UNIVERSITY OF MISKOLC Faculty of Mechanical Engineering and Informatics
Department of Fluid and Heat Engineering
and
OTTO VON GUERICKE UNIVERSITÄT MAGDEBURG Institute of Fluid Dynamics & Thermodynamics
Laboratory of Fluid Dynamics & Technical Flows
GAS-LIQUID MIXING IN A SPIRAL TUBE
MASTER’S THESIS
MSc Program in Energetics Engineering
Faragó Dávid
OFZ0JG
Magdeburg, Germany
2018
II
TASK DESCRIPTION FOR THE FINAL MSC THESIS
Faragó Dávid
OFZ0JG
II. year MSc Energy management engineering student
Topic: Fluid mechanics measurement
Title: Gas-liquid mixing in a spiral tube
Task in details:
1. Literature survey regarding the development of spiral mixers, including the gas-
liquid phase mixing and attempts to improve its efficiency!
2. Design a method to measure the evolving flow structures inside a helically coiled
pipe!
3. Create an experimental setup to execute the calibrations and the measurements!
Investigate at least three different states!
4. Evaluate the results, and make suggestions on the possibilities of improving the
reactors efficiency!
Supervisor at the Department of Fluid and Heat Engineering, University of Miskolc:
Dr. Bencs Péter, Head of Department, Associate Professor
Supervisor at the Department of Fluid and Heat Engineering, Otto von Guericke
Universität, Magdeburg
Kováts Péter, Assistant lecturer
Date of task issuing: 28th February, 2018
Deadline for submission: 7th May, 2018
Ph. ...................................................
Dr. Bencs Péter
Head of Department, Associate Professor
III
1. Location of final internship: .............................................................................
2. External advisor’s name: ..................................................................................
3. The thesis tasks require / do not require modification1
................................... ........................................
date supervisor
If modification is needed, please list on a separate sheet.
4. Dates of supervision:
................................... ........................................
................................... ........................................
................................... ........................................
date supervisor
5. The thesis is / is not ready for submission.
.................................. ........................................ ..........................
date supervisor advisor
6. The thesis contains ........ pages and the following documents:
........ drawings;
........ supplementary documents;
........ other supplements (CD, etc.).
7. The thesis is / is not ready to be sent to the external reviewer.1
The external reviewer’s name: .................................................
................................. .............................................
date Head of Department
8. Final evaluation of thesis:
External reviewer’s opinion: ...................................................
Departmental opinion: ........................................................
Decision of the State Examining Board: .........................................
Miskolc, ......................... ...........................................
President of the State Examining Board
1 Please underline appropriate text.
IV
DECLARATION OF AUTHORSHIP
I hereby certify that this thesis has been composed by me and is based on my own work,
unless stated otherwise. No other person’s work has been used without due
acknowledgement in this thesis. All references and verbatim extracts have been quoted,
and all sources of information, including graphs and data sets, have been specifically
acknowledged.
Date: ........................................... Signature: .................................................................
V
ABSTRACT
Curved tubes are used in many different industrial appliances because of their
advantageous effects on flow dynamics for mixing and heat transfer. One of the most
widespread implementation is the helically coiled tube reactor, which has a low cost of
production and can come in relatively small sizes if necessary. In the present thesis, a
helically coiled pipe, made of glass, will be investigated using tomographic particle image
velocimetry. The geometry itself makes the measurement quite challenging; tomographic
PIV is usually executed with relatively simple, high aspect ratio bodies (with one
dimension being several times smaller than the other two). This time, the scrutinized body
has sizes of the same order of magnitude in all three dimensions (at least the investigated
sections do).
To carry out the measurements, four cameras were mounted on a stationary frame in a
linear arrangement. Fourteen COB LED lights were facilitated as the light source with a
total power output of 1960 W. To avoid reflections, the helix was placed inside a view
box with a refractive index matched agent. The sides of the view box were perpendicular
to the camera angle of views, eliminating any distortive effects between the particles and
the lenses. Prior to each measurement, a perspective calibration took place, then 1000
double-frame images were recorded. This procedure was repeated four times in total for
four different velocities, providing us with images in different flow regimes; one in
laminar, two in transient, and one in the turbulent zone. During certain pre-processing
and post-processing steps, the sizes of individual images were reduced, the amount of
ghost particles and background noise was decreased. The volume was reconstructed using
FastMART calculation providing three dimensional volumes, then the vector fields were
calculated using the built-in cross correlation function of DaVis by comparing the two
frames of each individual images. The resulting vector fields were then exported and
investigated in through visualizing them in ParaView.
VI
ÖSSZEFOGLALÁS
Ívelt csővezetékeket számos különböző ipari készülékben használnak azok kedvező
keveredésre és hőátadásra gyakorolt áramlástechnikai hatása miatt. Az egyik
legelterjedtebb megvalósítás a csavarvonalas tekercselésű csőreaktor, amelynek gyártási
költsége viszonylag alacsony, és kompakt, kis kiszerelésben is elkészíthető. Ez olyan
technológiák esetén lehet jelentős, ahol korlátozott helyen kell megvalósítani a keverést
vagy hőátadást. Jelen diplomamunkában egy üvegből készült csavarvonalas tekercset
(hélixet) vizsgálunk meg tomográfiás részecskemegfigyelésen alapuló sebességmérés
(PIV – Particle Image Velocimetry) alkalmazásával. Maga a geometria is meglehetősen
nagy kihívást jelentett mérési szemszögből; a TOMO PIV-t általában viszonylag
egyszerű, síkszerű testek (olyan test, melynek egyik dimenziója sokszor kisebb, mint a
másik kettő). Ezúttal a vizsgált test kiterjedése mindhárom dimenzióban azonos
nagyságrendű (legalábbis a vizsgált szakaszokat tekintve).
A mérés elvégzéséhez négy kamera került rögzítésre egy merev keretre, lineáris
elrendezésben. A szükséges fényt 14 COB LED lámpa biztosította. A tükröződés
elkerülése érdekében a hélixet egy tízszög alapó plexihasáb belsejében helyeztük el, ami
aztán egy, az üveg törésmutatójával egyező törésmutatójú, vegyülettel került feltöltésre.
Mindennemű optikai torzulás elkerülése érdekében a kamerák úgy lettek beállítva, hogy
az általuk látott képszög merőleges legyen a plexihasáb adott oldalaira. Négyféle
sebességet vizsgáltunk különböző áramlástani zónákban (egy lamináris, két tranziens,
illetve egy turbulens esetet). Minden egyes mérés előtt kalibrációra került sor, majd 1000
double-frame kép került rögzítésre. Bizonyos pre-processing és post-processing lépések
véghezvitele során az egyes képek méretet lecsökkentettük, valamint a szellem
részecskék mennyiségét és intenzitását lecsökkentettük, a háttérzajt kiszűrtük. A teljes
térfogatot a DaVis FastMART számítási módszerével rekonstruáltuk, majd a vektor
mezőket a DaVis kereszt korrelációs számítással határozta meg a double-framed képek
különálló két képének összehasonlításával. Az eredményül kapott vektor mezőket
exportáltuk és ParaView programkörnyezetben vizualizáltuk, a kapott eredményeket
vizsgáltuk.
1
I TABLE OF CONTENTS
I Table of Contents .................................................................................................... 1
II Nomenclature .......................................................................................................... 3
III Introduction ............................................................................................................. 4
IV Aim of the project .................................................................................................... 6
V Measurement Method .............................................................................................. 7
V.1 Particle Image Velocimetry ................................................................................ 7
V.1.1 Working principle ....................................................................................... 8
V.1.2 Single frame, double exposure .................................................................... 9
V.1.3 Double frame, double exposure .................................................................. 9
V.2 Tomographic PIV ............................................................................................... 9
V.2.1 Ghost particles .......................................................................................... 13
VI Experimental Setup ............................................................................................... 15
VI.1 The frame ...................................................................................................... 18
VI.2 Adjusting cameras ........................................................................................ 22
VI.3 Adjusting area of interest – Scheimpflug criterion ....................................... 23
VI.4 Light source .................................................................................................. 24
VI.5 Camera .......................................................................................................... 25
VI.6 Calibration tests ............................................................................................ 26
VI.7 Refractive index matching ............................................................................ 30
VI.7.1 About ammonium thiocyanate .................................................................. 30
VI.8 Investigated cases ......................................................................................... 33
VII Tomographic PIV experiment ............................................................................... 36
VII.1 Perspective calibration .................................................................................. 36
VII.1.1 Defining experimental setup ................................................................. 37
VII.1.2 Defining coordinate system ................................................................... 37
VII.1.3 Calibration target ................................................................................... 38
VII.1.4 Recording images .................................................................................. 38
VII.1.5 Mark reconnaissance ............................................................................. 38
VII.1.6 Mapping function .................................................................................. 39
VII.2 Compute disparity vectors ............................................................................ 40
2
VII.3 Disparity vector post processing .................................................................. 41
VII.4 Correct calibration ........................................................................................ 41
VII.5 Recording images ......................................................................................... 42
VII.6 Image pre-processing .................................................................................... 43
VII.6.1 Time filter .............................................................................................. 43
VII.6.2 Applying 2D mask ................................................................................ 44
VII.6.3 Particle quality enhancement ................................................................ 47
VII.7 Volume reconstruction ................................................................................. 48
VIII Post-processing ...................................................................................................... 49
VIII.1 FastMART sum ............................................................................................ 49
VIII.2 Three-dimensional Matlab mask .................................................................. 50
VIII.3 Applying mask on FastMART images ......................................................... 56
VIII.4 Vector Calculation – Averaged vector field ................................................. 56
IX Results ................................................................................................................... 57
X Conclusion ............................................................................................................. 67
XI Summary ............................................................................................................... 68
XII Outlook .................................................................................................................. 69
XIII Acknowledgements ............................................................................................... 70
XIV References ............................................................................................................. 71
XV Appendix ............................................................................................................... 73
3
II NOMENCLATURE
𝑅𝑒 Reynolds number −
𝐷𝑒 Dean number −
𝑑 Internal diameter of the helically coiled pipe mm
𝐷 Diameter of the bounding cylinder of the helically
coiled pipe mm
𝑏 Coil pitch mm
𝑡 Time, time step s
𝑡 + ∆𝑡 Subsequent time step −
𝑑𝑡 Pulse separation μs
𝑓 Frequency Hz,1
𝑠
𝑄 Flow rate 𝑚
𝑠
3
,𝑚𝑙
𝑚𝑖𝑛
𝑣 Mean velocity 𝑚
𝑠
𝑚 Mass 𝑘𝑔
𝜌 Fluid density 𝑘𝑔
𝑚3
𝜇 Dynamic viscosity 𝑁 𝑠
𝑚2
𝜈 Kinematic viscosity 𝑚2
𝑠
4
III INTRODUCTION
Curved tubes are widely spread in both laboratory and industrial-scale applications.
