From Kinetic Theory to Hydrodynamics: re-imagining two fluid models of particle-laden flows

A number of important technologies involve the manipulation of particle-laden flows. These include pharmaceuticals manufacturing, power plant technologies, food processing, and many others. Various environmental protection and safety issues are rooted in the understanding of the dynamics of granular flows, for example, avalanches, sandstorms, and city air pollution. Models for these are traditionally derived from analogies with dilute gases at the statistical level, and from conventional fluid mechanics at the continuum level. Rapid granular flows are, however, known experimentally to display a variety of rheological and flow physics not seen in conventional fluid flows.

Previous research in modelling rapid granular flows has co-opted transport models developed for rarefied gases under strong non-equilibrium. This approach produces constitutive equations that incorporate high order gradient terms (the best known of which are the Burnett and super-Burnett set of equations). However, this higher order hydrodynamics is known to violate several fundamental thermodynamic and mechanical properties.

Alternative phenomenological approaches have been developed separately, which draw on continuum mechanics approaches. These, however, cannot at present always claim to provide good predictions of the various phenomena exhibited by rapid granular flows. Flow behaviour in the moderate solid volume fraction regime, and the transitions between different flow regimes, are still complex, controversial and problematic.

In this project we will attempt to resolve some of these problems by developing and testing sophisticated new models within a two-fluid approach to dilute granular flows. These models will be founded on a sound understanding of both the micro-scale fluid dynamics and the non-equilibrium particle statistics. Better resolution of the fundamental physics of both particle/particle and fluid/particle interactions will enable new constitutive equations that leapfrog the predictive capabilities of phenomenological models. Our new models will be implemented in the open source computational fluid dynamics software OpenFOAM, in a form suitable for both future research and industrial simulation.