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

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¥ ¥ ¥ § + ¥ ¥ ¥ 7 Investigation of the yz-plane length ªSÔÔ of . Another important fact is the shift of ªS··&¸ü×r¹&» ½ the ªSÙ¥ÙÇ¸º×p¹&» ½ and maximum with ×_ìË» increasing . This is shown more clearly in figure 7.14 for various wall distances of the fixed point. The symbols indicate the position of the maximum and the legend reveals the corresponding position in wall-units. The graphs labelled by the solid symbols indicate a correlation where a line at a ¹ particular -location of the first image measured at ì time is correlated with the second image acquired at ì‹¼ a line extracted from the second image at ìÇ¼Ê×_ì is correlated with the first image measured at ì . The asymmetry of the correlation shift for ¤×_ì indicates again that the flow structures, represented by this particular correlation function, reveal two dominant inclination angles relative to the wall, and it can be seen that the inclination of structures at closer wall distances relative to the location of the fixed point reveal the smaller inclination angle. The analysis of the spatio-temporal correlation functions of the velocity fluctuations and the Reynolds stresses indicate that the statistical properties of the log-law region is quite complex with respect to the ×rì . The opaque symbols indicate a correlation where R vv (∆t + =0) 1 0.8 0.6 0.4 0.2 =0) R (uv)(uv) (∆t 1 0.8 0.6 0.4 0.2 0 1 ¥ 0 200 ¥ ¥ 400 600 y + +∆y + ¦ 800 ¥ 1000 ¥ 0 1 ¥ 0 200 ¥ ¥ 400 600 y + +∆y + ¦ 800 ¥ 1000 ¥ 0.8 0.8 R vv (∆t + =2.3) 0.6 0.4 0.2 R (uv)(uv) (∆t + =2.3) 0.6 0.4 0.2 0 1 ¥ 0 200 ¥ ¥ 400 600 y + +∆y + ¦ 800 ¥ 1000 ¥ 0 1 ¥ 0 200 ¥ ¥ 400 600 y + +∆y + ¦ 800 ¥ 1000 ¥ 0.8 0.8 R vv (∆t + =4.6) 0.6 0.4 0.2 R (uv)(uv) (∆t + =4.6) 0.6 0.4 0.2 0 ¥ 0 200 ¥ ¥ 400 600 y + +∆y + ¦ 800 ¥ 1000 ¥ 0 ¥ 0 200 ¥ ¥ 400 600 y + +∆y + ¦ 800 ¥ 1000 ¥ FIGURE ˜ ÔÔ 7.13: ˜Sù ·Ô ú ù ·Ô:ú and correlation functions measured ˜uš ÐÏ žžž at © » š and ž ÆÐ žž ÆËÑ žž Æ Î§žž ÆÒ ž±ž ÆËÏ žž Æ¡ žž Æ œyž±ž Æ §ž±ž Æ¡¢ žž ÆÐ žžZž (see location of the maximum). Ï 150
¨ ¨ ¨ 7.3 Spatio-temporal correlations with ×_ñò¬\ ¨ ¨ ¨ ¨ ¨ ¨ first order moments of the velocity fluctuations within this domain. It could be shown that the structures of the spatio-temporal auto-correlation functions of the stream-wise (ªS·· ) and span-wise (ªSÙ&Ù ) velocity fluctuations are quite similar (shape, size and temporal decay) when the span-wise and wall-normal dependence is considered, whereas their cross-correlation ªS·Ù is necessarily zero due to symmetry. Also, the characteristic shift of the largest correlation value towards higher velocity regions with time agrees well. The wall-normal correlations, on the other hand, are relatively small and their maximum decreases fast with increasing time. As a consequence, the spatial extent of regions where most of the Reynolds stresses are produced must be relatively limited. The correlation function of the stream-wise vorticity component also reveals a short spatio-temporal correlation length and a displacement towards higher velocity regions. Although a consistent interpretation of the presented results is conceivable, the instantaneous velocity fields need to be analysed for further evidence. y + ,∆t + ) R uu (31+∆ 1 0.8 0.6 0.4 20.4 21.9 27.3 31.1 34.6 39.9 43.3 R uu (198+∆y + ,∆t + ) 1 0.9 0.8 0.7 185.4 198.4 196.3 198.5 200.6 205.2 216.4 y + ,∆t + ) R uu (52+∆ 0.2 1 0.8 0.6 0.4 ¨ 0 50 ¨ 100 ¨ © 150 200 y + +∆y + © 250 ¨ 300 34.1 41.6 48.5 52.6 56.6 63.6 77.1 R uu (301+∆y + ,∆t + ) 0.6 100 1 0.9 0.8 0.7 © 150 ¨ 200 © 250 300 y + +∆y + © 350 ¨ 400 288.1 298.6 299.1 301.3 302.4 305.6 326.3 y + ,∆t + ) R uu (101+∆ 0.2 1 0.8 0.6 0.4 ¨ 0 50 ¨ 100 ¨ © 150 200 y + +∆y + © 250 ¨ 300 90.4 99.4 98.8 101.2 104.4 111.2 132.3 R uu (398+∆y + ,∆t + ) 0.6 200 1 0.9 0.8 0.7 © 250 ¨ 300 © 350 400 y + +∆y + © 450 ¨ 500 394.7 387.5 398.6 400.8 402.9 421.4 0.2 ¨ 0 50 ¨ 100 ¨ © 150 200 y + +∆y + © 250 ¨ 300 0.6 300 © 350 ¨ 400 © 450 500 y + +∆y + © 550 ¨ 600 FIGURE 7.14: Representation of the ˜ ·· correlation at ˜$ûšÀœ§§žž in the vicinity of the maximum for various wall distances © » of the fixed point and temporal separation between the measurements (ÉKøÓ» š Ð ž Æ ÏcÆ Ð§ÆØÆ ž Æ ÈÐ§Æ È7ÏcÆ ÈKÐ ž ). 151
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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
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! 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 and 148: ô ô 7.3 Spatio-temporal correlati
Page 149: 7.3 Spatio-temporal correlations wi
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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