In collaboration with T. Weinhart (PostDoc), S. Luding, O. Bokhove, R. Hartkamp (PhD student) and D.Tunuguntla (PhD student, recently started).

The project investigates dry granular flows on inclined channels with local constrictions and obstacles, using discrete

element models (DEM) and Discontinuous Galerkin Finite Element Models (DGFEM). The effects of poly-dispersity and non-uniform shape of the particles will be studied for both rotating and non-rotating situations. The main challenges in the modeling of these flows is understanding the effect of rotation, particle segregation and how to deal with the co-existence of rapid and slow regimes.

Granular avalanche flows are common to natural environments and industry. They occur across many orders of magnitude.

Examples range from rock slides, containing upwards of 1000m3 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 influenced by many factors such as: poly-disperity; variations in density; non-uniform shape; complex basal topography; surface contact properties; coexistence of static, steady and accelerating material; and, flow obstacles and constrictions.

Discrete Particle Methods (DPMs) are an extremely powerful way to investigate the effects of these and other factors. With the rapid recent improvement in computational power the full simulation of the flow in a small hour glass of millions of particles is now feasible. However, complete DPM simulations of large-scale geophysical mass flow will, probably, never be possible.

One primary goal of the present research is to simulate large scale and complex industrial flows using  granular shallow-layer equations. So far we have taken the first step of using the DPM to simulate small granular flows of mono-dispersed spherical particles in steady-flow situations.  The DPM simulations undertaken to date will enable the construction of the mapping between the micro-scale and macro-scale variables and functions (the Micro-Marco transition), thus enabling construction of a closed set of continuum equations. These mappings (closure relations) can then be used in continuum shallow-layer models and compared with full DPM simulations (DPMs). For certain situations, precomputed closures should work; but, in very complicated situations the pre-established relations may fail.

So far the Micro-Macro transition has been investigated for basal friction (see pubs. [13,17]), closure relations required for shallow-granular models (i.e. velocity shape factor, normal stress difference and basal frictions), see pub. [13], and for binary size particles segregation, see pub. [14]. To perform the micro-macro transition for basal friction a new method of mapping micro-macro variables had to be developed that is valid near a boundary, see pub. [12]. Finally, the Micro-Macro transition has been used to investigate a framework for a fully three dimensional description of flowing granular materials, see pub. [19].

When simple precomputed closures law fail, heterogeneous, multi-scale modelling (HMM) is then an alternative in which the local constitute relations are directly used in the continuum model. In HMM, continuum and micro-scale models are dynamically coupled with a two-way communication between the different models in selective regions in both space and time, thus reducing computational expense and allowing simulation of complex granular flows.

In the future the project will focus on developing a heterogeneous multi-scale model, coupling macro-scale continuum with micro-scale discrete particle models, using integrated DEM and DGFEM. The coupling will be done at selective regions in space and time thus reducing computational expense and allowing simulation of the complex granular flows under study.