Particle Contact Force Research Articles

Momentum balance and stresses in a suspension of spherical particles in a plane Couette flow

Non-Brownian suspension of monodisperse spherical particles, with volume fractions ranging between ϕ = 0.05 and 0.38 and particle Reynolds numbers ranging between Rep = 0.002 and 20, in plane Couette shear flows is investigated using three-dimensional particle-resolved numerical simulations. We examine the effects of volume fraction and particle Reynolds number on the macroscopic and microscopic stresses in the fluid phase. The effective viscosity of the suspension is in a good agreement with the previous empirical and experimental studies. At Rep = 20, however, the effective viscosity increases significantly compared to the lower particle Reynolds number simulations in the Stokes flow regime. Examining the stresses over the depth of the Couette gap reveals that this increase in wall shear stresses at high particle Reynolds numbers is mainly due to the significantly higher particle phase stress contributions. Next, we examine the momentum balance in the fluid and particle phase for different regimes to assess the significance of particle/particle interaction and fluid and particle inertia. At the highest particle Reynolds number and volume fraction, the particle inertia plays a dominant role in the momentum balance and the fluid inertia is non-negligible, while the short-lived contact forces are negligible compared to these effects. For all other regimes, the fluid inertia is negligible, but the particle inertia and contact forces are important in the momentum balance. Reynolds stresses originated from velocity fluctuations do not contribute significantly to the suspension stresses in any of the regimes we have studied, while the reduction in the shear-induced particle rotation can be a reason for higher wall shear stress at Rep = 20. Finally, we study the kinematics of particles, including their velocity fluctuations, rotation, and diffusion over the depth of the Couette gap. The particle diffusion coefficients in the cross flow direction exhibit an abrupt increase at Rep = 20.

Fluid Coupled-DEM Simulation of Lateral Loading Experiment for Buried Pipe in Saturated Sand

Two-dimensional simulation was carried out using a fluid coupled-DEM (discrete element method) analysis on lateral loading experiments for a pipe buried in saturated sand. The interaction between soil and pore water was reproduced by dividing the model into solid and fluid phases. The variation of the excess pore water pressure was calculated on a fluid mesh based on the pore volume change and was then given to the soil particles in the solid phase. The head difference between the fluid meshes produced upward seepage to the soil model. Liquefaction was reproduced by the decrease of the contact force between the soil particles due to the upward seepage. The force-displacement curves obtained from lateral loading simulations showed good agreement with the experimental results under various effective stress conditions. Distribution maps of contact force and displacement of soil particles revealed displacement mechanism of the buried pipe and its surrounding soil. The variation of the void ratio and the excess pore water pressure with the pipe displacement could be reproduced to some extent, and the applicability of this analysis method to interaction problems has been verified.

Improving particle flow in liquid-solid countercurrent extraction tower by insert structure optimization: A combined study on experiments and DEM simulations

The particle velocity distributions in the liquid-solid countercurrent nylon 6 extraction tower equipped with different types of inserts were investigated by both cold-model experiments and 2D-DEM simulations. The cold-model experiment results near the insert were well interpreted by the distribution of the particle contact force acquired from the DEM simulation. Compared with the disordered particle flow caused by a conventional single-funnel insert, the uniform particle flow could be realized by a special combination of single-funnel inserts with 53° and 35° dip angles of the upper and lower parts, respectively. In addition, a new type of insert, the multi-funnel insert, was found to be more beneficial in improving the uniformity of the particle velocity distribution because it made the particle contact force near the insert uniform. Furthermore, the mass flow state could be maintained in a wider range of discharge rate, which implied an enhancement of the operating flexibility of the tower equipped with the multi-funnel insert. These developed inserts have the potential to be applied in large-scale liquid-solid countercurrent extraction processes.

