Theore oretic tical al backgr groun und d and applicati ations ns of DEM Simon on Lo
Conten ents ts DEM equations ions DEM inter erac action ion models ls Examples es – Particle transport in horizontal pipes – Blast furnace – Mixing drum – Conveyer belt cases – Particle transport in gas-liquid flow in pipes Comparis ison on with EDEM Conclus lusio ions ns
DEM equat ations ions Linea ear moment ntum um of particle: le: d v i m F F F Drag Contact Other i dt Angular ar moment entum um: k d i I M i ij ij dt j 1 M F ij roll Contact i = rolling torque e opposes es particle e rot otation ion M ij = rolling frictio ion n coeffic icie ient nt. roll
DEM Interac raction ion Models ls What are DEM Interac actio ion n models ls? – DEM interaction models define the behaviour between particle-particle and particle-wall interactions – Interaction models are used to define different forms of behaviour between colliding DEM particles such as contact forces, heat conduction and bonding The follow owing ing slides es outlin ine e the followi owing ng DEM interac action ion models ls available le in STAR-CCM+: Hertz-Mindlin Contact Force Model – Walton-Braun Contact Force Model – Conduction Heat Transfer Model – Parallel Bonds Model – 4
DEM Interac raction ion – Hertz Mindlin lin Contac act This is a no-slip lip contac act model l used for modeli ling ng contac act betwee een n particles les The Hertz-Min Mindlin lin contact model l is a variant of the non-lin inear ear spring- dashpot contact model l based on the Hertz-Mind indlin in contac act theory The forces betwee een two wo particle les, A and B, are defined ed by the follow owing ing equations ons: F F F contact n t The normal and tangent ential al force, F n and F t , , are defined ed as follows ows: K d N v if K d K d C t t t t t t n n fs F K d N v n n n n n F K d C d t t t fs t d t where – K n and K t is the spring stiffness (normal and tangential) – d n and d t are the particle overlaps in the normal and tangential directions – N n and N t are the damping (normal and tangential) – v n and v t are the normal and tangential particle velocity 5 – C fs is the static friction coefficient
DEM Interac raction ion – Walton n Braun Contac act This is a plastic ic-elas lastic ic contact model l that is useful ul in situat uatio ions ns where the collis ision ion betwe ween en two wo particle les includes es plastic ic deformat ation. ion. This is typical al for mater erials ials where the collision ion leads to mater erial ial deformat ation ion and the impact energy is dissipat ated ed during g the collision. ion. – The model is characterized by the following equations: – When the contact is loading: d F n K n K 1 . 6 RY Y E YieldStres sFraction 1 1 0 0 When contact is unloading: – 1 K d d d d K ( 1 E ) F K ( ) n 2 1 deformatio n max f n 2 deformatio n E f where • E is the material Young’s Modulus • E f is a user-controllable energy fraction defining the amount of energy recovered during unloading • YieldStressFraction is a user-controllable model property defining the onset of plastic deformation • d is the contact model overlap • d max is the max overlap reached during loading 6 • n is the contact normal vector
DEM Interac raction ion – Partic icle le Bonding ng Parallel el particle e bonds s is a model el that introd oduces es attra ractive e inter er-particle e forc rces es to the particle e syst stem em. The bonded ed particle e model el uses s the concep ept of a massl sless ess bar connec ecting a pair of bonded ded articles. es. The bar can transm smit forc rce and torqu rque e between en particles es and it is also subject ect to cracking g under er load The e parallel el bond forc rces es are represen resented ed in the follow owing gove overn rning equ quations ons: Force and torque on a particle due to parallel bonds is: – F F n F t M M n M t i n i s i i n i s i where, • F n and M n denote the normal components of forces and torques with respect to the contact plane • F s and M s denote the shear components of forces and torques with respect to the contact plane 7
DEM Interac raction ion – Conduction ion Heat Trans nsfer er Two wo particles es are assum umed ed to exc exchang nge e heat through conduc uction ion when they ey are physical ally ly in in contac act The heat conduction on between en two wo contac acting ing particle les takes place via the followin wing mechan anis isms: Particle-to-Particle Direct Heat Transfer through Contact Area Radius – Q Q K A T T pp , ij pp , ij eff c j i K K 2 A r i j K c c eff K K i j where, • K i and K j are the thermal conductivities of contacting particles I and J, respectively • r c is the contact area radius • T i and T j are the temperatures of contacting particles I and J, respectively 8
Parti ticle le transpor ort t in pipe - Marcus experim imen ent
Non-spheric herical al partic icle le flow ow in pipe - Vasque uez experime iment nt Elli lipsoid soidal al partic icles les with an effectiv ive e diamet eter er of 4mm. Shape e defined ned by method od of bonded ded spheres es. Sphere eres overlap ap each ot other r and relat ativ ive e positio ions ns remain in fix at all time. Drag ag force by Haider er and Levens nspiel iel.
Validation Case – Blast furnace Case Description Lab experiments to validate DEM for solid descent in a blast furnace. Cold Model, mono-sized particles. Raceway modeled by creating a space in front of tuyere(s). Ref : Zhou et al, 2005, ISIJ, vol. 45, no. 12, pp 1828 – 1837.
Validation Case – Blast furnace Particle filling process
Validation Case – Blast furnace
Examples les
Comp mpet etit itiv ive e analysis sis – basic charac acteristi eristics STAR AR-CCM+ CCM+ EDEM EM – Distributed memory (MPI) – Shared memory (OpenMP) • Domain decomposition • Loop parallelism • Cluster friendly • Single workstation – 2d, 3d – 3d – Volumetric representation – Surface representation • + Allows to solve coupled • + Almost no surface preparation problems • - Makes coupling difficult • - Extra work required for – Single purpose solver code meshing – Rich, multi physics framework
Compet etit itiv ive e analysis is STAR-CCM+ EDEM Spherical particles x x Rigid composites x x Breakable flexible clumps x Custom coding Hertz Mindlin x x Hysteretic model x x Parallel bonds x x Cohesion x x Linear spring Can use hysteretic model x JKR Can use cohesion model x Electrostatics 2 way coupled Limited Particle/flow interaction 2 way coupled No longer supported
Compet etit itiv ive e analysis is STAR-CCM+ EDEM Heat transfer particle-particle, Particle-particle particle-flow, particle-particle radiation Interfaces General Parallel planes Particle shape editor x x Moving geometry Rigid body motion Rigid body motion Easy to setup – no meshing required Transient post processing Track files Full solution replay
Compet etit itiv ive e analysis is Concl clusi sion on – Competitive in terms of implemented features – Advantage for complex physics • Reuse of feature implemented for general Lagrangian framework • Ability to implement more complex physics due to the background FV discretization – Further improvements • Simplify the workflow for complex moving geometries • Transient post processing and solution history
Future ure develop opmen ent Physic ics – Liquid bridges, capillary forces, free surface-particle interaction in VOF – Mass transfer, drying, coating – Smooth simulation physics decomposition DEM, FEA, EMP – Surface only DEM Perform ormance nce and scalab abilit ility – Improved cache coherency for single workstation runs – Dynamic particle centric load balancing GUI I and usabilit lity – Transient post processing and solution snapshots – CAD import and interpolation of particle shape by sphere trees
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