Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 5.3.1 - Simulation of detailed flow behaviour in a Wurster type coating process based upon DEM and two-fluid models
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00125
 Material Information
Title: 5.3.1 - Simulation of detailed flow behaviour in a Wurster type coating process based upon DEM and two-fluid models Industrial Applications
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: van Wachem, B.
Remmelgas, J.
Niklasson-Björn, I.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: Wurster-type fluidized bed
two-fluid model
discrete element modeling
 Notes
Abstract: Discrete element or Lagrangian models have become a very useful and versatile tool to study the hydrodynamical behaviour of particulate flows. For example, they are very attractive because phenomena such as coating, drying, agglomeration, and break-up can be incorporated in a straightforward manner. In these models, Newton’s equations of motion are solved for each particle, and a collision model is applied to handle particle encounters. The motion of the fluid phase is determined from the volume averaged governing equations in an Eulerian framework. Although recent increases in computational power has significantly increased the applicability of discrete element models, their usefulness is still limited to systems involving on the order of one or a few million particles. For commercial-scale production processes involving large numbers of particles, other models such as two-fluid models must be employed. In the two-fluid approach, where both phases are treated as volume averaged, fully interpenetrating continua, it is much more difficult to include phenomena such as agglomeration and break-up. In this study, fluid mechanics calculations using a discrete element model (DEM) are employed to study the flow behaviour in a laboratory-scale Wurster-type coating process computationally. The results from the DEM calculations are compared to predictions based upon simulations using a two-fluid model in the context of studying the flow behavior in and around the jets that emanate from the orifices in the distributor plate. For the overall flow behavior, it is found that the two different models give predictions that are similar. However, for the detailed flow behavior in the immediate vicinity of the distributor plate and the atomization nozzle, the results differ. The DEM model predicts that the air jets near the distributor plate and the atomization nozzle persists further into the particle bed than for the two-fluid model. However, the effect of the jets on the behavior of the particles is greater for the two-fluid model. While the effect of the atomization jet on the time-averaged particle distribution for the two-fluid model, it is hardly discernible for the DEM model. For both models, however, the effect of the jets near the distributor plate is limited to the region in the immediately downstream of the distributor plate.
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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Bibliographic ID: UF00102023
Volume ID: VID00125
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 531-vanWachem-ICMF2010.pdf

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


Simulation of detailed flow behaviour in a Wurster-type fluidized bed based upon
Discrete Element and Two-Fluid Modelling


Berend van Wachem,* Johan Remmelgast and


Ingela Niklasson-Bjntm


Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ
t Pharmaceutical Development, AstraZeneca R&D, MOlndal, Sweden
Keywords: Wurster-type fluidized bed, Two-Fluid Modelling, Discrete Element Modelling




Abstract

Discrete element or Lagrangian models have become a very useful and versatile tool to study the hydrodynamical
behaviour of pariculate flows. For example, they are very attractive because phenomena such as coating, drying,
agglomeration, and break-up can be incorporated in a straightforward manner. In these models, Newton's equations
of motion are solved for each particle, and a collision model is applied to handle particle encounters. The motion
of the fluid phase is determined from the volume averaged governing equations in an Eulerian framework. Although
recent increases in computational power has significantly increased the applicability of discrete element models, their
usefulness is still limited to systems involving on the order of one or a few million particles. For commercial-scale
production processes involving large numbers of particles, other models such as two-fluid models must be employed.
In the two-fluid approach, where both phases are treated as volume averaged, fully interpenetrating continue, it is
much more difficult to include phenomena such as agglomeration and break-up.
In this study, fluid mechanics calculations using a discrete element model (DEM) are employed to study the flow
behaviour in a laboratory-scale Wurster-type coating process computationally. The results from the DEM calculations
are compared to predictions based upon simulations using a two-fluid model in the context of studying the flow
behavior in and around the jets that emanate from the orifices in the distributor plate. For the overall flow behavior,
it is found that the two different models give predictions that are similar. However, for the detailed flow behavior in
the immediate vicinity of the distributor plate and the atomization nozzle, the results differ. The DEM model predicts
that the air jets near the distributor plate and the atomization nozzle persists further into the particle bed than for the
two-fluid model. However, the effect of the jets on the behavior of the particles is greater for the two-fluid model.
While the effect of the atomization jet on the time-averaged particle distribution for the two-fluid model, it is hardly
discernible for the DEM model. For both models, however, the effect of the jets near the distributor plate is limited to
the region in the immediately downstream of the distributor plate.


