Publications

Shi, Nan;
Numerische Untersuchung wandnaher Transport- und Strukturbildungsprozesse in turbulenter Rayleigh-Bénard-Konvektion, 2013. - Online-Ressource (PDF-Datei: VI, 93 S., 36,81 MB) : Ilmenau, Techn. Univ., Diss., 2013
Parallel als Druckausg. erschienen

In der vorliegenden Dissertation wurde die Struktur der Grenzschichten in turbulenter Rayleigh-Bénard-Konvektion durch dreidimensionale direkte numerische Simulationen untersucht. Zuerst wurde die Konvektion in einer zylindrischen Zelle mit einem Seitenverhältnis von Eins bei den Rayleighzahlen Ra = 3*10^9 und Ra = 3*10^10 und bei fester Prandtlzahl Pr = 0.7 betrachtet. Ähnlich wie bei den experimentellen Ergebnissen in der gleichen Konfiguration und für die gleiche Prandtlzahl wichen die Grenzschichten der Geschwindigkeits- und Temperaturfelder von den Vorhersagen der Prandtl-Blasius-Pohlhausen Theorie ab. Die Abweichungen werden kleiner, wenn ein dynamisches Reskalieren der Daten mit einer instantan definierten Grenzschichtdicke durchgeführt und die Analyseebene mit der momentanen Richtung der großskaligen Zirkulation in der geschlossenen Zelle ausgerichtet wurde. Die physikalischen Gründe für die Abweichungen der Grenzschichtprofile von der klassischen Prandtl-Blasius-Pohlhausen und Stewartson-Theorien für erzwungene und natürliche Konvektion wurden im Detail untersucht. Die numerischen Ergebnisse zeigen, dass wichtige Annahmen für die klassischen laminaren Grenzschichttheorien für erzwungene und natürliche Konvektion verletzt werden, wie die strikte Zweidimensionalität der Dynamik oder der Stationarität. Schließlich wurde die Grenzschichtdynamik bei drei unterschiedlichen Prandtlzahlen Pr = 7, 0.7, 0.1 bei Ra = 3*10^9 und [Gamma] = 1 verglichen. Hier zeigte sich, dass mit zunehmender Prandtlzahl dynamisches Skalieren die Vereinbarung mit der Prandtl-Blasius-Pohlhausen Theorie verbessert. Die thermische Plumeablösung scheint eine der Hauptursachen für die Abweichungen von der klassischen Grenzschichttheorie. Mit abnehmender Prandtlzahl wird die thermische Grenzschichtdicke dicker. Der Winkel der momentanen großskaligen Zirkulation hat wenigere Fluktuation für die größere Prandtlzahl. Mit abnehmender Prandtlzahl nimmt die mittlere Amplitude der momentanen großskaligen Zirkulation zu.

http://www.db-thueringen.de/servlets/DocumentServlet?id=23592

Scheel, Janet D.; Emran, Mohammad Shah; Emran, Mohammad Shah *1976-*; Schumacher, Jörg;
Resolving the fine-scale structure in turbulent Rayleigh-Bénard convection. - In: New journal of physics, ISSN 1367-2630, Bd. 15 (2013), 113063, insges. 32 S.

We present high-resolution direct numerical simulation studies of turbulent Rayleigh-Bènard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in particular the statistics of the kinetic energy and thermal dissipation rates in the bulk and the whole cell. The fluctuations of the energy dissipation field can directly be translated into a fluctuating local dissipation scale which is found to develop ever finer fluctuations with increasing Rayleigh number. The range of these scales as well as the probability of high-amplitude dissipation events decreases with increasing Prandtl number. In addition, we examine the joint statistics of the two dissipation fields and the consequences of high-amplitude events. We have also investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We demonstrate that global transport properties, such as the Nusselt number, and the energy balances are partly insensitive to insufficient resolution and yield correct results even when the dissipation fields are under-resolved. Our present numerical framework is also compared with high-resolution simulations which use a finite difference method. For most of the compared quantities the agreement is found to be satisfactory.

https://doi.org/10.1088/1367-2630/15/11/113063

Tympel, Saskia; Boeck, Thomas; Schumacher, Jörg
Laminar and transitional liquid metal duct flow near a magnetic point dipole. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 735 (2013), S. 553-586

The flow transformation and the generation of vortex structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces acting on the fluid elements. The duct is of square cross-section. The dipole is located above the top wall and is centred in spanwise direction. Our model uses the quasistatic approximation which is applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at small hydrodynamic Reynolds numbers Re as well as the transitional time-dependent regime at higher values which may generate a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes and their dependence on Re and on the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared: streamwise-, spanwise- and wall-normaloriented dipole axes. The most efficient generation of turbulence at a fixed distance above the duct follows for the spanwise orientation, which is caused by a certain configuration of Hartmann layers and reversed flow at the top plate. The enstrophy in the turbulent wake grows linearly with Ha which is connected with a dominance of the wall-normal derivative of the streamwise velocity.

http://dx.doi.org/10.1017/jfm.2013.491

Doumenc, Frederic; Chénier, E.; Trouette, B.; Boeck, Thomas; Delcarte, C.; Guerrier, Béatrice; Rossi, Maurice
Free convection in drying binary mixtures: solutal versus thermal instabilities. - In: International journal of heat and mass transfer, ISSN 1879-2189, Bd. 63 (2013), S. 336-350

Free convection occuring during the drying of plane layers of polymer solutions may be due to various mechanisms, based on buoyancy or Marangoni effect, of thermal or solutal origin. This theoretical and numerical work provides all the required tools to analyze thoroughly the problem. In this transient flow, different methods (frozen time, non-normal, nonlinear methods) are proposed to predict critical times for convection onset and threshold values for convection. Nonlinear and non-normal methods give similar results, within the uncertainty inherent to any transient problem. It is shown that, when linear stability analysis indicates the presence of several instability mechanisms, it is necessary to invoke nonlinear arguments to establish the leading mechanism. The proposed methodology is then applied to experimental results from the literature for two polymer solutions (Polyisobutylene/toluene and Polystyrene/toluene).

https://doi.org/10.1016/j.ijheatmasstransfer.2013.03.070

Kumar, Bipin; Schumacher, Jörg; Shaw, Raymond A.
Cloud microphysical effects of turbulent mixing and entrainment. - In: Theoretical and computational fluid dynamics, ISSN 1432-2250, Bd. 27 (2013), 3/4, S. 361-376

Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence timescales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered.

http://dx.doi.org/10.1007/s00162-012-0272-z