Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 6.5.4 - Formation of fibers in streamwise streaks close to a plane wall
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 Material Information
Title: 6.5.4 - Formation of fibers in streamwise streaks close to a plane wall Particle-Laden Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kvick, M.
Håkansson, K.
Lundell, F.
Söderberg, L.D.
Prahl Wittberg, L.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: fiber suspension flows
fiber streaks
wall bounded turbulent flow
 Notes
Abstract: In papermaking, the structure and mechanical properties of the final, dry paper are to a large extent determined by the flow of a low concentration (< 1%) cellulose fibre suspension early in the process. A key flow device is the headbox nozzle, a 2D contraction that generates a thin and wide fibre suspension sheet that is jetted out onto permeable forming wires, where the paper is formed. Aiming at understanding how the mass and orientation distributions are affected by the flow along internal surfaces of the nozzle a turbulent fibre suspension flow near a wall is investigated in this study. The experimental setup consists of an inclined open rectangular channel made of glass with reservoirs in the upstream and downstream position. A pump is used to transfer the suspension from the downstream to the upstream reservoir. The suspension flows down the inclined channel driven by gravity. Cellulose acetate fibres with a density f = 1300 kg/m3 and an aspect ratio of rp = 7; 14 and 28 are used. The flow Reynolds number is varied between 500 and 20000 by adjusting the angle of inclination of the channel and the thickness of the water layer flowing down the channel. By analyzing images taken from beneath, through the glass bottom of the channel, on the fully developed flow, fibres are detected using a steerable filter. The position and orientation of the fibres in the flow parallel plane are obtained and the evolution of fibre-streaks in time are visualized. The width of the fibre-streaks are compared with the empirical value of 50l+ for low velocity streaks in turbulent boundary layers, where l+ is the viscous length scale. The result show that the fibre-streaks scale in the same manner as the viscous sublayer streaks in a turbulent wall bounded flow. It is shown that the fibres do not form streaks for all cases studied, only in a certain range of flow and particle Reynolds number there is an occurrence of fibre-streaks. In the case when fibres have not formed streaks, most of the fibres have an orientation aligned with, or close to, the flow direction.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00161
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 654-Kvick-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Fibre Streaks in Wall Bounded Turbulent Flow


M. Kvick*, K. Hfkansson*, F. Lundellt, L. D. SOderberg* and L. Prahl Wittberg,t

Wallenberg Wood Science Center, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
t Linn6 FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
t Innventia AB, SE-114 86 Stockholm, Sweden
kvick@mech.kth.se, karlh@mech.kth.se and fredrik@mech.kth.se
Keywords: Fibre suspension flows, Fibre streaks, Wall bounded turbulent flow




Abstract

In papermaking, the structure and mechanical properties of the final, dry paper are to a large extent determined by the
flow of a low concentration (< 1 .) cellulose fibre suspension early in the process. A key flow device is the headbox
nozzle, a 2D contraction that generates a thin and wide fibre suspension sheet that is jetted out onto permeable forming
wires, where the paper is formed. Aiming at understanding how the mass and orientation distributions are affected
by the flow along internal surfaces of the nozzle a turbulent fibre suspension flow near a wall is investigated in this
study. The experimental setup consists of an inclined open rectangular channel made of glass with reservoirs in the
upstream and downstream position. A pump is used to transfer the suspension from the downstream to the upstream
reservoir. The suspension flows down the inclined channel driven by gravity. Cellulose acetate fibres with a density
pf 1300 kg/m3 and an aspect ratio of rp 7, 14 and 28 are used. The flow Reynolds number is varied between
500 and 20000 by adjusting the angle of inclination of the channel and the thickness of the water layer flowing down
the channel. By analyzing images taken from beneath, through the glass bottom of the channel, on the fully developed
flow, fibres are detected using a steerable filter. The position and orientation of the fibres in the flow parallel plane are
obtained and the evolution of fibre-streaks in time are visualized. The width of the fibre-streaks are compared with
the empirical value of ~ 501+ for low velocity streaks in turbulent boundary layers, where 1+ is the viscous length
scale. The result show that the fibre-streaks scale in the same manner as the viscous sublayer streaks in a turbulent
wall bounded flow. It is shown that the fibres do not form streaks for all cases studied, only in a certain range of flow
and particle Reynolds number there is an occurrence of fibre-streaks. In the case when fibres have not formed streaks,
most of the fibres have an orientation aligned with, or close to, the flow direction.


