The significance of coherent flow structures for the turbulent mixing ...

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Contents 4.7 Monochromatic aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.8 Feasibility study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5 Investigation of the xy-plane 69 5.1 The statistical description of turbulence . . . . . . . . . . . . . . . . . . . . 69 5.2 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.3 Statistical properties of the flow . . . . . . . . . . . . . . . . . . . . . . . . 75 5.3.1 Single point statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.3.2 Spatial auto- and cross-correlation functions . . . . . . . . . . . . . . 79 5.4 Properties of coherent velocity structures . . . . . . . . . . . . . . . . . . . . 90 5.4.1 Shear-layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.4.2 Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.4.3 Sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6 Investigation of the xz-plane 97 6.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.2 Statistical properties of the buffer layer . . . . . . . . . . . . . . . . . . . . . 101 6.2.1 Single point statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2.2 Spatial auto-correlation functions . . . . . . . . . . . . . . . . . . . 105 6.2.3 Spatial cross-correlation functions . . . . . . . . . . . . . . . . . . . 109 6.3 Spatio-temporal buffer layer statistics . . . . . . . . . . . . . . . . . . . . . 114 6.4 Properties of coherent velocity structures . . . . . . . . . . . . . . . . . . . . 121 6.4.1 Low-speed streaks . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.4.2 Sweeps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6.4.3 Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 ¢¡¤£¦¥ ¢¡¤£§¥ ¢¡¨£©¥ ¢¡ 7 Investigation of the yz-plane 135 7.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7.2 Statistical properties of the log-law region . . . . . . . . . . . . . . . . . . . 138 7.2.1 Spatial correlations with . . . . . . . . . . . . . . . . . . . . 141 7.2.2 Spatial cross-correlations with . . . . . . . . . . . . . . . . 143 7.3 Spatio-temporal correlations with . . . . . . . . . . . . . . . . . . . 146 7.4 Spatio-temporal correlations with . . . . . . . . . . . . . . . . . . . 152 7.5 Properties of coherent velocity structures . . . . . . . . . . . . . . . . . . . . 155 7.5.1 Loop-shaped structures . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.5.2 Sweeps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.5.3 Stream-wise vortices . . . . . . . . . . . . . . . . . . . . . . . . . . 160 8 Summary 163 Bibliography 169 Commonly used symbols 177 Index 180 4
1 Introduction One of the fascinating phenomena of natural science is the turbulent state of the macroscopic flow motion in fluid-mechanics. Beside the omnipresent variety and beauty of the turbulent motion, the inherent fascination and attraction is strongly connected with the enormous difficulties associated with a mathematical and physical understanding. The principal difficulty, with respect to an inviscid fluid or a classical gas of point particles in equilibrium, results from the strong non-linearity in the conservation equation and the dissipative character e.g. the flux of energy from the large scales or eddies into progressively smaller and smaller ones. As a general mathematical solution of non-linear, non-equilibrium systems is out of reach from the present point of view, the properties of idealised flows with simple geometries are examined experimentally and numerically. Of primary interest is the two-dimensional turbulent boundary layer flow of an incompressible fluid along a flat plate with zero pressure gradient, because this flow reveals simultaneously two characteristic phenomena of turbulence, namely the effects of near-wall turbulence and the effects of intermittency, e.g the interaction of the turbulent boundary layer with the laminar outer flow according to figure 1.1. This particular flow evolves from a laminar boundary layer flow when the Reynolds number £¡ is sufficiently high. In this case flow disturbances with a particular wavelength grow, become unstable and share the energy from the mean motion over the degrees of freedom by non-linear interaction. rot U = 0 1.2 δ U / U δ y 0.4 δ rot U = 0 δ x 1 FIGURE 1.1: Instantaneous structure of a turbulent boundary layer and mean velocity profile after [37] Beginning with the early channel and pipe flow measurements, published by Laufer [68, 69], and the zero pressure gradient boundary layer benchmark investigations along a flat plate by Klebanoff [55], turbulent boundary layers have been examined extensively because of their technological importance, their significance for the development of fundamental turbulence models and for the validation of numerical flow simulations [89, 96]. The bulk of the quantitative investigations has been performed with intrusive single-point measurement techniques [21] such as pressure probes and hot-wire anemometer, but also non-intrusive flow visualisations techniques have been frequently applied to examine qualitatively the global features of 5
Page 1 and 2: The significance of coherent flow s
Page 3: Contents 1 Introduction 5 2 Particl
Page 7 and 8: As order can be always observed whe
Page 9 and 10: were not considered in detail in th
Page 11 and 12: varying signal can be transformed i
Page 13 and 14: 2 Particle Image Velocimetry The tr
Page 15 and 16: 2.1 Principles It is of fundamental
Page 17 and 18: ’ ’“ ” ”• Ž Ž Ž Ž
Page 19 and 20: ¹ and 2.2 Generation of appropriat
Page 21 and 22: 2.2 Generation of appropriate trace
Page 23 and 24: 2.3 Registration of the particle im
Page 25 and 26: 2.3 Registration of the particle im
Page 27 and 28: ë ë 2.3 Registration of the parti
