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HIGH TEMPERATURE CYCLONES
by
PETER A. PATTERSON, M.Eng.
A thesis submitted to the Faculty of Graduate Studies and Rp.search of McGill university in partial
fulfillment of the requirements for the degree of Doctor of Philosophy
Department of Chemical Engineering McGill University, Montreal
0Peter patterson, 1989
February, 1989
• +1 National Ubrary . of canada
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ISBN 0-315-52508-8
Canada
HIGH TEMPERATURE CYCLONES
P.A. Patterson
Chemical Engineering Department McGill University, Montreal
Quebec, Canada H3A 2A7
ABSTRACT
Gas-solids separation was studied in a 102 mn, dia~eter
conventional cyclone operated with air heated to
te~peratures between 300 K and 2 000 K. Cyclone pressure
drops, fractional and overall collection efficiencies were
measured as functions of temperature, gas throughput, dust
loading and cyclone geometry. Alumina and silica of 100 %
less than 44 pm mass median diameter were used as test
dusts. Inlet velocities ranged from 3 to 42 mis and inlet
dust loadings were between 0.3 and 215 g/m3.
Empirical models were derived to correlata the experimental
results for the cyclone collection efficiency, press~re
drop, tangential velocity and 50 % cut size. The
performance of the cyclones at very high temperatures was
not significantly different from the room temperature
behavior, provided that the effect of ternperature on
particle, gas and flow properties was adequately treated.
cyclone à heute temp6rature
P.A. Patterson
RÉSUMÉ
La séparation gaz-solides fut étudiée dans un cyclone
conventionnel de 102 mm de diamètre opéré dans l'air
chauffé à des températures entre 300 et 2 000 K. La chute
de pression dans le cyclone et les efficacités de
collection fractionnelle et totale ont été mesurées en
fonction de la température, de la charge en poussières, de
la géométrie du cyclone et du débit de gaz le traversant.
Des poussières d'alumine et de silice de moins de 44 pm de
diamètre moyen furent utilisées comme particules d'essai.
La vitesse et la charge en ~~ussière à l'entrée du cyclone
variaient de 3 à 42 mjs et de 0.3 à 235 gjm3 respectivement.
Des modèles empiriques ont été dérivés afin de corréler les
résultats expér •. lllentaux sur l'efficacité de collection, la
perte de pression, la vitesse tangentielle et le diamètre
de pertes à 50%. La performance des cyclones à haute
température comparé à ceux opérant à te~pérature ambiante
est sensiblement la même en autant que les effets de
température sur les particules et les propriétés du gaz et
du flux soient traités adéquatement.
TO MY FATHER
ACKNOlfLEOOEHBNTS
The author wishes to thank all those who contributed
directly or indirectly to the presentation of thi~ ehesis:
Prof. Munz for his guidance, patience and generosity
throughout the course of this project.
Ors. W.H. Gauvin, M.E. Weber, D. Berk, A. Mujumdar and
J.L. Meunier; the plasma group: Earle, Roberto, Paul S.,
Paul P., Peter T., Maysa, Murray, Gang-Qiang, Bogdan; summer
students: John, Colin, Bruno and Gillian for their advice,
practical assistance and moral support.
The Chemical Engineering non-academic staff: Mr. Krish, Mr.
Dumont, Mr. Habib, Alain, Walter, Herb, Don, Lou, Pat and
Anne for their professional 'assistance.
Mr. stanl~y Henry of the Electrical Engineering workshop for
solving many electrical problems (inclùding my TV).
The Natural Sciences and Engineering Research council of
Canada, and the Ministry of Education of Quebec for their
financial support.
And most of all, my family for their love and support.
'. ., ,. ".
• / ~ . .
.'
TABLE OP CONTENTS
-ABSTRACT
RÉSUMÉ
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
I.J:ST OF FIGURES
LIST OF TABLES
GENERAL INTRODUCTION
CHAPTER 1
:HAPTER 2
GENERAL CYCLONE THEORY AND PRACTICE
Introduction Types of cyclones High Temperature cyclone Studies Summary
EXPERIMENTAL PROCEDURES
Introduction
Experimental Apparatus The cyclone The Plasma Generator The cyclone Inlet Channel The Inlet and Out let Diagnostic
Sactions The Particle Feeder The Particle Sample Train
Data Acquisition and Analysis Particle selection Criteria Characterization of the Powders operating Procedure
Summary
ii
~
i
ii
'1
xi
1
3 3 5
23
25
25 25 27 30 32
35 37
40 40 42 49
52
C CHAPTER 3 GAS AND PARTICLE FLOW PATTERNS
Literature Review 53
Experimental Results and Discussion 62 Particle Deposition Patterns 63 Pressure and Velocity Measurements 67
The Pressure Probe 67 Tlle Pressure Probe Location 72 Room Temperature Experiments 73
Profiles Obtained with Large 73 diameter gas outlet
Profiles obtained with small 81 Diameter Gas Outlet
Profiles for small vs Large 85 Diameter Gas Outlet
High Temperature Runs 88 Comparisons with Predicted Profiles 94 Correlation of the Experimental 95
Summary 104
CHAPTER 4 COLLECTION EFFICIENCY STUDY
Introduction 106
Lit3rature Review 107 Modelling the Collection Performance 107
of Cyclones The Rosin et al. Study 112 The Lapple Study 115 The Sproull Study 116 The Leith and Licht Study 118 The Deitz Study 121 The Mothes and Loffler Study 125 Effect of OUst Load on Collection 131
Efficiency summary of Literature Review 138
Experimental Results and Discussion 140 Operating Conditions 140 Correlation with Dimensionless Groups 141 Effect of operating Conditions on 149
Grade Efficiency Curves Comparisons with Predicted Grade 158
Efficiency CUrves Comparisons with Predicted Overall 160
Collection Efficiencies The Loading Effect 163
C The Rosin et al. Model 165
Hi
o
CRAPTER 5
The Lapple Model The Sproull MOdel The Leith and Licht Model The Masin and Koch Hodel The Deitz Model The Mothes and Loffler Model
Summary
CYCLONE PRESSURE DROP STUDY
167 171 171 174 174 178
181
Li~erature Review 184 The Effect of OUst Load on 196
Pressure Drop
Experimental Results and Discussion 201 Analysis of the Euler Number 202 Predicted vs Experimental Pressure 209
Drops su~ary 221
CONCLUSIONS 224
CONTRIBUTIONS TO KNOWLEDGE 227
RECOMMENDATIONS 229
NOMENCLATURE 230
REFERENCES 238
APPENDIX 1 - RAW DATA 246
APPENDIX 2 - TEMPERATURE MEASUREMENT 247
iv
Figure
1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
1-9
1-10
2-1
2-2
2-3
2-4
2-5
2-6a
2-6b
c
HaT OP lIGURES
Four basic types o! cyclones (CapIan, 1977)
Examples of some commercial cyclones (perry and Chilton, 1973)
The variation of air viscosity with temperature.
The A.P.T. test rig and grade efficiency curves (parker et al., 1981).
Correlation of the A.P.T. data (Parker et al., 1981).
Dimensions of the Exxon miniplant cyclones (Hoke et al., 1980).
Comparisons of Exxon data with the Leith and Licht model (Hoke et al., 1980).
cyclone dimensions in stream 1 of the CURL test rig (Pillai and Wood, 1981).
Comparisons of CURL data with the Leith and Licht (1972) model (pillai and Wood, 1981).
The Grimethorpe cyclone and data (Wheeldon et al., 1986).
The experimental apparatus (Il, 12, 13 are electrical isolation sections).
The test cyclone.
The inlet diagnostics section.
The outlet diagnostics section.
The Tafa particle feeder.
The particulate sampling train.
Orientation of the slots on successive stages of the cascade impactor.
v
6
8
11
13
15
16
19
21
22
26
28
33
34
36
38
39
2-7
2-8
2-9
2-10
3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
3-9
3-10
3-11
3-12
3-13
3-14
3-15
photographs of the test dusts: a) alumina, b) silica. '
In1et particle size distributions of alumina
Inlet pa~icle size distributions of silica
Effect of inlet velocity and dust load on dispersion and measured size distribution
The van Tongeren (1975) cyclone with rust bypass
The velocity profiles of ter Linden (1949)
Particle deposition patterns on the walls of the cyclone.
The 5-channel pressure probe (Reydon, 1978)
Pressure probe location and coordinate system
Total velocity profiles vs inlet flowrate for cyclone Cl.
Tangential velocity profiles vs flowrate for cyclone Cl.
Radial velocity profiles vs flowrate for cyclone Cl.
Axial .elocity profiles vs flowrate for cyclone Cl.
Oiagram showing the flow zones in the cyclone
Tangential velocity profiles vs flowrate cyclone C2.
Radial velocity profiles vs flowrate for cyclone C2.
Axial velocity profiles vs flowr.ate for cyclone C2.
Tangential velocity profiles vs gas outlet configuration for an inlet velocity of 8 mis
Radial velocity profiles vs gas outlet configuration for an inlet velocity of 8 mis
vi
43
44
45
48
55
57
64
69
71
74
76
77
79
82
83
84
86
87
c 3-16
3-17
3-18
3-19
3-20
3-21
3-22
3-23
3-24
4-1
4-2
4-3
4-4a
4-4b
4-5
4-6
Axial velo city profiles vs gas out 1 et configuration for an inlet velocity of 8 m/s
éomparison of tangential velocity profiles at high and lo~ temperatures.
Comparison of radial velocity profiles at high and low temperatures.
Comparison of axial velocity profiles at high and low temperatures.
Wall tangential velocity/mean inlet velocity vs annulus Reynolds number.
comparison of experimental with predicted tangential velocity profiles: cyclone Cl at 300 K.
Comparison of experimental with predicted tangential velocity profiles: cyclone Cl at 1300 K.
Comparison of experimental with predicted tangential velocity profiles: cyclone C4 at 300 K.
Comparison of experimental with predicted tangential velocity profiles: cyclone C4 at 1300 K.
Theoretical vs actual grade efficiency curves (stairmand, 1975).
TI.e Staimand (1951) cyclones and grade efficicncy curves.
T"e nomalized grade efficiency curve and cyclone configuration of Lapple (1951).
The cyclone cross-section for the Leith and Licht (1972) model.
Comparison of the Leith and Licht model with other models.
The geometry for the Deitz (1979) model.
Comparison of the Deitz (1979) model with experimental data.
vii
89
91
92
93
97
98
101
102
103
110
114
117
119
119
123
126
4-7
4-8
4-9
4-10
4-11
4-12
4-13
4-14
4-15
4-16
4-17
4-18
4-19
4-20
4-21a
4-21b
4-21c
The geometry for the Mothes,and Loffler 128 (1984, 1988) model.
Comparisons of theory with experiment for 132 the Mothes and Lo:fler (1984, 1988) model.
/ariation of separation efficiency due to 139 agglomeration with particle size (Mothes and Loffler, 1985).
dpa vs Re.stin 0.5 both both dusts. 145
dpa vs separation number for both dusts. 148
Penetration vs Re.stino.5 for both dusts 150
Penetration vs separation number for alumina 151
Penetration vs separation number for silica 152
Grade efficiency curves showing the effects 153 of temperature, inlet velocity and dust load.
Grade efficiency c~rves showing the effects 155 of particle type and dust load.
Grade efficiency curves showing the effects 157 of outlet dimensions and dust load.
Grade efficiency curves suowing comparison 159 of experimental with predicted data for poor operating conditions.
Grade efficiency curves showing comparison 161 of experimental with predicted data for good operating conditions.
Experimentally measurêd collection efficiency 166 vs dust loading.
Predicted vs experimental overall collection 168 efficiency for the Rosin et al. (1932) model with no load correction.
Predicted vs experimental overall collection 169 efficiency for the Rosin et al. (1932) model with A.P.I. (1975) loa' correction.
Predicted vs experimental overall collection 170 efficiency for Rosin et al. (1932) model with A.P.I. (1975) load correction (A = 0.26)
viii
c
c
4-22 Predicted vs experimental overall collection 172 efficiency for Lapple (1951) model with A.P.I. (1975) load correction (A = 0.26).
4-23 predicted vs experimental overall collection 173 efficiency for Sproull (1970) model with A.P.I. (1975) load correction (A = 0.26).
4-24 Pr.edicte~ vs experimEntal overall efficiency 175 for Leith & Lic:lt (1972) model with A.P.I. (1975) load correction (A = 0.26).
4-25 Predicted vs experimental overall efficiency 176 for Masin & Koch (1984) model with A.P.I. (1975) load correction. (A = 0.26).
4-26 Predicted vs experimental overall efficiency 177 for the Deitz (1981) model with A.P.I. (1975) load correction (A = 0.26).
4-27 Predicted vs experimenta1 overa1l efficiency 179 for the Mothes & Laffler (1984) model with A.P.I. (1975) load correction (A = 0.26).
4-28 Predicted vs experimental overall efficiency 182 for a modified Mothes & Laffler (1984) model with A.P.I. (1975) load correction (A = 0.26).
~-1 Total and static pressure profiles measured 190 by ter Linden (1949).
5-2 Variation of pressure drop reduction with 198 dust load (Sproull, 1966).
5-3
5-4
5-5
5-6
5-7
Variation of pressure drop ratio and velocity profiles with dust load (Yuu et al. 1978).
Variation of pressure drop with barrel velocity he ad for dust-free flow.
Variation of pressure drop with barrel velocity head for dust-laden gas.
Variation of zero-load Euler number with cyclone geometric parameter.
V~riation of Euler number ratio with dust load.
ix
200
204
205
207
208
5-8
5-9
5-10
5-11
5-12
5-13
5-14
5-15
A2-1
A2-2
comparison of experimental data·with pressure drop ~redicted by the Wheeldon et al. (1986) model. <
Comparison of experimental data with pre&sure drop predicted by the Masin and Koch (1986) model.
Comparison of experimental data with pressure drop predicted by the Shepherd and Lapple (1939, 1940) model.
Comparison of experimental data with pressure drop predicted by the Ca~al and Martinez-Benet (1982) model.
Compar~ ~ of experimental data with pressurt urop predicted by the Stairmand (1949) mvdel.
Comparison of experimental data with pressure drop predicted by the Alexander (1949) model.
comparison of experimental d~ta with pressure drop predicted by thp. model derived from the experimental data (method 1).
comparison of experimental data with pressure drop predicted by the model derived from the experimental data (method 2).
Measured vs corrected tempcrature for runs with alumina.
Measured vs corrected temperature for runs with silica.
x
212
213
215
216
218
219
220
222
255
256
Table
4-1
4-2
5-1
5-2
Al-l
Al-2
Al-3
Al-4
Al-5
c
Lxsr OF TABLES
Summary of correlation coeffi~ients for dimensionless group study
Summary of Performance Xndices for collection efficiency models
Co~~a~ison of Euler numbers
Summary of Performance Indices for pressure drop models
Alumina Experimental Data - High Temperature - 5.08 cm outlet
Alumina Experimental Data - High Temperature - 2.54 cm outlet
Alumina Experimental Data - room temperature
Silica Experimental Data - high temperature
silica Experimental Data - room temperature
xi
~
144
164
203
210
247
248
249
250
251
o
GENERAL INTRODUCTION
c
GENERAL, INTRODUCTION •
The separation of-solids from gases at high temperatures is
a very important problem in the areas of .energy conservation
and conversion. Processes SUCII as advanced coal conversion, . . combustion and biomass conversion produce large quantities
of gas at temperatures above 1 000 K which are contaminated
with micron-sized particles. In some cases, these gases
must be cleaned at high tempe ratures to minimize the loss in
enthalpy. Recent developments in high te~perature plasma
processing are also expected to require high temperature gas
cleaning.
Conventional cyclones are popular for l1igh temperature gas
cleaning because of their simplicity and low maintenance
requirements. They are currently the only gas cleaning
device which can be used on an indus trial scale at very high
temperatures. Despite the apparent simplicity of the equip
ment and its governing principles, the characterization of
particle removal performance is still not clearly defined
and ia largely empirical (Zhou et al., 1988: Mothes and Lof
fler, 1988). only limited experimental data have been
reported for high temperature operation, and these are
insufficient for thorough evaluation of the effects of tem
perature on the particle collection mechanism&.
o 2
The objective of this study was ~o gain a fundamental under-
standing of the behavior of conventional cyclones and to
study how they performed at very high temperatures. Collec
tion efficiencies an1 pressure drops w~re m~asured at gas
temperatures up to 2 000 K with silica and alumina as the
test dusts. The gas throughput, dust loading and cyclone
geometry were the other operating variables. Standard con
ditions are defined as 298 K and 101 kpa in this thesis.
The thesis is arranged in six chapters. Chapter 1 gives a
broad overview of cyclone practice and a review of rele~ant
studies of cyclones at elevated temperatures. Chapter 2
contains descriptions of the experimental apparatus and
procedures. Chapter 3 deals with the flow patterns in cyc
lones with discussion~ of published studies and observations
made in the presenc study. Chapters 4 and 5 de scribe col
lection efficiency and pressure drop studies with emphasis
on math~catical models capable of predicting cyclone perfor
mance. The raw experimental da~a are included in the appen
dices.
CRAP'rER 1
GENERAL CYCLONE TJŒORY AND PRAC'l'ICE
c
o ClIAP'l'BR 1
GBNERAL CYCLONE THBORY AND PRACTICB
INTRODUCTION
cyclones have been used for over a cent«~ to separate sol
ids fro~ gases (1885, German patent 39219). Their simple
design, high efficiency for large partic1es and 10w mainte
nance costs still cake them the most common gas c1~aning
device in use today. The various types of cyclones common1y
used are described briefly in this chaptcr, fo110wed by a
discussion of their use at high temperatures.
TYPBS OP' CYCLONES
The necessary e1ements of a cyclone are the f10w inlet which
produces the vortex, an axial outlet for cleaned gas, and a
dust discharqe or collector (The~ore & Buonicore, 1976;
caplan, 1977; Heumann, 1983). These three elements have
been coJW.l.ned in many ways and Flgure 1-1 shows the four
basic classifications. The combination of tangential inlet
with axial dust discharge (known as the ~onventional cyc
lone), is the most common arrangem~nt and was the focus of
this study.
lAI TO"'l'/I"o' illll' ..... GI.cI>Or;1
CCI Aue' iIIlI' GIlet dllotho'VI
4
-
~ 1
IBI T.IIQtIll ••• "" .. pt fi phI'OI c""l'IOu;.
lOI Al .. ' 1/1'" Pt'Ipft.rol CSIKhO,'iI'
Figure 1-1 Four basic types of cyclones (Caplan, 1977).
-0
5
CYclones are used either as individual units, as a composite
of two or more swirl chambers, or as banks of small units in
parallel to form a multicyclone (Figure 1-2). The diameter
can vary from around one centimeter (miniature sampling cyc
lones) to several meters in commercial units. Many accesso
ries sucn as inlet vanes, baffles and vortex shields have
been used in attempts to enhance the dust collection and
reduce the pressure drop; however, improving one of these
usually results in making the other worse.
HIGH TEMPERATURE CYCLONE STODIES
cyclones are popular for high temperature gas cleaning
because of their simplicity and low maintenance require
ments. The largest application of cyclones ;3 for the
recovery of regenerated catalyst fines in petroleum refinery
cata1ytic cracking units (Saxena et al., 1982). In modern
units, temperatures can approach 973 K and pressures,
400 kPa.
The~e has been recent interest in hot gas cleanup systems
for pressurized f1uidized bed combustion of coal in power
generation. Applica~ions at temperatures up to 1 500 K and
pressures up to 5 000 kpa are being considered, with cyc
lones as the primary gas c1eaning device (Razqaitis,
6
.. ....
.......... _~5r-o..r ... .....
Figure 1-2
v--........ III
C" Cil
_fl_ ... - .... '----""" .....
Ccl
III
Examples ot some commercial cyclones (Perry and Chilton, 1973)
T
1977: Heyer and Edwards, 1978: Horrison, 1979: Gil~s, 1981,
1982: Henry et al., 1981, 1982). Only limited experimental
data have been reported for cyclones oper~ting at very high
temperature and these-a:? insufficl"_-t- for the evaluation of
the effects of temperature and press_. • on the particle col
lection mechanisms.
The principal effect of high temperatures on the performance
of cyclones, is that the gas viscosity illcreases, leading to
an increase in the drag force on the particles and a
subsequent decrease in the inertial separation potential of
the cyclone. Figure 1-3 shows that the viscosity of air
increases by a factor of three as the temperature increases
from 300 to 2 000 K.
The gas density on the other hand varies inversely with tem
perature leading to an enhancement in the collection effi
ciency at elevated temperatures. However, the density
effect is usually negligible since the determining factor is
the difference between particle and gas densities, and the
particle density remains much higher than the gas density.
Theoretical models for cyclone performance do not usually
conta in the operating temperature as an explicit function,
but rather, it appears implicitly ~~ a function of visco
sity, gas density and other terms such as the vortex law
exp one nt en).
,~
7.0r-1 -----------------1
6.0 co •
0 a.. 6.0 • 10
0 -x 4.0 >-t-H CI)
8 3.01 ./
CI) H >
2.0
1.0~1~----==------~------~------~------J 200 600 Hm 1400
TEWERATURE. K 1800 2200
Fi9u~e 1-3 The variation of air viscosity with temperature.
~
0>
o
9
0n9 ol the earliest _tudies of cyclones at high temperatures
was repo~ted by Parent ~1946). He studied cyclones of 5.0
and 7.6 cm diameter at temperature~ up to 1 030 K using fly
ash of les& than 1~0 pm as the ' ~st dust. He observed the
inverse variation of efficiency with temperature, and the
direct variation with gas throughput. The dust loads stu
died were very low (0.0003 to 0.005 g/m3) and did not influ
ence the collection efficiency in this range.
Later, Alexander (1949) studied cyclones measuring 3.2 to
120 cm in diameter operated at temperatures up to 1 373 K.
The only high temperature results published, were for a
10 cm cyclone. He used silica dust with a mear diameter of
5.0 pm, and he measured static pr&ssures, ve Jcities and
directions of flow within the cyclone using a symmetrical
Pitot probe. The collection efficiencies were determined
for total catches and not fractional catches (with frac
tional catches, the dust is divided into several size ranges
or fractions, and the amount caught in each fraction is
measuxed). The empirical correlations devcloped by Alex
ander are discussed in Chapters 3 and 5 of this thesis.
Yellot~ and Broadley (1955), described tests done on 5.0 and
7.6 cm diameter Aerotec cyclones (reported earlier by Par
ent, 1946), and on a variety of straight-through tubes rang-
10
ing in diameter from 21 to 41 cm. The tests were carried
out at temperatures up to 977 K and pressures up to 500 kPa.
The tubes were tested both individually and Ir. batteries of
up to 60 units in parallel. The expected de crea se in ove
rall collection efficiency with increasing gas temperature
was observed. ~ellott and Broadley measured overall collec
tion efficiencies only and not fractional collection effi
ciencies.
More recent'y, smith et al. (1979) described the development
and calibration of a five-stage cyclone sampling system,
with the cyclones ranging from 1.5 to 4.5 cm in diameter.
They used particles ranging frQm 0.3 to 8.0 pm in diameter
and with densities between 1.03 and 2.04 g/cm3 • Tests were
carried out at temperatures up to 477 K and flow rates up to
0.03 m3/min at atmospheric pressure. They found that the
50 % cut-size was proportional to (pppo.5/Qm) where m was
between 0.63 and 1.11.
Parker et al. (1981) reported an experimental study carried
out at Applied Particulate Technologi~s (A.P.T.). The test
cyclone was a 5.0 cm diameter conventional cyclone operated
at temperatures up to 973 K, pressures up to 2 500 kPa, a~d
inlet velocities up to 5.2 mis (Figure 1-4a). They showed
that the collection efficiency decreased sharply with
increased temperature (Figure 1-4b), and that available the-
o
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..... ... ... ...
'" .. , . ... .. . ... .. . ur ~~~~~=::.:.:...._-..J !--!- --- ,a'" I, ••••• • t. " ........
"'''110' ................ " •. , •• ~ __ .. lM> .... UcH 11).
Figul:e 1-4 The A.P.T. test (Parker et .' 1.. 1
rig and grade efficiency curves 19~1).
c
12
oretical models could not predict the observed effects of
temperature and pressure (?igure 1-4c). However, their 50 %
cat-size data (expressed as aerodynami~ diameters) corre
l~ted weIl against the product of a Reynolds number and the
square root of a Stokes number (Figure 1-5).
The Reynolds number was based on the cyclone diameter and
the mean inlet velocity, while the Stokes number was based
on the mass median diameter of the feed dust (dpg)' the
inlet veloci~t (Vi) and the hydraulic diameter of the
inlet (dH). This definition of the Stokes number differs , from the usual practice of using the 50 % cut-size and the
c~clone diameter. In crder to avoid confusion, the Parker
et al. definition will be referred to as the inlet Stokes
number (Stin) and the other one as the cyclone Stokes num
ber (stso). The inlet Stokes number was given as:
(1-1)
Unexpectedly, me st of the cor~~lation for the Parker et al.
data was due te the Reynolds number and this could not be
explained by the authors. The inverse variation of cut-size
with Reynolds number is inconsistent, since the gas density
term in the numerator incorrectly predicts that decrcasing
the gas density (by increasing the temperature for example)
o
c • • • • ~ • :II ::! • ~ ,. u .. • •
, .... •••• •••• 1 •••
, ... ••••
o •• o •• o ••
0.1
0.1
13
8
o ...... 1 ..... 1&
o 0 00
00
tO' ,,' 1,4 tO"
Figure 1-5
Data correlation wilh 50% eut diameters.
Correlation of the A.P.T. data (parker et al., 1981).
c
14
would lead to higher cut-sizes. The Parker et al. work 1s
discussed further in Chapter 4.
Hoke et al. (1980, Ernst et al., 1982) studied the perfor
mance of three cyciones in series in a pressurized fluidized
bed co~ustion miniplant at Exxon. The cyclones had diame
ters of 15.2, 17.8 and 32.4 cm respectively, and other
dimensions as shown in Figure 1-6. The co~ustor was oper
ated at up to 1 173 K and 900 kPa.
The first cyclone was used primari1y to recycle flyash to
the co~ustor, so that the secondary cyclone was in effect
the first clean-up cyclone. The overall collection effi
ciency of the secondary cyclone was 90-95 % with the col
lected dust having a mean diameter of 20-25 pm, while the
dust penetrating the cyclone had a mean size of 3.0 to
5.0 pm. The tertiary cyclone collected around 90 % of the
dust leaving the second cyclone. About 80 % of the dust
penetrating the third cyclone was less than 5 pm with an
average particle size of around 1 to 3 pm. The final par
ticle concentration was usually 0.03 to 0.15 g/m3 at room
t~perature and pressure. These efficiencies were higher
than those predicted by available models (for example Leith
and Licht, 1972) and could not be explained by the authors
(Figure 1-7).
o
SYMIOL
15
CYCLCNE DE!JGN DIMlNliIONS
-IwlINL!r D t
sa:nCN 1.
DE!OlmCN
Inl.t T,.,. ...,.1 Di ..... 1It
Inlat Wlcth In"t Hel"'" ·O"' .. t PIpe in_lion ..... 1 H.l;ht ConoHolght Out"t PIpe or ..... 1It O"' .. t/ln .. t JMIo DI_lit of C#.e DI Ionf'-"Ctlon
T T ho ".
1 l T l
DIMENSIONS ICMI CYCLONE CYCLONE CYCLONE
NO. 1 NO. 2 NO. 3
T~ntlal 32.4 7.62
25.4 20.3 43.2 45.7 14.6 0.17
12.7 a.cyc ..
Tan;entlel 17.1 4.45
10.2 13.3 35.6 35.6 .. ., 1.37 '.0
CI-.
Tongontlal 15.2 3.'1 7.62
Il.4 40.' 20.3 6.2 1.~
'.0 CI~
Dimensions ot the Exxon ~iniplant cyclones (Hoke et al., 1980).
~
~ -~ Q !!i z 2 Id :t 0 u
TEiTlAAY CYCLONE COLLECTION EFFICIENCY (IUN 105)
1 1 ~_. a. ~ .... 100 • ..
J ............. .. • • .........
111
60'-'renure
....... ...... ...... ......... 700 k'. uS'e 14.' MII'/.In 15 "ue
...... , •
.... '\ ......
• •
TeMj>l ... ture Flow rate Inlat V.loclty 'renure cltop 4 k'.
' ... ...... .. ... .............
• IAlSTON FILT(J/C..:lUllU COUNTEI • CASCADE IMPACTOI .. LEml AND lICIIT MODEL (nILOaETICAl)
1
•
............ r
• 01 lIt , 1 1 1 l' , 1 l , , , ~
15 10 9 • 7 6 5 4 3 2 1 .9 •• .7 .6 .5
PAITICLE SIZE, .....
Figuro 1-7 Compnrioono ot Exxon dntn with tho I.oith and Licht modol (lloko ot nl., 1980).
~
... CIl'
)
o
o
17
An evaluation of several particulate samp1ing systens was
also done in the Exxon study. The streacs-entering and
leaving the third cyclone were sampled with a Balston Filter
particulate sampling system, and a high-temperature high
pressure (HTHP) sampling system containing either a 5-cy
clone sampler (mentioned earlier, Smith et. al., 1979), a
University of Washington 7-stage cascade impactor, or an
Applied Particle Technology (APT) high-tecperature high
pressure cascade impactor. The Balston filter elements con
sisted of borosilicate glass fibers bonded with an epoxy
resin.
