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High-efficiency industrial cyclone separator: A CFD study
Journal Pre-proof High-efficiency industrial cyclone separator: A CFD study Dzmitry Misiulia, Sergiy Antonyuk, Anders Gustav Andersson, Tord Staffan Lundström PII:
S0032-5910(19)30887-3
DOI:
https://doi.org/10.1016/j.powtec.2019.10.064
Reference:
PTEC 14831
To appear in:
Powder Technology
Received Date: 20 January 2019 Revised Date:
10 September 2019
Accepted Date: 15 October 2019
Please cite this article as: D. Misiulia, S. Antonyuk, A.G. Andersson, T.S. Lundström, High-efficiency industrial cyclone separator: A CFD study, Powder Technology (2019), doi: https://doi.org/10.1016/ j.powtec.2019.10.064. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.
High-efficiency industrial cyclone separator: a CFD study Dzmitry Misiuliaa,∗, Sergiy Antonyukb , Anders Gustav Anderssonc , Tord Staffan Lundstr¨omc a
Department of Machines and Apparatus for Chemical and Silicate Production, Belarusian State Technological University, 13a Sverdlova str., 220006 Minsk, Belarus b Institute of Particle Process Engineering, University of Kaiserslautern, D-67653 Kaiserslautern, Germany c Division of Fluid and Experimental Mechanics, Department of Engineering Sciences and Mathematics, Lule˚ a University of Technology, SE-971 87 Lule˚ a, Sweden
Abstract The flow within an industrial scroll-inlet high-efficiency cyclone separator has been studied using RSM and LES simulations. Of particular interest is the effect of the gas outlet configuration, i.e. outlet scroll and radial bend, on the flow pattern, pressure drop and cyclone efficiency. A surprising phenomenon is that the inner vortex splits into two vortices for the cyclone with a conventional outlet pipe while if the cyclone is equipped with an outlet scroll or radial bend there is no split. The outlet scroll and radial bend increase the pressure losses by 5.1% and 6.4%, respectively. These installations, moreover, significantly destabilize the pressure losses and the amplitude of instantaneous pressure drop oscillations increases from 0.65% ∗ Corresponding author. Tel.: +375 17 2202694, fax: +375 17 3276217. Postal address: Department of Machines and Apparatus for Chemical and Silicate Production, Belarusian State Technological University, 13a Sverdlova str., 220006 Minsk, Belarus. Email addresses: [email protected] (Dzmitry Misiulia), [email protected] (Sergiy Antonyuk), [email protected] (Anders Gustav Andersson), [email protected] (Tord Staffan Lundstr¨om)
Preprint submitted to Powder Technology
September 10, 2019
to 16.2% and 33.96%, respectively. The investigated outlet scroll and radial bend have practically no effects on the cyclone efficiency since the flow in the main separation zone is not affected by the gas outlet configuration. Keywords: Cyclone separator, Computational Fluid Dynamics, vortex breakdown, pressure drop, collection efficiency
1
1. Introduction
2
Gas cyclones are the most popular tools for the separation of solid par-
3
ticles from gases in industrial applications. Their popularity is due to their
4
simplicity, reliability, relatively low manufacturing costs and ability to work
5
under high pressures and temperatures.
6
The usage of high-efficiency cyclone separators is increasing especially
7
those that function without bag filters due to very high separation capability,
8
i.e. ACS Hurricane cyclones and ReCyclone systems [1, 2].
9
Gas cyclones are used as a pre-separator of a two or three-stage system,
10
as the only separation stage or as the final separation stage. In the first case,
11
when two or more cyclones are connected in series, an outlet scroll is normally
12
installed directly after and on top of the first stage cyclone. Sometimes,
13
due to practical reasons, a radial bend is attached to the gas outlet pipe
14
(vortex finder) instead of a scroll. In the second case when cyclone exhausts
15
directly into the atmosphere they commonly contain just a cylindrical outlet
16
pipe or one that is covered with a shallow cone to keep rain out a so-called
17
rain hat [3]. Outlet scrolls may also be installed on any cyclone wherein the
18
exhaust gas is to undergo a significant reduction in velocity, i.e. its expansion
19
to the atmosphere. The smooth expansion of the gas as it passes through
2
20
the scroll reduces the tangential velocity of the gas flow and converts a part
21
of its kinetic energy stored with the tangential velocity into static pressure.
22
Without such a scroll, the gas would undergo an abrupt expansion with an
23
instantaneous loss of kinetic energy. Thus, a well-designed outlet scroll will
24
imply a pressure recovery and this is the main reason of installing it. A
25
small pressure drop reduction can also be reached with a radial bend at the
26
outlet [4] but this is not its main purpose.
27
Several experimental and numerical works on the cyclone aerodynamics
28
and its performance with different gas outlet configurations have been carried
29
out. Muschelknautz (as it is quoted in [5]) investigated the effect of a
30
number of pressure recovery configurations including an outlet scroll, and
31
found that the outlet scroll reduced the pressure drop by 12% as compared to
32
the pressure drop with a conventional cylindrical, sharp-edged vortex finder.
33
Funk [3] experimentally investigated the pressure drop of a cyclone with
34
rectangular and radial evas´es at the outlet. One conclusion was that the
35
pressure drop in a cyclone can be reduced by between 8.7 and 11.9% with
36
the addition of a radial evas´e assuming that the separation efficiency is not
37
affected since the evas´e is outside of and downstream from the cyclone.
38
Kahrimanovic et al. [6] studied a cyclone with two configurations of the
39
radial diffuser at the gas outlet, a ”horizontal” one and an ”inclined” one
40
which was arranged at an angle of 30◦ with respect to the horizontal dif-
41
fuser. These two gas outlet configurations were compared with the radial
42
bend which was referred to as a normal outlet. With the ”horizontal” radial
43
diffuser 30% of pressure was recovered while with the more efficient but com-
44
plicated ”inclined” geometry the enhancement in pressure recovery was only
3
45
2-3%. A small enhancement with the ”inclined” diffuser was explained by
46
the larger radius of the diffuser plate. It was also concluded that the parti-
47
cle separation in the cyclone was not strongly affected by the radial diffuser
48
placed downstream the vortex finder.
49
The main goal with this work is to investigate the flow pattern and per-
50
formance of a high-efficiency industrial cyclone separator with a conventional
51
gas outlet pipe and reveal the effects of adding an outlet scroll or a radial
52
bend using Computational Fluid Dynamics (CFD) simulations.
53
2. Numerical modelling
54
2.1. Governing equations
55
A Eulerian-Lagrangian approach was applied to model two-phase gas-
56
solid flow in a cyclone. The gas phase was treated as an incompressible
57
isothermal flow using an Eulerian approach and the Lagrange method was
58
applied for the solid particles. These particles were tracked through the
59
cyclone.
60
2.1.1. Governing equations for continuous phase
61
62
The Reynolds-averaged Navier-Stokes (RANS) equations for the incompressible isothermal gas phase can be written as: ∂ui = 0, ∂xi
63
∂ui ∂ui 1 ∂p ∂ + uj =− + ∂t ∂xj ρ ∂xi ∂xj
(1) ∂ui 0 0 ν − ui uj ∂xj
(2)
64
where ui is the time-averaged (mean) gas velocity; u0i is the fluctuating gas ve-
65
locity; u0i u0j is the fluctuating Reynolds stress contribution; ν is the kinematic
66
viscosity of the gas; ρ is the gas density; p is the mean static pressure. 4
67
The Reynolds stress model (RSM) (as reported in [7]) has been proven
68
as the most appropriate RANS turbulence model for the prediction of highly
69
swirling flows in a cyclone separator and it was therefore applied in this
70
study. A separate differential Reynolds stress transport equation was solved
71
for each Reynolds stress components according to: ! ∂u0 u0 i j 2 k2 ∂ ν + 3 Cs ∂xk ∂u0i u0j ∂u0i u0j 2 − = Pij − δij + Φij , + uk ∂t ∂xk ∂xk 3 1 0 0 uu 2 i j
(3)
is the turbulence
72
where Cs is an isotropic diffusion coefficient; k =
73
kinetic energy; is turbulence dissipation rate; Pij is the exact production
74
term; δij is the Kronecker delta (δij = 1 if i = j and δij = 0 if i 6= j); Φij is
75
a pressure-strain correlation.
76
The exact production term is defined as: Pij = −u0i u0k
77
∂uj ∂ui − u0j u0k . ∂xk ∂xk
(4)
The pressure-strain correlation acts to drive turbulence towards an isotropic
78
state by redistributing the Reynolds stresses and can be split into two parts,
79
a slow, also known as the return-to-isotropy, term and a rapid term which
80
are defined as:
81
Φij,1
82
Φij = Φij,1 + Φij,2 , 1 = − Cs1 aij + Cs2 aik ajk − amn amn δij , 3
(5)
√ 1 Φij,2 = − Cr1 Pij aij + Cr2 kSij − Cr3 kSij amn amn + 2 2 +Cr4 k aik Sjk + ajk Sik − akl Skl δij + Cr5 k (aik Θjk + ajk Θik ) 3
5
(6)
(7)
83
where Cs1 , Cs2 , Cr1 , Cr2 , Cr3 , Cr4 , Cr5 are the model coefficients; aij is an
84
anisotropy tensor; Sij is a mean strain rate tensor; and Θij is a vorticity
85
tensor. These tensors are given by u0i u0j 2 aij = − δij , k 3 1 ∂ui ∂uj + , Sij = 2 ∂xj ∂xi 1 ∂ui ∂uj Θij = . − 2 ∂xj ∂xi
86
87
88
A transport equation for turbulence dissipation rate is written as ∂ νt ∂ ν + σRS ∂ ∂ ∂xk + uk = (C1 Pk − C2 ) + , ∂t ∂xk k ∂xk
(8) (9) (10)
(11)
89
where C1 and C2 are model coefficients; σRS is a turbulent Schmidt number;
90
νt is the turbulent kinematic viscosity νt = CµRS
91
k2
(12)
where CµRS is a model coefficient.
