040603 Four topics for further development of dem to deal with industrial fluidization issues, ICMF plenary2004
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040603 Four topics for further development of dem to deal with industrial fluidization issues, ICMF plenary2004

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This summarizes the outcome of my DEM research in 2004, presented at Yokohama, as a plenary lecture of ICMF (Intl Conf Multi-phase Flow).

This summarizes the outcome of my DEM research in 2004, presented at Yokohama, as a plenary lecture of ICMF (Intl Conf Multi-phase Flow).

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040603 Four topics for further development of dem to deal with industrial fluidization issues, ICMF plenary2004 040603 Four topics for further development of dem to deal with industrial fluidization issues, ICMF plenary2004 Presentation Transcript

  • Four Topics for FurtherDevelopment of DEM toDeal with IndustrialFluidization IssuesMasayuki Horio and Wenbin ZhangDepartment of Chemical Engineering,Tokyo University of Agriculture andTechnology,Koganei Tokyo, 184-8588 Japan,masa@cc.tuat.ac.jp
  • Come & Visit Tokyo Univ. A&Tat Koganei (25min from Shinjuku)
  • 渦Chemical Engineers in ICMF
  • From Burton to Fluid Cat. Cracking Chemical Engineers’ Unforgettable Memory The FCC Development (1940-50)Capacity in world total [%]
  • product Competition and Evolution product product of Fluid Catalytic Plants in 1940-50 product steam steam air kerocenekerocene & steam air& steam product kerocene air & steam FCC Plant development air in Catalytic Cracking ofkerocene& steam air steam Kerocene(1940-50)
  • Post cloud mdern Era: Natural Science and Engineering Science The presence of column wall makes research much easier hail artificial plant volcanic plateauAIChE Fluor Daniel Lectureship AwardLecture (2001)
  • My background-1974 Fixed/Moving Bed Reactors and iron-making Processes1974- Fluidization Engineering 75-99 Pressurized Fluidized Bed Combustion Jets, Turbulent Transport in Freeboard 82-89 Scaling Law of Bubbling Fluidized Bed 89-92 Scaling Law of Clustering Suspensions 93- DEM Simulation Waste Management, Material Processes1997- Sustainability and Survival Issues Biomass Utilization, Appropriate Technology
  • When Professor Tsuji et al. 1993 proposed anexcellent idea of applying the concept ofdiscrete/distinct element method of Cundall et al.(1979) to fluidized beds borrowing the fluid phaseformulation from the two phase model,I (Horio) almost immediately decided to join in thesimulation business of fluidized beds fromchemical engineers view points.This was because with his approach the realindustrial issues, such as agglomeration, gassolid reactions and/or heat transfer, can bedirectly incorporated into the model without thetedious derivation of stochastic mechanics,which is not only indirect but also sometimesimpossible from analytical reasons.
  • DEM, the last 10 yearsDEM: Discrete Element Method Fluid phase: local averaging Particles: semi-rigorous treatment User friendly compared to Two Fluid Model & Direct Navier-Stokes Simulation•A new pressure/tool to reconstruct particle reaction engineering based on individual particle behavior•Potential for more realistic problem definition/ solutionOur code development: SAFIRE Simulation of Agglomerating Fluidization for Industrial Reaction Engineering
  • Normal and tangential component of Fcollision and Fwall Fn = k nD x n - h dx n n dt Ft = m Fn x t Ft > m Fn x t Ft = k tD x - h dx t  m Fn t t Ft dt h = 2g g = ( ln e ) 2 km ( ln e ) 2 + p 2 SAFIRE (Horio et al.,1998~) Rupture joint h c Attractive force Fc Surface/bridge force (Non-linear spring) kn Normal dumping h n w/wo Normal Lubrication Normal elasticity No tension joint Tangential dumping h t Tangential elasticity k tSAFIRE is an extended Tsuji-Tanaka modeldeveloped by TUAT Horio group Friction slider m w/wo Tangential Lubrication Soft Sphere Model with Cohesive Interactions
