Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Influence of Horizontal Tubes, Averaging Periods and Extraction Methods on the
Hydrodynamics of Bubbling GasSolid Fluidized Beds
T.W. Asegehegn, M. Schreiber and H.J. Krautz
Brandenburg University of Technology Cottbus, Chair of Power Plant Technology
WaltherPauerStrasse 5, D03046 Cottbus, Germany
teklay.asegehegn@tucottbus.de
Keywords: Fluidized Bed Hydrodynamics; Numerical Study; Horizontal Tubes; Extraction Methods; Averaging Periods
Abstract
In this paper numerical studies using EulerianEulerian Two Fluid Model (TFM) of two dimensional gassolid bubbling
fluidized beds with and without immersed horizontal tubes were performed. The influences of tubes, averaging time and
extraction methods on the bed hydrodynamics were investigated. The results were compared with experimental data and
correlations available in the literature.
The overall pressure drops obtained from the simulations were found to be independent of the way of extraction, while the bed
expansion showed significant variation with the extraction techniques. The study also showed that the length of averaging
periods influence the timeaveraged bed properties. Investigations of bubble properties showed that horizontal tubes were the
main source of bubble breakup. Thus, the calculated mean bubble diameters and rise velocities were found to be lower with
tubes than without for the same bed geometry and superficial velocity. Similarly, the simulation showed higher vertical solid
velocity between the tube columns. For the beds with immersed tubes, defluidized regions were observed at the upper part of
the tubes where solid particles rested without moving. On the other hand, the lower parts of the tubes were usually covered
with gas pockets. These effects were seen to reduce with increasing superficial velocity.
Introduction
Fluidized beds are widely applied in process and chemical
industries such as combustion, drying, polymerization,
cracking of hydrocarbons, heat exchange, etc. In many of
these applications tubes are usually inserted to enhance the
rate of heat transfer and chemical conversion. The operation
and efficiency of fluidized bed reactors therefore strongly
depend on the geometry and arrangement of the immersed
tubes. Despite the significant influence of these immersed
tubes is on the hydrodynamics of the reactors, many
researchers have been concerned mainly on the
improvement of the heat transfer coefficient between the
tubes and the emulsion phase. However, it is the variation of
bubble properties and solid motion as a result of the tubes
which controls the rate of heat transfer and chemical
conversion.
Some researchers have been investigated the influence of
horizontal tube on bubble hydrodynamics, Yates et al. 1990,
Hull et al. 1999, Almstedt and coworkers (Olsson et al. 1995,
Wiman & Almstedt 1997) to mention few. However, these
results couldn't provide an indepth understanding of the
bubbling behavior of fluidized beds. This could be mainly
due to the lack of appropriate measurement devices for
bubble properties in the presence of such obstacles. Bubbles
vary in size and velocity over the bed volume; hence
measurement of bubble distribution and their characteristics
over the whole bed geometry is not possible by many of the
experimental procedures. In recent years, due to rapid
growth of computer capacity, numerical simulation is
becoming a powerful tool in determining the macro and
microscopic phenomena of gassolid fluidized beds.
Numerical simulations are more flexible and less expensive
to perform parametric studies of different bed geometries
and operating conditions. Moreover, they can provide
intensive data of bubble characteristics of the complete
volume of the reactors. On the other hand, these numerical
results require intensive validation with experiments before
using them as a fundamental tool for the scaleup and design
procedures of fluidized beds.
In general, two types of computer models are widely applied
today, the Two Fluid Model (TFM) based on the
EulerianEulerian approach (Anderson & Jackson 1967) and
the Discrete Particle Model (DPM) based on the
EulerianLagrangian approach (Tsuji et al. 1993, Hoomans
et al. 1996). DPM is a more fundamental approach for
fluidized bed applications, but its demand of very high
computational effort has made it more prohibitive and
limited to only few particles and very small fluidized beds.
On the other hand, the TFM requires less computational
time, thus, it remains to be the only realistic approach for
parametric investigation of fluidized beds of engineering
scales (van Wachem et al. 2001, van der Hoef et al. 2008).
For the past few years the TFM has been utilized intensively
for parametric investigations of the macroscopic bed and
bubble characteristics of fluidized beds. However, its
validation with experiments still remains insufficient for a
wide range of reactor geometry and operating conditions.
None of the CFD models available today are
comprehensively validated and verified with experiments
Paper No
and theories. Regarding beds with immersed tubes, even
only few numerical studies have been performed so far,
Bouillard et al. (1989), Gamwo et al. (1999), Gustavsson &
Almstedt (2000), Pain et al. (2001), Yurong et al. (2004).
Most of these investigators studied the overall solid
distributions in an attempt to study the erosion
characteristics of the tubes. Numerical studies of bubble
hydrodynamics in the presence of immersed horizontal
tubes are very limited so far. Thus, the validity of the CFD
models for complex bed geometries and operating
conditions is not well established.
One important aspect influencing the validation process is
the method of extracting data from numerical simulations.
These methods widely vary among the researches and not
enough attention was given by many of them. It is believed
that the difference in extracting fluidized bed characteristics
(bubble properties, bed expansion, pressure drop, etc.) from
numerical results could influence the accuracy of results
hence the validation process in similar way as using
different models. Patil et al. (2005) showed that different
averaging period for bubble diameter at a given pined height
of a bed result in different mean bubble diameter. Hulme et
al. (2005) showed the differences in defining the solid
volume fraction threshold to define a bubble led to different
average bubble diameter. In the literature, it is also possible
to find different ways of defining the bed expansion ratio
(Lofstrand et al. 1995, Llop et al. 2000, Geldart 2004,
Taghipour et al. 2005). These inconsistencies and
differences in the literature could somehow influence the
validation process in substantial magnitude. In principle, it
is not arguable to use similar definition and way of
extraction for both the numerical and experimental results
during validation. However, the error deviation between the
experiment and numerical results could vary with different
definitions of the parameters and ways of extraction used. In
addition, the accuracy and validity of a given extraction
method or definition may vary with bed geometry and
operating condition. In another meaning, one way of
extraction or definition could provide an excellent
agreement for a given case of bed geometry and operating
condition, as usually is claimed by the researches in their
work, while it may fail in different cases. Thus, consistent
and uniform definitions of parameters and ways of
extracting numerical results should be adopted in the
fluidized bed research to properly validate the CFD models
under all reactor design and operating conditions.
