Stability of operation of an apparatus containing a granular bed fluidized by a gas stream

The results of numerical experiments on the investigation of the stability of the fluidization process relative to finite perturbations and its behavior upon crossing the boundary of stability are presented.Notation H bed height - H₀, H_* bed heights in motionless and steady fluidized states - g free-fall acceleration - k₁, k₂ coefficients of resistance of gas-supply system and gas-distributing device, respectively - M molecular weight of gas - m mass of bed per unit cross-sectional area - p^*, p⁰ pressure at inlet and outlet of apparatus - Q₀, Q_b minimum fluidization velocity and average velocity of gas in the bubble phase - q, q_v total mass-flow rates of gas supplied to the bed and to the free cavity - R gas constant - S cross-sectional area of bed - V volume of cavity below gas-distributing grid accessible to the gas - gas density - T absolute temperature - c,, q₀ parameters introduced into (4) - t time - z dimensionless bed height - x dimensionless time - A, B, C, D, N, n dimensionless complexes introduced into (5) - v dimensionless volume - parameter introduced into (5) - z_* dimensionless bed height in steady fluidized state - circular frequency Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 889–892, November, 1977.     

Stability of plates from a granular composite with physically nonlinear inclusions and a damageable matrix

We present formulation and solution of the problem on the bifurcational stability of rectangular plates from granular composites with a damageable matrix and physically nonlinear inclusions. Translated from Problemy Prochnosti, No. 2, pp. 91–101, March–April, 2009.     

Density-driven sinking dynamics of a granular ring in sheared granular flows

This study reports experimental findings on the sinking dynamics of a heavy granular ring caused by the density-driven segregation effect in sheared granular flows. Specifically, this study systematically investigates the influences of the density ratio, shear rate, and solid fraction of the granular material on the sinking behavior of a heavy granular ring. The parameters of the dimensionless sinking depth and sinking rate, respectively, describe the change in the granular ring position and quantify the particle sinking speed. Experimental results show that both the dimensionless sinking depth and the sinking rate increase as the bottom wall velocity (shear rate) and solid fraction increase. The dimensionless sinking depth and the sinking rate also exhibit a linear relation. The dimensionless sinking depth does not increase monotonically as the density ratio increases. The sinking rate increases linearly with the final steady-state sinking depth for the same heavy granular ring structure, regardless of the wall velocity (shear rate), solid fraction, and density ratio.     

History-dependent deformation of a rotated granular pile governed by granular friction

We experimentally examined the history dependence of the rotation-induced granular deformation. As an initial state, we prepared a quasi-two-dimensional granular pile whose apex is at the rotational axis and its initial inclination is at the angle of repose. The rotation rate was increased from 0 to 620 (rpm) and then decreased back to 0. During the rotation, deformation of the rotated granular pile was captured by a camera. From the acquired image data, granular friction coefficient $\mu$ was measured as a function of the ratio between centrifugal force and gravity, $\mathrm{\Gamma }$. To systematically evaluate the variation of $\mu$ both in the increasing (spinning up) and decreasing (spinning down) rotation-rate regimes, surface profiles of the deformed granular piles were fitted to a model considering the force balance among gravity, friction, and centrifugal force at the surface. We found that $\mu$ value grows in the increasing $\mathrm{\Gamma }$ regime. However, when $\mathrm{\Gamma }$ was reduced, $\mu$ cannot recover its initial value. A part of the history-dependent behaviors of the rotated granular pile can be understood by the force balance model.     

Mixtures of granular materials

Balance laws are given for a mixture of granular materials of a type described by Goodman and Cowin. Constitutive equations are given for the case of two dry granular constituents, and consequences of the entropy principle are found.     

Creep of granular materials

This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.     

Compaction of granular mixtures

We propose a lattice model for studying the compaction of granular mixtures under taps. Two granular species are considered: small grains with low mobilities and T-shaped grains characterized by a larger ability to move. When those grains are mixed together, the compaction dynamics is mainly controlled by the volume fraction x of the small grains. Segregation have been found on the top layers of the pile. The grain mobilities have been studied for different values of the volume fraction x. An effective grain mobility has been defined for the mixture. This mobility is given by the linear combination of the mobility of both pure species minus a non-linear interaction term. Finally, the compaction speed depends on the fraction of the anisotropic grains.     

Stability analysis of the tunnel face in the cohesive-frictional soils considering the arch effect and rotational mechanism

ABSTRACT

This article proposes a new 3D failure mechanism to analyze the stability of the tunnel face driven by a closed shield in cohesive-frictional soils. The failure mechanism consists of a single block in the lower part defined by logarithmic-spiral and a distributed force caused by the weight of a half-ellipsoid in the upper part. The logarithmic-spiral surface represents the shear band and the distributed force is applied to simulate the arch effect. The arch effect and rotational mechanism are considered simultaneously. Comparisons among the proposed mechanism, numerical simulation and existing mechanism are conducted. The results show that the proposed mechanism provides improved limit support pressure values, and the failure patterns of the proposed mechanism agree well with those of the numerical simulation and experimental tests. This verifies that the proposed mechanism is effective and reasonable.     

Impact response of granular layers

Motivated by the wave tailoring potential of granular media, this study aims at evaluating force transmission through granular layers made of spherical particles. 2D simulations based on Hertzian contact law between adjacent particles are performed on two distinct systems: (1) layers consisting of ordered bimaterial lattices, and (2) single material layers with random packing. For the ordered systems, force transmission properties are found to vary with material mismatch and layer thickness. Transmitted force-decay in random configurations is substantially higher than those in the ordered systems.

