Interplay between advective, diffusive and active barriers in (rotating) Rayleigh–Bénard flow

Our understanding of the material organization of complex fluid flows has benefited recently from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify transport barriers in three-dimensional (3-D) turbulent flows. Specifically, theoretical advances have been incorporated into numerical algorithms that extract the most influential advective, diffusive and active barriers to transport from data sets in a frame-indifferent fashion. To date, however, there has been very limited investigation into these objectively defined transport barriers in 3-D unsteady flows with complicated spatiotemporal dynamics. Similarly, no systematic comparison of advective, diffusive and active barriers has been carried out in a 3-D flow with both thermally driven and mechanically modified structures. In our study, we utilize simulations of turbulent rotating Rayleigh–Bénard convection to uncover the interplay between advective transport barriers (Lagrangian coherent structures), material barriers to diffusive heat transport, and objective Eulerian barriers to momentum transport. For a range of (inverse) Rossby numbers, we identify each type of barrier and find intriguing relationships between momentum and heat transport that can be related to changes in the relative influence of mechanical and thermal forces. Further connections between bulk behaviours and structure-specific behaviours are also developed

Dynamics of Coherent Structures in Turbulent Rayleigh-Bénard Convection by Lagrangian Particle Tracking of Long-Lived Helium Filled Soap Bubbles

We present spatially and temporally resolved velocity and acceleration measurements of turbulent Rayleigh-Bénard convection covering the complete volume of a cylindrical sample with aspect ratio one. Using the "Shake-The-Box" Lagrangian particle tracking algorithm, we were able to instantaneously track more than 500,000 particles in the complete sample volume (~ 1 m³), corresponding to mean inter-particle distances down to 5-8 Kolmogorov lengths. We used the data assimilation scheme "FlowFit" with continuity and Navier-Stokes-constraints to interpolate the scattered velocity and acceleration data via continuous 3D B-Splines on a cubic grid and to recover the smallest flow scales. The measurements were enabled by a dedicated bubble fluid solution, which we developed for generation of longlived helium filled soap bubbles, allowing for long-term optical flow measurements at large scales in gaseous fluids. We show Lagrangian and Eulerian visualizations of the large-scale circulation (LSC) as well as small scale structures, such as thermal plumes and turbulent background fluctuations and unveil the dynamics of their complex interplay. By employing principal component analysis in the rotating frame of the LSC, we are able to describe the characteristic dynamics of the LSC with the first three POD modes with an accuracy of 95% by using only 50% of the turbulent kinetic energy of the flow

Thermal Flows

Flows of thermal origin and heat transfer problems are central in a variety of disciplines and industrial applications. The present book entitled Thermal Flows consists of a collection of studies by distinct investigators and research groups dealing with different types of flows relevant to both natural and technological contexts. Both reviews of the state-of-the-art and new theoretical, numerical and experimental investigations are presented, which illustrate the structure of these flows, their stability behavior, and the possible bifurcations to different patterns of symmetry and/or spatiotemporal regimes. Moreover, different categories of fluids are considered (liquid metals, gases, common fluids such as water and silicone oils, organic and inorganic transparent liquids, and nanofluids). This information is presented under the hope that it will serve as a new important resource for physicists, engineers and advanced students interested in the physics of non-isothermal fluid systems; fluid mechanics; environmental phenomena; meteorology; geophysics; and thermal, mechanical and materials engineering

Ein Gas-Kinetic Scheme Ansatz zur Modellierung und Simulation von Feuer auf massiv paralleler Hardware

