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bump around a post
” has to be made, and analytical approaches we fear fail because of the
dramatic consequences of small perturbations.
Figure 3.5
Experimental points of the particle diameter divided by the gap, versus the row shift fraction,
ε
.
For this work (in black) and that of Huang
et al.
(in grey), open points represent bump mode
and solid points represent zigzag mode. Zigzag mode particles follow the streamlines, while
bump mode particles follow the array slope,
ε
.
A feeling for the sensitivity of the motion of particulates to local variations in the
stream flow can be seen by simply examining the velocity field in an array of posts in the
vicinity of the stall points. At the stall point analytical techniques fail and it is necessary to
go to hydrodynamic code simulations, although even those fail when a particle is present!
We will not go into this complex subject here, nor will we attempt to discuss the harder
problem of addressing the number of steps required to sufficiently resolve the space
between particles and posts and the number of post interactions required to accrue a
significant bump displacement in a computational simulation.
We present, to get some flavour for the problem, a full N-S simulation of the fluid
flows around the posts in a bump array using the software package COMSOL.
14
There are
three figures, which present firstly the velocities and pressure profiles (Figure 3.6) and
secondly the forces moving the particles (Figure 3.7 and Figure 3.8).
There is always a danger when working with simulations that intuition gets
thrown out the window and with that a real understanding of the physics of the problem.
However we find these simulations most illuminating. To illustrate some of the fluid
dynamic behaviour in a bump array, we chose a two-dimensional geometry based on
reference [12] with ε set to 0.1. However, the methods presented here should be general
since the full N-S equation is used. A two-dimensional simulation should be a good
approximation over much of the channel, although aspects such as the Dean flow we
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