Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Axial mixing in rotating drums using magnetic resonance imaging using bran as a model for solid state fermentations

Magnetic resonance imaging (MRI) is an easily automated, reliable technique to investigate axial mixing within rotating drums. Moist bran can be clearly differentiated from dry bran using MRI allowing a non-segregating tracer for axial mixing. For a 20-cm diameter drum, the axial dispersion coefficient in the particle bed was 0.51 cm s(-2). Axial dispersion is scale-dependent.

Terässiilojen mitoitusohjelman kehittäminen

Siiloja käytetään jauhemaisten ja rakeisten aineiden varastointiin ja annosteluun maataloudessa sekä mm. lasi-, laasti- ja tasoiteteollisuudessa. Tällaiset laitokset toimitetaan usein kokonaistoimituksina, joissa tavanomaisten teräsrakenteiden kustannusvaikutus voi olla jopa 30 % koko toimituksen arvosta. Niinpä osaltaan siilojen tehokkaalla mitoituksella ja erilaisiarakenneratkaisuja vertailemalla voidaan alentaa toimitusten kokonaiskustannuksia. Tässä diplomityössä perehdyttiin siilojen rakenteisiin ja niiden lujuustekniseen mitoitukseen etenkin tuentaratkaisujen osalta. Mitoituksen osalta työssä perehdyttiin pääasiassa uusiin Eurooppalaisiin standardeihin SFS-EN 1991-4 ja SFS-EN 1993-4-1. Niiden mukaan määritetään mitoituskuormat sekä tehdään lujuustekninen mitoitus. Työn tuloksena laadittiin Microsoft Excel -pohjainen mitoitusohjelma, jolla voidaan nopeasti mitoittaa siilojen olennaisimmat teräsrakenteet. Ohjelmalla voidaan määrittää mitoitus koskien siilon lieriön ja kartion seinämiä sekä tuentaratkaisuja. Ohjelma nopeuttaa erityisesti tarjousvaiheen suunnittelua ja antaa pohjan varsinaiselle siilojen yksityiskohtaiselle mitoittamiselle ja suunnittelulle.

Solid transport in a pyrolysis pilot-scale rotary kiln: Preliminary results?stationary and dynamic results

Experiments for the investigation of the flow of granular solids in a pyrolysis pilot-scale rotary kiln are presented. These experiments consisted first in measuring the volumetric filling ratio (steady-state experiences) for several operating conditions and second in recording the exit flow rates after a positive or negative step in one of the operating parameters (dynamic experiences). A dynamical model computing the evolution of the flow rate of granular solids through the kiln has been developed based on Saeman model [Chem. Eng. Prog. 47 (1951) 508]. The simulations are compared with experimental results; the model gives good results for the rolling mode, but for the slipping mode too. (C) 2004 Elsevier B.V. All rights reserved.

Degradation of detergent (linear alkylbenzene sulfonate) in an anaerobic stirred sequencing-batch reactor containing granular biomass

This study aimed to determine the efficiency of an anaerobic stirred sequencing-batch reactor containing granular biomass for the degradation of linear alkylbenzene sulfonate (LAS), a surfactant present in household detergent. The bioreactor was monitored for LAS concentrations in the influent, effluent and sludge, pH, chemical oxygen demand, bicarbonate alkalinity, total solids, and volatile solids. The degradation of LAS was found to be higher in the absence of co-substrates (53%) than in their presence (24-37%). Using the polymerase chain reaction and denaturing gradient gel electrophoresis (PCR/DGGE), we identified populations of microorganisms from the Bacteria and Archaea domains. Among the bacteria, we identified uncultivated populations of Arcanobacterium spp. (94%) and Opitutus spp. (96%). Among the Archaea, we identified Methanospirillum spp. (90%), Methanosaeta spp. (98%), and Methanobacterium spp. (96%). The presence of methanogenic microorganisms shows that LAS did not inhibit anaerobic digestion. Sampling at the last stage of reactor operation recovered 61 clones belonging to the domain bacteria. These represented a variety of phyla: 34% shared significant homology with Bacteroidetes, 18% with Proteobacteria, 11% with Verrucomicrobia, 8% with Fibrobacteres, 2% with Acidobacteria, 3% with Chlorobi and Firmicutes, and 1% with Acidobacteres and Chloroflexi. A small fraction of the clones (13%) were not related to any phylum. Published by Elsevier Ltd.

