MechE Colloquium: Coupling rheology and segregation in granular flows
Event details
| Date | 28.09.2021 |
| Hour | 12:15 › 13:15 |
| Speaker | Prof. Nico Gray, Department of Mathematics, University of Manchester, Invited Professor at the Environmental Hydraulics Laboratory (LHE) of the school of Architecture, Civil and Environmental Engineering (ENAC) |
| Location | Online |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract:
During the last fifteen years there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the μ(I)-rheology (where μ is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This paper details theoretical and numerical frameworks (based on OpenFOAM®) which unify these currently disconnected endeavours. Coupling the segregation with the flow, and vice versa, is not only vital for a complete theory of granular materials, but is also beneficial for developing numerical methods to handle evolving free surfaces. This general approach is based on the partially regularized incompressible μ(I)-rheology, which is coupled to the gravity-driven segregation theory of Gray & Ancey (J. Fluid Mech., vol. 678, 2011, pp. 353–588).
These advection–diffusion–segregation equations describe the evolving concentrations of the constituents, which then couple back to the variable viscosity in the incompressible Navier–Stokes equations. A novel feature of this approach is that any number of differently sized phases may be included, which may have disparate frictional properties. Further inclusion of an excess air phase, which segregates away from the granular material, then allows the complex evolution of the free surface to be captured simultaneously. Three primary coupling mechanisms are identified: (i) advection of the particle concentrations by the bulk velocity, (ii) feedback of the particle-size and/or frictional properties on the bulk flow field and (iii) influence of the shear rate, pressure, gravity, particle size and particle-size ratio on the locally evolving segregation and diffusion rates. The numerical method is extensively tested in one-way coupled computations, before the fully coupled model is compared with the discrete element method simulations of Tripathi & Khakhar (Phys. Fluids, vol. 23, 2011, 113302) and used to compute the petal-like segregation pattern that spontaneously develops in a square rotating drum.
Link to the paper: https://doi.org/10.1017/jfm.2020.973
And movie: https://static.cambridge.org/content/id/urn:cambridge.org:id:article:S0022112020009738/resource/name/S0022112020009738sup006.mp4
Bio:
Nico Gray is a professor of Applied Mathematics in the Department of Mathematics and the Manchester Centre for Nonlinear Dynamics at The University of Manchester. He is an expert on granular flows and the particle segregation that takes place within them. This has applications to a wide range of common industrial processes, as well as to geophysical flows such as avalanches and debris flows. Nico holds a BSc in Mathematics from the University of Manchester, a PhD from the University of Cambridge and a Habilitation in Continuum Mechanics and Geophysical Mechanics from the Technical University of Darmstadt in Germany.
During the last fifteen years there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the μ(I)-rheology (where μ is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This paper details theoretical and numerical frameworks (based on OpenFOAM®) which unify these currently disconnected endeavours. Coupling the segregation with the flow, and vice versa, is not only vital for a complete theory of granular materials, but is also beneficial for developing numerical methods to handle evolving free surfaces. This general approach is based on the partially regularized incompressible μ(I)-rheology, which is coupled to the gravity-driven segregation theory of Gray & Ancey (J. Fluid Mech., vol. 678, 2011, pp. 353–588).
These advection–diffusion–segregation equations describe the evolving concentrations of the constituents, which then couple back to the variable viscosity in the incompressible Navier–Stokes equations. A novel feature of this approach is that any number of differently sized phases may be included, which may have disparate frictional properties. Further inclusion of an excess air phase, which segregates away from the granular material, then allows the complex evolution of the free surface to be captured simultaneously. Three primary coupling mechanisms are identified: (i) advection of the particle concentrations by the bulk velocity, (ii) feedback of the particle-size and/or frictional properties on the bulk flow field and (iii) influence of the shear rate, pressure, gravity, particle size and particle-size ratio on the locally evolving segregation and diffusion rates. The numerical method is extensively tested in one-way coupled computations, before the fully coupled model is compared with the discrete element method simulations of Tripathi & Khakhar (Phys. Fluids, vol. 23, 2011, 113302) and used to compute the petal-like segregation pattern that spontaneously develops in a square rotating drum.
Link to the paper: https://doi.org/10.1017/jfm.2020.973
And movie: https://static.cambridge.org/content/id/urn:cambridge.org:id:article:S0022112020009738/resource/name/S0022112020009738sup006.mp4
Bio:
Nico Gray is a professor of Applied Mathematics in the Department of Mathematics and the Manchester Centre for Nonlinear Dynamics at The University of Manchester. He is an expert on granular flows and the particle segregation that takes place within them. This has applications to a wide range of common industrial processes, as well as to geophysical flows such as avalanches and debris flows. Nico holds a BSc in Mathematics from the University of Manchester, a PhD from the University of Cambridge and a Habilitation in Continuum Mechanics and Geophysical Mechanics from the Technical University of Darmstadt in Germany.
Practical information
- General public
- Free