饱和砂土中泥浆渗透的变形-渗流-扩散耦合计算模型

传统的泥浆渗透计算中没有考虑土体变形和浆液流速的影响.根据泥浆颗粒的质量守恒定律推导了耦合流速的浓度扩散方程,并通过在浓度方程中引入沉积系数进一步计算得到沉积颗粒的质量;同时,以沉积量作为耦合项对毕奥固结方程中的水量连续方程进行了修正,在此基础上建立了变形-渗流-扩散耦合的控制方程及其变分原理. 采用有限单元法求解基本方程,运用了时间增量法与直接迭代法,并利用一维试验验证计算方法的可靠性,并与赫齐格的经典模型的计算结果进行了比较,结果表明,本文建立的模型的计算结果可以较好地预测各组试验中颗粒的沉积规律,且吻合程度优于仅考虑颗粒对流和扩散的传统计算方法. 最后,将泥浆在槽壁中的渗透简化为二维问题并进行了计算,计算结果与工程认识相符合,泥浆的沉积填充效应随深度的增加而增大,施工时需要严格控制浅层作业段的机械垂直度;成槽机的下斗抓挖时机可以根据地层填充的致密程度进行计算,对现场施工具有一定的指导意义.      

Transport modeling of sedimenting particles in a turbulent pipe flow using Euler–Lagrange large eddy simulation

A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity.     

Combination of CFD and DOE to analyse solid particle erosion in elbows

Solid particle erosion is a major concern in the engineering industry, particularly where transport of slurry flow is involved. Such flow regimes are characteristic of those in alumina refinement plants. The entrainment of particulate matter, for example sand, in the Bayer liquor can cause severe erosion in pipe fittings, especially in those which redirect the flow. The considerable costs involved in the maintenance and replacement of these eroded components led to an interest in research into erosion prediction by numerical methods at Rusal Aughinish alumina refinery, Limerick, Ireland, and the University of Limerick. The first stage of this study focused on the use of computational fluid dynamics (CFD) to simulate solid particle erosion in elbows. Subsequently an analysis of the factors that affect erosion of elbows was performed using design of experiments (DOE) techniques. Combining CFD with DOE harnesses the computational power of CFD in the most efficient manner for prediction of elbow erosion. An analysis of the factors that affect the erosion of elbows was undertaken with the intention of producing an erosion prediction model.     

Investigation of dense slurry suspensions with coaxial mixers: Influences of design variables through tomography and mathematical modelling

The coaxial mixers enhance the suspension of concentrated slurries in an agitated reactor. In this research work, the complex slurry suspension and dissemination behavior in a coaxial slurry mixing system (comprised of a close clearance anchor rotating with a low speed and an inner axial impeller rotating with a high speed) was analyzed employing ERT (electrical resistance tomography, a non-intrusive flow visualization technique), and computational fluid dynamics (CFD). The numerical models were validated by comparing the axial solid concentration profiles generated using the ERT data and the CFD simulation results. The influences of various important parameters such as the diameter of the inner axial impeller, the inner impeller type, and the inner impeller spacing on the hydrodynamic characteristics of the slurry suspensions in a coaxial mixing vessel were thoroughly analyzed. The radial and axial velocity profiles of solid particles were generated using the validated mathematical models. The assessment of energy loss due to the solid–solid collisions, the particle–fluid frictions, and the particle–vessel wall collisions was conducted. The evaluation of optimum inner impeller clearance and inner impeller diameter is essential to attain a high degree of solids suspension and dissemination in a coaxial slurry mixing system.     