Complex flow structures can be achieved with a considerably low energy cost. Due to
their versatile applicability, the development of curved geometries has been an important
issue of research in recent years. Most industrial appliances (such as power production,
chemical industry, electronics, cooling systems, air conditioning systems etc.) use some
kind of curved tubes mostly for mixing, heat and/or mass transfer. Apart from industrial
devices, curved structures can also be found in the human body, such organs are blood
vessels, the lungs, etc. Curved tubes can be used for single-, or multiphase transfers,
including liquid – liquid, liquid – gas, and liquid – solid systems.
Curved geometries can be divided into five main groups; their respective images are
represented in figure III-1 [1].
a) Helically coiled pipes: constant curvature, constant pitch
b) Torus: constant curvature, zero pitch
c) Serpentine tubes: periodically curved tubes, zero pitch
d) Spirals (Archimedean spirals)
e) Twisted tubes
Figure III-1 Different types of curved geometries [1]
The fluid flow in a curved tube is affected by unbalanced centrifugal forces, which
generate secondary flows resulting in the change of flow structure. Generally, in linear
pipes the velocity of the core region is higher than the velocity near the walls. In curved
geometries, this core region, affected by the centrifugal forces, shifts towards the outward
walls. An example of the emerging flow structure is shown in figure III-2 [1]. On the left
side of the image (a) the velocity profile is depicted as contours with the velocity being
the highest near the outer wall. On the right side (b), the vorticity is visualized in the same
cross-section.
5
Figure III-2 Exemplary image of evolving flow structure in a curved tube [1]
The secondary motion of the particles due to the secondary flows affect the dispersive
properties of the flow much like turbulent flow does; enhances cross sectional mixing,
improves the heat and heat-mass transfer coefficient. On the other hand, the border
between turbulent region and laminar region is shifted, and a wide transient region
appears where structured secondary flows appear together with the primary flow. These
secondary flow structures can be reached with a significantly lower Reynolds number
than actual turbulent flow structures, making the technology applicable for devices where
the working agent possesses high kinetic viscosity or the achievable velocity, or available
space is limited. In continuous processes (such as oil refining, natural gas refining, power
generation…), the use of curved geometries proved to be more efficient than traditional
appliances while also maintaining a lower energy consumption. In most industrial
chemical processes, mixing is an essential step of the whole process, and has a major
effect on productivity, efficiency, and yield. Conventional technologies usually imply
high energy input to reach a high degree of mixing. In a mixing vessel, the high energy
dissipation causes temperature rise, in tubular structures on the other hand high pressure
drops and inhomogeneous shear layers can appear. Coiled tubes have been investigated,
and have been reported to achieve a high degree of mixing even with low velocities. They
also have no moving parts, which greatly reduces maintenance and ensures a longer
lifetime. Curved tubes are also simple to manufacture, and are available in a broad range
of materials [1, 2, 3].
One of the most widespread curve geometry is the helically coiled tube, which provides
an enhanced mixing performance and heat transfer efficiency while also being compact
and relatively easy to design and produce. The improved mixing feature and better heat
transfer is thanks to the emerging secondary flows inside the pipe due to the perpendicular
centrifugal forces. The performance of helically coiled pipes depend on many factors,
hence there are numerous ways to improve their efficiency. Performance improvement
methods can be divided into two main groups; active and passive techniques. Active
methods require some type of external energy input, such as electricity, acoustic force or
vibrations, etc. Passive methods rely on more advanced, complex geometries or additives
(such as propellers, springs) to improve the performance [4, 5].
6
IV AIM OF THE PROJECT
The aim of the present thesis is to find the best possible solution to carry out the three
dimensional tomographic PIV measurement of a single phase fluid flow inside a helically
coiled pipe. Since the body to be investigated is rather complex, this is quite an unusual
and unique TOMO setup. Our purpose is to minimize the amount and intensity of ghost
particles, filter out background noises, and obtain the reconstructed volumes and vector
fields within a reasonable time.
It is also an essential part of this thesis to give an overview of the basic industrial uses of
different curved pipes, to describe particle image velocimetry, with the facilitated Tomo
PIV unfolded more comprehensively.
Defining the velocities for the different cases of the measurement and describing the
different flow regimes prior to measurements is also a part of the work. Expected fluid
structures are described as well. After obtaining the vector fields for each investigated
cases, visualizing the resulting flow characteristics inside the helically coiled pipe and
deducting conclusions are the final goals of this thesis.
7
V MEASUREMENT METHOD
V.1 Particle Image Velocimetry
Humans have tried to visualize and understand the motion of gas and liquid fluids for
centuries. Many experimental setups have seen the light during the course of finding
better solutions, such as flow visualization using smoke, or making the fluid motion
visible by adding paint to the flow. Some of many important aspects of a measurement
are the detail and accuracy of acquired results. These methods were capable of visualizing
the said motions, but to obtain usable data, a more complex and well established method
was necessary. With the rapid technological advancement in past decades, it quickly
became possible to utilize the developments in the fields of optics, electrotechnics,
LASER, and computer technologies to provide reliable and accurate results of simple or
complex flow structures Modern experimental fluid mechanics are capable of providing
instantaneous scalar or vector fields for the whole area of interest [6, 7].
One such technique is the particle image velocimetry (PIV). A conventional PIV
measurement is a non-intrusive optical method that can provide an instantaneous flow
velocity field in a single plane. Although non-intrusive, the technique requires seeding
particles to operate. Particles should be neutrally buoyant and micron-sized. The exact
size, type and density of particles mixed with the working fluid can vary for every
measurement. For example, in air some kind of water aerosol or oil can be used, while in
water or other liquids, usually solid particles or bubbles are used. For the PIV of flames,
solid particles are used. Figure V-1 shows a conventional, two dimensional PIV
arrangement with one camera [6, 8, 9, 10].
Figure V-1 Working principle of a conventional 2C-2D PIV measurement [8]
8
1 Double pulsed PIV laser 2 Sheet optics
3 Light sheet 4 Field of view
5 Main flow, including particle seeds 6 Camera lens
7 Image plane 8 One interrogation zone
Since the recording cameras need a clear view of particles, the medium must be
transparent. Obtained results can be used in microfluidics, spray automation and
combustion processes. The obtained results are similar to that of CFD simulations (such
as Large Eddy Simulations), hence the data can be used to validate or further improve
existing models [6, 8, 9, 10].
The following list summarizes the main attributes of PIV [6, 10].
Nature: non-intrusive, requires seeding particles
Can provide snapshots of flow fields
Statistics, spatial correlations and many other data can be obtained from the results
Measurement area depends on experimental setup, can vary on a large scale
(𝑚𝑚2 to 𝑚2)
Provides similar results as certain CFD models
Velocity range: from very low (~0) to supersonic
Two or three dimensional, can provide two or three velocity components
Instantaneous flow field in investigated area / volume
V.1.1 Working principle
Using a precisely timed light source, the area of interest is illuminated twice with a short
time gap between the two pulses. Conventional PIV systems usually facilitate a light sheet
created from double pulsed laser beam, but for certain arrangements, different light
sources can be applied as well. For example, tomographic PIV requires a homogeneous
volume illumination, which can be achieved with high power LED lights. In this case,
LED lights can be equally, or even more effective than laser generated light. Particle
images are recorded simultaneously with the light pulses by high speed camera. The time
gap between two pulses can vary depending on the peak velocity and seeding properties
of the measured flow; an appropriate displacement of particles is essential for a good
correlation [8, 10].
Acquired images are then divided into smaller parts, called the interrogation zones. For
each interrogation zone, one vector field is calculated. Particles that leave the
interrogation zone are lost, reducing the amount of particles, which contribute to the
correlation. Also, particles inside an interrogation zone must move homogeneously in the
same direction, else the statistically calculated vector fields will show spurious results.
Therefore, the size of interrogation zones is selected to be large enough to contain an
adequate amount of particles, but not too large, so the particle movement remains
homogeneous [8, 10].
Images can be recorded in two different modes [8]:
Single frame, double exposure: both exposures are recorded in one frame
Double frame, double exposure: two images are recorded, one for each pulse
9
V.1.2 Single frame, double exposure
In this case, the first and the second exposures are saved in a single image. The
interrogation windows are resolved by autocorrelation. Autocorrelation function can be
visualized by three dominant peaks, of which the central is referred to as the self-
correlation peak. Two identical displacement-correlation peaks are located axisymmetric
to the self-correlation peak. The fact that they are axisymmetric to the middle peak shows
zero displacement of particles, which can be explained with the method of recording.
Since two exposures were recorded in one frame, it is unknown which particle location
belongs to the first exposure, and which to the second one. That makes the autocorrelation
somewhat ambivalent. Autocorrelation peaks are close to the central peak, and are
relatively low, which renders them sensitive to background noises. For a better
correlation, a lower particle density is suggested as both exposures are recorded in the
same image, essentially doubling the number of particles in every image. Since only one
image is being stored, the method is much faster and requires less free storage space [8].
V.1.3 Double frame, double exposure
Unlike in single frame mode, frames are recorded for both exposures separately. Both
frames are divided into identical interrogation zones, which are solved by cross-
correlation. As the frames are recorded at different times with different exposures, the
background may differ in both frames. The correlation peaks, however, are higher, and
unequivocal, hence smaller displacements can be detected than with autocorrelation.
Using the standard PIV setup with 1 camera, a 2D vector field can be obtained with 2
velocity components (2D2C). In this case, the third velocity component is not perceptible.
Using a stereoscopic arrangement with 2 cameras enables the measurement of 3 velocity
components on a single plane (2D3C). By recording a volume with two or more cameras,
volumetric velocimetry, also known as tomographic PIV, can be performed (3D3C). By
decreasing the seeding density, particle tracking velocimetry (PTV) can be classified in
the same manner. Since one of the main focuses of the present thesis is tomographic PIV,
it explained in more detail [8].
V.2 Tomographic PIV
Many, if not most, flows of engineering interest are turbulent, hence they are always
three-dimensional (3D) and can only be described by knowing all three velocity
components (3C). While stereoscopic PIV measurements can provide us with all three
velocity components, it can solely do so in two dimensions. For a successful imaging of
turbulent flows, vortex dynamics, and complex geometries, a method is required that can
capture the properties in higher dimensions. Demanding a time resolved solution or the
temporal development of a process essentially introduces time as an additional dimension
[11, 12, 13].
10
Figure V-2 shows a representation of the measurement domains and components of
different methods.
