Biomedical Engineering Reference
In-Depth Information
Fig. 9.9
Velocity vector plot in the
y
-
z
plane in the presence of
τ
+
=
20 with mass loading of 20 %
in
a
one-way coupling and
b
four-way coupling
As a result, the particle aerodynamic interaction could influence the particle collision
rate, as well as the particle and fluid phase fluctuations. The collisions were assumed
to be binary since multiple collisions are extremely rare at the particle concentrations
that were considered.
To perform a direct numerical simulation, the CFD code used a pseudo-spectral
method for computing the fluid velocity field. That is, the fluid velocity is expanded
in a three-dimensional Fourier-Chebyshev series. The fluid velocity field is expanded
in Fourier series in the
x
- and
z
-directions, while a Chebyshev series is used in the
y-direction. The code uses an Adams-Bashforth-Crank-Nickolson (ABCN) scheme
to compute the nonlinear and viscous terms in the Navier-Stokes equation and per-
forms three fractional time steps to advance the fluid velocity from time step (
n
)
to time step (
n
1). The details of the numerical techniques were described by
McLaughlin (1989).
Particles were uniformly distributed in the channel, and the initial velocity of each
particle was set equal to the local fluid velocity evaluated at the centre of the parti-
cle. All results are averaged over the simulation time, and over the streamwise and
spanwise directions. Figure
9.9
a, b shows the results of one-way coupling compared
with four-way coupling which indicates that the presence of solid particles damps the
turbulence fluctuations and also decreases the number of eddies. Two-way coupling
refers to particle-fluid interactions only while four-way coupling is also inclusive
of particle-particle interactions. At sufficiently low particle volume fraction, two-
way coupling is adequate; however, with higher particle loadings, the collisions will
become dynamically significant and four-way coupling is required.
+
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