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.

Impact from this project will be academic, industrial, environmental and societal. With the target of effective low-carbon economies by 2050, national governments are instituting ambitious climate and energy policies in order to reduce CO2 emissions. These policies require both increased efficiency of current industrial processes, as well as new process design. Among the clean power plant technologies under development are Fluidized Bed Reactors. This research project is about creating an advanced kinetic theory that will ultimately help the simulation and design of industrial processes involving the flow of solid grains or particles. The major deliverable is a tractable design methodology (as software) that will provide enhanced capabilities to manufacturers of new products and future energy-generation processes. This software will be a design tool for a diverse range of transformative technologies that have potential for major societal and economic impact.

These opportunities are reflected in-project by collaborations with two major overseas organisations (see Letters of Support). As early-adopters of the project outcomes, they will be immediate beneficiaries of this project, and assist us in identifying new technology application areas. They have identified clear long-term potential in this research for the technical capabilities they will need to provide to customers and stakeholders in the future.

In addition to conventional routes to international academic impact, we plan a series of user engagement activities that include workshops and new training courses to accelerate the adoption of both the software and the new modelling methodologies within industrial and academic networks. Both academic and industrial users of the open-source software outcomes will benefit from being enrolled in a new community of multidisciplinary engineers engaged in improved granular flow simulation for design.