Theoretical background and applications of DEM. Simon Lo

Transcription

1 Theoretcal backgroud ad applcatos of DEM Smo Lo

2 Cotets DEM equatos DEM teracto models Examples Partcle trasport horzotal ppes Blast furace Mxg drum Coveyer belt cases Partcle trasport gas-lqud flow ppes Comparso wth EDEM Coclusos

3 DEM equatos Lear mometum of partcle: m dv dt F Drag F Cotact F Other Agular mometum: I M d dt j k j M j j1 roll F Cotact M j roll = rollg torque opposes partcle rotato = rollg frcto coeffcet.

4 DEM Iteracto Models What are DEM Iteracto models? DEM teracto models defe the behavour betwee partcle-partcle ad partcle-wall teractos Iteracto models are used to defe dfferet forms of behavour betwee colldg DEM partcles such as cotact forces, heat coducto ad bodg The followg sldes outle the followg DEM teracto models avalable STAR-CCM+: Hertz-Mdl Cotact Force Model Walto-Brau Cotact Force Model Coducto Heat Trasfer Model Parallel Bods Model 4

5 DEM Iteracto Hertz Mdl Cotact Ths s a o-slp cotact model used for modelg cotact betwee partcles The Hertz-Mdl cotact model s a varat of the o-lear sprgdashpot cotact model based o the Hertz-Mdl cotact theory The forces betwee two partcles, A ad B, are defed by the followg equatos: F The ormal ad tagetal force, F ad F t, are defed as follows: where cotact F F K d F t N v Ktdt Ntvt Ft Ktdt C fsdt dt K ad K t s the sprg stffess (ormal ad tagetal) d ad d t are the partcle overlaps the ormal ad tagetal drectos N ad N t are the dampg (ormal ad tagetal) v ad v t are the ormal ad tagetal partcle velocty 5 C fs s the statc frcto coeffcet f K d t t K d C fs

6 DEM Iteracto Walto Brau Cotact Ths s a plastc-elastc cotact model that s useful stuatos where the collso betwee two partcles cludes plastc deformato. Ths s typcal for materals where the collso leads to materal deformato ad the mpact eergy s dsspated durg the collso. The model s characterzed by the followg equatos: Whe the cotact s loadg: F Whe cotact s uloadg: F where K 1 d K1 1. 6RY0 1 K2( d ddeformato K2 K 1 E ) E s the materal Youg s Modulus f E f s a user-cotrollable eergy fracto defg the amout of eergy recovered durg uloadg YeldStressFracto s a user-cotrollable model property defg the oset of plastc deformato d s the cotact model overlap d max s the max overlap reached durg loadg 6 s the cotact ormal vector Y 0 d E YeldStressFracto deformato d max (1 E f )

7 DEM Iteracto Partcle Bodg Parallel partcle bods s a model that troduces attractve ter-partcle forces to the partcle system. The boded partcle model uses the cocept of a massless bar coectg a par of boded artcles. The bar ca trasmt force ad torque betwee partcles ad t s also subject to crackg uder load The parallel bod forces are represeted the followg goverg equatos: Force ad torque o a partcle due to parallel bods s: F where, F F t s M M M s t F ad M deote the ormal compoets of forces ad torques wth respect to the cotact plae F s ad M s deote the shear compoets of forces ad torques wth respect to the cotact plae 7

8 DEM Iteracto Coducto Heat Trasfer Two partcles are assumed to exchage heat through coducto whe they are physcally cotact The heat coducto betwee two cotactg partcles takes place va the followg mechasms: Partcle-to-Partcle Drect Heat Trasfer through Cotact Area Radus Q pp, j Qpp, j K eff A c T j T A 2 c r c K eff K K K j K j where, K ad K j are the thermal coductvtes of cotactg partcles I ad J, respectvely r c s the cotact area radus T ad T j are the temperatures of cotactg partcles I ad J, respectvely 8

9 Partcle trasport ppe - Marcus expermet

10 No-sphercal partcle flow ppe - Vasquez expermet Ellpsodal partcles wth a effectve dameter of 4mm. Shape defed by method of boded spheres. Spheres overlap each other ad relatve postos rema fx at all tme. Drag force by Hader ad Levespel.

11 Valdato Case Blast furace Case Descrpto Lab expermets to valdate DEM for sold descet a blast furace. Cold Model, moo-szed partcles. Raceway modeled by creatg a space frot of tuyere(s). Ref : Zhou et al, 2005, ISIJ, vol. 45, o. 12, pp

12 Valdato Case Blast furace Partcle fllg process

13 Valdato Case Blast furace

14 Examples

15 Compettve aalyss basc characterstcs STAR-CCM+ Dstrbuted memory (MPI) Doma decomposto Cluster fredly 2d, 3d Volumetrc represetato + Allows to solve coupled problems - Extra work requred for meshg Rch, mult physcs framework EDEM Shared memory (OpeMP) Loop parallelsm Sgle workstato 3d Surface represetato + Almost o surface preparato - Makes couplg dffcult Sgle purpose solver code

16 Compettve aalyss STAR-CCM+ EDEM Sphercal partcles x x Rgd compostes x x Breakable flexble clumps x Custom codg Hertz Mdl x x Hysteretc model x x Parallel bods x x Coheso x x Lear sprg Ca use hysteretc model x JKR Ca use coheso model x Electrostatcs 2 way coupled Lmted Partcle/flow teracto 2 way coupled No loger supported

17 Compettve aalyss Heat trasfer STAR-CCM+ partcle-partcle, partcle-flow, partcle-partcle radato EDEM Partcle-partcle Iterfaces Geeral Parallel plaes Partcle shape edtor x x Movg geometry Rgd body moto Rgd body moto Easy to setup o meshg requred Traset post processg Track fles Full soluto replay

18 Compettve aalyss Cocluso Compettve terms of mplemeted features Advatage for complex physcs Reuse of feature mplemeted for geeral Lagraga framework Ablty to mplemet more complex physcs due to the backgroud FV dscretzato Further mprovemets Smplfy the workflow for complex movg geometres Traset post processg ad soluto hstory

19 Future developmet Physcs Lqud brdges, capllary forces, free surface-partcle teracto VOF Mass trasfer, dryg, coatg Smooth smulato physcs decomposto DEM, FEA, EMP Surface oly DEM Performace ad scalablty Improved cache coherecy for sgle workstato rus Dyamc partcle cetrc load balacg GUI ad usablty Traset post processg ad soluto sapshots CAD mport ad terpolato of partcle shape by sphere trees