Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time

Explicit numerical simulation of non-creeping single phase flow in porous media

Porous media and transport within them play important roles across industries and beyond, including in water and pollutant transport in soils, flow in petroleum and geothermal reservoirs, and water treatment in deep bed filtration to list just a few key examples. The study of such flows has traditionally been dominated by experiment. Simulation is, however, playing an increasing role in this field both because of the advent of X-ray microtomography (XRMT), which now permits the mapping of pore structures down to sub-micrometer resolution, and the ubiquitous availability of powerful compute clusters built on cheap commodity machines. Simulation in this context involves solving for the flow field in a model of a porous solid derived from XRMT - in this sense, the simulations mimic reality and are hence termed by us as explicit numerical simulation (ENS). The particular challenge in doing ENS is correctly solving the flow problem in extremely complex geometries. This challenge has led to the use of various methods such as lattice-gas automata (LGA) and the related lattice-Boltzmann method (LBM), which are particularly suited to resolving flows in complex geometries. All of this work to date has been restricted to low velocity flows termed Darcy flows because of limitations associated with LGA, LBM and other methods. There is, however, a range of applications where higher speed flows are of relevance and hence extension of the ENS approach to higher speed flows in porous media is important. This has been done here using an LGA model that does not include the deficiency of more standard LGA models that restricts them to slow flows. The thesis first details this little-known and used LGA model before demonstrating it on a range of benchmark problems. The model is then used to predict ab initio the hydrodynamic properties of a random packing from the Darcy to the turbulent regime. Comparison with experiment is excellent. The approach is then used to study, for the first time to our knowledge, the interstitial flow patterns from the Darcy to turbulent regimes

On Microstructural Analysis of Porous Media Existing in Fuel Cells Using the Lattice Boltzmann Method

This Licentiate thesis aims to gain understanding related to the fluid behavior in porous media existent in fuel cells (FCs) at microscale. In order to achieve this; the widely used methodology for solving problems in porous media has been applied, the Lattice Boltzmann Method (LBM). LBM presents several advantages to solve problems where the microstructural architecture is complex. The introductory part presents the scope of the thesis and the different parts include in the document. Different characteristics of the FCs are given, as well as the parts where the porous media are found within the FCs are presented. The mechanism of energy conversion for two selected kind of FCs is explained, and the simplified electrochemical reactions involved in such conversion are presented. The second part of the thesis corresponds to the LBM explanation and the solution of several physical problems. The simulations are carried out at different Re in order to prove the ability of LBM for solving problems at different regimes, and to get knowledge about the boundary conditions implemented. The simulation results performed in this part are basically at macroscale. Momentum equation and energy equation form part of the results obtained using the LBM. All the simulations are validated with corresponding previous studies, which show a relatively high accuracy of the method. Finally, the simulation results of the fluid behavior in porous media are presented. Both, randomly generated and a reconstructed porous domain from a real image are analyzed. Microstructure parameters such as porosity, gas-phase tortuosity and permeability are obtained after using the LBM. The results obtained are compared with previous studies, and the posibble future work is detailed in the last chapter

Progress in particle-based multiscale and hybrid methods for flow applications

This work focuses on the review of particle-based multiscale and hybrid methods that have surfaced in the field of fluid mechanics over the last 20 years. We consider five established particle methods: molecular dynamics, direct simulation Monte Carlo, lattice Boltzmann method, dissipative particle dynamics and smoothed-particle hydrodynamics. A general description is given on each particle method in conjunction with multiscale and hybrid applications. An analysis on the length scale separation revealed that current multiscale methods only bridge across scales which are of the order of O(102)−O(103) and that further work on complex geometries and parallel code optimisation is needed to increase the separation. Similarities between methods are highlighted and combinations discussed. Advantages, disadvantages and applications of each particle method have been tabulated as a reference

Double population cascaded lattice boltzmann method

Lattice Boltzmann Methods (LBM) are powerful numerical tools to simulate heat and mass transfer problems. Instead of directly integrating the N-S equations, LBM solves the discretized form of the Boltzmann Transport Equation (BTE), keeping track of the microscopic description of the systems. Therefore, LBM can solve fluid flows with great stability and computational efficiency, especially complex geometry fluid flows. For thermal flows, double distribution function (DDF) LBM scheme is the most popular and successful approach. But it is evident from the literature that existing double distribution function (DDF) LBM approaches, which use two collision operators, involve collision schemes which violate Galilean invariance, therefore producing instabilities for flows with high Re and Ra numbers. In this thesis, a double population cascaded lattice Boltzmann method is developed to improve the DDF LBM scheme from this drawback. The proposed method reduces the degree of violation of Galilean invariance, increasing the stability and accuracy of the LBM scheme. The scheme was implemented to simulate advection-diffusion, forced convection and natural convection heat transfer problems. The proposed scheme was also successfully tested for turbulent flow regimes and 3-D fluid flow in porous media. The results obtained from this work are in strong agreement with those available in the literature obtained through other numerical methods and experiments.Os métodos de ”Lattice”Boltzmann (LBM) são potentes ferramentas numéricas para simular problemas de transferência de massa e calor. Ao invés de integrar diretamente as equações de Navier-Stokes, o método LBM resolve, de forma discretizada, a equação de transporte de Boltzmann, acompanhando a descrição microscópica dos sistemas. O método LBM pode solucionar fluxo de fluidos com grande estabilidade e eficiência computacional, especialmente fluxos em geometrias complexas. Para fluxos térmicos, o esquema LBM de dupla função de distribuição (DDF) é a abordagem mais popular e bem sucedida. Mas é evidente, a partir da literatura, que as abordagens LBM de dupla função de distribuição (DDF), as quais utilizam dois operadores de colisão, envolvem esquemas de colisão que violam a invariância de Galileu, produzindo instabilidades para fluxos com números Re e Ra altos. Nesta tese, o método de ”Lattice”Boltzmann em cascata de dupla população em cascata é desenvolvido para corrigir o esquema DDF LBM. O método proposto reduz o grau de violação da invariância de Galileu, aumentando a estabilidade e acurácia do método LBM. O método foi implementado para simular problemas de advecção, difusão, convecções natural e forçada típicos de transferências de calor. O esquema proposto foi também bem sucedido em regimes de fluxo turbulento e em escoamentos 3-D em meios porosos. Os resultados obtidos neste trabalho estão fortemente de acordo com experimentos e métodos numéricos disponíveis na literatura

