Ontwikkeling van reflectiepunt, schaduw en interferometrische planaire technieken ter bepaling van de diameter van luchtbellen Development of Glare Point, Shadow and Interferometric Planar Techniques for Gas Bubble Sizing Sam Dehaeck

Ontwikkeling van reflectiepunt, schaduw en interferometrische planaire technieken ter bepaling van de diameter van luchtbellen Development of Glare Point, Shadow

and Interferometric Planar Techniques for Gas Bubble Sizing

Sam Dehaeck

Promotoren: prof. dr. ir. J. Vierendeels, prof. dr. ir. J.P.A.J. van Beeck Proefschrift ingediend tot het behalen van de graad van

Doctor in de Ingenieurswetenschappen: Werktuigkunde-Elektrotechniek Vakgroep Mechanica van Stroming, Warmte en Verbranding

Voorzitter: prof. dr. ir. R. Sierens

Faculteit Ingenieurswetenschappen

Academiejaar 2006 - 2007

Dankwoord

Het dankwoord. Het laatste stukje tekst dat nog geschreven moet worden en dan is mijn doctoraatsthesis klaar.

Dat is toch iets om even bij stil te staan want het doctoraat is toch min of meer de puberteit van elke onderzoeker.

De tijd waarin je voor het eerst op je eigen benen moet leren staan en je eigen onderzoeksdoelen moet uitzetten.

Een tijd ook waarin je tijdschriften probeert te verleiden om je artikels te publiceren en waarbij je noodzakelijker wijze soms een blauwtje oploopt. Daarnaast duiken er, zoals bij elke puberteit, vele existentiële vragen op zoals;

Ben ik wel goed bezig? Waar was ik nu weer mee bezig? Is dit niet al allemaal eens onderzocht?

Op zo’n momenten, was ik zeer dankbaar dat ik met mijn promotor Jeroen van Beeck kon praten. Hij vond op miraculeuze wijze altijd de tijd en het geduld om naar mijn ideëen te luisteren. Daarnaast hebben zijn subtiele hints me ook vaak geholpen in het uitzetten van de grote lijnen van mijn onderzoek. Samen met Michel Riethmuller wil ik jullie ook bedanken voor het originele idee van mijn doctoraat, want een goede start is toch al de halve race.

Een tweede steunpilaar van dit onderzoek was Jan Vierendeels. Bedankt voor het opvolgen en blijvend steunen van mijn doctoraat. Samen met Erik Dick wil ik jullie ook bedanken om me naar het VKI te sturen. Zonder jullie was ik waarschijnlijk nooit begonnen met experimenteel onderzoek, een discipline waar ik me heel goed thuis voel. Verder wil ik ook de rest van de vakgroep bedanken, en in het bijzonder Rita, voor de broodnodige hulp bij de administratieve kant van een doctoraat.

Daarnaast wil ik ook de professoren van het EA departement van het Von Karman Instituut bedanken (M.

Riethmuller, JM. Buchlin, J Anthoine, ..) voor de interesse en de vele vragen tijdens de jaarlijkse doctor- aatspresentaties. Verder bedank ik ook de technische staf van het Von Karman Instituut (Guillaume, Didier, Jacques,...) voor de snelheid en inventiviteit waarmee mijn technische probleempjes werden opgelost.

Ook een warme groet naar de verschillende professoren en vorsers in de Mutech groep; Johan, Annick, Jan, Herman (2x), Réné, Paola, David, Tim, Thomas, Wouter, Steven, Pavel, Flora, ... Bedankt voor de vele interes- sante gesprekken die we gehad hebben en de interesse naar mijn werk. Jullie waren het die zin gegeven hebben aan dit doctoraat. Heidi wil ik ook bedanken voor de leuke uurtjes in de trein en in de auto op weg naar één of ander industrieterrein in the middle of nowhere. En niet te vergeten voor de bellenmetingen in de reactor, zeker één van de hoogtepunten uit dit doctoraat.

De mede-doctoraatstudenten van het VKI (Bart, Thomas, Alberto, Mike, Sandy, Rosaria, Raimondo, An en vele anderen) voor de interessante gesprekjes (en spelletjes frozen bubble) tijdens de middagpauzes. Ik wil ook de verschillende stagiairs niet vergeten waarmee ik heb mogen samenwerken; Aurianne, Vassilios, Dora, Rocco en Sedat. Stuk voor stuk hebben jullie bijgedragen tot deze thesis en ik hoop dat jullie er ook een beetje trots op zijn. Tot slot nog de medetreinpendelaars; Tom, Johan, Nadège, Mickaël & Pierre. Jullie vriendschap heeft van het (soms eindeloze) wachten op de trein een mooie tijd gemaakt.

Daarnaast wil ik ook mijn ouders bedanken voor hun niet aflatende steun en liefde. Mijn broer, voor de leuke telefoongesprekken, de ontspannende middagetentjes en de plezante avondjes uit. Tenslotte wil ik ook Han- nah bedanken, mijn kersverse bruid, voor alweer enkele van de mooiste jaartjes van mijn leven. Vanaf het gezamenlijk schrijven van onze IWT-projectaanvragen in ons nieuwe appartementje tot het bijstaan in de the- sisschrijfmarathon, jij was er altijd om naar me te luisteren, me te helpen en in me te blijven geloven. Ik dank je hiervoor met heel mijn hart.

Veel leesplezier!

Sam.

