Couette flow of granular materials
TL;DR: In this paper, the flow of granular materials between rotating cylinders is studied using a continuum model proposed by Rajagopal and Massoudi (A method for measuring material moduli for granular material: flow in an orthogonal rheometer, DOE/PETC/TR90/3, 1990).
Abstract: The flow of granular materials between rotating cylinders is studied using a continuum model proposed by Rajagopal and Massoudi (A method for measuring material moduli for granular materials: flow in an orthogonal rheometer, DOE/PETC/TR90/3, 1990). For a steady, fully developed condition, the governing equations are reduced to a system of coupled non-linear ordinary differential equations. The resulting boundary value problem is non-dimensionalized and is then solved numerically. The effect of material parameters, i.e., dimensionless numbers on the volume fraction and the velocity fields are studied.
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TL;DR: In this article, the creep motion in aeolian sand transport is studied using two typical granular flow models and the expression of creep flux is theoretically revealed that creep fraction (the contribution of creep to the overall sand flux) changes with wind velocity and grain size.
31 citations
01 Jan 2010
TL;DR: An exact analysis of the natural convection in unsteady Couette flow of a viscous incompressible fluid confined between two vertical parallel plates in the presence of thermal radiation is performed in this paper.
Abstract: An exact analysis of the natural convection in unsteady Couette flow of a viscous incompressible
fluid confined between two vertical parallel plates in the presence of thermal radiation is performed. The flow
is induced by means of Couette motion and free convection currents occurring as a result of application of
constant heat flux on the wall with a uniform vertical motion in its own plane while constant temperature on the
stationary wall. The fluid considered here is a gray, absorbing-emitting but non-scattering medium, and the
Rosseland approximation is used to describe the radiative heat flux in the analysis. The dimensionless
governing partial differential equations are solved using Laplace transform technique. Numerical results for the
velocity, the temperature, the skin-friction, the Nusselt number, the volume flow rate and the vertical heat flux
are shown graphically. The effect of different parameters like thermal radiation parameter, Grashof number,
Prandtl number and time are discussed. It is observed that the momentum and thermal boundary layer thickness
decreases owing to an increase in the value of the radiation parameter. An increase in the Grashof number is
found to increase the velocity of air and water and to decrease the skin-friction at the moving plate.
29 citations
Cites background from "Couette flow of granular materials"
...3 16 y T k T y T k t T C h p ′ ∂ ′ ∂ ′ + ′ ∂ ′ ∂ = ′ ∂ ′ ∂ σ ρ (6)...
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...(1), (6) and (3) reduces to the following non-dimensional form of equations:...
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TL;DR: In this paper, the authors used the constitutive relation derived by Rajagopal and Massoudi [Rajagopal, K. R. and M. Massoum, 1990] to predict the normal stress differences between two horizontal flat plates.
15 citations
TL;DR: In this article, a low shear mixing device consisting of a box with two moving walls and three static walls was used again to study granular mixing as a function of particle size.
13 citations
Cites background from "Couette flow of granular materials"
...The latter works were performed in two dimensions and with monosized particles [15–23]....
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TL;DR: In this article, a low shear mixing device consisting of a box with two moving walls and three static walls was developed to study granular mixing, and experiments at different wall velocities and wall displacements were run to obtain an in depth understanding of the internal behavior of granular materials in three dimensions.
13 citations
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TL;DR: In this article, a large number of spherical grains of diameter D = 0.13 cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums.
Abstract: Dispersions of solid spherical grains of diameter D = 0.13cm were sheared in Newtonian fluids of varying viscosity (water and a glycerine-water-alcohol mixture) in the annular space between two concentric drums. The density σ of the grains was balanced against the density ρ of the fluid, giving a condition of no differential forces due to radial acceleration. The volume concentration C of the grains was varied between 62 and 13 %. A substantial radial dispersive pressure was found to be exerted between the grains. This was measured as an increase of static pressure in the inner stationary drum which had a deformable periphery. The torque on the inner drum was also measured. The dispersive pressure P was found to be proportional to a shear stress λ attributable to the presence of the grains. The linear grain concentration λ is defined as the ratio grain diameter/mean free dispersion distance and is related to C by λ = 1 ( C 0 / C ) 1 2 − 1 where C 0 is the maximum possible static volume concentration. Both the stresses T and P , as dimensionless groups T σ D 2 /λη 2 , and P σ D 2 /λη 2 , were found to bear single-valued empirical relations to a dimensionless shear strain group λ ½ σ D 2 (d U /d y )lη for all the values of λ C = 57% approx.) where d U /d y is the rate of shearing of the grains over one another, and η the fluid viscosity. This relation gives T α σ ( λ D ) 2 ( dU / dy ) 2 and T ∝ λ 1 2 η d U / dy according as d U /d y is large or small, i.e. according to whether grain inertia or fluid viscosity dominate. An alternative semi-empirical relation F = (1+λ)(1+½λ)ηd U /d y was found for the viscous case, when T is the whole shear stress. The ratio T/P was constant at 0·3 approx, in the inertia region, and at 0.75 approx, in the viscous region. The results are applied to a few hitherto unexplained natural phenomena.