92
The RSM model developed by Speziale, Sarkar and Gatski [8] was used in
93
this study. This RSM model uses a quadratic relation for the pressure-strain
94
correlation and is more accurate than the other RSM models particularly for
95
swirling flows [9]. The RSM model coefficients are listed in Table 1.
96
For a proper prediction of the flow field at the wall a scalable wall func-
97
tion [10] was applied.
98
2.1.2. Governing equations for dispersed phase
99
The dispersed phase was calculated using particle transport modelling
100
where representative spherical particles were tracked through the flow. The 6
101
tracking was carried out by forming a set of ordinary differential equations
102
in time for each representative particle, consisting of equations for position
103
and velocity using forward Euler integration [10, 11] according to: xnp = xop + uop ∆t,
104
up =
dxp , dt
(13) (14)
105
where xp was a particle position; up was a particle velocity; the superscripts
106
o and n referred to old and new values respectively; t was time; ∆t was a
107
time step.
108
In forward integration, the particle velocity calculated at the start of the
109
time step was assumed to prevail over the entire step. At the end of the time
110
step, the new particle velocity was calculated using the analytical solution
111
to the particle momentum equation as: − → − → π 3 d→ up − dp ρp = FD + FG 6 dt
(15)
112
where dp was the particle diameter; ρp was the particle density; FD was an
113
aerodynamic drag force acting on the particle; FG was a net force due to
114
gravity being equal to the gravitational force subtracted with the buoyant
115
force.
116
The aerodynamic drag force was defined as: πd2p 1 F D = CD ρ |u − up | (u − up ) 2 4
(16)
117
where CD was the drag coefficient derived from the Schiller Naumann corre-
118
lation according to [10]:
24 0.687 CD = max 1 + 0.15Rep , 0.44 Rep 7
(17)
119
where the particle Reynolds number was: Rep =
120
dp |us | . ν
(18)
The net force due to gravity was in its turn given by FG =
121
where g was gravity.
122
2.2. Cyclone geometry
π 3 d (ρp − ρ) g 6 p
(19)
123
A high-efficiency industrial gas cyclone STsN-40 [4] with an internal di-
124
ameter of 0.3 m was studied. As previously described the three outlet con-
125
figurations were investigated, an ordinary outlet pipe, an outlet scroll and a
126
radial bend as shown in Fig. 1. The geometrical dimensions of the cyclone
127
are given in Table 2.
128
2.3. Boundary conditions and numerical settings
129
A velocity profile for a fully developed air flow was applied at the in-
130
let. All cyclones were investigated at an area-averaged inlet velocity of
131
win = 24.5 m s−1 , that being the optimal velocity for this type of
132
cyclone (according to [4]), see Fig. 2. The recommended inlet velocity range
133
for the investigated cyclone is 16.8 – 24.5 m s−1 . Therefore, the cyclone with
134
an ordinary outlet pipe was also investigated at area-averaged inlet velocities
135
of 16.8 and 20.7 m s−1 . The area-averaged inlet velocity was computed as
136
the ratio of the volumetric flow rate to the inlet cross-sectional area as:
win = 8
Q , ab
(20)
137
where Q was the volumetric flow rate; a and b were the inlet width and
138
height.
139
At the outlet, an opening boundary condition with zero pressure normal
140
gradient that allows the air to cross the boundary surface in both directions
141
was used. The air density and dynamic viscosity were set to 1.205 kg m−3
142
and 1.831×10−5 Pa s, respectively. A medium turbulence intensity of 5% was
143
set both at the inlet and the outlet. A non-slip smooth wall boundary con-
144
dition was applied on all other boundaries. In two-phase simulations, 25000
145
representative particles 0.2−4 µm in diameter (1000 particles for 25 different
146
diameters) with a density of 1930 kg m−3 , random initial positions and zero
147
slip velocity were injected at the inlet. For a proper particle tracking solu-
148
tion, 100 integration steps per element were applied [10, 12, 13]. To reduce
149
the computational time, the particles reaching the side wall and bottom of
150
the dust hopper were terminated by applying the parallel and perpendic-
151
ular coefficients of restitution of 0.0 on these surfaces. For all other walls,
152
these coefficients were set to 0.8 which is commonly applied to many different
153
materials [14].
154
The time step ∆t was 1×10−5 – 5×10−5 s that resulted in a mean volume-
155
averaged Courant number of 0.16–0.51 for all cases (Table 3). The root-mean-
156
square scaled residuals were set below 2×10−5 which required, in average, 5
157
loop iterations within a time step.
158
The simulations were performed on a 64-bit Linux cluster at Lule˚ a Uni-
159
versity of Technology using a commercial solver ANSYS CFX 15.0 (ANSYS,
160
Inc., Canonsburg, Pennsylvania, USA). During simulations, tangential ve-
161
locities at some points in the cyclone body, area-averaged total and static
9
162
pressure at different sections, total pressure drop, volume-averaged turbu-
163
lence kinetic energy and turbulence eddy dissipation as well as area-averaged
164
y + were monitored to be sure that the flow inside the cyclone had reached its
165
fully developed state (statistically steady-state). After that, an arithmetic
166
averaging was initiated.
167
3. Grid independence study
168
A grid independence study was performed for a cyclone separator with
169
an ordinary gas outlet pipe. Five high quality grids with 0.327, 0.551, 0.871,
170
1.211 and 3.601 million elements were generated, No 1–5 in Table 3. For
171
a proper near the wall treatment with scalable wall function in RSM, the
172
thickness of the first grid nearest the wall should result in y + from 11.06 to
173
300. The mean area-averaged values of y + for all 5 grids were in this range,
174
see Table 3.
175
The effects of the grid size on the time-averaged tangential and axial
176
velocities in the cyclone body along the x-axis (y = 0, z = 0) can be seen
177
in Fig. 3. The velocities are normalized with the area-averaged inlet velocity
178
win .
179
All meshes captured the inverted ”W”-shape of the tangential velocity
180
profile, but the axial velocity profiles predicted with the coarsest mesh signif-
181
icantly differed from the others. The maximum tangential velocity increased
182
with the increase in number of mesh elements (Fig. 3). However increasing
183
the number of elements in the mesh from 0.871 million had negligible effects
184
on the tangential and axial velocity distributions. To conclude, the flow pat-
185
tern in a cyclone can be quite accurately captured with a mesh consisting 10
186
of 0.871 million elements. Using a finer mesh will not lead to significant
187
changes in velocity profiles but will increase the computational time. There-
188
fore, meshes with the same element size were created for the cyclones with
189
an outlet scroll (No 6 in Table 3) and radial bend (No 7 in Table 3), as shown
190
in Fig. 4.
191
Due to a lack of information in the literature regarding pressure and
192
velocity distributions in the investigated cyclone with its scroll inlet, there
193
are no reliable data to perform a validation study. Based on the results
194
of previous studies of a reverse-flow cyclone separator with a helical-roof
195
inlet [7, 10, 11, 12, 13] that showed good agreement between the numerical
196
and experimental data, it is likely that the numerical model and settings can
197
adequately predict the flow pattern in this cyclone as well. Nevertheless,
198
in order to exclude some uncertainty, Large Eddy Simulations (LES) of a
199
cyclone with an ordinary gas outlet pipe were performed using the dynamic
200
Smagorinsky-Lilly model [15] and the results were compared with the RSM
201
simulations (No 8 and 9 in Table 3).
202
LES simulations require much finer mesh and the mesh size should prefer-
203
ably be in the dissipation range of the turbulent length scale where motions
204
experience viscous effects. Based on mean volume-averaged turbulence ki-
205
netic energy and eddy dissipation the length scales and ranges for the cyclone
206
were defined according to [11, 16] and are sketched in Fig. 5.
207
The simulations were performed with a mesh consisting of 7.25 million
208
elements. It can be seen from Fig. 5 that the average mesh element size
209
for the cyclone was within the dissipation range of the universal equilibrium
210
range.
11
211
The tangential and axial velocity profiles predicted with the RSM and
212
LES models are shown in Fig 6. The tangential velocity predicted with LES
213
were slightly higher. Both the RSM and LES models revealed the same
214
profiles for tangential and axial velocities and agreed well.
215
4. Results and discussion
216
4.1. Effects of the gas outlet configuration on the flow pattern in the cyclone
217
The contour plots of the time-averaged static pressure, tangential velocity
218
and axial velocity in the cyclone body and in the vortex finder for the three
219
gas outlet configurations are shown in Fig. 7. The radial profiles of the tan-
220
gential and axial velocity components along the x-axis at three cut sections
221
along the cyclone axis (z = 0, 0.15 and 0.3 m) are presented in Fig. 8. Since
222
the geometrical axis of the outlet scroll and radial bend did not coincide with
223
the cyclone geometrical axis (z-axis) which was used as the axis of rotation
224
for computing the tangential and axial velocities, the contour plots of the
225
static pressure and velocity field in the scroll outlet and radial bend are not
226
shown in Fig. 7.
227
Static pressure in a cyclone (Fig. 7) has its minimum value in the vortex
228
core region, i.e. near or at the geometrical axis of the cyclone and increases
229
towards the periphery where it reaches its maximum value. The difference
230
between the maximum and minimum values, i.e. the difference in static
231
pressure at the cyclone wall and its centerline was about 4.6 kPa in the cy-
232
clone with the ordinary outlet pipe. Placing the outlet scroll and radial bend
233
downstream the vortex finder increased this difference to 6.3 and 5.1 kPa
234
respectively. 12
235
The maximum tangential velocity was approximately twice as large as the
236
inlet velocity and was practically constant along the cyclone axis (Fig. 7).
237
The radial profile of the tangential velocity distribution had an inverted ”W”-
238
shape and was almost independent of the z-axis (Fig. 8). The outlet scroll
239
and radial bend had insignificant effects on the tangential velocity field in
240
the cyclone body.