Contents

List of symbols and acronyms vii

Samenvatting ix

Summary xiii

List of publications xvii

1 Introduction 1

1.1 Bubbly Applications . . . . 1

1.2 Overview of Bubble Sizing Techniques . . . . 2

1.2.1 Introduction . . . . 2

1.2.2 Acoustical Measurements . . . . 3

1.2.2.1 Passive Acoustics . . . . 3

1.2.2.2 Linear Active Acoustics . . . . 3

1.2.2.3 Non-Linear Active Acoustics . . . . 4

1.2.2.4 General Remarks on Acoustical Techniques . . . . 5

1.2.3 Optical Measurements . . . . 5

1.2.3.1 Phase Detection Probes . . . . 5

1.2.3.2 Laser Diffraction Particle Sizing . . . . 6

1.2.3.3 Phase Doppler Anemometer . . . . 7

1.2.3.4 Backlighting . . . . 8

1.3 Outline of the Thesis . . . . 9

2 Glare Points 11 2.1 Introduction . . . . 11

2.2 Spherical Bubbles . . . . 12

2.3 Glare Point Measurement Techniques . . . . 13

2.4 Wall Deflection . . . . 17

2.5 Non-Spherical Bubbles . . . . 17

2.6 Glare Point Width . . . . 19

CONTENTS

2.7 Conclusions . . . . 21

3 Glare Point Velocimetry and Sizing (GPVS) 23 3.1 Introduction . . . . 23

3.2 Basic GPVS . . . . 24

3.2.1 Spherical Bubbles . . . . 24

3.2.2 Non-Spherical Bubbles . . . . 26

3.3 Extended GPVS . . . . 27

3.3.1 Configuration . . . . 27

3.3.2 Extra Information . . . . 28

3.3.3 Different Observation Angles . . . . 30

3.4 Uncertainty Analysis . . . . 30

3.4.1 Uncertainty Analysis of the Conversion Factor α

. . . . 30

3.4.2 Uncertainty Analysis of the Inter Glare Point Distance Measurement δ

. . . . 32

3.4.3 Uncertainty Analysis of the Calibration Constant C . . . . 32

3.5 Experiments . . . . 33

3.5.1 Goals . . . . 33

3.5.2 Experimental Set-Up . . . . 33

3.5.3 Size Calibration Basic GPVS . . . . 34

3.5.4 Velocity Calibration Basic GPVS . . . . 35

3.5.5 Refractive Index Determination . . . . 35

3.5.6 Alignment Verification . . . . 36

3.5.7 Extended GPVS at 90

. . . . 36

3.6 Designing a GPVS Experiment . . . . 37

3.6.1 Introduction . . . . 37

3.6.2 Working Domain . . . . 37

3.6.3 Obtaining the Maximum Precision . . . . 39

3.6.4 Limited Depth-of-Field . . . . 40

3.7 Discussion . . . . 41

3.8 Conclusions . . . . 42

4 Interferometric Particle Imaging (ILIDS) 43 4.1 Introduction . . . . 43

4.2 Experimental Set-Up . . . . 45

4.3 Multi-Frequency ILIDS . . . . 45

4.3.1 Introduction . . . . 45

4.3.2 Power Spectrum Analysis . . . . 46

CONTENTS

4.3.3 Experimental Verification . . . . 48

4.3.4 Choice of the Observation Angle . . . . 48

4.4 Formula . . . . 49

4.5 Uncertainty Analysis . . . . 50

4.5.1 Introduction . . . . 50

4.5.2 Uncertainty Analysis of the Conversion Factor α

. . . . 51

4.5.3 Uncertainty Analysis of the Fringe Frequency Determination F . . . . 52

4.5.4 Uncertainty Analysis of the Calibration Constant C

. . . . 54

4.5.4.1 Fringe Counting . . . . 54

4.5.4.2 Full Experimental Calibration . . . . 55

4.5.4.3 Semi-Experimental Calibration . . . . 55

4.5.4.4 Theoretical Calibration . . . . 56

4.5.4.5 Comparison of Experimental and Theoretical Calibration . . . . 58

4.5.4.6 Calibration Conclusions . . . . 59

4.6 Designing a Maximum Precision ILIDS Configuration . . . . 60

4.6.1 Calibration Procedure . . . . 60

4.6.1.1 Short Stand-Off Distances . . . . 61

4.6.1.2 Large Stand-Off Distances . . . . 61

4.6.1.3 Transit Region . . . . 62

4.6.2 Design Guidelines . . . . 63

4.7 Discussion . . . . 64

4.8 Conclusions . . . . 65

5 Backlighting 67 5.1 Introduction . . . . 67

5.2 Gradient Pair Method . . . . 68

5.2.1 Principle . . . . 68

5.2.2 Intermediate Results after the Gradient Pair Method . . . . 70

5.3 Clustering . . . . 72

5.3.1 Choice of a Clustering Technique . . . . 72

5.3.2 Connectivity Based Pre-Clustering . . . . 73

5.3.3 Clustering Parameters . . . . 73

5.4 Validation . . . . 74

5.5 Experiments . . . . 75

5.6 Discussion . . . . 77

5.7 Conclusions . . . . 78

CONTENTS

6 Glare Circles 79

6.1 Introduction . . . . 79

6.2 Theoretical Background . . . . 80

6.2.1 Glare Circles . . . . 80

6.2.2 Bubble Diameter Measurements . . . . 80

6.2.3 Refractive Index Measurements . . . . 81

6.3 Experiments . . . . 82

6.3.1 Sizing Experiments . . . . 82

6.3.2 Refractive Index Measurements . . . . 83

6.4 Uncertainty Analysis . . . . 84

6.4.1 Common Uncertainties . . . . 84

6.4.2 Bubble Sizing . . . . 85

6.4.3 Refractive Index Measurements . . . . 85

6.5 Discussion . . . . 85

6.6 Conclusion . . . . 86

7 Laser Marked Shadowgraphy (LMS) 87 7.1 Introduction . . . . 87

7.2 Principle . . . . 88

7.3 Processing . . . . 90

7.4 Experiments . . . . 92

7.4.1 Experimental Set-Up . . . . 92

7.4.2 Bubble Diameter in Function of Rotational Speed . . . . 92

7.5 Discussion . . . . 93

7.6 Conclusions . . . . 94

8 Fourier Calibration 95 8.1 Introduction . . . . 95

8.2 Principle . . . . 95

8.3 Uncertainty Analysis . . . . 97

8.3.1 Introduction . . . . 97

8.3.2 Uncertainty in the Positioning of the Target . . . . 97

8.3.3 Uncertainty in the Image Processing . . . . 98

8.4 Applications . . . . 100

8.4.1 Rotation along the Optical Axis . . . . 100

8.4.2 Varying Magnification . . . . 100

8.4.3 In- versus Out-Focus Calibration . . . . 100

CONTENTS

8.5 Conclusions . . . . 102

9 Comparing Backlighting, GPVS, ILIDS and LMS 103 9.1 Working Domain . . . . 103

9.2 Uncertainty Analysis . . . . 105

9.3 Void Fraction Limits . . . . 106

9.4 Experimental Comparison . . . . 107

9.5 Discussion . . . . 108

9.5.1 Backlighting . . . . 108

9.5.2 ILIDS . . . . 109

9.5.3 GPVS . . . . 111

9.5.4 LMS . . . . 114

10 Conclusions 117 10.1 Overview of the Thesis . . . . 117

10.2 Overview of the Techniques . . . . 119

10.3 Remaining Goals . . . . 120

Bibliography 121

A Colour Separation Artefacts A.1

A.1 Introduction . . . . A.1 A.2 Overview of Image Processing . . . . A.2 A.3 Colour Separation Artefacts . . . . A.4 A.3.1 Blooming Effect . . . . A.4 A.3.2 Colour Interpolation Artefacts . . . . A.6 A.3.2.1 Introduction . . . . A.6 A.3.2.2 Linear Algorithm . . . . A.6 A.3.2.3 Threshold Based Variable Gradient Method . . . . A.7 A.3.3 Effect of Compression . . . . A.8 A.4 Conclusions . . . . A.9

B Droplet Measurements with ILIDS B.1

B.1 Introduction . . . . B.1

B.2 Glare Point Locations . . . . B.1

B.3 Uncertainty Analysis . . . . B.2

B.4 Designing a Maximum Precision Configuration . . . . B.4

B.5 Conclusions . . . . B.6

CONTENTS

C Void Fraction Limits C.1

List of Symbols and Acronyms

This list contains the symbols and acronyms, which are used throughout the text. Symbols with more local uses are not included. This is especially true for chapter 5, where all symbols are local. Occasionally, some symbols have a different meaning than in this list, but this will be apparent from their context.

General Symbols

α Conversion factor relating the distance between two glare points to the bubble diameter γ Collecting angle, i.e. the opening angle from the bubble centre to the aperture edges δ Distance between two glare points

δ

Distance between two glare points in pixels

θ Observation angle, i.e. the angle between the laser propagation direction and the connecting line bubble-camera

λ Wavelength

τ Angle between light ray and tangent at the interface ϕ Tilt angle of ellipse

∆φ Fringe spacing

Φ

Out-focus disc size in pixel C Calibration value

D

The bubble diameter

F Frequency

I Intensity

M Optical magnification

N Amount of interactions between the light ray and the bubble R The bubble radius

Re Reynolds number S

Physical size of a pixel

a Principal radius of an ellipse, i.e. half the long axis b Secondary radius of an ellipse, i.e. half the short axis d

Distance bubble-aperture

f Focal length of the lens

f

F-number of the objective, i.e. focal length divided by aperture diameter g Out-focus distance of the CCD-plane

h Camera displacement from the in-focus position n

Refractive index of the liquid

r

Radius of the aperture s

Distance lens-image s

Distance lens-object t Laser-sheet thickness

v Velocity

LIST OF SYMBOLS AND ACRONYMS

w Distance between glare point and reference ray from the centre of the bubble x

Newtonian image distance, i.e. distance to the image minus focal length x

Newtonian object distance, i.e. distance to the object minus focal length

Acronyms

2D Two-dimensional BFP Back Focal Plane BPP Back Principal Plane CCD Charge Coupled Device CRLB Cramer-Rao Lower Bound FFP Front Focal Plane

FFT Fast Fourier Transform FPP Front Principal Plane GO Geometrical Optics GPD Global Phase Doppler

GPVS Glare Point Velocimetry and Sizing GW Glare point Width

ILIDS Interferometric Laser Imaging for Droplet Sizing IPI Interferometric Particle Imaging

LMS Laser Marked Shadowgraphy NA Numerical Aperture

PIV Particle Image Velocimetry

PSF Point Spread Function

PTV Particle Tracking Velocimetry

SNR Signal to Noise Ratio

Samenvatting

Luchtbellen treden op in tal van industriële toepassingen. In de elektrochemische industrie worden er bellen ge- produceerd bij de hydrolyse van water, de productie van chloor en als nevenreactie in metaaldepositieprocessen.