Analysis of Industrial Granular Flow Applications by Using Advanced Collision Models

Granular flow phenomena are frequently encountered in the design of process and industrial plants in the traditional fields of the chemical, nuclear and oil industries as well as in other activities such as food and materials handling. Multi-phase flow is one important branch of the granular flow. Granular materials have unusual kinds of behavior compared to normal materials, either solids or fluids. Although some of the characteristics are still not well-known yet, one thing is confirmed: the particle-particle interaction plays a key role in the dynamics of granular materials, especially for dense granular materials. At the beginning of this thesis, detailed illustration of developing two models for describing the interaction based on the results of finite-element simulation, dimension analysis and numerical simulation is presented. The first model is used to describing the normal collision of viscoelastic particles. Based on some existent models, more parameters are added to this model, which make the model predict the experimental results more accurately. The second model is used for oblique collision, which include the effects from tangential velocity, angular velocity and surface friction based on Coulomb's law. The theoretical predictions of this model are in agreement with those by finite-element simulation. I n the latter chapters of this thesis, the models are used to predict industrial granular flow and the agreement between the simulations and experiments also shows the validation of the new model. The first case presents the simulation of granular flow passing over a circular obstacle. The simulations successfully predict the existence of a parabolic steady layer and show how the characteristics of the particles, such as coefficients of restitution and surface friction affect the separation results. The second case is a spinning container filled with granular material. Employing the previous models, the simulation could also reproduce experimentally observed phenomena, such as a depression in the center of a high frequency rotation. The third application is about gas-solid mixed flow in a vertically vibrated device. Gas phase motion is added to coherence with the particle motion. The governing equations of the gas phase are solved by using the Large eddy simulation (LES) and particle motion is predicted by using the Lagrangian method. The simulation predicted some pattern formation reported by experiment.

Pneumatic Conveying of Granular Materials in a Pilot Scale Downer-Riser System

Studies regarding the field of this work aim to substitute industrial mechanical conveyors with pneumatic conveyors to overcome the disadvantages in solids flow regulation and risks posed to production and health. The experimental part of this work examines how the granular material properties, fluidizing airflow rate, equipment geometry, and pressures along the pipes affect the mass flow rate through the system. The results are compared with those obtained from previous experiments conducted with alumina. Experiments were carried out with a pilot scale downer-riser system at Outotec Research Center Frankfurt. Granular materi-als used in this work are named as sand, ilmenite, iron ore 1 and iron ore 2.

Granular Attrition due to Rotary Valve in a Pneumatic Conveying System

The rotary valve is a widely used mechanical device in many solids-handling industrial processes. However, it may also be responsible for most of the attrition effects occurring in a typical process. In this study, the attrition effects occurring in a rotary valve operating as a stand-alone device and as part of a pneumatic conveying system were investigated. In the former case granular attrition was carried out at three different rotary valve speeds and the experimental results obtained were found to be in good agreement with the Gwyn correlation. In the latter case three typical air flow rates were used in the pneumatic conveying system. The size distribution of the attrition product obtained at the lowest air flow rate used was not adequately described by the Gwyn correlation. The attrition process and mechanisms involved were analysed and the minimum size of the attrition product obtained from both modes of operations was found to be similar.

Study on Granular Dynamics in Vertically Vibrated Beds using Tracking Technique

The study of granular material is of great interest to many researchers in both engineering and science communities. The importance of such a study derives from its complex rheological character and also its significant role in a wide range of industrial applications, such as coal, food, plastics, pharmaceutical, powder metallurgy and mineral processing. A number of recent reports have been focused on the physics of non-cohesive granular material submitted to vertical vibration in either experimental or theoretical approaches. Such a kind of system can be used to separate, mix and dry granular materials in industries. It exhibits different instability behaviour on its surface when under vertical vibration, for example, avalanching, surface fluidization and surface wave, and these phenomena have attracted particular interest of many researchers. However, its fundamental understanding of the instability mechanism is not yet well-understood. This paper is therefore to study the dynamics of granular motion in such a kind of system using Positron Emission Particle Tracking (PEPT), which allows the motion of a single tracer particle to be followed in a non-invasive way. Features of the solids motion such as cycle frequency and dispersion index were investigated via means of authors’ specially-written programmes. Regardless of the surface behaviour, particles are found to travel in rotational movement in horizontal plane. Particle cycle frequency is found to increase strongly with increasing vibration amplitude. Particle dispersion also increased strongly with vibration amplitude. Horizontal dispersion is observed to always exceed vertical dispersion.

