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Frictional boundary condition for lattice Boltzmann modelling of dense granular flows

Published online by Cambridge University Press:  17 October 2023

G.C. Yang Open the ORCID record for G.C. Yang [Opens in a new window] ,
Y.J. Huang ,
Y. Lu Open the ORCID record for Y. Lu [Opens in a new window] ,
C.Y. Kwok ,
Y.D. Sobral Open the ORCID record for Y.D. Sobral [Opens in a new window]  and
Q.H. Yao
G.C. Yang
Affiliation:
School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, PR China
Y.J. Huang
Affiliation:
School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, PR China
Y. Lu*
Affiliation:
Department of Civil Engineering, Hong Kong Chu Hai College, Hong Kong, PR China Department of Civil Engineering, The University of Hong Kong, Haking Wong Building, Pokfulam Road, Hong Kong, PR China
C.Y. Kwok
Affiliation:
Department of Civil Engineering, The University of Hong Kong, Haking Wong Building, Pokfulam Road, Hong Kong, PR China
Y.D. Sobral
Affiliation:
Departamento de Matemática, Universidade de Brasília, Campus Universitário Darcy Ribeiro, 70910-900 Brasília DF, Brazil
Q.H. Yao
Affiliation:
School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, PR China
*
†Email address for correspondence: helenlu@chuhai.edu.hk
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Abstract

Hydrodynamic approaches that treat granular materials as a continuum via the homogenization of discrete flow properties have become viable options for efficient predictions of bulk flow behaviours. However, simplified boundary conditions in computational fluid dynamics are often adopted, which have difficulty in describing the complex stick–slip phenomenon at the boundaries. This paper extends the lattice Boltzmann method for granular flow simulations by incorporating a novel frictional boundary condition. The wall slip velocity is first calculated based on the shear rate limited by the Coulomb friction, followed by the reconstruction of unknown density distribution functions through a modified bounce-back scheme. Validation is performed against a unique plane Couette flow configuration, and the analytical solutions for the flow velocity profile and the wall slip velocity, as functions of the friction coefficient, are reproduced by the numerical model. The transition between no-slip and partial-slip regimes is captured well, but the convergence rate drops from second order to first order when slip occurs. The rheological parameters and the basal friction coefficient are calibrated further against the discrete element simulation of a square granular column collapsing over a horizontal bottom plane. It is found that the calibrated continuum model can predict other granular column collapses with different initial aspect ratios and slope inclination angles, including the basal slip and the complex internal flow structures, without any further adjustments to the model parameters. This highlights the generalization ability of the numerical model, which has a wide range of application in granular flow predictions and controls.

JFM classification

Granular media: Avalanches Multiphase and Particle-laden Flows: Particle/fluid flow Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , A21
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Yang et al. Supplementary Movie

Comparison of granular column collapse simulations using the discrete element and the lattice Boltzmann methods.

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