Grain Size Reduction in Granular Flows of Spheres: The Effects of Critical Impact Energy

1992 ◽  
Vol 59 (2S) ◽  
pp. S17-S22 ◽  
Author(s):  
M. W. Richman ◽  
A. A. Oyediran
Keyword(s):  
Impact Energy ◽  
Constitutive Relations ◽  
Granular Flows ◽  
Binary Collision ◽  
Granular Temperature ◽  
Balance Equations ◽  
Shear Rates ◽  
Time Variations ◽  
Granular Shear ◽  
Induced Stresses

We extend methods employed to derive recent kinetic theories for rapid noncomminuting granular flows, to homogeneous flows in which a fraction of the repeated collisions produce tiny fractures on the particles’ peripheries and gradually reduce their effective diameters. The theory consists of balance equations for mass, momentum, and energy, as well as constitutive relations for the pressure tensor and collisional rates of mass and energy lost. We improve upon the work of Richman and Chou (1989) by incorporating into the constitutive theory the critical impact energy below which no mass loss occurs in a binary collision. The theory is applied to granular shear flows and, for fixed shear rates, predicts the time variations of the solid fraction, granular temperature, and induced stresses, as well as their extreme sensitivities to small changes in the critical impact energy.

scholarly journals Self-diffusion scalings in dense granular flows

Soft Matter ◽  
2021 ◽  
Author(s):  
Riccardo Artoni ◽  
Michele Larcher ◽  
James T. Jenkins ◽  
Patrick Richard
Keyword(s):  
Shear Rate ◽  
Solid Fraction ◽  
Granular Flows ◽  
The Self ◽  
Granular Temperature ◽  
Restitution Coefficient ◽  
Self Diffusion ◽  
Diffusivity Tensor ◽  
Dense Granular Flows

The self-diffusivity tensor in homogeneously sheared dense granular flows is anisotropic. We show how its components depend on solid fraction, restitution coefficient, shear rate, and granular temperature.

scholarly journals SLOW DENSE GRANULAR FLOWS AS A SELF-INDUCED PROCESS

2001 ◽  
Vol 04 (04) ◽  
pp. 441-450 ◽  
Author(s):  
OLIVIER POULIQUEN ◽  
YOËL FORTERRE ◽  
STÉPHANE LE DIZES
Keyword(s):  
Simple Model ◽  
Shear Flow ◽  
Granular Material ◽  
Granular Flows ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Stress Fluctuation ◽  
The Media ◽  
Granular Shear ◽  
Dense Granular Flows

A simple model is presented for the description of steady uniform shear flow of granular material. The model is based on a stress fluctuation activated process. The basic idea is that shear between two particle layers induces fluctuations in the media that may trigger a shear at some other position. Based on this idea, a minimum model is derived and applied to different configurations of granular shear flow.

The influence of image analysis methodology on the calculation of granular temperature for granular flows

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
A. M. Taylor-Noonan ◽  
D. Gollin ◽  
E. T. Bowman ◽  
W. A. Take
Keyword(s):  
Image Analysis ◽  
Granular Flows ◽  
Granular Temperature ◽  
Analysis Methodology

scholarly journals Stability analysis of rapid granular chute flows: formation of longitudinal vortices

2002 ◽  
Vol 467 ◽  
pp. 361-387 ◽  
Author(s):  
YOËL FORTERRE ◽  
OLIVIER POULIQUEN
Keyword(s):  
Stability Analysis ◽  
Kinetic Theory ◽  
Three Dimensional ◽  
Granular Flows ◽  
Granular Temperature ◽  
Instability Mechanism ◽  
Longitudinal Vortices ◽  
Spontaneous Formation ◽  
Wide Range ◽  
Inclined Planes

In a recent article (Forterre & Pouliquen 2001), we have reported a new instability observed in rapid granular flows down inclined planes that leads to the spontaneous formation of longitudinal vortices. From the experimental observations, we have proposed an instability mechanism based on the coupling between the flow and the granular temperature in rapid granular flows. In order to investigate the relevance of the proposed mechanism, we perform in the present paper a three-dimensional linear stability analysis of steady uniform flows down inclined planes using the kinetic theory of granular flows. We show that in a wide range of parameters, steady uniform flows are unstable under transverse perturbations. The structure of the unstable modes is in qualitative agreement with the experimental observations. This theoretical analysis shows that the kinetic theory is able to capture the formation of longitudinal vortices and validates the instability mechanism.

MATERIAL ELEMENT MODEL AND THE GEOMETRY OF THE ENTROPY FORM

2010 ◽  
Vol 07 (06) ◽  
pp. 1021-1042 ◽  
Author(s):  
M. DOLFIN ◽  
M. FRANCAVIGLIA ◽  
S. PRESTON ◽  
L. RESTUCCIA
Keyword(s):  
Phase Space ◽  
Constitutive Relations ◽  
Element Model ◽  
Continuum Thermodynamics ◽  
Balance Equations ◽  
Ferroelectric Crystal ◽  
Material Element ◽  
Closure Conditions ◽  
The Continuum ◽  
Crystal Element

