Effect of particle polydispersity on micromechanical properties and energy dissipation in granular mixtures

A series of numerical tests was conducted to study the micromechanical properties and energy dissipation in polydisperse assemblies of spherical particles subjected to uniaxial compression. In general, distributed particle size assemblies with standard deviations ranging from 0% to 80% of the particle mean diameter were examined. The microscale analyses included the trace of the fabric tensor, magnitude and orientation of the contact forces, trace of stress, number of contacts and degree of mobilization of friction in contacts between particles. In polydisperse samples, the average coordination numbers were lower than in monodisperse assemblies, and the mobilization of friction was higher than in monodisperse assemblies due to the non-uniform spatial rearrangement of spheres in the samples and the smaller displacements of the particles. The effect of particle size heterogeneity on both the energy density and energy dissipation in systems was also investigated.     

Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum

Despite the wide applications of powder and solid mixing in industry, knowledge on the mixing of polydisperse solid particles in rotary drum blenders is lacking. This study investigates the mixing of monodisperse, bidisperse, tridisperse, and polydisperse solid particles in a rotary drum using the discrete element method. To validate the model developed in this study, experimental and simulation results were compared. The validated model was then employed to investigate the effects of the drum rotational speed, particle size, and initial loading method on the mixing quality. The degree of mixing of polydisperse particles was smaller than that for monodisperse particles owing to the segregation phenomenon. The mixing index increased from an initial value to a maximum and decreased slightly before reaching a plateau for bidisperse, tridisperse, and polydisperse particles as a direct result of the segregation of particles of different sizes. Final mixing indices were higher for polydisperse particles than for tridisperse and bidisperse particles. Additionally, segregation was weakened by introducing additional particles of intermediate size. The best mixing of bidisperse and tridisperse particles was achieved for top–bottom smaller-to-larger initial loading, while that of polydisperse systems was achieved using top–bottom smaller-to-larger and top–bottom larger-to-smaller initial loading methods.     

Resonance scattering characteristics of double-layer spherical particles

Based on the principle of ultrasonic resonance scattering, sound-scattering characteristics of double-layer spherical particles in water were numerically studied in this paper. By solving the equations of the scattering matrix, the scattering coefficient determined by the boundary conditions can be obtained, thus the expression for the sound-scattering function of a single double-layer spherical particle can be derived. To describe the resonance scattering characteristics of a single particle, the reduced scattering cross section and reduced extinction cross section curves were found through numerical calculation. Similarly, the numerically calculated sound attenuation coefficient curves were used to depict the resonance scattering characteristics of monodisperse and polydisperse particles. The results of numerical calculation showed that, for monodisperse particles, the strength of the resonance was mainly related to the particle size and the total number of particles; while for polydisperse particles, it was primarily affected by the particle size, the coverage of the particle size distribution and the particle concentration.     

Spectrum of density fluctuations in a particlefluid system—II. Polydisperse spheres

This paper presents an extension of the analysis shown in Part I to a polydisperse particle-fluid system. The density autocorrelation is shown to be a function of two quantities, a generalized Overlap function for which an analytical expression is derived, and the radial distribution function (RDF). In Fourier transform space, the density spectrum again appears to be a strong function of the mean particle size, and secondarily the mean particle separation distance. One unusual result is previously observed oscillations in the density spectrum of a monodisperse system of particles are severely dampened or even eliminated in the polydisperse case, depending on the width of the particle size distribution. Apparently contributions from different particle correlations interfere with each other, thereby reducing the coherent oscillations seen in the monodisperse particle-fluid system. Furthermore at large wavenumbers, the spectrum decays with a −2 power-law, independent of the shape of the particle size distribution. This behavior can be traced to the Overlap function which controls the behavior of the spectrum beyond the first peak. Remarkably the −2 power-law spectrum is determined by the shape of the particles (i.e. spheres) rather than their spatial distribution (RDF).

