Large-scale flow structures in turbulent Rayleigh-Bénard convection: dynamical origin, formation, and role in material transport. - Ilmenau : Universitätsbibliothek, 2023. - 1 Online-Ressource (xiv, 134 Seiten)
Technische Universität Ilmenau, Dissertation 2023
Thermische Konvektion ist der essentielle Mechanismus durch welchen Wärme in vielen natürlichen Strömungen übertragen wird und weist zugleich oftmals eine Hierarchie von verschiedenen Strömungsstrukturen auf. Jedes Umfeld kann dabei über seine eigenen charakteristischen Randbedingungen verfügen, wobei die solare Konvektionszone das wohl bekannteste Beispiel mit ausgeprägter Strukturhierarchie repräsentiert. Die Entstehung Letzterer und die Rolle der involvierten Strömungsmuster bzgl. des materiellen Transports stellen wichtige offene Fragen der Wissenschaft dar. Die vorliegende Arbeit (1) erweitert unser Verständnis von der Beeinflussung großskaliger Strömungsstrukturen durch verschiedene Randbedingungen und (2) untersucht diese Muster aus der Perspektive materiellen Transports. Zu diesem Zweck wird Rayleigh-Bénard Konvektion - ein Paradigma natürlicher thermischer Konvektion - mittels direkter numerischer Simulationen untersucht. Das erste wesentliche Ergebnis wird durch eine explorative Studie verschiedener idealisierter mechanischer und thermischer Randbedingungen erreicht. Es wird gezeigt, dass Letztere die Natur der großskaligen Strömungsstrukturen fundamental bestimmen. Wird eine konstante Wärmestromdichte aufgeprägt, so kann eine allmähliche Aggregation kleinerer Konvektionszellen zu einer die gesamte Domäne füllenden Konvektionsstruktur - welche in Analogie zur astrophysikalischen Motivation als Supergranule bezeichnet wird - für alle zugänglichen Rayleigh- und Prandtl-Zahlen beobachtet werden. Es wird zudem gezeigt, dass schwache Rotation um die vertikale Achse imstande ist, den Aggregationsprozess zu beschränken. Der dynamische Ursprung und die Formierung der Supergranulen werden im Kontext von Instabilitäten und spektralen Kaskaden analysiert. Das zweite wesentliche Ergebnis wird durch die Analyse der Entwicklung von masselosen Lagrange'schen Partikeln im klassischen, durch konstante Temperaturen angetriebenen Szenario erzielt. Unüberwachtes maschinelles Lernen wird dazu benutzt, kohärente Regionen zu identifizieren, welche anschließend mit den großskaligen Strömungsstrukturen in Verbindung gebracht und bzgl. ihres Wärmetransportes in verschiedenen Fluiden analysiert werden. Abschließend wird eine neue evolutionäre Clustering-Methode entwickelt, welche künftig auf die Supergranulenaggregation angewendet werden kann. Diese Arbeit beschreibt einen neuen Mechanismus der Selbstorganisation von Strömungen und erweitert damit unser Verständnis großskaliger Strömungsstrukturen thermischer Konvektion. Die Einfachheit des untersuchten dynamischen Systems erlaubt eine Übertragung auf verschiedenste natürliche Strömungen sowie deren erfolgreichere Interpretation.
