A greyscale volumetric lattice Boltzmann method for upscaling pore-scale two-phase flow

Unified mesoscopic modeling and GPU-accelerated computational method for image-based pore-scale porous media flows

Numerical studies of interfacial phenomena in liquid water transport in polymer electrolyte membrane fuel cells using the lattice Boltzmann method

Pore network models are useful for studying transport in porous materials in a computationally efficient way. Extraction of networks from volumetric images has evolved over the years, starting with medial axis-based approaches to more recent watershed segmentation. This paper reconsiders the classic medial axis method, which offers several advantages such as speed and topological correctness, and develops a modernized, updated, and improved version. The new method is named Medial Axis Guided Network Extraction Tool (MAGNET). It works by analyzing the skeleton of a porous material to identify pore centers at junctions and endpoints. Additional pore bodies are found on long throats using two different approaches. This work includes an efficient tool for calculating the cross-sectional area of throats with irregular shape by using walkers with an infinite mean-free path to probe the geometry orthogonal to the medial axis at the point of the throat constriction. This extra step was critical for obtaining an equivalent diameter needed to calculate the permeability. Lastly, MAGNET was written with computational efficiency in mind. The skeletonization approach was itself 4.2X faster than the SNOW watershed segmentation for a 10003 image. Additionally, a parallelized skeletonization was applied by processing the image in blocks with sufficient overlap which resulted in a 5.5X speed-up compared to the serial approach. To validate the output, MAGNET was tested on a 4003 voxel image of a Berea sandstone, and the flow and capillary properties of the extracted network were compared to the results from SNOW and the lattice-Boltzmann method. Structural information such as pore and throat size distribution and mercury intrusion curves was compared, and noticeable similarity was achieved. Crucially, the permeability predicted by MAGNET was within 5% of the lattice-Boltzmann prediction on the same image.

Computational Fluid Dynamics (CFD) uses numerical methods to solve problems involving fluid flows, e.g. in automotive engineering, energy, civil engineering, and aerospace. One of these methods is the lattice Boltzmann method (LBM). Beside giving accurate results for a wide range of complex flows, the LBM lends itself to efficient implementations on massively parallel systems such as the general-purpose computing on graphics processing units (GPGPU). This work considers the cumulant LBM, which overcomes some problems of classical LBMs, such as the violation of the Galilean invariance, the spurious coupling of the degrees of freedoms, and the hyper-viscosity. In order to enable the cumulant LBM for complex CFD engineering problems, this work focuses on the discretization of the computational domain and the analysis of turbulent flows in the near-wall region.
\nThe grid generation for LBM deals with several issues such as the second order boundary definition, the free shape grid refinement, and the level wise load balancing for parallel meshes. While discretizing complex geometries, these issues have to be handled simultaneously.
\nTurbulent flows close to walls are characterized by high velocity gradients in a thin region called the boundary layer. In order to resolve numerically the boundary layer, a grid with a high resolution is required resulting in a high computational cost for the simulation. Empirical functions can be used for modelling the boundary layer, allowing to estimate the quantities at the wall even with coarse grids, and thus increasing the efficiency of the numerical simulation.
\nIn this work, a new grid generator that addresses the LBM discretization issues is implemented. It creates free shape multi-level three-dimensional meshes with second order accurate boundary definition for very complex geometries. It can be applied for generating grids of complex bodies, such as cars, porous media, and urban areas.
\nRegarding the near-wall region treatment, a new wall function is introduced. It uses local information at the boundary nodes for recovering the quantities at the wall. For generating a proper turbulence for wall bounded flows, a new set of relaxation parameters is introduced, which eliminates the spurious dependence of the error on the bulk viscosity.
\nIn conclusion, this work addresses two important aspects for enabling the cumulant LBM for complex fluid flow problems: grid generation and boundary treatment for turbulent flows.

