Transcript Document

Modelling Fiber Suspensions
Flows Using Rheological Data
M. Graça Rasteiro
COSt Action FP1005 meeting
Nancy, 13-14 October 2011
Portugal
Overview
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Objectives
Overview of work being developed
Rheological characterization
Pilot rig
CFD model
Results
Future work
Objectives
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Flow properties of pulp suspensions are
important for the optimization of most unit
operations
in
pulp
and
paper
making.
Therefore, it is necessary to understand the
specific
hydrodynamic
features
of
fibre
suspensions.
Objectives
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Pulp suspensions flowing in pipes exhibit
three basic types of shear flow mechanisms:
Plug Flow
water
P
L
Plug flow
Mixed Flow
Transition
Turbulent
flow
flow
Turbulent Flow
Vmax
VWT
VW
Vred
Objectives
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Construction of a flow model able to predict
the flow behaviour of pulp fibre suspensions
represents an important step in this area.
Strategy: Pseudo-Homogeneous Model
Knowledge of the rheological behaviour is
essential for the construction of a realistic
model.
The k  
Turbulence Model is one of the
simplest and most used turbulence models for
industrial applications. Modifications to the
k- ε model can lead to an efficient description
of the flow of concentrated fiber suspensions.
Overview of the research developed
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Rheological
characterization
suspensions
(different
fiber
consistencies).
-new rotational
developed at UCM
rheometer
of
fiber
types
and
(Searl
effect)
Development of models for the rheology of
fiber suspensions.
(Carla A.F. Ventura, A. Blanco, C. Negro, F.A.P. Garcia, P. Ferreira, M.G. Rasteiro, "Modelling Pulp
Fibre Suspension Rheology", Tappi J, 6, 7, 17-23 (2007).)
Identification of the main parameters with a
stronger impact on the rheology of fiber
suspensions.
(Carla A.F. Ventura, A. Blanco, C. Negro, F.A.P. Garcia, P. Ferreira, M.G. Rasteiro, "Modelling Pulp
Fibre Suspension Rheology", Tappi J, 6, 7, 17-23 (2007).)
Overview of the research developed
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Pilot rig for the study
suspensions in pipes.
of
the
flow
of
fiber
-Flow
tests
varying
fiber
type,
suspension
consistency, temperature, pipe diameter and material.
Identification of the main parameters
stronger impact on the flow regimen.
with
a
(Carla Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro; "Flow Dynamics of Pulp Fibre Suspensions", Tappi J,
7, 8, 20-26 (2008).)
New set of design correlations for friction factor
vs Reynolds number based on a statistical design,
showing the dependence on consistency and pipe
diameter for two flow regimes.
(Carla A.F. Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro, "Modelling Pipe Friction Loss of Pulp Fibre
Suspensions", CHERD (2011) – in revision.)
Modelling of the
pipesturbulent
approach.
flow of
regime
fiber suspensions in
–
pseudo-homegeneous
(Carla A.F. Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro, "Modelling the Turbulent Flow of Pulp
Suspensions”, I&ECR, 50,16, 9735–9742 (2011).)
Rheological characterization
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New plate rotational Rheometer – Searl effect
5
3
4
2
5
1-Analytical scales;
2-Arms to measure torque;
3-Rotor;
4-Vessel;
5-Computer connected to the
scales;
6-device to control
velocity.
6
1
6
Induces
uniform fibre distribution
1
5
Measures shear in the rotor (mobile plate) and
in the vessel (fixed plate)
Calculates the difference between torque
applied by the rotor and torque transmitted by
the fluid to the vessel
Rheological characterization
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Suspensions tested:
Fibre length
(mm)
Consistencies %
Recycled pulp
1.14±0.04
1.4 – 4.23
Eucalypt bleached
kraft pulp
0.71±0.03
1.45 – 3.5
Eucalypt (90%) + pine (10%)
bleached pulp
0.61±0.06
0.9 – 3.2
Pine unbleached kraft pulp
2.56 ±0.14
0.8 – 3.6
Pulp Type
(w/w)
Rheological characterization
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Typical Rheograms
ap (Pa.s)
 (Nm-2)
C=3.2%
C=2.5 %
C=2.2 %
C=1.9 %
C=1.6%
C=1.2 %
C=0.9 %
pine + eucalyptus suspension
Rheological characterization
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Herschel-Bulkley model
y - yield stress
k – consistency coefficient
n – flow index
-Using an experimental design the influence of
fibre characteristics (length), consistency and
temperature on y were evaluated.
- n an k are mainly influenced by consistency
- Yield stress increases with consistency and fibre length
- Temperature has got a negative effect on yield stress
See: Ventura C, Blanco A, Negro C, Ferreira P, Garcia F, Rasteiro M,
Tappi J, 6 (7) 17 (2007)
Flow model
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Pseudo-Homogeneous Model
Objective:
To model the turbulent flow of
suspensions in pipes using CFD(FEM).
pulp
fibre
Modified k-ε model.
COMSOL Multiphysics Software, version 3.5
Pilot rig
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Pilot Rig
Pilot rig
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Pilot Rig
Experimental Results- pressure drop
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Pipe -3”SS
Pulp type effect
400
∆P(mm H2O/m pipe)
350
300
250
200
150
100
50
0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Velocity(m/s)
recycled pulp suspension C=4.2%
pulp suspension C=3.4%
pine Pulp
eucalypt pulp suspension C=3.5 %
Details of Governing Equations
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Equation for k
k  IT 
2
Equation for ε
3
k 2