This work presents a simulation approach based on a Gas Kinetic Scheme (GKS) for the simulation of fire that is implemented on massively parallel hardware in terms of Graphics Processing Units (GPU) in the framework of General Purpose computing on Graphics Processing Units (GPGPU). Gas kinetic schemes belong to the class of kinetic methods because their governing equation is the mesoscopic Boltzmann equation, rather than the macroscopic Navier-Stokes equations. Formally, kinetic methods have the advantage of a linear advection term which simplifies discretization. GKS inherently contains the full energy equation which is required for compressible flows. GKS provides a flux formulation derived from kinetic theory and is usually implemented as a finite volume method on cell-centered grids. In this work, we consider an implementation on nested Cartesian grids. To that end, a coupling algorithm for uniform grids with varying resolution was developed and is presented in this work. The limitation to local uniform Cartesian grids allows an efficient implementation on GPUs, which belong to the class of many core processors, i.e. massively parallel hardware. Multi-GPU support is also implemented and efficiency is enhanced by communication hiding. The fluid solver is validated for several two- and three-dimensional test cases including natural convection, turbulent natural convection and turbulent decay. It is subsequently applied to a study of boundary layer stability of natural convection in a cavity with differentially heated walls and large temperature differences. The fluid solver is further augmented by a simple combustion model for non-premixed flames. It is validated by comparison to experimental data for two different fire plumes. The results are further compared to the industry standard for fire simulation, i.e. the Fire Dynamics Simulator (FDS). While the accuracy of GKS appears slightly reduced as compared to FDS, a substantial speedup in terms of time to solution is found. Finally, GKS is applied to the simulation of a compartment fire. This work shows that the GKS has a large potential for efficient high performance fire simulations.Diese Arbeit präsentiert einen Simulationsansatz basierend auf einer gaskinetischen Methode (eng. Gas Kinetic Scheme, GKS) zur Simulation von Bränden, welcher für massiv parallel Hardware im Sinne von Grafikprozessoren (eng. Graphics Processing Units, GPUs) implementiert wurde. GKS gehört zur Klasse der kinetischen Methoden, die nicht die makroskopischen Navier-Stokes Gleichungen, sondern die mesoskopische Boltzmann Gleichung lösen. Formal haben kinetische Methoden den Vorteil, dass der Advektionsterms linear ist. Dies vereinfacht die Diskretisierung. In GKS ist die vollständige Energiegleichung, die zur Lösung kompressibler Strömungen benötigt wird, enthalten. GKS formuliert den Fluss von Erhaltungsgrößen basierend auf der gaskinetischen Theorie und wird meistens im Rahmen der Finiten Volumen Methode umgesetzt. In dieser Arbeit betrachten wir eine Implementierung auf gleichmäßigen Kartesischen Gittern. Dazu wurde ein Kopplungsalgorithmus für die Kombination von Gittern unterschiedlicher Auflösung entwickelt. Die Einschränkung auf lokal gleichmäßige Gitter erlaubt eine effiziente Implementierung auf GPUs, welche zur Klasse der massiv parallelen Hardware gehören. Des Weiteren umfasst die Implementierung eine Unterstützung für Multi-GPU mit versteckter Kommunikation. Der Strömungslöser ist für zwei und dreidimensionale Testfälle validiert. Dabei reichen die Tests von natürlicher Konvektion über turbulente Konvektion bis hin zu turbulentem Zerfall. Anschließend wird der Löser genutzt um die Grenzschichtstabilität in natürlicher Konvektion bei großen Temperaturunterschieden zu untersuchen. Darüber hinaus umfasst der Löser ein einfaches Verbrennungsmodell für Diffusionsflammen. Dieses wird durch Vergleich mit experimentellen Feuern validiert. Außerdem werden die Ergebnisse mit dem gängigen Brandsimulationsprogramm FDS (eng. Fire Dynamics Simulator) verglichen. Die Qualität der Ergebnisse ist dabei vergleichbar, allerdings ist der in dieser Arbeit entwickelte Löser deutlich schneller. Anschließend wird das GKS noch für die Simulation eines Raumbrandes angewendet. Diese Arbeit zeigt, dass GKS ein großes Potential für die Hochleistungssimulation von Feuer hat

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Thermal Flows

Flows of thermal origin and heat transfer problems are central in a variety of disciplines and industrial applications. The present book entitled Thermal Flows consists of a collection of studies by distinct investigators and research groups dealing with different types of flows relevant to both natural and technological contexts. Both reviews of the state-of-the-art and new theoretical, numerical and experimental investigations are presented, which illustrate the structure of these flows, their stability behavior, and the possible bifurcations to different patterns of symmetry and/or spatiotemporal regimes. Moreover, different categories of fluids are considered (liquid metals, gases, common fluids such as water and silicone oils, organic and inorganic transparent liquids, and nano-fluids). This information is presented under the hope that it will serve as a new important resource for physicists, engineers and advanced students interested in the physics of non-isothermal fluid systems; fluid mechanics; environmental phenomena; meteorology; geophysics; and thermal, mechanical and materials engineering