  • COMBUSTION Spray Agglomerating AGGLOMERATION Granulation/Coating Fluidization FB w/ Immersed Ash Tubes : Melting FB of Particles w/Pressure Effect I-H Solid Bridging van der Waals Rong-Horio 1998 Tangential 2000 FB w/ Interaction Kuwagi-Horio Lubrication Immersed Iwadate-Horio Effect 1999Coal/Waste Tubes 1998 Kuwagi-HorioCombustion Parmanently Rong-Horio 2000 in FBC Wet FB 1999 Mikami,Kamiya, Fluidized Bed DEM Horio Started from 1998 Particle-Particle Dry-Noncohesive Bed Single Char Heat Transfer Tsuji et al. 1993 Combustion Rong-Horio Natural Phenomena in FBC 1999 Rong-Horio OTHER 1999 Lubrication Force Effect SAFIRE Olefine Scaling LawAchievements Polymerization Noda-Horio for DEM Scaling Law for DEM PP, PE Structure of 2002 Computation Computation Kaneko et al. Emulsion Phase Kajikawa-Horio 2000~ Kuwagi-Horio 1999 2002~ Kajikawa-Horio Catalytic Reactions 2001CHEMICAL REACTIONS FUNDAMENTAL LARGE SCALE SIMULATION
  • AGGLOMERATION Industrial Issues & DEM■ Agglomerating Fluidization by Liquid Bridging by van der Waals Interaction by Solid Bridging through surface diffusion through viscous sintering by solidified liquid bridge Coulomb Interaction■ Size Enlargement by Spray Granulation (Spraying, Bridging, Drying) by Binderless Granulation (PSG)■ Sinter/Clinker Formation in Combustors / Incinerators (Ash melting) in Polyolefine Reactors (Plastic melting) in Fluidized Bed of Particles (Sintering of Fe, Si, etc.) in Fluidized Bed CVD (Fines deposition and Sintering)
  • CHEMICAL REACTORS Industrial Issues & DEM Heat and Mass Transfer gas-particle particle-particle Heterogeneous Reactions Homogeneous Reactions Polymerization Catalytic Cracking (with a big gas volume increase) Partial Combustion (high velocity jet)COMBUSTION / INCINERATION Boiler Tube Immersion Effect Particle-to-Particle Heat Transfer Char Combustion Volatile Combustion (Gas Phase mixing / Reaction) Combustor Simulation
  • 10m m Sintering of 2xneck 2xneck steel particles neck diameter, 2 neck diameter in Fluidized Bed Reduction (a) 923K (b) 1123KSteel shot :dp=200m m, H2, 3600s SEM images of necks 30 Calculated from after 3600s contact 25 surface diffusion model 20 Neck diameter 2x 15 10 d p=200 m m d p=20 m m 5 0 700 800 900 1000 1100 1200 1300 Temperature [K] Neck diameter determined from SEM images after heat treatment in H2 atmosphere Solid Bridging Particles (Mikami et al , 1996)
  • Model for Solid Bridging Particles1. Spring constant: Hooke type (k=800N/m) Duration of collision: Hertz type2. Neck growth: Kuczynski’s surface diffusion model 1/ 7 4 56gd 3 x neck = DS rg t kBT Ds = D0,s exp (-Es /RT) -2 5 D0,s =5.2x10 m/s, E =2.21x10 J/mol (T>1180K)3. Neck breakage Fnc = s neck  Aneck Ftc = t neck  Aneck Kuwagi-Horio Kuwagi-Horio 1999
  • Kuwagi-Horio Steel shot Cross section 6mm 200mm rg = 10mm neckSurface Roughness and Multi-point Contact Kuwagi-Horio 1999
  • 1273K, u 0 = 0.26 m/s, Dt=0.313s Kuwagi-Horiot= 0.438s 0.750s 1.06s 1.38s 1.69s 2.00s 2.31s 2.63s 2.94s 3.25s Snapshots of Solid Bridging Particles without Surface Roughness Kuwagi-Horio 1999
  • dp =200mm, T=1273K, u0 =0.26m/s Kuwag i-Horio(a) Smooth surface (b) 3 micro-contact points (c) 9 micro-contact points (Case 1) (Case 2) (Case 3)Agglomerates (or “dead "dead zones") grown on the wallthe1.21 s). (t = 1.21 s). Fig.7 Agglomerates (or zones”) grown on (t = wall Kuwagi-Horio 2000
  • Intermediate condition Weakest sintering Strongest sintering condition condition(a) Smooth surface (b) 3 micro-contact (c) 9 micro-contact points points Kuwagi-Horio d p =200mm, T=1273K, u 0=0.26m/s Agglomerates Sampled at t = 1.21s Kuwagi-Horio 1999
  • Poly-Olefine Reactor Simulation, Kaneko et al. (1999) fluid cell uyEnergy balanceGas phase : ( ) ∂εu T ) ∂ Tg ε ( i g 1 particle + = Q ∂t ∂i x ρcp,g g g uxParticle : vy ε Tg dTp Vpcp,pρp dt H ( = Rp (- Δ r ) - hp Tp - Tg S ) Qg vx Tpn 6(1- ε ) Qg = dp ( hp Tp - Tg ) external gas film E heat transfer hpn Rp = k exp ( ) w cPr RTp coefficient 1 (different for each particle) 1 Nu = 2.0 + 0.6 Pr Rep 3 2 (Ranz-Marshall equation) Nu = hpdp / kg Pr = cp,gμ / kg g Rep = u - v ρdp / μ g g
  • Particle circulation Kaneko et al. 1999(artificially generated by feeding gas nonuniformly from distributor nozzles) t=9.1 sec t=6.0 sec t=8.2 sec 393 (120℃) 343 293 T [K] (20℃) 2.5umf 2.5umf 2umf 2umf 3umf 3umf 3umf 9.3umf Ethylene polymerization 15.7umf Number of particles=14000 Gas inlet temp.=293 K Hot spot u0=3 umf Tokyo University of Agriculture & Technology Idemitsu Petrochemical Co.,Ltd.