One additional parameter which is usually overlooked
without much attention but could also influence the
validation process is the averaging period for analyzing the
timeaveraged fluidized bed properties. In the literature, it is
possible to find averaging periods ranging from 1 to 18s
which shows the wide difference in treating this value
among the researchers (Gamwo et al. 1999, Taghipour et al.
2005, Patil et al. 2005, Rong & Horio 2001, Xie et al. 2008).
It is unquestionable that longer averaging periods will
provide better accuracy of results; however, higher demand
of computational time has forced to use only few seconds of
real flow time. The most important issue here is to find an
optimum length of averaging time such that one can attain a
more representative result of the fluidized bed properties
with acceptable computational effort. This may depend on
many parameters mainly bed geometry and superficial
velocity and it is difficult to provide a general value for all
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
bed geometries and operating conditions.
In this paper numerical studies of gassolid fluidized beds
were performed to investigate the influence of horizontal
tubes on the bubble characteristics, mean bubble diameter
and rise velocity. In addition, the influence of different
extraction methods for pressure drop and bed expansion,
and influence of averaging time on the simulation results
was investigated.
Nomenclature
Symbo
A
A,B
Cd
d
e
Fr
g
go
h
I
I2D
I
J
k
n
p
P
q
Re
t
u'
Greek
Is:
Area (m2)
Constants in Syamlal et al. (1993) drag model
Drag coefficient
Diameter (m)
Coefficient of restitution
Constant in Johnson et al. (1990) friction model
(Nm2)
Gravitational acceleration (ms2)
Radial distribution function
Height (m)
Unit tensor
Second invariant of the deviatoric stress tensor
Granular energy transfer (kgm S3)
Granular energy diffusion coefficient (kgm 's 1)
Constant in Johnson et al. (1990) friction model
Constant in Johnson et al. (1990) friction model
Pressure (Pa)
Diffusion of fluctuating energy (kgs3)
Reynolds number
Time (s)
Velocity (ms1)
Fluctuating velocity (ms1)
letters:
B Interphase drag coefficient (kgm3s1)
7 Dissipation of fluctuating energy (kgm S3)
e Volume fraction
O Granular temperature (m2S2)
A Bubble coalescence parameter
P Shear viscosity (Pas)
g Bulk viscosity (Pas)
p Density (kgm3)
r Shear stress tensor (Nm2)
( Angle of internal friction (o)
f' Specularity coefficient
Subscripts:
B Bubble
col Collisional
f Frictional
g Gas phase
int Initial
kin Kinetic
KTGF Kinetic Theory of Granular Flow
max Maximum
mf Minimum fluidization
min Minimum
p Particle
s Solid phase
sl Slip
t Terminal
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Numerical Modeling
In this study the EulerianEulerian Two Fluid Model
(TFM) with closure equations based on the Kinetic Theory
of Granular Flow (KTGF) was used. The TFM treats both
the gas and the solid phase as fully interpenetrating
continue. For each phase the conservation equations of
mass and momentum are solved. The first breakthrough of
the TFM was reported by Anderson & Jackson (1967).
They derived local averaged equations from the equation
of motion of a single solid particle and the NavierStokes
equation of fluid flow. The latest development of the model
came from the KTGF, an extension of the kinetic theory of
dense gases (Chapman & Cowling 1970). The approach
was first applied to granular flows by Jenkins & Savage
(1984) and Lun et al. (1984). Later Ding & Gidaspow
(1990) and Gidaspow (1994) applied it to dense gassolid
fluidized beds. The model equations and parameters used
in this study are discussed in detail below.
Governing Equations
The conservation of mass for both the gas and the solid
phase can be written as:
a(E gp) + ( gpug) = 0
at +
a(EsPs)
a+ V7 (EspsUs)= 0
at
and for Pg > 0.8
3 g(1 ) 2.65
S 4 d ug up us g
Where
Cd = 2 Rep
0.44
The particle Reynolds number is given by:
EgP gpUg Usldp
Rep =
Pg
Syamlal et aL (1993) drag model
S=C (l ( use
4 u 2d, Ut
where
(2
Cd = 0.63 +
and
The volume fractions are related as:
Es + Eg = 1
The conservation of momentum for the gas and the solid
phase are described by:
a (ESgpug)
at + V (EgPgUgg)
= V (Tg) EsVP (ug Us) + EgPgg (4)
a(EsPss)
d(e u) + V (Espsusus)
at
= V (Ts) EsVP VP + (ug us) + Esps (5)
The interphase momentum transfer coefficient P represents
the drag between the phases and is mainly modeled
empirically. In the literature several models for this
coefficient were reported (e.g. Wen & Yu 1966, Gibilaro et
al. 1985, Syamlal et al. 1993, Gidaspow 1994, Di Felice
1994). However, in this study the most common and
frequently used drag models of the Syamlal et al. (1993)
and Gidaspow (1994) were investigated. The expressions
for both models are listed below.
Gidaspow (1994) drag model
For sg < 0.8
p= 150 ( ) + 1.75(1 E g us (6)
c9 (d) dp
ut = 0.5 (A 0.06Rep
+ (0.06Rep)2 + 0.12Rep(2B
with
A = 4.14 B
A = .14 B
0.8E .28
2.65
F
A) + A2)
,Eg < 0.85
,Eg > 0.85
Kinetic Theory of Granular Flow (KTGF)
As the result of averaging, the Two Fluid Model requires
closure equations to describe the rheology of the
particulate phase, i.e., the solid phase viscosity and solid
pressure. There are two major approaches studied in
describing the solid rheology. The first approach, which
was mainly applied in the early computer modeling, is the
Constant Viscosity Model (CVM) (see e.g. Gidaspow &
Ettehadieh 1983, Kuipers et al. 1992). This approach treats
the solid phase viscosity to be constant and solid pressure
to be a function of the modulus of elasticity of the powder,
which in turn is assumed to be a function of local porosity
only. The second approach derives these solid properties
from the principle of Kinetic Theory of Granular Flow
(KTGF). KTGF takes the non ideal particleparticle
collisions to describe the dependence of the rheologic
properties of the fluidized particles on local particle
concentration and the fluctuating motion of the particles.