241
The axial velocity field in the cyclone with different gas outlet configura-
242
tions could be divided into two zones, an outer zone with negative velocity
243
values and an inner zone with positive velocity values. The outer zone de-
244
termined the downwardly directed outer vortex and the inner one defined
245
the size of the upwardly directed inner vortex. Not the outlet scroll nor a
246
radial bend had a noticeable effect on the axial velocity distribution in the
247
outer zone but they did effect the inner zone. This can be explained by some
248
transformation of the inner vortex which precesses around the cyclone axis.
249
Fig. 9 represents the iso-surfaces of the vorticity around z-axis of −3000 s−1 .
250
A very interesting phenomenon, a ”vortex-breakdown with bifurcated double
251
helix” occurred in the cyclone separator with an ordinary outlet pipe. The
252
onset of the ”vortex-breakdown” was a bit upstream the vortex finder where
253
the upwardly directed inner vortex divided into two vortices which then en-
254
tered the vortex finder. As a result, there were two vortices in the vortex
255
finder which broke up at the gas outlet section.
256
The revealed vortex-breakdown with bifurcated double helix occurred in
257
the cyclone separator with an ordinary outlet pipe at different inlet velocities
258
over the whole recommended operation range of 16.8 – 24.5 m s−1 . Fig. 10
259
shows the vortex-breakdown phenomenon at area-averaged inlet velocities
13
260
of 16.8, 20.7 and 24.5 m s−1 . The inlet velocity did not affect the vortex-
261
breakdown but changed the swirl intensity in the cyclone and vortex finder.
262
Such a ”vortex-breakdown” phenomenon can be also seen in Fig. 11 which
263
represents the instantaneous tangential and axial velocity contour plots in the
264
vortex finder. The contour plots predicted with the RSM and LES model
265
are similar and show good agreement.
266
Such a vortex breakdown with bifurcated double helix in a swirling flow
267
was reported by Meliga et al. [17]. Also, Karniadakis and Sherwin [18] iden-
268
tified such an onset of the ”vortex-breakdown” with Direct Numerical Sim-
269
ulations (DNS) using a Fourier series approximation in the axial direction.
270
Spiral modes of instability were found to cause a lateral expansion of the
271
cross-section of the vortex core, and a corresponding drop in axial velocity.
272
When the assumption of axial periodicity was neglected, as in a fully three-
273
dimensional DNS, this then led to an axial stagnation point – indicative of
274
vortex breakdown. Vortex tip stabilization has been also explored at the
275
bottom of a cyclone [19, 20, 21].
276
Surprisingly, such a ”vortex-breakdown” phenomenon does not occur if
277
the outlet scroll or radial bend is placed downstream the vortex finder. More-
278
over, the phenomenon does not appear in other cyclone geometries with the
279
ordinary gas outlet pipe, see for instance [11, 22].
280
The time-averaged parameters of the flow at the gas outlet are not rep-
281
resentative since the flow at the gas outlet is unstable and there is a strong
282
precession of the vortex core [11]. Instead, 15 streamlines coloured by abso-
283
lute velocity in the vortex finder, outlet scroll and radial bend are presented
284
in Fig. 12. The flow in the conventional vortex finder is still quite swirling
14
285
at the outlet and the maximum absolute velocity reaches 70 m/s. In fact, a
286
well-designed outlet scroll should reduce the velocity due to expansion of the
287
cross-sectional area. However, these simulations showed that the velocities
288
in the outlet scroll and radial band were higher than in the ordinary outlet
289
pipe and the streamlines were not structured, especially in the outlet scroll.
290
With the investigated outlet scroll design the velocity at the outlet was not
291
reduced and as a result there maybe higher pressure losses at the outlet.
292
4.2. Effects of the gas outlet configuration on the cyclone performance
293
294
Cyclone performance is characterized by pressure drop and collection efficiency.
295
Pressure drop is an important cyclone performance characteristic since it
296
determines operation cost of a cyclone which is proportional to the energy
297
required to overcome these pressure losses. The instantaneous total pressure
298
drop across the cyclone with the three different gas outlet configurations
299
is shown in Fig. 13 whereas the time-averaged total pressure drop and the
300
pressure losses in the cyclone body (upstream the vortex finder inlet) and
301
in the vortex finder and gas outlet (downstream the vortex finder inlet) are
302
plotted in Fig. 14.
303
Surprisingly, both the outlet scroll and bend outlet increased the total
304
pressure drop across a cyclone instead of the opposite. Moreover, they lead
305
to dramatical increase in oscillations of the instantaneous pressure drop. The
306
amplitude of these oscillations (i.e. the difference between the maximum and
307
minimum value of the instantaneous pressure drop) was very small in the
308
cyclone separator with the conventional outlet pipe and was equal to 0.65%
309
of the average total pressure drop. However installing the outlet scroll and 15
310
radial bend downstream from the vortex finder increased the amplitude of
311
oscillations to 16.2% and 33.96%, respectively (Fig. 13).
312
Fig. 14 shows that the pressure losses in the cyclone body upstream from
313
the vortex finder, i.e. the pressure losses from the cyclone inlet to the vortex
314
finder inlet, were nearly 2000 Pa and were almost independent of the gas out-
315
let configuration downstream from the vortex finder. This can be explained
316
by the fact that the gas outlet configuration has minor effects on the velocity
317
distribution in the cyclone body. Placing the outlet scroll and radial bend
318
downstream from the vortex finder, however, increased the pressure losses in
319
the vortex finder and downstream from it, i.e. from the vortex finder inlet
320
to the cyclone gas outlet. This can be explained by higher velocities in the
321
outlet scroll and radial bend (Fig. 12).
322
Time-averaged pressure drop coefficients (based on the inlet velocity and
323
mean axial velocity in a cyclone body) of a cyclone with different gas outlet
324
configurations are listed in Table 4. It shows that the installation of an out-
325
let scroll and radial bend downstream from the vortex finder increased the
326
dimensionless pressure losses, the Euler number, by 5.1% and 6.4% respec-
327
tively. A negative effect in pressure drop reduction with the scroll outlet was
328
also reported by Lazarev [4] and Idel’chik [23]. The investigated radial bend
329
(R = 1.5D) was probably too abrupt and located too close to the vortex
330
finder. These negative effects can be overcome by optimization of the gas
331
outlet design.
332
The effects of the outlet scroll and radial bend on the cyclone collection
333
efficiency are presented in Fig. 15. The investigated gas outlet configurations
334
had almost no effect on the cyclone grade efficiency curve, as expected, since
16
335
the outlet scroll and radial bend were downstream from the vortex finder
336
and did not significantly affect the flow field in the cyclone body where the
337
particles are separated from the gas flow. The predicted cut-size of all cy-
338
clones was practically the same and about 1.1 µm. Cyclones with such a
339
small value of the cut-size (i.e. high separation capability) can be used as a
340
final separation stage in industry.
341
5. Conclusions
342
An industrial high-efficiency cyclone separator with three different gas
343
outlet configurations (conventional outlet pipe, outlet scroll and radial bend)
344
has been computationally investigated using Reynolds stress model simula-
345
tions and Large eddy simulations and the effects of the outlet scroll and radial
346
bend placed downstream the vortex finder on the flow pattern and cyclone
347
performance have been revealed. The following conclusions can be drawn:
348
• a unique ”vortex-breakdown with bifurcated double helix” phenomenon
349
occurs in the high-efficiency cyclone separator with an ordinary outlet
350
pipe. The observation is that the inner vortex split into two vortices.
351
This is a phenomenon that has never been found in cyclone separators
352
before. This phenomenon does not appear if the outlet scroll or radial
353
bend is placed downstream the vortex finder. Additional studies are
354
needed to reveal the reason and nature for the double helix;
355
• an outlet scroll and radial bend have insignificant effects on the velocity
356
field in a cyclone body except regarding the axial velocity distribution
357
in the inner vortex as described above;
17
358
• installation of an outlet scroll and radial bend downstream from the
359
vortex finder increases the dimensionless pressure losses by 5.1% and
360
6.4% respectively. Moreover it significantly destabilizes the pressure
361
losses by increasing the amplitude of instantaneous pressure drop os-
362
cillations from 0.65% to 16.2% and 33.96% respectively;
363
364
365
366
• the outlet scroll and radial bend have almost no effect on the cyclone separation capability; • the geometry of the investigated scroll outlet is not properly designed and needs to be optimized;
367
• placing the radial bend (R = 1.5D) right downstream from the vortex
368
finder is not recommended since it leads to high pressure losses. This
369
negative effect can be probably overcome by increasing the bend radius
370
and placing the radial bend further downstream from the vortex finder.
371
Future extension of this work is firstly to investigate the reasons and
372
nature of the unique ”double spiral vortex-breakdown” phenomenon, and
373
secondly optimize the gas outlet configuration in terms of minimum pressure
374
losses.
375
Acknowledgements
376
377
This work was partially performed with financial support provided by Swedish Institute through the Visby Programme to the first author.
18
378
379
380
381
382
383
384
385
386
387
388
References
[1] A.Alves, J.Paiva, R.Salcedo, Cyclone optimization including particle clustering, Powder Technology 272 (2015) 14–22. [2] Advanced Cyclone Systems, Hurricane and ReCyclone systems. http://www.acsystems.pt/, 2017 (accessed 7 March 2018). [3] P.A. Funk, Reducing cyclone pressure drop with evas´es, Powder Technology 272 (2015) 276–281. [4] V.A.Lazarev, Cyclones and Vortex Dust Traps: A Handbook, 2nd ed., Ozon-NN, Nizhnii Novgorod, Russia, 2006. [5] A.C. Hoffmann, L.E. Stein, Gas Cyclones and Swirl Tubes, 2nd ed., Springer Berlin Heidelberg New York, 2008.
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[6] D. Kahrimanovic, S. Puttinger, G. Aichinger, S. Pirker, Minimizing
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pressure drop in cyclone separators measurements and numerical sim-
391
ulations, 11th World Filtration Congress, 16-20 April, 2012, Graz, Aus-
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tria.