Study of sedimentation of non-cohesive particles via CFD–DEM simulations

The sedimentation process of granular materials exists ubiquitously in nature and many fields which involve the solid-liquid separation. This paper employs the coupled computational fluid dynamics and discrete element method (CFD-DEM) to investigate the sedimentation process of non-cohesive particles, including the hindered settling stage and the deposition stage. Firstly, the coupled CFD-DEM model for sedimentation is validated by the hindered settling velocity at different solid volume concentrations of suspension (0.05~0.6). Two typical modes of sedimentation are also presented by the concentration profiles and the equal-concentration lines. Then, the comparisons between mono- and poly-dispersed particle system are detailed. In the sedimentation of the poly-dispersed particle system, the segregation phenomenon is simulated. Furthermore, this segregation effect reduces with the increase of the initial solid concentration of suspension. From the simulations, the contact force between every pair of particles can be obtained, hence we demonstrate the "effective stress principle" from the view of the particle contact force by giving the correspondence between the particle contact force and the "effective stress", which is a critical concept of soil mechanics. We also demonstrate the effective stress principle from the view of the contact force acting on particles. Moreover, the deposition stage can be simulated by CFD-DEM method, therefore the solid concentrations of sediment bed on different conditions are studied. Based on the simulation results of maximum solid concentration and the theory of sedimentation, this paper also discusses a method to calculate the critical time when sedimentation ends of two typical modes of sedimentation.

Numerical simulation study on macroscopic mechanical behaviors and micro-motion characteristics of gangues under triaxial compression

This paper describes the numerical research that studied the macroscopic mechanical behavior and the microscopic particle movement of gangue with different gradation under different confining condition and loading rate. Two types of compression tests, confined compression tests and triaxial compression tests were simulated using the commercial numerical modeling software PFC3D. Most of the gangues are irregular convex polyhedron in shape. When under compression, huge contact force can be generated between particles result in interlocking effect. In order to reproduce the interaction between gangues, this research used Clump Template tool in PFC3D to generate clusters of particles to represent tailing particles. Following observations were made based on numerical modeling result: 1) reasonable particle gradation can significantly improve the anti-deformation capacity and decrease lateral stress coefficient of gangue. 2) In triaxial compression tests, the load bearing capacity of gangue increases with the increase of confining pressure. 3) Distribution of particles axial displacement showed ‘horizontal layering’ feature in confined compression tests, and showed ‘concave layering’ feature in triaxial compression tests. In triaxial compression tests, particles close to the mid-height and the sides of the sample have most significant lateral displacement, forming a triangular zone of significant lateral displacement. It is also found that smaller particles move more actively while the large particles have their own “movement inertia”. 4) With the increase of confining pressure, the number of the contact force chains and the maximum contact force between particles within the sample increases gradually, also the interpenetration degree of the contact force chains gradually increased. Meanwhile, the number of contact force chains and the maximum contact force are comparatively higher by using confined compression condition than the confining pressure at the same stress state. 5) Large size gangue particles play the main role in anti-deformation and transfer of axial stress; the surface contact force of large particles is significantly greater than that of the small particles. 6) Faster loading rate may increase the measured load bearing capacity of the gangue sample under the same confining condition.

DEM study to determine the relationship between particle velocity fluctuations and contact force disappearance

Particle pulsation, which includes velocity and force fluctuations, has already widely existed during the discharge from a silo or hopper. To clarify the characteristics of particle pulsation, in this work, discharge from a 3D conical silo was simulated using the platform with the discrete element method (DEM). The velocity and total force fluctuations were quantitatively analyzed during the initial duration of the discharge and the relationship between velocity fluctuation and contact force disappearance was investigated. Furthermore, the effects of hopper half angle and static friction coefficient (between particle and wall) on velocity fluctuation and contact force disappearance were discussed. The results indicate that both the velocity and total force fluctuations can be divided into three stages and there is a one-to-one corresponding relationship in the violent fluctuation stage. The crest time of velocity fluctuation is the same as the time of contact force disappearance (i.e., particle motion is freely falling body) which only occurs in the violent fluctuation stage. Compared to the larger hopper half angle, the velocity fluctuation exhibits a larger amplitude and higher frequency and the contact force disappearance frequently occurs at the smaller hopper half angle. The velocity fluctuation presents an irregular small amplitude, with no occurrences of contact force disappearance below the critical value of the static friction coefficient, while the velocity fluctuation shows a regular large amplitude, with occurrences of contact force disappearance beyond the critical value. The results are useful for understanding the dynamic behavior of a rice particle during discharge from the conical silo.

