About smoothing and time-averaging of particle velocity (Us)

Dear CFDEM community,

I am simulating a pipe flow using DNS-DEM with smoothing model since the particle size is larger than the mesh size. The model works fine as the predicted concentration profiles and velocities are in good agreement with experimental data. However, regarding the averaged particle velocity (Us) in a cell, smoothing for the Us is performed to “fill in” values in cells void of particles and values calculated in the cells (via Lagrangian-To-Euler mapping) are NOT changed, as suggested by the code

******************************************************************************
solve
(
fvm::ddt(vSmoothField)
-fvm::laplacian( DT_, vSmoothField)
==
NLarge / deltaT * vSmoothField.oldTime() //add source to keep cell values constant
-fvm::Sp( NLarge / deltaT, vSmoothField) //add sink to keep cell values constant
);
*******************************************************************************

I am wondering

1) What should be the smoothing lengthscale for Us?

Typical smoothing length for voidfraction and Ksl is 3*dp (particle diameter), and as the documentation suggests, the smoothing lengthscale for Us should be the equal or larger than that used for voidfraction and Ksl. I've ran simulations with different smoothing lengthscale for Us from 1dp to 4dp, the results indicate no difference on the concentration and bulk flow velocity prediction, except the particle velocity (Us) profile is different due to different smoothing scale, which is expected. Is this because the "Us" is only smoothed to "fill" in cells void of particles, and smoothing length for Us doesn't have much effect on the results?

2) How to correctly get time-averaged Us since it's been smoothed? I've attached a mean velocity profile plot, the blue line is time-averaged fluid velocity U, red line is the time-averaged smoothed Us and black cross is time-averaged particle velocity (vs) in liggghts. There is a huge difference between the two particle velocity profiles. Is there anyway that maybe we don't need to smooth the particle velocity and set particle velocity as fluid velocity in cells void of particles, as to get a better fit as suggested by the black cross symbols. Thanks.

Cheers,
Enzu