Lattice Boltzmann Method Model Research Articles

Study on Gas Diffusion Layer Structure Tolerant to Flooding in PEFC by Scale Model Experiment and LBM Simulation

To improve the performance of a polymer electrolyte fuel cell (PEFC), it is essential to control liquid water behavior in the cell. Gas diffusion layer (GDL) plays an important role for the water transport. As the structure of GDL is quite complex and small with the scale order of 200 mm thickness, measurement of liquid water behavior in the GDL is difficult, and only a few results are reported with X-ray measurement and pore-network simulation. Therefore, the water transport in GDL is still unclear and there may be some room for improving the structure of GDL. The objective of this study is to evaluate the effects of different degree of isotropic fiber directions and uneven hydrophobic and hydrophilic structure of GDL for the water transport. For the analysis enlarged scale model experiment and high-speed Lattice Boltzmann Method (LBM) are applied. In the previous research of the authors, the effects of the GDL fiber direction on the cell performance was investigated using anisotropic GDL, and the results of the experiments showed that the cells with perpendicular fibers are more tolerant to flooding than cells with fibers parallel to the channel direction (1). The fiber direction is important factor for the water control in the GDL. The fiber direction perpendicular to the channel discharged liquid water under libs more smoothly. Similarly, there is a report which shows that better cell performance was obtained with the GDL with cyclic hydrophobic and hydrophilic lines (2). The fiber direction and wettability of GDL are important factors for the water control in the GDL, but the water behavior in the structures have not been observed and the effect of these factors on water transport is not clear yet. The authors proposed a scale model experiment with similarity to the actual behavior. In the experiment silicon oil is used for the liquid water and water for air. With this combination of the fluids, buoyancy effects are set similar with the actual system in enlarged models with 300 times of the actual size. Additionally, the authors have developed LBM model with high speed computation to make it possible to simulate the space covering the GDL width and channel. Figure 1 is a result comparing the scale model and LBM simulation. The figure shows the liquid water distribution in GDL. Figure 1 (a) is experimental results with an enlarged scale model and Fig. 1 (b) is simulation result by LBM. The two figures show similar water distribution. Figure 2 shows two different fiber structures with LBM simulation. Figure 2 (a) is the structure of anisotropic fiber and Fig. 2 (b) is the one of isotropic fiber. The fibers have a diameter of 8μm and orientation is set to give based on electrical resistivity with the actually measured GDLs with different isotropy. Sizes of the each GDL structure is 270μm × 270μm × 200μm and porosities is 75%. Liquid water is introduced from a hole placed at the bottom center of the boundary, which corresponds to MPL boundary. The contact angle of solid wall (GDL fibers, MPL, side wall) is set 130º. Figure 3 shows the difference in water distributions in two different fiber structures with LBM simulation. Figure 3 (a) shows the result for anisotropic and Fig.3 (b) shows the result for isotropic fiber. The water tends to spread along with fiber direction in the anisotropic GDL, whereas water transports upwards randomly in the isotropic GDL. It is known that water tends to retain in the GDL under ribs and smooth removal of the water is important to avoid flooding. The anisotropic GDL may guide the liquid water toward channel direction from under the rib, when the fiber direction is placed perpendicular to the rib direction. In the final full paper, the water transport characteristics with different fiber orientations and wettability will be demonstrated in detail. Reference (1) K. S. S. Naing, Y. Tabe, and T. Chikahisa, J. Power Sources, 196 (2011) 2584-2594. (2) A. Forner-Cuenca, J. Biesdorf, V. Manzi-Orezzoli, L. Gubler, T. J. Schmidt and P. Boillat, J. Electrochemical Society, 196 (13) F1389-F1398 (2016). Figure 1

Simulation of forced convection in non-Newtonian fluid through sandstones

ABSTRACTNumerical simulation is carried out to study forced convection in non-Newtonian fluids flowing through sandstones. Simulation is carried out using lattice Boltzmann method (LBM) for both shear-thinning and shear-thickening, by varying the power law index from 0.5 to 1.5 in Carreau–Yasuda model. Parameters involved in LBM and Carreau model are identified to achieve numerical convergence. Permeability and porosity are varied in the range of 10−10–10−6 and 0.1–0.7, respectively, to match actual geometrical properties of sandstone. Numerical technology is validated by establishing Darcy's law by plotting the graph between velocity and pressure gradient. Consequently, investigation is carried out to study the influence of material properties of porous media on flow properties such as velocity profiles, temperature profiles, and Nusselt number.