As a result of shearing of the particulate phase, particles
Paper No
,Rep < 1000
,Rep > 1000
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
collide resulting in a random granular motion. This particle
velocity fluctuation generates an effective pressure in the
particulate phase, together with an effective viscosity that
resists shearing of the particle assembly. Analogous to the
thermodynamic temperature for gases, the model introduce
the granular temperature as a measure of the particle
velocity fluctuations. Thus, it assumes the solids viscosity
and stress to be a function of this granular temperature,
which in turn varies with time and position in the fluidized
bed. The granular temperature 8 is defined based on the
solid fluctuating velocity u 'with:
g = [(g )( (V )I
+ tg ((Vug) + (Vug)T)]
The bulk viscosity g is usually set to zero for gases, the
shear viscosity [g is assumed to be constant.
Solid Phase Shear Stress Tensor
The solid phase is also assumed to be Newtonian and the
stress tensor is modeled using the Newtonian stressstrain
relation as:
1
0 = U'2
3
The variation of the particle velocity fluctuations is
described by a separate conservation equation, the
socalled granular temperature equation:
3 ((EspsO) +V (Psus)
2+ .( u, at 0(epu" O )
= (Ps + s):Vu V q y (15)
The left hand side of this equation is the net change of
fluctuating energy. The first term on the right hand side is
the generation of fluctuating energy due to local
acceleration of the particles, which include the solid
pressure and shear tensor. The second term is the diffusion
of fluctuating energy defined by a gradient of the granular
temperature with a diffusion coefficient k:
T+= [ s(( + (V us) )
+ + ((VU)+ (US)]
In fluidized beds the bulk and shear viscosities of the
particulate phase are of the same order and thus the bulk
viscosity is not neglected. Both variables are explained
below.
Solid Bulk Viscosity
The solid bulk viscosity describes the resistance of the
particle suspension against compression and expansion. In
this study the expression given by Lun et al. (1984) was
used:
4 0
S= EsPsdpo(1 + e) 
A21
q = kVO
The third term on the right hand side is the dissipation of
fluctuating energy due to inelastic collision and the last
term is the exchange of fluctuation energy between gas and
solid phase, which accounts for the loss of granular energy
due to friction with the gas.
Instead of solving the complete granular temperature
equation, Syamlal et al. (1993) proposed an algebraic form
of the equation. They assume a local equilibrium between
generation and dissipation of the granular energy as these
terms are the most dominant terms in dense regions. The
convection and diffusion terms can be neglected. Boemer
et al. (1997) and van Wachem et al. (2001) showed that
simplifying the partial differential equation with the
algebraic form hardly affects the simulation results while
significant computational time can be saved. By neglecting
the convection and diffusion terms and retaining only the
generation and the dissipation terms, equation (15) reduces
to:
0 = (PsI + T): Vu, y (17)
In this study this algebraic form was used.
Closure Equations
Gas Phase Stress Tensor
Since gases are usually assumed to be Newtonian fluids,
the stress tensor is modeled using the Newtonian
stressstrain relation as:
Solid Shear Viscosity
The shear viscosity represents the tangential forces due to
translational and collisional interaction of particles. In
general, it is written as the sum of a collisional and a kinetic
part:
Ps,KTGF = Ls,col + Ls,kin
The shear viscosity expression given by Gidaspow (1994)
was used in this study:
40
ps,coi = EsPsdpgo(1 + e) (22)
5 w
10 psd 4 ( 2
Ps,kin =V + 9os(l+ e) (23)
96 (1 + e)Es0 5
Radial Distribution Function
The radial distribution function can be interpreted as the
probability of a single particle touching another particle
(probability of particle collision) in the solid phase. Thus,
its value increases with increasing solid volume fraction.
The function allows a tight control of the solids volume
fraction, so that the maximum packing is not exceeded and
more accurate flow characteristics can be achieved. In this
study the expression of Lun et al. (1984) was used.
Paper No
Paper No
9o = 1 E ) ] (24)
s,max/
Solid Pressure
The solid pressure represents the normal solidphase forces
due to particleparticle interactions and it prevents the solid
phase from reaching unrealistic high solid volume
fractions. It is usually written as the sum of a kinetic and a
collisional term as given by Lun et al. (1984):
Ps,KTGF = EpsO + 2goE2ps(1 + e)
Frictional Models
When particles are closely packed as in the case of dense
fluidized beds, the behavior of the granular flow is not
adequately described by the kinetic theory, which assumes
collisions to be binary and quasiinstantaneous. In regions
with high particle volume fractions, multiparticle contacts
frictionall effects) dominate the stress generation
mechanism. Hence, it is necessary to include this frictional
stress in the model. Similar to the shear stress, the
frictional stress is composed of the frictional shear
viscosity and frictional solid pressure, which includes the
tangentional and normal frictional forces. The frictional
values are simply added when the solid volume fraction
exceeds a certain value E.,.., which is usually set to 0.5
(see e.g. van Wachem et al. 2001).
Ps = Ps,KTGF + sf (26)
Ps = Ps,KTGF + Ps,f (27)
In this work the Schaeffer (1987) model for the frictional
shear viscosity and the Johnson et al. (1990) model for the
frictional pressure are used:
Ps sin p
2sf si (28)
P, = Fr ( mi (29)
Es,max E)P
Numerical Simulation Procedure and Boundary
Conditions
Bed Geometry and Simulation Parameters
In this paper two different bed geometries from literature
were investigated. Figure 1 shows the overall bed
geometries of both beds. In figure la the setup of
Taghipour et al. (2005) is shown. The bed is pseudo2D
with im in height and 0.28m width. Glass beads with an
initial fixed bed height of 0.4m were used. A uniform
quadratic mesh with size of 5mm was used. The geometry
was used to investigate the extraction methods and
averaging periods for the analysis of timeaveraged bed
hydrodynamics.
In the second part of this paper geometries from Hull et al.
