Combined effects of prescribed pressure gradient and buoyancy in boundary layer of turbulent Rayleigh-Bénard convection. - In: European journal of mechanics, ISSN 1873-7390, Bd. 57 (2016), S. 64-74
Boundary layers of the velocity and temperature fields are essential for the transport of heat and momentum in turbulent Rayleigh-Bénard convection. Here we study the combined effects of a prescribed pressure gradient and buoyancy for a boundary layer flow by an extension of the two-dimensional, steady Falkner-Skan model. The resulting model, which couples the evolution of the velocity field to that of the temperature field, is used for a comparison with the dynamics in the vicinity of the isothermal bottom plate in a fully turbulent Rayleigh-Bénard convection flow in a closed cylindrical cell. The obtained set of boundary layer equations is solved numerically and the results are compared with direct numerical simulation data at a Rayleigh number Ra = 3 × 10^9 and for Prandtl numbers Pr = 0.7 and Pr = 7. The additional buoyancy effects improve the agreement with the data for the lower of the two Prandtl numbers. The improvements remain however very small for the larger Prandtl number. In the latter case, the simulation data show a much weaker coherence and strength of the large-scale circulation. Pressure gradients are then generated by local impacts of colder fluid at the bottom rather than by a coherent circulation which fills the whole convection cell.
http://dx.doi.org/10.1016/j.euromechflu.2016.02.001
The eruptive regime of mass-transfer-driven Rayleigh-Marangoni convection. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 791 (2016), S. R4-1-R4-12
The transfer of an alcohol, 2-propanol, from an aqueous to an organic phase causes convection due to density differences (Rayleigh convection) and interfacial tension gradients (Marangoni convection). The coupling of the two types of convection leads to short-lived flow structures called eruptions, which were reported in several previous experimental studies. To unravel the mechanism underlying these patterns, three-dimensional direct numerical simulations and corresponding validation experiments were carried out and compared with each other. In the simulations, the Navier-Stokes-Boussinesq equations were solved with a plane interface that couples the two layers including solutal Marangoni effects. Our simulations show excellent agreement with the experimentally observed patterns. On this basis, the origin of the eruptions is explained by a two-step process in which Rayleigh convection continuously produces a concentration distribution that triggers an opposing Marangoni flow.
http://dx.doi.org/10.1017/jfm.2016.63
Hierarchical Marangoni roll cells : experiments and direct numerical simulations in three and two dimensions. - In: Computational methods for complex liquid-fluid interfaces, (2016), S. 481-501
Many technological processes, such as extraction, evaporation, or absorption are accompanied by solutal Marangoni instability. This type of convection, which is driven by gradients in interfacial tension, can significantly influence process performance in industrial production. The patterns originating from this convection are of a complex and unsteady nature. One particularly remarkable feature is the formation of hierarchical structures, that is, larger patterns emerging on a background of smaller flow patterns. For the example of liquid-liquid extraction, hierarchical roll cells were already observed in the early experiments on solutal Marangoni convection [1-5]. Despite the continuing research [6-13], the details of the multiscale patterns and the mechanisms underlying the hierarchy formation remained unresolved for a long time. Only recently, a thorough characterization of hierarchical Marangoni roll cells could be achieved by a combination of highly resolved three-dimensional (3D) simulations and specifically designed validation experiments [14,15]. However, the hierarchical nature requires the use of a well adapted numerical technique and of large parallel computers to simultaneously resolve both the very fine and the large-scale features of solutal Marangoni convection. To reduce computational cost compared to full 3D simulations, two-dimensional (2D) models are frequently employed [9,16]. Experimentally, such a reduction can be realized to a certain degree in the Hele-Shaw (HS) cell. Here, the liquids are placed between two parallel plates that are sufficiently close together such that the fluid motion becomes mainly 2D [17]. This can be represented by gap-averaged equations [6,7] which - contrary to pure 2D models - take into account the influence of wall friction. Despite the benefits of the HS cell, differences may arise by reducing 3D dynamics to a 2D situation. In this chapter, we present mathematical models, which are able to reproduce the hierarchical patterns observed in the experiments. Therefore, particular focus is laid on providing sufficiently comparable situations in experiments and simulations. The methods are applied to an exemplary two-layer system where hierarchical Marangoni roll cells develop due to the mass transfer of a weakly surface-active solute. In combination with the validation experiments, the results of the simulations provide new insights into the hierarchical nature of the patterns. On this basis, we discuss the applicability of the simplified theoretical models and point out limitations when comparing experimental and numerical results.