Verder treden luchtbellen op in het continu gieten van staal, in waterzuiveringsinstallaties, in fermentatiepro- cessen en nog vele andere domeinen. Deze ver uit elkaar liggende industrietakken hebben allemaal belang bij verbeteringen in de experimentele meettechnieken waarmee de betreffende bellenstromingen onderzocht worden.

Voor het opmeten van de diameter en snelheid van deze gasbellen gebruikt men bij voorkeur een planaire en niet intrusieve techniek. Dergelijke technieken hebben het voordeel dat ze de stroming niet verstoren en met een enkele meting meteen een ruimtelijk overzicht kunnen bieden (bvb. van een gedeelte van een elektrochemische elektrode). De meest courante 2D optische techniek die aan deze eisen voldoet is de schaduwmethode. Hierbij worden de luchtbellen diffuus belicht en hun schaduw wordt met een digitale camera geregistreerd (figuur 1(a)).

Deze techniek heeft echter verscheidene nadelen. Het belangrijkste hiervan is dat alle bellen tussen de lichtbron en de camera afgebeeld worden en men dus niet de preciese afstand tussen de bel en de camera kent. Aangezien de optische vergroting (meestal) afhankelijk is van deze afstand, treden er grote fouten op in het berekenen van de echte belgrootte uitgaande van de afgebeelde schaduwgrootte.

Een andere techniek, genoemd Interferometric Laser Imaging for Droplet Sizing (ILIDS), werd reeds 20 jaar geleden ontwikkeld en maakt recent een steile opmars in het meten van bolvormige druppels (Koenig et al.

[1986], Ragucci et al. [1990], Glover et al. [1995]). Bij deze techniek gebruikt men een 2D laservlak dat haaks staat op de kijkrichting van de camera. Enkel druppels in dit vlak (van enkele mm dik) worden afgebeeld door de camera, waardoor het hierboven vermelde probleem van de schaduwtechniek grotendeels geëlimineerd wordt.

Bij ILIDS steunt men op het feit dat het licht dat naar de camera wordt verstrooid afkomstig is van specifieke punten op het druppeloppervlak; de zogenaamde reflectiepunten. Alhoewel deze techniek ontwikkeld is op druppels, wordt het principe geïllustreerd op gasbellen in figuur 2. Deze figuur toont dat wanneer deze punten uit-focus worden afgebeeld, er een interferentiepatroon ontstaat zoals zichtbaar in figuur 2 en 1(b). Aan de hand van de frequentie van dit patroon kan men de diameter bepalen. In een variant van ILIDS wordt de foto in-focus genomen, waardoor de twee reflectiepunten zichtbaar zullen zijn zoals ook aangegeven in figuur 2 en 1(c).

Zoals Hess [1998] aantoonde kan men aan de hand van de afstand tussen twee reflectiepunten ook de diameter bepalen. Doorheen de tekst wordt deze techniek Glare Point Velocimetry and Sizing (GPVS) genoemd.

∗Merk op dat nog andere interactie-ordes zich een weg kunnen banen naar de camera, maar deze hebben een veel lagere intensiteit (voor de getoonde observatie hoek) en zijn daarom niet zichtbaar.

Figuur 1: De vijf optische 2D meettechnieken die onderzocht werden in deze thesis geïllustreerd op één bel (a)

Schaduwmethode (b) ILIDS (c) GPVS (d) Reflectiecirkels (e) LMS

SAMENVATTING

Figuur 2: Principe van GPVS en ILIDS.

Echter, deze optische technieken werden voornamelijk ontwikkeld voor druppels. Door het grote belang van gasbelmetingen in o.a. de elektrochemische industrie, is het onderwerp van deze thesis dan ook het ontwikkelen van niet-intrusieve 2D optische meettechnieken ter bepaling van de gasbelgrootte. Aangezien het onderzoek van ILIDS op druppels reeds had aangetoond dat deze techniek (en zijn variant GPVS) vele voordelen heeft in vergelijking met de schaduwmethode, was de originele doelstelling van dit doctoraat dan ook onderzoeken hoe de meetprincipes van GPVS en ILIDS overgedragen konden worden op het meten van gasbellen.

De eerste concrete resultaten hieromtrent werden gemeld in Dehaeck et al. [2005] (en hoofdstuk 3). Hierin werden drie nieuwe configuraties voorgesteld voor het meten van luchtbellen met GPVS, waaronder die van figuur 2. Numeriek onderzoek hieromtrent heeft aangetoond dat deze opstellingen preciezer zijn, toepasbaar in grotere concentraties aan bellen en bovendien leiden tot kleinere fouten in snelheidsmetingen dan de enige opstelling tot dan toe gekend voor het meten van gasbellen met ILIDS van Niwa et al. [2000]. In een variant van de opstelling in figuur 2, werd een tweede laservlak gebruikt met een omgekeerde richting als het originele laservlak. Dit leidt tot het verschijnen van een derde reflectiepunt. Met deze extra informatie is het mogelijk om de refractie-index van het medium te bepalen, zoals we experimenteel hebben aangetoond. Daarnaast kan dit extra punt ook gebruikt worden om niet-bolvormige bellen te detecteren. Dit is belangrijk aangezien numerieke simulaties hebben aangetoond dat de meetfout voor niet-bolvormige bellen kan oplopen tot 16% voor een niet- bolvormigheid van 10%. De configuratie die door ons werd voorgesteld, kan deze fout beperken tot 4%.

In hoofdstuk 4 wordt er dan gekeken naar de beste toepassing van deze nieuwe inzichten voor belmetingen met ILIDS (een combinatie van Dehaeck and van Beeck [2007d] en Dehaeck and van Beeck [2007e]). Dit leidt tot een nieuwe ILIDS configuratie waarin dezelfde niet-bolvormigheidsdetectie kan gebeuren als voor GPVS maar nu met slechts één laservlak. Daarnaast werd ook voor het eerst een volledige onzekerheidsanalyse van ILIDS uitgevoerd, zowel voor druppels als bellen. Eén van de belangrijke nieuwe resultaten hierin was dat de meetfout voor niet-bolvormige druppels kan oplopen tot 5.5% voor een niet-bolvormigheid van 10% (appendix B). Daarnaast toonde deze analyse ook aan dat de calibratie van ILIDS één van de belangrijkste foutenbronnen is. Dit feit is nog niet voldoende gekend in de ILIDS gemeenschap aangezien de meeste auteurs hun cali- bratiemethode en de geassocieerde onzekerheid niet vermelden. Om deze onduidelijkheid in de verschillende calibratiemethodes op te helderen, werden de verschillende calibratiemethodes uitgebreid met elkaar vergele- ken, zowel theoretisch als experimenteel. Daarnaast wordt ook veel aandacht besteed aan het optimaliseren van deze calibratietechnieken.

Naast het bereiken van de originele doelstelling, i.e. nieuwe configuraties ontwikkelen voor het meten van

gasbellen met GPVS en ILIDS, werden ook verscheidene andere technieken onderzocht of ontwikkeld. Zo

werd in hoofdstuk 5 (gebaseerd op Dehaeck and van Beeck [2007a]) een nieuw beeldverwerkingsprogramma

ontwikkeld dat in staat is om ellipsvormige schaduwen van een variabele grootte te herkennen in een foto van

de schaduwmethode (e.g. figuur 1(a)). Hierbij werd uitgegaan van een bestaand algoritme van Rad et al. [2003]

SAMENVATTING

dat reeds in staat was om cirkels te detecteren. Dit algoritme werd gegeneraliseerd naar de detectie van ellipsen en aanzienlijk versneld.