Nomenclature


Roman symbols
g gravitational constant (Ins 2)
h height of water layer (m)
1 length (m)
n number density (-)
Re Reynolds number (-)
u velocity (nms1)
Greek symbols
a inclination-angle of plate (-)
3 fibre orientation angle (-)
AZ spanwise displacement (m)
v kinematic viscosity (smn 2)
p density (kgmi3)
0 peak location (-)
T shear stress (kgm i1 2)


Subscripts
f fibre
h bulk
p particle
s surface of water layer
H20 water
Superscipts
+ viscous scale



Introduction

In papermaking, the mass and orientation distribution of
cellulose fibres, therefore also the mechanical properties
of the paper, are highly dependent on the flow in the
headbox nozzle. The headbox is a 2D contraction that
generates a thin, wide fibre suspension sheet that is jetted







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


out onto permeable forming wires, where the paper is
formed.
The highly complex flow in a headbox, where the flow
is both turbulent and elongated, together with the pres-
ence of several surfaces, motivates studying the behavior
of fibres in turbulent boundary layers. An increased un-
derstanding of fibres in wall bounded turbulent flow will
give a better understanding on the effects of the headbox
on the final paper. Not only the distribution of the fibre
orientations, i.e. their individual direction in the flow, but
also the the overall fibre orientation and the distribution
of the fibres in the cross direction (spanwise) is of in-
terest. When making paper, the orientation of the fibres
and the basis weight of the paper are the factors that de-
cides the mechanical properties of the paper. Ideally, an
isotropic orientation distribution and a homogenous ba-
sis weight is desired.
Earlier experiments have been conducted by Carlsson
(2009), who mainly investigated orientation and distri-
bution of cellulose fibres in laminar flow. In this study,
although the experimental setup is the same as the one
used by Carlsson (2009), the emphasis will lie on study-
ing fibres in turbulent shear flow. Jeffery (1922), de-
rived the equations of motion for ellipsoidal particles in
inertialess shear flow. He found that the particles ro-
tated in stable orbits, the so called Jeffery orbits. The
equations have since they first were derived been devel-
oped to work for more advanced flows, e.g. any symmet-
ric body, sedimentation effects, wall effects etc. Earlier
work have demonstrated that fibres in shear flow experi-
ence these kind of motions.
It is well known that in a turbulent flow, there exists
coherent structures in the boundary layer, known as vis-
cous sublayer streaks. These turbulent streaks scale with
the viscous length scale 1:


v
-Tall


(1)


where u ^wa. is the friction velocity and v the kinematic
viscosity. It has been found that the width of the streaks
are approximately 501+.
Several experiments and numerical simulations have
been performed regarding particles in turbulent bound-
ary layers. Kaftori et al. (1995) studied the deposition
of spherical particles in streaks while Ninto and Gar-
cia (1996) used both sand (non-symmetrical particles)
and spherical particles. To the authors best knowledge,
experiments regarding formation of fibre-streaks in tur-
bulent shear flow has not been conducted earlier. Al-
though, simulations regarding this phenomena exists,
e.g. Mortensen (2007).
In the present study, fibres in a turbulent wall bounded
flow are studied experimentally, effort is put into finding
out when fibres gather in streaks. Moreover, the distri-


Reservoir
I


Reservoir


Figure 1: Schematic drawing of the experimental setup.


butions of the fibre orientation are of interest, both for
the cases when fibre-streaks are and are not present. In
addition, experiments are conducted using a solution of
water and polyethylene oxide, modifying the turbulence
in the flow.


