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.

浸入运动边界-格子Boltzmann方法4种固含率计算方法对比研究

为了达到流固耦合,格子Boltzmann方法(LBM)可采用浸入运动边界法(IMB)实现移动颗粒边界上的无滑移条件.该耦合方式(IMB-LBM)中固含率计算方法对流固耦合计算精度和效率有影响.对常用的固含率4种计算方法,即蒙特卡洛法(MCM)、单元分解法(UDM)、近似多边形法(APM)和闭合边界法(CBM),分别阐述其具体算法,对比了它们的计算精度和计算效率;最后通过圆盘颗粒非连续变形分析方法(DDDA)与IMB-LBM耦合模型下的一个多颗粒沉降流固耦合算例,对比分析了它们在流固耦合计算过程中的耗时.结果表明:1)CBM无误差,MCM和UDM在随机点数取1000,子单元数取100时误差稳定在1%以下,APM在颗粒直径大于格子长度10倍时,误差小于0.44%;2)MCM和UDM的计算精度及耗时分别与随机点数和子单元数相关,它们的计算耗时大于APM和CBM;3)计算效率上,APM>CBM>UDM>MCM,其中CBM计算耗时略微大于APM,APM和UDM计算耗时分别比MCM少2个和1个数量级.该结果可为IMB-LBM耦合模型中固含率计算方法优选提供借鉴.

基于LBM的典型建筑布局树木风环境模拟

在建筑方案设计阶段定量评估景观绿植对建筑风环境影响,对于提高行人区域热舒适性具有重要实践意义。结合格子玻尔兹曼计算流体力学方法和多孔介质模型,开展了边界层流场-建筑-树木耦合模拟和关键参数验证,针对城市街道区域典型矩形建筑平面布局存在的风速加速现象,开展树木挡风效应分析。研究结果表明:模拟方法能够重现出与试验吻合一致的树木尾流区平均风速和湍流特征;基于不同阻力系数的树木透孔率对树木背风区下游1H~3H范围内挡风效应影响明显;基于等效原则提出的圆柱体简化模型能够计算出与树木原型一致的挡风效应变化规律;建筑两侧和迎风端布置合理间距的树木能够减小矩形建筑两侧风速加速比和加速区域面积,可以通过经济合理的树木布置方案实现建筑周围风环境舒适度优化和通风廊道畅通。研究成果可应用于景观植被风环境优化设计,为方案设计阶段绿色建筑自然通风评估提供新的计算参考。

PF-LBM耦合模型下Al-Cu合金的枝晶生长和气泡形成

基于Shan-Chen多相流的格子玻尔兹曼方法模拟复杂多相流系统,探索气泡在液相中的生长和运动.研究了Al-4.0wt.%Cu合金在凝固过程中枝晶与气泡的相互作用,各向异性对凝固组织的影响以及枝晶与气泡共存时溶液密度的变化情况.结果表明:在定向凝固枝晶生长模型中,气泡先在枝晶底部析出,压差导致气泡上升,流动的过程中会与枝晶产生相互作用且会出现气泡合并与消失的情况,在枝晶间密集通道处大气泡会变成蠕虫形状.模拟区域的高长比会影响枝晶和气泡的生长情况,当高长比较小时更容易产生短而小的气泡,高长比较大时更容易产生蠕虫状气泡.在等轴枝晶生长模型中,气泡在枝晶间析出,随着枝晶的生长,气泡同样会发生合并与消失的情况,并且在受到挤压时发生形变.

基于LBM的泡沫金属与翅片相变储能系统性能对比分析

为了研究翅片和泡沫金属铜对相变储能系统性能的影响,使用四参数随机生长法(QSGS)构建了孔隙密度(PPI)分别为20PPI、30PPI的泡沫铜复合相变材料模型,并构建了等铜质量的翅片相变材料模型。在此基础上,采用格子玻尔兹曼(LBM)数值模拟方法对相变材料(PCM)的储/放热过程进行了数值模拟,基于努塞尔数、液相率、PCM流动速度、PCM熔化/凝固时间对比分析了添加翅片以及添加泡沫金属结构对相变材料换热性能的影响。结果表明,在储热过程中,由于泡沫金属的存在会抑制熔化过程中对流换热的发展,双翅片结构的努塞尔数高于泡沫金属结构,熔化时间更短,相比于20PPI、30PPI泡沫铜复合相变材料分别缩短了28.55%、17.5%;在放热过程中,泡沫金属的存在会增加热传导面积,泡沫金属结构的凝固速度高于翅片结构,30PPI泡沫金属结构的凝固时间相比于翅片、20PPI泡沫铜复合相变材料分别缩短了65.80%、20.24%。综合考虑储放热两个过程,30PPI泡沫金属结构的总储放热时间最短,相比于翅片、20PPI泡沫铜复合相变材料分别缩短了27.81%、15.32%。在耗费相同金属材料的条件下,采用泡沫结构是更为有效的提升储能效率的手段。

