Translational Granular Temperatures Research Articles

Collisional dissipation rate for binary mixtures of aspherical particles

The homogeneous cooling process of binary mixtures of large aspherical particles and small spheres is modeled using DEM. The dissipation rate increases with the increasing total solid volume fraction of the mixture. For a specified total solid volume fraction of the mixture, the dissipation rate increases with the increasing fraction ratio of small spheres in the mixture. Energy equipartition analysis shows that the translational and rotational components of the granular temperature for the large aspherical particles are generally equivalent. Energy equipartition is also present between the translational granular temperature for the large and small particles. Both particle aspect ratio and shape irregularity affect the collisional dissipation rate. The collisional dissipation rate increases with the aspect ratio (AR) for the same particle shape. For the same AR, the collisional dissipation rate of more-irregular oval-like particles are larger than less-irregular rod-like particles. The collisional dissipation rate decreases with the increasing particle sphericity.

Numerical study on the effect of drum on the flow behavior of binary-size particles in rotating drums

The flow behavior of binary-sized particles in a horizontal rotating cylinder drum (RCD) and rotating ellipsoidal drum (RED) based on the discrete element method (DEM) is predicted. The simulations in this work study the influence of flattening on the flow of binary-sized particles. The flow characteristics such as the mixing indices, the resulting contact forces, the translational granular temperature, the configurational temperature and the energy dissipation are predicted or calculated in the simulations. The results show that the changes in flattening and particle diameter can affect the flow significantly. At a high rotating speed, the mixing degree of binary-sized particles in the RED can be improved. The resulting contact forces gradually increase with the increasing of rotating speed and flattening. The large particle's velocity is larger than that of the small one. The change of rotating angle causes the oscillation of translational granular temperature and configuration temperature.

Comparison of computational fluid dynamics–discrete element method and discrete element method simulations for a screw conveyor

AbstractFlow behavior of particles is simulated by means of discrete element method (DEM) in a screw conveyor. The gas flow is considered by the Euler model. The subgrid scale model turbulence model is applied to solve gas turbulence. A detailed description of the model equations applied has been presented. The comparison between computational fluid dynamics (CFD)‐DEM (i.e., considering gas flow) and DEM (i.e., not considering gas flow) simulation results is performed. Predicted mass flow rate with CFD‐DEM model is in better agreement with experiments by Roberts and Wills comparing with DEM results. The effects of incline angle and filling rate on the flow behavior of particles are predicted. The simulation results show that the gas flow has a major impact on particle flow behavior at a high rotation speed, whereas the velocity of particles increases with an increase of rotation speed. As the filling rate rises, both the translational granular temperature and the rotational granular particle temperature decline, which means that the particles fluctuation turns weak. While with an increase of incline angle, from the horizontal to vertical, the translational granular temperature is increased, but the rotational granular temperature reduces and then goes up. In brief, translational motion is a main mode of motion in a screw conveyor.

Numerical simulation of flow behavior of particles in an inverse liquid–solid fluidized bed with a jet using CFD-DEM

Flow behavior of particles in an inverse fluidized bed with a jet is simulated by means of DEM-CFD. The lubrication forces are considered. By changing the jet velocity, the distribution of particles is obtained within the bed. The distributions of velocity and concentration of particles are analyzed at different jet velocities. The rotational and translational granular temperatures are calculated in an inverse fluidized bed with a jet. Simulations indicate that the flow behavior of particles is divided into three stages: particles flow downward; particles flow upwards and a dynamic balance is reached in the bed. Quality of fluidization can be improved through increasing jet speed, liquid viscosity, restitution coefficient of particles and particle density. An agreement between the numerical simulation and experimental results has been achieved in an inverse liquid–solid fluidized bed.

Partial slip boundary conditions for collisional granular flows at flat frictional walls

We derive new boundary conditions (BCs) for collisional granular flows of spheres at flat frictional walls. A new theory is proposed for the solids stress tensor, translational and rotational energy dissipation rate per unit area and fluxes of translational and rotational fluctuation energy. In the theory we distinguish between sliding and sticking collisions and include particle rotation. The predictions are compared with literature results obtained from a discrete particle model evaluated at a given ratio of rotational to translational granular temperature. We find that the new theory is in better agreement with the observed stress ratios and heat fluxes than previous kinetic theory predictions. Finally, we carry out two fluid model simulations of a bubbling fluidized bed with the new BCs, and compare the simulation results with those obtained from discrete particle simulations. The comparison reveals that the new BCs are better capable of predicting solids axial velocity profiles, solids distribution near the walls and granular temperatures. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1853–1871, 2017

Modification of kinetic theory of granular flow for frictional spheres, part II: Model validation

