Imaging of water-sided gas-concentration fields at a wind-driven, wavy air-water interface [Elektronische Ressource] / presented by Alexandra Gabriela Herzog

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Dissertationsubmitted to theCombined Faculties for the Natural Sciences and forMathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural Sciencespresented byDipl. Phys. Alexandra Gabriela Herzogborn inSchorndorfOral Examination 21.10.2010Imaging of Water-sided Gas-Concentration Fields at aWind-Driven, Wavy Air-Water InterfaceReferees: Prof. Dr. Bernd JähneProf. Dr. Ulrich PlattThe aim of this study is to develop improved measurement techniques todetermine depth dependent water-sided gas concentration fields under a wind-driven free surface that is strongly wave-influenced. In comparison to previousstudies the pH-LIF method was improved by using a novel fluorophore, a morepowerful Laser and an optimized optical setup. This configuration allows forthe first time high temporal resolution imaging of concentration fields under astrongly wave-influenced surface in two spatial dimensions. Two measurementtechniques based on Laser-induced fluorescence have been improved and devel-oped, respectively: On the one hand, the theory of a spectral reconstructionapproach was improved, that allows an arbitrary orientation of the illuminatedcross section. Here, depth-dependent concentration fields can be estimated byinverse modeling. On the other hand, a novel measurement technique, staticpattern LIF (SP-LIF), has been developed from side-LIF by applying a dis-cretized illumination.

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Dissertation
submitted to the
Combined Faculties for the Natural Sciences and for
Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
presented by
Dipl. Phys. Alexandra Gabriela Herzog
born in
Schorndorf
Oral Examination 21.10.2010Imaging of Water-sided Gas-Concentration Fields at a
Wind-Driven, Wavy Air-Water Interface
Referees: Prof. Dr. Bernd Jähne
Prof. Dr. Ulrich PlattThe aim of this study is to develop improved measurement techniques to
determine depth dependent water-sided gas concentration fields under a wind-
driven free surface that is strongly wave-influenced. In comparison to previous
studies the pH-LIF method was improved by using a novel fluorophore, a more
powerful Laser and an optimized optical setup. This configuration allows for
the first time high temporal resolution imaging of concentration fields under a
strongly wave-influenced surface in two spatial dimensions. Two measurement
techniques based on Laser-induced fluorescence have been improved and devel-
oped, respectively: On the one hand, the theory of a spectral reconstruction
approach was improved, that allows an arbitrary orientation of the illuminated
cross section. Here, depth-dependent concentration fields can be estimated by
inverse modeling. On the other hand, a novel measurement technique, static
pattern LIF (SP-LIF), has been developed from side-LIF by applying a dis-
cretized illumination. For the first time, a reliable estimate of the water surface
even under a nearly vanishing near surface concentration gradient, has become
possible. Now, the found and classified coherent structures in the near surface
turbulence under wind shear can be compared to the results of direct numerical
simulations to reveal the dominating transport mechanisms under varying con-
ditions.
Ziel der Arbeit ist die Entwicklung einer verbesserten Messtechnik, welche es
ermöglicht unter wellenverzerrter Oberfläche das wasserseitige Gaskonzentra-
tionsfeld zu bestimmen. Im Vergleich zu vorherigen Studien wurde die pH-LIF
Messtechnik durch einen neuen Fluoreszenzfarbstoff, einen leistungsstärkeren
Laser und einen optimierten optischen Aufbau verbessert, was nun erstmals
zeitlich hochaufgelöste Messungen unter stark wellenbeeinflußter Grenzschicht
in zwei räumlichen Dimensionen erlaubt. Für die Durchführung dieser Exper-
imente wurde ein völlig neuer, chemisch inerter Wind-Wellen Kanal konzip-
iert, realisiert und weitgehend charakterisiert. Zwei Messtechniken basierend
auf Laser-induzierter Fluoreszenz wurden weiter beziehungsweise neu entwick-
elt: Zum einen wurde die Theorie eines spektralen Ansatzes weiterentwickelt
und in numerischen Simulationen getestet, welcher eine beliebige Orientierung
des beleuchteten Querschnitts erlaubt. Die tiefenabhängigen Konzentrations-
felder werden hierbei mit Hilfe inverser Modellierung bestimmt. Zum anderen
wurde aus der Seiten-LIF Methode durch eine diskretisierte Beleuchtung die
neue Messmethode Static Pattern LIF entwickelt. Hierdurch wird nun erst-
malseinezuverlässigeDetektionderWasseroberflächeauchinAbwesenheiteines
starkenKonzentrationsgradienteninderGrenzschichtermöglicht. Diemitdieser
Methode gefundenen und klassifizierten kohärenten Turbulenzstrukturen unter
Windscherung können nun mit Ergebnissen der Direkten Numerischen Simula-