Determination of Hydrogen–Water Relative Permeability and Capillary Pressure in Sandstone: Application to Underground Hydrogen Injection in Sedimentary Formations

This paper presents fundamental analysis and micromechanical understanding of dense slurry behavior during settling in narrow smooth and rough slots. Particularly, this study seeks to contribute toward better understanding of dynamics of particle–particle and particle–wall interactions in viscous fluids using simple experiments. The findings of this study are applicable in a wide variety of problems, for example sediment transport, flow and transport of slurry in pipes, and industrial applications. However, the results interpretation focuses on better understanding of proppant flow and transport in narrow fractures. A sequence of experiments image frames captured by video camera is analyzed with particle image velocimetry (GeoPIV). The measurements include vertical velocities and displacement vectors of singular and agglomerated particles and larger area of formed slurry. Results present novel insights into the formation and effects of agglomerates on general slurry settling, and are supplemented with a comparison with previously published theoretical and empirical relationships. This work also emphasizes a role of particle–particle interactions in promoting agglomeration in viscous fluid. Particularly, a thin layer of viscous fluid between approaching particles dissipates particle kinetic energy due to lubrication effect. Lubrication effect is more pronounced when particles are constrained between two narrow walls and interact frequently with each other. Fluid tends to flow around agglomerated particles, and agglomerates remain stable for prolonged time periods gravitationally moving downward. The relative amount and size of agglomerated affects general settling of the slurry. It was found that fluid viscosity due to lubrication effect promotes agglomeration, and therefore, the overall slurry settling relatively increases at higher fluid viscosities. The results of the presented work have impact on various industrial and engineering processes, such as proppant flow and transport in hydraulic fractures, sand production in oil reservoirs, piping failure of dams and scour of foundation bridges.     

耐磨环氧胶粘涂层冲蚀磨损特性的研究

本文对气固冲蚀和浆体冲蚀条件下耐磨环氧胶粘涂层的磨损特性进行了研究。结果表明,这种涂层的冲蚀磨损是由粘结剂的磨损和抗磨填料的磨损所组成;填料粒度和磨料粒度都对涂层的气固冲蚀磨损有影响,但在给定的试验条件下,填料粒度对涂层的浆体冲蚀磨损影响甚微。文章指出,耐磨环氧胶粘涂层在气固冲蚀和浆体冲蚀下的磨损机理相似,但磨损规律却有所不同;耐磨环氧胶粘涂层尤其适用于浆体冲蚀的场合,可以明显地提高机械过流部件的使用寿命。     

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.     

Analysis of minimum specific energy consumption and optimal transport concentration of slurry pipeline transport systems

Slurry pipeline transport is widely used in several industrial processes. Calculating the specific power consumption (SPC) and determining the best working conditions are important for the design and operation of transportation systems. Based on the Shanghai Jiao Tong University high-concentration multi-sized slurry pressure drop (SJTU-HMSPD) pipeline-resistance-calculation model, the SJTU-SPC model for calculating the power required to transport a unit volume of solid materials over a unit pipeline length is established for a slurry transport system. The said system demonstrates a uniformity coefficient in the 1.26–7.98 range, median particle size of 0.075–4 mm, particle volume concentration of 10–60%, and pipeline diameter of 0.203–0.8 m. The results obtained were successfully verified against existing experimental data. The influence of parameters, such as particle-gradation uniformity coefficient, median particle size, pipe diameter, and particle volume concentration, on the SPC were analysed. The results revealed that the greater is the uniformity coefficient, the smaller is the minimum specific energy consumption and the larger the optimal transport concentration for a constant, median particle size slurry. As observed, the optimal transport concentration for broad-graded sand equalled approximately 48%. These results supplement the conclusions of existing research, indicating that the optimal transport concentration is approximately 30% and provides theoretical support for high concentration transportation of broad graded slurry.     

Scaling granular material with polygonal particles in discrete element modeling

Despite advancements in computational resources, the discrete element method (DEM) still requires considerable computational time to solve detailed problems, especially when it comes to the large-scale models. In addition to the geometry scale of the problem, the particle shape has a dramatic effect on the computational cost of DEM. Therefore, many studies have been performed with simplified spherical particles or clumps. Particle scaling is an approach to increase the particle size to reduce the number of particles in the DEM. Although several particle scaling methods have been introduced, there are still some disagreements regarding their applicability to certain aspects of problems. In this study, the effect of particle scalping on the shear behavior of granular material is explored. Real granular particles were scanned and imported as polygonal particles in the direct shear test. The effect of particle size distribution, particle angularity, and the amount of scalping were investigated. The results show that particle scalping can simulate the correct shear behavior of the model with significant improvement in computational time. Also, the accuracy of the scalping method depends on the particle angularity and particle size range.     