(1999) were used to investigate the influence of immersed
tubes on the fluidized bed hydrodynamics. Three different
tube arrangements were investigated, staggered (S3),
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
inline (13) and without immersed tubes (NT). The beds
were 2D, 0.2m wide and im high. The detail dimensions
can be found in Hull et al. (1999) and the staggered
arrangement is reproduced as shown in figure lb. A
triangular mesh for the beds with tubes and quadratic mesh
for the bed without tubes of 8mm size was used with slight
refinement of up to 5mm near the tube surfaces to capture
the higher velocity gradients there.
Figure 1: Geometry of the simulated bed geometries (a)
Taghipour et al. (2005) and (b) the staggered arrangement
of Hull et al. (1999). Drawings are not to scale.
For the solution purpose the commercial CFD code Fluent
6.3 (Fluent 2006) was used. The QUICK and second order
upwind scheme were used for the spatial discretization of
the continuity and momentum equations respectively while
time was discretized using first order implicit. The
PhaseCoupled SIMPLE algorithm was used for the
pressurevelocity coupling. Time steps of 5x10 5 to 104s
and convergence criteria of 103 for the residual of all
quantities were used. Table 1 shows additional simulation
parameters used in this work.
Table 1: Physical properties and simulation parameters
Taghipour et al. Hull et al.
(2005) (1999)
Gas density (kgm3) 1.2 1.2
Gas viscosity (Pas) 1.79 x 105 1.79 x 105
Particle density (kgm3) 2500 2700
Particle diameter (lm) 275 230
Minimum fluidization
1 0.065 0.047
velocity (ms )
Minimum fluidization
void fraction
Bed height at minimum
fluidization (m)
Initial void fraction
Initial bed height (m)
Restitution coefficient
Superficial velocity (ms1)
Maximum particle packing
Limit
Specularity coefficient
Time step size (s)
0.4
0.9
0.15 0.55
0.65
0.25
104
0.9
0.15 0.35
0.63
0.25
5x105
Paper No
Boundary Conditions
At the inlet the velocity inlet boundary condition with
uniform superficial velocity of the gas phase was set. At
the outlet, the pressure outlet boundary condition was set
for the mixture phase and the height of the free board was
made long enough such that a fully developed flow was
achieved for the gas phase. At the walls the gas phase was
assumed to have a no slip boundary condition. For the
particulate phase the partial slip boundary condition of
Johnson & Jackson (1987) was used:
Ust cf'npesSog
 (Ts) n + u,0
WslJ 2 23Es,max
+ (n Ts,f n) tan ( = 0 (30)
The initial conditions of the first case (Taghipour et al.
2005) were set to a fixed bed condition while for the
second case (Hull et al. 1999) the initial conditions were to
the minimum fluidization as given in table 1.
Results and Discussion
The simulations were performed for 15s of real flow time
and the first 3s were neglected to reduce the startup effect.
Averaging Period
Due to the unsteady nature of bubbling fluidized beds, bed
properties are usually averaged over a certain period of
time for parametric study. In experimental analysis, the
length of averaging time is not of great importance as one
can perform experiments for quit long time as much as
hours if necessary. In contrary, the length of averaging time
in numerical simulations is of great concern. At the present
status of CFD models for multiphase flows and computer
power it is impractical or impossible to perform simulation
more than few seconds of real flow time for an average
laboratory or test scale fluidized bed. On the other hand,
the accuracy of the timeaveraged bed and bubble
characteristics will improve with increasing averaging
periods. Thus, finding an optimum value of the averaging
period in relation to the computational effort and accuracy
of the results is of critical aspect in validating numerical
results. Usually researches choose averaging period mainly
based on their computer capacity and simulation time and
only few have mentioned that they perform sensitivity
analysis to investigate the influence of different averaging
times (Patil et al. 2005 for example). In this part of the
study a wide range of averaging period (1 to 12s) was
investigated. For the analysis, timeaveraged plots of void
fraction and vertical solid velocity at different heights were
used. For this case the bed from Taghipour et al. (2005)
was used with a superficial velocity of 0.38 ms1, which is
6 times the minimum fluidization velocity.
From figure 2 it can be seen that the bed properties are
sensitive to the averaging periods. Especially within the
first few seconds the averaged values may vary relatively
strong. With increasing averaging time these fluctuations
reduced and the shape of the graphs didn't change after an
averaging period of 7s which can be said that the averaged
values reached "steady state", i.e the time averaged value
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
is independent of the averaging periods. From the two
figures it can be concluded that an averaging period of 7s
is enough from the analysis of particle characteristics for
this bed.
080
075 (a)
070
0 65
0 60
0 55
050 is 2s 3s 4s
000 005 010 015 020 025
Bed Width (m)
, 06
E 04
S02
0 00
S04
O 04
S06
E 08
> 10
(b)
Bed Width (m)
)0 010 015 025
1s 2s 3s 4s
5s 6s 7s and more
Figure 2: Timeaveraged plots for different averaging
periods at a height of 0.4m above the distributor,
u=0.38ms'1 (a) void fraction and (b) solid vertical velocity
In a similar comparison we have observed that after 8s of
averaging period the mean bubble properties showed no
major difference with increase in time. Hence, for the
presented cases it was found that an averaging period of 8s
is satisfactory for analyzing the timeaveraged fluidized
bed properties. Increasing the averaging period further will
lead to higher computational time without significant
improvement in accuracy of the numerical results.
