Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory

Using the results of recent numerical simulations, we extend an existing kinetic theory for dense flows of identical, nearly elastic, frictionless spheres to identical, very dissipative, frictional spheres. The existing theory incorporates an additional length scale in the expression for the collisional rate of dissipation; this length scale is identified with the size of a cluster of correlated particles. Parameters of the theory for very dissipative, frictional spheres are set using the results of physical experiments on inclined flows of spheres over a rigid, bumpy base in the absence of sidewalls. The resulting theory is then tested against the results of physical experiments on flows of the same material over the surface of an erodible heap when frictional sidewalls are present.     

NUMERICAL SIMULATION OF GRANULAR COUETTE FLOWS BETWEEN TWO ROUGH PARALLEL PLATES

This paper presents a numerical method for calculating the granular Couette flows between two parallel plates. A kinetic model which includes the frictional energy loss effects is employed, and the equations of motion are solved using a numerical iterative method. The boundary conditions are satisfied by ensuring the balance of momentum and energy at such boundaries. The mean velocity, the fluctuation kinetic energy and the solid volume fraction profiles are evaluated under a variety of conditions. The mean velocity profiles are compared with the molecular dynamic simulation results, and good agreement is observed. The study shows that the slip velocity may vary considerably depending on the surface roughness, coefficient of restitution and friction coefficient.     

Kinetic theory applied to inclined flows

We apply the continuum equations of a kinetic theory to predict the features of uniform, steady, inclined flows of identical, frictional, inelastic spheres over a rigid, bumpy base between vertical, frictional side walls. Numerical solutions of these equations over a range of mass flow rates exhibit features seen in physical experiments and numerical solutions in the absence of side walls. For the densest flows, we employ a phenomenological extension of kinetic theory that involves a length scale associated with particle correlations. When a dense flow is thick enough, an algebraic balance between the production and dissipation of fluctuation energy reproduces the relation between mass flow rate and mass hold-up obtained when solving the boundary-value problem of the extended theory.     

Jamming in granular shear flows of frictional,polydisperse cylindrical particles

In this work, frictional, cylindrical particle shear flows with different size distributions (monodisperse, binary, Gaussian, uniform) are simulated using the Discrete Element Method (DEM). The influences of particle size distribution and interparticle friction coefficient on the solid phase stresses, bulk friction coefficient, and jamming transition are investigated. In frictional dense flows, shear stresses rise rapidly with the increasing solid volume fraction when jamming occurs. The results suggest that at the jamming volume fraction, stress fluctuation and granular temperature achieve the maximum values, and the rate of the stress increase with increasing solid volume fraction approaches the peak value. Meanwhile, the degree of cylindrical particle alignment approaches a valley value. In the polydisperse flows, the jamming volume fraction exhibits significant dependences on the fraction of the longer particles and the particle size distribution. Two models considering the effect of particle size distribution are discussed for predicting the jamming volume fractions of polydisperse flows with frictional, cylindrical particles.     

Dense inclined flows of inelastic spheres

We outline an extension of the hydrodynamic equations for dense flows of identical, inelastic spheres that incorporates an additional length scale in the expression for the collisional rate of dissipation. This length scale is identified with the length of a particle chain. In steady, fully developed inclined flows, the resulting theory predicts that at a given angle of inclination a range of flow depths is possible, that such flows possess a region of uniform volume fraction, and that this volume fraction decreases as the angle of inclination increases. The balance of particle fluctuation energy, integrated through the depth of a flow, results in a relation between the mean flow velocity, the depth, and the angle of inclination that collapses experimental data taken over a range of inclination angle.     

Extended kinetic theory applied to dense,granular, simple shear flows

We apply the extended kinetic theory (EKT) to the dense, simple shear flow of inelastic hard spheres. EKT is a phenomenological extension of kinetic theory which aims at incorporating in the simplest possible way the role of pre-collisional velocity correlations which are likely to occur at a concentration larger than the freezing point. The main effect of that correlation is the decrease in the rate at which fluctuating energy is dissipated in inelastic collisions. We use previously published results of numerical simulations performed using an event-driven algorithm to obtain analytical expressions for the radial distribution function at contact (which diverges at a concentration lower than the value at random close packing for sheared inelastic spheres) and the correlation length (i.e., the decreasing factor of the dissipation rate) at different values of the coefficient of restitution. With those, we show that when the diffusion of fluctuating energy of the particles is negligible, EKT implies that three branches of the analytical relation between the ratio of the shear stress to the pressure and the concentration (granular rheology) exist. Hence, for a certain value of the stress ratio, up to three corresponding values of the concentration are possible, with direct implications on the existence of multiple solutions to steady granular flows.     

