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CFD MODELLING OF FLUIDIZED BED SYSTEMS
Kari Myöhänen, Vesa Tanskanen, Timo Hyppänen, Riitta Kyrki-Rajamäki
Lappeenranta University of Technology, P.O.Box 20,
FI-53851 Lappeenranta, Finland
kari.myohanen@lut.fi, vesa.tanskanen@lut.fi, timo.hyppanen@lut.fi, riitta.kyrki-rajamaki@lut.fi
Abstract: Gas-solid fluidized bed systems are used for various purposes, such as for
energy production and in petrochemical processes. Because of the high volume
fraction of the solid phase, the fluid dynamics of the solids have a major effect on
mixing of reactants and the performance of the overall processes. The fluidized bed
systems can be simulated by computational fluid dynamics (CFD), but the
complicated processes set limits for the modelling. This paper presents the current
status of CFD modelling capabilities and modelling examples.
Keywords: modelling, multiphase, computational fluid dynamics, FCC, CFB
1 INTRODUCTION
The advantages of gas-solid fluidized beds are
numerous, for example: fluidization of particles
enables controlled handling of solids; good solids
mixing and the large thermal inertia of solids produce
nearly isothermal conditions; heat flow and reaction
rates between gas and solids are high due to large
gas-particle contact area; heat transfer from
suspension to heat exchanger surfaces is enhanced by
the solids; constant movement of particles and the
large interparticle forces enable operation close to
melting temperature of solids. Hence, the fluidized
beds are used for gasification, combustion, catalytic
cracking and various other chemical and
metallurgical processes.
The fluid dynamics of solids have a large effect on
various phenomena, such as the mixing of different
reactants and heat transfer. Thus, as a starting point
for a more comprehensive model, first the fluid
dynamics of the solids would have to be modelled
correctly. Because of large volume fraction of solids,
the best alternative is usually the Eulerian approach,
in which different gas and solid phases are treated as
interpenetrating continua and momentum and
continuity equations are defined for each phase.
Bubbling fluidized beds have been modelled with
relatively good results, but modelling of circulating
fluidized bed (CFB) applications remains to be a
challenge (Arastoopour, 1999; van Wachem et al.,
2001; Cruz et al., 2002). The following article
concentrates on hydrodynamic modelling of CFB
applications. The paper presents the theories and
software for multiphase modelling. Modelling
examples are presented, which show the challenges
and possibilities of the CFD modelling.
2 FLUIDIZED BED APPLICATIONS
The following presents two examples representing
circulating fluidized beds: fluid catalytic cracking
and circulating fluidized bed combustion.
The fluid catalytic cracking (FCC) is used for
converting crude oil into a variety of higher-value
light products, such as gasoline (Fig. 1). Hot catalyst
(650 – 700 °C) flows from the regenerator to the
3 EULERIAN MULTIPHASE MODELLING bottom of the riser and meets the liquid feed, which
is vaporized. The mean size of the FCC particles is
about 40 – 80 µm and particle density 1100 – 1700
kg/m3, representing Geldart group A. Inside the riser,
the feed vapor is cracked by the catalyst. Fluidization
velocity in the riser is 6 – 28 m/s, increasing towards
top due to molar expansion. The net solids flow is
400 – 1200 kg/m
3.1 Modelling theories
Substantial development of multiphase CFD
techniques occurred in late 1970’s. In 1975, Harlow
and Amsden introduced a numerical method called
IMF – Implicit MultiField solution method (Witt,
1997). On the other field, Spalding (1981) proposed
an extension to the SIMPLE (Semi-Implicit Method
for Pressure-Linked Equations) algorithm of Patankar
and Spalding (1972). This method is called IPSA
(Inter-Phase Slip algorithm) and is used in many
multiphase codes like Phoenics and CFX (Witt,
1997). Also, some other SIMPLE modifications have
been used, such as PC-SIMPLE in Fluent (Fluent
manual 2001) Table 1 lists properties of different
solution methods.
2
s. At the top of the riser, the
catalyst is separated from reaction products and
returned back to regenerator.
For the continuum equations, following set of
equations is used in most of the models (van
Wachem et al., 2000):
()
()
solidsfor
t
gasfor
t
ss
s
gg
g
0
0
=⋅∇+
∂
∂
=⋅∇+
∂
∂
v
v
α
α
α
α
(1)
, where α is volume fraction and ‘g’ and ‘s’ denotes
gas and solid phases. Moreover, α
g
+ α
s
= 1, has to be
satisfied.
Fig. 1. Side-by-side FCC unit (King, 1992).
The continuity equations are basic physics, but
several different approaches exist for the phase
momentum equations. According to Witt (1997), the
three most common models can be classified as
• Model A: Pressure drop shared between phases
(Ishii, 1975; Harlow and Amsden, 1975)
• Model B: Pressure drop in gas phase only.
