Discrete Element Modelling of Particulate Media by Chuan-Yu Wu - Original PDF

دانلود کتاب Discrete Element Modelling of Particulate Media by Chuan-Yu Wu - Original PDF

Author: Chuan-Yu Wu

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In numerical simulations of dense two-phase flow involving particulate materials the Discrete Element Method (DEM) has proved particularly effective in capturing the complex hydrodynamics of the solid phase. 1 DEM-based granular solid dynamics, including collisions and persistent contact with elaborate force-displacement laws, friction and cohesion have shown to be superior to traditional fluid-like, continuum approaches, which typically require coarse approximations and the introduction of artificial variables like solids pressure and viscosity. However, computational limitations of DEM models do not allow adding also the burden of flow simulations resolved at the level of particle-particle interstices, so that typically an averaged scale approach, with computational cell sizes of the order of a few particle diameters, is used. 2 .3 As a consequence, formulations of the drag force acting on individual particles are required to close the set of equations to solve for the solid and fluid phases. While many drag force models for monodisperse systems have been proposed in the literature, as discussed below, expressions for such force on a particle in a multi-particle system is currently the subject of extensive research work

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4 Discrete Element Modelling of Particulate Media (2) where Pi, U and P are the fluid density, fluid velocity and pressure, respectively, sis the volumetric fraction of the fluid (or voidage ), 't" is the deviatoric stress tensor, S is the fluid- particle inter-phase momentum exchange density and g the acceleration of gravity. The corresponding equations for each particle of the solid phase follow the conventional DEM approach, i.e.: (3) (4) where m, V, I, a and a are the particle mass, volume, moment of inertia, linear and angular acceleration, respectively. The forces considered are gravity, contact forces fc, pressure gradient and drag force fd, in the order of appearance in Equation (3). Note that the last two terms arise from the interaction with the fluid. In the rotational direction only torques arising from contact forces are considered. Interphase coupling is achieved by connecting the momentum exchange density source termS in Equation (2) with the drag force acting on individual particles, i.e.: (5) where the w1 coefficient plays the role of distance weighting function per unit volume. 2.2 Drag force Expressions accounting for the influence of velocity and voidage on the drag force exerted on individual particles have been often derived based on established correlations for the pressure drop across fixed beds of a single material of diameter D. In general terms, the modulus of the dissipative pressure gradient is related to the modulus of the drag force by: (6) Extensive studies in the literature led to a number of common, relatively accurate expressions valid for monodisperse suspensions that cover many orders of magnitude of the Reynolds number and from dense packing to highly dilute systems, like the combination ofErgun 3 and Wen and Yu 5 or DiFelice's formula. 6 In the case of disperse systems or when multiple particulate solids are present simultaneously, the drag force acting on a particle becomes much more difficult to evaluate. This is also related to the fact that experimental accessibility to such datum is very limited. The first theoretical advancements indeed appeared as a result of fully resolved simulations of fluid flow through static arrays of spheres. In particular, van der Hoef et a1., 7 based on lattice-Boltzmann simulations of the flow through random arrays o