The study found that while the Balston fil ter could give
good concentration measurecents, problens arose in obtaining
the particle size distribution. The Coulter Counter which
was used to measure the size of the dust col1ected on the
Balston filter, gives the volumetrie diameter whereas the
cyclone sees the aerodynamic equivalent diameter. It was
also not certain whether or not Agglomeration occurred in
the cyclone or in the fil ter, and to what degree agglomer
ates were redispersed before being measured by the counter.
The 5-cyclone sampler was four.d to be unsuitable for HTHP
sampling due to: 1) the very dilute nature and small size of
the ~articulates in the flue gas stream: 2) the size resolu
tion of the cyclone train which was too poor: and 3) system
c
18
leaks and contamination from anti-seize compounds in the
fittings.
The results obtained from the 7-stage cascade impactor were
indeterminate since it was run at flowrates which were too
high, leading to wash-off of parti cl es from the early stages
to later stages. On the other hand, good results were
obtained with the APT cascade impactor containing inconel
shim substrates. The flyash particles were very adhesive at
the samplinq conditions, allowing the use of the bare metal
substrates.
Pillai and Wood (1981. also Lane et al. 1982. Hoy and Rob
erts, 1980) reported on a 1 OOO-hour test program on a
PFBC facility at the Coal utilization Research Laboratory
(CURL) in Leatherhead England. The off-gas from the cOmbus
tor in the test rig was split into two streams, each con
taining three cyclones in series. The stream-1 cyclones had
diameters of 50.8, 39 and 33 cm respectively with dimensions
as shown in Figure 1-8. The cyclones were tested at temper
atures up to 1 088 K, pressures up to 6uO kpa and inlet
velocities up to 33 mis.
The overall collection efficiency of the first cyclone
agreed we11 with that predicted by the Leith and Licht
model, whereas the second and third cyclone overall effi-
(1
Figure 1-8
H
19
~ 1 •
1 s o i
1
L.I----!-I--; 1
1 1 1
STAGE 1 B:%ao.c::rr.ttr 101
• _lr-S1 0/0.0.46 bIO.o.21 A/D.O.30 5/0.0.9 h/C.'.l1 H/D.J.eo
9/0'0.'5
STAGE 2 SOCy DoOn'<' ... ID.
·390IMI"-]""" 0/0_0'6 b/D.D.21 A/O,0.19 5/0'0.9 n/C. !.32 H/D.J80 . 9/0.0.27
STAGE J
aoor :loG.,.'''' '0' • J30_lr-., 0/0 .o.~
b/C.0.19 .4/0_0.5 5/0.0.9
"'0.'.5 H/O.'.O BIO. 0.38
Cjclone dimensions in stream 1 of the CURL test :dg (Pillai and Wood, 1981)_
c
(
c
20
ciencies were poorly pred~cted by the same model.
Figure 1-9 shows that the grade efficiencies for thp three
cyclones did not agree with those predicted by the Laith and
Licht model.
It was also found that for the second cyclone in stream-l,
there was a decrease in the grade efficiency for particles
above 4.0 pm. The stage-3 cyclone on the other hand, had
flat grade efficiencies for particles in the range 0.8 to
15 pm (Figure 1-9). The reasons given for this unexpected
behavior were: 1) large errors due to the sma11 amount of
material collected by the cyclone; 2) the dust was too fine
for inertial separation; and 3) agglomeration of particles
after collection by the cyclones resulting in lower calcu
lated efficiencies for larger particles.
Wheeldon et al. (1936) reported on the performance of two
parallel pairs of cyclones in the off-gas stream of the Gri
methorpe PFBC facility in South Yorkshire, England. Each
pair consisted of two cyclones operating in series. The
cyclones were 1.2 m in diameter with the proportions shown
in Figure 1-10a. The operating pressure varied between 6
and 12 atmospheres, temperatures between 900 and 1 183 K,
velocities between 16 and 27 mis and du st loads up to
140 91m3 • Efficiencies up to 98.6 % with cut-sizes of
around 3.5 pm uere measured.
"'or-,..--:--, l , ft ,"~"'"
" " ' . . " " ••
• ; JO
i 10
~
i • 1 ~Ll. ..•.. , . t "-:.. .. t &. •••••
~ 10 ••• ••
~ . ~ 1 1 S~·\%I: 1
l " " di .. III fi tJ tt
ft • • ••••
"
;; 1 ..
21
· ... . · ... .
· ... , f :
. 1 1 ~ kl ..
i '" .. "1
:,-.-.. , ... -- "'-*--
: .~: -~ .. - .. . . . .. .
f i r" , .
..
! ..
l ,,,''l'~GE. Z. , 1
... h-• ...i...-_--,,;;-, -_.-:L........:~!J.L~l- _1--I-J.....L..l-!.U,!.
Figure 1-9
.. ,., ...... :"" .... I~.'
· ..... · ... , 1 ..
1 1 1 , l '
.. Comparisons of CURL data with the Leith and Licht (1972) model (Pillai and Wood, 1981).
c
...,.t-.a. ..... •
•
fi IIIIJ'
,]
u .. _ fi"'"''''''
1 ~
i i
•
22
STOlU !.Mf' '0' Jtt4.1:!'( .IJIQ UCOtClh' UC\O!!fi
yruY1 "un MI 19.19!t§
.. "" .... . ". "..., c"a ....
~ .. .. • ft •
• "NI' • Ne...,.., U'''''I''',,-...
:r ~.:·t'·' .. le •
Il .. H .. .M
K' ,. 'M
• ( i 1
•• Il " • • » J 1 M ; • ~ • • & ., • .. 'm ... " .......... C'lQ,I;oC ...... " •• '
" " " H
• Nltru. , _hIN. • ..n. ..... ,.atM ._'IPUIIM
IIC#M1UUR G .... O[ q'l!!!5! 1!:!,V!.S fat ne ""UIX '!SR S(l1'!!9HIJ an2!!fS
--..
-_...-........ ,AdCl lIrCo ....... -
Figure 1-10 The Grimathorpe cyclone and data (Wheeldon et al., 1986).
.23
The ~yclone collection performancè'was characterized by a
cyclone Stokes number defined by the 50 % cut diameter, the
gas velocity in the body of the cyclone [vb = 4Q/~dc2], and
the cyclone diameter:
stso = d pS02ppVb
18pdc (1-2)
The StokeF number varied inversely with collection effi-
ciency and dust load (Figure 1-10b) while the operating
prp.ssure had no influpnce on the collection efficiency. The
effect of temper~ture was accounted for by the viscosity
term in the Stokes number. The grade efficiency curves
(Fiqure 1-10c) showed 'fish-hook' tails explained by the
authors as being due to agglomeration of fine p~rticles in
the cyclone; the agglomerates later break down during the
particle size analysis. The reason for the reduction in
e!ficiency above 8 pm for the secondary cyclones was not
clear, but the authors felt that it was due to strongly
bonded agglomerates with effective densities lower than the
individual particle àensities.
SUHK1.RY
cyclones are used for high temperature particulat~ removal
c
24
mainly because of their simplicity and low maintenance
requirements. Most of the published studies of cyclones
operating at high temperatures were for applications in the
petroleum industry or in fluidized bed coal combustion sys
tems. These studies included cyclones varying from 1.5 to
120 cm in diameter operating at temperatures up to 1 380 K.
Comparisons of operating data with predicted grade effi
ciency curves and total collection efficiency data showed
that the performance of cyclones is still not adequately
predicted over a wide range of operating conditions.
CHAP'rER 2
EXPERIMENTAL PROCEDURES
c
(
INTRODUCTION
mmnER2
EXPERIMENTAL PROCEDURES
The first section of this chapter contains descriptions of
the experimental apparatus. This is followed by an outline
of the particle selection criteria and dust characteriza
tion, and conclu~es with an outline of the operating and
analytical procedures.
EXPERIMENTAL A~PARATUS
A schematic diagram of the experimental test rig is shown in
Figure 2-1. The main components were the cyclone, the
plasma generating system to heat the air stream, the par
ticle feeder, the inlet and outlet diagnostic sections, and
the particle sampling train. T,lese components are discussed
in the following sections. The cyclone and the inlet and
outlet channels were made out of 316L stainless steel and
were thp~ally insulated.
The cyclone
A sche~atic diagram of the cyclone and its dimensions is
e ~
,
T') 'k AIR VENT ~ pnRTICLE
l uÛl FEE DER
H PlRSHR 'R:l "'TE"PERATURE TORCII PARTlCLES
PRESSURE ~Ffl~1 Il 12 18
PLASMA 1 1 •
'''88.']1' GENERATOR
r l CYCLONE VENTURI ® 1 1 nlllER I!l
AIR PARTlCLE8 IN TEIIPERRTURE --~ J 1 BlH
- --
Figuro 2-1 Tho oxporimontnl nppnrntus (Il, I2, I3 nro oloctricnl isolntion soctions).
N CI
c
27
shown in Figure 2-2. The cyclone had a 10.2 cm i.d. diame
ter barrel and a rectangular inlet measuring 2.54 cm by 5.08
cm on the inside. The cyclone dimensions were measurable to
within 1 mm. The top of the cyclone was constructed with
the flexibility to change the dimensions of the gas outlet
duct: outlet diameters of 2.54 and 5.08 cm, and engagement
heights of 7.0 and 10.8 cm were studied. The four outlet
configurations were labeled as follows: Cl - 5.08 cm diame
ter by 10.8 cm long. C2 - 2.54 cm èiameter by 10.8 cm long.
C3 - 5.08 cm diameter by 7.0 cm long and. C4 - 2.54 cm
diameter by 7.0 cm long. Cyclone C3 was the standard design
of Lapple (1951. Perry & Chilton, 1973). The dust was col
lected in a sealed bin below the cone of the cyclone and
weighed at the end of each run.
The Plasma Generator
A 35 kW TAFA radio frequency plasma generating system was
used to heat air from room temperature to above 2 000 K.
The system consisted of a LEPEL 35 kW rectifier operating at
a frequency ot 4 MHz, and a TAFA Hodel 56 plasma torch. The
plasma vas confined by a 5.08 cm (2 inches) i.d. water
cooled quartz tube as it passed through the torch. The
presence of this quartz tube limited the operation of the
torch to around atmospheric pressure.
28
o
cm
de 10.2 œ 2.54. 8.OB bo 2.154 ho 8.OB
S 7.0. 10.8 ZI 20.3 ~ 20.3 Zo 18.2 1 2.154
CYC. œ S -lIt-Na.
CI 8.08 10.8 Zo CZ 2.154 10.8
l C3 8.08 7.0 C4 2.154 7.0
Figure 2-2 The test cyclone.
c
29
The use of a plas=a torch to supply the required heat is a
novelty in the study of cyclones at high te=peratures. The
torch allows the use of a wide variety of gases in a con
trolled che=ical at=osphere at te=peratures which cannot be
achieved in co=bustion syste=s, and by electrical resistance
heating ele=ents. The use of air (whose physical and ther
=odyna=ic properties are weIl known) instead of a co=bustion
product with =ore che=ical species, reduces uncertainties in
calculations involving the gas properties.
The plas=a torch was always started with argon since it is a
=onato=ic gas and ionizes much easier than air to for= the
plas=a. The energy efficiency of this type of plasma gener
ating system is of the order of 20 to 40 percent and it
varies with gas throughput~ thus, around 8 to 16 k~ was
transferred to the gas passing through the torch. The flow
rate of air passing through the torch was between 0.05 and
0.11 m3/min and the temperature of the gas was between 2 000
K and 6 000 K at the exit of the torch (ba~ed on a heat bal
ance).
A second strea= of air at roo= te=perature was added to the
plasma in a "tee" section just below the exit of the torch,
and a third stream (used as the particle carrier gas) was
added in a Venturi section about 15 c= further downstream.
o
30
. The resulting cixtures were around 2 000 K and less, with
flowrates between 0.19 and 1.18 standard c3/cin. The maxi
cuc error licits on the measured temperatures and flowrates
were cstiDated to be ± 2 % of the determined values.
The torch was at a potential of around 1 000 volts during •
operation. Whenever the cyclone vas connected to the torch,
the large cass of cetal acted as an electrical energy sink
even when the cyclone vas not grounded. This forced the
torch to operate at very high powers and resulted in the
crackinq of cany quartz tubes. This problec was solved by
insertinq three electrical isolation sections in the inlet
channel thus breaking the single metal cass into four iso
lated sections and reducing the voltage tetween the torch
and the cyclone in three steps.
The cyclone Inlet Channel
The cyclone inlet channe! began with a 5.08 CD diameter 90
degree elbow through which part of the supplementary air was
fed (Figure 2-1). The elbow was conncctcd to one leg of a
tee section and the second leg of the tee was connected to
the plasca torch. The other part of the supplecentary air
was injected through four tubes ot 5 am internal diameter
• placed tangentially around the top of the tee section just
c
31
below the exit of the torch. The outlet of the tee was
separated from a Venturi section by a donut-shaped block of
transite (an asbestos composite) measuring 5.08 cm thick by
5.08 cm inside diameter by 10.2 cm outside diameter (Il in
Figure 2-1). This transite block was the first of the three
electrica1 isolation sections mentioned above.
The Venturi section was 15.2 cm long and had diameters of
5.08 cm at each end and 2.54 cm at the throat. Two 5 mm
i.d. particle feed ports were instal1ed in the wall at the
throat of the Venturi, perpendicular to the wall and diame
trical1y opposed to each other. The particles were fed this
way in order to take advantage of the high turbulence in the
expanding section of the Venturi to disperse the particles.
The second electrical isolation section was placed after the
Venturi mixer and was again a transite donut, but measuring
only 2.54 cm thick (12 in Figure 2-1).
A 30.5 cm long rectangular section with a 2.54 cm by 5.08 cm
cross-section followed the Venturi. The purpose of this
section was to give the flow a chance to develop before
reaching the inlet diagnostic section. A three mm thick
asbestos gasket placed between these two sections was used
as the third electrical isolati~n section (13 in Fig-
ure 2-1).
o
32
The Inlet and outlet Diagnostic sections
The inlet and outlet diagnostic sections contained probes
for the measurement of temperature, pressure and for par
ticle sampling, as shown in Figures 2-3 and 2-4. The inlet
diagnostic section was rectangular, 15 cm long and ended 10
cm upstream of the cyclone barrel. The outlet diagnostic
section was 5.08 cm in diameter and the probe tips were 15
cm beyond the roof of the cyclone when the 5.08 cm diameter
out let was used, and 23 cm from the roof when a 2.54 cm out-
let diameter was used. The longer outlet was made by
inserting a 2.54 to 5.08 cm expansion section between the
cyclone outlet and the diagnostic section.
The static pressure was measured through a 3.2 mm tube in
the wall of the inlet duct perpendicular to the flow, while
the impact pressure was measured through a similar tube pro
jecting into the channel and parallel to the flow. The dif
ferences between the static and impact pressures were used
to compute the inlet velocity while the cyclone pressure
drop was measured by the difference between the inlet and
outlet static pressures. The pressures were measured by an
HKS Baratron Type 77 electronic pressure meter in the range
of 0.1 to 400 N/m2 (0.001 to 3 mmHg), and by a Magnehelic
mechanlcal gage in the range 400 to 2 450 N/m2 (3 to 20
,.,
WALL THERMOCOUPLE
\---t~ " PRESSURE PROBES
PARTICLE SAMPLE PROBE
Figure 2-3 Tho inlet diagnostics section.
~ --
THERMOCOUPLE
~
~
o
THERMOCOUPLE -_---==== PARTICLE:_~'=== SAMPLE PROBE
PRESSURE PROBES
34'
~ALL "..." THERMOCOUPLE
Figure 2-4 The outlet diagnostics section.
(
c
35
mmHg). Both devices were estimated to have maximum error
limits c' ± 2 % of the scale reading.
The inlet gas temperature was measured by a 3.2 lDlD dialnet~r
chromel-alumel (type-K) thermocouple aligned paralle: to the
flow and ';'n the same plane as the .ressure and particle
eampling probes. The wall temp~rature was measured directly
cpposite the gas tEmperature thermocouple and was l'sed to
corrEct the temperatu~e measured by the gas thermocouple for
radiation heat losses (see calculations in Appendix A2).
The temperatures were recorded by à Thermo Ele~ccl~ 24 chan
nel strip-chart recorder.
The Particle peedcr
A TArA vibrating bowl feeder was used to fEed the test dust
into th., cyc~o ... e inlet channE'l. The feeder (shown in Figure
2-5) consisted of a conical storage hopper which fed th2
powder onto a bowl with a spiralling ramp around its
perimeter. The bowl was made to ~ibrate with an amplitude
proportional to the voltage applied to the vibrator, and
ticles in the bowl liIoved at a proportio •• ate1:~te upward in a
spira'. and through a hole at the top of the ramp. The
feeder was emptied after each run and the amount ~f powder
fed was determined by weight differ.ence. Fe~d =ates of up
SEEDED GAS OUT
, '
36
. .
~ GAS IN
1+-4--- STORAGE CANISTER
f4--4--- VIBRATING BOWL
I---j.--- VIBRATOR
Figure 2-5 The Tafa particl~ feeder.
37
to 700 g/min. with al'lmina and 160 g/min. with silica were
used. The maximum error limits for the dust feed rate were
estimated to be ± 1 g/min.
The Partic1e Samp1ing Train
The particle sampling train is shown schemat.cally in Fig
ure ~-6. Only one cascade impactor was available, 50 samp
ling was done on only one stream (either the inlet or the
outlet) in an experiment. The sample probe was a 5 mm
inside diameter stainless steel tube tapered at the end to
form a nozzle which was aligned parallel to the axis of the
channel.
The probe was connected to a Sierra 220 cascade impactor
where particle size distributions were measured for aervJy
namic diameters in the r~nge of 50 to 0.1 p~. The impactor
was supplied with 10 stages but only the first seven were
used since the last three stages measured particle sizes
below 0.1 pm in diameter and introduced large pressure drops
into the impactor. The cut··sizes of the impactor stages
were determined from data supplied by the manufacturer.
Each impactor stage had four rectanqular slots in a spoke
like arrangement centered on the axis of the impactor.
c
> -- --- -- -- --or
. . •
., > > Il :::r
. .. CASCADE II1PACTOR
MAIN STREAM
METER
ŒSJ---RECORDER
FLOW TRANSDUCER SAMPLE
r-----:::>~ ST REA M
PUMP
Figure 2-6a The particulate sarnpling train.
o
.c.> 1~{
"
,"," ,
, , "\
"
" '\.
c
39
o o
pol.~ ----of g=
_---A--~ ..... ..•. .... ....
.. .~
~ "
~ .... , ,
~L.i<J ~··········ï ............. Ë···········] ........ -............
/)r~~ </ , , , , . , . , ........
position of slot.s on oc' .. ocsnt stoges
Figure 2-6b Orientation of the slots on successive stages of the cascade impactor.
o
o
40
The slots were rotated through 45 degrees cn adjacent stages
leading to a circumferential rather than a radial flow of
gas between stages. This arrangement minimized particle
losses at the cyli~drical walls. The slots on the lst stage
measured 3.6 mm by 13 mm while those on the 7th stage were
4 0.15 mm by 5.8 mm.
Fiberglass was used as the collection substrate on each
plate and for the back-up filter. The substrates supplied
by the manufacturer had slots of one size only measuring
4 mm by 14 mm, which meant that a significant area around
the slots on the smaller stages. This situation was
improved by designing a die and cutting new substrates with
smaller slots (measuring 2 mm by 13 mm) which were used on
stages five to seven.
The flowrate of gas through the impactor was monitored using
a Matheson Series 8110 mass flow transducer which preceded
the sampling pump used to ensure a steady flow of gas
through the sample train.
DATA ACQUISITION AND ANALYSIS
Particle selection criteria
The du st used in most of the previous studies of cyclones at
c
41
high tempe ratures was usually flyash having fairly wide size
distributions, and densities that were not precisely known.
Salcedo (1981) showed that the particle density cou Id vary
between size fractions for powders consisting of several
chemical species. The varied composition and wide size dis
tribution of flyash. together with inaccuracies in the par-. ticle size determination could lead to difficulties in eval-
uating the fractional collection efficiencies and in com-
pleting fractional mass balances. Furthermore, at very high
temperatures, combustion of some of the flyash particl~s
could occur within the cyclone, leading to more uncertain
ties in evaluating the cyclone performance.
Considering the above, the following criteria were specified
in choosing the test dusts:
1. They should have relatively high melting points.
2. They should not react with air at temperatures below
2 000 K.
3. Their densities should be weIl defined.
4. They should be readily available.
Several refractory oxides meet these criteria and alumina
(grade C70-FG obtained from ALCAN) and silica (grade AC-8130
obt~ined from Anachemia) were selected for this research.
The powders were sieved and the fraction below 44 pm used in
o
o
this study. The fine particle size was used because the
collection efficiency is known to be close to 100 % above 50
pm and it was more beneficial to study the sizes where the
performance is uncertain. The particle densities were 3.9
and 2.6 for the alumina and silica respectively.
Characterization of the Povders
Analyses were done to determine the particle size distribu
tion, shape and density using microscopes, an x-ray sedi
graph and agas pycnometer in addition to the cascade impac
tor.
An optical microscope (Reichert - Zetopan) and a scanning
electron microscope (model JEOL CX100) were used to observe
the shape and size of samples collected on each stage of the
cascade impactor and from the cyclone inlet and bin. These
observations showed that the alumina particles were mostly
rounded but a few were elongated whereas, the silica par
ticles were more angular and also had some elongated par
tic les (Figure 2-7a,b).
In both cases, individual as well as clusters of particles
vere observed. For alumina, the individual particle sizes
ranged from 0.4 to 30 pm while the loosely agglomerated
clusters measured up to 140 pm in diameter. The silica
(
a
(
b
( Figure 2-7
43
alumina
sllica
Photographs ot the test dusts: a) alunina, h) silica.
~ • Q
60 lUI Inlet. 1lJat. No. V.locl tu Lood
ml. glrrfl
40/- c ffi03 16 23 o MilS 21 28
N +M36 27 3
~ "MOI 7 6
• OAA3Q 4 120
~ 00 III Sed 1 grq:.h
~ ~ 20r ! 1 II' 1 \. \\ \\ X \ t .... ~
\0 t- ~
.~--I ",., t'A
\.0 \0.0 60.0 PARTICLE SIZE. f..I1l
, , Figure 2-8 Inlct particlo sizo distributions ot alumina.
~ ~
60 lUl Inlet Ibtt No. Veloolty Lood
mie glnP
40~ OSAOI 28 2 c SItIU 9 3
N
3J~ + SII'IX3 6 9 051004 6 9
• .SItœ 9 9
~ • Sad 1 grq:tl
~ ~ 20~ /' ~d>-r"'." \ 1\ 1 ~
~ ~ ~ \II ... !Il
10
0 '- 1 ft !
0.2 !! [J-I 1.0 10.0 60.0
PffiTIQ.e SIZE. f-ITI
Figura 2-9 Inlet particle size distributions of silica.
,
o
46
agglomerated less than the alumina with clusters up to
around 70 pm and discrete particles between 0.15 and 40 pm
being observed.
The theoretical cut-size for each impactor stage fell within
the range of particle sizes observed by the microscope for
both alumina and silica. The SEM observations also con
firmed that there was an overlap of particle sizes on adja
cent stages, but the average particle size decreased pro
gressively from the top to the bottom of the impactor.
A Micromeritics Sedigraph 5000D-Particle Size Analyzer was
used as another way of measuring the particle size distribu
tion. with this technique, the powdered sample was dis
persed in a liquid and the ra~e of settling was detected by
an X-ray beam. Stokes' law was assumed and the rate of set
tling was related to the particle size and density, and the
liquid density and viscosity. The output of the instrument
was a plot of the cumulative percent undersize versus the
Stokes equivalent spherical diameter.
Figures 2-8 and 2-9 show comparisons of size distributions
obtained with the sedigraph comparcd with cascade impactor
distributions for alumina and silica. The distributions
obtained with the sedigraph are shown for comparison but
were not used since the cyclone sees the aerodynamic diame-
c
ter as measured by the impactor, rathar than the diameter
of particles settling in a liquid as rneasured by the sedi
graph. The distribution measured by the sedigraph also
depended on the degree of dispersion or flocculation of the
particles in the test liquid.
The inlet size distribution measured by the cascade impactor
depended on the inlet velocity and on the dust load. Theor
etically, at high velocities and low or intermediate dust
loads, the incoming particles are weIl dispersed so the
measured size distribution is closest to the true distribu
tion (Figure 2-10a). At low velocities and low or interme
diate dust loads, the largest particles settle in the inlet
channel so the size distribution ente ring the cyclone is
finer than the original distribution (Figure 2-10b). At
very high dust loads, agglomeration of the particles results
in a coarse size distribution (Figure 2-10c).
These trends were experimentally ob~erved and the inlet dis
tributions measured under various operating conditions are
shown in Figures 2-8 and 2-9. The ~lumina and silica were
bimodally distributed. The major peak for alumina occurred
at around 4 to 5 #m with the minor peak occurring at around
25 #m. For silica, the trend was reverse~ with the major
peak occurring around 25 #m and the minor peak or sadd le
point around 4 to 5 #m.
48
• • • • • • • HIg, Velocltl:l • • • (0) • • • • • • Law 01'" Mad 1 un Lccd • •
• • • • •
•
Law Veloeltl:l
Law 01'" HIg, Loo:f • (b) •
~.... . ...... .. ~ .
, . ... .; .. • • • • •• ••••••••• • . • e. .' ... " . . ' .. •• • • • : . . . .. . . . .
HIg, Locd
Medlun 01'" HIg, Veloel tl:l
•
Figure 2-10 Effect of inlet velocity and dust load on dispersion and measured size distribution.
c
49
The inlet 50 % cut-sizes varied from 2.5 to 5.1 ~m for alu
mina a~d 4.5 to 10.~ ~~ with silica while the dp16/dp84
ratio varied from 0.11 to 0.19 for alumina and 0.12 to 0.18
for si1ica. dp16 and dp84 are the particle sizes be10w
which 16 % and 84 % of the particles lie. For a log-normal
size dis~ributiont the standard deviation is given by ~ither
dp84/dp50 or dp50/dp16t so dp16/dp84 is equiva1ent to the
inverse of the variance and is a measure of the width of the
distribution.
OPERATïNG PROCErryREB
The following procedure was followed for a typical r:n:
l ._ 1mpactor substrates were weighed an~ the impactor
installed in the sample line.
2. The particle feeder WQS loaded with a • 'own ~ass of
powder.
3. The plasMa generator was warmeu up and the torch ignited
with argon.
4. The plasma gas was switched ta air after around two to
50
five minutas of stable operation with argon.
5. The system is allowed to heat up for between five and 30
minutes depending on the test beirag done.
6. The sample pump was turned on and the sample flow
adjusted to the predetermined isokinetic flowrate.
7. ~bout one minute later, the parti~le feeder was
turned on at the pres et voltage and the feed was main
tained for the d~sired time (usually 3 minutes).
8. The feeder was switched off, the sample pump turned ~ff,
th.. pl'!.sma generator turned off and the gas flow
stopped, all within five seconds.
9. The mass of powder left in the feeder at tha end of the
run was measured and subtractea from the initial '!.mount
to determine the amount of powder fed.
10. Tite impactor substr,ates were re-weighed to determine the
m~ss collected on each stage.
11. The cyclone was allowed to cool bcfore the inlet
section, the roof and the bin were opened and the dust
deposited in tt-"! inlet chan .. «l, on the walls of the
c
51
cyclone and in the coll~ction bin were collected
separately.
The mass of powder ~ntering the cyclone (HF) was taken as
the difference betwaen the powder fed by the feeder and that
deposited in ~he inlet. The powder collected (HC) was taken
as the S~4 of the powder deposited ~n the walls ~ç the cyc
lone and that collected in the bill. The inlet size distri
but.ùn (xif) wa~ Qeasured with the cascade impactor on the
inlet for some initial rvn~ and then th~ impactor was used
on the outlet for subsequent runs to mcasure the outl~t dis
tribution (xio)' The operating conditions were matched in
choosing the appropriate inlet size distribution for mass
balance calculations. The mass balanc,'s were completed over
the length of time for which powder was fed:
Ovarall mdSS balance:
(7.-1)
Fractional mass ~alance:
(2-2)
The two unknowns - the out~et mass (Ho) and the collected
dust size distribution (xie) - were determined from these
o 52
equations and the ~verall and fractional collection effi
ciencies given by Mc/MF and (McXif)/(MFxif) respectively.
SU!lHARY
A 10.2 CD i.d. cyclone with four out let configurations w~s
used in this study. The high temperatures were attained
using an induction plasma sYf".tem ol'?rating with air. Inlet
and outlet diagnostic sections enabled the measuremLnts of
temperature pressures and gas and particle flowrates. Mass
balances yielded overall and fractional collection effi
ciencies and the pressures measurements yielded the cyclone
pressure drop.
CHAP'l'ER 3
GAS AND PARTICLE FLOW PATTERNS
CllAPTBR 3
GAS ~ PAR'l'ICLB PLOW PATTBRNS
LI'l'BRA'l'URB RBVlmf
Some earlier experimental studies of flow patterns and col
lection performance in cyclones were reported by prockat
(1930), Whiton (1932), Rosin et al. (1932), van Tongeren
(1935), Shepherd and Lapple (1939, 1940), Alexander (1949),
ter Linden (1949), Iinoya (1954) and Smith (1962). These
and other works have been reviewed by Stern et al. (1955),
Jackson (1963), Caplan (1977) and more recently by Saxena et
al. (1982), ogawa (1984) and Leith (1984).