(Anderson and Jackson, 1967)
• Model C: Relative velocity model.
(Gidaspow 1978,1994)
In bare form, the model A has been considered as ill-
posed and the model B well-posed. However,
addition of viscosity or extra terms, such as granular
pressure, lift force and virtual mass, can make the
model A well-posed. It is not well known what
combined effects these terms have, and often the
main interest of codes has been in granular pressure
term (Witt, 1997). Confusingly, in the current CFD
models, there are two typical sets of governing
equations; by Jackson (1997) or by Ishii (1975)
(Table 2). The difference is not anymore clearly in
the pressure drop, but in the fluid stress-strain tensor
effect on the granular phase. In Eqs. (2) - (3), β is
drag coefficient, P
Fig. 2. CFB boiler (EC Chorzów Elcho, adapted from
Foster Wheeler reference material).
In a circulating fluidized bed boiler (Fig. 2), the
fluidization velocity is typically about 5 m/s at full
load. The solids are coarser and denser than in FCC,
particle size 100 – 300 µm and particle density 1800
– 2600 kg/m
3
(Geldart group B). The fuels used in
CFB combustion include coal, oil shale, petroleum
coke, lignite, wood, biomass and different wastes.
Typical furnace temperatures are 800 – 900 °C and
net solids flow in furnace 10 – 100 kg/m
2
s.
s
is granular pressure and
τ
is
stress-strain tensor. It seems that most of the codes
use Ishii (1975) type equations, but especially stress
terms may be handled differently.
Table 1. Commonly used solution algorithms.
IMF IPSA Other SIMPLE extensions
Properties -Point-relaxation iterative
technique
-Volume fractions solved from individual
phase mass conservation equations
PC-SIMPLE:
-Volume fractions are obtained from phase
continuity equations.
-Pressure and phase coupling
terms treated implicitly
-Pressure correction equation derived from
global mass conservation
-Velocities are solved coupled by phases,
but in a segregated fashion. Velocities are
solved simultaneously for all phases.
-Convective, viscous and
body force terms treated
explicitly
-PEA (partial elimination algorithm) is
used in implicit solution of interphase
coupling terms.
-Pressure correction equation is based on
total volume continuity. Pressure and
velocities are corrected to satisfy the
continuity constraint.
-As in SIMPLE, convective and diffusive
fluxes are handled implicitly and variables
have to be relaxed.
Software K-FIX CFX,PHOENICS,STAR-CD, FLUENT4 Fluent (PC-SIMPLE),
MFIX (extension)
Table 2. Momentum equations.
Jackson (1997)
()
()
gvvvv
v
gvvvv
v
sssgs
s
s
g
sss
s
ss
ggsgg
g
ggg
g
gg
PP
t
P
t
ραβτατααρ
ραβατααρ
+−+∇−⋅∇+∇−⋅∇=
⎥
⎦
⎤
⎢
⎣
⎡
∇+
∂
∂
+−−∇−⋅∇=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∇+
∂
∂
(2)
Ishii (1975)
()
()
gvvvv
v
gvvvv
v
sssgs
s
sss
s
ss
ggsgg
g
ggg
g
gg
PP
t
P
t
ραβτααρ
ραβατααρ
+−+∇−⋅∇+∇−=
⎥
⎦
⎤
⎢
⎣
⎡
∇+
∂
∂
+−−∇−⋅∇=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∇+
∂
∂
(3)
3.2 Codes for multiphase modelling
Of the dozens of different CFD software packages
only few include possibility for Eulerian multiphase
modelling. The following is a list of codes most
commonly referenced in the literature:
• Phoenics (www.cham.co.uk)
• Fluent (www.fluent.com)
• CFX (www.ansys.com)
• Star-CD (www.cd-adapco.com)
• Estet-Astrid (www.simulog.fr)
• MFIX (www.mfix.org)
It is possible to implement user defined modifications
to any of these codes. The following presents only
the originally programmed features.
Phoenics was released in 1981 and it can be
considered as a prototype code for many of the later
CFD softwares. Phoenics uses IPSA algorithm and
solves type A momentum equations, but IPSA has
been implemented for two phases only. According to
Muehlbauer (2004), Phoenics uses so called drift-flux
method for more than two phases having the same
range of properties.
Fluent was launched in 1983, but the multiphase
models have been more developed in the later
versions only. Eulerian multiphase modelling with
more than two phases, including granular material,
can be calculated. For the pressure-velocity coupling,
Fluent uses Phase Coupled SIMPLE algorithm.
Kinetic theory is applied and the momentum equation
of granular phase is of Ishii (1975) type A, where
viscosity, granular temperature and lift force can be
included. For fluid-solid momentum exchange
coefficient, Fluent offers Syamlal-O’Brien and
Gidaspow models for granular modelling. For dilute
systems, Wen and Yu model can be used as well. For
solid-solid momentum exchange coefficient Syamlal-
O’Brien-symmetric model can be used. Fluid-fluid
momentum transfer can be calculated using Schiller-
Naumann or Morsi-Alexander exchange coefficients.