Lattice Boltzmann method (LBM) is a new attractive computational approach for simulating isothermal multi-phase flows in computational fluid dynamics (CFD). It is based on the kinetic theory and easy to be parallelized. This study aims to analyze the performance of parallel LBM programming for the incompressible two-phase flows at high density and viscosity ratio. For this purpose, a liquid drop impact on a wetted wall with a pre-existing thin film of the same liquid is simulated by using the parallel LBM code. During the simulations, the domain decomposition, data communication and parallelization of the LBM code using the message passing interface (MPI) library have been investigated. The computational results show that the parallel LBM code exhibits a good high performance computing (HPC) on the parallel speed-up.

Augmenting X-ray micro-CT data with MICP data for high resolution pore-scale simulations of flow properties of carbonate rocks

PurposeThe purpose of this paper is the examination of fluid flow around NACA0012 airfoil, with the aim of the numerical validation between the experimental results in the wind tunnel and the Lattice Boltzmann method (LBM) analysis, for the medium Reynolds number (Re = 191,000). The LBM–large Eddy simulation (LES) method described in this paper opens up opportunities for faster computational fluid dynamics (CFD) analysis, because of the LBM scalability on high performance computing architectures, more specifically general purpose graphics processing units (GPGPUs), pertaining at the same time the high resolution LES approach.Design/methodology/approachProcess starts with data collection in open-circuit wind tunnel experiment. Furthermore, the pressure coefficient, as a comparative variable, has been used with varying angle of attack (2°, 4°, 6° and 8°) for both experiment and LBM analysis. To numerically reproduce the experimental results, the LBM coupled with the LES turbulence model, the generalized wall function (GWF) and the cumulant collision operator with D3Q27 velocity set has been used. Also, a mesh independence study has been provided to ensure result congruence.FindingsThe proposed LBM methodology is capable of highly accurate predictions when compared with experimental data. Besides, the special significance of this work is the possibility of experimental and CFD comparison for the same domain dimensions.Originality/valueConsidering the quality of results, root-mean-square error (RMSE) shows good correlations both for airfoil’s upper and lower surface. More precisely, maximal RMSE for the upper surface is 0.105, whereas 0.089 for the lower surface, regarding all angles of attack.

The objective of this work is to gain the mechanical understanding of the water management in the proton exchange membrane fuel cell (PEMFC). Water is a by-product of the fuel cell reaction and its amount is proportion to the current of fuel cell output. Water is used to retain the proper hydration level in the PEM. At the same time, condensed water in the flowfield and the gas diffusion layer (GDL) reduces oxygen transport to the oxygen reduction reaction (ORR) area. Therefore, excess accumulation of condensed water causes to lower the performance, particularly at the higher current densities. Detailed simulation of two-phase water in the GDL is significantly important to understand the water management.This work shows the successful in development of a multi-scale calculation technique that incorporates various scales of numerical model in a fuel cell and simultaneously performed a prediction. The outcomes of this work are, (i) development of two-phase fluid model in the micro-scale porous structure of GDL, and (ii) integration of this micro-scale GDL fluid model with a state-of-the-art macro-scale flowfield fluid model to predict two-phase water in the fuel cell. Figure 1 gives the concept of modeling approach at each component of the fuel cell. The flowfield in the bipolar plate and MEA models are calculated using traditional computational fluid dynamics (CFD) method with existing PEMFC model [1-3]. The two-phase fluid in the micro-scale porous structure of GDL is numerically predicted by Lattice Boltzmann Method (LBM) [4-5]. The solution of each iteration from CFD and LBM are required to simultaneously exchange for the next iteration until all solutions are converged, especially at the interfaces. In this figure, it shows the flowfield is transformed into the macro-scale CFD model and the image of detail structured GDL is converted into micro-scale LBM model. Actual porous structure imaging of GDL is obtained by the nano-scale high special resolution x-ray computed tomography. Figure 2 shows an example of the predictions from the simulation when the macroscopic flowfield model is combined with the microscopic GDL model while performing the calculation. The predictions give the detail distributions of variables in every components of the multiscale model. In this figure, the current density distribution on MEA surface, the liquid water transport inside the GDL, and the temperature of solid and fluid phases inside the GDL are presented.