https://doi.org/10.22032/dbt.58334
Spatial prediction of the turbulent unsteady von Kármán vortex street using echo state networks. - In: Physics of fluids, ISSN 1089-7666, Bd. 35 (2023), 11, 115141, S. 115141-1-115141-15
The spatial prediction of the turbulent flow of the unsteady von Kármán vortex street behind a cylinder at Re = 1000 is studied. For this, an echo state network (ESN) with 6000 neurons was trained on the raw, low-spatial resolution data from particle image velocimetry. During prediction, the ESN is provided one half of the spatial domain of the fluid flow. The task is to infer the missing other half. Four different decompositions termed forward, backward, forward-backward, and vertical were examined to show whether there exists a favorable region of the flow for which the ESN performs best. Also, it was checked whether the flow direction has an influence on the network's performance. In order to measure the quality of the predictions, we choose the vertical velocity prediction of direction (VVPD). Furthermore, the ESN's two main hyperparameters, leaking rate (LR) and spectral radius (SR), were optimized according to the VVPD values of the corresponding network output. Moreover, each hyperparameter combination was run for 24 random reservoir realizations. Our results show that VVPD values are highest for LR ≈ 0.6, and quite independent of SR values for all four prediction approaches. Furthermore, maximum VVPD values of ≈ 0.83 were achieved for backward, forward-backward, and vertical predictions while for the forward case VVPDmax = 0.74 was achieved. We found that the predicted vertical velocity fields predominantly align with their respective ground truth. The best overall accordance was found for backward and forward-backward scenarios. In summary, we conclude that the stable quality of the reconstructed fields over a long period of time, along with the simplicity of the machine learning algorithm (ESN), which relied on coarse experimental data only, demonstrates the viability of spatial prediction as a suitable method for machine learning application in turbulence.
https://doi.org/10.1063/5.0172722
Reduced-order modeling of two-dimensional turbulent Rayleigh-Bénard flow by hybrid quantum-classical reservoir computing. - In: Physical review research, ISSN 2643-1564, Bd. 5 (2023), 4, 043242, S. 043242-1-043242-13
Two hybrid quantum-classical reservoir computing models are presented to reproduce the low-order statistical properties of a two-dimensional turbulent Rayleigh-Bénard convection flow at a Rayleigh number Ra=105 and Prandtl number Pr=10. These properties comprise the mean vertical profiles of the root mean square velocity and temperature and the turbulent convective heat flux. The latter is composed of vertical velocity and temperature and measures the global turbulent heat transfer across the convection layer; it manifests locally in coherent hot and cold thermal plumes that rise from the bottom and fall from the top boundaries. Both quantum algorithms differ by the arrangement of the circuit layers of the quantum reservoir, in particular the entanglement layers. The second of the two quantum circuit architectures, denoted H2, enables a complete execution of the reservoir update inside the quantum circuit without the usage of external memory. Their performance is compared with that of a classical reservoir computing model. Therefore, all three models have to learn the nonlinear and chaotic dynamics of the turbulent flow at hand in a lower-dimensional latent data space which is spanned by the time-dependent expansion coefficients of the 16 most energetic proper orthogonal decomposition (POD) modes. These training data are generated by a POD snapshot analysis from direct numerical simulations of the original turbulent flow. All reservoir computing models are operated in the reconstruction or open-loop mode, i.e., they receive three POD modes as an input at each step and reconstruct the 13 missing modes. We analyze different measures of the reconstruction error in dependence on the hyperparameters which are specific for the quantum cases or shared with the classical counterpart, such as the reservoir size and the leaking rate. We show that both quantum algorithms are able to reconstruct the essential statistical properties of the turbulent convection flow successfully with similar performance compared with the classical reservoir network. Most importantly, the quantum reservoirs are by a factor of four to eight smaller in comparison with the classical case.
https://doi.org/10.1103/PhysRevResearch.5.043242
Strongly superadiabatic and stratified limits of compressible convection. - In: Physical review fluids, ISSN 2469-990X, Bd. 8 (2023), 10, 103505, S. 103505-1-103505-19
Fully compressible turbulent convection beyond the Oberbeck-Boussinesq limit and anelastic regime is studied in three-dimensional numerical simulations. Superadiabaticity ε and dissipation number D, which measures the strength of stratification of adiabatic equilibria, cause two limits of compressible convection - nearly top-down-symmetric, strongly superadiabatic convection and highly top-down-asymmetric, strongly stratified convection. The highest turbulent Mach numbers Mt follow for a symmetric blend of these two limits, which we term the fully compressible case. Particularly, the strongly stratified convection case leads to a fluctuation-reduced top layer in the convection zone, a strongly reduced global heat transfer, and differing boundary layer dynamics between top and bottom. We detect this asymmetry for growing dissipation number D also in the phase plane, which is spanned by the turbulent Mach number Mt and the dilatation parameter δ, which relates the dilatational velocity fluctuations to the solenoidal ones. A detailed analysis of the different transport currents in the fully compressible energy budget relates the low-D convection cases to the standard definition of the dimensionless Nusselt number in the Oberbeck-Boussinesq limit.