Extraction Methods
In order to investigate their influence, different methods of
extracting pressure drop and expansion ratio from the
simulations were studied and compared with experimental
data given by Taghipour et al. (2005). The pressure drop is
the easiest parameter to be accurately measured or read
from numerical simulation. One option is to read the
timeaveraged static pressure at the bottom (inlet section)
of the bed with the reference pressure in the freeboard
region set to zero. The second option is to use a linear
extrapolation of the pressure versus bed height plot (linear
regression). This method was mainly used in experimental
studies. In figure 3 the pressure drops extracted with these
two different methods are plotted against experimental
data. Both give almost identical and constant values over
the whole velocity range. In parallel study, the bed
pressured drop didn't vary with the drag models used and
both models predicted similar bed pressure drop over the
whole range of superficial velocities.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
6000
5000
a.
a 4000 
3000
2000
1000
0
0 01 02 03 04 05 06 07
Superficial Velocity (ms1)
Figure 3: Pressure drop versus superficial velocity
In contrary to the bed pressure drop, estimating the
expanded bed height is difficult as it varies with time. One
method very often used for experiments is to assume a
linear relationship between pressure drop and bed height
and the height at which the pressure drop become zero can
be defined as the expanded bed height. Another possibility
is to use the height at which the timeaveraged value of the
bed pressure drop or the solid volume fraction drops below
some certain limit. In this paper after some trials 0.1% and
5% of their maximum value were chosen. Figure 4 shows
the bed expansion ratio (defined as the ratio of the
expanded bed height to the initial fixed bed height) as a
function of superficial velocity and comparison with the
experimental results of Taghipour et al. (2005). The results
showed that the extracted value of the expansion ratio was
highly sensitive to the used method and deviations of more
than 20% compared to the experimental data may occur.
Over the whole velocity range both the 0.1% pressure drop
and 5% solid volume fraction approach gave better
agreement with the experiment.
00 01 02 03 04 05
Superficial Velocity (ms1)
06 07
Figure 4: Expansion ratio versus superficial velocity for
Gidaspow (1994) drag model
In a similar way the influence of the two drag models on
the bed expansion ratio was investigated. Figure 5 shows
the expansion ratio predicted using the two drag models
(equations 69 and 1013) and comparison with the
experimental data. The Syamlal drag model showed a
slightly lower expansion than Gidaspow. This is consistent
with the findings of other researchers, e.g. Taghipour et al.
(2005).
0 0.1 0.2 0.3 0.4 0.5
Superficial Velocity(ms1)
0.6 0.7
Figure 5: Bed expansion ratio predicted by the two drag
models and comparison with experimental data
Tube Influence
Bubble Properties
Bubble properties were calculated from the volume
fraction contour produced by Fluent. There is no clear
definition of bubble boundaries. However, many previous
investigators defined the boundary to be 0.8 for the gas
volume fraction (Hulme et al. 2005) and this definition was
adopted in this study as well. The beds were divided into
equal horizontal sections of 0.01m height. Taking into
account the bubble breakup and coalescence, the bubble
properties like projected area, centroids were calculated for
each bubble in each section in time interval of 0.02s.
It was observed that tubes were the main cause for bubble
splitting. Small bubbles were usually formed at the bottom
of the bed. They rise and grew by coalescence until they
reached the first row of the tubes which then split and
further grew by coalescence until they reach the next row
of tubes. This continued until the last row of tubes after
which large bubbles were formed up to they finally erupted
at the top of the bed. In general, this mechanism was seen
to reduce the averaged bubble properties such as diameter
and rise velocity in the vicinity of the tube bank. Moreover,
the shape of the bubbles in the tube bank region is not
similar to that of the tube free region. Bubbles in the tube
free region of the bed were seen to be nearly circular as
can be seen from the results of the bed without tubes and
on the region below and above the tube banks in the case
of S3 and 13 tube arrangements. In the tube bank region
bubbles were observed to elongate in the vertical direction
when they moved between tube rows.
Bubble Diameter
The bubble diameter was calculated from the area
equivalent, AB, using equation 31 below.
dB = 7r
21A
For beds without internals different correlations are
available in the literature to predict bubble size in 2D bed.
In this paper the expression used by Hull et al. (1999) was
chosen and is written as:
Paper No
   
4 4 
 ^ '^ ^ ^
Taghipour et al (2005)
 e  Facetera_ e .... ..
A Linear regression
Paper No
B 8(u ur.)(23/4 1) 3]2/ (32)
dB = I + d3/2 (
Where h is the height above the distributor and dB,mt is the
initial bubble diameter. For a porous plate distributor, it
can be written as (Mori & Wen 1975):
dB,int = 0.00376(u Uf)2 (33)
0035
 0030
E
0025
.* 0020
S0015
S0010
0 0005
0 000
000 005 010 015 020 025 030 035
Bed Height (m)
Figure 6: Timeaveraged bubble diameter for the staggered
(S3) tube arrangement
0050
*Simulation 13
0 045   
 Simulation S3
S0040
50040 *Simulation NT .
0 *Equation Hulletal (1999)
S00 03 
0 025  
0 0020 
c 0015
20010
0005
0000
000 005 010 015 020 025 030 035
Bed Height (m)
Figure 7: Timeaveraged bubble diameter for the staggered
(S3), inline (13), without tubes (NT) beds and equation 32
In figure 6 the simulation results and experimental data of
Hull et al. (1999) for the staggered (S3) bed geometry is
shown. The numerical simulation is in good agreement
with the experimental data in the majority of the bed. The
difference between the two results occurred near the lower
and upper parts of the tube rows. The slight
underprediction of the simulation on the lower side of the
tube rows can be explained due to the fact that small
bubbles were observed to form at the bottom of the tubes
which resulted in significant change of the bubble
hydrodynamics around the tube bank region. This was
explained in our previous study (Asegehegn & Krautz
2009). On the other hand the slight overprediction of the
simulation results on the upper side of the tube rows is not
clearly known and it needs further investigations. In figure
7 the comparison between the mean bubble diameters for
the three beds and equation 32 is shown. No major
difference between the inline and staggered tube
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
arrangements were observed. For both beds with tubes the
mean bubble diameter is smaller than the bed without
tubes. This is due to the higher bubble breakup resulted
from the presence of tubes which eventually reduced the
bubble size. For the bed without immersed tubes the
simulation showed good agreement with equation 32.
Bubble Velocity
The bubble rise velocity was calculated from the difference
in the vertical coordinate of the centriod between
consecutive time frames and dividing by the time interval.
In figure 8 comparisons of the simulation results with
experimental data of Hull et al. (1999) for the staggered
tube arrangement is shown.