Granular temperature is an important factor in
calculation of granular viscosities. Differential
equation for granular temperature is possible, but due
to convergence problems, the simplified algebraic
form is useful. For granular kinetic part of viscosity,
Syamlal-O’Brien and Gidaspow models can be used,
and for the frictional part, Schaeffer’s expression is
available. Lun et al. expressions can be used for
granular bulk viscosity, solids pressure and radial
distribution function.
For turbulence modelling Fluent offers, in multiphase
cases, k-ε-models (Standard, RNG, realizable) and
now also Reynolds Stress model. In these k-ε-
models, turbulence can be modelled by ‘mixture’,
‘dispersed’ or ‘k-ε per phase’ models. In the
dispersed model, k-ε-equations are solved for the
primary phase and Tchen’s theory is used for the
dispersed phases. (Fluent manual 2001).
The commercial version of
CFX was published in
1990. The version CFX 5 was based on unstructured
mesh and later, when ANSYS Inc. bought CFX, the
name was changed to ANSYS CFX. CFX uses IPSA
method as solution algorithm. Model A equations
(+additional terms) are solved and kinetic theory is
applied for granular flows. There are no restrictions
in the amount of phases. Furthermore, for the
dispersed phases, a so called MUSIG (Multiple Size
Group) scheme is applicable for bubbly flows.
According to Muehlbauer 2004, the single-phase k-
ε- and Reynolds Stress models are generalized to
multiphase situation (at least in CFX-4). As some
additional implementations; optional Sato’s model is
available for bubble-induced turbulence, turbulent
dispersion force exists for phasic momentum
equations, and optional turbulent diffusion term is
available for phasic continuity equations. In May,
2006, Ansys bought the Fluent Inc., which is likely to
cause changes to these two codes.
STAR-CD applies IPSA algorithm in multiphase
calculations and the momentum equation for a phase
is according to Ishii (1975). At the moment, the
Eulerian model in STAR-CD allows only two phases,
but the extension to multiple phases is in progress.
According to Muehlbauer (2004), turbulence is
modelled based on high Reynolds number k-ε-model.
Modified k-ε-equations are solved for the continuous
phase and the dispersed phase turbulence is
correlated using semi-empirical models. Particles
effects on turbulence field are taken account by
additional terms.
Simulog/
Estet-Astrid, N3S and many other codes
allow Eulerian multiphase calculations as well, but in
this survey it is not possible to examine these
packages in more details.
MFIX (Multiphase Flow with Interphase
eXchanges), developed at the National Energy
Technology Laboratory (NETL), has been used for
CFB simulations and as a test-stand for multiphase
equations (Benyahia
et al., 2006). The code itself is
based on a generally accepted set of multiphase
equations. In kinetic theory, modified Princeton
model is used.. Syamlal-O’Brien and Gidaspow
models exist for the drag correlation for fluid-solid
momentum transfer. Additionally, Wen-Yu
correlation (dilute case) and Hill-Koch-Ladd
correlation are available. The latter one is valid for
one solid phase only. For solid-solid momentum
exchange coefficient Syamlal-O’Brien-symmetric
can be used. MFIX documentation informs that Yu-
Standish correlation (multi-component) and Fedor-
Landell correlation (binary mixture of powders) are
available for calculation of solids maximum packing
in polydisperse systems. For heat transfer coefficient,
Gunn correlation is applied for Nusselt number in
granular phase. The turbulence model in MFIX is
quite similar to dispersed k-ε-model in Fluent. For
turbulence interaction terms, Simonin’s and
Ahmadi’s models are optional in that model. For
calculation of granular temperature, differential and
algebraic equations are available. However, the
turbulence kinetic energy ‘k’ for granular phase is
replaced by the granular temperature, which forms
still a differential equation. For the granular
quantities like solids pressure, viscosities and
granular conductivity, Simonin and Ahmadi
expressions are optional. For frictional viscosity,
Schaeffer or Princeton models are available.
3.3 Common problems in Eulerian modelling
Axial density or velocity profiles are not realistic
with current drag models.
According to Kallio
(2005), the CFD simulations underpredict the solids
concentration in the bottom region of a CFB. Kallio
mentions, that this is due to underestimation of the
average slip velocity and overestimation of the
average gas-solid drag force. These problems are
results of mismatch between the computational mesh
size and the assumption of homogenous conditions
inside of each control volume. Kallio obtained better
results by using a simple drag model based on Ergun
(1952) and modified Poikolainen (1992) models. In
this model, some empirical correlations are needed to
calculate the ratio of the slip velocity to the terminal
velocity, but this term is not very sensitive.