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[7] D.Misiulia, A.G.Andersson, T.S.Lundstr¨om, Computational investiga-
394
tion of an industrial cyclone separator with helical-roof inlet, Chemical
395
Engineering and Technology 38 (8) (2015) 1425–1434.
396
[8] C.G.Speziale, S.Sarkar, T.B.Gatski, Modelling the pressure-strain corre-
397
lation of turbulence: an invariant dynamical systems approach, Journal
398
of Fluid Mechanics 227 (1991) 245–272. 19
399
400
[9] ANSYS CFX-Solver Theory Guide, Release 15.0, ANSYS, Inc, Canonsburg, Pennsylvania 2013.
401
[10] D.Misiulia, K.Elsayed, A.G.Andersson, Geometry optimization of a
402
deswirler for cyclone separator in terms of pressure drop using CFD
403
and artificial neural network, Separation and Purification Technology
404
185 (2017) 10–23.
405
[11] D.Misiulia, S.Antonyuk, A.G.Andersson, T.S.Lundstr¨om, Effects of
406
deswirler position and its centre body shape as well as vortex finder
407
extension downstream on cyclone performance, Powder Technology 272
408
(2018) 14–22.
409
[12] D.Misiulia, A.G.Andersson, T.S.Lundstr¨om, Large eddy simulation in-
410
vestigation of an industrial cyclone separator fitted with a pressure re-
411
covery deswirler, Chemical Engineering and Technology 40 (4) (2017)
412
709–718.
413
[13] D.Misiulia, A.G.Andersson, T.S.Lundstr¨om, Effects of the inlet angle
414
on the collection efficiency of a cyclone with helical-roof inlet, Powder
415
Technology 305 (2017) 48–55.
416
[14] C.T. Crowe, J.D. Schwarzkopf, M. Sommerfeld, Y. Tsuji, Multiphase
417
flows with droplets and particles, 2nd ed., CRC Press, Boca Raton,
418
Florida, USA 2012.
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[15] D.K.Lilly, A proposed modification of the Germano subgrid-scale closure method, Physics of Fluids A 4 (3) (1992) 633635.
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[16] S.B. Pope, Turbulent Flows, IOP Publishing. 2001.
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[17] P. Meliga, F. Gallaire, J.-M. Chomaz, A weakly nonlinear mechanism for
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mode selection in swirling jets, Journal of Fluid Mechanics 699 (2012)
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216–262.
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427
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[18] G.E. Karniadakis, S.J. Sherwin, Spectral/hp element methods for computational fluid dynamics. Oxford University Press, 1999. [19] J.J. Derksen, Separation performance predictions of a Stairmand highefficiency cyclone, AIChE Journal 49 (6) (2003) 1359–1371.
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[20] W. Peng, A.C. Hoffmann, P.J.A.J. Boot, A. Udding, H.W.A. Dries,
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A. Ekker, J.Kater, Flow pattern in reverse-flow centrifugal separators,
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Powder Technology 127 (2002) 212–222.
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[21] C. Cort´es, A. Gil, Modeling the gas and particle flow inside cyclone
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separators, Progress in Energy and Combustion Science 33 (2007) 409–
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452.
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[22] L.S. Brar, K.Elsayed, Analysis and optimization of multi-inlet gas cy-
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clones using large eddy simulation and artificial neural network, Powder
437
Technology 311 (2017) 465–483.
438
439
440
[23] I.E. Idel’chik, Handbook of Hydraulic Resistance, 3rd ed., Begell House, 1996.
Nomenclature and units
441
21
Upper-case Roman CD
[–]
drag coefficient
Cr1−r5
[–]
RSM model coefficient
Cs
[–]
isotropic diffusion coefficient
Cs1 ,Cs2
[–]
RSM model coefficient
CµRS
[–]
RSM model coefficient
C1 ,C2
[–]
RSM model coefficient
Co
[–]
Courant number
D
[m]
cyclone body diameter
De
[m]
vortex finder diameter
Eu
[–]
Euler number normalized by mean axial velocity in a cyclone body
Euin
[–]
Euler number normalized by inlet velocity
FD
[N]
drag force
FG
[N]
net force due to gravity
L
[m]
characteristic length scale
N
[–]
number of mesh elements
Rep
[–]
particle Reynolds number
Sij
[s−1 ]
mean strain rate tensor
Q
[m3 s−1 ]
volumetric gas flow rate
a
[m]
cyclone inlet height
aij
[–]
anisotropy tensor
b
[m]
cyclone inlet width
dp
[m]
particle diameter
Lower-case Roman
22
g
[m2 s−1 ]
gravity
k
[m2 s−2 ]
turbulence kinetic energy
l
[m]
length scale
lDI
[m]
length scale which splits the universal equilibrium range into inertial subrange and dissipation range
lEI
[m]
length scale that forms the demarcation between the energy containing range and the universal equilibrium range
l0
[m]
integral scale
lη
[m]
Kolmogorov length scale
p
[Pa]
static pressure
∆p
[Pa]
total pressure drop across a cyclone
r
[m]
radius
s
[m]
vortex finder length
t
[s]
time
∆t
[s]
time step
u
[m s−1 ]
gas velocity
up
[m s−1 ]
particle velocity
wax
[m s−1 ]
axial component of gas velocity
win
[m s−1 ]
inlet gas velocity
wt
[m s−1 ]
tangential component of gas velocity
xp
[m]
particle position
y+
[−]
dimensionless parameter
δij
[–]
Kronecker delta 23
[m2 s−3 ]
turbulence eddy dissipation
ν
[m2 s−1 ]
kinematic viscosity
νt
[m2 s−1 ]
turbulent kinematic viscosity
ρ
[kg m−3 ]
gas density
ρp
[kg m−3 ]
particle density
σµRS
[–]
RSM model coefficient
θij
[s−1 ]
vorticity tensor
Φij
[m2 s−3 ]
pressure-strain correlation
Other symbols ¯
time-averaged (mean)
0
fluctuating
hi
volume-averaged
area-averaged
Abbreviations CFD
Computational Fluid Dynamics
DNS
Direct Numerical Simulations
LES
Large Eddy Simulations
RANS
Reynolds-averaged Navier-Stokes
RSM
Reynolds stress model
24
Tables
442
Table 1: RSM model coefficients
CµRS 0.1
σRS
Cs
1.363 0.22
Cs1
Cs2
Cr1
Cr2
Cr3
Cr4
1.7
1.05
0.9
0.8
0.65 0.625
Cr5
C1
C2
0.2
1.44 1.83
Table 2: Cyclone dimensions (normalized by cyclone diameter D)
a
b
De
d
d1
d2
H
h
hc
h1
h2
l
s
0.38 0.16 0.4 0.2 0.7 0.15 3.3 1.6 1.6 0.8 0.1 0.5 0.4
443
25
Table 3: Numerical settings
Number Case No
Gas outlet
of mesh
configuration elements, N, 106
Numerical model
∆t, −5
10
hCoi
y+
sec
1
pipe
0.327
RSM
5
0.447
104.1
2
pipe
0.551
RSM
5
0.471
90.29
3
pipe
0.871
RSM
5
0.491
91.00
4
pipe
1.211
RSM
5
0.505
91.51
5
pipe
3.601
RSM
2
0.260
54.91
6
scroll
0.999
RSM
5
0.526
95.10
7
bend
0.975
RSM
5
0.534
93.48
8
pipe
7.25
LES
1
0.164
34.78
9
pipe
7.25
RSM
1
0.181
33.8
26
Table 4: Pressure drop coefficients (time-averaged Euler numbers) of a cyclone with different gas outlet configurations
Pressure drop coefficients
Gas outlet configuration
(Euler numbers)
pipe
scroll
bend
Euin
8.41
8.84
8.95
Eu
1404
1475
1494
27
Figure captions
444
445
Figure 1: Cyclone with different gas outlet configurations.
446
Figure 2: Inlet velocity contour plot.
447
Figure 3: Predicted time-averaged tangential and axial velocities along
448
449
450
the x-axis (y = 0, z = 0) normalized by area-averaged inlet velocity. Figure 4: Meshes for a cyclone with the investigated gas outlet configurations.
451
Figure 5: Eddy sizes for the turbulent flow within the cyclone.
452
Figure 6: Predicted with RSM and LES time-averaged tangential and
453
axial velocities along the x-axis (y = 0, z = 0) normalized by area-averaged
454
inlet velocity.
455
456
Figure 7: Time-averaged static pressure, tangential velocity and axial velocity in the cyclone body and in the vortex finder.
457
Figure 8: Time-averaged tangential and axial velocity profiles in the cy-
458
clone body along the x-axis at three different z positions (z = 0, 0.15, and
459
0.3 m).
460
461
Figure 9: Iso-surfaces with the vorticity around z-axis of −3000 s−1 for the three configurations.
462
Figure 10: Iso-surfaces with the vorticity around z-axis of −2000, −2500
463
and −3000 s−1 at area-averaged inlet velocity of 16.8 (a), 20.7 (b) and
464
24.5 m s−1 (c) respectively.
465
466
467
468
Figure 11: The instantaneous tangential and axial velocity contour plots obtained with RSM and LES. Figure 12: Streamlines in the vortex finder and different gas outlet configurations. 28
469
470
471
472
473
474
Figure 13: Instantaneous total pressure drop across the cyclone with different gas outlet configurations. Figure 14: Pressure losses in the cyclone with different gas outlet configurations. Figure 15: Collection efficiency of a cyclone with different gas outlet configuration.
475
29
Highlights • A unique ”double spiral vortex-breakdown” appear in the cyclone with conventional outlet pipe; • An outlet scroll and radial bend have insignificant effects on the velocity field in the main separation zone; • Installation of the outlet scroll and radial bend increases the pressure losses by 5.1% and 6.4% respectively; • The outlet scroll and radial bend increase the amplitude of pressure drop oscillations from 0.65% to 16.2% and 33.96% accordingly; • The outlet scroll and radial bend have practically no effects on the cyclone separation capability.
