Energy stability of magnetohydrodynamic flow in channels and ducts. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 987 (2024), A33
We study the energy stability of pressure-driven laminar magnetohydrodynamic flow in a rectangular duct with a transverse homogeneous magnetic field and electrically insulating walls. For sufficiently strong fields, the laminar velocity distribution has a uniform core and convex Hartmann and Shercliff boundary layers on the walls perpendicular and parallel to the magnetic field. The problem is discretized by a double expansion in Chebyshev polynomials in the cross-stream coordinates. The linear eigenvalue problem for the critical Reynolds number depends on the streamwise wavenumber, Hartmann number and the aspect ratio. We consider the limits of small and large aspect ratios in order to compare with stability models based on one-dimensional base flows. For large aspect ratios, we find good numerical agreement with results based on the quasi-two-dimensional approximation. The lift-up mechanism dominates in the limit of a zero streamwise wavenumber and provides a linear dependence between the critical Reynolds and Hartmann numbers in the duct. As the aspect ratio is reduced away from unity, the duct results converge to Orr's original energy stability result for spanwise uniform perturbations imposed on the plane Poiseuille base flow. We also examine different possible symmetries of eigenmodes as well as the purely hydrodynamic case in the duct geometry.
https://doi.org/10.1017/jfm.2024.393
Reduced order modeling of thermal convection flows: a reservoir computing approach. - Ilmenau, 2024. - 1 Online-Ressource (xx, 164 Seiten)
Technische Universität Ilmenau, Dissertation 2024
In dieser Arbeit wird das Potenzial von Machine-Learning-Algorithmen (ML) zur Verbesserung der Parametrisierung von großskaligen atmosphärischen Simulationen untersucht. Herkömmliche Ansätze verwenden oft Vereinfachungen oder rechenintensive Methoden. Diese Arbeit beabsichtigt, einen physikalisch konsistenten und rechnerisch effizienten Ansatz einzuführen, der Reservoir Computing (RC) und Datenkompression nutzt, um subgitter-skalige Merkmale aus direkten numerischen Simulationen (DNS) der thermischen Konvektion zu extrahieren. Hierbei wird der hochaufgelöste Simulationsdatensatz zuerst durch Proper Orthogonal Decomposition (POD) oder ein Autoencoder-Netzwerk (AE) vorverarbeitet, um die Datenmenge zu reduzieren. Anschließend wird ein RC-Modell auf diesem reduzierten Datenraum trainiert, um zukünftige Strömungszustände ohne die Lösung der nichtlinearen Bewegungsgleichungen vorherzusagen. Die Vorhersagen des kombinierten POD-RC-Modells werden anhand der Originalsimulationen validiert. Das Modell reproduziert die strukturellen und statistischen Merkmale von trockenen und feuchten Konvektionsströmungen und eröffnet somit neue Wege für die dynamische Parametrisierung des subgrid-skaligen Transports in grob aufgelösten Zirkulationsmodellen. Des Weiteren untersucht die Studie die Verallgemeinerungseigenschaften eines AE-RC-Modells basierend auf einem wärmeflussgetriebenen zweidimensionalen turbulenten Konvektionssystem. Dabei zeigt sich, dass das AE-RC-Modell die räumliche Struktur und statistischen Eigenschaften der ungesehenen physikalischen Felder korrekt wiedergibt. Schließlich liegt der Fokus auf der Parametrisierung der konvektiven Grenzschicht (CBL) mithilfe eines Generative Adversarial Networks (GAN), das auf hochaufgelösten DNS-Daten einer dreidimensionalen CBL trainiert wird. Es wird gezeigt, dass die Methode durch eine physikalisch informierte Reskalierung der begrenzten Trainingsdaten in der Lage ist, das CBL-Wachstum und die damit verbundene Musterbildung zu reproduzieren. Die GAN-Ergebnisse stimmen mit Standard Mass-Flux Parametrisierungen überein und liefern zusätzlich die horizontale Anordnung der turbulenten Strömung, die mit dem Mass-Flux-Ansatz nicht erreicht werden kann. Obwohl die Implementierung von ML-basierten Parametrisierungsschemata in großskaligen Modellen nicht im Fokus steht, trägt diese Arbeit dazu bei, unser Verständnis des Potenzials und der Grenzen dieser Modelle im Kontext der Klimamodellierung und numerischen Wettervorhersage zu vertiefen.