Figure V-2 Measurement methods divided by the number of measured components and
investigated dimensions [11]
In tomographic PIV, the measured domain is three-dimensional as opposed to
stereoscopic PIVs two-dimensional domain. In Tomo-PIV measurements a homogeneous
illumination is required for the volume of interest, which foreshadows the demand for a
more powerful light source. With respect to planar PIV measurements, the tomographic
PIV requires a significantly larger amount of light to achieve necessary homogeneity of
illumination. The light scattered by seeding particles in the illuminated volume is
collected by a number of cameras (usually at least four), then the projected images are
recorded on the host computer. It is recommended that at least four cameras are used in
tomographic PIV [11, 12, 13].
11
Cameras can be arranged in a cross configuration or in a linear configuration, as shown
in figure V-3. Cross configuration can generally result in more accurate measurements,
but linear configurations are also acceptable when setting up a cross configuration is not
possible for some reason [11, 12, 13].
Figure V-3 Typical tomographic PIV camera arrangements: cross- and linear
configurations [14]
12
Image V-4 shows the working principle of a tomographic PIV measurement that implies
double-frame recording method of initial particle images.
Figure V-4 Working principle of a Tomo-PIV measurement implying double-frame
recording and cross correlation [11]
The recorded image-pairs are the input for the tomographic reconstruction algorithm. The
pattern of the original particles in the three dimensional space is reconstructed by a
mathematical reconstructing algorithm, which yields a three dimensional distribution map
of light intensity in the investigated volume.
To obtain accurate relation of the location of particles compared to the measurement
domain, a calibration procedure is needed. During the process, a target with a pattern of
equidistant dots on either a single, or two planes is moved in the depth directions, and
images are recorded in several depths encompassing the measurement domain. The
parameters of the calibration target are well known, and so are the exact locations of the
target in the domain. For tomographic PIV, the precision is rather strict. Any perturbations
13
can cause the invalidation of a calibration, in such cases, the solution is to recalibrate.
Performing the calibration is advised to be done just before, or just after a measurement,
inside the frame of a couple minutes. Still, there is always a mechanical loose between
cameras and mounts, there can be vibrations, or slight changes in temperature… therefore
performing digital calibration corrections is also advised [11, 14].
Using the acquired reconstructed volumes, performing a three-three dimensional cross-
correlation analysis will provide the desired velocity vector field.
V.2.1 Ghost particles
The reconstruction is a large, underdetermined problem, therefore there is no exact,
unique solution for it. When the lines-of-sight of installed cameras intersect in a point that
does not correspond with a real particle, or with the same particle, these points are
perceived as artefacts in the reconstructed volume; the so called ghost particles. Image V-
5 illustrates the generation of ghosts in the case of a two-dimensional setup with two
viewing cameras. The filled circles represent real particles, empty circles show the
possible locations of emerging ghost particles. As for the colours, blue stands for particle
positions in the time instant 𝑡, while red represents particle positions in 𝑡 + ∆𝑡. Same
goes for the lines; they represent the lines-of-sight through real particles in the same
manner as the circles represent the particles’ positions. Where blue lines intersect, a real
or ghost particle is depicted in the time instant 𝑡, where red lines intersect, a real or ghost
particle is depicted in 𝑡 + ∆𝑡. As for real measurements, real and ghost particles cannot
be distinguished as easily. Particle positions occur as intensity peaks in images, however
we don’t know which intensity peak stands for the real particle and which for the fake
[11, 14].
Figure V-5 The generation of ghost particles [14]
The lines-of-sight through every particle can intersect with the other cameras’ line-of-
sight in a number of points. Several conclusions can be deducted from such a simplified
abstract: increasing the amount of particles in an interrogation zone will result in an
increased number of random intersections. Also, the larger the particles, the more likely
these random intersections will occur. Increasing the number of cameras will decrease
the chance of ghost particles, since random intersections for more cameras are less likely
to appear.
14
It is possible that the number of ghost particles exceeds that of the actual particles in the
reconstructed volume. Ghost particles will result in an underestimation of velocity
magnitude, and can result in biased peak detection during correlation [11, 14].
In summary, the three main influencing factor of the quantity of ghost particles [13]:
Seeding particle density: the higher the density, the more ghosts are likely to
appear
Seeding particle size: the larger the particles, the more ghosts are likely to appear
Number of cameras: more properly set up cameras can significantly cut the
number of ghosts in the reconstructed volume
Besides the main factors, camera and background noise, contaminations inside the
decagonal tank – hereinafter referred to as the view box – also slightly contribute to the
amount of ghost particles in the reconstructed volume. The number of ghosts can also be
reduced post measurement by applying different filters by taking advantage of the fact
that the intensity of ghosts is usually much lower than that of real particles. Applied
methods are described in section VII.6 – Image pre-processing [11].
15
VI EXPERIMENTAL SETUP
As a helically coiled pipe is quite an unusual target for a Tomo-PIV measurement, the
setup itself is also quite unique.
For an image clear of any kind of distortions and reflections, a perpendicular view at the
target object is suggested. Obtaining the three dimensional flow pattern with all three
velocity components requires different camera angles, and preferably four cameras.
Cameras need to face the target from different angles, opposing cameras see the target
from practically the same angle, resulting in a vast amount of ghost particles. For this
measurement, a linear configuration of four cameras were used as illustrated in figure VI-
1 [14, 15].
Figure VI-1 The applied camera arrangement from the front (left), and from the side
Cameras have a perpendicular view on the sides of the decagonal tank. This arrangement
helps to decrease the amount of optical distortions from recorded images. figure VI-2
summarizes the geometric properties of said tank, figure VI-3 summarizes the bounding
geometrical properties, and figure VI-4 shows the specific properties of the helically
coiled pipe. The cameras are viewing the target from an angle – they are perpendicular to
the sides of the tank, but not the actual target – hence calibration was necessary prior to
each image recording.
16
Figure VI-2 Geometric properties of the view box
Figure VI-3 Geometric properties of the helically coiled pipe (helix) including the
linking tube on both sides
The relatively long linear part after the first initial bend following the inlet serves as a
kind of equalizer zone; by the end of this linear section the effects of the bend are not
present, hence the flow is laminar when it enters the coiled section of the pipe. For an
accurate inspection of the evolution of flow structure inside the helically coiled pipe it is
essential that the initial flow does not contain any turbulent properties – in other words,
is laminar.
17
Figure VI-4 Specific geometric properties of the helix
As it can be depicted from the above image, the cross-section of the helix is not a perfect
circle, but rather an ellipse. The given values were measured and then reproduced in CAD,
however, our helix is not fully accurate. The pitch ratio varies and wall thickness is not
the same throughout the whole part. Figure VI-5 shows a photograph of the helix inside
the view box, with a laser sheet to help in setting the helix in position.
Figure VI-5 A photo showing the location of the helix inside the view box with the help
of a laser sheet
18
VI.1 The frame
The first step was setting up a suitable frame for the experiment to hold the cameras, the
helix and the tank. The frame has to be stable since it has to hold a large amount of weight,
and the slightest displacements can cause the invalidation of the calibrations. It also has
to provide an aid to securely and steadily lead the cables of the cameras to the processing
computer. The facilitated frame is shown in figure VI-6.
Figure VI-6 The facilitated frame
19
Next, four cameras were installed according to figure VI-7, and were linked to the host
computer. To minimize distortions, the arrangement ensures that all camera views are
normal to their corresponding side of the decagonal tank, meaning that the angle between
each individual cameras is exactly 36°. The thick camera cables are visible in the
background. In this setup, the Scheimpflug adapters acted solely as a link between camera
and cable, their angles were set to zero. The tank is already filled with a refractive index
matched solution (explained in section VI.7 – Refractive index matching). The helix itself
is pretty much invisible in this case, what we can see is the air inside it. Figure VI-8 shows
the setup from a different angle.
Figure VI-7 System arrangement from the side
Camera cables along with most linking and power supply cables were lead along the
frame instead of being laid on the ground, since working with fluids and electrical devices
could be dangerous without certain precautions. The host computer was relatively far
from any liquid (around 1.5 meters), making sure it wouldn’t get wet.
20
Figure VI-8 System arrangement as seen from behind the cameras
21
Figure VI-9 shows a schematic of the basic principle of the experimental setup including
the parts it consists of, and the main height values.
Figure VI-9 Schematic of the working principle of the system
1 Fluid level 2 Primary fluid reservoir
3 Helically coiled pipe (helix) 4 View box
5 Pump 6 Frame
7 Secondary fluid reservoir
22
As it can be perceived from the schematic, the main driving force of the fluid is the height
difference between the fluid level in the primary reservoir and the end of the pipe in the
secondary reservoir. A pump was used to resupply fluid to the primary tank in between
two measurements. To eliminate the effects of vibrations caused by the pump, it was
turned off during the measurements, and restarted when needed. The pipe was fixed on
top of the secondary reservoir, therefore the change of fluid level in the secondary tank is
irrelevant; not so much in the primary reservoir however. By eliminating the pump and
the factor of fluid level rise in the secondary reservoir, a nearly constant flow could be
obtained with the only limiting factor being the fluid level subsidence inside the primary
tank, which is further investigated in section VII.5 – Recording images. As visible, the
helically coiled pipe is situated in the middle of the view box; the centre line of the helix
and the centre line of the decagonal tank is coincident. The height difference between the
primary reservoirs fluid level and the centre line of the helix is 1.3 m, the height difference
between the centre line of the helix and the end of the pipeline is 0.8 m, adding up to a
total of 2.1 m height difference between the top and the bottom (without taking fluid level
subsidence into account).
A controllable traverse system was then installed so the calibration plate could be semi-
automatically moved in both depth directions, making later calibration processes much
simpler, and also more accurate.
VI.2 Adjusting cameras
To see if the cameras are in the right position, the tank, with the helix inside was filled
with water. Cameras were mounted with a 3D camera mount that provided an adjustable
angle in all rotational directions. Any translations were done by replacing the mounting
bracket – which was the link between the camera and the frame. Therefore, adjusting
camera angles was very simple, adjusting their position translation-wise on the other
hand, took several tries.
We used the “Grab” function of DaVis to see if the cameras are in their correct positions;
the Grab feature of DaVis provides a live image of selected camera views, hence any
adjustments are rather simple to supervise. The images in Grab mode are not stored.
Although the exact coordinates were calculated for each camera, setting them up was still
challenging. We used a laser sheet to project the origin to several points on the frame,
then measured the distances for each coordinates. After done, using the live image the
cameras were adjusted in a way, that the helix in all four images were the same size, and
in the same position.
However, since there is a mechanical loose between the lenses and the mounts, and the
helix exactly unmoveable inside the view box either, it is almost impossible to set the
cameras exactly as ought to. After all cameras were able to see the whole diameter of the
bounding cylinder of the helix – although only a section of the full length – the calibration
plate was pulled down, and set in the middle of the decagonal tank [8].