Does the granular matter?

Granular materials, such as sand, gravel, powders, and pharmaceutical pills, are large aggregates of macroscopic, individually solid particles, or “grains.” Far from being simple materials with simple properties, they display an astounding range of complex behavior that defies their categorization as solid, liquid, or gas. Just consider how sand can stream through the orifice of an hourglass yet support one's weight on the beach; how it can form patterns strikingly similar to a liquid when vibrated, yet respond to stirring by “unmixing” of large and small grains. Despite much effort, there still is no comprehensive understanding of other forms of matter, like ordinary fluids or solids. In what way, therefore, is granular matter special, and what makes it so difficult to understand? An emerging interdisciplinary approach to answering these questions focuses directly on the material's discontinuous granular nature.

The influence of substrate kinetics on the microbial community structure in granular anaerobic biomass

The development of a strong, active granular sludge bed is necessary for optimal operation of upflow anaerobic sludge blanket reactors. The microbial and mechanical structure of the granules may have a strong influence on desirable properties such as growth rate, settling velocity and shear strength. Theories have been proposed for granule microbial structure based on the relative kinetics of substrate degradation, but contradict some observations from both modelling and microscopic studies. In this paper, the structures of four granule types were examined from full-scale UASB reactors, treating wastewater from a cannery, a slaughterhouse, and two breweries. Microbial structure was determined using fluorescence in situ hybridisation probing with 16S rRNA-directed oligonucleotide probes, and superficial structure and microbial density (volume occupied by cells and microbial debris) assessed using scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The granules were also modelled using a distributed parameter biofilm model, with a previously published biochemical model structure, biofilm modelling approach, and model parameters. The model results reflected the trophic structures observed, indicating that the structures were possibly determined by kinetics. Of particular interest were results from simulations of the protein grown granules, which were predicted to have slow growth rates, low microbial density, and no trophic layers, the last two of which were reflected by microscopic observations. The primary cause of this structure, as assessed by modelling, was the particulate nature of the wastewater, and the slow rate of particulate hydrolysis, rather than the presence of proteins in the wastewater. Because solids hydrolysis was rate limiting, soluble substrate concentrations were very low (below Monod half saturation concentration), which caused low growth rates. (C) 2003 Elsevier Ltd. All rights reserved.

Towards a better understanding of granular material processes: The coupling of a computational fluid dynamics framework with micro-mechanical models

Abstract not available

Importance of granular structure in the initial conditions for the elliptic flow

We show the effects of the granular structure of the initial conditions of a hydrodynamic description of high-energy nucleus-nucleus collisions on some observables, especially on the elliptic-flow parameter upsilon(2). Such a structure enhances production of isotropically distributed high-p(T) particles, making upsilon(2) smaller there. Also, it reduces upsilon(2) in the forward and backward regions where the global matter density is smaller and, therefore, where such effects become more efficacious.

Systematic investigation of a family of gradient-dependent functionals for solids

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. On a test set of 60 solids, we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding.

Gradient-dependent density functionals of the Perdew-Burke-Ernzerhof type for atoms, molecules, and solids

One of the standard generalized-gradient approximations (GGAs) in use in modern electronic-structure theory [Perdew-Burke-Ernzerhof (PBE) GGA] and a recently proposed modification designed specifically for solids (PBEsol) are identified as particular members of a family of functionals taking their parameters from different properties of homogeneous or inhomogeneous electron liquids. Three further members of this family are constructed and tested, together with the original PBE and PBEsol, for atoms, molecules, and solids. We find that PBE, in spite of its popularity in solid-state physics and quantum chemistry, is not always the best performing member of the family and that PBEsol, in spite of having been constructed specifically for solids, is not the best for solids. The performance of GGAs for finite systems is found to sensitively depend on the choice of constraints stemming from infinite systems. Guidelines both for users and for developers of density functionals emerge from this work.