  • Uniform gas feeding Nonuniform gas feeding particle temp. particle velocity particle temp. particle velocity vector vector t=9.1 sec t=8.2 sec : Upward motion 2umf 2umf 3umf 3umf 3umf : Downward motion 15.7umf Stationary circulation Stationary solid revolution helps Petrochemical Co.,Ltd. Tokyo University of Agriculture & Technology Idemitsu the formation of hot spots.
  • A Rough Evaluation of Heat Transfer Between Particlesradiation A B 0.4 nm contact point heat transfer A Bconvection particle-thinned film-particle Rong-Horio 1999 heat transfer when l AB < 2r + d : particle-particle heat conduction
  • Four Topics for Further Development of DEM1. PSD2. Large Scale Computation via Similar Particle Assemblage Model3. Surface Characterization and Reactor Simulation4. Lubrication Force and Effective Restitution Coefficient
  • PSD IssueDerivation of CDcorresponding to ErgunCorrelation and A Case StudyMaster Thesisby Nobuyuki Tagami
  • 1. PSD What We need for moving from Uniform Particle Systems to Non-uniform Ones ○ 3D Computation ○ Contact Model with Particle Size Effect Fookean to Herzean Spring ○ Fluid-Particle Interactions Today’s topic 1) not from Ergun (1952) Correlation 2) not indifferent to particle arrangement
  • 1. PSD Apparent Drag Coefficient that corresponds to Ergun Correlation (1) Bed Pressure Drop Correlation (Ergun(1952)) ΔP * /DL = ΔP/ΔL - ρ f g = (1 - ε ) 150 (1 - ε )μ f ( )  + 1.75ρ f u - v  u - v d p : Particle diameter  ε : Void fraction d p   d p   ρ f : Fluid density (2) Equation of motion for fluid (1D) u : Fluid velocity ΔP ( ) v : Particle velocity -ε - nFpf + ερ f g = 0 n = (1 - ε )/ πd p 3 /6 ΔL (3) Drag Coeff. 8 F pf → Apparent Drag Coeff. CD  200(1 - ε )μ f p d p ρf u - v 2 2 C D, Ergun = + 2.33 d pρ f ε u - v
  • 1. PSD Extension of CD,Ergun 200(1 - ε )μ f C D,Ergun = + 2.33 d pρ f ε u - v 200(1 - ε )μ f C D,Ergun = + 2.33 d pρ f ε u - v
  • 1. PSD The Sum of Drag Force Consistent with Ergun Correlation ? Error was within the Accuracy ofdp1/dp2 Number of Ergun Correlation ±25%. F i,C D,Ergun[mm/mm] particles Binary System Fi,Ergun1.00 300001.50 / 4444 /0.750 35556 1.25 ρ p = 2650kg/m 3 1.00 ρ f = 1.204kg/m 3 μ f = 18 μ Pa s 0.75 u 0 = 0.811  1.122m/s (t  0.5s) = 1.122m/s (t  0.5s)
  • 1. PSD PSD Effect: A Case Study Run1 Run2 Run3 Diameter [mm] 3.00 4.50/3.00/2.25 4.50/2.25 Number [#] 30000 2963/10000/23703 4444/35556 Vol. Fraction 1 0.333/0.333/0.333 0.500/0.500 Surface to Volume Mean Diameter: dsv=Σ(Ndp3)/Σ(Ndp2) = 3.00 mm Total solid volume = 4.24×10-4m3, Total solid surface area = 8.48×10-1m2Young’s modulus: 80GPa, Poisson ratio: 0.3, friction coefficient: 0.3(Glass beads) Contact Force Model Normal:Hertz’ Model Tangential: ‘no-slip’ Solution of Mindlin, and Deresiewicz (1953)
  • Comparison of the three cases Run 1 Run 2 Run 3 3.00mm 4.50 / 3.00 / 2.25 4.50 / 2.25 mm mmu0 = 1.438→2.938m/s (t<1sec), u0 = 2.938m/s (t≧1sec)
  • 1. PSD Run3 Large particles become more mobile receiving forces from smaller ones
  • 2. SPA Fluidization XI, May 9-14, 2004, Ischia (Naples), Italy The Similar Particle Assembly (SPA) Model, An Approach to Large-Scale Discrete Element (DEM) Simulation Kuwagi K.a, Takeda H.b and Horio M.c,* aDept. of Mech. Eng., Okayama University of Science, Okayama 700-0005, Japan bRflow Co., Ltd., Soka, Saitama 340-0015, JapancDept. of Chem. Eng., Tokyo University of Agri. and Technol., Koganei, Tokyo 184-8588, Japan
