Compression, Consolidation, Permeation & Flow of Ultrafine Cohesive Powders Abbas Kamranian Marnani, Katja Mader-Arndt and Jürgen Tomas Mechanical Process Engineering, Faculty of Process and Systems Engineering, Otto von Guericke University Magdeburg Problem Definition Objectives Cooperation Experimental Methods Analytical Description DFG-Graduate School 1554 “Micro-Macro-Interactions in Structured Media and Particle Systems” 1. Process and handling problems of ultrafine, cohesive powders (d<10 µm) Dosing & Packing Product design Conveying Transport Macroscopic permeation and flow properties Particle size d µm Permeability k f in m/s Force ratio F H0 /F G 10 – 100 10 -7 – 10 -5 1 – 100 1 – 10 10 -9 – 10 -7 100 – 10 4 0.01 – 1 10 -13 – 10 -9 10 4 – 10 8 2. Decreasing particle size d: decreasing pore size and permeability and increasing ratio of adhesion force/weight force Goal: Understanding of physical particle properties at Flow-around Approach Contact Detachment Sliding Ultrafine, dry and adhesive particles (1) Combination of Fluid Dynamics (CFD) and Discrete Element Method (DEM) by PFC 3D and fluid coupling (2) Measurement of macroscopic powder properties (compression, consolidation and permeation tests) (3) Evaluation of the process (experiments – simulations) Flow & Permeation of Powders Modeling & Simulation L. Tobiska – U MD: Numerics of CFD-DEM coupling A. Kharaghani – U Magdeburg Pore network and flow simulations D. Thevenin – U Magdeburg (MD) Fluid Mechanics, CFD & DEM coupling A. Bertram – U Magdeburg: Fundamentals of constitutive laws S. Luding – U Twente: Calibration of DEM simulations K. Mader-Arndt – U MD Model “Stiff particles with soft contacts” 1) Compression test and model-based data evaluation New Home-built Test Rig 3) Model-based data evaluation of compression and shear work 2) Micro-macro aspects of cohesive powder consolidation and shear 5) Micro-macro aspects of hindered powder flow Air permeation resistance = particle flow-around drag + macroscopic powder bed resistance (pressure drop) Macroscopic powder flow resistance in a convergent hopper = cohesive flow resistance + air permeation resistance 4) PI-flow chart and side view of compression, consolidation & permeation cell Process Variables Hopper Discharge and Laminar Permeation through a Cohesive Powder Bridge Differential equation of motion Permeation resistance acc. to Molerus 1 Discharge velocity-time law Stationary discharge velocity Characteristic discharge (relaxation) time Velocity-displacement law Differential equation Displacement-time law Discharge time Only numerically solvable lam , 76 lam , 76 St , s lam , 76 b a min t 1 t t tanh v 2 ) ( B g t t tanh g dH / dp b b 1 g dt ) t ( dh + ⋅ ε ⋅ ⋅ ε ⋅ ⋅ ρ − − ⋅ = ( ) ( ) − ⋅ + − + ⋅ − − + ⋅ − ρ − − ⋅ ⋅ = 1 t t tanh ln ' b t 1 2 1 1 t t tanh ln ' b t 1 2 1 ' b t 1 t t tanh ln ' b t 1 1 g dH / dp b b 1 t g ) t ( h lam , 76 lam , 76 lam , 76 lam , 76 lam , 76 lam , 76 2 2 lam , 76 b a min 2 lam , 76 ρ − − ⋅ = ⋅ ε ⋅ ε ⋅ + ⋅ θ + + g dH / dp b b 1 g v v ) ( B g v b tan ) 1 m ( 2 dt dv b a min St , s 2 ε ⋅ ⋅ ε ⋅ − ⋅ θ + = St , s lam , 76 lam , st v 2 ) ( B g t 1 tan ) 1 m ( 2 b v 2 / 1 b a min 2 st , s lam , 76 g dH / dp b b 1 b tan ) 1 m ( g 2 v 2 ) ( B g t − ρ − − ⋅ θ + + ε ⋅ ⋅ ε ⋅ = lam , 76 lam , 76 St , s lam , 76 b a min t 1 t t tanh v 2 ) ( B g t t tanh g dH / dp b b 1 g ) t ( v + ⋅ ε ⋅ ⋅ ε ⋅ ⋅ ρ − − ⋅ = ) ( B Re 24 1 95 . 0 1 2 1 1 95 . 0 1 692 . 0 1 Re 24 Eu 2 3 3 3 3 B ε ⋅ = ε − − ε − ⋅ + ε − − ε − ⋅ + ⋅ = 1 Molerus, O., (1993). Principles of Flow in Disperse Systems. Chapman & Hall, London Data of a very cohesive limestone powder (d 50 = 1.2 µm) [ ] [ ] lam , 76 ' ) 0 ( lam , 76 St , s St , s ' ) 0 ( lam , 76 St , s b a min ) 1 ( t 1 v ln h b tan ) 1 m ( 4 ) ( B t g v tanh v 2 ) ( B g v ln h b tan ) 1 m ( 4 ) ( B t g v tanh g dH / dp b b 1 g ) h ( v − + ⋅ θ + ⋅ ε ⋅ ε ⋅ ⋅ ε ⋅ ε ⋅ + ⋅ θ + ε ⋅ ε ⋅ ⋅ ρ − − ⋅ =