The hydrodynamics of a dense solid–gas fluidized bed is studied, using a two fluid model (TFM) based on our newly developed kinetic theory of granular flow (KTGF) for rotating rough particles. The TFM simulations are validated by comparing with PIV-DIA experimental data (Buist et al., 2014) and results obtained from discrete particle model (DPM) simulations of the bubbling fluidized bed. The TFM model predictions agree well with the experimental results for the time-averaged particle axial velocity and solids volume fraction. The predicted levels of the translational granular temperatures and solids circulation patterns compare reasonably well with the results obtained from the DPM simulations. The predicted rotational granular temperature in our TFM simulations shows an almost uniform distribution in the bed as a result of the assumptions that both the local mean rotational velocity and the gradient of the rotational granular temperature at the wall are zero, indicating directions for future improvement. A comparison between TFM simulations using the present KTGF model, and a more simple kinetic theory for rapid flow of slightly frictional, nearly elastic spheres derived by Jenkins and Zhang (2002), is carried out to investigate the influence of particle friction in the fluidized bed. The present KTGF model leads to better agreement with DPM simulations and experimental results for the axial particle velocity profiles and solids volume fraction distribution.

Predicted configurational and translational granular temperatures of particles for low-velocity intruder impacting on granular bed using DEM

The impact and penetration process of a cubic intruder on granular bed is simulated by means of Distinct Element Method (DEM) using PFC commercial code. The excavation stage of cratering is represented by numerical simulation, and the simulated size and penetration depth of the cubic intruder are consistent with experiments. The configurational temperatures are calculated from overlaps of particles, and the translational granular temperatures are calculated from translational velocities of particles. The generalized granular temperature is proposed to show the relation between the fluctuation translational velocity and the fluctuation velocity of deformation of particles. The major finding of this study is the configurational temperature and translational granular temperatures increase rapidly, reach maximum, and then decrease at the impact and penetration process of the intruder. The variations of energy dissipation are analyzed on the basis of generalized granular temperature in the impact and penetration process of the intruder through the granular bed.

Simulations of dynamic properties of particles in horizontal rotating ellipsoidal drums

Flow behavior of particles in the horizontal rotating ellipsoidal drum (RED) is predicted by means of the discrete element method (DEM). The effect of flattening of the ellipsoidal drum on flow regimes of particles is simulated because of its importance to industrial applications, and because the underlying flow of particles is not fully explained yet. Different flow regimes are produced by varying flattening. The resulting contact forces between the drum wall and particles are predicted in the horizontal RED and horizontal rotating cylinder drum (RCD). The flow of particles in the horizontal RED becomes significantly different to that in the horizontal RCD due to the increase of flattening of the ellipsoidal drum. At high rotation speed, a crescent shaped flow mode is observed at the orientation angle of 90° and a showery raining mode is observed at 120°. The results show that the resulting contact forces between the particles and the drum wall increase with the increase of flattening and rotation speed. The velocity of particles is changed with the orientation angle of the horizontal RED. The translational granular temperature and configurational temperature are calculated from simulated instantaneous translational velocity and displacement of particles, respectively. The simulated translational granular temperature and configurational temperature increase with the increase of flattening and rotation speed. The rate of energy dissipation through collisions and contact interactions of particles is predicted in the horizontal RED and RCD.

Numerical simulation of different flow regimes in a horizontal rotating ellipsoidal drum

Flow regimes of particles are predicted by means of discrete element method (DEM) in a horizontal rotating ellipsoidal drum (RED) at different rotation speeds and flattening. The macroscopic behavior of the particle flow is produced in a horizontal RED at specified rotation speed, and compared to the motion of particles in the horizontal rotating cylinder drums (RCD). Simulations indicate that there are two different flow regimes in one round with the rotating angles of the horizontal RED. The particle bed became more dilated with the increase of rotation speed. The evolution of resulting contact forces between particles and drum walls is predicted in the horizontal RED at different rotation speeds and flattening. Simulated mixing index indicates that the mixing of particles is improved at the low rotation speed and the segregation of particles is enhanced at the high rotation speed in the horizontal RED. The translational granular temperature and con temperature are calculated from simulated instantaneous velocity and displacement of particles. The predicted configurational and translational granular temperatures increase with the increase of rotation speeds and flattening in the horizontal RED. The rate of energy dissipation based on the generalized granular temperature is increased with the increase of rotation speeds in the horizontal RED.

Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.