0 70
' 060
S050
0
_
S040
^ 030
0 20
010
S 010 
2
000 005 010 015 020 025
Bed Height (m)
030 035
Figure 8: Timeaveraged bubble rise velocity for the
staggered (S3) tube arrangement
080
oso
S070
E
.060 
S050
n. 040
0 030
S020
S010
000
000 005 010 015 020
Bed Height(m)
025 030 035
Figure 9: Timeaveraged bubble rise velocity for the
staggered (S3), inline (13) and without tubes (NT) beds
The results showed good agreement. Similar to the mean
diameters, the rise velocities were lower at the bottom of
the tubes and were explained in our previous publication
(Asegehegn & Krautz 2009). The higher velocity predicted
by the simulation on the upper part of the tube rows can be
explained partly due to the two bubble motion mechanisms
explained above. As a result of the elongation of a bubble
and stretching over the surface of the tubes, the centroid of
the bubble moved farther than if it was circular. Such
phenomena were not reported in the experimental study of
Hull et al. (1999). In their explanation they associated the
lower rise velocity at the upper part of the tube rows to the
decrease in bubble diameter due to splitting. In fact this
was also observed in the simulation results, figure 8 and 9.
*Simula tion .__ __  
+Hulletal (1999)
          
                   
  
*Simulation
UHulletal (1999)
             
7Simulation 13
.SimulationS3
hSim ulation NT
              
     _       
               
I
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
However, the simulation showed higher rise velocity as a
bubble moved between the tubes. In general, in the tube
bank regions of the fluidized beds with immersed tubes the
bubble rise velocity depends not only on the bubble size
but also on the bubble shape. A comparison of the mean
rise velocities for all the three bed geometries is shown in
figure 9. The mean bubble rise velocity of the bed without
internals is higher than the beds with internals which
reflects the presence of larger bubbles in the case of the no
tube bed. Regarding the two tube arrangements, the inline
predicted slightly higher bubble rise velocity on the upper
part of the bed. This could be due to the unrestricted
motion of bubbles between the tubes.
Solid Motion and Circulation
Though it is difficult to predict the individual particle
motion and circulation using the Two Fluid Model, it can
sufficiently predict the averaged particle velocities and
solid volume fraction distribution across the bed. To
investigate the solid motion and distribution, the
timeaveraged contours and graphs of the solid vertical
velocity and volume fractions were analyzed. Figure 10
shows the timeaveraged solid volume fraction contour of
the three bed arrangements. For all beds lower solid
concentration at the centre and higher concentration at the
wall of the beds were observed. This is mainly due to the
presence of bubbles at the centre of the beds. This was
more pronounced for the beds with tubes. Figure 11 shows
the averaged solid volume fraction with bed height and can
be well seen that tubes reduce the concentration of solids
in their vicinity.
I,
057
054
Ol 0
I05
047
041
o P o o o o o(
0 3S
0019
f063
Figure 10: Timeaveraged solid volume fraction for no
tube, staggered and inline arrangement, u=0.25ms1
Around the tubes, defluidized regions were observed at the
top of tubes where solid particle rest without moving.
While at the bottom very low solid concentration were
observed and in most cases stagnant bubbles were attached
to it. Such phenomena were reported by other investigators
as well, Glass & Harrison (1964), Loew et al. (1979),
Sitina & Whitehead (1986) to mention few. This was also
observed in our preliminary experimental investigations
which is not included in this paper. These phenomena were
found to reduce with increasing superficial velocity.
From figure 12 it can be seen that solid particles moved
upwards near the centre of the bed and downwards along
the wall of the bed.
SU 4U
* 030
In
an on
010
UUU I  
000 010 020 030 040 050
Solid Volume Fraction ()
060
Figure 11: Timeaveraged solid volume fraction with
height of the bed, u=0.25ms1
Figure 13 shows the timeaveraged vertical solid velocity
for the three tube arrangements and two different
superficial velocities (0.15ms1 and 0.35ms 1) at three
different locations above the distributor. Right below the
second row (y=0.18m), right above the second row
(y=0.21m) and between the second and the third row
(y=0.22m). For the no tube bed the vertical solid velocity
increased with bed height, while this was not usually the
case for the beds with internal tubes. For both tube
arrangements the particles were observed to have higher
vertical velocity between the tubes, where this was more
pronounced for the inline case at higher superficial
velocity. For the staggered arrangement, with increasing
superficial velocity relatively uniform vertical velocities
were observed. This is mainly due to the restriction of flow
as the particles move upwards. For the inline on the other
hand they can move between the columns throughout the
tube bank region without restriction which would give a
higher vertical velocity in between the tube columns.
In general, the vertical solid velocity increases between the
tubes while it is nearly stagnant along the tubes. The
staggered arrangement showed relatively uniform and
lower velocity distribution in the tube bank region as
compared to the inline case, which was observed to
behave as a channellike flow inbetween the tube
columns.
062
055
05
044
039
033
OZ/
02
015
01
0042
0015
00/3
013
nis
oOO
0*0
000
Figure 12: Timeaveraged solid vertical velocity in ms1 for
no tube, staggered and inline arrangement, u=0.25ms1
Paper No
*NT
 NT
.S3
            
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
u=0.35ms1
S02
So
S01
Soo
S00
' 0
0
2 01
o 1
02
03
04
03
i
.g 00
0
ol
4?
0 02
O
01
04
012
03
04
03
E 02
 01
*g 00
.c ol*
0
02
03
E 04
2 02
NT >
o 00
0(
2> 02
04
06
08
06
in
E 04
S3
o 02
(
U)
E 04
o 02
S00
0
(0
04
Figure 13: Timeaveraged solid vertical velocity for the three beds at three different heights above the distributor; a and b for
beds without tubes, c and d for staggered arrangement and e and f for inline arrangement. Graphs on the left hand side are
for superficial velocity of 0.15ms1 and those on the right hand side are for superficial velocity of 0.35ms1.
Conclusions
Numerical simulations using the EulerianEulerian Two
Fluid Model (TFM) were performed for two dimensional
gassolid fluidized beds with and without immersed
horizontal tubes. In the first part of this paper the influence
of different techniques of extracting the timeaveraged
values of pressure drop and bed expansion, and the
influence of averaging time were discussed. It was found
that different extraction methods of the timeaverage value
led to different results. The expanded bed height, and
therefore the expansion ratio, was best defined at a height
where the time average solid volume fraction drops below
5% of the maximum or the pressure drop reached below
0.1% of the overall bed pressure drop. Moreover, it is
necessary to perform sensitivity analysis to make sure that
the averaging period doesn't influence the final simulation
results. Depending on the bed geometry and operating
condition an optimum averaging time should be selected
such that the mean properties didn't vary considerably with
higher averaging period.
