Lattice Boltzmann simulation of solute transport in a single rough fracture

In this study, the lattice Boltzmann method （LBM） was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves （BTCs） for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers （Re）. The results show that the rough frac~＇e wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.     

NUMERICAL STUDY OF THE RELATIONSHIP BETWEEN APPARENT SLIP LENGTH AND CONTACT ANGLE BY LATTICE BOLTZMANN METHOD

The apparent slip between solid wall and liquid is studied by using the Lattice Boltzmann Method (LBM) and theShan-Chen multiphase model in this paper. With a no-slip bounce-back scheme applied to the interface, flow regimes under differentwall wettabilities are investigated. Because of the wall wettability, liquid apparent slip is observed. Slip lengths for different wallwettabilities are found to collapse nearly onto a single curve as a function of the static contact angle, and thereby a relationshipbetween apparent slip length and contact angle is suggested. Our results also show that the wall wettability leads to the formation of alow-density layer between solid wall and liquid, which produced apparent slip in the micro-scale.     

NUMERICAL STUDY OF NON-AQUEOUS PHASE LIQUID TRANSPORT IN A SINGLE FILLED FRACTURE BY LATTICE BOLTZMANN METHOD

In this article,the Non-Aqueous Phase Liquid(NAPL)transport in the single filled fracture was studied with the Shan-Chen multi-component multiphase Lattice Boltzmann Method(LBM)with special consideration of wettability effects.With the help of the model,the contact angle of the non-wetting phase and wetting phase interface at a solid wall could be adjusted.By considering a set of appropriate boundary conditions,the fractured conductivity was investigated in condition that the NAPL blocks the channels in the single filled fracture.In order to study the wettability effects on the NAPL transport,a constant driving force was introduced in the Shan-Chen multi-component multiphase LBM.Flow regimes with different wettabilities were discussed.Simulated results show that the LBM is a very instrumental method for simulating and studying the immiscible multiphase flow problems in single filled fracture.     

LATTICE BOLTZMANN METHOD WITH DOUBLE MESHES

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＩｎｒｅｃｅｎｔ ｙｅａｒｓ ,ｔｈｅｏｒｙａｎｄａｐｐｌｉｃａｔｉｏｎｓｏｆＬａｔｔｉｃｅＢｏｌｔｚｍａｎｎｍｅｔｈｏｄ (ＬＢＭ )ｈａｖｅｍａｄｅｒａｐｉｄ ｐｒｏｇｒｅｓｓ ,ｍａｋｉｎｇＬＢＭｃｏｍｐｅｔｉｔｉｖｅｔｏｔｈｅｃｏｎｖｅｎｔｉｏｎａｌａｐｐｒｏａｃｈｅｓｉｎＣｏｍｐｕｔａｔｉｏｎａｌＦｌｕｉｄＤｙｎａｍｉｃｓ (ＣＦＤ )ａｎｄａｎａｌｔｅｒｎａｔｉｖｅｗａｙｔｏｓｉｍｕ ｌａｔｅｔｈｅｆｌｕｉｄｆｌｅｌｄ[1] .ＴｈｅｋｅｙｉｄｅａｂｅｈｉｎｄＬＢＭｉｓｔｈ…     

APPLICATION OF LBM-SGS MODEL TO FLOWS IN A PUMPING-STATION FOREBAY

A 2-D Lattice Boltzmann Method (LBM) coupled with a Sub-Grid Stress (SGS) model is proposed and validated by flows around a non-submerged spur dike in a channel. And then the LBM-SGS model is further applied to flows in a pumping-station forebay. Shallow water equations are numerically solved by the LBM and the turbulence can be taken into account and modeled efficiently by the Large Eddy Simulation (LES) model. The bounce-back scheme of the non-equilibrium part of the distribution function is used at the inlet boundary, the normal gradient of the distribution function is set as zero at the outlet boundary and the bounce-back scheme is applied to the solid wall to ensure non-slip boundary conditions. Firstly, the model successfully predicts the flow characteristics around a spur dike, such as circulating flow, velocity and water depth distributions. The results are verified by the experimental data and compared to the results obtained by conventional Smagoringsky Model (SM) of LES. Finally, the LBM-SGS model is used to further predict the flow characteristics in a forebay, such as secondary flow and water level. The comparisons show that the model scheme has the capacity to simulate complex flows in shallow water with reasonable accuracy and reliability.     

Investigation of cavitation bubble collapse near rigid boundary by lattice Boltzmann method

The dynamics of the bubble collapse near a rigid boundary is a fundamental issue for the bubble collapse application and prevention. In this paper, the bubble collapse is modeled by adopting the lattice Boltzmann method(LBM) and is verified, and then the dynamic characteristics of the collapsing bubble with the second collapse is investigated. The widely used Shan-Chen model in the LBM multiphase community is modified by coupling with the Carnahan-Starling equation of state(C-S EOS) and the exact difference method(EDM) for the forcing term treatment. The simulation results of the bubble profile evolution by the LBM are in excellent agreements with the theoretical and experimental results. From the two-dimensional pressure field evolution, the dynamic characteristics of the different parts during the bubble collapse stage are studied. The role of the second collapse in the rigid boundary damage is discussed, and the impeding effect between two collapses is demonstrated.     