In hoofdstuk 6 (gebaseerd op Dehaeck and van Beeck [2007b]) wordt dieper ingegaan op de heldere cirkels die verschijnen binnenin de schaduw van luchtbellen zoals zichtbaar in figuur 1(d). We tonen aan dat deze cirkels ook afkomstig zijn van reflectiepunten. Het optreden van deze cirkels werd reeds theoretisch voorspeld door van de Hulst and Wang [1991] en Bongiovanni et al. [1997]. Experimentele resultaten en het gebruik hiervan ter bepaling van de beldiameter en de refractie-index zijn echter nieuw. Naast een analytische afleiding van de noodzakelijke formules, werd hierin ook experimenteel aangetoond dat de beldiameterbepaling met behulp van de reflectiecirkels bijna een grootte-orde nauwkeuriger is dan de traditionele diameterbepaling aan de hand van de schaduwdiameter. Maar misschien een nog interessantere toepassing van deze reflectiecirkels is de bepaling van de refractie-index van de vloeistof. We zullen aantonen hoe deze grootheid gemeten kan worden tot op de tweede decimaal nauwkeurig en dit zonder dat enige calibratie nodig is!

Hoofdstuk 7 (gebaseerd op Dehaeck and van Beeck [2007c]) voert echter nog een grotere verbetering van de schaduwtechniek in: Laser Marked Shadowgraphy of LMS. Hierin wordt de schaduwtechniek gecombineerd met de GPVS techniek van hoofdstuk 3 (figuur 1(e)). Op deze wijze, geniet de schaduwtechniek van de goede lokalisatie van het meetvolume die het laservlak van GPVS met zich meebrengt. Dit vermindert de meetonzek- erheid ten gevolge de afstand bel-camera maar verhindert ook dat uit-focus belletjes gemeten zouden worden.

In experimenten wordt aangetoond dat de meetfout tot 20% zou bedragen met de gewone schaduwtechniek, terwijl die nu tot 1% kan beperkt worden met LMS. Daarnaast kan de groottebepaling van bolvormige bel- letjes met GPVS gebeuren, wat tot precisere metingen leidt dan de schaduwtechniek. GPVS heeft echter ook voordeel bij de samenwerking aangezien de robuustheid van de beeldverwerking vergroot wordt. Dit is voor- namelijk omdat een zwarte cirkel met twee intense punten op gekende locaties een veel sterkere ’handtekening’

van de bel levert dan gewoon twee lichtvlekjes die op dezelfde hoogte moeten staan. Deze techniek werd vervolgens toegepast voor het opmeten van beldiameterdistributies in een elektrochemische reactor.

Het enige stuk van de puzzel dat nu nog ontbreekt is een efficiënte calibratiemethode voor de in-focus tech- nieken (GPVS, Schaduwtechniek, Reflectiecirkels en LMS). Dit wordt verholpen in hoofdstuk 8 waarin een algoritme op basis van de Fourier transformatie wordt voorgesteld. Experimenten tonen aan dat deze meth- ode uitermate geschikt is voor het calibreren van typische GPVS experimenten waarbij het meetvlak niet noodzakelijk loodrecht staat op de kijkrichting van de camera. De hierbijhorende verandering van de opti- sche magnificatie met de locatie in de foto, kan perfect opgemeten worden en vervolgens gebruikt worden als calibratiecurve.

Tenslotte worden in hoofdstuk 9 de verschillende meettechnieken met elkaar vergeleken. Deze vergelijking gebeurt op basis van hun werkdomein (afstand camera-bel versus beldiameter), de bereikbare precisie en ook de maximaal toelaatbare concentraties aan bellen. Deze analyses tonen aan dat de verschillende meettechnieken die voorgesteld werden in deze thesis elk hun specifiek toepassingsgebied hebben waarin ze uitblinken. Op basis hiervan kunnen de volgende richtlijnen opgesteld worden:

• Indien de bellen niet bolvormig zijn (i.e. groter dan ± 1mm) is de keuze duidelijk: LMS (hoofdstuk 7). Deze techniek is de enige die kwantitatieve resultaten kan leveren in dit geval. De schaduwtechniek alleen (i.e. zonder het laservlak) kan dit ook maar hierbij is het meetvolume niet goed bepaald. Dit kan leiden tot aanzienlijke meetfouten. Merk wel op dat deze lokalisatie in bepaalde gevallen al gegeven kan zijn door de geometrie, e.g. de belcreatie op één enkel capillair. In dit geval, is een laservlak niet noodzakelijk en is de gewone schaduwtechniek even efficiënt.

• Voor bolvormige bellen zijn er verschillende mogelijkheden. Indien de diameterverdeling van een lage

concentratie van microbelletjes (<0.5mm) gemeten moet worden, dan is ILIDS (hoofdstuk 4) de aangewezen

kandidaat. Met deze techniek kunnen standaard lenzen gebruikt worden op een comfortabele afstand voor

het meten van microbelletjes. Men moet echter wel in rekening nemen dat snelheidsmetingen op basis

van ILIDS beeldjes en de lokalisatie van de belletjes (e.g. voor concentratiemetingen) een grootte-orde

minder nauwkeurig zijn dan de diametermetingen.

SAMENVATTING

• Tenslotte, indien het aantal belletjes in het gezichtsveld te groot is en de ILIDS beeldjes beginnen te

overlappen of wanneer de snelheidsmetingen een betere resolutie nodig hebben of wanneer dicht bij de

wand moet gemeten worden dan zijn in-focus technieken onmisbaar. Voor matige bellenconcentraties

biedt LMS het beste compromis (hoofdstuk 7). De toegevoegde robuustheid in de beeldverwerking ten

opzichte van GPVS is hierbij de doorslaggevende factor. Echter, GPVS (hoofdstuk 3) lijkt de beste op-

tie voor het meten in de hoogste bellenconcentraties. Dit voornamelijk omdat bij GPVS enkel de bellen

tussen het meetvolume en de lens goede metingen kunnen verstoren, terwijl bij LMS (en de schaduwtech-

niek) ook de bellen tussen het meetvolume en de achterkant van de testsectie voor problemen zorgen.

Summary

Bubbly flows appear in many industrial applications. In electrochemistry, bubbles emerge on the electrodes in e.g. hydrolysis of water, the production of chloride and as a side-reaction in metal plating. Bubbles also appear in the continuous casting of steel, waste water treatment, fermentation processes and many other domains.

All of these industries benefit from advances in the experimental bubble measurement devices they use to characterise the bubbly flow.

For measuring the diameter and velocity of these gas bubbles, a non-intrusive, planar measuring technique is preferably used. These techniques have the advantage that they do not disturb the flow and they can provide a spatial overview (e.g. of an entire electrode) with a single measurement. The most common 2D optical technique that satisfies these criteria is backlighting (or shadowgraphy). Here, the bubbles are illuminated from the back and their shadow is recorded by a camera (figure 1(a)). This technique has several disadvantages though. The most important one being that all the bubbles between the light source and the camera are imaged.

Therefore, one does not know the distance between the bubble and the camera precisely. As the magnification of the camera depends on this distance (in general), sizing errors are the inevitable result.

Another technique, called Interferometric Laser Imaging for Droplet Sizing (ILIDS), was developed over 20 years ago but is recently becoming a serious competitor for measuring spherical droplets (Koenig et al. [1986], Ragucci et al. [1990], Glover et al. [1995]). In this technique, a laser-sheet is created and placed at an angle with the viewing direction of the camera. Only droplets in this plane (of several mm thick) are imaged by the camera and therefore, the above mentioned issue with backlighting is almost absent here. ILIDS is based on the fact that light that is scattered towards the camera is coming from specific points on the droplet surface;

the so-called glare points. Although this technique was developed for droplets, the principle is illustrated on bubbles in figure 2. This figure shows that when these glare points are imaged out-focus, an interference pattern as shown in figure 2 (and 1(b)) emerges. The frequency of this interference pattern is used to size the bubble.

In a technique closely related to ILIDS, the camera is placed in-focus and only two glare points are visible as shown in figure 2 and 1(c).

As demonstrated by Hess [1998], the distance between these glare points can also be used to size the bubble. Throughout the text, this technique will be denoted by Glare Point Velocimetry and Sizing (GPVS).

However, these optical techniques were mainly developed for droplets. Because measuring bubbles is that important for e.g. the electrochemical industry, the main goal of this thesis was to develop non-intrusive 2D optical techniques for bubble sizing. As the investigation of ILIDS on droplets had already shown that this

†Note that other interaction orders also reach the camera but these have a significantly lower intensity and are therefore not visible in the image (or at least for the shown position of the camera).

