Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P1.69 - On CFD practices for cyclone simulation
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 Material Information
Title: P1.69 - On CFD practices for cyclone simulation Industrial Applications
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Ropelato, K.
Fontes, C.E.
Fusco, J.M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: cyclone
gas-solid
separation
multiphase flow
RSM
CFD
 Notes
Abstract: Cyclones have been applied in dust separation for more than a hundred years. Great effort has been dedicated in order to find new techniques to reduce the pressure drop and to increase the collection efficiency. In Fluid Catalytic Cracking unit (FCC), on petroleum industry for instance, cyclones usually have diameters from 0,70 to 1,8 meters. CFD techniques are powerful tools to be used by researchers on the pursuit of a better equipment. In this paper the developed CFD model was validated against the traditional studies made by Dirgo et al. (1985) (to analyze the pressure drop in different inlet velocities for a single phase) and by Qian et al. (2009), to analyze the pressure drop considering 15 m/s inlet velocity and a gas-solid flow). Particles size of used Talcum powder was 6.39 μm and a two-way coupling was adopted. In order to analyze the cyclone anisotropy effects, tetrahedrical and hexahedrical meshes were built and their results were compared for different inlet velocities for Dirgo et al. (1985) cyclone. Almost all cyclone simulations presented by open literature do not consider the hopper length, this work shows that its influence on the simulation results must be considered. A set of CFD cyclone simulation cases is presented applying a three-dimensional unstructured mesh and using a Reynolds Stress Model turbulence model. The observed numerical pressure drop was compared against experimental data. Different geometries and meshes were used. Simulation results showed good agreement with experimental data.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Resource Identifier: P169-Ropelato-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


On CFD practices for cyclone simulation


Karolline Ropelato*, Carlos Eduardo Fontes*, and Jose Mozart Fuscot


ESSS Engineering Simulation and Scientific Software, Rio de Janeiro, RJ, Brazil.

CENPES PETROBRAS Research and Development Center, Rio de Janeiro, RJ, Brazil.

ropelatoiidesss.com.br and mozartfiidpetrobras.com.br



Keywords: Cyclone, gas-solid, separation, multiphase flow, RSM, CFD.



Abstract

Cyclones have been applied in dust separation for more than a hundred years. Great effort has been dedicated in order to find
new techniques to reduce the pressure drop and to increase the collection efficiency. In Fluid Catalytic Cracking unit (FCC),
on petroleum industry for instance, cyclones usually have diameters from 0,70 to 1,8 meters. CFD techniques are powerful
tools to be used by researchers on the pursuit of a better equipment. In this paper the developed CFD model was validated
against the traditional studies made by Dirgo et al. (1985) (to analyze the pressure drop in different inlet velocities for a single
phase) and by Qian et al. (2009), to analyze the pressure drop considering 15 m/s inlet velocity and a gas-solid flow). Particles
size of used Talcum powder was 6.39 pLm and a two-way coupling was adopted.
In order to analyze the cyclone anisotropy effects, tetrahedrical and hexahedrical meshes were built and their results were
compared for different inlet velocities for Dirgo et al. (1985) cyclone. Almost all cyclone simulations presented by open
literature do not consider the hopper length, this work shows that its influence on the simulation results must be considered.
A set of CFD cyclone simulation cases is presented applying a three-dimensional unstructured mesh and using a Reynolds
Stress Model turbulence model. The observed numerical pressure drop was compared against experimental data. Different
geometries and meshes were used. Simulation results showed good agreement with experimental data.


