The significance of coherent flow structures for the turbulent mixing in wall-bounded flows [Elektronische Ressource] / vorgelegt von Christian J. Kähler

Informations

• Publié par: georg-august-universitat_gottingen
• Publié le: 01 janvier 2004
• Nombre de lectures: 44
• Langue: English
• Poids de l'ouvrage: 29 Mo

Extrait

The significance of coherent flow
structures for the turbulent mixing in
wall-bounded flows
Dissertation
zur Erlangung des Doktorgrades der
Mathematisch-Naturwissenschaftlichen Fakultaten¨ der
Georg-August-Universitat¨ zu Gottingen¨
Vorgelegt von
Christian J. Kahler¨
aus Buchholz i. d. Nordheide
Gottingen¨ 2004D7
Referent: Professor Dr. H. Eckelmann
Korreferent: Dr. D. Ronneberger
Tag der mundlichen¨ Prufung:¨ 1. July 2004Contents
1 Introduction 5
2 Particle Image Velocimetry 13
2.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Generation of appropriate tracer-particles . . . . . . . . . . . . . . . . . . . 16
2.2.1 Description of the experiment . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Particle size analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3 Flow visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Registration of the particle images . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1 Principles of CCD sensors . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2 Quantum efficiency and signal-to-noise ratio . . . . . . . . . . . . . 25
2.3.3 CCD architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Particle image analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.1 Particle image density, loss of pairs and velocity gradients . . . . . . 30
2.4.2 Signal-peak detection and displacement determination . . . . . . . . 31
3 Stereo-scopic Particle Image Velocimetry 37
3.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1.1 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.2 Scheimpflug condition . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Evaluation of stereo-scopic image pairs . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Determination of the mapping function . . . . . . . . . . . . . . . . 42
3.2.2 Image warping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.3 Vector field warping . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.4 Interrogation window warping . . . . . . . . . . . . . . . . . . . . . 45
3.3 Calibration validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Multiplane Stereo Particle Image Velocimetry 49
4.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Four-pulse-laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.1 Performance of spatial light-sheet separation . . . . . . . . . . . . . 53
4.2.2 Generation and controlling of the timing sequence . . . . . . . . . . 54
4.3 Modes of Operation I – In-plane flows . . . . . . . . . . . . . . . . . . . . . 55
4.4 of II – Out-of-plane flows . . . . . . . . . . . . . . . . . . 57
4.5 Simplified recording system . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.6 Polarisation effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3Contents
4.7 Monochromatic aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.8 Feasibility study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5 Investigation of the xy-plane 69
5.1 The statistical description of turbulence . . . . . . . . . . . . . . . . . . . . 69
5.2 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.3 Statistical properties of the flow . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3.1 Single point statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3.2 Spatial auto- and cross-correlation functions . . . . . . . . . . . . . . 79
5.4 Properties of coherent velocity structures . . . . . . . . . . . . . . . . . . . . 90
5.4.1 Shear-layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.4.2 Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4.3 Sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6 Investigation of the xz-plane 97
6.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2 Statistical properties of the buffer layer . . . . . . . . . . . . . . . . . . . . . 101
6.2.1 Single point statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.2 Spatial auto-correlation functions . . . . . . . . . . . . . . . . . . . 105
6.2.3 cross-correlation . . . . . . . . . . . . . . . . . . . 109
6.3 Spatio-temporal buffer layer statistics . . . . . . . . . . . . . . . . . . . . . 114
6.4 Properties of coherent velocity structures . . . . . . . . . . . . . . . . . . . . 121
6.4.1 Low-speed streaks . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.4.2 Sweeps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.4.3 Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7 Investigation of the yz-plane 135
7.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.2 Statistical properties of the log-law region . . . . . . . . . . . . . . . . . . . 138
7.2.1 Spatial correlations with . . . . . . . . . . . . . . . . . . . . 141
7.2.2 Spatial cross-correlations with . . . . . . . . . . . . . . . . 143
7.3 Spatio-temporal correlations with . . . . . . . . . . . . . . . . . . . 146
7.4 with . . . . . . . . . . . . . . . . . . . 152
7.5 Properties of coherent velocity structures . . . . . . . . . . . . . . . . . . . . 155
7.5.1 Loop-shaped structures . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.5.2 Sweeps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.5.3 Stream-wise vortices . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8 Summary 163
Bibliography 169
Commonly used symbols 177
Index 180
4

1 Introduction
One of the fascinating phenomena of natural science is the turbulent state of the macroscopic
flow motion in fluid-mechanics. Beside the omnipresent variety and beauty of the turbulent
motion, the inherent fascination and attraction is strongly connected with the enormous dif-
ficulties associated with a mathematical and physical understanding. The principal difficulty,
with respect to an inviscid fluid or a classical gas of point particles in equilibrium, results from
the strong non-linearity in the conservation equation and the dissipative character e.g. the
flux of energy from the large scales or eddies into progressively smaller and smaller ones. As
a general mathematical solution of non-linear, non-equilibrium systems is out of reach from
the present point of view, the properties of idealised flows with simple geometries are exam-
ined experimentally and numerically. Of primary interest is the two-dimensional turbulent
boundary layer flow of an incompressible fluid along a flat plate with zero pressure gradient,
because this flow reveals simultaneously two characteristic phenomena of turbulence, namely
the effects of near-wall turbulence and the effects of intermittency, e.g the interaction of the
turbulent boundary layer with the laminar outer flow according to figure 1.1. This particular
flow evolves from a laminar boundary layer flow when the Reynolds number
is sufficiently high. In this case flow disturbances with a particular wavelength grow, become
unstable and share the energy from the mean motion over the degrees of freedom by non-linear
interaction.
U / U1.2 drot U = 0
y
rot U = 00.4 d
x
1
FIGURE 1.1: Instantaneous structure of a turbulent boundary layer and mean velocity profile after [37]
Beginning with the early channel and pipe flow measurements, published by Laufer [68,
69], and the zero pressure gradient boundary layer benchmark investigations along a flat plate
by Klebanoff [55], turbulent boundary layers have been examined extensively because of their
technological importance, their significance for the development of fundamental turbulence
models and for the validation of numerical flow simulations [89, 96]. The bulk of the quanti-
tative investigations has been performed with intrusive single-point measurement techniques
[21] such as pressure probes and hot-wire anemometer, but also non-intrusive flow visualisa-
tions techniques have been frequently applied to examine qualitatively the global features of
5




dd
1 Introduction
the flow [15, 24, 25, 28, 54, 57, 58, 59, 79, 81, 84, 92, 103, 110]. Although the conclusive-
ness of these visualisations is often questionable, because of the complexity of the turbulent
motion and inherent problems associated with the interpretations of the flow visualisation re-
sults as discussed by Hama [26], these investigations have improved the understanding of
turbulence to a large extent, because it was possible to detect coherent flow structures such
as low-speed streaks, shear-layers, stream-wise vortices and loop-shapedes and to
illustrate their significance for the turbulent mixing in wall-normal direction. In the follow-
ing years, a number of partially contradicting vortical models have been proposed, designated
as hairpin, horseshoe or lambda vortices in the literature [83, 98, 99], to link the coherent
structures and processes identified as illustrated in figure 1.2