Author:
SUNDARAM SHIVSHANKAR,COLLINS LANCE R.
Abstract
Direct numerical simulations of heavy particles suspended in a
turbulent
fluid are performed to study the rate of inter-particle collisions as a
function of
the turbulence parameters and particle properties. The particle volume
fractions
are kept small (∼10−4) so that the system is well
within the
dilute limit. The fluid velocities are updated using a pseudo-spectral
algorithm
while the particle forces are approximated
by Stokes drag. One unique aspect of the present simulations is that the
particles
have finite volumes (as opposed to point masses) and therefore particle
collisions
must be accounted for. The collision frequency is monitored over several
eddy
turnover times. It is found that particles with small Stokes numbers behave
similarly to the
prediction of Saffman & Turner (1956). On the other hand, particles
with
very large
Stokes numbers have collision frequencies similar to kinetic theory (Abrahamson
1975). For intermediate Stokes numbers, the behaviour is complicated by
two effects:
(i) particles tend to collect in regions of low vorticity (high strain)
due
to a centrifugal
effect (preferential concentration); (ii) particle pairs are less strongly
correlated with
each other, resulting in an increase in their relative velocity. Both effects
tend to
increase collision rates, however the scalings of the two effects are
different, leading
to the observed complex behaviour. An explanation for the entire range
of Stokes
numbers can be found by considering the relationship between the collision
frequency
and two statistical properties of the particle phase: the radial distribution
function and the relative velocity probability density function. Statistical
analysis of the data, in
the context of this relationship, confirms the relationship and provides
a quantitative
description of how preferential concentration and particle decorrelation
ultimately
affect the collision frequency.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
496 articles.
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