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

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£ £ £ £ ¿ 7 Investigation of the yz-plane in stream-wise direction according to section 5.3.2 it is evident that the maximum ªSÔÔ of decreases quite rapidly with increasing temporal delay and vanishes already ×rìË»\¬ for at c while the other correlations still show a significant correlation which is above ª«§N¬ö®c¯ 0.6 ªS·· for and around 0.4 in case ªSÙ&Ù of . Another interesting effect becomes visible when the correlation functions in the near-wall region are considered. It can be seen that ªSÔÔ the ªSÙ&Ù and correlations decrease quite rapidly with respect ªS·· to and relative to the decrease of the correlation function at larger wall locations of the fixed point. This implies that structural changes within the near-wall region are quite large. When the width of the correlation and the curvature around the maximum are considered, the total size decreases only very little with increasing temporal separation but the curvature of the maximum becomes weaker. This indicates the dissipation of the small-scales due to action of the viscosity. The large-scales, on the other hand, are only weakly affected within the same time. This implies that the structures which become visible for large time separations can be considered as a low-pass representation of the dominant velocity structures. This point will be discussed in the next section. 1 1 0.8 0.8 R vv (∆t + =0) 0.6 0.4 0.2 R (uv)(uv) (∆t ÷ +=0) 0.6 0.4 0.2 0 1 £ 0 100 £ £ 200 300 y + +∆y + ¤ 400 £ 500 £ 0 1 £ 0 100 £ £ 200 300 y + +∆y + ¤ 400 £ 500 £ 0.8 0.8 R vv (∆t + =1) 0.6 0.4 0.2 R (uv)(uv) (∆t ÷ +=1) 0.6 0.4 0.2 0 1 £ 0 100 £ 200 £ y + +∆y + 300 £ 400 £ 500 £ 0 1 £ 0 100 £ 200 £ y + +∆y + 300 £ 400 £ 500 £ 0.8 0.8 R vv (∆t + =5) 0.6 0.4 0.2 R (uv)(uv) (∆t ÷ +=5) 0.6 0.4 0.2 0 £ 0 100 £ £ 200 300 y + +∆y + ¤ 400 £ 500 £ 0 £ 0 100 £ £ 200 300 y + +∆y + ¤ 400 £ 500 £ FIGURE ˜ ÔÔcÄ Éø » Í 7.11: (left) ˜Sù ·Ô ú ù ·Ô:ú Ä Éø » Í and (right) correlation functions measured ˜$ûš at and © » š Ñ ž Æ Î§ž ÆËÏ ž ÆÐ žž ÆËÑ žž Æ Îžž ÆÒ ž±ž (see location of the maximum). œ§§žž 148
7.3 Spatio-temporal correlations with ¢¡¤£¦¥ To estimate the average decay of the flow structures being responsible for the production of §©¨¨ turbulence, the correlation was calculated, see right column of figure 7.11 and 7.13. The rapid § ¨¨ decay of for increasing is mainly caused by the small correlation 1 1 R uu (∆t + =0) 0.8 0.6 0.4 0.2 R ww (∆t + =0) 0.8 0.6 0.4 0.2 0 0 1 0 200 400 600 y + +∆y + 800 1000 −0.2 1 0 200 400 600 y + +∆y + 800 1000 R uu (∆t + =2.3) 0.8 0.6 0.4 0.2 R ww (∆t + =2.3) 0.8 0.6 0.4 0.2 0 0 1 0 200 400 600 y + +∆y + 800 1000 −0.2 1 0 200 400 600 y + +∆y + 800 1000 R uu (∆t + =4.6) 0.8 0.6 0.4 0.2 R ww (∆t + =4.6) 0.8 0.6 0.4 0.2 0 0 1 0 200 400 600 y + +∆y + 800 1000 −0.2 1 0 200 400 600 y + +∆y + 800 1000 R uu (∆t + =23) 0.8 0.6 0.4 0.2 R ww (∆t + =23) 0.8 0.6 0.4 0.2 0 0 0 200 400 600 y + +∆y + 800 1000 −0.2 0 200 400 600 y + +∆y + 800 1000 FIGURE ! #"%$ 7.12: (left) )(( #"%$ and (right) correlation functions measured +*,.-0/1324242 at 5 -613287/924287:324287;3242877?4242@7AB2=287C32=287D3242@7/242=2 and (see location of the maximum). '& '& 149
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The significance of coherent flow s
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Contents 1 Introduction 5 2 Particl
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1 Introduction One of the fascinati
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As order can be always observed whe
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were not considered in detail in th
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varying signal can be transformed i