The last decade the Lattice Boltzmann method has evolved into a powerfull solver for flow through porous media, where the solid phase is represented fully resolved on the computational grid (Hill, 2001). Packed and stored fresh agricultural produce are frequently modeled as porous media and therefore we envision Lattice Boltzmann to be an important tool for simulating heat and mass transport in these systems via forced or natural convection. However, practical package and storage systems have too large lengthscales for fully resolved simulations. Consequently, simulations on the full system scale have to be performed at the volume-averaged scale. For the volume-averaged scale closure relations are needed such as the drag force, effective diffusivity or conductivity. Also here Lattice Boltzmann can play a vital role. Lattice Boltzmann is also capable of simulations at the volume-averaged scale, though it has not frequently used for this scale. With this capability, we can build a multiscale simulation approach, similar to what is developed for fluidized beds (van der Hoef, 2004). In this contribution we will present the general framework, and applications of Lattice Boltzmann to forced flow through package with spherical produce (fully resolved), natural convection in bulk containers of seed potatoes (volume-averaged) (van der Sman,1997 & 1999), and some benchmark problems like natural convection in cavity (van der Sman, 2006) and flow in a channel with a porous layer (Beavers and Joseph benchmark). References o Hill R.J., Koch D.L., and Ladd A.J.C. Moderate-Reynolds-number flows in ordered and random arrays of spheres JOURNAL OF FLUID MECHANICS 448: 243-278 (2001). o van der Hoef M.A., Annaland M.V., Kuipers J.A.M. Computational fluid dynamics for dense gas-solid fluidized beds: a multi-scale modeling strategy. CHEMICAL ENGINEERING SCIENCE 59 (22-23): 5157-5165 (2004). o van der Sman R.G.M. Solving the vent hole design problem for seed potato packagings, with the Lattice Boltzmann scheme. INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS 11 (3-4): 237-248 (1999). o VanderSman R.G.M. Lattice-Boltzmann scheme for natural convection in porous media INTERNATIONAL JOURNAL OF MODERN PHYSICS C 8 (4): 879-888 (1997) o van der Sman R.G.M. Lattice Boltzmann scheme for natural convection on square and rectangular grids. in revision Phys. Rev. E (2006). IUFoST 2006 DOI: 10.1051/IUFoST:20060990

In this work, results from a 2-D Lattice Boltzmann (LB) solver are presented simulating flow past rectangular square cylinders at low Reynolds numbers (< 250). The LBGK equation is a hyperbolic equation that approximates the Navier Stokes equations in the nearly incompressible limit. It is a system of 9 one dimensional partial differential Hamiltonian-Jacobian equations, consisting of an advection and diffusive portion. The LB method is an alternative computational fluid dynamics (CFD) method used to numerically predict incompressible viscous flow. The current LB method uses a statistical mechanics formulation to solve the Boltzmann equation. The LB model captures the nonlinear Navier Stokes advection terms using linear streaming operators. In this thesis, the LB model is classified as an explicit, Lagrangian, finite-hyperbolicity and weakly compressible approximation of the Navier Stokes equations. The momentum flux tensor is captured locally as opposed to a pressure field eliminating the need to solve the Poisson equation. This allows the fluid structure interactions (FSI) behavior to be calculated elegantly at the interface through the mesoscopic momentum transfer between the fluid and structure. At this level, the forces are simultaneously calculated. The LB equations are discretized both in time and phase space using a standard D2Q9 lattice model. Validation tests for flow around single square cylinders at different aspect ratio at low Reynolds numbers are presented. Good agreement with other investigators is achieved. Flow past multiple bluff bodies (representing building in a city) is also presented. The vortex shedding simulations presented provide preliminary indications in terms of St that the LB method can be used to simulate high Re flow.