  • Development of Computer Pormance 1.0E+16 Fastest computer models Nishikawa et al. (1995) Performance [MFLOPS] Seki (2000) 1.0E+13 Oyanagi(2002) 15 to 20 years Single processor for PC 1.0E+10 Moores Law 1.0E+7 1.0E+4 1.0E+1 1,940 1,960 1,980 2,000 2,020 Year
  • 2. SPA How to deal with billions of particles? TFM (Two-fluid model) DSMC (Direct Simulation Monte Carlo) Difficult to deal with realistic particle-particle and particle-fluid interactions including cohesiveness DEM (Discrete Element Method) One million or less particles with PC in a practical computation time Hybrid model of DEM and TFM (Takeda & Horio, 2001) Similarity condition for particle motion (Kazari et al., 1995) Imaginary sphere model (Sakano et al., 2000)
  • 2. SPA Similar Particle Assembly (SPA) ModelAssumptions(0. Particles are spherical)1. A bed consists of particles of different species having different properties, i.e. particle size, density and chemical composition, and it has some local structure of their assembly.2. Of each group (species) N particles are supposed to be represented by one particle at the center of them. This center particle is called a representative particle for the group.3. The representative particles for different groups can conserve the local particle assembly similar.
  • m times larger system(a) (b) of the same particles as the smaller bed A particle Represented volume for N particles Similar structure (c) + (d) + + + + i +x + + x+Dx i’ x x+mDx original system m times larger system Particle Coordination Scaling
  • 2. SPAPreparation(1) All particles are numbered: i=1~NT.(2) Subspace: ( Gk  d p ,  p )(3) Group number of particles: (( ) ki  k d pi ,  pi  Gk )(4) Equation of motion for particle i:  p 3  dv i p 3   pi  d pi  = Ffi +  Fpij +  pi  d pi g 6  dt j i 6  Ffi: particle-fluid interaction force Fpij: particle-particle interaction force
  • 2. SPA Governing Equations Equation of motion for original particle:  p 3  dv i p 3   pi  d pi  = Ffi +  Fpij +  pi  d pi g 6  dt j i 6  Equation of motion for m-times larger volume:  p 3  dv i p 3   pi  d pi  = Ffi +  F pi j +  pi  d pi  g * * 6  dt j  i 6  where d pi = md pi  p 3  dv i p 3  m  pi  d pi  3 = Ffi +  F pi j + m  pi  d pi g * * 3 6  dt j  i 6    If F +* fi F * pi j = m  Ffi +  F pij 3    , v i = v i j  i  j i    (1 -  )2 m f (u - v)  f (u - v) u - v   FPi = 150 + 1.75(1 - )  Ncell    2 d pi d pi   p Fpi =  CD f  2 (u - v l ) u - v l d pi 2 8
  • Computation Conditions for Case 1Particles Geldart Group: DParticle diameter: dp [mm ] (a) 1.0 (b) 3.0 (c) 6.0Particle density: p [ kg/m3 ] 2650Number of Particles (a) 270,000 (b) 30,000 (c) 7,500Restitution coefficient 0.9Friction coefficient 0.3Spring constant: k [ N/m ] 800 (Dt=2.58x10-5s)BedColumn size 0.5×1.5mDistributor Porous mediumGas AirViscosity: mf [Pa.s ] 1.75x10-5Density: f [kg/m3 ] 1.15
  • 0.262s 0.528s 0.790s 1.05s 1.31s 1.58s 1.84s 2.10s 2.36s 2.62s (a) Original bed (dp=1.0mm) (b) SPA bed (representative particle, dp’=3.0mm) (c) SPA bed (representative particle, dp’=6.0mm) Snapshots of Dry Particles
  • p=2650kg/m3, Column : 0.5×1.5m, u0=1.2m/sof lower half set particles [m] 0.4 d p =1.0mm (Original bed) Dry (fluid cell: 134x333) 0.3 Average height 0.2 d p =1.0mm (Original bed) d p =3.0mm (SPA bed) d p =6.0mm (SPA bed) 0.1 (fluid cell: 22x56) u0: increasing u0: decreasing0 decreasing U + 0 0 1 2 3 4 5 Time [s] Average height of dry particles initially located in the half lower region