Experimental characterization of turbulent superstructures in large aspect ratio Rayleigh-Bénard convection

Die Untersuchung von thermisch induzierten Strömungen hat in den letzten Jahrzehnten eine enorme Aufmerksamkeit erfahren, um geophysikalische und astrophysikalische Systeme besser verstehen zu können. Hierfür hat sich das sogenannte Rayleigh-Bénard Modell als eines der meist untersuchten fluidmechanischen Systeme etabliert, da es die kaum abzubildende Komplexität von natürlichen Systemen in ihrer Mannigfaltigkeit auf ein Fluidvolumen reduziert, welches von unten isotherm erwärmt und von oben isotherm gekühlt wird. Trotz dieser Reduzierung an Komplexität können mit diesem Modell die wesentlichen Eigenschaften von thermischer Konvektion abgebildet werden. Die Strömung in einem solchen System, welche als Rayleigh-Bénard Konvektion bekannt ist, weist Strömungsstrukturen auf unterschiedlichsten Längenskalen auf. In der vorliegenden Arbeit werden die sogenannten Superstrukturen untersucht. Diese sich in horizontaler Richtung weit erstreckenden Strukturen treten in Erscheinung, wenn die horizontale Dimension der Fluidschicht wesentlich größer als der vertikale Abstand zwischen der erwärmten Unterseite und der gekühlten Oberseite ist. Da die Superstrukturen bisher im Wesentlichen anhand von numerischen Simulationen untersucht wurden, soll in dieser Arbeit erstmals vom experimentellen Standpunkt ein besserer Eindruck gewonnen werden. Zur Untersuchung der Superstrukturen wird eine Rayleigh-Bénard Zelle mit den Abmessungen l × w × h = 700 mm × 700 mm × 28 mm und folglich mit einem Aspektverhältnis von Γ = l/h =25 aufgebaut. Bei allen Experimenten wird diese Zelle mit Wasser als Arbeitsmedium befüllt. Um die Rayleigh-Bénard Strömung zu untersuchen, werden thermochrome Flüssigkristalle als Impfpartikel der Strömung beigefügt, sodass simultane Messungen des Temperatur- und Geschwindigkeitsfeldes in horizontalen Ebenen der Zelle vorgenommen werden können. Während das Geschwindigkeitsfeld mittels der Bewegung der thermochromen Flüssigkristalle im zeitlichen Verlauf anhand der etablierten Partikelbild-Geschwindigkeitsmessung (Particle Image Velocimetry) bestimmt wird, basiert die Messung des Temperaturfelds auf der farblichen Erscheinung der thermochromen Flüssigkristalle, welche unter der Beleuchtung von Weißlicht temperaturabhängig ist. Im Hinblick auf die genaue Bestimmung der Temperatur wird diese Messtechnik umfänglich charakterisiert, wobei die wesentlichen Einflussfaktoren auf die Messunsicherheit diskutiert werden. Da die Untersuchung der turbulenten Superstrukturen mittels dieser Messtechnik den optischen Zugang zur flachen Rayleigh-Bénard Zelle erfordert, ist der Aufbau speziell konstruiert und ermöglicht die Beobachtung der Strömung durch eine transparente Kühlplatte. Der Entwicklungsprozess wird in der Arbeit aus ingenieurstechnischer Sicht genauestens erklärt. Bei der Auswertung der Messungen kommen die großskaligen Strukturen sowohl im Temperaturfeld als auch im Geschwindigkeitsfeld zum Vorschein. Die Größe der Superstrukturen wird untersucht in Abhängigkeit der Rayleigh-Zahl Ra, welche den thermischen Antrieb der Strömung beschreibt und in der vorliegenden Arbeit etwa im Bereich 2 × 10^5 ≤ Ra ≤ 2 × 10^6 variiert wird. Auf der Basis dieser Messungen, welche jeweils einen großen Zeitraum abdecken, wird das Langzeitverhalten der Superstrukturen analysiert, womit deren langsam voranschreitende Umstrukturierung gezeigt wird. Da die kombinierte Messung des Temperatur- und Geschwindigkeitsfeldes in den horizontalen Messebenen die Berechnung des lokalen Wärmestroms ermöglicht, wird diese Möglichkeit ebenfalls demonstriert. Um die experimentellen Ergebnisse dieser Arbeit bewerten zu können, werden jene mit den Resultaten aus numerischen Simulationen verglichen.Aiming at a better understanding of geophysical and astrophysical settings, the investigation of thermally driven fluid flows has attracted great attention in the last decades. In this context, the so-called Rayleigh-Bénard model has established as one of the most