Transcript MODELOWANIE PRZEPŁYWU MASY PAPIERNICZEJ

CFD Modelling of the Flow Inside
an LC Refiner
Dariusz Asendrych, Grzegorz Kondora
Częstochowa Univ. of Technology, Poland
A joint meeting
COST Action FP1005
Fibre suspension flow modelling - a key for innovation
& competitiveness in the pulp & paper industry
ERCOFTAC SIG 43
Fibre suspension flows
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Outline
 Introduction / Motivation
 Numerical model



Simplified / full geometry
Boundary conditions
Governing equations
 Results


Simplified geometry - Diverging grooves
Full geometry - General flow pattern
 Summary / Perspectives
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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LC refiner
plate disc refiner
Geometry – assumptions
simplified
typical refiner filling
• neglected housing  axisymmetric outlet
(instead of point outlet)
• neglected axial part of inlet, radial inlet
applied
• periodicity of discs geometry - singlesegment (30 degrees of angular extent 1/12)
full
• 12 segments
• housing
• single-pipe outlet
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Boundary conditions
 simplified filling
• geometry and mesh - GAMBIT
 inlet - VELOCITY INLET
• mesh: 6 / 24 mln cells
 outlet - PRESSURE OUTLET
• FLUENT 6.3 / 13
PERIODIC B.C.
INTERFACE for sliding meshes
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Governing equations
• pulp suspension treated as a single-phase continuum (N-S, continuity)
• flow character assumed to be laminar (confirmed by simulation results)
• pulp modelled as either Newtonian or non-Newtonian fluid
U
p  2
 U  U  
 U
t
 
U  0
  f γ 
where
γ
or
μ  const
- rate of deformation tensor
• fibre-fibre and fibre-wall interactions are neglected - main goal was to
analyze the LC refining hydraulics
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Pulp material properties
Newtonian fluid - constant apparent viscosity
softwood pulp, Cm = 4%, fibre lenght = 1400 μm, diameter = 26 μm
ln(l/d) = 3,986
ln(μr) = 5,91
μr = 370
μpulp = μr · μwater = 370 · 0,001003 = 0,371 Pa·s
source:Radoslavova, Silvy, Roux, 1996,,TAPPI Papermakers Conf., Philadelphia
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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General flow pattern
reverse flows in stator disc

enhanced internal
circulation
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Diverging grooves
αdiv = 0.0 deg
αdiv = 0.25 deg
αdiv = 0.50 deg
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Diverging grooves
intensification
of reverse flow
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Diverging grooves
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Diverging grooves
• mass flux exiting stator grows
• power consumption decreases
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Full refiner
simulation
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Full refiner geometry model
• housing included
• pipe outlet
• 12 segments
outlet
collector
outlet pipe
inlet
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Velocity magnitude
rotor
stator
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Pressure distribution
rotor
p
[bar]
7
6
stator
5
4
3
2
1
0
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Pressure distribution
5
p
[bar]
r*
1
4
0
3
2
5
1
p
[bar]
4
3
2
1
r* [-]
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Pressure distribution
p
[bar]
gap
7
6
5
4
3
2
1
0
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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LC refiner flow model - Fox et al.
Fox, T.S., Brodkey, R.S. Nissan, A.H., 1979, TAPPI J., 62 (3)
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Pressure distribution - CFD vs Fox et al.
exit
region
0
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
1
2
3
4
5
6
7 [bar]
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Mass flux at filling outlet
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Mass flux at filling outlet
full refiner
single-segment refiner
2
1
0
-1
-2
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Flow reversals in stator
full refiner
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Summary / Perspectives
Simplified geometry model
• qualitative agreement with experimental observation - adequate numerical model
• divergent grooves:
 modify pressure distribution and enhance flow reversals
 no energy penalty - improved flow quality
Full geometry model
• circulation / exit regions - analogy to Fox et al.
• existence of the backflows in the stator
• mass flow rate distributions stongly non-uniform and rotor position dependent
General
•
•
•
•
no fibres included...
CFD can really help - useful tool in process optimisation
time consuming simulations
ongoing simulations / data processing for varying conditions
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Thank You for Your Attention
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Reynolds number - Laminar vs Turbulent
gap
groove
Re is low enough to justify the assumption about laminar flow character
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Grid tests
Investigated parameters:
• succesive ratio
• interval count at the cross-section
• interval count along the groove
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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CFD vs experiment
velocity vectors
axial velocity
simulation
literature
[Lumiainen] - LDA
• refiner grooves occupied by spiral vortices
• tertiary flows (momentum exchange between discs)
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
[Fox et al.]
• good qualitative agreement
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Pulp material properties
non-Newtonian pulp model
  f(D)
source [Ventura et al.]
D - deformation rate tensor
  f (  II )
istan
refining regime
II - 2nd invariant o D
( D )     Ai  exp(ti /  II )
 II
i
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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Solution monitoring
mass flux at selected
groove outlet
progressing solution (time step No)
CFD Modelling of the Flow Inside an LC Refiner
COST FP1005 / SIG 43 meeting, 24-26.X.2012, Trondheim
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