In the second part of the paper the influence of immersed
tubes on bubble hydrodynamics were studied. The
presence of horizontal tubes was the main cause of bubble
breakup which eventually reduces the mean bubble
diameter and rise velocity. The shape and mechanism of
Paper No
u=0.15ms1
(b) y=o 18m
 ^ B __ ^
y=O 21m
Ay=0 22m
10 05 010 0 0
Bed Width (m)
 l
(c) y=O 18m
  _2_1_m ......
*y=0 22m
 u 21
)0 005 010 015 0
Bed Width
    d  
(e)  y=O 18m
e Iy=O 21m
DO 0
   
() y=O 18m
Sy=0 21 m
?_y=O 22m
      ^ .yo 
   J <JF^ = 22 
OlO
)0 05 010 015 1 0
 
Paper No
bubble movement in the vicinity of the tube banks differed
significantly from the tube free region of the bed. In
addition, the simulation results showed higher vertical
velocity between the tube columns while the maximum
velocity was observed at the center of the beds without
tubes. With regard to the two tube arrangements, the
staggered one showed more uniform solid distribution in
the tube bank region. In the inline arrangement the solids
were seen to move between the tube columns to form a
channellike flow with relatively higher vertical solid
velocity. For both arrangements defluidized regions were
observed at the upper part of the tubes, which is more
pronounced in the inline case. On the other hand, the lower
parts of the tubes were usually covered with gas pockets.
These effects were observed to reduce with increasing
superficial velocity.
In general, the Two Fluid Model is capable of predicting
the main characteristics of bubble behavior and solid
motion with complex geometries. It is a promising tool for
parametric investigation of fluidized bed reactors. However,
intensive experimental validations are required before
using it as a commanding method for scaling up and design
procedures of these systems. Moreover, intensive
investigations with more dense tube arrangements are
needed to verify the bubble characteristics and solid
motion for better understanding of the influence of
immersed tubes.
Acknowledgements
The authors gratefully acknowledge the funding of this
research project by the "Entrepreneurial
Regions"Initiative established by the German Federal
Ministry of Education and Research and the International
Graduate School supported by the Brandenburg University
of Technology Cottbus and the Brandenburg Ministry of
Higher Education, Research and Culture.
References
Anderson, T.B. & Jackson, R. A Fluid Mechanical
Description of Fluidized Beds: Equations of Motion. I &
EC Fundamentals, Vol. 6, 527539 (1967)
Asegehegn, T.W. & Krautz, H.J. Hydrodynamic simulation
of gassolid bubbling fluidized bed containing horizontal
tubes. Proceedings of the 20th International Conference on
Fluidized Bed Combustion, Vol. II, Xi'an, China (2009)
Boemer, A.; Qi, H. & Renz, U. Eulerian simulation of
bubble formation at a jet in a twodimensional fluidized
bed. Int. J. Multiphase Flow, Vol. 23, 927944 (1997)
Bouillard, J.X.; Lyczkowski, R.W. & Gidaspow, D.
Porosity distributions in a fluidized bed with an immersed
obstacle. AIChE Journal, Vol. 35, 908922 (1989)
Chapman, S. & Cowling, T.G. The Mathematical Theory
of NonUniform Gases. Cambridge University Press,
Cambridge (1970)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Deen, N.G.; van Sint Annaland, M.; van der Hoef, M.A. &
Kuipers, J.A.M. Review of discrete particle modeling of
fluidized beds. Chem. Eng. Sci., Vol. 62, 2844 (2007)
Di Felice, R. The voidage function for fluidparticle
interaction systems. Int. J. Multiphase Flow, Vol. 20,
153159 (1994)
Ding, J. & Gidaspow, D. A Bubbling Fluidization Model
Using Kinetic Theory of Granular Flow. AIChE Journal,
Vol. 36, 523538 (1990)
Fluent Inc. Eulerian Model Theory. FLUENT 6.3 User's
Guide, Chapter 23.5 (2006)
Gamwo, I.K.; Soong, Y. & Lyczkowski, R.W. Numerical
simulation and experimental validation of solids flows in a
bubbling fluidized bed. Powder Technol., Vol. 103,
117129(1999)
Geldart, D. Expansion of Gas Fluidized Beds. Ind. Eng.
Chem. Res., Vol. 43, 58025809 (2004)
Gibilaro, L.G.; Di Felice, R. & Waldram, S.P Generalized
friction factor and drag coefficient correlations for
fluidparticle interactions. Chem. Eng. Sci., Vol. 40, 1817
1823 (1985)
Gidaspow, D. Multiphase Flow and Fluidization:
Continuum and Kinetic Theory Descriptions. Academic
Press, Boston (1994)
Gidaspow, D. & Ettehadieh, B. Fluidization in
twodimensional beds with a jet. 2. Hydrodynamic
modeling. Ind. Eng. Chem. Fundamen. Vol. 22, 193201
(1983)
Glass, D.H. & Harrison, D. Flow patterns near a solid
obstacle in fluidized bed. Chem. Eng. Sci., Vol. 19,
10011002 (1964)
Gustavsson, M. & Almstedt, A.E. Numerical simulation of
fluid dynamics in fluidized beds with horizontal heat
exchanger tubes. Chem. Eng. Sci., Vol. 55, 857866 (2000)
Hoomans, B.PB.; Kuipers, J.A.M.; Briels, W.J. & Van
S ....ii W.PM. Discrete Particle Simulation of Bubble and
Slug Formation in a TwoDimensional GasFluidized Bed:
A HardSphere Approach. Chem. Eng. Sci., Vol. 51,
99118 (1996)
Hull, A.S.; Chen, Z.; Fritz, J. W. & Agarwal, P K.
Influence of horizontal tube banks on the behavior of
bubbling fluidized beds: 1. Bubble hydrodynamics.
