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Modelling Fiber Suspensions Flows Using Rheological Data. COSt Action FP1005 meeting Nancy, 13-14 October 2011. M. Graça Rasteiro. Portugal. Overview. UNIVERSITY of COIMBRA. Objectives Overview of work being developed Rheological characterization Pilot rig CFD model Results - PowerPoint PPT Presentation
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Modelling Fiber Suspensions Flows Using Rheological Data
M. Graça Rasteiro COSt Action FP1005 meeting Nancy, 13-14 October 2011
Portugal
Objectives
Overview of work being developed
Rheological characterization
Pilot rig
CFD model
Results
Future work
OverviewUNIVERSITY of COIMBRA
Objectives
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.
UNIVERSITY of COIMBRA
Plug Flow
Mixed Flow
Turbulent Flow
Pulp suspensions flowing in pipes exhibit three basic types of shear flow mechanisms:
Objectives
water
Plug flow
Turbulent
flow
Transition
flowL
P
maxV WTV WV redV
UNIVERSITY of COIMBRA
Objectives
Construction of a flow model able to predict the flow behaviour of pulp fibre suspensions represents an important step in this area.
The 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.
k
UNIVERSITY of COIMBRA
Strategy: Pseudo-Homogeneous Model
Knowledge of the rheological behaviour is essential for the construction of a realistic model.
Overview of the research developed
Rheological characterization of fiber suspensions (different fiber types and consistencies).
-new rotational rheometer (Searl effect) developed at UCM
UNIVERSITY of COIMBRA
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
Pilot rig for the study of the flow of fiber suspensions in pipes.
-Flow tests varying fiber type, suspension consistency, temperature, pipe diameter and material.
UNIVERSITY of COIMBRA
Identification of the main parameters with a stronger impact on the flow regimen.(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 flow of fiber suspensions in pipes- turbulent regime – pseudo-homegeneous approach. (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
New plate rotational Rheometer – Searl effect
UNIVERSITY of COIMBRA
Induces uniform fibre distribution
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
1
2
34
5
6
1-Analytical scales;2-Arms to measure torque;3-Rotor;4-Vessel;5-Computer connected to the scales;6-device to control velocity.
5
5
1
6
Rheological characterization
Suspensions tested:
UNIVERSITY of COIMBRA
Pulp TypeFibre length
(mm)
Consistencies %
(w/w)
Recycled pulp 1.14±0.04 1.4 – 4.23
Eucalypt bleachedkraft 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
Rheological characterization
Typical Rheograms
UNIVERSITY of COIMBRA
(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
ap (Pa.s)
Rheological characterization
y - yield stress
k – consistency coefficient
n – flow index
UNIVERSITY of COIMBRA
-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
Herschel-Bulkley model
- 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)
Objective:
Flow model
To model the turbulent flow of pulp fibre suspensions in pipes using CFD(FEM).
UNIVERSITY of COIMBRA
Pseudo-Homogeneous Model
COMSOL Multiphysics Software, version 3.5
Modified k-ε model.
Pilot rig
Pilot Rig
UNIVERSITY of COIMBRA
Pilot rig
Pilot Rig
UNIVERSITY of COIMBRA
Pulp type effect Pipe -3”SS
Experimental Results- pressure drop
0
50
100
150
200
250
300
350
400
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
Velocity(m/s)
∆P
(mm
H2O
/m p
ipe)
recycled pulp suspension C=4.2% eucalypt pulp suspension C=3.5 %pine Pulp suspension C=3.4%pulp
UNIVERSITY of COIMBRA
Details of Governing Equations
Equations for the turbulence intensity and length scales
Turbulence damping assumed – I and l were adjusted depending on fiber type
and consistency.
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Equation for ε
2TIk
Equation for k
TL
k 23
81
Re
hDT II
hT DlL
I – turbulence intensity scaling parameter
l - turbulence length scaling parameter
Viscosity was supplied as a function of local shear rate in the pipe cross-section (data extracted from the rheograms).