Introduction

The Wurster bed coating process is used frequently in
the pharmaceutical industry. For example, it is em-
ployed to deposit a drug substance or a film on pellets
for controlled-release formulations. The development of
such a process, from the laboratory to the commercial
scale, is difficult, and scale-up is always a challenge.
There have been a number of studies dealing with
scale-up of fluidized beds. For example, Glicksman and
co-workers (Glicksman 1984, 1988) analyzed the equa-
tions of motion to develop a set of scaling rules. These
scaling rules were later considered by van Ommen et al.
(2006), who evaluated them computationally and found
that similitude between scales could not be obtained us-
ing any of the proposed rules. Despite the extensive re-


search in this field, scale-up of fluidized bed processing
remains a challenge. Given the fact that it is challenge
for a fluidized bed, it is obviously also a challenge for
a Wurster bed, i.e. a spouted bed with a draft tube, that
involves a droplet spray.

One reason for the difficulty in scale-up of fluidized
beds is obvious: the particle size does or should not
change upon scale-up while the geometrical configura-
tion of the processing equipment does. This is obviously
the case also for Wurster beds, though in this case it can
be expected to be more difficult since the flow profile is
not uniform throughout the cross section. That is, for
Wurster beds the distributor plate has been specifically
designed in order to create or at least enhance the circu-
lating behavior that is characteristic of spouted beds.







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


A non-uniform flow profile throughout the cross-
section is also obtained immediately downstream of the
distributor plate due to the gas jets that emerge from the
orifices in the distributor plate. These jets may penetrate
the bed and result in bypass or attrition. The effect of the
jets in determining the flow behavior obviously depends
on the length of the jets compared to the dimensions of
the vessel. In particular, the influence of the jets may
be expected to be greater for small vessels and they are
thus a complication that must be dealt with in order to
understand how scale-up can be expected to affect pro-
cess and, more imlli'i .lm.ll \ product performance.
In this work, the flow behavior in a laboratory-scale
Wurster bed is studied computationally using discrete el-
ement and two-fluid models in order understand how the
predictions between the two models differ. For the lat-
ter model, the solids phase is modeled using a constant
particle-phase viscosity. The results are employed to un-
derstand how the atomization jet and the gas jets formed
by the the distributor plate affect the performance of the
process.


Computational models

The computational model includes two-phase flow of air
and particles in a model of a Wurster bed that includes
an inlet section, a distributor plate including a wire mesh
screen, an atomization nozzle, and a product chamber. A
sketch of the cross section of the (axisymmetric) geom-
etry is shown in Figure 1. Figure 1 also shows a close-
up of the geometry near the spray nozzle. In reality, the
nozzle consist of an annular air inlet and a circular liquid
inlet, as also indicated in Figure 1.
Following Karlsson et al. (2009) the nozzle is mod-
eled as an inlet with a velocity of 40 m/s. In order to
study the influence of the nozzle on the global flow be-
havior, calculations are carried out for two nozzle diam-
eters: 0.4 mm and 4 mm corresponding to volumetric
flow rates of 0.02 and 2 m3/h at at the relevant con-
ditions for the atomization flow, i.e. a temperature of
20 C and a pressure of 1 atm.
In previous work, Karlsson et al. (2009), the model
of the distributor plate was simplified by representing it
as three annular regions, as shown in Figure 2, where
each region is homogeneous. A different velocity was
specified in each region in order to create a non-uniform
flow profile at the bottom of the bed. Specifying the
velocity at the bottom of the bed is a good approximation
if the pressure drop across the distributor plate is large
compared to the pressure drop across the particle bed
because then the flow distribution through the plate will
not be affected by the flow behavior in the bed. As an
alternative to specifying the velocity at the bottom of the
bed, one may include an inlet plenum and model flow


H =60mm
r---


L,=320mm


G-dF 15 mm


D1 =100 mm
(a) Vessel geometry
Dnoe


(b) Geometry near spray nozzle


Figure 1: Sketches of geometry of Wurster bed and ge-
ometry near spray nozzle.





















