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

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* Ó , ß ) , Á ß ½ ) 5 Investigation of the xy-plane *+ -, , À.* case of the upper ÎUÓ · ³ Z·(' Ó vector field the range is and *ÕÀ for the lower image . In both cases the region where the production of turbulence ÎVÓzÁ · ³ Z·(' takes place (red colour) is embedded in the typical low-speed regions close to the wall, and it should be noted that on top of the low-speed region a vortex can be observed, as already mentioned at the end of the previous section. It is evident that these vortices pump low-speed fluid away 400 350 300 250 y + 200 150 100 50 0 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 400 y [???] x [???] 350 300 250 200 150 100 50 y + x + 0 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 y [???] FIGURE 5.17: In-plane velocity fluctuations and distribution of the instantaneous Reynolds shear-stress ß¥ß (red: /.021 , blue: /3054 ) measured at çNì . x [???] ËBíî 94
* Ó , Ó * Á , Â 5.4 Properties of coherent velocity structures from the wall and this is associated with the production of turbulence because 6(7 is negative. In addition it becomes visible that upstream of the low-speed region a well developed shearlayer appears. Compared to the previously discussed shear-layer angle, here the angle is large in relation to the wall. 5.4.3 Sweep In this section the interaction between the shear-layer and the near-wall structures with the surrounding high momentum flow structures coming from larger wall distances under conservation of their momentum will be investigated. The extended high momentum flow structures moving towards the wall are called sweeps in the literature, see page 71. Figure 5.18 shows two examples which were selected due to the strong intensity in the Reynolds shearstresses 6(7 component that is approximately 20 times larger than the average value shown in figure 5.4. In case of the top vector field, for example, the non-dimensional range is , þ .* , *: þ and for the lower figure ÎUÓ 697.8$6 ' ) . It should be ÎVÓŒÓ 6(7.8$6 ' ) Ó mentioned that nearly no measured velocity field indicates a higher value which means that the structures can be considered as dominant concerning the production of turbulence. However, these velocity field represents general features which can be frequently observed even when the peak intensity of the Reynolds shear stress is lower. It can be seen from both velocity fields that sweeps are relatively simple large-scale eddy structures which transfer high momentum fluid towards the wall as assumed in the mixing-length theory by Prandtl. The word eddy implies a local flow region (or structure) over which the simultaneous velocity fluctuations are coherent or correlated [89, 100] and not a circulatory motion. As the variation of the stream-wise velocity inside the sweep is relatively small, the significance of this flow structure with regard to the production to turbulence is basically determined by the velocity fluctuation in wall-normal direction. This becomes important in case of boundary layer control for example, because a velocity disturbance in wall-normal direction is much more efficient than a disturbance in stream-wise direction. However, as a large part of the sweeps is located farther away from the wall, the potential artifical disturbance must be intense enough to reach the flow structure. The results presented in this chapter clearly indicate the existence of coherent structures, their geometrical properties, and their significance for the turbulent mixing in wall-bounded flows. In the following chapters the interaction of these structures will be further examined in order to find out which structures are fundamental and which ones are only secondary, which ones are dominant and which ones are irrelevant. 95
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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
Page 43 and 44: Ð È Ñ ù Ñ ù Ð È Ð È Ñ ù
Page 45 and 46: 3.2 Evaluation of stereo-scopic ima
Page 47 and 48: ú ¦ 3.3 Calibration validation by
Page 49 and 50: 4 Multiplane Stereo Particle Image
Page 51 and 52: £ è ¤ ó 4.2 Four-pulse-laser S
Page 53 and 54: £ ¤ £ £ 4.2 Four-pulse-laser Sy
Page 55 and 56: ( ì ( æ ( ì è ð ( ( ( ( ( ( ì
Page 57 and 58: æ ( | | | | | | | ì æ õ æ õ
Page 59 and 60: 4.5 Simplified recording system 4.5
Page 61 and 62: 4.7 Monochromatic aberrations refle
Page 63 and 64: º¹ n 4.7 Monochromatic aberration
Page 65 and 66: 4.8 Feasibility study experiments i
Page 67 and 68: 4.8 Feasibility study 10 20 30 40 5
Page 69 and 70: é¥î ëÝïñð€òôó 5 Invest
Page 71 and 72: I L § § § : ? ; õ : I I I W
Page 73 and 74: 5.2 Experimental set-up α4 α3 α2
Page 75 and 76: { : { L Ø { 9 D { 9 D T W ð 9
Page 77 and 78: : T ž ž ò 5.3 Statistical pro
Page 79 and 80: ¾ ¾ 5.3.2 Spatial auto- and cross
Page 81 and 82: ½ Ë 5.3 Statistical properties of
Page 83 and 84: ½ Ë 5.3 Statistical properties of
Page 85 and 86: ô ó ñ ½ ñ ô ó 5.3 Statistica
Page 87 and 88: æ å ä ã ã ã ½ Ë ä æ å ½
Page 89 and 90: æ æ å ä À Â ½ 5.3 Statistica
Page 91 and 92: ½ 5.4 Properties of coherent veloc
Page 93: » % %QÄ ¾ Ó turbulent velocit
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
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¿ 7.2 Statistical properties of th
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ô ô 7.3 Spatio-temporal correlati
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7.3 Spatio-temporal correlations wi
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¨ ¨ ¨ 7.3 Spati
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£ 7.4 Spatio-temporal correlations
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7.5 Properties of coherent velocity
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¿ 7.5 Properties of coherent veloc
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¿ 8 Summary The first part of this
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aperture, it is shown how to elimin
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¡ ¿ tures keep their spatial orga
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Bibliography [1] ACARLAR MS, SMITH
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[30] HINSCH K (1995) Three-dimensio
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[60] KNEUBÜHL FK, SIGRIST MW (1995
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[93] SMITH CR, METZLER SP (1983) Th
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Z k l l l l l { l R q ‡ ˆ ’
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Ø á a Õ Œ v momentum thickness,
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Index Kolmogorov micro-scale . . .
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Acknowledgement First of all I woul
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Lebenslauf von Christian Joachim K
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