Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session A2: Convection and Buoyancy-Driven Flows I: Rayleigh-BĂ©nard Convection |
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Chair: Eric Brown, University of California, Merced Room: 23A |
Sunday, November 18, 2012 8:00AM - 8:13AM |
A2.00001: Comparison between 2D and 3D turbulent Rayleigh-Benard convection Erwin van der Poel, Richard Stevens, Detlef Lohse We provide a detailed comparison between the results for 3D and the computationally much cheaper 2D numerical simulation of Rayleigh-B\'enard (RB) flow. The 2D character of the LSC in both 2D and 3D flows hints towards a large similarity, in particular for integral quantities. Moreover, theoretical concepts for the scaling relations in turbulent RB convection are not specific to 2D or 3D. We compare the global transport quantities, boundary layer profiles, and flow topology of 2D and 3D convection to find at which control parameters differences and similarities can be found. One of the pronounced differences is the limited motion of the LSC in 2D, which increases the accumulation of energy in corner-rolls, leading to large scale wind reversals and high sensitivity of global output parameters on the roll-state. [Preview Abstract] |
Sunday, November 18, 2012 8:13AM - 8:26AM |
A2.00002: Supercritical Quasi-conduction States and Multiple Stable Flows in Stochastic Rayleigh-B\'{e}nard Convection Daniele Venturi, George Karniadakis Stochastic bifurcations and stability of natural convection within two-dimensional square enclosures are investigated by using different stochastic modeling approaches. Deterministic stability analysis is carried out first to obtain steady state solutions and primary bifurcations. It is found that multiple stable steady states coexist, in agreement with recent results, within specific ranges of Rayleigh number. Stochastic simulations are then conducted around bifurcation points and transitional regimes. The influence of random initial conditions and random perturbations in the temperature distribution at the horizontal walls is also investigated. It is found that random noise renders the bifurcation process to convection imperfect and it extends the range of stability of quasi-conduction states beyond the classical onset of convection. In particular, subcritical and nearly supercritical quasi-conduction stable states are observed within the range of Rayleigh numbers Ra=0-4000. Analysis of the stochastic bifurcation diagrams also shows the presence of a stochastic drift phenomenon in the heat transfer coefficient, especially in the transcritical region. Such stochastic drift is investigated further by means of a sensitivity analysis based on functional ANOVA decomposion. [Preview Abstract] |
Sunday, November 18, 2012 8:26AM - 8:39AM |
A2.00003: Geometry-dependence of dynamics of the large-scale circulation in turbulent Rayleigh-Benard convection Eric Brown, Russell Hawkins We present a simple model for the geometry-dependence of dynamics of the large-scale circulation (LSC) in turbulent Rayleigh-Benard convection. This extends a previous model of stochastic ordinary differential equations (ODEs) developed to describe LSC dynamics in an aspect ratio 1 upright cylinder. The large-scale circulation exhibits behavior such as spontaneous meandering of the orientation, cessations of the flow, and various oscillation modes, which can change with the geometry of the container. Specifically, in experiments with a sideways cylinder the LSC orientation is found to align with the longer diameters, and new oscillation modes around and between these longest diagonals were found. These changes in dynamics with geometry can be accounted for with the addition of a shape-dependent potential term to the stochastic ODE model that represents the pressure forcing from the sidewall. For the sideways cylinder, the potential is analogous to a Duffing oscillator. The agreement between model predictions and observations suggests the possibility of describing LSC flows in arbitrary geometries with a relatively simple stochastic ODE model. [Preview Abstract] |
Sunday, November 18, 2012 8:39AM - 8:52AM |
A2.00004: Comparison between rough and smooth plates within the same Rayleigh-Benard cell Eleonore Rusaouen, Julien Salort, Fanny Seychelles, Jean-Christophe Tisserand, Matthieu Creyssels, Olivier Liot, Bernard Castaing, Francesca Chilla A Rayleigh-Benard cell consist in a tank filled of a fluid on which a temperature difference is imposed thanks to a cold plate at top and a hot at bottom. Movement is induced by the buoyancy force. Considering most of experimental apparatus previously used all around the world, both plates are smooth. Recently, the effect of roughness on thermal transfer had become a subject of interest. The present experiment is an asymetrical rough Rayleigh-Benard cell. Indeed the hot plate is rough whereas the cold plate is still smooth. Previously, tests conducted with 2mm high roughness showed independence of the two plates and a heat flux enhancement on the rough plate, which appeared to be greater than expected from the surface increase. This regime was caracterized by a $Nu \propto Ra^{1/2}$ law. New results obtained with a 4mm high roughness also show this flux enhancement and the independent behaviour of the plates. But a transition appears at high Rayleigh from the 1/2 power law regime to a 1/3 one. Former results obtained in the same symetrical smooth/smooth cell also showed a 1/3 law. But the rough 1/3 regime reveals a multiplier coefficient of 1.6 with the smooth one. [Preview Abstract] |
