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.

Numerical modeling of fluid-particle interaction in granular media

Fluid-particle interaction underpins important behavior of granular media. Particle-scale simulation may help to provide key microscopic information governing the interaction and offer better understanding of granular media as a whole. This paper presents a coupled computational fluid dynamics and discrete element method （CFD-DEM） approach for this purpose. The granular particle system is modeled by DEM, while the fluid flow is simulated by solving the locally averaged Navier-Stokes equation with CFD. The coupling is considered by exchanging such interaction forces as drag force and buoyancy force between the DEM and CFD. The approach is benchmarked by two classic geomechanics problems for which analytical solutions are available, and is further applied to the prediction of sand heap formation in water through hopper flow. It is demonstrated that the key characteristic of granular materials interacting with pore water can be successfully captured by the proposed method.

Effective thermal conductivity in granular media with devolatilization:the Lattice Boltzmann modelling

Flow thermomechanics in reactive porous media is of importance in industry including the thermal processing of fossil fuel(coking understood as a slow pyrolysis)involving devolatilisation.On the way to provide a detailed description of the process,a multi-scale approach was chosen to estimate effective transport coefficients.For this case the Lattice Boltzmann method(LBM)was used due to its advantages to accurately model multi-physics and chemistry in a random geometry of granular media.After account for earlier studies,the paper presents description of the model with improved boundary conditions and a benchmark case.Results from meso-scale LBM calculations are presented and discussed regarding the spatial resolution and the choice of relaxation parameter along its influence on the accuracy compared with empirical formulae.Regarding the estimation of effective thermal conductivity coefficient it is shown that occurrence of devolatilization has a crucial effect by reducing heat transfer.Some quantitative results characterise the propagation of thermal front;also presented is the evolution of effective thermal conductivity.The work is a step forward towards a physically sound simulation of thermal processing of fossil fuel.

Pore structure of ore granular media by computerized tomography image processing

The pore structure images of ore particles located at different heights of leaching column were scanned with X-ray computerized tomography (CT) scanner, the porosity and pore size distribution were calculated and the geometrical shape and connectivity of pores were analyzed based on image process method, and the three dimensional reconstruction of pore structure images was realized. The results show that the porosity of ore particles bed in leaching column is 42.92%, 41.72%, 39.34% at top, middle and bottom zone, respectively. Obviously it has spatial variability and decreases appreciably along the height of the column. The overall average porosity obtained by image processing is 41.33% while the porosity gotten from general measurement method in laboratory is 42.77% showing the results of both methods are consistent well. The pore structure of ore granular media is characterized as a dynamical space network composed of interconnected pore bodies and pore throats. The ratio of throats with equivalent diameter less than 1.91 mm to the total pores is 29.31%, and that of the large pores with equivalent diameter more than 5.73 mm is 2.90%.

Evolvement of permeability of ore granular media during heap leaching based on image analysis

The column leaching experiment of ore granular media was carried out with the home-made multi-functional experimental apparatus and the pore structure of ore granular media was scanned by the X-ray computed tomography machine before and after leaching.The porosities of each section before and after leaching were calculated based on CT images processing,and the permeability of each zone before and after leaching were also calculated with Carman-Kozeny equation.The permeability evolvement law was disclosed.The results indicate that before leaching the permeability of the ore granular media in different height has not much difference and the value ranges from 5.70×10-4mm 2to 1.11×10 -3mm 2,where the lowest one locates in the bottom zone.After leaching the permeability distributes inhomogeneously along the height of the column and the value ranges from 3.44×10 -4 mm 2 to 2.25×10 -2 mm 2 ,where the lowest one is in the same place.Except for the bottom zone,the permeability of other zones increases after leaching,especially the top zone.Through comparison of the permeability at bottom zone before and after leaching,the whole permeability after leaching decreases by 39.65%that coincides with the measured experimental data.

Wave propagation and energy dissipation in viscoelastic granular media

In terms of viscoelasticity, the relevant theory of wave i n granular media is analyzed in this paper. Under the conditions of slight deforma tion of granules, wave equation, complex number expressions of propagation vecto r and attenuation vector, attenuation coefficient expressions of longitudinal wa ve and transverse wave, etc, are analyzed and deduced. The expressions of attenu ation coefficients of viscoelastic longitudinal wave and transverse wave show th a t the attenuation of wave is related to frequency. The higher the frequency is, the more the attenuation is, which is tested by the laboratory experiment. In a ddi tion, the energy dissipation is related to the higher frequency wave that is abs orbed by granular media. The friction amongst granular media also increase the e nergy dissipation. During the flowing situation the expression of transmission f actor of energy shows that the granular density difference is the key factor whi ch leads to the attenuation of vibrating energy. This has been proved by the exp eriment results.