(a)
Reflection plane


(b)

Figure 2: Sketch of the distributor plate.





through the three annular regions of the plate using a
different pressure loss coefficient for each annulus. A
case in which there is such a coupling between the inlet
and the product chambers has, in fact, been considered
by Johansson et al. (2006), though only for a distributor
plate the creates a uniform flow profile throughout its
cross section.


In both the aforementioned cases the presence and be-
haviour of the orifices is neglected. While this may be
a reasonable approximation in most cases, it is not ob-
vious that the effect of the jets on the behavior of the
bed can be neglected for small-scale beds. In this work,
the detailed geometry of the distributor plate is included.
The distributor plate is modeled as sketched in Figure 2,
which shows the smallest repeat-unit (a 30-degree slice)
from which the distributor plate may be recreated by ro-
tational translations. In Figure 2 it may be noted that the
30-degree slice has reflection symmetry with respect to
the indicated plane so that it may be possible to model
the flow using as little as 1/24th of the full geometry.


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


Air Particles
Boundary U[m/s] a [-] U [m/s] a [-]
Jet 44 1.0 0.0 0.0
Inlet 1.4 1.0 0.0 0.0

Table 1: Inlet boundary conditions.


Condition Air Particles
Wall slip No slip Free slip
Outlet volume fraction 1.0 0.0
Outlet pressure 1 atm

Table 2: Outlet and wall boundary conditions.



Fluid-Phase Model


In the calculations, air is assumed to have properties
corresponding to a temperature of 60 C and a pressure
of 1 atm (for both the atomizing and fluidizing air (see
Karlsson (2007))). Air is thus modeled as an incom-
pressible fluid with a density of 1.1 kg/m and a viscosity
of 2.0 x 10 5 Pas (see Table 3). The volumetric flu-
idization flow rate of 40 m3/h at a temperature of 20 C
and a pressure of 1 atm corresponds to a a flow rate
of 40 m3/h at a temperature of 60 "C and atmospheric
pressure, which gives an average velocity of 1.6 m/s for
an inlet with an outer diameter of 100 mm diameter and
an inner diameter of 15 mm. The outlet at the top of the
expansion chamber is modeled as a pressure outlet. The
boundary conditions are summarized in Tables 1 and 2.
The interaction of the air with the particles is included
by accounting for the volume that the particles occupy
and through the drag force that the particles exert on the
fluid, which to a first order approximation is linear in the
relative velocity between the fluid, vf, and the particles,
vp. Details of the derivation of the governing equations
may be found in Anderson and Jackson (1967). The con-
tinuity equation becomes


d(afpf) dOf(aPfv)
at 9xi


Condition
Density [kg/m3]


Air
1.1


Particles
1.5 x 103


Viscosity [Pa s] 2.0 x 10 0.10
Maximum packing [-] 1.0 0.65


Diameter [pm]


N/A


480


Table 3: Properties of air and particles.







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


and the momentum equation becomes

O(afpfv) 09 afPf v3 ) 09oxa 3)
at p Oxp Ox(T


Sf OxJ
a _X


phases J f
+TfV3f+S3+ 1 1(f,P) :-


where af is the local volume fraction of the fluid phase;
pf is the density of the fluid; p is th pressure; Tf the
source term linear in the velocity field; S} the additional
source terms; and T7 the stress tensor of the fluid, given
by


T + 7) + A f W- (3)
a \x3 0x^ ) \ 3 ) ax"

where pf is the shear viscosity and A1 represents the
bulk viscosity of the fluid, which is assumed to be zero.
In equation (2), ,3(,p) is the momentum transfer coeffi-
cient, assumed in this work to be in the form due to Wen
and Yu Wen and Yu (1966)

S3 CD apaf vP 265, (4)
4 dp f

where CD is the drag coefficient for an individual parti-
cle (assumed to be spherical)

S24(1 + 0.15Re 687) Re < 1000
S0.44, Re > 1000 (5)

The equations are discretized by the finite volume
method and the subsequent set of linearized equations
is solved for the whole domain, in conjunction with the
appropriate equations for the particle phase.

