Compression, Consolidation, Permeation & Flow of Ultrafine ... · Compression, Consolidation,...
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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 − − ⋅ =
Transcript of Compression, Consolidation, Permeation & Flow of Ultrafine ... · Compression, Consolidation,...
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 kf in m/s Force ratio FH0 /FG
10 – 100 10-7 – 10-5 1 – 100
1 – 10 10-9 – 10-7 100 – 104
0.01 – 1 10-13 – 10-9 104 – 108
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 PFC3D 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 Molerus1
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,76lam,76St,s
lam,76b
amin
t1
tttanh
v2)(Bg
tttanh
gdH/dp
bb1g
dt)t(dh
+
⋅
ε⋅⋅ε⋅
⋅
ρ
−−⋅
=
( ) ( )
−
⋅
+−
+
⋅
−
−
+
⋅
−
ρ
−−⋅⋅=
1t
ttanhln'bt12
11t
ttanhln'bt12
1
'bt1
tttanhln
'bt11
gdH/dp
bb1tg)t(h
lam,76lam,76lam,76lam,76
lam,76lam,7622
lam,76b
amin2lam,76
ρ
−−⋅=⋅ε⋅ε⋅
+⋅θ+
+gdH/dp
bb1gv
v)(Bgv
btan)1m(2
dtdv
b
amin
St,s
2
ε⋅⋅ε⋅
−⋅θ+
=St,slam,76
lam,st v2)(Bg
t1
tan)1m(2bv
2/1
b
amin
2
st,slam,76 g
dH/dpb
b1b
tan)1m(g2v2
)(Bgt
−
ρ
−−⋅θ+
+
ε⋅⋅ε⋅
=
lam,76lam,76St,s
lam,76b
amin
t1
tttanh
v2)(Bg
tttanh
gdH/dp
bb1g
)t(v+
⋅
ε⋅⋅ε⋅
⋅
ρ
−−⋅
=
)(BRe24
195.01
21
195.01692.01
Re24Eu
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 (d50 = 1.2 µm)
[ ]
[ ]lam,76
')0(
lam,76
St,s
St,s
')0(
lam,76
St,s
b
amin
)1(
t1vlnh
btan)1m(4
)(Btgv
tanhv2
)(Bg
vlnhb
tan)1m(4)(Btg
vtanh
gdH/dp
bb1g
)h(v−
+⋅θ+⋅
ε⋅ε⋅
⋅ε⋅ε⋅
+⋅θ+
ε⋅ε⋅
⋅
ρ
−−⋅
=
