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CFD analysis of flow field in square cyclones

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Author's personal copy
CFD analysis of
ow
eld in square cyclones
Arman Raou
, Mehrzad Shams
, Homayoon Kanani
Department of Mechanical Engineering, K.N. Toosi University of Technology, Pardis St., Mollasadra St., Vanak Sq., Tehran, Iran
a b s t r a c ta r t i c l e i n f o
Article history:
Received 19 August 2008Received in revised form 30 September 2008Accepted 6 November 2008Available online 27 November 2008
Keywords:
CFDSquare cycloneTwo phaseFlow
eld
In this study, computational
uid dynamic method is used to predict and evaluate the
ow
eld inside asquare cyclone. The
ow
eld is calculated using 3D Reynolds-averaged Naveir
–
Stokes equations. TheReynolds stress transport model (RSTM) is used to simulate the Reynolds stresses. The Eulerian
–
Lagrangiancomputational procedure is implemented to predict particle trajectory in the cyclone. The Newton's secondlaw is used to study the particle trajectory with modeling the drag and gravity forces acting on the particles.The velocity
uctuations are simulated using the discrete random walk (DRW). Two square cyclones whichhave different geometries are studied. The cyclones are simulated at different
ow rates. The details of the
ow
eld are studied in the cyclones and the effect of varying the
ow rates is observed. Tangential velocityis investigated in different sections inside the square cyclone. Contour of pressure and turbulence intensity isshown for different inlet velocities inside the cyclones. It is observed that different geometries, also differentinlet velocities, could affect on the pressure drop. The collection ef
ciency and the
ow patterns obtainednumerically are compared with the experimental data and good agreement is observed.© 2008 Elsevier B.V. All rights reserved.
1. Introduction
Due torelative simplicity tofabricate, lowcost tooperate,and welladaptabilitytoextremelyharshconditions, cycloneshavebecomeoneof the most important gas
–
solid separators which are preferablyutilized in both engineering and process operations. Cyclone is a keypart for the circulating
uidized bed (CFB) boiler which has greateffects on the combustion ef
ciency, the circulation rate and thedesulfurizationef
ciencybythecirculationofthesolidparticlesinthefurnace.Theperformanceofacycloneiscriticaltotheboiler'ssafeandeconomic operation. The arrangement and structure of the cyclonehave in
uence on the overall arrangement of a boiler.Conventional cyclone which has circular cross section was thecommonly used cyclone for the CFB boiler. With the development of large CFB boilers, the huge bodyof the conventional cyclone became amajor shortcoming because of the thick refractory wall that needs along period to start the boiler. An alternative way to overcome theseproblems is the use of square cyclone. A square cyclone has moreadvantages over the conventional cyclone including convenientconstruction, easier membrane wall arrangement, shorter start
–
stoptime and at the same time easy integration with the boiler [17].A considerable number of experimental investigations have beenperformed on the square cyclones. Wang et al. [17] studied theseparation mechanism of a square cyclone at high inlet particleconcentration. They proposed an instantaneous separation modelbased on experimental observation and measurement. Junfu et al. [6]investigated the square cyclone at 75 t/h CFB boiler and presented amodel to study the cyclones. Effects of different parameters includinglength, diameter of vortex
nder, and inlet velocity onperformance of squarecycloneswerestudiedbyQiangetal.[11].SuandMao[15]used
a three-dimensional particle dynamic analyzer (3D-PDA) to under-stand the nature and characteristics of the suspension
ow in thesquare cyclone separator and found out the factors affecting particlemotion. The turbulent
ow
eld inside a square cyclone wasexperimentally investigated by Su [16] to study the mechanism of particle separation and provide guidance for the optimization of itsstructure. Junfu et al. [7] evaluated the performance of advancedwater-cooled square cyclone with curved inlet. The results werecompared with other cyclones through
y ash analysis and showedthat the overall performance of the square cyclone in such capacity iscompatible with the conventional cyclones.Laser Doppler anemometry (LDA) and hot-wire anemometry arefrequently employed to study the
ow pattern in the cyclonesexperimentally. Recently, research efforts by computational
uiddynamics are frequently carried out for the resolution of
ow
eldand dust particle behavior with different degrees of numerical andmodeling accuracy in order to assist in the time consuming experi-mental works. In conjunction with the complex
ow structure,numerical simulation is momentarily not able to completely sub-stitute experiments but can reduce, to a certain degree, experimentalcosts for design and optimization.
