MICRO-PIV MEASUREMENT OF FLOW THROUGH FORMING FABRICS
BY
FATEHJIT SINGH
B.TECH, INDIAN INSTITUTE OF TECHNOLOGY RORRKEE, 2010
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
in
THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES
(Mechanical Engineering)
THE UNIVERSITY OF BRITISH COLUMBIA
(Vancouver)
December, 2013
© Fatehjit Singh, 2013
Abstract
This thesis describes an experimental investigation of the flow field upstream of forming fabrics
that are typically used in the paper making process. Micro Particle Image Velocimetry was used
to measure the velocity distribution upstream of a forming fabric. The velocity upstream of two
different types of forming fabrics, namely Monoflex D60TM and IntegraTM, was studied. As
expected, the experiments show the existence of a highly variable drainage velocity field
upstream of both fabrics. The drainage velocity over the holes can be several times greater than
the drainage velocity above the fabric filaments. Since fines and filler tend to follow fluid
streamlines, one would therefore expect substantially higher fines and filler concentrations in the
holes between the filaments as compared over fabric knuckles. The decay in drainage velocity
variations can be represented by the equation Aexp −
Bz
D
+ C, where A and B are constant and
C is the uncertainty in the experimental setup. D and z represent the fabric‟s filament diameter
and distance above the fabric surface.
It is expected that the response of pulp fibers to the velocity variations caused by the fabric‟s
weave structure is strongly correlated to their length. The fibers with a length greater than 1.5
mm experience a weighted-average velocity field along their length that is approximately
uniform. The deposition of short fibers with length <1500 μm is strongly influenced by the
fabric‟s weave structure. The experiments also indicate that for fines and filler materials, the
different filament diameters and weave patterns among the fabrics are irrelevant since their
length scale is smaller than the gap between the fabric filaments. In general, the fabric with finer
weave pattern results in more uniform fiber deposition.
ii
To study the fiber mat formation, thin layers of fibers were deposited onto the fabric. It was
observed that as the grammage increases from 1 g/m2 to 5 g/m2, the normalized standard
variations in drainage velocity field increases from 15% to 61%. The thickness of the boundary
region (i.e. the upstream region affected by the disturbance generated by the fabric and fibers)
also increases from 1.5D to 3.0D.
iii
Preface
The presented thesis represents a culmination of work and learning that has taken place over a
period of almost two years (2011-2013). The first chapter of the thesis describes the technical
background, literature review and motivation behind this work, with the remaining chapters
presenting the design, data measurements and conclusions drawn from it.
Versions of the data presented in Chapter 2 & 3 of this thesis have been published in the 24th
CANCAM 2013 conference under the title of “Micro-PIV measurement of flow through a
forming fabric”.
The design of the test section and the flow loop described in Chapter 2 was done primarily by
Fatehjit Singh under guidance of Dr. Green Sheldon and Dr. Boris Stoeber. The Image
processing techniques used for data analysis are standard technique defined and tested by other
researchers working in similar fields.
Fatehjit Singh conducted all the experiments and analysis described in this thesis. Sheldon I.
Green‟s and Boris Stoeber‟s role in the thesis was primarily supervisory.
iv
Table of Contents
Abstract .......................................................................................................................................... ii
Preface ........................................................................................................................................... iv
Table of Contents ...........................................................................................................................v
List of Figures .............................................................................................................................. vii
List of Symbols ...............................................................................................................................x
Acknowledgements ...................................................................................................................... xi
Dedication .................................................................................................................................... xii
Chapter 1: Introduction ................................................................................................................1
1.1
Histroy............................................................................................................................. 1
1.2
Papermaking ................................................................................................................... 2
1.2.1 Former types ............................................................................................................... 4
1.2.2 Forming fabrics ........................................................................................................... 6
1.2.3 Forming section .......................................................................................................... 8
1.2.4 Wiremarks ................................................................................................................... 9
1.3
Micro-Particle Image Velocimetry ............................................................................... 10
1.4
Background on flow through forming fabrics .............................................................. 13
Chapter 2: Experimental Design ................................................................................................17
2.1
Test Section and flow loop ........................................................................................... 17
2.2
Depth of Correlation ..................................................................................................... 22
Chapter 3: Experimental Results ...............................................................................................27
3.1
Drainage velocity for Monoflex D60TM ........................................................................ 27
3.2
Drainage velocity for IntegraTM .................................................................................... 34
v
3.3
Velocity field effect on fibers and fines ........................................................................ 38
3.4
Single fiber experiments ............................................................................................... 40
3.5
Fiber deposition experiments ........................................................................................ 43
Chapter 4: Conclusion and Future work ...................................................................................48
4.1
Conclusion .................................................................................................................... 48
4.2
Future work ................................................................................................................... 49
References .....................................................................................................................................50
Appendices ....................................................................................................................................53
Appendix A ............................................................................................................................... 53
Appendix B ............................................................................................................................... 55
vi
List of Figures
Figure 1.1 Schematic explaining the different sections in papermaking process ........................... 3
Figure 1.2 Scheme of Fourdrinier former ....................................................................................... 4
Figure 1.3 Scheme of Twin Wire former ........................................................................................ 5
Figure 1.4 Single layer, double layer and triple layer forming fabric............................................. 7
Figure 1.5 Co-ordinate system for multilayer forming fabric......................................................... 8
Figure 1.6 Jet impingement and dewatering in forming section ..................................................... 9
Figure 1.7 Principle of Particle Image Velocimetry ..................................................................... 12
Figure 1.8 Velocity fields obtained directly above the fabric surface .......................................... 15
Figure 2.1 Schematic diagram of Micro-PIV setup ...................................................................... 17
Figure 2.2 a) Top view of test section indicating the position of forming fabric, fabric holder and
metallic screens inside the flow channel. b) 3D sketch of test section ......................................... 19
Figure 2.3 Fabric holder ................................................................................................................ 19
Figure 2.4 Shows the new microscope stage and micropositioner arrangement on the top of the
microscope .................................................................................................................................... 20
Figure 2.5 Schematic diagram of flow loop for the test section ................................................... 21
Figure 2.6 (a) Shows a single μ-PIV image with low particle image density. (b) Result of
carrying out image overlapping operation on 50 μ-PIV image pairs ............................................ 24
Figure 2.7 Shows the μ-PIV image obtained from the experiments. The image on right has been
obtained by applying the power filter technique on the left image............................................... 25
Figure 3.1 Monoflex D60TM forming fabric ................................................................................. 28
Figure 3.2 Drainage velocity field at different distance from the fabric surface .......................... 30
vii
Figure 3.3 Normalized drainage velocity as a function of normalized distance upstream of the
knuckle of the forming fabric ....................................................................................................... 31
Figure 3.4 Normalized Drainage velocity (Ṽ𝑧) along the machine direction line at different height
