Pore-scale Lattice Boltzmann Method Research Articles

Improved lattice Boltzmann method to simulate liquid flow in nanoporous media: Coupling molecular dynamics simulations and theoretical model

Understanding the mechanisms of nanoconfined liquid flow in nanoporous media is crucial for many scientific and engineering applications such as enhanced shale oil recovery and water purification. However, due to molecular interactions which cause slip boundary and heterogeneous viscosity/density in nanoscale space, the conventional continuity equations are no longer applicable. Besides, the pore size in popular molecular dynamics simulation (MDS) is too small to meet the engineering application, and the pore-scale lattice Boltzmann method (LBM) is difficult to accurately consider molecular interactions in complicated nanoporous media. In this work, we summarize and establish four theoretical models for liquid flow in nanopores, which are region-separation model, effective viscosity model, apparent viscosity model, and apparent slip length model. Then, through comparative analysis, we indicate that the apparent viscosity model is most suitable for coupling LBM. Based on apparent viscosity model which comprehensively considers slip boundary and heterogeneous viscosity/density, we present a local-apparent-viscosity LBM (LAV-LBM) to simulate liquid flow in nanoporous media. According to LAV-LBM simulations, the effects of molecular interactions, porous media geometry, and wall wettability on apparent permeability of water flow in nanoporous media are discussed. Finally, we couple MDS results with the proposed model to calculate apparent permeability of shale oil flow in inorganic and organic media, which provides a basic model for the upscaling method from molecule-scale to pore-scale simulations.

Simulation of Water Flow in a Nanochannel with a Sudden Contraction or Expansion.

Water flow in a nanoscale channel is known to be affected by strong water-wall interactions; as a result, the flow considerably deviates from the conventional continuum flow. Nanochannel with a sudden contraction or expansion is the most fundamental morphological nanostructure in many nanoporous systems such as shale matrix, mudrock, membrane, etc. However, the nanoconfinement effects of water flow in nanoporous systems and its effect on macroscopic flow behavior are still evolving research topics. In this work, our recently developed pore-scale lattice Boltzmann method (LBM) considering the nanoscale effects is extended to directly simulate water flow in nanoporous systems. The results show that the flow rate is dramatically decreased in hydrophobic nanopores because of additional flow resistances at the contraction and expansion junctions. This indicates that the bundle of capillary models or the permeability averaging method overestimates the water flow rate in nanoporous media if the contraction/expansion effects between different nanopores are ignored. This work highlights the importance of wettability of the nanochannel in the determination of dynamic water flow behaviors in the contraction/expansion nanosystem. Other important aspects, including velocity distribution, flow patterns, and vortex characteristics as well as pressure variation along the flow direction, are for the first time revealed and quantified. Large differences can be found comparing gas or larger-scale water flows through the same system. A new type of pressure variation curve along the axis of flow direction is found in the hydrophobic nanochannel with a sudden contraction/expansion. This work provides the fundamental understanding of water transport through the nanoscale system with contraction and expansion effects, giving implications to a wide range of industry applications.

Pore scale simulation for melting of composite phase change materials considering interfacial thermal resistance

The convective melting process and thermal performance of phase change materials (PCMs) incorporating porous skeleton in the one-side-heated rectangular cavity are investigated numerically in this work. A pore-scale lattice Boltzmann method (LBM) with implicit scheme is developed to explore the solid–liquid phase change process. The interfacial thermal resistance between the skeleton and PCMs is considered by interfacial conditions treatment. The random porous microstructure is generated by quartet structure generation set (QSGS) which is used to compute effective thermal conductivity in LBM. The validations of the current model are employed by the two-phase series conduction model and previous numerical results. The effects of porous structure, skeleton material, and thermal interfacial conditions on heat transfer characteristics are systematically investigated. The computational results show that the melting rate and effective thermal conductivity increase with the reducing porosity and the high thermal conductivity of the skeleton material accelerate the melting process. In addition, the consideration of interactions in the LBM leads to a significant difference. When the thermal interfacial resistance is set to be 1 × 10−4 m2 W/K, the temperature drop is very large in two-phase conduction, the melting rate decreases remarkably in the phase change process. The present simulation is also suitable for optimizing the porous structure to prepare various composite PCM in the thermal energy storage field.