Experimental Setup & Analyzing Techniques

The experimental setup, shown in figure 1, consists of
an inclined channel made of glass with length 2 m and
width 0.56 m. Water is pumped to an upstream reser-
voir and allowed to flow down the plate driven by grav-
ity alone. Reservoirs are located upstream and down-
stream of the glass plate in order to reduce disturbances
in the flow. In both reservoirs, submersible pumps are
placed to stir the suspension and prevent sedimentation
of fibres. The system requires a liquid volume of 120 1
to function properly. At a downstream position where
the turbulent flow is fully developed, a CCD-camera is
mounted underneath the glass-plate to acquire images of
the fibre suspension flow from below. The setup makes
it possible to alter the angle of the glass-plate (a) and
the height (h) of the water layer flowing down the plate.
The accuracy is it "'. and it for the angle and the
height respectively.
The variations of the above parameters are limited
by the experimental setup, the angle is varied between
0.03 0.2 degrees and the height between 6 12 mm,
the complete test matrix is found in table 1. The height
of the water layer is measured at several positions to
ensure that there are no local acceleration of the flow.

Flow situation
The velocity profile for the fluid flow down the inclined
plate is, with laminar approximations, given by;

u --y(2h y) sin a, (2)
2v
v is the kinematic viscosity of water, g is the gravita-
tional constant and y is the wall normal coordinate vary-
ing from y = 0 at the surface of the glass-plate to y = h












Table 1: Parameter variations. Rows represents the an-
gles of inclination and columns the heights of
the water layer.
a h 6 8 10 12
S0.03 X X X
S0.07 X X X
S0.10 X X X
S0.14 X X X
S0.17 X X X
S0.21 X X -


at the surface of the water layer. The maximum veloc-
ity, given by the velocity at the surface of the water layer
is u(y h) Us. The bulk Reynolds number is de-
fined by the height of the water layer h and the angle of
inclination a as:

hUs gh3 sin a
Rh = 2v2- (3)
v 2v2
Using values from table 1, the bulk Reynolds number is
found to be within the range of 500 -20000 3.7'. An-
other important dimensionless parameter is the particle
Reynolds number:


R Twall
Pp V2


.11.1? sin a
v2


with values between 100 2000 1 '". One of the
most intriguing aspects with this experimental setup is
that since the flow is driven by gravity alone and since
the gravitational force is balanced by the force from the
glass-plate, the wall shear stress is defined by;

Twall = pgh sin a. (5)
It is well known that the coherent turbulent structures
in the flow, scale with the viscous length scale 1+, de-
fined by;

I+ =- h (6)

where u 7n.w is the friction velocity and is directly
related to the wall shear stress. Although the exact
structure of the turbulent boundary layer streaks is
not certain, the width of the streaks has been well
investigated and reported to be approximately 501+, by
e.g. Zacksenhouse et al. (2001).

Fibre suspension
The fibre suspension consists of water with den-
sity PH20 1000 kg/m3 and a dilute concentration
(0.008 < nl3 < 0.033) of cellulose acetate fibres. The
fibres have a density of pf 1300 kg/m3, a diameter


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


of df 70 pm and the fibre lengths are If 0.5 mm,
1.0 mm and 2.0 mm giving aspect ratios of rp 7, 14
and 28. Since the density ratio Pf/PH20 is greater than
unity, the fibres will sediment in the flow. To increase the
visibility of the fibres, the fibres are dyed using a black
textile dye from Nitor.
Furthermore, experiments are conducted using a mix-
ture of water and a polymer, polyethylene oxide (PEO,
Polyox WSR-301), as the liquid phase to investigate
the effects of an altered turbulence in the flow. The
solution have a concentration of 40 ppm PEO. After the
polymers have been added to the fluid, the solution is
stirred daily but otherwise left standing for five days to
ensure that the solution is homogenous. The viscosity
of the solution is measured for different shear rates
using a Brookfield viscometer and is found to be similar
to water. Flow rate measurements also gives similar
results compared to water. For PEO experiments only
fibres with an aspect ratio of 14 are used.

Measurement and analysis procedure

A CCD-camera (Prosilica GE-680) placed underneath
the glass-plate is connected to a light source through
a data acquisition hardware from National Instruments
(NI USB-6008). By controlling the light source it is as-
sured that the exposure time is short enough for the im-
ages to become sharp. The images are acquired using
a frequency of 0.14 0.30 Hz, depending on the flow
velocity, to make sure that the images are statistically
independent of eachother. For each case, 150 images
are acquired, this is found to be sufficient for the streak
width and fibre-orientation-distribution to converge. A
typical image is shown in figure 2, where the fibres are
black, the streamwise direction is upward. The differ-
ences in background intensity is due to surface waves
and reflections of the light source.