Lattice Boltzmann method and its application in the modelling of high intensity focused ultrasound (HIFU)

High-intensity focused ultrasound (HIFU) is a breakthrough of noninvasive targeted therapeutic technique for tumor treatments. The operational procedure of HIFU is to concentrate the ultrasound energy into the focal region by using the ultrasound transducer, and the focused ultrasound energy is sufficient to rapidly rise the temperature of tumor located at the focal region up to above 65°C and locally destroy the tumor for coagulation necrosis. The ultrasound transducer is the key component in HIFU treatment to generate the high-intensity focused ultrasound energy, the dimension of focal region generated by the transducer is closely relevant to the safety of HIFU treatment. Therefore, it is necessary to simulate the acoustic field numerically for estimating the performance, optimizing the parameters and reducing the design cost of the focused ultrasound transducer. Besides, the common spherical transducer is the most widely used transducer in HIFU, but the size of its focal region still could not satisfy the requirements of some sophisticated applications. So, it is necessary to adopt some new kinds of focused ultrasound transducers with better focusing performance. Aiming at these issues, we presented a numerical simulation method called the lattice Boltzmann method (LBM) in this paper. It is a novel fluid dynamic simulation approach based on mesoscopic kinetic theory, which takes prominent advantages of distinct physical meaning, easy implementation and excellent parallel performance. The LBM has shown great potential in numerical simulations of complex flows that would be difficult for traditional methods. Firstly, we reviewed the developments and applications of the LBM. Then, we revealed the inherent relationship between the LBM and the Boltzmann equation, and presented two basic LBM models called the single-relaxation-time (SRT) model and multiple- relaxation-time (MRT) model, recovered the corresponding macroscopic Navier-Stokes equations respectively via the Chapman−Enskog expansion, presented two common boundary conditions called the non-equilibrium extrapolation scheme and the BFL scheme. Besides we introduced the conversion method between the physical units and lattice units based on dimensional analysis. After that, we built an axisymmetric multiple-relaxation-time (AMRT) LBM model with the BFL scheme, and simulated the acoustic fields generated by concave ultrasound transducers of different field angles respectively by the AMRT model, Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and spheroidal beam equation (SBE). Results indicated that the AMRT model could be used to describe the acoustic field generated by the concave ultrasound transducer, and the transducer with bigger field angle had a better focusing performance. Lastly, we presented a novel spherical cavity transducer with two open ends for providing subwavelength focal region and sufficient pressure gain. We investigated the standing wave acoustic field generated by the spherical cavity ultrasound transducer via the AMRT model and experimental measurements. Results indicated that the AMRT model could be used to describe the standing wave filed generated by the spherical cavity ultrasound transducer, and this device exhibited much better focusing performance than the traditional concave ultrasound transducer, and could meet the requirement of some sophisticated HIFU treatments. The main aim of this work is to solve some practical problems for the numerical modeling of acoustic field in the HIFU treatments and provide new sights into the acoustic simulations.

Consistent lattice Boltzmann modeling of low-speed isothermal flows at finite Knudsen numbers in slip-flow regime: Application to plane boundaries.

