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.

Mobility and dynamic erosion process of granular flow:insights from numerical investigation using material point method

In order to understand the dynamics of granular flow on an erodible base soil,in this paper,a series of material point method-based granular column collapse tests were conducted to investigate numerically the mobility and dynamic erosion process of granular flow subjected to the complex settings,i.e.,the aspect ratio,granular mass,friction and dilatancy resistance,gravity and presence of water.A set of power scaling laws were proposed to describe the final deposit characteristics of granular flow by the relations of the normalized run-out distance and the normalized final height of granular flow against the aspect ratio,being greatly affected by the complex geological settings,e.g.,granular mass,the friction and dilatancy resistance of granular soil,and presence of water in granular flow.An index of the coefficient of friction of granular soil was defined as a ratio of the target coefficient of friction over the initial coefficient of friction to quantify the scaling extent of friction change(i.e.,friction strengthening or weakening).There is a characteristic aspect ratio of granular column corresponding to the maximum mobility of granular flow with the minimum index of the apparent coefficient of friction.The index of the repose coefficient of friction of granular flow decreased gradually with the increase in aspect ratio because higher potential energy of granular column at a larger aspect ratio causes a larger kinetic energy of granular soil to weaken the friction of granular soil as a kind of velocity-related friction weakening.An increase in granular mass reduces gradually the indexes of the apparent and repose coefficients of friction of granular soil to enhance the mobility of granular flow.The mobility of granular flow increases gradually with the decrease in friction angle or increase in dilatancy angle of granular soil.However,the increase of gravity accelerates granular flow but showing the same final deposit profile without any dependence on gravity.The mobility of granular flow increases gradually by lowering the indexes of the apparent and repose coefficients of friction of granular flow while changing the surroundings,in turn,the dry soil,submerged soil and saturated soil,implying a gradually increased excessive mobility of granular flow with the friction weakening of granular soil.Presence of water in granular flow may be a potential catalyzer to yield a long run-out granular flow,as revealed in comparison of water-absent and water-present granular flows.In addition,the dynamic erosion and entrainment of based soil induced by granular flow subjected to the complex geological settings,i.e.,the aspect ratio,granular mass,gravity,friction and dilatancy resistance,and presence of water,were comprehensively investigated as well.

Particle dynamics in dense shear granular flow

The particle dynamics in an annular shear granular flow is studied using the discrete element method, and the influences of packing fraction, shear rate and friction coefficient are analyzed. We demonstrate the existence of a critical packing fraction exists in the shear granular flow. When the packing fraction is lower than this critical value, the mean tangential velocity profile exhibits a rate-independent feature. However, when the packing fraction exceeds this critical value, the tangential velocity profile becomes rate-dependent and varies gradually from linear to nonlinear with increasing shear rate. Furthermore, we find a continuous transition from the unjammed state to the jammed state in a shear granular flow as the packing fraction increases. In this transforming process, the force distribution varies distinctly and the contact force network also exhibits different features.

Numerical simulation of two-dimensional granular shearing flows and the friction force of a moving slab on the granular media

This paper studies some interesting features of two-dimensional granular shearing flow by using molecular dynamic approach for a specific granular system. The obtained results show that the probability distribution function of velocities of particles is Gaussian at the central part, but diverts from Gaussian distribution nearby the wall. The macroscopic stress along the vertical direction has large fluctuation around a constant value, the non-zero average velocity occurs mainly near the moving wall, which forms a shearing zone.. In the shearing movement, the volume of the granular material behaves in a random manner. The equivalent fl＇iction coefficient between moving slab and granular material correlates with the moving speed at low velocity, and approaches constant as the velocity is large enough.

Estimating the maximum impact force of dry granular flow based on pileup characteristics

The maximum normal impact resultant force(NIRF)is usually regarded as the sum of the static earth pressure of the dead zone and the dynamic impact pressure of the flowing layer.The influence of the interaction between the flowing layer and dead zone on the impact force is ignored.In this study,we classified two impact models with respect to the pileup characteristics of the dead zone.Then,we employed the discrete element method to investigate the influences of the pileup characteristics on the impact force of dry granular flow on a tilted rigid wall.If the final pileup height is equal to the critical value,the maximum NIRF can be estimated using a hydrostatic model,because the main contribution to the maximum NIRF is the static earth pressure of the dead zone.If the final pileup height is less than the critical value,however,the particles in the dead zone are squeezed along the slope surface by the impact ofthe flowing layer on the dead zone,and because of shear effects,the flowing layer causes an entrainment in the dead zone.This results in a decrease in the volume of the dead zone at the moment of maximum NIRF with increases in the slope angle.As such,the maximum NIRF mainly comprises the instant impact force of the flowing layer,so hydro-dynamic models are effective for estimating the maximum NIRF.Impact models will benefit from further study of the components and distribution of the impact force of dry granular flow.

