How to control/achieve the expected particle volume fraction in CFDEMcoupling simulations

Hello All,

I am simulating a particle-fluid flow case using cfdemPisoSolver.

My physical problem is like this.
The geometry is a cylinder (D1=4.5" and L=21.75cm) and there is a hole (D2=0.4") on the side of the cylinder. The central axis of the cylinder is y-direction and so y=0-21.75.
Boundary conditions could be like this:
Inlet: fixed fluid velocity (vfluid=1033cm/s) pointing into the cylinder and the particle could be injected from the inlet (y=0) and has the same velocity as the fluid;
Outlet: fixed pressure (P=0);
Hole (its position is around y=9-10): fixed fluid velocity (vhole=13073cm/s) pointing out of the cylinder, which means the particle&fluid would flow outside the cylinder through the hole.

My simulation condition is the "injected" particle volume fraction is 0.043.
I have tried two particle insertion approaches.
Approach 1:
fix ins nve_group insert/stream seed ${seed6} distributiontemplate pdd1 maxattempt 50000 all_in yes massrate ${Propp_mr} mass ${tot_mass} vel constant 0 ${vfluid} 0 overlapcheck yes insertion_face ins_face extrude_length 0.1
# The insertion_face is y=0 cross-section, which means this approach injects the particles at y=0.
# I monitored the particle volume fraction of the regions before the hole (y=0-2; 2-4; 4-6; 6-8).
Approach 2:
region simwell cylinder y 0 0 5.715 1 4 units box #5.715cm is the cylinder radius
variable insertstep equal round(3/${vfluid}/${simstep}/1.5)
fix ins nve_group insert/pack seed ${seed6} distributiontemplate pdd1 maxattempt 50000 all_in yes vel constant 0 ${vfluid} 0 insert_every ${insertstep} overlapcheck yes volumefraction_region ${conc} region simwell ntry_mc 50000
# For Approach 2, you can see that I have a particle insertion "region" y=1-4 instead of injecting particles at y=0.
# I monitored the particle volume fraction for the regions y=1-4 (insert region) and 5-8.

My questions/problems are as follows.
1. With Approach 1, for most cases, I can have the volume fraction as the expected value 0.043. But in some cases, the particle volume fraction is smaller than 0.043. Specifically, for example, the case with vfluid=1033cm/s and vhole=13073cm/s, I could achieve the expected volume fraction. But for the case with vfluid=52cm/s and vhole=654cm/s (other simulation parameters are the same), the particle volume is smaller than 0.043.

2. With Approach 2, I found that it is not trivial to achieve the expected particle volume fraction. The particle volume fraction in the insert region (y=1-4) is always smaller than 0.043, and the region y=5-8 might be smaller or larger than 0.043, which depends on the "insertstep" value. The "insertstep" parameter could affect the particle volume fraction a lot. When "insertstep" is larger, the particle volume fraction (in the region y=5-8) is smaller. When "insertstep" is smaller, the particle volume fraction (in the region y=5-8) is larger.

Your valuable comments/suggestions would be very very appreciated!

Best regards,
Min