2,445 citations
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01 Nov 1992TL;DR: In this article, Coulomb's method of wedges and differential slices were used to determine the stress and strain rate of Coulomb material, and the conical yield function was used to predict mass flow rate.
Abstract: 1. Introduction 2. The analysis of stress and strain rate 3. The ideal Coulomb material 4. Coulomb's method of wedges 5. The method of differential slices 6. Determination of physical properties 7. Exact stress analysis 8. Velocity distributions 9. The conical yield function 10. The prediction of mass flow rate Problems Appendices Index.
953 citations
Esso1
692 citations
TL;DR: In this article, a constitutive equation appropriate for flow of cohesionless granular materials at high deformation rates and low stress levels is proposed, which consists of an extension and a reinterpretation of the theory of Goodman & Cowin (1972).
Abstract: A constitutive equation appropriate for flow of cohesionless granular materials at high deformation rates and low stress levels is proposed. It consists of an extension and a reinterpretation of the theory of Goodman & Cowin (1972), and accounts for the non-Newtonian nature of the flow as evidenced by Bagnold's (1954) experiments. The theory is applied to analyses of gravity flows in inclined chutes and vertical channels. Experiments were set up in an attempt to generate two-dimensional shear flows corresponding to these analyses. Velocity profiles measured by a technique which makes use of fibre optic probes agree qualitatively with the theoretical predictions, but direct comparison is inappropriate because of unavoidable side-wall friction effects in the experiments. The existing measure of agreement suggests that the most prominent effects have been included in the proposed constitutive relations. Tests in the inclined chute revealed the possible existence of surge waves and granular jumps analogous to hydraulic jumps.
480 citations
TL;DR: In this paper, the results obtained during rapid shearing of several dry, coarse, granular materials in an annular shear cell were described, and the main purpose of the tests was to obtain information that could be used to guide the theoretical development of constitutive equations suitable for the rapid flow of cohesionless bulk solids at low stress levels.
Abstract: Experimental results obtained during rapid shearing of several dry, coarse, granular materials in an annular shear cell are described. The main purpose of the tests was to obtain information that could be used to guide the theoretical development of constitutive equations suitable for the rapid flow of cohesionless bulk solids at low stress levels. The shear-cell apparatus consists of two concentric disk assemblies mounted on a fixed shaft. Granular material was contained in an annular trough in the bottom disk and capped by a lipped annular ring on the top disk. The bottom disk can be rotated at specified rates, while the top disk is loaded vertically and is restrained from rotating by a torque arm connected to a force transducer. The apparatus was thus designed to determine the shear and normal stresses as functions of solids volume fraction and shear rate.Tests were performed with spherical glass and polystyrene beads of nearly uniform diameters, spherical polystyrene beads having a bimodal size distribution and with angular particles of crushed walnut shells. The particles ranged from about ½ to 2 mm in size. At the lower concentrations and high shear rates the stresses are generated primarily by collisional transfer of momentum and energy. Under these conditions, both normal and shear stresses were found to be proportional to the particle density, and the squares of the shear rate and particle diameter. At higher concentrations and lower shear rates, dry friction between particles becomes increasingly important, and the stresses are proportional to the shear rate raised to a power less than two. All tests showed strong increases in stresses with increases in solids concentrations. The ratio of shear to normal stresses showed only a weak dependence upon shear rate, but it increased with decreasing concentration. At the very highest concentrations with narrow shear gaps, finite-particle-size effects became dominant and differences in stresses of as much as an order of magnitude were observed for the same shear rate and solids concentration.
418 citations