Experimental Study on the Mobility of Channelized Granular Mass Flow

Granular mass flows （e.g., debris flows/avalanches） in landslide-prone areas are of great concern because they often cause catastrophic disasters as a result of their long run-out distances and large impact forces. To investigate the factors influencing granular mass flow mobility, experimental tests were conducted in a flume model. Granular materials consisting of homogeneous sand and non- homogeneous sandy soil were used for studying particle size effects. Run-out tests with variable flow masses, water contents, and sloping channel confinement parameters were conducted as well. The results indicated that granular mass flow mobility was significantly influenced by the initial water content; a critical water content corresponding to the smallest flow mobility exists for different granular materials. An increase in the total flow mass generally induced a reduction in the travel angle （an increase in flow mobility）. Consistent with field observations, the travel angles for different granular materials decreased roughly in proportion to the logarithm of mass. The flume model tests illustrate that the measured travel angles increase as the proportion of fine particles increases. Interestingly, natural terrain possesses critical confinement characteristics for different granular mass flows.

Numerical simulations of dense granular flow in a two-dimensional channel:The role of exit position

Molecular dynamics simulations have been performed to elucidate the influence of exit position on a dense granular flow in a two-dimensional channel. The results show that the dense flow rate remains constant when the exit is far from the channel wall and increases exponentially when the exit moves close to the lateral position. Beverloo’s law proves to be successful in describing the relation between the dense flow rate and the exit size for both the center and the lateral exits.Further simulated results confirm the existence of arch-like structure of contact force above the exit. The effective exit size is enlarged when the exit moves from the center to the lateral position. As compared with the granular flow of the center exit, both the vertical velocities of the grains and the flow rate increase for the lateral exit.

Discharge flow of granular particles through an orifice on a horizontal hopper:Effect of the hopper angle

We experimentally investigate the effect of the hopper angle on the flow rate of grains discharged from a twodimensional horizontal hopper on a conveyor belt.The flow rate grows with the hopper angle,and finally reaches a plateau.The curve feature appears to be similar for different orifice widths and conveyor belt-driven velocities.On the basis of an empirical law of flow rate for a flat-bottom hopper,we propose a modified equation to describe the relation between the flow rate and hopper angle,which is in a good agreement with the experimental results.

A Statistical Estimation Model for the Impact Force of Dry Granular Flow Against Rigid Barrier

The impact force on retaining structure,which is caused by granular flow comprised of dry particles originated from shallow landslide failure,still lacks systematic studies.In order to support the potential design requirement of structure used to resist this kind of impact,a series of dry granular impact experiments are conducted on one rigid barrier model.According to parametric analysis results,one nonlinear regression model is proposed to correlate total normal impact force at critical time(Fcr)with its influential parameters.Further,we complete a systematic statistics analysis and obtain a subsequent optimum regression equation based on the proposed model.According to experience and dimension balance,the equation is modified and finally transformed into one non-dimensional equation,which shows good agreement between predicted and observed results.

Three-dimensional Simulation of Gas/Solid Flow in Spout-fluid Beds with Kinetic Theory of Granular Flow

A three-dimensional Eulerian multiphase model, with closure law according to the kinetic theory of granular flow, was used to study the gas/solid flow behaviors in spout-fluid beds. The influences of the coefficient of restitution due to non-ideal particle collisions on the simulated results were tested. It is demonstrated that the simulated result is strongly affected by the coefficient of restitution. Comparison of simulations with experiments in a small spout-fluid bed showed that an appropriate coefficient of restitution of 0.93 was necessary to simulate the flow characteristics in an underdesigned large size of spout-fluid bed coal gasifier with diameter of 1m and height of 6m. The internal jet and gas/solid flow patterns at different operating conditions were obtained. The simulations show that an optimal gas/solid flow pattern for coal gasification is found when the spouting gas flow rate is equal to the fluidizing gas flow rate and the total of them is two and a half times the minimum fluidizing gas flow rate. Be-sides, the radial distributions of particle velocity and gas velocity show similar tendencies; the radial distributions of particle phase pressure due to particle collisions and the particle pseudo-temperature corresponding to the macro-scopic kinetic energy of the random particle motion also show similar tendencies. These indicate that both gas drag force and particle collisions dominate the movement of particles.

