Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session PS: Convection III |
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Chair: Nigel Kaye, Clemson University Room: 203B |
Tuesday, November 25, 2008 11:35AM - 11:48AM |
PS.00001: Aspect ratio dependence of heat transport in Rayleigh-B\'{e}nard convection Mohammad Emran, Jorge Bailon-Cuba, Joerg Schumacher The variation of heat transfer with respect to two of the three dimensionless control parameters in confined convection, namely the Rayleigh number and Prandtl number, has been the focus of most experiments and simulations. The dependence of the third parameter- the aspect ratio $\Gamma=D/H$, with $D$ is the diameter and $H$ is the height of the cell- has, however, been studied little. We, therefore, want to investigate the aspect ratio dependence of convective turbulence in a cylindrical cell by three-dimensional direct numerical simulations. The study emphasizes on two questions: Does the turbulent heat transport at a fixed Rayleigh number $Ra$ depend on the aspect ratio variation? Which changes in the global flow structures are associated with the aspect ratio variation? The analysis is conducted at several $Ra$ with a fixed Prandtl number of $0.7$. In addition, we quantify the fraction of the total kinetic energy that is contained in large-scale flow patterns by the so-called snapshot analysis. [Preview Abstract] |
Tuesday, November 25, 2008 11:48AM - 12:01PM |
PS.00002: Proper orthogonal decomposition of turbulent thermal convection Jorge Bailon-Cuba, Joerg Schumacher The determination of the empirical eigenfunctions, which result from the Proper Orthogonal Decomposition (POD) procedure, is considered for Rayleigh-B\'enard convection in rectangular boxes. Periodic boundary conditions correspond to continuous symmetries and eigenmodes in the lateral translation-invariant directions, which are Fourier modes. These symmetries reduce the dimensionality of the eigenvalue problem. Free-slip boundary conditions in the vertical direction $y$, correspond to so-called discrete symmetries which can be handled by group theoretical considerations, with a significant increase in the available database. Several data sets at different Rayleigh number, are analyzed. We study how much kinetic energy is contained in the first POD modes, and how it changes with Rayleigh number. The most energetic POD modes give us also a hint on the dynamic dominance of coherent flow patterns, and how well the original inhomogeneous flow can be modeled with a reduced number of modes. [Preview Abstract] |
Tuesday, November 25, 2008 12:01PM - 12:14PM |
PS.00003: Thermal convection at high Rayleigh and Prandtl numbers Sophie Androvandi, Anne Davaille We conducted laboratory experiments to study the convective patterns developping in a fluid with strongly temperature-dependent viscosity. As the viscosity ratio $\gamma$ increases, the thermal structure of the tank becomes asymmetric, the more viscous cold thermal boundary layer (TBL) at the top becoming thicker than the bottom hot TBL, and moving much more slowly (``sluggish lid regim''). For high Rayleigh numbers($> 10^{6}$) and intermediate viscosity ratios ($\gamma < 4000$), the temperature and velocity fields show that three different scales of convection develop: the largest convective scale is cellular, with cold downwelling sheets of viscous fluid encasing hotter, less viscous, parts of the tank. Within each of those cells develop several (typically $3$ to $7$) hot $3D$ upwelling plumes. Upon impinging under the cold TBL, each plume in turn generates locally a small ring of cold material which does not reach the bottom of the tank. A regim diagram of the multiscales convection existence and scaling laws describing the characteristics of the instabilities have been obtained. [Preview Abstract] |
Tuesday, November 25, 2008 12:14PM - 12:27PM |
