颗粒群碰撞搜索及CFD-DEM耦合分域 求解的推进算法研究

在采用计算流体力学-离散元耦合方法(computational fluiddynamics-discrete element method, CFD-DEM)进行固液两相耦合分析时, 颗粒计算时间步的选取直接影响到耦合计算精度和计算效率. 为此, 本文选取每个目标颗粒为研究对象, 引入插值函数计算时间步的运动位移, 构建可变空间搜索网格; 通过筛选可能碰撞颗粒建立搜索列表, 采用逆向搜索方式判断碰撞颗粒, 从而提出一种改进的DEM方法(modified discreteelement method, MDEM). 该算法在颗粒群与流体耦合计算中, 颗粒计算初始时间步选取不受颗粒碰撞时间限制, 通过自动调整和修正实现大步长, 由颗粒和流体耦合条件实时更新流体计算时间步, 使颗粒计算时间步选取过小导致计算效率低、选取过大导致颗粒碰撞漏判的问题得以解决, 为颗粒与流体耦合的数值模拟提供了行之有效的计算方法. 通过两个颗粒和多个颗粒的数值模拟, 得到的颗粒间碰撞力、碰撞位置及次数, 与理论计算结果的相对误差均低于2%, 与传统的DEM碰撞搜索算法相比, 在选取的3种计算时间步均不会影响计算精度, 且有较高的计算效率. 通过多个颗粒与流体的耦合数值模拟, 采用传统的CFD-DEM方法, 只有颗粒计算时间步选取10$^{-6}$ s或更小才能得到精确解, 而采用本文方法取10$^{-4}$ s也能够得到精确解, 避免了颗粒碰撞随时间步增大而出现的漏判问题, 且计算耗时降低了16.7%.      

Superquadric DEM-SPH coupling method for interaction between non-spherical granular materials and fluids

The research on the coupling method of non-spherical granular materials and fluids aims to predict the particle–fluid interaction in this study. A coupling method based on superquadric elements is developed to describe the interaction between non-spherical solid particles and fluids. The discrete element method (DEM) and the smoothed particle hydrodynamics (SPH) are adopted to simulate granular materials and fluids. The repulsive force model is adopted to calculate the coupling force and then a contact detection method is established for the interaction between the superquadric element and the fluid particle. The contact detection method captures the shape of superquadric element and calculates the distance from the fluid particle to the surface of superquadric element. Simulation cases focusing on the coupling force model, energy transfer, and large-scale calculations have been implemented to verify the validity of the proposed coupling method. The coupling force model accurately represents the water entry process of a spherical solid particle, and reasonably reflects the difference of solid particles with different shapes. In the water entry process of multiple solid particles, the total energy of the water entry process of multiple solid particles tends to be stable. The collapse process of the partially submerged granular column is simulated and analyzed under different parameters. Therefore, this coupling method is suitable to simulate fluid–particle systems containing solid particles with multiple shapes.     

Effect of Shape on Inertial Particle Dynamics in a Channel Flow

Particle dynamics in a channel flow are investigated using large eddy simulation and a Lagrangian particle tracking technique. Following validation of single-phase flow predictions against DNS results, fluid velocities are subsequently used to study the behaviour of particles of differing shape assuming one-way coupling between the fluid and the particles. The influence of shape- and orientation-dependent drag and lift forces on both the translational and rotational motion of the particles is accounted for to ensure accurate representation of the flow dynamics of non-spherical particles. The size of the particles studied was obtained based on an equivalent-volume sphere, and differing shapes were modelled using super-quadratic ellipsoid forms by varying their aspect ratio, with their orientation predicted using the incidence angle between the particle relative velocity and the particle principal axis. Results are presented for spherical, needle- and platelet-like particles at a number of different boundary layer locations along the wall-normal direction within the channel. The time evolution and probability density function of selected particle translational and rotational properties show a clear distinction between the behaviour of the various particles types, and indicate the significance of particle shape when modelling many practically relevant flows.     

Experimental Study on the Effective Particle Diameter of a Packed Bed with Non-Spherical Particles

An experimental study is conducted to determine the characteristics of frictional pressure drops of fluid flow in porous beds packed with non-spherical particles. The objective is to examine the applicability of the Ergun equation to flow resistance assessment for packed beds with non-spherical particles. The experiments are carried out on the POMECOFL facility at KTH. Hollow spheres and cylinders are used to pack the beds. Either water or air is chosen as the working fluid. The experimental data show that the Ergun equation is applicable to all the test beds if the effective particle diameter used in the equation is chosen as the equivalent diameter of the particles, which is the product of Sauter mean diameter and shape factor of the particles in each bed.     

