  Two-way coupled DNS simulation of particle-laden turbulent Couette-flow [1],
in the volume fraction regime $\phi>10^{-4}$, showed a discontinuous decrease
of turbulence intensity beyond a critical volume fraction
$\phi_{cr}\sim7.875\times10^{-4}$. Due to the presence of high inertial
particles, the drastic reduction of shear production of turbulence is found to
be the main cause for the discontinuous attenuation of turbulence. In this
article, particle-phase statistics is explored. The two-way coupled DNS reveal
that the mean-square velocity profiles in cross-stream (y) and span-wise (z)
directions are flat and increase with $\phi$ as the higher frequency of
collision helps in transferring streamwise momentum to span-wise and
wall-normal directions. Whereas, streamwise fluctuations decrease and tend
become flatter with increase in loading. In the regime with $\phi>\phi_{cr}$,
the particle velocity fluctuations drive the fluid phase velocity fluctuations.
Additionally it is observed that one-way coupled DNS and Fluctuating Force
Simulation (FFS) [2] are capable to predict the particle phase statistics with
reasonable accuracy in the regime $\phi<\phi_{cr}$ where wall-particle
collision time and inter-particle collision time is lesser than viscous
relaxation time of the particles. For, $\phi>\phi_{cr}$, a significant error in
the prediction from one-way coupled DNS and FFS is observed due to the
limitation of FFS in capturing the turbulence attenuation and the change in
mean fluid velocity profile. A modified FFS model (M-FFS) is successfully
developed in this article with modified mean fluid velocity profile and
zero-diffusivity.