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4 مدل‌سازی عنصر گسسته محیط ذرات (2) که در آن Pi، U و P به ترتیب چگالی سیال، سرعت و فشار سیال هستند، یعنی کسر حجمی سیال (یا voidage)، 't' تنش انحرافی است. تانسور، S چگالی تبادل تکانه بین فازی سیال- ذره و g شتاب گرانش است. I، a و a به ترتیب جرم ذرات، حجم، ممان اینرسی، شتاب خطی و زاویه ای هستند. نیروهای در نظر گرفته شده عبارتند از گرانش، نیروهای تماس fc، گرادیان فشار و نیروی پسا fd، به ترتیب شکل ظاهری در رابطه (3). توجه داشته باشید که دو ترم آخر از برهمکنش با سیال ناشی می شود.در جهت چرخش فقط گشتاورهای ناشی از نیروهای تماس در نظر گرفته می شود. جفت بین فازی با اتصال منبع چگالی تبادل مومنتوم termS در معادله (2) با نیروی پسا عمل کننده حاصل می شود. روی ذرات منفرد، به عنوان مثال: (5) که در آن ضریب w1 نقش تابع وزن فاصله در واحد حجم را ایفا می کند. 2.2 نیروی کشش عباراتی که تأثیر سرعت و خلأ بر نیروی پسا اعمال شده بر ذرات منفرد را محاسبه می کند، اغلب بر اساس همبستگی های ثابت شده برای افت فشار در بسترهای ثابت یک ماده واحد با قطر D به دست آمده است. به طور کلی، مدول گرادیان فشار اتلافی با مدول نیروی پسا مرتبط است: (6) مطالعات گسترده در ادبیات منجر به تعدادی عبارات رایج و نسبتا دقیق معتبر برای تعلیق های تک پراکنده شد که مرتبه های بزرگی از عدد رینولدز و از متراکم را پوشش می دهد. بسته بندی به سیستم های بسیار رقیق، مانند ترکیب Ergun 3 و Wen و Yu 5 یا فرمول DiFelice. در مورد سیستم های پراکنده یا زمانی که چندین ذره جامد به طور همزمان وجود دارند، ارزیابی نیروی کششی که بر یک ذره وارد می شود بسیار دشوارتر می شود. این همچنین به این واقعیت مربوط می شود که دسترسی تجربی به چنین داده هایی بسیار محدود است. اولین پیشرفت های نظری در واقع در نتیجه شبیه سازی های کاملاً حل شده از جریان سیال از طریق آرایه های ساکن کره ها ظاهر شد. به طور خاص، van der Hoef et a1., 7 بر اساس شبیه سازی شبکه-بولتزمن جریان از طریق آرایه های تصادفی o

 