轴对称Boltzmann模型方程统一算法与空天飞行环境喷管流动模拟

拦截机动飞行器周围大范围区域存在主喷/侧喷流/羽流影响,而传统的纳维-斯托克斯(Navier-Stokes,N-S)方程不能很好模拟发动机喷管扩张段出口附近流动情况,需要一种新的方法来处理这种全流域流动问题。为解决该问题,针对特定轴对称喷管内流动,本文通过数学推导确立描述不同克努森数稀薄环境条件下的轴对称喷管内流动Boltzmann模型方程,初步建立适于该模型方程的数值格式与气体动理论统一算法。通过开展同轴圆筒间的定常/非定常旋转流动以及轴对称喷管内流动数值计算研究,发现统一算法计算流场与其他途径得到的结果吻合较好,验证了统一算法在全局克努森数喷管流动模拟的适应性和可靠性。通过与低密度风洞实验对比,喷管出口核心区羽流结构一致,羽流轴线压力分布一致,表明统一算法可以有效解决喷管入口压缩段到扩张段多流域混合,尤其是出口附近稀薄气体真空低压环境流动问题。

含孔板微通道内随流气泡运动的两相格子Boltzmann模拟

带有气泡的两相流系统存在于各种工业过程中,涉及复杂的相界面变化,但气泡在管道中伴随液相流动时,通过孔板的运动过程尚未有充分的研究结果.相场格子Boltzmann模型在模拟复杂界面方面具有优势,适合研究气泡两相流在含孔板微通道内的运动,分析We数、气泡相对大小和孔板表面润湿性等因素对气泡动力学特性的影响.数值计算结果显示,随着We数增加,气泡表面张力减小,导致其穿过孔板结构时更易被撕裂,峰值速度降低.在研究的参数范围内存在两个临界直径比,这两个临界值将气泡通过孔板的运动分成三种形态,而且临界直径比会随We数的增加而减小.另外,随着接触角的增大,孔板表面对气体的吸附能力加强,气泡与孔板表面的接触面积增加,引起穿过孔板气泡的质量减少和气泡通过的速度增加.

基于格子Boltzmann方法的钉扎螺旋波反馈控制

螺旋波是心室跳动过速和纤维性颤动的根源,钉扎螺旋波相对于自由螺旋波来说更难消除.本文采用格子Boltzmann方法求解,以FitzHugh-Nagumo模型为对象,研究了使用反馈控制法消除钉扎螺旋波.数值结果表明,无论钉扎螺旋波钉在圆形障碍物还是矩形障碍物上,反馈控制法对其都具有很好的控制作用.此外,通过数值模拟系统研究了可激性系数、反馈控制信号幅度、记录反馈信号时间和障碍物的大小对钉扎螺旋波的控制情况.研究表明,钉扎螺旋波消除有三种情况.首先,反馈控制信号幅度和可激性系数与钉扎螺旋波消除所需的时间有关,反馈控制信号幅度越大或可激性系数越小,钉扎螺旋波消除越快.其次,障碍物大小和可激性系数影响着能成功消除钉扎螺旋波下记录反馈信号时间与加入反馈控制时间之间对应的时间间隔.最后,在保持加入反馈控制时间不变的情况下,记录反馈信号时间影响着能成功消除钉扎螺旋波所需的最小反馈控制信号幅度.

LBM晶格结构对纳米薄膜超快传热过程影响

超快激光加热技术在微纳米器件制造中发挥着重要作用,研究超快激光作用在靶体内部的超快传热过程对器件的热设计有着重要意义。文章基于格子玻尔兹曼方法研究了纳米薄膜的超快传热过程,围绕不同晶格结构对比分析了纳米薄膜内部的能量密度分布,探索了薄膜内部的声子输运特性。结果表明:纳米薄膜受到激光加热后,在应用D2Q9和D2Q5模型得到的结果中,薄膜内部能量均以“波状”形式传递且整体趋势相同,但D2Q9模型得到的数值要略低于D2Q5模型;通过对比应用D1Q3与D2Q9模型得到的结果,发现沿薄膜厚度方向上的能量密度差异较大,说明研究纳米薄膜内部超快传热过程时,不能忽略沿薄膜径向传递的能量。

THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

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.