The first nonequilibrium effect experienced by gaseous flows in contact with solid surfaces is the slip-flow regime. While the classical hydrodynamic description holds valid in bulk, at boundaries the fluid-wall interactions must consider slip. In comparison to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type condition for the fluid tangential velocity. This makes its numerical modeling a challenging task, particularly in complex geometries. In this work, this issue is handled with the lattice Boltzmann method (LBM), motivated by the similarities between the closure relations of the reflection-type boundary schemes equipping the LBM equation and the slip velocity condition established by slip-flow theory. Based on this analogy, we derive, as central result, the structure of the LBM boundary closure relation that is consistent with the second-order slip velocity condition, applicable to planar walls. Subsequently, three tasks are performed. First, we clarify the limitations of existing slip velocity LBM schemes, based on discrete analogs of kinetic theory fluid-wall interaction models. Second, we present improved slip velocity LBM boundary schemes, constructed directly at discrete level, by extending the multireflection framework to the slip-flow regime. Here, two classes of slip velocity LBM boundary schemes are considered: (i) linear slip schemes, which are local but retain some calibration requirements and/or operation limitations, (ii) parabolic slip schemes, which use a two-point implementation but guarantee the consistent prescription of the intended slip velocity condition, at arbitrary plane wall discretizations, further dispensing any numerical calibration procedure. Third and final, we verify the improvements of our proposed slip velocity LBM boundary schemes against existing ones. The numerical tests evaluate the ability of the slip schemes to exactly accommodate the steady Poiseuille channel flow solution, over distinct wall slippage conditions, namely, no-slip, first-order slip, and second-order slip. The modeling of channel walls is discussed at both lattice-aligned and non-mesh-aligned configurations: the first case illustrates the numerical slip due to the incorrect modeling of slippage coefficients, whereas the second case adds the effect of spurious boundary layers created by the deficient accommodation of bulk solution. Finally, the slip-flow solutions predicted by LBM schemes are further evaluated for the Knudsen's paradox problem. As conclusion, this work establishes the parabolic accuracy of slip velocity schemes as the necessary condition for the consistent LBM modeling of the slip-flow regime.

Challenges and opportunities in modelling of proton exchange membrane fuel cells (PEMFC)

Challenges and opportunities in modelling of proton exchange membrane fuel cells (PEMFC)

Application of the lattice Boltzmann method for simulation of the mold filling process in the casting industry

The aim of this work is the development of the lattice Boltzmann model for simulation of the mold filling process. The authors present a simplified approach to the modeling of liquid metal-gas flows with particular emphasis on the interactions between these phases. The boundary condition for momentum transfer of the moving free surface to the gaseous phase is shown. Simultaneously, the method for modeling influence of gas back pressure on a position and shape of the interfacial boundary is explained in details. The problem of the lattice Boltzmann method (LBM) stability is also analyzed. Since large differences in viscosity of both fluids are a source of the model instability, the so-called fractional step (FS) method allowing to improve the computation stability is applied. The presented solution is verified on the bases of the available reference data and the results of experiments. It is shown that the model describes properly such effects as: gas bubbles formation and air back pressure, accompanying liquid-gas flows in the casting mold. At the same time the proposed approach is easy to be implemented and characterized by a lower demand of operating memory as compared to typical LBM models of two-phase flows.

A novel Lattice Boltzmann method for the dynamics of rigid particles suspended in a viscoelastic medium

We suggest a novel numerical algorithm based on the lattice Boltzmann method (LBM) to investigate particulate systems in which solid particles are suspended in a viscoelastic medium. In this model, polymer solution is described by the viscoelastic fluid based on the advection-diffusion LBM model, and it is coupled with the smoothed profile method (SPM) which describes the motion of rigid particles. To validate the present algorithm, we test three benchmark problems (two-dimensional simulation); viscoelastic flow past a cylinder, a single particle migration in a viscoelastic Couette flow, and dynamics of two particles in a viscoelastic Couette flow. Simulation results are carefully analyzed, and they are compared with previous simulation results implemented by finite element method (FEM) and finite volume method (FVM). In all test results, hydrodynamic properties and the motion of the particles induced by viscoelasticity are correctly captured, and they qualitatively as well as quantitatively correspond to previous reports. We conclude that both viscoelasticity and multi-body hydrodynamic interactions can be well incorporated in this new LBM algorithm. The present study has its significance as a first report, which strictly solves the flow behavior of solid particles immersed in a viscoelastic medium on the LBM framework.

Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures

The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass–Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures.

A Finite Difference Lattice Boltzmann Method to Simulate Multidimensional Subcontinuum Heat Conduction

In this paper, a lattice Boltzmann method (LBM)-based model is developed to simulate the subcontinuum behavior of multidimensional heat conduction in solids. Based on a previous study (Chen et al., 2014, “Sub-Continuum Thermal Modeling Using Diffusion in the Lattice Boltzmann Transport Equation,” Int. J. Heat Mass Transfer, 79, pp. 666–675), phonon energy transport is separated to a ballistic part and a diffusive part, with phonon equilibrium assumed at boundaries. Steady-state temperature/total energy density solutions from continuum scales to ballistic scales are considered. A refined LBM-based numerical approach is applied to a two-dimensional simplified transistor model proposed by (Sinha et al. 2006, “Non-Equilibrium Phonon Distributions in Sub-100 nm Silicon Transistors,” ASME J. Heat Transfer, 128(7), pp. 638–647), and the results are compared with the Fourier-based heat conduction model. The three-dimensional (3D) LBM model is also developed and verified at both the ballistic and continuous limits. The impact of film thickness on the cross-plane and in-plane thermal conductivities is analyzed, and a new model of the supplementary diffusion term is proposed. Predictions based on the finalized model are compared with the existing in-plane thermal conductivity measurements and cross-plane thermal conductivity molecular dynamics (MD) results.

Multi-Scale Modeling of Transports inside PEMFC By Combining Multi-Phase CFD Fuel Cell Model with Lattice Boltzmann Method

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.

A lattice-Boltzmann scheme of the Navier–Stokes equation on a three-dimensional cuboid lattice

The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or a cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, either by adding a free parameter in the definition of moments or by extending the equilibrium moments. These models satisfy all isotropy conditions and are fully consistent to the Navier–Stokes equations. Here we developed a lattice Boltzmann model on a 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed the moment equations, derived from our MRT–LBM model through the Chapman–Enskog analysis, to be fully consistent with the Navier–Stokes equations. A second-order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities. The form of the second-order term and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the shear viscosity can be adjusted, independent of the stress-moment relaxation parameter, thus potentially improving the numerical stability of the model. The resulting cuboid MRT–LBM model is then validated through benchmark simulations using the laminar channel flow, the turbulent channel flow, and the 3D time-dependent, energy-cascading Taylor–Green vortex flow. The second-order accuracy of the proposed model is also demonstrated. The aspect ratios for numerical stability appear to be constrained at high flow Reynolds numbers, especially for turbulent flow simulations, an aspect requiring further investigation.

GPU accelerated numerical study of PCM melting process in an enclosure with internal fins using lattice Boltzmann method

Latent heat thermal energy storage (LHTES) has many applications in engineering fields such as electronic cooling, thermal storage of solar energy, heating and cooling in buildings, waste heat utilization and so on. The advantages of LHTES over sensible thermal energy storage or chemical energy storage techniques are high energy density and phase change at nearly constant temperature. Unfortunately, the low thermal conductivity of PCMs increases the thermal gradient in the energy storage system and impedes the heat transfer efficiency. However, high thermal conductivity fins could be used to promote the melting process in PCM enclosures. As a powerful numerical method developed during the past two decades, lattice Boltzmann method (LBM) was used to simulate the conjugate heat transfer in the solid walls, fins and PCM region. By changing the velocity field and diffusivities, only one distribution function was needed to simulate the melting with natural convection in PCMs and conduction in fins and enclosure surfaces. As a result, the thermal boundary conditions on the interfaces of PCMs, fins and solid walls were satisfied automatically. By using enthalpy-based multiple-relaxation-time (MRT) LBM model, the iteration steps for the latent-heat source term were avoided. Under this case, the conjugate convective heat transfer with phase change is modeled efficiently. The graphics processing units (GPU) computing becomes attractive since the advent of CUDA which includes both hardware and programming environment in 2007. Consequently, the developed MRT LBM code is further implemented to run on GPU. High computation speed was achieved. The melting process in PCMs was investigated for different materials of fins and walls, number of fins, fin configurations, hot wall temperature, thermal boundary conditions, and inclination angle of the PCM cavity. Lattice Boltzmann method implemented on GPU was demonstrated as an efficient approach to study the PCM melting process with internal fins.