https://doi.org/10.22032/dbt.59964
Connecting finite-time Lyapunov exponents with supersaturation and droplet dynamics in a turbulent bulk flow. - In: Physical review, ISSN 2470-0053, Bd. 109 (2024), 4, 045101
The impact of turbulent mixing on an ensemble of initially monodisperse water droplets is studied in a turbulent bulk that serves as a simplified setup for the interior of a turbulent ice-free cloud. A mixing model was implemented that summarizes the balance equations of water vapor mixing ratio and temperature to an effective advection-diffusion equation for the supersaturation field s(x,t). Our three-dimensional direct numerical simulations connect the velocity and scalar supersaturation fields in the Eulerian frame of reference to an ensemble of cloud droplets in the Lagrangian frame of reference. The droplets are modeled as point particles with and without effects due to inertia. The droplet radius is subject to growth by vapor diffusion. We report the dependence of the droplet size distribution on the box size, initial droplet radius, and the strength of the updraft, with and without gravitational settling. In addition, the three finite-time Lyapunov exponents λ1 ≥ λ2 ≥ λ3 are monitored which probe the local stretching properties along the particle tracks. In this way, we can relate regions of higher compressive strain to those of high local supersaturation amplitudes. For the present parameter range, the mixing process in terms of the droplet evaporation is always homogeneous, while it is inhomogeneous with respect to the relaxation of the supersaturation field. The probability density function of the third finite-time Lyapunov exponent, λ3 < 0, is related to the one of the supersaturation s by a simple one-dimensional aggregation model. The probability density function (PDF) of λ3 and the droplet radius r are found to be Gaussian, while the PDF of the supersaturation field shows sub-Gaussian tails.
https://doi.org/10.1103/PhysRevE.109.045101
Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh-Bénard convection. - In: European journal of mechanics, ISSN 1873-7390, Bd. 103 (2024), S. 69-85
We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh-Bénard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of time-dependent flow networks. These are based on trajectories of Lagrangian tracer particles that are advected in the flow. We identify coherent sets in the Lagrangian frame of reference as those sets of trajectories that stay closely together for an extended time span under the action of the turbulent flow. Depending on the choice of the measure of coherence, sets with different characteristics are detected. First, the application of a recently proposed evolutionary spectral clustering scheme allows us to extract granular coherent features that are shown to contribute significantly less to the global heat transfer than their spatial complements. Moreover, splits and mergers of these (leaking) coherent sets leave spectral footprints. Second, trajectories which exhibit a small node degree in the corresponding network represent objectively highly coherent flow structures and can be related to supergranules as the other stage of the present flow hierarchy. We demonstrate that the supergranular flow structures play a key role in the vertical heat transport and that they exhibit a greater spatial extension than the granular structures obtained from spectral clustering.
https://doi.org/10.1016/j.euromechflu.2023.08.007
Supergranule aggregation: a Prandtl number-independent feature of constant heat flux-driven convection flows. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 980 (2024), A46, S. A46-1-A46-13
Supergranule aggregation, i.e. the gradual aggregation of convection cells to horizontally extended networks of flow structures, is a unique feature of constant heat flux-driven turbulent convection. In the present study, we address the question if this mechanism of self-organisation of the flow is present for any fluid. Therefore, we analyse three-dimensional Rayleigh-Bénard convection at a fixed Rayleigh number Ra ≈ 2.0 × 10^^ 5 across 4 orders of Prandtl numbers Pr ∈ [10^−2, 10^2] by means of direct numerical simulations in horizontally extended periodic domains with aspect ratio Γ = 60. Our study confirms the omnipresence of the mechanism of supergranule aggregation for the entire range of investigated fluids. Moreover, we analyse the effect of Pr on the global heat and momentum transport, and clarify the role of a potential stable stratification in the bulk of the fluid layer. The ubiquity of the investigated mechanism of flow self-organisation underlines its relevance for pattern formation in geophysical and astrophysical convection flows, the latter of which are often driven by prescribed heat fluxes.