https://doi.org/10.1103/PhysRevFluids.8.103505
Compressible turbulent convection in highly stratified adiabatic background. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 972 (2023), R4, S. $pR4-1-R4-12
Buoyancy-driven turbulent convection leads to a fully compressible flow with a prominent top-down asymmetry of first- and second-order statistics when the adiabatic equilibrium profiles of temperature, density and pressure change very strongly across the convection layer. The growth of this asymmetry and the formation of an increasingly thicker stabilized sublayer with a slightly negative mean convective heat flux Jc(z) at the top of the convection zone is reported here by a series of highly resolved three-dimensional direct numerical simulations beyond the Oberbeck–Boussinesq and anelastic limits for dimensionless dissipation numbers, 0.1 ≤ D ≤ 0.8, at fixed Rayleigh number Ra = 10^6 and superadiabaticity ϵ = 0.1. The highly stratified compressible convection regime appears for D > Dcrit ≈ 0.65, when density fluctuations collapse to those of pressure; it is characterized by an up to nearly 50 % reduced global turbulent heat transfer and a sparse network of focused thin and sheet-like thermal plumes falling through the top sublayer deep into the bulk.
https://doi.org/10.1017/jfm.2023.724
Assessing non-Oberbeck-Boussinesq effects of convection in cryogenic helium. - In: Physical review fluids, ISSN 2469-990X, Bd. 8 (2023), 9, 094606, S. 094606-1-094606-18
The present study investigates the non-Oberbeck-Boussinesq (NOB) effects which arise due to the temperature dependence of material properties in cryogenic helium experiments of turbulent Rayleigh-Bénard convection. Here we quantify these effects solely by the difference of the measured mean temperature at the center of the closed cell, Tc, from the arithmetic mean temperature obtained from the prescribed fixed and uniform temperatures at the top and bottom copper plates of the apparatus, Tm = (Tbot + Ttop) /2. To this end, the material properties such as specific heat at constant pressure, dynamic viscosity, thermal conductivity, the isobaric expansivity, and the mass density are expanded into power series with respect to temperature up to the quadratic order with coefficients obtained from the software package HEPAK. A subsequent nonlinear regression that uses deep convolutional networks delivers a dependence of the strength of non-Oberbeck-Boussinesq effects in the pressure-temperature parameter plane. Strength of the NOB effects is evaluated via the deviation of the mean temperature profile ξNOB ≡ Tm − Tc from the top-bottom-symmetric Oberbeck-Boussinesq case ξNOB = 0. Training data for the regression task are obtained from 236 individual long-term laboratory measurements at different Rayleigh numbers which span eight orders of magnitude.
https://doi.org/10.1103/PhysRevFluids.8.094606
Simulation of magnetohydrodynamic flows of liquid metals with heat transfer or magnetic stirring. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 23 (2023), 3, e202300153, S. 1-8
We discuss the effects of nonhomogeneous magnetic fields in liquid metal flows in two different configurations. In the first configuration, we briefly report the impact of fringing magnetic fields in a turbulent Rayleigh-Bénard convection setup, where it was shown that the global heat transport decreases with an increase of fringe-width. The convective motion in regions of strong magnetic fields is confined near the sidewalls. In the second configuration, we numerically study the effects of an oscillating magnetic obstacle with different frequencies of oscillation on liquid metal flow in a duct. The Reynolds number is low such that the wake of the stationary magnetic obstacle is steady. The transverse oscillation of the magnet creates a sinusoidal time-dependent wake reminiscent of the vortex shedding behind solid obstacles. We examine the behavior of the streamwise and spanwise components of the Lorentz forces as well as the work done by the magnets on the fluid. The frequency of the oscillation of the streamwise component of Lorentz force is twice that of the spanwise component as in the case of lift and drag on solid cylindrical obstacles. The total drag force and the energy transferred from the magnets to the fluid show a nonmonotonic dependence on the frequency of oscillation of the magnetic obstacle indicative of a resonant excitation of the sinusoidal vortex shedding.