23
VI.3 Adjusting area of interest – Scheimpflug criterion
To obtain a large amount of data per image, the helically coiled pipe was divided into
different sections lengthwise. This arrangement also assures a better contribution to the
correlation. To keep the area of interest in focus, Scheimpflug adapters were used.
The Scheimpflug criterion states that if the image plane, the lens plane, and the object
plane does not intersect in the same point, deficiencies in the resulting images will occur.
Said deficiencies are from two sources. First, the particles that are out of the plane are
completely ignored and therefore lost. Second, the particles farther from the focus point
are getting blurry, and their perspective size is altered by the false mapping of the
cameras. Scheimpflug adapters alter the image plane in a way that the three planes will
intersect in one point, resulting in a high field of view and depth of field. Figure VI-10
illustrates an example of the acquired result without, and with an angled adapter [8, 16].
Figure VI-10 Calibration target with (left) and without an angled Scheimpflug setting
The image with the neutral adapter becomes obscure on the edges, while the one with an
applied Scheimpflug adapter is sharp in the whole volume, but is slightly darker.
Using the traverse system, the plate was then moved to the borders of our area of interest,
which in this case means ± 21 cm from the middle. The Scheimpflug adapters were then
adjusted so the three planes would intersect in a single point, resulting in sharp pictures.
The process was done by using the Grab function of DaVis 8.4, the same feature that was
used while setting the cameras themselves.
After, the calibration plate was removed from the tank and the helix was placed inside.
Using the grab function again, the cameras were slightly adjusted until we had a clear
view on the helix in both depth directions.
24
Figure VI-11 Fully open (left) and partially closed Scheimpflug adapters
Figure VI-11 shows the same Scheimpflug adapter in an open and an angled state. By
angling, the depth of field greatly increases, but the amount of light that can reach the
image plane is vastly reduced, resulting in sharper, but much darker images.
VI.4 Light source
Generally, for PIV measurements, the facilitated light source is provided by a LASER.
We decided to try LED lights as our light source to see if we can achieve processable
results. LED lights are a significantly cheaper, safer source of illumination, and are also
much simpler to deploy and operate. For the calibration test, the facilitated fluid was
water. The different refractive indexes of water and glass causes reflections and
distortions, however, our main goal now is to get the cameras in their correct positions.
In later measurements, with the piping and everything else in place, adjusting the cameras
to a greater extent would require major changes, hence would be quite difficult. First, 8
high power COB (Chip on Board) LEDs (Luminus CXM-32) were applied, 4 on top, and
4 on the bottom of the view box. The nominal performance of the 8 LEDs was 1120 W.
To control the flashlights’ timing, a programmable timing unit (PTU X) was used. The
PTU X controller provides a highly accurate timing for the pulses, and can be operated
from a PC [15]. The arrangement of the LED lights is shown in figure VI-12.
25
Figure VI-12 LED arrangement on the view box
VI.5 Camera
For the 3D tomographic PIV measurement, four LaVision Imager sCMOS (scientific
complementary metal–oxide–semiconductor) scientific imaging cameras were used – see
the picture. The camera operates in Global Shutter mode, which means that images will
start and end their exposures at the same time. On a side note, the
other possibility is Rolling Shutter mode where individual
rows, instead of waiting for the whole frame to finish, begin
the exposure of the next frame. While much
faster, Rolling Shutter mode is not
recommended for flashlight illuminated
cases, because of the possible time
difference between the exposures of
individual rows [15, 17].
For timing, the required mode for flashlight featured measurements – such as PIV – is the
double-frame mode, in which there is a short time gap between the end of the initial
exposure and the start of the following one. For the sCMOS camera, this time gap is
minimum 120 nanoseconds. This may limit the frequency of the flashlight. Table VI-1
sums up the main technical data of Imager sCMOS [15]:
26
Table VI-1 Main technical data of Imager sCMOS
Resolution (height x width) 2560 x 2160 pixels
Pixel size (height x width) 6.5 x 6.5 μm2
Quantum efficiency 57%
Imaging frequency (frame rate) 50 fps
Quantum efficiency shows the rate at which the camera can produce electric charge from
incoming photons. Cameras were equipped with Tokina 100 mm F2.8 MACRO lenses.
VI.6 Calibration tests
Different particle sizes and particle densities were tested to find a proper mixture for the
TOMO evaluation. The results showed that LED lights were able to provide enough
illumination for the two cameras in the middle, but were not sufficient for the cameras on
the top and the bottom. Theoretically, all four cameras should have provided almost
equally bright and sharp results, as they were at an equal distance from the helix, they
were located on the perimeter of a circle – of which the centre was the helix – along with
the other two cameras. There were two differences; one is the angle at which the cameras
were looking at the helix, and the Scheimpflug adapters’ settings. The former could be
responsible for lower illumination, since LED lights were not placed symmetrically for
each cameras. The latter could alter the focal distance at which the object is visible for
the camera, hence altering the relative amount of light reaching the lenses.
First, different LED arrangements were tested to see if it was possible to provide nearly
homogeneous illumination by leaving the Scheimpflug adapters set in the previous
positions. In addition to the previously placed 8 COB LEDs, 3 were added to both sides
of the decagonal tank, adding up to 14 applied high power COB LEDs, adding up 1960
W nominal power output in total. The new arrangement is shown on figure VI-13.
27
Figure VI-13 Modified LED arrangement on the view box
This LED arrangement proved to be able to provide much better, the illumination seemed
to be more homogeneous and the brighter in general. Figure VI-14 shows two images
with both LED arrangement showing the differences in the amount of illumination. The
two images share the same intensity scale to provide a rational basis of comparison. The
photo on the left side was taken with using 8 COB LEDs arranged as shown in figure VI-
12, the right side image was take while using 14 COB LEDs arranged according to figure
VI-13. As visible, particle intensity has increased by leaps and bounds. The intensity of
reflections won’t matter later on, since they will mostly be eliminated by using a refractive
index matched agent.
28
Figure VI-14 Particle intensity with 8 LED arrangement (left), and 14 LED
arrangement
Unfortunately, the views of the two more oblique cameras were still obscure. It was time
for the effects of the Scheimpflug adapters to be scrutinized.
Scheimpflug adapters are usually used to increase the depth of field on objects that are
not perpendicular to camera lenses. In this case, the calibration plate was used to set the
Scheimpflug adapters to the correct angle. Figure VI-15 shows a photo of the setup with
different Scheimpflug angles for the cameras.
29
Figure VI-15 A photo of tilted Scheimpflug adapters
The minor differences in angle caused major changes in focal distances. Furthermore,
higher angles drastically reduce the amount of incident light, which was the reason behind
the obscure picture of outer cameras. However, Scheimpflug adapters are mostly
necessary for planes, since our target was a rotationally symmetric body, every camera
was already perpendicular to it, without the adapters. Therefore, for the actual
measurements, the use of Scheimpflug adapters was unnecessary. We set the Scheimpflug
adapters to the same axis as their corresponding cameras, and checked if the calibration
was possible this way. In this case, Scheimpflug adapters acted solely as a link between
cameras and cables. Since DaVis was able to recognize most of the dots on the calibration
plate – which is shown on figure VII-4 in a later section – we continued with this setup.
To obtain sharp images for the whole area, the aperture was set to 32. Setting the camera
aperture to the maximal value drastically decreases the amount of light that a camera can
capture, which implies a high intensity light source to illuminate the investigated volume.
The fourteen installed COB LED lights with a total performance of 1600 W proved to be
sufficient for this case.
30
VI.7 Refractive index matching
The refractive index of air, water and glass are entirely different, therefore the obtained
images are distorted and contain a vast amount of reflections. Reflections could easily be
annihilated from later calculations by using a mask or a filter, but the deficiencies left
behind by them contain valuable data that are being lost. Distortions on the other hand
are much harder to eliminate. A plausible solution to eliminate these effects is to use
index-matched agents. For a flow inside a linear pipe, it would be sufficient to match the
refractive index of the fluid with the walls. With more complex geometries – which the
helically coiled pipe most certainly is – a tank can be used with sides that are
perpendicular to the camera views. The tank is often referred to as the view box. Inside
the view box, an index match liquid surrounds the investigated model. The flowing agent
inside the model is the same fluid that is inside the view box, and its refractive index is
approximately the same as the models. It is important that the cameras are arranged
perpendicularly to the sides of the decagonal tank (because it is the only boundary
between the camera and the target with different refractive indexes). Figure VI-16 shows
an example of unmatched and matched index cases. The difference is clearly visible, the
magnitude of refraction errors is greatly reduced after the index matching [8]. One
suitable fluid is the ammonium thiocyanate solution. On the left side image, the glass is
already essentially invisible; what we see is the air trapped inside the tube. After releasing
the air, the end of the tube fills with the agent rendering the part unseeable.
Figure VI-16 The end of the pipe filled with air (left) and ammonium thiocyanate
VI.7.1 About ammonium thiocyanate
The ammonium thiocyanate is the salt of thiocyanic acid, a highly hygroscopic, colourless
and odourless crystalline material. It is highly soluble with water and ethanol. It can be
used in many fields, including chemical analysis, photography, as a fertilizer etc.
According to PubChem data, ammonium thiocyanate is classified as an irritant,
environmentally hazardous – especially to aquatic biomes [18].
31
Ammonium thiocyanate is:
o Harmful if swallowed
o Harmful in contact with skin
o Harmful if inhaled
o Very toxic to aquatic life
o Very toxic to aquatic life with long lasting effects
o Harmful to aquatic life with long lasting effects
The solution has almost the same properties as water. The density was calculated by
measuring the mass of 100 𝑚𝑙 ammonium thiocyanate solution, the result was 1132
𝑘𝑔𝑚3⁄ . It is highly corrosive to metals, especially iron, brass and copper. Its kinematic
viscosity is 1.198 ∙ 10−6 𝑚2
𝑠⁄ . In this case, the refractive index of the solution is 1.468
(measured with an optical device). It is important, that the kinematic viscosity of the
solution is relatively low (close to that of waters), since at higher values it would not be
possible to obtain turbulent flows [18].
Figure VI-17 shows what ammonium thiocyanate does when left alone for a while, and
its immediate effects on the metallic parts of the calibration plate.
Figure VI-17 Ammonium thiocyanate precipitation (left) and the agents effect on the
calibration plate
32
It is interesting to note that with glycerine, at the saturation for the required refractive
index, the kinematic viscosity would be around 1122 ∙ 10−6 𝑚2
𝑠⁄ . At this rate the system
would need circa 25 𝑚𝑠⁄ flow velocity, or 45 𝑙
𝑚𝑖𝑛⁄ flow rate just to reach the very edge
of the boundary of laminar flow.