https://doi.org/10.1017/jfm.2024.56
Non-intrusive, transferable model for coupled turbulent channel-porous media flow based upon neural networks. - In: Physics of fluids, ISSN 1089-7666, Bd. 36 (2024), 2, 025112, S. 025112-1-025112-13
Turbulent flow over permeable interfaces is omnipresent featuring complex flow topology. In this work, a data-driven, end-to-end machine learning model has been developed to model the turbulent flow in porous media. For the same, we have derived a non-linear reduced order model (ROM) with a deep convolution autoencoder. This model can reduce highly resolved spatial dimensions, which is a prerequisite for direct numerical simulation, by 99%. A downstream recurrent neural network has been trained to capture the temporal trend of reduced modes; thus, it is able to provide future evolution of modes. We further evaluate the trained model's capability on a newer dataset with a different porosity. In such cases, fine-tuning could reduce the efforts (up to two-order of magnitude) to train a model with limited dataset (10%) and knowledge and still show a good agreement on the mean velocity profile. Especially, the fine-tuned model shows a better agreement in the porous domain than the channel and interface areas indicating the topological feature is less challenging for training than the multi-scale nature of the turbulent flows. Leveraging the current model, we find that even quick fine-tuning achieves an impressive order-of-magnitude reduction in training time by approximately O(102) and still results in effective flow predictions. This promising discovery encourages the fast development of a substantial amount of data-driven models tailored for various types of porous media. The diminished training time substantially lowers the computational cost when dealing with changing porous topologies, making it feasible to systematically explore interface engineering with different types of porous media.
https://doi.org/10.1063/5.0189632
Wall-attached convection under strong inclined magnetic fields. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 979 (2024), A53, S. A53-1-A53-27
We employ a linear stability analysis and direct numerical simulations to study the characteristics of wall modes in thermal convection in a rectangular box under strong and inclined magnetic fields. The walls of the convection cell are electrically insulated. The stability analysis assumes periodicity in the spanwise direction perpendicular to the plane of a homogeneous magnetic field. Our study shows that for a fixed vertical magnetic field, the imposition of horizontal magnetic fields results in an increase of the critical Rayleigh number along with a decrease in the wavelength of the wall modes. The wall modes become tilted along the direction of the resulting magnetic fields and therefore extend further into the bulk as the horizontal magnetic field is increased. Once the modes localized on the opposite walls interact, the critical Rayleigh number decreases again and eventually drops below the value for onset with a purely vertical field. We find that for sufficiently strong horizontal magnetic fields, the steady wall modes occupy the entire bulk and therefore convection is no longer restricted to the sidewalls. The aforementioned results are confirmed by direct numerical simulations of the nonlinear evolution of magnetoconvection. The direct numerical simulation results also reveal that at least for large values of horizontal magnetic field, the wall-mode structures and the resulting heat transfer are dependent on the initial conditions.
