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

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¡ ¡ 7 Investigation of the yz-plane all cross-correlations. In order to examine the dynamical properties of the flow represented by the correlations in the left column, a positive span-wise velocity fluctuation which is located at the fixed point will be assumed first. It can be seen from the sign of the correlation that å positive fluctuation induces a vertical motion towards the wall, which is located upstream of the horizontal velocity structure Ã (negative values), and a motion away from the wall located downstream of the coherent structure. The argumentation can be reversed when a motion å Û with is considered. At larger wall distance it can be deduced from the secondary peaks near the wall that a horizontal motion in Ã positive (å direction ) induces also a quite local downstream motion, but the location of this coherent motion is relatively close to the location of the fixed point with respect to the position where an upward motion can be observed. In addition, it can be concluded from the increasing height of the correlation value that the coherence of this near-wall motion increases if the location of the fixed point is farther away from the wall. When the correlations shown in the right column of figure 7.9 are analysed in the same way, it can be seen that a vertical motion at the fixed point location with ã induces a horizontal motion towards ×pÃ»Ü¬2 in the near-wall region and away from the centre at higher wall locations. A vertical motion towards the wall, on the other hand, induces a horizontal motion away from the centreline at ×pÃ » ¬\ due to continuity. As the correlations do not allow to differentiate between primary and secondary motion it is also conceivable to interprete the results in a different way. For example, it can also be stated that a horizontal motion towards the centreline induces a vertical motion away from the wall at the location of the fixed point. This argumentation was usually applied for the interpretation of the results in chapter 6. The basis for this interpretation is the assumption that the kinetic energy of the vertical motion is not sufficient to alter the turbulence structure to a large extent, especially near the wall. This can be deduced from the rms-profiles shown in figure 7.3. Anyway, the three dimensional size, shape and interaction of the flow structures is now fully determined if the results presented in chapter 5 and 6 are taken into account. 7.3 Spatio-temporal correlations with çéèTê ë To examine the dynamical aspects of the organised flow structures, the temporal evolution of the primary correlations as a function of the wall-normal ¹&» coordinate and time delay will be analysed in the following. It might be argued that it is easier to perform such an analysis when the orientation of the measurement plane is parallel to the î±ïð main ×_ìË»À¬3ìäŸí flow direction. However, it should be kept in mind that due to the small size of the correlations in span-wise direction the results may be strongly biased if the measurement plane is not perfectly aligned with respect to maximum of the correlation in physical space, or, if the 3D correlation is slightly tilted in span-wise direction due to the limited number of samples, for example. Both effects can be avoided by using the experimental configuration applied here. To obtain correct results a two-dimensional correlation was calculated from which two orthogonal lines being parallel to the coordinate axis were extracted, and the location of the global maximum was used to determine the intersection point of the lines to be extracted (the one-dimensional correlation function depends on the coordinates of the points from which the values are taken from the four-dimensional correlation function). For the calculation of the two-dimensional correlation functions a line at a particular wall location was extracted from the measurement acquired at ì time and correlated with the result measured ìÇ¼¢×_ì at . The distance between both measurement planes is zero in order to study the convective de- 146
ô ô 7.3 Spatio-temporal correlations with ×_ñò¬\ ô ô š cay of the flow structures. Figure 7.10 and figure 7.11 reveal the primary correlations measured ª«§p¬3®c¯c at and figure 7.12 and figure 7.13 show the corresponding results for the ¿ ° investigation. Clearly visible is the different size and shape of the correlations ª«§¬ and the variations in the temporal decay. Due to the different size of the correlation functions 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 ô 0 100 ô 200 ô y + +∆y + 300 ô 400 ô 500 ô −0.2 1 ô 0 100 ô 200 ô y + +∆y + 300 ô 400 ô 500 ô R uu (∆t + =1) 0.8 0.6 0.4 0.2 R ww (∆t + =1) 0.8 0.6 0.4 0.2 0 0 1 ô 0 100 ô ô 200 300 y + +∆y + õ 400 ô 500 ô −0.2 1 ô 0 100 ô ô 200 300 y + +∆y + õ 400 ô 500 ô R uu (∆t + =5) 0.8 0.6 0.4 0.2 R ww (∆t + =5) 0.8 0.6 0.4 0.2 0 0 1 ô 0 100 ô ô 200 300 y + +∆y + õ 400 ô 500 ô −0.2 1 ô 0 100 ô ô 200 300 y + +∆y + õ 400 ô 500 ô R uu (∆t + =10) 0.8 0.6 0.4 0.2 R ww (∆t + =10) 0.8 0.6 0.4 0.2 0 0 ó 0 100 ó 200 ó y + +∆y + 300 ó 400 ó 500 ó −0.2 ó 0 100 ó 200 ó y + +∆y + 300 ó 400 ó 500 ó 147 FIGURE ˜ ·$· 7.10: (left) ˜ Ù&Ù and (right) correlation functions measured ˜šuœ§§žž at © » and ž Æ Î§ž ÆËÏ ž ÆÐ žž ÆËÑ ž±ž Æ Îžž ÆÓÒ žž (see location of the maximum). Ñ
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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
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 and 142: 7.2 Statistical properties of the l
Page 143 and 144: ¿ 7.2.2 Spatial cross-correlations
Page 145: ¿ 7.2 Statistical properties of th
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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