  • 0.262s 0.528s 0.790s 1.05s 1.31s 1.58s 1.84s 2.10s 2.36s 2.62s (a) Original bed (dp=1.0mm) (b) SPA bed (representative particle, dp’=3.0mm) (c) SPA bed (representative particles, dp’=6.0mm)Snapshots of Wet Particles (V=1.0x10-2)
  • p=2650kg/m3, Column : 0.5×1.5m, u0=1.2m/sof lower half set particles [m] 0.4 d p =1.0mm (Original bed) Wet (fluid cell: 134x333) 0.3 Average height 0.2 d p =6.0mm (SPA bed) d p =3.0mm (SPA bed) 0.1 d p =1.0mm (Original bed) (fluid cell: 22x56) u0: increasing decreasing U u0: decreasing0 + 0 0 1 2 3 4 5 Time [s] Average height of wet particles initially located in the half lower region
  • 2. SPA 10,000 10,000 Umf = 0.72m/s dry wet (V=1.0x10-2) 8,000 8,000 Umf = 0.70m/sDP [Pa] DP [Pa] 6,000 6,000 4,000 d p =1.0mm 4,000 d p =1.0mm d p=3.0mm d p =3.0mm 2,000 2,000 d p =6.0mm d p =6.0mm 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 U0 [m/s] U0 [m/s] (a) Dry particles (b) Wet particles Umf from Wen-Yu correlation = 0.57m/s Comparisons of umf
  • 2. SPA CPU time for real 1s on Pentium 4 2.66GHz Dry [s] Wet [s] Original bed 27,300 27,600 (dp=1mm) (7hrs 34min) (7hrs 39min) SPA bed 1,760 1,870 (dp’=3mm) (29min) 1/15 (31min) 1/15 SPA bed 426 508 (dp’=6mm) (7min) 1/64 (8min) 1/55
  • Computation Conditions for Case 2Single bubble fluidization of two-density mixed particlesColumn 0.156x0.390m p=3000kg/m3Nozzle width 4mm p=2000kg/m3Particle (original) dp 1.0mm p 2000, 3000 kg/m3Gas Air f 1.15kg/m3 0.7m/s 0.7m/s mf 1.75x10-5Pa.s 15m/s (0.482s) Fig: Initial state
  • p=3000kg/m3 p=2000kg/m3t=0.056s t=0.111s t=0.167s t=0.223s t=0.278s (a) dp=1.0mm (original bed) (b) dp’=2.0mm (SPA bed)Single Bubble Behavior of Two-Density Particles
  • p=3000kg/m3 p=2000kg/m3t=0.278s t=0.557s t=0.835s t=1.114s t=1.392s (a) dp=1.0mm (original bed) (b) dp’=2.0mm (SPA bed)Single Bubble Behavior of Two-Density Particles
  • Z 0.14 SPA model 0.14 SPA model [m] 0.12 0.12 0.12 0.10 0.1 0.1 0.08 0.08 0.08 Original bed z [m] Original bed 0.06 0.06 0.06 0.04 0.04 0.04 Bubble region 0.02 0.02 0.02 (No particles exist.) 0 0 0 0.5 1 1.5 2 2.5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 (a) t=0.056s Gas velocity [m/s] Particle velocity averaged in each fluid cell [m/s] Z 0.14 0.14 [m] SPA model 0.12 0.12 0.12 Original bed 0.10 0.1 0.1 Original SPA 0.08 z [m] 0.08 bed 0.08 model 0.06 0.06 0.06 0.04 0.04 0.04 0.02 0.02 0.02 0 0 0 0.5 1 1.5 2 2.5 3 0 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Gas velocity [m/s] Particle velocity averaged (b) t=0.111s in each fluid cell [m/s]Vertical velocity distributions of particle and gas phases along the center line
  • 2. SPA SPA concept: promising. Similar Particle Assembly (SPA) model for large-scale DEM simulation Validations (comparisons with the original) Non-cohesive particles >Slug flow occurred at the beginning of fluidization: similar >Bubble diameter: almost the same >Bubble shape: not clear with large representing volume >Umf: fair agreement Cohesive particles: the same tendency as the above Binary (density) System: >Bubble: similar >Particle mixing: similar
  • 3. More Realistic Surface Characterization Measurement of Stress-Deforemation Characteristics for a Polypropylene Particle of Fluidized Bed Polymerization for DEM Simulation M. Horio, N. Furukawa*, H. Kamiya and Y. Kaneko *) Idemitsu Petrochemicals Co.