LT
Equations for the turbulence intensity and length scales
I T  I Re
1
8
Dh
LT  l Dh
I – turbulence intensity scaling parameter
l - turbulence length scaling parameter
Turbulence damping assumed – I and l were adjusted depending on fiber type
and consistency.
Viscosity was supplied as a function of local shear rate in the pipe
cross-section (data extracted from the rheograms).
Results - Modelling
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Experimental data
Consistencies %
Pulp Type
SS Pipes and PE Pipes
3” and 4”
Recycled pulp
Eucalypt bleached kraft pulp
1.4 – 4.23
1.45 – 3.5
Eucalypt (90%) + pine (10%) bleached
pulp
0.9 – 3.2
Pine unbleached kraft pulp
0.8 – 3.6
Results - Modelling
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Turbulence parameters values
Pulp type
Recycled
Eucalypt
Eucalypt
+ pine
Pine
Turbulence Parameters
very low consistencies
low consistencies
Consistency (%)
0.72
0.60
0.61
1.40
1.80
2.30
2.70
I
0.01
0.01
0.01
0.009
0.008
0.007
0.005
l
0.005
0.005
0.005
0.005
0.005
0.005
0.005
Consistency (%)
0.77
0.91
1.4
1.5
I
0.09
0.09
0.007
0.003
l
0.005
0.005
0.005
0.005
Consistency (%)
0.71
0.77
0.9
1.2
1.3
I
0.07
0.05
0.01
0.005
0.003
l
0.005
0.005
0.005
0.005
0.005
Consistency (%)
0.66
0.76
0.8
1
I
0.01
0.01
0.0005
0.0003
l
0.005
0.005
0.005
0.005
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Results - Modelling
Comparison between predicted and experimental
pressure drop (Pa/m) for the turbulent regime
1800
2000
1500
1600
Recycled 0.61%
Recycled 0.76%
600
Recycled 1.4%
Recycled 1.8%
300
Recycled 2.3%
Recycled 2.7%
Predicted
900
1200
Eucalypt 0.77%
800
Eucalypt 0.91%
Eucalypt 1.4%
400
Eucalypt 1.5%
0
0
0
300
600
900
1200
Experimental
1500
1800
0
400
a) recycled
1800
1800
1500
1500
1200
1200
900
eucalypt+pine 0.71%
eucalypt+pine 0.90%
600
1200
eucalypt+pine 1.20%
1600
2000
Experimental
900
pine 0.66%
600
eucalypt+pine 0.77%
300
800
b) eucalypt
Predicted
Predicted
Predicted
1200
pine o.76%
pine 0.8%
300
pine 1%
eucalypt+pine 1.30%
0
0
0
300
600
900
1200
1500
1800
0
300
Experimental
c) eucalypt+pine
d) pine
600
900
Experimental
1200
1500
1800
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Results - Modelling
Turbulence intensity scaling parameter versus
suspension consistency
1
Recycled Pulp
Low Consistencies
Eucalypt Pulp
0.1
Eucalypt/Pine Pulp
I
Pine Pulp
0.01
0.001
High Consistencies
0.0001
0.00
0.50
1.00
1.50
Consistency (%)
2.00
2.50
3.00
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Future work
▪ Introduce in the model experimental information on
the turbulence damping.
▪ Modify the transport equations
include mechanistic damping terms.
for
k
and
ε
to
Establish
quantitative
correlations
for
the
turbulence intensity and length scales, as a function
of fiber characteristics and consistency.

▪ Model the intermediate regime (plug of fibers +
water annulus).
 Acquire experimental information on the fiber plug
evolution with Reynolds number (different fiber types
and consistencies), using tomographic techniques.
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Acknowledgments:
European Project NODESZELOSS;
FCT Project FIBERFLOW;
UCM;
RAIZ – Instituto Investigação da Floresta e Papel;
Gopaca, S.A.;
Prado Karton, S.A.;
Soporcel - Grupo Portucel Soporcel;
CELTEJO - Empresa de Celulose do Tejo, S.A.;
Carla Ventura
Carla Cotas
Joy Iglesias
F. Garcia
Paulo Ferreira
UNIVERSITY of COIMBRA
Thank you for your
attention
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Conclusions
▪ The pressure drop profiles obtained using COMSOL
Multiphysics Software agree very well with the experimental
results obtained.
▪ The use of the k-ε Turbulence Model, associated with the
rheological data acquired in a specially built viscometer,
revealed to be a good strategy for the prediction of
pressure drop values for fibre suspension flow.
▪ For very low consistencies the I value
influenced by the consistency increase.
is
minimally
▪ For relatively high values of consistency, as consistency
increases, the I values decrease for all the pulps tested.
This boundary is dependent on the fibre type.
The turbulence damping is higher in the case of the pine
suspensions (longer and stiffer fibres), being lower for
the recycled fibres suspension.

