Large-scale grid-enabled lattice Boltzmann simulations of complex fluid flow in porous media and under shear

Well-designed lattice Boltzmann codes exploit the essentially embarrassingly parallel features of the algorithm and so can be run with considerable efficiency on modern supercomputers. Such scalable codes permit us to simulate the behaviour of increasingly large quantities of complex condensed matter systems. In the present paper, we present some preliminary results on the large-scale three-dimensional lattice Boltzmann simulation of binary immiscible fluid flows through a porous medium, derived from digitized X-ray micro-tomographic data of Bentheimer sandstone, and from the study of the same fluids under shear. Simulations on such scales can benefit considerably from the use of computational steering, and we describe our implementation of steering within the lattice Boltzmann code, called LB3D, making use of the RealityGrid steering library. Our large-scale simulations benefit from the new concept of capability computing, designed to prioritize the execution of big jobs on major supercomputing resources. The advent of persistent computational grids promises to provide an optimal environment in which to deploy these mesoscale simulation methods, which can exploit the distributed nature of computer, visualization and storage resources to reach scientific results rapidly; we discuss our work on the grid-enablement of lattice Boltzmann methods in this context.     

A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method

Fluid flow analyses for porous media are of great importance in a wide range of industrial applications including, but not limited to, resin transfer moulding, filter analysis, transport of underground water and pollutants, and hydrocarbon recovery. Permeability is perhaps the most important property that characterizes porous media; however, its determination for different types of porous media is challenging due its complex dependence on the pore-level structure of the media. In the present work, fluid flow in three-dimensional random fibrous media is simulated using the lattice Boltzmann method. We determine the permeability of the medium using the Darcy law across a wide range of void fractions (0.08 ? ? ? 0.99) and find that the values for the permeability that we obtain are consistent with available experimental data. We use our numerical data to develop a semi-empirical constitutive model for the permeability of fibrous media as a function of their porosity and of the fibre diameter. The model, which is underpinned by the theoretical analysis of flow through cylinder arrays presented by [Gebart BR. Permeability of unidirectional reinforcements for RTM. J Compos Mater 1992; 26(8): 1100–33], gives an excellent fit to these data across the range of ?. We perform further simulations to determine the impact of the curvature and aspect ratio of the fibres on the permeability. We find that curvature has a negligible effect, and that aspect ratio is only important for fibres with aspect ratio smaller than 6:1, in which case the permeability increases with increasing aspect ratio. Finally, we calculate the permeability tensor for the fibrous media studied and confirm numerically that, for an isotropic medium, the permeability tensor reduces to a scalar value.     

Flow of non-newtonian fluid through porous media

This article shows the solutions of the nonlinear equations describing the transient flow of power law fluids through a porous medium. These are obtained by means of a generalized Boltzmann transformation approach for several cases of practical interest in interpretation of well-flow tests of short duration, used currently in oil reservoir engineering for obtaining the reservoir properties. A formulation of a moving boundary problem for a short time, appearing during the production of fluids by elastic decompression, is used in deriving the exact solutions in closed form for certain cases. The presence of a decompression front is physically demonstrated and its location in the reservoir at a given time is determined. The limitations associated with the generalized Boltzmann transformation approach in solving the nonlinear equations of power law fluid flow in oil reservoirs are shown and discussed with regard to the interpretation of the well-flow test analysis.     

Transient gas flow through porous media

The problem of transient, one-dimensional flow of an ideal gas through a deformable porous layer is considered. Due to the assumption of small displacement gradients, the mathematical model leads to a formulation in terms of a nonlinear partial differential equation familiar in gas flow theory. For the limiting case of zero surface pressure analytic short time and long time solutions are presented. These are matched at an intermediate value of time giving an accurate approximate solution. The general case of non-zero surface pressure is treated numerically using Galerkin's method. The analytical character of the early time solution is discussed for this general case.     

Physical and computational scaling issues in lattice Boltzmann simulations of binary fluid mixtures

We describe some scaling issues that arise when using lattice Boltzmann (LB) methods to simulate binary fluid mixtures--both in the presence and absence of colloidal particles. Two types of scaling problem arise: physical and computational. Physical scaling concerns how to relate simulation parameters to those of the real world. To do this effectively requires careful physics, because (in common with other methods) LB cannot fully resolve the hierarchy of length, energy and time-scales that arise in typical flows of complex fluids. Care is needed in deciding what physics to resolve and what to leave unresolved, particularly when colloidal particles are present in one or both of two fluid phases. This influences steering of simulation parameters such as fluid viscosity and interfacial tension. When the physics is anisotropic (for example, in systems under shear) careful adaptation of the geometry of the simulation box may be needed; an example of this, relating to our study of the effect of colloidal particles on the Rayleigh-Plateau instability of a fluid cylinder, is described. The second and closely related set of scaling issues are computational in nature: how do you scale-up simulations to very large lattice sizes? The problem is acute for systems undergoing shear flow. Here one requires a set of blockwise co-moving frames to the fluid, each connected to the next by a Lees-Edwards like boundary condition. These matching planes lead to small numerical errors whose cumulative effects can become severe; strategies for minimizing such effects are discussed.     