Cyclones operate by converting the inertia of the incoming
stream to centrifugal forces in a confined vortex, causing
the parti cl es to move towards the wall and be separated from
the gas. The gas flow pat~ern has been described by van
Tongeren (1935) as a combination of double-eddy and a dou
ble-spiral flow patterns as shown in Figure 3-1. The upper
eddy is formed in the annulus between the cyclone wall and
the exit 1uct, with a weak up~ard flow along the outer wall.
The dOUble-spiral p~ttern refers to the downward spiralling
flow around the walls of the cyclone and the upward flow in
the core below the gas exit duct.
c
(
c
54
According to van Tongeren, dust accumulates under the rooi
of t~e cyclone and is supported by the upward force of the
upper eddy current. Eventually, the weight of the dust is
sufficient to overcome the effect of the cddy current so it
falls suddenly and some of it escapes tbrough the gas out
let. If the particles are sticky (for example hot flyash)
the accumulation on the r~of can form a sol id blcck which
does not fall readily and may haoper the operation of the
cyclone. Some cyclones (such as the one shown in Figure
3-1) are modified to take advantage of the upper eddy by
having a dust bypass which skims the dust from tha top of
the cyclone and re-injects it just above the dust outlet.
The gas ente ring the annular region at the top of the cyc
lone is s~~cezed by the gas already in the cyclone, to about
half of the inlet width (Theodore & Buonicore, 1976). Inlet
vanes, helical and Involute inlets have been used in
atte~pts to reduce the effects of this Interference between
the two gas streams. Inlet vanes tend to decrease the col
lection efficiency since they retard the formation of a vor
tex in the annulus.
Theodore and Buonicore (1976) also pointed out that the con
ical portion of the cyclone is not necessary to reverse the
dIrection of the vortex although it reduces the length of
cyclone needed to do so. The cone brings tho pa~icles to a
o
û
o
lower
55
Inner ~'\J...i?~--- sp 1 ra 1
eddy outer
IU'!}\,~"+---------it-
spI raI
Figure 3-1 The van Tongeren (1935) cyclone vith dust bypass.
(
(
56
central point making them easier to handle and dispose.
Care should be taken not to make the cone too small; other
wise the vortex core will contact the wall and re-entrain
the collected dust.
Ter Linden (1949) measured static pressures and three compo
nents of gas velocities inside a cyclone with a helical
inlet. Figure 3-2 shows that the tangential velocity is the
main component except at the core where the upward axial
velocity is predominant. The tangential velocity increased
from the wall to the center, reaching a maximum at about
65 % of the distance from the wall to the axis, then
decreased quickly as the axis was approached. The tangen
tial velocity in the outer part of the cyclone up to the
maxima was given as a function of the velocity at the wall
(Vtw) and a vortex exponent (n):
(3-1)
with n = 0.52. According to ter Linden, the wall velocity
does not deviate much from the velocity of the gas in the
inlet duct.
The r~dial velocity measured by ter Linden was relatively
small and directed inward from the wall to around the radius
o
J 1
/
VIridoo olT..,...wVcIoàq Y,IDoI_ Vcb=7 Y ... ~_Io.C"-
---T.....,.w-,.. ------~.._,..
57
T!aL.~ , ,UTC~ .. a 1
tnQl"Jf'r ... ,."",&IS Id ac.t 1
ri i
j -n,:!:\~I7"""'~l~~7t"::""';d lI'.t.rc "fUUI.I •• • _,.,.cw,.,,· ",ocm •
.. , "'lUS"' SICI .~~~~~~~~~~
.\ 1
\ /W\ / ~"1 \ 1 \ 1 \ 1 ''r-I--l-'Ir-i
Figure 3-2 The velocity profiles of ter Linden (1949).
c
58
of the exit duct, and directed outwards from the axis to
around the gas exit duct radius. The axial velocity pro
files revealed the reversal of flow in the cyclone, with the
axial flow being downward close to the wall and upward in
the core.
Alexander (1949) measured static pressures and ve10cities in
cyclones of 3.2 to 120 cm in diameter. He observed that if
the cyclone was sufficient1y long, the vortex did not run
the full length and was completely reversed at a distance
below the gas exit duct that he termed the "natural length".
This length depended on the cyclone geometry but not on the
gas velocity and was given by the empirical expression:
[d 2] 1/3
Ln = 2.3 de A~ (3-2)
Alexander also derived expressions f~r the ratio of the tan
gential velocity at the wall to the mean inlet velocity, and
for the vortex exponent as fun ct ions of cyclone diameter and
temperature:
(3-3)
n = (3-4)
fi
59
(3-5)
with dc in centimeters.
Abrahamson et al. (1978) discussed in some detail, the
effects of particle bouncinq on the walls, aqqlomeration,
dust pick-up from the collection bin, and saltation from the
walls and bin. (Saltation is the entrainment of particles
from the surface of a layer of p~rticles into a qas stream).
He measured velocity and static pressure distributions in
du st collection bins of various sizes attached to a 30 cm
diameter cyclone at room temperature. He found thdt the
vortex in the cyclone persists in the bin and that there is
a considerable exchanqe of qas between the cyclone and the
bin. Abrahamson also found that the collection efficiency
varied' inversely with the level of dust in the bin and
directly with the inlet dust concentration. No mathematical
modellinq was presented in his study.
Meissner and Loffler (1978) developed an empirical model to
describe the tanqential velocity profile in the cyclone bar
rel at room temperature. The velocity at the wall is higher
than the me an inlet velocity due to the vena contracta in
the entry reqion. He found that for friction-free flow, the
c
60
wall velocity (Vtw*) was related to the me an inlet velocity
(vi) by the expression:
= - --- + 0.889 [-0.204 bc ]-1
(3-6)
This equation predicts that the tangential velocity at the
wall would be 1.27 times the mean inlet velocity for the
cyclone used in the present study, with both the 2.54 and
5.08 diameter gas outlets. A wall friction coefficient (ee)
was used to account for the friction at the walls, and the
wall velocity (Vtw) was determined to be:
Vtw 1 [[ -- = ----* 0.25 vb eehz
where:
h * z
~ h *Vt *] O. 5 ] + ~e z w _ 0.5 Vb
(3-7)
(3-8)
with Vb being the gas velocity in the cyclone barrel, hc
the height of the inlet and hz the height of the cylindrical
portion of the cyclone barrel.
Meissner and Loffler did a differential angular momentum
balance to calculate the radial variation of tangential
o
61
velocity as:
Vtw r [ [rJ] - = - 1 + D 1-Vt rc r
(3-9)
where:
+ h] sin ~c
(3-10)
D is a parameter accounting for the exchange of angular
momentum between the wall and the gas and ~c is the angle
the cone makes with the cylindrical portion of the cyclone.
The wall friction coefficients of the body (ee)' the top of
the cyclone (eD) and the conica! section (eK) were measured
and found to lie between 0.0065 and 0.0075 for cyclones with
smocth walls at room temperature.
The radial velocity in the outer part of the cyclone was
determined by assuming that the gas flowed uniformly into
the core region through an imaginary cylinder formed by the
axial extension of the gas outlet duct. The radial velocity
was then given by:
(3-11)
(
c
c
62
the conclusion that stso varied inversely with dust lQad.
Pursuing the same argument and using an anëlysis s;milar to
Wheeldon et al., it was calculated that the cyclone used in
this study would have sts l varying between 1.0 x 10-4 and
2.2 x 10-4 depending .~~ the gas outlet configuration. In
comparison. the measured stso varied between 4.0 x 10-4 and
3.6 x 10-1 , and ~here was no corrblation between stso and
the dust load. It was concluded that a single stso for ea.,
cyclone configuration did not adequately charac~erize the
performance of thb cyclone in tàis study.
Parker et al. (198\) showed that their data could r corre
lal~d by plotting the p:od~ct of the Reynolds number (Re)
anà the s~uare root of the inlet Stokes number (~tin)
a;ainst the experimen~ally dete~dined SO % cut-size on log
log coordin
'63
Particlo Deposition Patter"s
A ribbon-like pattern was som× formed by t~· pùrticles
on the ~alls of the cyclone depending on the inlet flowrate
and dust concentration. The width of the ribbon in the
axial direction was equal. to the height of the inlHt at the
entrance to the cyclor.e. and increased te. about twice that
height after about cn~ ro',tion (Figure 3-3a). These pat-
t!.l:ns indicated that: the -:jas made between three and six
rotations in moving down the cyclone.
Relatively co~centrated depo~its of particles usually accum
ulated in the corners formed by the intersection of the roof
an~ the r.ycJone barrel, and by the roof and the gas outlet
duct. These deposits are evidence of the ?èdv formed in the
upper sectior. of the cyclone as first described by van Ton
geren (1935). ·rlJ.e occurrence of these eddies was further
confirmed by the pres~nce of streaks in the deposited layer
close te. the roof. These streaks were djrected upwards at
angles of around 20 to 30 degrees t~ the horizontal on the
wall of the cyclone barrel.
The deposition patterns also indicat~d that ~~e flow in the
annu~.l!s bE'tween the cyclone wall and the gas outl~t duct was
highly turbulent especially in the region where the incoming
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a
b
Figure 3-3
64
particle deposition patt3rns on the ~alls of the cyclone.
c
65
flow met the flow already in the cyclone (Figure 3.3b).
~his behavi~u~ was most noticeable for runs with low or
in~ermediate du st loads (less than 10 g/m3); then it was
clear that the deposits on both the barrel and the outer
wall of the gas outlet duct were thicker than on the sur
T.vunding walls, and the deposition pattern r.ad a rough
appearance.
There was a tendency for the deposits on the cyclone barrel
to start aDout one to five centimeters further downstream of
the entrance at high temperatures than at lower tempera
tures. This occurrence could not be zttributed entirely to
the temperature due to the relationship between the volumet
rie flowrate, inlet velocity, dust loading and temperature.
It is however consistent in that it shows that the particles
reach the ~all at a later time, leading tu lower collection
efficiencies.
Deposits on the inner wall of the gas exit tube started at
around 0.5 to l cm above the lower edge, and exten~ed
upwards. A pattel~ of streaks was observed, upwardly
inclined at more than 45 degraes to the horizont~l for most
runs. This pattern is consist6nt with the notion that the
inner vortex has a higher axial co~ponent than the outer
vortex. It is also consistent with the theory that par
ticles are separated fro~ the upward inner vortex as weIl as
o
66
from the downward outer vorte~. Models such as the Dietz
(1981) and Mothes and Laffler (1984, 1988) models take this
into account, whereas models such as the Rosin et al. (1932)
model assume that separation occurs only as the gas moves
downward.
The absence of particles within 0.5 to 1 cm of the lower
edge on the inside of the gas outlet duct, can be attributed
to the small inward flow of gas being entrained beneath the
lip of the duct from the eddy current in the upper part of
the cyclone. This stream of gas tend~ to contain only the
fine st particles, and !orms a layer of gas of lON dust con
centration at the bottom of the gas exit. This layer
extends for up to 1 ~ into the gas outlet before the gas is
fully mixed with the inner vortex leaving the cyclone.
Particle deposition patterns indicated that the vortex usu
ally ran the full length of the cyclone and that there was a
region of high swirl at the base of the cone when the larger
(5.08 cm ) diameter outlet was used. This ter.dency was best
illustrated by the presence of deep grooves in the dust
deposited at the bottom of the cone, for runs in which high
dust loads were used.
Alexancler's (1949) empirical equation predicted that the
natural length would be 12 cm for the 2.54 cm diameter out-
67
let and 23 cm for the 5.08 cm diameter outlet for the cyc
lone used in this study. Alexander also stated that the
vortex in cyclones that were slightly longer ~han thr calcu
lated natural lenqth, is likely to run the full length of
the cyclone. This appeared to be the case with the 5.08 cm
diameter outlet. The actual length of the cyclone below the
gas out let duct was either 1.3 or 1.5 times the calculated
natural length with the 5.08 cm diameter outlet. This com
pares with ratios ~i 2.5 and 2.8 for the 2.54 cm diameter
outlet.
PRESSURE 2UlD VELOCITY HEASOREHBNTS
The Pressure Probe
A three-dilUp.nsional 5--channel pressure probe (shown in Fig
ure 3-4) was us cd tIJ maasut'e ve~.ocity and static pressure
profiles in the cyclone. T.he prcbe waz manufactur,d by
United Sensors and Control corporation (~odel No.
DA-250-48-H-44-Cd) and was previously used anù d~scribed in
detail by Bank (197~) and Reydon (1978).
The probe was ~ounted on a stand which allowcd it t~ bB
rotate:i through 360 degrees aro:.md its major axis aud to be
moved known distances along the same axis. 'fhe probe was
68
6.4 mm in diameter and had five taps of 0.8 ~ inside diame
ter arranged on flat wedges that were eut into the cyl indri
cal surface of the probe about 13 mm from the tip. This
arrangement allowed the measurement of total and static
pressures at a point, and hence the calculation of the total
velocity and its co~ponents.
Referring to Figure 3-4, hole Pl was centrally located and
permitted the calculation of the total velocity (dynamic)
pressure. Taps P2 and P3 were on planes ± 45 degrees to the
plane of Pl and all~wed the measurement of the yaw angle
pressures and the stream static pressure. Taps P4 and P5
were in the same plane as Pl and wera used to determine the
pitch angle pressures. The differential pressures were
measured by an MKS Baratron electronic pressure transducer
and a Magnehelic mechanical gage (described in Chapter 2).
Velocity-static pressure measurements were made by first
aligning the probe with tap Pl in a horizontal plane and
facing the flow. In this position, the angle to the hori
zontal was zero and the pressure (P3-P2) was measured. The
probe was then rotated until (P3-P2) was zero (that is P3 =
P2) and the angle through ~hich the probe was rotated was
measured as the angle the flow ~ade with the horizontal
plane (.1». At this fixed angle (4)), the pressures
(PI-Patm)' (P2-Patm), (Pl-P2) and (P~-P5) were measured.
69
. , . '. " . ,. :,.1' ..
• f' •
4
Figure 3-4 The 5-channel pressure probe (Reydon, 1978).
o
70
The velocity pressure (PT-PS)' the direction of the velocity
vector relative to the probe (e), and the static pressure
relative to atmospheric pressure were calculated from the
following equations (Reydon, 1978):
(3-13)
K(e) (3-14)
F(e) (3-15)
(3-16)
The magnitude of the total velocity and its three components
were given by the following equations, using the coordinate
system shown in Figure 3-5c:
(3-17)
Vt = V sin(e) (tangential) (3-18)
Vz = V sin(~) cos(e) (axial) (3-19)
vr = V cos(~) cos(e) (radial) (3-20)
71
(b)
lae •• o
Vz
1)-------
c Figur~ 3-5 Pressure probe location and coordinate system.
o
o
72
In the above equations, C, K, and F are calibration factors
for the probe that were supplied by the manufacturer, and Cp
is a standard pressure probe coefficient that is approxi
mately 1.
The Pressure Probe Location
The location of the pressure probe in the cyclone is shown
in Figure 3-5a,b. The probe was inserted radially through a
port in the wall of the cyclone, 13 cm from the roof and
perpendicular to the axis of the inlet channel. Four gas
outlet duct configurations, (Cl to C4 in Figure 2-2), were
used. The cross-sectional area of the probe projecting into
the cyclone varied from 0.8 to 3.25 cm2 , depending on its
radial position. This probe area corresponded to around 1
to 4 % of the cyclone cross-sectional area when viewed from
above.
Since gas velocity distributions have been measured in
detail by other researchers (Shepherd & Lapple, 1939; ter
Linden, 1949; Alexander, 1949; Iinoya, 1954; Ogawa, 1984),
the measurements made in the present research were done
mainly to verify that some of the standard assumptions about
the flow pattern were applicable to the cyclone used in this
research.
c
c
73
Room Temperature Experiments
Profiles Obtained with Large Diameter Gas Outlet
Velocity profiles were measured at room temperature using
the four outlet configurations (Figure 2-2) and mean inlet
velocities between 2.75 and 15.2 mis. The measured veloci
ties were normalized by dividing by the calculated mean
inlet velocities. The radial position (r) was normalized by
dividing by the cyclone radius (rc).
Figure 3-6 shows the variation of the total velocity (V)
across the radius of the cyclone with the outlet configura
tion Cl (5.08 cm diameter, 10.8 cm long). The mean inlet
velocities for the three profiles shown were 2.75, 7.75 and
15.2 mis. The legend in this figure also shows the inlet
flowrate in standard litres per minute (slpm). The total
velocities increased from the wall towards the center,
peaked at around 0.35 of the cyclone radius, and then
decreased towards the axis of the cyclone. Furthermore, the
velocity ratios varied directly with inlet velocity at each
radial position so that the profiles were parallel to each
other across most of the cyclone.
@
2.8
2.61-
2.41-
2.21-
>- 2.0 l-I-U 1.81-0 ~ 1.61-
1- 1.41-t~~
2 1.21-...... ~ 1.0
5 0.81-1-
0.61-
0.4L 0.2
0.0 0.1
Outlet IÀCt
-_.0... ..... -- ......... IJ-" .... 0 .... ....
Ynlet Flowrate slpm mis
o t 177 16.20 A BOO 7.76 o 213 2.76
••••••••• A ..... "'"-A···· ....... - 0 ." .... ...- - --.. "" ." ". '-1----__
0 . ~
•••••• • .. A. •.•••••••• 0" • •• /.1 .••••.•.•••..• ll. ~o O~~ ........ A
1
O 'l .t:.
1 1 1 1 1 1
0.3 0.4 0.6 0.6 0.7 0.8 RADIAL POSITION. r/R
-0
--'-
0.9
Figure 3-6 Total velocity profiles vs inlet flowrate for cyclone Cl.
9
1.0
~
" "
75
The maxima in the velocity profiles usually occurred at
radial positions that were less than the gas outlet radius.
These maxima indic?~~ a transition from a strongly spiral-
1ing region to a core region with little rotational motion.
The radius of the core region was about 0.7 of the outlet
tube radius, which is within the range of 0.5 to 1.0 as
stated by many researchers (for example sta~ .~and, 1951,
Leith & Licht, 1972: Deitz, 1981).
Figure 3-7 shows the tangential velocity profiles corre
sponding to the total velocity profiles of Figure 3-6. The
shapes of these profiles and their magnitude are very simi
lar to the total velocity profiles especially in the outer
part of the cyclone. This indicates that the tangential
component was dominant across most of the cyclone except in
the innermost region around the axis.
Figure 3-8 shows the radial velocity profiles for the runs
discussed above. This figure shows that the radial velocity
was relatively low and directed inwards from the wall
towards the center in the outer part of the cyclone. On the
other hand, the radial velocity was directed outwards from
the axis to around 0.35 of the cyclone radius, coinciding
with the maxima in the total and tangcntial velocity pro
files. The radial component iF sometimes neglected or is
assumed to be constant along the length of the cyclone.
~
2.8
2.61-
2.41->-1- 2.21-..... u Cl 2.01-...J W :> 1.81-1-w 1.61--1 Z :::: 1.41-...J a: 1.21-..... 1-Z 1.01-w (!)
~ 0.81-1-
0.61-
0.41-
0.2 0.0
_.
Out/et tu::t
,.-,.-1:1- .. C""~ .............
"0
A •• ••••• .. ·····A.... .. ......
Inlet Flowrate alpm mla
01177 16.20 A 600 7.76 o 213 2.76
U e. .... .... .... ... .. . _ .. c.. •• ' '" . A .' 0'" 'oU."-
Y,,' .......... ---C-
.' "·A-; ....... --• .. ... A. "'0 " .. O
..... ' . ...... A
o
_. _L -'- -'-
0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 1.0 RADIAL POSITION. r/R
Figure 3-7 Tangential velocity profiles vs flowrate for cyclone Cl.
~
àI
@
t .el 1 1.4 OuUat [u;t
t .21-
t .ot ~ 0.8 .... g 0.6
lnlat Flowrata slpm mis
c 1177 ÂBOO o 213
16.20 7.75 2.75
rrl 0.4 __ g-----~c-----~ St. ::>: ----. -_·ü tu 0.2 ~g.:;,. "...... ...... " .............. ,u ............ .
-' ~ 0.0 / .... ~ I~"
§ ~~:: /.:,/ a::: .'·u -0 6 .... . 0 .....
-0.8 t ····
-t.O~----~----~----~----~----~~----~----~-----L----~----~
0.0 O. t 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 RADIAL POSITION. r/R
Figure 3-8 Radial velocity profiles vs flowrate for cyclone Cl.
t .0
o
::l
c
78
The corresponding axial velocity profiles for the same runs
are shown in Figure 3-9. This figure shows that the three
normalized velocity profiles are indistinguishabJe under the
experimental conditions. The figure clearly shows the down
ward flow of gas close to the wall and the reversed flow in
the inner part of the cyclone. The interface between the
dowllflow and upflow regions occurred at around 0.6 of the
cyclone radius and did not coincirle with either the gas out
let radius, or the maxima in the tangential and total velo
city profiles.
These observations led to conclusions similar to those made
by pervov (1974), that there are three regions in the cyc
lone when viewed from above (Figure 3-10):
1) a downward spiralling outer region around the wall,
2) an upward strongly rotating inner annular region and
3) an innermost core where the flow is mainly axially
upward with little or no spiralling motion.
The transition between regions 1 and 2, occurred at around
0.6 of the cyclone radius while the transition between
regions 2 and 3 occurred at around 0.35 of the cyclone
radius (or around 0.7 of the gas outlet radius).
e
1.8
1.6t-
1.4 t-
1.2t-
>- 1.0t-t-G 0.8t-e ~ 0.6t-
I:ü 0.4 t-
Outlet tblt
~~ ....... .... ...... 6: .. ..........
Inlet Flowrate alpin mis
CII77 16.20 .t::. eoo 7.76 o 213 2.76
2 0.2" I-t
~ 0.0 I-t ~ -0.2t-
..,,;.: ••••• "!- ...... r.1
·····.'Ii·............ ....,.. ______________ ~ 1
o~~&', .. ~ .. "':-0:.",
'~""6-., < ""0 - ..... Li
-0.4t-
-0.6t -0.8~---~---~---~---~---~---~--~------~---~~
0.0 O. t 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 t .0 RAOIFL POSITION. r/R
Figure 3-9 Axial velocitl' profiles vs flowrate for cyclone Cl.
o
" ID
c
c
boundorld between downflow end upflow
80
,----.... .. .. .. "," .. , " , ,
1 \ 1 \
1 \ 1 \
1 1 1 1 \ 1 \ 1 \ 1 \ 1
gos outl et duct
core raglon
Figure 3-10 Diagram showing the flow zones in the cyclone.
81
Profiles obtained vith Small Diameter Gas Outlet
Figure 3-11 shows tangential velocity profiles obtained with
gas o4tlet configuration C2 (2.54 cm diameter and 10.8 cm
long). There was a distinc~ change in the slopes of the
curves half way between the axis and the wall, and maxima at
around 0.25 of the cyclone radius. The location of the max
ima in this case coincided with the outlet tube radius,
(compared to 0.5 to 0.75 outlet diameters with the larger
outlet).
The corresponding radial velocity profiles are shown in Fig
ure 3-12. A relatively constant inward flow in the outer
part of the cyclone anà flow in the opposite direction
within the core was again observed. The transition was
around 0.25 of the cyclone radius, coinciding with the
radius of the gas outlet duct and the maxima in the tangen
tial velocity profiles.
The axial velocity profiles for cyclone C2 are shown in Fig
ure 3-13. The transition from the downflow to the upflow
regions occurred halfway between the axis and the wall. This
coincided with the location of the change in elope of the
tangential velocity profiles. This figure also shows that
the axial velocity increased sharply within the core and
~
2.8
2.6
2.4
(latlat Il.ct
.0- ..... , , , , "
Inlat Flowrata slpm mis
~ 2.2 ' '0 ' , 'A....... , l ,'_ •••.•• ,
Clin A BOO o 213
16.20 7.76 ....
g 2.0 l ,,' -"A, ' " " , ~ ~ ,
l " •••• ,
2.75 ...J w ::-t-w ...J :z .... ....... ...J a:: .... t-:z w Cl)
:z a: t-
1.8
1.6
1.4
1.2
' ,,' " '0 R ~ , . '. .. .... .... ..... ....... 0
"À ...... " ........ 0-......... ........... A '0.-,.
./ 0............... ~ ............. A .......... /:1
/' "0 - ~· .. · ......... A o
1.0 o
0.2'~---L---L---L--~--~--~--~--....I---....I-~
0.0 O. t 0.2 0.3 0.4 0.5 0.6 0.7 0.8 o.g t .0 RADIAL POSITION. r/R
Figure 3-11 Tangantial velocity profiles vs flowrate cyclone C2.
~
CI
""
o
1.6
1.4
1.2
1.0
?: 0.8 1-4 g 0.6
~ 0.4
~ 0.2 1-4 0.0
~ -0.2 1-4
n..sUat n..sct lnlet Flowrata .Ipm mla
Clin 15.20 A 600 7.75
,O-~......... 0 ZI3 Z.75 I/!i.·····... .....0 '.: ...... -...........
L- Â.... -0------0 ( •••••••• /1 ------,R:: . ............. ----.1':1 1 ~ • A······........ . ............ ~ 1 0 3
:"1
/' :, , , , , , ~ -0.4
-0.6 Â: , , -0.8
, , 1
-1.0 0.0 0.1
--'-
0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 1.0 RADIAL POSITION. rlR
Figure 3-12 Radial velocity profiles vs flowrate for cyclone C2.
o
CD
'"
~
1.81 U 1 \
1.6 ~ \ 1 ~llel D.x:l A \
1.4 ~ '. \ '. \ ·e. \ 1.2 t- ... \ '. \ e.. \
>- 1.01-l
0.8t
O -'. \
~\ .. 'q
'"4 ' I-! . , -', ,
Q '.' - -'. , -'. , '.' 'f, ~
U
~ 0.6
Inlel Flowrate slpm mis -
U 1177 16.20 A eoo 7.76 o 213 2.76
fij 0.41-
2 0.21-
&,':., ~~ ,
o~~ I-!
~ 0.0 a: ~ -0.21-a:
"~Q~ , ...... . u .. ..
.... 0 .. ~~:.:.· ..... -A ~::r -,
-0.8 ' ---J 0.0 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 1.0
RADIA- POSITION. rlR
Figure 3-13 Axial velocity profiles vs flowrate for cyclone C2.
~
0>
"'"
o
o
85
became stronger with increased flowrate.
Profiles for Bmall vs Large Diameter Gas Outlet
Figure 3-14 shows a comparison of tangential velocity pro
files for the four gas outlet configurations (Cl ~o C4) at
a me an inlet velocity of 7.75 m/s. These plots show that
the profiles were similar for the same outlet diameter, and
that the length of the outlet did not greatly affect the
profiles. Furthermore, the velocities were similar in the
outer half of the cyclone but were noticeably higher with
the smaller diameter gas outlet in the inner regions.
The radial velocity profiles in Figure 3-15 show the almost
constant inward drift of gas from the wall towards the cen
ter, and the flow in the opposite direction in the central
region. The radial velocity was high~= for the small outlet
diameter configurations since the same flow had to enter the
core at a smaller radius. This is consistent with the
hypothesis that the gas passes into the core through an
imaginary cylinder of radius ri' and the radial velocity is
given as [vr = Q/2~rilj.
Figure 3-15 also shows the tendency for the change in direc
tion of ~he radial velocity to be closer to the ~xis with
~
2.8
2.6 Gas Outlat D..ct Dlcmatar Length
2.4
2.2 >-:: 2.0 u Cl 1.8 ...J w > 1.6 1-w 1.4 ...J z ..... 1.2 " ...J a: 1.0 ..... 1-
ffi 0.8 (!) z: a: 0.6 1-
0.4
0.2 0.0 0.1
.. 0-- ......... , --- ~ ...
dalDo sIDo
""/-----. .....::2" ,,~ '~.
OCI CC2 lIE Cl .C4
0.6 0.26 0.6 0.26 cI'. ,,~
• cr.:;::::::.~.. ······~Iil .... -:.~n__ • .... ............. -..-;:-.- --1.0 1.0 0.7 0.7
... III
... . ........ ._-.".... . -~--~
~ll lIE
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 RADIAL POSITION. r/R
Figure 3-14 Tangential velocity profiles vs gas outlct configuration for an inlet velocity of 8 rn/s.
1.0
~
ex> ."
e
1.6
1.41-
1.21-
1.01-
0.81- c-~ .. , .. , .... ''-'"'''' c .. ~~
Gas Oull B l Il..cl DlanelQr Length
OCI CC2 lIEC3 -C4
CdelDe) (aIDe)
0.6 1.0 0.26 1.0 0.6 0.7 0.26 0.7
~ 0.61-.... 1 1 • ...- ... 0-___ LI , . '. ___ ·----....;.;.==.::.=...::.::.ac -..0
;/ "" •••••••••••• • •••••••••••• ·lIE·· •••••••••••. >IL ............ li: g 0.41--' ~ 0.21-
, . .... .. ___ -.()----o---..("'":;.--- v :/ ... ····0 , ..
t- 0 0 ... w • , -' , z 02 ' . ...... - . , . .. .... ,/:Il ~ -0.4 Î ......... c/ c ciIL ..... .,/' ~ -0.6 ~I;/
-0.8 -' -1.0~'--~~--~--~--~~--~--~----L---~--~--~
0.0 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.0 t .0 RADIAL POSITION. r/R
Figure 3-15 Radial ve10city profiles vs gas outlet configuration for an inlet velocity of 8 rn/s.
o
0> ...
c
88
the short cutlets (C3, C4) than with the long outlets (Cl,
C2). The reason for t.his is that the core was shaped like
an inverted cone with the base being the bottom of the gas
outlet duct. Since the probe location was fixed axially,
the short outlet corresponded to a longer distance below the
gas exit duct, and the observed core diameter was therefore
smaller.