基于LBM的翼伞伞型曲面化气动特性研究

翼伞是应用于空降空投领域的一类重要气动减速装置,该文总体目标为采用格子玻尔兹曼方法研究不同翼伞曲面化伞型的气动仿真特性。在进行与试验数据的验证后,仿真分析不同伞型的气动曲线,得到其变化趋势和系数值差异。进行详细的流动特性分析对不同伞型的气动特性差异原因,还分析气室、小孔2种气流结构对气动特性的影响。采用传统有限元方法进行补充解释分析。结果充分证明格子玻尔兹曼方法进行翼伞气动仿真的可靠性。加入曲面化的伞型其升阻特性有明显提高,同时反映出气动特性的鲁棒性。气室结构对升阻特性提高有较大影响,而小孔结构影响程度较小。上述结论对翼伞试验和仿真研究具有重要的借鉴和指导意义。

KdV方程的格子Boltzmann模型求解

浅水波模型被广泛地用于模拟水波传播的动力学行为。很多问题,如强非线性问题、非平衡问题、实际应用中发生的问题等,使得传统的理论研究手段通常无能为力。文章首先给出了格子Boltzmann方法(LBM)的基本理论,然后利用经典的一维五速度(D1Q5)的离散速度模型,给出Korteweg-de Vries(KdV)方程中含有修正项的格子Boltzmann(LB)模型推导公式,最后进行数值模拟,将KdV方程的精确解和模拟解进行比较,然后验证修正模型的精确性。实验结果表明,用格子Boltzmann方法对KdV方程进行求解,其模拟解和精确解吻合度较高。

Investigation of Acoustomagnetoelectric Effect in Bandgap Graphene by the Boltzmann Transport Equation

We study the acoustomagnetoelectric (AME) effect in two-dimensional graphene with an energy bandgap using the semiclassical Boltzmann transport equation within the hypersound regime, (where represents the acoustic wavenumber and is the mean free path of the electron). The Boltzmann transport equation and other relevant equations were solved analytically to obtain an expression for the AME current density, consisting of longitudinal and Hall components. Our numerical results indicate that both components of the AME current densities display oscillatory behaviour. Furthermore, geometric resonances and Weiss oscillations were each defined using the relationship between the current density and Surface Acoustic Wave (SAW) frequency and the inverse of the applied magnetic field, respectively. Our results show that the AME current density of bandgap graphene, which can be controlled to suit a particular electronic device application, is smaller than that of (gapless) graphene and is therefore, more suited for nanophotonic device applications.

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.

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.

利用LBM方法模拟金属氢化物储氢罐内氢气脱附的传热与传质

采用一个二维数学模型来评估金属氢化物储氢罐中氢气脱附过程中的传热和传质。模拟采用了具有D2Q9结构的格子玻尔兹曼方法(LBM),对加热流体温度、出口压力及流体与金属氢化物罐之间的对流传热系数等操作参数进行了研究,以确定它们对脱附过程性能的影响。加热液体的温度对脱附过程有重大影响。随着流体温度的升高,由于床层温度大幅上升,氢气脱附量急剧增加。此外,出口压力的降低也会显著加快脱附速度。在对流系数达到一定量前,氢气脱附会得到加强。

A particle-resolved heat-particle-fluid coupling model by DEM-IMB-LBM

Multifield coupling is frequently encountered and also an active area of research in geotechnical engineering.In this work,a particle-resolved direct numerical simulation(PR-DNS)technique is extended to simulate particle-fluid interaction problems involving heat transfer at the grain level.In this extended technique,an immersed moving boundary(IMB)scheme is used to couple the discrete element method(DEM)and lattice Boltzmann method(LBM),while a recently proposed Dirichlet-type thermal boundary condition is also adapted to account for heat transfer between fluid phase and solid particles.The resulting DEM-IBM-LBM model is robust to simulate moving curved boundaries with constant temperature in thermal flows.To facilitate the understanding and implementation of this coupled model for non-isothermal problems,a complete list is given for the conversion of relevant physical variables to lattice units.Then,benchmark tests,including a single-particle sedimentation and a two-particle drafting-kissing-tumbling(DKT)simulation with heat transfer,are carried out to validate the accuracy of our coupled technique.To further investigate the role of heat transfer in particle-laden flows,two multiple-particle problems with heat transfer are performed.Numerical examples demonstrate that the proposed coupling model is a promising high-resolution approach for simulating the heat-particle-fluid coupling at the grain level.

基于LBS的旅游路线推荐系统设计

为满足日益增长的高品质、多样化、个性化旅游需求,采用基于位置的服务(Location Based Services,LBS),结合用户行为分析和智能算法处理,设计旅游路线推荐系统。该系统由个性化路线推荐模块、消息推送模块、用户管理模块、人工智能模块等构成。系统性能测试结果表明,该推荐系统能显著提高旅游规划效率和用户满意度,可为旅游行业智慧化服务模式发展提供技术支持。