(116b) Head Formation in Bidisperse Shallow Granular Flows

Size-segregation plays an important role in many industrial and natural systems. This is particularly relevant for shallow granular flows, where segregation has a significant influence on the flow behavior. Applications range from industrial chutes and hoppers to the prediction of natural hazards.

In these situations, particles segregate vertically by size, with larger particles on top of smaller particles. As the surface velocity of such flows is larger than the mean velocity, the larger material is transported to the flow front. This causes size-segregation in downstream direction, resulting in a flow front composed of purely large particles. As large particles are generally more frictional, the mobility of the flow front is reduced, resulting in a so-called bulbous head.

One of the main challenges of simulating granular flows is the enormous number of particles they contain, which makes discrete particle simulations too computationally expensive to be practically useful. Continuum methods are able to simulate the bulk flow and segregation behaviour of such flows, but have to make averaging approximations to reduce the huge number of degrees of freedom to the relevant continuum fields. We use a depth-averaged model to predict the flow profile for such flows, based on flow height, depth-averaged velocity and particle-size distribution [1]. Small-scale periodic discrete particle simulations are used to determine the material parameters of the continuum model.

In this talk, we show that the bulbous head structure emerges naturally from this depth-averaged continuum framework, and that the long-time behaviour of this solution of the depth-averaged continuum model converges to a novel travelling wave solution [2]. Furthermore, we validate a simple 1D continuum level simulation against a computationally expensive 3D particle simulation, where we see surprisingly good agreement between both approaches, considering the approximations made in the continuum model. We conclude that the travelling distance and height of a bidisperse granular avalanche can be well predicted by our continuum model.

REFERENCES

[1] M. J. Woodhouse, A. R. Thornton, C. G. Johnson, B. P. Kokelaar and J. M. N. T. Gray, J. Fluid Mech., 709, 543-580 (2012)
[2] I.F.C. Denissen, T. Weinhart, A. Te Voortwis, S. Luding, J.M.N.T. Gray and A.R. Thornton, under review with J. Fluid Mech. (2017)