| Summary: | 博士 === 國立臺灣大學 === 應用力學研究所 === 85 === The average settling velocity of small heavy particles under a body force
field is studied numerically in homogeneous turbulence
generated by the direct nu
merical simulation(DNS) of the continuity and Navier-Stokes equations.The flow
field experienced by a particle is highly nonuniform, which is primarilydue t
o the coherent structures in turbulence. In isotropic turbulence, more particl
es tend to accumulate in the low vorticity regions with larger local downward
fluid velocities. The drag on the particle is less there, and thus the averag
e settling velocity of particles in turbulence is greater than that in still
fluid. It is found in the present study that the phenomenon of particle accumu
lation is controlled mainly by the small eddies with scalelw corresponding to
the maximum of the dissipation (vorticity) spectrum.However, the magnitude of
the increase of average settling velocity dependsstrongly on the large energet
ic eddies. As lw is in general of one order greater than the Kolmogorov length
scale, this study suggests that the large eddy simulation is also suitable fo
r the present problem provided that the smallest resolved scale is greater tha
n lw/2.5. When the mean shear is present, the intense vorticity is found to b
e or ganized in coherent, tubular or sheet-like, elongated vortices. Such vort
ices are orientated approximately along the direction of principal elongation
of the mean strain.The flow field is packed rather tightly with mainly two typ
es of basic fluid motion : the solid body rotation associated with the tubular
vorticesand the plane strain motion associated with the sheet-like vortices.
the flow field is quite compact in comparison with that in isotropic turbulenc
e. For particle settling through such sheared flow field under a body force pe
rpendicular to the mean flow, it is found that the particles lead the fluid in
the streamwise direction and fall faster (or slower) than the particles in st
ill fluid for small (or large) particle inertia and body force. The magnitudes
of the relative velocity components between the particle and the fluid in a
turbulent shear flow are greater (or less) than those in a corresponding lamin
ar shear flow for particles with small (or large) particle inertia and free fa
ll veloci ty. The preferential sweeping model proposed by Wang & Maxey(1993) f
or isotropic turbulence is modified here for understanding the behavior of the
settling velocity of particles in sheared turbulence. The present results may
find applications in the environmental engineering and the modelling of two-p
hase suspension flow.
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