S0032-5910(19)30887-3
DOI:
https://doi.org/10.1016/j.powtec.2019.10.064
Reference:
PTEC 14831
To appear in:
Powder Technology
Received Date: 20 January 2019 Revised Date:
10 September 2019
Accepted Date: 15 October 2019
Please cite this article as: D. Misiulia, S. Antonyuk, A.G. Andersson, T.S. Lundström, High-efficiency industrial cyclone separator: A CFD study, Powder Technology (2019), doi: https://doi.org/10.1016/ j.powtec.2019.10.064. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.
High-efficiency industrial cyclone separator: a CFD study Dzmitry Misiuliaa,∗, Sergiy Antonyukb , Anders Gustav Anderssonc , Tord Staffan Lundstr¨omc a
Department of Machines and Apparatus for Chemical and Silicate Production, Belarusian State Technological University, 13a Sverdlova str., 220006 Minsk, Belarus b Institute of Particle Process Engineering, University of Kaiserslautern, D-67653 Kaiserslautern, Germany c Division of Fluid and Experimental Mechanics, Department of Engineering Sciences and Mathematics, Lule˚ a University of Technology, SE-971 87 Lule˚ a, Sweden
Abstract The flow within an industrial scroll-inlet high-efficiency cyclone separator has been studied using RSM and LES simulations. Of particular interest is the effect of the gas outlet configuration, i.e. outlet scroll and radial bend, on the flow pattern, pressure drop and cyclone efficiency. A surprising phenomenon is that the inner vortex splits into two vortices for the cyclone with a conventional outlet pipe while if the cyclone is equipped with an outlet scroll or radial bend there is no split. The outlet scroll and radial bend increase the pressure losses by 5.1% and 6.4%, respectively. These installations, moreover, significantly destabilize the pressure losses and the amplitude of instantaneous pressure drop oscillations increases from 0.65% ∗ Corresponding author. Tel.: +375 17 2202694, fax: +375 17 3276217. Postal address: Department of Machines and Apparatus for Chemical and Silicate Production, Belarusian State Technological University, 13a Sverdlova str., 220006 Minsk, Belarus. Email addresses: [email protected] (Dzmitry Misiulia), [email protected] (Sergiy Antonyuk), [email protected] (Anders Gustav Andersson), [email protected] (Tord Staffan Lundstr¨om)
Preprint submitted to Powder Technology
September 10, 2019
to 16.2% and 33.96%, respectively. The investigated outlet scroll and radial bend have practically no effects on the cyclone efficiency since the flow in the main separation zone is not affected by the gas outlet configuration. Keywords: Cyclone separator, Computational Fluid Dynamics, vortex breakdown, pressure drop, collection efficiency
1
1. Introduction
2
Gas cyclones are the most popular tools for the separation of solid par-
3
ticles from gases in industrial applications. Their popularity is due to their
4
simplicity, reliability, relatively low manufacturing costs and ability to work
5
under high pressures and temperatures.
6
The usage of high-efficiency cyclone separators is increasing especially
7
those that function without bag filters due to very high separation capability,
8
i.e. ACS Hurricane cyclones and ReCyclone systems [1, 2].
9
Gas cyclones are used as a pre-separator of a two or three-stage system,
10
as the only separation stage or as the final separation stage. In the first case,
11
when two or more cyclones are connected in series, an outlet scroll is normally
12
installed directly after and on top of the first stage cyclone. Sometimes,
13
due to practical reasons, a radial bend is attached to the gas outlet pipe
14
(vortex finder) instead of a scroll. In the second case when cyclone exhausts
15
directly into the atmosphere they commonly contain just a cylindrical outlet
16
pipe or one that is covered with a shallow cone to keep rain out a so-called
17
rain hat [3]. Outlet scrolls may also be installed on any cyclone wherein the
18
exhaust gas is to undergo a significant reduction in velocity, i.e. its expansion
19
to the atmosphere. The smooth expansion of the gas as it passes through
2
20
the scroll reduces the tangential velocity of the gas flow and converts a part
21
of its kinetic energy stored with the tangential velocity into static pressure.
22
Without such a scroll, the gas would undergo an abrupt expansion with an
23
instantaneous loss of kinetic energy. Thus, a well-designed outlet scroll will
24
imply a pressure recovery and this is the main reason of installing it. A
25
small pressure drop reduction can also be reached with a radial bend at the
26
outlet [4] but this is not its main purpose.
27
Several experimental and numerical works on the cyclone aerodynamics
28
and its performance with different gas outlet configurations have been carried
29
out. Muschelknautz (as it is quoted in [5]) investigated the effect of a
30
number of pressure recovery configurations including an outlet scroll, and
31
found that the outlet scroll reduced the pressure drop by 12% as compared to
32
the pressure drop with a conventional cylindrical, sharp-edged vortex finder.
33
Funk [3] experimentally investigated the pressure drop of a cyclone with
34
rectangular and radial evas´es at the outlet. One conclusion was that the
35
pressure drop in a cyclone can be reduced by between 8.7 and 11.9% with
36
the addition of a radial evas´e assuming that the separation efficiency is not
37
affected since the evas´e is outside of and downstream from the cyclone.
38
Kahrimanovic et al. [6] studied a cyclone with two configurations of the
39
radial diffuser at the gas outlet, a ”horizontal” one and an ”inclined” one
40
which was arranged at an angle of 30◦ with respect to the horizontal dif-
41
fuser. These two gas outlet configurations were compared with the radial
42
bend which was referred to as a normal outlet. With the ”horizontal” radial
43
diffuser 30% of pressure was recovered while with the more efficient but com-
44
plicated ”inclined” geometry the enhancement in pressure recovery was only
3
45
2-3%. A small enhancement with the ”inclined” diffuser was explained by
46
the larger radius of the diffuser plate. It was also concluded that the parti-
47
cle separation in the cyclone was not strongly affected by the radial diffuser
48
placed downstream the vortex finder.
49
The main goal with this work is to investigate the flow pattern and per-
50
formance of a high-efficiency industrial cyclone separator with a conventional
51
gas outlet pipe and reveal the effects of adding an outlet scroll or a radial
52
bend using Computational Fluid Dynamics (CFD) simulations.
53
2. Numerical modelling
54
2.1. Governing equations
55
A Eulerian-Lagrangian approach was applied to model two-phase gas-
56
solid flow in a cyclone. The gas phase was treated as an incompressible
57
isothermal flow using an Eulerian approach and the Lagrange method was
58
applied for the solid particles. These particles were tracked through the
59
cyclone.
60
2.1.1. Governing equations for continuous phase
61
62
The Reynolds-averaged Navier-Stokes (RANS) equations for the incompressible isothermal gas phase can be written as: ∂ui = 0, ∂xi
63
∂ui ∂ui 1 ∂p ∂ + uj =− + ∂t ∂xj ρ ∂xi ∂xj
(1) ∂ui 0 0 ν − ui uj ∂xj
(2)
64
where ui is the time-averaged (mean) gas velocity; u0i is the fluctuating gas ve-
65
locity; u0i u0j is the fluctuating Reynolds stress contribution; ν is the kinematic
66
viscosity of the gas; ρ is the gas density; p is the mean static pressure. 4
67
The Reynolds stress model (RSM) (as reported in [7]) has been proven
68
as the most appropriate RANS turbulence model for the prediction of highly
69
swirling flows in a cyclone separator and it was therefore applied in this
70
study. A separate differential Reynolds stress transport equation was solved
71
for each Reynolds stress components according to: ! ∂u0 u0 i j 2 k2 ∂ ν + 3 Cs ∂xk ∂u0i u0j ∂u0i u0j 2 − = Pij − δij + Φij , + uk ∂t ∂xk ∂xk 3 1 0 0 uu 2 i j
(3)
is the turbulence
72
where Cs is an isotropic diffusion coefficient; k =
73
kinetic energy; is turbulence dissipation rate; Pij is the exact production
74
term; δij is the Kronecker delta (δij = 1 if i = j and δij = 0 if i 6= j); Φij is
75
a pressure-strain correlation.
76
The exact production term is defined as: Pij = −u0i u0k
77
∂uj ∂ui − u0j u0k . ∂xk ∂xk
(4)
The pressure-strain correlation acts to drive turbulence towards an isotropic
78
state by redistributing the Reynolds stresses and can be split into two parts,
79
a slow, also known as the return-to-isotropy, term and a rapid term which
80
are defined as:
81
Φij,1
82
Φij = Φij,1 + Φij,2 , 1 = − Cs1 aij + Cs2 aik ajk − amn amn δij , 3
(5)
√ 1 Φij,2 = − Cr1 Pij aij + Cr2 kSij − Cr3 kSij amn amn + 2 2 +Cr4 k aik Sjk + ajk Sik − akl Skl δij + Cr5 k (aik Θjk + ajk Θik ) 3
5
(6)
(7)
83
where Cs1 , Cs2 , Cr1 , Cr2 , Cr3 , Cr4 , Cr5 are the model coefficients; aij is an
84
anisotropy tensor; Sij is a mean strain rate tensor; and Θij is a vorticity
85
tensor. These tensors are given by u0i u0j 2 aij = − δij , k 3 1 ∂ui ∂uj + , Sij = 2 ∂xj ∂xi 1 ∂ui ∂uj Θij = . − 2 ∂xj ∂xi
86
87
88
A transport equation for turbulence dissipation rate is written as ∂ νt ∂ ν + σRS ∂ ∂ ∂xk + uk = (C1 Pk − C2 ) + , ∂t ∂xk k ∂xk
(8) (9) (10)
(11)
89
where C1 and C2 are model coefficients; σRS is a turbulent Schmidt number;
90
νt is the turbulent kinematic viscosity νt = CµRS
91
k2
(12)
where CµRS is a model coefficient.
