We study finite-inertia effects on the collision rate of bidisperse heavy particles in
a turbulent gas, using direct numerical simulations and kinematic descriptions. As
shown previously for a monodisperse system (Sundaram & Collins 1997; Wang,
Wexler & Zhou 2000), a statistical mechanical description of the average collision
kernel consists of two parts, namely a description of the relative velocity between two
colliding particles (the turbulent transport effect) and of the non-uniform particle distribution
due to dynamic interaction of particles with coherent vortex structures (the
accumulation effect). We first show that this description remains valid and accurate
for a bidisperse system involving two groups of particles of inertial response time
τp1 and τp2, respectively. Numerical
results for the turbulent transport effect and the accumulation effect have been obtained as a function of
τp1 and τp2. Interestingly, the
accumulation effect in a bidisperse system is bounded above by that of a monodisperse
system. An explanation for this observation is given, in terms of the correlation
between concentration fields of the two size groups. Simulations show that particles
from two size groups were found in different regions of a vortex, thus reducing the
net accumulation effect in a bidisperse system. The turbulent transport effect, on
the other hand, is bounded below by the level in a monodisperse system, due to a
differential inertia effect. The above observations imply that the size polydispersity
enhances the turbulent transport effect but weakens the accumulation effect, relative
to a monodisperse system.
A simple eddy–particle interaction (EPI) model was developed and shown to give
a reasonable prediction of the collision kernel, except for a small parametric region
where both τp1 and τp2 are on the
order of the ow Kolmogorov time τk and thus
the accumulation effect must be included. A more accurate model incorporating both
the turbulent transport effect and the accumulation effect has also been developed.
The model would provide an upper bound on the collision rates for a non-dilute
bidisperse system, since turbulence modulation and particle-particle interactions are
not considered in this model.
Finally, some consideration is given to the effect of nonlinear drag on the collision
kernel. The results show that the drag nonlinearity can increase the collision kernel
slightly (less than 10%) at large particle inertia.