On boundary conditions for fluid flow in porous media

We continue the study undertaken in [11] of boundary conditions at the surface between a porous medium and a free fluid flow. Two different kinds of phenomena may appear, according to the direction of the averaged gradient of pressure in the porous medium, oblique or normal to the surface. General results about the matching of the different flow regions and boundary conditions are given, as well as examples. The interface layer in the case of a normal gradient of pressure is studied in detail.     

Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using Lattice Boltzmann Method

In this paper the Lattice Boltzmann Method (LBM) is utilized to investigate the effects of uniform vertical magnetic field on the flow pattern and fluid–solid coupling heat transfer in a channel which is partially filled with porous medium. Al₂O₃–water nanofluid as a work fluid with temperature sensitive properties is forced to flow into the channel while the top and bottom walls of the channel is heated and kept at a constant temperature. In the present study, with respect to previous works and experimental data, a new correlation is presented for density of Al₂O₃–water nanofluid as a function of temperature. The result also shows that the step approximation which is used for the complex boundaries of porous medium is reliable. Finally, the effect of various volume fractions of nanoparticles (ϕ = 0%, 3%, 5% and 7%) and different magnitude of magnetic field (Ha = 0, 5, 10 and 15) on the rate of heat transfer are thoroughly explored. In accordance with the results, by raising the nanoparticle volume fraction, average temperature and velocity at the outlet of the channel increase and the average Nusselt number rises dramatically. In addition, the increase the Hartmann number leads to the slow growth in the average Nusselt number, although the outlet average temperature and velocity shows a little drop.     

Lattice Boltzmann simulations of bubble formation in a microfluidic T-junction

A lattice Boltzmann equation method based on the Cahn-Hilliard diffuse interface theory is developed to investigate the bubble formation process in a microchannel with T-junction mixing geometry. The bubble formation process has different regimes, namely, squeezing, dripping and jetting regimes, which correspond to the primary forces acting on the system. Transition from regime to regime is generally dictated by the capillary number Ca, volumetric flow ratio Q and viscosity ratio λ. A systematic analysis is performed to evaluate these effects. The computations are performed in the range of 10(-4)相似文献   

Towards aeroacoustic sound generation by flow through porous media

In this work, we present single-step aeroacoustic calculations using the Lattice Boltzmann method (LBM). Our application case consists of the prediction of an acoustic field radiating from the outlet of a porous media silencer. It has been proved that the LBM is able to simulate acoustic wave generation and propagation. Our particular aim is to validate the LBM for aeroacoustics in porous media. As a validation case, we consider a spinning vortex pair emitting sound waves as the vortices rotate around a common centre. Non-reflective boundary conditions based on characteristics have been adopted from Navier-Stokes methods and are validated using the time evolution of a Gaussian pulse. We show preliminary results of the flow through the porous medium.     

Gate elements at injection locations in numerical simulations of flow through porous media: applications to mold filling

Mold filling in polymer and composite processing is usually modelled as a special case of Darcy flow in porous media. The flow pattern and the time necessary to fill the mold depend on the ‘gate’ locations where resin is injected into the closed mold. In composite manufacturing, these are commonly outlets of small tubes transporting resin from a reservoir and their diameters are several orders of magnitude smaller than the mold dimensions. Similar size issue is also encountered in other applications of flow through porous media, such as oil and water pumping and drilling. Traditionally, these inlets are modelled by pressure or flow rate boundary condition as applied at a node of the finite element mesh that represents the injection gate. The omission of the inlet radius in the model results in a mathematical singularity as the mesh gets refined. The computed pressure or flow field depends on the mesh size and does not converge to the accurate solution, as the finite element mesh is refined. It is possible to deal with this phenomenon by modelling the inlet geometry more accurately but this approach is inefficient, as it requires additional degrees of freedom and, above all, significantly complicates the modelling process if the inlet location is not fixed a priori. This paper presents a more efficient alternate solution. It uses special ‘gate’ elements embedded in the mesh around the injection locations. Instead of adjusting the geometrical modelling of the injection location, the adjacent elements use modified shape functions to accurately model pressure field in the neighbourhood of small radial inlet. The proper pressure field shape‐functions for ‘gate’ elements based on linear finite elements are derived. The implementation in an existing mold filling simulation and how the ‘gate elements’ are automatically selected is described. An example to demonstrate the use of ‘gate’ elements and convergence towards the accurate solution with mesh refinement is presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Lattice Boltzmann simulations of contact line motion in a liquid-gas system

We use a lattice Boltzmann algorithm for liquid-gas coexistence to investigate the steady-state interface profile of a droplet held between two shearing walls. The algorithm solves the hydrodynamic equations of motion for the system. Partial wetting at the walls is implemented to agree with Cahn theory. This allows us to investigate the processes which lead to the motion of the three-phase contact line. We confirm that the profiles are a function of the capillary number and a finite-size analysis shows the emergence of a dynamic contact angle, which can be defined in a region where the interfacial curvature tends to zero.     