Experiment and simulation of slurry flow in irregular channels to understand proppant transport in complex fractures

Slurry flow and proppant placement in irregular fractures are crucial to evaluate hydraulic fracturing stimulation but need to be better understood. This study aims to investigate how irregular fracture affects proppant transport and distribution using laboratory experiments and micro-scale numerical models. The unresolved method of the computational fluid dynamics (CFD) and the discrete element method (DEM) considers Saffman lift force, Magnus force, and virtual mass force to accurately capture the frequent interaction between proppant and slickwater. Experimental results validated the reliability of the optimized CFD-DEM model and calibrated primary parameters. The effects of crack height and width, bending angle, and distance between the crack and inlet on particle distribution were studied. The results indicated that the improved numerical method could rationally simulate proppant transport in fractures at a scale factor. The small crack height causes downward and upward flows, which wash proppant to the fracture rear and form isolated proppant dunes. A wider region in the fracture is beneficial to build up a large dune, and the high dune can hinder particle transport into the fracture rear. When the crack is close to the inlet, the primary fracture without proppants will close to hinder gas production. The smaller the bending angle, the smaller the proppant dune. A regression model can precisely predict the dune coverage ratio. The results fundamentally understand how complex fractures and natural cracks affect slurry flow and proppant distribution.     

Theoretical analysis of capillary-driven nanoparticulate slurry flow during a micromold filling process

The microcasting technique for the fabrication of microstructures mainly involves two consecutive steps, namely, the capillary-driven flow of nanoparticulate slurry in micromolds and sintering of the resulting preform. During the mold-filling step, particle settling leads to a spatial particle distribution in the preform, which affects the subsequent sintering kinetics, and in turn, and causes a shape distortion in the final sintered product. This paper presents a comprehensive theoretical model which is adopted to account for the capillary-driven flow and simultaneous particle settling behavior during the filling step. Numerical simulations are performed over a wide range of parameters to illustrate the effects of four nondimensional groups on the fill time and particle distribution, and to develop design windows, which may serve as guidelines in the design of particle properties, slurry composition, and mold dimensions to maintain a desired level of homogeneity in particle distribution.     

柔性微粒介电泳分离过程的多尺度模拟

介电泳分离是一种高效的微细颗粒分离技术,利用非均匀电场极化并操纵分离微流道中的颗粒. 柔性微粒在介电泳分离过程中同时受多种物理场、多相流和微粒变形等复杂因素的影响,仅用单一的计算方法对其进行模拟存在一定的难度,本文采用有限单元——格子玻尔兹曼耦合计算的方法处理这一难题.介观尺度的格子玻尔兹曼方法将流体看成由大量微小粒子组成,在离散格子上求解玻尔兹曼输运方程,易于处理多相流及大变形问题,特别适合模拟柔性颗粒在介电泳分离过程中的变形情况.另一方面,介电泳分离过程的模拟需求解流体、电场和微粒运动方程,计算量相当庞大,通过有限单元法求解介电泳力,提高计算效率.利用这种多尺度耦合计算方法,对一款现有的介电泳芯片分离过程进行了模拟.分析了微粒在电场作用下产生的介电泳力,揭示了介电泳力与电场变化率等因素之间的关系.对微粒运动轨迹及其变形的情况进行了研究,发现微粒的变形主要与流体剪切作用有关.这种多尺度耦合计算方法,为复杂微流体的计算提供了一种有效的解决方案.      

Differentially weighted direct simulation Monte Carlo method for particle collision in gas–solid flows

In gas–solid flows, particle–particle interaction (typical, particle collision) is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles (e.g., agglomeration and fragmentation) in spite of their initial monodisperse particle distribution. The conventional direct simulation Monte Carlo (DSMC) method for particle collision tracks equally weighted simulation particles, which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions. In this study, a new differentially weighted DSMC (DW-DSMC) method for collisions of particles with different number weight is proposed within the framework of the general Eulerian–Lagrangian models for hydrodynamics. Three schemes (mass, momentum and energy conservation) were developed to restore the numbers of simulation particle while keeping total mass, momentum or energy of the whole system unchanged respectively. A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency. The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best. Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC, compared with the equally weighted DSMC. Meanwhile, computational cost can be largely reduced in contrast with direct numerical simulation.     

