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

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Ž Á § Âc Ã c ¬ ¬ Å Å Í Å | ~ ~ ¯ ~ x W V ~ ¢ ~ ~ ~ Ž Ÿ Reynolds number based on tracer particle diameter, c e Reynolds number based on boundary layer thickness, c e ‰ _P¹ x outward interaction, ¬ with ¬¾ÆY and ÆÇY T inward interaction, ¬ with ¬¾ÈY and ÈÇY l x x x x l Commonly used symbols I particle image density pressure fluctuation © turbulent kinetic energy, ª Tz« ¬ ª u® d u®¯ d a7_ [ d Q h°hFj Q D spatial cross-correlation global maximum of correlation (signal peak) Q/±³²´±£µ correlation of velocity fluctuation ¬· and ¬7¸ QKR p_P¹ Reynolds number based on stream-wise measurement position, c eIº _P¹ QKRS | ~ ¼ } ¼ Reynolds number based on momentum c e ŒP_P¹ thickness, co-ordinates of the signal peak in correlation plane time QKR QKR» Ž¡½ non-dimensional time, Ž¡½¾TŠŽ°¬ d delay between two laser illuminations _P¹ rÀ Ž¿TŠŽ e c » c ~ Â ~ Ã free-stream velocity mean velocity at the boundary layer edge instantaneous velocity component º in -direction instantaneous velocity component ¢ in -direction instantaneous velocity component Ÿ in -direction mean velocity components º in ¢ , Ÿ and -direction components of velocity fluctuations º in ¢ , Ÿ und -direction ¬ turbulence level, Á ¬4T « ¬ d _ c ¬Ä½ ¯ ½ non-dimensional velocity fluctuations, ¬Ä½GTŠ¬ _ ¬ ½ friction ¬ velocity, p particle velocity ¬ rms root mean square value of ¬ , ¬ rms T « ¬ d ¬ ] w_€a y sweep, ¬ with ¬GÆY and ÈÉY ~ Ì image co-ordinates ¤ space co-ordinate in stream-wise direction º space co-ordinate in wall-normal direction ¢ space co-ordinate in span-wise direction Ÿ [ ejection, ¬ with ¬GÈÉY and ÆY ÅËÊ displacement in physical space Ÿ ½ viscous or wall units, º ½ T º ¬ _P¹ º ½ ¢ ½ º ~ Ÿ 0 light-sheet thickness _–¹ º ½ non-dimensional displacement, º ½ T º ¬ Greek symbols off-axis angle ‰ boundary layer thickness ‰KTm‰ ` c TŠY)nÏÎ–Î c e f 178 ‰ depth of focus, ‰ T\[Pq^s diff`@t u V f _ÐtÑd
Ø á a Õ Œ v momentum thickness, Œ T integral correlation length, Ø Ú¸ÛT eÒÓ Ó À À eÒÓ › Ý eÒÓ À Þ À l l ¢ l ¢ displacement thickness, ‰€‹T ½ non-dimensional boundary layer thickness ‰ “ÔV ‰^‹ total energy cK_ c e × VON KÁRMÁN constant cÖ_rc e cK_ c e “ÔV wavelength of laser light Ǜ º f Ú¸ v ½ v dissipation length, v Ù¸ÛT¨V _ y non-dimensional streak spacing in Ÿ -direction dÄÝ³ÞFß dynamical viscosity Ù¸ Q/Ú¸ …à| ² µ density of the fluid, VPnÏ[ kg/mâ (air) kinematical viscosity, ¹ T á _^a ¹ p tracer particle density, ã ä€W kg/mâ (olive oil), Î)Vå[ kg/mâ (DEHS) a standard deviation of index (here è ) æ·ç mol molecular shear stress, ] mol T áËé é ¢ ] cK_ components of the vorticity fluctuation in Ÿ -direction w wall shear stress, ] w TÑêìëîí ] ð áËé cg_ é ¢ ] tur turbulent shear stress, ] tur T a ¬ }wï Abbreviations CCD DLR DNS DPIV FFT HFI HWA LML LES MPSPIV PDF PIV RANS RMS SPIV Charge Coupled Device Deutsches Zentrum für Luft- und Raumfahrt e.V. Direct Numerical Simulation Digital Particle Image Velocimetry Fast Fourier Transformation Hermann Föttinger Institut Hot-Wire Anemometer Laboratoire de Mecanique de Lille Large Eddy Simulation Multiplane Stereo Particle Image Velocimetry Probability Density Function Particle Image Velocimetry Reynolds Averaged Navier-Stokes Simulation Root Mean Square Stereo-scopic Particle Image Velocimetry 179
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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
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ß ß 6.2 Statistical properties
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g ˆ g ˆ 6.2 Statistical propertie
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— ¯ 6.2 Statistical properties o
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å å ç æ æ ã ã ã å å è æ
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6.2.3 Spatial cross-correlation fun
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6.2 Statistical properties of the b
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6.2 Statistical properties of the b
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performed at and the second at
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6.3 Spatio-temporal buffer layer st
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M M æ æ æ æ æ æ ã ã ã H M
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V W V 6.4 Properties of coherent ve
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6.4 Properties of coherent velocity
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6.4 Properties of coherent velocity
Page 127 and 128: 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 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: Z k l l l l l { l R q ‡ ˆ ’
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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