The effect of an asymptotically large pressure gradient on the correlation of several important higher-order moments is revisited for the polydisperse system. The relatively simple relationships developed for the monodisperse system are lost in the polydisperse case because particles of different sizes will be influenced differently by an applied pressure gradient. The result is moments that are of different order in velocity can no longer be related to each other (as they were in the monodisperse system), even in this idealized flow. A more comprehensive understanding of this phenomenon can only be achieved through direct numerical simulation or experiment.     

Effect of particle size distribution on micro- and macromechanical response of granular packings under compression

The role of particle size heterogeneity on micro- and macromechanical properties of assemblies of spherical particles was studied using DEM simulations. The response to an imposed load of a granular material composed of non-uniformly sized spheres subjected to uniaxial confined compression was investigated. A range of geometrical and micro-mechanical properties of granular packings (e.g., void fraction, contact force distribution, average coordination number and degree of mobilisation of friction at contacts between particles) were examined, and provided a more accurate interpretation of the macroscopic behaviour of mixtures than has previously been available. The macromechanical study included stress transmission, stiffness and angle of internal friction of the granular assemblies.The degree of polydispersity showed slight effect on both, the void fraction and the elastic properties of the system. The tendency for increase in the lateral-to-vertical pressure ratios was observed with an increasing degree of particle size heterogeneity; however, the different pressure ratios calculated for samples with various degrees of polydispersity lay within the range of data scatter.     

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.     

An analytical approach for the closure equations of gas–solid flows with inter-particle collisions

This work examines the effect of inter-particle collisions on the motion of solid particles in two-phase turbulent pipe and channel flows. Two mechanisms for the particle–particle collisions are considered, with and without friction sliding. Based on these collision mechanisms, the correlations of the various velocity components of colliding particles are obtained analytically by using an averaging procedure. This takes into account three collision coordinates, two angles and the distance between the centers of colliding particles. The various stress tensor components are obtained and then introduced in the mass, linear momentum and angular momentum equations of the dispersed phase. The current approach applies to particle–particle collisions that result from both the average velocity difference and the turbulent velocity fluctuations. In order to close the governing equations of the dispersed phase, the pseudo-viscosity coefficients are defined and determined by the time of duration of the inter-particle collision process. The model is general enough to apply to both polydisperse and monodisperse particulate systems and has been validated by comparisons with experimental data.     

Dilation and breakage dissipation of granular soils subjected to monotonic loading

Dilation and breakage energy dissipation of four different granular soils are investigated by using an energy balance equation. Due to particle breakage, the dilation curve does not necessarily pass through the origin of coordinates. Breakage energy dissipation is found to increase significantly at the initial loading stage and then gradually become sta-bilised. The incremental dissipation ratio between breakage energy and plastic work exhibits almost independence of the confining pressure. Accordingly, a plastic flow rule consid-ering the effect of particle breakage is suggested. The critical state friction angle is found to be a combination of the basic friction between particles and the friction contributed by par-ticle breakage.     

Determining a representative element volume for DEM simulations of samples with non-circular particles

Numerical studies on the number of particles or system size required to attain a representative element volume (REV) for discrete element method (DEM) simulations of granular materials have almost always considered samples with spherical or circular particles. This study considers how many particles are needed to attain a REV for 2D samples of 2-disc cluster particles where the particle aspect ratio (AR) was systematically varied. Dense and loose assemblies of particles were simulated. The minimum REV was assessed both by considering the repeatability of static packing characteristics and the shearing behaviour in biaxial compression tests, and by investigating the effect of sample size on the measured characteristics and observed shearing behaviour. The repeatability of the data considered generally improved with increasing sample size. The packing characteristics of the dense samples were more repeatable suggesting that the minimum REV reduces with increasing packing density. The minimum REV was observed to be sensitive to the characteristic measured. Although the overall responses of the samples during shear deformation were similar irrespective of the sample sizes, the smaller the sample size, the higher the fluctuations observed in the responses. Analysis of the coefficient of variation of the fluctuations around the critical state stress ratio can provide insight as to whether a REV is attained. The particle AR influences the effect of sample size on shearing characteristics and thus the minimum number of particles required to attain a REV; this can be explained by the influence of AR on the number of contacts within the samples.     