Eulerian-Eulerian Particle-Phase Model

In the Eulerian-Eulerian two-phase flow model, the par-
ticle and fluid phases are assumed to be continuous and
fully interpenetrating Newtonian-like fluids; the mate-
rial parameters are summarized in Table 3. The parti-
cle phase is thus modelled by equations similar to Equa-
tions 1 and 2. However, in the particle phase momen-
tum equation a term involving the gradient of a solids
pressure has also been included to prevent the parti-
cle volume fraction from exceeding its maximum value,
ap,max-
The particle-phase stress is modeled using a constant
particle-phase viscosity of p = 0.10 Pas based upon
values reported on in the literature Grace (1970). The
particle phase pressure is modeled using the solids pres-
sure model proposed by Gidaspow,

Pp = Goe( .-.-), (6)


Figure 3: The computational mesh employed for two-
phase Eulerian-Eulerian flow predictions.


where Go is the reference modulus of elasticity and c
is the compaction modulus. In this work, a reference
modulus of elasticity of 1 Pa, a compaction modulus of
20, and a maximum particle volume fraction of 0.65 are
employed. The material parameters are summarized in
Table 3. The computational model for two-phase flow
does not include flow through the distributor plate. In-
stead, inlet boundary conditions are imposed at locations
that correspond to the the orifices in the distributor plate.
Figure 3 shows a typical mesh for this case.


Eulerian-Lagrangian Two-Phase Flow Model

A discrete element model (DEM) proposed by Cundall
and Strack Cundall and Strack (1979) is used to model
the particles. The individual trajectories of the particles
are determined in the Lagrangian framework, where par-
ticle collisions are modelled via the soft-sphere model
proposed by Tsuji et al Tsuji et al. (1991), which ac-
counts for some non-reversible deformation.
The trajectories of individual particles are considered
(i.e. described in a Langrangian framework) and New-
ton's 2nd law is solved for each particle, accounting for
the fluid-particle, particle-particle, and particle-wall in-
teractions, and approximating the integral with the Ver-
let algorithm.
Newton's 2nd law for the particles is written as


Vp m+ pg


vpVp


N
+ [Fw+ Fpp]


MP =- 13(f,p)-V v
dv Vp (
m^= ^[v







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


and for the rotational momentum
dwc
I = Tp (8)

where mp is the mass of the particle; Vp is the volume of
the particle; II is the moment of inertia; Tp the torque
acting on the particle; wp is the rotational velocity; vp is
the translational velocity; and 3 is the momentum trans-
fer coefficient (see Equation 4). In addition, Fpw and
Fpp are the particle-wall and particle-particle interaction
forces, respectively. The right hand side terms of equa-
tion (7) are outlined in table 4.


Table 4: Terms of right hand side of equation(7)

Term Force type

/v (vf- vp Drag force
mpg Body force due to gravity
VpVPf Force due to the pressure gradient
Fp Particle-wall contact force
Fpp Particle-particle contact force


Implementation of particle collisions
The particle-particle and particle-wall interactions as
taken into account in this work are assumed to be local;
i.e. no long-range forces are included. If each particle
pair is considered in order to determine this interaction,
the resulting computational effort would scale as N2,
N being the number of particles. In order to develop
a more efficient scheme, a particle-mesh algorithm is
adopted in which each of the particles is assigned a cell
in the particle mesh based upon its location. Using this
particle-mesh, each particle is only tested for interaction
against particles located in the same or directly neigh-
bouring particle mesh cells. Although this method re-
quires a more complex algorithm it leads to a scaling of
N logN, making it a lot more favourable for large num-
bers of particles. The particle collisions are modelled
by the soft-sphere model as described by Cundall and
Strack Cundall and Strack (1979). In brief, this model
uses a spring-dashpot-slider arrangement to describe the
particle behaviour before, during and after a collision.
The damping coefficient used, described by Tsuji and
co-workers Tsuji (1994); Tsuji et al. (1991) is, however,
used since it is related to the coefficient of restitution.
The normal and tangential contact forces are given by
the sum of forces due to the spring and dashpot. From
Hertzian contact theory the normal and tangential con-
tact forces are,

Fij = (-kn,6 .1. G n)n (9)