Figure 1: The five optical 2D measuring techniques that were investigated in this thesis, illustrated on a single

bubble (a) Backlighting (b) ILIDS (c) GPVS (d) Glare Circles (e) LMS

SUMMARY

Figure 2: Principle of GPVS and ILIDS.

technique (and GPVS) has many advantages compared to backlighting, the original aim was to investigate how the measuring principles of GPVS and ILIDS could be transferred to measuring gas bubbles.

The first results in this respect were reported in Dehaeck et al. [2005] (chapter 3). Here, three new configurations were proposed to measure bubbles with GPVS (including the one of figure 2). It was shown numerically how these configurations were more accurate, applicable in larger bubble concentrations and lead to smaller velocity errors than the only configuration known at this time for the measurement of bubbles with ILIDS (Niwa et al.

[2000]). In one of these configurations, a second laser-sheet was used that is opposed to the original one, which creates a third glare point. With this extra information it is possible to measure the refractive index of the liquid, as was shown experimentally. This extra point can also be used to detect non-spherical bubbles. This is vital as numerical simulations have showed that the sizing error on bubbles with a non-sphericity of 10% can go up to 16%! With the proposed configuration, this error can be reduced to approximately 4%.

Chapter 4 then investigates how to implement these improvements in GPVS to bubble measurements with ILIDS (a combination of Dehaeck and van Beeck [2007d] and Dehaeck and van Beeck [2007e]). This resulted in a new ILIDS configuration in which the same non-sphericity detection is achieved with a single laser-sheet.

Next to this, a complete uncertainty analysis of ILIDS was performed for the first time, both for bubbles and droplets. One of the innovative results here was that the sizing error for measuring non-spherical droplets (of 10%) can go up to 5.5% (appendix B). This analysis also showed that the calibration of ILIDS is one of its most important error sources. This fact is relatively unknown in the ILIDS community as most researchers do not mention their calibration procedure, nor the associated uncertainty. To clarify the differences in the various calibration procedures, they were compared theoretically and experimentally. Based on this analysis, it was shown how to optimise the calibration.

As the original goals, i.e. develop new configurations for sizing bubbles with GPVS and ILIDS, were reached in the two previous chapters, other techniques were also investigated or newly developed in the remainder. In this respect, chapter 5 (based on Dehaeck and van Beeck [2007a]) introduces a novel image processing algorithm, which can detect ellipsoidal shadows of a variable size in an image (e.g. figure 1(a)). To this end, the algorithm of Rad et al. [2003], which was already capable of detecting circles, was extended to detect ellipses and made considerably faster.

Chapter 6 (based on Dehaeck and van Beeck [2007b]) investigates the appearance of bright circles inside the

shadows of bubbles as shown on figure 1(d). It will be demonstrated how these circles are also caused by glare

points. In fact, the appearance of these ’glare circles’ was already predicted theoretically by van de Hulst and

Wang [1991] and Bongiovanni et al. [1997]. However, experimental results and the idea to use them to measure

the diameter and refractive index of the bubble has not been demonstrated so far (to our knowledge). Next to

an analytical derivation of the necessary formulae, we show experimentally that bubble diameter measurements

based on this glare circle are approximately one order of magnitude more precise. However, perhaps more

SUMMARY

interesting is the application of this glare circle to measure the refractive index of the surrounding liquid. We demonstrated how to obtain this quantity accurate up to the second decimal without the need for a calibration!

In chapter 7 (based on Dehaeck and van Beeck [2007c]), another improvement of regular backlighting is in- troduced: Laser Marked Shadowgraphy (LMS). This technique is a combination of backlighting and GPVS (figure 1(e)). In this way, backlighting benefits of the good localisation of the measurement volume offered by the laser-sheet. This decreases the sizing error caused by the uncertainty in the distance bubble-camera. It also avoids the sizing of out-focus bubbles. We showed experimentally how regular backlighting could lead to sizing errors of up to 20% due to the sizing of out-focus bubbles whereas LMS can limit this error to 1%. Nev- ertheless, sizing spherical bubbles is done preferably with GPVS due to the increased precision it brings. Now, GPVS also benefits from the collaboration with backlighting as the presence of the circular shadows makes the image processing more robust. This is because a black circle with two bright points at specific locations is a much stronger ’signature’ than just two glare points that should be at the same pixel row. This technique was then applied to measure bubble diameter distributions in an electrochemical reactor.

Now, the only piece of the puzzle that is missing is a good calibration method for the in-focus techniques (GPVS, backlighting, glare circle sizing and LMS). This is remedied in chapter 8 in which an algorithm based on the Fourier transform is proposed. Experiments have shown that this technique is capable of calibrating targets that are placed at an angle with the viewing direction of the camera, a situation quite common in GPVS.

The resulting change in the magnification across the field of view (caused by the varying distance bubble- camera) can be measured and used as a calibration curve to obtain more accurate results.

Finally, in chapter 9, the introduced techniques are compared on the basis of working domain (stand-off distance of the camera versus the bubble diameter), precision and achievable void fraction. These comparisons showed that each presented technique has its own preferred working domain. Thus, the following guidelines were extracted concerning which 2D optical technique to use in a given situation:

• When the bubbles are not spherical (i.e. larger than 1mm) the choice is clear: LMS. This technique was introduced in chapter 7 and is the only technique able to obtain quantitative data in this case. Backlighting can provide this information as well, but its measurement volume is not well-defined. As a result, void fraction measurements are inaccurate and out-focus bubbles are measured as well, which leads to large measurement errors. Note that in some occasions, the localisation can be provided by the experimental set-up, e.g. bubble formation on a single needle, in which case regular backlighting is sufficient.

• When the bubbles are spherical there are different possibilities. When the diameter distribution of a dilute cloud of micro-bubbles (<0.5mm) should be measured, the ILIDS configuration suggested in chapter 4 is probably the best option. With this technique, regular lenses can be used at a comfortable stand-off distance. However, one should take into account that velocity measurements and the localisation of the bubbles for the void fraction maps are one order of magnitude less accurate than the bubble diameter.

• When the void fraction in the bubble cloud is too large to avoid overlapping images with ILIDS or when

the velocity measurements should have a better resolution or when one needs to measure close to the

wall, in-focus techniques are necessary. For moderate bubble concentrations, using LMS (chapter 7)

provides the best compromise. The increased robustness of the image processing over regular GPVS is

its main advantage. However, GPVS (chapter 3) still appears to be the best option to measure in high

bubble concentrations. This is due to the fact that only those bubbles between the measurement volume

and the lens are important and not the ones between the laser-sheet and the backlighting source as for

LMS (and backlighting).

List of Publications

S. Dehaeck, J.P.A.J. van Beeck, and M.L. Riethmuller. Extended glare point velocimetry and sizing for bubbly flows. Experiments in fluids, 39(2):407–419, August 2005. doi: 10.1007/s00348-005-1004-6.

S. Dehaeck and J.P.A.J. van Beeck. Designing a maximum precision interferometric particle imaging set-up.

Experiments in fluids (in press), 2007. doi: 10.1007/s00348-007-0286-2.

S. Dehaeck and J.P.A.J. van Beeck. A clustering approach to ellipse detection. Computer Vision and Image Understanding (submitted), 2007.

S. Dehaeck and J.P.A.J. van Beeck. Multi-Frequency Interferometric Particle Imaging for Gas Bubble Sizing.

Experiments in fluids (submitted), 2007.

S. Dehaeck and J.P.A.J. van Beeck. Simultaneous Determination of Bubble Diameter and Relative Refractive Index Using Glare Circles. Applied Optics (submitted), 2007.

S. Dehaeck and J.P.A.J. van Beeck. Laser marked shadowgraphy. Experiments in fluids (submitted), 2007.

P. Planquart, S. Dehaeck, J.-M. Buchlin, and ML Riethmuller. Experimental investigation of bubbly flow, annular flow and transition in a downward cocurrent two-phase flow. In Abstracts of the 5th International conference on multiphase flows, 2004.

S. Dehaeck, J.P.A.J. van Beeck, and M.L. Riethmuller. Glare Point Velocimetry and Sizing (GPVS): Introduc- tion of a new optical 2D measuring technique for bubbly flows. In 12th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, 2004.