  • Computation conditionsParticlesNumber of particles nt 14000Particle diameter dp 1.0×10-3 mRestitution coefficient e 0.9Friction coefficient μ 0.3Spring constant k 800 N/mBedBed size 0.153×0.383 mTypes of distributor perforated plateGas velocity 0.156 m/s (=3Umf)Initial temperature 343 KPressure 3.0 MPaNumerical parametersNumber of fluid cells 41×105Time step 1.30×10-5 s
  • 0 7 15 ΔT [K]Snapshots of temperature distribution in PP bed (without van der Waals force)
  • Ha = 5×10-20 JHa = 5×10-19 J0 7 15 ΔT [K] Snapshots of temperature distribution in PP bed (with van der Waals force)
  • 3. Surface Characterization Experimental determination of repulsion force
  • 3. Surface Characterization Catalyst TiCl3 0.35 Pressure 0.98 MPa 0.3 Diameter[mm] Temperature 343 K 0.25 Reactor stage φ14 mm 0.2 0.15 0.1 0.05 0 0 10 20 30 40 50 60 Time [min] PP growth with time The micro reactor 0 min 1 min 2 min 5 min 10 min 15 min 20 min 30 min 60 min Optical microscope images Polymerization in a Micro Reactor
  • 3. Surface Characterization 1: material testing machine’s 10 stage 2: electric balance 9 3: table 7 8 4: polypropylene particle 5: aluminum rod 6 5 6: capacitance change 1 4 3 7: micro meter 2 8: nano-stage 9: x-y stage 1 10: cross-head of material testing machine Force-displacement meter
  • k ~100 N/m Fdp0.5x1.5 (Hertzean spring) 10 -3 10-3 10-3 dp = 597μm dp = 597μm dp = 597μm 3rd 10-4 10-4 10-4 Force [N]Force [N] Force [N] 2nd 3rd 10-5 10-5 10-5 2nd 2nd 2nd 1st 1st 1st 10-6 10-6 10-6 10 -8 10-7 10 -6 10 -5 10 -8 10-7 10 -6 10 -5 10 -8 10 -7 10-6 10-5 Displacement [m] Displacement [m] Displacement [m] x dp=597mm FE-SEM images: whole grain and its surface Repeated force-displacement characteristics of a polypropylene particle
  • Fdp0.5x1.5 (Hertzean spring) 10 -3 10-3 10-3 dp = 487μm dp = 487μm dp = 487μm 10 -4 10-4 10-4 3rd Force [N]Force [N] Force [N] 3rd 2nd 10 -5 1st 10-5 10-5 2nd 1st 1st 2nd 2nd 1st 1st 1st 10 -6 10-6 10-6 10-8 10 -7 10 -6 10 -5 10 -8 10-7 -6 10 10 -5 10-8 10-7 10-6 10 -5 Displacement [m] Displacement [m] Displacement [m] x dp=487mm FE-SEM images: whole grain and its surface Repeated force-displacement characteristics of a polypropylene particle (maximum load from first cycle)
  • 3. Surface Characterization FE-SEM image of the top particle after three times pressing
  • 3. Surface Characterization Particle surface morphology changes by collisions Plastic deformation in the case of PP Hertz model stands OK Experimental Determination of Cohesion Force: Now on going
  • 4. Lubrication Force Lubrication Force and effective Restitution Coefficient W. Zhang, R. Noda and M. Horio Submitted to Powder Technology
  • 4. Lubrication Force Restitution Spring constant coefficient ? ? Heat transfer, agglomeration Realistic collision process Fluidization behavior ‘Near Contact’ force: Interparticle forces Lubrication forceField force: Contact force:Electrostatic Van der Waals forceforce Liquid and solid bridge force Impact force
  • 4. Lubrication ForceClassical lubrication theory For Liquid-Solid Systems; Tribology, filtration etc.Why not in Gas-solid systems?  Lubrication force negligible ?  Introduction of “Stokes Paradox” ? Two solid surfaces can never make contact in a finite time in any viscous fluid due to the infinite lubrication force when surface distance approaches zero Can we avoid the paradox practically or essentially?
