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MASTER THESIS S

Ali Halabia

LAPPEENRANTA UNIVERSITY OF TECHNOLOGY Department of Energy and Environmental Technology

DRAG FORCE AND FRICTIONAL RESISTANCES IN VERTICALLY VIBRATED DENSE GRANULAR MEDIA

Supervisor: Examiner:

Professor Piroz Zamankhan Professor Lasse Koskelainen

The Energy and Environmental Technology Department Council has approved the topic of this thesis on 7.9.2005. Lappeenranta, January 31, 2006

Ali Halabia Leirikatu 2 C 7, 53600 Lappeenranta GSM 050-5960567

ABSTRACTLAPPEENRANTA UNIVERSITY OF TECHNOLOGY Department of Energy and Environmental Technology Ali Halabia

DRAG FORCE AND FRICTIONAL RESISTANCES IN VERTICALLY VIBRATED DENSE GRANULAR MEDIA Thesis for the degree of Master of Science in Technology, 2006 101 pages, 33 figures, 10 tables and 2 appendices Supervisor: Examiner: Professor Piroz Zamankhan Professor Lasse Koskelainen

Keywords: granular materials; drag force; vibration; friction The objective of this thesis is to shed light on the vertical vibration of granular materials for potential interest in the power generation industry. The main focus is investigating the drag force and frictional resistance that influence the movement of a granular material (in the form of glass beads) contained in a vessel, which is subjected to sinusoidal oscillation. The thesis is divided into three parts: theoretical analysis, experiments and computer simulations. The theoretical part of this study presents the underlying physical phenomena of the vibration of granular materials. Experiments are designed to determine fundamental parameters that contribute to the behavior of vibrating granular media. Numerical simulations include the use of three different software applications: FLUENT, LS-DYNA and ANSYS Workbench. The goal of these simulations is to test theoretical and semiempirical models for granular materials in order to validate their compatibility with the experimental findings, to assist in predicting their behavior, and to estimate quantities that are hard to measure in laboratory.

TIIVISTELMLAPPEENRANNAN TEKNILLINEN YLIOPISTO Energia- ja Ympristtekniikan osasto Ali Halabia VASTUSVOIMA JA KITKAVASTUKSET PYSTYSUUNTAISESSA VRHTELYSS OLEVASSA TIIVIISS RAKEISESSA MATERIAALISSA Diplomity, 2006 101 sivua, 33 kuvaa, 10 taulukkoa ja 2 liitett Ohjaaja: Professori, TkT Piroz Zamankhan

Tarkastaja: Professori, TkT Lasse Koskelainen Hakusanat: rakeinen materiaali; vastusvoima; vrhtely; kitka

Rakeisilla materiaaleilla on mahdollisia energiateollisuuden sovellutuksia, kuten esimerkiksi leijukerrospoltto. Tmn diplomityn tavoitteena on valaista rakeisen materiaalin kyttytymist pystysuuntaisen vrhtelyn alaisena. Erityisesti tyss on keskitytty tarkastelemaan vastus- ja kitkavoimia, jotka vaikuttavat rakeisen materiaalin liikkeeseen astiassa, joka on sinimuotoisessa vrhtelyliikkeess. Diplomity koostuu kolmesta osasta: teoreettisesta tarkastelusta, kokeellisesta osasta ja tietokonesimulaatioista. Teoriaosassa ksitelln vrhtelevn rakeiseen materiaaliin liittyvi fysikaalisia ilmiit ja kokeellisessa osassa pyritn vastaavasti mrittelemn perusparametrit, jotka vaikuttavat vrhtelyss olevan rakeisen materiaalin kyttytymiseen. Simulaatio-osan numeerisessa laskennassa on kytetty FLUENT, LS-DYNA ja ANSYS Workbench ohjelmistoja. Tmn simulaatio-osan tavoitteena on testata teoreettisten ja puoliempiiristen rakeisen materiaalin mallien soveltuvuutta kokeiden tuloksien avulla. Simulaatioiden tavoitteena on mys ennustaa kyseisten mallien kyttytymist ja arvioida suureita joita on vaikea mitata kokeellisesti.

