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

XIV REFERENCES

[1] Subhashini Vashisth, Vimal Kumar and Krishna D. P. Nigam, “A review on the

potential applications of curved geometries in process industry,” Industrial &

Engineering Chemistry Research, vol. 47, no. 10, pp. 3291-3337, 2008.

[2] Krishna D. P. Nigam, Roy Shantanu and Sharma Loveleen, “Single phase mixing in

coiled tubes and coiled flow inverters in different flow regimes,” Chemical

Engineering Science, vol. 160, pp. 227-235., 2017.

[3] Vimal Kumar, Mohit Aggarwal and Krishna D. P. Nigam, “Mixing in curved tubes,”

Chemical Engineering Science, vol. 61, pp. 5742-5753., 2006.

[4] Andrew Michael Fsadni and Justin P. M. Whitty, “A review on the two-phase heat

transfer characteristics in helically coiled tube heat exchangers,” International

Journal of Heat and Mass Transfer, vol. 95., pp. 551-565., 2016.

[5] Paisar Naphon and Somchai Wongwises, “A review of flow and heat transfer

characteristics in curved tubes,” Renewable and Sustainable Energy Reviews, vol.

10., pp. 463-490., 2016.

[6] Prof. Dr. Paripás Béla, Prof. Dr. Szabó Szilárd, Kocsisné Dr. Baán Mária, Dr. Tolvaj

Béláné and Dr. Bencs Péter, Lézeres mérési- és megmunkálási eljárások a

gépészetben, Miskolc, Egyetemváros: Nemzeti Tankönyvkiadó, 2011.

[7] Adrian and J. Ronald, Particle imaging techniques for experimental fluid mechanics,

Annual Reviews Inc., 1991.

[8] LaVision GmbH, Product-Manual for DaVis 8.4 - FlowMaster D84, Göttingen,

2017.

[9] V. A. Reyes, F. Z. Sierra-Espinosa, S. L. Moya and F. Carrillo, “Flow field obtained

by PIV technique for a scaled building-wind towermodel model in a wind tunnel,”

Energy and Buildings, vol. 107, pp. 424-433., 2015.

[10] Dantec Dynamics, “Particle Image Velocimetry (PIV),” [Online]. Available:

https://www.dantecdynamics.com/particle-image-velocimetry. [Accessed 10 April

2018].

[11] F. Scarano, “Tomographic PIV: Principles and practice,” Measurement Science and

Technology, vol. 24, 2012.

[12] LaVision GmbH, Tomo-PIV Seminar, October 28th, 2016, Göttingen, 2017.

[13] LaVision GmbH, Tomographic PIV - Volumetric Flow Field Imaging, Göttingen,

2017.

72

[14] LaVision GmbH, Product-Manual for DaVis 8.4 - FlowMaster Tomographic PIV,

Göttingen, 2017.

[15] LaVision GmbH, Product-Manual for DaVis 8.4 - FlowMaster Getting Started,

Göttingen, 2017.

[16] Ayak K. Prasad and Kirk Jensen, “Scheimpflug stereocamera for particle image

velocimety to liquid flows,” Applied Optics vol. 34, pp. 7092-7099., 1995.

[17] QImaging, “Rolling Shutter vs. Global Shutter,” 2014.

[18] PubChem Database, “Ammonium Thiocyanate,” [Online]. Available:

https://pubchem.ncbi.nlm.nih.gov/compound/ammonium_thiocyanate#section=Top.

[Accessed 26 February 2018].

[19] Damaris Elisabeth Pohl, Masterarbeit - Charakterisierung des Sauerstoffübergangs

und des Strömungsfeldes in einem Helixreaktor mittels optischer Messverfahren,

Magdeburg: OVGU - Institut für Strömungstechnik und Thermodynamik, 2017.

[20] Ligrani M. Philipp, “A study of Dean vortex development and structure in a curved

rectengular channel with aspect ratio of 40 at Dean numbers up to 430,” 1994.

[21] R. W. Dean, “XVI. Note on the motion of fluid in a curved pipe,” The London,

Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 4, no.

20, pp. 208-223., 1927.

[22] LaVision GmbH, Product-Manual for DaVis 8.4 - DaVis D84, Göttingen, 2017.

[23] Kováts Péter, Fabio J. W. A. Martins, Dominique Thévenin and Katharina Zähringer,

Tomographic PIV Measurements in a Helically Coiled Reactor, Magdeburg, 2018.

[24] LaVision GmbH, Product-Manual for DaVis 8.4 - Programmable Timing Unit (PTU

X), Göttingen, 2017.

[25] LaVision GmbH, Product-Manual for DaVis 8.4 - Imager sCMOS, Göttingen, 2017.

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 -