Introduction

Cyclones have been applied in dust separation for more than
a hundred years. Most attention has been given to find new
techniques intending to reduce the pressure drop and to
increase the collection efficiency (Chen (2007),
Ramachandran (1991)).
In the last forty years, researches have been looking for
specific points to enhance the efficiency of cyclones. Some
examples of these researches were Zens (1975), who
analyzed how cyclone geometry affect vortex length and the
size of the cyclone dipleg. Bryant et al. (1983) made a series
of experiments to visually observe the vortex length and
confirmed its independence of inlet velocity over the normal
ranges of operation. At the same time, Bryant et al. (1983)
analyzed the effect on the pressure drop of a minor amount
of solids in the gas stream. During the Fourth Fluid
Catalytic Cracking Symposium (1983), Tenney and Allen
presented a study entitled "Cyclones Fact and Fiction".
They discuss some important aspects, such as:
the number of parallel cyclone units and the
number of cyclones stages;
cyclones proportions, dipleg sizes and wall
thicknesses:
the type of valves or splash plates to be used on
diplegs.
Cyclones popularity is due to their simplicity, the fact that


they are inexpensive to manufacture, compact, contain no
moving parts and require very little maintenance when
properly designed. However, the disadvantage of these
equipment is that the pressure drop and consequent power
requirement are large compared to those of simple settling
chambers (Ayers, 1983).
The combination between computational advances and
experimental knowledge of cyclones behaviour allow the
use of CFD (Computational Fluid Dynamics) techniques for
better understanding the fluid dynamics behavior inside
these equipment. The literature presents many CFD studies
on cyclones. Gimbun et al. (2005) presented a CFD
calculation to predict and evaluate the effects of temperature
and inlet velocity on the pressure drop of gas cyclones. The
authors used a RSM turbulence model to predict the
pressure drop in cyclones. The CFD models predicted
excellently the cyclones pressure drops.
A new mechanical device, used to improve gas flow inside
cyclones producing smaller pressure drops, was presented
by Noriler et al. (2l1~14. The implementation of the
mechanical device generates a pressure drop decrease of
about 20%. Cort~s and Gil (2007) made a consistent review
of cyclones' models developed for the flow field inside
inverse flow region. The models analyzed by the authors
evaluated the velocity distribution, collection efficiency and
studied the application of CFD to cyclones. The authors
concluded that the complexity of the flow inside the





























































Table 1: Cyclones characteristics.
Dirgo et al. Qian et al.
Dimension (1985) (2009)
[m] [m]
Cyclone diameter, D 0.305 0.205
Gas outlet diameter, De 0.152 0.063
Inlet height, a 0.152 0.094
Inlet width, b 0.061 0.042
Outlet duct length, S 0.152 0.185
Cyclone height, H 1.220 0.778
Cyclone height, h 0.457 0.269
Dust outlet diameter, B 0.114 0.082


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Paper No


cyclones is due to instability, as modern experimental and
numerical techniques have demonstrated.
Despite these many related works, open literature doesn't
present many studies on high diameters cyclones. In
petroleum industry, for instance, cyclones have diameters
between 0.70 to 1.8 meters and hoppers length of equal size.
The present study takes part in a more general work on
numerical prediction of turbulent dispersed two-phase flows
in cyclones.
The validation of the developed CFD model was performed
by comparisons against two cases: the study developed by
Dirgo et al. (1985) and the study developed by Qian et al
(2009). The gas flow fields were calculated for cyclones
with different inlet section angles by means of
computational fluid dynamics (CFD) technology, and the
inner flow field of these cyclones were compared. The
pressure drop obtained by Qian (2009) was used to validate
de multiphase CFD model used on this work.
Many different types of cyclones configuration have been
proposed, but the reverse-flow cyclone with a tangential
inlet (Figure 1) is the mostly often used. Table 1 shows the
dimension for Dirgo et al. (1985) and Qian et al. (2009)
cyclones geometries used in the present study.
Dirgo et al. (1985) tested five air flows to evaluate the
pressure drop (5, 10, 15, 20, 25 m/s).Qian et al. (2009)
conducted the experiments using a inlet gas velocity of 15
m/s. Talcum powder of mean particle size of 6.39 pLm and
with a density of 2750 kg/m3 was used. The inlet particle
load was 10g/Nm3, particle porosity of 3.6 10-6
Elghobashi (1994) proposed a classification for gas-solid
suspensions based on porosity. When the suspension is very
dilute, say a < 10-6, Shows that particles have no effect on
the turbulent motion of the continuous phase, but their
motion can be governed by the turbulent motion of the
continuous phase if their inertia is sufficiently small
("one-way coupling"). When the particle volume fraction is
increased, say up to a = 10-', the effects of the presence of
particles on the turbulent motion of the continuous phase
can be observed, the "two-way coupling"
Despite the fact the simulation presented characteristics of
dilute flow, regions of high values of particle concentration
were noticed along the domain. Because of this behaviour a
two-way approach was adopted.