ACKNOWLEDGMENTSThis thesis work has been carried out in the Laboratory of Computational Fluid Dynamics at Lappeenranta University of Technology during the second half of year 2005. I would like to express my sincere thanks to my supervisors Professor Piroz Zamankhan and Professor Lasse Koskelainen for reviewing this thesis and for their continuous help and professional guidance. I wish to thank Lappeenranta University of Technology for providing me with a stipend and giving me the chance to make this thesis. I am also grateful for Docent Pertti Kolari for the support he has offered. Very kind thanks go to all my friends in Lappeenranta and to my colleagues at the Laboratory of CFD. I owe my family in Finland and Palestine special warm thanks for their patience, love and encouragement, especially my parents to whom I dedicate this work.

Mie ite! Ali Halabia Lappeenranta, January, 2006

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TABLE OF CONTENTSNOMENCLATURE .......................................................................................................3 1. INTRODUCTION ..................................................................................................8 1.1 1.2 1.3 1.4 2. 2.1 Motivation and Background ...........................................................................8 Static and Dynamic Behavior of Granular Materials ...................................10 Review of Previous Related Work ...............................................................11 Objectives and Thesis Structure ...................................................................13 Drag Force: A Continuum Approach ........................................................... 15 Drag of Immersed Bodies .....................................................................15 Fluid Flow Over A Sphere: Friction and Pressure Drag.......................16 Drag Force: A Statistical Mechanics Approach ...........................................19 Viscosity .......................................................................................................21 Viscosity of Gases ................................................................................ 22 Viscosity of Liquids.............................................................................. 23 Viscosity of Solids................................................................................ 23 Elastic Binary Collisions and Hertz Contact Theory....................................23 Geometry of Solid Surfaces in Contact ................................................24 Hertz Theory of Elastic Contact ...........................................................28 The Coefficient of Restitution ..............................................................29 Experiment Setup for Binary Collision ................................................31 Experiment With The Ultrasonic Motion Detector ..............................34 Analysis of Experiment Results............................................................36 Simple Viscoelastic Material Models ...................................................39 Finite Element Analysis........................................................................40

SINGLE-PARTICLE DYNAMICS ..................................................................... 15 2.1.1 2.2.2 2.2 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.5.6

Inelastic Binary Collisions............................................................................29

3.

DYNAMICS OF A SYSTEM OF PARTICLES..................................................46 3.1 3.2 3.3 3.4 General Overview.........................................................................................46 Vertical Vibration of Granular Materials .....................................................46 Experimental Techniques for Studying Granular Materials .........................48 Procedure and Setup of the Vibro-Fluidized Bed Experiment .....................49

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3.5 3.6 3.6.1

Experimental Results ....................................................................................53 Discrete and Continuum Formulation of Granular Flows ............................57 Introductory Remarks ...........................................................................57 Computer Simulation and Modeling Methods .....................................58 Lagrangian Models ...............................................................................58 Eulerian versus Lagrangian Description of Particle Motion ................63 Continuum Theory of Granular Flows .................................................64 Continuum Modeling of Granular Flows .............................................65 Volume Fractions..................................................................................67 Governing Conservation Equations ......................................................68 Interphase Exchange Coefficient ..........................................................71 Solids Pressure......................................................................................74 Solid Shear Stresses.............................................................................. 75 Granular Temperature...........................................................................76 Turbulence Models ...............................................................................76 RSM Dispersed Turbulence Model ......................................................77

3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 3.7 3.7.1 3.7.2 3.7.3 3.7.4 3.7.5 3.7.6 3.7.7 3.7.8 3.8 4. 4.1 4.2 4.3 5. 5.1 5.2

CFD Eulerian Multiphase Model..................................................................67

CFD Simulations and Results.......................................................................78 Background about Modal Analysis ..............................................................86 Model Construction in ANSYS Workbench ................................................86 Results of Modal Simulations.......................................................................88 Summary of the Thesis Core Points .............................................................91 Future Research Work ............................................................