     

Hydrodynamics of a granular medium

The hydrodynamic characteristics of loose granular media are studied experimentally, with due allowance for particular aspects of the pore space structure (the sinuous nature of the paths of penetration and the efficiency with which the intergranular spaces take part in filtration); the results show that Re 80, up to Reynolds numbers of Re_cr 5.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 3, pp. 452–459, September, 1971.     

Experimental study of granular stratification

The flow of binary granular mixtures made of sand (rough) and glass spheres (smooth) into a vertical Hele Shaw cell give rises to heaps exhibiting different internal structures. We first give the phase diagram of heap morphologies classified as a function of the size ratio of rough to smooth particles. Granular stratification is one type of observable structure, which consists in the formation of alternating layers through the pile, and is found to occur only for a size ratio greater than 1.5. We present an experimental study of stratification and report that the wall separation and the mass flux can modify the layering process.     

Shakedown of unbound granular material

Compacted unbounded granular materials are extensively used as sub-layer in pavement design. Most pavement design guides assume that they are responsible for the degradation and deformation of the roads and railways that they support. Biaxial tests are usually employed to investigate the elasto-plastic response of these materials to cyclic loading. A particularly interesting question is whether a limit load exists, below which the excitations shake down, in the sense that the material does not accumulate further deformations. We have carried out a detailed study of the elasto-plastic behavior of a simple model of unbound granular matter submitted to cyclic loading. The dissipated energy throughout the simulation has been used for the characterization of the different regimes of responses.     

Asymptotic behaviour of granular materials

The concept of the asymptotic behaviour of particulate materials is described, including its enhancement by considering asymptotic states in extension. A 3D discrete element model with elastic spherical particles and the granulometry of a real sand is set up. The numerical sample is stretched from different initial states, and the influence of the strain rate direction on the final state is studied within the stress ratio, void ratio and mean stress space. Asymptotic behaviour is clearly observed, although the grains remain intact (no grain crushing is considered). The extension asymptotic states were observed, and the notion of a normal extension line is introduced. The extension asymptotic states coincide with the peak states observed in the shear tests with constant stress path direction in dense samples.     

Microstructural mechanics of granular media

A geometrically and physically linear micromechanical theory for elastic granular media is presented, based on the identification of the constituent grains with the nodes of a Bravais lattice. Adjacent particles are permitted to displace normally and transversely to each other, and to rotate with respect to the doublet axes. Thus, microstrains of the axial, torsional, and shear type are generated. The conjugate microstresses are then defined. Through a variational formulation, the microstress equations of motion are derived, together with natural boundary conditions and the transition from the microstresses to the macrostresses. The principles of thermodynamics are employed to derive the most general, invariant, and appropriately symmetric microconstitutive equations, and to close the system of field equations for the granular medium, subject to both adiabatic and non-adiabatic processes. The problem of a granular semispace loaded by compressive boundary force is solved as an application, and the existence of locally tensile microstresses is determined, while the associated macrostresses are computed to coincide with the well-known Flamant's solution and thus to be compressive everywhere.     

Using PIV to measure granular temperature in saturated unsteady polydisperse granular flows

The motion of debris flows, gravity-driven fast moving mixtures of rock, soil and water can be interpreted using the theories developed to describe the shearing motion of highly concentrated granular fluid flows. Frictional, collisional and viscous stress transfer between particles and fluid characterizes the mechanics of debris flows. To quantify the influence of collisional stress transfer, kinetic models have been proposed. Collisions among particles result in random fluctuations in their velocity that can be represented by their granular temperature, T. In this paper particle image velocimetry, PIV, is used to measure the instantaneous velocity field found internally to a physical model of an unsteady debris flow created by using “transparent soil”—i.e. a mixture of graded glass particles and a refractively matched fluid. The ensemble possesses bulk properties similar to that of real soil-pore fluid mixtures, but has the advantage of giving optical access to the interior of the flow by use of plane laser induced fluorescence, PLIF. The relationship between PIV patch size and particle size distribution for the front and tail of the flows is examined in order to assess their influences on the measured granular temperature of the system. We find that while PIV can be used to ascertain values of granular temperature in dense granular flows, due to increasing spatial correlation with widening gradation, a technique proposed to infer the true granular temperature may be limited to flows of relatively uniform particle size or large bulk.     

Gravitational flow of granular materials

The free flow of granular materials through an orifice in a horizontal bottom has been investigated. An equation is proposed for calculating the mass flow rate.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 15, No. 5, pp. 870–874, November, 1968.     

Isostaticity in granular matter

Recent work (PRL V81, 1998, p. 1634) has proven that cohesionless granular packings are isostatic in the limit of low applied pressure, and suggested that this property is responsible for the peculiar static behavior of granular materials. On disordered isostatic systems, stress–stress response functions are power-law distributed, with a cutoff that grows exponentially with distance. If the external pressure is increased sufficiently, excess contacts are created, the packing becomes hyperstatic, and the medium behaves as a normal elastic continuum. I discuss here these ideas briefly, and also report on numerical results (mainly stress distributions) from a simple two-dimensional model of packings which captures the essential physics of stress transmission in granulates under varying load conditions. Received 30 March 2000     

Stresses in granular materials

When circularly polarised light is passed through a granular material under boundary stresses patterns—‘light stripes’—are seen in the resulting images which have been traditionally associated with the directions of major principal stresses in the equivalent continuum. In this paper the passage of polarised light through a single spherical particle under stress is studied experimentally and analytically. The effect of placing the particle within a layer of particles, a layer of thickness 2–3 particles, and within a mass of particles is investigated experimentally. The appearance of light stripes is a visual reinforcement of effects seen at the particle level provided the level of stresses in individual particles is low. The implications for quantitative photoelastic interpretation of granular media are discussed.