
Research Article


CFD Modeling of Heat and Mass Transfer in the Fluidized Bed Dryer 

M. Keshavarz Moraveji,
S.A. Kazemi
and
R. Davarnejad



ABSTRACT

Heat and mass transfer during drying process in a fluidized bed dryer have been modeled with Computational Fluid Dynamics (CFD) method. An Eulerian Eulerian two fluid model incorporating kinetic theory was used for simulation of gassolid flow. Governing equations were discretized based on finite volume in twodimension and discretized algebraic equations were solved iteratively with Semi Implicit Method for Pressure Linked Equations (SIMPLE) method. The effects of operating conditions involving inlet gas velocity, inlet gas temperature, inlet solid temperature, initial solid moisture and particle size on the drying process were investigated. The modeled data were in good agreement with the experimental data obtained from the literature.





Received: June 19, 2010;
Accepted: November 14, 2010;
Published: December 27, 2010


INTRODUCTION
Recently various methods for drying process of solids have been developed.
Thermal efficiency of the fluidized bed dryers is most important item for variety
of drying applications (Mujumdar, 1995; Strumillo
and Kudra, 1996). In this type of dryers, the drying gas in a boiling bed
unit fluidizes the solids. Mixing and heat transfer processes are very rapid.
The exit gas is usually saturated with vapor for any allowable fluidization
velocity. These dryers may also be operated batch wise (Souraki
and Mowla, 2008). There is interest in predicting the hydrodynamic behavior
of fluidized beds.
While there are several experimental procedures for measuring heat and mass
transfer phenomena in the fluidized bed, the use of CFD tools for providing
valuable information for design of the reactor, scale up and optimization has
attracted considerable attention in the recent years (Hekmat
et al., 2010; Azizi et al., 2010).
Two methods have been typically used for CFD modeling of gassolid flows, namely,
EulerianLagrangian method and EulerianEulerian approach. In the EulerianLagrangian
approach, the computational demand rises sharply with the number of traced particles,
which constrains its applicability to high concentration flows. In the EulerianEulerian
method, which is used in the current study, two phases are mathematically treated
as interpenetrating continua. The theoretical fundamental and equations for
twofluid method is explained in detail in the literature (Ishii,
1975; Gidaspow, 1994).
Researchers have conducted several numerical studies to describe fluidized
bed drying process. Hoebink and Rietema (1980a) and
Kerkhof (1994) presented some models based on temperature
and humidity as homogeneous variables. Thomas and Varma
(1992) showed a model which solid particles receded evaporation interface.
The diffusive models were studied by Hoebink and Rietema
(1980b), Zahed et al. (1995) and Van
Ballegooijen et al. (1997). They considered the humidity profiles
inside the particles. Palancz (1983) proposed a mathematical
model for continuous fluidized bed drying based on the twophase fluidization.
According to this model, the fluidized bed was divided into two phases involving
a bubble and an emulsion phase. An improvement in Palancz's model was carried
out by Lai and Chen (1986). Garnavi
et al. (2006) continued Palancz's work. They considered variation
of bubble size along the bed height as well. Chandran et
al. (1990) investigated single and spiral fluidized beds in a batch
and continuous system. Tsotsas (1994) and Groenewold
and Tsotsas (1997) modeled the heat and mass transfer in a batch fluidized
bed using a normalized decreasing transfer rate related to the humidity of a
single particle.
Hajidavalloo and Hamdullahpur (2000a, b)
and proposed a mathematical model for heat and mass transfer simulation in a
fluidized bed drying for large size particles. Wang and
Chen (2000) studied bed dynamics in a fluidized bed as a perfect mixer without
bubbles. Syahrul et al. (2002) were used mass,
energy and entropy balances in a batch fluidized bed dryer by assuming perfect
mixing of particles. Wildhagen et al. (2002)
showed a threephase model involving solid (as lumped), interstitial and bubble
gas (as a perfect plug flow). Vitor et al. (2004)
studied the effective heat and mass transfer coefficients estimated between
interstitial gas and solid phases in drying process of biomass in a batch fluidized
bed dryer. Burgschweiger and Tsotsas (2002) experimentally
considered and theoretically modeled a continuous fluidized bed drying under
steady state and dynamic conditions.
Izadifar and Mowla (2003) presented a model for a continuous
fluidized bed dryer. According to this model, moisture content of particle and
the latent heat of desortion vaporization were not constant values. Souraki
et al. (2009) modeled the drying process of small spherical porous
particles in a microwave fluidized bed dryer assisted with inert glass beads
particles. Ishii (1975) used a twofluid model for a packed
bed dryer. BasiratTabrizi et al. (1983, 2002)
extended Ishii’s model for a fluidized bed dryer. BasiratTabrizi
et al. (1983) showed a model to simulate drying process for twodimensional
cylindrical cases.
In this study, CFD method was used for heat and mass transfer studying during
drying process. The EulerianEulerian twofluid model was used to simulate the
gassolid flow. The modeling results are compared with the experimental data
reported by BasiratTabrizi et al. (1983) and
also compared with results from commercial CFD software (Fluent 6.3).
Computational fluid dynamic model: The conservation of mass and momentum
and constitutive relations were studied elsewhere (Azizi
et al., 2010). Here, the heat and species conservation equations
are briefly summarized.
Heat transfer modeling: Thermal energy equations for the gas phase are derived as following: The thermal energy balance for the solid phases is given as: The heat transfer between the gas and the solids is a function of temperature difference between the gas and solid phases: The heat transfer coefficient is related to the particle Nusselt number using the following equation: The Nusselt number is determined applying the following correlation (Gunn, for a porosity range of 0.351.0 and a Reynolds number up 10^{5}: Mass transfer modeling: In a complete mixing fluidized bed dryer, the surface moisture of the samples (at the end of drying process) will be assumed to be at equilibrium with the drying air. The species equation for the gas phase is: where, X_{g} is the mass fraction and R_{g }is the rate of formation of gas species (evaporation rate). The species equation for the solid phase is as the following: where, R_{sm} is the moisture evaporation from the particle surface.
Numerical simulation: The governing equations were discretized using
finite volume method (the secondorder upwind scheme) and discretized algebraic
equations were solved iteratively with SIMPLE method (Ergun,
1952). The CFD opensource code MFIX is used for the present study (Azizi
et al., 2010). The convergence criterion (for time zone) of 10^{4}
is specified for the relative error between successive iterations. The computational
domain consists 35 grids in radial and 40 grids along the axis of the bed. So,
