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*Aspects of Particle Sedimentation in Dilute Flows at Finite
Reynolds numbers*

The purpose of these studies is to examine dilute
two-phase flows at finite Reynolds numbers along two main themes. First,
to investigate the sedimentation of solid particles arranged in a regular
periodic lattice and to determine both sedimentation rates and flow characteristics
over a range of finite Reynolds numbers and particle concentrations up
to 20%. This is a canonical problem in sedimentation theory and should
provide useful insights into the dynamics of two-phase flow. Second, to
investigate a simplified, approximate method for calculating dispersed
two-phase flow using a force-coupling model that employs the fluid force
on the individual particles to represent the particulate phase as a
distributed
body force action on the fluid phase. This makes the equations of motion
for finite Reynolds number flows suitable to be solved numerically, and
to be independent of the choice of algorithms.
A spectral/*hp* element
direct numerical method is also used to solve the time dependent
Navier-Stokes equations for flow through
periodic arrays of cylindrical and spherical particles.
The DNS calculations more
accurately model the flow dynamics and is used
to validate the results of the force-coupling model.

The two dimensional problem was used as a test of the DNS and the
results agree well with those of other numerical simulations. Analyzing the three dimensional
problem proved to be informative. Determining the relationships between
the superficial velocity or sedimentation velocity, the external force
on the particles and flow structure as the volume fraction and Reynolds
number are varied were the main goals. For Stokes flow conditions the sedimentation
velocity decreases as the volume fraction is increased. At finite Reynolds
numbers, this is countered by an interaction between the particles and
the wakes when the system is dilute. As the volume fraction increases,
the velocity is hindered by the particles and the settling rate decreases
so that the flow experiences a *blocking effect*. Flow separation
is delayed till higher Reynolds numbers. Comparing the force-coupling model
for spherical particle motion in dilute flows to the DNS show that it successfully
captures the flow dynamics and reproduces observed flow characteristics
from experimental data as well. As a first approximation method it proves
to be efficient and consistent.