Vibrating Liquefaction Experiment and Mechanism Study in Saturated Granular Media

By the vibrating liquefaction experiment of tailings and fine-ores of iron, it is observed and noted that the change of pore water pressure when the vibrating liquefaction takes place. Based on relevant suppositions, the equation of wave propagation in saturated granular media is obtained. This paper postulates the potential vector equation and the velocity expression of three kinds of body waves under normal conditions. Utilizing the wave theory and the experimental results, the influence of three body waves on pore water pressure and granules has been analyzed in detail. This revealed the rapid increment mechanism of pore water pressure and the wave mechanism of vibrating liquefaction.

ROTATIONAL RESISTANCE AND SHEAR-INDUCED ANISOTROPY IN GRANULAR MEDIA

This paper presents a micromechanical study on the behavior of granular materials under confined shear using a three-dimensional Discrete Element Method （DEM）. We consider rotational resistance among spherical particles in the DEM code as an approximate way to account for the effect of particle shape. Under undrained shear, it is found rotational resistance may help to increase the shear strength of a granular system and to enhance its resistance to liquefaction. The evolution of internal structure and anisotropy in granular systems with different initial conditions depict a clear bimodal character which distinguishes two contact subnetworks. In the presence of rotational resistance, a good correlation is found between an analytical stress-force-fabric relation and the DEM results, in which the normal force anisotropy plays a dominant role. The unique properties of critical state and liquefaction state in relation to granular anisotropy are also explored and discussed.

Discrete simulation and micromechanical analysis of two-dimensional saturated granular media

In this study, a novel approach to incorporate the pore water pressure in the discrete element method （DEM） to comprehensively model saturated granular media was developed. A numerical model was constructed based on the DEM by implanting additional routines in the basic DEM code; pore water pressure calculations were used with a two-dimensional （2D） model to simulate the undrained behavior of satu- rated granular media. This model coupled the interaction of solid particles and the pore fluid in saturated granular media. Finally, several 2D undrained shear tests were simulated. The test results showed that the model could predict the response of the saturated granular soil to shear loading. The effect of initial compaction was investigated. Biaxial tests on dense and loose specimens were conducted, and the effect of the initial density on the change in shear strength and the volume change of the system was inves- tigated. The overall behavior of loose and dense specimens was phenomenologically similar to the real granular material. Constant volume tests were simulated, and the results were compared to those from the coupled model. Induced anisotropy was micromechanically investigated by studying the contact force orientation. The change in anisotropy depended on the modeling scheme. However, the overall responses of the media obtained usinz the couoled and constant volume methods were similar.

Sound scattering in dense granular media

The sound propagation in a dense granular medium is basically characterized by the ratio of wavelength to the grain size. Two types of wave transport are distinguished: one corresponds to coherent waves in the long wavelength limit, the other to short-wavelength scattered waves by the inhomogeneous contact force networks. These multiply scattered elastic waves are shown to exhibit a diffusive characteristics of transport over long distances of propagation. Determination of the transport mean free path l * and the inelastic absorption (Q-1) allows the inference of the structural properties of the material such as the heterogeneity and internal dissipation. The relevance of our experiments for seismological applications is discussed. Moreover, we apply the correlation technique of the configuration-specific sound scattering to monitoring the dynamic behaviour of the granular medium (irreversible rearrangements) under strong vibration, shearing and thermal cycling, respectively.

Fractal analysis of granular ore media based on computed tomography image processing

九组矿石样品的代表性的图象被 X 光检查获得计算断层摄影术(CT ) 扫描仪。基于 CT 图象分析，稳固的矩阵的分数维的尺寸，毛孔空格和每件样品的矩阵 / 毛孔接口被使用框数测量方法。有粒子尺寸，孔，和渗出物系数的三种分数维的尺寸的关联被调查。结果证明为这些样品的所有图象，矩阵阶段有最高的尺寸，由矩阵毛孔接口的毛孔阶段，和尺寸列在后面有最小的价值；当毛孔阶段的尺寸与孔断然并且线性地联系时，矩阵阶段和矩阵毛孔接口的尺寸否定地并且线性地与孔被相关；矩阵毛孔接口的分数维的尺寸与渗出物系数否定地并且线性地联系。矩阵 / 毛孔接口的更大的分数维的尺寸为解决方案流动显示更不规则的复杂隧道，导致低渗透。