Pore-scale simulation of salt fingers in porous media using a coupled iterative source-correction immersed boundary-lattice Boltzmann solver

In the conventional representative elementary volume-scale models, details of fluid movement, thermal transfer and mass transport in the porous media are relatively hard to capture, while the understanding of them is crucial in many diverse engineering and environmental applications such as running nuclear power facilities or pollutant diffusion in soil environment. In this paper, a pore-scale lattice Boltzmann method (LBM) modeling of double diffusion systems in saturated porous media is developed to investigate the role played by pore structure in the behavior of salt finger phenomena together with their fluid flow mechanism. An iterative source-correction immersed boundary method is developed to describe the solid skeleton with different boundary conditions for velocity field, heat transfer, and mass transport, respectively. The natural convection in a vertical annulus and the conjugate heat transfer problem in a two-layer horizontal annulus are employed to verify the accuracy and the applicability of the immersed boundary method for Dirichlet-type, Neumann-type and conjugate heat transfer boundary conditions, respectively. Comparisons between the present results and existing investigation show a very good agreement and demonstrate that the double diffusive process in porous media can be predicted with a good accuracy by the proposed model. Subsequently, the instability evolution process of salt finger-type of double diffusive convection in porous media is investigated, with a focus on the structure and behavior of salt fingers and the kinetic energy evolution. The obtained simulation results show that in saturated porous media, relatively large vertical mass fluxes can be generated even if the density distribution is of dynamical stability.

Prediction of effective diffusivity of porous media using deep learning method based on sample structure information self-amplification

Effective diffusivity is one of the basic transport coefficients used to describe the mass transport capability of a porous medium. In this study, a deep learning method based on a convolutional neural network (CNN) with sample structure information self-amplification is proposed to predict the effective diffusivity of a porous medium, which is considerably influenced by the morphological and topological parameters of the porous medium. In this method, the geometric structures of three-dimensional (3D) porous media are reproduced via a stochastic reconstruction method. Datasets of the effective diffusivities of the reconstructed porous media were first established by the pore-scale lattice Boltzmann method (LBM) simulation. A large number of geometric structures of 3D porous media are obtained using the proposed sample structure information self-amplification approach. The 3D geometric structure information and corresponding effective diffusivities are directionally applied to a CNN for training and prediction. The effective diffusivities of media with porosities ranging from 0.48 to 0.58 are employed as training datasets, and the effective diffusivities of media with a broader porosity range of 0.39 to 0.79 are predicted by CNN. The CNN model can achieve a fast and accurate prediction of the effective diffusivity. The relative error between the CNN and LBM is 0.026%–8.95% with porosities ranging from 0.39 to 0.79. For a typical case with a porosity of 0.5, the computation time required by the CNN model is only 3 × 10−4 h, while the computation time for the same case is 16.96 h using the LBM. These findings indicate that the proposed deep learning method has a powerful learning ability; it is time-saving, provides accurate predictions, and can serve as a promising and powerful tool to predict the transport coefficients of complex porous media.

Pore-scale modeling of oxygen transport in the catalyst layer of air-breathing cathode in membraneless microfluidic fuel cells

The air-breathing membraneless microfluidic fuel cell is one of the potential micro-fuel cells. Different from conventional membrane-based micro-fuel cells, its cathode catalyst layer directly contacts with flowing aqueous electrolyte. This makes it essential to well understand the oxygen transport, dissolve and reaction in cathode catalyst layer of the microfluidic fuel cell. For the first time, a pore-scale Lattice Boltzmann method model is developed for the cathode catalyst layer with an underneath electrolyte microchannel. The various nanostructured catalyst layers are numerically reconstructed. The effects of key components (ionomer and catalyst mass fractions) and geometric parameters (porosity, isotropy) on oxygen transport and reaction are investigated and discussed. The modeling results suggest that local oxygen concentration and reaction rate are closely correlated to nanostructure. Oxygen transfer can be enhanced by increasing the porosity yet ionomer is found to be extra resistance. The ionomer and catalyst mass fractions have complex effects on oxygen transfer and reaction. Vertical-anisotropic catalyst layers benefit oxygen transfer, thus ordered nanostructure of cathode catalyst layer holds great potentials to enhance performance. The electrolyte flow rate shows the minimum influence on oxygen transfer and reaction. The modeling results can provide insights into multiphysics interaction and characteristics of oxygen transport in air-breathing cathode and also be reference for flow in porous media involving electrochemical reactions.

Pore-scale investigation on effects of void cavity distribution on melting of composite phase change materials

Composite Phase Change Materials (PCMs) incorporated with metal foams are promising candidates for thermal management for space exploration. However, void cavities are generated as a result of the volume change of PCM during the melting process, introducing a resistance to heat transfer due to the low thermal conductivity of the void. In this work, the effects of void cavity distribution on the conduction-dominated melting of composite PCMs under microgravity conditions are studied by a two-dimensional pore-scale lattice Boltzmann method, in which a microstructural description of the metal foam is experimentally characterized with the help of X-ray micro-Computed Tomography. Two typical distribution patterns of void cavities are analsed and computed performance is compared (1) a near-wall void cavity, and (2) randomly distributed void cavities. The evolutions of temperature distributions and melting interfaces are compared, and the average liquid fraction and energy stored per width are deduced to describe the energy storage performance. Moreover, the influence of the volume fraction of void cavities is investigated by comparing temperature distributions and energy storage performances of composite PCMs with four different volume fractions of void cavities (0%, 3.7%, 7.6%, 15.2%). After introducing void cavities, the energy stored per width is reduced by 5.7%, 12.3% and 20.2% for randomly distributed void cavities when volume fraction of void cavities is 3.7%, 7.6%, and 15.2%, respectively, and reduced by 42.2%, 64.1% and 79.7% for the near-wall void cavity, respectively. This work initiates the study of the effects of void cavity distribution on composite PCMs, which will stimulate work on structural optimization of thermal management systems.