  • Davies’ development of lubrication theory to gas-solid systems dh = -v(t ) = -(v1 + v2 ) v1 dt dv m = -F (t ) = - FL dt r H(r,t) h(0,t) p(r,t) • identical and elastic • head-on collision v2 • rigid during approaching Assumptions in classical lubrication theory  Initial gap size h0 is assumed to be much smaller than particle radius  Upper limit of integration of pressure for lubrication force is extended to infinity  Paraboloid approximation of undeformed surface  Fluid is treated as a continuum 3mRv  3H (r , t ) = h(0, t ) + r / R 2 p(r , t ) = FL , =  2prp(r , t )dr = pmR 2v / h 2(h + r 2 / R) 2 0 2
  • Examination of the assumptions in gas-solid systems R: particle Ratio of lubrication force FL,R/FL,¡Þ 10 radius Ratio of FL,0 to other forces 1.0 8 0.9 FL,0/Fd 6 0.8 h0: initial 4 0.7 separation 0.6 2 FL,0/G 0.5 0 0.4 0.01 0.1 1 0.0 0.2 0.4 0.6 0.8 1.0 h0/R Relative initial distance Order-of-magnitude estimation  FL, =  2prp(r , t )dr 0 • FCC particles: 50mm, v0=ut, at 20C R FL, R =  2prp(r , t )dr accurate 0 • Comparison of initial lubrication force to other forces more reasonable with large • Particle radius as “near contact lubrication effect area area” or “lubrication effect area”
  • Numerical solutions for pressure distributionPressure h0=0.01R h0=0. 1R h0=R Relative radial distance r/R numerical analytical with paraboloid approximation • Pressure decays to zero much more slowly than that with paraboloid approximation • Contribution of pressure in the outer region to the lubrication force may play an important role • Numerical calculations for lubrication force are needed
  • Avoidance of “Stokes Paradox”• Assume that minimum surface distance equals to surface roughness• Whether the fluid remains as a continuum is determined by the relative magnitudeof surface distance to mean free path of fluid molecules Case 1: hmin>l0 FL ,num h h K1 (h) = = 1.041 - 0.281lg - 0.035 lg 2 FL ,ana R R 25Ratio of lubrication force to 1 1  initial value FL,0 at h0 R 3 20 contact FL ,ana (h) =  2prpdr = pmR 2v -  0 2 h h+R 15 10 approaching  Surface roughness of FCC is observed 5 to be one tenth of particle radius detaching 0 0.0 0.2 0.4 0.6 0.8 1.0  Maximum lubrication force is reached hmin/h0 Ratio of surface distance h/h when roughness make contact 0 • FCC particle: 50mm, v0=ut/5  To realistic particles, stokes paradox is avoided • Fluid: Continuum
  • Avoidance of “Stokes Paradox” Case 2: hmin<l0 • Particles in this case have relatively smaller roughness • Non-continuum fluid effect should be considered in the last stage of approaching • Maxwell slip theory (Hocking 1973) was adopted v0=ut/2 FL ,num, slip h h 1E-6 K 2 ( h) = = 1.309 - 0.082 lg - 0.009 lg 2Lubrication force FL (N) Non-continuum fluid FL ,ana,slip R R v0=ut/5 1E-7 Continuum fluid pmR 2v   h + 6l0   h + R + 6l0  1E-8 FL ,ana, slip = (h + 6l0 ) ln  h  - (h + R + 6l0 ) ln  h + R      2 12l 0  1E-9 l0>>h 1E-10 pmR 2v  6l0  FL ,ana, slip = ln   2l0  h  1E-11 1E-8 1E-7 1E-6 1E-5 1E-4 Surface distance h (m)  Increase of lubrication force is slowed down in close approaching distance • GB particle: 50mm, v0=ut/5  Treatment of fluid as a non-continuum • Fluid: Non-continuum helps us avoid the infinite lubrication force