Direct numerical simulation of CO2 hydrate dissociation in pore-scale flow by applying CFD method

Summary The lattice Boltzmann method (LBM), a kind of mesoscopic method based on kinetic theory, is widely used in computational fluid dynamics and acoustic wave. Compared with the traditional wave equation, LBM has many advantages, such as great ease of implementation, near-infinite potential for the parallelization, flexible handling of boundary conditions and simulating complex phenomena easily. In this abstract, LBM is introduced to simulate acoustic wave propagation with viscous sponge layers (VSL), where the relaxation time, which is related to the kinematic shear viscosity, varies as different functions and the reflected wave absorbing effects are compared. Numerical results demonstrate that the situation when the relaxation time in VSL varies as a cubic function has a better absorbing ability for boundary reflection, which is of vital importance for seismic wavefield simulation by LBM.

A numerical study of the MRT-LBM for the shallow water equation in high Reynolds number flows: An application to real-world tsunami simulation

Soft rock is one of the common geological conditions in coal mine underground water reservoir engineering. The cross-scale correlation analysis of water erosion soft lithology deterioration is very important for the safety and stability of coal mine underground reservoir (CMUR) engineering. To address the issues of grain crowding and segmentation difficulties in cross-scale correlation analysis, as well as the limitations of traditional etching methods, this study proposes an image grain segmentation method based on deep learning algorithms, utilizing scanning electron microscopy and image processing techniques. The method successfully segments crowded grains and eliminates the interference from misplaced particles. In addition, indoor uniaxial compression tests were conducted to obtain the mechanical properties of sandstone samples with different water content. By quantitatively characterizing the macroscopic and microscopic deterioration degree of red sandstone samples with different water contents, the relationship between the strength changes of rock samples and the petrographic parameters such as grain size and grain shape is analyzed, and the influence law of soft lithology deterioration in CMUR engineering is revealed. The results indicate: (1) Water significantly weakens the mechanical properties and stability of soft rock. With increasing water content, the strength of sandstone samples continuously decreases, and the failure mode transitions from brittle to ductile failure. (2) The deterioration of micro-micro structures is the main cause of the decrease in mechanical properties of water-eroded soft rock. Grain size, grain area, and aspect ratio are negatively correlated with water content, indicating that hydrophilic minerals in soft rock dissolve under the action of water, leading to rock damage. (3) Grain size, area, and aspect ratio can serve as significant indicators for quantifying the strength changes of water-eroded soft rock. The research findings can be applied to stability assessment and disaster prevention in CMUR engineering.

Soil water retention curve (SWRC) as the constitutive relationship of hydro-mechanical coupling bridge of unsaturated soil has been experimentally investigated decades regarding impacts from dynamic effects in sandy soil and deformation in soft soil. However, due to inaccessibility of observation of microscale dynamic capillary behavior in geotechnical testing scale, most of the experimental methods can only provide the deviation between static SWRC and dynamic SWRC on drainage and imbibition. With the development of Computational Fluid Dynamic (CFD) simulation, several numerical methods so far can be utilized to investigate the soil water retention behavior in both micro- and macro-scale and upscaling between them, such as pore network model, Navier-Stokes integrated with Volume of Fluid and Level Set Method. Nevertheless, none of them provide a vision of interaction between fundamental fluid fractions in order to replicate the physical behavior of fluid tension from their mathematical expression. Compared to those CFD methods, Lattice Boltzmann Methods (LBM) is formulated on microscale for simulation of fluid dynamics. In addition to the interaction forces between fluid-fluid and fluid-solid phases, it fundamentally replicates the physical meaning of immiscible multiphase flow behavior in porous media. Therefore, LBM is selected to investigate the dynamic effect in soil water retention behavior in this study. The aim is to investigate the dynamic capillary pressure (soil suction in soil mechanics) varying with the saturation of each phase in a Representative Elementary Volume (REV) domain.