upstream of the forming fabric ..................................................................................................... 32
Figure 3.5 Normalized standard deviation in Vz as a function of normalized elevation above the
fabric ............................................................................................................................................. 33
Figure 3.6 Velocity fields at different distance upstream from the fabric surface ....................... 36
Figure 3.7 Normalized standard deviation in Vz as a function of normalized elevation above the
fabric ............................................................................................................................................. 37
Figure 3.8 Velocity field after circular averaging of the flow field .............................................. 38
Figure 3.9 Normalized standard deviation of the flow field immediately upstream from the fabric
surface after applying an averaging circulat filter with different diameters for Monoflex D60TM
and IntegraTM ................................................................................................................................ 39
Figure 3.10 A gold wire is attached to Monoflex D60TM single layer fabric in two different
orientations of (a) 0° and (b) 30° relative to the horizontal filaments .......................................... 41
Figure 3.11 Drainage velocity field (m/s) for to Monoflex D60TM single layer fabric immediately
upstream from the fabric (a) without a gold wire and (b) with a gold wire attached to the fabric 42
Figure 3.12 The drainage velocity (𝑉𝑧) as a function of (a) normalized Z distance with respect to
the fiber diameter d and (b) CMD*............................................................................................... 43
Figure 3.13 The pink dotes on the fabric surface are the trapped microparticles ......................... 45
Figure 3.14 Normalized standard deviation of the drainage velocity upstream of the Monoflex
D60TM fabric surface as a function of normalized distance from the fabric surface, for different
levels of fiber deposition ranging from 1 g/m2 (GSM1) to 5 g/m2 (GSM5) ................................. 46
viii
Figure 3.15 Exponential function fit at 5 g/m2 curve. The exponential curve intersects the fixed
uncertainty offset line at z/D =2.5 ................................................................................................ 47
Figure A1 Normalized drainage velocity as a function of normalized distance upstream of
different knuckle positions of the forming fabric. The experiment was run at a free stream
velocity 𝑉𝑚𝑒𝑎𝑛 = 0.35 m/s .......................................................................................................... 54
Figure B1 The drainage velocity (𝑉𝑧) as a function of CMD* at different points along the gold
wire ............................................................................................................................................... 56
Figure B2 The drainage velocity (𝑉𝑧) as a function of normalized Z distance (with respect to the
fiber diameter d) obtained at different location above the gold wire ............................................ 57
ix
List of Symbols
CMD Cross machine direction
CMD* Normalized distance in cross machine direction
D Filament diameter
DOC Depth of correlation
d Fiber diameter
𝑑𝑝 Particle‟s diameter
f f-number of imaging system
GSM Gram per square meter
l Filament length
M Magnification
MD Machine Direction
MD* Normalized distance in machine direction
NA Numerical aperture
NSD Normalized Standard Deviation
PIV Particle Image Velocimetry
p Power factor
Re Reynolds number based on the filament diameter
Vz Drainage Velocity
𝛿𝑐𝑜𝑟𝑟 Depth of correlation
λ Wavelength of light
ɛ Threshold parameter
x
Acknowledgements
I want to express my enduring gratitude to my supervisors Prof. Sheldon I. Green and Prof. Boris
Stoeber for their continuous guidance and exceptional patience during my research.
I would like to thank my friends Peter, Yu Chen, Troy, Drew, Jingmei, Anupam and Suman for
their help during the process of this project. I would also like to thank George Soong and Nici
Darychuk for their continuous assistance in labs and office.
AstenJohnson Inc. and NSERC are gratefully acknowledged for their financial supports.
Special thanks are owed to my beloved parents and my sister for their endless encouragement
and financial support throughout my years of education.
xi
Dedication
To my parents and sisters.
xii
Chapter 1: Introduction
Paper is a versatile material with many uses. Whilst the most common is for writing and printing
upon, it is also widely used as a packaging material, in cleaning products, in a number of
industrial and construction processes, and even as a food ingredient. Global consumption of
paper is approximately 400 million tons per year.
Paper has for a long time been the carrier of knowledge and history over generations. Today, in
the era of electronics, internet and computers, paper may no longer be the most popular means of
transmission of knowledge and information in some parts of world, but it certainly maintains its
central role in the packaging industry throughout the globe. Paper has also shown potential to
find a unique place in upcoming biomedical devices like micro-PADs (micro-fluidics paperbased analytical devices) [1]. Its high market availability and properties like biocompatibility,
wicking and light weight make it an excellent platform for biomedical devices. Papers containing
conducting carbon or metal fibers respond to electrical and magnetic stimulus and are being used
in different research areas. Apart from the increasing popularity of paper in biomedical devices,
the demand of paper is still high in developing economies where paper is used for printing and
writing, which requires paper sheets that possess a uniform density distribution. Methods for
producing uniform paper are thus very important, and are the motivation of this research work.
1.1
History
The word “Paper” is derived from an ancient Greek word papyrus, which stands for the Cyperus
papyrus plant. The papyrus was used in ancient Egypt and other Mediterranean cultures for the
purpose of writing. Paper as known in modern days was invented by the ancient Chinese in the
2nd century BC during the Han Dynasty and spread slowly to the west via the Silk Road.
1
Papermaking and
manufacturing
in
Europe
started
in
the
Iberian
Peninsula,
today's Portugal and Spain and Sicily in the 10th century and slowly spread to Italy and South
France reaching Germany by 1400 A.D.
Until the 18th century, paper sheets were manufactured one at a time by hand and their quality
was dependent on the skill of the individual craftsman. However this was a tedious and time
consuming process. At the end of the 18th century, Nicholas Louis Robert introduced a machine
which could produce paper in a continuous process. This first type of machine is now known as
Fourdrinier former. The major component of this machine is a moving endless belt of wire,
which drains water from the pulp suspension and forms a continuous wet sheet. The wet sheet is
dried and pressed to produce the final paper product. A number of significant inventions during
the early 19th century provided the basis for the modern papermaking machine which can
produce high quality paper at a much faster rate but even today, paper machines still follow the
same basic principles, in which the sheet is formed over a continuous wire (i.e. forming fabric) at
the wet end.
1.2
Papermaking
Papermaking involves four basic processes: forming, pressing, drying and calendaring. At the
forming stage, a dilute suspension of pulp in water, generally about 0.7% consistency (defined as
the percentage of weight of fibrous material in the suspension), is forced through a woven
forming fabric. The water passes through the voids in the forming fabric while the pulp fibers
and most of the fines and fillers get deposited on the top surface, creating a pulp mat [2 & 3].
After the forming section the pulp mat enters the nip of two rolls running under pressure in the
pressing section. Under the effect of pressure between the two rolls, water is removed from the
2
pulp mat and its compactness and strength is increased. The paper mat consistency leaving the
press section can be above 40 %. The drying section of the paper machine, as its name suggests,
dries the paper by passing it over a number of steam heated cylinders that evaporate the
moisture. Paper dryers are typically arranged in groups called sections and are run at lower
speeds to compensate for the sheet shrinkage. In the calendaring section, the paper is passed
through a number of rolls to make the paper surface smooth and glossy. After calendaring, the
paper is wound into a roll called a tambour or reel, and stored for final cutting and shipping.
In the next section we will discuss the major types of papermaking machines (Former types)
used in industry.
Figure 1.1 Schematic explaining the different sections in the papermaking process.
3
1.2.1
Former types
Fourdrinier Former
The fourdrinier former were the first machines that lead to the continuous production of paper. In
this kind of former the jet from the headbox is sprayed on the forming fabric moving in the
horizontal direction. The jet comes out through a rectangular opening of adjustable height which
is called the slice. At the end of the forming section wet web leaves the former and is passed on
to the next section in the process.
In the earlier versions of this former dewatering occurs only in downward direction due to effect
of gravity but with time significant modifications were made to increase the rate of dewatering
by using foil elements, dry and wet suction boxes [4]. There are certain downsides of using this
type of former. Firstly, because of unidirectional dewatering process the paper produced has
different properties on different sides, secondly at higher speeds the belt in the machine becomes
unstable and this limits the running speed of these kinds of formers.
Figure 1.2 Scheme of Fourdrinier former
4
Twin-Wire Formers
Twin wire formers were introduced in the 1950s to overcome the disadvantage of slow
dewatering rates and low running speed in Fourdrinier formers. The Twin Wire Machine or Gap
former uses two vertical wires in the forming section, thereby increasing the dewatering rate of
the fiber slurry while also giving uniform properties on both sides of the paper [2]. The two
forming fabrics also provide better stabilization allowing the manufacturers to run the machine at
higher speeds. Since the dewatering rate and running speed are higher for twin wire formers,
their running length is comparatively short as compared with traditional Fourdrinier formers.