the total grids will be around 1400. When the grids increase to 3000 (50x60)
or decrease to 600 (20x30) the modeling results (velocity and temperature distributions)
will not change significantly. Therefore, the obtained results in this range
will be independent of meshes number. The initial bed of solids is packed into
the bottom of the bed up to 0.6 m of bed height. The bottom of the bed is defined
as inlet velocity to specify a uniform inlet gas velocity. Pressure boundary
conditions were employed at the top of the freeboard which is set to a standard
value of 1.0132x10^{5} Pa.
RESULTS AND DISCUSSION In the present study the Wheat grains was used as solid particles with initial temperature of 298 K, initial moisture content of 0.25 kg kg^{1}, density of 1200 kg m^{3} and diameter of 3 mm. The air enters the bed with initial moisture content of 0.015 kg kg^{1}. The wall temperature was assumed to be in the adiabatic condition. Results of this simulation were obtained after 250 sec. The operating conditions effects such as the inlet gas velocity, inlet gas temperature, inlet solid temperature, initial solid moisture and particle size on the drying process were also investigated.
According to the Fig. 1 and 2, temperature
and moisture content of solid profiles are in good agreement with the experimental
data obtained by BasiratTabrizi et al. (1983).
Figure 17 show the temperature and moisture
content changes profile at various drying times. The required time for moisture
content and moisture content equilibrium will be obtained from moisture content
versus time curve.
 Fig. 1: 
Temperature of solid in fluidized bed at various gas velocities
(4 and 5 m sec^{1}) at temperature of 373 K 
 Fig. 2: 
Moisture content of solid in fluidized bed at various gas
velocities (4 and 5 m sec^{1}) at temperature of 373 K 
 Fig. 3: 
Temperature of solid in fluidized bed at various gas temperatures
(343 and 373 K) at velocity of 4 m sec^{1} 
 Fig. 4: 
Moisture content of solid in fluidized bed at various gas
temperatures (343 and 373 K) at velocity of 4 m sec^{1} 
 Fig. 5: 
Moisture content of solid in fluidized bed at various particle
diameters (1 and 3 mm) 
Figure 1 and 2 show the effect of initial
air velocity on drying process at gas temperature of 373 K. The profiles of
temperature and moisture content of solid show that these parameters have no
significant effect on dryer performance.
 Fig. 6: 
Moisture content of solid in fluidized bed at various initial
solid temperatures (288, 298 and 308 K) 
 Fig. 7: 
Moisture content of solid in fluidized bed at various initial
moisture contents of solid (0.2, 0.25 and 0.3) 
The higher air velocity at a constant temperature can make the drying time,
shorter. Figure 3 and 4 show temperature
and moisture content profiles at two air temperatures (343 and 373 K) and constant
gas velocity (4 m sec^{1}).
As shown in Fig. 3 and 4, drying process with a low gas temperature reaches steady state condition faster than the higher gas temperature. The moisture content is at a high gas temperature is low. So, it causes a faster drying process. Further, two distinct zones in drying process are observed in these figures. At the first part the solids temperature increased versus time up to the saturation temperature. This temperature approximately is 367 K at higher gas temperature (373 K) and 340 K at lower gas temperature (343 K). At the first part, moisture content of solids (drying rate) decreased versus time up to the final moisture content which was around 0.049 kg kg^{1} at higher gas temperature and 0.08 kg kg^{1} at lower gas temperature. At the second part, the steady state condition and the particle temperature was equal to the saturation temperature and moisture content of solid was constant. As shown in Fig. 3 and 4, there is a good agreement between theoretical data obtained from this work and the experimental data obtained from the literature however there are some deviations between those data (theoretical and experimental) related to the moisture contents.  Fig. 8: 
Mean volume fraction of air in the bed (near wall (at x =
0.07 m)) 
 Fig. 9: 
Mean axial of air at two locations along the bed width (near
wall (at x = 0.07 m)) 
The particle size effect on moisture content of solid has been shown in Fig. 5. As the particle diameter was decreased versus time, the drying rate was increased. The moisture content sharply reached equilibrium condition at smaller particles (d_{p} = 1 mm).
Figure 6 and 7 show the effect of the inlet
moisture content and inlet temperature of the solid particles on the moisture
content of solid. The inlet moisture content of particles had a significant
effect on the dryer performance but the inlet temperature of the particles had
no effect on it. Therefore, the fluidized bed dryer is more sensitive to the
inlet gas temperature, initial solid moisture and particles size.
Figure 8 shows mean volume fraction of air along the bed height (on dryer wall while its radius is around 0.07 m). It shows an enhancement from the inlet zone to the outlet zone of bed. Figure 9 shows mean axial air velocity at two locations along the radius of bed (center and near the wall) and compared results from our modeling with modeling results from commercial CFD software (Fluent 6.3).
Figure 10 to 12 show the mean radial
velocity of air at four locations (y = 0.1, 0.3, 0.6 and 1.1 m) along the axis.
The velocity profiles show a good agreement between the data obtained from simulation
results and results from the Fluent software however some deviations are observed
near the inlet zone of the bed (at y = 0.1 m).
 Fig. 10: 
Mean radial velocity of air at one location near the inlet
zone of the bed (y = 0.1 m) 
 Fig. 11: 
Mean radial velocity of air at two locations in the middle
zone of bed (y = 0.3 and 0.6 m) 
 Fig. 12: 
Mean radial velocity of air at one location near the outlet
zone of the bed (y = 1.1 m) 
Figure 9 to 12 show when the air passes
through the bed, near the inlet zone (at y = 0.1 m) and in the middle of the
bed height (at y = 0.3, 0.6 m), mean air velocity is minimum near the wall bed
(x = 0) and is maximum in the middle of the bed width (x = 0.07). Mean air velocity
of the outlet zone of the bed (at y = 1.1 m) is maximum near the walls and decreases
in the middle of the bed width. The maximum amount of air velocity is around
the radial center of the bed (at y = 0.3 m).
CONCLUSIONS A two fluid Eulerian model was used for modeling the heat and mass transfer in a fluidized bed dryer including wet wheat grains. The modeling was used to predict moisture and temperature distributions of solid at various drying times. The drying curve showed constant and decreasing rates. The operating conditions effects such as inlet gas velocity, inlet gas temperature, inlet solid temperature, initial solid moisture and particles size on the drying process were investigated. The modeling results showed a good agreement between the calculated data and the reported data in the literature.
NOMENCLATURE
a 
= 
Specific surface (1/m) 
c 
= 
Specific surface kJ kg^{1} °C 
C_{DZ} 
= 
Two phase grag coefficient 
d 
= 
Particle diameter (m) 
D 
= 
Molecular diffusion (m^{2} sec^{1}) 
g 
= 
Gracity (m sec^{2}) 
G (ε_{g}) 
= 
Solid stress modulus 
h_{v} 
= 
Heat transfer dimensionless 
k 
= 
Thermal conductivity (kJ kg^{1} °C) 