A hybrid finite difference-boundary element procedure for the simulation of turbulent MHD duct flow at finite magnetic Reynolds number. - In: Journal of computational physics, ISSN 1090-2716, Bd. 304 (2016), S. 320-339
A conservative coupled finite difference-boundary element computational procedure for the simulation of turbulent magnetohydrodynamic flow in a straight rectangular duct at finite magnetic Reynolds number is presented. The flow is assumed to be periodic in the streamwise direction and is driven by a mean pressure gradient. The duct walls are considered to be electrically insulated. The co-evolution of the velocity and magnetic fields as described respectively by the Navier-Stokes and the magnetic induction equations, together with the coupling of the magnetic field between the conducting domain and the non-conducting exterior, is solved using the magnetic field formulation. The aim is to simulate localized magnetic fields interacting with turbulent duct flow. Detailed verification of the implementation of the numerical scheme is conducted in the limiting case of low magnetic Reynolds number by comparing with the results obtained using a quasistatic approach that has no coupling with the exterior. The rigorous procedure with non-local magnetic boundary conditions is compared with simplified pseudo-vacuum boundary conditions and the differences are quantified. Our first direct numerical simulations of turbulent Hartmann duct flow at moderate magnetic Reynolds numbers and a low flow Reynolds number show significant differences in the duct flow turbulence, even at low interaction level between the flow and magnetic field.
https://doi.org/10.1016/j.jcp.2015.10.007
Simulations of solutal Marangoni convection in two liquid layers : complex and transient patterns. - Ilmenau : Universitätsbibliothek, 2015. - 1 Online-Ressource (vi, 189 Seiten)
Technische Universität Ilmenau, Dissertation 2015
Stofftransport über die Grenzfläche zwischen nicht mischbaren Flüssigkeiten ist in der Lage Konvektion durch Dichtegradienten (Rayleigh-Konvektion) oder Gradienten in der Grenzflächenspannung (Marangoni-Konvektion) zu erzeugen. Direkte numerische Simulationen eines Zweischichtsystems wurden durchgeführt, um zwei klassische Experimente aus diesem Bereich zu reproduzieren und zu erklären. Dazu wurden die Navier-Stokes-Boussinesq- und die Transportgleichung für einen gelösten Stoff in zwei, durch eine ebene Grenzfläche gekoppelten Schichten, für all drei Raumdimensionen gelöst. Eine Pseudo-Spektral-Methode wurde zur numerischen Lösung der Gleichungen eingesetzt, wobei Fourier-Moden in beiden horizontalen Richtungen und Chebyshev-Moden in der vertikalen Richtung eingesetzt wurden. Der anfänglich nur in einer Phase gelöste Stoff diffundiert in die andere Phase, welches im Laufe des Stofftransportes Konvektion auslöst. Zwei unterschiedliche Stoffsysteme wurden simuliert, zuerst das ternäre Gemisch aus Cyclohexanol, Wasser und Butanol. Dabei ist Butanol zu Beginn nur in der oberen organischen Phase gelöst. Da Butanol die Grenzflächenspannung sowie Dichte verringert, entsteht Marangoni-Konvektion mit einer stabilisierenden Dichteschichtung. Die durchgeführten Simulationen reproduzierten erfolgreich die experimentell bekannten mehrskaligen Strömungsmuster. Eine zweistufige Hierarchie von Konvektionszellen wurde beobachtet: große, langsam wachsende Zellen, welche kleinere, stetig bewegte Zellen einschließen. Die Ursache für den Musteraufbau wurde durch zwei Mechanismen, Vergröberung und eine lokale Instabilität, erklärt. Die zeitliche Entwicklung der Muster wurde mit