Closure relations for shallow granular flows from particle simulations

The discrete particle method (DPM) is used to model granular flows down an inclined chute with varying basal roughness, thickness and inclination. We observe three major regimes: arresting flows, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed: for small inclinations the flow can be highly energetic and strongly layered in depth; whereas, for large inclinations it can be non-uniform and oscillating. For steady uniform flows, depth profiles of density, velocity and stress are obtained using an improved coarse-graining method, which provides accurate statistics even at the base of the flow. A shallow-layer model for granular flows is completed with macro-scale closure relations obtained from micro-scale DPM simulations of steady flows. We obtain functional relations for effective basal friction, velocity shape factor, mean density, and the normal stress anisotropy as functions of layer thickness, flow velocity and basal roughness.     

Pipe-Wall Friction in Vertical Sand-Slurry Flows

This article describes the results of extensive laboratory tests of vertical flows of three sand fractions (0.12, 0.37, and 1.84 mm sands) in a 150 mm pipe. The tests revealed an interesting phenomenon of a surprisingly low contribution of the medium sand to the total friction of the mixture flow in the vertical pipe. The frictional pressure drop in highly concentrated flows at high velocities was lower for slurries of the medium sand than for slurries of both the fine sand and the coarse sand. The solids friction at the pipe wall is analyzed taking into account effects of particle-particle interactions and particle-liquid interactions in the boundary layer of a vertical flow of settling slurry. The analysis suggests that the observed phenomenon is associated with the hydrodynamic liquid lift force acting on solid particles traveling near a pipe wall. This off-wall force seems to be more effective for the medium sand particles than for the fine sand particles and coarse sand particles interacting with liquid in the boundary layer of the mixture flow. The excessive frictional pressure drop due to the presence of solids in vertical flows seems to be primarily produced by the combined effect of the Bagnold collisional force (the force that colliding particles exert against the pipe wall) and the liquid lift force acting on solid particles in the near-wall zone of the slurry flow.     

Effect of boundary vibration on the frictional behavior of a dense sheared granular layer

We report results of 3D discrete element method simulations aiming at investigating the role of the boundary vibration in inducing frictional weakening in sheared granular layers. We study the role of different vibration amplitudes applied at various shear stress levels, for a granular layer in the stick-slip regime and in the steady-sliding regime. Results are reported in terms of friction drops and kinetic energy release associated with frictional weakening events. We find that a larger vibration amplitude induces larger frictional weakening events. The results show evidence of a threshold below which no induced frictional weakening takes place. Friction drop size is found to be dependent on the shear stress at the time of vibration. A significant increase in the ratio between the number of slipping contacts to the number of sticking contacts in the granular layer is observed for large vibration amplitudes. These vibration-induced contact rearrangements enhance particle mobilization and induce a friction drop and kinetic energy release. This observation provides some insight into the grain-scale mechanisms of frictional weakening by boundary vibration in a dense sheared granular layer. In addition to characterizing the basic physics of vibration-induced shear weakening, we are attempting to understand how a fault fails in the earth under seismic wave forcing. This is the well-known phenomenon of dynamic earthquake triggering. We believe that the granular physics are key to this understanding.     

“Phonon” conductivity along a column of spheres in contact

We calculate energy conduction and dissipation along a column of spheres linked with linear springs and dashpots to illustrate how grains in simultaneous contact may produce a constant “phonon” conductivity of granular fluctuation kinetic energy. In the core of dense unconfined granular flows down bumpy inclines, we show that phonon conductivity dominates its counterpart calculated from gas kinetic theory. However, the volume dissipation rate of phonon fluctuation energy is of the same order as the kinetic theory prediction.     