Twin wire formers can be further divided into two types: hybrid formers and gap formers. As the
name suggests the hybrid former use both traditional Fourdrinier forming and twin-wire forming.
In gap formers the jet is directly sprayed between the two forming fabrics. The Figure 1.3 shows
a schematic of a gap former.
Figure 1.3 Scheme of Twin Wire former
5
1.2.2
Forming Fabric
The forming fabric or "wire" of a paper machine is the continuous belt or belts of mesh screen
upon which the paper sheet is formed. In the past, the forming fabric was made of bronze wire
and hence called the wire. These fabrics had a short life expectancy because they were
susceptible to fatigue and corrosion. Today, fabrics are made from synthetic fibers such as
polyester and nylon which provide better durability and allow running the fabrics at higher
speeds and enhanced width. The forming fabric structure is a complex three-dimensional woven
matrix, which consists of machine direction (MD), and orthogonal cross machine direction
(CMD) filaments in single or multiple layers. Figure 1.4 shows different types of fabrics
available in the market and highlights their structural differences. Figure 1.5, shows the
coordinate system of a multiple-layer forming fabric. The Z direction is perpendicular to the
MD-CMD plane. The forming fabric has two surfaces. The paper side, is the side in contact with
the sheet of paper. The machine or wear side is the side in contact with the elements that support
and move the fabric.
A forming fabric is designed to perform three basic functions: drainage, support and transport.
The forming fabric allows large volumes of water to flow through its structure in a short span of
time, allowing the increase of the fiber mat consistency. The influence of the forming fabric on
the flow normally is critical only at the initial phase of the fiber mat formation. Once a web of
fibres is formed, it begins to control the drainage. The solid surface of forming fabric provides
the crucial support for retains the fibers and fillers. The fabric also acts as a medium of transport
by passing the sheet to the next section i.e. pressing [5].
6
Figure 1.4 Single layer, double layer and triple layer forming fabric
The multiple-layer forming fabric is currently the most popular in industry. The fabric is unique
because filaments on either side of the sheet are distinct. On the paper side, the fabric filaments
are very fine which help in improving the fiber mass uniformity in the paper thereby increasing
its smoothness. On the machine side, the filament diameter is kept large to improve the fabric‟s
resistance to wear and decrease running resistance [6], [7]. Looking at the history of fabric
design, it is evident that the concept of multilayer forming fabric is quite successful and
addresses a number of performance issues simultaneously.
7
Figure 1.5 courtesy to AstenJohnson Inc, Co-ordinate systems for multilayer forming fabrics.
1.2.3
Forming section
At the forming stage, a dilute suspension of pulp in water, generally about 0.2 to 1.0%
consistency, is forced through a woven forming fabric. The dilute suspension exits the headbox
through a rectangular opening of adjustable height called the slice and gently lands on the
moving fabric. The speed of the moving fabric is kept within a 3% range of the speed of the
incoming jet of suspension. During the dewatering, the fines and filler materials in the pulp
suspension follow the flow streamlines, and are distributed in a fashion that depends on the
distribution of the velocity upstream of the forming fabric. The water passes through the voids in
the forming fabric while the pulp fibers and most of the fines and filler get deposited on the top.
The non-uniform structure of a forming fabric causes flow non-uniformities that alter the
distribution of filler in the sheet [8]. It is known that non-uniformities of the wet fibrous mat are
difficult to change at subsequent stages, i.e. pressing and drying. Therefore, the non-uniformities
introduced in the forming section of the wet fibrous mat will have a profound effect on the
8
structure of the printed end product. It has been shown that the velocity distribution of the flow
upstream from forming fabric strongly affects the final paper quality [8&9].
Figure 1.6 Jet impingement and dewatering in forming section
1.2.4
Wire Marks
A wire mark is the mark left on the paper web due to the formation wire i.e. the forming fabric.
Wire marks are undesirable as they can cause printing problems and substandard optical results.
There are two major types of wire marks: topographical wire marks and hydrodynamic wire
marks. Topographic wire marks refer to the three dimensional paper surface caused by the fabric
surface geometry i.e. knuckles and holes [10]. Topographic wire marks are caused in part by
fiber bending and in part by the geometry of the fabric, whereas a hydrodynamic wire mark is
caused by unevenly distributed hydrodynamic forces of the flow through forming fabric, which
results in an uneven fiber and filler distribution in the paper web [11].
9
The focus of the proposed research is on hydrodynamic wire marks, i.e. uneven fiber and filler
mass distribution caused by hydrodynamic forces. Since the hydrodynamic forces placed on
fibers are directly related to the velocity distribution of the flow around them, investigating the
hydrodynamic wire mark involves an examination of the velocity distribution upstream of the
forming fabric, where the paper web is formed. It has been shown earlier that the downstream
velocity does not have a significant effect on the velocity patterns upstream.
1.3 Micro Particle Image Velocimetry.
Particle Image Velocimetry (PIV) is an optical, non-intrusive method of flow visualization. It has
become one of the most widespread techniques for investigating the fluid flow because it allows
instantaneous measurements of the flow field in the plane or volume without disturbing the flow
or fluid properties. Moreover, this technique presents the advantage of resolving gradient based
quantities like vorticity.
The experimental set-up of a PIV system consists of multiple components based on the intended
application. Some of the most essential components are

a source of Illumination

a camera

a data acquisition system
Since PIV is an optical measurement technique, a transparent working medium and optical
access to the area of investigation are required. In most of the applications, one also needs to add
tracer particles to the flow. These particles can be fluorescent or non-fluorescent in nature and
need to be illuminated in the plane of flow. The light emitted or scattered by these particles is
10
recorded in the form of digital images and the displacement of particles is calculated by cross
correlating the image pairs.
In the simplest set-up, the PIV recordings can be done using a lamp of continuous white light and
a digital camera that records successive images [12]. For higher velocity flows, one needs to
reduce the time between successive images to a very small value to avoid losing significant
number of particles in an image pair. Under such conditions, one can use pulsed light sources
which are in sync with digital camera by a timing unit. The time delay between these light pulses
can vary from nanoseconds to few milliseconds. In general, the time delay between the light
pulses must be long enough to register finite particle displacement between the images and short
enough to avoid losing any particles due to their out-of-plane motion. The synchronization is
done in a way that the first light pulse is set at the end to the first camera recording and the
second pulse is set at an arbitrary time in the second recording. In this manner the time interval
„Δt‟ becomes equal to time interval between the two synchronized light pulses and stays
independent of camera frame rate [13].
The quality of particle images can be improved by using fluorescence imaging. Excited
fluorescent particles emit light at a certain wavelength whereas the remaining objects in the test
section either reflect or scatter the light at the original wavelength. An optical filter can be placed
between the test section and the digital camera which allows only the light emitted by the
fluorescent particles to reach the camera. Using this setup, a fairly improved image of particles is
obtained which is free from any light originating from the test section and background noise.
To calculate the displacement, digital PIV recording are subdivided into smaller regions called
“interrogation windows” [12]. Based on the displacement of particles inside the interrogation
11
window, an average displacement vector is generated. The velocity is calculated by the ratio of
average displacement and time interval between successive images.
Figure 1.7 Principle of Particle Image Velocimetry.
