(379g) Adapting Data Processing to Compare Model and Experiment Accurately: A Discrete Element Model and Magnetic Resonance Measurements of a 3D Cylindrical Fluidized Bed | AIChE

(379g) Adapting Data Processing to Compare Model and Experiment Accurately: A Discrete Element Model and Magnetic Resonance Measurements of a 3D Cylindrical Fluidized Bed


Boyce, C. M. - Presenter, University of Cambridge
Dennis, J. S., University of Cambridge
Holland, D. J., University of Cambridge
Scott, S. A., University of Cambridge


Despite the widespread practical importance of fluidized
beds, the underlying physics of these systems is still not well understood [1].
This lack of understanding is due in part to the fact that fluidized beds are difficult
to measure because they are opaque, and non-intrusive measurement techniques
such as magnetic resonance (MR) must be employed. Additionally, granular matter
in fluidized beds can possess gas-, liquid-, and solid-like properties [2],
making it very difficult to model accurately. In order to predict the behaviour
of fluidized beds, two characteristics must be modelled properly: (1) the
contact forces between the particles and (2) the interaction forces between the
particles and the fluid. The difficulties in measuring and modelling granular
systems potentially lead to experimental results and simulations with a
combination of known and unknown inaccuracies. Thus, in order to cross-validate
these models and measurements, it is important to compare their results in as
direct a manner as possible. This paper describes the cross-validation of a
computational model and magnetic resonance measurements of a 3D cylindrical
bubbling fluidized bed; the model was processed in a manner that simulated the
acquisition process of the experiment to provide a direct comparison between
the two.

A discrete element
model (DEM) to simulate individual particles combined with computational fluid
dynamics (CFD) to model fluid flow was used here to simulate a bubbling
fluidized bed. The authors developed a 3D cylindrical DEM-CFD model by
integrating a discrete element model in which particles are tracked in
rectangular coordinates and contained by tubular walls with a CFD grid modelled
in cylindrical coordinates. A novel structured CFD grid, shown in Figure 1, was
setup such that the volumes of the fluid cells were kept constant and of
similar shape, to ensure the volume-averaged fluid equations for modelling
unresolved fluid flow around particles [3], were satisfied. The accuracy of a
DEM-CFD model is unclear because of inherent assumptions and inaccuracies in parameters
describing the contact mechanics between particles as well as a drag law
describing the force of interaction between fluid and particles.

Thus, the DEM-CFD model
required validation by experiment. Magnetic resonance (MR) was chosen for
experimental comparison because it has proven effective at measuring a variety
of physical aspects of fluidized beds [4,5,6], it does
not require tracer particles, and it can make measurements on 3D cylindrical
fluidized beds. An inherent problem of MR is the complex and indirect
tomographic measurement techniques it requires. It is unclear how the mathematical
sampling and post-processing methods used to convert the raw MR measurements
into images, and derived quantities such as particle velocity,
affect the results of measurements on dynamic systems such as fluidized beds.
Thus, it is desirable to cross-validate MR measurements by comparison with
computational models.

In this study, the
DEM-CFD model developed was used to simulate an MR experiment measuring
time-averaged particle velocity in a bubbling fluidized bed, conducted by
Holland et al. [7]. The time averaged
velocity was measured in the x-z
plane with a 5 mm slice in the y-direction
at the centre of a 44 mm diameter bed, as shown in Figure 2. The bed contained
1.2 mm diameter particles with a settled height of 30 mm and was fluidized at
twice the minimum fluidization velocity, 2 U/Umf. In the experiment, a pulse sequence of
magnetic field gradients, shown in Figure 3, was used to manipulate MR signal
from oil contained in poppy seeds and ultimately measure the time-averaged
velocity of the particles over an acquisition time of ~30 minutes. This same
pulse sequence was simulated on the particle positions output from the DEM-CFD
model over a timespan compressed to 20 seconds, in order to directly compare
the results measured by model and experiment.

Additionally, other,
simpler averaging techniques were applied to the particle positions and
velocities output from the DEM-CFD simulation to provide a comparison with the
MR-type acquisition and averaging procedure. A frame-based technique averaged
together the average particle velocity in individual pixels at ?frames? in
time, separated by 10 ms intervals, over the total simulation
time. In contrast, particle-based averaging techniques gave equal weighting to
the velocity of each particle which passed through a pixel. The MR-type average
was expected to be closer to a particle-based average, since MR signal is
proportional to the volume of the particle from which it is produced. However,
it was unclear how far other complications in the MR acquisition process would
cause the MR-type average to deviate from a particle-based average in a dynamic
fluidized bed system and how far this average would deviate from a frame-based
average. Additionally, since technical complications in MR required signal from
particles to be weighted by a 5 mm Gaussian slice, shown in Figure 3, as
compared to being bounded by a simple 5 mm ?top-hat? slice, a particle-based
average was conducted with both of these slices to see how the different slices
affected the final average.