Lattice Boltzmann simulation of a laminar square jet in cross flows

A three-dimensional, nineteen-velocity (D3Q19) Lattice Boltzmann Method (LBM) model was developed to simulate the fluid flow of a laminar square jet in cross flows based on the single relaxation time algorithm. The code was validated by the mathematic solution of the Poiseuille flow in a square channel, and was further validated with a previous well studied empirical correlation for the central trajectory of a jet in cross flows. The developed LBM model was found to be able to capture the dominant vortex, i.e. the Counter-rotating Vortex Pair (CVP) and the upright wake vortex. Results show that the incoming fluid in the cross flow channel was entrained into the leeside of the jet fluid, which contributes to the blending of the jet. That the spread width of the transverse jet decreases with the velocity ratio. A layer-organized entrainment pattern was found indicating that the incoming fluid at the lower position is firstly entrained into the leeside of the jet, and followed by the incoming fluid at the upper position.

Simulation of micro flow in the transition regime using effective-viscosity-based multi-relaxation-time lattice Boltzmann model

With the rapid development of micro-electro-mechanical systems (MEMS), microscale rarefied gas flows have received considerable attention in the past decades. Recently, the lattice Boltzmann method (LBM) emerges as a promising way to study the flow in MEMS for its kinetic nature and distinctive computational features. Various LBM models have been used to simulate the microscale and nanoscale flow, among which the two-dimensional and nine-velocities (D2Q9)-based LBM is most widely accepted due to its extremely simplicity and high efficiency. However, the D2Q9-based LBM encounters great difficulties in the transition regime due to the rarefaction effects on mean free path and gas viscosity. An effective way to improve the capability of the existing LBM model is to incorporate an effective viscosity into the relaxation time, which can improve the accuracy of LBM model while keeping the simplicity and efficiency of LBM. However, the existing D2Q9-based LBM models with effective viscosity cannot give satisfactory predictions of the none-equilibrium phenomenon at moderate or high Knudsen (Kn) number both in accuracy and efficiency. To solve the above problem, in this study, an effective mean free path function proposed by Dongari et al. (Dongari N, Zhang Y H, Reese J M 2011 J. Fluids Eng. 133 071101) via modular dynamics mean is introduced into the D2Q9 multi-relaxation-time lattice Boltzmann model (MRT-LBM) to account for the effect of Knudsen layer in transition flow regime, and the viscosity in the MRT-LBM model is modified correspondingly. The combination of the bounce-back and specular reflection boundary condition is used to deal with the velocity slip, and the relaxation time and the reflection coefficient are properly set to eliminate the numerical artifact on the boundaries as the kinetic boundary condition is used. Micro Couette flow at Kn=0.1-6.77, and periodic Poiseuille flow at Kn=0.1128-2.2568, respectively, are numerically investigated by using the proposed MRT-LBM model, and the numerical results, including the non-dimensional velocity profile and the mass flow rate, are verified by the direct simulation Monte~Carlo (DSMC) data, the linearized Boltzmann solutions and the existing LBM model. The calculation results demonstrate that in transition regime, with the increase of Knudsen number, the dimensionless slip velocity at the wall significantly increases. It is shown that the velocity profiles predicted by the present MRT-LBM model agree well with the DSMC data and linearized Boltzmann solutions up to Kn=4.5 in Couette flow, which is much more accurate than that obtained from the existing LBM model. And the present LBM model gives at least the same order of accuracy in the prediction of velocity profile and mass flow rate as the existing LBM model in periodic Poiseuille flow. What is more, the Knudsen minimum phenomenon of flow in the microchannel is successfully captured at around Kn=1. The results demonstrate that the proposed model can enhance the ability of LBM in capturing the non-equilibrium phenomenon in micro flow in the transition regime both in accuracy and efficiency.