With the advent of microfluidics devices it became very important to study the flow field at a
micron scale. Today these microfluidics devices are used in a number of industries including
computers, automotive and biomedical industry. In some of most recent advancements,
microfluidics devices are being used as supersonic nozzles, micro-thrusters and flow control
devices in the aerospace industry and are being developed and used in the biomedical industry
for drug delivery and patient monitoring. This lead to the development of a wide range of
diagnostic techniques for experimental microfluidics research. A number of common
macroscopic full field measurement techniques have been extended to microfluidics length
scales with minor modifications. PIV at micron length scales is known as micro PIV. A typical
micro PIV system is assembled about an inverted microscope system. The microfluidics
12
device/test section of interest is placed on the microscope stage directly above the objective lens.
The light enters the microscope through an aperture and is focused onto a small region of the
microfluidics device.
Some of the working difference between PIV and μ-PIV are as follows:

In standard PIV, a light sheet is used to illuminate the region under observation. As such
the depth of the interrogation volume is equivalent to the thickness of the laser sheet. In
the case of μ-PIV we deal with objects at micron length scales as such it is not always
possible to generate a laser sheet in micrometric dimensions. As a result, the entire
volume is illuminated and the thickness of the measurement is defined by the depth of
field of the microscope objective. In experiments this thickness is better defined as the
depth of correlation which will be discussed in the later sections [14].

Unlike standard PIV, in μ-PIV experiments the positioning of the camera and the light
source is not flexible because of the inherent constraints introduced by the design of
microscopes.
1.4
Background on Flow through Forming Fabrics
Paper consists of a network of fibers that is deposited onto the surface of the forming fabric in
the forming section. The distribution of fibers in the finished paper is hardly affected by the
following process steps such as drying and pressing. The deposition of fibers on the fabric‟s
surface depends on the pulp properties such as fiber length, fiber coarseness and suspension
consistency [15], all of which have an impact on suspension mobility and suspension uniformity.
Winters et al. conclude in their work that at a given grammage, reducing the fiber length and
pulp suspension consistency reduces the basis weight variation. They also state, that the effect of
13
the fiber length becomes more significant at higher grammage, while flexibility effect is more
dominant at lower grammage [16].
Another factor that leads to non-uniform basis weight of the fiber mat related to the non-uniform
hydrodynamic forces that exist across the forming fabric because of the fabric‟s weave structure.
The design of this structure is the result of a long empirical design process with the goal of
improving the fabric‟s performance including durability, drainage capacity and fiber retention. It
has been shown that reducing the knuckle height on the paper side of the fabric increases the
paper uniformity [17]. The present work aims at studying the uniformity of the flow field
upstream of the fabric due to the fabric structure as this affects the uniformity of the paper.
It has been shown that the velocity distribution is itself affected by the structure of the forming
fabric at the beginning of fiber deposition with this effect reducing as more and more fibers get
deposited. It was found that the drainage rate is higher when fibers are oriented across the long
knuckles of a single layer fabric [18]. In the past decade several changes have occurred in the
design of forming fabric. Danby, R. in 1986 investigated the impact of multilayer fabrics on
sheet and wire mark formation, finding that coarse filaments on the machine side layer of the
fabric increase multilayer fabric longevity [19]. He also found that sheet quality is improved by
using finer filaments on the paper side layer.
Due to the high complexity of the forming fabric‟s three-dimensional structure, previous
research on flow through forming fabrics considered simplifications of the fabric geometry.
Huang et al. carried out a numerical investigation of flow through banks of cylinders at low
Reynolds numbers (smaller than 150), finding that a downstream row of 14 cylinders has little
influence on an upstream row of cylinders provided that the surface separation between the rows
exceeds 0.7 times the upstream cylinder diameter [20 & 21]. Gilchrist et al. measured the
14
upstream velocity profile and pressure drop of the flow through two rows of cylinders [22]. The
flow through the forming fabric has been extensively modeled using FluentTM at the Pulp and
Paper Center, UBC [23 & 24]. It was seen that that the flow non-uniformity caused by the fabric
weave is restrained to a short distance above the fabric. However, even this non-uniformity is not
particularly felt by fibers, whose length scale results in an averaging of the local velocity field. It
was also seen that uneven filament spacing produces only a highly localized change in the flow
field.
Figure 1.8 Velocity fields obtained directly above the fabric surface [23]
Detailed simulation results had been generated for velocity patterns upstream of forming fabrics.
But for validation purposes a proper experimental method to study the forming fabric is yet to be
developed. Owing to the extremely small scale of the filaments of forming fabrics, traditional
experimental techniques (Pitot-static tubes, PIV, and LDV) cannot be used to measure the
detailed flow field through the fabric. Peng and Green [25] made PIV measurements on an 80×
scale model of a forming fabric (at this scale, the resolution limits of PIV do not preclude
15
accurate measurements). They showed that the RMS variation of machine direction velocities are
about 10 % of the average Z direction velocity at the distance of 0.25D above the fabric. The
deviation of the Z direction velocity decreases from 15.1% at a plane 0.25D upstream of the
fabric to 3.8% at a plane 1.5D upstream of the fabric, implying that the non-uniformity caused by
the fabric weave is constrained to a short distance above the fabric. Immediately adjacent to the
fabric (0.25D upstream) the local drainage velocity varies by a factor of 2.2 from peak to crest,
this implies that there may be areas over the fabric where the fines (short, broken fibers with
length less than 75 μm) and filler materials initially accumulate 2.2 times faster than in adjacent
areas.
The process of making a scale-model of forming fabrics is both expensive and time consuming.
Further, the fabric model is not a perfectly scaled replica of the original fabric as certain
simplifications to the real geometry are necessary to develop robust CAD representations of the
fabric. The aim of the present work is to demonstrate a μ-PIV technique for the direct
measurement of forming fabric flow. Investigating a range of different forming fabrics using this
technique has the benefits of being fast, reliable, and inexpensive.
In the present research, we will be using original forming fabric samples in the test setup for
making the study even more accurate. Similar studies are been conducted presently at the
Georgia Institute of Technology using magnetic resonance imaging on forming fabrics to
understand the micro-flow phenomenon of wicking [26].
16
Chapter 2: Experimental Design
2.1 Test section and flow loop
As discussed in the previous section, the small scale of the forming fabric structure makes it very
difficult to use standard experimental techniques in determining the velocity patterns near the
forming fabric. Micro-PIV was selected to carry out experiments directly on the fabrics because
it provides instantaneous measurements of in-plane flow field at an appropriate spatial resolution
for fabric and fiber studies. The micro-PIV optics is shown in Figure 2.1. The experiments were
carried out at the Pulp and Paper Centre at UBC.
Figure 2.1 Schematic diagram of Micro-PIV setup
The next step was the construction of a flow loop that mimics the conditions inside the forming
section. The test section for studying forming fabric needs to fulfill the following criteria:
17
1) It should allow the study of different types of forming fabric, with filament diameters between
125
and
400
microns
and
a
fabric
repeat
structure
area
between
2.4 × 2.2 mm2 and 4.2 × 4.3 mm2
2) The drainage velocity through a forming fabric varies between 0.05 to 0.5 m/s [27]. The flow
loop must provide steady flow in this velocity range to mimic the actual dewatering conditions
prevalent during the forming process.
3).The test section should be compact enough to fit on a microscope stage and must provide
optical access for carrying out micro-PIV experiments.
To fulfill the above criteria a test section was made from a lexan (polycarbonate) block. The test
section in shown in Figure 2.2 and its outer dimensions are 80 × 50 × 10 mm. The inside flow
channel dimensions are 60 × 10 × 10 mm, thus providing a cross sectional area of 100 mm2 for
the flow. The test section‟s cross-sectional area of 100mm2 is large enough to study a fabric
structure repeat without being too affected by boundary layer effects. A glass slide is attached on
the top and bottom surface of the test section to provide optical access. The circular holes at
either side of the test section (see figure 2.2 b) are fitted with barbed plastic tubing connecting
the test section with a storage tank providing a constant head driven flow.