Figure 4 shows a
comparison between the experimental MR results for time averaged particle velocity
and those from the DEM-CFD simulation with the simulated MR pulse sequence. The
model and measurements are cross-validated by the similarity in velocity
profiles. Notably, the experimental profile extends further upward in the bed
and has a higher maximum particle speed than the DEM-CFD velocity profile.
These differences can be attributed to inaccuracies in modelling the
fluid-particle interaction force: spherical particles were used in the DEM-CFD
simulation, giving them a lower surface-area-to-volume ratio than the
non-spherical poppy seeds used experimentally and thus a lower drag force.
Additionally, the drag correlation of Beetstra et al. [8] used here has been
demonstrated to significantly underestimate the average drag force on particles
in a fluidized bed [9].

Figure 5 provides a
comparison between the different averaging techniques used to time-average
particle velocity from the DEM-CFD data. The comparison shows very little
difference between MR-type averaging, particle-based averaging with a 5 mm top-hat
slice, and particle-based averaging with a Gaussian-weighted 5 mm slice. Thus,
this comparison shows that, despite the complex acquisition and processing
procedure, MR measurements do provide a particle-based time average in dynamic
systems and a 5 mm Gaussian slice yields equivalent results to a 5 mm top-hat
slice in these systems. Additionally, the frame-based average provides a
similar velocity profile, yet much greater upwards and downwards particle
speeds than the other averages. This demonstrates that different averaging
techniques on the exact same data can yield vastly different results. Thus,
great care should be taken when comparing results from different modelling and measurement
techniques for cross-validation, as it may be the averaging technique, as
opposed to validity of the techniques, which causes discrepancies.


[1] P. G. de Gennes, Rev. Mod. Phys. 71, S374 (1999).

[2] H. M. Jaeger, S. R. Nagel, and R. P. Behringer,
Rev. Mod. Phys. 68, 1259 (1996).

T. B. Anderson, and R. Jackson, Industrial & Engineering Chemistry
Fundamentals 6, 527 (1967).

[4] C. R.
Müller, J. F. Davidson, J. S. Dennis, P. S. Fennell, L. F. Gadden,
A. N. Hayhurst, M. D. Mantle, A. C. Rees, and A. J. Sederman, Chemical Engineering Science 62, 82 (2007).

[5] C. R.
Müller, J. F. Davidson, J. S. Dennis, P. S. Fennell, L. F. Gadden,
A. N. Hayhurst, M. D. Mantle, A. C. Rees, and A. J. Sederman, Phys. Rev. Lett. 96, 154504 (2006).

[6] D. J.
Holland, C. R. Müller, J. F. Davidson, J. S. Dennis, L. F. Gladden, A. N, Hayhurst, M. D. Mantle, and A. J. Sederman,
Journal of Magnetic Resonance 187,
199 (2007).

[7] D. J.
Holland, C. R. Müller, J. S. Dennis, L. F. Gladden, and A. J. Sederman, Powder Technology 182, 171 (2008).

[8] R, Beetstra, M. A. van der Hoef, and
J. A. M. Kuipers, Chemical Engineering Science 62, 246 (2007).

[9] S. H. L. Kriebitzsch, M. A. van der Hoef,
J. A. M. Kuipers, Chemical Engineering Science 91, 1 (2013).


(Colour online) Horizontal cross
section of novel CFD grid. Different colours denote different CFD cells. More
CFD cells are used in the annuli further from the centre, such that the fluid
cells have a constant volume to ensure the same accuracy in the volume-averaged
fluid equations.

(Colour online) Plot of 5 mm y-slice in
fluidized bed (left). Plot of Gaussian and top-hat signal
weighting functions versus y-position in the fluidized bed (right).

Pulse sequence modelled for MR-type
post processing of time averaged axial velocity measurements (Reproduced from
Holland et al. [7]).

(Colour online) Comparison of average
axial velocity images from: (a) experimental MR imaging [5] and (b) MR-type
post-processing of the DEM simulation. Image (c) gives the difference map
between (b) and (a). The resolution of each image is 1.04 mm (z) by 0.94 mm

(Colour online) Comparison of average
axial velocity images of DEM simulation with different averaging methods: (a)
MR-type post-processing, (b) Gaussian-slice particle-based average, (c)
?top-hat? slice, particle-based average, and (d) frame-based average. The
resolution of each image is 1.04 mm (z) by 0.94 mm (x).