A lattice Boltzmann model for heat and mass transfer phenomena with phase transformations in unsaturated soil during freezing process

In this paper, a mesoscopic numerical model for simulating the heat and moisture transport phenomena in frozen soil during freezing process is presented. The model includes a stochastic generation-growth method for reconstructing the soil structure with given macroscopic geometric parameters, a lattice Boltzmann method (LBM) model for solving multiphase fluid flow and a LBM model for solving heat conduction with phase change in porous media. By using the present model, freezing process in sandy loam soil is demonstrated. Two types of boundary condition, prescribed temperature and adiabatic boundary conditions are employed in the given cases. All the numerical results show good agreement with experimental results. Considering the mesoscopic nature of LBM, the proposed model is a potential alternative to traditional continuum models.

Pore-scale numerical investigations of fluid flow in porous media using lattice Boltzmann method

Purpose – Lattice Boltzmann method (LBM) is employed to explore friction factor of single-phase fluid flow through porous media and the effects of local porous structure including geometry of grains in porous media and specific surface of porous media on two-phase flow dynamic behavior, phase distribution and relative permeability. The paper aims to discuss this issue. Design/methodology/approach – The 3D single-phase LBM model and the 2D multi-component multi-phase Shan-Chen LBM model (S-C model) are developed for fluid flow through porous media. For the solid site, the bounce back scheme is used with non-slip boundary condition. Findings – The predicted friction factor for single-phase fluid flow agrees well with experimental data and the well-known correlation. Compared with porous media with square grains, the two-phase fluids in porous media with circle grains are more connected and continuous, and consequently the relative permeability is higher. As for the factor of specific porous media surface, the relative permeability of wetting fluids varies a little in two systems with different specific surface areas. In addition, the relative permeability of non-wetting fluid decreases with the increasing of specific surface of porous media due to the large flow resistance. Originality/value – Fluid-fluid interaction and fluid-solid interaction in the SC LBM model are presented, and schemes to obtain immiscible two-phase flow and different contact angles are discussed. Two-off mechanisms acting on the wetting fluids is proposed to illustrate the relative permeability of wetting fluids varies a little in two systems with different specific surface.

Lattice Boltzmann Method for the Simulating Extrudate Swell of Viscoelastic Fluid

The main objective of this work is to develop a new approach based on the Lattice Boltzmann method (LBM) to simulate the extrudate swell of an Oldroyd B viscoelatic fluid. Two lattice Boltzmann equations are used to solve the Navier-Stokes equations and constitutive equation simultaneously at each time iteration. The single LBM model is used to track the moving interface in this paper. To validate the accuracy and stability of this new scheme, we study the steady 2D Poiseuille flow firstly, finding the numerical results be in good accord with the analytical solution. Then the die-swell phenomenon is solved, we successfully acquire the different swelling state of an Oldroyd B fluid at different time.

Lattice Boltzmann simulation of multicomponent noncontinuum diffusion in fractal porous structures.

A lattice Boltzmann method (LBM) of multicomponent diffusion is developed to examine multicomponent, noncontinuum mass diffusion in porous media. An additional collision interaction is proposed to mimic the Knudsen diffusion caused by the collision interaction between gas molecules and solid pore walls. Using the improved LBM model, the ternary mixtures diffusion is simulated in fractal porous structures which are reconstructed by the random midpoint displacement algorithm. The effects of fractal characteristics and Knudsen diffusion resistance on the multicomponent diffusion in porous structures are investigated and discussed. The results indicate that the smaller fractal dimension enhances the diffusion rate of gas mixtures in fractal porous structures. When the dimensionless Knudsen diffusion coefficient is less than 20, the presence of Knudsen diffusion resistance reduces the rate of mass diffusion in porous structures obviously, especially for the species with larger molecular weight.