Sunday, November 18, 2012 8:52AM - 9:05AM |
A2.00005: Lagrangian tracking of an instrumented particule in Rayleigh-Benard flow Fanny Seychelles, Xavier Riedinger, Julien Salort, Eleonore Rusaouen, Matthieu Gibert, Yoann Gasteuil, Olivier Liot, Bernard Castaing, Francesca Chilla Thermal convection is present in different systems from astrophysical to geophysical flows. Most experiments and numerical studies are carried from eulerian point of view. The heat transfer from a local perspective is not well understood. Lagrangian description could provide the missing insights on the local mixing and transport mechanisms in thermal convection. We present here a lagrangian measurement in a Rayleigh B\'enard convection. To be more precise, we have conceived a sphere particle with embarked thermometers and radio emitter. Our experimental setup is a rectangular vessel with height H=40 cm and section 40 cm x 10 cm filled with water. The walls are made of polymethylmetacrylate, the top plate is cooled by controlled thermal bath, and the bottom plate is heated by electrical resistance. Using a camera for optical tracking, we obtain at the same time the position and temperature measurement of the particle. We present here the results of a new sensor on statistics of temperature, velocity and heat transport in an original Rayleigh Benard convection, where the top plate is smooth and the bottom plate is rough. [Preview Abstract] |
Sunday, November 18, 2012 9:05AM - 9:18AM |
A2.00006: Spatial Dependence of Boundary Layers in Simulations of Rayleigh-B\'enard Convection Janet Scheel, Jorge Munoz We present results from a systematic study of the thermal and viscous boundary layers obtained from simulations of Rayleigh-Benard convection in a cylindrical container of aspect ratio one (diameter = depth). We extract local boundary layers at a variety of locations in the container for Rayleigh numbers between $1\times 10^5-1 \times 10^9$ and for Prandtl numbers from $0.021-0.7$. We find some spatial dependence of boundary layer thicknesses, but these results highly depend on the method of extracting boundary layer thickness. We find similar results for the scaling of boundary layer thickness with Rayleigh number. This is an extension of our study of boundary layers performed in the center of the cell (J.D. Scheel et al., JFM, 2012). We compare our results to others, including the work by Wagner, et al., JFM, 2012. [Preview Abstract] |
Sunday, November 18, 2012 9:18AM - 9:31AM |
A2.00007: Reynolds number measurements for turbulent Rayleigh-B\'enard convection with $0.17 < Pr < 0.88$ James Hogg, Guenter Ahlers We report Reynolds-number measurements from space-time cross-correlation functions of shadowgraph images taken of turbulent Rayleigh-B\'enard convection in a cylindrical cell of height $L = 9.5$ mm and aspect ratio $\Gamma = 10.6$. The fluids were pure gases with Prandtl-numbers $Pr\approx0.7$ and gas mixtures with $0.17 \leq Pr < 0.7$. The Rayleigh-number range was $10^{5} \leq Ra \leq 10^{8}$. The elliptic approximation of He and Zhang\footnote{G.-W. He and J.-B. Zhang, Phys. Rev. E, \textbf{73}, 055303 (2006).} was used to calculate the mean flow velocity $U$ and the rms fluctuation velocity $V$. For this system $U$ was close to zero, and the Reynolds number $Re_{V}$ based on $V$ had $Ra$- and $Pr$-dependences consistent with the Grossmann-Lohse model.\footnote{S. Grossmann and D. Lohse, Phys. Rev. E, \textbf{66}, 016305 (2002).} [Preview Abstract] |
Sunday, November 18, 2012 9:31AM - 9:44AM |
A2.00008: Heat transport by turbulent Rayleigh-B\'enard convection for $Pr \simeq 0.8$ and $4 \times 10^{11} < Ra < 2 \times 10^{14}$: ultimate-state transition for aspect ratio $\Gamma$ = 1.00~ Dennis P.M. van Gils, Xiaozhou He, Denis Funfschilling, Guenter Ahlers, Eberhard Bodenschatz We report experimental results for heat transport by Rayleigh-B\'enard convection (RBC) in a cylindrical sample with aspect ratio $\Gamma \equiv D/L = 1.00$ ($D= 1.12$ m is the diameter and $L = 1.12$ m is the height) over the range $4 \times 10^{11} < Ra < 2 \times 10^{14}$ at $Pr \simeq 0.8$. For $Ra < Ra_1^* \simeq 2 \times 10^{13}$ we find $Nu = N_0 Ra^{\gamma_{\mathrm{eff}}}$ with $\gamma_{\mathrm{eff}}$ = 0.321 $\pm$ 0.002 and $N_0 = 0.0776$, consistent with classical turbulent RBC in a system with laminar boundary layers (BLs) below the top and above the bottom plate and with the prediction of Grossmann and Lohse$^{(1)}$. For $Ra > Ra_1^*$ the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for $\Gamma = 0.50$$^{(2)}$, we interpret this phenomenon as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of $Ra_1^*$ as it does for $\Gamma = 0.50$. [Preview Abstract] |
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