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

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

Simulation study on PEM fuel cell gas diffusion layers using x-ray tomography based Lattice Boltzmann method

The Polymer Electrolyte Membrane (PEM) fuel cell has a great potential in leading the future energy generation due to its advantages of zero emissions, higher power density and efficiency. For a PEM fuel cell, the Membrane-Electrode Assembly (MEA) is the key component which consists of a membrane, two catalyst layers and two gas diffusion layers (GDL). The success of optimum PEM fuel cell power output relies on the mass transport to the electrode especially on the cathode side. The carbon based GDL is one of the most important components in the fuel cell since it has one of the basic roles of providing path ways for reactant gases transport to the catalyst layer as well as excess water removal. A detailed understanding and visualization of the GDL from micro-scale level is limited by traditional numerical tool such as CFD and experimental methods due to the complex geometry of the porous GDL structural. In order to take the actual geometry information of the porous GDL into consideration, the x-ray tomography technique is employed which is able to reconstructed the actual structure of the carbon paper or carbon cloth GDLs to three-dimensional digital binary image which can be read directly by the LB model to carry out the simulation. This research work contributes to develop the combined methodology of x-ray tomography based the three-dimensional single phase Lattice Boltzmann (LB) simulation. This newly developed methodology demonstrates its capacity of simulating the flow characteristics and transport phenomena in the porous media by dealing with collision of the particles at pore-scale. The results reveal the heterogeneous nature of the GDL structures which influence the transportation of the reactants in terms of physical parameters of the GDLs such as porosity, permeability and tortuosity. The compression effects on the carbon cloth GDLs have been investigated. The results show that the c applied compression pressure on the GDLs will have negative effects on average pore size, porosity as well as through-plane permeability. A compression pressure range is suggested by the results which gives optimum in-plane permeability to through-plane permeability. The compression effects on one-dimensional water and oxygen partial pressures in the main flow direction have been studied at low, medium and high current densities. It s been observed that the water and oxygen pressure drop across the GDL increase with increasing the compression pressure. Key Words: PEM fuel cell, GDL, LB simulation, SPSC, SPMC, x-ray tomography, carbon paper, carbon cloth, porosity, permeability, degree of anisotropy, tortuosity, flow transport

CFD. Conventional and Lattice Boltzmann methods. Study of LBM: Basic theory and applications. Simulation of a fluid in a wind tunnel

Treballs Finals de Grau d'Enginyeria Química, Facultat de Química, Universitat de Barcelona, Curs: 2021-2022, Tutor: Joan Llorens LlacunaThe aim of this work is to examine Lattice Boltzmann method (LBM) to see their possible application in Chemical Engineering problems. LBM is considered an efficient alternative method to conventional computational fluid dynamics (CFD) in some fluid dynamics problems, in which conventional numerical methods are limited. LBM does not rely on numerical resolution of Navier-Stokes equation (NSE) like conventional CFD does. Contrary to CFD, LBM does not need fluid mechanics equations to describe fluid behaviour. Thus, mathematical complexity is reduced, and the efficiency of the method increases. LBM is based on statistical probabilities of movement of fluid, specifically, particles, in streaming and collision processes. This method is founded, mainly, on the kinetic theory, which will be analysed in depth to understand the basis of the technique. Thus, LBM can describe fluid behaviour without solving LBM, as CFD have application on Transport Phenomena simulation in fluid flow. In particular, conventional CFD is mainly implemented for industrial, environmental and physiological fluid fields. Once studied the basis of the main representative methods of either microscopic and mesoscopic level and analysed its concepts entailed, a comparison among conventional CFD and emerging LBM, included in the work, permits simulating fluid behaviour efficiently by choosing the befitted technique. Likewise, limitations and applications of each method will be remarked. Small errors, simple application of the method, extensibility, higher parallelization and small-time procedure are some of the characteristics required for a well suitable method to simulate fluid flows