S. Dehaeck and J.P.A.J. van Beeck. Development of a PIV set-up for measuring bubbles. In International Workshop on Micro PIV and Applications in Microsystems, Delft, April 2005.

S. Dehaeck and J.P.A.J. van Beeck. Demonstration and characterisation of a new interferometric particle

imaging configuration for bubbles. In 13th International Symposium on Application of Laser Techniques to

Fluid Mechanics, Lisbon, 2006.

1

Introduction

1.1 Bubbly Applications

Bubbles appear in a myriad of applications in which they can serve different purposes. Sometimes they are vital, sometimes they are a nuisance but sometimes they can even be deadly. To start with a cheerful application, the importance of bubbles in fizzy drinks will be discussed. Anybody would agree that champagne is mostly about the bubbles. Recently, this application and more specifically the birth, rise and collapse of champagne bubbles was studied by Liger-Belair [2003] (under sponsorship of Moët & Chandon and Pommery amongst others!).

A typical picture of a bubble train in champagne from these authors is shown in figure 1.1(a). New bubbles are formed frequently on e.g. fibres from tea towels with a size of several tens of micrometres. In its rise, the bubble continues to grow and accelerate due to the continued absorption of carbon dioxide. At the surface, the bubble will eventually pop and the ensuing rush of liquid to fill the void left by the bubble will result in the creation of a liquid jet, which can be observed in figure 1.1(b). This jet then breaks up in a fine mist of micro- droplets. Next to being fascinating in itself, this whole process is also essential for the taste of champagne. Due to their molecular structure, the aromatic components tend to adhere to the bubble surface. As a result, these aromatic components will rise with the bubble. Liger-Belair [2003] hypothesised that when the bubble finally collapses, these components will be caught in the liquid jet and subsequently in the mist of micro-droplets.

As evaporation progresses faster on small droplets, this would liberate the aroma in a more efficient way than without the effervescence.

The origin of these bubbles can be found in the second alcoholic fermentation, which takes place in the bottle.

As with any (alcoholic) fermentation process, yeasts are injected which convert the sugar present into alcohol

and carbon dioxide. When the bottle is uncorked, this leads to a super-saturation of the champagne with

carbon dioxide, which drives the bubble creation. However, the making of alcoholic beverages is only one

example in which a mass-culture of micro-organisms is used to create useful products. In general, this is

called fermentation and it is a key industrial process that provides essential ingredients for common food,

beverage and pharmaceutical products. The best known example of industrial fermentation is probably the

mass-production of baker’s yeast. Another interesting application is the production of Human Serum Albumin

(HSA) by a genetically modified yeast (Barr et al. [1992], Kobayashi et al. [2000]). HSA is an important protein

component of human plasma and is used in the treatment of severe burns or blood loss. Before the advent of

genetic engineering, HSA was obtained from blood donors. Yet, due the risk of infection (by e.g. HIV) other

production processes were sought for and found with the help of genetics. Currently, a massive amount of yeast

cells, which are genetically engineered to produce HSA, are grown in a medium that is rich in nutrients. From

CHAPTER 1. INTRODUCTION

Figure 1.1: (a) Bubbles rising in a glass of champagne (b) Liquid jet formed upon the collapse of a bubble.

(Photographs courtesy of Gerard Liger-Belair)

the necessary nutrients, the delivery of oxygen imposes the most stringent limitation due to the low solubility of oxygen in water. Therefore, air and even pure oxygen bubbles are pumped into the system to enhance the mass transfer. Nevertheless, studies have shown that scaling up these bioreactors often results in a dramatic loss of productivity (sometimes up to 50%!) due to the poor aeration of the tank (Moo-Young and Blanch [1981]). As a result, different ways to obtain a more homogeneous bubble distribution and avoid ’dead zones’ where cells could be oxygen-starved are being examined. Another improvement in the oxygen delivery that is investigated is the use of smaller bubbles. This results in a higher oxygen delivery due to the increase in both the interfacial area and the hold-up time of the bubbles. As a result, sparging with micro-bubble dispersions (MBD) is under heavy research as it provides bubbles with diameters of 20-1000 µm compared to 3-5 mm in normal fermenters (Kaster et al. [1990]).

Finally, another application where bubbles arise is in cardiac surgery. During such a procedure, the blood is deviated through an extra-corporeal circuit. Micro-bubbles can be entrained through the connection between the device and the artery and get pumped around the body. These gaseous micro-emboli then can get trapped and block small arteries at different locations, thus causing severe damage. The most dangerous location to get trapped is obviously the brain. This can lead to neurocognitive impairment or death. In fact, studies have reported that 50-70% of the patients undergoing coronary artery bypass grafting surgery experience some sort of neurocognitive impairment in the week following the surgery. Luckily, some of these micro-emboli dissolve/disappear and only 30-40% still have the symptoms after 3 months (e.g. Shaw et al. [1985]). As a direct result, studying the capacity of these extra-corporeal circuits to remove some of the entrained bubbles (or reduce them in size), as done by Dickinson et al. [2006], literally becomes a matter of life or death.

1.2 Overview of Bubble Sizing Techniques

1.2.1 Introduction

The above mentioned applications have in common that a detailed characterisation of the bubbles is necessary for the optimisation of the corresponding systems. When looking at the available tools for measuring bubble sizes, we note that there are many different techniques available based on very different physical principles.

An overview of several of these techniques will be given next. However, only techniques capable of measuring

bubble diameter distributions will be discussed. As a result, capacitance measurements and other techniques

which only measure void fractions, i.e. the volumetric concentration of air in the measurement volume, will

not be discussed.

1.2. OVERVIEW OF BUBBLE SIZING TECHNIQUES

Figure 1.2: (a) Release of a bubble from an injection needle (b) Registered pressure fluctuation from the release in (a) (Pictures and pressure profile reproduced from Manasseh [2004] with permission)

1.2.2 Acoustical Measurements

1.2.2.1 Passive Acoustics

Bubbles are a particularly well-suited target for acoustical measurements as the damping on volumetric os- cillations is rather small (e.g. Leighton [1994]). As a result, bubbles will oscillate when they detach from an injection needle, growing and shrinking with a frequency which is inversely proportional to their diameter (Minnaert [1933]). The proportionality constant depends on the liquid pressure and density and only marginally on the surface tension (Longuet-Higgins et al. [1991]). Now, these oscillations create an oscillating pressure field, i.e. a sound that can be heard by a human ear for bubbles larger than 0.3mm in water.

Now, the creation of sound upon release is used in passive acoustics to size the bubbles. Pictures from Manasseh [2004] of the release and the registered pressure fluctuation are shown in figure 1.2(a) and (b) respectively.

The greyed-out area in the transducer output corresponds to the time in which the images were taken. The frequency of the registered fluctuation is then extracted and used to size the released bubble. However, as Manasseh et al. [2001] showed, the frequency of the sound shifts as the bubble continues to oscillate, possibly due to the asymmetrical nature of the release. Thus, only the first periods of the sound can be used for quan- titative measurements. Nevertheless, successful measurements have been performed by Manasseh [2004] in an industrial scale bioreactor. In a way, these tests also highlighted some of the advantages of this technique.

Bubbles of ± 1mm can be measured with regular hydrophones, which can be integrated into working reactors.

Additionally, the signal processing can be performed in real time and the amount of data recorded is moderate (certainly compared to storing thousands of digital images). Therefore, this technique is an excellent tool for the supervision of industrial processes.

1.2.2.2 Linear Active Acoustics

For bubbles smaller than 300µm, regular hydrophones cannot detect the high frequencies involved and spe- cialised equipment becomes necessary. In addition, the intensity of the emitted sound decreases with the di- ameter squared making passive acoustics virtually impossible (Manasseh [2004]). In this case, more or less an inverted approach is preferred. Sound of different frequencies is sent into the flow and the attenuation, reflection or propagation of this sound by the presence of a bubble cloud is recorded and investigated. For measurements based on the attenuation, one uses the fact that bubbles absorb much more energy of the fluctuating pressure field when the frequency is close to its own natural frequency (which is determined by its radius). As a result, the amount of attenuation at a particular frequency is proportional to the amount of bubbles that are resonating.