Powder Technology 191 (2009) 349
–
357
Corresponding author. Tel.: +98 912 359 6236; fax: +98 21 88877273.
E-mail address:
shams@kntu.ac.ir (M. Shams).0032-5910/$
–
see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.powtec.2008.11.007
Contents lists available at ScienceDirect
Powder Technology
journal homepage: www.elsevier.com/locate/powtec
Author's personal copy
CFD has a great potential to predict the
ow
eld characteristicsand particle trajectories inside the cyclone as well as the pressuredrop [4]. The complicated swirling turbulent
ow in a cyclone placesgreat demand on the numerical techniques and the turbulencemodels employed in the CFD codes. CFD was widely used toinvestigate
ow
eld inside conventional cyclones. It has beenshown in the previous works on the prediction of the cycloneperformance under different operating temperatures and inletvelocities (Gimbun et al., 2005). Raou
et al. [13] used computatio-nal
uid dynamics to simulate and optimize vortex
nder of conventional cyclones. Although many numerical works have beenconducted on the conventional cyclones, there is a little numericalstudy about square ones. As numerical investigations of squarecyclones could have an important role to better understanding of the
ow parameters, this study is intended to obtain detailed
ow information by CFD simulation within square cyclones. Twocases with different geometries are selected to study. Case 1 is thesquare cyclone studied by Wang et al. [17] with upward outlet.Also, a square cyclone investigated by Su and Mao [15] issimulated numerically, as case 2. The square cyclones are modeledat different
ow rates and
ow
elds are evaluated inside thesecyclones. Contours of pressure and turbulence intensity withinthe cyclones are shown. Tangential velocity pro
les and velocityvectors in different sections are investigated. The numerical resultsare compared with experimental data and good agreement isobserved.
2. Flow simulation
For an incompressible
uid
ow, the equations of continuity andbalance of momentum for the mean motion are given as
A
u
i
A
x
i
=0
ð
1
Þ
A
u
i
A
t
+
u
j
A
u
i
A
x
j
=
−
1
ρ
A
p
A
x
i
+
m
A
2
u
i
A
x
j
A
x
j
−
AA
x
j
R
ij
ð
2
Þ
where
u
i
is the mean velocity,
x
i
is the position,
p
is the meanpressure,
ρ
is the constantgasdensity,
v
is thekinematicviscosity, and
R
ij
=
u
i
′
u
j
′
¯¯¯¯¯ is the Reynolds stress tensor. Here,
u
i
′
=u
i
−
u
i
is the
i
th
uid
uctuation velocity component.
Fig. 1.
The geometry of cyclone for (a) case 1 and (b) case 2, unit: mm.350
A. Raou
et al. / Powder Technology 191 (2009) 349
–
357
Author's personal copy
The RSTM provides differential transport equations for evaluationof the turbulence stress components i.e.,
AA
t R
ij
+
u
k
AA
x
k
R
ij
=
AA
x
k
v
t
σ
k
AA
x
k
R
ij
−
R
ik
A
u
j
A
x
k
+
R
jk
A
u
i
A
x
k
−
C
1
e
k R
ij
−
23
δ
ij
k
−
C
2
P
ij
−
23
δ
ij
P
−
23
δ
ij
e
ð
3
Þ
where the turbulence production terms are de
ned as
P
ij
=
−
R
ik
A
u
j
A
x
k
−
R
jk
A
u
i
A
x
k
;
P
= 12
P
ij
ð
4
Þ
with
P
beingthe
uctuationkineticenergyproduction.