Figure 2: Example of an image acquired during exper-
iment. Fibres have been dyed black for bet-
ter visibility. The streamwise direction is up-
ward.







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010



Not streak
v Streak *
* r = 28


10
mC 10,


10 *


Figure 3: Intensity distribution of an image.


0

-02--
0 5 10 15 20 25
AZ [mm]

Figure 4: Autocorrelation where the intensity in each
image has been summated in the streamwise
direction. The correlation is obtained us-
ing the resulting intensity distribution and the
mean is taken for the whole set of images.



The field of view of is 100 x 56 mm2 with a resolu-
tion of 1920 x 1080 pixels. The depth of field of the
lens used is greater than the depth of the water layer at
all times. Hence, all fibres are sufficiently sharp to be
detected. The camera settings are kept constant during
all experiments.
The images are processed by first subtracting the
background noise. The fibres position (x- and z-
coordinate in the image), and orientation angle 3 (3 0
in the streamwise direction and 3 = 90 in the spanwise
direction) are found using a second order ridge detector
within the class of steerable filters, Carlsson (2009),
Jacob and Unser (2004). The filter has earlier been
evaluated by Carlsson (2009), where the effect of noise
and unsharpness of the images on the orientation angle


Figure 5: Parameter space where the fibres form streaks
or not for all cases, excluding experiments
with PEO.


were found to be less than 1 for moderate levels of
disturbances. To analyze the width of the fibre-streaks
in the flow, the intensities of the processed images are
summated in the streamwise direction. This leads to an
intensity distribution graph shown in figure 3, where
a high intensity indicates a high fibre concentration.
Since the streaks are not parallel to the flow direction,
only part of the images are used. For each intensity
distribution an autocorrelation is calculated and an
average is obtained for all images in the set. This
results in a correlation graph, depicted in figure 4. The
mean streak width is found as the first minimum of the
correlation. Since this point is not well defined, in this
study the interception point with zero correlation is set
to half the mean width of the streaks instead. Similar
methods have been used earlier, by e.g. Lagraa et al.
(2004). Even if a correlation has a negative minimum
value, this is not a guarantee that streaks are observed
by the eye. Therefore, a condition is set where the
minimum correlation has to be lower than -0.05 for
the set to have streaks. This value has been found by
investigating images with and without streaks and their
corresponding correlations.



Results & Discussion

Fibre streaks

In the parameter space investigated, it is of interest to
find out when the fibres tend to gather at the surface of
the glass-plate and form fibre streaks. In figure 5 the
variations of Rep and Reh are shown together with the
occurrence of streaks. As can be observed from this fig-








7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


S. 2AZo/h
S- 501 /h
07 - -70/h


- 08

02
S06
o8
0
0)
S04
E
0 02


0-
0


002
0018


2 25
x 104


Figure 6: Streak width normalized with the height of the
water-layer versus the bulk Reynolds number
for all cases where fibres form streaks, exclud-
ing experiments with PEO.



ure, fibres tend to form streaks for high bulk Reynolds
number and low particle Reynolds number. Moreover,
there are three different regions with no overlap in fig-
ure 5. Each region correspond to one aspect ratio and
thus the effect of aspect ratio can not be isolated.
Through the comparison of the width of the fibre-
streaks with the value of 501 a well known width for
turbulent boundary layer low-velocity streaks, figure 6
clearly shows that the width of the two types of streaks
scale in the same manner, where 2AO is the streak
width obtained from the autocorrelation, normalized
with the height of the water layer. Equation 6 has been
used to calculate the viscous length scale 1+. As is
shown in figure 5, no streaks are formed for fibres
with length, 28, while for fibre lengths rp 7
most experiments resulted in distinct fibre streaks.
Furthermore, depicted in the figure, there is a region
where for the same fibre length (rp 14), streaks occur
only for larger values of Reh.