Study of fluid cell coarsening for CFD-DEM simulations of polydisperse gas–solid flows

Particle polydispersity is ubiquitous in industrial fluidized beds, which possesses a significant impact on hydrodynamics of gas–solid flow. Computational fluid dynamics-discrete element method (CFD-DEM) is promising to adequately simulate gas–solid flows with continuous particle size distribution (PSD) while it still suffers from high computational cost. Corresponding coarsening models are thereby desired. This work extends the coarse-grid model to polydisperse systems. Well-resolved simulations with different PSDs are processed through a filtering procedure to modify the gas–particle drag force in coarse-grid simulations. We reveal that the drag correction of individual particle exhibits a dependence on filtered solid volume fraction and filtered slip velocity for both monodisperse and polydisperse systems. Subsequently, the effect of particle size and surrounding PSD is quantified by the ratio of particle size to Sauter mean diameter. Drag correction models for systems with monodisperse and continuous PSD are developed. A priori analysis demonstrates that the developed models exhibit reliable prediction accuracy.     

Machine Learning for heat radiation modeling of bi- and polydisperse particle systems including walls

We investigated the ability of four popular Machine Learning methods i.e., Deep Neural Networks (DNNs), Random Forest-based regressors (RFRs), Extreme Gradient Boosting-based regressors (XGBs), and stacked ensembles of DNNs, to model the radiative heat transfer based on view factors in bi- and polydisperse particle beds including walls. Before training and analyzing the predictive capability of each method, an adjustment of markers used in monodisperse systems, as well as an evaluation of new markers was performed. On the basis of our dataset that considers a wide range of particle radii ratios, system sizes, particle volume fractions, as well as different particle-species volume fractions, we found that (i) the addition of particle size information allows the transition from monodisperse to bi- and polydisperse beds, and (ii) the addition of particle volume fraction information as the fourth marker leads to very accurate predictions. In terms of the overall performance, DNNs and RFRs should be preferred compared to the other two options. For particle–particle view factors, DNN and RFR are on par, while for particle–wall the RFR is superior. We demonstrate that DNNs and RFRs can be built to meet or even exceed the prediction quality standards achieved in a monodisperse system.     

可破碎颗粒体在动力载荷下的耗能特性

采用离散元的数值方法, 通过连接键将若干小颗粒绑定为一个具有不规则外形的大颗粒体, 设置不同连接键强度模拟了颗粒体在外加动力载荷下破碎过程, 并探讨其中系统能量耗散特性. 计算结果表明, 颗粒体的破碎程度决定了系统能量耗散率, 即内部耗能占外界输入能量的比例. 破碎率越高, 颗粒间相互摩擦和碰撞越剧烈,系统能量耗散率越高. 同时, 在循环载荷下系统内颗粒体破碎绝大部分发生在加载初期, 随着颗粒体的分解破碎速率逐渐减小, 系统耗能能力也随之降低.      

Effects of Particle Size Non-Uniformity on Transport and Retention in Saturated Porous Media

Short-pulse injection experiments are investigated to study the effects of particle size non-uniformity on the transport and retention in saturated porous media. Monodisperse particles (3, 10, and 16 \(\upmu \hbox {m}\) latex microspheres) and polydisperse particles (containing 3, 10, and 16 latex microspheres) were explored. The obtained results suggest considering not only the particle sizes but also their polydispersivity (particle size non-uniformity) in transport and retention. Although, the density of the suspended particles is close to that of water, results reveal a slow transport of particles compared to the dissolved tracer whatever their size and flow velocity. The recovered particles in the mixture experiments show that the retention of large particles (10 and 16 \(\upmu \hbox {m}\)) enhances the retention of small ones (3 \(\upmu \hbox {m}\)). However, the straining of 10 and 16 \(\upmu \hbox {m}\) particles in “mixture experiments” is smaller than their straining in “monodisperse experiments”. A linear relationship summarizing the simultaneous effect of particle sizes and flow velocity on deposition kinetics coefficient is proposed.     

