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

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5 Investigation of the xy-plane of conservation equations for the Reynolds stresses [37, 89]. Of primary interest are ÎV¼ÐÏ'Ñ the ÎÐ¼ÐÑÏ and correlations and their dependence on the wall distance, because these functions are mainly responsible for the turbulent mixing in wall-bounded flows according to the Reynolds equation in the boundary layer approximation on page 70. For the interpretation it is important to keep in mind that the first subscript indicates the velocity component at the fixed point while the second one indicates the component which is spatially shifted for the calculation of the cross-correlation. There are two surprising results, namely the different height of the correlation in the vicinity of the wall and the shift of the maximum towards the wall (when the stream-wise velocity component is fixed) or away from the solid boundary (when the wallnormal velocity component is fixed). This result will be further examined in chapter 6. 5.4 Properties of coherent velocity structures The multi-point correlations presented in the previous section furnish information about the average size, shape and coherence of the flow structures being present in the flow field, and they provide valuable details required for the interpretation of near-wall turbulence in terms of Reynolds equation and multi-point correlation equations. However, as the flow structures have a history of development while they are transported downstream, the spatial correlation functions include realizations of a large number of structures at various stages of their life history. As the details about the individual flow structures are averaged out by the statistical approach, the organisation of the individual coherent flow structures, their significance for the production of turbulence and their relation with respect to proposed vortex models will be investigated in the following. Unfortunately, this is not a trivial task because the selection of typical structures is subjective as the outcome of such an approach is always strongly coupled with the specified criteria. In other words, it is always possible to find structures which nicely match with the models proposed in the first chapter or structures with other desired properties. In order to minimise this well known problem, several techniques have been successfully exploited in the past, such as the variable interval time averaging (VITA) method, which compares the short term variance of a flow variable with respect to a chosen threshold level, or the variable interval space averaging (VISA) method, which allows to detect structures with similar spatial structure. However, these methods, which were mainly developed for the analysis of time-resolved hot-wire measurements, are not well suited for the analysis of PIV velocity fields. Therefore flow structures will be investigated here which appear frequently and with sufficient strength in the essential Reynolds stress component. The first criterion selects structures which are dominant with regard to their occurrence and the second one identifies structures which are dominant in terms of turbulent mixing and production of turbulence. 5.4.1 Shear-layer The basic coherent flow structure that can be easily observed in the áEÄ -plane of a turbulent boundary layer (stream-wise wall-normal) is the so called shear-layer. When moving with the appropriate convection velocity, or after subtracting the local mean velocity, this structure appears as a slightly-inclined low-speed region, often several thousand wall-units in length and some 100 wall-units in height (their width is largely unknown). The inclination angle of the shear-layers relative to the wall was the subject of several studies [9, 28, 50, 62, 80]. The general consensus is that this angle depends on the distance from the wall, as indicated by the 90
½ 5.4 Properties of coherent velocity structures results in figure 5.5 and 5.6, but the exact values are still a point of discussion. The results, based on the analysis of space-time correlation measurements, vary between 4 and 7 degrees in the viscous sub-layer and 11 and 20 degrees in the buffer region [63]. This observation is fully consistent with the average results presented in section 5.3.2. On the top of these layers, vortices with a strong span-wise vorticity component can be observed frequently [74, 38], but it is an open question whether these vortices are a result of a Kelvin-Helmholtz instability, like 400 350 300 250 + y 200 150 100 50 0 50 100 150 200 250 300 350 400 450 500 550 600 650 400 y [???] x [???] 350 300 250 y + 200 150 100 50 0 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 y [???] x [???] + x FIGURE 5.15: Velocity fluctuations measured at çNì ËBíî ß¥ß ( is colour coded). 91
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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
Page 39 and 40: › B › B › J ù ž & 3.1 Princ
Page 41 and 42: 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: æ æ å ä À Â ½ 5.3 Statistica
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
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7.2 Statistical properties of the l
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¿ 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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