Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: A hard-sphere approach

Abstract

A discrete particle model of a gas-fluidised bed has been developed and in this the twodimensional motion of the individual, spherical particles was directly calculated from the forces acting on them, accounting for the interaction between the particles and the interstitial gas phase. Our collision model is based on conservation laws for linear and angular momentum and requires, apart from geometrical factors, two empirical parameters: a restitution coefficient and a friction coefficient. A sequence of collisions is processed using techniques which find their application in hard-sphere simulations which are commonly encountered in the field of molecular dynamics. The hydrodynamic model of the gas phase is based on the volume-averaged Navier-Stokes equations. Simulations of bubble and slug formation in a small twodimensional bed (height 0.50 m, width 0.15 m) with 2400 particles (dp = 4 mm, material: aluminium, p = 2700 kg m-3) showed a strong dependency of the flow behaviour with respect to the restitution and friction coefficient. A preliminary experimental validation of our model was performed using a small scale "two-dimensional" gas-fluidised bed (height 0.30 m, width 0.15 m, depth 0.015 m) with 850/~m ballotini glass particles (p = 2930 kgm-3) as the bed material. Results compared fairly well with the results of a simulation which was performed with 40,000 particles using realistic values for the restitution and friction coefficients which were obtained from simple independent experiments.

Eulerian–Eulerian simulation of dense solid–gas cylindrical fluidized beds: Impact of wall boundary condition and drag model on fluidization

“…The most detailed description is the Discrete Particle Model (DPM) or the Lagrangian-Eulerian framework where the solid phase consists of individual particles interacting with each other and the continuous gas phase [3][4][5]. Current computational resources, however, limit the number of solid particles that can be tracked simultaneously making the approach only feasible for dilute solid-phase flows [6].…”

Energy absorption during compression and impact of dry elastic-plastic spherical granules

“…In the last ten-fifteen years, these methods found many applications in the mechanics of bulk materials, i.e. flow behaviour and discharge of silos [8,49,50], filling and packing [111], shearing [25,35,47,61,103], heap formation [13,36,65], bed configuration and loading conditions in fall mills [63,69,105], compression behaviour [68,78], mixing and transportation [12,27,44,52,54,107], fluidised bed processes [31,40,41,58,66,90,102,104,110,112], heat exchange processes [41,50].…”

“…The time step of DEM calculations that ensures numerical stability is proportional to the mass of the smallest particle in the system [6]. Therefore in the DEM/DPM-models the granules are usually represented as homogeneous particles [31,40,58,66,67,78,110] and the influence of their microstructure is neglected. Based on the assumption of a continuous matter, contact theory and continuum mechanics can be used to describe the mechanical behaviour of a granule without breakage through experimentally observed mechanical parameters like modulus of elasticity, yield point, contact stiffness.…”

Sur le volume élémentaire représentatif de la loi de perte de charge d'Ergun

“…Le fondement théorique de ces lois provient de l'analogie avec l'expression de la perte de charge dans un tube cylindrique. Cette analogie permet d'obtenir des expressions théoriques corrigées expérimentalement par un facteur multiplicatif proche de 2 en raison de la tortuosité [12] pour donner en définitive les lois respectives de Blake-Kozeny et de Burke-Plummer :…”

“…La modélisation de l'écoulement du fluide interstitiel repose sur la résolution directe des équations de Navier-Stokes à l'échelle de la particule, écrites sous forme adimensionnelle : (9) (10) avec : (11) et : (12) où i = 1, ..., 3 et j = 1, ..., 3. Le mouvement du fluide sur la surface des particules est soumis aux conditions d'adhérence, à savoir que la vitesse du fluide en ces points est égale à la vitesse des particules, nulle dans le cas présent.…”