A combined method using Lattice Boltzmann Method(LBM)and Finite Volume Method(FVM)to simulate geothermal reservoirs in Enhanced Geothermal System(EGS)

With the development of industrial activities,global warming has accelerated due to excessive emission of CO_(2).Enhanced Geothermal System(EGS)utilizes deep geothermal heat for power generation.Although porous medium theory is commonly employed to model geothermal reservoirs in EGS,Hot Dry Rock(HDR)presents a challenge as it consists of impermeable granite with zero porosity,potentially distorting the physical interpretation.To address this,the Lattice Boltzmann Method(LBM)is employed to simulate CO_(2)flow within geothermal reservoirs and the Finite Volume Method(FVM)to solve the energy conservation equation for temperature distribution.This combined method of LBM and FVM is imple-mented using MATLAB.The results showed that the Reynolds numbers(Re)of 3,000 and 8,000 lead to higher heat extraction rates from geothermal reservoirs.However,higher Re values may accelerate thermal breakthrough,posing challenges to EGS operation.Meanwhile,non-equilibrium of density in fractures becomes more pronounced during the system's life cycle,with non-Darcy's law becoming significant at Re values of 3,000 and 8,000.Density stratification due to buoyancy effects significantly impacts temperature distribution within geothermal reservoirs,with buoyancy effects at Re=100 under gravitational influence being noteworthy.Larger Re values(3,000 and 8,000)induce stronger forced convection,leading to more uniform density distribution.The addition of proppant negatively affects heat transfer performance in geothermal reservoirs,especially in single fractures.Practical engineering considerations should determine the quantity of proppant through detailed numerical simulations.

An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM)

The lattice Boltzmann method （LBM） is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanoparticles： TiO2, Ag, Cu, and A1203. The Brinkman and Maxwell-Garnetts models are used to simulate the viscosity and the effective thermal conductivity of nanofluids, respectively. Results from the performed numerical analysis show good agreement with those obtained from other numerical meth- ods. A variety of the Rayleigh number, the nanoparticle volume fraction, and the aspect ratio are examined. According to the results, choosing copper as the nanoparticle leads to obtaining the highest enhancement for this problem. The results also indicate that the maximum value of enhancement occurs at λ =2.5 when Ra = 106 while at A = 1.5 for other Rayleigh numbers.

On the spreading behavior of a droplet on a circular cylinder using the lattice Boltzmann method

The study of a droplet spreading on a circular cylinder under gravity was carried out using the pseudo-potential lattice Boltzmann high-density ratios multiphase model with a non-ideal Peng–Robinson equation of state. The calculation results indicate that the motion of the droplet on the cylinder can be divided into three stages: spreading, sliding, and aggregating.The contact length and contact time of a droplet on a cylindrical surface can be affected by factors such as the wettability gradient of the cylindrical wall, the Bond number, and droplet size. Furthermore, phase diagrams showing the relationship between Bond number, cylinder wall wettability gradient, and contact time as well as maximum contact length for three different droplet sizes are given. A theoretical foundation for additional research into the heat and mass transfer process between the droplet and the cylinder can be established by comprehending the variable rules of maximum contact length and contact time.

Exploration of the coupled lattice Boltzmann model based on a multiphase field model:A study of the solid-liquid-gas interaction mechanism in the solidification process

A multiphase field model coupled with a lattice Boltzmann(PF-LBM)model is proposed to simulate the distribution mechanism of bubbles and solutes at the solid-liquid interface,the interaction between dendrites and bubbles,and the effects of different temperatures,anisotropic strengths and tilting angles on the solidified organization of the SCN-0.24wt.%butanedinitrile alloy during the solidification process.The model adopts a multiphase field model to simulate the growth of dendrites,calculates the growth motions of dendrites based on the interfacial solute equilibrium;and adopts a lattice Boltzmann model(LBM)based on the Shan-Chen multiphase flow to simulate the growth and motions of bubbles in the liquid phase,which includes the interaction between solid-liquid-gas phases.The simulation results show that during the directional growth of columnar dendrites,bubbles first precipitate out slowly at the very bottom of the dendrites,and then rise up due to the different solid-liquid densities and pressure differences.The bubbles will interact with the dendrite in the process of flow migration,such as extrusion,overflow,fusion and disappearance.In the case of wide gaps in the dendrite channels,bubbles will fuse to form larger irregular bubbles,and in the case of dense channels,bubbles will deform due to the extrusion of dendrites.In the simulated region,as the dendrites converge and diverge,the bubbles precipitate out of the dendrites by compression and diffusion,which also causes physical phenomena such as fusion and spillage of the bubbles.These results reveal the physical mechanisms of bubble nucleation,growth and kinematic evolution during solidification and interaction with dendrite growth.