92
The RSM model developed by Speziale, Sarkar and Gatski [8] was used in
93
this study. This RSM model uses a quadratic relation for the pressure-strain
94
correlation and is more accurate than the other RSM models particularly for
95
swirling flows [9]. The RSM model coefficients are listed in Table 1.
96
For a proper prediction of the flow field at the wall a scalable wall func-
97
tion [10] was applied.
98
2.1.2. Governing equations for dispersed phase
99
The dispersed phase was calculated using particle transport modelling
100
where representative spherical particles were tracked through the flow. The 6
101
tracking was carried out by forming a set of ordinary differential equations
102
in time for each representative particle, consisting of equations for position
103
and velocity using forward Euler integration [10, 11] according to: xnp = xop + uop ∆t,
104
up =
dxp , dt
(13) (14)
105
where xp was a particle position; up was a particle velocity; the superscripts
106
o and n referred to old and new values respectively; t was time; ∆t was a
107
time step.
108
In forward integration, the particle velocity calculated at the start of the
109
time step was assumed to prevail over the entire step. At the end of the time
110
step, the new particle velocity was calculated using the analytical solution
111
to the particle momentum equation as: − → − → π 3 d→ up − dp ρp = FD + FG 6 dt
(15)
112
where dp was the particle diameter; ρp was the particle density; FD was an
113
aerodynamic drag force acting on the particle; FG was a net force due to
114
gravity being equal to the gravitational force subtracted with the buoyant
115
force.
116
The aerodynamic drag force was defined as: πd2p 1 F D = CD ρ |u − up | (u − up ) 2 4
(16)
117
where CD was the drag coefficient derived from the Schiller Naumann corre-
118
lation according to [10]:
24 0.687 CD = max 1 + 0.15Rep , 0.44 Rep 7
(17)
119
where the particle Reynolds number was: Rep =
120
dp |us | . ν
(18)
The net force due to gravity was in its turn given by FG =
121
where g was gravity.
122
2.2. Cyclone geometry
π 3 d (ρp − ρ) g 6 p
(19)
123
A high-efficiency industrial gas cyclone STsN-40 [4] with an internal di-
124
ameter of 0.3 m was studied. As previously described the three outlet con-
125
figurations were investigated, an ordinary outlet pipe, an outlet scroll and a
126
radial bend as shown in Fig. 1. The geometrical dimensions of the cyclone
127
are given in Table 2.
128
2.3. Boundary conditions and numerical settings
129
A velocity profile for a fully developed air flow was applied at the in-
130
let. All cyclones were investigated at an area-averaged inlet velocity of
131
win = 24.5 m s−1 , that being the optimal velocity for this type of
132
cyclone (according to [4]), see Fig. 2. The recommended inlet velocity range
133
for the investigated cyclone is 16.8 – 24.5 m s−1 . Therefore, the cyclone with
134
an ordinary outlet pipe was also investigated at area-averaged inlet velocities
135
of 16.8 and 20.7 m s−1 . The area-averaged inlet velocity was computed as
136
the ratio of the volumetric flow rate to the inlet cross-sectional area as:
win = 8
Q , ab
(20)
137
where Q was the volumetric flow rate; a and b were the inlet width and
138
height.
139
At the outlet, an opening boundary condition with zero pressure normal
140
gradient that allows the air to cross the boundary surface in both directions
141
was used. The air density and dynamic viscosity were set to 1.205 kg m−3
142
and 1.831×10−5 Pa s, respectively. A medium turbulence intensity of 5% was
143
set both at the inlet and the outlet. A non-slip smooth wall boundary con-
144
dition was applied on all other boundaries. In two-phase simulations, 25000
145
representative particles 0.2−4 µm in diameter (1000 particles for 25 different
146
diameters) with a density of 1930 kg m−3 , random initial positions and zero
147
slip velocity were injected at the inlet. For a proper particle tracking solu-
148
tion, 100 integration steps per element were applied [10, 12, 13]. To reduce
149
the computational time, the particles reaching the side wall and bottom of
150
the dust hopper were terminated by applying the parallel and perpendic-
151
ular coefficients of restitution of 0.0 on these surfaces. For all other walls,
152
these coefficients were set to 0.8 which is commonly applied to many different
153
materials [14].
154
The time step ∆t was 1×10−5 – 5×10−5 s that resulted in a mean volume-
155
averaged Courant number of 0.16–0.51 for all cases (Table 3). The root-mean-
156
square scaled residuals were set below 2×10−5 which required, in average, 5
157
loop iterations within a time step.
158
The simulations were performed on a 64-bit Linux cluster at Lule˚ a Uni-
159
versity of Technology using a commercial solver ANSYS CFX 15.0 (ANSYS,
160
Inc., Canonsburg, Pennsylvania, USA). During simulations, tangential ve-
161
locities at some points in the cyclone body, area-averaged total and static
9
162
pressure at different sections, total pressure drop, volume-averaged turbu-
163
lence kinetic energy and turbulence eddy dissipation as well as area-averaged
164
y + were monitored to be sure that the flow inside the cyclone had reached its
165
fully developed state (statistically steady-state). After that, an arithmetic
166
averaging was initiated.
167
3. Grid independence study
168
A grid independence study was performed for a cyclone separator with
169
an ordinary gas outlet pipe. Five high quality grids with 0.327, 0.551, 0.871,
170
1.211 and 3.601 million elements were generated, No 1–5 in Table 3. For
171
a proper near the wall treatment with scalable wall function in RSM, the
172
thickness of the first grid nearest the wall should result in y + from 11.06 to
173
300. The mean area-averaged values of y + for all 5 grids were in this range,
174
see Table 3.
175
The effects of the grid size on the time-averaged tangential and axial
176
velocities in the cyclone body along the x-axis (y = 0, z = 0) can be seen
177
in Fig. 3. The velocities are normalized with the area-averaged inlet velocity
178
win .
179
All meshes captured the inverted ”W”-shape of the tangential velocity
180
profile, but the axial velocity profiles predicted with the coarsest mesh signif-
181
icantly differed from the others. The maximum tangential velocity increased
182
with the increase in number of mesh elements (Fig. 3). However increasing
183
the number of elements in the mesh from 0.871 million had negligible effects
184
on the tangential and axial velocity distributions. To conclude, the flow pat-
185
tern in a cyclone can be quite accurately captured with a mesh consisting 10
186
of 0.871 million elements. Using a finer mesh will not lead to significant
187
changes in velocity profiles but will increase the computational time. There-
188
fore, meshes with the same element size were created for the cyclones with
189
an outlet scroll (No 6 in Table 3) and radial bend (No 7 in Table 3), as shown
190
in Fig. 4.
191
Due to a lack of information in the literature regarding pressure and
192
velocity distributions in the investigated cyclone with its scroll inlet, there
193
are no reliable data to perform a validation study. Based on the results
194
of previous studies of a reverse-flow cyclone separator with a helical-roof
195
inlet [7, 10, 11, 12, 13] that showed good agreement between the numerical
196
and experimental data, it is likely that the numerical model and settings can
197
adequately predict the flow pattern in this cyclone as well. Nevertheless,
198
in order to exclude some uncertainty, Large Eddy Simulations (LES) of a
199
cyclone with an ordinary gas outlet pipe were performed using the dynamic
200
Smagorinsky-Lilly model [15] and the results were compared with the RSM
201
simulations (No 8 and 9 in Table 3).
202
LES simulations require much finer mesh and the mesh size should prefer-
203
ably be in the dissipation range of the turbulent length scale where motions
204
experience viscous effects. Based on mean volume-averaged turbulence ki-
205
netic energy and eddy dissipation the length scales and ranges for the cyclone
206
were defined according to [11, 16] and are sketched in Fig. 5.
207
The simulations were performed with a mesh consisting of 7.25 million
208
elements. It can be seen from Fig. 5 that the average mesh element size
209
for the cyclone was within the dissipation range of the universal equilibrium
210
range.
11
211
The tangential and axial velocity profiles predicted with the RSM and
212
LES models are shown in Fig 6. The tangential velocity predicted with LES
213
were slightly higher. Both the RSM and LES models revealed the same
214
profiles for tangential and axial velocities and agreed well.
215
4. Results and discussion
216
4.1. Effects of the gas outlet configuration on the flow pattern in the cyclone
217
The contour plots of the time-averaged static pressure, tangential velocity
218
and axial velocity in the cyclone body and in the vortex finder for the three
219
gas outlet configurations are shown in Fig. 7. The radial profiles of the tan-
220
gential and axial velocity components along the x-axis at three cut sections
221
along the cyclone axis (z = 0, 0.15 and 0.3 m) are presented in Fig. 8. Since
222
the geometrical axis of the outlet scroll and radial bend did not coincide with
223
the cyclone geometrical axis (z-axis) which was used as the axis of rotation
224
for computing the tangential and axial velocities, the contour plots of the
225
static pressure and velocity field in the scroll outlet and radial bend are not
226
shown in Fig. 7.
227
Static pressure in a cyclone (Fig. 7) has its minimum value in the vortex
228
core region, i.e. near or at the geometrical axis of the cyclone and increases
229
towards the periphery where it reaches its maximum value. The difference
230
between the maximum and minimum values, i.e. the difference in static
231
pressure at the cyclone wall and its centerline was about 4.6 kPa in the cy-
232
clone with the ordinary outlet pipe. Placing the outlet scroll and radial bend
233
downstream the vortex finder increased this difference to 6.3 and 5.1 kPa
234
respectively. 12
235
The maximum tangential velocity was approximately twice as large as the
236
inlet velocity and was practically constant along the cyclone axis (Fig. 7).
237
The radial profile of the tangential velocity distribution had an inverted ”W”-
238
shape and was almost independent of the z-axis (Fig. 8). The outlet scroll
239
and radial bend had insignificant effects on the tangential velocity field in
240
the cyclone body.
