Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.

/pdf/lattice-gas-cellular-automata-and-lattice-boltzmann-models-2kkc77jjx8.pdf

Lattice-Gas Cellular Automata and Lattice Boltzmann Models

https://cyberleninka.org/article/n/22310.pdf

Pore-scale imaging and modelling

Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction

Extensive lattice-Boltzmann simulations were performed to obtain the drag force for random arrays of monodisperse and bidisperse spheres. For the monodisperse systems, 35 different combinations of the Reynolds number Re (up to Re = 1,000) and packing fraction were studied, whereas for the bidisperse systems we also varied the diameter ratio (from 1:1.5 to 1:4) and composition, which brings the total number of different systems that we considered to 150. For monodisperse systems, the data was found to be markedly different from the Ergun equation and consistent with a correlation, based on similar type of simulations up to Re = 120. For bidisperse systems, it was found that the correction of the monodisperse drag force for bidispersity, which was derived for the limit Re = 0, also applies for higher-Reynolds numbers. On the basis of the data, a new drag law is suggested for general polydisperse systems, which is on average within 10% of the simulation data for Reynolds numbers up to 1,000, and diameter ratios up to 1:4

Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres

Gas-solid fluidized beds are widely applied in many chemical processes involving physical and/or chemical transformations, and for this reason they are the subject of intense research in chemical engineering science. Over the years, researchers have developed a large number of numerical models of gas-fluidized beds that describe gas-solid flow at different levels of detail. In this review, we discriminate these models on the basis of whether a Lagrangian or a Eulerian approach is used for the gas and/or particulate flow and subsequently classify them into five main categories, three of which we discuss in more detail. Specifically, these are resolved discrete particle models (also called direct numerical simulations), unresolved discrete particle models (also called discrete element models), and two-fluid models. For each of the levels of description, we give the general equations of motion and indicate how they can be solved numerically by finite-difference techniques, followed by some illustrative examples of a fluidized bed simulation. Finally, we address some of the challenges ahead in the multiscale modeling of gas-fluidized beds

Numerical Simulation of Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy

Tracer dispersion has been simulated in three-dimensional models of regular and random sphere packings for a range of Peclet numbers. A random-walk particle-tracking (PT) method was used to simulate tracer movement within pore-scale flow fields computed with the lattice-Boltzmann (LB) method. The simulation results illustrate the time evolution of dispersion, and they corroborate a number of theoretical and empirical results for the scaling of asymptotic longitudinal and transverse dispersion with Peclet number. Comparisons with nuclear magnetic resonance (NMR) spectroscopy experiments show agreement on transient, as well as asymptotic, dispersion rates. These results support both NMR findings that longitudinal dispersion rates are significantly lower than reported in earlier experimental literature, as well as the fact that asymptotic rates are observed in relatively short times by techniques that employ a uniform initial distribution of tracers, like NMR.

Pore-scale simulation of dispersion

Pore-scale simulations of monodisperse sphere packing and fluid flow in cylinders have reproduced heterogeneities in packing density and velocity previously observed in experiment. Simulations of tracer dispersion demonstrate that these heterogeneities enhance hydrodynamic dispersion, and that the degree of enhancement is related to the cylinder radius, R. The time scale for asymptotic dispersion in a packed cylinder is proportional to R2/DT, where DT represents an average rate of spreading transverse to the direction of flow. A generalization of the Taylor–Aris model of dispersion in a tube provides qualitative predictions of the long-time dispersion behavior in packed cylinders.

Hydrodynamic dispersion in confined packed beds

Simulation of ordered packed beds in chromatography.

The effective longitudinal dispersion constant, D(L)(eff), in cylindrical packed beds is larger than in the bulk due to the existence of radial inhomogeneities induced by the cylinder walls. For dense random packed beds, D(L)(eff) can be several times larger than the bulk value, even for arbitrarily large cylinder radius, R. The time-scale for attaining asymptotic dispersion rates in a cylindrical geometry is neither the convective nor the diffusive time-scale, but rather D(T)/R(2), where D(T) is the bulk transverse dispersion rate. Similar effects are predicted for packed beds confined in ducts of any cross-sectional geometry. The case of a rectangular duct, compared with an infinite slit, provides an intuitive model for the influence of walls in the limit as R goes to infinity.

Enhanced dispersion in cylindrical packed beds.

A computer simulation of a section of the interior region of a liquid chromatographic column is performed. The detailed fluid flow profile is provided from a microscopic calculation of low Reynolds number flow through a random packed bed of nonporous spherical particles. The fluid mechanical calculations are performed on a parallel processor computer utilizing the lattice Boltzmann technique. Convection, diffusion, and retention in this flow field are calculated using a stochastic-based algorithm. This computational scheme provides for the ability to reproduce the essential dynamics of the chromatographic process from the fundamental considerations of particle geometry, particle size, flow velocity, solute diffusion coefficient, and solute retention parameters when retention is utilized. The simulation data are fit to semiempirical models. The best agreement is found for the “coupling” model of Giddings and the four-parameter Knox model. These models are verified over a wide range of particle sizes and fl...

Robert S. Maier

Papers

Pore-scale simulation of dispersion

Hydrodynamic dispersion in confined packed beds

Simulation of ordered packed beds in chromatography.

Enhanced dispersion in cylindrical packed beds.

Simulation of packed-bed chromatography utilizing high-resolution flow fields: comparison with models.