Can unresolved CFDEM account for flow over a bed surface?

Submitted by fturney on Tue, 10/09/2018 - 19:14

I have been scouring the internet for an answer to this question and I can't seem to find anyone who has truly dissected it so I'll post the question here. If anyone knows of a paper or forum post that already addresses the following concerns that would, of course, be really helpful.

It seems to me, there are a number of errors that could occur in unresolved CFDEM when the fluid cell straddles the fluid-solid interface (the bed surface). Consider a tightly-packed static bed with fluid velocities perpendicular to the surface of the bed that will eventually dislodge some particles. Fluid speed drops rapidly beneath the surface of the bed where speed is nearly 0 less than 10 particle diameters deep. Consider fluid cells as cubes with side lengths equal to 4*(particle diameter), and also assume particles are monodisperse. Such is the case for my proposed sediment transport modeling.

I see two potential problems,

1) If the fluid cell straddles the bed surface (such that half the cell contains a static well-packed bed, and the other half contains empty fluid), on a sub-grid scale there is a sharp gradient in fluid volume fraction and fluid velocity from above the bed to beneath the bed. Despite that, my understanding is that the drag force on each particle is calculated using the fluid velocity and fluid volume fraction for the whole cell. This implies that particles that are one or two particle diameters deep into the bed will experience nearly the same drag force as exposed particles at the surface. This is unphysical as in reality particles at the surface will be protecting or sheltering particles beneath them from high wind speeds. The impact of this will be that particles beneath the surface will experience unrealistically high drag forces and the bed will become de-stabilized and move in an unrealistic way.

2) If the fluid cell straddles the bed surface, then the exact orientation of cell over the bed surface will impact the drag forces on any given particle within the cell, which is again unphysical. I've attached a drawing that shows the strange problem of cell orientation about the bed surface. Case A: If the cell contains mostly fluid, then the fluid volume fraction will be high, the wind speed will be high, and the drag force will be high on particles near the surface. Case B: If the cell contains mostly particles then the fluid volume fraction will be low, the wind speed will be low, and the same surface particles in case A will experience lower drag forces. This implies that choosing the correct orientation of the fluid cell about the bed surface would be very important to dislodgement of particles from the bed and that with a deformable surface (such as a developing ripple) it would be impossible to generate truly physical results.

I believe both these problems can be fixed by modifying the drag coefficient with an exposure term that quantifies a given particles exposure to the flow. Particles that are tightly packed and have particles on all sides should have very low drag coefficients and particles that are near the surface should have higher drag coefficients. I think a relevant exposure parameter to include would be based on something like the sum of the 8 or so nearest neighbor particles. I think such a modification could be quantitatively investigated using resolved CFDEM as the ground truth.

If anyone has any advice or reasons why these problems are not really problems I would be very grateful to hear your opinions.

Thanks,
Francis

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