Figure 1: Cyclone with dimensions.


Nomenclature


amisotropy tensor
SSG model constants
Drag force
Source term
identity tensor

turbulence kinetic energy
pressure
prOduction term
Q-criterion
Reynolds Number
SSG model constants
rate of strain
time
fluid velocity


Greek letters
a porosity
a turbulence dissipation rate
9L dynami1c viscosity
p density
a stress tensor
z time of interaction between particle motion and
continuous phase
pressure strain


Subsripts
C1RS, S1, S2,

eRS, cs, cel, cs2





Superscrips


SSG model constants
SSG model constants
SSG model constants
continuous
particle
Turbulent


transpose of a matrix


Mathematical Formulation


The high curvature of the average streamlines, high swirl
intensity and radial shear and the adverse pressure gradients
and recirculation zones produce an anisotropic turbulence




























K1 r3 21
a=- v-I(0



S = dVv+(VI)T)(1


W= VT(V')T (12)

where a is the anisotropy tensor, S strain rate and W
YOrticity tensor. The RSM-SSG model constants are shown
in Table 2 and Table 3.

Table 2: Values of SSG model constants.
epRSSeRS cs 081 c,2
0.1 1.36 0.22 1.45 1.83

Table 3: Values of SSG model constants.
Csl Cs2 Crl Cr2 Cr Cr4 Cr5
1.7 -1.05 0.9 0.8 0.65 0.625 0.2


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

pressure-strain term can be split into two parts:


Paper No


inside a cyclone (Cortis (2007)). Reynolds Stress Models
perform better than eddy-viscosity models for such flows
(Kaya and Karagoz (2008); Slack et al. (2000), Wang et al.
(2006)).
The conservation equations of the flow phases can be
written in an Eulerian referential, in continuous integral or
differential form, based on the theorem of transport. The
conservation equations can be written in a generalized form.
Time-averaged mathematical models, together with the
Reynolds decomposition model, can be written as follows:


4 = 4 +4


I, is the iloit term, also known as the return to isotropy
term and ~2 is called the "rapid" term. The two terms are:


3 )


Mass conservation equation,


~z= -Cr1Pa +CrpKS +CrpKSzj~ +

(1) Crpr aS +Sa -S


+V-(py)= 0


Crs plc aWT + WaT


Momentum conservation equation,


+ V (pv) = V -a-V -pwv+ F (2)

Where p is the fluid density, P~is the Reynolds Stress
Tensor, F represents the momentum exchange with disperse
phase Appears as a source inside the source term of the
continuous phase equation. This term and appears only in
two-way coupling cases. Finally, a is the stress tensor
defined as:


where CL represents the molecular viscosity, v the fluid
velocity, p the pressure and I is the identity tensor.
The model considered a quadratic order closure based on the
conservation equation for Reynolds stress component of
Speziale-Sarkar-Gatsi (SSG) Speziale et al. (1991)'
represented as follow:

8 pvy)
dt \V(- /

S+-Cs p Vv +P + psI ()
38 3

The turbulence dissipation E equation has the form:


The particle equation of motion,
Riley (1983), can be written for
density to fluid density as:


derived by Maxey and
large ration of particle


dv,
=f
dt


8(ps)
t+ V (pve) =

''- 1'"1(5)


P is the production term and is the pressure-strain:


P =-p y(~VT) +(VYvy (6)

The pressure-strain acts to drive turbulence towards an
isotropic state by redistributing the Reynolds stresses. The


f represents the drag force modelled by Schiller Naumann
drag force correlation. This should only be used for solid
spherical particles, or for fluid particles that are sufficiently
Small that they may be considered spherical. The Schiller
Naumann drag force correlation (Equation 14) is derived for
flow past a single spherical particle, it is only valid in the
dilute limit of very small solid phase volume fractions.