Differentially weighted direct simulation Monte Carlo method for particle collision in gas-solid flows

In gas-solid flows,particle-particle interaction(typical,particle collision) is highly significant,despite the small particles fractional volume.Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles(e.g.,agglomeration and fragmentation) in spite of their initial monodisperse particle distribution.The conventional direct simulation Monte Carlo(DSMC)method for particle collision tracks equally weighted simulation particles,which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions.In this study,a new differentially weighted DSMC(DW-DSMC) method for collisions of particles with different number weight is proposed within the framework of the general Eulerian-Lagrangian models for hydrodynamics.Three schemes(mass,momentum and energy conservation) were developed to restore the numbers of simulation particle while keeping total mass,momentum or energy of the whole system unchanged respectively.A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency.The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best.Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC,compared with the equally weighted DSMC.Meanwhile,computational cost can be largely reduced in contrast with direct numerical simulation.     

A spectral projection method for the analysis of autocorrelation functions and projection errors in discrete particle simulation

Discrete particle simulation is a well‐established tool for the simulation of particles and droplets suspended in turbulent flows of academic and industrial applications. The study of some properties such as the preferential concentration of inertial particles in regions of high shear and low vorticity requires the computation of autocorrelation functions. This can be a tedious task as the discrete point particles need to be projected in some manner to obtain the continuous autocorrelation functions. Projection of particle properties on to a computational grid, for instance, the grid of the carrier phase, is furthermore an issue when quantities such as particle concentrations are to be computed or source terms between the carrier phase and the particles are exchanged. The errors committed by commonly used projection methods are often unknown and are difficult to analyse. Grid and sampling size limit the possibilities in terms of precision per computational cost. Here, we present a spectral projection method that is not affected by sampling issues and addresses all of the above issues. The technique is only limited by computational resources and is easy to parallelize. The only visible drawback is the limitation to simple geometries and therefore limited to academic applications. The spectral projection method consists of a discrete Fourier‐transform of the particle locations. The Fourier‐transformed particle number density and momentum fields can then be used to compute the autocorrelation functions and the continuous physical space fields for the evaluation of the projection methods error. The number of Fourier components used to discretize the projector kernel can be chosen such that the corresponding characteristic length scale is as small as needed. This allows to study the phenomena of particle motion, for example, in a region of preferential concentration that may be smaller than the cell size of the carrier phase grid. The precision of the spectral projection method depends, therefore, only on the number of Fourier modes considered. Copyright © 2008 John Wiley & Sons, Ltd.     

Direct numerical simulation of particle–fluid systems by combining time-driven hard-sphere model and lattice Boltzmann method

A coupled numerical method for the direct numerical simulation of particle–fluid systems is formulated and implemented, resolving an order of magnitude smaller than particle size. The particle motion is described by the time-driven hard-sphere model, while the hydrodynamic equations governing fluid flow are solved by the lattice Boltzmann method (LBM). Particle–fluid coupling is realized by an immersed boundary method (IBM), which considers the effect of boundary on surrounding fluid as a restoring force added to the governing equations of the fluid. The proposed scheme is validated in the classical flow-around-cylinder simulations, and preliminary application of this scheme to fluidization is reported, demonstrating it to be a promising computational strategy for better understanding complex behavior in particle–fluid systems.     

Normalized SPH without boundary deficiency and its application to transient solid mechanics problems

Smoothed particle hydrodynamics (SPH) method is a powerful tool for modeling solid mechanics problems, especially for large deformation problems. However, it suffers from boundary deficiency and difficulty of boundary condition treatment. In this work, a normalized SPH method is proposed to overcome these problems. The method is based on a newly developed normalized particle approximation. To derive this particle approximation, a normalized kernel approximation which is accurate for derivatives of linear functions everywhere in a problem domain is constructed, and all integral terms of the normalized kernel approximation including boundary terms are discretized by particle summations. The normalized particle approximation is free of matrix inversion, consequently attractive in computational stability and simplicity compared with other corrective particle approximations. Its approximation accuracy is demonstrated by calculating derivatives of test functions. Based on this particle approximation, the formulation of the normalized SPH method for transient solid mechanics problems is derived. Moreover, a direct method of treating traction boundary conditions is presented by making use of the boundary term of the normalized particle approximation. The accuracy and capability of the normalized SPH method are validated by the calculation of elastic wave propagation in solids and compared with commonly used SPH method.