Lattice Boltzmann simulations of incompressible liquid-gas systems on partial wetting surfaces

A three-dimensional Lattice Boltzmann two-phase model capable of dealing with large liquid and gas density ratios and with a partial wetting surface is introduced. This is based on a high density ratio model combined with a partial wetting boundary method. The predicted three-dimensional droplets at different partial wetting conditions at equilibrium are in good agreement with analytical solutions. Despite the large density ratio, the spurious velocity around the interface is not substantial, and is rather insensitive to the examined liquid and gas density and viscosity ratios. The influence of the gravitational force on the droplet shape is also examined through the variations of the Bond number, where the droplet shape migrates from spherical to flattened interface in tandem with the increase of the Bond number. The predicted interfaces under constant Bond number are also validated against measurements with good agreements.     

On-chip high-pressure picoliter injector for pressure-driven flow through porous media

A high-pressure (> 3 MPa) on-chip injector has been developed for microchip applications including HPLC. The mechanical injector is implemented using in situ photopolymerization of fluorinated acrylates inside wet-etched silica microchips. The injector allows reproducible injections as small as 180 pL with < 250 ms duration. The injector operated robustly over 60 days and over 1000 injections. The injector is unique among polymer-based valves as it functions in aqueous, acetonitrile, and mixed buffers at high pressures without detectable leakage.     

Lattice Boltzmann simulation of flow past a non-spherical particle

Lattice Boltzmann method was used to predict the fluid-particle interaction for arbitrary shaped particles. In order to validate the reliability of the present approach, simulation of flow past a single stationary spherical, cylindrical or cubic particle is conducted in a wide range of Reynolds number (0.1 < Re_p < 3000). The results indicate that the drag coefficient is closely related to the particle shape, especially at high Reynolds numbers. The voxel resolution of spherical particle plays a key role in accurately predicting the drag coefficient at high Reynolds numbers. For non-spherical particles, the drag coefficient is more influenced by the particle morphology at moderate or high Reynolds numbers than at low ones. The inclination angle has an important impact on the pressure drag force due to the change of projected area. The simulated drag coefficient agrees well with the experimental data or empirical correlation for both spherical and non-spherical particles.     

Lattice Boltzmann simulation of the flow of binary immiscible fluids with different viscosities using the Shan-Chen microscopic interaction model

We present a lattice Boltzmann study of the flow of a binary fluid where the fluid components have different viscosities. For this purpose, a microscopic interaction model (due to Shan & Chen) is used. The model is validated for Poiseuille flow of layered immiscible binary fluids and the dispersion of a capillary wave. We then study the unstable displacement of a viscous fluid by a less viscous fluid in a two-dimensional channel. Although a finger-like structure was observed in many simulations, it is not clear if this structure was produced due to viscous fingering or due to other effects.     

Generalised solution to the problems of transient flow of fluid in porous media

The application of Green's function to problems of unsteady fluid flow in porous media is developed. The result indicates that the problem of fluid flow can be vizualised as being equivalent to that of finding an appropriate source function to describe the physical problem. For cases where the appropriate instantaneous Green's function for the system can be found, the required fluid flow problem is easily solved. The application of this very powerful approach is demonstrated for the case of an oil well producing in an infinite oil reservoir body (the infinite line source case), and that of partially penetrating or restricted-flow entry oil/water well in a confined stratum, (the finite line source system).     

A dynamic mesh refinement technique for Lattice Boltzmann simulations on octree-like grids

In this contribution, we present our new adaptive Lattice Boltzmann implementation within the Peano framework, with special focus on nanoscale particle transport problems. With the continuum hypothesis not holding anymore on these small scales, new physical effects—such as Brownian fluctuations—need to be incorporated. We explain the overall layout of the application, including memory layout and access, and shortly review the adaptive algorithm. The scheme is validated by different benchmark computations in two and three dimensions. An extension to dynamically changing grids and a spatially adaptive approach to fluctuating hydrodynamics, allowing for the thermalisation of the fluid in particular regions of interest, is proposed. Both dynamic adaptivity and adaptive fluctuating hydrodynamics are validated separately in simulations of particle transport problems. The application of this scheme to an oscillating particle in a nanopore illustrates the importance of Brownian fluctuations in such setups.