Abstract
ABSTRACTThis 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.
Highlights
Bingham plastics or viscoplastic materials – such as cement mortar, slurries, and suspensions – are widely used in hydraulic and civil engineering
The accuracy of the multiple-relaxation-time lattice Boltzmann model (MRT-lattice Boltzmann model (LBM)) approach has been studied by Chai et al (2011) and it is second-order accurate in space, which is affected by fluid compressibility
The present results indicate that increasing Bingham number (Bn) substantially increases the drag coefficient in the system when Reynolds number (Re) is constant, while increasing Re decreases the drag coefficient for the same values of Bn; Newtonian fluids are characterized by this phenomenon
Summary
Bingham plastics or viscoplastic materials – such as cement mortar, slurries, and suspensions – are widely used in hydraulic and civil engineering. The traditional methods of computational fluid dynamics (CFD), such as the finite-volume method (Neofytou, 2005; Xu, Yuan, Repke, & Wozny, 2012) and the finite-element method (Bell & Surana, 1994; Ozmen-Cagatay & Kocaman, 2011), are the most common numerical techniques used to simulate Bingham plastic flows. Such traditional methods often produce inaccuracies in cases of complex geometries and boundary conditions
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