The axial profiles shown in Figure 3-16 ~erc ~imilar in the
outer part of the cyclone with the transition between upf!ow
and downflow occurring at around 0.6 of the cyclone radius.
On the other hand, ti~e axial velocity in the inner region
was higher with the smaller diameter outlet than with the
larger outlet since the same amount of gas had to flow
through the smaller diameter channel.
High Temperature Runs
Measurements with the pressure probe at high ~emperatures
were limited because parts of the probe were bonded with
silver solder. This meant that the probe could not be used
at very high temperatures for the length of time needed to
make extensive measurements. In order to take the non
isothermal conditions into account, the average temperature
between the inlet and outlet to the cyclone was used to
e
1.8
1.6
1.4
1.2
1.0
>- 0.8 1-
t; 0.6 0 m 0.4'· > 1- 0.2 w ...J :z 0.0 .... "-...J -0.2 a: .... ~ -0.4
-0.6
-0.8 0.0 0.1
Gas eut 1 at I:lJot Dlcmatar Length
deIDc aIDe
OCI OC2 lIEC3 .C4
0.6 0.26 0.6 2.6
-~~ ..... . ........... , "~·············lIE
0.. ";::':"""':::---"::0
~""::~
1.0 1.0 0.7
7
0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 1.0 RADIAL POSITION. r/R
Figure 3-16 \~ial velocity profiles vs gas outlet configuration for an inlet velocity of 8 rn/s.
o
CI) co
,
c
90
calculat the velocities from the presRure measurements. In
the worse case, the temperature in the outer region would be
close to the ir.let temperature, while the temperaturc in the
inner region would be close to the outlet temperature.
Figure 3-17 shows tangential velocity profiles obtained with
outlet configuration C3 (5.08 cm diameter, 7.0 cm long) for
flowrate~ of 0.6 and 1.18 standard m3jmin at room and ele
vated temperatures. These plots show that the profiles were
similar except for the high temperature 0.6 stal1ard m3jmin
run, which was lower than the others except close to the
axis. A probable explanation for the low profile ls that
this run had the highest temperature of the four shown
(1 300 K); thus the gas viscosity was highest and
consequently, the transference of rotational velocity was
least.
The radial velocity profiles (Figure 3-18) were similar in
the outer part of the cyclone except for the high tempera
ture 0.6 standard m3jmin run, which was again much lower
than the others, and indicated that the inward flow of gas
extended much cl oser to the axis than in the other cases.
The axial velocity profiles (Figure 3-19) also show that the
hottest run had lower velocity ratios than the others across
the cyclone.
e
2.8
2.61-
2.41-:0-r- 2.21-.... g 2.01--J w
1.8~ > r-
1.61-w -J :z:
1.41-.... ...... -J a: 1.2 t-.... t-:z: 1.0 t-w CD ~ 0.81-t-
0.6 t-
0.4 t-
0.2 0.0
, 1 ,
C
_.
1
, , ,
•
,
Outl et IlJot GIn VIn TIn C Ipm) Cmls) CK)
c 600 7.16 + 1177 16.20 A 600 33.00 01177 44.00
1 --+ ............ /~---~ .... + /, ... -~ ~
,... --- O::-----~â: _+ /' - ·_~---C ~ 1::., ......... . "
........ 1::.,...... A A ............
....... ~ •...•......•
1 1 _.
1
300 300
1300 000
•
0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 1.0 RADIAL POSITION. r/R
Figure 3-17 cornparison of tangential velocity profiles at high and low ternperatures.
o
co -
..
~
1.8
1.61- Out! et CU::t 1 Gin Vin Tin (Ipm) (mis) CK)
1.41- -o BOO 7.76 300 1.21- +l1n 16.20 300
Il BOO 33.00 1300 >-t-
1.01- o lIn 44.00 000 I-f g 0.81-..J g! 0.61-
l:ü 0.41--' :s 0.21-...... ëÈ 0.0 t-4
ê -0.21-0::
-OAt -0.6
-0.8 0.0
_l~ __ ..1. -'- • ..L • ..J. ..J.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 1.0 RADIAL POSITION. rlR
Figura 3-18 comparison of radial valocity pr~filas at high and low tcmpcraturas.
~
co N
e
1.8
1.6 l-
1.41-
1.21-
>-1.01-
.... ~ 0.81-e irl 0.61- c.. > 1- 0.41-w ~ 0.21-... :::i 0.0 a: ~ -0.21-a:
-0.41-
Outlet D.J:=t 1 Gin Vin Tin (Ipm) (mla) CK) -C 600 7.76 300
+ lIn 16.20 300 A eoo 33.00 1300 o lIn 44.00 000
-----~---~ Il.............. ~ .. _+~_ .... ~~:-:-_____ _ ............... ~.~
~. ~~ •••••••• I\.
""0 .. -0.6t _0.81.--.1.--.1.---'----'---'---'---1---'---1----1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 O.g 1.0 RADIAL POSITION. r/R
Figur~ 3-19 comparison of axial volocity prOfiles at high and low temporatures.
o
,~
Comparisons vith predicted Profiles
Tangential velocity profiles in cyclones are usually deter
mined by assuming an appropriate vortex law model with the
one in equation 3-1 being the most common. This equation
requires the determination of a vortex exponent and the
velocity at a known radial position (usually at the wall).
Alexander's (1949) models for the wall velocity (equa
tion 3-3) and the vortex exponent (equations 3-4 and 3-5)
are perhaps the most widely used expressions for this pur
pose. Equations 3-4 and 3-5 predicted vortex exponent val
ues of 0.5 at room temperature and 0.2 at 1 300 K for the
cyclone used in this study.
There is no fo~al definition of the wall velocity: strictly
speaking, the velocity at the wall is zer , with a sharp
drop occurring within the boundary layer. In the analysis
of flow patterns within cyclones, the wall velocity is not
usually taken as zero, but is taken to be the free stream
velocity just outside the boundary layer. Because of the
difficulty of making measurements close to the wall, the
wall velo city is usually dete~ined by extrapolation of the
measured profile to the wall, ignoring any points that indi
cate the sharp drop in velocity within the boundary layer.
This method is adequate when the sha~~ drop in velocity is
95-
observed close to the wall, but becomes subjective vhen the
decrease in velocity is graduaI.
The tangential velocity at the wall (Vtw) has been taken to
h'ive va ..... les ranging from around one to several times the
mean inlet velocity. The measurements made in this study
indicated that the velocity close to the wall was usually
between 0.9 and 1.2 times the me an inlet velocity. This
compares with Alexander's model (equation 3-3) which pre
dicted wall velocities of 1.52 and 1.07 times the inlet
velocity for outlet diameters of 2.54 and 5.08 cm respec
tively. Muschelknautz's (1972, 1980) presented a plot which
predicts values of 0.95 and 1.25 for the 2.54 and 5.0a cm
dia~eter outl~ts in the cyclone used in this study. Meis
sner and Loffler's (1978) model (equation 3-6) predicted a
value of 1.27 for both outlet diameters.
Correlation of the Experimental Data
The measurements made in this study showed that the tangen
tial velocity at the wall depended on the inlet gas velo
city, temperature and the outlet diameter. This combination
of variables suggests that a Reynolds number might be used
to correlate the wall velocity with the flow conditions and
outlet dimensions. A Reynol~ number (Rea) was defined
c
96
based on the me an inlet velocity (vi), and the hydraulic
diameter of the annulus between the outlet duct and the
wall:
(3-21)
This Reynolds number was correlated with the wall to inlet
vclocity ratio using a power law model. The resulting plot
is shown in Figure 3-20, with the regrcssion coefficient
being 0.95 and the model given by:
(3-22)
Equation 3-1 was used to calculate the local tangential
velocity in the outer part of the cyclone while the velocity
in the core was assumed to be directly proportional to the
radial position. The radius of the core region was taken to
be at 0.75 of the gas outlet radius. Equation 3-22 was used
to calculate the wall velocity and the vortex exponent was
calculated by Alexander's models (equations 3-4 and 3-5).
The resulting curve is shcwn as the solid line labeled "new
model" in Figure 3-21. This figure shows the experimental
data compared with predicted velocities using the 2.54 cm
~ 0
2.0 1
Vtw/Vln - 0.202 Reo. teg
R - 0.95
~ t-i
H ~
a yaY'ê • • 1
~ t-i _0---
~ ------,.
0
1.0 ~ 0>
0.8 ' ' ,
Œ3 IE4 REYtU.DS t-Ut-I3ER
Figuro 3-20 Wnll tnngentinl volocitY/menn inlot velocity vs nnnulus Reynolds number.
tE6
co ....
~
2.8l 2.6; /
2.4 ~ / ,/'. \~ "'Uat [).ct 1
. / \. / / \ ""-1: 2.21-
1.8 / ' • "-tii t . / .... -.. " " -1.6 / /' .... ............... '" "'
Z
' •• ' ". ... • , .. ' ". ... ........
0-4
g 2.01--1 w >
0-4 • ,...... ... .. ........
...... / ' , .. ' ". .. '-... . /
'.' ...... ............ -1 ' • " .. a: ,.iI ..... .... .. - ,. '" - . t- J' , ,.... . ...... -'" -....... Z /
'/ .•••• :-........... ,: .... --.,. ~ w" .... =- ~ CD ~.,~... • ••••••• ::-.11- ' ..
Z 0 / 1: •• ~ ... ",.8 J -, '"--0- ... -..;: ••••
0.6 /il --• Experimentai
O.4t A'l , 0.2 ( - ,
0.0 O. t 0.2
..... Alexa lder C 1949) --- Naw IfOdel - ·-Malaenar & Loffler C 1972) ---Maleener & Loffler Cvtw - vin)
-'- --L --'- , , 0.3 0.4 0.6 0.6 0.7
RADIAL POSITION. r/R
_. 0.8 0.9 t .0
Figure 3-21 comparison ot experimental with predicted tangential velocity profiles: cyclone Cl nt 300 K.
~
10 CI
o
o
99
diameter gas outlet at room temperature and an inlet velo
city of 7.75 ~/s. The other profiles shown in this figure
are: the original Alexander (1949) model with the wall velo
city calculated from equation 3-3; the Heissner and Loffler
(1978) model (equation 3-9); and the Heissner and Loffler
model with the wall velocity being equal to the mean inlet
velocity instead of that calculated from equation 3-6.
Figure 3-21 shows that the Alexander model with both the
original and the new wall velocity agreed well with the
experimental data. On the other hand, the Heissner and
Loffler models greatly over-predicted the tangential velo
cities across the cyclone. The high values calculated by
the Heissner and Loffler model can be explained by cons id
ering equations 3-9 and 3-10. For the cyclone used in this
study, D was approximately 0.04, so equation 3-9 reduces to:
Vt _rc = (0.96 to 1) Vtw r
(3-23)
Comparing this equation with equation 3-1, the vortex
exponent in the Heissner and Loffler model is approximately
1.0, which is expected only for a gas of zero viscosity and
with no friction~l effects. The vortex exponent of 0.5
predicted by Alexander's model is more reasonable and was
confirmed by the experi~ental data.
c
c
100
Figure 3-22 shows a similar plot obtained at a temperature
of 1 300 K with the same outlet configuration. In this
case A1exander's model under-predicèed the vortex exponent,
giving a value of 0.2 while a value of 0.3 fitted the data
better. The Meissner and Loffler model once again greatly
over-predicted the velocities across the cyclone radius.
Figure 3-23 is a similar plot obtained with the small
(2.54 cm) diameter gas outlet at room temperature. There
was aga in good agreement between the experimental data and
the profile predicted by the new model except ~or the point
at a relative radius of 0.25. In this case, the predictions
of both the Alexander and the Meissner and Loffler models
were much greater than the measured velocities. The expla
nation for the high values predicted by the Meissner model
was the same as above (n approximately equal to 1.0),
whereas the over-prediction of the Alexander model over
prediction was due to the high wall velocity ratio cal cu
lated for the small diameter outlet (1.52). Once again, the
calculated vortex exponent (0.5) agreed with the experimen
tal data like it did in Figure 3-21.
Figure 3-24 shows the results of another high temperature
run but with the small diameter outlet. We again see that
the vortex exponent was under-estimated at high temperature
c
2.8 l 1 \ 1 2.6; / .. ~.I Outlet D..Ict
2.41->-1- 2.21-..... u o 2.01--'
. / ' \ / l' \.
/ ' '\ ". . / \, "'-. / ' ,,"'"
1- 1.8 . ,1 ,,,-.,,,,, ~ 1.6 / / '''.. ."",.
w >
~ 14 /. , " "'-... ...... . / •...... ..................... -.1 .. - •.•.• "' .... a: 1 2· ..... ............... .... ............ ...... 1 ' .. ,.--- ... - .............. --..... .... , ....... - .................... .... 1- /.. .. ---_ • . •..• ~ ..••••. z 1 0 .. - " - ------ - .... ~ W • • •• , .- --------, .' , . --CD l, .. ', ~ 0.8 1) ...... / • Experimentai 1- . , o 6 1/ ..... ~' . "'AlaXŒldar C IQ4Q)
. Il .. .,' ---New modal 0.4 t f' . ./' -·-Melsener 8 Laffler (IQ72)
... ; ---Meleener 8 Laffler Cvtw - vin) .. -, 0.2 y 1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 RADIAL POSITION. r/R
0.8 o.g 1.0
Figure 3-22 Comparison of experimental with prcdicted tangential velocity profiles: cyclone Cl at 1300 K.
.,
... o ...
~
2.8
2.6
2.4
ç 2.2 ..... g 2.0 -l
~ 1.8
l:i:i t .6 2 ...... t.4 ~ CI: t.2 )-t
~ 1.0 C!' ~ 0.8 t- 0.6
0.4
.- 1-- ". -~ '. . . . . IT f /\ .......... .\ \ /
•• : 1 \ "':'\ '\. I f,' \, .. ~,...... . '1 , '\ ••• "
/',' ! ! ", ', ..... , ... , .. ".~ . .., " ..... : l ", •••••••• :1 .... '" .~ •••• ., ., '" ...... . Il ! ' ", '.', " ....................... . . , .""' "-., : 1 ........ '~ .........
. , " . "~ Il . • """.... ___ , il " ________ .. __ " ~-, . li If ___ ' ____ ,
fi If li/i
,
:J :1 ./ , i, il :, i ri
• experimentai ..... Alextnder \: t(49)
---New IIlOCYJI - ·-t-te1 eer.er 8 Laffler C 1972) ---Meleener 8 Laffler Cvtw - vin)
0.2 111 '.
0.0 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.0 R~IAL POSITION. rlR
1.0
Figure 3-23 Compar~son of experimental with predicted tangential velocity profiles: cyclone C4 at 300 K.
~
... o N
e
2.81 1 1 1 \ \
2.6 • j l '
2.4 Il \, >-., \ ~ 2.2 Il ...... . u . '. , o ., / ..... "
2.0 " i ......... "' ""-.... , ...... "-...... ...... -" ....... ,
1 6 L. Il : ... "" .................. :~ .. . • l" j. '''" ~: .................. .
, 1.4 II f· ,"'-"""-.. •• .......... .............--.1 ., ...... - ......--......
a: 1 2 l'1' f " -------- • ............ ...... . ---_ ....... ~ t;: : 1 --------- ---........, ru tOi 1 ---------':.-
~ 0:8 ~ l/ • Experimentai t- (} 6 1 f / .... Alexmcler (1949)
• i' --- New model o 4 K j/ -.-Melsenar 8 Laffler (1972) • f/ ---Malaenar 8 Latr'ier (vtw - vin)
0.2LM.~i--~-- ~ __ ~ ____ ~ __ ~ ____ L-__ -L __ ~~ __ ~ __ ~
0.0 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.0 1.0 RAOIFL POSITION. rlR
Figure 3-24 compa~ison of experimental with predicted tangential velocity profiles: cyclorJ C4 at 1300 K.
o
~
:3' ,
'.
(
c
104
by the Alexander model: a value of 0.2 was predicted while
0.3 fit the data better. In addition to that, the predic
tions of the original Alexander model were consistently
hi~her due to the high calculated wall velocity ratio
(1.52) •
BUHKARY
It was found that the tangential velocity profileb depended
on the wall velocity and vortex exponent. Experimental
measurements showed that the wall to inlet velocity ratio
depend on the flow conditions and the outlet diameter. A
Reynolds number was defined for the annulus between the cyc
lone wall and t.he gas outlet duct, and this number was cor
related wi~h t.he wall to inlet vElocity ratio.
In general, the new wall velocity model along with Alex
ander's vortex exponent model agreed with the experimental
lata for room temperature runs with both the small and large
diameter outlets. At high temperatures, the vortex exponent
was under-estimated by the ~lexander Dodel. A vortex
exponent of 0.3 fit the data better than the predicted 0.2.
Furthermore, the wall velocity was overpredicted by the
Alexander model for the small diameter gas outlet (2.54 cm),
while the new model gave better estima tes with both the
105
small and large diameter gas outlets. It is recommended
that the new wall velocity model (equation 3-22) be used
with the Alexander vortex exponent model to determine the
tangential velocity profiles.
c
CRAP'l'ER ..
COLLECTION EFFICIENCY STODY
c
106
CRAPTER 4
COLLECTION EPJ'ICIEHCY STUDY
INTRODUCTION
The variables affecting the performance of cyclones can be
classified into four groups:
1. Particle properties - density, size and shape.
2. Gas properties - te~perature, pressure, density, viscosity.
3. Cyclone geo~etry - inlet, outlet barrel di~ensions.
4. System properties - gas and particle flowrat~, inlet velocity, dust load.
The accurate prediction of the perforv.ance of cyclones over
a wide range of operating conditicns is understandably a
formidable task when the nuœber of variables is considered.
Detailed n~erical ~odels nave been developed to design and
predict the performance of cyclones, however, it is ~ore
often the case tb~t a si~ple easy-to-use model is required
for prelimtll<1!.ry or nun-critical applications. Many si~pli
fi cd an~lytical modcls have been developed for this purpose
and so~e of these are discussed below.
c
107
This chapter examines the performance of cyclones as meas
ured by the collection efficiency or the particle eut-size.
A reviev is presented of the existing theoretical ~odels
used for correlating and predicting the collection perfor
mance, followed by discussions of the experimenta1 results
obtained in the present study.
LITERA'l'URE REVIn
Hodel1ing The Collection Performance of cyclones
For a particle in the cyclone, the main forces acting on it
are the centrifugal force (Fe) tending to ~ovc it to the
wall and the viscous drag force (Fv ) acting in the opposite
direction. There are other forces, such as gravit y,
diffusion, thermophoresis and electrostatic forces, which
are negligible in most cases but would have to be considered
in some systems (Calvert and Parker, 1976). The resultant
of these forces determines the motion of the particle.
In this study, the gravit y force was negligible because of
the small mass of the particles, while electrostatic forces
were also negligible since the partiel es were not chargpd
and the cyclone was grounded. Diffusion and thermophoretic
forces could not be ruled out withollt some preliminary cal-
o
o
108
culations since very fine particles «44 p=) vere used in
this study. At least one model (Mothes and Loftler, 1984,
1988) takes diffusion effects into consideration, as will be
discussed later.
Studies by Talbot et al. (1980), Dwyer (1967), Derjaguin and
Yala=ov (1965), Fuchs (1964) and others, have shown that in
order for thercophoretic forces to be significant, particle
sizes must be of the order of 1 p= or less, while tempera
ture gradients must be of the order of 50 Kjcm or greater.
The temperature gradient in the radial direction had the
greatest effect on the dust separation in the cyclone. The
highest temperature gradient in this study was esti=ated to
be arou~d 100 Kjcm at the wall of the barrel with the wall
being at a lower temperature than the gas. At the same
time, less than 10 \ of the particles were below 1 pm and at
best, about 30 \ of these were estimated to be in the high
ature gradient region close to the wall. These conditions
are marginal for thercophoresis to occur and at best, the
collection efficiency WGuld be enhanced for the 3 \ of sub
micron-sized particles close to the wall. The thercopho
reeic effect was negligible for mose runs and marginal at
best, so it was ignored in this study.
A simplified force balance taking into account only the cen-
c
109
trifugal and viscous forces gives:
(4-1)
Assucing that the particles are spherical, and that Stokes
law is valid for the viscous drag on the particles, the '
force balance beco~es:
(4-2)
,
This equation is the starting point for ~ost of the theoret
ical cyclone ~odels. Theoretically, at a given radial poai
tion there is a critical size of particle (of given density)
for which these forces just balance so that there is no net
radial ~ovement of the particle. If the radial position is
at the exit duct radius, then this particle size is often
referred to as the "theoretical cut-size". If all of the
particles came in at the same radial position then the effi
cieney would be 100 t for all particles greater than the
cut-size, and zero for smaller particles. The shape of a
plot ot collection efficieney versus particle size (grade or
fractional efficieney curve) for the Ideal cyclone will then
be a step function as shown in Figure 4-1.
In practice, the particles enter at difterent radial posi-
o
100
UJ N ... Cf)
C UJ l-Cl: 1-Cf)
1- 50 a: c UJ :> 0 z: UJ 0:
~
0
1 1 1 1 1 1 1 1 1 1 1 1 I 1 1
ac tua 1 curV.
\ "1 1
1
110
Th.or.t Ica 1 curV~
:on. of r.duc.d .ffl c I.nc 'l du. to • dd'lln;, bou:'lcln; •••
zon. of Incr.as.d _.fficl.nc'l du. to
collision, flocculatlon •••
PARTICLE SIZE •
th.or.tlcal lI:ut-slz~
Figure 4-1 Theoretical vs actual grade efficiency curves (Stair.aand, 1975).
(
111
tions and many particles smaller than the theoretical cut
size are separated with the coarser particles due to agglom
eration and their radial position upon entering the cyclone.
In addition to that, many particles coarser than the theo
retical cut-size escape vith the clean gas due to secondary
flows, bouncing from the walls and short-circuiting from the
inlet duct directly into the gas outlet stream. As a
result, the grade efficiency curve tends to be "sn shaped
and the cut-size refers to the particle size collected with
50 t efficiency (Figure 4-1).
stairmand (1951) described the preparation and use of grade
efficiency curves to evaluate the performance of cyclones
and to predict their behavior over a limited range of oper
ating conditions about which the curves were prepared. He
gave experimental data for tests performed on a 20 cm diame
ter "high efficiency" cyclone and a "high gas rate" cyclone
of the same diameter (Figure 4-2). In both cases, the per
formance curves were always concave downwards and asymptoti
cally approached 100 t collection efficiency with increasing
particle size, and ~p.ro efficiency for decreasing particle
size.
Abrahamson and Allen (1986) defined a dimensionless effec
tive particle size by taking the square-root of the ratio of
the radial particle velocity to the radial gas velocity at
112
the qas outlet radius. This definition was claimed to brinq
toqether the grade efficiency curves for a wide variety and
sizes of cyclones. An important difficulty in usinq this
method is the uncertainty involved in determining the gas
and particle radial velocities in the cyclone.
The ultimate objective of theoretical cyclone studies is to
be able to predict the grade efficiency curves for given
cyclone dimensions and operating conditions. This curve
allows the determination of the overall collection effi
ciency as weIl as the cut-size. If the curve cannot be pre
dicted, it is still desirable to be able to predict the ove
raIl collection efficiency or the critical and cut-sizes.
Some studies aimed at achieving these goals are discussed
below.
The Rosin, Rammler and Intelmann study
One of the earliest theoretical cyclone studies was done by
Rosin et al. (1932). They made several simplifying assump
tions, the main one being that the qas stream kept the shape
of the inlet duct as it moved do~ the cyclone. They also
assumed that the tangential velocity was equal to the me an
inlet velocity and that the particle acceleration and the
radia~ gas velocity were negligible. The force balance in
c
(
(
113
equation 4-2, was reduced to equating the centrifugaI and
viscous drag forces resulting in:
(4-3)
They went on to show that the smallest particle that
could be collected in the cyclone can be determined by the
e::pression:
dpmin (4-4)
This diameter is usually referred to as the 100 % critical
cut-size. The main problem with using equ~'\on 4-4 is that
the number of rotations made by the gas (Ns ) must be known
beforehand or must be predicted by one of the few
correlations a"ailable (API, 1975: crawford, 1976). One of
these correlations, presented by Theodore and Buonicore
(1976) was given as:
(4-5)
where the effective cyclone volume (Vc ) is divided by the
gas flowrate (Q) to obtain the mean residence time, which is
"","
C, .... , ... tor" _n. •
.,,. .. u,. w,· ,u,.
.... -ur' "-'1i:~::l;:!.JL
•
--1%.1-
.. 1
• "
... . i~
.,"~ YiUUtl.
"'''lf.
114
~
'a ~'O
ï 10
"10 " ~so w w.., ~ :i sa
>0
10
o
TUT CU"VI 10" Ik 1 •• CYC:WHr SO '.twc&NtlT. 'VILOQTY l ,"'/cc. soua C[N$UT IH AI" AT wc.
1 1 1 1 1
1
10 20)O~SOtO ..... TCLC .. tt~
'ttfir".."u cvn. (01 hi,,. f6:ocllq qdOltC
1
,.
niT OJ .. vl 10 .. ' ... ..: .. eTCtONt. JO ""M INtn vlLoan 1&",«, ,QUO DU'I"n IN ~ .. AT ~c.
100
,0 .10
.~
C '0 • 2 tO
t so w
11 40
2'0 • '0
10
o
1/
1/
1
10 '0 )0 .0 so 60 10 , .... ,tC"C "" o.<aoflt)
HI,,. i" ,.'" qd.,.. :,,,,,, "tpfII1.,., 'u(fltNlt(. (V,.,. rI' AIt" 'f' ,.1. (rdOftC
Figure 4-2 The stairmand (1951) cyclones and grade efficiency curvas.
t
.115
then multipliE'd by vi to obtain the mean length of the path
the gas makes in the cyclone. Theodore & Buonicore also
stated that for large diameter cyclones, the number of spi
rals correlates well with the inlot ve!ocity and can be
expressed approximately as:
Ns = 1.54 ln(vi) - 0.37 with vi in mis (4-6)
Ter Linden (1949), developed a similar model to the Rosin et
al. model and showed that the largest particle that will not
be collected in the cyclone is given by ta king the radial
position (in equation 4-3) to be that of the gas outlet
duct:
(4-7)
~he main diffioulty in using this expression is in knowlng
the radial and t.angential velocities of the gas (vrg
and Vt).
The Lapp10 stUdy
Lapple (1951) showed that the 50 % cut-size r.ould be given
by an e~lation analogous to Rosin et al.'s equ~tion (4-4),
o
116
if the inlet width (S) is used instead of the cyclone diame-
ter:
(4-8)
Lapple then established a normalized grade efficiency curve
for which the fractional collection efficiency was plotted
against t~e particle size (dp) divided by the cut-size
(dp50) calculated by equation 4-8 (Figure 4-3b). This
normalized curve is applicable to cyclones with the configu
ration shown in Figure 4-3a, which corresponds to cyc:one C3
used in this study (see Figure 2-1).
The Sproull study
Sproull (1970) proposed a particle collection effidency
model of the form:
e .. 1 - e-wO (4-9)
wh.1re
w = (4-9a)
c
c
1! I~ ~ ê<i 8 70 oa. 60 • eo ;; 40 'a ~ ,:: u c .. ~ 'ü
" o
30
20
, , • •
:/
Il
117
•
Section A-A
• • 1 ••
• • • • • 1 l , • 1 1
1 1 1 ........ Il 1/ 1 lA' 1
" 1 1 1 1
. . • • 1 1
1 1 1
1 1 1 1 1
· • i !
· · : i • ~ • , 1 • : •
• , •• • • 1
1 1
/ 1 1 ~ '~ n40S 07 W 3.0 4.0 50 7.0 10.0 8 Fbrflde size mio,lOp/Dpcl
Rebtioruhip betwcen conection efticicncy and pmicle size for cyclODes oE Fig.
Figure 4-3 The normalized grade etticiency curve and cyclone configuration 0: Lapple (1951).
118
In this equation, 0 is the surface area of the bal" -lof the
cyclone divided by the gas throughput. The drift wüocity
(w) is equivalent to the radial velocity vrp in equation 4-3
with r being replaced by the cyclone diameter (de>. '1:he
drift velocity is the main uncertainty in this mod~l, and
the exponential function causes the calculated collection
efficiency to be sensitive to the variables affecting this
velocity.
The Leith , Licht 8tudy
Leith and Licht (1972), used a different approach to the
earlier researchers and attempted to account for the contin
ual back-mixing of uncollected particles due to turbulence
and secondary flows within the cyclone. They assu~ ., that a
uniform concentration of uncollected dust is maintained in
the gas flowing through any horizontal cross-section of the
cyclone. Referring to Figure 4-4a, they considered a hori
zontal cross-section of the cyclone. In time dt, all par
ticles a distance dR or less from the wall will move to the
wall and be collected. Heanwhile, particles travel a dis
'cance Rda tangentially and dz vertically. The number of
parti~les in che sector is:
c
Figure 4-4a
Figure 4-4b
c
119
The cyclone cross-section for the Leith a~d Licht (1972) model.