Lattice Boltzmann simulation study of anode degradation in solid oxide fuel cells during the initial aging process

For present solid oxide fuel cells(SOFCs),rapid performance degradation is observed in the initial aging process,and the dis-cussion of the degradation mechanism necessitates quantitative analysis.Herein,focused ion beam-scanning electron microscopy was em-ployed to characterize and reconstruct the ceramic microstructures of SOFC anodes.The lattice Boltzmann method(LBM)simulation of multiphysical and electrochemical processes in the reconstructed models was performed.Two samples collected from industrial-size cells were characterized,including a reduced reference cell and a cell with an initial aging process.Statistical parameters of the reconstructed microstructures revealed a significant decrease in the active triple-phase boundary and Ni connectivity in the aged cell compared with the reference cell.The LBM simulation revealed that activity degradation is dominant compared with microstructural degradation during the initial aging process,and the electrochemical reactions spread to the support layer in the aged cell.The microstructural and activity de-gradations are attributed to Ni migration and coarsening.

A High-Accuracy Curve Boundary Recognition Method Based on the Lattice Boltzmann Method and Immersed Moving Boundary Method

Applying numerical simulation technology to investigate fluid-solid interaction involving complex curved bound-aries is vital in aircraft design,ocean,and construction engineering.However,current methods such as Lattice Boltzmann(LBM)and the immersion boundary method based on solid ratio(IMB)have limitations in identifying custom curved boundaries.Meanwhile,IBM based on velocity correction(IBM-VC)suffers from inaccuracies and numerical instability.Therefore,this study introduces a high-accuracy curve boundary recognition method(IMB-CB),which identifies boundary nodes by moving the search box,and corrects the weighting function in LBM by calculating the solid ratio of the boundary nodes,achieving accurate recognition of custom curve boundaries.In addition,curve boundary image and dot methods are utilized to verify IMB-CB.The findings revealed that IMB-CB can accurately identify the boundary,showing an error of less than 1.8%with 500 lattices.Also,the flow in the custom curve boundary and aerodynamic characteristics of the NACA0012 airfoil are calculated and compared to IBM-VC.Results showed that IMB-CB yields lower lift and drag coefficient errors than IBM-VC,with a 1.45%drag coefficient error.In addition,the characteristic curve of IMB-CB is very stable,whereas that of IBM-VC is not.For the moving boundary problem,LBM-IMB-CB with discrete element method(DEM)is capable of accurately simulating the physical phenomena of multi-moving particle flow in complex curved pipelines.This research proposes a new curve boundary recognition method,which can significantly promote the stability and accuracy of fluid-solid interaction simulations and thus has huge applications in engineering.

Experimental Study of Heat Transfer in an Insulated Local Heated fromBelow and Comparison with Simulation by Lattice Boltzmann Method

In this paper,experimental and numerical studies of heat transfer in a test local of side H=0.8 m heated from below are presented and compared.All the walls,the rest of the floor and the ceiling are made from plywood and polystyrene in sandwich form(3 mmplywood-3 cm polystyrene-3 mmplywood)just on one of the vertical walls contained a glazed door(2 H/3×0.15 m).This local is heated during two heating cycles by a square plate of iron the width L=0.6 H,which represents the heat source,its temperature Th is controlled.The plate is heated for two cycles by an adjustable set-point heat source placed just down the center of it.For each cycle,the heat source is switched“on”for 6 h and switched“off”for 6 h.The outdoor air temperature is kept constant at a low temperature Tc<Th.All measurements are carried out with k-type thermocouples and with flux meters.Results will be qualitatively presented for two cycles of heating in terms of temperatures and heat flux densitiesϕfor various positions of the test local.The temperature evolution of the center and the profile of the temperature along the vertical centerline are compared by two dimensions simulation using the lattice Boltzmann method.The comparison shows a good agreement with a difference that does not exceed±1℃.

