Measurements of Turbulence at High Reynolds Numbers
From Eulerian Statistics Towards Lagrangian Particle Tracking
von Christian Küchler
Datum der mündl. Prüfung:2020-12-16
Erschienen:2021-03-18
Betreuer:Prof. Dr. Eberhard Bodenschatz
Gutachter:Prof. Dr. Eberhard Bodenschatz
Gutachter:Dr. Michael Wilczek
Gutachter:Prof. Dr. Rainer Grauer
Zum Verlinken/Zitieren:
http://dx.doi.org/10.53846/goediss-8490
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Description:Dissertation
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Zusammenfassung
Englisch
The effective description and fundamental understanding of turbulent flows remains elusive to modern physics despite centuries of research and its great importance in numerous fields. The theoretical difficulties of the topic (nonlinear, nonlocal, or unclosed equations) are accompanied by the multiscale characteristics, large number of degrees of freedom, and strong sensitivity to initial conditions that make numerical and laboratory experiments equally challenging. One potential way to unravel the dynamics underlying turbulent motions is the separation of inertial forces from viscous forces, i.e. the study of turbulence at very large Reynolds numbers. The Max Planck Variable Density Turbulence Tunnel (VDTT) is a facility well-suited for the study of such large Reynolds numbers under controlled conditions. Its active grid allows the creation of turbulence at Taylor-scale Reynolds numbers Rλ > 6000 that can be investigated with state-of-the-art subminiature hot wires and whose turbulence generation can be controlled with great flexibility. This allows the study of fine details of the turbulence energy spectrum, such as the bottleneck effect, which are difficult to investigate even at small Rλ. We show for the first time experimentally that the bottleneck effect decreases with increasing Reynolds number up to Rλ ≈ 5000 confirming previous numerical studies at lower Reynolds numbers. A very influential phenomenological model is the seminal self-similar model of the velocity increment statistics by Kolmogorov and its intermittency refinements. In this thesis the cornerstones of this scaling theory are confirmed approximately throughout the range of Rλ studied (150-6000) using hot wire data from the VDTT. This constitutes the most extensive dataset in this range of Rλ to the author’s best knowledge. The local scaling exponents of the increment statistics becomes Rλ-independent for Rλ > 2000. They do however not allow the immediate identification of an inertial range scaling exponent, but carry the imprints of the turbulence decay and certain dissipative effects. The effect of decay is more dramatic, but can be explained by a model for the statistics of decaying turbulence. This allows the extraction of an inertial range scaling exponent that agrees with those obtained by the extended self-similarity technique. The dissipative effects take the form of log-periodic oscillations on the scaling functions, whose exact physical origin remains elusive. The remainder of the thesis deals with the design and implementation of a particle tracking system in the VDTT. The system allows the measurement of statistics in the Lagrangian framework, where instead of a multi-location measurement, individual fluid parcels are followed throughout the flow and multi-time statistics are obtained. The setup records the motion of cellulose particles of Stokes numbers between 0.0001 and 2 illuminated by a high-power laser using four stationary high-speed cameras. It is shown that the setup is capable of acquiring acceleration statistics and record particle tracks of up to 15 viscous time scales. This allows the systematic investigation of Lagrangian turbulence at Rλ > 2000 where such investigations were impossible hereto- fore.
Keywords: Turbulence; Fluid Physics; Fluid Dynamics; Flow Measurement