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The Taylor-Couette (TC) flow, the flow confined between two concentric independently rotating cylinders, is used as a perfect model to investigate shear flow over concave surfaces and one of the paradigmatic systems of the physics of fluids. In this thesis, an experimental investigation of the turbulent TC flow in a very wide gap geometry with a radius ratio 𝜂 = 0.1 is performed. The physical and dynamic behavior of the flow is studied in a geometry that has rarely been investigated before the current study, which makes this study unique. The study aims to understand the effect of curvature on the TC flow, particularly in cases where the circumferential length of the inner cylinder is smaller than the gap width. The flow is studied in the different rotation regimes: counter-rotating, co-rotating, and purely inner cylinder rotating regimes up to shear Reynolds numbers Re_s≤ 150000. The flow field has been qualitatively studied using visualization techniques. By probing the different flow parameters, familiar coherent TC flow patterns appear, in addition to newly observed patterns we assume only exist for very wide gap TC flows. For a more detailed quantitative study, a time-resolved velocity field measurement has been conducted using the High-speed Particle Image Velocimetry technique through the system end plate. The radial and azimuthal velocity components in the 2D horizontal plane are measured at different axial positions, in order to scan the axial variance of the flow. The recorded flow field is used to compute the angular momentum transport in terms of the quasi-Nusselt number (Nu_ω). The results show a maximum of Nu_ω for low counter-rotating rates of −0.011 ≤ μ_max ≤ −0.0077, which is associated with large-scale structures that span the entire gap. Moreover, the Nu_ω decreases for counter-rotation rates higher than μ_max until it reaches a minimum value and then tends to increase again for higher counter-rotation cases. The space-time behavior of the turbulent flow field for the high counter-rotating cases shows the existence of newly observed patterns next to the outer cylinder wall that propagates inward, enhancing the angular momentum transport and resulting in a second maximum in transport for higher counter-rotating rates. For the pure rotating inner cylinder, the momentum transport scaling with the shear rate Nu_ω ∼ Re_s^α has been studied, and it shows a transition in scaling to 𝛼 = −0.76 for all flows with Re_(s )≥ 25000. This new scaling reveals the transition of the flow from the classical turbulent regime to the ultimate one, where this transition is accompanied by a clear change in the flow behavior. Moreover, the flow in the co-rotating regime and particularly in the centrifugal stable regime (𝜇 > +0.01) is investigated. The Velocity measurements show the presence of disturbed flow near the inner cylinder, where the measured velocity profiles showed a clear deviation from those predicted by laminar flow for flows up to 𝜇 = +0.04.
Stratified vortices can be found from small to large scales in geophysical and astrophysical flows. On the one hand, tornadoes and hurricanes can lead to devastation and even a large
number of casualties. On the other hand, vortices can distribute heat and momentum in the atmosphere which is important for a habitable environment on Earth. In the astrophysical context, accretion disks (from which solar systems are formed) can be seen as stratified vortices. In such systems, understanding the mechanisms that can result in an outward transport of angular momentum is a central problem. For a planet or star to be formed in a disk, angular momentum has to be carried away from its center to allow matter aggregation by gravity; otherwise, its rotation speed would be far too large, avoiding this matter aggregation (and the consequent star formation) to happen. In such gas systems, turbulence is the most likely mechanism to achieve such a large angular momentum transport. However, it was shown that the flow profile of accretion disks is stable with respect to purely shear instabilities, and the question arises about how the turbulence can be generated. Among other candidates, the strato-rotational instability (SRI) has attracted attention in recent years. The SRI is a purely hydrodynamic instability that can be modeled by a classical Taylor-Couette (TC) system with stable density stratification due to axial salinity or temperature gradients.
In this thesis, a combined experimental and high-performance computing study of new specific behaviors of the strato-Rotational Instability (SRI) is performed. The density stratification causes a change in the marginal instability transition when compared to classical non-stratified TC systems, making the flow unstable in regions where – without stratification – it would be stable. This characteristic makes the SRI a relevant phenomenon in planetary and astrophysical applications, particularly in accretion disk theory.
Despite many advances in the understanding of strato-rotational flows, the confrontation of experimental data with non-linear numerical simulations remains relevant, since it involves
linear aspects and non-linear interactions of SRI modes which still need to be better understood. These comparisons also reveal new non-linear phenomena and patterns not yet observed in the SRI, that can contribute to our understanding of geophysical flows.
The linear-theory assumption is a fundamental approach for the study of waves in fluids. The governing equations are linearized by assuming the perturbations are small so that the consequences of nonlinear terms are negligible. Nevertheless, if a wave approaches a critical level, in which the wave amplitude grows so as to create an instability of the background flow, the assumption of linearity may not hold any longer. In this case, the nonlinear terms are required to be taken into consideration.
In this thesis, two experimental setups have been proposed for the study of two scenarios, in which the nonlinear effects become significant and a traditional linear solution is no longer valid.
The first experiment focuses on an inertially oscillating rotating fluid. In the thesis, we present experimental results from a system that is simpler than classical precession experiments but still shows very similar wave interactions and a collapse to turbulence. This system consists of a partly filled rotating annulus that rotates about its symmetry axis slightly tilted with respect to the gravity vector.