Mass-front velocity of dry granular flows influenced by the angle of the slope to the runout plane and particle size gradation

The mass-front velocities of granular flows results from the joint action of particle size gradations and the underlying surfaces.However,because of the complexity of friction during flow movement,details such as the slope-toe impedance effects and momentum-transfer mechanisms have not been completely explained by theoretical analyses,numerical simulations,or field investigations.To study the mass-front velocity of dry granular flows influenced by the angle of the slope to the runout plane and particle size gradations we conducted model experiments that recorded the motion of rapid and long-runout rockslides or avalanches.Flume tests were conducted using slope angles of 25°,35°,45°,and 55° and three particle size gradations.The resulting mass-front motions consisted of three stages:acceleration,velocity maintenance,and deceleration.The existing methods of velocity prediction could not explain the slowing effect of the slope toe or the momentum-transfer steady velocity stage.When the slope angle increased from 25° to 55°,the mass-front velocities dropped significantly to between 44.4% and59.6% of the peak velocities and energy lossesincreased from 69.1% to 83.7% of the initial,respectively.The velocity maintenance stages occurred after the slope-toe and mass-front velocity fluctuations.During this stage,travel distances increased as the angles increased,but the average velocity was greatest at 45°.At a slope angle of 45°,as the median particle size increased,energy loss around the slope toe decreased,the efficiency of momentum transfer increased,and the distance of the velocity maintenance stage increased.We presented an improved average velocity formula for granular flow and a geometrical model of the energy along the flow line.

Simulation of pore scale fluid flow of granular ore media in heap leaching based on realistic model

Two-dimensional images of the granular ore media with different grain sizes were obtained from the X-ray computed tomography.Combined with the digital image processing and finite element techniques,the original grayscale images were transformed into the finite element models directly.By using these models,the simulations of pore scale fluid flow among particles were conducted with the COMSOL Multiphysics,and the distribution characteristics of fluid flow velocity and pressure were analyzed.The simulation results show that there exist obvious preferential flow and leaching blind zone in each granular medium.The flow velocity at pore throat is larger than that of pore body and the largest velocity reaches 0.22 m/s.The velocity decreases gradually from the center of pore throat and body to the surface of particles.The flow paths of granular media with larger grain size distribute equally,while the fluid flow velocities in most of areas of granular media with smaller grain size are lower,and some of them approach to zero,so the permeability is very low.There exist some pore clusters with different pressures,which is the basic reason for the uneven flow velocity distribution.

Flow Behaviors of Gas-Solid Injector by 3D Simulation with Kinetic Theory of Granular Flow

由 Eulerian 途径的一个煤气固体的注射者的流动行为上的计算研究被执行。煤气的阶段与 k- 被建模狂暴的模型和粒子阶段与小粒的流动的运动理论被建模。由 Eulerian 二液体的模型(TFM ) 的模拟与由分离元素方法(DEM ) 和实验的相应结果相比。它被看模仿的结果在对的合理同意的那 TFM 试验性并且模仿的 DEM 结果。基于 TFM 模拟，煤气固体的流动模式，煤气的速度，粒子速度和静电干扰在不同开车喷气速度， backpressure 和会聚的节角度下面的压力被获得。结果证明平均轴的煤气的速度严厉地减少了然后稍微在水平传送增加了到经常的价值的时间尖叫。轴的粒子速度开始增加了然后减少的时间一般水准，但是在会聚的节的插头区域，粒子速度显著地再次增加了到最大的价值。总体上，静态的压力分发变化趋势被发现在驾驶煤气的速度， backpressure 和会聚的节角度上独立。然而，静态的压力随会聚的节角度和煤气的喷气速度的增加增加了。到 backpressure 的静态的压力的差别与增加 backpressure 增加了。

Experimental Study of Seepage Properties of Non-Darcy Flow in Granular Coal Gangues

By using the steady-state seepage method, a patent seepage device together with the MTS815.02 Rock Me- chanics Test System is used to test the seepage properties of non-Darcy flow in a granular gangue with five different grain sizes during the compaction. The experimental results show that the seepage properties are not only related to the stress or displacement level, but also to the grain size, the pore structure of the granular gangue, and the current porosity. The permeability and the non-Darcy flow coefficient can be fitted respectively by the cubic polynomials and the power functions of the porosity. Formally, the flow in granular gangue satisfies the Forchheimer’s binomial flow, but under the great axial and confining pressure and owing to the grain’s crushing, the flow in granular gangues is different from that in rock-fills which are naturally piled up. As a result, the non-Darcy flow coefficient may be negative.

A Fractal Model for the Effective Thermal Conductivity of Granular Flow with Non—uniform Particles

The equipartition of energy applied in binary mixture of granular flow is extended to granular flow withnon-uniform particles. Based on the fractal characteristic of granular flow with non-uniform particles as well as energyequipartition, a fractal velocity distribution function and a fractal model of effective thermal conductivity are derived.Thermal conduction resulted from motions of particles in the granular flow, as well as the effect of fractal dimension oneffective thermal conductivity, is discussed.