24
f= (1+0.15Re0 687)
Re


The Q-Criterion (Haller, 2005) was used to analyze regions
of vorticity and it is the first three-dimensional vortex
criterion which defines a vortex as a spatial region where:


n =-pl- pV- I+~[~+ VT+V)LT












Dirgo's cyclone pressure drop was measured at each inlet
velocity. The downstream pressure taps were located
between the cyclone and the flow straightened so that only
losses due to the cyclone were included.
The simulations were executed on two computers. Each of
them has eight 3 GHz cores with 24 GBytes of memory.
A characteristic time step of 10-3 WaS considered in the
simulation. Tree days of simulation were necessary to
guarantee the convergence.
The pressure drop of single phase simulations results were
compared to those of Dirgo et. al. (1983). and have shown a
good agreement with the experimental data, as one can see
in Figure 3. It is important to stress that, for low velocities at
inlet of the cyclone, results as good as 0.07% of deviation
were obtained. Figure 3 shows that, for both tetrahedrical
and hexahedrical meshes, with or without hopper, results
show good agreement with experimental data.
Figure 3 also shows that, at higher velocities, around 20 m/s,
the hexahedrical mesh shows better results. The reason for
this may be the less dissipative nature of this kind of mesh
element. One may see that, even for the highest velocity, the
hexahedrical mesh is the only one that still shows good
results. It is important to verify that the tetrahedrical mesh
without hopper shows approximately 50% of deviation from
experimental data. This may be due to the fact that the
original Dirgo's article reported experiments in which a
cyclone with hopper was used. This results shows that the
presence of this device is extremely important in
simulations concerning CFD if one wants to reproduce
actual physical behaviour inside cyclones.


3500
3000 o ExpenmentalDGOea
a 50 HCyclone wthutHopper



1000-
500-

510 15 20 25 30
Velocity (mis)
Figure 3: Cyclone pressure drop.


Q-Criterion was also analyzed to compare the influence of
geometric and mesh configuration under four different inlet
velocities (10 m/s; 15 m/s; 20 m/s; 25 m/s), as one can see at
Figure 4.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Paper No


Results and Discussion


the Euclidean norm of the vorticity tensor (W) dominates
that of rate of strain (S) for the detection of coherent vortex.


Numerical Method

The computation model of the cyclones, was built using
Ansys Design Modeler and is discretized the elements using
ICEM-CFD. The simulations where performed on
discretized governing equations based on element-based
finite volume method (EbFVM) available on ANSYS CFX.
Hexahedrical and tetrahedrical meshes have been used with
roughly the same number of nodes (270,000). A mesh
refinement was made at the core annulus region to capture
the low pressure region, Figure 2. The single-phase models
have been generated as three-dimensional (3D), transient
and the continuous phase (air) has been modelled using the
RSM-SSG turbulence model. A high resolution scheme was
used to model the advection terms of the momentum
equation.
The gas-solid simulation for the Qian et al. (2009) case
consider the Euler-Lagrange and two-way coupling for the
Qian et al. (2009) cyclone was conducted using a
hexaedrical mesh with the same number of nodes of the
single phase studies.






















(a) (c)
Figure 2: Representations of a typical cyclone mesh used in
this study: (a) Tetrahedrical mesh, (b) hexahedrical mesh,
(c) tetrahedrical mesh detail and (d) hexahedrical mesh
detail.


- ar2 -|S|2 > 0






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Tetra Tetra Hexa Tetra Tetra Hexa


Paper No


Tetra Tetra Hexa


Tetra Tetra Hexa


Mna
210hOI

1~14

(~LSh~

~.2Y*106

OmO~r00
Ir11


(d)


(c)


(b)


Figure 4: Vortex core region with Q-Criterion. Inlet velocities: (a) 10 m/s; (b) 15 m/s; (c) 20 m/s and (d) 25 m/s.