In the experiments, we find a resonant collapse when the forcing frequency corresponds with a resonant frequency of the rotating tank. Two types of instability can be triggered: a parametric triadic instability, in which two free Kelvin modes arise and form a triad with the forced Kelvin mode, and a shear-type instability related to the nonlinearly excited geostrophic flow. The latter instability gives rise to a barotropic mode that interacts with the forced mode and generates secondary modes. We also observed dependency of the mode frequencies on the Ekman number, which can, at least partly, be explained by a Doppler shift due to the mean flow. Finally, we try to connect our data to a low-order dynamical system based on the weakly nonlinear theory that describes the main features of single triad interaction in precession experiments.
The second experiment concerns the study of undular bores (or tidal bores), in which the nonlinearity plays an important role. An experiment has been performed in which undular bores are produced in an open circular channel. More specifically, two different cases have been investigated: a single bore case with a rigid boundary setup and a bore colliding case with a periodic lateral boundary setup. Bores are generated by abruptly releasing a barrier that separates fluids with different surface levels. Up to our knowledge, this is the first experimental study of undular bores in a circular channel. For a setup without barriers, this geometry accomplishes in a natural way the periodic lateral boundary conditions, which is very often used in numerical simulations. The experimental results have been compared with the nonlinear numeric simulations and achieved an excellent agreement.
Resonance phenomena are ubiquitous in Nature. Resonance means that a system can accumulate large amounts of kinetic energy. In rotating flows inertial waves provide a mechanism for resonance by redistributing momentum, kinetic energy and helicity.
In order to investigate inertial waves a Taylor-Couette system was investigated which consists of a homogeneous liquid confined between two coaxial cylinders and two rigid lids. The inner cylinder is slightly conical (frustum) to break the vertical mirror symmetry. Inertial waves were excited by two different forcing configurations: the frustum in libration and the lids together with the outer cylinder in libration. Libration means that the rotation rate of the wall is modulated with a fixed amplitude and frequency of the order of the mean rotation rate. Direct numerical simulations (DNS) were conducted with a numerical solver in terrain-following coordinates.
DNS results reveal that inertial wave excitation is localised at the edges of the confinement, which is in very good agreement with recent laboratory measurements of Seelig (2014, PhD thesis, BTU Cottbus - Senftenberg). A model of the wave excitation mechanism was developed with the aid of boundary layer theory. The model suggests that a difference in the boundary layer mass flux (Ekman flux) excites the waves by driving an excess Ekman pumping velocity at the edges. The DNS results exhibit this flux difference, and the simulated kinetic energy spectra of the waves exhibit the frequency dependency predicted by the model.
However, DNS results also exhibit helical vortices at the edges which are not part of the model. Conservation properties suggest that these vortices are merely a compensating phenomenon which tends to stabilise the boundary layer flow. The details of this flow, however, appear less important for the wave excitation.
Response spectra of the kinetic energy, the dissipation rate, the helicity, and the quality factor were computed in order to assess resonance conditions. Simulated resonance peaks have a width of only 1/20th of the mean rotation rate. At these peaks, the kinetic energy was found to increase by a factor 10-50 even though viscous forces were still rather large (Ekman number of the order 1/100,000 with the length scale given by the mean radial gap width).
The flow patterns found at those resonances were investigated and found to be in very good agreement with the spatial patterns obtained by laboratory measurements and geometric ray tracing. The DNS results suggest that there are two types of resonance in rotating flows: modes and wave attractors. In contrast to a mode, a wave attractor exhibits net focusing of wave energy and occupies a finite frequency band. DNS results show that the wave attractor resonance frequency adjusts within the frequency band which suggests that wave attractor resonances complement 'classical' mode resonances and may, thus, be relevant in various applications.
Fortschrittliche Braunkohlenverbrennungstechniken für die dezentrale Energieversorgung gehören zu den Forschungszielen an der BTU Cottbus (Brandenburgischen Technischen Universität Cottbus) und am ERI (Energieressourcen-Institut). Ein Schwerpunkt dabei ist die Entwicklung eines neuen Verbrennungssystems – der Zykloidfeuerung. Begleitend hierzu wurden mit der vorliegenden Arbeit erstmals grundlegende Untersuchungen zur Strömungsdynamik in der Brennkammer durchgeführt und ein numerisches Modell der isothermen Brennkammerströmung aufgestellt. Da eine messtechnische Erfassung des heißen, partikelbeladenen Strömungsfeldes in der Zykloidfeuerung nicht möglich war, wurde dieses modelliert und ein isothermes Brennkammermodell errichtet. Für die Strömungsmessungen wurde ein Heißfilmanemometer eingesetzt und zur numerischen Simulation kam das kommerzielle Programm FLUENT zur Anwendung. Im Brennkammermodell wurde ein dreidimensionales, stark verdralltes Strömungsfeld durch die Messungen ermittelt, welches die Simulationsergebnisse gut wiederspiegeln. Durch die Verbindung messtechnischer Untersuchungen und numerischer Simulationen konnte das isotherme Strömungsfeld vollständig dargestellt und Abhängigkeiten herausgearbeitet werden. Es liegen damit umfangreiche, grundlegende Erkenntnisse zum Strömungsverhalten im Brennkammermodell und dessen Abhängigkeiten vor. Diese sind grundsätzlich auf isotherme Strömungsverhältnisse in der realen Zykloidbrennkammer anwendbar.