Direct Numerical Simulations and
Experiments of a Small Fluidized Bed

Y. (Yali) Tang^*,
N.G. (Niels) Deen, E.A.J.F. (Frank) Peters, J.A.M. (Hans) Kuipers

Department
of Chemical Engineering and Chemistry, Eindhoven University of Technology,
Eindhoven, The Netherlands

 (^*
Corresponding E-Mail: y.tang2@tue.nl
)

Keywords: direct numerical simulation,
immersed boundary method, fluidized bed, PIV,DIA

Abstract

Gas-fluidized
beds are frequently applied in the chemical, environmental, petrochemical,
metallurgical and energy industries, where exist large-scale operations
involving physical (coating, drying and granulation) and chemical
transformation.  The numerical prediction of fluidization in engineering
scale equipment can, in practice, only be achieved with continuum models such
as the two-fluid model. In recent years, discrete element model have also
become increasingly popular for modelling gas fluidized beds. A common feature
of all these models is that the gas-solid interactions are not directly
resolved, but rather described via closures with parameters (porosity,
velocity) determined by the volume-averaging approach.  However, it has
been demonstrated that the gas-solid drag force as calculated in these models
with volume-averaged parameters shows a departure from the true drag force,
even when the most accurate and suitable drag correlations are used¹.
On the other hand, direct numerical simulations (DNS) treats the gas-particle
interactions ab initio, such that the flow is fully resolved and ?truly?
predicted. At present, fully resolved simulation of large industrial equipment
is not feasible. However, thanks to the drastically increasing computer power
and improvement of parallelization algorithm, DNS of actual fluidization with
more than thousands of particles (at lab scale) has been achieved^2,3.
This might suggest DNS as a promising and effective tool for quantitative
understanding of gas-solid flows, which is crucial for efficient design and
optimal operation of fluidized beds.

In
this work we experimentally validate our DNS fluidization code using coarse
grids. We carry out both DNS and experiments of a small pseudo-2D fluidized
bed, with the bed width, depth and height 0.1, 0.015 and 0.4 m respectively.
Air is used as a fluidization agent, with density ρ_g
= 1.2 kg/m³ and viscosity μ_g
= 1×10^-5 kg/(m·s) (for simulation
setting). The bed is filled with 5000 spherical glass beads with a uniform
particle diameter d_p = 0.0025
m  and density ρ_p= 2526 kg/m³. The minimum fluidization velocity is
determined U_mf = 1.33 m/s, and our
experiments have been performed with gas feed
U_g of 2-2.6 m/s
corresponding to (1.5-2)U_mf.

Two
experimental techniques are used in this work: particle image velocimetry (PIV) and digital image analysis (DIA). These
techniques have been widely used for the measurement of solids motion in
pseudo-2D fluidized beds. PIV is a non-intrusive optical technique based on the
comparison of two images recorded with a very small time delay by a high speed
CCD camera. For the analysis, every image is divided into interrogation zones,
where cross-correlation on two consecutive images is employed to obtain an
average displacement of the particles in the selected interrogation zone. The
PIV image pairs are post-processed using the commercial software package DaVis (LaVision). A multi-pass
algorithm using interrogation zones of 64×64 and 32×32 pixels, respectively, is
employed to reconstruct the corresponding vector image. DIA is an image
post-processing algorithm, in which the gas and solids are discriminated on the
basis of the pixel density. With the 2D intensity of PIV images, a correlation
is used to reconstruct the instantaneous profile of 3D solids volume fraction,
which in turn is used to correct the PIV velocity vectors.

The
simulations are performed using an immersed boundary method (IBM). The main
characteristics of our IBM are: the governing equations that describe the fluid
flow are solved on a fixed and structured Eulerian
grid with the grid spacing much smaller than the particle size; the particles
are represented by sets of Lagrangian marker points,
and the dynamics of the particles are governed by the Newtonian equations of
motion; particle-particle and particle-wall interactions are handled by a hard
sphere model; the coupling between gas and solid phases is implemented by
enforcing no-slip boundary conditions at the surface of the particles, via a
forcing term that is calculated at the position of each marker point and
subjected to the transport equations. Since the flow is solved on the entire
domain including the volume occupied by the solids, the inertia of the
artificial fluid inside a particle is subtracted from the force density.

Figure
1 shows a snapshot of IBM simulation of the fluidization of 5000 particles. The
time step to update the gas flow is set to ∆t = 1×10^-5
s. With the correction for grid size effects, we use relatively coarse grids
with the grid spacing h = d_p/10.
Constant pressure outflow boundary condition is used at the top, and no-slip
boundary conditions are used for all the side walls. The gas is uniformly
injected through the bottom with the superficial velocity corresponding to the
experiments. The collision coefficients of normal restitution, tangential
restitution and sliding friction are set to 0.97, 0.33 and 0.1, respectively.
In order to analyze the dynamic behavior of the bed and compare to the
experimental results, the average height of all particles, the pressure drop,
the time-averaged solids volume fraction, the time-averaged solids velocity and
the granular temperature are computed from the simulation results. Figure 2
shows the profile of time-averaged solids volume fraction and the solids volumetric
flux vectors from PIV & DIA for superficial velocity U_g
= 2.4 m/s. The solids circulation pattern can be clearly seen from the
time-averaged lateral profile of solids flux. For comparison with IBM
simulation results, the average bed height and the pressure drop are measured
as well.

In
this work, direct numerical simulations of an actual gas-fluidized bed using
IBM with coarse grids is validated with dedicated one-to-one experiments.
Drastic reduction of the computational cost by using coarse grids with
effective calibration makes it feasible of large DNS modelling. Besides, DNS of
fluidization can provide insights and data to correct for the deviation
resulting from volume-averaging approach, which is a major step forward in
discrete element modelling and two-fluid modeling of fluidized beds.

Figure
1. A snapshot of IBM simulation of a small fluidized bed.

Figure
2. Left: profiles of solids volume fraction; Right: solids flux vectors
(multiplication of particle velocity and volume fraction m³/(m²Â·s)).

References

1.      Kriebitzsch
SHL, van der Hoef MA, Kuipers JAM. Drag
force in discrete particle models?Continuum scale or single particle scale? AIChE
J. 2013;59:316-324.

2.      Kriebitzsch
SHL, van der Hoef MA, Kuipers JAM. Fully
resolved simulation of a gas-fluidized bed: A critical test of DEM models.
Chem. Eng. Sci. 2013;91:1-4.

3.     
Pan T-W, et al.
Fluidization of 1204 spheres: simulation and experiment. J. Fluid Mech. 2002;451:169-191.