Page 29 and 30: ýÿþ¡ û û ¢ ¢ £ôþ¡ î¥
Page 31 and 32: or = ö D Q ù ù ?xö ù Y[Z]\ & &
Page 33 and 34: ñ † † † † † † † †
Page 35 and 36: ˜ E ˜ T ˜ T 2.4 Particle image
Page 37 and 38: 3 Stereo-scopic Particle Image Velo
Page 39 and 40: › B › B › J ù ž & 3.1 Princ
Page 41 and 42: Æ e¼c’„ïG ù # #dc’e › B
Page 43 and 44: Ð È Ñ ù Ñ ù Ð È Ð È Ñ ù
Page 45 and 46: 3.2 Evaluation of stereo-scopic ima
Page 47 and 48: ú ¦ 3.3 Calibration validation by
Page 49 and 50: 4 Multiplane Stereo Particle Image
Page 51 and 52: £ è ¤ ó 4.2 Four-pulse-laser S
Page 53 and 54: £ ¤ £ £ 4.2 Four-pulse-laser Sy
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( ì ( æ ( ì è ð ( ( ( ( ( ( ì
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æ ( | | | | | | | ì æ õ æ õ
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4.5 Simplified recording system 4.5
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4.7 Monochromatic aberrations refle
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º¹ n 4.7 Monochromatic aberration
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4.8 Feasibility study experiments i
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4.8 Feasibility study 10 20 30 40 5
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é¥î ëÝïñð€òôó 5 Invest
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I L § § § : ? ; õ : I I I W
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5.2 Experimental set-up α4 α3 α2
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{ : { L Ø { 9 D { 9 D T W ð 9
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: T ž ž ò 5.3 Statistical pro
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¾ ¾ 5.3.2 Spatial auto- and cross
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½ Ë 5.3 Statistical properties of
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½ Ë 5.3 Statistical properties of
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ô ó ñ ½ ñ ô ó 5.3 Statistica
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æ å ä ã ã ã ½ Ë ä æ å ½
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æ æ å ä À Â ½ 5.3 Statistica
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½ 5.4 Properties of coherent veloc
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» % %QÄ ¾ Ó turbulent velocit
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* Ó , Ó * Á , Â 5.4 Properties
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! 6 Investigation of the xz-plane O
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6.1 Experimental set-up the (virtua
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ß ß 6.2 Statistical properties
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g ˆ g ˆ 6.2 Statistical propertie
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— ¯ 6.2 Statistical properties o
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å å ç æ æ ã ã ã å å è æ
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6.2.3 Spatial cross-correlation fun
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6.2 Statistical properties of the b
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6.2 Statistical properties of the b
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performed at and the second at
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6.3 Spatio-temporal buffer layer st
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M M æ æ æ æ æ æ ã ã ã H M
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V W V 6.4 Properties of coherent ve
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6.4 Properties of coherent velocity
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Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
d d 6.4 Properties of coherent velo
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'§ 'Î ª ¿ ¦ '§ ')( 7 Investi
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% { s s s s 7.1 Experimental set-up
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‘ — s 7.2 Statistical propertie
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7.2 Statistical properties of the l
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¿ 7.2.2 Spatial cross-correlations
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¿ 7.2 Statistical properties of th
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ô ô 7.3 Spatio-temporal correlati
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7.3 Spatio-temporal correlations wi
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¨ ¨ ¨ 7.3 Spati
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£ 7.4 Spatio-temporal correlations
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Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
¿ 7.5 Properties of coherent veloc
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¿ 8 Summary The first part of this
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aperture, it is shown how to elimin
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¡ ¿ tures keep their spatial orga
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Bibliography [1] ACARLAR MS, SMITH
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[30] HINSCH K (1995) Three-dimensio
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[60] KNEUBÜHL FK, SIGRIST MW (1995
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[93] SMITH CR, METZLER SP (1983) Th
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Z k l l l l l { l R q ‡ ˆ ’
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Ø á a Õ Œ v momentum thickness,
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Index Kolmogorov micro-scale . . .
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Acknowledgement First of all I woul
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Lebenslauf von Christian Joachim K
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