241
The axial velocity field in the cyclone with different gas outlet configura-
242
tions could be divided into two zones, an outer zone with negative velocity
243
values and an inner zone with positive velocity values. The outer zone de-
244
termined the downwardly directed outer vortex and the inner one defined
245
the size of the upwardly directed inner vortex. Not the outlet scroll nor a
246
radial bend had a noticeable effect on the axial velocity distribution in the
247
outer zone but they did effect the inner zone. This can be explained by some
248
transformation of the inner vortex which precesses around the cyclone axis.
249
Fig. 9 represents the iso-surfaces of the vorticity around z-axis of −3000 s−1 .
250
A very interesting phenomenon, a ”vortex-breakdown with bifurcated double
251
helix” occurred in the cyclone separator with an ordinary outlet pipe. The
252
onset of the ”vortex-breakdown” was a bit upstream the vortex finder where
253
the upwardly directed inner vortex divided into two vortices which then en-
254
tered the vortex finder. As a result, there were two vortices in the vortex
255
finder which broke up at the gas outlet section.
256
The revealed vortex-breakdown with bifurcated double helix occurred in
257
the cyclone separator with an ordinary outlet pipe at different inlet velocities
258
over the whole recommended operation range of 16.8 – 24.5 m s−1 . Fig. 10
259
shows the vortex-breakdown phenomenon at area-averaged inlet velocities
13
260
of 16.8, 20.7 and 24.5 m s−1 . The inlet velocity did not affect the vortex-
261
breakdown but changed the swirl intensity in the cyclone and vortex finder.
262
Such a ”vortex-breakdown” phenomenon can be also seen in Fig. 11 which
263
represents the instantaneous tangential and axial velocity contour plots in the
264
vortex finder. The contour plots predicted with the RSM and LES model
265
are similar and show good agreement.
266
Such a vortex breakdown with bifurcated double helix in a swirling flow
267
was reported by Meliga et al. [17]. Also, Karniadakis and Sherwin [18] iden-
268
tified such an onset of the ”vortex-breakdown” with Direct Numerical Sim-
269
ulations (DNS) using a Fourier series approximation in the axial direction.
270
Spiral modes of instability were found to cause a lateral expansion of the
271
cross-section of the vortex core, and a corresponding drop in axial velocity.
272
When the assumption of axial periodicity was neglected, as in a fully three-
273
dimensional DNS, this then led to an axial stagnation point – indicative of
274
vortex breakdown. Vortex tip stabilization has been also explored at the
275
bottom of a cyclone [19, 20, 21].
276
Surprisingly, such a ”vortex-breakdown” phenomenon does not occur if
277
the outlet scroll or radial bend is placed downstream the vortex finder. More-
278
over, the phenomenon does not appear in other cyclone geometries with the
279
ordinary gas outlet pipe, see for instance [11, 22].
280
The time-averaged parameters of the flow at the gas outlet are not rep-
281
resentative since the flow at the gas outlet is unstable and there is a strong
282
precession of the vortex core [11]. Instead, 15 streamlines coloured by abso-
283
lute velocity in the vortex finder, outlet scroll and radial bend are presented
284
in Fig. 12. The flow in the conventional vortex finder is still quite swirling
14
285
at the outlet and the maximum absolute velocity reaches 70 m/s. In fact, a
286
well-designed outlet scroll should reduce the velocity due to expansion of the
287
cross-sectional area. However, these simulations showed that the velocities
288
in the outlet scroll and radial band were higher than in the ordinary outlet
289
pipe and the streamlines were not structured, especially in the outlet scroll.
290
With the investigated outlet scroll design the velocity at the outlet was not
291
reduced and as a result there maybe higher pressure losses at the outlet.
292
4.2. Effects of the gas outlet configuration on the cyclone performance
293
294
Cyclone performance is characterized by pressure drop and collection efficiency.
295
Pressure drop is an important cyclone performance characteristic since it
296
determines operation cost of a cyclone which is proportional to the energy
297
required to overcome these pressure losses. The instantaneous total pressure
298
drop across the cyclone with the three different gas outlet configurations
299
is shown in Fig. 13 whereas the time-averaged total pressure drop and the
300
pressure losses in the cyclone body (upstream the vortex finder inlet) and
301
in the vortex finder and gas outlet (downstream the vortex finder inlet) are
302
plotted in Fig. 14.
303
Surprisingly, both the outlet scroll and bend outlet increased the total
304
pressure drop across a cyclone instead of the opposite. Moreover, they lead
305
to dramatical increase in oscillations of the instantaneous pressure drop. The
306
amplitude of these oscillations (i.e. the difference between the maximum and
307
minimum value of the instantaneous pressure drop) was very small in the
308
cyclone separator with the conventional outlet pipe and was equal to 0.65%
309
of the average total pressure drop. However installing the outlet scroll and 15
310
radial bend downstream from the vortex finder increased the amplitude of
311
oscillations to 16.2% and 33.96%, respectively (Fig. 13).
312
Fig. 14 shows that the pressure losses in the cyclone body upstream from
313
the vortex finder, i.e. the pressure losses from the cyclone inlet to the vortex
314
finder inlet, were nearly 2000 Pa and were almost independent of the gas out-
315
let configuration downstream from the vortex finder. This can be explained
316
by the fact that the gas outlet configuration has minor effects on the velocity
317
distribution in the cyclone body. Placing the outlet scroll and radial bend
318
downstream from the vortex finder, however, increased the pressure losses in
319
the vortex finder and downstream from it, i.e. from the vortex finder inlet
320
to the cyclone gas outlet. This can be explained by higher velocities in the
321
outlet scroll and radial bend (Fig. 12).
322
Time-averaged pressure drop coefficients (based on the inlet velocity and
323
mean axial velocity in a cyclone body) of a cyclone with different gas outlet
324
configurations are listed in Table 4. It shows that the installation of an out-
325
let scroll and radial bend downstream from the vortex finder increased the
326
dimensionless pressure losses, the Euler number, by 5.1% and 6.4% respec-
327
tively. A negative effect in pressure drop reduction with the scroll outlet was
328
also reported by Lazarev [4] and Idel’chik [23]. The investigated radial bend
329
(R = 1.5D) was probably too abrupt and located too close to the vortex
330
finder. These negative effects can be overcome by optimization of the gas
331
outlet design.
332
The effects of the outlet scroll and radial bend on the cyclone collection
333
efficiency are presented in Fig. 15. The investigated gas outlet configurations
334
had almost no effect on the cyclone grade efficiency curve, as expected, since
16
335
the outlet scroll and radial bend were downstream from the vortex finder
336
and did not significantly affect the flow field in the cyclone body where the
337
particles are separated from the gas flow. The predicted cut-size of all cy-
338
clones was practically the same and about 1.1 µm. Cyclones with such a
339
small value of the cut-size (i.e. high separation capability) can be used as a
340
final separation stage in industry.
341
5. Conclusions
342
An industrial high-efficiency cyclone separator with three different gas
343
outlet configurations (conventional outlet pipe, outlet scroll and radial bend)
344
has been computationally investigated using Reynolds stress model simula-
345
tions and Large eddy simulations and the effects of the outlet scroll and radial
346
bend placed downstream the vortex finder on the flow pattern and cyclone
347
performance have been revealed. The following conclusions can be drawn:
348
• a unique ”vortex-breakdown with bifurcated double helix” phenomenon
349
occurs in the high-efficiency cyclone separator with an ordinary outlet
350
pipe. The observation is that the inner vortex split into two vortices.
351
This is a phenomenon that has never been found in cyclone separators
352
before. This phenomenon does not appear if the outlet scroll or radial
353
bend is placed downstream the vortex finder. Additional studies are
354
needed to reveal the reason and nature for the double helix;
355
• an outlet scroll and radial bend have insignificant effects on the velocity
356
field in a cyclone body except regarding the axial velocity distribution
357
in the inner vortex as described above;
17
358
• installation of an outlet scroll and radial bend downstream from the
359
vortex finder increases the dimensionless pressure losses by 5.1% and
360
6.4% respectively. Moreover it significantly destabilizes the pressure
361
losses by increasing the amplitude of instantaneous pressure drop os-
362
cillations from 0.65% to 16.2% and 33.96% respectively;
363
364
365
366
• the outlet scroll and radial bend have almost no effect on the cyclone separation capability; • the geometry of the investigated scroll outlet is not properly designed and needs to be optimized;
367
• placing the radial bend (R = 1.5D) right downstream from the vortex
368
finder is not recommended since it leads to high pressure losses. This
369
negative effect can be probably overcome by increasing the bend radius
370
and placing the radial bend further downstream from the vortex finder.
371
Future extension of this work is firstly to investigate the reasons and
372
nature of the unique ”double spiral vortex-breakdown” phenomenon, and
373
secondly optimize the gas outlet configuration in terms of minimum pressure
374
losses.
375
Acknowledgements
376
377
This work was partially performed with financial support provided by Swedish Institute through the Visby Programme to the first author.
18
378
379
380
381
382
383
384
385
386
387
388
References
[1] A.Alves, J.Paiva, R.Salcedo, Cyclone optimization including particle clustering, Powder Technology 272 (2015) 14–22. [2] Advanced Cyclone Systems, Hurricane and ReCyclone systems. http://www.acsystems.pt/, 2017 (accessed 7 March 2018). [3] P.A. Funk, Reducing cyclone pressure drop with evas´es, Powder Technology 272 (2015) 276–281. [4] V.A.Lazarev, Cyclones and Vortex Dust Traps: A Handbook, 2nd ed., Ozon-NN, Nizhnii Novgorod, Russia, 2006. [5] A.C. Hoffmann, L.E. Stein, Gas Cyclones and Swirl Tubes, 2nd ed., Springer Berlin Heidelberg New York, 2008.
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[6] D. Kahrimanovic, S. Puttinger, G. Aichinger, S. Pirker, Minimizing
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pressure drop in cyclone separators measurements and numerical sim-
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ulations, 11th World Filtration Congress, 16-20 April, 2012, Graz, Aus-
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tria.
