Rapid Flows Of Granular Materials Research Articles

Numerical Investigation of the Propagation of Shock Waves and Dead Zones in Rapid Flows of Granular Materials using SPH Method

Numerical Investigation of the Propagation of Shock Waves and Dead Zones in Rapid Flows of Granular Materials using SPH Method

A continuum–kinetic theory approach to the rapid flow of granular materials: the effects of volume fraction gradient

We study the fully developed flow of granular materials down an inclined plane. The model uses ideas from both continuum and kinetic theories, where the form of the constitutive relation for the stress tensor is derived using standard techniques in continuum mechanics (cf. Rajagopal and Massoudi, DOE Report, DOE/PETC/TR-90/3, 1990); the material properties are derived using the kinetic theory approximation proposed by Boyle and Massoudi (Int. J. Eng. Sci. 28 (1990) 1261–1275), which includes the effects of the gradient of the volume fraction. The equations are non-dimensionalized and the system of non-linear ordinary differential equations is solved numerically.

Couette flows of a granular monolayer—an experimental study

An experimental study concerning rapid flows of granular materials in a two-dimensional planar granular Couette flow apparatus is performed. The device is capable of generating particulate flows in the grain-inertia regime at different shearing rates and solid volume fractions. Multi-color spherical glass particles are sheared across an annular test-section for several wall angular velocities. A video recorder is used to record the motion of particles and consecutive images are stored and analyzed by an image processing technique for evaluating individual grain velocities. Experimental data for the mean velocity, the root-mean-square (RMS) fluctuation velocity components and the solid volume fraction profiles are obtained. The resulting mean velocity profiles have a roughly linear variation for the range of solid volume fractions and shear rates studied. The solid volume fraction profiles exhibit non-uniform variations with the highest concentration occurring near the center of the shearing cell. The RMS fluctuation velocities are roughly constant, with the streamwise fluctuation being somewhat larger than the cross-stream direction. The experimentally measured flow properties are in reasonable agreement with the earlier theoretical and simulation results.

Rapid flow of granular materials with density and fluctuation energy gradients

A constitutive relationship for the stress tensor of granular materials during the rapid flow regime that includes the effects of density gradient and fluctuating velocity is proposed. Explicit expressions for various stress components are obtained and simple examples are presented. It is shown that this continuum-based model is capable of predicting normal stress differences. The model also contains many earlier models as its special cases. The results also show that the model may be suitable for analyzing rapid, as well as slow, motions of granular materials.

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.

A turbulence model for rapid flows of granular materials part I. basic theory

A one-equation closure model for rapid flows of granular material is developed. A complete system of equations governing the transport of mass, momentum and fluctuation energy is derived. The functional dependences of the material parameters on the solid volume fraction are obtained and several simple examples are presented. A stress transport model for rapid flows of granular materials is also outlined.

A turbulence model for rapid flows of granular materials part II. Simple shear flows

Using the one-equation turbulence model of Part I, rapid flows of granular materials are studied. The equations governing the transport of mass, linear momentum and fluctuation energy are considered. For simple shear flows, the dependences of the stress—shear rate relationship on the coefficient of restitution and solid volume fraction are studied. Couette and gravity flows of granular materials in rapid flow regimes are analyzed. Velocity, solid volume fraction and fluctuation energy profiles are calculated. The results are compared with those of the other theoretical models and the existing experimental data. It is shown that the predictions of the turbulence model agree reasonably well with the experimental data.

A kinetic model for rapid flows of granular materials

A kinetic model for rapid flows of granular material is considered. An evolution equation for the first order distribution function is developed which includes the effects of intergranular friction force in an average sense. The collision operator is approximated by the BGK relaxation model. The fundamental equations of motion including an equation for dynamics of the fluctuation energy are derived and discussed. The gravity and the plane Couette flows of granular materials are treated as examples of the applications of the present theory.

Towards a turbulent modeling of rapid flow of granular materials

From the global equations of balance for particulate media and via a special ensemble averaging technique, the local equations governing the mean motion and the random fluctuations in a rapid flow of granular materials are derived. The resulting equations resemble those of a compressible turbulent flow. Approximate expressions for the components of the fluctuation stress tensor are obtained which are completely computable and in this sense are rather new. The order of magnitude analysis of these stresses indicate that they are in complete agreement with available experimental results. Furthermore, an explicit equation is derived for the evolution and transport of random fluctuation energy which is coupled with the energy dissipation due to fluctuating stress tensor and the mean motion.

New constitutive equations for the rapid flow of granular materials

Presented is an analytical description of the rapid two dimensional shearing flow of granular materials which results in expressions for the normal as well as the shear stress in terms of various flow parameters. The rapid flow regime here is in accord with the grain-inertia-dominated flow of granular materials as described by Bagnold. Both gradients of velocity and microrotation of grains are taken into account and the final constitutive equations resemble those of a non-Newtonian microfluid for which the stresses depend on the square of the velocity gradients, the square of microrotation gradients, as well as the product of velocity gradients and microrotation gradients.