Lattice Boltzmanm方法在计算流体力学中的应用

Lattice Boltzmanm方法(简称LBM)是一种基于分子运动论和统计力学理论的流体计算方法。详细分析了LBM的基本理论,系统介绍了曲线固体边界处理的新方法。与Navier-Stokes方程相比较,LBM在算法及复杂边界处理等方面更具有优势。该方法在多相流、多组分流、热传导、颗粒悬浮、紊流及微小流束等问题的模拟中已得到广泛应用。     

SIMULATION OF SOLUTE TRANSPORT IN A PARALLEL SINGLE FRACTURE WITH LBM/MMP MIXED METHOD

This article deals with the solute transport in a single fracture with the combination of the Lattice Boltzmann Method （LBM） and Modified Moment Propagation （MMP） method, and this mixed method is proved to have several advantages over the LBM and Moment Propagation （MP） mixed method which leads to negative concentrations under some conditions in computation. The disadvantage of LBM/MP has been overcome to a certain extent. Also, this work presents an LBM solution of modeling single fractures with uniformly or randomly distributed grains, which can provide a new path of applying the LBM in solute transport simulation in fractures.     

INCOMPRESSIBLE MULTI-RELAXATION-TIME LATTICE BOLTZMANN MODEL IN 3-D SPACE

Multi-Relaxation-Time Lattice Boltzmann Method(MRT LBM) is of better numerical stability and has attracted more and more research interests.The previous MRT LBM included artificial compressible effects.To overcome the disadvantage,an incompressible MRT LBM has been proposed in two dimensions recently.In this article,we present incompressible MRT LBMs in 3-D space,with example of nineteen-velocity.The equilibria in momentum space are derived from an earlier incompressible Lattice Bhatnagar-Gross-Krook(LBGK) ...     

Modelling of solute transport in a filled fracture: Effects of heterogeneity of filled medium

In this paper, the developed lattice Boltzmann method(LBM) is used to model the solute transport in a filled fracture under a heterogeneous advective velocity field. The results of the developed LBM in modelling the solute transport are compared with the published experimental data. The numerically derived BTCs indicate that the distribution of the filled medium in the fracture has a significant effect on the characteristics of the BTCs, even with the same porosity. The heterogeneity of the filled medium is responsible not only for the heterogeneous advective velocity field but also for the early arrival and long tails of the BTCs. The long tailings of the BTCs increase their length with the increase of the duration of the input pulse. Furthermore, the BTCs obtained from the LBM simulations are well consistent with the two-region model(TRM). The fitting results show that the fractional mobile region varies with the distribution of the filled medium. The long tailings of the BTCs increase their length with the increase of the immobile region while the concentration peak value increases with the increase of the mobile region.     

Three-dimensional prediction of reservoir water temperature by the lattice Boltzmann method: Validation

The water temperature stratification in large reservoirs might have serious ecological and environmental consequences. The modeling of the temperature distribution and its history is of great importance both for studying the underlying mechanisms and for controlling the adverse effects. To develop an effective and efficient method for simulation of temporal and spatial temperature variations, a lattice Boltzmann method(LBM) model for 3-D thermal buoyancy flows is proposed and validated by the temperature data measured in a model reservoir. This paper discusses important aspects of the LBM and its turbulence model, analyzes the gravity sinking mechanism of cold currents, and demonstrates the complexity of the temperature redistribution process. Good agreement between the simulated and measured results shows that the newly developed method is feasible and powerful, and it will be used for the water temperature prediction in actual reservoirs in a near future.     

基于格子玻尔兹曼方法的液滴撞击移动液膜过程模拟

采用可调节表面张力的大密度比格子玻尔兹曼伪势模型模拟了液滴撞击移动液膜的过程,并进一步分析了雷诺数、韦伯数和初始液膜运动速度对液冠演化的影响。结果表明:初始液膜运动速度会增大上游液冠处撞击后液膜运动速度不连续性,促进上游液冠变形,同时减小了下游液冠处撞击后液膜运动速度不连续性,对下游液冠演化具有抑制作用;上游液冠高度随雷诺数增大而增大,但不随韦伯数的变化发生改变,而下游液冠高度则随着雷诺数和韦伯数的增大而减小,但雷诺数和韦伯数均不影响到液冠半径的演化;随着初始液膜运动速度增大,上、下游液冠高度减小,但液冠半径增大。格子玻尔兹曼伪势模型模拟结果与试验结果和理论分析一致,证明格子玻尔兹曼伪势模型可以有效模拟复杂液膜条件下液滴撞击液膜过程。     

A LATTICE BOLTZMANN SUBGRID MODEL FOR LID-DRIVEN CAVITY FLOW

In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the twodimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.     