Numerical modeling of slippage and adsorption effects on gas transport in shale formations using the lattice Boltzmann method

Shale formations consist of numerous nanoscale pores within a range of 2 nm–50 nm; the shale gas flow within this size range under typical shale reservoir pressure and temperature will fall into the slip flow or the transitional flow regime 0.001 < Kn < 10. Besides nano-pores in shale, there exist a number of mesoscopic and macroscopic pores with size larger than 50 nm, and many micrometer fractures. Natural gas, mainly methane, flows through nanoscale pores, mesoscale, and macroscopic pores or fractures during the production period. Gas slippage described by the Klinkenberg effect reduces viscous drag near the pore walls and influences permeability. In shale, the majority of gas molecules are adsorbed in kerogen that is considered to be organic source rocks. Within nano-pores and meso-pores, Darcy's law cannot effectively describe this type of transport phenomena due to its continuum assumption. Alternatively, the kinetic-based lattice Boltzmann method (LBM) becomes a strong candidate for simulating an organic-rich shale reservoir that contains a large number of nano-pores. In this paper, we present a multiple-relaxation-time (generalized) LBM, which is considered to be one of the most efficient LBM models. For gas flow in a confined system, its molecular mean free path is corrected depending on the size of the confined system and the distance of the gas molecules from the pore walls. Gas slippage on pore walls is captured with a combined bounce-back specular reflection boundary condition. In addition, adsorbed gas in shale has a significant influence on gas transport in shale gas production. Here, we propose to incorporate inter-molecular and adsorptive forces into the generalized LBM algorithm to capture gas adsorptions in organic nano-pores. Therefore, this approach is able to simulate gas flow with adsorption effect. Many factors are believed to control the flow mechanisms in these types of pores, including the pore size distribution, the specific surface area, and the adsorptive feature of the pore walls. The simulation results agree well with the existing data for high Knudsen flows between 2D parallel plates. Accounting for the adsorption and slippage effects, flow phenomena are investigated by varying different controlling factors in both simple and complex structures. The permeability of methane is also determined for complex porous geometries.

Lattice Boltzmann simulation of the three-dimensional motions of particles with various density ratios in lid-driven cavity flow

An estimation of solid particle dynamics through a fluid has been studied. Although traditional computational fluids dynamics models can predict multiphase flow and the interactions between the fluid and solid particles, a high level of accuracy of an appropriate numerical model for this type of difficulty is still in demand. Some researchers examining this problem dedicated their research to the particle motions under the influence of gravity. Therefore, in this study a modern computational fluid dynamic model, the Lattice Boltzmann Method (LBM), was proposed to predict the three-dimensional cubic lid-driven cavity flow and combined with the Lagrangian approach on the prediction of solid particles in the range of different density ratios. To solve the term, flow fluid, the mesoscale numerical scheme of the Multi Relaxation Time (MRT) lattice Boltzmann method was used to simulate the objects at higher stability. In the present study, the different densities of the particles were considered and the effects of gravity were included in the calculation. The 4th Runge-Kutta method was functioned to determine the effect of an external force on a particle because this method is accurate enough compared to other known numerical schemes. The hard sphere model was used to model particle-particle and particle-wall collisions. The solid particle subtleties determined using a numerical fluid dynamic simulation of LBM showed good agreement with the reputable benchmark results by previous researchers. Furthermore, according to the results, the dependency of the particle trajectories on the magnitude of the density of the particles can be observed. The results revealed the significant effect of collision, drag force, gravity force, and vortex structure on a particle's trajectory. Consequently, the LBM model is suitable for this type of problem, and the proposed model is expected to have a wide range of applications.