- • B .. ,. r-y '19561
_. St ... , r....,. (1'101
-- PrCSCfll TheOlJ
.z
comparison of the Leith and Licht model with other models.
120
(4-10)
and the number of particles removed from the sector is:
Hence, the fraction of particles removed in time dt is:
-d(np) = 2rcdR - (dR)2 = np rc2
2dR (4-11)
Integrating up to the average residence time for a particle
in the cyclone yields a predictive equation for the collec
tion efficiency given by:
E = 1 - exp[-2(~)1/(2n+2)]
where:
p d 2v (n+1) p p tw
18pdc
(4-12)
(4-13)
(4-14)
c
c
121
(4-15)
(4-16)
The three di~ensionless para=eters in equation 4-12 are: G -
a geometric design constant: ~ - a ~odified i~paction par
a=eter si~ilar to the Stokes nucber: and n - the vortex 1aw
exponent. Figure 4-4b shows a co~parison of~he Leith and
Licht ~odel with experi~ental data of stair=and (1951) and
other theoretical ~odels.
The Leith and Licht ~odel does not take into account par
ticle agglo~eration and the loading effect, both of which
improve the collection efficiency. The ~odel is therefore
likely to underesti~ate the perfo~ance of the cyclone in
non-di lute syste~. continuation of the work of Leith and
Licht led to the fo~ulation of overall design approaches
and other developments by Leith and Kehta (1973), Koch and
Licht (1977), Asla=i and Licht (1978) and Kasin and Koch
(1984).
The Deitz study
Dietz (1979, 1981) identified two other features of the
o
122
Leith and Licht model which were inadequately treated.
Firstly, although the distribution ot gas rcsidence times
within the cyclone is recognized, only the average residence
time i~ used in their analysis (the shorter residence times
can lead to lower collection efficiency). Secondly, the
Licht and Leith model is not consistent with the actual gas
flow pattern. If turbulent mixing is an important factor in
determining cyclone efficiency, then the interchange of par
ticles between the upflowinq and downflowing sections of the
cyclone must be included. Thus, by assuming that the gas is
uniformly mixcd across a horizontal section of the cyclone,
Leith and Licht ignore the reverse flow nature of the cyc
lone.
In an attempt to o~ercome the deficiencies of the Leith and
Licht model, Deitz developed an analytical expression for
the collection efficiency, based on a three-region model for
the fluid flow in the cyclone. The three regions are the
entrance region, the downflow (annular) region, and the
upflow (core) region (Figure 4-5). TUrbulence is assumed to
main tain uniform radial concentration profiles in each
region, and particle interchange is allowed between the
annular and core regions. Conservation of particles in each
regicn requires that:
·1
c
I-!-l t
1 • Oc ........
1 1
1 ..
1 1 • 1 1 ........ 1 1
2 1 1 1 " n 1 ...... 1 • 1
1 1 1 1 1 1
123
z·o
I-~
a..w 1
z· 1
i 1 , , , 1
~ 1
u~ i 1 1 Z 1
~t ! 1 -'a..w 1
-;-çw( 1 1 1 1 l , 1 1 1 ! ! 1
r···, Ile
Figure 4-5 The geo=etry for the Deitz (1979) =odel.
1 1
o
124
Region 1:
(4-17)
Region 2:
(4-18)
Region 3: ,
(4-19)
Qv(z) is the axial volucetric flowrate, rw(z) is the
particle flux to the cycl?ne wall, rv(z) is the radius of
the core region and rv(z) is the flux of particles fro~ the
annular region to the core region. Stokes' law was used for
the drag force which was ~quated with the centrifugaI force
in order to dete~ine the radial particle velocity. It was
further assuced that:
1. The radial gas velocity into the core region is constant.
2. The tangential velocity do es not vary axially.
3. A ~odified free vortex law describes the radial variation of the tangential velocity.
4. The radius of thE: core region is equal to that of the exit tube.
:
The reà~lt was a model for the efficiency of the cyclone
c given by:
where:
_
r~c~u:.rw:....+_r~v:...v~r=--+_r..:v_U~r KO = 2rvur
125
(4-20)
(4-21)
(4-22)
(4-23)
Ur and vr are the radial velocities of the particle and gas
respectively. The Dietz model agreed weIl with data
obtained from the secondary cyclone of the Exxon miniplant
(Ernst et al., 1982; Hoke et al.,1980) as shown in Figure
4-6. The Exxon cyclone had a diameter of 18 cm and was
operated (for the selected data) at up to 948 K, 10 kPa and
55 mIs inlet velocity.
The Mothes , Lorf1er study
Mothes and Loffler (1984, 1988) reported the development of
a model similar to Dietz's (1981i but with four regions
o • --.0-,-
'" w_ .... '-'" -~-<-o--~-----.... c;,._ ,,-
• ,;. .. .... •• .... nt
1)0.
. ,. ...
.. '" l'l' • ,~. . - .~ .
.... .... -•• .. .. '!II' ... ... H' : .. ~.
:h"- :". .. th ..
. ...... h.· h.·
. . --
•• • ... ,~. ... • •• • • .... n-l' U " .- ... ...
lO' •• ., :.,. .. :,. .. :,. ... .... .. ' h.' -
.. . ... Compuison bttwtfll dat-o". aM: tI~rimcct rOf SHOII'oJlI,~ CJcloot al [UN'S mialp!aal (ru J%.l~
126
,:\ _u
('[ l' ,
" • -- .. . . .. . COlipariao.'mrcn lMor7 ,ocI npcrl:atDI rOf .... 04 .... " '7_ al E .... \ ..wpla .. (na
l%.l~
i:l II
• .
i~ li •
--"
,
, ,
. . ---
, , ,
.. .. ;
Computl4D bd"Cflllhrory and npcrfllltilf fot ICCOM..ult (JdODC Il [su.", mmiplanl (nlll ... o4ll~
--
_.
•
. --- . .. ... eoaparisoa bdwua iMoI'J.04 Uptr"'.tDlrot
ucoa41Uct C)'doDt &1 Essoa" miniplard (ruD lf']~
•
•
. -- .. .. .. .. . Co.pathoa ~wtu 1Mor7'" npcrl""'1 rot ItCODd1taCt Cldo .. Il [11011°, .infplant (m n.4~
Fiqure 4-6 , Comparison of the Deitz (1979) model with experimental data.
c
127
instead of three. The new model takes into account the
friction occurring at the walls of the cyclone (which affects
the velocity profiles), and a particle diffusivity which
accounts for the influence of turbulence on the particle
separation. The qualitative results presented include:
1. The tangential velocity depends only on the radius and
does not vary axially. The radial profile is determined
by the cyclone geometry, wall roughness and particle
concentration.
2. The mean motion of the particles primarily determines
the cut of the cyclone while the diffusive (turbulent)
motion influences the shape of the grade efficiency
curve.
3. Particles must be prevented f.rom entering the upward
flow and must be deposited on the wall during their r~s
idence time.
4. Re-entrainment of particles occurs in the lower part of
the cyclone and from the hopper due to increased turbu
lence.
The physical cyclone model used by Mothes and Loffl~r (1984,
1988) is shown in Figure 4-7. The radius ra of the actual
(1
Figure 4-7
Exil cice
128
"
l,II' 1.ld
',l':'f=iC'W1\c.l,rj hl''''': I,~I'.II
I,lz-4Z .
i,lII i.1II ri
1r:-~':"""''':'''''''..l''H----' Ij--------I--'-0' . 1 i,I','1- i- C 1 j
~------~--------~~
The geometry for the Mothes and Loffler (1984, 1988) mode!.
129
c'llinder and cone cyclone was changed to ra* = (VcI'lth)o.e.
instead of changing the cyclone height (as Deitz did). This
method does not affect the radial ve1ocity, which is
important in determining the remova1 efficiency. The three
ve1oc1ty comp~nents were given in Chapter 3 (equations 3-9
to 3-12). The axial vo1um~tric f10wrate was given by:
Q(z) (4--24)
Mass balances simi1ar to Deitz yieid2d the fo11)wing expres
sions for each region:
Region 1:
(4-25)
( 4-26)
w(ra *) :. - (4-27)
Region 2:
d dz[Q(Z)C2(Z)] = -2~ra*j2(ra*) + -~~ij2,4(ri) (4-28)
j2(r~*) = w(ra~)C2{Z) (4-29)
(4-30)
with:
Region 3:
= ppX2Vt 2 (·>:i)
18Jlr i
13v
j2(1)~!ra2-ri2)-j4(1)~ri2_j3(ra*)2~ra*(h-l) .. 0
j3(ra*) = W(ra*)c3 - mw/2~ra*(h-l)
1 = h - (h-ht)/lO
assuming 10 % of gas flows through this region
Region 4:
with j2,4 given by equation 4-30.
These equations were solved for cl(z) to c4(z) and the
cc:lection efficiency calculateâ as:
(4-31)
(4-32)
(4-33 )
(4-34 )
(4-35)
_C::,.4 (.:...h-=t~) e .. 1 - ( 4-36)
The Mothes and Loffler model agreed best with their exper
imental data when a particle diffusivity of 0.0125 m2/s was
c
131
used (Figure 4-8e). The mcdel predicted the effect of other
operating parameters uith varying degrees-of success (Fig
ure 4-8a,d). The mcdel al 50 compared iavorably with the
models of Deitz (1981) and Muschelknautz (1972) ln predict
ing the shape of gr~de efficiency curves (Figure {-Sf). 1c
should be noted that in Figure 4-8f, the curve predict~d by
th~ Leith and Licht (1972) model was straight anè over
predicted the collection efficiency for small particle
size:>: a similar trend was noticed with most ·,f the data
obtained in the present study.
Effect of Dust Load on Collection Efficiency
Increasing the cIust load has two opposing effects on the
collection efficiency: firstly, it causes a decrease in the
tangential velocity and as a result decreases the separation
potential. Barth (1956), Muschelknautz (1967, 19'/0) and
measurements by Yuu et al. (197S) attributed this to an
increase in the friction factor at the \.11 in the presence
of particles. On the other hand as the dust concentration
increases, particle collisions increase and fine particles
which would not be removed individually, are swept to the
wal1s along with the larger particles. The scrubbing effect
is usual1y dominant and depends on the du st concentration as
weIl ~s on the size distribution of the fred dust.
'1, .,71'':)",' ~!~ - 1 ~ I .... u ". r ... "n .. /-
~ ';!
t' ••• 'a 1 .,-a s U',-·t~l,. -CAO_
oz c _'s· .ut. ,. o.. 0. 0'111 .-'t~ OAll' •
1 i .. l! w ,
u os , • • . .. Pa~Sln c/~ ..
E!f.ç: çf dllo:'\,ftr cf eXit pIpe en u-. ctr.~ •• ,..ey of stS':.tJ"on.
""Ç7j ..
, •• Ion .. ~ ~ •• n· a. n •• otn .. S .......
c..tcqs-'i,
.. ,. r.r-f-_~. O'It •
..~ .
Etred 01 ln. width 01 En •• ntranct on """'ICllncy of stPlratlOn.
,.In-"III 0./.'" .. -UH_ • .... en_ .... " Il .". uns'· .·Un_ ..... ... ...... ,. ., ..... u .. li
.l. ____ ~~~~::::~ ____ ~.~': ... ::n:m:J:.u::J'.
u u z " ... ,,,.l'IJCIt weaJ".m
Elttct of coefflClenl of ~tUd. "If'us-on on ln. ,tf'JCltncy of stp.lrauon.
1. , •• t.C'h ..
-â '.I""='" ~
t;·,u~.
.... t) .. .. a" .. ·.n· a •• , S'
1! o..uus-',. •• ~ j
,,,. ~
us. • U li , , • 1 ..
PutlC" SIle ""-
Eftec1 of gu UlfOug"put on th, tlflCl.ncy of stp.)/lElon.
.~
• '.n~""' • '".OH ..
S ... I.,n,.. , • c • ." ilS ", ... ,. OI-
~ 1 a..'OflU,.),. • JIf
,. • !JI
~ .. ! •
" U UI , • . .. E!ftct 01 cycrone " .. gnl on th, tlf-a,ncy 01
""'"tlon.
~
8 " ~ a a 1 .. ~ .. 5
'1 •• n-". ,. ... " .. .. ItJ"_ Il • 's· I·un .. ",,1"" ./ .... 0'" a,.to,n-'" 'JCtn'"fMiI.
......
-,,/' . //
/// ~ ,I-l ... '..... 111711
• ,1 -....... l'U)I l,' -DoM. IIUIt
;0.." ~ - .... " ........ ,.·,U' ·,~J~----~.~I~--~----·,;-----~,--~.~~.~ ..
PII'ICIt sau rI".n
Companson of VlfIOUS fNU'I.mauul mfIC"'J.
Figur-a 4-8 Comparisons of theory with experiment for the Mothes and Latfier (1984, 1988) model.
'L'
c
c
133
Ogawa (1985) analyzed the effuct of dust load on the collec
tion efficiency using a model based on the probabilities of
interchange of deposited and dispersed dusts withit. the cyc
lone. He showed that the eff.iciency depends on thb dust
load according to an expression of the form:
(4-37)
where bl is a dimensionless number and kl (m3jg) is a
coefficient d~pending on the inlet size distribution, cyc
lone dimensions and inlet velocity. bl and kl were measured
to he 0.032 and -0.0157 for a 90 mm diameter conventional
cyclone with flyash (2.06 pm mean diameter) at velocities of
14 to 16 mjs. The small negative k indicates that the co]
lect;on efficiency decreased slightly with dust load con
trary to expectations. On the other hand, in the same
study, the measured efficiency increased with dust load for
axial cyclones of roughly the same diameter.
Ogawa (1982) referred to another empirical expression devel
oped by the American PetroleU3 Institu~e (API, 1955):
[c ]0.2 Ea = 100 - (100-Eo) c: (4-38)
o
o
134
where the subscript "0" refers to a reference load arbi
trarily taken as one unit (1 gr/ft3).
A more recent correlation developed by the API (1975) was
based on plots of overall collection efficiency vs du st load
on probability - log coordinates. The model was of the
form:
pee) = P(Eo) + A log L (4-39)
where pee) and P(Eo) are the probabilities associated with
the collection efficiencies at zero loaa (Eo) and higher
loads (E), A is an experimentally determined parameter and L
is the du st loading in gr/ft3 (1 gr/ft3 = 2.29 g/m3). The
parameter A was numerically fitted by Hasin and Koch (1986)
to a polyncmial in the base efficiency:
A = 0.67 - 2.11Eo + 5.63E02 - 4.oeo3 (4-40)
Approximating the probability function by In[(l-e)/E], equa
tion 4-39 became:
In(l-e) = In[ 1~ ] 1+eo ( -1)
(4-41)
• Masin and Koch also used a correlation developed by Sproull
c
(
135
(1966) to account for the effect of 10ad on the effective
viscosity of the system:
(4-42)
Hasin and Koch used these 10ad corrections and a saltation
correction to modify the Leith and Licht (1972) model,
resulting in the expression:
•
[ ~AiG ]0.41/(n+l)
= -2.3 SF 2 LF.dc
(4-43)
where LF is the viscosity load correction in equation 4-42,
~ and G are the stokes number and the cyclone configuration
factor defined by Leith and Licht (equatioll 4-13 and 4-14),
and n is the vortex exponent. The saltatio.1 factor (SF) was
used to account for the decrease in efficiency that occurs
at high velocity as a result of re-entrainme.lt of particles
from the cyclone walls. A correlation dcveloped by Kalen
and Zenz (1973) was used to calculate the saltation velocity
and the saltation factor defined as:
with k { = 0.41 for 1 < vi/vs < 2.5 = -0.31 otherwise
(4-44)
o
136
The resulting correlation was claimed to improve the collec
tion efficiency predictions over a wide range of operating
conditions. however, with the high degree of empiricism in
the model and the scatter still remaining in the data, the
authors reconmended experimental verification for critical
applications.
Mothes and Loffler (1985) noted that the agglomeration pro
cess consists of two parts: firstly, the particle motion
leading to collisions, and se~ondly, the impact behavior
after the collision. The relative motion of the particles
can be due to several things:
1. Different terminal velocities to the wall of particles of different sizes.
2. The relative motion of neighboring particles caused by the velocity gradient of the gas.
3. Particles following the turbulent velocity fluctuations.
4. Electrostatic effects with charged particles.
The first effect is usually the dominant one in cyclones.
Mothes and Loffler analyzed the agglomeration process in
three steps: first, the deposition efficiency of fine par
ticles on a large particle settling towards the wall was
determined. second, the gas volume cleaned by a large par-
c
137
ticle on its way to the cyclone wall was determined: and
third, the change of fine particle concentration caused by
the cleaning effect of the large particles was calculated.
The resulting expression for the collection efficiency under
high load conditions (e) was given as:
e(x) = l - [l-eo (X)][l-eA(X)]
EA(x) = 1 - exp[-CV(XG).Vx(XG,x)]
(4-45)
(4-46)
where eA(x) is the separation efficiency due to agglo~er
ation, Cv(XG) is the effective vol~e concentration of the
cleaning big particles, and Vx(XG,x) is the gas vol~e
cleaned by a big particle. Vx(XG,x) takes into account the
relative velocity between the large and s~all particles, and
the deposition efficiency of fine particles on a big par
ti~le.
Mothes and Loffler showed that for a 15 PD cleaning par
ticle, the variation of deposition efficiency with the size
of the smaller particles was calculated to have a maximua
(at 2 to 3 pm). This maxim~ occurred since the impact
efficiency varied directly with particle size while the
adhesion probability varied inversely with particle size
(large particles rebound almost co~pletely after collision).
The result was that the calculated separation efficiency due
to agglo~eration also had ~axi~a when plotted against par-
o
o
ticle size as shown in Figure 4-9.
The main problem with using this model is in defining the
size of the cleaning particle. In a system with a continu
ous size distribution, there is a continuous distribution of
cleaning particle sizes and a simultaneous distribution of
small particle sizes. It is therefore not expected that a
weIl defined maximum will be observed in the plot of effi
ciency due to agglomeration versus particle size.
summary of Literature Review
It has been shown that the collection efficiencies of cyc
lones depend on the properties of the dusts, the gas proper
ties system properties, (especially the gas flowrate and
inlet dust load) , and the cyclone geometry. The large number
of variables make mathematical modelling of cyclone oper
ations a non-trivial task. The result is that prediction of
cyclone performance still depends mainly on empirical corre
lations. llevertheless, a few models based on fundamenta!
theory have met with varying degrees of success in
predicting the collection efficiencies over a reasonable range of
operating conditions.
c
" -~ >-u c .. ~OS -.. C .2 -'" ~ '" Co .. ..
0 Q2
Figure 4-9
c
139
1 1 1 c.tg/mJ C/C:et't ~t:,..~·"
, .. 150 mm .000
t. 1 SOm", b •• LSmm
2500 h. 1220'"'" Y •• Il'mls
COIl"'''''9 petllel. "'t
1000
9 •• soo ~'. o.,
SO 100 ~
0-' 0.6 o.s 1 15 2 3 , 6 8 10 20
particle size x/llm
Variation of separation e!ficiency due to agglomeration with particle siz~ (Mothes and Lo!!ler, 1985).
140
EXPERIMENTAL RESULTS AND DISCUSSION
operating Conditions
The raw experimental data are tabulated in Tables A1-1 to
Al-5 of Appendix 1. The principal controllable variable was
the volumetrie gas flowrate which directly affected the
inlet velocity, gas temperature, dust loading an~ cyclone
pressure drop. The flowrate had a strong influence on tem
perature because the flow of gas through the torch was con
fined to a range of 0.05 to 0.11 standard m3/min and the
power of the generator was maintained near its design limit
of 40 kW when used with air. The power could not be
increased when the supplementary air at room temperature was
mixed with the plasma: this resulted in a drop in tempera
ture inversely proportional to the flowrate of supplementary
air.
The maximum flowrate used at room temperature was around
1.18 standard m3/min, giving an inlet velocity of 15 mis.
The highest flowrate used at high temperature was 0.98 stan
dard m3/min, resulting in temperatures of around 900 K and
inlet velocities of around 40 mis. The lowest flowrates
used were around 0.2 standard m3/min; this was the lower
limit necessary to avoid melting the cyclone inlet duct
close ~o the exit of the torch. The highest tempe rature of
(
(
141
2 000 Kwas obtained at a flow rate of 0.194 standard m3/min
and an inlet velocity of 17 mis. The dust load varied from
0.3 to 23S q/m3 for alumina and from 1.1 to 80 q/m3 for
silica.
Correlation With DimenRionless Groups
In evaluating the performance of cyclones we can examine the
variation of either the overall or the fractional collection
efficiency with changes in specifie variables (for example
inlet velocity, dust load, temperature), or with dimension
less groups such as the Reynolds or Stokes numbers.
A common practice is to characterize the cyclone performance
by the cyclone Stokes number (stSO ) defined in equation 1-2.
The data of Wheeldon et al. (1986) and the measurements made
in this study showed that it was difficult to characterize
the cyclone by a single number such as the Stokes number.
For example, the cyclones in the Wheeldon et al. study were
predicted to have a single stso of 1.29 x 10-4 while the
measured values ranged between 0.4 x 10-4 and 1.96 x 10-4•
This variation was attributed to the variation in dust load,
and a plot was shown of stso versus du st load (Figure
1-10b). The author of this thesis thinks that the scatter
in this plot was too great to justify the lines drawn and
142
the conclusion that stso varied inversely with dust load.
Pursuing the same argument and using an analysis similar to
Wheeldon et al., it was calculated that the cyclone used in
this study would have stso varying between 1.0 x 10-4 and
2.2 x 10-4 depending on the gas outlet configuration. In
comparison, the measured stso varied between 4.0 x 10-4 and
3.6 x 10-1 , and there was no correlation between stso and
the dust load. It was concluded that a single stso for each
cyclone configuration did not adequately characterize the
performance of the cyclone in this study.
Parker et al. (1981) showed that their data could be corre
lated by plotting the product of the Reynolds number (Re)
and the square root of the inlet Stokes number (st in)
against the experimentally determined SO % cut-size on log
log coordinates. The cut-size was reported as aerodynamic
diameters (dpa ) defined as the physical diameter (dPSO)
times the square root of the product of the slip correction
parameter (C') and the particle density (pp). The Reynolds
number was based on the cyclone diameter and the mean inlet
velocity, while the Stokes number was based on the mass
median diameter of the feed du st and the hydraulic diameter
of the inlet (equation 1-1).
The inlet Stokes number (stin) defined by Parker et al. is
c
(
143
interesting in that it is based on kncwn operating condi-
tiors (dp~l' Pp' ·'i' Il. H) and can be used as a predictive
parameter if it can be co~related against the collection
eff~ ciency or the 50 % cut-size. On the ':ltth· ... nd, the
cyclo.le Stokes numbe= (st50) ls used to chal.'acterize the
cyclone and consists of independent variables (pp' vb' Ilr
de) and the dependent variahle (dp50).
Their method was tested with our data and Figure 4-10 shows
the results obtained with silica and alu~ina, compared with
the data of Parker et al. (1981). We see that our data fol
lowed the expected trend but that the slope of the Parker et
al. data was steeper. The correlation coefficient (R) ~as
0.67 for our data whereas it was 0.97 for t~e Parker data.
Further aralysis showed that most of th, correlation for the
Parker et al. data was due to the Reynolds number \~ = 0.97)
rather than the Stokes number (R = 0.~9) while the opposite
was true for our data (R = 0.71 for stin' and 0.55 for Re).
The results of these analyses are shown in Table 4-1 along
'Ii th the critical R required for significance at the 95 \
confid~nce level.
The variation ~f cut-size with Reynolds numbar is theoretic~lly
inconsistent, since the gas density term in the num~rator of the
Reynolds number inco~rectly predicts that decreasing the gas d~n-
144
TABLE C-:l,
summary of Correlation coefficients tor Dimension1ess Group study
CORRELATION COEFFICIENT
Independent Re.St. 0.5 St in. L'oc. Er<! Variables ln Re st in
y - dpai c - 0.2; d - 2
Alumina 0.67 0.58 0.70 0.87 Silica 0.66 0.49 0.79 0.91 Both 0.67 0.5S 0.71 0.85 Parker 0.97 0.97 0.59 0.60
Y = l-e; c = 0.5; d - 2
Alumina 0.63 0.58 J.60 0.90 Silica 0.51 0.37 0.63 0.92 Both 0.50 0.46 0.46 0.72
Critical R at 95 % confidence level
Alumina 0.34 0.;:7 0.27 0.38 Silica 0.40 0.32 0.32 0.44 Both 0.25 0.21 0.21 0.29 Parker 0.52 0.43 0.43 0.58
c
145
~-:~------------------~~ - -~ ~ ln o -
10 • o ,..,. c
"I:f O+J -en
+
(') o -
•
~
N
" .... -,., CI .Sl /:: ::s s:: 1/1 CI :.: o "'" CIl ~
1 CIl 'tl ..... o s:: >. CI CI:
CIl >
oa Co
'tl
o .... 1 ...
sity (by increasing the temperature for example) would lead to
higher cut-sizes. Since stin includes the inlet v~!ocity and the
gas viscosity (as does Re) and also takes into account the inlet
particle size and the particle density, it is justifiable to use
the Stokes number alone or with dimensionless groups other than
the Reynold~ number.
Considering the wide range of du st loads used in this study
and the tendency for the collection efficiency to increase
with increased load, it was felt that a loading factor
should be included with the Stokes number for correlating
the data. 1 dimen"ionless load factor Lv was defined as the
inlet volumetrie dust load: the volume oe particles per unit
volume of gas at the inlet conditions.
The rationale behind using this parameter was that the load
effect is due to eh~ in~reased number of particle-particle
collisions and the prob~oility of collisions occurring is
s~rongly dependent on the volume occupied bl the particles"
In Addition to that, the defined paramcter also takes the
temperature of the g~s Into account and for a given mass
flowrate of gas and particles, increasing the temperature
iowers th~ dust load, leading to lower collection efficten
cies.
It has been shown by other wo~kers (Alexander, 1949 for
c
(
c
147
example) and in this study that the collection efficiency
increases (or cut-size decreases) as the ratio of barrel
diameter to gas outlet diameter increases. This prompted
the definition of aecond dimensionless pa~ameter (Er = dclde) which was included with the Stokes number for
correlating the data. The cyclona diameter in the numerator
replaces that in thp Reynolds number so the combinat ion of
Stinl Lv and Er is theoretic~lly more cor.sistent than the
Re.stino.5 combination. A new separation number was defined
as:
(4-47)
Non-linear regression analyses on our data determined that c
and d should be 0.2 and 2 respectively for correlation
against the 50 % aerodynamic diameter. Figure 4-11 shows
the resulting plot for silica and alumina and for the data
of Parker using the same values for c and d. The correla
tion coefficient was 0.85 for the combined alumina and sil-
Ica data whil~ it was 0.60 for the Parker data (Table 4-1).
The correlations with alumina and silica con$idered sepa-
rately were higher than when they were combined. The model
for the combined data was:
d p 50 = 3Sn-O. 2 w~th Sn = St- .T_~0.2.Er2 1n -v (4-48)
148
,... -(1) CD -.., •
0 ... ID lB 2 8 :; N
• <3 ~ ON •
~=i 0
--0 • • • <3d1 a:UlD.. 0"0 0:
0<3+ '41: <3~~ <39 0
ft i :> 'a <1
+ 8~ + + + t <l' 't:/ .t +
++ + J + + 0
o • o
N 0
o -0
0
-
++
+
-·b -.
• o (')
• • - o
'D L-W . 0 > -l .
C ,.J
en
• CI
"" CI ::s '0
J:
"" o ,Q
~
~ ~ CI ,Q JO ::s s: s: o .... "" e ~ Co CI (Il
~ ., 'Oc.
... ... 1 ...
(
(
c
When the overall collection efficiency data were studied
instead of the 50 % cut-size, it was found that the penetra
tion (l-e) rather than the efficiency (e) should be used for
the log-log plot. There was much scatter in the plot of
penetration vs the Reynolds-Stokes number combination used
by Parker et al. as shown in Figure 4-12.
The new separation parameter showed a much st ronger rela
tionship with the penetration and was best correlated with c
a~d d (in equation 4-47) being 0.5 and 2 respectively. The
resulting plots are shown in Figures 4-13 and 4-14 for alu
mina and silica respectively and the corr~lation coeffi
cients are given in Table 4-1.
Effect o~ Operating conditions on Grade Efficiency CUrvos
The grade efficiency curves are usually more useful for ana
lyzing the performance of cyclones since they show how the
efficiency varies with particle size and can be integrated
to give the overall collection efficiency. They are also
use fuI for evaluating how weIl a theoretical model works,
since a theory which accurately predicts the shape of the
grade efficiency curve is also likely to successfully pre
dict the effect of changes in the operating conditions.
Three figures of grade efficiency curves are discussed here
~~
I.OOL~--------------------------------------------~
o
OAlunlna ASlllca
R - 0.60 .-. A A
Cl "'''' '" 0 ,6 '" '" o ~ 0 ~A - 8 '" 0 0
Ct
::: 0 Il' (J '" '" '" '" !li 0",-" 0 0.