Fibre orientation
The fibre orientation distribution is highly dependent
on the length of the fibres. Figure 7 show one sample
distribution for each aspect ratio; 7, 14 and 28. The
distribution for rp 28 has a large peak at 3 0
(streamwise) and most fibres are oriented with an angle
3 between -45 and 45 degrees. Fibres with rp 14
have a more homogenous orientation distribution, with
a peak at 3 = 0 and two peaks at 3 30. The
fibres with rp 7 are mostly located in the region
45 < 3 < 135. In figure 7 it can also be seen that there
are two peaks at 3 z 65 and 3 z 115 for rp 7.
These peaks will move closer to 3 90 as the particle


Figure 7: Orientation distribution for rp 7, rp 14
and rp 28. 3 0 and 3 90 is in
the streamwise and spanwise direction respec-
tively. The distributions are from experiments
with Reh A 8000. Rep z 32 for rp 7,
Rep z 165 for rp 14 and Re, 1113 for
r 28.



135 Peak Locat
Peak Location


120

105


= 90

75

60


20 40 60
Re
P


80 100


Figure 8: Peak in fibre orientation distribution versus
particle Reynolds number for fibres with rp
7. Peaks from dashed line in figure 7 are
marked with A.



Reynolds number is increased. In figure 8 the location
(() of the two peaks from several orientation distribu-
tions are plotted versus Rep, as can be observed from
that plot the two peaks merge into one at Rep 70. In
addition to the results in figures 7 and 8, it is observed
that when no streaks are found the peak at 3 = 0 grows
for all aspect ratios.

Effects of non-newtonian fluid
When the polymer polyethylene oxide (PEO) is added


05 1 15
Reh


re =7
S re =14
.... re =28







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


001
0 009


Not streak
10 Streak
n Not streak PEO
0 Streak PEO


"'p


Figure 9: Parameter space where the fibres form streaks
or not for all cases. The arrow refers to the
orientation distributions in figure 10.


to the flow, the fluid may experience non-newtonian
behavior. Addition of polymers to turbulent flow has
been shown to reduce drag, e.g. White et al. (2004). The
physical explanation for this is still under investigation.
In our study, the purpose of adding a polymer is to alter
the turbulence in the flow and to investigate whether
this has any effects on the fibre orientation and the
streakiness. Even though the addition of PEO has no
effect on the viscosity of the fluid, there are notable
differences compered to using pure water as the liquid
phase. Fibres in a PEO solution have a higher tendency
to form streaks and the streaks present are more distinct
compared to the water case. As shown in figure 9,
streaks occur both at higher and lower Reh when
polymers are present. There are two differences in the
orientation distributions compared to the water case,
see figure 10. Firstly, the peak at 3 0 is smaller and
secondly, the peaks that are found at 3 + 30 for water
are located closer to 3 + 40.



Conclusions

An experimental study has been performed to study the
behavior of cellulose acetate fibres in turbulent wall
bounded flow. A fibre suspension flowed down an in-
clined plate driven by gravity, producing a turbulent
shear flow. A CCD-camera was mounted below the in-
clined glass-plate to acquire images of the fibres in the
flow, and a steerable filter was used to detect the fibres
orientation and position in the images.
Experiments were performed for three different fibre
lengths; the angle of inclination and the height of the
water-layer were varied. Streaks were quantified by an-


Figure 10: Fibre orientation distribution for fibre as-
pect ratio 7, for water and PEO. Similar
bulk Reynolds number and particle Reynolds
number.


alyzing the autocorrelation of a set of images. It was
found that when fibre-streaks occurred they scaled in the
same manner as the viscous sub-layer streaks. However,
not all fibres gathered in streaks, for fibres with rp 28
not a single streak could be observed. Fibre-streaks were
formed for high Reh and low Rep.
Investigating fibre-orientation-distributions it has been
found that fibres that do not form streaks tend to have
an orientation aligned with, or close to, the flow direc-
tion. Streaks formed with rp 14-fibres had a close
to homogenous distribution, while the rp 7-fibres lo-
cated in streaks where mostly oriented between 45 and
135 degrees.
Fibres with rp 14 in PEO solution forms streaks
at both higher and lower Reh then in pure water. The
orientation distribution for fibres with rp 14 have a
smaller peak at 3 0 and the side peaks are located
closer to 3 + 40 compared to when no polymers are
present.


Acknowledgements

Thoughts and comments from Dr. Allan Carlsson are
greatly acknowledged. The study was funded by Wal-
lenberg Wood Science Center and the Swedish Research
Council.


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" 102


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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


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