Modelling Fluid-Structure Interaction Problems with Coupled DEM-LBM

When studying the properties and behaviour of particulate systems, a multi-scale approach is an efficient way to describe interactions at different levels or dimensions; this means that phenomena taking place at one scale will inherently impact the properties and behaviour of the same system in a different scale. Numerical representation and simulation of fluid-structure interaction (FSI) systems is of particular interest in the present work. Conventional computational fluid dynamics (CFD) methods involve a top-down approach based on the discretisation of the macroscopic continuum Navier-Stokes equations; cells are typically much larger than individual particles and the hydrodynamic force is calculated for all the solid particles contained in singular a cell. Unlike traditional CFD solvers, the lattice Boltzmann method (LBM) is an alternative approach to simulate fluid flows in complex geometries in a mesoscale level. In LBM the fluid is deemed as a collection of cells, each one containing a particle that represents a density distribution function with a velocity field. The distinct element method (DEM) is in charge of handling the motion of particles and calculating the interparticle contact forces. The two methodologies LBM and DEM were selected among the available approaches to be combined in a single computational code to represent FSI systems. The key task to undertake was the implementation of a coupling code to exchange information between the two solvers LBM and DEM in a correct and efficient manner. The calculation of hydrodynamic forces exerted by the fluid on the particles is the major challenge in coupled FSI simulations. This was addressed by including the momentum exchange method, based on the link bounce-back technique, together with the immersed boundary method to deal with moving particles immersed in a fluid. In addition, in order to better understand the dynamics of FSI systems in a mesoscale level, the present work paid special attention to the accurate representation of individual particles displaying irregular geometries instead of the preferred spherical particles. This goal was achieved by means of X-ray microtomography digitisation of particles, allowing the capture of complex micro-structural features such as particle shape, texture and porosity. In this way a more realistic particle representation was achieved, extending its use to the implementation into computational simulations. The DEM-LBM coupling implementation carried out was tested quantitatively and qualitatively based on theoretical models and experimental data. Different cases were selected to simulate the dynamic process of packing particles, particle fluidisation and segregation, particles sedimentation, fluid permeability calculations and fluid flow through porous media. Results and predictions from simulations for a number of configurations showed good agreement when compared with analytical and experimental data. For instance, the relative error in terminal velocity of a non-spherical particle settling down in a column of water was 4.2%, showing an asymptotic convergence to the reference value. In different tests like the drag on two interacting particles and the flow past a circular cylinder at Re = 100, the corresponding deviations from the references published were 20% and 8.23% respectively. The extended Re range for the latter case followed closely the reference curve for the case of a rough cylinder, indicating the effects of the inherent staircase-like boundary in digital particles. Three dimensional simulations of applications such as fluidisation and sedimentation showed the expected behaviour, not only for spherical particles but also considering complex geometries such as sand grains. A symmetric array of spheres and randomly mixed particles were simulated successfully. Segregation was observed in a case configured with particles with different size and density. Hindered settling was also observed causing the slow settling of the small particles. Incipient fluidisation of spherical and irregular geometries was observed in relatively large computational domains. However, the minimum fluidisation velocity configured at the inlet was commonly 10 times larger than the calculated from the Ergun equation.