0
0 '" 0 '" 0 ~ ft 0 '" ' 0- '" <>.r"" S. 0 _ ~ '" - ~ ~o~ _ ~ 0 "co A 00 ~ ·0.10 00 A Z 0
8 0 0 ~ 0
i o ot ' ", , , , , , , , , , ft 1
• 103 t04 t05 6xt05 Re· eSt In)O.6
Figure 4-12 penetration vs Reynolds number-(stokes number)lj2 for both dusts.
~
1.00, ..,
,.., a a -~ .... W
1 -..., Z 0.101-a t-f
;
AllIlllna
c OCI cold " ~Ct ~t
'" ~ CC3 hot c .......... ~ ~ li( C4 cold
.N:::....k f + C4 hot
~~ë/!~A + 0 - 0.6 ~~KO ~ d-2
00 c R - 0.00
49 ,.",
++~
0.01' ,,' • 1 0
-1 •• " pl
, , ft
1 • "pl ro '''11'
st'n.LyC.Erd 102
Figure 4-13 Penetration vs separation number tor alumina.
~
-ur -
152
N 0 -
+ j"
o .(.lI
% • cs
u ooi
0 ~
O<l . - ooi c:I
't;<l ,. 0
./: <l
II ... L.. ,. W CI
0 • .Il 0 El
o P<l > ::2 ...J s::
O:ll<l • s:: C 0
ooi o+J ~
CI) CI ,. - cs ~<l c.
CI c:I
<lI c:I >
<lt
s:: 0
ooi
SI ~ 1J 1J 10 cs
fi 8] 8] • • ,. ON 0 ~
CI • 1 • s::
--~~ - CI (/) UUUU Cl1J c::: 1 Ilo
O<lll+ . 0 - ... ri
• 1 ... 8 0 - CI - 0 ,. • • • ::2 - 0 0 C'
[001/;;3-1] 'NOI18~!3N3d ooi ~
~ ~
l00t- lK-·_·_·)I{_·- ---- .-~._ _--- -::-:,.-_ ..... ·u - -----~ .,. .. ---- -0---- - - - --
00 1 /" .......... .---N ' .. ...".-/ .. .,/ • 80 . + ,,,0",,..,
>-u 70 1 1 / .. / m • , 1
I-t
60 1 / " / u I-t
H: . , P / w
60 1 j Ij RLn Vin Tin Cln eff Z 0 40 l' f/ No. mis K g/m3 Z I-t t-U :JO ! fI 0 SAOB 3 2Q5 4B 73 w -' J )1{ SAOQ 15 295 4A 00 -' 0 20. + SAZ8 15 1664 50 86 u
IO~ L 1 <> SA29 17 1836 3 61
al.. j, a 2 4 6 8 10 12 14
PARTICLE SIZE. 1..1111
Figure 4-15 Grade efficiency curves showing the effects of temperature, inlet velocity and du st load.
-(Il Col
154
to illustrate some of the trends found in this study.
Figure 4-15 shows four grade efficiency curves obtained with
silica at the conditions shown in the legend. The overall
and fractional collection efficicncy increased as the curves
go from right to left and from bottom to top. The right
hand side of the curves pass through points around 30 ~m and
are not extrapolated as they might appear to be.
Runs SAOS and SA09 in this figure showed that for similar
temperatures and dust loads, the collection efficiency was
significantly higher at the higher inlet velocity for par
ticle sizes up to around 10 ~m and were both close to 100 %
above 10 ~m. Runs SA09 and SA2S show that for the same
inlet velocity and similar loads, the efficiency varied
inversely with temperature. The difference was not as dra
matic as the velocity effect, and was most significant
between 1 and 6 ~m.
Runs SA2S and SA29 in the same figure illustrate that
increasing the dust load resulted in significantly higher
collection efficiencies. The curve obtained at the lower
dust load (SA29) did not approach 100 %, but leveled off at
around 95 %. The largest differences occurred between runs
SA09 and SA29 and showed that for similar velocities, the
combined effect of two favorable conditions (low temperature
~ ~
toot- ~ n----A----~------------~""n-n---~ .. -/Jr9- ".......... .•........ ................................... .. ............. ,.,::... ---.----.--.
001-PC'" .,..,-' _. '-'
fJr-o-:t N
r~ •
~ Il RLn Vin TIn Cln eff .... 00 u No. mis K g/m 3 Z ....
~ 60 o AA43 16 298 1 89
B 40 A AA48 16 298 4 93 ....
~ 3J c SAil 16 298 6 87
lIE SAf6 16 298 f 78 20
10 ~ c,
o,ojl~ 0 2 4 6 8 fO f2 14
PARTICLE SIZE. f-ITl
Figure 4-16 Grade efficiency curves showing the effects of partic1e type and dust load.
-(Il (Il
156
and high load) resulted in much higher efficiencies th an the
combined effect of unfavorably high temperature and low dust
load.
Figure 4-16 shows grade efficiency curves for runs obtained
with silica and alumina at room temperature and agas flow
rate of 1.18 standard m3jmin. The efficiencies were rela
tively high and the grade efficiency curves were almost
identical (except for run SA1S) because of the favorable
conditions of low temperature and high gas flowrates.
Lines AA43 and SA1S show that for a dust load of 1 gjam3,
the efficiency was higher with alumina for all particle
sizes as expected by its higher density. The four lines
show that with silica, the overall efficiency increased 9 %
(going from 78 to 87 %) as the load went from 1 to S gjam3,
while it went up 4 % for a similar increase in du st load
with alumina. In general, the load effect was larger with
silica than it was with alumina, and the silica grade effi
ciency curves were lower than the alumina curves. This is
consistent with the premise that the load effect depends
largely on the volume occupied by the particles.
Figure 4-17 shows grade efficiency plots obtained with alu
mina at high temperatures and at a flowrate of 0.213 stan
dard m3jmin. Run AA48 and AC01 were obtained with the
~
N ~
>-
~ .... (--~ a ....
~
-- -----l lOO [ ~... ,. .. : . .!!.:!::.-. ~'""':~~:;'--~;;..::o.~.oo.::... ... _ .... '
l " ." ................. . •
001- /;).:9 ao 70
00
60
40
.'~ ù :, , :,
'J!., lb' . ~
li • 1
li :li 1- Il
li
RLn No.
o AA05
A AA48 rl ACQl
li( AD12
Vin rn/a
16
17 17 16
Tin Cln aff K 91m3 Z
1773 18(Y'1
1803
174::1
2\ 77 36 84
35 84 20 84
2Ot- '.:
lOt- i/ 0~.~o~-----~-------:6----~8----~10~--~12~--~14 024
PMTICLE sr:l:. J-m
Figure 4-17 Grade efficiency curves showing the effects of outlet dimensions and dust load.
~
-ln ~
158
5.08 cm diameter out let and outlet J.engths of 10.8 and
7.0 cm respecti~ely. The curves and the overall collec~ion
efficiency were the sa~e, showing that the outlet length did
not notice"lbly affect the performance of the c~·clone. On
the other h~nd, the outlet diameter had a seronger effect on
the collection effici~ncy as illustrated ~y line AA05
(5.08 cm diameterj and AD12 (2.54 ~~ diameter).
O~her comparisons of grade efficiency curves could be made
for other operating and geometric vaciabJ.es but the discus
sion becomes too exhaustivp. when a large number of data are
being analy?ed. At this point, it becomes cl~ar why it is
~aluable t have a theoretlcal model which accurately pre
dict~ the grade efficiency curves ~ver a wide range of
operating conditions.
Compariaons With Predicted Grade Effi'::i1lDCY CUrves
The exper::~ntal grade efficiency data were com~arpd wi~h
tha predjctions of the models of Rosin et a~. (1937.), Lapple
(1951), Sproull (1970), Leith and Licht (197 2), Masin and
Koch (1986), Deitz (1981), anù Mothes and Laffler (1984,
1988) • r'lgure 4-18 shows the data obtained for one exper
iment compared with the predictions of the theoretical ~od
els- The legand shows the type of particle, \ohe experimen-
~
N
•
~ .... U .... Hi z o ....
~ 8
l00 l -~.~=~-•• .,....-- - - - ':':':":"ft ...................... ::: ·!lI. 1 - - -
/ ......... -..,..-.- --.. .. ..... ----- -;"...-- 'li __ .---. .---
00 L / ..... -;:;,-- __ .-r . __ .. ..,....-.
BOt- / j';:..---;>,/ .... ........... .... ~ ;'/ ,: ,
70l- // /,:1/ , .. ~./ , 1 : ,/
, ! : 1.
6Ol- 1,/,' /y 6Ol- ri / 1
1 .~
-10 l- -'1 ! .1l 3Ol- J ;: ft
\ //. . ," 2Ol- 1 I~r" 10 l- ?,~ ...
( .. ' ~
aL.' • '
• 5111 ca. 17 mie • 1836 K.
S/i2Q
3 g/m3 BI %
• Experlr:lllC"ltel Date ••••••• Roeln et cl. (IQ'J2) -. - LDp/lle ll96l) - - Sproull (1070) ---- Lai th 4 Llcht (\072) -Haaln 4 Koch (1084) ---- Del tz (W81l --- Mothes 4 Loffler (1B84)
a 2 4 6 8 10 12 1-1 PARTICLE srzE. pm
Figure (-18 Grade efficiency cu~ves showing comparison of experimental with prcdicted data for poor opcrating conditions.
~
-01 <D
160
tal run number, inlet velocity, dust load, inlet temperature
and overall collection efticiency. For this experiment,
there was wide disagreement amongst the predictions of the
various models, with th~ ~itz model agreeing best with the
experimental results.
Figure 4-19 is a similar plot for an experiment a~ room teM
perature, with alumina. The hi1her particle density and low
temperature in this case lrsultcd in a higher overall col
lection efficiency (93 %). Furthermore, the predicted grade
efficiency curves agrp.ed better th an in the previous case
and are cl oser to the experimental data. The curves pre
dicted by the Leith and Licht Dodel and~' the Masin et al.
model were usually flattar th,m the other models .md usually
overpredicted the efficiencies in the small part1cle size
range. In general, it was found that the agreement amongst
the moè,ls was best under favorable operating conditions
(hi"" overall collection efficiency) and worst for poor
operating cor~itions.
C~Apariaona wit~ predicted OVerall Collection Efficiencieo
In ord9r to make a better comparis~n of how weIl the models
worked over a wide range of operating conditions, the pre
dicted overall collect.on efriciencies and 50 % cut-sizes
~
N
•
~ I-t c.J
~ (5 ....
~
....... .:.:.::.:.:.. -'I:"'Z.---:""I.-----------~ . .;~.:_.a~", ,-IIIIt'lii __ " Z,,,""""':::" :,,"';I~' - - 11--.;....--.v~ '- ..... --- __ ' . ;;..- --. . ,' ....
1 ex}
00
80 'ft ./ /,.//
70 t- 1;' !4~" ''fIl Alunlna AA46
16 nt/a. 3 glm3
300 K. 03 r 60H / ~l 50 ri! ,IV • Experimentai Data 40 rI . ······Rosln et al. (1932)
'i -'-L~ple(I001) h ~ - - Sproull (1970)
~ ,t -"- Lei th 4 Llcht (1972)
~() i~ - Hasln 4 Koch (1984) ~ ----Caltz (1981)
10 .1/ --- Mothes 4 Loffler (1984)
OIJr~----~----~----~------~----~----~----~
30
o 2 4 6 8 to t2 14 PARTIa..e SIZe. f-IITI
Figure 4-19 Grade efficiency curves showing comparison of experimental with predicted data for good oparating conditions.
e'\
-'" o
162
were plotted against the experimentally determined values.
The original assucptions made in deriving each model was
used along with Masin and Koch's (1986) approximation to the
load correction of the API (1975), (equations 4-40 and
4-41).
A performance index similar to that used by Rudnick et al.
(1986) and Leith (1987), was used to asses how well the
models predicted the experimental overall collection effi-
ciencies. The efficiencies were transformed into the number
of transfer units (N) defined by:
N = -ln P (4-49)
where P is the penetration (1-e). This transformation
serves the purpose of giving equal weights to the same per
centage differences at low and high efficiencies. Troe per
formance index (PI) was defined for each model as:
PI = I(Nm-Np)2 ~ I(A2) ( 4-50) nm nm
where Hm and Np are the measured and pred~cted number of
transfer units, and nm is the number of measurements made.
The performance index can be shown to be made up of two
parts: the variance of Ais:
(
n-1 (I(â»2 n(n-1)
163
(4-51)
where â avg is the mean difference between Nm and Np. For
large n~, equations 4-50 and 4-51 qive:
(4-52)
This indicates that PI consists of a measure of t~e average
difference between Hm and Np (âavg2), and a measure of the
scatter about the parity line of the theory vs experiment
plot (oô 2 ). The ~erformance index varies inversely with the
>-ccuracy with which the ~odel predicts the data, so the best
mcdal should have the lowect index. The resuîting plots are
disc~ssed in the followinq sections and the performance
indices and regression coefficients are summarized in
Table 4-2. The colle~~ion ef~iciencie~ are plotted instead
of the penetrations si~ce collection efficiency is the more
~h~ Lcading Et!ect
7he experimental efficiency was plottp.d against the dust
0
164
TABLE 4-2
summary ot Pertormance Indices tor Collection Etticiency Modela
Model Method* R
Rosin et al. (1932) a) 0.325 b) 0.536 c) 0.511
Lapple (1951) a) 0.264 b) 0.524 c) 0.493
Sproull (1970) a) 0.142 b) 0.409 c) 0.293
Leith & Licht (1972) a) 0.544 b) 0.581 c) 0.700
Masin & Koch (1984) a) 0.544 b) 0.719 c) 0.701
Deitz (1979) a) 0.524 b) 0.644 c) 0.693
Mothes & Laffler (1984) a) 0.720 b) 0.742 c) 0.886
Modified Mothes & Laffler 0.892
* a) mod&l with no load correction b) model with API (1975) load correction
(eqn. 4-39) with A given by eqn. 4-40
PI
0.517 1.006 0.301
0.791 0.744 0.284
1.045 2.7911 2.224
0.261 1.448 0.380
0.261 0.231 0.377
0.694 0.790 0.214
0.451 0.816 0.089 0.085
c) model with API (1975) load correction and A = Ae (Fig. 4-20)
c
165
load on probability-log scales (as in the API study) giving
the graph shown in Figure 4-20. The general trend of effi
ciency increasing with load was observed. The slope of the
regression line through the data was 0.26 and was taken as
the experimentally dete~ined load correction exponent (Ae).
The slope is dimensionless assuming that the reference load
is 1 g/m3 • The value of 0.26 for Ae compares with the
values determLned from equation 4-40 where A varied between
0.67 and 0.19 as the efficiency varied between 0 \ and
100 %. The performance index was usually lower when Ae was
used, compared to when the A from equation 4-40 was used
with the models tested.
The Rosin et al. Hodel
One of the main requirements for using the Rosin et al.
(1932) model is that the number of spirals made by the gas
in the cyclone must be Known. Particle deposition patterns
on the walls indicat~d that the gas made at least two rota
tions in the upper part of the barrel and one to four more
turns close to the bot tom of the cone for a total of three
to six spirals. Equation 4-5 predicted that the number of
spirals would vary between 5.0 and 6.5 and equation 4-6 pre
dicts 0.7 to 5.5 spirals for the range of flowrates used in
this study.
~
00.0
97.6 N
• ~ 00.0
t-4 U t-4
~OO.O
Z "0 o _
~OO.O 70.0
60.0
o alunlna cold <> .1 1 ICXJ co Id C alunlna hot - 1011 val • • "alunlna hot - hlgh val. + slllCXJ hot - 1011 vsl. • si 1 ICXJ hot - hlgh vol •
• o 0 •
• <> ----o • • <>~.....---.
• n c;-; <> -- -00 C C+
<>,
• • • + +
C
g
+
slope Cf\,) - 0.26
60.0 1 , , , ft , , , ft , , , t 1 0 , , , , , ft 1
0.3 1.0 10.0 100.0 300.0 INLET OOST LOAOING. g/m3
Figure 4-20 Experimentally measured collection effic!ency vs dust loading.
~
-Cl Cl
c
167
Figure 4-21a shows the experimenta1 overall collection effi
ciencies plotted against the efficiency predicted by the
Rosin et al. model using the more fundamental equation (4-5)
to determine the number of spirals in the cyclone. The
loading effect was not taken into account in this figure.
We see that there was much scatter in the data and that the
predicted values were generally lower than the experimental
values. The performance index was 0.52.
The Hasin and Koch load correction model (equations 4-40 and
4-41) was used with the Rosin model to give the plot shown
in Fi~Jre 4-21b. This correction resulted in the calculated
efficiencies being higher than the experimental efficien
cies. The agreement was better when the experimentally
determined Ae (0.26) was used instead of equation 4-40.
This is shown in Figure 4-21c where the performance index
was 0.43 in this case.
The Lapple model
The Lapple (1951) model was based on a normaljzed grade
efficiency plot (Figure 4-3) with the 50 t cut-size being
the same as that calculated for the Rosin et al. models.
The agreement betv~en the experimental and calculated effi-
e ~
100 1
cuolcna ~I.try
o CI - cold li! OO~ CI - hot
+ ca - hot N 'IJ. C3 - hot
• c C4 - cold
ti li C4 - hot
iD eo A-a .... R - 0.32 u PI - 0.62 ....
Hi
o .0(".61. IJ. Y II1II •••
Il 7--" (f/JO C • ~ + + IJ.
• - • 0.-(J C C
~. c+
~ 70
• y '" li q. l(-o _ Cl
00 ~
.... ~ Q.
IJ. li
00
00
o 0
'lJ CD C
60 ~K ___ .....L ___ --JL..-___ ..L-_
60 00 70 eo 00 100
EXPERltverrAL EFFIClEOCV. %
Figure 4-21a predicted vs experimental overall collection efficiency for the Rosin et al. (1932) model with no load correction.
~
lm. cuo1ona QlnlWtry OK lE lE.o'-~ ~
o CI - cold ~ fil; •
oo~ CI - hot
o lE-' '=1/+
+ C2 - hot .0 '. 7c:ff D
N A C3 - hot
OEA 0 0 0
ci 0 C4 - cold
0
• C4 - hot lE lE lE cV
§ 00 R - 0.64 lE • A;/ • D
8 PI - 1.01
~ 70~ // D
~ A
u .....
~ n. BO
A - 0.67 - 2.11Eo + 6.63EQ2 - 4.0E03
0060 00 70 8) 00 lm
E>.?ERltENTFl. EFFICIel::Y. %
Figure 4-2lb Predicted vs experimental overall collection eiCiciency for the Rosin et al. (1932) model with A.P.l. (1975) load correction.
~
-0> .D
@ ~
100 1
A - 0.26 lIE. lIO li( R - 0.51 . ~~ PI - 0.00
001-.. ~~. []
• 00" Q [] + + 11.~ ~
N ri' 016/ g"D + D • ~
lKl .... • 0 11&
ifi Il [] .... • U .... n/ o 0 lb li( []
fi) 70 Il cyolona 1-u geomatru ....
~ o CI - cold II( CI - hot n. 00 + c..~ - hot Il C3 - hot
[] [] C4 - cold • C4 - hot
1/ 60
60 00 70 lKl 00 \00
EXPERltENTFL EFFIClEOCY. %
Figure 4-21c Predicted vs experimental overall collection efficiency for Ro~in et al. (1932) model with A.P.I. (1975) load correction (A = 0.26)
-... 0
171
ciencies was again best when the experimentally determined
load exponent (Ae) was used with the load correction mod~l
of equation 4-39. The resulting plot is shown in Fig-
ure 4-22. Furthermore, the Lappl model predicted the
experimental data with roughly the same degree of accuracy
as the Rosin et al. model Figure 4-21c. The performance
indices were both around ~.3.
The sproull model
The predictions of the Sproull (1970) model (equation 4-9)
along with the load correction of equation 4-39 and Ae are
shown in Figure 4-23. In thi~ case, the efficiencies calcu
lated for runs at high temperatures were distinctly higher
than the e~~erimental values. On the other hnnd the room
temperature predictions agreed rensonably well with the
experimental data. The large deviations at high lempera
tures we~e due to the higher velocities (for a given mass
flowrate) being squared in equation 4-9a.
The Leith and Licht model
Th~ efficiencies predicted by the Leith and Licht (1972)
model (equation 4-12) with the load correction of equation
~ ~
100 1
A - 0.26 R - 0 • ..0 -Jt9/ • PI - 0.28
001- · ~.O •••• "!..~ •• N o.... ~ + +
"~80 + •
~ o· 0 0 0 eo •• 0 • ..... . A 0 [leP 0 u • .....
~ • 0. 0 70
~ 0 cyclone
A geaœtry .. ~ --
~ OCt - cold • CI - hot a.. 00 + C2 - hot
0 A C3 - hot o C4 - cold • C4 - hot
1/ 60
60 00 70 80 00 100
EXPERUENTfl. s=FIClel:Y. %
Figure 4-22 Predicted vs experimental overall collectior. efficiency for La~ple (1951) model with A.P.l. (1975) load correction (A = 0.26).
-" 1\)
e ~
100, li li li( ~p. r+ill1 +
A - 0.26 .... V R - 0.29 li il 0 PI -~2.22 ~ li 0 C
-. li OO~ ;e 001- li o 0 C li o 0 :r ..
J o c
o 0 •
t n/ 0
m c c .... u .... lb
70
~ c
c:uolone gaanatry ....
m OCt - cold li CI - hot
0- 00 + C2 - hot ~ C3 - hot C C4 - cold • C4 - hot
1/ 60
100 60 00 70 00 00
EXPERItENTFL EFFIClEOCV. %
Fig. 4-23 Predicted vs experimental overall collection efficiency for Sproull (1970) model with A.P.l. (1975) load correction (A D 0.26).
-'" (..)
lU
4-39 are shown in Figures 4-24. The agreement b9tween the
calculated and experimental values were not as good as with
the Rosin et al. and the Lapple models. The Licht and Leith
model tended to overestimate the collection efficiency at
both low and high temperatures.
The Hasin end Koch model
Figure 4-25 shows the results obtained with the Hasin and
Koch (1984) model (equation 4-43). The load correction in
this case was given by equation 4-39 and was accompanied by
a saltation correction as discussed in the literature
review. These corrections tended to overestimate the col
lection effic.Jncies when either A (from equation 4-40) or
the experimentally determined Ae (0.26) was used.
The Deitz model
The graph obtained from the Deitz (1981) model (equa-
tion ~-20) along with the load correction of equation 4-39
is shown in Figure 4-26. The load-corrected efficiencies
obtained with either the calculated A (equation 4-40) or the
experimental Ae (0.26) was better than for the other models
discussed so far. This was not surprising since this model
o 0
100 1
A - 0.26
• Il ~~~11 + R - 0.70 PI • 0.38 Il lB~ • Il Il Il i\'llltllElflI(i P+ 0 001- ($> • .e Pt. 9>. C/
N ~II • ~ A ~ 0
• Il A O~~ • ~
Il 80 • t-4 A u
t-4
~
~ 70
CUOICX'l9 geallstry
t-4
~ o CI - cold • CI - hot Il.. 00 + C2 - hot A C3 - hot DC4-cold • C4 - hot
1/ 60
50 00 70 80 00 100 EXPERltENTFl. s=FICIENCY. %
Figure 4-24 Predicted vs experim~ntal overall efficiency for Leith & Licht (1972) modal with A.P.I. (1975) load correction (A a 0.26).
-.... (Il
~
100 1
CllPIc:v-. get F 1 ti'\l
o CI - cold • 00 f.W CI - hot
+ C2 - hot .. .A C3 - hot
• D C4 - oold
~ • C4 - hot • 80
R - ~.72 • M u PI - 0.23 M
~
~ 70r /'
M
~ eo"
A - 0.87 - 2.IIEa + 5.C3EQe - 4.0e03
mK ~
m eo 70 80 00 100 EXPERllENTFL EFFICIecV. %
Figure 4-25 Predicted vs experimontal overall efficiency for Masin & Koch (1984) model with A.P.l. (1975) load correction. (A - 0.26).
~
-" C1l
~
100 1
A - 0.2C 0 R - 0.e9 :<J~ll PI - 0.21
001-IIi
VO 0
Il 1l0~~~ ~ N Il.':8>0++ • o ~ 1l0' 0 Il
~ Oll 1l~~1l0 • ao t-t 0ll :QA 0+ u IV t-t :/ . ~
70 Il 0
m A • CUOlone u ()QOmBtry t-t
~ OCI - cold • Il CI - hot 0... :rl + C2 - hot
0 A C3 - hot o C4 - cold • C4 - hot
1/ 60
60 00 70 ao 00 100 EXPERltENTfL EFFICIEflCV. %
Figure 4-26 Predicted vs experimcntal overall efficiency for the Deitz (1981) model with A.P.l. (1975) load correction (A a 0.26).
o
-.... ....
178
takes into account some of the inconsistencies of previous
models as discussed earlier. However, it was observed that
the efficiencies calculated for the runs with the small
diamgter gas outlet (C2 and C4) were noticeably lower than
for the larger diameter outlet. At this point, this was not
too much of a concern since the larger diameter is the more
standard size for cyclonen.
The Hothes and Lottler model
Figure 4-27 shows the collection efficiencies predicted by
the Mothes and Loffler (1984, 1988) model plotted against
the experimentally determined values. This model was given
as equations 4-24 to 4-36 in this chapter. ~~~tion 4-39
was again used for the load correction nlong with Ae' The
agreement between the calculated and experimental values was
better than for the,other models. as reflected in the lower
performance index of 0.089.
Several ~odifications were m~de in an attempt to improve the
predictions of the original Mothes and Loffler model. , "
Firstly, it was shown in Chapter 3 that Mothes and Loffler
used a tangential vclocity model (equation 3-9) that consis
tently over-estimated the velocities measured in the present
study. The Mothes and Loffler velocity model was thus
8 0
\00 1
A - 0.28 R - 0.89 :~~iI + PI - 0.089 ,. .
001- ~ .~~.~QJI .Q~"9> + N
0°· .'i (~o. •
~ 80
o~~ H U • II H
~ 70
~ Il CUOlcna gaonat l1l
H
~ OCI - cold • CI - hot
D- 00 • + C2 - hot Il C3 - hot II C4 - cold • C4 - hot.
t/ 60
60 00 70 80 00 100 EXt~ItENTfl.. EFFICIBCV. %
Fig. 4-27 Predicted vs experimental overall efficiency for the Mothes & Loffler (1984) model with A.P.l. (1975) load correction (A a 0.26).
, , ,
" ,
,
oc • ,
, " " ,
, "
" • >
" .. • \
~
' ~ .. " , ,
c
180
replaced with the one derived from the experimental data
obtained in this study (equation 3-22). Alexander's models
(equ~tions 3-2 and 3-5) were used to calculate the vortex
exponent and the tangential velocit~' at the boundary between
the inner core and the outer vortex. The diameter of this
boundary was taken to be 0.75 of the outlet duct diameter,
instead of the actual outlet diameter.
Another modification was to calculate the particle diffusi
vit Y instead of using a fixed assumed value. Mothes and
Laffler estimated that the particle diffusivity was between
0.00625 and 0.2, with a value of 0.0125 working best with
'cheir data. This was cOIr:lared with the range of 0.05 to
0.01 found by Abrahamson (1981). Weinstock (1978) showed
that the particle turbulent diffusion coefficient could be
given by the expression:
[m-l]vo'Lo
Dt = m 4'11°.5 (4-53)
where m is a constant taken as 5/3, vo ' is the root Mean
square fluctuating velocity and Lo is the outer scale length
of the turbulence. Abrahamson (1981) showed that vo ' could
be taken as approximately O.lvtw and 10 as 'IIrc. He also
showed that for the particle sizes used in this study, we
can ignore the correction for diffusivities of larger par-
181
ticles which do not follow the gas flow completely. These
relationships were used to calculate the particle diffusi
vit Y for each expcriment. The calculated values ranged from
0.004 to 0.04 under the experimental conditions used in this
study.
The modifications discussed above were applied to the Mothes
and Laffler model and used along with the A.P.l. (1975) load
correction (equation 4-39). Figurs 4-28 shows that the data
was symmetrically distributed about the parity line and
there was no segregation of the data according to cyclone
geometry or operating temperature. The maximum deviation
between predicted and experimental efficiencies was around
8 %, which was reasonable considering the complexity of the
flow within the cyclone and the wide range of operating con
ditions. The performance index was 0.085. These factors
make the modified Mothes and Laffler model the most success
ful of the models tested for predicting the overall collec
tion effiencies in this study.
SUHHARY
The conclusions drawn from the experimental study regarding
the collection efficiency dnd cut-size are summarized as
~ ~
100 1
A - 0.26 Rf - 0.89 .~~rr .. + PI - 0.1:85
001- ""'IVoy • of
•• ·C};D ... ;~cl1I N • .L{~(p + • o Of!
~ 80 o· -Vo!!'·01 .... O· li" A u .... _/ D
~ ~
70 A CUOlone
gElaIIBt ru 1 U .... o CI - cold
~ • • CI - hot 80 + C2 - hot
A C3 - hot D C4 - cold • C4 - hot
1/ 60
60 80 70 80 00 100 1-'D?6813c EXPERltENTFL EFFICIBCY. %
Fig. 4-28 Predicted vs experimental overall efficiency for a modified Mothes & Loffler (1984) model with A.P.l. (1975) load correction (A = 0.26).
-Cl> -~
182
follows:
1) The overall collection efficiency varied inversely vith
temperature for the same inlet velocity and dust load.