Effect of base roughness on size segregation in dry granular flows

This paper presents simulations of dry granular flows along a sloping channel using the discrete element method. The kinetic sieving and squeeze expulsion theories are utilized to study the effects of base roughness on size segregation and the underlying mechanisms. Basal friction has a significant influence on flowing regimes inside the granular body, and a larger base friction accelerates the size segregation process. The front zone of the granular body is more likely to be collision dominated with increasing base friction; as a result, the energy dissipated by frictional shearing decreases, and damping energy due to particles collisions is enhanced. Meanwhile, granular flows become much looser, and collisions between particles increase rapidly. It is shown that the differences in the kinetics among grains of mixed sizes and the mechanical effects of particle contacts can explain the mechanism of size segregation. The parameter representing the intensity of particles exchange also increases as base friction increases. The forces acting on particles are also affected by base friction. The dimensionless contact force describing the contribution of contact channel-normal stress increases as base friction increases, which indicates that a higher dispersive trend has developed inside the granular body.     

Depth-averaged relations for granular-liquid uniform flows over mobile bed in a wide range of slope values

The behavior of liquid-granular flows, driven by gravity, is experimentally analyzed. Two types of free-surface uniform flow can take place, having different boundary conditions at the bottom. The first one runs over a fixed surface behaving as a solid (non-deformable) impermeable wall; the second one runs over a mobile-bed at rest, formed by the same loose grains and liquid of the flowing mixture. In the paper we will mark the differences between the two, but focus on the latter one. The experiments span over, and characterize, the possible flow regimes. In mobile-bed uniform flows it has been found that the Froude number reduces as the slope increases. Accordingly, there is an increment of the solid-concentration. These results are meaning that as slope increases a progressive dominance and thickening of frictional layers over collisional ones is taking place through the flow depth. Same behaviours have been observed by changing the type of grains in the flowing mixture. These findings contrast with the case of flows over a solid wall, where different trends are observed. Application of force balances by means of Coulomb law provides interesting confirmation of what observed and allows to take into account the surface-tension effects, which come into play when the particles on top are going to desaturate. Experimental data have also been employed to assess the applicability of kinetic theories to wet granular flows. Energy and momentum balances, under the hypothesis of no contribution in the liquid phase (except for the added mass concept) to shear stress and to the energy processes, are applied throughout the flow depth of the solid phase. Although depth-averaged quantities come out to have a trend similar to the experimental one, deficiencies in the theoretical approach, mainly due to its inability to represent frictional contacts, are clearly detected. Same conclusions may be drawn by applying the quite simple Bagnold theory. Altogether, a more appropriate theory able to deal with both collisional and frictional mechanisms, including the transition between, is demanded.     

Volume fraction and velocity fields of nearly uniform granular flows in a narrow channel geometry with smooth bed

The combined knowledge of the velocity and volume fraction fields is crucial for investigating the dynamics of granular flows, especially in the dense-collisional regime where both frictional and collisional dissipation mechanisms are significant. A laboratory investigation on steady dry granular flows in a straight channel is reported, where slip conditions are allowed at the basal surface and side walls. The stochastic-optical method (SOM), proposed by Sarno et al. (2016) for estimating the volume fraction in granular mixtures, is applied for the first time to granular flows. The velocity at the free surface and at the flume sidewall is measured by using a multi-pass particle image velocimetry (PIV) approach. The measurements of the velocity and volume fraction reveal a superimposition of different dynamic structures, which can be distinguished by means of a volume fraction threshold. Additionally, the profiles of measured volume fraction are exploited to estimate the pressure distribution, so as to numerically describe the velocity profiles by using the μ(I) rheology. It is found that the employment of the experimental volume fraction is superior in describing the flow dynamics, especially near the free surface.     

Granular fluids with solid friction and heating

We perform large-scale molecular dynamics simulations to study heated granular fluids in three dimensions. Granular particles dissipate their kinetic energy due to solid frictional interaction with other particles. The velocity of each particle is perturbed by a uniformly-distributed random noise, which mimics the heating. At the early stage of evolution, the kinetic energy of the system decays with time and reaches a steady state at a later stage. The velocity distribution in the steady state shows a non-Gaussian distribution. This has been characterized by using the Sonine polynomial expansion for a wide range of densities. Particles show diffusive motion for densities below the jamming density \(\phi _\mathrm{J}\).     

Flow Control Through the Use of Topography

In this work, optimal shaft shapes for flow in the annular space between a rotating shaft with axially-periodic radius and a fixed coaxial outer circular cylinder, are investigated. Axisymmetric steady flows in this geometry are determined by solving the full Navier-Stokes equations in the actual domain. A measure of the flow field, a weighted convex combination of the volume averaged square of the L₂-norm of the velocity and vorticity vectors, is employed. It has been demonstrated that boundary shape can be used to influence the characteristics of the flow field, such as its velocity component distribution, kinetic energy, or even vorticity. This ability to influence flow fields through boundary shape may be employed to improve microfluidic mixing or, possibly, to minimize shear in biological applications.     