The saturation of the solution was based on a previous study of the university [19]. The
ideal saturation is 53.86 wt%, around 15 kg of the solution was necessary. The inner
temperature was always 20 °C, distillate water’s density at this temperature is 998.23
𝑘𝑔𝑚3⁄ [18].
Water Ammonium thiocyanate
Calculated mass 7.486725 kg 8.739375 kg
Measured mass 7.487 kg 8.739 kg
After we measured the necessary amounts, we began to add the salt to the distillate water,
giving it time to dissolve. Due to the relatively large volume, three separate mixers were
used in the process. Although larger mixers would have been able to mix this amount in
one, their metallic parts would have contaminated the agent. The mixers, which were used
in the process were either plastic, or ceramic coated metallic devices. Ammonium
thiocyanate, when dissolving, absorbs a huge amount of heat, cooling its surroundings
significantly. Ice started to form on the outside wall of the mixers, indicating that the
temperature of the solution dropped below zero. Since the saturation point of a liquid is
dependent on its temperature, we needed to wait for it to warm up to the original
temperature, 20 °C (we were concerned about heating a hazardous agent in a plastic
bottle). After about 4-5 hours, the solutions in the three mixers were transparent,
indicating a roughly complete dissolution, so we decided to mix the three parts into one,
and let the solution settle overnight.
The solution is highly reactive and tends to precipitate on free surfaces. The view box and
the reservoirs were filled up with ammonium thiocyanate solution.
For the measurement, the calibration plate was changed to a new one for two reasons;
first, the previous calibration plate was made of aluminium, and the solution tends to react
with metals and form a red cloud inside the fluid. Second, the plate was too short to cover
the whole region for all cameras, all views and didn’t have enough points in one plane for
the DaVis calibrations. The new calibration plate was made of plastic, and was high
enough to cover all camera views.
33
VI.8 Investigated cases
Before running the measurements, several cases have been predetermined based on our
suspicions considering the flow. When a fluid moves in a straight pipe, that after a while
becomes curved, the centripetal forces will cause the fluid to change its direction of
motion. If the flow is not fully turbulent, but has enough energy for vortices to form, then
the so-called Dean-vortex pairs become visible [20]. Figure VI-18 shows an abstract of
what can loosely be called the path lines of a vortex pair in a cross section of a circular
pipe [21].
Figure VI-18 Dean-vortex pairs in a cross section of a circular curved pipe [21]
The centre line – denoted by capital “C” – acts as a sort of a border between the upper
and the bottom flows. The velocity components of particles always lie in the central plane,
hence a particle that is inside this plane – theoretically – never leaves it. This phenomenon
essentially divides the whole volume into two with two independent flows. The arrows
represent the main direction of the particles’ motion. As for the central plane, particles
move from the inside region to the outside due to centrifugal forces. The motion of the
particles is represented by the path lines, however, they don’t actually form a closed path.
The representation is superposed with the motion along the pipe, resulting in a screw-like
helical motion along the channel. Two equidistant points from the centre line are denoted
by the capital letters “A” and “B” stand for what could be understood as the “focus” of
the vortex pair; the streamlines through these points are circles coaxial with each other
and parallel to the centre plane. The direction of the helical motion of the two vortices are
the opposites of one another [21].
34
The Dean-number is a dimensionless property used in fluid dynamics, and can be defined
as expressed in equation (1).
𝐷𝑒 =𝑣 𝑑
𝜈√
𝑑
𝐷= 𝑅𝑒√
𝑑
𝐷 (1)
Where De is the Dean-number, Re is the Reynolds number, c is the mean streamwise
velocity of the fluid, d is the internal equivalent diameter of the pipe, D is the diameter of
the bounding cylinder of the helically coiled pipe. All of the above properties are applied
to the flow domain; the wall thickness does not play a role in the evolution of the flow
structure [21].
At low Dean-numbers (𝐷𝑒 < 40) the flow is fully laminar. At higher Dean-numbers
(𝐷𝑒 = [64 … 75]) vortex pairs develop and become the primary instability of the flow.
Between these two regions, the flow shows unsteady secondary turbulences, but the Dean
vortices are not yet recognizable. With increasing Dean-numbers, the amplitude of
secondary instabilities starts to increase exponentially. The flow develops fully turbulent
properties at about a Dean-number of 400 [20, 21].
The velocity expressed from equation (1):
𝑣 =𝐷𝑒 𝜈
𝑑√
𝐷
𝑑 (2)
Table VI-1 shows some theoretical cases. They mostly acted as touchstone for later
measurements; the flow rates were set according to these values to obtain a laminar,
transient and turbulent flow structures.
Table VI-2 Theoretical cases overview
Case
Nr. 𝐷𝑒
𝑑
[𝑚𝑚] 𝐷
[𝑚𝑚] 𝜂 [𝑃𝑎 𝑠] 𝜌 [
𝑘𝑔
𝑚3] 𝜐 [𝑚2
𝑠] 𝑣 [
𝑚
𝑠] 𝑄 [
𝑚𝑙
𝑚𝑖𝑛] 𝑅𝑒
1 64 6 27 0.001349 1131.9 1.1918E-06 0.03 45.75 135.76
2 75 6 27 0.001349 1131.9 1.1918E-06 0.03 53.61 159.10
3 200 6 27 0.001349 1131.9 1.1918E-06 0.08 142.97 424.26
4 700 6 27 0.001349 1131.9 1.1918E-06 0.29 500.38 1484.92
5 3500 6 27 0.001349 1131.9 1.1918E-06 1.47 2501.90 7424.62
To change the flow rate, a simple clamping tool was used (see figure VI-19). For low
velocities, the flow rates were determined by measuring the volume flowing out over
predetermined time steps and then averaging the results. For higher velocities, the mass
of the flowing out fluid was measured and then, knowing the density of ammonium
thiocyanate solution, it was calculated to flow rate. We had to resolve from the use of
more advanced flow meters and taps, since their metallic parts would contaminate the
solution.
35
Figure VI-19 The clamping tool used to control the flow rate
The flow rates were set and measured before each separate measurement cases. Table VI-
2 sums up all investigated cases except for the fourth case, which solely describes the
flow properties without the clamping tool – it is the maximal flow rate that can be
achieved with the current setup.
Table VI-3 Investigated cases
Case
Nr. 𝑄 [
𝑚𝑙
𝑠] 𝑄 [
𝑚𝑙
𝑚𝑖𝑛] 𝑐 [
𝑚
𝑠] 𝑅𝑒 𝐷𝑒
1 0.77 46 0.0390 164 70
2 1.20 72 0.0612 257 111
3 7.92 475 0.4032 1692 728
4 20.00 1200 1.0186 4273 1839
As already mentioned, the helix was divided into parts lengthwise. Starting from the inlet,
four different areas are investigated. Each of these areas are share a half of a coil with
their neighbouring parts, assuring a better quality coupling between them in the post
processing. The helix and the view box are linked together with solid coupling; hence
they are moved together when changing to a different area of interest. The shifting
direction of the box with the helix inside is strictly perpendicular to all camera views,
hence one calibration for every velocity was enough. The calibration plate was also
independent from the view box, therefore moving the box sideways and then recalibrating
the same views as before would not change the calibration in any noticeable way.
Calibrating involves taking the helix out and replacing it with the calibration plate, then
repeating this method the other way around. This whole process puts quite some strain on
the entire unit. On the other hand, performing only one calibration takes about the same
amount of time as recording all 4000 images for one case, with taking the necessary
relocations of the view box into account.
36
VII TOMOGRAPHIC PIV EXPERIMENT
The flow rate was measured individually for each case. Prior to the measurements, tracer
particles were mixed in with ammonium thiocyanate. White polyamide tracer particles –
Vestosint 2178 – were used as seeding particles with a size of 20 𝜇𝑚.
Since the lines-of-sights are not perpendicular to the surface of the helically coiled pipe
and the investigated volume quite vast, perspective calibrations were carried out before
each investigated cases. Note that calibration could be done either just before, or right
after a measurement. The fluid inside the tank was stirred, resulting in a motion of
accumulated contaminations. Images were recorded in this state, and they were later used
to create the disparity map for the volume self-calibration. The following flowchart
illustrates the process of calibration [14].
Figure VII-1 shows a flowchart of calibration and tomographic reconstruction steps.
These steps are thoroughly explained in this chapter.
Figure VII-1 Calibration (left), and tomographic reconstruction flowchart
VII.1 Perspective calibration
For a tomographic PIV experiment, a volume calibration is needed, during which several
planes are recorded and taken into account. Calibration was done following the
instructions of DaVis 8.4 [15].
37
VII.1.1 Defining experimental setup
Type of calibration was set to advanced, 4 cameras were defined in the same coordinate
system.
VII.1.2 Defining coordinate system
For the calibration we used 11 image planes with 4 mm gaps between each, ending in ±20
mm in both depth directions. Originally, 21 planes were recorded starting from the
middle, with 2 mm wide gaps between every plane, in case we needed more planes for
proper results. However, 11 planes proved to be sufficient. Figure VII-2 shows an abstract
of plate positions with arrows indicating the direction of the cameras’ lines-of-sight and
the angle at which the cameras are looking at the target. The open decagon represents the
view box, the blue ring in the middle stands for the helically coiled pipe. Of course, the
helix and the calibration plate were not ever in the view box at the same time. The grey
rectangle denoted as the calibration plate shows the proportional side view of the target,
the other equidistant lines in front of the calibration plate represent the faces of the target
in different positions. The thicker, red line located in the middle is the origin.
Figure VII-2 Calibration plate positions inside the view box
38
VII.1.3 Calibration target
The calibration target can be either two- or three dimensional. Two dimensional
calibration plates have equidistant dots on a single plane, while three dimensional plates
have them on usually two separate planes. For the measurement, we are using a self-made
2D plate with the parameters shown on figure VII-3. The triangle in the middle serves as
a reference point, DaVis can differentiate it from the circles, and hence it is not interfering
with the mark identification. As shown on the magnified image, the distance between
individual marks is 3 mm in both directions.
Figure VII-3 Properties of the facilitated calibration target
VII.1.4 Recording images
After making sure that there were no contaminations or bubbles between the cameras and
the plate (e.g. on camera lenses, on the walls of the view box or the helix), the images
were acquired in every plane as previously illustrated in figure VII-4.
VII.1.5 Mark reconnaissance
After recording the images, the same marks on every view was identified. Since we used
a self-made calibration target, automatic mark recognition could not be used. Instead, we
selected the same marks for all cameras, all views, and all planes. The process required a
certain order of mark selection. To make it easier to identify the marks on each plane, in
the middle of the plate there were a black square and a triangle, compared to the positions
of these we were able to find the appropriate points. For the edges however, these figures
were not in view. To be able to recognize the correct dots, we used a simple laser sheet.