Evaluation of coarse-grained CFD-DEM models with the validation of PEPT measurements

Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) is a commonly used numerical method to model gas-solid flow in fluidised beds and other multiphase systems. A significant limitation of CFD-DEM is the feasibility of the realistic simulation of large numbers of particles. Coarse-graining (CG) approaches, through which groups of multiple individual particles are represented by single, larger particles, can substantially reduce the total number of particles while maintaining similar system dynamics. As these three CG models have not previously been compared, there remains some debate, however, about the best practice in the application of CG in CFD-DEM simulations. In this paper, we evaluate the performance of three typical CG methods based on simulations of a bubbling fluidised bed. This is achieved through the use of a numerical validation framework, which makes full use of the high-resolution 3D positron emission particle tracking (PEPT) measurements to rigorously validate the outputs of CFD-DEM simulations conducted using various different coarse-graining models, and various different degrees of coarse-graining. The particle flow behaviours in terms of the particle occupancy field, velocity field, circulation time, and bubble size and velocity, are comprehensively analysed. It is shown that the CG simulation starts to fail when the size ratio between the bed chamber and the particles decreases to approximately 20. It is also observed, somewhat surprisingly, that the specific CG approach applied to interparticle contact parameters does not have a substantial effect on the simulation results for the bubbling bed simulations across a wide range of CG factors.     

Modeling particle sedimentation in viscous fluids with a coupled immersed boundary method and discrete element method

Numerical techniques have increasingly been used to model fluid–particle two-phase flows. Coupling the immersed boundary method (IBM) and discrete element method (DEM) is one promising approach for modeling particulate flows. In this study, IBM was coupled with DEM to improve the reliability and accuracy of IBM for determining the positions of particles during the sedimentation process within viscous fluids. The required ratio of the particle diameter to the grid size (D/dx) was determined by comparing the simulation results with the analytical solution and experimental data. A dynamic mesh refinement model was utilised in the IBM model to refine the computational fluid dynamics grid near the particles. In addition, an optimum coupling interval between the IBM and DEM models was determined based on the experimental results of a single particle sedimentation within silicon oil at a Reynolds number of 1.5. The experimental results and the analytical solution were then utilised to validate the IBM–DEM model at Reynolds numbers of 4.1, 11.6, and 31.9. Finally, the validated model was utilised to investigate the sedimentation process for more than one particle by modeling the drafting-kissing-tumbling process and the Boycott phenomenon. Benchmark tests showed that the IBM–DEM technique preserves the advantages of DEM for tracking a group of particles, while the IBM provides a reliable and accurate approach for modeling the particle–fluid interaction.     

Simulation of proppant transport at intersection of hydraulic fracture and natural fracture of wellbores using CFD-DEM

Proppants transport is an advanced technique to improve the hydraulic fracture phenomenon, in order to promote the versatility of gas/oil reservoirs. A numerical simulation of proppants transport at both hydraulic fracture (HF) and natural fracture (NF) intersection is performed to provide a better understanding of key factors which cause, or contribute to proppants transport in HF–NF intersection. Computational fluid dynamics (CFD) in association with discrete element method (DEM) is used to model the complex interactions between proppant particles, host fluid medium and fractured walls. The effect of non-spherical geometry of particles is considered in this model, using the multi-sphere method. All interaction forces between fluid flow and particles are considered in the computational model. Moreover, the interactions of particle–particle and particle–wall are taken into account via Hertz–Mindlin model. The results of the CFD-DEM simulations are compared to the experimental data. It is found that the CFD-DEM simulation is capable of predicting proppant transport and deposition quality at intersections which are in agreement with experimental data. The results indicate that the HF–NF intersection type, fluid velocity and NF aperture affect the quality of blockage occurrence, presenting a new index, called the blockage coefficient which indicates the severity of the blockage.     