A LATTICE BOLTZMANN METHOD FOR SIMULATION OF A THREE- DIMENSIONAL DROP IMPACT ON A LIQUID FILM

A single-phase free surface tracking model based on the Lattice Boltzmann Method （LBM）, which has capability of simulating liquid-gas system with the assumption that the gas phase has only negligible influence on the liquid phase, is utilized to simulate the flow of a drop impacting on a liquid film. Three typical outcomes in the flows, i.e., deposition, crown and splash, which have been observed in the previous experiments, are obtained in the present three dimensional numerical simulations. The numerical results are consistent with the experimental and analytical results available.     

基于郎之万方程和LBM的Janus颗粒自驱运动模拟

Janus颗粒由于本身的自驱动特性在生物能源医药等领域具有广阔的应用前景,然而其自驱动特性研究目前还不完善。该文基于格子Boltzmann方法(LBM)和郎之万方程,结合反弹边界格式建立了模拟球形Janus颗粒自驱动的动力学模型,利用爱因斯坦关系式对运动方程中的布朗力进行修正,相对于涨落LBM大幅降低了计算量,提高了计算效率。通过模拟2μm球形Janus颗粒的自驱运动并与实验结果对比得出,采用该方法模拟所得颗粒运动特性与实验相符,验证了该方法的可行性与准确性。通过在特定情况下扩散系数与扩散泳力的关系图与实验结果的对比,可得出不同燃料浓度作用下Janus颗粒受到扩散泳力的大小,为后续实验和数值模拟工作的展开提供了有力的支撑。     

LATTICE BOLTZMANN METHOD SIMULATIONS FOR MULTIPHASE FLUIDS WITH REDICH-KWONG EQUATION OF STATE

In this article we state that the compression factor of the Redlich-Kwong Equation Of State (EOS) is smaller than that of van der Waals EOS. The Redlich-Kwong EOS is in better agreement with experimental data on coexistence curves at the critical point than the van der Waals EOS. We implement the Redlich-Kwong EOS in the Lattice Boltzmann Method (LBM) simulations via a pseudo-potential approach. We propose a new force, which can obtain computational stationary and reach larger density ratio. As a result, multi-phase flows with large density ratio (up to 1012 in the stationary case) can be simulated. We perform four numerical simulations, which are respectively related to single liquid droplet, vapor-liquid separation, surface tension and liquid coalescence of two droplets.     

Numerical simulation of dam break flow impact on vertical cylinder by cumulant lattice Boltzmann method

The purpose of this study is to apply the cumulant lattice Boltzmann method(LBM)to simulate high Reynolds number free surface flows.The single-phase cumulant LB...     

SIMULATION OF THE TWO PHASE FLOW OF DROPLET IMPINGEMENT ON LIQUID FILM BY THE LATTICE BOLTZMANN METHOD

A Lattice Boltzmann Method (LBM) with two-distribution functions is employed for simulating the two-phase flow induced by a liquid droplet impinging onto the film of the same liquid on solid surface.The model is suitable for solution of twophase flow problem at high density and viscosity ratios of liquid to vapor and phase transition between liquid and its vapor.The roles of the vapor flow,the density ratio of liquid to vapor and the surface tension of the droplet in the splashing formation are discussed.It is concluded that the vapour flow induced by the droplet fall and splash in the whole impinging process may affect remarkably the splash behaviour.For the case of large density ratio of liquid to vapor a crown may engender after the droplet collides with the film.However,for the case of small density ratio of liquid to vapor a "bell" like splash may be observed.     

Orientation of the fiber suspending in the flow through a tube containing a sphere

Fiber suspensions flow through a tube containing a sphere in the dilute and concentrated regimes is simulated numerically with the Lattice Boltzmann Method (LBM). The numerical results of fiber orientation distribution based on a statistical scheme are obtained and agree qualitatively with the experimental ones for the flow through a parallel plate channel containing a cylinder. The results show that the sphere in the tube results in a change in the fiber orientation distribution downstream of the sphere along the flow and transverse directions. The influences of the sphere on the fiber orientation distribution are more significant for the concentrated suspensions than for the dilute one. The effect of the initial fiber orientations on the fiber orientation distribution is significant upstream of the sphere but small downstream of the sphere.     

LATTICE BOLTZMANN SCHEME TO SIMULATE TWO-DIMENSIONAL FLUID TRANSIENTS

ＮＯＭＥＮＣＬＡＴＵＲＥｐα ———ｐｒｅｓｓｕｒｅｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎｐ(0 )α ———ｅｑｕｉｌｉｂｒｉｕｍｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎｅα———ｌｏｃａｌｐａｒｔｉｃｌｅｓｔｒｅａｍｖｅｌｏｃｉｔｙｒ———ｌｏｃａｔｉｏｎｏｆｃｏｍｐｕｔａｔｉｏｎａｌｇｒｉｄｎｏｄｅδｔ ———ｔｉｍｅｉｎｃｒｅｍｅｎｔτ———ｔｈｅＢＧＫｒｅｌａｘａｔｉｏｎｐａｒａｍｅｔｅｒα———ｉｎｄｅｘｏｆｐａｒｔｉｃｌｅｓｔｒｅａｍｄｉｒｅｃｔｉｏｎｂ———ｔｈｅｎｕｍｂｅｒｏｆｐａ…