Results - Modelling
Experimental data
UNIVERSITY of COIMBRA
Pulp Type
Consistencies %
SS Pipes and PE Pipes
3” and 4”
Recycled pulp 1.4 – 4.23
Eucalypt bleached kraft pulp 1.45 – 3.5
Eucalypt (90%) + pine (10%) bleached pulp
0.9 – 3.2
Pine unbleached kraft pulp 0.8 – 3.6
Turbulence parameters values
Pulp type Turbulence Parameters very low consistencies low consistencies
Recycled
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
Eucalypt
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
Eucalypt + pine
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
Pine
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
UNIVERSITY of COIMBRA Results - Modelling
Results - Modelling
Comparison between predicted and experimental pressure drop (Pa/m) for the turbulent regime
UNIVERSITY of COIMBRA
0
300
600
900
1200
1500
1800
0 300 600 900 1200 1500 1800
Experimental
Pre
dict
ed
Recycled 0.61%
Recycled 0.76%
Recycled 1.4%
Recycled 1.8%
Recycled 2.3%
Recycled 2.7%
0
400
800
1200
1600
2000
0 400 800 1200 1600 2000
Experimental
Pre
dic
ted
Eucalypt 0.77%
Eucalypt 0.91%
Eucalypt 1.4%
Eucalypt 1.5%
0
300
600
900
1200
1500
1800
0 300 600 900 1200 1500 1800
Experimental
Pre
dic
ted
eucalypt+pine 0.71%
eucalypt+pine 0.90%
eucalypt+pine 0.77%
eucalypt+pine 1.20%
eucalypt+pine 1.30%
0
300
600
900
1200
1500
1800
0 300 600 900 1200 1500 1800Experimental
Pre
dic
ted
pine 0.66%
pine o.76%
pine 0.8%
pine 1%
c) eucalypt+pine d) pine
a) recycled b) eucalypt
Results - Modelling
Turbulence intensity scaling parameter versus suspension consistency
UNIVERSITY of COIMBRA
0.0001
0.001
0.01
0.1
1
0.00 0.50 1.00 1.50 2.00 2.50 3.00
Consistency (%)
I
Recycled Pulp
Eucalypt Pulp
Eucalypt/Pine Pulp
Pine Pulp
Low Consistencies
High Consistencies
Future work
▪ Introduce in the model experimental information on the turbulence damping.
▪ Modify the transport equations for k and ε to include mechanistic damping terms.
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.
UNIVERSITY of COIMBRA
Acknowledgments:
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.;
European Project NODESZELOSS;
FCT Project FIBERFLOW;
UCM;
Carla Ventura
Carla Cotas
Joy Iglesias
F. Garcia
Paulo Ferreira
UNIVERSITY of COIMBRA
Thank you for your attention
UNIVERSITY of COIMBRA
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 is minimally influenced by the consistency increase.
▪ 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.
UNIVERSITY of COIMBRA
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 1 2 3 4 5 6 7
Velocity (m/s)
Pre
ssu
re D
rop
(P
a/m
)
Pine 0.76% - experimental
Pine 0.76% - predicted
Pine 1.0% - experimental
Pine 1.0% - predicted
005.0
0003.0%1
005.0
01.0%76.0
l
IC
l
IC
Results - Modelling
Comparison with experimental data
UNIVERSITY of COIMBRA
Results and Discussion
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
First, the numerical implementation was validated with water. Then, the pulp’s physical characteristics were introduced in the model.
UNIVERSITY of COIMBRA
Results and Discussion
Numerical ImplementationUNIVERSITY of COIMBRA
Kinetic energy profile for the recycled fibre suspension
0.72% consistency
Results and Discussion
Numerical ImplementationUNIVERSITY of COIMBRA
Kinetic energy profile for the recycled fibre suspension
2.7% consistency
Governing Equations
0 u
Fuupuut
u T
2
2
1 TT
k
T UUkUkt
k
k
CUUk
CUt
TT
T2
2
2
12
1
C 1C 2C k Constant
Value 0.09 1.44 1.92 1.0 1.3
Continuity equation
Conservation of momentum
Transport Equation for k
Transport Equation for ε
model constants:
UNIVERSITY of COIMBRA
Standard k-ε model
2kCT
Numerical Implementation
For the CFD modelling the Chemical Engineering module of COMSOL Multiphysics Software version 3.5 was used.
Geometry
4 m
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.
UNIVERSITY of COIMBRA
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 ImplementationUNIVERSITY of COIMBRA
Physics and Boundaries
Numerical Implementation
Inlet 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.
Outlet Boundary “Normal Stress, Normal Flow” function
Wall Logarithm wall function,
Symmetry Boundary
Axial Symmetry
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Friction Factor
D
uC
L
Hf
2
2
Du
Re
.
RevsC f
Friction factor results
Friction Factor: Eucalypt pulp
Re
Cf
Friction Factor: distinct pulps
0.001
0.010
0.100
1.000
10.000
10 100 1000 10000 100000Re
Cf
recycled pulp suspension C=4.2% eucalypt pulp suspension C=3.5%eucalypt/pine pulp suspension C=3.2% pine pulp suspension C=3.4%water line
Friction factor results
Friction Factor
Correlations for 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;
fC
Rheological characterization
Typical rheogram for a pulp fibre suspension
UNIVERSITY of COIMBRA
Rate of shear, γ
Sh
ear
stre
ss,
δ
Newtonianfluid
τD
τY
Rheological characterization
Typical Rheograms
UNIVERSITY of COIMBRA
C=3.6%C=3.3 %C=2.9 %C=2.3 %
C=1.9%C=1.5 %C=1.0 %
Pine suspension
(Nm-2) ap (Pa.s)
0
50
100
150
200
250
300
350
400
0 2000 4000 6000 8000 10000
(1/s)
(N
/m2)
pine C=3.6%
pine C=3.3%
pine C=2.9%
pine C=2.3%
pine C=1.9%
pine C=1.5%
pine C=1.0%0.01
0.1
1
10
0 2000 4000 6000 8000 10000 12000
dV/dx (1/s)
pine C=3.6%
pine C=3.3%
pine C=2.9%
pine C=2.3%
pine C=1.9%
pine C=1.5%
pine C=1.0%