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2 Particle Image Velocimetry The tr
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2.1 Principles It is of fundamental
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’ ’“ ” ”• Ž Ž Ž Ž
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¹ and 2.2 Generation of appropriat
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2.2 Generation of appropriate trace
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2.3 Registration of the particle im
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2.3 Registration of the particle im
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ë ë 2.3 Registration of the parti
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ýÿþ¡ û û ¢ ¢ £ôþ¡ î¥
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or = ö D Q ù ù ?xö ù Y[Z]\ & &
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ñ † † † † † † † †
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˜ E ˜ T ˜ T 2.4 Particle image
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3 Stereo-scopic Particle Image Velo
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› B › B › J ù ž & 3.1 Princ
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Æ e¼c’„ïG ù # #dc’e › B
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Ð È Ñ ù Ñ ù Ð È Ð È Ñ ù
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3.2 Evaluation of stereo-scopic ima
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ú ¦ 3.3 Calibration validation by
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4 Multiplane Stereo Particle Image
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£ è ¤ ó 4.2 Four-pulse-laser S
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£ ¤ £ £ 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
Page 97 and 98: ! 6 Investigation of the xz-plane O
Page 99 and 100: 6.1 Experimental set-up the (virtua
Page 101 and 102: ß ß 6.2 Statistical properties
Page 103 and 104: g ˆ g ˆ 6.2 Statistical propertie
Page 105 and 106: — ¯ 6.2 Statistical properties o
Page 107 and 108: å å ç æ æ ã ã ã å å è æ
Page 109 and 110: 6.2.3 Spatial cross-correlation fun
Page 111 and 112: 6.2 Statistical properties of the b
Page 113 and 114: 6.2 Statistical properties of the b
Page 115 and 116: performed at and the second at
Page 117 and 118: 6.3 Spatio-temporal buffer layer st
Page 119 and 120: M M æ æ æ æ æ æ ã ã ã H M
Page 121 and 122: V W V 6.4 Properties of coherent ve
Page 123 and 124: 6.4 Properties of coherent velocity
Page 133 and 134: d d 6.4 Properties of coherent velo
Page 135 and 136: '§ 'Î ª ¿ ¦ '§ ')( 7 Investi
Page 137 and 138: % { s s s s 7.1 Experimental set-up
Page 139 and 140: ‘ — s 7.2 Statistical propertie
Page 141 and 142: 7.2 Statistical properties of the l
Page 143 and 144: ¿ 7.2.2 Spatial cross-correlations
Page 145 and 146: ¿ 7.2 Statistical properties of th
Page 147: ô ô 7.3 Spatio-temporal correlati
Page 151 and 152: ¨ ¨ ¨ 7.3 Spati
Page 153 and 154: £ 7.4 Spatio-temporal correlations
Page 161 and 162: ¿ 7.5 Properties of coherent veloc
Page 163 and 164: ¿ 8 Summary The first part of this
Page 165 and 166: aperture, it is shown how to elimin
Page 167 and 168: ¡ ¿ tures keep their spatial orga
Page 169 and 170: Bibliography [1] ACARLAR MS, SMITH
Page 171 and 172: [30] HINSCH K (1995) Three-dimensio
Page 173 and 174: [60] KNEUBÜHL FK, SIGRIST MW (1995
Page 175 and 176: [93] SMITH CR, METZLER SP (1983) Th
Page 177 and 178: Z k l l l l l { l R q ‡ ˆ ’
Page 179 and 180: Ø á a Õ Œ v momentum thickness,
Page 181 and 182: Index Kolmogorov micro-scale . . .
Page 183 and 184: Acknowledgement First of all I woul
Page 185: Lebenslauf von Christian Joachim K
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