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

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7 Investigation of the yz-plane wall structures presented in the previous chapter, and the ªSÔÔÅ¸Õ¹¥»‹Ö=¹¥»n¼r×r¹¥»‹ÖØ×pÃ» ½ correlation, shown in the upper left image of figure 7.6, indicates the spatial extent of the dominant flow structures which are moving towards and away from the wall. With increasing wall distance from the fixed point, the correlations increase in size but it should be noted that the total size is always below the size of the ªS·· correlation. When the ªSÙ¥ÙÚ¸º¹&»nÖ=¹&»‰¼[×p¹&»ÇÖØ×pÃ» ½ correlation in figure 7.7 is considered, it can be concluded that the various primary correlations are always stretched in the direction of the velocity fluctuation. However, the dimension of the stretching which is related to the region where a correlated motion can be observed is quite different. Another interesting feature is the butterfly shape of the ªSÙ¥Ù correlation, especially ¹ »ÜÛ ° for . The fact that the correlation is further away from the wall with ÝÞÃ » Ý increasing indicates that the influence of a span-wise motion being present ¹ » ¬5Âc at , for example, is quite limited. This might be related to the fact that the span-wise motion is restricted by the R (y + =30) vv R (y + =200) vv + y + ∆ + y + y + ∆ + y + y + ∆ + y R (y + =50) vv R (y + =300) vv R (y + =100) vv R (y + =400) vv 142 ∆ z + ∆ z + FIGURE 7.6: ˜ ÔÔÄ © »nÆ © »pÈ8É © »¾ÆËÉÌw»¾Í correlation measured at © » šßÎ§ž ÆËÏ ž ÆÐ žž ÆËÑ žž Æ Î§ž±ž ÆÒ žZž .
¿ 7.2.2 Spatial cross-correlations with ²L³¢´âµ The left column in figure 7.8 shows the ªSÔ· cross-correlation function measured at ¹¥»5¬ ¿ 7.2 Statistical properties of the log-law region R (y + =30) ww R (y + =200) ww y + ∆ y + y + ∆ y + y + ∆ y + R (y + =50) ww R (y + =300) ww R (y + =100) ww R (y + =400) ww ∆ z + ∆ z + FIGURE 7.7: ˜ Ù¥ÙnÄ © » Æ © » È8É © » ÆËÉÌ » Í correlation measured at © » šßÎ§ž ÆËÏ ž ÆÐ žž ÆËÑ žž Æ Î§ž±ž ÆÓÒ žž . presence of the streaks which are attached to the wall according to the section 6.4. However, the situation is reversed. In this case the correlation function drops down to zero ¹&»‰¬ at ¹&»8à with Ã»Á¬u at but for Ý Ã»áÝ larger a significant correlation with the near-wall motion can be found. ¥Ö ° ¥Ö c (top to bottom) with the ã component fixed while the ä signal was shifted in the ¹ Â Ã and directions. The right column reveals the opposite case where ä the component was fixed ã while was shifted. The negative sign of the cross-correlations, represented by the dashed lines, indicates again that the transport of relatively low-momentum fluid outward into higher 143
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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
Page 91 and 92: ½ 5.4 Properties of coherent veloc
Page 93 and 94: » % %QÄ ¾ Ó turbulent velocit
Page 95 and 96: * 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: 7.2 Statistical properties of the l
Page 145 and 146: ¿ 7.2 Statistical properties of th
Page 147 and 148: ô ô 7.3 Spatio-temporal correlati
Page 149 and 150: 7.3 Spatio-temporal correlations wi
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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