## Computational multi-scale modeling of super-dispersed multiphase flows

### Organization:

Funded by: IMPACT

Postdoc: Thomas Weinhart

Supervisor: Onno Bokhove / S. Luding

Collaboration: Dr. A.R. Thornton

### Description:

Dry granular avalanche flows are a common occurrence in both the natural geophysical environment and industry, and occur across many orders of magnitude. Common examples range from: rock slides,

containing upwards of 1000m^3 of material; to the flow of sinter, pellets and coke into a blast furnace for iron-ore melting; down to the flow of sand in an hour-glass.

The dynamics of these flows are complicated by many factors; for examples: polydisperity, variation in density, non-uniform shape, surface contact properties, flow obstacles and constrictions, etc...

Molecular Dynamics (DPM) algorithms are an extremely powerful tool to investigate the effects of these and other factors and with the rapid recent improvement in computational power the full simulation of the

flow in a small hour glass is now obtainable. However the full DPM simulation of real geophysical mass flow, will probably, never be possible.

Continuum models are able to simulate the volume of real geophysical flows, but have to make averaging approximations reducing the properties of over a trillion individual particles to a handful of averaged quantities. Once these average parameters have been tuned via experiment or historical data these models can be surprisingly accurate; but, a model tuned for one flow configuration often has no prediction power for other setup. DPM can be used to obtain the mapping between the microscopic and macroscopic parameters allowing determination of the macroscopic data without the need for a-piori knowledge. In simple situations it is possible to pre-compute the translation between the particle and continuum; but, in more complicated situations heterogeneous multiscale modelling is required (HMM). In HMM continuum and micro models are dynamically coupled with two way feedback between the models. The coupling is done in

selective regions in space and time, thus reducing computational expense and allowing simulation of the complex granular flows.

We start by consider the flow of granular material down an inclined chute. The flow can be described by a macroscopic model with the exception of the basal friction coefficient, which requires microscopic modeling with a shorter spatial and temporal step size.

For the HMM the macroscopic behaviour is described by a Discontinuous Galerkin discretization of the shallow water equations with unknown bottom friction coefficient. A Discrete Particle Model is used to compute the undetermined basal friction coefficient and hence close the model. The microscopic model requires a short time scale, but is assumed to relax rapidly in time. The model is implemented in hpGEM.

The model is tested against the Pouliquen-Jenkins flow rule for rapid granular flow along an inclined chute with rough base. We simulate granular flows through a contraction and show speed comparisons with the microscopic model to demonstrate the effectiveness of the algorithm.

The DPM code developed as part of this project is available for public use, for more information please via the codes website at http://www2.msm.ctw.utwente.nl/athornton/MD/