Results - Modelling
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Comparison with experimental data
Pressure Drop (Pa/m)
2000
1800
Pine 0.76% - experimental
1600
Pine 0.76% - predicted
1400
Pine 1.0% - experimental
1200
C  0.76%
Pine 1.0% - predicted
1000
800
600
C  1%
400
200
0
0
1
2
3
4
Velocity (m/s)
5
6
7
I  0.01
l  0.005
I  0.0003
l  0.005
Numerical Implementation
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Results and Discussion
First,
the
numerical
implementation
was
validated
with
water.
Then,
the
pulp’s physical
characteristics
were introduced
in the model.
Simulated pressure drop for the flow of the recycled pulp suspension with 2.7% (w/w)
consistency, at a velocity of 4.8 m/s.
Numerical Implementation
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Results and Discussion
Kinetic
energy
profile for the
recycled
fibre
suspension
0.72% consistency
Numerical Implementation
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Results and Discussion
Kinetic
energy
profile for the
recycled
fibre
suspension
2.7% consistency
Governing Equations
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 u  0
Continuity equation
Conservation of momentum



u
T
  u   u   p    u  u   F
t
Standard k-ε model
T   C 
k2

Transport Equation for k


k

    T
t
k

 
1
k   U  k   T U  U T
2
 


2
 
Transport Equation for ε




    T
t


model constants:
 
1

   U    C 1  T U  U T
2
k
 

Constant
Value
C
0.09
C 1
1.44

2
C 2
1.92
  C 2
2
k
k
1.0

1.3
Numerical Implementation
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For the CFD modelling the Chemical Engineering module of
COMSOL Multiphysics Software version 3.5 was used.
Geometry
4m
The
system
to
be
modelled is basically
a linear pipe (3 in
diameter and 1 m long)
where
a pulp fibre
suspension is flowing.
2D axial symmetry.
Numerical Implementation
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2D axial symmetry: mesh mode
In
order
to
reach
accurate
results
for
the pressure drop, the
mesh
selected
was
a
mapped mesh consisting
of
quadrilateral
elements.
The mesh is more
refined
near
the
wall to resolve the
viscous sublayer.
Numerical Implementation
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Physics and Boundaries
Inlet Boundary
Outlet Boundary
Wall
Symmetry
Boundary
Plug type cross section velocity profile;
The existence of particles, such as fibres, in a fluid flow induces a
turbulence damping, thus the L and I values should be smaller then usually
assumed for homogeneous fluids
Since the turbulent length scale is mentioned to be mainly dependent on the
system geometry, it’s value was assumed to be constant for all the fibre
types and all the consistencies. The intensity scale parameter was adjusted
according to the pulp fibre type and concentration.
“Normal Stress, Normal Flow” function
Logarithm wall function,
Axial Symmetry
Friction Factor
H
u2
 2 Cf 
L
D
uD
Re 

 .
 
 
 
C f vs Re
Friction factor results
Friction Factor: Eucalypt pulp
1.00000
3.50%
3.20%
2.90%
2.50%
0.10000
1.80%
1.50%
Cf
0.77%
0.01000
0.00100
100.00
1000.00
10000.00
Re
100000.00
1000000.00
Friction factor results
Friction Factor: distinct pulps
10.000
Cf
1.000
0.100
0.010
0.001
10
100
1000
Re
recycled pulp suspension C=4.2%
eucalypt/pine pulp suspension C=3.2%
water line
10000
100000
eucalypt pulp suspension C=3.5%
pine pulp suspension C=3.4%
Friction Factor
Correlations for C f not only as a function of
Reynolds number, but also showing the dependence
on consistency and pipe diameter for a range of
pulp suspensions and for two different flow
regimes were obtained;
Rheological characterization
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Shear stress, δ
Typical rheogram for a pulp fibre suspension
τY
τD
Newtonian
fluid
Rate of shear, γ
Rheological characterization
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Typical Rheograms
10
1
Ψ (Pa.s)
 (Nm-2)
ap (Pa.s)
0.1
0.01
0
2000
4000
6000
dV/dx (1/s)
C=3.6%
C=3.3 %
C=2.9 %
C=2.3 %
C=1.9%
C=1.5 %
C=1.0 %
Pine suspension
8000
10000
1200