基于Lattice Boltzmann方法的瓦斯渗流模拟研究

为了更好地处理瓦斯渗流中的吸附-解吸问题和复杂边界条件,Lattice Boltzmann方法(LBM)被引入到瓦斯渗流模拟研究中。给出了考虑Klinkenberg效应和吸附-解吸特性的LBM瓦斯渗流方程和建模方法,得到了2种因素对渗流的影响,模拟研究获得了煤体中瓦斯压力在时间上的演化和空间上的分布规律、不同裂隙分布对瓦斯流动的影响,对比分析了抽放压力及抽放孔布置对瓦斯抽放效果的影响等,并初步探索了煤体细观结构图像处理与LBM相结合的瓦斯渗流模拟研究新思路。

基于Lattice Boltzmann模型的液-液混合流模拟

引入了一种二元Lattice Boltzmann Model(LBM),实现了两种液体组成的混合流的模拟.不同于其它的类似模型,它区分考虑了流体的粘性和扩散特性,可以很容易地模拟各种互溶或者不互溶的混合流现象.此外,由于LBM的运算大都是线性的局部运算,这使得它很容易在可编程图形处理器(Graphics Process Unit,GPU)上进行加速,从而进行实时模拟.给出了若干二元混合流的模拟结果.

基于Lattice Boltzmann方法的方柱绕流模拟

从分子动力论出发,探讨了模拟不可压缩粘性流动的Lattice Boltzmann(LB)方法.根据粒子平衡分布函数和非平衡反弹思想,提出了高效的出口边界条件处理格式.结合区域分裂技术设计了适合集群计算机运算的LB并行算法,并用C++程序语言开发了LB并行计算程序.通过对不同雷诺数时的方柱绕流模拟,验证了本文方法的有效性,同时详细分析了雷诺数对方柱绕流特性的影响.

基于区域分裂的非均匀Lattice Boltzmann方法

基于区域分裂技术 ,设计了一种使用非均匀网格的LatticeBoltzmann(LB)模型 .其基本思想是 :将流场分解为若干个规则的子区域 ,在每个子区域使用均匀网格上的LB模型求解 ,子区域的边界条件利用插值方法决定 .用该模型对二维圆柱绕流问题进行了模拟 。

用Lattice Boltzmann方法模拟二维水力过渡过程

本文旨在探索用LatticeBoltzmann方法模拟二维水力过渡过程的可行性 .应用Chapman Enskog展开技术 ,导出了一套多尺度方程 ,将LB方程和其所对应的宏观方程联系起来 ;根据水力过渡过程基本方程的特点 ,建立了计算二维水力过渡过程的一个LB模型 ;应用该模型对一维正弦波的传播、一维断波的传播与反射、二维拐角衍射波等典型算例 ,以及近似为二维问题的混凝土蜗壳在机组甩负荷和起动工况下的水力过渡过程进行了模拟分析 .研究表明用LB方法模拟多维水力过渡过程是可行的 ,值得进一步探讨 .

用Lattice Boltzmann方法计算流体对曲线边界的作用力

通过分析格子Boltzmann方法中边界受力的计算方法,研究了两种用LB方法计算边界受力的方法———动量转换法和应力积分法,其中动量转换法较为可靠、准确,且易于执行.应用LB方法模拟了圆柱绕流问题,并计算出圆柱的阻力系数.通过模拟凹坑表面的层流流动,发现随着Re数的增大,凹坑表面的阻力系数逐渐接近平板的阻力系数.