= 
Moisture evaporation 
Pr 
= 
Prandtl No. 
P 
= 
Pressure (kPa) 
Re 
= 
Reynolds number, as defined in text 
r 
= 
Radial distance from the centerline (m) 
T 
= 
Temperature (°C) 
t 
= 
Time (sec) 
u 
= 
Radial velocity (m sce^{1}) 
v 
= 
Axial velocity (m sce^{1}) 
x 
= 
Moisture content (kg_{w}/kg_{s}) 
z 
= 
Elevation (m) 
Greek symbols:
β 
= 
Gassolid drag coefficient 
γ_{0} 
= 
Heat of vaporization (kJ kg^{1}) 
ε 
= 
Void fraction 
μ 
= 
Viscosity (kg msec^{1}) 
ρ 
= 
Density (kg m^{3}) 
σ 
= 
Evaporation coefficient (kg m^{2} sec) 
τ 
= 
Stress (kPa) 
Subscripts:
Dz 
= 
Grag in zdirection 
g 
= 
Gas 
p 
= 
Particle 
pg 
= 
Gas on the surface of a particle 
r 
= 
Radial 
rr 
= 
Radialstress 
s 
= 
Solid 
sz 
= 
Solidaxial 
v 
= 
Vapor 
z 
= 
Axial 
zz 
= 
Axialstress 

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