In this work we analyze and compare the model of the material (elastic) element and the entropy form developed by Coleman and Owen with that one obtained by localizing the balance equations of the continuum thermodynamics. This comparison allows one to determine the relation between the entropy function S of Coleman–Owen and that one imported from the continuum thermodynamics. We introduce the Extended Thermodynamical Phase Space (ETPS) [Formula: see text] and realize the energy and entropy balance expressions as 1-forms in this space. This allows us to realizes I and II laws of thermodynamics as conditions on these forms. We study the integrability (closure) conditions of the entropy form for the model of thermoelastic element and for the deformable ferroelectric crystal element. In both cases closure conditions are used to rewrite the dynamical system of the model in term of the entropy form potential and to determine the constitutive relations among the dynamical variables of the model. In a related study (to be published) these results will be used for the formulation of the dynamical model of a material element in the contact thermodynamical phase space of Caratheodory and Hermann similar to that of homogeneous thermodynamics.

Investigating Multiphase Turbulence Statistics of Large-Scale Two-Way Coupled Gravity-Driven Flows

2014 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Kinetic Theory ◽  
Turbulent Kinetic Energy ◽  
Particle Velocity ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Granular Temperature ◽  
Particle Phase ◽  
Simulation Results ◽  
Filtering Approach

Starting from the kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-average (RA) equations were recently derived for the particle phase in a collisional gas-particle flow by Fox [1]. The turbulence model solves for the RA particle volume fraction, the phase-average (PA) particle velocity, the PA granular temperature, and the PA particle turbulent kinetic energy (TKE). A clear distinction is made between the PA granular temperature, which appears in the kinetic theory constitutive relations, and the particle-phase turbulent kinetic energy, which appears in the turbulent transport coefficients. Mesoscale direct numerical simulation (DNS) can be used to assess the validity of the closures proposed for the unclosed terms that arise due to nonlinearities in the hydrodynamic model. In order to extract meaningful statistics from simulation results, a separation of length scales must be established to distinguish between the PA particle TKE and the PA granular temperature. In this work, we introduce an adaptive spatial filter with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The filtering approach is applied to fully-developed cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. Simulation results show a strong correlation between the local volume fraction and granular temperature, with maximum values located just upstream of clusters (i.e., where maximum compressibility of the particle velocity field exists), and negligible particle agitation is observed within clusters.

scholarly journals Modeling the Hydro-Mechanical Coupling Behavior of Unsaturated Geotechnical Materials Based on Non-Equilibrium Thermodynamic Theory

2020 ◽  
Vol 10 (16) ◽  
pp. 5668
Author(s):  
Guangchang Yang ◽  
Yang Liu ◽  
Peipei Chen
Keyword(s):  
Yield Criterion ◽  
Constitutive Relations ◽  
Thermodynamic Theory ◽  
Granular Temperature ◽  
Equilibrium Thermodynamic ◽  
Energy Functions ◽  
Mechanical Coupling ◽  
Coupling Behavior ◽  
The Relationship ◽  
Non Equilibrium

A new hydro-mechanical model for unsaturated geotechnical materials based on the non-equilibrium thermodynamic theory is presented in this paper. Common concepts, such as yield criterion and flow rules, are not involved in the constitutive relationships, and are replaced with the thermodynamic concepts of granular temperature, granular entropy, migration coefficients, and energy functions. The dissipation system and the migration coefficient relationships are theoretically determined, and the constitutive relations of non-elastic deformation and granular temperature are obtained by dissipation relations and thermodynamic identity. Thus, the relationship between dissipation mechanism and macro mechanical behavior can be established by migration coefficients and energy functions. The model can reflect the complex hydro-mechanical coupling behavior of unsaturated geotechnical materials subjected to various mechanical paths. The validity of the model is verified by comparing the modeling results with experimental data, and reasonable agreement is achieved.

scholarly journals Charge transport equation for bidisperse collisional granular flows with non-equipartitioned fluctuating kinetic energy

2021 ◽  
Vol 926 ◽  
Author(s):  
Lise Ceresiat ◽  
Jari Kolehmainen ◽  
Ali Ozel
Keyword(s):  
Kinetic Energy ◽  
Charge Transport ◽  
Transport Equation ◽  
Solid Phase ◽  
Constitutive Relations ◽  
Kinetic Equations ◽  
Three Dimensional ◽  
Granular Flows ◽  
Transport Equations ◽  
Hydrodynamic Equations

Starting from the Boltzmann–Enskog kinetic equations, the charge transport equation for bidisperse granular flows with contact electrification is derived with separate mean velocities, total kinetic energies, charges and charge variances for each solid phase. To close locally averaged transport equations, a Maxwellian distribution is presumed for both particle velocity and charge. The hydrodynamic equations for bidisperse solid mixtures are first revisited and the resulting model consisting of the transport equations of mass, momentum, total kinetic energy, which is the sum of the granular temperature and the trace of fluctuating kinetic tensor, and charge is then presented. The charge transfer between phases and the charge build-up within a phase are modelled with local charge and effective work function differences between phases and the local electric field. The revisited hydrodynamic equations and the derived charge transport equation with constitutive relations are assessed through hard-sphere simulations of three-dimensional spatially homogeneous, quasi-one-dimensional spatially inhomogeneous bidisperse granular gases and a three-dimensional segregating bidisperse granular flow with conducting walls.

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