Divergence in hopper flow using DDPM and DEM Collision
 

Hello CFD community,

I am modeling a hopper type multiphase/granular flow of sand particles and air, driven by gravity, with the DDPM and “DEM Collision” models in Fluent 16.2. As I have read in other research, a transient approach is necessary for a hopper simulation, where first particles are injected into the domain and allowed to come to rest (with hopper outlet closed), and then the outlet is opened and particles/air flow out.

A number of time steps after injecting particles, I always get divergence due to “pressure correction” or “pressure coupling”.

Divergence happens after a number of time steps, but it is my impression that it is when the particles start to collide and interact. For example, if I inject a burst of particles from the right boundary (as shown in the attached image showing Volume Fraction of particles), a logical solution is found at each time step until the particles hit the tapered surface, at which point it immediately diverges. (In this setup, the top, tapered-top, left, and bottom surfaces are walls, and the right surface is a “pressure-inlet” with an injection along the surface. Gravity is pulling particles to the left. )

I have tried and checked many parameters to get convergence:
- Set Under-Relaxation factors to 0.01
- Time step 5e-5
- Particle diameter is definitely less than element size
- Gravity on/off (doesn’t seem to make a difference)
- DPM Collision settings – reduced dramatically down to k = 100 and eta = .2
- Solving Volume Fraction equations only (neglecting fluid) – works, but when turning fluid equations back on it immediately diverges.
- Solvers – PC Simple or Coupled, tried both
- Granular material properties and models – tried various and used recommendations from research
- Mesh Info – Maximum Orthogonal Skew is .013, Minimum Orthogonal Quality is .99, and Maximum Aspect Ratio is 1.9. I believe these all show an adequate mesh.

Any advice on why I have this consistent divergence would be very helpful and appreciated. I have not yet found a good example or tutorial on this type of dense flow using Fluent, but if/when I solve this I will post the details to help the CFD community!

can you share your case file. let me try it myself first.

Hi,

Just a thought. Before you inject your particles into the hopper, is it filled with air? Did you assign air as the primary phase here? Did you also patch it in the hopper zone?

-BB

Thanks for your thoughts and ideas!

I am attaching a cas and data file showing injected particles which have not yet hit the tapered section.

Yes, air is the primary phase, and I initialize the domain to have a volume fraction (of sand) of 0, so it is filled with air only.

The files are now attached to this post.

Hello did you get a solution for your case?
 

Hello did you make sure that the parcel size is less than minimum cell size in your mesh?

Hello and thank you for the reply-

Yes, I did indeed check this and tried various parcel sizes, even a single particle per parcel. I did not ever find a real solution, though I will say that the Ansys tutorial "Modeling bubbling fluidized bed using DDPM+DEM" was very helpful.

While not 100% positive, I believe some of my problems were arising from the fact that the width of my geometry is ~10 mm, and the particles are ~.3 mm in diameter. I believe the mesh size should be several times the particle size - let's say 5. This means my geometry can only have 10/(5*.3), or ~seven cells across, which is not very fine mesh at all! The tutorial works fine, but when keeping all else the same and reducing the geometry size I get divergence every time (even after trying all sorts of things).

During this study, I also built a Matlab script to output an injection or ".inj" file, which I will attach in (.txt format), that lets you inject a group of particles given some x, y, and z boundaries. I hope others will find this useful!