v
t
istheturbulent(eddy) viscosity; and
σ
k
=1,
C
1
=1.8,
C
2
=0.6 are empirical constants [8].The transport equation for the turbulence dissipation rate,
ε
, is given as
A
e
A
t
+
u
j
A
e
A
x
j
=
AA
x
j
m
+
m
t
σ
e
A
e
A
x
j
−
C
e
1
e
kR
ij
A
u
i
A
x
j
−
C
e
2
e
2
k
:
ð
5
Þ
In Eq. (5),
k
=
12
u
V
i
u
V
i
is the
uctuation kinetic energy, and
ε
is theturbulence dissipation rate. The values of constants are
σ
ε
=1.3,
C
ε
1
=1.44 and
C
ε
2
=1.92.The dispersion of small particles is strongly affected by theinstantaneous
uctuationof
uidvelocity.Theturbulence
uctuationsare random functions of space and time. In this study, a discreterandom walk (DRW) model is used for evaluating the instantaneousvelocity
uctuations. The values of
u
′
,
v
′
and
w
′
that prevail during thelifetime of the turbulent eddy,
T
e
, are sampled by assuming that theyobey a Gaussian probability distribution. In this model the instanta-neous velocity in the
i
th direction is given as
u
V
i
=
f
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u
V
i
u
V
i
:
q
ð
6
Þ
In Eq. (6),
ζ
is a zero-mean, unit-variance, normally distributed,random number,
ﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u
V
i
u
V
i
q
is the local root mean-square (RMS)
Fig. 2.
Generated mesh of the cyclones for (a) case 1 and (b) case 2.
Table 1
False time steps used for the simulationParameters False time stepPressure 0.2
u
(
x
-velocity) 0.4
v
(
y
-velocity) 0.4
w
(
z
-velocity) 0.4
k
(turbulent kinetic energy) 0.5
ε
(turbulent dissipation rate) 0.5Reynolds stresses 0.5
Fig. 3.
Comparison of numerical, mathematical and experimental [17] result forcollection ef
ciency in the case 1.351
A. Raou
et al. / Powder Technology 191 (2009) 349
–
357
Author's personal copy
uctuation velocity in the
i
th direction; and the summation conven-tion on
i
is suspended.The characteristic lifetime of the eddy is de
ned as a constantgiven by
T
e
=2
T
L
ð
7
Þ
where
T
L
is the eddy turnover time given as
T
e
=0.3(
k/
ε
) in the RSTM.The other option allows for a log-normal random variation of eddylifetime that is given by
T
e
=
−
T
L
log
r
ð Þ ð
8
Þ
where
r
is a uniform random number between 0 and 1. The particle isassumed to interact with the
uid
uctuation
eld, which stays
xedovertheeddylifetime.Whentheeddylifetimeisreached,anewvalueoftheinstantaneousvelocityisobtainedbyintroducinganewvalueof
ζ
in Eq. (6).There are two main approaches to modeling multiphase
owsthat account for the interactions between the phases. These are theEulerian
–
Eulerian and the Eulerian
–
Lagrangian approaches. Theformer is based on the concept of interpenetrating continua, forwhich all the phases are treated as continuous media with propertiesanalogous to those of a
uid. The Eulerian
–
Lagrangian approachadopts a continuum description for the liquid phase and tracks thediscrete phases using Lagrangian particle trajectory analysis.Inpresent study, onewaycoupling method is used to solve of two-phase
ow and the Eulerian
–
Lagrangian approach is implemented forsimulationofseconddiscretephase(particles).Inthismodel,theairisthe continuous phase and the particles are treated as the disperseddiscrete phase. The volume-averaged and steady state Navier
–
Stokesequation is solved for the gas phase. The particle motions aresimulated by the Lagrangian trajectory analysis procedure. Forcesacting on the dispersed phases include drag and gravity. The discrete-phase equations are solved with the Runge
–
Kutta for particles.To calculate the trajectories of particles in the
ow, the discretephase model (DPM) was used totrackindividual particles through thecontinuum
uid. The particle loading in a cyclone separator istypically small, and therefore, it can be safely assumed that the
Fig. 4.