Ibsen
et al. (2000) noted that two-phase modelling is
not able to capture the hydrodynamic behaviour of
particles with different diameters. Ibsen
et al,
obtained more realistic results, especially in dilute
conditions, by increasing the amount of solid phases
of different particle diameters. In the simulations of
multiple phases, the major drawback is the
simulation time, which increases steeply when the
amount of phases increases.
Simulation times are long, convergence is poor
and stability problems occur when multiple
phases exist.
Convergence problems and long
computing time make large scale simulations with
more than two phases very challenging. At the
beginning of a simulation, some of these problems
can be reduzed by using small under-relaxation factor
for the volume fraction, and trying to avoid zero
volume fractions as an initial condition. In close-to-
symmetrical cases, 2D-results can be used for
initialization of 3D-problems, which may reduce the
required stabilization time. Mixture based models can
be used as initialization tools before starting real
Eulerian calculations, but these mixture models may
not work properly with dense and large particle
phases. A quite clear solution would be to reduce the
time-step size below the characteristic time of flow,
but this makes 3D simulations of large scale units
practically impossible. Furthermore, because of flaws
in current granular models and numerical schemes,
sudden divergences can be possible even with a very
small time-step.
4
EXAMPLE STUDY
Figure 2 presents a schematic diagram of the studied
furnace and Table 3 lists the main boiler data. The
fuel is fed to four feeding points at the front wall and
three points at the back. Circulating bed is fluidized
by primary air through the grid. Secondary air is
introduced at level 2 – 4 m from grid. From the
furnace, the gas and solids enter the separator, which
separates the solids from flue gas. The separated
solids flow to internal heat exchanger units
(INTREX). Part of the bed material enters the
INTREX units directly from furnace. From the
INTREX units, the bed is returned back to furnace.
Fig. 4. Model geometry in 3D-calculations.
Table 3. Boiler data.
Capacity (electr., thermal) 102 MWe, 250 MWth
Furnace dim.ensions 14.3 m × 6.7 m × 43.8 m (w×d×h)
Fuel Subbituminous coal
In each case, the model was first calculated without
fuel feeding in order to establish stable process
conditions. This could take several days, depending
on the case and the starting point. After the stable
conditions were reached, the fuel feeding was started
and simulated for 5 to 15 seconds. As expected, the
measured vertical solid concentration profile could
not be exactly simulated (Fig. 5 – 7). Because of this,
the results are qualitative.
Total flue gas flow 125 kg/s
Bed temperature 802 °C
Primary air share 60%
The calculations were performed by Fluent version
6.2.16 (Tanskanen, 2005). Table 4 summarizes
essential model options.
Table 3. Model options.
Fluid-solid drag Syamlal-O’Brien
Solid-solid drag Syamlal-O’Brien-symmetric
Granular viscosity Syamlal-O’Brien
Gran. bulk viscosity Lun et al
Frictional viscosity Schaeffer
Granular temperature Algebraic
Solids pressure Lun et al
Phases Flue gas, ρ
g
=0.329 kg/m
3
Bed, dp=175 µm, ρ = 2548 kg/m
3
Fig. 5. Example of volume fraction of bed.
p
Fuel, dp = 32-4000 µm, ρ = 1262 kg/m
3
p
The purpose of the work was to study the penetration
and mixing of fuel and char at the lower part of the
furnace. The model volume was restricted to a 15 m
height section of the furnace. First, the case was
modelled in two dimensions (Fig. 3) and the effect of
different parameters was studied (particle size,
secondary air, etc.). Finally, the case was modelled as
a three-dimensional slice of furnace (Fig. 4).
Fig. 6. Solid concentration profile in 2D-calculations.
Fig. 3. Model geometry in 2D-calculations.
Fig. 7. Solid concentration profile in 3D-calculations.
At the moment, the multiphase CFD codes and
models are not yet developed to their final form.
Especially the physics of granular material is not
completely known and the CFD calculations of more
than two phases in circulating fluidized bed
conditions are quite challenging. Many of the
phenomena in fluidized bed systems are three-
dimensional in nature and include multiple phases,
but modelling these conditions is time-consuming
and the results are unreliable. However, the data of
CFD studies can be utilized for better understanding
of the process, if care is taken and the results
compared with experience and measurements.
Based on calculation results, the particle size of fuel
has relatively small effect on penetration and mixing
of fuel in dense bed zone (Fig. 8). This further
emphasis the need to model the fluid dynamics of
bed correctly. Figure 9 presents the volume fraction
of fuel at 2.5 seconds after start of feeding in 3D-
calculation. The 3D simulation was calculated in a
Linux cluster with 5 x 2 GHz processors. With mesh
of 216200 cells, the simulation of 2.5 seconds took
about two months of calculation time.
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5
CONCLUSIONS
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