Boundary conditions for collisional granular flows of frictional and rotational particles at flat walls

Collisions between frictional particles and flat walls are determined using Coulomb friction and both tangential and normal restitution, and pseudothermal states of particles are described by both the translational and rotational granular temperatures. Then, new models for the stresses and the fluxes of fluctuation energy for the collisional granular flows at the walls are derived. These new models are tested and compared with the literature data and models. The ratio of rotational to translational granular temperatures is shown to be crucial on accurately predicting the shear stress and energy flux and is dependent on the normalized slip velocity as well as the collisional parameters. Using a theoretical but constant value for this ratio, predictions by the new models could still agree better with the literature data than those by the previous models. Finally, boundary conditions are developed to be used within the framework of kinetic theory of granular flow. © 2014 American Institute of Chemical Engineers AIChE J 60: 4065–4075, 2014

Simulations of configurational and granular temperatures of particles using DEM in roller conveyor

The configurational temperature and translational and rotational granular temperatures of particles are simulated by means of discrete element method (DEM) in the roller conveyor. Motion of particles in the roller conveyor is predicted with the change of rotation speed. The distributions of velocity and volume fraction of particles are obtained along bed height. The translational and rotational granular temperatures are calculated from simulated instantaneous translational and angular velocities of particles. The configurational temperatures of particles are calculated from simulated instantaneous overlaps of particles. The simulated results show that the translational and rotational granular temperatures and configurational temperature of particles decrease with the increase of solids volume fractions. The predicted configurational temperatures are larger than that translational and rotational granular temperature, indicating that the rate of energy dissipation do contributes by sliding and rolling contact deformation of elastic particles in the roller conveyor. The lowest translational granular temperature means that the rotational mechanism dominates in the roller conveyor. The influence of rotation speeds of rollers on granular temperatures and configurational temperature is analyzed.

Euler–Euler modeling of a gas–solid bubbling fluidized bed with kinetic theory of rough particles

Kinetic theory of granular flow is extended for rough particles. Both the translational and rotational granular temperatures are introduced to characterize the random fluctuations of particles. Sliding and sticking mechanisms are distinguished in the binary collision model with the friction coefficient and coefficients of normal and tangential restitution. Collision integrals are performed to produce new expressions of the constitutive relations for rough particles. Flat wall boundary conditions for rough particles are proposed according to the particle–wall collisions. The present model is incorporated in Euler–Euler simulations of a bubbling gas–solid fluidized bed. The computed bed expansion dynamics and flow patterns are validated with experimental measurements and Euler–Lagrange simulations. The ratio of rotational to translational granular temperatures is found to be influenced by the particle volume fraction and the fluidization velocity. Comparison among the present model, the original smooth particle model and another rough particle model is also carried out.

Simulation of motion of particles in reciprocating grates using DEM

Abstract Motion of monosize particles and binary mixture in the reciprocating grate is simulated by means of Discrete Element Method (DEM). The flow behavior of monosize particles and the mixing and segregation processes of binary mixture with identical densities but different sizes subjected to horizontal reciprocating grates are investigated in this study. The spatial distributions of velocity and volume fraction of particles are predicted. The contact force and granular temperature of particles are calculated in a reciprocating grate. The mechanism causing the mixing and segregation of binary mixture is strongly dependent on the momentum exchange of each species which is related to the granular temperature of mixture components. The simulation results show that the translational granular temperatures of small particles are higher than those of large particles, indicating that the translational granular temperatures do not equilibrate for the binary mixture system. The kinetic energy of large particles is higher than that of small particles. The influence of amplitude and frequency on motion of particles is analyzed.

Discrete particle modeling of granular temperature distribution in a bubbling fluidized bed

The discrete hard sphere particle model (DPM) is applied in this work to study numerically the distributions of particle and bubble granular temperatures in a bubbling fluidized bed. The dimensions of the bed and other parameters are set to correspond to those of Müller et al. (2008). Various drag models and operational parameters are investigated to find their influence on particle and bubble granular temperatures. Various inlet superficial gas velocities are used in this work to obtain their effect on flow characteristics. It is found that the superficial gas velocity has the most important effect on granular temperatures including bubble granular temperature, particle translational granular temperature and particle rotational granular temperature. The drag force model affects more seriously the large scale variables such as the bubble granular temperature. Restitution coefficient influences all granular temperatures to some degree. Simulation results are compared with experimental results by Müller et al. (2008) showing reasonable agreement.

Hydrodynamics of Nearly Smooth Granular Gases

Hydrodynamic equations of motion for a monodisperse collection of nearly smooth homogeneous spheres have been derived from the corresponding Boltzmann equation, using a Chapman-Enskog expansion around the elastic smooth spheres limit. Because in the smooth limit the rotational degrees of freedom are uncoupled from the translational ones, it turns out that the required hydrodynamic fields include (in addition to the standard density, velocity, and translational granular temperature fields) the (infinite) set of number densities, n(s,r, t), corresponding to the continuum of values of the angular velocities. The Chapman-Enskog expansion was carried out to high (up to 10th) order in a Sonine polynomial expansion by using a novel computer-aided method. One of the consequences of these equations is that the asymptotic spin distribution in the homogeneous cooling state for nearly smooth, nearly elastic spheres, is highly non-Maxwellian. The simple sheared flow possesses a highly non-Maxwellian distribution as well. In the case of wall-bounded shear, it is shown that the angular velocity injected at the boundaries has a finite penetration length.