准静态侵入颗粒介质的底边界效应仿真分析

论文基于球形离散元方法研究颗粒介质的底边界效应,仿真刚体圆柱准静态侵入有限厚度颗粒介质直至底边界的过程,探究侵入物所受阻力与侵入深度间关系.结果表明,圆柱准静态侵入颗粒层至池底的阻力-深度曲线,前段呈类静水压力线性,接近底边界的后段呈类指数增长形式;在距底数个粒径范围内阻力存在波动,波长近似颗粒直径.与圆柱底固连的倒锥形固化区颗粒存在动态更新,侵入接近底边界时固化区瓦解,局部颗粒阻塞与疏通决定阻力增长趋势;圆柱底面以下的颗粒力链在接近底边界时转化为圆柱底与颗粒池底之间的“底-底”力链,力链受挤压后平均颗粒数的递减很好地解释了阻力振荡的波动性.

隔离层下单漏斗放矿力链演变的参数敏感性分析

利用PFC软件,以同步充填留矿法为背景,选取隔离层厚度A、隔离层界面摩擦因数B、矿石颗粒摩擦因数C及颗粒半径D作为正交试验的四种影响因素,对力链特征参数的一般变化规律进行分析,研究影响力链演变的参数及其敏感性。结果表明:力链数量先减少后增加;力链长度的概率分布曲面呈指数形式递减,短力链所占比例逐渐减少,长力链所占比例逐渐增加;力链强度表现出先减少后增加的规律;力链强度的概率分布先呈指数式上升,后呈指数式递减;四种因素对正交试验指标影响的主次顺序为CDAB;对应的最优方案为颗粒摩擦因数0.8、颗粒半径0.008 m、隔离层厚度0.004 m、隔离层界面摩擦因数0.5,此时散体介质体系在放矿过程中最为稳定。

固液混合物振动筛分机理研究

振动筛分技术是固液混合物分离的一种手段,被广泛应用于钻井液固相控制、河道淤泥处理和煤矿脱水等领域。现有研究对固液混合物的振动筛分机理缺乏认识,限制了振动设备筛分效率的提升空间。针对这一问题,采用计算流体力学与离散单元耦合法(CFD DEM)研究了固液混合物振动筛分机理。首先,利用Hertz-Mindlin JKR Cohesion接触模型引入湿颗粒之间的碰撞行为;其次,应用多孔介质描述了筛网的细孔特征;然后,运用动网格模拟了筛网的直线振动轨迹;最后,分析了固相颗粒物料的动力学特性和液相流动特性,并对比研究了振动系统的振幅和振动频率对固液混合物筛分效率的影响。研究结果表明,增加振幅和振动频率可提高固液混合物筛分效率,但当振幅大于3.0 mm和频率大于22.3 Hz时,振动筛对固液混合物的筛分效率影响的敏感性减弱;振幅小于或等于3.0 mm和频率小于或等于22.3 Hz时,固液混合物振动筛分效率对振幅的变化最敏感,振动频率次之;固液混合物的透筛区域集中在筛网长度比小于20%的区域。

Influence of Ti on Microstructure and Magnetic Properties of FePt Granular Films

在室温下,应用对靶直流磁控溅射设备在普通玻璃基片上制备了FePt(30 nm)／Ti(t nm)颗粒膜样品,随后,在真空中进行了原位退火。详细研究了Ti衬底层对FePt颗粒膜的微结构和磁特性的影响。X射线衍射图谱表明样品形成了较有序的L10织构,Ti和FePt形成了三元FePtTi合金。当Ti层厚度t=5 nm、退火温度Ta=500℃时,样品具有高度有序的L10织构、小的颗粒尺寸和优异的磁特性。矫顽力超过了6．7 kOe,饱和磁化强度为620emu／cc。并且具有较小的开关场分布。结果表明FePt／Ti颗粒膜系统可作为超高密度磁记录介质的候选者。

Influence of vibration on granular flowability and its mechanism of aided flow

Regarding flowing granular media as weak transverse isotropic media, the phase velocity expressions of wave P, wave SH and wave SV were deduced, the propagation characteristics of waves in flowing granular media were analyzed. The experiments show that vibration has great influence on granular fluidity. The wavefront of wave P is elliptic or closely elliptic, the wavefront of wave SH is elliptic, and the wavefront of wave SV is not elliptic. Wave propagation in the granular flowing field attenuates layer after layer. The theory and experiment both substantiate that the density difference is the key factor which leads to the attenuation of vibrating energy. In terms of characteristics of wave propagation one can deduce that vibrating waves have less influence on flowability of granules when the amplitude and frequency are small. However, when the amplitude and frequency increase gradually, the eccentricity of ellipsoid, the viscosity resistance and inner friction among granules, and shear intensity of granules decrease, and the loosening coefficient of granules increases, which shows the granules have better flowability.

