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Which scaling law to apply for coarse-graining?

Hi all,

i'm struggling with some coarse-graining simulations for a simple angle of repose test and wanted to tap into the knowledge of other users.

In literature there are some approaches on how to scale material parameters when scaling down the particle sizes. For example Chen [1] uses scaling laws for the surface energy and the Young's Modulus. If i apply them, i see however, that for smaller particle sizes this does not fit the original simulation. Chen gives as rules: surface energy scales with CGF ^2 and Young's Modulus scales with CGF ^2.5.

I myself scale the surface energy so that the total cohesion force in the JKR model is the same for all particle sizes. This gives reasonable results when scaling up, when scaling down however it gives also to low angles of repose (however not as bad as Chen)

As this is such an important topic in DEM simulation i wanted to ask, what other users usually use to scale there particles up or down?

Thanks!

[1] https://api.repository.cam.ac.uk/server/api/core/bitstreams/c34dbffb-ef12-4168-a735-488925715606/content

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Stephen Cole

Hi Clemens,

It would be good to hear from some other EDEM users as you say. For myself I'd say the Angle of Repose test doesn't fit well for scaling particles as it can be quite a dynamic case and the inertia of the particles influences the results. You also want to ensure the coordination number in the system remains approximatly the same.

Something like a shear cell test is better for coarse graining if we are looking at more semi-static flows.

For the EEPA model and powders we have some guidance here:

EDEM Technical report: Calibrating DEM models for Powder Simulation

Regards

Stephen

Clemenslischka

Hi Clemens,

It would be good to hear from some other EDEM users as you say. For myself I'd say the Angle of Repose test doesn't fit well for scaling particles as it can be quite a dynamic case and the inertia of the particles influences the results. You also want to ensure the coordination number in the system remains approximatly the same.

Something like a shear cell test is better for coarse graining if we are looking at more semi-static flows.

For the EEPA model and powders we have some guidance here:

EDEM Technical report: Calibrating DEM models for Powder Simulation

Regards

Stephen

Hi Stephen,

very much appreciate your answer! Glad to hear, that angle of repose test is indeed a challenge when scaling the particles. In light of this i'm quite satisfied with the results. Coordination number, total mass and heigth of the different cases seem to be acceptable.

I'm thinking on using the parameters to test them in a different setup, the rotating cylinder. What confuses me a bit a the moment is the Cohesion Force. I exported the normal overlap of the particles and calculated the Cohesion Force based on the JKR model description in the manual. With an average normal overlap of 0.0002 mm i calculate a normal force that is 2000 times lower than the gravitational force per particle, which gives me very low Bond numbers <0. Is this in general the correct way to calculate the Cohesion force by hand with the normal overlap? Other studies give Bond numbers > 1 or > 10 in DEM simulations for cohesive powders.

Thank you!

Stefan Pantaleev_21979

Hi Stephen,

very much appreciate your answer! Glad to hear, that angle of repose test is indeed a challenge when scaling the particles. In light of this i'm quite satisfied with the results. Coordination number, total mass and heigth of the different cases seem to be acceptable.

I'm thinking on using the parameters to test them in a different setup, the rotating cylinder. What confuses me a bit a the moment is the Cohesion Force. I exported the normal overlap of the particles and calculated the Cohesion Force based on the JKR model description in the manual. With an average normal overlap of 0.0002 mm i calculate a normal force that is 2000 times lower than the gravitational force per particle, which gives me very low Bond numbers <0. Is this in general the correct way to calculate the Cohesion force by hand with the normal overlap? Other studies give Bond numbers > 1 or > 10 in DEM simulations for cohesive powders.

Thank you!

Hi Clemens,

In the dynamic flow regime I 'd scale the adhesion parameters to maintain the bond number (as apposed to the scaling for the quasi-static flow regime where the adhesion energy per unit volume is maintained). I'd also keep the stiffness un-scaled although the effect of the stiffness on low stress dynamic flows is not very significant in any case. As Stephen is says, scaling in the dynamic flow regime is complex and limited so I'd expect the scaling to hold for factors of between 2 and 4.

Some useful papers:

Mohajeri, M. J. et al. (2020) ‘A hybrid particle-geometric scaling approach for elasto-plastic adhesive DEM contact models’, Powder Technology. The Authors, 369, pp. 72–87. doi: 10.1016/j.powtec.2020.05.012.

Saruwatari, M. and Nakamura, H. (2021) ‘Coarse-Grained Discrete Element Method of Particle Behavior and Heat Transfer in a Rotary Kiln’, Chemical Engineering Journal. Elsevier B.V., p. 130969. doi: 10.1016/j.cej.2021.130969.

Of the above the first one is very similar to my advice above, is most practical but is also inadequate for scaling the AoR for factors beyond 2. The second paper goes further by scaling the damping and stiffness and good results are shown up to scaling factor of 4 (things start to break down progressively after that).

Best regards,

Stefan