39
It did not interfere with the calibration or the measurement in any way, and provided a
unique and noticeable benchmark.
VII.1.6 Mapping function
After identifying three marks on each recorded plane on all four views, by running the
“Fit mapping function” DaVis identified all recognizable marks on the whole plane using
a polynomial 3rd order method.
Figure VII-4 shows an image of the view of camera 2 (second camera from the bottom);
the brighter line in the middle is the linear projection of the laser sheet. The green-framed
circles are the marks that were recognized, of which the three with the circle inside around
the triangle are the ones that we originally marked as references.
Figure VII-4 Identification of target marks
The general settings for the fit mapping function are:
Fit model 3rd order polynomial
Handedness Right handed
Scale factor 64.8828 pixel/mm
Size of dewarped image 2760 x 2476
40
VII.2 Compute disparity vectors
Disparity vectors are used for the volume self-calibration, of which the goal is to eliminate
any remaining calibration inaccuracies, since however strictly the calibration process was
done, some errors will always appear. The lines-of-sight of the cameras are known from
the volumetric calibration. Ideally, the lines-of-sight of all cameras intersect in one point,
but since some calibration errors are always present, lines-of-sight do not intersect in a
single point. Figure VII-5 shows an abstract of a three camera setup exemplifying the
result of calibration errors. Ideally, the X, Y, Z refer to the coordinates of the intersection
point. In this case, blue represents the true lines-of-sight, which don’t intersect in a single
point. The middle point denoted with the X, Y, Z coordinates in this case denote a ‘best
guess’ intersection point, which is determined by triangulation. After obtaining a
triangulated intersection point, the lines-of-sight are projected back to each camera
sensors (marked by red lines). If the position of the projected intersection point and the
original sensor positions are known, the disparity vectors can be calculated for each
cameras [14].
Figure VII-5 Lines-of-sight intersections in case of a three camera setup [14]
Disparity vectors are calculated for each individual particle. The investigated volume is
then divided into a discrete number of sub volumes. A disparity map is created for each
sub volume by applying a Gaussian blur on each disparity vector inside the sub volume,
then summing the results.
The quality of disparity maps can be increased by using a series of images to determine
the disparity maps. The results will have less noise and more distinguished peaks. Figure
VII-6 shows the difference between evaluating different numbers of images.
41
Figure VII-6 Exemplary disparity maps generated from different numbers of images
[14]
In our case, the fluid inside the view box was stirred, resulting in a motion of accumulated
contaminations and particles inside it. A whole set was recorded, and then all images were
used to create the disparity maps. From the disparity maps, a disparity vector is created
for each sub volumes.
VII.3 Disparity vector post processing
After obtaining the disparity vectors from the previous step, vector post-processing steps
can be executed to smoothen the disparity field and obtain more reliable vectors.
VII.4 Correct calibration
Using the obtained disparity field, the correction is applied on the current calibration. The
new calibration is generated and stored in the current project folder. After correcting the
calibration, the software returns to the disparity map generation step, and repeats the
process in an iteration-like method. The steps are repeated until the remaining calibration
inaccuracies reach a sufficiently low value, which in case of a Tomo-PIV measurement
is suggested to be a maximum of 0.1. Table VII-1 summarizes the RMS (root mean
square) inaccuracy values after the final step in the current measurement for each camera.
Table VII-1 Calibration inaccuracies after the final step
Camera 1 Camera 2
Plane nr. 1 to 10 Plane nr. 1 to 10
Z position of plane [mm] -18.9 to 18.9 Z position of plane [mm] -18.9 to 18.9
Average RMS to fit
[pixel] 0,0209
Average RMS to fit
[pixel] 0,0211
Camera 3 Camera 4
Plane nr. 1 to 10 Plane nr. 1 to 10
Z position of plane [mm] -18.9 to 18.9 Z position of plane [mm] -18.9 to 18.9
Average RMS to fit
[pixel] 0,0195
Average RMS to fit
[pixel] 0,0200
42
VII.5 Recording images
For each cases of the measurement, the following procedure took place.
1. Filling up the primary reservoir with particle filled ammonium thiocyanate
solution using the pump.
2. Turning off the pump.
3. Opening the pipeline, recording images.
4. Closing the pipeline, returning to the first step.
During the first step, the pipeline is closed, but filled up with the solution. The line should
only be closed off when it doesn’t contain any air bubbles, since they act as enormous
resistances, jamming the steady flow of the solution slowing, or even completely stopping
it.
The second step is crucial to prevent vibrations, which would affect the results, caused
by the pump. The pipeline is still closed.
Water level subsidence has little to no effect on the flow rate. Figure VII-7 shows the
deviation between the averaged flow rates of three measurements. During a full
measurement, less than half of the tank capacity flows out, accounting for a maximal 5
cm water level subsidence. The results of the flow tests show that this height change is
not significant from the viewpoint of our measurement.
Figure VII-7 The effect of fluid level subsidence on average flow rate
If the effect was more considerable, it could be neutralized by using a tank with a larger
floor area as the primary fluid reservoir.
Each camera recorded 5 times 200 images individually for every lengthwise section for
every case. Having four lengthwise sections and four investigated velocities accounts for
16000 recorded images in total. Recording sessions were partitioned to minimize the
effect of fluid level subsidence in the primary reservoir; since the solution was not time
resolved anyway, the actual physical time of the recording does not affect the results as
8,00
8,25
8,50
8,75
9,00
9,25
9,50
9,75
10,00
10 20 30 40 50 60
Time [s]
Average flow rate [ml/s]
43
long as the characteristic features of the measurement environment don’t change. The
divided parts can be seen in figure VII-8.
Table VII-2 summarizes the applied settings; 𝑓 stands for the sampling frequency at
which the images were recorded. Its value is somewhat arbitrary; in this case it was
chosen with the fluid level subsidence in mind. For lower velocities, five hertz meant only
a slight change in fluid level, while for higher velocities we preferred to have a higher
sampling frequency to reduce the time necessary for recording 200 images. Having the
sampling frequency doubled essentially halves the recording time as well as the amount
of height change.
The value of 𝑑𝑡 is the time delay between recording two PIV frames. In conventional PIV
measurements facilitating laser pulses as the light source, 𝑑𝑡 is often referred to as pulse
separation. Since in this case it can be understood the same way – although we use
controlled COB LED pulses – hereinafter it is referred to as pulse separation as well. The
value of pulse separation affects the distance that one particle can travel between two
frames; if the value is too low, then the vectors in the post processing are going to be too
small, if too high, then many particles will leave the interrogation zones resulting in
spurious results. Generally, a movement of around 5 pixels is applicable [15].
Table VII-2 Investigated cases and measurement settings
Case
Nr. 𝑄 [𝑚𝑙
𝑚𝑖𝑛] 𝑐 [
𝑚
𝑠] 𝑅𝑒 𝐷𝑒 𝑓 [𝐻𝑧] 𝑑𝑡 [𝜇𝑠]
1 46 0.0390 164 70 5 2000
2 72 0.0612 257 111 5 1800
3 475 0.4032 1692 728 10 300
4 1200 1.0186 4273 1839 10 200
VII.6 Image pre-processing
Image pre-processing is an important step before commencing with the vector calculation.
It can help to improve the quality of the final results and also to decrease file sizes, which
can significantly reduce the computational time of the vector fields [8].
VII.6.1 Time filter
High intensity, stationary contaminations – such as bubbles, aggregated particles, and
other non-moving artefacts – can be filtered out by subtracting the minimum of a number
of images from the time series from the source. The number of images that are take into
account per image is called the filter length, the minimum can be calculated forward,
backward, or symmetrically. In our case the calculation was set symmetrical with a filter
length of three. Figure VII-8 illustrates the working principle of a symmetrical three
image wide time filter [14, 22].
44
Figure VII-8 Schematic of the working principle of symmetrical time filter with a filter
length of 3 [22]
The first two, and the last two images are identical. By taking three subsequent images
into account to calculate the minimum, only non-moving objects will appear on the target
images, and by subtracting these from the source images only the stationary
contaminations are eliminated [22].
VII.6.2 Applying 2D mask
Using a mask, a prescribed region of the geometry can be marked as valid or masked out.
Masked out pixels are not lost, nor deleted, but they are not used in further calculations.
There are three basic ways to generate a mask for the images [14].
Geometric mask
As the name suggests, geometric mask is created by applying geometric shapes, defined
by the user, as a mask.
Algorithmic mask
Algorithmic masks make use of the different intensity of certain areas, and use this
information to create a mask (e.g. by applying a threshold criteria).
Load mask from disk
Loading an existing mask created in an external program (such as Matlab).
Methods can also be combined to obtain an ideal mask. In this step, a two-dimensional
geometric mask was defined for all cameras, which is shown in figure VII-9 for all
sections of the helix. This image can also provide an overview of the lengthwise sections
of the helix used in this measurement [14, 22].
45
Figure VII-9 The final 2D masks
After creating the binarized mask, it was multiplied with the source images, resulting in
the original intensity where the value of the mask was ‘1’, and eliminating everything
else by multiplying the source value by ‘0’.
This version of DaVis does not support three-dimensional masks, or any kind of masks
in different planes, therefore in a later step, an external three-dimensional mask is also
applied to the images. The main reason that other planar masks are not supported by
DaVis is probably that tomographic PIV measurements usually include a planar flow with
one dimension being significantly smaller than the other two (high aspect ratio). This is
not the case in our measurement, the helix is a complex geometry and can not at all be
considered a planar body. The helix is also hollow in the middle; by applying a 2D mask,
most of the ghosts outside of the helix actually disappeared as shown in figure VII-10,
but in the hollow region, the same amount of ghosts stayed, especially on the farther side
from the cameras, as shown in figure VII-11. The main advantage of applying this two-
dimensional mask is that it greatly reduces the size of the images, thus making subsequent
steps that much faster and less memory intensive.
46
Figure VII-10 Particle intensities from a side view of the helix
Generally, higher intensities are bound to real particles, while ghost particles possess
lower intensities. From the above image it can be perceived that a lot of ghosts have really
been masked out, but some still remain.
47
Figure VII-11 Particle intensities from a frontal view of the helix
Most of the ghosts inside helix are still there. Without even noting, it can be deducted that
the cameras were viewing the helix from the right side in figure VII-12 just by looking at
the particle intensities. The ghosts inside the helix still remain a problem, and it cannot
be solved inside DaVis, hence an external mask will later be facilitated based on the
different intensities values of ghosts and real particles.