Therefore, probing the flow with different frequencies allows one to obtain a bubble size distribution. Some of the possible configurations are reviewed by Vagle and Farmer [1998] for the measurement of bubbles in breaking waves. However, these measurements require the assumption that the bubbles are homogeneously

∗On the pressure transducer output shown, a negative voltage corresponds to a positive pressure.

CHAPTER 1. INTRODUCTION

Figure 1.3: Received acoustic signal from a resonating bubble

distributed in the space between the transmitter and the receiver. This is a rather restrictive assumption, which excludes it for several practical applications.

1.2.2.3 Non-Linear Active Acoustics

Another approach in active acoustics is to insonify a volume with two acoustic signals as suggested by New- house and Shankar [1984]. These signals have a very different frequency (and intensity) and the one with the lowest frequency is called the ’pumping’ signal (f

) whereas the second frequency is much higher (and much more intense) and is called the ’imaging’ signal (f

). In a measurement, the frequency of the pumping signal is varied until the natural frequency of the bubble under investigation is found and the bubble starts to resonate.

In this case, the imaging signal will be reflected in a different/non-linear way. This implies that the received signal when both frequencies are used simultaneously is not the same as the mathematical sum of the received signals when each frequency would be applied separately. Instead, the imaging signal will be reflected with an intensity that is modulated by the pumping frequency. This has been represented schematically in figure 1.3. On this figure, the varying intensity is clearly noticeable as the bubble is resonating. This can be understood from the fact that the resonating bubble will scatter more of the imaging signal when it grows and less as it shrinks again. In contrast, when the bubble is not resonating, the detected signal will have a constant amplitude. Thus, a frequency analysis of the received signal will show frequency components at f

± f

when the bubble is resonating. As these peaks will be absent when the bubble under investigation is not resonating, the presence of peaks at these frequencies can be used to classify the scattering object as a bubble with a natural frequency equal to the pumping signal frequency. Thus, a sweep with the pumping frequency through the relevant natural frequencies corresponding to a given diameter range, allows for an accurate sizing of a given bubble. However, as was shown by e.g. Phelps and Leighton [1996], this modulation also occurs for bubbles close to their res- onating frequency. As a result, a finite range of bubble diameters will essentially lead to the same output signal, thus limiting the precision of the experiments (c.f. diffraction in optics). Phelps and Leighton [1996] discuss an improved implementation which can improve this limit and show experimental results where a precision of 1.2% was achieved for bubbles with a radius of 1.61mm.

The resulting system can be used to measure bubbles in optically opaque media as blood to measure the size of entrained gaseous emboli in extra-corporeal circuits (e.g. Dickinson et al. [2006]). It could even be used to monitor decompression sickness in astronauts and divers through the skin (c.f. an ultra-sound scan of a foetus)!

This is definitely an advantage of the acoustical techniques with respect to optical techniques.

1.2. OVERVIEW OF BUBBLE SIZING TECHNIQUES

Figure 1.4: (a) Working principle of optical probes (b) Sample signal showing two passing bubbles (c) Two-tip configuration (d) Sample signal of two-tip configuration

1.2.2.4 General Remarks on Acoustical Techniques

Concluding the overview of the acoustical techniques, we might state that the precision of the recent non- linear active acoustical techniques is certainly comparable to optical techniques. Also the passive acoustical measurements obtain an accuracy of ± 2%, as reported by Vazquez et al. [2005]. However, one must always verify if the assumptions used to relate the natural frequency to the bubble diameter, are valid in the present experiment. This is because the resonant frequency of the bubble is influenced by the damping present in the system. This damping is linked to the dissipation of energy in the oscillating bubble by viscous losses, thermal dissipation and acoustic radiation. All three of these terms need to be modelled theoretically, which introduces uncertainty in the results. Furthermore, it was shown that bubble-bubble interactions could lower this resonance frequency as well (c.f. Strasberg [1953]), possibly biasing measurements in dense bubble clouds. A final remark that we wish to add here is that the presented techniques are point measurement techniques (although this

’point’ can be made quite large). As a consequence, only a single bubble can pass the measurement volume at any given time (except for the attenuation experiments), which limits the measurable amount of bubbles present in the flow. Additionally, when a bubble diameter evolution over a certain distance needs to be characterised, many different measurements are necessary at different positions. In this way, only time-averaged diameter distribution fields can be obtained, which makes the technique unsuitable to characterise transient phenomena.

1.2.3 Optical Measurements

1.2.3.1 Phase Detection Probes

Air and water not only have wildly different acoustical properties, they also have a different optical refractive

index. This leads to a phenomenon called total internal reflection where light cannot escape a denser medium

when the impact angle with the interface is too large. This effect is used by optical probes as illustrated in

figure 1.4(a). The light ray travelling through the optical fibre can refract through the tip when immersed in

water as the refractive index of water is close to that of the fibre. On the contrary, when a bubble passes by,

the tip will pierce the surface and the light ray will be totally reflected at the fibre-air interface due to the

large difference in refractive index. As a result, the light sensitive diode connected to the fibre will receive a

large amount of light and its voltage will rise considerably as shown in figure 1.4(b). This technique was first

described by Miller and Mitchie [1970]. Note that similar phase detection probes can also be constructed based

CHAPTER 1. INTRODUCTION

Figure 1.5: Principle of Fraunhofer diffraction particle sizing technique.

on the different electrical resistance of wires in the presence of air versus water (Neal and Bankoff [1963]) or use simple hot-wires as the heat transfer properties are also radically different.

Independent of the origin of the signal, relating the time spent in air to the diameter of the passing bubble is tricky and for this, one needs to know the local velocity of the bubbles. To this end, one can use a two-tip configuration as shown in figure 1.4(c). The sample signal in figure 1.4(d) shows that the arrival time of the different bubbles will be displaced by a certain amount ∆T . Measuring this average displacement (e.g. by cross-correlation of the two signals) allows the determination of the velocity of the bubbles. Then, a physical length can be calculated for T

and T

. However, it is clear that these lengths not only depend on the diameter of the pierced bubble but also on the distance to the centre of the bubble. Consequently, only a statistical diameter distribution of the bubbles can be obtained under a number of assumptions. These assumptions were stated by e.g. Cartellier [1999] of which the most stringent in our opinion is the need for a unidirectional speed of the bubbles which, in addition, is not correlated with their size. As a result, reliable results cannot be obtained for e.g. a naturally rising bubble column. Another restriction is the minimum measurable bubble diameter as the finite tip size and the increasing resilience to piercing as the bubble gets smaller will lead to a bouncing away of the smallest bubbles. Larger bubbles, on the other hand, will be deformed, thus changing the residence time. This can reach differences of up to 10% (Barrau et al. [1999]), which will result in a bias error in the diameter measurements. Nevertheless, these intrusive point measurements do have one exceptional advantage, the ability to measure inside high void fraction flows (no real upper limit) and provide fairly accurate void fraction profiles there. As most industrial applications (e.g. continuous casting of steel, Planquart et al.

[2004]) have an important void fraction that excludes the use of photographic techniques, these probes have an important working domain which they share with other void fraction measurement tools as capacitance tomography.

1.2.3.2 Laser Diffraction Particle Sizing

Another optical technique is based on the Fraunhofer diffraction of a collimated laser beam on passing a cloud of particles. The basis for this technique was laid by Swithenbank et al. [1977] and was subsequently commer- cialised by Malvern Instruments. The principle of this technique is displayed in figure 1.5. Due to the presence of bubbles in the path of the laser beam, the far field light intensity pattern will consist of the original laser beam plus a set of concentric rings due to Fraunhofer diffraction. As the radius of these rings is correlated with the particle diameter, a diameter distribution (averaged over the line of sight of the beam) can be calculated from the intensity at different radial distances. This is exactly the principle of the device shown in figure 1.5.

Due to the use of a Fourier lens the Fraunhofer pattern can be retrieved at a convenient distance at which the

1.2. OVERVIEW OF BUBBLE SIZING TECHNIQUES ring detector is located. This consists of a series of circular detectors (generally 30), which average the amount of light retrieved for a small range of radial distances. As mentioned, a range of radial distances corresponds to a range of particle sizes and therefore one can relate the relative intensity of each of these rings to the volume concentration of that particular particle size class.