18
(a)
(b)
Figure 2.2 a) Top view of the test section indicating the position of the forming fabric, the fabric holder and the
metallic screens inside the flow channel. b) 3D sketch of the test section. The arrows indicate the direction of flow.
Upstream of the fabric are two flow conditioning metallic screens for improving the flow
uniformity and reducing large-scale turbulence.
The forming fabric is placed in the central rectangular region and supported using a thin-walled
rectangular insert support (see figure 2.3) which keeps it in a rigid position perpendicular to the
surface of the glass slide.
Figure 2.3 Fabric holder
19
The experiments also require great precision in placing and locating the fabric. A typical manual
microscope stage provides a resolution of 500 microns in the X-Y plane. Given the dimensions
of the fabric filament there was a requirement for a higher resolution micro-positioning stage.
Also it was not possible to lower the existing microscope stage far enough to scan throughout the
depth of the test channel, given the limited working distance of the microscope objective.
Therefore a new microscope stage was built using a KM-165u micropositioner. The
micropositioner provides a resolution of 5 microns in the X-Y plane. As seen in Figure 2.4, the
micropositioner is fixed on a steel sheet which has precisely drilled holes of various diameters to
allow the objective lens to pass through and to attach itself rigidly with the microscope.
Figure 2.4 Shows the new microscope stage and micropositioner arrangement on the top of the microscope.
Figure 2.5 shows a schematic of the flow loop. It consists of a centrifugal pump, valves, and inlet
and outlet tanks designed to provide a constant head pressure for the experimental test section.
20
The inflow tank provides fluid to the pump, and is slightly elevated in order to prime the pump
before operation.
The outlet tank receives the flow from the pump and supplies it to the test section. To maintain a
constant head, the outlet tank is provided with an overflow line which maintains the water level
inside the tank at a constant height.
Outlet Tank
Overflow Line
Test Section
Valve
Inlet Tank
Centrifugal Pump
Figure 2.5 Schematic diagram of the flow loop including the test section.
21
2.2 Depth of correlation
The basic principle of μ-PIV is the same as that of PIV. The velocity field is measured by
determining the displacement of particles in the flow between two laser pulses. Since μ-PIV is
used in experiments involving small length scales, the equipment used in capturing these digital
particle images is slightly different from the equipment used for conventional PIV.
One critical working difference is with the laser used to illuminate the micro-particles. In PIV a
very thin laser sheet defines the plane on which the PIV measurements are made. It is not
possible to create a suitably thin sheet in μ-PIV. Rather, the entire flow field is illuminated and
the plane on which measurements are made is the plane in which illuminated particles are
approximately in focus. The thickness of that plane is the depth over which particles significantly
contribute to the cross-correlation, and is commonly expressed in terms of a depth of correlation.
The depth of correlation (DOC) is defined as twice the distance from the object plane to the
nearest plane in which a particle becomes sufficiently defocused so that it no longer contributes
significantly to the cross-correlation analysis [28]. The DOC is an important parameter in
defining the out-of-plane spatial resolution for the experiment. The in-plane resolution is a
function of many variables and is dependent on the size of the interrogation window selected
during the cross-correlation analysis.
Analytically the DOC, 𝛿𝑐𝑜𝑟𝑟 can be defined by the expression,
𝛿𝑐𝑜𝑟𝑟 = 2
1− 𝜀
𝜀
∗ 𝑓 2 𝑑 2 𝑝 + 5.95 𝑀 + 1
2 4
2𝜆 𝑓
𝑀2
0.5
,
(1)
With the particle diameter 𝑑𝑝 , the wavelength of light λ, and the magnification and the f-stop of
the imaging system M and f, respectively. ɛ is the threshold parameter below which the
defocused particle images no longer contribute significantly to the displacement-correlation peak
and is normally set equal to 0.01. As the DOC increases, particles farther from the focal plane
22
contribute to the cross-correlation, leading to larger velocity errors if there are significant out-ofplane gradients of the velocity.
To remove the error caused by the finite DOC, a number of techniques have been discussed in
the literature. According to equation (1), the DOC can be reduced by increasing the
magnification of the objective lens or by reducing the particle diameter. Therefore different
combinations of particle size and objective magnification were tested to minimize the DOC.
High magnification objective lenses (40× and 50×) offer DOC in the range of 5-25 μm
depending upon the particle diameter, but they dramatically reduce the field of view. This can be
a severe limitation in our case where a large field of view is desirable to cover the entire fabric
repeat pattern in one image. On the other hand, with a lower magnification (4×) objective lens,
the DOC can be as large as 200 μm, which can lead to significant errors because of velocity
averaging over this slice thickness, and the fabric pattern in that direction is associated with
significant velocity variations.
1, 5 and 10 μm diameter particles were tested at different magnifications. The smaller particle
sizes have a favorably smaller DOC in range of 3-20 μm, but they suffer from poor signal to
noise ratio when focusing deeper in the flow channel. It was determined that 5 μm particles are a
good compromise between visibility and DOC. Most experiments were done with 5 μm particles
and a 10× objective lens, leading to a DOC of 50 μm or less.
Apart from making physical changes in the measurement system, a number of image processing
techniques have been put forward and tested for reducing the error caused by the DOC. Image
overlapping has been shown to effectively reduce the DOC and improve the measurement
accuracy [29]. The technique has shown very promising results in boundary layer flows where
velocity gradients are significantly large. The image overlapping technique was initially
23
introduced to artificially increase the particle image density in the PIV images with steady flow.
This technique constructs a new image by selecting the maximum intensity value at each pixel
from a given set of PIV images. This is equivalent to collecting the brightest particles from the
given image set and results in better correlation, a higher particle density, and higher density of
velocity vectors. The same technique also leads to a reduction in DOC because a number of
defocused particles are replaced by brighter in-focus particles. However, if two particles from
different images are in close proximity, image processing techniques may interpret the two
images as a single particle. Figure 2.6 shows a typical result of this image processing operation.
(a)
(b)
Figure 2.6 (a) Shows a single μ-PIV image with low particle image density. (b) Result of carrying out image
overlapping operation on 50 μ-PIV image pairs. Particle images obtained observing 5 μm particles with M=10 ×,
NA= 0.3 objective lens.
Olsen et al. proposed a data processing scheme that they labeled the “power filter technique” for
modifying the DOC. The power filter raises the image intensity at each point in the image to a
24
certain value „p‟. They showed that for images with the power filter technique applied the DOC
is given by:
𝛿𝑐𝑜𝑟𝑟 = 2
1−
1
ɛ2𝑝
1
ɛ2𝑝
0.5
∗ 𝑓 2 𝑑 2 𝑝 + 5.95 𝑀 + 1
2
2 4
𝜆 𝑓
𝑀2
The depth of correlation can be increased or decreased by a factor of two for power-filter values
of 0.67 and 2.0, respectively [30]. Experiments were in good agreement with the theoretical
values predicted by the model.
Figure 2.7 shows the result of this image processing operation applied to a typical μ-PIV image.
Rossi et al. studied the effect of particle image intensity and image preprocessing on the DOC
and concluded that it is very difficult to completely remove the bias error caused by a finite DOC
[31]. It is shown that various image preprocessing techniques developed for reducing the DOC
are only partially successful and can reduce the error by a factor between 0.5 and 1. The correct
quantification of the DOC is a subject of current research.
(a)
(b)
Figure 2.7 (a) The μ-PIV particle image obtained observing 5 μm particles with M=10 ×, NA= 0.3 objective lens.
