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

More documents

Recommendations

Info

ƒ„ „ ƒ ƒ„ ƒ„ „ ƒ ƒ„ ƒ„ „ ƒ … … … … … 7 Investigation of the yz-plane of the data. As the flow structures and their spatial organisation change while they are transported downstream, the various correlation values yield information about their life history. This is in some extent similar to the image analysis in PIV where the position, size, shape and intensity of the signal-peak in the correlation domain yield statistical information about the size and shape of the particle images themselves as well as information about the magnitude, direction and homogeneity of the displacement of the particle ensemble in between the two illuminations. The main difference lies in the fact that the fluid mechanical correlations presented in the following are ensemble averages calculated over hundreds of realizations, whereas in PIV the ensemble average is replaced by the spatial average of a single realization. This implies that in our case the statistical process leading to the fluid mechanical correlation functions must not necessarily be ergodic as required for PIV image analysis. Intensity Intensity x ∆ ~ x ∆τ ∆t t x ∆x ∆τ … … … ∆t ∆ ~ x t FIGURE 7.2: Optimised light-sheet positioning to reduce loss-of-correlation due to unpaired particle image pairs, induced by out-of-plane (F† " Ø‡mù motion mm). Different light-sheet shadings indicate different states of polarisation. Left: Timing diagram for measuring all components of the space-time correlations tensor K+ Ø for and KJ various . Right: Timing diagram for measuring all components of the space-time correlations tensor for K‰ˆ Ø and various KJ . 7.2 Statistical properties of the log-law region To ensure that the experimental arrangement was properly aligned relative to the flow direction, the main statistical flow properties were calculated and compared with the results presented in chapter 5. The top row of figure 7.3 shows the non-dimensional mean velocity profile in linear and semi-logarithmic representation. It can be seen that the functional dependence agrees fairly well with the graph from the measurements presented in chapter 5. This demonstrates the accuracy of the stereoscopic PIV method because the mean streamwise velocity in figure 7.3 corresponds to the out-of-plane velocity component in the present investigation. To estimate the quality of the camera and light-sheet alignment, the statistical properties of the fluctuations in the near-wall region were calculated. The distribution of the velocity fluctuations and , the stream-wise vorticity a‹x and two components of the |‹Š:Œ Reynolds stress tensor ( Œ and | ) are exactly symmetrical so that a high flow quality and very accurate alignment of the laser and recording system can be assumed in the following. Any misalignment of the light-sheet with respect to the wall and mean flow direction or incorrect estimated camera positions would appear as a displacement of the distributions of certain magnitude and direction and, thus, indicate how to improve the setup or to correct the results. 138
‘ — s 7.2 Statistical properties of the log-law region 25 30 U + mean 20 15 10 5 ’ yz−result “ xy−result U + mean 25 20 15 10 5 0 3 Ž 0 100 Ž 200 Ž y + 300 Ž 400 Ž 500 Ž 0 a.u. Ž Ž 1 10 100 y + 1000 Ž v + rms w + rms u + rms 2 1 PDF (u + ) PDF (v + ) PDF (w + ) a.u. Ž Ž 1 10 100 y + PDF(uv) PDF(vw) PDF(uw) 1000 Ž a.u. ” −7.5 • −5.0 – −2.5 0.0 2.5 5.0 7.5 u i + PDF (ω x ) Ž −1 0 1 u i u j Ž Ž −300 −200 −100 0 100 ω x [1/s] 200 Ž 300 Ž FIGURE 7.3: Flow characteristics. Upper row: Mean velocity profile at ˜$v›šLœ§§žž . Centre row: Intensities and distribution of the velocity fluctuations. Lower row: Distribution of the Reynolds stresses and stream-wise vorticity. The distribution, on the other hand, is not symmetrical and possesses a negative mean value indicating that turbulence is produced on average. Slight differences between both investigations can be only observed in the left graph of the centre row for |ŸŒ o2h . In this domain, q the maximum of the stream-wise and wall-normal velocity fluctuations is lower with respect to the reference investigation due to the different spatial resolution in wall-normal direction. However, q hc for the values nicely match apart from the component of the velocity s¢¡ fluctuation which is slightly underestimated in ÎŸq the -investigation. This can be explained by the fact that the out-of-plane motion in ÎŸq the -investigation is quite small referring to the inplane motion in contrast to qÏ the -investigation. This is supported by the hot-wire comparison shown in figure 5.3 on page 77. It can be seen that the PIV results match with the hot-wire investigations for the and component while a slight systematic deviation can be observed in case of the component. However, it should be mentioned that this systematic difference Œ | 139
Page 1 and 2:
The significance of coherent flow s
Page 3 and 4:
Contents 1 Introduction 5 2 Particl
Page 5 and 6:
1 Introduction One of the fascinati
Page 7 and 8:
As order can be always observed whe
Page 9 and 10:
were not considered in detail in th
Page 11 and 12:
varying signal can be transformed i
Page 13 and 14:
2 Particle Image Velocimetry The tr
Page 15 and 16:
2.1 Principles It is of fundamental
Page 17 and 18:
’ ’“ ” ”• Ž Ž Ž Ž
Page 19 and 20:
¹ and 2.2 Generation of appropriat
Page 21 and 22:
2.2 Generation of appropriate trace
Page 23 and 24:
2.3 Registration of the particle im
Page 25 and 26:
2.3 Registration of the particle im
Page 27 and 28:
ë ë 2.3 Registration of the parti
Page 29 and 30:
ýÿþ¡ û û ¢ ¢ £ôþ¡ î¥
Page 31 and 32:
or = ö D Q ù ù ?xö ù Y[Z]\ & &
Page 33 and 34:
ñ † † † † † † † †
Page 35 and 36:
˜ E ˜ T ˜ T 2.4 Particle image
Page 37 and 38:
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 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 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: % { s s s s 7.1 Experimental set-up
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 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
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?