Ftij = -ktet I' Get (10)
where G is the velocity vector of particle i relative to
particle j, Get is the slit velocity vector at the contact
point. The subscripts n and t represent the normal and
tangential components respectively and 6 is the displace-
ment, or overlap, of particles i and j during collision.
Three parameters are required by the soft-sphere model;
stiffness (k), damping coefficient (r) and the coefficient
of friction (p). The parameter p is a well known empiri-
cal quantity, stiffness and the damping coefficient can be
estimated using equations

n = a.Mkn (11)

Tpt = aVMkt (12)
where M = ; and m is the mass of the particle.
Note that for wall collisions m, -- oc, hence M = p.
The relationship between a and the coefficient of restitu-
tion is well defined by Tsuji et al Tsuji et al. (1991). The
spring constants are, based upon elastic deformation,


4 1 a4( 1
56 \ +-


( 2 (Ti 2 7j ri + rj 2' 1
kt \ i + G ri (14)

where r is the radius of the particles, a the Poisson's ra-
tio; E the Young's modulus, G the shear modulus (given
by G 2(E( ) and 6, the magnitude of the deforma-
tion in the normal direction. Note as above, when a par-
ticle reaches a wall, r, -- oc, hence, =+ 1

Results

Calculations of the Eulerian-Eulerian simulations were
performed with Ansys CFX versions 11.0 and 12.0,
whereas the Eulerian-Lagrangian simulations were per-
formed with the in-house code Multiflow.

Single-phase flow of air
Computations of the single-phase flow of air are em-
ployed to determine the details of the flow around the
distributor plate and the atomizer nozzle in order to cal-
culate inlet boundary conditions for the multiphase flow
simulations. Figure 4 shows an example of the flow
visualized through the bottom plate. Although Figure
4 shows results for a case with a nozzle diameter of
4.5 mm, the details of the atomization flow do not affect
the flow distribution through the distributor plate. For
example, the same flow distribution is obtained when
the atomization flow is turned off. In any case, the in-
let boundary conditions for the cases including the two-
phase flow will use the single-phase velocity distribution


Ej rirj








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


Velocity
10.0
8.8
7.5
6.2
5.0
3.8
2.5
1.2
0.
[m s^-1]





Figure 4: The air velocity
phase flow calculations


as predicted by the single-


Orifice Small Medium Big
Velocity 10 9.4 8.0


Table 5: Inlet boundary conditions for two-phase flow
calculations.


across the plate, as shown in Table 5. The resulting flow
profile of these boundary conditions is shown in Figure
5 for the Eulerian-Lagrangian simulations.


Eulerian-Eulerian two-phase flow predictions

Results are presented for a case for which the atomiza-
tion flow enters the vessel through an opening with a
diameter of 0.4 mm and with a velocity of 40 m/s. The
flow in this case is expected to be dominated by the in-
fluence from the jets that emanate from the holes in the
distributor plate, though the atomization flow still has
an effect due to its high velocity. Figure 6 shows a snap-
shot of the particle distribution at one instant in time that
later may be compared with a similar snapshot for the
DE-model.
The flow field may also be examined in terms of
the mass flow of particles into and out of the Wurster
tube. Figure 7 shows the instantaneous as well as time-
averaged particle mass flow rate into the bottom of the
Wurster tube and out of top of the Wurster tube. Al-
though there are considerable fluctuations in the mass
flow rates, the particle mass flow rate into the Wurster
tube at the bottom is clearly greater than the particle
mass flow rate out of the tube at its top. That is, par-


Figure 5: The modelled air velocity 0.5 mm above the
distributor plate as modelled in the Eulerian-Lagrangian
simulations.


Figure 6: Snapshot of a particle isovolume correspond-
ing to a volume fraction of 0.15 at t 3.79 s.







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


Figure 7: The particle mass flow rate through the bot-
tom of the Wurster tube. The time-average mass flow
rates for an averaging period of 2 s are shown with thick
curves.