Image-based modelling for fluid flow and permeability prediction within continuously-evolving mushy zone during melting and solidification

Mushy zone permeability is a key parameter that characterizes the fluid flow resistance within the two-phase mixed region during solid-liquid phase transitions. It plays an important role in accurately modelling the melting and solidification processes as well as the related latent heat storage performance. In our previous research, series images of the transient microstructures within the continuously-evolving mushy zone during both paraffin’s melting and solidification have been experimentally obtained by using a confocal optical microscope system. Thus, in this study, based on those experimentally-obtained images, the liquid flow and related permeability within the transient mushy zone were calculated using a pore-scale lattice Boltzmann method. The calculated flow velocity and predicted permeability have been verified against the corresponding reported analytical solutions. In addition, the mechanism behind the microscopic flow was presented and analysed. Moreover, the effects of image resolution on the fluid flow calculation were also studied. It was found that difference in the microstructures between melting and solidification results in distinctly various distributions of local velocity fields within the mushy zone, but makes little difference to the maximum velocity and the average permeability. The results also indicate that the image resolution imposes great effects on the predicted liquid flow by blurring and omitting tiny structures within the mushy zone in lower-resolution images. In addition, the predicted permeability increases more gently with the local liquid fraction as compared with our previously proposed correlations. Therefore, this work presents detailed information on fluid flow within mushy zone with continuously-evolving microstructures, and provides more insights into the fluid dynamics of the solid-liquid phase change.

Effect of supergravity on heat transfer characteristics of PCM with the pore-scale lattice Boltzmann method

Latent thermal energy storage has been recommended as an effective technique to the thermal management system of space exploration due to its excellent ability of storing thermal energy. In the current work, the melting process of phase change material under supergravity conditions (3g, 5g, 7g) are numerically investigated by a pore-scale lattice Boltzmann method with the real microstructure of metal foam. A comparative study is carried out to illustrate the influence of gravitational acceleration and metal foam on melting performance of phase change material. Results indicate that natural convection accelerates the motion velocity of the upper PCM, and leads to the inhomogeneous distribution of melting front. Moreover, with the increasing gravitational acceleration, there is a transition of the dominated heat transfer mechanism from conduction to convection, which attributes to the stepped-up natural convection effect, and thus melting front gets even steeper and melting rate is significantly increased. Besides, the existence of metal foam significantly distorts the melting front and enhances the melting rate.

Pore-scale investigation of gravity effects on phase change heat transfer characteristics using lattice Boltzmann method

Latent heat thermal energy storage (LTES) has been recommended to complicated aerospace systems due to the excellent ability of storing thermal energy in recent years. Metal foam, as an effective additive to enhance the effective thermal conductive coefficient of phase change materials, has been wildly used in the LTES system. In support of the future space exploration, solid–liquid phase change within metal foam under different gravitational accelerations and corresponding heat transfer characteristics are investigated in this work to enhance understanding of heat transfer capability in reduced gravity conditions. A pore-scale lattice Boltzmann method with the double distribution functions is developed to study the solid–liquid phase change problems with the natural convection heat transfer in metal foam. Here, microstructure of metal foam is experimentally obtained by the use of X-ray computed tomography. Two numerical validation cases are performed, one for fluid–solid conjugate heat transfer problem, and the other for melting process in a square cavity without the porous media. The presented lattice Boltzmann results are in good agreement with previous analytical and numerical results. Based on the analysis of temperature and velocity fields during melting within metal foam, it is found that the clockwise circulation, caused by the temperature gradient, leads to the inhomogeneous distribution of liquid–solid interface along vertical direction. What’s more, gravity effects on the temperature and velocity fields together with the average Nusselt number and liquid fraction coefficient are investigated. Results show that with the decrease of gravitational accelerations from 1g to 0g, the maximum vertical velocity reduces and the thickness of velocity boundary layer thickens accordingly, and results in the pronounced reduction of average Nusselt number and melting rate. The natural convection appears to be even more tenuous as gravitational acceleration decreases, leading to the dominant heat transfer mechanism transited from convection to conduction, and finally alleviating the phase change process. The liquid fraction under 0g, 0.01g and 0.1g conditions are 54.6%, 58.9% and 67.9% respectively of that under 1g conditions at Fo = 0.06. In addition, porosity effects on phase change heat transfer characteristics are discussed by comparing the liquid fraction with porosity of 0.9, 0.94 and 1. It is found that metal foam with lower porosity shows higher effective thermal conductivity and outstanding heat transfer performance, while the restriction on natural convection should not be neglected, especially for melting region which is dominated by natural convection.