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Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

Song-Gui Chen, Chuan-Hu Zhang, Yun-Tian Feng, Qi-Cheng Sun, Feng Jin, Yuntian Feng Orcid Logo

Engineering Applications of Computational Fluid Mechanics, Volume: 10, Issue: 1, Pages: 347 - 360

Swansea University Author: Yuntian Feng Orcid Logo

DOI (Published version): 10.1080/19942060.2016.1169946

Abstract

This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathemati...

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Published in: Engineering Applications of Computational Fluid Mechanics
Published: 2016
URI: https://cronfa.swan.ac.uk/Record/cronfa28924
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Abstract: This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re) and Bingham number (Bn). These results reveal the flow behavior of Bingham plastics.
Keywords: Bingham plastic, multiple-relaxation-time, lattice Boltzmann model, parallel frame, drag coefficient
College: College of Engineering
Issue: 1
Start Page: 347
End Page: 360