tion verglichen werden, um Rückschlüsse auf dominante Transportmechanismen
zu ziehen.Nihil tam difficile est, quin quaerendo investigari possit
TerentiusContents
I Introduction 17
1 Introduction 19
II Theoretical Background 27
2 Basic Theory of Transport Processes across the Air-Water
Boundary Layer 29
2.1 The Fundamental Transport Mechanisms: Diffusion and Turbu-
lence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.1 Diffusive Transport . . . . . . . . . . . . . . . . . . . . . . 30
2.1.2 Turbulent Transport . . . . . . . . . . . . . . . . . . . . . 32
2.2 Differential Equations of Transport . . . . . . . . . . . . . . . . . 34
2.2.1 Conservation of Momentum: The Navier-Stokes Equation 35
2.2.2ation of Mass: Fick’s Transport Equation of Mass 36
2.2.3 Transformation to Flux Equations . . . . . . . . . . . . . 37
2.2.4 Limits of Validity . . . . . . . . . . . . . . . . . . . . . . . 37
2.3 Boundary Conditions on Gas Transfer . . . . . . . . . . . . . . . 38
2.3.1 Boundary Conditions due to Flow Regimes: Boundary
Layer and Bulk . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.2 Boundary Condition due to Properties of Trace Gas and
Solvent Medium Water . . . . . . . . . . . . . . . . . . . . 40
2.3.3 Summary of Boundary Conditions . . . . . . . . . . . . . 43
2.4 Classification Parameters of Transport across a (free) Interface . 44
2.4.1 Definition of the Boundary Layer Thickness in Transfer
Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4.2 Transfer Velocity . . . . . . . . . . . . . . . . . . . . . . . 46
2.4.3 Transfer Time . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.5 Modeling and Simulating Gas Transfer . . . . . . . . . . . . . . . 47
2.5.1 Shear flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5.2 Ways of Simplifying the Transport Equations: Linearized
1D-Transport models . . . . . . . . . . . . . . . . . . . . . 49
2.5.3 Full Transport Equations: Direct Numerical Simulation
-DNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 56
7III Measurement Technique 57
3 Method for Visualizing Dissolved Gas in the Water-Phase:
Laser-Induced Fluorescence 59
3.1 Relation to Previous Works . . . . . . . . . . . . . . . . . . . . . 60
3.2 ContributionandImprovementsregardingFluorophoreandTracer
Gas in this Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Introduction to Fluorescence . . . . . . . . . . . . . . . . . . . . . 61
3.4 The pH-Indicator Method: Fluorophore as Tracer for Gas Con-
centration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1 Indicator Reaction as Basis of Detection of Acid/Alkaline
Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.2 Relation between Intensity of Fluorescence Signal to Con-
+
centration of H O . . . . . . . . . . . . . . . . . . . . . . 653
3.4.3 The Core of the pH-Method: Conservation of Mass Flux . 68
3.4.4 Theoretical Sensitivity of Fluorescence Detection to Con-
centration Changes . . . . . . . . . . . . . . . . . . . . . 73
3.5 The pH-Method in Comparison to the Oxygen Quenching Tech-
nique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.6 Properties of Tracer Hydrogen Chloride . . . . . . . . . . . . . . 76
3.6.1 Dissociation Reaction of HCl in Water . . . . . . . . . . . 76
3.6.2 Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.6.3 Partial Pressure over Highly Saturated HCl Solution . . . 78
3.6.4 Diffusion Coefficient . . . . . . . . . . . . . . . . . . . . . 78
3.6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.7 Fluorescent Dye for LIF-Measurements: HPTS . . . . . . . . . . 80
3.7.1 Desirable Properties of a Fluorophore used for LIF . . . . 80
3.7.2 The fluorophore used for measurements: HPTS . . . . . . 81
3.7.3 Absorption Characteristics of HPTS . . . . . . . . . . . . 84
3.7.4 Fluorescence Characteristics of HPTS . . . . . . . . . . . 87
3.7.5 Comparison of HPTS to Commonly Used Fluorescein . . 91
3.7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4 Realizations of LIF-Setups for Measuring Depth-Dependent
Gas Concentration under a Wave-Influenced Water Surface 95
4.1 Contribution in this Study . . . . . . . . . . . . . . . . . . . . . . 96
4.2 The Classic Approach: Tilted Side-Camera Setup . . . . . . . . . 97
5 The Spectral Reconstruction Approach (SPERA) 99
5.1 Intention of the Method . . . . . . . . . . . . . . . . . . . . . . . 100
5.2 Relation to Previous Works . . . . . . . . . . . . . . . . . . . . . 100
5.3 Contribution and Improvements in this Study . . . . . . . . . . . 101
5.4 Basic Principle of the SPERA Technique . . . . . . . . . . . . . . 102
5.5 Physical Description of Regarded Absorption/ Emission Processes 103
5.6 Discretization of the Emission-Absorption Equation . . . . . . . . 107
5.6.1 Estimation of the Remaining Rest or Error Term . . . . . 1115.6.2 Estimation of the Needed Concentration of the Absorber
Dye for a Given Spatial Resolution z . . . . . . . . . . . 113