As can been in all cases, the hopper itself modifies
significantly the flow field in the cyclone, showing, once
more, its importance in the simulation.
For the cases with hexahedrical mesh, when compared with
its similar for tetrahedrical one, the results show that the
latter tends to be more dissipative than the first, resulting in
a poorer shaped core. This behaviour becomes more visible


as the velocity in the inlet increases.
One of the criteria used during simulations in order to check
their convergence was the difference between the absolute
pressure at the inlet and the overflow of the cyclone, which
accounts for the pressure drop. Figure 5 shows the results
obtained for this variable.


Tetra Tetra Hexa


Tetra Tetra Hexa


Tetra Tetra Hexa Tetra Tetra Hexa


(a)


(b)


(c) (d)


Figure 5: Absolute Pressure. Inlet velocities: (a) 10 m/s; (b) 15 m/s; (c) 20 m/s and (d) 25 m/s.


The results agreed with those showed in Figure 4,
presenting small differences among the cases when the inlet
velocity is low and bigger differences when the velocity
approaches its maximum value. Once again, the
hexahedrical mesh conserves better the vortex core and the
gradient pressure (region of low pressure in the middle,


assigned by the intense blue colour, and a region of higher
pressure, marked by the red colour outskirt the center).
Figure 6 shows, for each case studied, a plane for the axial
velocity plotted in order to verify the results achieved for
the absolute pressure.


Ibt~L~RIW
lml~m

IOlhm """l"""i



soosn

oa~a~a~l
Im]

































Table 4: Pressure drpresults.
Qian et al Error
Numerical (09 %

AP (Pa) 1550.74 1536.85 0.9

Figure 7 shows the Q-Criterium, absolute pressure. Axial
velocity and streamline for Qian's cyclone. During the
simulation, regions of particle volume fraction with values
higher than 1 were observed. This behaviour happens
because the Lagrangian approach predicted regions of
particle accumulation. The time of interaction between
particle motion and continuous phase (zcp) fluctuations is
defined by Peirano et al. (1998), Figure 7 (e).


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Paper No


(a) (b) (c) (d)
Figure 6: Axial velocity. Inlet velocities: (a) 10 m/s; (b) 15 m/s; (c) 20 m/s and (d) 25 m/s.


Figure 6 also show the differences between the results
achieved by hexahedrical and by tetrahedrical mesh, as well
as the influence of the hopper presence. As expected, the
presence of a hopper increases the length of the equipment,
letting the vortex to grow more inside the cyclone. This
characteristic makes the vortex thinner than the one that is
developed by a cyclone without a hopper.
The second part of this work consisted in the determination
of the pressure drop in a gas-solid cyclone considering the
studies developed by Qian etcl 1o/ rf is ,'.
The cyclone pressure drop was calculated as the difference
between the inlet and the average vortex pressure at the
finder exit (overflow region). The pressure in the overflow
was tracked during the simulation to evaluate the solution
stability. Table 4 shows that the CFD numerical results
presented an excellent agreement with Qian's experimental


values (less than 1% of error).


Velodly u
25.0

16.2


r.5 .

-1.2 i

-10.0
[m s -11


OCealeron



3.01xi+05


2.000**05

1 tonesoB


1000**04


2.275e-4

1.550e-0


L250a-05


1.0000-05


Figure 7: Qian cyclone. (a) Vortex core region with Q-Criterion, (b) Pressure, (c) Axial velocity and (d) Streamline.


Conclusions

The simulations were carried out using the RSM-SSG
model of Speziale et. al. (1991) for turbulence and a high
order advection scheme on 3D meshes. The influences of
the mesh, as well as the presence of a hopper were tested.
The results for pressure drop showed that both, tetrahedrical


and hexahedrical meshes, were good enough to represent
the experimental data for low velocities at the inlet of the
cyclone. As the velocity rises to higher values the
hexahedrical mesh have shown its superiority and should be
used. Considering the experimental apparatus used in Dirgo
et al.(1983), the influence of a small hopper presence was
also analysed and verified. Actually, the combination of the


Tetra Tetra Hexa Tetra Tetra Hexa Tetra Tetra Hexa


Tetra Tetra Hexa






;1Ylh

I i



-c-1, i,


Absolute Pressure
102500.0

I102125.0

101750.0

101375.0


101000.0
[P]






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Braz. J. Chem. Eng., January-March, Vol. 21, N 1, pp.