This can be attributed to the increase in viscosity with
temperature.
2) The efficiency increased with dust load and the load effect
was stronger at high temperature than at low tempera-
ture. The load effect was also strongest at low loads
and decreased as the load increased.
3) The efficiencies obtained with the smaller diameter
!2.54 cm) outlet were about 5 to 10 % h!gher than with
the larger (5.08 cm) outlet.
4) There was generally wide disagreement amongst the pre
dictions of the theoret.l.,.al models for the same operat
ing conditions. The ClJ.sa'Jreement was widest for poor
operating conditions (low collection efficiencies).
5) The best agreement between calculated and experimental
collection efficiencies was obtained v.lt~ the ~othes and
Loffler (1984, 1988) model. The agreement vas improved
when t.he model was modified to include some of the
results obtained in this study.
<,
CHAPTER 5
CYCLONE PRPoSSURE DROP STUDY
c
~~ER5
CYCLONE PRESSURE DROP STODY
LITERATORE REVIEW
The cyclone pressure drop is one of the important factors
that determines the operating co st of cyclones. The pres
sure drop is usually expressed as the number of inlet velo
city heads (NH) where the inlet velocity head is defined as
(PfVi 2f2), where [pf ~ Pg + Cv(pp-Pg)] and Cv is the volume
of dust per unit volume of gas, thus:
(5-1)
Licht (1980) summarized the phenomena that contribute to the
total pressure drop across the cyclone as follows:
1. Loss due to frictional flow in the entrance duct.
2. Exit loss due to the sudden expa~sion of the gas stream from the inlet duct into,the barrel.
3. Friction loss at the walls in the body of the cyclone.
4. Kinetic energy loss due to turbulence within the cyclone.
•
c
185
5. Entrance loss due to the sudden contraction of the gas stream at the entrance to the exit duct.
6. Static he ad loss due to the difference in elevation between the inlet and outlet ducts.
7. Recovery of energy in the.outlet duct.
8. Loss duc to frictional flow '~rough the outlet duct.
The kinetic energy losses (4) are usually the most important
and most models are developed around this. The operating
temperature is not usually considered explicitly but is
taken into account through the variables that it aff~cts
(for example the gas density and viscosity).
Perhaps the most cited study of pressure drop in cyclones
was that of Shepherd and Lapple (1939, 1940), who used a
30 cm glass cyclone of conventional design. They studied
the effects of cyclone size, dust loading, cyclone geometry
and internaI modifications (baffles and vanes for example)
on the cyclone pressure drop. Impact and static pressures
were measured in the cyclone with a Pitot proba consisting
of two adjacent 2.0 mm i.d. copper tubes • •
Shepherd and Lapple found that the pressure drop for a given
cyclone arrangement, when expressed in terms of inlet velo-
186
city heads (Na), was independent of gas flowrate. The same
study found that the cyclone friction loss increased when
the inlet width, inlet height and exit duct length were
increased. In contrast, the pressure drop decreased with
increased exit duct diameter, and increased dust loading.
straightening vanes inserted in the exit duct and extended
below it, ~lso reduced the pressure drop whereas, baffles
placed below the exit duct usually resulted in an increase
in the pressure drop across the cyclone. The effects of
these variables on the collection efficiency were not dis-
cussed by the authors.
Shephord and Lapple supported their experimental str1y with
a theoretical treatment of the pressure drop in the cyclone:
starting with the Bernoulli theorem, the pressure drop
acroes the cyclone expressed as number of velocity heads
(Na) was given by:
(5-2)
wher~ Fcv is the friction loss factor associated with the
cyclone barrel, Fev is that in the exit duct, Ai and Ao are
the inlet and outlet areas respectively. Fev can be evalu
ated f.rom the Fanning equation and was given by:
c
4 fLe [Ai] 2 Fev = -- --de Ao
187
(5-3)
where "f" may be read from an appropriate curve or may be
assumed to be 0.005 for normal cyclone operating conditions.
Le and de are the equivalent length and diameter of the exit
duct respectively. It was assumed that the frictior loss
factor in the cyclone (Fcv) was equivalent to the energy
required to produce the high velocity inner vortex observed
in reverse flow cyclones. Assuming negligible entrance
los ses and the vortex law exponent (n) equal to 0.5,
together with a correlation of their experimental data,
Shepherd and Lapple obtained the expression:
(5-4)
where kwas 7.5 when an inlet vane was used and 16 without
the inlet vane. Substituting equations 5-3 and 5-4 into
equation 5-2 resulted in the expression:
(5-5)
This model is one of the standard models used for the theo-
o
188
retical treatment of pressure drop in cyclones and is often
approximated by using only the first term on the right hand
side of the equation.
staircand (1949) did a theoretical de~lvation of the pres
sure drop in a cyclone considering los ses i~ the inlet, the
cyclone and the exit duct. The three components combine to
give the total pressure loss according to the expression:
(5-6)
where ~ is the ratio of the tangential velocity at ~he mean
inlet radius to the mean inlet velocity and was given by:
(5-7)
where As is the inlet area, As is the surface area exposed
to the rotating gas and f is the friction factor. 9 was
calculated to be approximately 0.5 and 0.4 for the 2.54 cm
and 5.08 diameter gas outlets for the cyclones used in this
study.
Ter Linden (1949) measured static and total pressures in a
cyclone (diameter not given) a .. d obtained the profiles shown
c
169
,.
in Figure 5-1. These ~rofiles show that the pressure was , .
high throughout t~e cyclone except for a core of low pres-
sure in the center of the cyclone. The lo~ pressure core
extended the full length of the cyclone into the dust bun~er
and was roughly 0.4 times the diameter of the gas exit duct.
The low pressure existing in the dust collection bin (or
outlet valve) is important since if it is not air tight, air
would be drawn into the bottom of the cyclone, carrying dust
with it and thus lowering ~~e collection efficiency. Ter
Linden did not give a mathematical model to describe the
observed pressure distributions.
Alexander (1949, 1950) developed a model based on the theory
that the cyclone pressure drop is due ta the sum of the
energy losses by gas in passing between the wall and exit
radii, and the energy lost ln the outgoing gas. The first
component was in turn made up of the difference between two
elements: 1) the pressure difference between a layer of gas
at the wall, and a layer of gas at the outlet radius (poten
tial energy); and 2) the difference in velocity (kinetic)
energy between the wall and the outlet radius. The energy
lost in the outgoing gas was also made up of two components:
1) the energy lost by the gas in going from the outlet
radius to a smaller radius r; and 2) the ro~ational ener~l
of the gas contained within the outlet radius.
Figure :3-1
STAnc: na:uat., "' YUOCTT_'·U t1(TI.(J l'II SIC.I
1 •
• INUT 1
190,
, L __ q
srArc n~i-----=:=m~==-----: +to l1It. fNATlI. 4
vtlOCTT-10·' tUTlU tu SIC.
\ • • • • • • \ \
DUST CUIUT
/ / 1
Toul a:>d Satie P=su:cs al Dilf=l Poicu iD • Cyclone
---Swic~ -:.---- ToaJ p=
Total and static pressure profiles measured by ter Linden (1949).
c
191
The resulting model derived by Alexander for pressure drop
expressed as number of wall velocity heads (NHw) was:
(5-8)
fA is a factor accounting for the energy loss in the out
going gas and varies between 1.9 and 2.4 as the vortex expo
nent (n) varies between zero and 0.8. The wall velocity was
shown to be approximately 2.15[Ai/(dcde)]0.5 times the inlet
velocity, so the right hand side of the equation should be
multiplied by 4.62[Ai/(dcdel] to obtain thp. number of inlet
velocity heads.
The American petroleum Institute (API, 1975), used a model
in which the total pressure drop was considered ta be made
up of five components:
1. Inlet contraction loss.
2. Solids contraction loss.
3. Barrel loss.
4. ReversaI loss.
5. Exit contraction loss.
The first two components apply to cyclones which are
immersed in a vessel such as above a fluidized bed combus-
192
tor. The inlet contraction loss was given as:
(5-9)
where kl is a function of the ratio of the cyclone inlet ... area to the external vessel area, and is approximately 0.5
for a ratio uf zero. The solid~ acr.eleration loss depends
on the dust load (Ca~ and was givcn as:
(5-10)
The particle velaci.c.ies in the inlet (vpi) and in the
external vessel (vpv) are usually taken as the gas velocity
for fine particles.
The barrel loss (dPb) was taken as the equivalent of the
straight -;lpe loss evaluated at the inlet velocity (Vi),
with the diameter being the inlet hydraulic diameter (dH)'
and the length being that described by Ns rotations of the
gas around the barrel, thus:
(5-11)
where i is the Fanning friction factor with the Reynolds
c
c
193
number evaluated at the inlet conditions.
The reversaI head loss is due to the flow going from the
barrel to the exit pipe and was taken as one inlet velocity
head:
(5-12)
The exit contraction loss is the difference between the
velocity head based or. the superficial velocity through the
barrel cross-section (PgVb2/2), and that in the exit pipe
(PgVe2/2), and was given by:
with k1 in this case being a function of the ratio of the
cyclone cross-sectional area to the exit duct area.
Masin and Koch (1986} gave a working form of the API model
as:
(5-14)
194
CasaI and Hartinez-Benet (1982) did a statistical analysis
of published experimental data to derive the following equa-
tion for the pressure drop across the cyclone based on the
number of inlet velocity hcads:
[A. ] 2
NH = 11.3 d:2 + 3.33 inlet velocity heads (5-15)
This expression is similar to the simplified Shepherd and
Lapple model but with the number of velocity heads given a
non-zero intercept. The model was claimed to fit the
selected data better than more complicated expressions given
for example by Shepherd and Lapple (1939), Stairmand (1949),
and Alexander (1949).
Masin and Koch (1986) recommended using the Shepherd and
Lapple (1939) or the CasaI and Martinez-Benet (1982) models
for pressure drops up to 0.2 Pa. For higher pressure drops,
they suggested using the API (1975) model modified so that
the maximum change in vclocity was considered for calcul at
ing the expansion or contraction losses. This was done by
using the greater of the in let or outlet velocity to deter
mine the friction factor, and by replacing the first term in
equation 5-14 with (l+Pg).
Wheeldon et al. (1986) analyzed their data by defining the
c.
c
195
pressure drop in terms of the velocity in the body of the
cyclone (vb) and the Euler number (Eu), where Eu is the
number of barrel velocity heads:
1 dP = EU0'2PgVb2 (5-16)
with
vb = 4Qv
(5-16a) ?Id 2 c
They added a term to the Shepherd and Lapple (1939) model to
account for the height of the cyclone, and showed that the
Euler number under zero load (Elle)' could be estimated by
the expression:
(5-17)
The constant in this equation was based on an Euler number
of 320 for the standard Stairmand (1949) high efficiency
cyclone. Equation 5-17 predicted an Euler number of 535 for
both the primary and secondary cyclones used in the Wheeldon
et al. study. On the other hand, the experimental data
yielded values of 296 for the primaries and 534 for the sec
ondaries even though both sets were geometrically similar.
The low value for the primaries was attributed to the higher
o
196
dust loadings going into these units.
The Effect of Dust Load on Pressure Drop
It hag ge~€rally been found that the pressure drop decreases
as the inlet dust load is increased (Kriegel, 1968; Knowl
ton and Bachovchin, 1977; Bryant et al., 1983). This is
contrary to the effect whereby the effective gas density
increases with dust load and should cause a corresponding
increase in the pressure drop. The observed pressure drop
reduction must therefore be exp1ained by other phenomena.
One factor is that increasing the dust load is usua1ly
accompanied by an increase in the overall collection effi
ciency. Consequently, there are fewer particles in the out
let gas stream so the energy loss in the outlet region is
lower and results in lower pressure drops ~t high inlet dust
loads.
Sproull (1966) used an analysis of pressure drop in a pipe
described by Fanning's equation:
dP = p v 2 -f~ dx
2rH (5-18)
(
197
Replacing f with data from Moody (1944), this equation
was given as:
(5-19)
where ks is a constant, dl 3S the pipe diameter and x is the
length of the pipe. If dust is added to the gas for a fixed
flowrate, then only the density (Pg) and viscosity (p) ~ould
be affected. Since the added dust increases the effective
density, then the observed pressure drop reduction must be
due to a decrease in the effective gas viscosity. Equa
tion 5-19 was used to generate the plot ~f viscosity vs du st
loading shown in Figure 5-2. An empirical expression was
given by equation 4-42 for the visccsity-Ioad effect.
Barth (1956) and Muschelknautz (1967, 1970) attributed the
reduction in pressure drop to the increase in the fricticn
factor at thR walls, and the consequent decrease in the tan
gential velocities in thR cyclone. Experimental studies by
Yuu et al. (1978) founr éhat in general, the pressure 6rop
was lowered by 35 % for loads between 0.2 and 50 g/m3 and by
larger amounts above 50 g/m3 (Figure 5-3a). This trend was
linked to the observation that at low loads, the uarticles
which stuck to the walls, w~re confined to a small area of
the ~alls, whereas at higher loads, this area suddenly
~~
0
-10
N \
• -20 z a {"6 .~" ... ti ::l
-~ ID 1 ?:
1, 1.3
~
... -40 B
x
U) ~ 1.1 ~ ... • > hl 1 ... > 0.91" -1-60
0.7' '-00 o 60 100 160 200 260
ruST LORD. l;J/"~
Figure 5-2 Variation of pressure drop reduction with dust load (Sproull, 1966).
~
-Il) ())
-'
c
c
199
widened to cover the entire cyclone barrel.
Yuu et al. (1978) also showed that the pressure drop
decreased as the inlet velocity was increased up to 10 mIs
then remained constant at ~igher velocities. It was post
ulated that the amount of particles sticking to the walls
varied directly with the inlet veloc:ty. The measured
radial profiles of tangential velocity varied inversely with
dust load (Figure 5-3b) and it was shown that the velocities
outside of the wall region, were lowered when the walls were
deliberately coated with particles and dust-free air was
passed through the cyclone (Figure 5-3c).
Briggs (1946) showed that for a constant '·olumetric flow
rate, the pressure drop varied with dust load according to
the expression:
(5-20)
with Ca beinq the du st lo~d in g/m3 and dPo the pressure
drop at zero load. Masin and Koch (1986) used a similar
load correction while Wheeldon et al. (1986) used an expres
sion of a simiiar form but with constants proposed by Smo
lik (1975):
(5-21)
1.0
0.7 r~ .
t-~
• . •
• • • . . • • 6
200
. . ... ~ '-' • . . ..... • Ui -20nys
1 •• · ... ·1 t ..... /d .64 !-... -. "&t·-• 1IC .... ~ -..: XXI:(
Sig ... Maten~1 10 ... 1"",1 '.(q/ml • e., · , o ,P.V.C.Powderl ·163 A 1 Fly ôISh i 27 " 1 Mang.nese 1 18 .
OJQ2'OJ 0.5 0.7 1 2 3
u.leOCmI.,
• ! :5
°o~----'-i~~--~;-----~ re ... , u, YS , (U,· 11.0 =1 ... ).
1.33 a? 2.00
0(" cl?" 4.37
• • , •• li • · 5 7 10 20 30 50 70 100 200 JOO C (gtm'l
" YS C.
"
la
-. .,.. "\i •
o 50 r ("""1 IQCI r.4
Dis<n'boéoo ::( ...... :éo;I.doœa il lino aac&o
Figu:-:e 5-3 Variation of pressure drop ratio and velocity profiles with dust load (Yuu et al. 1978).
,
c
c
201
The difference between the pressure drop (or Euler number)
ratios predicted by equations 5-20 and 5-21 increases with
load. For example, below 0.1 g/m3 both equations give a
ratio of close to one whereas at 100 g/m3 equation 5-20
gives a ratio of ~.5 and equation 5-21 gives 0.91. The
Briggs model (equation 5-20) has been used extensively, and
gives a more conservative estimate of the pressure drop.
The loading effect could also be affected by the size dis
tribution of the dust. This can happen due to agglomeration
and settling of the particles for example. Sproull (1966)
mentioned that a coarse dust is less effective than a fine
dust at the same concentration in reducing the friction
factor or the effective viscosity of the gas.
EXPERIMENTAL RESULTS AND DISCUSSION
The pressure drop across the cyclone was measured in each
experiment as described in Chapter 2. The measured pressure
drops ranged from 50 to 2 700 Pa and are listed with the
experimental data in Tables A1-1 to Al-5 of Appendix 1. The
data were analyzed in terms of the Euler number in a way
similar to Wheeldon et al. (1986). The measured pressure
drops were then compared with the predictions of models by
202
Shepherd and Lapple (1939,1940), Alexander (1949), cas al and
Martinez (1~82), Masin and Koch (1986) and Whee1don et al.
(1986). The load effect was accounted for by the Briggs'
(1946) expression (equation 5-20), and by "the Smolik (1975)
model (equation 5-21).
Ana1ysis of the Eu1ar HUmber
The Euler numbers defined by equation 5-16 were calculated
from equation 5-17 to vary between 271 and 1219 for the
cyclone configurations used in this study. These values are
listed in column 2 of Table 5-1. In comparison, the expe
rimentally determined zcro-load Euler numbers (EUe> varied
between 199 and 722 (column 3 of TaDle 5-1).
The experimental Euler numbers were determined by plotting
the cyclone pressure drop against the pressure drop associ
ated witn one barrel velocity head, and measuring the slope
of the regression line for each cyclone geometry. Fig-
ure 5-4 shows the plot obtained with the cyclone under dust
free conditions while Figure 5-5 shows the plot obtained
with the dust-laden gas. These figures show that the Euler
numbers were higher for the smaller diameter gas outlets (C2
and C4) and that the length of the gas outlet affected the
Euler number.
~ ~
'l'AB LB 5-1
COKPARISON OP BULBR NUKBBRS
ZERO-LOAD (EUC> MEAN WITH LOAD
Eqn. 5-17 Fig. 5-4 Eqn. 5-22 Fig. 5-5
stairmand (1949) 320 206
'" Whooldon ot al. (1986) 0 Co>
primarios 545 352 296
Socondarios 545 352 534
This study - Cl 305 238 197 202
C2 1219 646 787 540
C3 271 199 175 153
C4 1083 722 698 622
o
:nxl
i 2600 •
~2CXX)
1600
ce ~Ioo)
m~
1 CUO lone gaometru o CI -ce AC3 lIE C4
00-"'" o 1 2 3 4 6 6 7 a 0 10 8ffiREL vaOCITY I-EAO. Pa
Figuro 5-4 variat:ion of proDDuro drop wit:h barrol volocit:y hoad tor dUDt:-troo tlow.
~
.. o ~
~
:DX). } }
cE 2600 •
~2(XX)
WI&D 0.
œ ~ICXXJ
cuolarw gea.try
o CI -C2 AC3 lIEC4
îlE
lIE
lIE §
600 ~ ,Ji) _~ ~ ~ 0
o/; .. ~. ." ·
1 o
:Eu-640
o
•
o 1 2 3 4 6 6 7 8 9 10 a:F.R8.. vaOCITY I-ERJ. Pa
Figuro 5-5 Variation of rt'oDGUrO drop with barX'ol volocity hoad for dUDt-lndon gaG.
~
N o ln
., 206
A more general way to determine the zero-load Euler number
(Eue) was by fitting the right han~ side of equation 5-17 to
the experimental data. This was done by plotting the zero
load pressure drop against the group of variables on the
right-hand side of equation 5-17 and measurinq the slope of
the regression line (Figure 5-6). The slope was 18 so the
resulting equation was:
(5-22)
The new set of zero-load Euler numbers (Eue) predieted by
equation 5-22 are given in eolumn 4 of Table 5-1.
Taking the dust loading into aeeount, equation 5-20 ean be
rewritten in the form:
(5-23)
thus a plot of [l-Eu/Eue ] versus Ca on log-log eoordinates
should yield a straight line with a slope of nbn and an
intereept nan• Figure 5-7 shows this plot with the exper-\
imental regression line shown as the sol id line with the . , equation:
~
HXX) 1
CUOIa-. 0011- g.DII.try
Eml- o CI I::.œ
! 700L cc) 1( CC
fXX)
~003 r:l
400
:m
ZOCI
lOCI
rJ a la
Cl>~ ,'" _,of
II(
1(
1(
1::.
B'N', .. trlo do do dol! do paranetlllr - ba ha dei ZI+ZZ-S
20 30 40 GEOtETRIC PARREfER
60
Figure 5-6 Variation of zero-load Euler numbor with cyclono goomotric parametcr.
~
'" ~
o
....
i
2.001r---------------------------------------~
1.00
cuoltnl .,......try
OCI - oold lIE CI - hot +C2 - hot AC3 - hot Il C4 - oold • C4 - hot
• lIE ... (fll lIE +" A A .... ,
"'-~+~ lIE- ...... ~ •
lIE OQ,~ lb ....... . • (j Il ..... .
Il .' + .. ' .!.. 0.10
0.'31
_.~_O.~ c ....
• • . ....... 0·'6 , Il •••••••••• ~ .....
\~~- .
... ... ...'"
0:' ......... tI:.o ......
O$Y,'" # ...... lIE
~ ... ",
...... \' ...... ...... ... .' .' •••• . ...
.... . ' .' .' .' .' .... .... .. '
.' ~ .... o-..... .,. . ... ~. .' .' ....... , .. ·····0
.... 0.01 l , ft , r' ,.- ft ft , , ft , ft , , , ft ft , , 1
0.6 1.0 10.0 100.0 600.0 II'LET OOST LORJ. glm3
Figure 5-7 Variation of Euler number ratio with dust load.
~
~ o 0>
,
c
209
(5-24)
The dotted line in Figure 5-7 was obtained from the Brjggs ,
(1945) equation (5-20), while the broken line represents the
Wheeldon et al. (1986) model (equation 5-21). The plot
shows that there was much scatter in the data and that the
Wheeldon et al. model would predict the performance with
roughly the same degree of accuracy as the experimental
regression line. The Briggs model on the other hand gives a
more conservative estimate of the load effect as mentioned
earlier.
Predicted vs Exp~rimenta1 pressure Drops
The evaluation of the models was completed by plotting the
predicted pressure drop against the experimental pressure
drop on log-log scales. A performance index similar to that
described in Chapter 4 (equations 4-49 to 4-52) was used to
measure the agreement between the experimental data and the
predictions of the theoretical models. The ca1culated per
formance indices are summarized in Table 5-2 along with the
me an deviation squared and the variance. The devlation is a
measure of the distribution about the parity line while the
variance is a measure of the scatter in the data.
210.
o TA3LE 5·2
SUl'l'l'lary of Perforlllnce Indices for Prnsure Drop Models
Wl>El FIGURE tJ.2 0 2 PERFORAANCE NO. INDEX
~eeldon et .1. (1986) 5·a 0.0606 0.1304 0.1909 (equotlons 5·17 and 5·21)
Ma.ln , Koch (1986) 5·9 0.2712 0.3278 0.5990 (equotlons 5·14 and 5·20)
Shepherd , lapple (1939, 1940) 5·10 0.5223 0.1577 0.6799 (equotlons 5·5 and 5·20)
Ca.al , Martlnez·Benet (1982) 5·11 0.3778 0.2844 0.6622 (equotlons 5·15 and 5·20)
Stalnoond (1949) 5·12 0.3098 0.1214 0.4312 (equotlons 5·6 and 5·20)
Ale.onder (1949) 5·13 0.0407 0.0952 0.1359 (equotlons 5·a and 5·20)
ExperimentaI model 1 5·14 0.0029 0.0816 0.0845 (<qUItlon 5·24, Fig 5·4)
ExperimentaI DOdeI 2 5·15 0.0060 0.0816 0.0925 (equotlons 5·22 and 5·24)
c
211
Figure 5-8 sho~s the experiment~lly determined pressure drop
plotted agalnst the pressure drop predicted by the models
used by Wheeldon et al. (1936). These were given as equa
tion 5-17 along with the load correcti~n given by equa-
tion 5-21. The figure shows tha~ the pressure drops were
reasonably weIl predicted but with a tendency fo!" the :>re
dicted values to be higher than the experimental values. The
largest deviations occurred for runs with high du st loads,
in which case equation 5-21 predicted large decreases in the
pressure drop due to the dust loading.
It can also be seen that ~ost of the room temperature pre
di,ctions agrep.d excellently with the experimental values
while the high temperature predictions wece generally higher
than the experimental values. The high predictions cou Id be
due to two factors: firstly, at high temperatur~s the velo
cities ",ere hiq~er for the same mass flowrates so t. ... 2 c:t1cu
lated number of velocity heads were much higher. Secondly,
the du~t load decreased at higher temperatures (for the same
mass fl,wrates) so the calculated Euler numbers were gener
ally t. tc;'her fct' the high temperature runs. The performance
index was 0.19 with the scatter in the data (variance) being
higher than the deviation from the patity line.
Figure 5-9 shows a similar plot for the pressure drops pre-
c
lOOllO~ 71
~ •
& 151CXX1
~ § 100
1
CUCllona g.cmat.ry
OC1 - cold .C1 - hot +œ - hot 11 C3 - hot CC4 - cold • C4 - hot
•• o~ • '" y
li( I_~
11 • ! ~é-(J1f" ~)..r0
J.!-,~6 I~:~/o
L.~O li( _ 1~"'A 0
0- 0 cg 0 70 -o
IOV '!'l''' ",t", ",'
la 100 ICXX1 10CXX1 EXPERltENTFL PRESSl..RE œtF. Pa
Figare 5-8 Comparison of experimental data with pressure drop predicted by the Wheeldon et al. (1986) model.
o
,.. -,..
~
J(XY.Xh 71
.f • es
P.ilOOl
~ Œ
§ 100
ID ~
cuolona gIICI.etry
OCt - oold lE Ct - hot +C2 - hot AC3 - hot CC4 - oold .C4 - ho~ ... **- li(
A .- ... ~!fl •• CC
/i-.. CI) • C . IllE "'.r.tI + al>
jt/lt:P+ 00
li( ii:l~ ! C C
0<0000
o C QI
oC)
IO~V---~~~~~~--~--~~~~~--~~~~~-u
10 100 1000 10000 EXPERlt-ENTfL PRESSl..R: œlF. Pa
Figure 5-9 comparison of experimcntal data with pressure drop predicted by the Masin and Koch (1986) model.
~
N -w
214
dicted by the Hasin and Koch (1986) version of the
API (1975) mode1 (equation 5-14). In t~is case, the loading
effect was accounted for by the model \~sed by Hasin & Koch
(equation 5-20). The scatter in thir. plot was more than
with the Wheeldon et al. model, and in most cases the pre
dicted values were lower than the experimental values. The
performance index was higher in this case (0.60) and both
the deviaticn and the variance were high. The discrepancy
betw~en the calculated values at low and high temperatures
was more noticeable in this case.
Figure 5-10 sho~'s the plot obtained for the Shepherd and
Lapple (1939, 1940) model as determined from equations 5-5
and 5-20. In this case only the first term of equation 5-5
was used with the constant k having a \l'alue of 16. A simi
lar distribution was obtained for the predictions of the
Casal and Hartinez-Benet (1982) model (equation 5-15) as
shown in Figure 5-11. The similarity in the plots was due
to the similarity between the two models as discussed ear
lier in this chapter. In both cases, the predicted pressure
drops were ~?stly higher than the experimental values, and
in a few cases, the predicted values were almost one order
of ~agnitude higher. The performance indices were 0.68 and
0.66 respectively with the higher contributions coming from
the deviations from the parity line.
~
1 (XXX) r 71
e. •
~Icœ
~ § 100
1
ouolcne gtICIl.try
OC! - oold -CI - hot +C2 - hot AC3 - hot CC4 - oold • C4 - hot.
• rI'. .. ~ ~
_ + J< -
A +1 ?~
iil"lilE~/-~/ _ ,Ir - -,.~A 0
Q C0<o0 Or?"
o 0
la v , ,o,.J
la 100 1000 1 (XXX) EXPERllENTfL PRESSlŒ ŒUF. Pa
Fi9ure 5-10 Comparison of exparimcntal data with pressure drop predicted by the Shcpherd and Lapplo (1939, 1940) mo~el.
~
1\) .. CIl
9
HXXXh 51
~ •
~Icxx)
§ 100
1
CVllcna Q«X,.lry
OCI - cold .CI - hot +C2 - hot AC3 - hot C C4 - cold .C4 - hot
.... ~ ••• C
+
+11 g Dt A I*~
... I!IE/ ~llliiii .... 00
c r.n •• i" • !»lIE A ..n () ./
0<h0' _0
° 10~V--~~~~~~--~~~~~~~--~~~~~
100 1000 10000 10 EXPERltENTFL PREsst..R: œœ. Pa
Figure 5-11 cOhlparison of experimental data with pressure drop predictod by tho Casai and Martinoz-Donot (1982) modol.
~
j\) .. 01
c
(
217
The pressure drops calculated from the Stairmand (1949)
model were generally lower than the experimental values as
shown in Figure 5-12. Equation 5-6 was used along with
Briggs' (1946) load correction model (equation 5-20). There
was little segregation of the data for the cold and hot
runs. The performance index was 0.43 vith the main contri
bution coming from the deviation from the parity line.
The predictions of the Alexander (1949) model (equation 5-8)
are shown in Figure 5-13. The Briggs modql (equation 5-20)
vas used aga in to determine the loading effect. The plot
shows that there was good agreement between the predicted
and experimental values throughout the range of pressure
drops. Furthermore, there was no segregation between the
low and high temperature data. The performance index was
0.14 which vas the lowest of the theoretical models tested.