Effects of grid size on predictions of bed expansion in bubbling fluidized beds of Geldart B particles: A generalized rule for a grid-independent solution of TFM simulations

Numerical simulations of gas–solid fluidized beds based on the kinetic theory of granular flow exhibit a significant dependence on domain discretization. Bubble formation, bubble size and shape all vary greatly with the discretization, and the use of an inappropriate scale resolution leads to inaccurate predictions of fluidization hydrodynamics. In this study, grid-independent solutions of the two fluid model were examined by comparing the bed expansions obtained from numerical simulations with experimental results and empirical predictions, based on bubbling fluidized beds of Geldart B particles. Grid independence was achieved with a grid resolution equal to 18 times the particle diameter. The simulation results were compared with previously published data for verification purposes. The results of this work should provide a guideline for choosing the appropriate grid size and thereby minimize the time and expense associated with large simulations.     

Numerical prediction of particle slip velocity in turbulence by CFD-DEM simulation

Turbulent environment improves the flotation recovery of fine particles by promoting the particle–bubble collision rate, which directly depends on the particle slip velocity. However, the existing slip velocity models are not applicable to fine particles in turbulence. The mechanism of turbulence characteristics and particle properties on the slip velocity of fine particles in turbulence was unclear. In this study, a coupled ANSYS FLUENT and EDEM based on computational fluid dynamics (CFD) and discrete element method (DEM) were used to simulate the slip velocity of fine particles in the approximately homogenous isotropic turbulence, which was excited by the grid. The reliability of the used CFD-DEM simulation method was validated against the slip velocity measured by the particle image velocimetry (PIV) experiments. In particular, the effects of the particle shapes, particle densities, and turbulence intensities on the slip velocity have been investigated with this numerical method. Numerical results show that particle shapes have no significant effect on fine particles between 37 and 225 μm. The slip velocity of the spherical particles increases with the turbulence intensity and particle density. Based on the simulated data, a model which has a correlation coefficient of 0.95 is built by using nonlinear fitting.     

气固两相流介尺度LBM-DEM模型

LBM-DEM耦合方法通常是指一种颗粒流体系统直接数值模拟算法,即是一种不引入经验曳力模型的计算方法,颗粒尺寸通常比计算网格的长度大一个量级,颗粒的受力通过表面的粘性力与压力积分获得,其优点是能描述每个颗粒周围的详细流场,产生详细的颗粒-流体相互作用的动力学信息,可以探索颗粒流体界面的流动、传递和反应的详细信息及两相相互作用的本构关系,但其缺点是计算量巨大,无法应用于真实流化床过程模拟。本文针对气固流化床中的流体以及固体颗粒间的多相流体力学行为,建立了一种稠密气固两相流的介尺度LBMDEM模型,即LBM-DEM耦合的离散颗粒模型,实现在颗粒尺度上流化床的快速离散模拟。该耦合模型采用格子玻尔兹曼方法(LBM)描述气相的流动和传递行为,离散单元法(DEM)用于描述颗粒相的运动,并利用能量最小多尺度(EMMS)曳力解决气固耦合不成熟问题,以提高其模拟精度。通过经典快速流态化的模拟,验证了介尺度LBM-DEM耦合模型的有效性。模拟结果表明介尺度LBM-DEM模型是一种探索实验室规模气固系统的有力手段。     

Numerical simulation of uranium tetrafluoride fluorination in a multistage spouted bed using the improved CFD-DEM chemical reaction model

A CFD-DEM reaction coupling model was established to simulate UF₄ fluorination process, in which heat and mass transfer, heterogeneous chemical reaction, and particle shrinkage model were considered. The gas behavior was described by the conservation laws of mass, momentum, and energy. The solid phase is modeled with the discrete element method, considering the gas–solid interphase force, contact force, heat transfer, and chemical reaction models based on the discretized surface. Each particle can be individually tracked and associated with specific physical properties. The proposed CFD-DEM reaction coupling model based on particle shrinking reaction model with discretized surface was validated by the experimental and literature results at first. Then a multistage conical spouted bed was proposed and the process of UF₄ fluoridation reaction in it was investigated. The fluidization characteristics and the concentration distribution of gaseous products in the spouted bed with an extended gas velocity range were obtained and analyzed. In addition, the effects of different parameters, such as superficial gas velocity, temperature, fluorine concentration, on fluoridation rate and the fluorine conversion rate were investigated based on the proposed CFD-DEM reaction coupling model. The results obtained in this work are beneficial for method development of the chemical reaction simulation research in particle scale using the CFD-DEM model, and useful for operation and equipment parameters design of the uranium tetrafluoride fluorinate industrial process in the future.     

Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers

This paper describes a complete framework to predict the behaviour of interacting non-spherical particles with large Stokes numbers in a turbulent flow. A summary of the rigid body dynamics of particles and particle collisions is presented in the framework of Quaternions. A particle-rough wall interaction model to describe the collisions between non-spherical particles and a rough wall is put forward as well. The framework is coupled with a DNS-LES approach to simulate the behaviour of horizontal turbulent channel flow with 5 differently shaped particles: a sphere, two types of ellipsoids, a disc, and a fibre. The drag and lift forces and the torque on the particles are computed from correlations which are derived using true DNS.The simulation results show that non-spherical particles tend to locally maximise the drag force, by aligning their longest axis perpendicular to the local flow direction. This phenomenon is further explained by performing resolved direct numerical simulations of an ellipsoid in a flow. These simulations show that the high pressure region on the acute sides of a non-spherical particle result in a torque if an axis of the non-spherical particle is not aligned with the flow. This torque is only zero if the axis of the particle is perpendicular to the local direction of the flow. Moreover, the particle is most stable when the longest axis is aligned perpendicular to the flow.The alignment of the longest axis of a non-spherical particle perpendicular to the local flow leads to non-spherical particles having a larger average velocity compared to spherical particles with the same equivalent diameter. It is also shown that disc-shaped particles flow in a more steady trajectory compared to elongated particles, such as elongated ellipsoids and fibres. This is related to the magnitude of the pressure gradient on the acute side of the non-spherical particles. Finally, it is shown that the effect of wall roughness affects non-spherical particles differently than spherical particles. Particularly, a collision of a non-spherical particle with a rough wall induces a significant amount of rotational energy, whereas a corresponding collision with a spherical particle results in mostly a change in translational motion.     

Direct-forcing immersed boundary lattice Boltzmann simulation of particle/fluid interactions for spherical and non-spherical particles

The lattice Boltzmann method (LBM) is a useful technique for simulating multiphase flows and modeling complex physics. Specifically, we use LBM combined with a direct-forcing (DF) immersed boundary (IB) method to simulate fluid–particle interactions in two-phase particulate flows. Two grids are used in the simulation: a fixed uniform Eulerian grid for the fluid phase and a Lagrangian grid that is attached to and moves with the immersed particles. Forces are calculated at each Lagrangian point. To exchange numerical information between the two grids, discrete delta functions are used. The resulting DF IB-LBM approach is then successfully applied to a variety of reference flows, namely the sedimentation of one and two circular particles in a vertical channel, the sedimentation of one or two spheres in an enclosure, and a neutrally buoyant prolate spheroid in a Couette flow. This last application proves that the developed approach can be used also for non-spherical particles. The three forcing schemes and the different factors affecting the simulation (added mass effect, corrected radius) are also discussed.     

基于CFD-DEM的高炉风口回旋区形状和传热特性数值模拟研究

采用计算流体力学-离散单元法(CFD-DEM)耦合方法,对高炉风口回旋区进行了数值模拟研究。首先通过与实验结果对比,验证了CFD-DEM模型的正确性;然后考察了不同气速对风口回旋区形状和传热特性及颗粒接触的影响。数值模拟结果表明:风口回旋区的大小和形状均受气速影响较大,在较大进气速度下,颗粒受到的曳力大于颗粒间的摩擦阻力并破坏颗粒间的桥力,形成较大尺寸的回旋区;且颗粒之间接触力较小,形成较大的空隙结构,更有利于热气体向周围扩散以强化传热。目前考察的三种气速结果表明:当气速为11m/s时,热量向下方传递速度最快;当气速为13m/s时,热量向上方传递速度最快;而当气速为15m/s时,热量向右方传递速度最快;此外,气速越大流态化越明显,颗粒间接触越少,接触力也越小。     

粒子法中自由表面粒子识别

针对移动粒子半隐式法MPS（Moving Particle Semi-implicit Method）基于粒子数密度来判断自由表面会出现将内部粒子误判为自由表面粒子的问题,提出了一种结合几何法和体积法的自由表面粒子判定方法。通过对溃坝问题进行数值模拟,结果表明,全新的自由表面粒子判定方法对流体平稳运动以及剧烈运动两种工况,都能准确地判断出自由表面粒子,解决了基于粒子数密度判断方法因粒子分布稀疏产生误判的问题。[JP2]这种全新的自由表面粒子判定方法对今后采用MPS方法计算两相流问题时,两种介质在界面处的传热传质计算有重要意义。     

Numerical simulation of the hydrodynamic interaction between a sedimenting particle and a neutrally buoyant particle

A new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi-static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.     

