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

Lead Research Organisation: Heriot-Watt University
Department Name: Sch of Engineering and Physical Science

Abstract

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.

Planned Impact

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.

Publications

10 25 50
 
Description Several gas phase models have been developed and tested (refer to list of publications). These models allowed better predictions of phenomena such as, shock waves, gas flows in micro-channels and other non-continuum effects in gases. Granular phase models being currently developed and tested incorporate physics that classical theory does not include. The models are being tested as to whether they capture various particle organization within particle-laden flows.
Exploitation Route Key outcomes of this funding may be taken forward by others to explore the safe design and operation of power plants (e.g. transport of solid fuel grains), handling of natural phenomena (e.g. pyroclastic flows from volcanoes), pharmaceutical manufacturing (e.g. conveying of pills), and clean technology (e.g. fine dust particle control). These outcomes can also be used to better understand phenomena such as cluster formation and wave patterns that occur in particle-laden flows and others. This funding outcomes may also be taken to investigate other applications, including windblown sand and the multiscale processes in avalanche flows or extension of the models to multiphase flows where the carrier fluid is a liquid rather than a gas.
Sectors Aerospace, Defence and Marine,Agriculture, Food and Drink,Chemicals,Electronics,Energy,Environment,Transport,Other

 
Description From Kinetic Theory to Hydrodynamics: re-imagining two fluid models of particle-laden flows
Amount £412,289 (GBP)
Funding ID EP/R007438/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 01/2018 
End 12/2021
 
Description The Leverhulme Trust: Research Project Grants
Amount £255,000 (GBP)
Funding ID RPG-2018-174 
Organisation Heriot-Watt University 
Sector Academic/University
Country United Kingdom
Start 11/2018 
End 01/2023
 
Description ICNAAM 2019 17th International Conference of Numerical Analysis And Applied Mathematics, Rhodes, Greece, September 2019, in AIP Proceedings 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact A talk: SK Dadzie and MH Lakshminarayana Reddy, Recasting Navier-Stokes equations: shock wave structure
description, ICNAAM 2019 17th International Conference of Numerical Analysis And Applied
Mathematics, Rhodes, Greece, September 2019, in AIP Proceedings
Year(s) Of Engagement Activity 2019
URL http://history.icnaam.org/icnaam_2019/icnaam.org/index-2.html
 
Description Presentation at 31st International Symposium on Rarefied Gas Dynamics held at Technology & Innovation Centre, University of Strathclyde, Glasgow (July 23-27, 2018) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I gave a presentation on "Thirty-Five Moment Theory for Dilute Smooth Hard Sphere Gases". It attracted people who are working on Moment closure methods and later benefited from discussions with them.
Abstract:
Modeling transport phenomena in a gas under rarefied conditions pose unique challenges. One needs to develop accurate hydrodynamic models that can be used for the modeling of flows in the rarefied regime - the well-known standard hydrodynamic equations are inappropriate since continuum hypotheses are violated. Rarefied gas flows are well described
by the Boltzmann equation and the solution to the same via Discrete Simulation Monte Carlo (DSMC) technique will be more useful, but this method is restrictive with regards to computational requirements. Due to the complexities associated in solving Boltzmann equation, there have been significant attempts made to formulate alternative solution methods that can provide an accurate description of a gas in the rarefied regime. Further, modeling rarefied or non-equilibrium gas flows requires a 'beyond Navier-Stokes-order' description in terms of an extended set of hydrodynamic fields. Moment closure methods play an important role in handling the behaviour of non-equilibrium gases by assuming the distribution function with more degrees of freedom. In general it is assumed that the addition of more moments in a closure approximation gives rise to a system of moment equations, which approximate non-equilibrium flows accurately. Best known approach for obtaining a closed moment system is the Grad's moment method, in which the distribution function is expanded in terms of Hermite polynomials in the components of the fluctuating velocity with the Maxwellian as weight function. In this work, we employ the Grad's method of moments to derive higher-order moment closure, namely, the 35-moment system, for smooth hard-sphere gas.
Year(s) Of Engagement Activity 2018
URL http://www.jwfl.ac.uk/event_detail.cfm?pid=07C7020B-AC36-4F5B-BA23-1BE3EC1C67D9
 
Description Presentation at UK Annual Workshop on Multiscale Fluid Dynamics, Scottish Universities Insight Institute, Glasgow (December 18 -19, 2018) 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Gave a talk on "Recasting Navier-Stokes: stationary planar shock wave problem revisited" at this workshop.
Year(s) Of Engagement Activity 2018
 
Description UKFN Special Interest Group (SIG) in Multiscale and Non-Continuum Flows 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact A talk on our current research progress at the UKFN Special Interest Group (SIG) in Multiscale and Non-Continuum FlowsWindermere, UK, December 2019 Invited by Prof Duncan Lockerby
Year(s) Of Engagement Activity 2018,2019
 
Description Workshop on Complex Heterogeneous Systems (CHeSs), Heriot-Watt University, UK, June 2018 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I gave a talk on entitled: "Constitutive Equations Beyond the Navier-Stokes-Fourier System" at this workshop.
Year(s) Of Engagement Activity 2018