Theore oretic tical al backgr groun und d and applicati ations - - PowerPoint PPT Presentation

Theore

• retic

tical al backgr groun und d and applicati ations ns

• f DEM

Simon

• n 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

• n with EDEM

Conclus lusio ions ns

DEM equat ations ions

Linea ear moment ntum um of particle: le: Angular ar moment entum um: = rolling torque e opposes es particle e rot

• tation

ion = rolling frictio ion n coeffic icie ient nt.

Other Contact Drag i i

F F F dt v d m   

 





 

k j ij ij i i

M dt d I

1

   

i Contact roll ij

F M       

roll



ij

M 

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

• wing

ing slides es outlin ine e the followi

• wing

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

• wing

ing equations

• ns:

The normal and tangent ential al force, Fn and Ft , , are defined ed as follows

• ws:

where

– Kn and Kt is the spring stiffness (normal and tangential) – dn and dt are the particle overlaps in the normal and tangential directions – Nn and Nt are the damping (normal and tangential) – vn and vt are the normal and tangential particle velocity – Cfs is the static friction coefficient

5

t n contact

F F F  

n n n n n

v N d K F                 

t t fs t t fs n n t t t t t t t

d d C d K C d K d K if v N d K F

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:

–

When contact is unloading: where

• E is the material Young’s Modulus
• Ef 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
• dmax is the max overlap reached during loading
• n is the contact normal vector

6 n K Fn d

1

 

1

6 . 1 RY K  

n K F

n deformatio n

) (

2

d d   

1 2

1 K E K

f



sFraction YieldStres E Y  

) 1 (

max f n deformatio

E  d d

DEM Interac raction ion – Partic icle le Bonding ng

Parallel el particle e bonds s is a model el that introd

• duces

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

• wing gove
• vern

rning equ quations

• ns:

–

Force and torque on a particle due to parallel bonds is:

where,

• Fn and Mn denote the normal components of forces and torques with respect to the

contact plane

• Fs and Ms denote the shear components of forces and torques with respect to the

contact plane

7

i s i n i

t F n F F  

i s i n i

t M n M M  

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

• n 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

where,

• Ki and Kj are the thermal conductivities of contacting particles I and J, respectively
• rc is the contact area radius
• Ti and Tj are the temperatures of contacting particles I and J, respectively

8

 

i j c eff ij pp ij pp

T T A K Q Q    

, , 2 c c

r A  

j i j i eff

K K K K K  

Parti ticle le transpor

• rt

t in pipe - Marcus experim imen ent

Non-spheric herical al partic icle le flow

• w 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

• d of

bonded ded spheres es. Sphere eres overlap ap each ot

• ther

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

STAR AR-CCM+ CCM+

– Distributed memory (MPI)

• Domain decomposition
• Cluster friendly

– 2d, 3d – Volumetric representation

• + Allows to solve coupled

problems

• - Extra work required for

meshing

– Rich, multi physics framework

EDEM EM

– Shared memory (OpenMP)

• Loop parallelism
• Single workstation

– 3d – Surface representation

• + Almost no surface preparation
• - Makes coupling difficult

– Single purpose solver code Comp mpet etit itiv ive e analysis sis – basic charac acteristi eristics

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-flow, particle-particle radiation Particle-particle 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

• n

– 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

Compet etit itiv ive e analysis is

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

• rmance

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

Future ure develop

• pmen

ent