Assessment of the kinetic–frictional model for dense granular flow

This paper aims to quantitatively assess the application of kinetic–frictional model to simulate the motion of dry granular materials in dense condition, in particular, the annular shearing in Couette configuration. The weight of frictional stress was varied to study the contribution of the frictional stress in dense granular flows. The results show that the pure kinetic-theory-based computational fluid dynamics (CFD) model (without frictional stress) over-predicts the dominant solids motion of dense granular flow while adding frictional stress [Schaeffer, D. G. (1987). Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 66(1), 19–50] with the solids pressure of [Lun, C. K. K., Savage, S. B., Jeffrey, D. J., & Chepurniy, N. (1984). Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 140, 223–256] in the CFD model improves the simulation to better conform available experimental results. The results also suggest that frictional stress transmission plays an important role in dense granular flow and should not be neglected in granular flow simulations. Compatible simulation results to the experimental data are seen by increasing the weight of frictional stress to a factor of 1.25–1.5. These improved simulation results suggest the current constitutive relations (kinetic–frictional model) need to be improved in order to better reflect the real dense granular flow.     

Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.     

Assessment of the kinetic-frictional model for dense granular flow

This paper aims to quantitatively assess the application of kinetic-frictional model to simulate the motion of dry granular materials in dense condition, in particular, the annular shearing in Couette configuration. The weight of frictional stress was varied to study the contribution of the frictional stress in dense granular flows. The results show that the pure kinetic-theory-based computational fluid dynamics （CFD） model （without frictional stress） over-predicts the dominant solids motion of dense granular flow while adding frictional stress [Schaeffer, D. G. （1987）. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 66（1）, 19-50] with the solids pressure of [Lun, C. NTK., Savage, S. B., Jeffrey, D. J., ＆ Chepurniy, N. （1984）. Kinetic theories for granular flow： Inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 140, 223-256] in the CFD model improves the simulation to better conform available experimental results. The results also suggest that frictional stress transmission plays an important role in dense granular flow and should not be neglected in granular flow simulations. Compatible simulation results to the experimental data are seen by increasing the weight of frictional stress to a factor of 1.25-1.5. These improved simulation results suggest the current constitutive relations （kinetic-frictional model） need to be improved in order to better reflect the real dense granular flow.     

不同重力场下颗粒冲击过程的离散元分析

开展不同重力场下颗粒材料冲击动力学研究有助于加深对颗粒运动机制的理解和深空探测任务的实施。本文采用离散元模拟对颗粒介质受球形冲击物的冲击过程进行了数值模拟，并与地球重力下冲击的试验结果进行对比验证。在此基础上，进一步研究了重力加速度对冲击物动力学的影响规律。计算结果表明，在所有重力加速度下，冲击物的穿透深度d与冲击速度v₀的关系可以用Poncelet模型表达；d与冲击物下落的总高度H表现为d～Hⁿ的幂律关系，当H<10 m时，d与H的幂率标度为0.322,而H>10 m时，d与H的幂率标度下降到0.211。此外，穿透深度小于冲击物半径时，重力加速度对冲击物减速过程无影响。在所有的重力加速度下，当冲击速度大于5 m/s时，冲击物的持续碰撞时间t_c是恒定的，且与重力的-1/2次方呈正比。     

On flows of granular materials

This article reviews the behavior of materials made up of a large assemblage of solid particles under rapid and quasi static deformations. The focus is on flows at relatively high concentrations and for conditions when the interstitial fluid plays an insignificant role. The momentum and energy exchange processes are then primarily governed by interparticle collisions and Coulomb-type frictional contact. We first discuss some physical behavior —dilatancy, internal friction, fluidization and particle segregation — that are typical to the understanding of granular flows. Bagnold's seminal Couette flow experiments and his simple stress analysis are then used to motivate the first constitutive theories that use a microstructural variable — the fluctuation energy or granular temperature — governing the subscale fluctuating motion. The kinetic theories formalize the derivation of the field equations of bulk mass, momentum and energy, and permit derivation of constitutive relations for stress, flux of fluctuation energy and its dissipation rate for simple particle assemblages and when frictional rubbing contact can be ignored. These statistical considerations also show that formulation of boundary conditions needs special attention. The frictional-collisional constitutive behavior in which both Coulomb-type rubbing contact and collisional encounters are significant are discussed. There is as yet no rigorous formulation. We finally present a phenomenological approach that describes rapid flows of granular materials under simultaneous transport of heat and close with a summary of stability analyses of the basic flow down an inclined plane.Dedicated to Professor Dr.-Ing. Franz Gustav Kollmann on the occasion of his sixtieth brithday     