Peirano, E., Leckner, B. Fundamentals of turbulent gas-solid
flows applied to circulating fluidized bed combustion.
Department of Energy Conversion. Chalmers university of
technology Gdteborg,Vol. 24, pp. 259-298 (1998).

Qian, F., Wu, Y. Effects of the inlet section angle on the
separation performance of a cyclone. IChemE. Vol. 87, pp.
1567-1572 (2009).

Ramachandran, G., Leith, David., Dirgo, J., Feldman.
Cyclone optimization based on a new empirical model for
pressure drop. Aerosol Science and Technology, Vol. 15, pp.
135-148 (1991).

Slack, M. D., Prasad, R.O., Bakker, A., Boysan, F.Advances
in cyclone modeling using unstructured grids. Trans
IChemE, Vol. 78, Part A, November, pp. 1098-1104 (2000).

Speziale, C.G., Sarkar, S. and Gatski, T.B. Modelling the
pressure-strain correlation of turbulence: an invariant
dynamical systems approach, J. Fluid Mechanics, Vol. 277,
pp. 245-272 (1991).

Tenney, E. D., Allen, R. L. Cyclones Fact and Fiction.
Katalistiks Fourth Fluid Catalytic Cracking Symposium,
May 18-19th (1983).

Wang, B. Xu, D. L., Chu, K. W., Yu, A. B. Numerical study
of gas-solid flow in a cyclone separator. Applied
Mathematical Modelling, Vol. 30, pp. 1326-1342 (2006).

Zens, F. A. Size cyclone diplegs better. Hydrocarbon
Processing, May, pp. 125-128 (1975).


Paper No


hopper presence and a hexaedrical mesh gave the best match
with the experimental results.
For all studied cases, the Q-criterion, the absolute pressure
and the axial velocity profiles were used to verify not only
the stability of the solution but also the characteristics of the
cyclone. In this way, for all purposes, under high velocity at
inlet, a hexahedrical mesh for the cyclone is recommended,
so as the presence of a hopper and its realistic geometric
representation. At low inlet velocity, however, a
tetrahedrical mesh may be enough to achieve a good
simulation and, given it is far easier to be built than
hexahedral meshes, it may be used. However, the limit
between "high" and "small" velocities was not explored.
The evaluated Euler-Lagrange, two-way coupling was
capable to predict the pressure drop in a multiphase cyclone
with good results. Particles effect can be neglected on the
turbulent motion for dilute suspension. Less than 1% of
difference was observed comparing CFD results with
experimental data obtained by Qian et al. (2009).

References

ANSYS-CFX Solver Theory Guide Reference Manual
(2009).

Ayers, W. W., Boysan, F., Swithenbank, J. Ewan, B. C. R.
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Bryant, H. S., Silverman, R. W., Zenz, F. A. How dust in gas
affects cyclone pressure drop. Hydrocarbon Processing,
June, pp. 87-90 (1983).

Chen, J., Shi, M. A universal model to calculate cyclone
pressure drop. Powder Technology, Vol. 171, pp. 184-191
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Cort~s, C., Gil, A. Modeling the gas and particle flow inside
cyclone separators. Progress in Energy and Combustion
Science, 33, pp. 409-452 (2007).

Dirgo, J. Leith, D. Cyclone collection efficiency:
comparison of experimental results with theoretical
predictions. Aerosol Science and Technology, Vol. 4, pp.
401-415 (1985).

Elghobashi, S. On predicting particle-laden turbulent flows.
Applied Scientific Research, v. 52, pp. 309-329, 1994.

Haller, G. An objective definition of a vortex. J. Fluid. Mech,
Vol. 525, pp. 1-26 (2005).

Kaya, F. and Karagoz, I. Performance analysis of numerical
schemes in highly swirling turbulent flows in cyclones.
Current Science, Vol. 94, n 10, May, pp. 1273-1278 (2008).

Maxey, M. R. And Riley, J., Equation of motion for a small
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(1983)

Noriler, D., Vegini, A. A., Soares, C., Barros, A.A.C., Meier,
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