https://doi.org/10.1017/jfm.2023.1087
Synchronising the Rayleigh-Bénard instability in a liquid metal flow using electromagnetic forces. - Ilmenau : Universitätsbibliothek, 2023. - 1 Online-Ressource (xiii, 125 Seiten)
Technische Universität Ilmenau, Dissertation 2023
Wie tickt die Sonne? Warum hat sie einen Elfjahresyzklus? Die Theorie des solaren Dynamos hat sich seit ihren Anfängen im frühen neunzehnten Jahrhundert weit entwickelt. Aber auch heute ist noch nicht vollends verstanden, wie das solare Magnetfeld entsteht. Die Qualität wissenschaftlicher Theorien wird dabei oft an ihrer Fähigkeit gemessen, das regelmäßige Kommen und Gehen der Sonnenflecken zu reproduzieren. Diese aktiven Regionen auf der Sonnenoberfläche sind ihrerseits ein Ausdruck der internen magnetischen Prozesse. Was aber, wenn der Sonnenzyklus tatsächlich von außen getaktet würde? Bereits im neunzehnten Jahrhundert war bekannt, dass eine bemerkenswerte Übereinstimmung von Sonnenfleckenzahlen und dem Rhythmus der am stärksten gezeitenwirksamen Planeten existiert. Dennoch schien ein kausaler Zusammenhang aufgrund der geringen Größe der Gezeitenkräfte immer unmöglich. Um dieses Rätsel zu ergründen wurde in den letzten Jahren ein möglicher Interaktionsmechanismus entwickelt. Er beruht auf periodischen Helizitätsschwankungen einer nicht achsensymmetrischen Instabilität, die durch schwache Gezeitenkräfte synchronisiert wird. Gegenstand dieser Arbeit ist es, fundamentale Aspekte dieses Mechanismus experimentell zu untersuchen. Der erste Teil der Arbeit behandelt die Frage, ob es experimentell möglich ist, mittels elektromagnetischen Kräften gezeitenähnliche Strömungen in einem Zylinder mit Flüssigmetall zu erzeugen. Wie sich herausstellt ist es tatsächlich möglich, ein gut definiertes, quasi-zweidimensionales Strömungsmuster zu erzeugen. In Kombination mit numerischen Daten, welche parallel am Institut erarbeitet wurden, konnte das Verhalten der Strömung charakterisiert werden. Im zweiten Teil der Arbeit werden die elektromagnetischen Kräfte periodisch und mit unterschiedlicher Frequenz und Stärke auf eine Rayleigh-Bénard Strömung im Zylinder appliziert. Diese Strömung kann so eingestellt werden, dass sie mit ihren natürlichen Helizitätsschwingungen ein gutes Modell für den interessierenden Prozess darstellt. Beim Anlegen der gezeitenähnlichen Kräfte zeichnet sich eine starke Interaktion mit der Rayleigh-Bénard Strömung ab. Dieser Zustand wurde mit einer Vielzahl von Analysetechniken untersucht, um die zugrundeliegenden Prozesse zu verstehen. Mit den gewonnenen Erkenntnissen wurde ein theoretisches Modell entwickelt, um die erhaltenen Strömungsmuster zu erklären. Es möge zu einem besseren Verständnis dieser Strömungen im Allgemeinen und des Solardynamo-Prozesses im Besonderen beitragen.
https://doi.org/10.22032/dbt.59530
Formation of the inlet flow profile for passive control of a magnetohydrodynamic liquid-metal flow in a channel. - In: High temperature, ISSN 1608-3156, Bd. 61 (2023), 3, S. 417-428
The paper describes an experimental attempt to affect the flow of liquid metal using a relatively small perturbation at an inlet to a long channel. The purpose is to form a flow structure which is stable in a strong magnetic field at high heat loads, enhance heat transfer, and achieve more predictable flow parameters. It is demonstrated that an obstacle in the form of a rod located transverse to the flow and parallel to the applied magnetic field and installed at the inlet can induce perturbations in the form of regular vortices observed along the flow at lengths as great as several tens of channel hydraulic diameters. The experiments confirm that thus generated vortices considerably change the structure of the isothermal MHD flow. In the case of mixed convection, such vortices suppress the development large-scale thermogravitational fluctuations in the flow and enhance heat transfer under certain flow conditions.
https://doi.org/10.1134/S0018151X23030033
Exploring the ultimate regime of turbulent Rayleigh-Bénard Convection through unprecedented spectral-element simulations. - In: SC '23: proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, (2023), 5, S. 1-9
We detail our developments in the high-fidelity spectral-element code Neko that are essential for unprecedented large-scale direct numerical simulations of fully developed turbulence. Major innovations are modular multi-backend design enabling performance portability across a wide range of GPUs and CPUs, a GPU-optimized preconditioner with task overlapping for the pressure-Poisson equation and in-situ data compression. We carry out initial runs of Rayleigh-Bénard Convection (RBC) at extreme scale on the LUMI and Leonardo supercomputers. We show how Neko is able to strongly scale to 16,384 GPUs and obtain results that are not possible without careful consideration and optimization of the entire simulation workflow. These developments in Neko will help resolving the long-standing question regarding the ultimate regime in RBC.
https://doi.org/10.1145/3581784.3627039