(b) The image has been obtained by applying the power filter technique, p=2.
25
Based on the optical setup and the size of particles used in the experiment, the DOC was
calculated as 50 μm. In our experiment we used the image overlapping and power-filter
techniques to further reduce the depth of correlation by a factor of about 2. We therefore estimate
the DOC of the experiments is 25 μm.
26
Chapter 3: Experimental Results
Experiments are conducted for two different type of forming fabrics. The μ-PIV measurements
are taken over one repeat pattern of the fabric; this requires recording images at different depths
at a certain location by adjusting the focal plane of the microscope, as well as displacing the test
section on the micropositioner stage parallel to the fabric to a different location to record the next
set of images. The in-plane resolution of the PIV velocity field (i.e. the size of the interrogation
window) and the depth increments are different for the two fabrics; they were chosen according
to the different filament diameters. At each measurement plane, a minimum of 50 image pairs
are captured using the camera. These image pairs are pre-processed including overlapping and
power filtering to increase the particle density in the resulting image pair, and to reduce the depth
of correlation, respectively. Finally, the velocity vectors are calculated using DavisTM 8.0 by
LaVision through cross-correlation of the images of each pair. This yields 2D velocity vector
fields for each plane; the drainage velocity, the velocity component perpendicular to the fabric
plane, is extracted from this data, and it is combined in MatlabTM to create a 3D matrix
containing the drainage velocity in the entire scan volume.
3.1 Drainage velocity for Monoflex D60 TM
Micro-PIV measurements were conducted at different planes perpendicular to the Monoflex
D60TM fabric surface shown in Figure 3.1.Monoflex D60TM is a single layer forming fabric. Its
filament diameter is D=400 μm and the spacing between filaments can vary from 300 to 400 μm.
The in-plane resolution of the measurements based on the size of the interrogation windows is 20
µm × 20 μm and the distance between measurement planes is about 62.5 μm. Figure 3.2 shows
the drainage velocity fields obtained upstream of the fabric at different distances from the fabric
27
surface. CMD* and MD* represent the normalized distance wrt to filament diameter (D) in
CMD and MD directions, respectively. It can be seen that in the plane exactly above the fabric‟s
surface multiple stagnation regions indicate the presence of fabric filaments. Similarly, multiple
higher velocity regions indicate the holes between the filaments. As we move away from the
fabric surface the variation in the velocity field is reduced until the velocity field becomes fairly
uniform and undisturbed by the fabric.
MD(y)
CMD(x)
Figure 3.1 Monoflex D60TM forming fabric. The yellow point marks the knuckle position used for plotting the
results shown in Figure 3.3.
28
(a)
(b)
(c)
(d)
29
(e)
(f)
Figure 3.2 Drainge velocity field (m/s) at different distances from the fabric surface at (a) z = 0 D, (b) z= 0.25 D, (c)
z = 0.50 D, (d) z = 0.75 D, (e) z = 1.0 D, (f) z = 1.25 D, (g) z= 1.5 D. CMD* and MD* represent the normalized
diatance wrt to filament diameter (D) in CMD and MD directions, respectively. The experiment was run at a free
stream velocity Vmean = 0.35m/s.
Figure 3.3 shows the normalized drainage velocity Ṽ𝑧 = (𝑉𝑧−𝑉𝑚𝑒𝑎𝑛)/𝑉𝑚𝑒𝑎𝑛 as a function of the
normalized distance, taken at one location above a fabric knuckle. Similar plots have been
obtained at other locations above the fabric and can be found in Appendix A. Flow nonuniformities associated with the forming fabric weave cease to be measurable farther than 1.5 D
upstream from the fabric. The results are in agreement with previous simulation and
experimental work done by Vakil et al. [24] and Peng and Green [25], respectively. In the
following sections, we will define this region as „boundary region‟ i.e. the upstream region
affected by the disturbance generated by the fabric.
30
Figure 3.3 Normalized drainage velocity as a function of normalized distance upstream of a knuckle of the
Monoflex D60TM fabric. The experiment was run at a free stream velocity Vmean = 0.35 m/s. The location of the
measurement is marked in Figure 3.1.
Figure 3.4 is analogous to Figure 3.3, but shows Ṽ𝑧 above a line on the fabric oriented in the
machine direction. The blue curve represents the velocity immediately above the forming fabric.
The three locations where Ṽ𝑧 is nearly at -1 indicate the stagnation points caused by individual
fabric filaments; in dimensional form the velocity in these locations is close to zero. The red,
green, and black curves indicate the Ṽ𝑧 at distances of 100 μm, 200 μm and 800 μm above the
forming fabric, respectively. The results shown in Figure 3.4 are consistent with those in Figure
3 – at 0.5 D (200 μm) upstream from the fabric, the velocity variations are dramatically reduced,
and at 2 D (800 μm) above the fabric there is no correlation between the fabric structure and the
velocity profile.
31
Figure 3.4 Normalized drainage velocity along a line in machine direction at different heights upstream of the
Monoflex D60TM fabric.
Two features of the black (800 μm) curve in Figure 3.4 should be pointed out. First, the curve is
not smooth. The fine scale features of the curve are caused by random errors in the PIV
measurements, which are believed to be caused primarily by the noise in the PIV images.
Increasing the number of PIV image pairs decreases this noise, but to eliminate it completely
would require a prohibitively large number of image pairs. A second feature of the velocity
profile is the generally lower velocities present near the center. We believe these may be caused
by slight porosity variations in the upstream screens.
Close to the fabric (100 μm or 0.25 D upstream) the highest Vz is 6 times greater than the lowest
Vz. Depending on the Stokes number and mobility of the fines and filler particles, this large
variation in velocity would be expected to lead to substantially higher fines and filler deposition
rates in the holes between filaments compared to over fabric knuckles.
32
Figure 3.5 compares simulations and experimental measurements of the normalized standard
deviation for the velocity in the Z-direction at different planes upstream of the forming fabric.
The simulations were done with a perfectly uniform approach flow. In contrast, in the
experiment the approach flow to the fabric is slightly curved owing to the non-uniformity of the
upstream screens. To compare the simulations and experiments, the background parabolic
variation is subtracted from all velocity measurements before computing the experimental
standard deviation. The experimental normalized standard deviation falls from a maximum value
of 34% at a plane immediately above the forming fabric to 4% at a distance of 600 μm (1.5D)
upstream.
Figure 3.5. Normalized standard deviation in Vz as a function of normalized elevation above the Monoflex D60TM
fabric. The red curve shows CFD values and the blue curve shows the results of μ-PIV experiments. The experiment
and the simulation were run at a free stream velocity Vmean = 0.35 m/s.
33
The experimental normalized standard deviation (NSD) values are consistently somewhat higher
than the values from the numerical simulations. The difference can be attributed primarily to the
fact that the simulations have only negligible uncertainty whereas the experiments have an
uncertainty of approximately 4%. This uncertainty is caused by errors associated with the PIV
technique. The difference can also be caused by the fact that for the idealized fabric, the crosssection of each filament is circular along its entire length. In reality, large-scale plastic
deformation of the filaments occurs at knuckles, and thus at these locations the idealized fabric
geometry did not accurately reflect the real geometry.
3.2 Drainage Velocity for IntegraTM
The As compared to Monoflex D60TM the fabric has a very fine weave pattern and is used for
printing paper. Experiments were also conducted to determine the velocity field upstream of
IntegraTM. Based on the smaller diameter of the filaments the distance between parallel
measurement planes was kept at 40 μm to provide sufficient resolution. The in-plane resolution
was kept the same as for the previous experiments i.e. 20 µm × 20 μm. Figure 3.6 shows the
drainage velocity field at different distances from the fabric.