Particle extrusion in elastohydrodynamic line contacts: Dynamic forces and energy consumption

The author’s model of particle entrapment and thermoviscoplastic indentation built and experimentally validated in recent publications is utilised to calculate the contact forces on ductile, isolated interference particles passing through elastohydrodynamic, rolling–sliding, line contacts. The model is detailed and enriched by supplementary equations. A parametric study deals with the effects of particle size and cold hardness, kinetic friction coefficient, rolling velocity and slide-to-roll ratio of the contact on the particle contact forces, mean friction coefficient, temperature, plastic work and power required to deform a particle, as well as on dent volume and plastic strain rates of the indented contact surfaces. A factual selection of optimal conditions and parameter values that minimise the disruption of a contaminated contact is thus greatly facilitated.

Cyclical pulsation properties of particles in cone silo

Intense particle pulsation during discharging may lead to the vibration of silo, even the failure of silo structure. To date, the studies related to particle pulsation have mainly concentrated in the following aspects: the noise caused by vibration of silo, the minimum decisive height to produce silo music and the factors affecting particle pulsation. However, the above studies cannot in depth analyze the motion state nor the flow law of all particles in silo. To explore the pulsation characteristics of particles, in this paper we simulate the discharging tests of ellipsoidal particles in deep silo with different half-cone angles based on the discrete element method, in order to reveal the mechanisms of particle pulsation and variation of contact force among the particles in the silo. In each simulation discharging test, the cylinder section of silo is divided into 4 fixed areas where flow behavior and the motion characteristics of particles are analyzed. The simulation results show that the velocity fluctuation of particles exists in the whole discharging process. At the early stage of discharging, the cyclical pulsation with large amplitude appears while irregular fluctuation with small amplitude occurs in the later stages. The study also finds that the dynamic characteristics of the axial force among particles are the same as those of velocity pulsation in the corresponding areas. Besides, the amplitude of particle pulsation shows an increase trend and the contact force of particles presents more periodic pulsation along the negative direction of outlet. The pulsation characteristics(velocity pulsation and force pulsation) of adjacent particle layers are similar, including similar waveform and identical cycle. During the intense pulsation stage, each minimum of the axial force of particles in the top layer is close to the gravity, indicating that the contact force among these particles disappears. Furthermore, the periodic pulsation of particles causes the contact force among particles to periodically disappear. It is noted that the stability of discharging, frequency, amplitude and duration of the intense pulsation increase with the decrease of the half-cone angle. In order to evaluate the fluctuation degree of the velocity pulsation, the standard deviation of particle velocities is used. Note that the particle velocities are no longer subjected to the influence of rising trend, which result is obtained by the finite difference method. The results show that the standard deviation gradually increases with the decrease of half-cone angle. This is because the increase of half-cone angle causes the time and amplitude of stable fluctuation to decrease. This numerical study of particle pulsation will provide the reference for safety design of discharging devices.

Evaluation of Soil State Variation using Bender Elements Within Centrifuge Models

Abstract In centrifuge modelling, in-flight soil conditions can vary horizontally depending on the location, i.e., from the center of model to a point close to the rigid wall. Moreover, loading history and earthquake shaking events affecting the particle contact force can influence the in-flight soil conditions. For reliable centrifuge modelling, therefore, it is important to evaluate the in-flight soil properties in a soil model at specific locations before target experiments are performed. A series of centrifuge model tests were undertaken on a uniform dry sand to investigate the in-flight soil parameters by measuring shear wave velocity (Vs) via bender elements (BE), as the Vs of the soil is directly related with soil properties. Three plausible conditions likely to influence the soil parameters were discussed in this paper: (i) boundary condition (location from the container boundary), (ii) load history (sequence of spinning up and down in the centrifuge), and (iii) earthquake shaking events. The Vs measured in the centrifuge was verified through comparison with resonant column (RC) test results. The results showed that the Vs is different in horizontal plane with locations within the model as well as with different loading events. The results also confirmed that the evaluation of in-flight soil properties before performing the test is important for interpreting the soil behavior accurately.