VII.6.3 Particle quality enhancement
To further improve the quality of the obtained images, a Gaussian smoothing of 5x5 pixels
was executed with a sharpening operation following it. The Gaussian smoothing increases
particle size while also blurs the image, a sharpening operation used after the Gaussian
smoothing can reduce the particle size to the original. The operation results in a significant
reduction of noise level in the background and a more distinguished borders for the
particles [14]. Then the intensity range was enhanced by the multiplication of intensity
values by a factor of 10. After that, a subtract constant was used to reduce the intensity of
noise. As a side effect, the intensities of the images were slightly decreased.
48
VII.7 Volume reconstruction
During this process, DaVis uses the raw data from individual recordings to reconstruct
the volume. The facilitated reconstructing method is FastMART (MART: Multiplicative
Algebraic Reconstruction Algorithm). FastMART can be utilized when the amount of
available RAM is high; in that case the algorithm can provide fast and precise results.
Although, the reconstructed volume of the original images (resolution: 2560 x 2160)
would take up about 68 GBs, and DaVis can use up to three times of this memory during
calculations (it simultaneously calculates on multiple levels), it would exceed the
available 128 GB RAM. Therefore, the resolution of the images was decreased by using
a binning software with a 2x2 binning. Image resolution after this step was 1379 x 1237,
and the reconstructed volume would be around 27 GB of available RAM. The software
can operate hard drives to run calculations, however, by decreasing the memory demand
of the calculations instead of forcing the calculations to the hard drive, plenty of time can
be saved [14, 23].
The facilitated FastMART settings:
MinLOS initialization
CSMART iterations: ................. 5
SMART iterations: .................. 16
SMOOTH iterations: .............. 20
SMOOTH strength: ............... 0.5
THRESHOLD: .................... 0.01
Number of cameras: ................... 4
Results were checked with a threshold of 0.01 and 0.005, and the results were almost
identical. Increasing the number of iterations hardly increases the computational time;
saving and loading images are accountable for the majority of elapsed time while
iterations account for a negligible amount. Since increasing the number of iterations
doesn’t really affect the total computational time, they were chosen to be relatively high.
The volume for the reconstruction was chosen to be “max” in the x and y directions, and
the depth direction “z” was set with a slight oversize. Table VII-3 sums up the exact
volume settings and the voxel size [23].
Table VII-3 Volume settings
min max min max
x -18.9948 23.5126 mm = 0 1379 voxel
y -16.8297 21.3006 mm = 0 1237 voxel
z -21 21 mm = -681.5 681.5 voxel
1380 x 1238 x 1364 voxel = 8.7 GB
49
VIII POST-PROCESSING
After the reconstruction, additional filters can be applied to enhance the vector field
obtained from the volume correlation [14]. To reduce the computing time, a 2x2 image
binning was used, reducing the 2560x2160 pixel images to images with a resolution of
1379x1237. The flowchart of our approach is shown on figure VIII-1.
Figure VIII-1 Post processing flowchart
VIII.1 FastMART sum
Following the FastMART volume reconstruction, the provided images were summed for
each investigated cases and each lengthwise sections accordingly. The summed up
volumes were used as the input of the Matlab program to create three dimensional masks
for all cases.
50
VIII.2 Three-dimensional Matlab mask
A generic 3D mask created in CAD could not be used because of the inaccuracies in the
geometry of the helix. To begin with, the cross-section is more likely ellipsoid than
circular, and there’s no way to actually obtain the exact properties for it since the wall
thickness may also vary. The pitch is also not exactly consistent, but an average can be
obtained by dividing the length of the coil by the number of turns. The relation of the
actual geometry and an accurate CAD projection is visualised in figure VIII-2. The filled
patterns represent the masked geometry, the hollow ellipses show the outer and inner wall
of the idealized generic tube. It is clear that a generic mask can not be facilitated in this
case.
Figure VIII-2 CAD projection compared to the generated mask
The creation of the mask was based on the different intensities of ghost and real particles.
By choosing a suitable threshold, the unnecessary particles could be removed from the
reconstructed volume and then the generated mask can be applied inside DaVis as an
external mask. The masking method was done in thirteen steps. The intensity was
converted into a percent value, where 1 is the maximum intensity of the chosen image,
and 0 stands for zero intensity. For the inlet part, the intensity boundary was set to 0.5
(with slight adjustments when needed), for all other sections it was set to 0.8 or 0.9 to
gain easily identifiable images. The reason behind the first sections lowered intensity
boundary lies in the fact that the inlet has a much higher intensity than the coils, meaning
that if the same value was used as for the rest of the cases, the coils would not stand out
enough from the background to be clearly distinguished from ghosts, or even the
background. Of course, some information regarding the inlet is lost this way, but it does
not matter, since it is defined in a separate step. Going through the whole method took
roughly 25 minutes for each individual case.
51
Step 1: choosing the source folder of the summed up FastMART reconstructed volume
and a target folder for the mask. The program loads the necessary data from the given
folders, and will later write the data for the mask in the destiny folder.
Step 2: after successfully loading the volume, the program draws an image of the helix
from front view on which we can select at least three points – as shown in figure VIII-3
– as the centreline of the helix. The program will then find the middle point and draw a
circle in the centreline using an extrapolation of selected points. The octagon form for
these images is expected, they correspond with the viewing angles of the cameras and
generally occur in TOMO related measurements (although might take different forms).
As it can be perceived, it is not an easy task for one to distinguish ghosts from particles;
the line between real and imaginary is quite smooth in this case.
Figure VIII-3 Marking the points for centreline extrapolation
Step 3: selecting the outside limits of the helically coiled pipe. This time, the program
only takes one point into account; the one that is farthest from the centre (which was
defined in the previous step).
52
Step 4: selecting the inside limits in the same manner as the outside limits, only this time
the program takes the closest point to the middle. Figure VIII-4 shows an image of the
three coaxial circles.
Figure VIII-4 The centreline, the outer and the inner border of the helix
Step 5: modifying outside limits if necessary according to the visual representation of the
helix in plane x-y as shown in figure VIII-5. Only the outer border can be modified, since
the inner border cannot be correctly perceived from this viewing angle.
Figure VIII-5 Outer border correction projected in x-y plane
53
Step 6: modifying outside limits if necessary according to the visual representation of the
helix in plane x-z as shown in figure VIII-6. Again, only the outer border can be modified.
Figure VIII-6 Outer border correction projected in x-z plane
Step 7: selecting the threshold to add to the mask (mostly used for the lengthwise section
of the helix with the inlet). Figure VIII-7 shows a threshold region with- and without the
inlet part.
Figure VIII-7 Threshold regions as depicted in the inlet (left), and all other sections
Step 8: the program asks if you wish to use the parameters given. If you do so, the program
continues, if not, you can start over the masking process from step 2.
54
Step 9: set initial threshold for the helical mask (value must be between 0 and 1): we use
0.1. The initial threshold is a mask that encompasses the whole geometry, and is much
larger than the real size of the helix. The mask will be shrank from this to a much thinner
one.
Step 10: the program shows the initial mask as shown in figure VIII-8, and asks if you
wish to continue; if you do not, you can give another value for the initial mask and
continue from step 9.
Figure VIII-8 The mask after applying the initial threshold
Step 11: set final threshold for the helical mask (value must be between 0 and 1): we
create a mask with both 0.8 and 0.75. This factor determines how much the initial
threshold gets shrank.
Step 12: the program asks if you wish to use the set value for the final threshold. If you
do so, the program continues, if not, you can set a new value and continue from step 11.
An image of the current mask is given as a reference as shown in figure VIII-9.
Figure VIII-9 The mask after applying the final threshold
55
Step 13: the data gets saved into the previously defined destination. Visual representations
of the final mask are provided in x-y, x-z, z-y planes as shown in figure VIII-10 to VIII-
12.
Figure VIII-10 The final mask as projected in x-y plane
Figure VIII-11 The final mask as projected in x-z plane
56
Figure VIII-12 The final mask from a frontal view
VIII.3 Applying mask on FastMART images
Applying mask on each individual, original FastMART images, not the summed ones.
VIII.4 Vector Calculation – Averaged vector field
After applying the 3D mask on the FastMART images, we proceeded with the vector
calculation. The displacement vectors are calculated in a multi-pass method in three steps,
as summarized in table VIII-1.
Table VIII-1 Volume correlation methodology
Step X size
[pixel]
Y size
[pixel]
Z size
[pixel]
Overlap
[%]
Peak Search
Radius
[voxel]
Binning Passes
1 48 48 48 75 4 4x4x4 2
2 40 40 40 75 2 2x2x2 2
3 32 32 32 75 1 - 4
In the first step, the window size is larger so that it can cover the maximum shifts in the
flow. The final interrogation window size is 32x32x32 voxels, with 75% overlap one
vector is calculated for every 8x8x8 voxels [14, 23].
57
IX RESULTS
Figure IX-1 shows a visual representation of the evolution throughout the helically coiled
pipe. In this case, the positive velocity value stands for an upwards direction. A similar
result was expected.
Figure IX-1 Velocity component y throughout the reconstructed body
Figure IX-2 shows a similar result with the z component of the velocity. These images
suggest that the obtained results are in fact apprehensive.
Figure IX-2 Velocity component z throughout the reconstructed body
58
Figure IX-3 shows a visualization of the x component of velocity from a side view, which
is the main direction of the flow. The limits of the legend in this case were chosen so that
the slight variations are more visible, the local maximums may exceed the actual limits.
Figure IX-3 Velocity component x throughout the reconstructed body from side view
Figure IX-4 shows the same representation from a frontal view. The arrow shows the
initial direction of the flow, indicating that the x component of the velocity magnitude
also gets slightly faster when travelling downwards. The stained characteristic of the
image can be imputed to the mask and the chosen velocity range.
Figure IX-4 Velocity component x throughout the reconstructed body from frontal view
59
Figure IX-5 shows the sections of investigation. The arrow represents the main flow
direction as well as the inlet of the helically coiled pipe. The gaps between parts of the
helix indicate the original lengthwise sections; the four lengthwise cases were recorded
simultaneously. One full loop of each lengthwise sections were assigned a capital letter,
and the full volume was cut to two slices by a vertical and a horizontal plane. Note that
the helix on the image is tilted to make both horizontal cross sections visible and
distinguishable. These cross sections are indicated by a brighter shade of the colour of
their corresponding section. The first segment streamwise was assigned with the number
1, each downstream sections got an incremented number, up to 5 for the last segment.
Table IX-1 sums up the angles of each individual cross section for every case, starting
with 0° for the first case in every lengthwise section.