(a)
34
( b)
(c)
(d)
35
(e)
(f)
Figure 3.6. Drainage velocity fields (m/s) at different distances upstream from the IntegraTM fabric surface (a) z =
0D, (b) z = 0.25D, (c) z = 0.50D, (d) z = 0.75D, (e) z = 1.00D, (f) z = 3.00D. The freestream velocity is 0.3 m/s.
As for the IntegraTM forming fabric multiple stagnation regions in the velocity field immediately
upstream from the fabric (Fig. 3.6 (a)) indicate the presence of fabric filaments. Similarly,
multiple higher velocity regions indicate the holes between the filaments. At larger distances
from the fabric surface the variation in the velocity field is reduced and the velocity field
becomes fairly uniform and undisturbed by the presence of the fabric.
Figure 3.7 shows the normalized standard deviation of the velocity in the Z-direction at different
distances upstream from the forming fabric. This plot allows the determination of the boundary
36
region thickness created by the fabric. The normalized standard deviation (NSD) decreases from
a maximum value of 45% immediately upstream from the forming fabric to 5% at a distance of
2.5D (=375μm) upstream. The standard deviation beyond a distance of 2.5D is close to 5%,
which represents the uncertainty of the μ-PIV measurements. The NSD curve can be fitted using
a decaying exponential function and a constant which represents the uncertainty in μ-PIV
measurements. For the curve shown in figure 3.7 the equation comes out to be,
NSD
1.9z
z
= 40.9 ∗ e(− D ) + 5
D
In general, the thickness of the boundary region can defined as the value of z/D at which,
z
NSD D − c
= 0.01
NSD 0 − c
Where „c‟ represents the uncertainty in μ-PIV measurements. For IntegraTM the boundary region
thickness comes out to be 2.5D.
Figure 3.7 Normalized standard deviation in Vz as a function of the normalized distance from the IntegraTM fabric.
The experiment was run at a free stream velocity 𝑉𝑚𝑒𝑎𝑛 = 0.30 m/s.
37
3.3 Velocity field effect on fibers and fines
The velocity field shown in Sections 3.1 and 3.2 are point wise velocities. Fibers have a finite
length and therefore will not respond to point wise velocity, but rather to some weighted-average
velocity along their length. To see the effect of this velocity averaging over the length of fibers
and fines, filters that average over a circular region are applied to the point wise velocity fields.
Figure 3.8 shows the effect of circular filters with diameters of 400 and 800 μm on the velocity
field obtained directly above the surface of Monoflex D60TM fabric (Figure 3.2 (a)). The velocity
variations are smoothened out as the filter diameter (which can be roughly equated to the fiber
length) is increased. Similar results have been obtained previously through numerical simulations
[18].
(a)
(b)
Figure 3.8 Velocity field (m/s) after circular averaging of the flow field in Fig. 3.2 (a) over a diameter of 400 μm
and (b) 800 μm directly upstream from the Monoflex D60 TM fabric surface.
More interesting results can be obtained by comparing the averaged velocity fields above the two
forming fabrics tested and comparing their standard deviations with each other. Figure 3.9 shows
38
the variation in the flow field felt by fibers of different lengths directly upstream from the surface
of Monoflex D60TM and IntegraTM fabrics. Figure 3.9 seems to indicate that the filament
diameter and the weave pattern of the fabric do not affect these variations significantly for very
short (< 200 μm) or very long (> 1,500 μm) fibers. The fibers that are longer than 1,500 μm will
deposit in a fairly uniform way irrespective of the fabric used. However, fibers with an
intermediate length are strongly affected by the fabric geometry.
Figure 3.9 Normalized standard deviation of the drainage velocity immediately upstream from the fabric surface
after applying an averaging circular filter with different diameters for Monoflex D60 TM and IntegraTM.
Fibers of different length experience a more uniform velocity field with Integra TM compared to
Monoflex D60TM. Owing to the coarser weave pattern of Monoflex D60TM, the fibers over a
broad range of lengths tend to experience higher non-uniformity in the flow field, and it can be
39
expected that this leads to a non-uniform fiber distribution on the forming fabric, and thus to a
non-uniform fiber distribution in the resulting paper.
3.4 Single fiber experiment
Initially, experiments were conducted to ascertain the effect of single fiber deposition on the
flow field upstream of the fabric. The understanding of changes in the flow field can provide
insight into the early stages of the fiber buildup process and on its impact on subsequent fiber
deposition and orientation. To conduct such experiments one needs to be aware of the fiber
location on the fabric surface in advance since it is difficult to determine the position and
orientation of this fiber using the microscope once the fabric sample is mounted inside the test
section. It is therefore necessary to position the fiber at a known location with a desired
orientation relative to the fabric filaments before starting an experiment. Pulp fibers are not
longer than 4-5 mm, making it extremely difficult to sew a fiber to the fabric surface. Therefore,
the pulp fibers were replaced with a gold wire of similar diameter. Gold wires can be obtained
commercially. The extended length of the gold wire provides the opportunity to sew it to the
fabric thereby securing it well in place at a fixed orientation.
The experiment is conducted over a certain region of fabric with and without the gold wire. The
area of study usually includes up to 2-3 filaments of the fabric. These tests were conducted using
the Monoflex D60TM single layer fabric. As shown in Figure 3.10, the wire is either placed
horizontally or at a given angle relative to a horizontal filament. The experiments are conducted
using the same optical setup and the same PIV settings as described earlier in Section 3.1. Since
the wire diameter is only about d=50 μm, the distance between measurement planes is reduced to
40
12.5 μm to provide a higher resolution in order to capture the effect of the single wire on the
flow field.
CMD
MD
(a)
(b)
Figure 3.10 A gold wire is attached to Monoflex D60TM single layer fabric in two different orientations of (a) 0° and
(b) 30° relative to the machine direction filaments. In (a) the blue marking over the gold wire represents the line
used for plotting the results shown in Figure 3.12(b).
Figure 3.11 shows the velocity field directly above the fabric surface with and without gold wire.
The position of the wire can be identified from the differences in the velocity fields. The effect of
the artificial fiber is highly localized and does not seem to affect the flow field over the fabric
significantly. Similar results are obtained for different orientations of the gold wire and are
documented in Appendix B.
41
(a)
(b)
Figure 3.11. Drainage velocity field (m/s) for to Monoflex D60TM single layer fabric immediately upstream from the
fabric (a) without a gold wire and (b) with a gold wire attached to the fabric. The two vertical low velocity regions
indicate the fabric filaments while the horizontal region of low velocity in (b) indicates the position of the gold wire.
Figure 3.12 shows the velocity upstream from the fabric along the Z and CMD both with and
without the gold wire. In CMD and Z directions, the extent to which presence of the gold wire
affects the flow field is about 2d and 4d, respectively, where d is the diameter of the gold wire. It
can therefore be concluded that a deposited fiber reduces the probability of fine or filler material
settlement in its vicinity. It should be noted that in both the figures a zero velocity is never
attained because of the finite size of the interrogation window.
42
(a)
(b)
Figure 3.12 The drainage velocity (Vz ) as a function of (a) normalized Z distance with respect to the fiber diameter
d and (b) CMD*.
43
3.5 Fiber deposition experiments
To gain a better understanding of the fiber deposition process, additional experiments were
conducted to assess the effect of multiple fibers deposited onto the fabric and the changes the
process brings to the flow field. A small volume of pulp-water suspension with a known total of
mass of fibers is injected into the test section upstream from the forming fabric using a syringe.
To insert the syringe into the test section, a single hole is drilled from the side of the test section.