Contour of static pressure (Pa) for two cyclones at different inlet velocities. Case 1 (a)
v
=22, (b)
v
=30 and case 2 (c)
v
=20, (d),
v
=28.32, unit: m/s.352
A. Raou
et al. / Powder Technology 191 (2009) 349
–
357
Author's personal copy
presence of the particles does not affect the
ow
eld (one-waycoupling).The equation of motion of small particles, including the effects of nonlinear drag and gravitational forces, is given by
du
P
i
dt
=3
vC
D
Re
p
4
d
2
S u
i
−
u
P
i
+
g
i
ð
9
Þ
dx
i
dt
=
u
P
i
:
ð
10
Þ
Here,
u
i
P
is the velocity of the particle and
x
i
is its position,
d
is theparticle diameter,
S
is the ratio of particle density to
uid density, and
g
i
is the acceleration of gravity. The buoyancy, virtual mass and Bassetforces are negligible because of the small
uid-to-particle densityratio. The
rsttermon theright-handside (RHS)ofEq.(10)isthedragforce due to the relative slip between the particle and the
uid. Thedrag force is, generally, the dominating force. According to [5], thedrag coef
cient,
C
D
, is given as
C
D
= 24
Re
P
for
Re
P
b
1
ð
11
Þ
C
D
= 24
Re
P
1+ 16
Re
2
=
3P
for 1
b
Re
P
b
400
ð
12
Þ
where, Re
P
is the particle Reynolds number de
ned asRe
P
=
d
j
u
j
−
u
P
j
j
m
:
ð
13
Þ
The particle equation of motion requires the instantaneousturbulent
uid velocity values at particle locations. The mean liquidvelocity was evaluated by the use of the Reynolds stress transportturbulence model (RSTM) and the
uctuation velocity componentswere calculated from Eq. (6). The drag coef
cient for sphericalparticles is calculated by using the correlations developed by Morsiand Alexander (1972). The ordinary differential equation (Eq. (10)) isintegrated along the trajectory of an individual particle. Collectionef
ciency statistics are obtained by releasing a speci
ed number of monodispersedparticlesat theinletof thecycloneand bymonitoringthe number escaping through the under
ow. Collisions betweenparticles and the walls of the cyclone were assumed to be perfectlyelastic (coef
cient of restitution is equal to 1) [13]. Also, particle
–
particle collision is negligible.
3. Results
Thesimulationsareperformedfortwocyclonetypeswithdifferentgeometries which have been studied experimentally by [17,15]. Fig. 1
shows the geometry and dimension of the studied cases. As seen inFig.1 (a) the cyclone of case 1 has an upwardoutlet that also plays therole of vortex
nder. The particles size range is 0
–
2 mm of a materialwhose density and average diameter are respectively 0.205 mm and2550 kg/m
3
[17]. The simulations are performed at inlet velocities of 22, 26, 30 and 34 m/s.As indicated in Fig.1 (b), the exhaust gas went through downwardexit in case 2. The particle used was glass beads of mean diameter of 30
–
40
m and density of 2400 kg/m
3
[15]. This cyclone is studied atinlet velocities of 20, 25.3 and 28.32 m/s.Foranalyzing the
ow in the cyclones, the numbersof 186,298 and258,976 hexahedral cells are generated for cases 1 and 2, respectively.Fig.2 shows thedetailsof thecomputationalgrid forthecyclones.Thehexahedral computational grids are generated by dividing the wholecyclone geometry into a numberof blocks. A
“
velocity inlet
”
boundarycondition is used at the cyclone inlet. A fully developed boundarycondition is used at the outlet. Grid re
nement tests are conducted inorder to make sure that the solution is not grid dependent. The
nitevolume methods have been used to discretize the partial differentialequation. The SIMPLE method is used for pressure
–
velocity couplingand the second-order upwind scheme is implemented to interpolatethe variables on the surface of the control volumes. Turbulence
uctuations are simulated using Reynolds Stress Transport Model(RSTM). The computation is continued until the solution convergedwith a total relative error of less than 0.0005. The Lagrangian methodis used for tracking of particles in the simulation. For investigation of particles trajectory inside the cyclones, seven and nine millions of particles are released at the inlet of cases 1 and 2, respectively. Thechoice of the time step in
uences the convergence behavior: if takentoo large the simulations diverge, if taken too small the computationtimes go up. For steady-state problems, the time steps are false timesteps. False time steps used for simulation of
ow
eld are broughtin Table 1. Time step of 0.2 ms is used for calculation of particletrajectories in the numerical model.It is dif
cult to understand the cyclone separation behaviorwithout some information about the
ow
eld. CFD is a very usefultool to obtain details of the
ow inside a cyclone. Fig. 3 shows the CFD
Fig. 5.
Pressure drop in the cyclones at different inlet velocities. (a) Static pressure dropand (b) Dynamic pressure drop.353
A. Raou
et al. / Powder Technology 191 (2009) 349
–
357

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