Modeling friction effects on the ballistic impact behavior of a single-ply high-strength fabric

It has been shown through experiments that interfacial friction affects the energy absorption of fabrics subjected to ballistic impact. However, how the friction plays a role is not well understood. In this paper, a commercially available finite element analysis code, LS-DYNA, is used to model the ballistic impact of a square patch of single-ply plain-woven fabric. Three types of boundary conditions are applied on the fabric: four edges clamped, two edges clamped, and four edges free. The friction between yarns at their crossovers and the friction between projectile and fabric are taken into account. Effects of the friction during the phase prior to yarn failure are parametrically studied. Simulation results show that at a given time, the fabric with high friction absorbs more energy than the fabric with no friction. For the boundary condition with four edges free, friction contributes to increasing the fabric energy absorption mainly through the mechanism of frictional sliding dissipated energy. For the boundary conditions with two or four edges clamped, the energy dissipated through frictional sliding only accounts for a very small portion of the total absorbed energy; however, both the yarn strain energy and the yarn kinetic energy are increased when there is friction. Friction has an indirect effect on the fabric energy absorption by influencing the number of yarns that become involved. Simulation results also indicate that the boundary conditions significantly affect the fabric deformation, stress distribution, and time history of energy absorption.     

Numerical simulation of hydrodynamic characteristics in a gas–solid fluidized bed

The fluidization of quartz particles as bed materials in the fluidized bed has significant influences on the combustion and gasification of refused derived fuels. Three-dimensional (3-D) simulations and analyses are performed for Geldart B particles using the computational fluid dynamics (CFD) method based on the kinetic theory of granular flows (KTGF) to investigate the hydrodynamic behavior. The drag models of Syamlal–O’Brien, Gidaspow, and Wen and Yu are selected to analyze the applicability of the kinetic model. The pressure drop, velocity distribution and solid volume fraction are studied numerically when the gas inlet velocity is changed. The results show that the increase of superficial gas velocity would lead to heterogeneous expansion of solid volume fraction and velocity distributions in both the dense phase zone and free board with a similar distribution pattern. The near wall particles form a dense phase structure with the solid volume fraction being greater than 0.3.     

Investigating the effects of grain boundary energy anisotropy and second-phase particles on grain growth using a phase-field model

A phase-field model was used to investigate the simultaneous effects of grain boundary energy anisotropy and the presence of second-phase particles on grain growth in polycrystalline materials. The system of grains with anisotropic grain boundary energies was constructed by considering models of low and high misorientation angles between adjacent grains. Systems without particles reached a steady state grain growth rate, and this rate decreased by including the grain boundary energy anisotropy. In addition, the presence of particles significantly altered the microstructures during grain growth. This study showed that for systems including particles, the critical average grain size to stop grain growth depends not only on the volume fraction and size of particles, but also on the grain boundary energy anisotropy.     

Effects of Reduced Gravity Conditions on Bubble Dispersion Characteristics in the Bubble Column

Bubble-liquid turbulent flow has an excellent heat and mass transfer behaviors than single gas or liquid flow. In order to analyze the effects of normal and reduced gravity on cold bubble-liquid two-phase turbulent flow in bubble column a second-order moment cold bubble-liquid two-phase turbulent model was developed to disclose the bubble dispersion characteristics. Under the reduced gravity condition, volume fraction caused by the decrease of buoyance force is larger than normal gravity level due to bigger bubble solid volume. In addition, bubble frequency is also decreased by in decrease of buoyance force. Normal and shear stresses have strongly anisotropic characteristics at every directions and have larger values under normal gravity than reduced gravity. The liquid turbulent kinetic energy has the two-peak bimodal distribution and weaker than bubble turbulent kinetic energy with one peak unimodal, which is caused by vigorous wake fluctuations. The correlation of fluctuation velocities between bubble and liquid has clearly anisotropic behaviors Under reduced gravity, the bubble motion has a little impact on liquid turbulent flow caused by slight buoyancy force, however, it will greatly reduce the liquid turbulent intensity due to energy cascade transport, which was transformed into bubbles or dissipated by interface friction. Bubble formation and detachment mechanisms affected by gravity conditions lead to the different levels of bubble dispersion distributions.