Many-body interactions in soft jammed materials.

In jammed packings of soft frictionless particles such as foams or emulsions, stress is transmitted via a network of mechanical contacts between neighbors. In generic simplified models of such materials, particle interaction energies are assumed to be pairwise additive. We report ab initio simulations of foam microstructures, showing that in general, this fundamental assumption is not justified: the conservation of bubble volumes introduces a many-body coupling between all the contacts of a given particle. It strongly modifies the relation between forces and displacements at individual contacts, in a way that cannot be captured by an effective two-body interaction. We report the impact of this effect on the linear and nonlinear elastic response of ordered bubble packings with coordination numbers ranging from 6 to 12, used as simple model systems, and we present an analytical model without free parameters which is valid as long as bubbles have an approximately spherical shape. It predicts the many-body coupling of particle contact forces, as well as the macroscopic mechanical response. For packing fractions approaching the jamming transition where contact forces go to zero, we derive an asymptotic two-body interaction law. It contains a logarithmic term, yielding a critical scaling that cannot be approximated by a power law.

Lateral solid mixing in gas-fluidized beds: CFD and DEM studies

We investigated lateral solid mixing in gas-fluidized beds using CFD and DEM. We ran 3D CFD simulations, comparing the results with those formerly obtained in 2D CFD simulations. We observed that the frictional stress model affects the numerical results. This was also observed in 2D simulations, but in 3D simulations the effect is less pronounced. The 3D simulations described the lateral solid mixing process more accurately than the 2D simulations, simulation dimensionality being an important factor. To analyse further the role of frictional stress models, we ran 3D DEM simulations, employing the soft-sphere approach to model the particle–particle contact forces. The simulation results agreed reasonably well with the empirical data, but their accuracy depended on the values used for the collision parameters; also, the 3D CFD simulations matched the empirical data more closely. Altogether, we concluded that the simulation dimensionality plays the dominant role in predicting lateral solid mixing accurately.

Formation mechanism of shock-induced particle jetting.

The shock dissemination of granular rings or shells is characterized by the formation of coherent particle jets that have different dimensions from those associated with the constituent grains. In order to identify the mechanisms governing the formation of particle jets, we carry out the simulations of the shock dispersal of quasi-two-dimensional particle rings based on the discrete-element method. The evolution of the particle velocities and contact forces on the time scales ranging from microseconds to milliseconds reveals a two-stage development of particle jets before they are expelled from the outer surface. Much effort is made to understand the particle agglomeration around the inner surface that initiates the jet formation. The shock interaction with the innermost particle layers generates a heterogeneous network of force chains with clusters of strong contacts regularly spaced around the inner surface. Momentum alongside the stresses is primarily transmitted along the strong force chains. Therefore, the clustering of strong force chains renders the agglomeration of fast-moving particles connected by strong force chains. The fast-moving particle clusters subsequently evolve into the incipient particle jets. The following competition among the incipient jets that undergo unbalanced growth leads to substantial elimination of the minor jets and the significant multiplication of the major jets, the number of jets thus varying with time. Moreover, the number of jets is found to increase with the strength of the shock loading due to an increased number of jets surviving the retarding effect of major jets.

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.