     

Effects of hydrophilic particles on bubbly flow in slurry bubble column

To investigate the effects of hydrophilic particles on slurry bubble flows in a bubble column, distributions of the local gas holdup and the bubble frequency are measured using an electric conductivity probe. Particles are made of silica and their diameter is 100 μm. The particle volumetric concentration C_S is varied from 0 to 0.40. The measured data imply that the presence of particles promotes bubble coalescence. The film drainage time for two coalescing bubbles in a quasi two-dimensional bubble flow in a small vessel is also measured to quantitatively evaluate the particle effect on coalescence. A particle-effect multiplier is introduced into a coalescence efficiency model by taking into account the data of film drainage time and is implemented into a multi-fluid model. The main conclusions obtained are as follows: (1) the local gas holdup and bubble frequency in slurry bubble flows decrease with increasing the particle concentration, (2) the hydrophilic particles enhance bubble coalescence and the enhancement saturates at C_S ≃ 0.45, (3) the particle effect on coalescence is well accounted for by introducing the particle-effect multiplier to the film drainage time, and (4) the multi-fluid model can give good predictions for the distribution of the local gas holdup in the slurry bubble column.     

Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column

A new approach for simulating the formation of a froth layer in a slurry bubble column is proposed. Froth is considered a separate phase, comprised of a mixture of gas, liquid, and solid. The simulation was carried out using commercial flow simulation software (FIRE v2014) for particle sizes of 60–150 μm at solid concentrations of 0–40 vol%, and superficial gas velocities of 0.02–0.034 m/s in a slurry bubble column with a hydraulic diameter of 0.2 m and height of 1.2 m. Modelling calculations were conducted using a Eulerian–Eulerian multiphase approach with k–ε turbulence. The population balance equations for bubble breakup, bubble coalescence rate, and the interfacial exchange of mass and momentum were included in the computational fluid dynamics code by writing subroutines in Fortran to track the number density of different bubble sizes. Flow structure, radial gas holdup, and Sauter mean bubble diameter distributions at different column heights were predicted in the pulp zone, while froth volume fraction and density were predicted in the froth zone. The model was validated using available experimental data, and the predicted and experimental results showed reasonable agreement. To demonstrate the effect of increasing solid concentration on the coalescence rate, a solid-effect multiplier in the coalescence efficiency equation was used. The solid-effect multiplier decreased with increasing slurry concentration, causing an increase in bubble coalescence efficiency. A slight decrease in the coalescence efficiency was also observed owing to increasing particle size, which led to a decrease in Sauter mean bubble diameter. The froth volume fraction increased with solid concentration. These results provide an improved understanding of the dynamics of slurry bubble reactors in the presence of hydrophilic particles.     

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A hybrid computational method coupling the lattice-Boltzmann (LB) method and a Langevin-dynamics (LD) method is developed to simulate nanoscale particle and polymer (NPP) suspensions in the presence of both thermal fluctuation and long-range many-body hydrodynamic interactions (HIs). Brownian motion of the NPP is explicitly captured by a stochastic forcing term in the LD method. The LD method is two-way coupled to the nonfluctuating LB fluid through a discrete LB forcing source distribution to capture the long-range HI. To ensure intrinsically linear scalability with respect to the number of particles, a Eulerian-host algorithm for short-distance particle neighbor search and interaction is developed and embedded to LB-LD framework. The validity and accuracy of the LB-LD approach are demonstrated through several sample problems. The simulation results show good agreements with theory and experiment. The LB-LD approach can be favorably incorporated into complex multiscale computational frameworks for efficiently simulating multiscale multicomponent particulate suspension systems such as complex blood suspensions.