- : -4s
t =2s


Time Is]


Figure 8: The particle accumulation in the Wurster tube.


tides that enter the Wurster tube through the bottom do
not make it out through the top but fall back down inside
the tube. Since particles enter the Wurster tube but do
not always make it out, there must be an accumulation
of particles inside the tube. Figure 8, which shows the
mass of particles in the Wurster tube is, clearly shows
that particles accumulate in the Wurster tube. The mass
of particles in the Wurster tube may be of interest since
this quantity can possibly be measured using tomogra-
phy. Figure 8 also shows the time-averaged mass of par-
ticles in the Wurster tube, calculated using an averaging
period of 2, 3, and 4 s. Figure 8 thus shows that the pro-
cess requires at least 6 s to reach a steady state and that
a steady, time-averaged solution can be calculated with
reasonably precision by forming an average over 2 s.
The fact that particles tend to accumulate in the
Wurster tube may also be seen by examining Figure


Figure 9: Contour plots of the time-averaged particle
volume fraction in a vertical cross-section through the
centerline of the vessel.


9, which shows the time-averaged particle volume frac-
tion at a vertical plane that passes through the center-
line of the vessel. In Figure 9, it can be seen that parti-
cles have accumulated in the atomization flow. Figure
10 shows the time-averaged air velocity for the verti-
cal plane shown in Figure 9. The terminal velocity of
a sphere with a density of 1500 kg/m3 and a diameter
of 480 pm can be estimated to 0.5 m/s and Figure 10
indeed shows that the particles in the atomization flow
tend to remain there because there is a balance between
interphase drag and gravity.
The jets that emanate from the distributor plate for
single phase flow of air may be clearly seen in Figure
4. However, Figure 9 shows that when the particles are
present the jets only penetrate a short distance into the
bed, at least on average. Whether this is problem or not
obviously depends on the number or mass of particles in
the vessel. If the amount of particles is small, the jets
can possible penetrate the entire bed which can result in
a fair amount of gas bypass. It must, however, be noted
that Figure 9 shows the time-averaged particle volume
fraction. At any point in time, by-pass may be much
more severe that indicated by Figure 9, as shown in Fig-
ure 11, which shows a snapshot of the particle volume
fraction at = 6.9 s.
In Figure 9, it may be seen that the particle volume
fraction is slightly higher next to the wall in the inside
of the Wurster tube. One mechanism by which parti-
cles end up near the inside of the Wurster tube may be
seen by examining the sequence of images in Figure 12,
which shows vector plots of the particle velocity super-
imposed on contour plots of the particle volume fraction.






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


3 ~~:-I


(a) t 3.67 s


A


Figure 10: Contour plots of the time-averaged air veloc-
ity fraction in a vertical cross-section through the center-
line of the vessel.


Figure 11: Contour plot of the particle volume fraction
at t = 2.1 s for mesh B.


(c) t= 3.75 s (d) t= 3.79 s

Figure 12: Vector plots of the particle velocity superim-
posed on contour plots of the particle volume fraction at
t = 3.67, 3.71, 3.75, and 3.79 s.

Eulerian-Lagrangian two-phase flow predictions
In the case of the Eulerian-Lagrangian simulations, no
symmetry plane was assumed and the computational
domain considered is the complete geometry. The mesh
of the geometry consists of approximately 400,000 cells
and it is shown in Figure 13. As in the simulations
based upon the Eulerian-Eulerian model, the diameter
of the atomizing nozzle is 0.4 mm and the fluid velocity
through this nozzle is set to 40 m/s.

To have the same number of particles in the Wurster
bed compared to the two-fluid simulation case, approxi-
mately 1.00 x 106 particles are inserted into the domain.
The same inlet velocity boundary conditions are applied
as in the two-fluid model simulation case, see Figure 5.
The simulations were run for a period of 9 s of physical
time, of which the first 4 s are discarded in order to
compute time-averages. The average fluid velocity
obtained in the Eulerian-Lagrangian simulations is
shown in Figure 14. The fluid velocity is comparable
to the air velocity obtained in the two-fluid simulation.
Although the air velocity through the central nozzle
is very high, the mass flow of air through this nozzle
is very small. Two snapshots of the locations of the
particles are shown in Figures 15 and 16 showing the
complete Wurster bed and half of the Wurster bed
respectively. The particles in both figures are coloured
by their velocity. The time-averaged volume fraction


(b) t 3.71 s






JAM








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


Figure 15: A snapshot after t 4 s of the locations
of all the particles in the Wurster bed. The particles are
coloured by their velocity.


Figure 13: Part of the surface mesh employed for two-
phase Eulerian-Lagrangian flow predictions.