Table IX-1 Cross section angles in different cases
A B C D
1 0° 0° 0° 0°
2 90° 90° 90° 90°
3 180° 180° 180° 180°
4 270° 270° 270° 270°
5 360° 360° 360° 360°
Figure IX-5 Investigated sections of the helix
Note that every segment denoted by number 3 is always the lowest point of the section,
while 1 and 5 are both the highest. The two horizontal segments are at identical height, it
is worth noting however, that in segments denoted by number 2 the is facing in the
direction of the gravitational acceleration, while in segments denoted by number 4 it is
facing opposite in the opposite direction. This gravitational effect can have a great impact
on the flow structure, especially at low velocities.
It is also important to note that segments denoted by 4 are the farthest from all cameras.
In this part of the helix, the intensity of ghosts was much higher than the rest of the target
volume, and the number of valid particles were at a minimum. It is surmised that obtained
results are more reliable on the side of the helix that was closer to the cameras. Despite
that, the calculated vector field on the farther side of the helix should still be a reasonably
accurate representation of the real flow field.
The flow structures are presented in figure IX-7 for section A with the four measured
flow rates. Images should be understood as figure IX-6 shows; each cross section was
60
rotated into the same position as the first one (e.g. the bottom one was mirrored to a
horizontal plane) for a better comparison.
Figure IX-6 The key to understanding the results
The following images should be understood accordingly.
Figure IX-7 Velocity profiles in section A for all cases
The legend represents the velocity magnitude for each of the flow rates; the minimum
range is identically zero, but the maximum range is exclusive for every flow rate. Since
the main point of the representation is to visualize the flow structure, the exact values are
not included this time.
61
As it can be perceived from these images, the effect of the initial bend is somewhat
neutralized by segment 3, then the effects of the helical pipe can be investigated. As for
the represented flow rates, the table IX-2 summarizes the theoretical flow properties.
Table IX-2 Flow domains in different cases
Case 𝑄 [𝑚𝑙
𝑚𝑖𝑛] 𝑐 [
𝑚
𝑠] Re De Flow domain
1 46 0.0390 164 70 Laminar
2 72 0.0612 257 111 Transient (Dean domain)
3 475 0.4032 1692 728 Transient
4 1200 1.0186 4273 1839 Turbulent
The obtained images illustrate these properties quite accurately. After the effects of the
initial bend have been dissipated, the flow structure in the slowest case resembles that of
a laminar flow quite well. As for the two transient instances, the maximal flow structure
slowly starts to shift towards the outer wall, and Dean vortex pairs start to show
themselves. At the fastest pace, the flow structure becomes rather unpredictable. greatly
capturing the essence of turbulent nature.
Figure IX-8 to IX-10 show the evolution of the flow structure in sections B, C, and D in
the same manner.
Figure IX-8 Velocity profiles in section B for all cases
62
Figure IX-9 Velocity profiles in section C for all cases
Figure IX-10 Velocity profiles in section D for all cases
63
For low velocities inside or close to the laminar zone, a shift in the location of the maximal
velocity can be noticed. In segment one, the velocity profile seems to be consistently
pushed toward the inside, in the following segment it is either in the middle or shifted
towards the outside, then again to the inner wall in segment 3 etc. To further investigate
the occurrence, section D has been divided into 12 cross sections. Figure IX-11 shows the
resulting velocity fields.
Figure IX-11 Cross sections of section D, sliced every 30 degrees
Figure IX-12 can help visualizing the data by showing the positions of the slices with the
helically coiled pipe. It can be concluded that the gravitational effect dramatically
influences the final flow structure when the
velocity of the flow is relatively small. In this case,
it is quite visible when the flow is directed
downwards, the location of the peak velocity starts
to shift towards the outside wall, since the
centrifugal forces effecting the flow are enhanced
by the gravitational force. While travelling
upwards, the peak velocity shifts towards the
middle, then to the inner wall of the tube.
Figure IX-12 30 degree slices
64
Starting from the first two loops from the inlet were sliced by eight planes, the first plane
being vertical and the rest rotated by 22.5 degrees each. Figure IX-13 summarises the
velocity field in the cross sections of the first two loops in case of 72 ml/min flow rate.
Figure IX-13 Velocity fields in cross sections downstream of the inlet
In the first half-loop (until about 225°), the mask cuts into the region, resulting in some
loss of data. The reason for this is that the first loop has a significantly larger radius
compared to the remaining ones. In the future, by facilitating a more suitable masking
method the results can be improved. Other than that, the vortex pairs can easily be
distinguished.
65
To investigate the evolution of downstream flow structures, a set of cross sections have
been exported from the cross section of the horizontal slices that were the closest to the
camera. The flow rate in this case is 72 ml/min, the flow regime is transient (Dean
domain). Figure IX-14 show these image sets with the helix to make it more
understandable.
Figure IX-14 Horizontal cross sections with the helix
Figure IX-15 shows these cross sections magnified. Note that in this cross section, the
fluid is travelling upwards. It can be perceived from these images that the double vortex
loses its impact by the sixth or seventh loop, and after that the flow becomes almost
laminar again, with a shifted peak velocity due to centrifugal forces of course.
Figure IX-15 Horizontal cross sections magnified
66
Figure IX-16 shows the streamlines in the first five loops with the inlet included. The
double vortex pairs can even be surmised from this image; the separated flow is
represented by a “ditch” between the two sides. Generally, particles stay within the vortex
and don’t leave it. The ditch was also visible on the raw images, which indicates that most
particles stayed with either one of the vortices, and not in-between them.
Figure IX-16 Streamlines in the first five loops
67
X CONCLUSION
The main goal is to improve the efficiency of this type of helical reactor. What is
efficiency? Efficiency is the relation of invested energy to mixing ratio, for example, but
the definition is unique for different purposes. Why should it be improved, is it relevant?
It is. For large-scale industrial appliances saving energy on wherever possible is important
on its own, not to mention that there usually is limited space for the reactors and
employing a mixer with a huge flow resistance is often not advised due to its negative
effects on the flow structure. A helical reactor can also be facilitated in the laminar region,
which makes it an essential compartment of low-velocity devices. Mixing high viscous
fluids is also possible with a suitable coiled pipe; reaching a high magnitude of velocity
in those cases would require an immense amount of energy input, which can be avoided
by working in the laminar or transient flow regime and still reaching an acceptable mixing
performance.
Our measurements reveal that Dean-vortex pairs appear for a relatively short section after
the initial bend. They can be resurrected by changing the bend direction (e.g. originally
the fluid is rotating clockwise, then changing the rotation to counter clockwise), or by
including a period of linear pipe then another helical section. If there is a bend with a
linear section after it, secondary flows still appear, but dissipate much faster. The coiled
feature of the pipe helps keeping them up for a longer distance, making the reaction that
much more effective.
Measurements like this one can be carried out with a relatively low budget (since LED
illumination is much cheaper than a LASER) to determine the flow structures of complex
bodies if necessary.
68
XI SUMMARY
A Tomographic Particle Image Velocimetry of a helically coiled pipe was carried out to
determine the evolving flow structure characteristics. Curved tubes are used in many
industrial appliances because of their versatility, they can come in various shapes and
sizes. The most widely used implementation of curved geometries is a helically coiled
reactor.
For the Tomo-PIV, four cameras were set up on a stiff frame in a linear configuration, all
focused on the helix. An aperture of 32 was used with 14 COB LED lights acting as the
main light source, outputting up to a power of 1960 W. A view box was set up and filled
with a refractive index matched agent to avoid reflections. The same agent was used
inside the pipe. The camera angles were perpendicular to the corresponding sides of the
view box, eliminating any distortions between lens and helix.
Then 1000 double-frame images were recorded with four different velocities in different
flow regimes, and four lengthwise sections of the helix, adding up to a total of 16000
images. During processing of the images, remaining distortions and reflections were
neutralized, the file sizes were decreased. The volume reconstruction was done by
FastMART; the reconstructed volumes were then evaluated by a multi-pass volume
correlation method that provided the vector fields for the results.
The results were then exported and visualized and ParaView. During the investigation of
the results, we came to several conclusions considering the flow structure; the Dean
vortex pairs were clearly visible, but started to dissipate after a couple of loops. The flow
is separated; particles from one vortex generally do not leave said vortex, eventuating in
a “ditch” between the vortex pairs, where the particles are quite scarce. At lower
velocities, the effect of gravity can exceed the effect of centrifugal force, disarraying the
flow structure.
69
XII OUTLOOK
A view box with a suitable geometry, where the sides don’t oppose each other, can
provide a possibility for non-linear camera arrangement, which generally results in more
accurate results. Instead of using glass pipe, a silicone pipe can be used, rendering index
matching unnecessary, and a suitable three-dimensional mask created in a CAD software
could also be used in this case.
A different vector calculation approach can also be facilitated where instead of averaging
the calculated vector fields, one vector field is calculated on the summed images. This
way, we can get an insight to the turbulent nature of the flow. However, there is no way
to eliminate calculation errors, so it is not as reliable as an averaged field. This method is
somewhat similar to facilitating an immense amount of particles and then calculating the
results from these images, but the ghosts in this case won’t mean a problem since the
volume is already reconstructed at the moment of summing.
70
XIII ACKNOWLEDGEMENTS
I would like to thank for the opportunity and for all the help of PD Dr.-Ing. Janiga Gábor,
Dr. Ing. Katharina Zähringer, and Dr. Bencs Péter. I would like to thank to my supervisor,
Kováts Péter for all his help during, and after the experiments, and Dr.-Ing. Fabio Martins
for his advices and for providing the Matlab code used for the 3D masking.
This research was supported by the European Union and the Hungarian State, co-financed
by the European Regional Development Fund in the framework of the GINOP-2.3.4- 15-
2016-00004 project, aimed to promote the cooperation between the higher education and
the industry.
The research was also supported by the EFOP-3.6.1- 16-00011 “Younger and Renewing
University – Innovative Knowledge City – institutional development of the University of
Miskolc aiming at intelligent specialisation” project implemented in the framework of the
Széchenyi 2020 program. The realization of these two projects is supported by the
European Union, co-financed by the European Social Fund.
71
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73
XV APPENDIX
Luminus CXM-32 Specifications
Manufacturer Luminus Devices
Product Category High Power LEDs - White
Product White CoB LEDs
Package/Case COB - Chip-on-Board
Illumination Colour White (Cool White)
Wavelength/Colour Temperature: 5000 K
Luminous Flux/Radiant Flux 17880 lm
Colour Rendering Index - CRI 80
Viewing Angle 120 deg
Lens Colour/Style Tinted
Forward Current 2.64 A
Forward Voltage 54 V
Power Rating 140 W
Mounting Style SMD/SMT
Length 38 mm
Width 38 mm
Maximum Operating Temperature + 105 °C
Minimum Operating Temperature -
Series CXM-32
Brand Luminus Devices
LED Size 38 mm x 38 mm
Lens Shape Round Flat
Lens Dimensions 32.8 mm
Product Type LED – High Power
Subcategory LEDs
Reverse Voltage -