List of Figures ................................................ XI
List of Tables ................................................ XII
List of Symbols, Acronyms and Abbreviations .................. XIII
1 Introduction ................................................. 1
1.1 Background .............................................. 1
1.2 Measurement Techniques .................................. 2
1.3 Challenges in Measurements of Turbulent Flows ........... 5
1.3.1 Dynamic range .................................... 5
1.3.2 Multiple components and dimensions ............... 6
1.3.3 Simultaneous measurement ......................... 6
1.3.4 Spatial resolution ............................... 7
1.3.5 Miniaturization .................................. 8
1.3.6 Temporal resolution .............................. 8
1.3.7 Measurement uncertainty .......................... 9
1.3.8 Summary on challenges and demands ............... 10
1.4 Scope .................................................. 10
1.5 Structure of Thesis .................................... 11
2 Sensor ...................................................... 12
2.1 Introduction ........................................... 12
2.2 Laser Doppler Velocity Profile Sensor .................. 12
2.2.1 Laser Doppler anemometry ........................ 13
2.2.2 Laser Doppler velocity profile sensor ........... 16
2.3 Calibration ............................................ 19
2.4 Resolution and Measurement Uncertainty ................. 20
2.5 Sensor Systems ......................................... 23
2.5.1 Homodyne WDM sensor ............................. 23
2.5.2 Heterodyne WDM sensor ........................... 24
2.5.3 FDM sensor ...................................... 27
2.6 Signal Processing ...................................... 28
2.6.1 Signal detection ................................ 29
2.6.2 Evaluation of positions and velocities .......... 31
2.6.3 Validation of signals ........................... 32
2.6.4 Validity of signal processing ................... 35
2.7 Statistical Analysis ................................... 35
2.7.1 Turbulence statistics ........................... 36
2.7.2 Velocity bias and correction schemes ............ 39
2.7.3 Slot techniques ................................. 41
2.7.4 Overlap of traverse and slot .................... 44
2.7.5 Statistical influence of slot width ............. 44
2.7.6 Outlier reduction ............................... 47
2.8 Summary ................................................ 48
3 Calibration ................................................. 50
3.1 Introduction ........................................... 50
3.2 Motivation ............................................. 51
3.3 Conventional Calibration Methods ....................... 52
3.3.1 State of the art ................................ 52
3.3.2 Calibration methods at TU Dresden: methods ...... 53
3.3.3 Uncertainty analysis of the methods at TU
Dresden ......................................... 56
3.4 Multiple Pinhole Method ................................ 61
3.4.1 Principle ....................................... 61
3.4.2 Procedure ....................................... 62
3.4.3 Uncertainty analysis ............................ 64
3.4.4 Origin of uncertainty ........................... 76
3.4.5 Extension: wire instead of pinholes ............. 77
3.5 Discussions ............................................ 78
3.6 Summary ................................................ 80
4 Laminar Flows ............................................... 82
4.1 Introduction ........................................... 82
4.2 Purpose ................................................ 82
4.3 Theory ................................................. 83
4.3.1 Uniform laminar flow ............................ 83
4.3.2 Laminar boundary layer .......................... 83
4.4 Sensors ................................................ 85
4.5 Flow Measurements ...................................... 85
4.5.1 Uniform laminar flow ............................ 85
4.5.2 Laminar boundary layer .......................... 90
4.6 Results ................................................ 91
4.6.1 Uniform laminar flow ............................ 91
4.6.2 Laminar boundary layers ......................... 92
4.7 Discussions ............................................ 93
4.8 Summary ................................................ 98
5 Turbulent Channel Flow ..................................... 100
5.1 Introduction .......................................... 100
5.2 Purpose ............................................... 100
5.3 Theory ................................................ 101
5.3.1 Two-dimensional flow ........................... 101
5.3.2 Fully developed flow ........................... 101
5.3.3 Governing equations ............................ 102
5.4 Literatures: State-of-the-Art ......................... 105
5.4.1 Experiments .................................... 105
5.4.2 Numerical simulations .......................... 106
5.5 Experimental Investigation of a Channel Flow .......... 107
5.5.1 Flow facility and instruments .................. 107
5.5.2 Velocity profile sensors ....................... 109
5.5.3 Calibration .................................... 110
5.5.4 Flow measurements .............................. 112
5.5.5 Measurement results ............................ 114
5.6 Discussions ........................................... 117
5.7 Summary ............................................... 121
6 Local Flow Acceleration .................................... 123
6.1 Introduction: Flow Acceleration ....................... 123
6.2 Purpose ............................................... 124
6.3 Evaluation of Flow Acceleration ....................... 124
6.4 Validation Experiments ................................ 126
6.5 Flow Measurement ...................................... 126
6.6 Results and Discussions ............................... 128
6.7 Summary ............................................... 130
7 Two-Point Correlation ...................................... 131
7.1 Introduction .......................................... 131
7.2 Purpose ............................................... 132
7.3 Problems and Solution ................................. 132
7.3.1 State-of-the-Art ............................... 132
7.3.2 Issues on two-point velocity correlation
measurement .................................... 134
7.3.3 Solution ....................................... 135
7.4 Two-point correlation ................................. 136
7.4.1 Theory ......................................... 136
7.4.2 Evaluation ..................................... 137
7.5 Measurement, of two-point correlation ................. 137
7.6 Results and Discussion ................................ 139
7.7 Summary ............................................... 141
8 Conclusions ................................................ 142
8.1 Further Challenges .................................... 142
8.2 Summary ............................................... 146
References .................................................... 151
A Tracer Particle ............................................ 164
A.l Particle Motion ....................................... 165
A.2 Forces Acting on Particle ............................. 166
A.3 Light Scattering ...................................... 167
A.4 Generation and Seeding ................................ 169
A.5 Summary ............................................... 170
В Turbulence Statistics and Uncertainty Estimate ............. 171
B.l Introduction .......................................... 171
B.2 Statistical Uncertainty ............................... 172
B.3 Required Number of Data Samples ....................... 173
B.4 Summary ............................................... 175
С Uncertainty Analysis of Conventional LDA System ............ 176
C.l Background ............................................ 176
C.2 Specifications of the LDA System ...................... 177
C.3 Procedure of Error Estimate ........................... 178
C.3.1 Instability of carrier frequency ............... 179
C.3.2 Estimate uncertainty of Doppler frequencies
(CRLB) ......................................... 179
C.3.3 Non-uniformity of fringe spacings .............. 180
C.4 Total Uncertainty ..................................... 185
C.5 Discussions ........................................... 185
C.6 Summary ............................................... 187
D List of Publications ....................................... 188
Acknowledgements .............................................. 193
Biography ..................................................... 196
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