The fibers are deposited in increments of 1 g/m2until the grammage reaches the value of 5 g/m2.
Throughout the experiment, the freestream velocity is kept constant by increasing the height of
the outlet tank as the flow resistance of the fabric increases with the amount of deposited fibers,
and a fixed region of the fabric is scanned for the μ-PIV measurements. The same optical settings
and micro-particles as described in Section 3.1 are used for the experiments. The tests are
conducted using a batch of fractionated fibers with an average length of 2.4 mm. Such a large
average length insures close to 100% fiber deposition on the fabric surface and minimizes fiber
loss through the fabric. Maintaining the 100% fiber deposition condition is crucial for two
reasons:
1) This allows one to calculate the mass of fibers deposited on the fabric surface. In the present
experimental test setup it is not possible to collect the runaway fibers.
2) If a number of fibers are allowed to pass through the fabric, they may later end on the surface
of screens placed upstream in the test section as the same fluid is re-circulated through the test
section. Any such blockage of the screens will generate flow non-uniformities downstream in the
test section.
The experiments are restricted to only initial fiber deposition because at higher grammage, the
fiber mat becomes relatively dense and starts to trap a significant amount of fluorescent micro44
particles, as shown in Figure 3.13. Therefore these experiments cannot be run at much higher
grammage values. Trapping of micro-particles not only adds its own effect on the flow field but
only leads to a very high-brightness region close to fabric surface because of fluorescent
emissions by the microparticles. The latter effect makes it very difficult to distinguish between
particle images and background noise in the flow, and therefore all the displacement information
is lost.
Figure 3.13 The pink dots on the fabric surface are the trapped microparticles
Figure 3.14 shows the normalized standard deviations of the drainage velocity obtained at
different planes above the fabric for different fiber deposition levels. The curve representing a
grammage of 1 g/m2 (GSM 1) is very similar to the curve obtained over bare fabric (Fig. 3.5).
Note that unlike other plots of the standard deviation of the drainage velocity shown in Sections
3.1 and 3.2, here the standard deviation is calculated at a distance 0.25 D above the fabric. It is
not possible to calculate the flow velocity closer to the fabric because fiber deposition on the
fabric surface makes optical access to this region difficult and would lead to unreliable PIV
results.
45
Figure 3.14 Normalized standard deviation of the drainage velocity upstream of the Monoflex D60TM fabric surface
as a function of normalized distance from the fabric surface, for different levels of fiber deposition ranging from 1
g/m2 (GSM1) to 5 g/m2 (GSM5). The freestream velocity is kept constant at 0.2 m/s.
There are two interesting facts that can be inferred from the data shown. At the same average
drainage velocity the variation in drainage velocity increases with increasing fiber deposition.
This can be explained through continuity. As more and more fibers are deposited on the fabric
surface the available open area for flow decreases. To maintain the same flow rate, therefore, the
flow must accelerate and pass with much higher velocity through the available open areas,
causing the normalized standard deviation to increase.
The second observation which can be made from Figure 3.14 is the extension of the boundary
region thickness, (i.e. the upstream region affected by the disturbance generated by the screen
46
and fibers network) with the growing fiber mass on the fabric. To measure this extension, the
curves representing 5g/m2 fiber deposition level is fitted with an exponentially decaying function
and constant representing the uncertainty in μ-PIV experiment.
NSD
1.5z
z
= 81.3 ∗ e(− D ) + 5
D
As defined in Section 3.2, the boundary region thickness can be calculated from the expression,
z
NSD D − c
= 0.01
NSD 0 − c
which comes out equal to 3D (see figure 3.15). Since the fiber deposition increases the velocity
variation close to the fabric, it takes a much larger distance for the variations to decay under the
action of viscous forces. Similar observations have been made in other experiment involving a
scaled model of forming fabric [32].
Figure 3.15 Exponential function fit at 5 g/m2 curve. The exponential curve approaches the experimental uncertainty
value of 5 % asymptotically.
47
Chapter 4 Conclusion and Future Work
4.1 Conclusions
Based on the above results and discussion, the following conclusions can be drawn:
1) The fabric‟s weave structure results in strong variations in the drainage velocity upstream of
the fabric. The drainage velocity over the holes can be significantly greater than the drainage
velocity (Vz) above the fabric filaments. Close to the Monoflex D60TM fabric (100 μm or 0.25 D
upstream) the highest Vz is 6 times greater than the lowest Vz. One would therefore expect
substantially higher fines and filler concentrations in the holes between the filaments as
compared with over the fabric knuckles.
2) The velocity field variations caused by the fabric weave are constrained to a short distance
above the fabric surface and decay exponentially with distance from the surface. The rate of
decay of these variations (and the boundary region length) varies for different kind of fabrics, but
typical values of the boundary region length are 1.5D.
3) The variations of filament diameter and the weave pattern among the fabrics do not affect the
velocity variations significantly for very short (< 200 μm) or very long (> 1,500 μm) fibers but
the deposition of fibers with intermediate length (200 μm < l <1500 μm) is most strongly
influenced by the variations in fabric‟s weave structure. In general, the fabric with finer weave
pattern is expected to result in more uniform fiber deposition.
4) The deposition of a single fiber onto the fabric surface makes a highly localized impact on the
velocity field over the fabric and reduces the probability of fine or filler material advection in its
vicinity.
5) During the initial phase of fiber deposition (for a grammage less than 5g/m2), the variations in
the drainage velocity field and the thickness of the boundary region tend to increase.
48
4.2 Future work
In the existing experimental test facility, experiments can only be conducted using very long
fiber lengths (l >1500 μm). In future it will be worthwhile to collect the fibers and fines which
pass through the fabric surface and make precise fiber mass measurements. This will allow
running the experiments with different kind of fibers, to understand the effect of parameters like
fiber length and fiber coarseness on paper formation.
The multi-fiber experiments are also restricted to initial fiber deposition. At higher grammage,
the fiber mat becomes relatively dense and starts to trap a significant amount of fluorescent
micro-particles, making it highly difficult to conduct PIV analysis. To overcome this problem,
experiments can be designed to use the fines as tracing particles. The process will involve the
development of a new optical setup and a complex algorithm to trace the motion of fines in the
flow.
49
Reference
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52
Appendices
Appendix A - Additional plots for Monoflex D60TM
The conclusion related to the boundary region of Monoflex D60 TM fabric (refer to section 3.1)
are based on the plots of the normalized drainage velocity Ṽ𝑧 = (𝑉𝑧−𝑉𝑚𝑒𝑎𝑛)/𝑉𝑚𝑒𝑎𝑛 as a function of
the normalized distance, taken at different location above a fabric knuckle. The figure A1 shows
the plots obtained from different locations above the fabric. All the plots are fairly similar and
points towards the fact that flow non-uniformities associated with the forming fabric weave
cease to be measurable farther than 1.5 D upstream from the fabric.
(a)
53
(b)
(c)
(d)
Figure A1. Normalized drainage velocity as a function of normalized distance upstream of different knuckle
positions of the forming fabric. The experiment was run at a free stream velocity of 0.35 m/s.
54
Appendix B - Additional plots for single fiber experiments
Figures B1 & B2 show the drainage velocity obtained at different location with and without the
gold wire. In CMD and Z directions, the extent to which the presence of the gold wire affects the
flow field is about 2d and 4d, respectively, where d is the diameter of the gold wire.
(a)
(b)
55
(c)
Figure B1. The drainage velocity (Vz) as a function of CMD* at different points along the gold wire.
(a)
56
(b)
(c)
Figure B2. The drainage velocity (Vz) as a function of normalized Z distance (with respect to the fiber diameter d)
obtained at different location above the gold wire.
57