Continuum modelling of a granular superstable heap #

Hollie Lloyd, J M N T Gray, C G Johnson, G K Reynolds

10:30 Wednesday in 4Q07.

Part of the Granular and multiphase flows session.

Abstract #

There are many advantages to having a predictive model for granular materials from both an industrial and geophysical perspective. The development of a rheological model which captures all granular behaviour remains a highly active area of research; complicated by the diverse behaviour granular systems exhibit. For flowing granular materials, a key development was the dependence of the granular inter-particle friction μ on the dimensionless inertial number I, and the functional form of this relationship known as the μ(I)-rheology. In this rheology, granular materials can be modelled as an incompressible, viscoplastic fluid, where the viscosity depends on the inter-particle friction; this has been widely used with success. When investigating the behaviour of granular materials, oftentimes small scale experiments are used which are only a few grain diameters wide and confined by transparent sidewalls; from which experimental measurements are taken. The influence of these confining sidewalls is frequently neglected, when the effects of such a confinement are non-negligible. By implementing a width averaged sidewall friction force; this effect is accounted for in a two dimensional system. Another limitation of granular material modelling is freefalling granular material. This behaviour exists in the granular gas regime; which is beyond the capability of the μ(I)-rheology. This limits the capacity of simulating filling problems; present in many industrial settings. Using numerical techniques, an artificial freefalling jet can be established, to allow for filling to occur. A granular superstable heap requires the successful implementation of wall friction forces and a freefalling jet in order to form, making it an appropriate test case to validate our model. In this work, numerical simulations are performed and compared with experimental and theoretical results to demonstrate its success.