Isothermal and Non-Isothermal Turbulent Flow over Solid Waves Transport and Structure

Kruse N.

An experimental study on transport phenomena in a turbulent flow withseparation in a wide water channel (aspect ratio 12:1) is presented. Thewavy bottom wall, characterized by the wavelength ♥ and the wave amplitude2a, is heated with a constant heat flux under non-isothermalcondition. Spatiotemporal information on the flow velocity is obtainedfrom digital particle image velocimetry (PIV). Digital particle imagethermometry (PIT) is used to assess simultaneously the temporal andspatial variation of velocity and temperature fields. The temperatureis measured with thermochromic liquid crystal particles (TLC) whichchange their reflected wavelengths as a function of the temperature.At isothermal conditions, measurements are performed at Reynolds numbersup to 20500, defined with the bulk velocity and the half-height of thechannel. Large ensembles of instantaneous velocity fields are decomposedinto orthogonal eigenfunctions. A projection of instantaneous snapshotsof the velocity field onto eigenfunctions is used to extract the time developmentof flow structures of defined kinetic energy. Large longitudinalstructures with a characteristic spanwise scale O{1.5Λ} can be foundby projecting instantaneous realizations of the flow onto the first twoeigenfunctions. Any interactions between coherent structures result in amerger into newer structures via complete, partial, and fractional pairingsor divisions. The structures retain the characteristic separation andcontribute significantly to the kinetic energy. The meandering motion ofO{1.5♥Λ}-scales provides a mechanism for the transport of momentum.To quantify how turbulence statistics and eigenfunctions in the outer part of the shear layer depend on the interaction with the wall, threewavy surfaces, characterized by different amplitude-to-wavelength ratios,are investigated. Similar dominant eigenfunctions with similar spanwisescales are obtained in the outer part of the wall shear layer. Theroot-mean-square of the streamwise and spanwise velocity fluctuations,Reynolds shear stress, Reynolds stress coefficients, and turbulent kineticenergy are approximately the same regardless the surface roughness,when normalized with the friction velocity. The structure of stress producingmotions in the outer flow could have a universal character, inthat they are influenced by turbulence producing processes in the innerflow only through the magnitude of the friction velocity.

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Table of contents :
Abstract……Page 5
Zusammenfassung……Page 7
List of Figures……Page 9
List of Tables……Page 13
Nomenclature……Page 25
1 Introduction……Page 33
2.1 Transport and Structure in Wall Turbulence……Page 39
2.1.1 Wall Flows……Page 40
2.1.2 Turbulent Flow over Wavy Surfaces with Separation……Page 41
2.1.3 Large-Scale Longitudinal Flow Structures……Page 43
2.1.4 Governing Turbulent Transport Equations……Page 46
2.2.1 Mathematical Background……Page 48
2.2.2 The Method of Snapshots……Page 50
3 Experimental Aspects……Page 53
3.1 Channel Facility……Page 54
3.1.1 Non-Heated Test Section……Page 56
3.1.2 Heated Test Section……Page 57
3.2.1 Digital Particle Image Velocimetry……Page 60
3.2.2 Tracer Particles……Page 66
3.3.1 Combined Particle Image Velocimetry/Liquid Crystal Thermometry Technique……Page 72
3.3.2 Thermochromic Liquid Crystal Particles……Page 78
3.4 Measurement Accuracy……Page 89
3.4.1 Spatial Resolution……Page 92
I Results on Isothermal Flow over Waves……Page 95
4 Dynamics of Large-Scale Structures……Page 97
4.1 Instantaneous Velocity Fields……Page 98
4.2 Proper Orthogonal Decomposition Analysis……Page 100
4.3 Temporal Evolution……Page 103
4.4 Spanwise Growth……Page 108
4.5 Summary……Page 110
5 Influence of Amplitude-to-Wavelength Ratio on Turbulence……Page 111
5.1 Introduction……Page 112
5.2 Surface Roughness……Page 115
5.3 Structural Information from Streamlines of the Velocity Field……Page 118
5.4 Statistical Quantities……Page 119
5.5.1 Results in the (y,z)-Plane……Page 130
5.5.2 Results in the (x,y)-Plane……Page 135
5.5.3 Results in the (x,z)-Plane……Page 139
5.6 Summary……Page 143
6 Reynolds Number Considerations……Page 145
6.1 Introduction……Page 146
6.2 Structural Information from Streamlines of the Velocity Field……Page 147
6.3 Statistical Quantities……Page 152
6.4.1 Results in the (y,z)-Plane……Page 157
6.4.2 Results in the (x,y)-Plane……Page 160
6.4.3 Results in the (x,z)-Plane……Page 163
6.4.4 Energetic, Large-Scale Motion……Page 166
6.5 Summary……Page 168
II Results on Non-Isothermal Flow over Waves……Page 171
7 Structure of Turbulent Heat Flux……Page 173
7.1.1 Previous Research……Page 174
7.1.2 Objectives……Page 175
7.1.3 Flow Situation……Page 176
7.2.2 Structural Information from POD Analysis……Page 180
7.3.1 Instantaneous Velocity and Temperature Fields……Page 185
7.3.2 Structural Information from POD Analysis……Page 192
7.3.3 Summary……Page 197
8 Concluding Remarks……Page 201
9.1 Effect of a Moving Wavy Wall on Turbulent Transport……Page 205
9.2 Measurements in Complex Geometries……Page 207
Bibliography……Page 211
Curriculum Vitae……Page 223