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.

Packing induced bistable phenomenon in granular flow:analysis from complex network perspective

The effects of packing configurations on the phase transition of straight granular chute flow with two bottlenecks axe studied. The granular flow shows a dilute- to-dense flow transition when the channel width is varied, accompanied with a peculiar bistable phenomenon. The bistable phenomenon is induced by the initial packing config- uration of particles. When the packing is dense, the initial flux is small and will induce a dense flow. When the packing is loose, the initial flux is large and will induce a di- lute flow. The fabric network of granulax packing is analyzed from a complex network perspective. The degree distribution shows quantitatively different characteristics for the configurations. A two-dimensional （2D） packing clustering coefficient is defined to better quantify the fabric network.

Saint-Venant Equations and Friction Law for Modelling Self-Channeling Granular Flows: From Analogue to Numerical Simulation

Rock avalanches are catastrophic events involving important granular rock masses (>106 m3) and traveling long distances. In exceptional cases, the runout can reach up to tens of kilometers. Even if they are highly destructive and uncontrollable events, they give important insights to understand interactions between the displaced masses and landscape conditions. However, those events are not frequent. Therefore, the analogue and numerical modelling gives fundamental inputs to better understand their behavior. The objective of the research is to understand the propagation and spreading of granular mass released at the top of a simple geometry. The flow is unconfined, spreading freely along a 45° slope and deposit on a horizontal surface. The evolution of this analogue rock avalanche was measured from the initiation to its deposition with high speed camera. To simulate the analogue granular flow, a numerical model based on the continuum mechanics approach and the solving of the shallow water equations was used. In this model, the avalanche is described from a eulerian point of view within a continuum framework as single phase of incompressible granular material. The interaction of the flowing layer with the substratum follows a Mohr-Coulomb friction law. Within same initial conditions (slope, volume, basal friction, height of fall and initial velocity), results obtained with the numerical model are similar to those observed in the analogue. In both cases, the runout of the mass is comparable and the size of both deposits matches well. Moreover, both analogue and numerical modeling gave same magnitude of velocities. In this study, we highlighted the importance of the friction on a flowing mass and the influence of the numerical resolution on the propagation. The combination of the fluid dynamic equation with the frictional law enables the self-channelization and the stop of the granular mass.

Numerical Simulation of a Granular Flow on a Smooth Inclined Plane

Unlike most fluids,granular materials include coexisting solid,liquid or gaseous regions,which produce a rich variety of complex flows.Dense flows of grains driven by gravity down inclines occur in nature and in industrialprocesses.To describe the granular flow on an inclined surface,several studies were carried out.We can cite in particular the description of Saint-Venant which considers a dry granular flow,without cohesion and it only takes into account the substance-substrate friction,this model proposes a simplified form of the granular flow,which depends on the one side on the angle of inclination of the substrate with respect to the horizontal plane and on the other side on the thickness of the substance H.The numerical simulation we have developed is first based on the Saint-Venant model,it allowed us to visualize the variation of the speed according to the thickness of the substance(from 0 to H)and to deduce the average speed of the substance on an inclined plane.However,this restrictive model does not take into account the effect of particle friction on the flow and considers that the thickness H is constant.To make our simulation more realistic,we opted for the Savage-Hatter model.We took into account the variation of the thickness on the particles speed,in addition we have studied the effect of the variation of many parameters on the granular flow,namely the temperature and the roughness of the substrate,the density and the compactness of the substance,we found that the speed of the particles increases and the treatment time decreases with an increase in temperature.

Evaluation of the Impact Force of Dry Granular Flow onto Rock Shed

In the design of rock sheds for the mitigation of risk due to rapid and long landslides, a crucial role is played by the evaluation of the impact force exerted by the flowing mass on the rock sheds. This paper is focused on the influencing factors of the impact force of dry granular flow onto rock shed and in particular on the evaluation of the maximum impact force. The coupled DEM-FEM model calibrated with small-scale physical experiment is used to simulate the movement of dry granular flow coupled with impact forces on the rock-shed. Based on the numerical results, three key stages were identified of impact process, namely startup streams slippery, impact and pile-up. The maximum impact force increases linearly with bulk density, and the maximum impact force exhibits a power law dependence on the impact height and slop angle respectively. The sensitivities of bulk density, impact height, and slope angle on the maximum impact force are: 1.0, 0.496, and 2.32 respectively in the benchmark model. The parameters with high sensitivity should be given priority in the design of the rock shed. The results obtained from this study are useful for facilitating design of shed against dry granular flow.