An obvious disadvantage of this technique is the fact that it is a line-of-sight technique. Therefore, obtaining an accurate representation of a spatially varying diameter distribution will require the use of tomographic tech- niques (e.g. Yongyingsakthavorn et al. [2007]), which are inherently less accurate than direct measurements with point or 2D techniques. However, this is countered by its reliability and its ability to measure in relatively dense clouds (laser beam attenuation up to 60% acceptable, Triballier et al. [2003]). Yet, the most important advantage of this technique, in our opinion, is its capability of measuring very small particles ( ≈ 0.1µm!) with a relatively simple set-up. This is smaller than the resolution limit of oil-immersion microscopes (i.e. 0.2µm) which are considerably more difficult to use.

1.2.3.3 Phase Doppler Anemometer

The Phase Doppler Anemometer (PDA), which was introduced by Durst and Zare [1975] amongst others, is based quite literally on the detection of the phase of the Doppler shifted light scattered by a particle. The standard configuration for these measurements is shown in figure 1.6. A pair of laser beams is made to cross in the desired measurement point and the scattered light is gathered by two detectors with a different position.

Assuming for simplicity that the PDA is operated in reflection mode, it is easy to understand that a bubble placed in this crossing point will scatter light from both the laser beams. Yet, the two beams will be externally reflected on different locations on the bubble surface in order to reach e.g. detector 1. This is also sketched in the figure.

Now, these two locations on the bubble surface are called glare points and we will describe them elaborately in chapter 2. Suffice it to say here that they can be regarded as secondary point sources of light. Now, these two point sources are coherent and therefore they create an interference pattern in the neighbourhood of detector 1. As a result, a second detector placed close to detector 1 will sample a different location of the interference pattern and will receive a different light intensity. Thus, there will be a certain phase difference between the two detected signals. The magnitude of this phase difference can be shown to be proportional to the bubble size (or more accurately the local curvature). This can be understood from the fact that the distance between the two secondary point sources is proportional to the radius and the fringe spacing of the generated interference pattern is inversely proportional to this separating distance.

When the bubble is moving, the situation becomes more complicated due to the Doppler effect. As the bubbles

have a velocity component in the direction of the beam propagation, the scattered frequency will be shifted

proportionally. As this shift will be different for the two beams, the two secondary point sources described in

the previous paragraph will have a different emitting frequency as well. As a result, the intensity detected by

each detector will be modulated by the difference of these two Doppler shifts. The resulting signal for both

detectors is shown in figure 1.6. Discussing a single signal first, we note that a periodic signal is obtained with

a frequency that is proportional to the velocity of the particle (and the intersecting angle of the beams). This

principle is used in Laser Doppler Anemometry (LDA or LDV) (e.g. Yeh and Cummins [1964], vom Stein

and Pfeifer [1969], Rudd [1969]...). Also note the burst-like appearance of the signal, which is due to the non-

uniform laser intensity across the measurement volume. Now, the signal from the second detector is exactly the

same as the first signal, except for a small phase difference. As mentioned in the previous paragraph, this phase

shift is originating from the different scattering locations on the bubble surface. It can be shown that this phase

difference is independent of the location of the particle in the measurement volume and hence of the velocity

of the particle. Therefore, it can be used to measure the bubble diameter, which is the working principle of the

PDA. From figure 1.6, it is clear that when this phase difference is larger than 2π, the calculated diameter will

be wrong. In this case, one can use the time-shift technique, as introduced by Albrecht et al. [1993]. In this

technique, the time difference between the two burst peaks is used to size the bubble. The phase Doppler and

the time-shift technique are only two extensions of the basic LDA-system to measure the bubble size. Other

extensions as the Shadow Doppler technique (e.g. Hardalupas et al. [1994]) exist also, which have their own

CHAPTER 1. INTRODUCTION

Figure 1.6: A sample Phase Doppler Anemometer configuration and its output signal.

distinct advantages. For a more elaborate discussion of these extensions, we refer to Albrecht et al. [2003].

The main advantage of these LDA-based techniques is that both the bubble size and its velocity are measured simultaneously with a non-intrusive technique without making restrictive assumptions. Compared with the void fraction probes, the bubbles will not be distorted on passing the measurement volume and one does not have to assume that the size and the velocity are uncorrelated. In addition, no complicated modelling as for the acoustical techniques is needed, which will reduce bias errors. Yet, note that this is again a point measurement technique.

1.2.3.4 Backlighting

Glancing at the measurement techniques from the previous sections, it is apparent that they are all point mea- surement techniques. This implies that measuring a diameter distribution that varies with the location requires many (sequential) measurements. As a result, only time averaged overviews can be obtained, which is crippling when transient phenomena are to be studied. In contrast, imaging techniques as backlighting (as was already shown in figure 1.1(a) and figure 1.2(a)) offer a two dimensional view of the flow and spatially varying phe- nomena can be measured with far less measurements. This technique is quite literally, just as old as mankind or perhaps more accurately as old as photography. An illuminating source is placed behind the bubble and its shadow is simply recorded with a camera. The general set-up and the working principle is shown in figure 1.7 where a diffuse light source is used to obtain a homogeneous lighting. Next to a simple set-up, the image processing is also very intuitive. Bubbles are easily distinguished manually from other light scattering sources and one can also size non-spherical bubbles. Due to its high robustness, its good accuracy and probably also due to its simple basics, backlighting is arguably the most popular technique for sizing bubbles. As a result, it has evolved into more or less a golden standard against which the other techniques should be calibrated.

Nevertheless, it has its own set of disadvantages, which will be discussed in more detail in the course of this

thesis.

1.3. OUTLINE OF THE THESIS

Figure 1.7: Principle and example picture of backlighting

1.3 Outline of the Thesis

A serious competitor for backlighting was developed by Koenig et al. [1986], Ragucci et al. [1990] and Glover et al. [1995]. This technique measures the size and velocity per droplet in a light-sheet and is known under various names as Interferometric Laser Imaging for Droplet Sizing (ILIDS) or Interferometric Particle Imaging (IPI). As can be seen from its name, it was originally intended for droplet sizing. The first adaptation of this technique to bubble sizing was done by Niwa et al. [2000]. However, this configuration has several drawbacks and the original goal of this thesis therefore was to investigate different configurations to improve bubble measurements with ILIDS. In a later stage, this was broadened to investigate/improve also other 2D optical bubble measurement techniques.

The basic theory needed to explain the scattering phenomenon on which these techniques are based, will be given in chapter 2. Although most of this chapter is simply a revision, the location of the glare points was also calculated for non-spherical bubbles for the first time. Chapter 3 then continues on this basis to investigate the use of a close variant of ILIDS that was introduced by Hess [1998] for droplet measurements. This technique will be called Glare Point Velocimetry and Sizing (GPVS) throughout the text. As the configuration of Niwa et al. [2000] is not suited for GPVS measurements, different configurations were introduced. In chapter 4, new possibilities for ILIDS measurements on bubbles were explored. In addition, the different calibration procedures for ILIDS were investigated in detail and compared.

A new image processing algorithm to detect bubbles in backlighting images with a variable size was developed in chapter 5. Chapter 6 then investigates the bright circles that appear inside these circular shadows and how these can be used to size bubbles and to measure the refractive index of the liquid. As backlighting and GPVS have an overlapping working domain, a combination of both techniques was investigated in chapter 7. This technique is called Laser Marked Shadowgraphy (LMS) and combines the best of both worlds. After a short deviation in chapter 8 on the calibration of the in-focus techniques (Backlighting, GPVS and LMS), a comparison between the different introduced optical 2D bubble measuring techniques is given in chapter 9.

This comparison is based on their working domain, precision and maximum void fraction. This is followed by a thorough discussion of the pro’s and con’s of each sizing technique. Chapter 10 then draws the main conclusions.

This is followed by the three appendices. In appendix A, the artefacts introduced by separating the colour channels in a single CCD-array colour camera are studied. This was necessary in some of our experiments.

Appendix B describes the uncertainties connected to ILIDS measurements on droplets. This was put in ap-

pendix to avoid confusion between bubbles/droplets. Finally, in appendix C, the void fraction limitations of the

introduced techniques were mathematically derived.