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The proceedings of the International Symposium on Discrete Element Modelling of
Particulate Media held at the University of Birmingham on 29-30 March 2012.
Special Publication No. 339
ISBN: 978-1-84973-360-1
A catalogue record for this book is available from the British Library
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Contents Two-Phase Systems FROM SINGLE PARTICLE DRAG FORCE TO SEGREGATION IN FLUIDISED BEDS A. DiRenzo and F. P. DiMaio ENHANCING THE CAP A CITY OF DEM/CFD WITH AN IMMERSED BOUNDARY METHOD C.-Y. Wu andY. Guo EFFECT OF SOLID AND LIQUID HEAT CONDUCTIVITIES ON TWO- PHASE HEAT AND FLUID FLOWS T. Tsutsumi, S. Takeuchi and T. Kajishima 3 10 21 GRAVITATIONAL SEDIMENTATION AND SEPARATION OF PARTICLES 30 IN A LIQUID: A 3D DEM/CFD STUDY L. Qiu and C.-Y. Wu DEM SIMULATION OF MIGRATION PHENOMENA IN SLOW, DENSE 39 SLURRY FLOW WITH BROWNIAN MOTION EFFECTS M.A. Koenders, M. Ibrahim and S.Vahid FORCE EVALUATION FOR BINGHAM FLUIDS USING MULTIPLE- RELAXA TION-TIME LATTICE BOLTZMANN MODEL S. Chen, Q. Sun and F. Jin 46 THE EFFECT OF INITIAL BED HEIGHT ON THE BEHAVIOUR OF A SOIL 51 BED DUE TO PIPE LEAKAGE USING THE COUPLED DEM-LBM TECHNIQUE X. Cui, J. Li, A.H.C. Chan and D. Chapman GRANULAR FLOWS IN FLUID 59 K. Kumar, K. Soga and J.- Y. Delenne Cohesive Systems A STUDY OF THE INFLUENCE OF SURF ACE ENERGY ON THE MECHANICAL PROPERTIES OF LUNAR SOIL USING DEM C. Modenese, S. Utili and G.T. Houlsby MODELLING OF THE CONTACT BEHAVIOUR BETWEEN FINE ADHESIVE PARTICLES WITH VISCOUS DAMPING K. Mader and J. Tomas 69 76 viii Contents REBOUND OF A PARTICLE FROM A SOLID SURFACE WITH A VISCOUS 86 OR NONLINEAR VISCOELASTIC LIQUID FILM IN THE CONTACT ZONE J. Bowen, D. Cheneler, J.W. Andrews, C-Y. Wu, M.C.L. Ward and M.J. Adams EFFECT OF THE PENDULAR STATE ON THE COLLAPSE OF GRANULAR 95 COLUMNS R. Artoni, F. Gabrieli, A. Santomaso and S. Cola INVESTIGATION OF DYNAMIC BEHAVIOUR OF A PARTICLE-LOADED 103 SINGLE FIBRE USING DISCRETE ELEMENT METHODS M. Yang, S.Q. Li, G. Liu and J. S. Marshall MODELLING OF THE FILTRATION BEHAVIOUR USING COUPLED DEM 113 ANDCFD S. Stein and J. Tomas Granular Flows DEM MODELLING OF SUBSIDENCE OF A SOLID PARTICLE IN GRANULAR MEDIA C.H. Goey, C. Pei and C.-Y. Wu NUMERICAL SIMULATION Of THE COLLAPSE OF GRANULAR COLUMNS USING DEM T. Zhao, G.T. Houlsby and S. Utili 123 133 DEM MODELLING OF THE DIGGING PROCESS OF GRAVEL: INFLUENCE 141 OF PARTICLE ROUNDNESS S. Miyai, T. Katsuo, T. Tsuji, T. Takayama and T. Tanaka DEM MODELLING OF HIGH SPEED DIE FILLING PROCESSES C.-Y. Wu, F. Ogbuagu and C. Pei 149 DEM ANALYSIS OF LOADS ON DISC INSERTS IMMERSED IN GRAIN 158 DURING SILO FILLING AND DISCHARGE R. Kobylka and M. Molenda THREE DIMENSIONAL DEM/CFD ANALYSIS OF SEGREGATION DURING SILO FILLING WITH BINARY MIXTURES OF DIFFERENT PARTICLE SIZES C.-Y. Wu andY. Guo 165 MODELING PACKING OF SPHERICAL FUEL ELEMENTS IN PEBBLE BED 175 REACTORS USING DEM H. Suikkanen, J. Ritvanen, P. Jalali and R. Kyrki-Rajamaki Contents ix Quasi-Static Deformation A NUMERICAL INVESTIGATION OF QUASI-STATIC CONDITIONS FOR 187 GRANULAR MEDIA C. Modenese, S. Utili and G.T. Houlsby EXPLORING THE CONTROLLING PARAMETERS AFFECTING SPECIMENS GENERA TED IN A PLUVIATOR USING DEM L. Cui DEM TRIAXIAL TESTS OF A SEABED SAND G. Macaro and S. Utili THE STEADY STATE SOLUTION OF GRANULAR SOLID HYDRODYNAMICS FOR TRIAXIAL COMPRESSIONS S. Song, Q. Sun and F. Jin 196 203 212 3D DEM SIMULATIONS OF UNDRAINED TRIAXIAL BEHAVIOUR WITH 219 PRESHEARING HISTORY G. Gong and A.H.C. Chan STRONG FORCE NETWORK OF GRANULAR MIXTURES UNDER ONE- 227 DIMENSIONAL COMPRESSION N.H. Minh and Y.P. Cheng VERIFICATION OF THE DOUBLE SLIP AND ROTATION RATE MODEL 236 FOR ELLIPTICAL GRANULAR FLOW USING THE DISTINCT ELEMENT METHOD L.Q. Li, M.J. Jiang and Z.F. Sherr MICRO MECHANICS OF SEISMIC WAVE PROPAGATION IN GRANULAR 245 MATERIALS J. O'Donovan, C. O'Sullivan and G. Marketos MICRO MECHANICAL STUDY ON SHEAR WAVE VELOCITY OF GRANULAR MATERIALS USING DISCRETE ELEMENT METHODS X. Xu, D. Ling, Y. P. Cheng andY. Chen 255 MECHANICAL BEHAVIOUR OF METHANE HYDRATE SOIL SEDIMENTS 264 USING DISCRETE ELEMENT METHOD: PORE-FILLING HYDRATE DISTRIBUTION Y. Yu, Y. P. Cheng and K. Soga ON THE EFFECT OF SOIL MODIFICATION WITH LIME USING GRADING 271 ENTROPY E. Irnre, J. Szendefy, J. Lorincz, P.Q. Trang and Vijay P. Singh SUBJECT INDEX 280

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