DEM investigation on conveying of non-spherical particles in a screw conveyor

Screw conveyors are extensively used in modern industry such as metallurgy, architecture and pharmaceutical due to their high-efficiency in the transportation of granular materials. And substantial efforts have been devoted to the study of the screw conveyors. Numerical method is an effective way to study screw conveyor. However, previous studies have mainly focused in the regime of spherical particles while the in-depth investigations for non-spherical particles that should be the most encountered in practical applications are still limited. In view of the above situations, discrete element method (DEM), which has been widely accepted in simulating the discrete systems, is utilized to investigate the conveying process of non-spherical particles in a horizontal screw conveyor, with particles being modeled by super-ellipsoids. In addition, a wear model called SIEM (Shear Impact Energy Model) is incorporated into DEM to predict the wear of screw conveyor. The DEM simulation results demonstrate that the particle shape is influential for the flow behaviors of particles and the wear of conveyor. The conveying performance evaluated quantitatively of both mass flow rate and power consumption is subsequently obtained to investigate the effect of sphericity of particle with different operation parameters. Moreover, particle collision frequency and collision energy consumption are acquired to investigate the possible particle breakage between particles and screw blade. The comparisons between particle–particle collision and particle–wall collision reveal that particles with large shape index have more possibility to be damaged in particle–wall impingement.     

An extended finite element method for the simulation of particulate viscoelastic flows

We present an extended finite element method (XFEM) for the direct numerical simulation of the flow of viscoelastic fluids with suspended particles. For moving particle problems, we devise a temporary arbitrary Lagrangian–Eulerian (ALE) scheme which defines the mapping of field variables at previous time levels onto the computational mesh at the current time level. In this method, a regular mesh is used for the whole computational domain including both fluid and particles. A temporary ALE mesh is constructed separately and the computational mesh is kept unchanged throughout the whole computations. Particles are moving on a fixed Eulerian mesh without any need of re-meshing. For mesh refinements around the interface, we combine XFEM with the grid deformation method, in which nodal points are redistributed close to the interface while preserving the mesh topology. Our method is verified by comparing with the results of boundary fitted mesh problems combined with the conventional ALE scheme. The proposed method shows similar accuracy compared with boundary fitted mesh problems and superior accuracy compared with the fictitious domain method. If the grid deformation method is combined with XFEM, the required computational time is reduced significantly compared to uniform mesh refinements, while providing mesh convergent solutions. We apply the proposed method to the particle migration in rotating Couette flow of a Giesekus fluid. We investigate the effect of initial particle positions, the Weissenberg number, the mobility parameter of the Giesekus model and the particle size on the particle migration. We also show two-particle interactions in confined shear flow of a viscoelastic fluid. We find three different regimes of particle motions according to initial separations of particles.     

Onset velocity of circulating fluidization and particle residence time distribution:A CFD-DEM study

Until now,the onset velocity of circulating fluidization in liquid-solid fluidized beds has been defined by the turning point of the time required to empty a bed of particles as a function of the superficial liquid velocity,and is reported to be only dependent on the liquid and particle properties.This study presents a new approach to calculate the onset velocity using CFD-DEM simulation of the particle residence time distribution(RTD).The onset velocity is identified from the intersection of the fitted lines of the particle mean residence time as a function of superficial liquid velocity.Our results are in reasonable agreement with experimental data.The simulation indicates that the onset velocity is influenced by the density and size of particles and weakly affected by riser height and diameter.A power-law function is proposed to correlate the mean particle residence time with the superficial liquid velocity.The collisional parameters have a minor effect on the mean residence time of particles and the onset velocity,but influence the particle RTD,showing some humps and trailing.The particle RTD is found to be related to the particle trajectories,which may indicate the complex flow structure and underlying mechanisms of the particle RTD.     

Direct simulation of liquid–gas–solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid–gas–solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary – in particular, if the bubble–particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble–particle interaction at a size ratio of 1–2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than 100,000 fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble–particle interaction problems correctly.