PS.00004: Time-dependent plume dynamics C.P. Caulfield, M.M. Scase, A.J. Aspden, S.B. Dalziel We generalize the classical turbulent plume model of Morton, Taylor \& Turner (1956) to consider time-varying isolated sources of buoyancy in both unstratified and stratified environments. When the source buoyancy flux is reduced rapidly, we find that the plume narrows transiently from the classical straight-sided similarity solution towards another straight-sided similarity solution originally considered in the context of statically unstable ambient density distributions by Batchelor (1954). We verify this behaviour quantitatively by considering a large ensemble of laboratory experiments. Our results suggest that plume pinch-off is typically quite difficult to achieve. Conversely, when the source buoyancy flux increases rapidly, we find that a transient ``bulge'' propagates up the plume, separating regions of the plume associated with the original and final plume source conditions. We identify scaling laws for the various properties of this bulge, which are verified numerically by an ensemble of large eddy simulations. We show that our model equations can also be applied directly to the starting plume model of Turner (1962) if the increased entrainment through the top of the starting plume is accounted for appropriately. [Preview Abstract] |
Tuesday, November 25, 2008 12:27PM - 12:40PM |
PS.00005: Probing modal dynamics of Rayleigh-B\'{e}nard convection using optical actuation Adam Perkins, Michael Schatz We report on a new experimental approach to investigate the dominant modes governing instability in Rayleigh-B\'{e}nard convection. ~The convective fluid is a gas that strongly absorbs incident infrared laser light. Laser light absorption results in localized heating, thereby altering the fluid flow. Rapid scanning of the light by servo mirrors allows actuation at multiple spatial points nearly simultaneously. This approach provides a tool for repeatedly imposing a given convection pattern, e.g., straight rolls. Selected perturbations are applied to this initial pattern, thus providing an ensemble of systems with nearby initial conditions. Modal dynamics are extracted from the subsequent pattern evolutions, monitored via time series of shadowgraph images. [Preview Abstract] |
Tuesday, November 25, 2008 12:40PM - 12:53PM |
PS.00006: Reducing the Dimensionality of Spatio-Temporal Data in Rayleigh- B\'{e}nard Convection using Homology {\&} Karhunen- Lo\`{e}ve Decomposition Huseyin Kurtuldu, Michael Schatz We present two different approaches to obtain a reduced dynamical description of spatio-temporal chaos in Rayleigh B\'{e}nard convection experiments. Computational Homology, a topological characterization technique, and Karhunen- Lo\`{e}ve (KL) decomposition are applied to time series of shadowgraph images. Homology computations for each image produce a set of non-negative integers called Betti numbers defining different characteristic topological properties of convective flows. Quantitative information is obtained from the probability distributions constructed from a time series of Betti numbers to identify different spatio-temporal states at different control parameters in experiments. For comparison, analogous information content at the same parameter values is captured by normalized eigenvalue spectra obtained by KL decomposition of shadowgraph images. We discuss strengths and weaknesses of these methods for characterizing spatio-temporal dynamics. [Preview Abstract] |
Tuesday, November 25, 2008 12:53PM - 1:06PM |
PS.00007: Centrifugal effects in rotating convection: nonlinear dynamics Francisco Marques, Juan M. Lopez Rotating convection in cylindrical containers is a canonical problem in fluid dynamics, in which a variety of simplifying assumptions have been used in order to allow for low-dimensional models or linear stability analysis from trivial basic states. An aspect of the problem that has received limited attention is the influence of the centrifugal force, because it makes it difficult or even impossible to implement the aforementioned approaches. In this study, the mutual interplay between the three forces of the problem, Coriolis, gravitational and centrifugal buoyancy, is examined via direct numerical simulation of the Navier--Stokes equations in a parameter regime where the three forces are of comparable strengths in a cylindrical container with the radius equal to the depth so that wall effects are also of order one. A variety of bifurcated solutions and several codimension-two bifurcation points acting as organizing centers for the dynamics have been found. A main result is that the flow has simple dynamics for either weak heating or large centrifugal buoyancy. The limit of zero centrifugal buoyancy is singular, and the bifurcations found by decreasing it are subcritical. Centrifugal effects primarily lead to the axisymmetrization of the flow and a reduction in the heat flux. [Preview Abstract] |
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