Powder Technol., Vol. 103, 230242 (1999)
Hulme, I.; Clavelle, E.; van der Lee, L. & Kantzas, A. CFD
Modeling and Validation of Bubble Properties for a
Bubbling Fluidized Bed. Ind. Eng. Chem. Res., Vol. 44,
42544266 (2005)
Paper No
Jenkins, J.T. & Savage, S.B. A Theory for the Rapid of
Identical, Smooth, Nearly Elastic Spherical Particles. J.
Fluid Mech., Vol. 130, 187202 (1984)
Johnson, PC.; Nott, P & Jackson, R. Frictionalcollisional
equations of motion for particulate flows and their
application to chutes. J. Fluid Mech., Vol. 210, 501535
(1990)
Johnson, PC. & Jackson, R. Frictionalcollisional
constitutive relations for granular materials, with
application to plane shearing. J. Fluid Mech., Vol. 176,
6793 (1987)
Kuipers, J.A.M.; Prins, W. & van S ....ii W.PM.
Numerical Calculation of WalltoBed HeatTranfer
Coefficients in GasFluidized Beds. AIChE Journal, Vol.
38, 10791091 (1992)
Llop, M.F.; Casal, J. & Arnaldos, J. Expansion of gassolid
fluidized beds at pressure and high temperature. Powder
Technol., Vol. 107, 212225 (2000)
Lofstrand, H.; Almstedt, A.E. & Andersson, S.
Dimensionless Expansion Model for Bubbling Fluidized
Beds with an without Internal Heat Exchanger Tubes.
Chem. Eng. Sci., Vol. 50, 245253 (1995)
Loew, O.; Shmutter, B. & Resnick, W. Particle behavior
and velocities in a largeparticle fluidized bed with
immersed obstacles. Powder Technol., Vol 22, 4557
(1979)
Lun, C.K.K.; Savage, S.B.; Jeffrey, D.J. & Chepumiy, N.
Kinetic theories for granular flow: inelastic particles in
Couette flow and slightly inelastic particles in a general
flowfield. J. Fluid Mech., Vol. 140, 223256 (1984)
Mori, S. & Wen, C.Y Estimation of Bubble Diameter in
Gaseous Fluidized Beds. AIChE Journal, Vol. 21, 109115
(1975)
Olsson, S.E.; Wiman, J. & Almstedt, A.E. Hydrodynamics
of a pressurized fluidized bed with horizontal tubes:
Influence of pressure, fluidization velocity and tubebank
geometry. Chem. Eng. Sci., Vol. 50, 581592 (1995)
Pain, C.C.; Mansoorzadeh, S. & de Oliveira, C.R.E. A
study of bubbling and slugging fluidised beds using the
twofluid granular temperature model. Int. J. Multiphase
Flow, Vol. 27, 527551 (2001)
Patil, D.J.; van Sint Annaland, M. & Kuipers, J.A.M.
Critical comparison of hydrodynamic models for gassolid
fluidized beds Part II: freely bubbling gassolid fluidized
beds. Chem. Eng. Sci., Vol. 60, 7384 (2005)
Rong, D. & Horio, M. Behavior of particles and bubbles
around immersed tubes in a fluidized bed at high
temperature and pressure: a DEM simulation. Int. J.
Multiphase Flow, Vol. 27, 89105 (2001)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Schaeffer, D.G. Instability in the evolution equations
describing incompressible granular flow. J. Diff. Eq., Vol.
66, 1950 (1987)
Shen, L.; Johnsson, F. & Leckner, B. Digital Image
Analysis of Hydrodynamics TwoDimensional Bubbling
Fluidized Beds. Chem. Eng. Sci., Vol. 59, 26072617
(2004)
Sitnai, O. & Whitehead, A.B. In: Fluidization. edited by
Davidson, J. F.; Clift, R. & Harrison, D., Academic Press,
London (1986)
Syamlal, M.; Rogers, W. & O'Brien, T.J., MFIX
Documentation: Theory Guide, National Technical
Information Service. DOE/METC94/1004, Springfield
(1993)
Taghipour, F.; Ellis, N. & Wong, C. Experimental and
computational study of gassolid fluidized bed
hydrodynamics. Chem. Eng. Sci., Vol. 60, 68576867
(2005)
Tsuji, Y; Kawaguchi, T. & Tanaka, T. Discrete Particle
Simulation of TwoDimensional Fluidized Bed. Powder
Technol., Vol. 77, 7987 (1993)
van der Hoef, M.A.; van Sint Annaland, M.; Deen, N.G. &
Kuipers, J.A.M. Numerical Simulation of Dense GasSolid
Fluidized Beds: A Multiscale Modeling Strategy. Annu.
Rev. Fluid Mech., Vol. 40, 4770 (2008)
van Wachem, B.G.M.; Schouten, J.C.; van den Bleek,
C.M.; Krishna, R. & Sinclair, J.L. Comparative Analysis of
CFD Models of Dense GasSolid Systems. AIChE Journal,
Vol. 47, 10351051 (2001)
Wen, C.Y & Yu, YH. Mechanics of fluidization. Chem.
Eng. Prog. Symp. Ser., Vol. 62, 100111 (1966)
Wiman, J. & Almstedt, A.E. Hydrodynamics, erosion and
heat transfer in a pressurized fluidized bed: influence of
pressure, fluidization velocity, particle size and tube bank
geometry. Chem. Eng. Sci., Vol. 52, 26772695 (1997)
Xie, N.; Battaglia, F. & Pannala, S. Effects of using two
versus threedimensional computational modeling of
fluidized beds: Part 1: Hydrodynamics. Powder Technol.,
Vol. 182, 113 (2008)
Yates, J.G.; RuizMartinez, R.S. & Cheesman, D.J.
Prediction of Bubble Size in a Fluidized Bed containing
Horizontal Tubes. Chem. Eng. Sci., Vol. 45, 11051111
(1990)
Yurong, H.; Huilin, L.; Qiaoqun, S.; Lidan, Y.; Yunhua, Z.;
Gidaspow, D. & Bouillard, J.X. Hydrodynamics of
gassolid flow around immersed tubes in bubbling
fluidized beds. Powder Technol., Vol. 145, 88105 (2004)