双重网格的Lattice Boltzmann方法

针对均匀网格的LatticeBoltzmann方法(LBM)计算效率较低的不足,引入有限差分方法(FDM)中双重网格算法的基本思想,结合LBM在连续流场上变量也连续分布的特点,推导出双重网格的LBM.这种算法充分利用粗、细两种网格各自不同的优点,加快了收敛速度,提高了流场的计算效率.通过模拟二维Poiseulle流动和后台阶流动两个算例,证明双重网格算法的计算时间明显地少于均匀网格算法的计算时间,计算结果正确可信.

基于lattice Boltzmann方法对裂隙煤体中瓦斯运移规律的模拟研究

基于lattice Boltzmann方法建立一个新的模拟裂隙煤体内瓦斯渗流的动力学模型,并利用该模型模拟二维裂隙煤体内瓦斯流动。模拟结果表明,采动压力差对瓦斯流动速度、孔隙瓦斯压力及瓦斯压力梯度都有很大的影响。在采动压力条件下,瓦斯在裂隙煤体中的流动压力具有波动性,波动幅度的大小与流场两端的压力差有关。在瓦斯压力达到峰值前的瞬时,孔隙瓦斯压力梯度很大。随着采动压力差的增大,瓦斯流动由层流过渡到紊流,同时孔隙压力出现发散,压力变化出现明显的非线性特征。基于lattice Boltzmann方法的模拟结果与用其他方法得到的瓦斯渗流规律比较吻合,表明lattice Boltzmann方法可有效模拟瓦斯在裂隙煤体中的运移规律,这为进一步探讨煤与瓦斯两相耦合机制、煤与瓦斯突出机制及瓦斯抽放方案的设计提供新的思路。

非平衡与多相复杂系统模拟研究——Lattice Boltzmann动理学理论与应用

在自然界和工程物理领域存在大量的非平衡、多相等复杂系统和复杂行为。Lattice Boltzmann(LB)方法起源于复杂系统复杂行为研究的格子气或元胞自动机模型;其中,现代版的Lattice Boltzmann Kinetic Model(LBKM)植根于非平衡统计物理学的基本方程—Boltzmann方程。本文从物理学视角评述LB方法,给出单松弛因子和多松弛因子LBKM构建的统一理论,介绍其在非平衡与多相复杂系统研究方面的应用。简单列举LB在多相流、可压流、材料动理学等方面的进展,重点介绍使用LB研究流体界面不稳定性、燃烧等问题的工作。本文所重点传递的信息为:可以通过宏观量研究系统的非平衡行为、可以提供系统偏离热力学平衡引发的宏观效应是LBKM建模优越于宏观连续介质建模的地方;除了可以从更基本的层面理解相应物理系统的特征、机制和规律外,这类研究结果可以为现有程序或软件中宏观模型的改进(例如修正项的构造)提供物理参考。

微通道人工泡状流的Lattice Boltzmann数值模拟

采用高频电控热激发汽泡的方式构造微通道人工泡状流,可以有效抑制微通道沸腾流动的不稳定性和强化传热。本文基于Lattice Boltzmann大密度比多相流复合模型,数值研究了通道内人工泡状流的流动和传热,通过比较分析不同发泡频率的泡状流,量化分析了汽泡运动和增长对微通道流动与传热的相互影响。一方面着重分析了汽泡运动对微通道运动边界层以及汽泡相变增长对热边界层的影响,另一方面也研究了边界层对汽泡动力行为的影响,所得结论对研究抑制微通道沸腾流动不稳定性和强化传热有参考意义。

用Lattice Boltzmann方法模拟方柱绕流

用LatticeBoltzmann方法模拟了两种情况下的方柱绕流:方柱位于流场的边壁和方柱位于流场的中央.在第1种情况中,分析了流场的流线、速度矢量分布以及方柱后面绕流形成的回流区长度随Reynolds数的变化曲线;在第2种情况中,除了给出稳定时流场的流线、速度矢量分布和压力分布以外,还模拟了Re=150时方柱后面形成的周期旋涡现象.两种情况下的计算结果与其他文献中的计算数值和试验数据是一致的.