studied fluid-mechanical systems, since this reduces the hardly representable complexity of the natural environment with its enormous diversity to a fluid volume, which is uniformly heated from below and cooled from above. Despite this reduction of the complexity, this model is capable of representing the main characteristics of thermal convection. The flow in such a system, well-known as the Rayleigh-Bénard convection, exhibits flow structures on a large range of length scales. In this work, the so-called turbulent superstructures are studied. These horizontally stretched structures, which appear when the fluid layer has a much larger horizontal extent compared to the vertical distance between the hot and cold boundary, have mainly been investigated with numerical simulations so far. Therefore, the aim of the present work is to get a better impression of the turbulent superstructures from the experimental point of view for the first time. For the investigation of the superstructures a Rayleigh-Bénard cell with dimensions of l × w × h = 700 mm × 700 mm × 28 mm, thus having an aspect ratio of Γ = l/h =25, is set up. Here, water is used as the working fluid in the cell for all the experiments. In order to analyze the Rayleigh-Bénard flow, thermochromic liquid crystals are applied as tracer particles in the flow, which allows to perform simultaneous measurements of the temperature and velocity field in horizontal planes of the cell. While the velocity field is measured via the temporal displacement of the thermochromic liquid crystals using the established Particle Image Velocimetry, the temperature field is determined by evaluating their color shade, which depends on the temperature upon illumination with white light. With regard to the accurate determination of the temperature, this measuring technique is extensively characterized and the main influencing factors on the measurement uncertainty are discussed. Since the investigation of the turbulent superstructures with this optical measuring technique requires optical access to the flat Rayleigh-Bénard cell, the setup is specially designed and allows to observe the flow through a transparent cooling plate. The design process from the engineering point of view is thoroughly explained. In the evaluation of the measurements the large-scale structures are uncovered in both the temperature and the velocity field. The size of the turbulent superstructures is investigated in dependency of the Rayleigh number Ra, which characterizes the thermal driving force of the flow and is here approximately varied in the range 2 × 10^5 ≤ Ra ≤ 2 × 10^6. On the basis of the measurements conducted over extended time intervals, the long-term behavior of the superstructures is analyzed, thereby demonstrating their gradual reorganization. Since the combined measurement of the temperature and of the velocity field in the horizontal planes enables to estimate the local heat flux, this possibility is presented as well. In order to assess the experimental results of this work, these are compared to the outcomes of numerical simulations

Experimental techniques for turbulent Taylor–Couette flow and Rayleigh–Bénard convection

Taylor–Couette (TC) flow and Rayleigh–B´enard (RB) convection are two\ud systems in hydrodynamics, which have been widely used to investigate\ud the primary instabilities, pattern formation, and transitions from laminar to\ud turbulent flow. These two systems are known to have an elegant mathematical\ud similarity. Both TC and RB flows are closed systems, i.e. the total energy\ud dissipation rate exactly follows from the global energy balances. From an\ud experimental point of view, the inherent simple geometry and symmetry in these\ud two systems permits the construction of high precision experimental setups.\ud These systems allowfor quantitative measurements of many different variables,\ud and provide a rich source of data to test theories and numerical simulations.\ud We review the various experimental techniques in these two systems in fully\ud developed turbulent states