82, 83, 87, 93 time-to-failure, 216, 217, 220 torque, by flapper plate, 212 total pressure, 63, 179, 207, 259, 301

loss of, 45, 60, 64 trajectory, 37, 40, 175 transition, II, 12, 203, 204, 279, 280, 294 Iransmitted intensity, 187 troubleshooting, 49, 137 tubesheet, 304 tube-sheet, 13 turbidity, 187, 188, 190 turbulence, 17

effect on mean flow pattem, 126, 243 effect on particle dispersion, 21 , 23, 43,

132, 157, 171 effect on pressure drop, 53, 291 in inlet transition piece, 279 in sampling probes, 183 in swirl vanes, 289, 294 measurement of, 178

turbulence model, 123- 133 Algebraic Stress Model, 127

333

k-E, 126 Large Eddy Simulation, 127, 130, 131 Reynolds Stress Model, 127

turbulent suspension, 107, !58, 253 turbulent viscosity, 126 turn-down ratio, 247 tuming point, 166 twin-scroll inlet, 246 two-phase, 162, 239, 243 , 255 two-stage, 107,203, 242,254, 306

ultrasonic, 185 unclassified, 108, 156-159, 300 underflow

bleed flow through, 169 blowdown, 20 I configuration, 193 entrainment in, 200 in gas-liquid cyclones, 243, 244, 256,

259,263,265,273 , 274 in parallel cyclones, 205, 207, 224,

267,296, 302,307 mass flow so Iids in, 41 , 180, 181 particle size, 184 piping, 109, 199, 222, 273, 307 plenum, 13, 206, 305 pressure/pressure drop, I 09, 200, 204,

206,212 , 259,260, 272- 274 pump, 273

underflow sealing, 80, 130, 193- 200, 222, 242

uniflow cyclone, 13 up-flow, 67, 106, 175, 197- 199, 205 , 206,

209

vacuum,21 , 29,59,205,215 , 233- 238 vane angle, 295 vane throat area, 296 variance, 190-192 velocity head, 18, 64, 88 vent line, 209, 210 venturi, 5, 18, 248, 249,279 venturi meter, 18 venturi-scrubber/cyclone, 248 vibration cast, 225 Vicker' s hardness, 231 voltage, electrical analogue, 207 volume distribution, 26-28, 35, 189, 190,

250 definition, 25

volume equivalent, 24, 138, 188 vortex,220

flow, 15, 17, 18,30- 33, 51 , 55 , 209, 244, 262

334

gas phase in foam-breaking cyclones, 266

inner/outer, 7, 37, 40, 55, 83, 90, 93, 118, 130, 156

intensity of, 45, 87, 171, 228,256 particle motion in, 22 pressure in, 33, 59, 82 reentrainment into, 284 stability, 169, 170,220,221

vortex breaker, 243, 244, 285 vortex cross, 244 vortex end, 30, 109, 145, 165- 170,209,

213,221,243,284- 287,291,296 vortex finder, 12, 38, 40, 77, 166, 169,

174, 225,228,230,311 and the surface es, 77 definition, 7 design of, 282, 286-290, 292 diameter. See diameter:ofvortex finder flow in and around, 38, 40, 46, 53, 54,

58,67- 70,100-103,128,129,138, 198,279

fouling of, 13,240 in demisting cyclones, 239-263 length, 7, 115 pressure and pressure drop in, 45, 51-

53, 59-74 82, I 09, 130, 174, 204, 205

wall area, I 03

vortexlength,83, 167- 170,204,296 vortex precession, 166, 167, 220 vortex stabilizer, 243, 284, 285, 287, 296 vortex tube, I 03, 166, 270, 271. See also

vortex finder

wall axial velocity, 100 wall deposits, 80, 106, 140, 145, 168, 169,

198 wall film, 239, 240 wall friction, 49-61, 74, 75, 91 , 100, 101 ,

I 08, 140, 163, 171 , 228, 243, 256, 259, 261

wallloss, 45, 52, 108, 204 wall probes, 222 wall ve1ocity, 51, 56, 57, 73, 74, 98, 118,

129 wave-plate, 268 waves, 243 wear, 3, 6, 10, 155, 168, 193, 201,215-

232,290,292,312 wear plates, 222, 223 Weber number, 250 weid overlaid, 39 wet-gas compressor, 242 WGC, 242 wrap-around, 279

x-50 cut-point, 43