Deep Bed Filtration Modelling of Formation Damage Due to Particulate Invasion from Drilling Fluids

A Deep Bed Filtration model has been developed to quantify the effect of solids invasion from drilling fluids on the permeability of rock formations. The calculated particle-trapping profiles are compared directly with experimental profiles from scanning electron microscopy and synchrotron X-ray diffraction tomography mapping. The computed permeability reduction as a consequence of particle invasion is in broad agreement with experiment. Backflow was modelled by reversing the flow rate, starting off with a situation where all particles either remain trapped or are all released. It appears that the experimentally observed 30% release of particles upon backflow is reproducible within the limits of the two extreme cases. When erosion is included in the model, a peak in the backflow pressure time series can be observed. This peak may be correlated with the experimentally observed flow initiation pressure, which is the backflow pressure needed to initiate flow after initial inflow filtration. Finally, we conclude that internal reservoir damage, within the limits of our 1-D single phase DBF model, may contribute to the experimentally observed flow initiation pressure.     

Statistics of particle interactions in dense granular material under uniaxial compression

Stress evolution in a dense granular material is closely related to interactions of contacting particles. We investigate statistics related to particle interactions and the relationship between the averaged local relative motion and the macroscopic motion. The validity of the Voigt and Reuss assumptions is examined, and extensions to these assumptions are proposed. Effects of history in the dense granular material are investigated. Statistical samples used in this paper are obtained using three-dimensional numerical simulations of dense granular media under uniaxial cyclical compression. The results show that stresses arise mostly from normal forces between particles, and direct contributions from frictional tangential forces between particles are small. Tangential friction, however, significantly increases the particle contact time, and thus reduces the rate of contact breakage. The contact breakage rate is demonstrated to be a stress relaxation rate. Therefore, stress increases significantly with friction between particles as a result of prolonged relaxation time.     

Prediction of segregation characterization based on granular velocity and concentration in rotating drum

In a binary granular system composed of two types of particles with different granule sizes and the same density, particle sorting occurs easily during the flow process. The segregation pattern structure is mainly affected by the granular velocity and granular concentration in the flow layer. This paper reports on the experimental velocity and concentration measurement results for spherical particles in a quasi-two-dimensional rotating drum. The relationship between the granular velocity along the depth direction of the flow layer and granular concentration was established to characterize structures with different degrees of segregation. The corresponding relationships between the granular velocity and concentration and the segregation pattern were further analyzed to improve the theoretical models of segregation (convection–diffusion model and continuous flow model) and provide a reference for granular segregation control in the production process.     

Smoothed particle hydrodynamics for coarse-grained modeling of rapid granular flow

We simulated rapid flow in transient plane Couette flows of granular particles using the smoothed particle hydrodynamics(SPH) solutions of a set of continuum equations.This simulation was performed to test the viability of SPH in solving the equations for the solid phase of the two-fluid model associated with fluidization.We found that SPH requires the handling of fewer particles in simulating the collective behavior of rapid granular flow,thereby bolstering expectations of solving the equations for the solid phase in the two-fluid modeling of fluidization.Further work is needed to investigate the effect of terms describing pressure and viscous stress of solids on stability in simulations.     

Nonlinear dynamics of excited plate immersed in granular matter

The interaction between granular matter and the elastic body is a complex issue due to the complex properties of granular matter. An experiment involving a sinusoidally excited plate buried in glass bead particles contained in a box is conducted. The motion behavior of the plate is observed and recorded by the strain gauge. The amplitude–frequency and phase–frequency curves are recorded to study the natural property of the plate in granular matter. In this experiment, jump phenomena are found in both the amplitude–frequency and phase–frequency planes in circumstances with smaller particle sizes, lower buried depths, and larger amplitudes of the excitation force. Otherwise, the period-doubling bifurcation, especially 3T, is found with the increase in the excitation force. These bifurcations usually occur in specific buried depth and excitation frequency band and require smaller particle sizes. The experiments with random-shaped particles exhibit no-jump phenomenon, but period-doubling bifurcation and chaos. These phenomena are sensitive to parameters and closely related to the varying process of the excitation frequency and force. Reasonable mechanisms are summarized qualitatively through some of our recent researches in this paper.