Design and performance analysis of a rotary traveling wave ultrasonic motor with double vibrators

This paper presents the development of a rotary traveling wave ultrasonic motor, in which a vibrating stator and vibrating rotor are combined in one motor. The stator and rotor are designed as similar structures an elastic body and a piezoelectric ceramic ring. In exciting of the piezoelectric ceramics, the elastic body of the stator and rotor will generate respective traveling waves, which force each other forward in the contact zone. Based on the elliptical rule of particle motion and matching principle of vibration, the design rules of two vibrators are determined. The finite element method is used to design the sizes of vibrators to ensure that they operate in resonance, and the simulation is verified by measuring the vibration with an impedance analyzer. It is found out that to maintain an appropriate contact between the stator and rotor, two vibrators need to be designed with close resonance frequencies, different vibration amplitudes, and be driven by an identical driving frequency. To analyze this innovative contact mechanism, particle velocity synthesis theory and contact force analysis using Hertz contact model are carried out. Finally, a prototype is fabricated and tested to verify the theoretical results. The test results show that the output performance of the motor driven by the two vibrators is significantly improved compared to the motor driven by a sole stator or rotor, which confirms the validity of the double-vibrator motor concept.

Design and analyses of open-ended pipe piles in cohesionless soils

Large open-ended pipe pile has been found to be advantageous for use in transportation projects. The current design method, however, is not adequately developed. To close this practice gap, this paper first summarized different design methods for open-ended pipe piles in sandy soils. A major factor for all the design codes is to properly account for the formation and effects of soil plug. The comparison indicates that there is a large variation in the base capacity evaluation among different methods due to the complex behaviors of soil plug. To close the knowledge gap, discrete element method (DEM) was used to simulate the soil plugging process and provide insight on the plugging mechanism. The simulation results show that the arching effect significantly increases the internal unit shear resistance along pipe piles. The porosity distribution and particle contact force distribution from DEM model indicate a large stress concentration occurs at the bottom of the soil plug. Besides, nearly 90% of the plug resistance is provided by the bottom half portion of the soil column. The soil-pile friction coefficient has a significant effect on the magnitude of plug resistance, with the major transition occurred for friction coefficient between 0.3 and 0.4.

$$K_{0}$$ K 0 of granular soils: a particulate approach

The coefficient of earth pressure at rest \(K_{0}\) of granular soils is revisited by discrete element method simulation. The effects of confining pressure, soil density and over-consolidation ratio (OCR) on the \(K_{0}\) value are investigated. The coefficients of earth pressure at rest defined in the conventional form \(K_{0}\) and in the incremental form \(K_{0}'\) are compared. Most importantly, the microstructure of the soils (i.e. coordination number, anisotropies of contact normal and contact force) is monitored during the tests and it is used to explore the microscopic factors affecting the \(K_{0}\) value of soils. The results suggest that \(K_{0}\) and \(K_{0}'\) generally approach a similar constant when the applied vertical stress is 6-10 times and 4 times of the initial isotropic stress, respectively. Meanwhile, the \(K_{0}\) value decreases as the void ratio decreases and the vertical stress increases. The OCR has a significant effect on the \(K_{0}\) value and for the same OCR the \(K_{0}\) value is quite different during unloading and reloading. Better predictions are obtained by Jaky’s equation and Mayne and Kulhway’s equation if peak friction angle is used. The analyses indicate that the \(K_{0}\) value depends on the coordination number of the soil, which is consistent with its density-dependent macroscopic behavior. The results also indicate that the \(K_{0}\) value is closely related to the anisotropy coefficients of contact normal \(\alpha _{r}\), normal contact force \(\alpha _{n}\) and tangential contact force \(\alpha _{t}\). During the initial \(K_{0}\)-loading, \(\alpha _{r}\), \(\alpha _{n}\) and \(\alpha _{t}\) keep nearly constant and the evolution of \(K_{0}\) during unloading and reloading is mainly resulted from the evolutions of \(\alpha _{n}\) and \(\alpha _{t}\). It reveals that the particle rearrangement is negligible and the soil mainly adjusts the particle contact force to resist the external load during the \(K_{0}\) loading and unloading.