  • Avoidance of “Stokes Paradox” Case 3: hmin is comparable to Z0 • When the surface distance can be approached to the dominant range of van der Waals force, ----- -7 FL m dv = - F (t ) = -( FL - Fvw ) 2.0x10 0.0 dt -7 F total AR -2.0x10 F Fvw = - Forces F(N) A: Hamaker constantForces F (N) -7 -4.0x10 vw 12h 2 -7 -6.0x10 -8.0x10 -7  Magnitude of van der Waals force -6 -1.0x10 increases more rapidly when h -> 0 -6 -1.2x10 hvw -1.4x10 -6  A characteristic distance hvw is 1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 defined to indicate the adhesive force Surface distance h (m) dominant region (~10-9m) • GB particle: 50mm, v0=ut/10  Consideration of adhesive force in the last approaching stage saves us • Fluid: Non-continuum again from Stokes Paradox
  • Effective Restitution Coefficient• Lubrication effect is actually a kind of damping effect, causing kinetic energydissipation during both approaching and separating stage• Restitution coefficient can be regarded as a criterion for evaluating thelubrication effect on collision process * Ste mv0 e = 1- where St = Ratio of particle inertia to viscous force St 6pmR 2 * * mvc mve Critical Stokes Number St = * Ste = * = 2Stc * c 6pmR 2 6pmR 2 • vc* is called “critical contact velocity” under which particles cannot make contact due to the repulsive lubrication force in the approaching stage • ve* is called “critical escape velocity” under which particles cannot escape from the lubrication effect area and will cease during the separation stage  h  2 h  3 h  f1 (h) = 0.962 ln   - 0.079 ln   - 0.004 ln   Case 1 St = f (h0 ) - f (hmin ) * e h+R h+R h+R 2 2 1  h   6l  1  h+R   ln 1 + 0  - ln 1 +  - 6l R Rf(h): characteristic function f 2 (h) =  6 +  ln 1 + 0  -  6 +       h+R   Case 2,3 36  l0  h  36  l0    h  6l0
  • Examples and discussion 1.0 1.0 Restitution coefficient e Restitution coefficient e ut hmin/h0=1/5 0.8 0.8 ut/5 0.6 0.6 ut/2 ut/20 hmin/h0=1/10 ut/10 0.4 0.4 ut/50 0.2 umf 0.2 hmin/h0=1/20 0.0 0.0 20 30 40 50 60 70 80 90 100 110 0.1 1 10 100 1000 Diameter of FCC particles dp (mm) Stokes Number St Case 1: FCC, hmin/h0=1/10 Case 1: FCC, different roughness Under same approaching velocity, effect of the lubrication force on largerparticles is less significant than on smaller particles The independent effects of particle size and approaching velocity on thecoefficient of restitution can be included in the consideration of Stokes numbers Collisions with Stokes numbers less than Ste* result in a restitution coefficientto be zero, consequently causing cluster and agglomeration to occur
  • Examples and discussion Restitution coefficient eRestitution coefficient e 1.0 1.0 0.8 0.8 0.6 0.6 0.4 ut 0.4 ut 0.2 ut /2 0.2 ut /5 ut /10 0.0 0.0 ut /20 ut /50 20 30 40 50 60 70 80 90 100 110 20 30 40 50 60 70 80 90 100 110 Diameter of GB d (mm) Diameter of smooth GB dp (mm) Case 2: GB, solid line: with slip, dotted Case 3: GB, solid line: with slip and van der line: without slip Waals force, dotted line: without slip  Consideration of non-continuum fluid weakens the lubrication effect and thus increases the values of the restitution coefficient  The lubrication effect is more significant in case 3 since particles can approach much more closely so that the effect of non-continuum fluid may be more significant
  • 4. Lubrication Force Remarks By numerically extending classical lubricationtheory into gas-solid systems, semi-empiricalexpressions for lubrication force are proposed. Evaluation of lubrication effect on collisionprocess are made according to restitutioncoefficient. Stokes Paradox is avoided by consideringsurface roughness, non-continuum fluid and vander Waals force. Further research should be aiming atincorporating lubrication force and an effectiverestitution coefficient into DEM simulation in thenear contact area.
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