https://doi.org/10.1002/pamm.202300153
Stability analysis of wall-attached Bénard-Marangoni convection in a vertical magnetic field. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 23 (2023), 2, e202300020, S. 1-8
The threshold for the onset of thermocapillary flow in a planar liquid layer heated from below is increased by a vertical magnetic field when the liquid is a good electric conductor. The magnetic damping effect is reduced when the induced eddy currents are blocked by insulating side walls. Neutral conditions for this specific Bénard-Marangoni stability problem with a vertical field and side walls are obtained numerically for three-dimensional perturbations assumed periodic in one horizontal direction. The domain is bounded by a free-slip wall at the bottom, a free surface at the top and two free-slip lateral walls in the other horizontal direction. Buoyancy forces and surface deformations are neglected and a constant heat flux is imposed on the free surface. Upon increasing the magnetic induction, the least stable modes become localized near the side walls and the convective threshold increases at a lower rate than for the least stable bulk mode.
https://doi.org/10.1002/pamm.202300020
Thermal boundary condition studies in large aspect ratio Rayleigh-Bénard convection. - In: European journal of mechanics, ISSN 1873-7390, Bd. 101 (2023), S. 283-293
We study the influence of thermal boundary conditions on large aspect ratio Rayleigh-Bénard convection by a joint analysis of experimental and numerical data sets for a Prandtl number Pr=7 and Rayleigh numbers Ra=105−106. The spatio-temporal experimental data are obtained by combined Particle Image Velocimetry and Particle Image Thermometry measurements in a cuboid cell filled with water at an aspect ratio Γ=25. In addition, numerical data are generated by Direct Numerical Simulations (DNS) in domains with Γ=25 and Γ=60 subject to different idealized thermal boundary conditions. Our experimental data show an increased characteristic horizontal extension scale ÜÞλ of the flow structures for increasing Ra , which due to an increase of the convective heat transfer also leads to an increase of the Biot number (Bi) at the cooling plate. However, we find the experimental flow structure size to range in any case in between the ones observed for the idealized thermal boundary conditions captured by the simulations: On the one hand, they are larger than in the numerical case with applied uniform temperatures at the plates. On the other hand, they are smaller than in the case of an applied constant heat flux, the latter of which leads to a structure that grows gradually up to the horizontal domain size. We are able to link this observation qualitatively to theoretical predictions for the onset of convection. Furthermore, we study the effect of the asymmetric boundary conditions on the heat transfer. Contrasting experimental and numerical data reveals an increased probability of far-tail events of reversed heat transfer. The successive decomposition of the local Nusselt number Nuloc traces this effect back to the sign of the temperature deviation ÜÞΘ, eventually revealing asymmetries of the heating and cooling plate on the thermal variance of the generated thermal plumes.
https://doi.org/10.1016/j.euromechflu.2023.06.003
Collective variables between large-scale states in turbulent convection. - In: Physical review research, ISSN 2643-1564, Bd. 5 (2023), 3, S. 033061-1-033061-19
The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states that are visited subsequently by the system in a Markov-type hopping process. In the present work, we analyze the short transition paths between these subsequent macroscopic system states by a data-driven learning algorithm that extracts the low-dimensional transition manifold and the related new coordinates, which we term collective variables, in the state space of the complex turbulent flow. We therefore transfer and extend concepts for conformation transitions in stochastic microscopic systems, such as in the dynamics of macromolecules, to a deterministic macroscopic flow. Our analysis is based on long-term direct numerical simulation trajectories of turbulent convection in a closed cubic cell at a Prandtl number Pr=0.7 and Rayleigh numbers Ra=10^6 and 10^7 for a time lag of 10^5 convective free-fall time units. The simulations resolve vortices and plumes of all physically relevant scales, resulting in a state space spanned by more than 3.5 million degrees of freedom. The transition dynamics between the large-scale circulation states can be captured by the transition manifold analysis with only two collective variables, which implies a reduction of the data dimension by a factor of more than a million. Our method demonstrates that cessations and subsequent reversals of the large-scale flow are unlikely in the present setup, and thus it paves the way for the development of efficient reduced-order models of the macroscopic complex nonlinear dynamical system.
https://doi.org/10.1103/PhysRevResearch.5.033061