Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique Page: 20 of 47
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constrain pebble motion while at the same time be transparent to fluid flow.
The comparisons between simulation results and experimental data are presented in Figures
16, 17 and 18. The overall agreement is very good, though there are some discrepancies. Initially,
simulation show that the pebbles move faster in the central region, and slower near the wall
with some of the pebbles near the wall moving in a downward direction (see Figure 16a). This
can be explained by the fact that the counter fluid flow is not distributed uniformly through
the cone section. There could be several reasons for this behavior. One reason may be that the
holes in the conical section were not modeled explicitly. Another, more likely reason, is that
our initial packing was not ideally conformed to the boundary of the container, thus leading to
higher porosity near the skin of the container than in the interior of the pebble bed, thus leading
to higher fluid flow rates near the outer boundary of the cylinder. However, it appears that those
local fluctuations do not affect the integral characteristics of the flow field. A comparison of the
simulated evolution of the bed bottom position with that observed during the experiment is
shown in Figure 17. The bed bottom position was taken as the lowest pebble position in the
central cylindrical slice of radius 5.1cm. The averaged pebble mass flow in the bed region was
about 4kg/(m2s) and about 60kg/(m2s (Figure 18) in the chute section.
We performed numerous parametric studies for different boundary conditions and contact
model parameters. The most important ones are presented and discussed. The averaged pebble
mass flux appears to be not very sensitive to changes in the damping coefficient do (Figure 19).
According to Tsuji et al. (1992) the damping coefficient is related to the restitution coefficient
(the ratio between particle velocities before and after collision) We compare results with no
damping (damping parameter 0), damping parameters 0.07 and 0.7 and the maximum difference
was less than 15%. Another study was done to quantify effects of the stiffness coefficient k, in
equations (22). Our numerical simulations showed that this parameter has a significant effect
on the results, and should be chosen very carefully. The characteristic time step for fluid flow
could be hundreds of times larger than the time step required to simulate contact interaction
between particles based on the stiffness estimated from the physical properties of the particles.
If we use real stiffness and explicit integration of contact forces, the computations become
prohibitively expensive. However, as demonstrated below, reasonable numerical solutions can be
obtained using a lower stiffness than that computed based on physical properties of the pebbles.
According to the Hertzian contact theory Hertz (1882), the relation between the normal force
F, and displacement 6 is given by
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Kanarska, Y; Lomov, I & Antoun, T. Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique, article, September 10, 2010; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc868095/m1/20/: accessed March 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.