Discrete element method of improved performance of railway ballast bed using elastic sleeper

With the development of high-speed and heavy-haul railway in China, problems like insufficient thickness of ballast bed and overlarge track stiffness are obvious. Ballast may break into small particles and their contact status will deteriorate under cyclic loading, resulting in ballast degradation. Discrete element method (DEM) was used to research improved performance of ballast bed using elastic sleeper. Clusters were generated by bonding spheres to model real ballasts, while broken bonds were utilized to distinguish breakage. Two kinds of ballast beds with elastic sleeper and conventional sleeper were established, respectively. After applying cyclic loading to the models, differences of mechanical properties between two models were analyzed by contrasting their dynamic behavior indexes, such as particle contact force, sleeper settlement, vibration velocity and acceleration, breakage characteristic. The results illustrate that compared with conventional sleeper, elastic sleeper increases sleeper settlement, while reduces ballast vibration and contact force between particles, which could depress ballast breakage.

Numerical Analysis on the Splitting Test of Open-Graded Large Stone Asphalt Mixture Based on Discrete Element Method

AbstractThe deficiencies of analyzing and calculating asphalt mixture as a perfectly elastic body in the existing structural design theory of asphalt pavement were amended by numerically simulating the splitting (indirect tensile) test of AC - 16, AC - 20, and OLSM - 25 (open-graded large stone asphalt mixture) from the microscopic view based on the discrete element method and 2D particle flow code. The aggregate particle contact forces, displacement vectors, numbers of micro-cracks as well as the distribution laws of the cylindrical specimens of AC - 16, AC - 20, and OLSM - 25 were also analyzed and compared by numerically simulating the splitting test. Results indicated that under the influence of peak axial force, the distribution form of the contact force between the aggregate particles in the specimens changed from being basically uniform into being relatively discrete. When the cylindrical specimen of asphalt mixture cracked, the displacement vector greatly varied from one another with the increase ...

Localisation in granular media: Particle approach, homogenisation and continuum modelling

AbstractThe individual motion of grains in granular material has a strong influence on the macroscopic material behaviour, which is in particular the case for the phenomena of strain localisation in shear zones and justifies the need for techniques that incorporate a micro‐macro transition. In this contribution, granular media are investigated in three steps. Firstly, a microscopic particle‐based modelling is set up, where individual grains are considered as rigid uncrushable particles while their motion is obtained through Newton's equations of state. The inter‐particle contact forces are thereby determined via constitutive contact‐force formulations, which have to account for the envisaged material behaviour. The second step is the homogenisation of the obtained particle's displacements and contact forces through a particle‐centre‐based strategy towards continuum quantities. Therefore, Representative Elementary Volumes (REV) are introduced on the mesoscale and the specific construction of the REV boundary leads to the understanding of granular media as a micropolar continuum. Finally, in order to verify the homogenisation strategy, a continuum based micropolar model is applied to model localisation phenomena and a comparative study of the results is carried out in a qualitative way. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Three-dimensional modeling of olive cake combustion in CFB

A comprehensive three-dimensional numerical model which includes gas–solid flow, chemical reaction, heat transfer and mass transfer has been established, to simulate the combustion of olive cake in circulating fluidized bed (CFB) reactor. The gas flow is solved by large eddy simulation (LES) approach. The particle phase is modeled by discrete particle method, in which the drag force, gravity, particle contact force and static-dynamic friction force are taken into account. The reactive model includes pyrolysis, combustion of char and volatile matters, SO2 emission, NO and N2O emissions, which has been coupled with gas–solid flow. Simulations were carried out in a CFB riser (diameter of 0.125 m and height of 1.8 m). Flow patterns, axial and radial distributions of voidage, gas and particle velocities, profiles of temperature and gas compositions under different operating conditions were obtained. The gas pollutant emissions in a riser were highly focused on. The results showed that gas and solid temperatures increase along the riser which reveals that waste combustion mainly takes place in the upper regions of the riser. The NO and N2O concentrations reach the peak values above the fuel inlet level owing to the equilibrium between the formation and reduction reactions. The SO2 concentration peaks close to the fuel inlet. An increase in excess air ratio causes the increase of NO and N2O emissions. However, no obvious variation tendency is observed for the SO2 emission.