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

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7.4 Spatio-temporal correlations with çéè £ ë £ 7 Investigation of the yz-plane ê In this section various one-dimensional spatio-temporal correlation functions calculated from measurements in spatially separated planes will be examined. This particular experimental arrangement allows to select a flow pattern at an upstream position and to measure the structural changes due to the mean velocity gradients and to the turbulent motion as a function of the spatial distance between the light-sheet pairs and the time delay between the measurements. Figure 7.15 to figure 7.17 reveal the primary correlation functions for various wall distances from the fixed point and time delays between the measurements. The results were obtained by cross-correlating the measurements acquired at different locations (325 wall-units streamwise separation between both measurement planes) while the downstream measurement was performed after the upstream measurement as indicated by the axis label. As the local mean velocity is approximately ¿ ä » according to figure 7.3, the structures selected at the upstream 1 1 0.8 0.8 R uu (∆t + =0) 0.6 0.4 0.2 R uu (∆t + =20) 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 uu (∆t + =8) 0.6 0.4 0.2 R uu (∆t + =25) 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 uu (∆t + =15) 0.6 0.4 0.2 R uu (∆t + =30) 0.6 0.4 0.2 0 £ 0 100 £ 200 £ y + +∆y + 300 £ 400 £ 500 £ 0 £ 0 100 £ 200 £ y + +∆y + 300 £ 400 £ 500 £ FIGURE 7.15: ˜ ·· correlation measured at ˜ášLœ§§žž and © » š location of the maximum) for various temporal delays (see axis label). 152 Ñ ž Æ Î§ž ÆËÏ ž ÆÐ žž ÆËÑ žž Æ Îžž ÆËÒ ž±ž (see
£ 7.4 Spatio-temporal correlations ×_ñ ¬\ with ¿ £ location are convected by about 130 wall-units (40% of the distance between the measurement planes) for a temporal delay ×_ìË» ¬é¯ of . Thus, the maximum correlation value is relatively low, especially near the wall, but it slightly increases with ¹ increasing due to the larger correlation length and larger local convection velocity. An other interesting effect is the shift of the maximum towards larger wall distances. However, both observations can be explained by means of the result shown in figure 5.5 on page 80. When the correlation in the lower left column is considered with the maximum ¹¥»"¬ ° at , the profile ×_ñ » ¬ Â "Â ° ¬! ¿#" ° at corresponds to the dashed graph in the left centre row of figure 7.15, provided the structural changes are negligible, so that it can be assumed that the flow structure convects down-stream with an average velocity of ° ä » (local mean velocity at ¹ » ¬ ° ) over 130 wall-units in ¿ stream-wise direction. In this case it can be estimated that the highest correlation value at ¿" ° is 0.54 in the lower left column of figure 5.5, which nicely matches with the results from the present investigation, and the corresponding position of the maximum is at . This implies that the general properties of the correlations can be well understood ×_ñ » ¬$ 1 1 ¹&»&% 0.8 0.8 R vv (∆t + =0) 0.6 0.4 0.2 R vv (∆t + =20) 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 + =8) 0.6 0.4 0.2 R vv (∆t + =25) 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 + =15) 0.6 0.4 0.2 R vv (∆t + =30) 0.6 0.4 0.2 0 £ 0 100 £ 200 £ y + +∆y + 300 £ 400 £ 500 £ 0 £ 0 100 £ 200 £ y + +∆y + 300 £ 400 £ 500 £ FIGURE 7.16: ˜ ÔËÔ correlation measured at ˜ š œ§§žž and © » š Ñ ž Æ Î§ž ÆËÏ ž ÆÐ žž ÆËÑ ž±ž Æ Î§ž±ž ÆÓÒ žž (see location of the maximum) for various temporal delays (see axis label). 153
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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
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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 and 150: 7.3 Spatio-temporal correlations wi
Page 151: ¨ ¨ ¨ 7.3 Spati
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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