5.7 Experimental Aspects . . . . . . . . . . . . . . . . . . . . . . . . 114
5.7.1 Fluorophore . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.7.2 Absorption Dye . . . . . . . . . . . . . . . . . . . . . . . . 114
5.7.3 Application of the Theoretical Model on Experiments . . 118
5.7.4 TestMeasurements: CombinationofFluorophoreandAb-
sorption Dye . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.8 Parameter Estimation Techniques . . . . . . . . . . . . . . . . . . 121
5.8.1 Statistics of LIF-Signals . . . . . . . . . . . . . . . . . . . 121
5.8.2 Numerical Simulation . . . . . . . . . . . . . . . . . . . . 122
5.8.3 Robust Estimator Used for Simulations . . . . . . . . . . 123
5.9 Results of the Numerical Simulations in Spectral Reconstruction
Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6 Novel Extension for Waves: Static Pattern-LIF (SP-LIF) 129
6.1 Review of Other Approaches for Measuring Concentration Pro-
files under Wave-Influence Surface Conditions . . . . . . . . . . . 129
6.2 Main Idea of SP-LIF: Discretization of Illumination . . . . . . . . 131
6.3 Separating Pattern and Concentration Signal: Basic Ideas of Im-
age Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4 Surface Topology from Refraction of the Static Laser-Pattern . . 136
6.4.1 Surface Orientation from Refraction Angle . . . . . . . . . 136
6.4.2 Determination of Local Angle of Pattern Structure in0
Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.4.3 Inverse: Angle of Refracted Beam Calculated from Sur-
face Slope m . . . . . . . . . . . . . . . . . . . . . . . . . 139s
6.5 Experimental Realization . . . . . . . . . . . . . . . . . . . . . . 139
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
IV Experimental Setup 143
7 Ocean Simulation: The Wind-Wave Tunnel 145
7.1 Main Design Criteria . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.2 Design Types of Wind-Wave Tunnels or Reasons for a Linear
Wind- Wave-Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.3 Short Technical Description . . . . . . . . . . . . . . . . . . . . . 149
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8 The Optical Setup 155
8.1 Illumination Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.1.1 Light Source . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.1.2 Sheet Optics . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.2 Detector Setup: The Imaging System . . . . . . . . . . . . . . . . 1638.2.1 Scheimpflug Setup: Significant Improvement of Optical
Resolution by Scheimpflug-Arrangement . . . . . . . . . . 164
8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
V Processing of Experimental Data 169
9 Image Processing 171
9.1 Relation to Previous Studies . . . . . . . . . . . . . . . . . . . . . 171
9.2 Improvement and Contribution by SP-LIF for Surface Detection . 172
9.3 Procedures for Analyzing SP-LIF Data . . . . . . . . . . . . . . . 173
9.3.1 Preprocessing: Removal of Dark Current and Scheimpflug
Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
9.3.2 Simple 13-Beam Illumination: Flat and Wavy Interface . . 173
9.3.3 Fine Pattern Illumination . . . . . . . . . . . . . . . . . . 175
9.4 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
9.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
9.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
10 Statistical Analysis of the Gained Data Sets 183
10.1 Statistical Analysis for Controlled-Flux Techniques in Compari-
son to Constant Concentration Techniques . . . . . . . . . . . . . 183
10.1.1 Estimation of Water-sided Statistical Quantities for Neu-
mann and Dirichlet-type of Boundary Condition . . . . . 184
11 Estimation of Systematic Error Sources 187
11.1 Errors Affecting the Concentration Signal . . . . . . . . . . . . . 187
11.1.1 Fluorophore . . . . . . . . . . . . . . . . . . . . . . . . . . 187
11.1.2 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . 191
11.1.3 Effects of Temperature Variation . . . . . . . . . . . . . . 194
11.1.4 Errors due to Illumination Refraction Perpendicular to
Observation Plane . . . . . . . . . . . . . . . . . . . . . . 196
11.2 Disturbances of Flow Regime in the Wind-Wave Tunnel . . . . . 196
11.2.1 Temperature Flows . . . . . . . . . . . . . . . . . . . . . . 196
11.2.2 Secondary Currents . . . . . . . . . . . . . . . . . . . . . 197
11.2.3 Heterogeneous Distribution of HCl Concentration in Air . 197
11.3 Error in Signal Processing . . . . . . . . . . . . . . . . . . . . . . 198
11.3.1 Wrong Estimation of Buffer Point . . . . . . . . . . . . . . 198
11.3.2 Violation of Lambert-Beer Decay by Strong Concentra-
tion Variations . . . . . . . . . . . . . . . . . . . . . . . . 199
11.3.3 Errors in Diffusivity of Gaseous Tracer . . . . . . . . . . . 199
11.4 Discussion of Special Error Sources of SP-LIF . . . . . . . . . . . 200
11.5 of Special Error of SPERA . . . . . . . . . . . 200
11.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201