Figures 5-14 and 5-15 show plots obtained from the models
derived from the experimental data obtained in this study.
In both cases, the Euler number was calculated from the
equation of t~e experimental regression line obtainad from
the plot of Euler number ratio vs dust loading (equation
5-24). The difference between the two plots was in the
method used to determine the zero-load Euler numl'2r (Eue).
Figure 5-14 (method 1) was obtained by determining the zero-
c
. '
Hxm, /1
e. •
& I5IŒXl
~ § 100
1
cuolone gecawtry
OCI - cold • CI - hot + C2 - hot. âC3 - hot C C4 - cold • C4 - hot.
~",D[J
c.~.[J
• • ~ ~D .... " • l.b~ "'"
.. ' il!90
~ ,.,,IIE"'.
1{4( illE
[J (DT '#Il. '0 (J
'" r~<oO 00
o
IO~o-°' 10
~~~~~~ ........ ~ .... ~~~~~~ ........ ~ .... ~~~~~~ 100 IŒXl IQ(XXl
EXPERlt-ENTfL ~E œoP. Pa
Figura 5-12 Compnrison of exporimentnl data with pressura drop pradictod by tho stnirmnnd (1949) modol.
~
N ... Cl)
~
HXXXh 71
e. •
~1(xx)
5 1'00
cuo 1 cne g.cn.t.ry
OCI - oold • CI - hot +C2 - hot AC3 - hot Il C4 - oold .C4 - hot
IJIJ • fi'!/d
•• ~,7.. A .. Jh.~ 11: 7f( (J'j)
o
+~I!~O
ft~ • 1( ,,6~
Il • riV. ~/cro -o~O
./
10 V ""'" ""... ""
10 100 1000 10000 EXPERlt-ENTFL PRESSl.Œ [R(F. Pa
Figura 5-13 compnrison of oxporlmontnl dntn with pro99uro drop prodictcd by tho Aloxnndor (1949) modol.
r\
N ... CD
c
.. HXXXh 51
~ •
~Hxx)
~ If
§ 100
1
cuolcna gIIQIl. t.ry
OCI - oold • CI - hot. +œ - hot. âC3 - hot c C4 - oold • C4 - hot.
• • • ~ll-c . .., • }IE.4
â ,/fFütJ
ttr!<>~ .~~ ..
.1y<-â7 08 c M d:r''b 0 00
o /6
10~K--~~~~~~--~~~~~~--~~~~~~
la 100 1000 10000 EXPERltENTFL PRESSlRE œcP. Pa
Figura 5-14 compnrioon of axparimantnl dntn with praosura drop pradicted by tha modal derived from the experilllentnl dntn (mcthod 1).
o
,.. '" o
,
c
221
load Euler numbers from the slopes of the plot of pressure
drop vs barrel velocity head (Figure 5-4). The points in
Figure 5-14 wcre symmetrically distributed about the parity
line as indicated by the low squared deviation of 0.0029.
The performance index was correspondingly low (0.084) indi
cating a reasonably good fit of the experimental data.
Figure 5-15 was obtained by determining Euc from its rela
tionship with the cyclone geometry (equation 5--22). The
performance index was higher than for Figure 5-14 reflecting
the increased uncertainty in using equation 5-22. Neverthe
less, it is more convenient to use this equation than it is
to determine the Euc for each cyclone configuration from
Figure 5-4. In any case, the decrease in the agreement
between the calculated and experimental values was small so
either method would yield similar result.
SUHMARY
Several theoretical models exist for calculating the pres
sure drop across thp. cyclone as a function of operating
conditions. The ~ressure drop is often analyzed in terms of
the number of inlet velocity heads (NH) or the number of
barrel velocity heads (Euler number, Eu). It has been found
that the pressure drop varies inversely with the inlet dust
o
HXXXh 7,
e.. • ~ 151ŒXl
i § 100
1
cuolone geaa.try
o CI - cald .CI - hot +C2 - hot AC3 - hot o C4 - cald .C4 - hot
. -• 4--0
l\/~ A ~lIE t:rC~
+ .... J(.. • v:r, ~ _ .,JA'if lIE li ;;1I(:i
lIE rt.A~ 08 o "'~~ CO '0 0
10~V~--~~~~~~----~~~~~~----~~~~~~
10 100 1000 1(0)0 EXPERltENTfL PRESSlŒ rRCP. Pa
Figure 5-15 comparison of experimental data with pressure drop predicted by the model derived from the experimental data (method 2).
@
1\) 1\) 1\)
c
223
load and some authors have proposed power law models to
de scribe the relationship.
The experimental data showed the expected inverse variation
of pressure drop with load, but there was much scatter in
the data. The model proposed by Alexander (_949) agreed
with the experimental data better than any of the existing
models tested. Empirical models were derived for the Euler
numbers without and with dust loads.
CONCLUSIONS
o
(
c
c
224
CONCLUSIONS
The main features of this study arc sUMmariz~ . as follows:
1. A 10.2 cm àiamr..t .. ;c cyclo.~~ Illas studied at room ana
elevated temperatures. Temperatures up to 2 000 K were
used and are higher than previously reported for
cyclones. Alumina and silica of less than 44 ~m mass
median diameter were used as test 1usts in air.
2.
'3.
Cyclone preG~UI~ d~op~, fractional and overall collec
tion efficier.~i?~ ware moasured as functions of tempera
ture, gas throughput, dust loading and gas outlet geo,3-
e.try.
Tangelltial, radial and dxial vel.:.city profiles were
measured in the cyclone barrel at room and elevated tem
peratures. The Alexander (1949) model (equations 3-3 to
3-5) predicted the profiles reasonably weil. An empiri
cal model (equatian 3-22) was derived to correlate the
tangential velocity at the wall with the Reynolds number
of the gas in the annulus between the cyclone wall and
the .)utl€>': duct.
4. The inlet dust loading had a strong effect on the col
lection eff!ciency and pressure drop. The load effect
225
., . increased rapidly at low dust loads (1 to 5 g/m~), and
1eveled off at loads above 50 g/m3•
5. A correlation was developed relating the 50 % cut-size
and the penetration to a dimensionless separation number
(Sn). The separation number was defined in equation
4-47 and comprised an inlet Stokes number (Stin)' the
inlet volumetrie dust loading (Lv) and the ratio of the
cyclone diameter to the gas out let diameter (Er).
S. The best agreement between calculated and experimental
overail collection efficiencies occured with the Mothes
and Loffler (1984, 1988) model (equations 4-26 to 4-36)
along with an A.P.I. (;955 or 1975) load correction
model (equation 4-39). The agreenent was improved when
the tangential velocities were calculated using the
model derived in this study (equation 3-22) and the vor
tex exponent calculated by the Alexander (1949) mode]s
(equations 3-4 to 3-5).
7. The pressure drop across the cyclone was best predicted
by the l.lexander (1949) model (equation 5-8) along with
the load correction model of Briggs (1946) (equation
~-20). The agreement between calculated and • experimental values was lmproved when the experimental
c
8.
c
226
data was fitted to a model for the Euler r~mbfJr under
load (equation 5-22).
The performance of the cyclones at very high temp~ra
tures was not significantly different from the room tem
perature operation, provided that the temperature effect
on the particle, gas and (low properties was adequately
treated.
CONTRIBUTIONS TO XNOWLEDGE
c
c
227
CONTRIBUTIONS TO XNOWLEDGE
The following contributions to knowledge have been made by
the author:
1. Collection efficiencies and pressure drops were measured
at temperûtures higher than previously :epo=ted for co~
vention~l cyclone~.
2. An empirical model was derived relating the wall tangen
tial velocity to the Reynolds nucber of the gas in the
annulus between the gas outlet and the cyclone barrel
(equation 3-22).
3. A new separation parameter (Sn) was defined which can
pre~ict the collection efficiency and cut-size from
known operating conditions (equation 4-47). The new
parameter includes an inlet Stokes number (stin)' the
inlet volumetrie dust load (Lv) and the ratio of the
cyclone diameter to the gas outlet diameter (Er).
4. An existing model (Mothes and Loffler (1984, 1988) was
modified to improve the predictions of collection effi
ciency. The modifications included the replacem
o
o
22&
s. A new coefficient was obtained for a relationship
between the zero-load Euler number and the cyclone
dimensions (equation 5-22).
6. New parameter values were obtained for a model relating
the Euler number to the inlet dust loading.
c
RECOHlŒNDATIONS
(
o
o
RECOKKEHDATIONS
Thp following are reco~endations for future work:
1. A study should be done at high pressures in addition to
the high tempe ratures used in this project. This would
require the use of a different type of heat source since
the RF torch used here cannot be used at high pressures.
2. Larger-sized cyclones should be studied at the high
temperatures used in this study. This would require
using a more powerful plasma generating system or pre
heating the air to a high temperature in order to handle
the larger gas flows.
3. A more extensive study of gas flow patterns in the
cyclone at very high temperatures should be done.
Ideally, a non-intrusive method of flow visualization
and velocity measurement (Laser-Doppler anemometry for
example) should be used. This could require making the
cyclone out of a transparent, high-temperature material
such as quartz.
4. A continuous system should be studied at high tempera
tures. This would address issues such as reentrainment
of particles trom the bins which can occur in batch sys-
c
c
229a
tems. This would require on-line weight and particle
size measurement instead of a cascade impactor.
o
NOHENCLATURE
(
(
c
a
A
Ae
Ai
Ao
At
b
B
bc
bl
c
C'
d
230
HOKENC~TURE
constant
load exponent, equation 4-39
experimental load exponent
inlet cross-sectional area, m2
outlet cross-sectional area, m2
thermocouple surface area, m2
constant
inlet width, m
inlet width, m
dimensionless coefficient
load parameter exponent
5-channel pressure probe calibration factor
inlet dust loading, g/m3
calibration factor of heat-flux gauge
no. concentration of particles, no./m3
reference dust load (usually 1 gr/ft3)
constant pressure heat capacity, J/kg/K
pressure probe calibration factor
volumetrie du st load, m3 dust/m3 gas
particle concentrations in region~ 1 to 4, g/m3
cyclone configuration number (Figure 2-1)
CUnningham slip correction factor
exponent of outlet diameter to cyclone diameter ratio
momentum exchange parameter
cyclone barrel diameter, m
dH
di!
dl
dp
Dp
dpa
dpc
dpg
dpmin
dpSO
dp84
dP
dPb
dPe
dP' ~
dPr
dPs
dPo
dt
Dt
da
Er
Eu
Euc
f
0 F
231
inlet hydraulic diameter [4hcbe/2(hc+bc)], m
difference between measured and predicted values
pipe diameter, m
particle diameter, m
particle diffusivity
aerodynamic cut-size [dpso(C'pp)o.s], m.(kg/m3)0.s
cyclone cut-size, m
mean mass diameter of the test dUGt, m
diameter of smallest particle that can be collected.
SO % cut-size, m
84 % cut-size, m
cyclone pressure drop, Pa
barrel pressure loss, Pa
exit contraction loss, Pa
inlet contraction pressure loss, Pa
reversaI pressure head loss, Pa
solids acceleration loss, Pa
zero-load pressure drop, Pa
thermocouple diameter, m
particle turbulent diffusivity
angle swept by particle in horizontal plane
outlet diameter ratio [de/de]
Euler number
zero-load Euler number
Fanning friction factor
S-channel pressure probe calibration factor
232
c energy loss factor
inertial force of a particle
Fc centrifugaI force acting on a particle
Fcv friction loss factor for cyclone barrel
Fev friction loss factor in the exit duct
Ftw shape factor from thermocouple to walls
Fv drag force acting on a particle
G geometric parameter
h cyclone height, m
hc inlet height, m
hf heat transfer coefficient, Wjm2jK
ht height of gas outlet duct, m
hz height of cylindrical portion of cyclone, m
hz* modified height of cylindrical portion of ~zclone, m
II-I3 electrical isolation sections in inlet duct.
jc dust outlet diameter, m
jl,4 particle fluxes, no.jm2js
k constant
K 5-channel pressure probe calibration factor
Ka inlet heightjcyclone diameter
Kb inlet widthjcyclone diameter
Kc volume parame ter
kf thermal conductivity of gas, WjmjK
kl load coefficient
ks constant
thermal conductivity of wall
233
constant
Ko geometric parameter
Kl flow parameter
K2 geometric parameter
L du st loading, gjm3
le height of cylindrical part of barrel, m
Le equivalent length of the exit duct, m
LF load factor
Lo turbulence scale length, m
Ln Ilatural length of vortex in cyclone barrel, m
Lv inlet volumetrie dust load, m3 particlesjm3 gas
m constant
mass of dust collected in cyclone, kg
mass of du st entering cyclone, kg
mass of dust leaving cyclone, kg
vortex exponent
N number of transfer units
Nm measured number of transfer units
NH inlet velocity head
NHw number of wall velocity heads
np number of particles in sector
Np predicted number of transfer units
Ns number of spirals made by gas in the barrel
Nu ~usselt number
P penet~ation, [l-e]
Patm atmospheric pressure, Pa
(
(
(
Nu Nusselt nwnber
P penetration, [l-e]
Patm atmospheric pressure, Pa
Ps static pr~ssure, Pa
PT total pressure, Pù
Pl -5 pressures measured by pressure probe taps, Pa
rI performance index
Pr Prandtl number
Q volumetrie flowrate, m3/min
Qin inlet volumetric flowrate, m3/min
Qo inlet volumetrie flo' 'rate, m3/min
Qv axial volumetric fl~wrate, m3/_ i n
r
R
radial position i~ cyclone, m
regression coefficient
ra* modified radiur of cyclone, m
rc cyc~?ne radius, m
re exit dllct radius, m
ri exit du ct radius, m
rv r.~dius of boundary between upflow and downflow
Re Reyno'is nu~ber [dcUcg/~Pg]
Rea ~eynolds number in annulus formed by gas exit duct
S engagement le~gth, m
Sc engagement length, m
SF saltation factor
5~. se~aration parameter [StinoLvCoErd]
inlet Stokes number [C'dplppuc..l/9~gdH]
235
Tin inlet gas temperature, K
Tt thermocouple temperature, K
Tw wall temperature, K
u tangent '.al velocity component, mis
Uc mean inl~t velocity, mis
ur radial velocity of pa~ticle at radius r, mis
Urw radial velocity of the particle at the wall, mis
v axial velocity component, mis
V gas velocity, mis
vb barrel velocity, lQv/~rc2], mis
Vc effective cyclone volume, m3
vi inlet gas velocity, mis
Vnl voll'me of cyclone at natural length, m3
vo ' root mean square fluc~uating velocity, mis
vpi inlet particle velocity, mis
vpv partjcle velocity in external vessel, mis
v r radial velocity, mis
vr~ radial particle veloc~t.y, mis
vrg radial gas velocity, mis
Vs volume in annulus formed by exit duct, m3
Vs saltation vclocity, mis
Vt tangential veloclty, miR
Vt;w wall tangential veloc!.ty , mis
Vtw~ wall tangential velocity for frictionless flow, mis
Vv gas velocity in external vessel, mis
·'x volume cleaned by a big particle, m3
c
236
Vz axial velocity, mis
Vl stairmand barrel velocity term
w radial velocity component, mis
x length of pipe, m
~lC mass fra?tion of i for collected dust
xif mass fraction of i for feed dust
xio mass fraction of i for escaping dust
xG di"meter -f bjg cleaning particlc, m
y tangential velocity at mean inlet radius/mean inlet
velocity
z axial distance, m
Greek symbols
rv,w particle fluxes no./m2/s
6 difference between measured and predicted values
E collection efficiency
Ea efficiency under load
EA separation efficiency due to agglomeration
~o zero load efficicncy
Et total emissivity
o angle flow makes with the axis of the pressu~e probe
# gas viscosity, Pa.s
#g gas viscosity, Pa.s
#app viscusity under load, Pa.s
e wall friction coefficients
Pf combined density of gas and particles, kg/m3
237
Pg gas density, kg/m3
Pp particle density, kg/m3
o Stefan-Boltzmann constant
~ impaction parameter
o specifie su~face area of the barrel of the cyclone
~ angle flow makes with the axis of the pressure probe
~c angle between cylindrical and conical sections
REPERENCES
c
REPERENCES
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APPENDIX 1
RAW DATA
(
c
APPENDIX 1
RAW DATA
OPERATING CONDITIONS , RA. DATA
Tables Al-l and Al-~ shuw data for experiments don~ at ele
vated tecperatures using alumina as the test dust, and for
c~· .lon/! out let diameters" 5.08 atld 2.54 cm respecti vely.
The rows in these tables ar: ~rranged :n order ?f decreasing
inlet temperature. Runs where the 50 % cut-size is not r'ven
~ere done with the câscade imp~ctor a~ the cyclone inlet 50
the fractional mass bala~ces could not ~e completed. m~ble
Al-3 shows d~ta for -oom temperature experiments done with
alumina; the rows in this table are arranged in order of
increasing inlet velocity. Data for exp~riments done wit~
silica are given in Tables Al-4 and Al-5 for high and low
tempe ratures respectivaly.
247
TAlLE AI'I AltnfN ExptrfDef'\tll DIU· "ft: leqletlture t::U\S • S.CS (a. outle!
_ .... Inlet Standard Inlet Pressure ~t COllection 50 X
Number Teœperlture Flowt,t- ~eloclty Drop Load Efflclency Cut'slze [::] ~;.h~ IWol (Pli (g,a'51 !XI !/Je]
Cyclone cotltt: S,08 ca dl~terc 10.8 ~ long
M20 2000 0.194 17 53 31.8 83.1 1.84 MI3 1886 0.194 16 64 22.5 71.8 M22 1870 0.210 17 67 21.4 85.6 1.65 A..'21 1863 ~ • .aG 19 al 22.9 84.5 1.68 M41 1816 0.194 15 61 1.4 44.7 2.25 M48 1799 0.213 17 67 35.2 84.0 1.79 M05 lm 0.213 16 71 20.9 76.8 ~.20
MOI 1758 0.213 16 80 18.4 73.0 M03 In6 0.<13 16 67 23.3 75.7 M06 1"20 0.213 16 61 27.0 74.4 2.18 M04 1720 0.213 16 67 24.~ 70.3
MI8 1696 0.274 20 133 15.4 82.9 1.99 M02 16&9 0.213 15 71 40.9 50.5
AA36 1604 0.329 '.3 213 4.4 78.5 1.86 Ml!- 1~66 0.351 24 248 1~.2 88.2 '.~2 MI7 1542 0.329 22 11'2 19.8 86.4 1.42 MI2 1541 0.329 22 208 18.9 91.3 MIO 1525 0.373 25 240 22.6 811.6 1.51 .wa til7 0.423 U 427 234.6 QI.9 0.27
HI5 1505 0.3~ 21 144 22.6 M.9 1.48 MI6 1489 0.329 21 208 28.2 82.9 .-.-. MOS 1487 0.329 21 19~ 4~.3 85.3 1.61
AA.1S 1486 0.424 27 '.GO 2.7 67.7 M09 1480 0.373 24 293 ze. ~ 82.9 1.87 AA37 \478 0.423 27 400 183.1 88.4 106 MI9 1459 0.421 27 3't3 15.2 91.~ I.Z4 MO' 1442 0.329 21 196 35.1 85.9 1.80 AA34 1433 0.421 26 413 4.3 31.1 1.82 Mil 1295 0.463 32 S33 30.7 80.5 1.67 AM7 1221 0.603 32 667 0.7 71.5 1.68 AA44 1206 0.603 31 539 13.0 92.5 1.06 AMO /71 0.984 41 1813 2.1 89.3 ~).26
AA39 927 0.084 39 \421 38.1 95.5 0.95
~.5!!1.!.tl: 5·98 ca dl ..... tsr. 7.0 ca lm
AC'l2 1847 0.213 17 93 1.4 55.7 2.n '':CI 1803 0.213 17 67 3S.4 84.0 1.7Ç AC04 1388 0.429 26 427 40.5 88.6 I.S8 AC03 1380 C.<29 26 413 ".0 75.9 1.91 AC06 1230 G '3 ~ 293 48.0 89.6 1.52 AC05 1208 0.603 " 681 1.8 79.e 1.62
248
IULE AI·2 Aluolna Exptrl~tal Data· HIgh I""POrat .. e Runs • 2.54 CD outlet
RU'I Inlet St~rd Inle! PrHsut"'t Oust COllectIon Cut-hu:ber Tecrptret'Jt'e Flowr.,« Velocfty Drop LNd Efffcloncy She
(KI ~/.Inl 1of,1 (Pa) (g/"J) (%) (JJa)
Cyelont> out'ft: 2.54 os df5ftettt'. 10.8 CIl tenq
AS02 1913 o.m 18 2!2 15.4 93.9 0.74 AS03 1564 0.329 22 629 15.8 94.8 D.2S A80~ 1554 0.329 22 629 18.7 97.9 0.23
Cyç!oneo outtet; 2.54 CIl dl!I!nIUfr. 7.0 aI.Jsei
ADOI 1791 0.213 16 300 2.5 79.1 I.al ADI2 1740 0.213 16 29l 20.3 84.4 1.54 AD02 IT<I 0.213 16 295 87.0 89.5 0.33 AD04 1560 0.429 29 U3 19.8 93.4 1.13 AD03 14:"'1 0.429 26 1421 0.9 87.5 1.21 AD06 1340 0.603 34 2646 4.5 93.5 0.71 ADOS I29T 0.603 33 2058 ~5.7 95.9 0.66
c
249
TABlE Al·3 Al~lna E~rlment •• Dlta • Rooœ Te=perltur~ Runs
RU'I Standord Inlet Pressure Oust C<llIectlon eut· Nu:ber f~?Wrate Veloclty Drcp Load Efflclency SI.e
~,.Inl IaIsl [Pol [g,.,ll !Xl [,.al
Cyc:1one outtfS: S.OS Ç! dl?SU''-, 10.8 CI! tons
Ml4 0.321 1 53 73.7 84.0 1.77 AA30 0.321 • ;1 120.2 81.6 M28 0.401 5 91 62.3 89.0 1.52 U29 0.401 5 ~< 75.9 89.7 1.53 Ml6 0.463 6 160 ~.5 90.8 1.47 M14 0.463 6 104 eo.5 86.9 1.65 AA25 0.561 7 20Ç 54.8 90.9 1.47 AA32 •• 574 7 260 15.3 86.5 1.22 Ml7 0.574 7 253 65.7 92.1 1.30 AA45 1.177 15 1039 0.3 84.3 1.14 M43 1.177 15 IOW 1.3 89.3 1.18 M46 1.177 15 1039 3.5 92.6 1.18 M.l 1.177 15 640 91.8 92.7 1.19
Cyel 2e' ouUtt, 2.54 ça dheu," , 7 ,Q ca long
ADl1 0.213 3 69 5.8 eo.5 1.90 AD07 0.213 3 64 44.5 86.4 1.67 ADl0 0.603 8 833 9.7 92.5 1.07 ADDa 1.050 13 2666 8.4 92.7 1.13 AD09 1.177 15 2~ 14.0 96.0 0.90
250
c
TAlLE AI·4 5111.0 Experleontol Ooto • High Teoperotur~ Runs
R .... Inlet stondord Inlet Pressure Oust Collection CUt· Nu=btr '~rature flowrlte Veloelty Drop Load (ft 1 el enc:y SI ..
[KI [,.l,_lnl t-/sl [Pol [gI,.l1 [%1 [11111
Cyete out(~t; 5,08 CIl dlet,,, , 10,8 Ç!!! 1"""
SA29 1835 0.213 17 77 3.1 61 3.05 SAZ2 1676 0.260 19 107 9.3 78 2.05 SAZ8 '664 0.213 15 53 50.3 M 1.80 SA20 1605 0.308 21 133 8.1 71 2.51 SAI8 1566 0.308 21 147 3.1 67 2.62 SA03 1539 0.423 28 413 2.1 73 2.46 SAOI 1505 0.423 28 413 1.9 79 SA2S 1499 0.305 20 160 61,7 90 1.52 SA16 1474 0.423 27 453 7.9 §6 1.46 SA23 1459 0.429 27 373 8.1 1!2 1.84 SAZ4 1432 0.429 27 373 53.9 90 1.57 SA19 1352 0.600 35 66; 4.5 76 1.93 SAZI 1300 0.603 34 539 11.6 88 1.41 SAZ7 1196 0.600 31 392 58.0 90 1.28 SAZ6 1048 0.600 36 588 49.6 89 1.28 SA17 991 0.9M 42 1331 9.1 89 1.20 SA16 846 0.936 34 1157 8.7 87 1.46
tyettn out"t; br" ce d'~te ... 1.0 ~
51>05 1876 0.213 17 293 13.9 84 1.75 SI>'J2 1439 0.429 26 1079 10.8 90 1.49 51>07 1256 0,603 32 lue 23.9 89 1.~3
SOO4 Il25 0.603 31 1866 14.1 91 1.11
c
251
TABLE AI·5 Sil l,a Experloental Oata • Roao Tooperature Runs
R .... Standar<l Intet Pressure Oust CoUectlon CUt· Nlr.Iler Flowrate V.loclty Orop L~ Efflcloncy Sile
~/1I1n] [Jo/si [l'al [g/.,ll IXI II/III
Cye1m ClUttetj 5.0& ca dfeUt, 10.8 ca long
SAlO 0.212 3 20 30.1 71 2.59 SA08 0.212 3 13 48.0 73 2.55 SAI2 0.424 5 107 15.8 79 2.12 SA07 o ~24 5 72 34.4 74 2.57 SAI4 J.424 5 85 38.9 84 2.00 SA04 0.869 Il 573 6.2 67 SA05 0.869 Il 467 6.9 78 1.74 SA06 0.869 Il 547 25.5 85 1.71 SAI5 1.177 15 1012 1.1 78 1.50 SAli 1.177 15 933 5.4 87 1.46 SA09 I.ITI 15 933 '~.2 90 1.39 SAI3 1.177 15 579 79.7 92 1.30
Cyclone outles; 2'54 ça dhnerrt , 7 .0 (li long
S003 0.213 3 43 56.3 87 1.91 SOO6 0.603 8 5M 46.1 92 1.14 SOOI 1.177 15 2353 22.3 95 0.96
c
APPENDIX 2
TEMPERATURE HEASUREHENT
o
o
252
APPENDIX 2
TEMPERATURE HEABUREHENT
The arrangement of the thermocouples for measuring the inlet
and outlet gas temperatures were shown in F;gures 2-3 and
2-4. The alignment of the tip of the thermocouples paraI leI
to the axes of the channel has the advantage that the tem
perature gradient along the tip of the thermocouple is
negligible, therefore conduction heat losses can be
neglected. A heat balance around the tip of the thermo
couple reduces to equating the convective and radiative heat
fluxes:
(A2-1)
where hf is an average heat transfer coefficient, At is the
surface area of the thermocouple, 0 is the Stefan-Boltzman
constant, Et is the total emissivity (0.98) and Ftw is the
view factor from the thermocouple to the wall (taken to be
one).
Since hf was not kno~n, a second equation was needed in
order to determine hf and Tg. Several empirical
correlations for forced convectiop heat transfer from a
sphere or cylinder to agas were tried including those of
Hilpert (1933), McAdam (1954) and Whitaker (1972). The
(
<:
(
253
correlations that generally gave the most conservative
estimates of Tg were some presented by Clift et al. (1978)
which were derived from a collection of published data:
Nu -= 1 + prl/3[1 + 1] 1/3 ReO•41 Re·Pr
Nu = 1 + 0.677ReC•47 100<Re:S:4000
Nu = 1 + 0.272ReO•S8 4 OOO<Re:S: leS
1<Re<100 (A2-2a)
(A2-2b)
(A2-2c)
where Nu [=hfdtfkf] is the Nusselt number. The Reynolds
number [Re -= pvdtfp] was based on the thermocouple diameter
with the gas properties evaluated at the film temperature
[(Tg+Tt)/2]. The Reynolds number ranged between 100 and
2 000. The Prandtl number [Pr = cpp/kf] was also determined
at the film temperature, and was always close to 0.7.
A trial and error procedure was used to determine hf and Tg
stllrting by guessing Tg, calculating h from equati.," A2-2,
calculating a new Tg from equation A2-1 and comparing it to
the guessed value. The assumed and calculated Tg usually
converged to within 1 K in two to six Iterations.
The wall temperature was measured by a thermucouple strapped
to the outer wall of the channels directly opposite the gas
temperature thermocouples. A heat-flux gauge was taped to
€}
2000 1
loocr A 1U'Tl1 na
o Inlet
1000 l- Il Outlet ~
• ~ 1400
ml200
~ 1000'· fi)
WOOD 12 8000
400~/ 1./
200 200 40CJ 00) BOO 1000 1 zoo 1400 1000
tEAStRED TEWERATlR:. K
Figure A2-1 Measured vs correctcd tcmpcraturc for runs with alumina.
1 BOO 2000
~
'" '" '"
~
2(XX) 1
1800~ Slllca '6
o lnlet
~ 100) [ C Outlet
Q>
~ • ~
2 0,
1400 ~tj
1 zoo 1
1000
~ !:Po:
800 Ole/'
w o:r Œ 0 00) u
-100
ZOO~V~ __ -L ____ ~ ____ ~~ ____ ~ ____ ~ ____ ~ ____ ~ ____ ~ ____ ~
zoo 400 00) 800 1000 1200 1-100 Hm 1800 2(XX) tEASt.RED TePERATœE. K
Figure A2-2 Measured vs corrected temperature for runs with silica.
~
N (II 0>