zwei unabhängigen Experimenten aus der Literatur verglichen. Dazu wurden Längenskalen und der optische Fluss aus Schlierenbildern abgeleitet. Neben einer guten qualitativen Übereinstimmung erschienen jedoch Simulationen verlangsamt im Vergleich mit den Experimenten. Parameterstudien zeigten, dass Konzentrationsänderungen von Butanol teilweise durch eine Reskalierung von Länge und Zeit berücksichtigt werden können. Bei dem zweiten Stoffsystem wurde die Übergangskomponente durch Isopropanol ersetzt (ähnliche Eigenschaften wie Butanol) und nun in der unteren wässrigen Phase gelöst. Hierfür konnten Simulationen die experimentell beobachteten Strukturen (Eruptionen) reproduzieren und deren Ursprung durch die Wechselwirkung von Rayleigh- und Marangoni-Konvektion erklären. Ein Vergleich mit experimentellen Ergebnissen zeigte eine gute qualitative Übereinstimmung, jedoch waren auch hier die experimentell ermittelten Geschwindigkeiten höher. Parameterstudien ergaben, dass Variationen in der Ausgangskonzentration teilweise durch eine Reskalierung der Zeit berücksichtigt werden können.
http://www.db-thueringen.de/servlets/DocumentServlet?id=27242
Das Institut für Thermo- und Fluiddynamik. - In: Jenaer Jahrbuch zur Technik- und Industriegeschichte, ISSN 2198-6746, Bd. 18 (2015), S. 147-174
The distinction of instability and turbulence between the Taylor-Couette flow and electrically driven flow in annular channel. - In: Proceedings, ISBN 978-2-9553861-0-1, (2015), S. 191-194
Numerical simulation of swirling flow in the pipe under non-uniform magnetic field. - In: Proceedings, ISBN 978-2-9553861-0-1, (2015), S. 171-174
Numerical simulation of a round jet in the presence of an axial magnetic field. - In: Proceedings, ISBN 978-2-9553861-0-1, (2015), S. 175-178
We report numerical simulations of a submerged round jet of conducting liquid issuing into a square duct in the presence of a uniform axial magnetic field. Starting from a quiescent initial condition, the spatial development of the jet is simulated until the transition or breakup zone is no longer evolving in space or the jet has reached the outlet while eventually be completely suppressed within the computational domain. For even stronger fields the laminar jet becomes unsteady again, which is presumably caused by a MHD pinching mechanism.
Quantification of free convection effects on 1 kg mass standards. - In: Metrologia, ISSN 1681-7575, Bd. 52 (2015), 6, S. 835-841
We determine the free-convection effects and the resulting mass differences in a high-precision mass comparator for cylindrical and spherical 1 kg mass standards at different air pressures. The temperature differences are chosen in the millikelvin range and lead to microgram updrafts. Our studies reveal a good agreement between the measurements and direct numerical simulations of the Boussinesq equations of free thermal convection. A higher sensitivity to the free convection effects is found for the spherical case compared to the cylindrical one. We also translate our results on the free convection effects into a form which is used in fluid mechanics: a dimensionless updraft coefficient as a function of the dimensionless Grashof number Gr that quantifies the thermal driving due to temperature differences. This relation displays a unique scaling behavior over nearly four decades in Gr and levels off into geometry-specific constants for the very small Grashof numbers. The obtained results provide a rational framework for estimating systematic errors in mass metrology due to the effects of free convection.
https://doi.org/10.1088/0026-1394/52/6/835