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[7] D.Misiulia, A.G.Andersson, T.S.Lundstr¨om, Computational investiga-
394
tion of an industrial cyclone separator with helical-roof inlet, Chemical
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Engineering and Technology 38 (8) (2015) 1425–1434.
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[8] C.G.Speziale, S.Sarkar, T.B.Gatski, Modelling the pressure-strain corre-
397
lation of turbulence: an invariant dynamical systems approach, Journal
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of Fluid Mechanics 227 (1991) 245–272. 19
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[9] ANSYS CFX-Solver Theory Guide, Release 15.0, ANSYS, Inc, Canonsburg, Pennsylvania 2013.
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[10] D.Misiulia, K.Elsayed, A.G.Andersson, Geometry optimization of a
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deswirler for cyclone separator in terms of pressure drop using CFD
403
and artificial neural network, Separation and Purification Technology
404
185 (2017) 10–23.
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[11] D.Misiulia, S.Antonyuk, A.G.Andersson, T.S.Lundstr¨om, Effects of
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deswirler position and its centre body shape as well as vortex finder
407
extension downstream on cyclone performance, Powder Technology 272
408
(2018) 14–22.
409
[12] D.Misiulia, A.G.Andersson, T.S.Lundstr¨om, Large eddy simulation in-
410
vestigation of an industrial cyclone separator fitted with a pressure re-
411
covery deswirler, Chemical Engineering and Technology 40 (4) (2017)
412
709–718.
413
[13] D.Misiulia, A.G.Andersson, T.S.Lundstr¨om, Effects of the inlet angle
414
on the collection efficiency of a cyclone with helical-roof inlet, Powder
415
Technology 305 (2017) 48–55.
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[14] C.T. Crowe, J.D. Schwarzkopf, M. Sommerfeld, Y. Tsuji, Multiphase
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flows with droplets and particles, 2nd ed., CRC Press, Boca Raton,
418
Florida, USA 2012.
419
420
[15] D.K.Lilly, A proposed modification of the Germano subgrid-scale closure method, Physics of Fluids A 4 (3) (1992) 633635.
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[16] S.B. Pope, Turbulent Flows, IOP Publishing. 2001.
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[17] P. Meliga, F. Gallaire, J.-M. Chomaz, A weakly nonlinear mechanism for
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mode selection in swirling jets, Journal of Fluid Mechanics 699 (2012)
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216–262.
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426
427
428
[18] G.E. Karniadakis, S.J. Sherwin, Spectral/hp element methods for computational fluid dynamics. Oxford University Press, 1999. [19] J.J. Derksen, Separation performance predictions of a Stairmand highefficiency cyclone, AIChE Journal 49 (6) (2003) 1359–1371.
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[20] W. Peng, A.C. Hoffmann, P.J.A.J. Boot, A. Udding, H.W.A. Dries,
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A. Ekker, J.Kater, Flow pattern in reverse-flow centrifugal separators,
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Powder Technology 127 (2002) 212–222.
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[21] C. Cort´es, A. Gil, Modeling the gas and particle flow inside cyclone
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separators, Progress in Energy and Combustion Science 33 (2007) 409–
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[22] L.S. Brar, K.Elsayed, Analysis and optimization of multi-inlet gas cy-
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clones using large eddy simulation and artificial neural network, Powder
437
Technology 311 (2017) 465–483.
438
439
440
[23] I.E. Idel’chik, Handbook of Hydraulic Resistance, 3rd ed., Begell House, 1996.
Nomenclature and units
441
21
Upper-case Roman CD
[–]
drag coefficient
Cr1−r5
[–]
RSM model coefficient
Cs
[–]
isotropic diffusion coefficient
Cs1 ,Cs2
[–]
RSM model coefficient
CµRS
[–]
RSM model coefficient
C1 ,C2
[–]
RSM model coefficient
Co
[–]
Courant number
D
[m]
cyclone body diameter
De
[m]
vortex finder diameter
Eu
[–]
Euler number normalized by mean axial velocity in a cyclone body
Euin
[–]
Euler number normalized by inlet velocity
FD
[N]
drag force
FG
[N]
net force due to gravity
L
[m]
characteristic length scale
N
[–]
number of mesh elements
Rep
[–]
particle Reynolds number
Sij
[s−1 ]
mean strain rate tensor
Q
[m3 s−1 ]
volumetric gas flow rate
a
[m]
cyclone inlet height
aij
[–]
anisotropy tensor
b
[m]
cyclone inlet width
dp
[m]
particle diameter
Lower-case Roman
22
g
[m2 s−1 ]
gravity
k
[m2 s−2 ]
turbulence kinetic energy
l
[m]
length scale
lDI
[m]
length scale which splits the universal equilibrium range into inertial subrange and dissipation range
lEI
[m]
length scale that forms the demarcation between the energy containing range and the universal equilibrium range
l0
[m]
integral scale
lη
[m]
Kolmogorov length scale
p
[Pa]
static pressure
∆p
[Pa]
total pressure drop across a cyclone
r
[m]
radius
s
[m]
vortex finder length
t
[s]
time
∆t
[s]
time step
u
[m s−1 ]
gas velocity
up
[m s−1 ]
particle velocity
wax
[m s−1 ]
axial component of gas velocity
win
[m s−1 ]
inlet gas velocity
wt
[m s−1 ]
tangential component of gas velocity
xp
[m]
particle position
y+
[−]
dimensionless parameter
δij
[–]
Kronecker delta 23
[m2 s−3 ]
turbulence eddy dissipation
ν
[m2 s−1 ]
kinematic viscosity
νt
[m2 s−1 ]
turbulent kinematic viscosity
ρ
[kg m−3 ]
gas density
ρp
[kg m−3 ]
particle density
σµRS
[–]
RSM model coefficient
θij
[s−1 ]
vorticity tensor
Φij
[m2 s−3 ]
pressure-strain correlation
Other symbols ¯
time-averaged (mean)
0
fluctuating
hi
volume-averaged
area-averaged
Abbreviations CFD
Computational Fluid Dynamics
DNS
Direct Numerical Simulations
LES
Large Eddy Simulations
RANS
Reynolds-averaged Navier-Stokes
RSM
Reynolds stress model
24
Tables
442
Table 1: RSM model coefficients
CµRS 0.1
σRS
Cs
1.363 0.22
Cs1
Cs2
Cr1
Cr2
Cr3
Cr4
1.7
1.05
0.9
0.8
0.65 0.625
Cr5
C1
C2
0.2
1.44 1.83
Table 2: Cyclone dimensions (normalized by cyclone diameter D)
a
b
De
d
d1
d2
H
h
hc
h1
h2
l
s
0.38 0.16 0.4 0.2 0.7 0.15 3.3 1.6 1.6 0.8 0.1 0.5 0.4
443
25
Table 3: Numerical settings
Number Case No
Gas outlet
of mesh
configuration elements, N, 106
Numerical model
∆t, −5
10
hCoi
y+
sec
1
pipe
0.327
RSM
5
0.447
104.1
2
pipe
0.551
RSM
5
0.471
90.29
3
pipe
0.871
RSM
5
0.491
91.00
4
pipe
1.211
RSM
5
0.505
91.51
5
pipe
3.601
RSM
2
0.260
54.91
6
scroll
0.999
RSM
5
0.526
95.10
7
bend
0.975
RSM
5
0.534
93.48
8
pipe
7.25
LES
1
0.164
34.78
9
pipe
7.25
RSM
1
0.181
33.8
26
Table 4: Pressure drop coefficients (time-averaged Euler numbers) of a cyclone with different gas outlet configurations
Pressure drop coefficients
Gas outlet configuration
(Euler numbers)
pipe
scroll
bend
Euin
8.41
8.84
8.95
Eu
1404
1475
1494
27
Figure captions
444
445
Figure 1: Cyclone with different gas outlet configurations.
446
Figure 2: Inlet velocity contour plot.
447
Figure 3: Predicted time-averaged tangential and axial velocities along
448
449
450
the x-axis (y = 0, z = 0) normalized by area-averaged inlet velocity. Figure 4: Meshes for a cyclone with the investigated gas outlet configurations.
451
Figure 5: Eddy sizes for the turbulent flow within the cyclone.
452
Figure 6: Predicted with RSM and LES time-averaged tangential and
453
axial velocities along the x-axis (y = 0, z = 0) normalized by area-averaged
454
inlet velocity.
455
456
Figure 7: Time-averaged static pressure, tangential velocity and axial velocity in the cyclone body and in the vortex finder.
457
Figure 8: Time-averaged tangential and axial velocity profiles in the cy-
458
clone body along the x-axis at three different z positions (z = 0, 0.15, and
459
0.3 m).
460
461
Figure 9: Iso-surfaces with the vorticity around z-axis of −3000 s−1 for the three configurations.
462
Figure 10: Iso-surfaces with the vorticity around z-axis of −2000, −2500
463
and −3000 s−1 at area-averaged inlet velocity of 16.8 (a), 20.7 (b) and
464
24.5 m s−1 (c) respectively.
465
466
467
468
Figure 11: The instantaneous tangential and axial velocity contour plots obtained with RSM and LES. Figure 12: Streamlines in the vortex finder and different gas outlet configurations. 28
469
470
471
472
473
474
Figure 13: Instantaneous total pressure drop across the cyclone with different gas outlet configurations. Figure 14: Pressure losses in the cyclone with different gas outlet configurations. Figure 15: Collection efficiency of a cyclone with different gas outlet configuration.
475
29
Highlights • A unique ”double spiral vortex-breakdown” appear in the cyclone with conventional outlet pipe; • An outlet scroll and radial bend have insignificant effects on the velocity field in the main separation zone; • Installation of the outlet scroll and radial bend increases the pressure losses by 5.1% and 6.4% respectively; • The outlet scroll and radial bend increase the amplitude of pressure drop oscillations from 0.65% to 16.2% and 33.96% accordingly; • The outlet scroll and radial bend have practically no effects on the cyclone separation capability.