Hydraulic permeability of (un)bounded fibrous media using the lattice boltzmann method

Several articles have been written regarding the hydraulic permeability of ordered and disordered fibrous media. Here, we explore wall effects on hydraulic permeabilities for ordered and disordered media using the lattice Boltzmann (LB) simulation method. Simulation results are found to be in excellent agreement with the semi analytic result of Sangani and Acrivos, and simulation results for disordered media are in good agreement with the results of Jackson and James and Higdon and Ford's fcc lattice. The macroscopic behavior, the hydraulic permeability, shows a distinct connection with the geometry of the system. This connection is explored and elucidated for ordered and disordered media. Finally, hydraulic permeabilities for bounded media at various wall separations are presented for both ordered and disordered media and results are compared with hydraulic permeabilities calculated for the unbounded media, and a phenomenological correlation is presented to facilitate rapid prediction of hydraulic permeabilities for both unbounded and bounded fibrous media.     

Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method

In many realistic fluid-dynamical simulations the specification of the boundary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we study these issues in the case of the lattice-BGK model. The objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice-BGK method and to introduce some new ideas useful in practical simulations. We begin with an evaluation of the widely used bounce-back boundary condition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non-slip wall is assumed to be at the boundary nodes. Moreover, for a specific inclination angle of 45 degrees, the scheme is found to be second-order accurate when the location of the non-slip velocity is fitted halfway between the last fluid nodes and the first solid nodes. The error as a function of the relaxation parameter is in that case qualitatively similar to that of flat walls. Next, a comparison of simulations of fluid flow by means of pressure boundaries and by means of body force is presented. A good agreement between these two boundary conditions has been found in the creeping-flow regime. For higher Reynolds numbers differences have been found that are probably caused by problems associated with the pressure boundaries. Furthermore, two widely used 3D models, namelyD₃Q₁₅andD₃Q₁₉, are analysed. It is shown that theD₃Q₁₅model may induce artificial checkerboard invariants due to the connectivity of the lattice. Finally, a new iterative method, which significantly reduces the saturation time, is presented and validated on different benchmark problems.     

Lattice‐Boltzmann and finite element simulations of fluid flow in a SMRX Static Mixer Reactor

A detailed comparison between the finite element method (FEM) and the lattice‐Boltzmann method (LBM) is presented. As a realistic test case, three‐dimensional fluid flow simulations in an SMRX static mixer were performed. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used as a highly efficient chemical reactor for viscous systems like polymers. The complex geometry of this mixer makes such three‐dimensional simulations non‐trivial. An excellent agreement between the results of the two simulation methods was found. Furthermore, the numerical results for the pressure drop as a function of the flow rate were close to experimental measurements. Results show that the relatively simple LBM is a good alternative to traditional methods. Copyright © 1999 John Wiley & Sons, Ltd.     

Influence of stagnant zones on transient and asymptotic dispersion in macroscopically homogeneous porous media

The role of stagnant zones in hydrodynamic dispersion is studied for creeping flow through a fixed bed of spherical permeable particles, covering several orders of characteristic time and length scales associated with fluid transport. Numerical simulations employ a hierarchical model to cope with the different temporal and spatial scales, showing good agreement with our experimental results on diffusion-limited mass transfer, transient, and asymptotic longitudinal dispersion. These data demonstrate that intraparticle liquid holdup in macroscopically homogeneous porous media clearly dominates over contributions caused by the intrinsic flow field heterogeneity and boundary-layer mass transfer.