Towards a Mathematical Model for Elastic Wave Propagation in Granular Materials

A theoretical model for the propagation of acoustic waves in dry granular media is presented within the framework of the nonlinear granular elasticity. An essential ingredient is the dependence of the elastic moduli on compression. For the purpose of illustration, we analyze the case of a time-harmonic plane wave propagation under isotropic compression. We derive explicit relations for the wave speed dependence with the confining pressure. The present approach provides an accurate description of acoustic wave propagation in granular packings and represents a powerful tool to interpret the results of current experiments.

Mysteries of Granular Planet

The behavior of self-organizing granular medium in its own gravitational field is considered. The study is led within an approach proposing the existence of only three types of mesoscopic states in the material: so named hydrostatic, columnar and arched mesoscopic states. The results of this study are not obvious. Indeed, in the center of granular gravitating ball, as it turns out, pressure may be absent, though it is well-known that the pressure in either non-compressible liquid or solid linear-elastic medium is maximal. Such an uncommon stress state takes place at the arched mesoscopic state. Using the Mohr-Coulomb condition has given that the arched state can embody when sinus of internal friction’s angle increases up to the threshold value 1/3. At the hydrostatic mesoscopic state granular medium is like a liquid. The study also has shown the transition between hydrostatic and non-hydrostatic stress states being sharp in granular gravitating ball that opposes the known results of the linear theory of elasticity. At the columnar mesoscopic state any gravitating granular ball cannot be.

散体介质复杂力链网络演化持续同调拓扑研究

力链网络是表征颗粒物质和散体介质细观力学本质特征以及研究其宏观结构力学行为的重要基础.由于力链构型的复杂性和多重形态,使得力链网络难以分析处理.拓扑数据分析(TDA)为定量描述力链网络提供了一种简单、有效且易处理的方法.基于拓扑数据分析中的持续同调理论,建立了散体颗粒从接触网络到力链网络,再到拓扑空间模型的分析方法.以放顶煤开采为例,采用光弹实验方法,追踪放顶煤开采力链演化过程,对顶煤与覆岩力链网络进行持续同调拓扑分析.研究表明:将采场中散体颗粒应力作为持续同调分析的阈值ε时,Betti数可以作为衡量采场来压的一个量化指标,采场顶部覆岩和工作面前方煤岩力链网络β0曲线呈抛物线形,且来压时抛物线峰值高于初始状态下的峰值.顶部覆岩β0峰值位于强力链范围,而工作面前方煤岩β0峰值位于次强力链范围.β1曲线呈L形,在[0.3,1]区间内,β1趋近于0,在[0,0.2]区间内与ε近似呈反比.持续同调拓扑研究为定量分析颗粒介质复杂力链网络演化和宏观力学行为提供了有效方法.

二维颗粒结构中非线性波的传播和脉冲衰减

有序颗粒介质在冲击振动缓解、能量捕获和吸收等领域具有重要的研究价值。本文运用赫兹接触理论建立二维颗粒链数学模型,在冲击激励作用下,研究二维颗粒系统中脉冲波的传播特性、能量传递规律和传递力的降低机理。二维均匀颗粒系统嵌入了耦合颗粒以传递动能,初始脉冲激励在2列颗粒链间发生能量交换和脉冲等分现象,脉冲波在激励施加点附近发生强能量散射,激发出混合型的非线性波,即纵向传播的近零频率孤立波与横向高频剪切波。与一维均匀颗粒链相比,二维颗粒系统的末端传递力峰值得到了大幅度降低。通过改变颗粒间的质量比,在二维均匀颗粒链中引入轻珠链构成非均匀结构,沿纵向传播的孤立波在轻-重颗粒交界面发生反射,能量被局部约束在轻珠链中,使得一系列低幅值脉冲波按照不同的波速,延时释放到颗粒链末端,导致末端传递力峰值的进一步降低。