VelocityPhase1 average
34.52126
110
V h o
-1
-0.1
0.01
0.005015


Figure 14: A snapshot after t 4 s of the velocity mag-
nitude of the air in the center of the Wurster bed. The
snapshot is taken from the two-phase flow calculations.


Figure 16: A snapshot after t 4 s of the locations of
all the particles in one side of the Wurster bed, showing
the location and velocities of the particles in the center
region. Particles are coloured by their velocity.







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


VFrac _average
1
0.975
0.95
0.925
0.9


Figure 17: The averaged fluid volume fraction shown in
a plane going through the center of the Wurster bed
one side of the Wurster bed, showing the location and


shown in a cross section of the Wurster bed is shown
in Figure 17. The figure is fairly symmetrical, which
implies that the statistics of the linear average is satisfac-
tory. This figure shows the particles are moved towards
the Wurster tube in the center of the bed. In Figure 18
the particle mass flow entering the Wurster tube, leaving
the Wurster tube and the difference between these two
fluxes is shown, analogously as in Figure 7 and 8 for the
Eulerian-Eulerian simulations.


Discussion

The comparison between the DE- and two-fluid model
simulation shows that the two models give approxi-
mately the same overall flow behavior, at least on aver-
age. For example, both models predict an accumulation
of particle inside the Wurster tube. However, the DE-
model predicts that the air jets from the distributor plate
and the atomizer penetrate further into the particle bed
than does the two-fluid model. Despite this difference,
the two-fluid model predicts that the effect on the jets
on the particles is greater. These differences most likely
depend on the choice of constitutive model for the parti-
cle phase, for example through the value of the viscosity
employed for the particle phase.
The fact that particles that enter the Wurster tube
through the bottom but do not exit through the top may
possibly create a problems. For example, if the parti-
cle concentration inside the Wurster tube increases there
is an increased risk for agglomeration. Having particles
that enter the Wurster tube but do not make it out may
also create a wider particle size distribution that causes
a corresponding increase in the variability of the final
drug product, such as its content of drug substance or
dissolution time.
In the context of optimizing process parameters, it


Figure 18: The particle mass flow rate in the bottom
and the outlet of the Wurster tube as predicted by the
Eulerian-Lagrangian simulations. Also, the difference
between these is shown; representing the local accumu-
lation of particle mass.


is thus of interest to calculate a measure of this back-
mixing. If particles that enter through the bottom of the
Wurster tube also make it out through the top, albeit at a
later time, there should be a correlation between the par-
ticle mass flow rate into the bottom of the Wurster tube
at some point in time t and the particle mass flow rate
out of the top of the Wurster tube at some later point in
time t + At. It may thus be of interest to calculate the
correlation function


CBT(t) lim -
T-oo T -t Jo


TmB(s) Th(t + s)ds


(15)
where Trbottom is the mass flow rate through the bot-
tom of the Wurster tube and rbtop is the mass flow rate
through the top of the Wurster tube. For example, Fig-
ure 19, which shows this correlation function normal-
ized by the variance of the flow through the bottom of
the Wurster tube for the two cases considered in the
Eulerian-Eulerian simulations, shows that an increase
in the atomization flow decreases the amount of back-
mixing inside the draft tube.


Conclusions

Fluid mechanics calculations using a discrete element
model (DEM) were employed to study the flow be-
haviour in a laboratory-scale Wurster-type coating pro-
cess computationally. The results from calculations us-
ing a DE-model were compared to predictions based
upon simulations using a two-fluid model in the context
of the flow behavior in and around the jets that emanate















D=0.4 mm
SD=4.5 mm
0. 10






005 --
0.00



*0 200 400 6
Time [ms]



Figure 19: The correlation function for the mass flow of
particles through the bottom and top of the Wurster tube.


from the orifices in the distributor plate. For the overall
flow behavior, it was found that the two different models
gave predictions similar predictions. However, for the
detailed flow behavior in the immediate vicinity of the
distributor plate and the atomization nozzle, the results
differ. It was found that the air jets near the distributor
plate and the atomization nozzle persisted further into
the particle bed for the DE-model than for the two-fluid
model. However, further away from the jet inlets, the ef-
fect of the jets on the behavior of the particles was found
to be greater for the two-fluid model than for the DE-
model. This difference may depend on the choice of
constitute model for the particle phase.


References

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


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