Gas–solid interaction force from direct numerical simulation (DNS) of binary systems with extreme diameter ratios

Fluid–particle systems as commonly encountered in chemical, metallurgical and petroleum industries are mostly polydisperse in nature. However, the relations used to describe fluid–particle interactions are originally derived from monodisperse systems, with ad hoc modifications to account for polydispersity. In previous work it was shown that for bidisperse systems with moderate diameter ratios of 1:2 to 1:4, this approach leads to discrepancies, and a correction factor is needed. In this work we demonstrate that this correction factor also holds for more extreme diameter ratios of 1:5, 1:7 and 1:10, although the force on the large particles is slightly overestimated when using the correction factor. The main origin of the correction is that the void surrounding the large particles becomes less in case of a bidisperse mixture, as compared to a monodisperse system with the same volume fraction. We further investigated this discrepancy by calculating the volume per particle by means of Voronoi tessellation.     

Numerical and experimental direct shear tests for coarse-grained soils

The presence of particles larger than the permissible dimensions of conventional laboratory specimens causes difficulty in the determination of shear strength of coarse-grained soils. In this research, the influence of particle size on shear strength of coarse-grained soils was investigated by resorting to experimental tests in different scale and numerical simulations based on discrete element method (DEM). Experimental tests on such soil specimens were based on using the techniques designated as "parallel" and "scalping" to prepare gradation of samples in view of the limitation of laboratory specimen size. As a second approach, the direct shear test was numerically simulated on assemblies of elliptical particles. The behaviors of samples under experimental and numerical tests are presented and compared, indicating that the modification of sample gradation has a significant influence on the mechanical properties of coarse-grained soils. It is noted that the shear strengths of samples produced by the scalping method are higher than samples by the parallel method. The scalping method for preparing specimens for direct shear test is therefore recommended. The micromechanical behavior of assemblies under direct shear test is also discussed and the effects of stress level on sample behavior are investigated.     

Microstructural investigations of the yielding behaviour of bidisperse magnetorheological fluids

Particle level simulations were used to investigate the effects of size bidispersity and particle size ratios on the static and yielding behaviour of magnetorheological fluids (MRF). The MRF were treated as linearly magnetisable, neutrally buoyant particles dispersed in a viscous carrier liquid. In the quiescent mode (static structures), the bidisperse suspensions were found to have a higher tendency to form straight chains than the monodisperse suspensions; this is consistent with previous findings. Under steady shearing, the bidisperse suspensions exhibited higher stress enhancement than the monodisperse systems. The stress enhancement in bidisperse suspensions is likely to be due to the population and orientation of interacting large particles in the bidisperse suspensions.     

Numerical simulation of fluid–particle hydrodynamics in a rectangular spouted vessel

A three-dimensional, Eulerian simulation was developed to describe isothermal, two-phase flow of the continuous (water) and dispersed (solid particles) phases in a rectangular spouted vessel. The mass and momentum conservation equations for each phase were solved using the finite volume technique, which treats each phase separately, while coupling them through drag, turbulence, and energy dissipation due to particle fluctuations. Particle–particle interactions via friction were also included.     

Representative elementary volume analysis of polydisperse granular packings using discrete element method

The representative elementary volume (REV) for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression. Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15, 10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.     

基于离散单元法的颗粒阻尼耗能减振特性研究

采用离散单元法并从能量耗散的角度研究颗粒阻尼对系统减振特性的影响。建立了颗粒介质细观下的法向、切向和滚动方向的粘弹性接触模型和能量耗散模型,通过冲击激励和简谐激励下系统振动响应的多参数能量耗散分析来研究颗粒阻尼的耗能机理和减振特性。数值试验表明,颗粒介质可以在一个较宽的振动幅值范围内有效的发挥其阻尼效应,其耗能具有阶梯状周期性的特点。填充率是影响颗粒阻尼耗能减振效果的主要工程可控参数并对系统共振频率产生重大影响,当填充率接近极值时,系统出现无阻尼共振及共振频率超出无颗粒系统固有频率的现象。系统在最优填充率下共振时,颗粒与箱体保持恒定相位差的超振幅稳态运动。较小粒径的颗粒可以提高能量耗散率并使振动系统更快趋向静平衡状态,而恢复系数和摩擦系数则对法向和切向耗能的比值有较大影响。