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 MS: Convection II |
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Chair: Laurette S. Tuckerman, PMMH-ESPCI-CNRS, France Room: 203B |
Tuesday, November 25, 2008 8:00AM - 8:13AM |
MS.00001: Bifurcation phenomena in cylindrical convection Laurette Tuckerman, K. Boronska, L. Bordja, L. Martin-Witkowski, M.C. Navarro We present two bifurcation scenarios occurring in Rayleigh-Benard convection in a small-aspect-ratio cylinder. In water (Pr=6.7) with R/H=2, Hof et al. (1999) observed five convective patterns at Ra=14200. We have computed 14 stable and unstable steady branches, as well as novel time-dependent branches. The resulting complicated bifurcation diagram, can be partitioned according to azimuthal symmetry. For example, three-roll and dipole states arise from an m=1 bifurcation, four-roll and ``pizza'' branches from m=2, and the ``mercedes'' state from an m=3 bifurcation after successive saddle-node bifurcations via ``marigold'', ``mitsubishi'' and ``cloverleaf'' states. The diagram represents a compromise between the physical tendency towards parallel rolls and the mathematical requirement that primary bifurcations be towards trigonometric states. Our second investigation explores the effect of exact counter-rotation of the upper and lower bounding disks on axisymmetric flows with Pr=1 and R/H=1. The convection threshold increases and, for sufficiently high rotation, the instability becomes oscillatory. Limit cycles originating at the Hopf bifurcation are annihilated when their period becomes infinite at saddle-node-on-periodic-orbit (SNOPER) bifurcations. [Preview Abstract] |
Tuesday, November 25, 2008 8:13AM - 8:26AM |
MS.00002: Reduced models to study Rayleigh-Benard convection in cylindrical geometry Maria Cruz Navarro, Laurent Martin Witkowski, Laurette Tuckerman, Patrick Le-Quere We propose to study Rayleigh-Benard convection instabilities in a cylinder of aspect ratio one. The isothermal disks hot (at the bottom) and cold (on the top) turn at the same angular velocity but in the opposite direction. Three numerical techniques are used: (i) temporal integration, (ii) a study of the eigenvalues from the linearized system (Newton/Arnoldi), (iii) a projection of Navier-Stokes equations on a limited number of eigenvectors reducing the system to a few ordinary differential equations. At this state of development, only the study of linear stability (ii) takes into account non-axisymmetric modes. In absence of rotation, the first bifurcation is axisymmetric. The rotation of the disks has the effect of delaying the transition towards convection for both axisymmetric and non-axisymmetric modes, although there is a critical rotation velocity value for which the flow becomes three-dimensional. Restricting to axisymmetric mode, the non-linear dynamic is rich when varying the temperature difference between disks and their angular velocity. The goal of our work is to check the ability of reduced models to capture such dynamic by comparing technique (i) with technique (iii). [Preview Abstract] |
Tuesday, November 25, 2008 8:26AM - 8:39AM |
MS.00003: Non-resonant Forcing in Rayleigh-B\'enard Convection Stephan Weiss, Gabriel Seiden, Eberhard Bodenschatz, Werner Pesch We report experiments on spatially forced Rayleigh-B\'enard convection in a large aspect ratio cell. The stability region of forced straight rolls in the parameter space spanned by the reduced Rayleigh number and the forcing wavenumber is determined and compared to the theoretical prediction. Intriguing patterns found away from the stability region such as localized coherent states and ``brick-wall'' patterns are described in detail. [Preview Abstract] |
Tuesday, November 25, 2008 8:39AM - 8:52AM |
MS.00004: Enhancement of Heat Transfer by Vibrations Valentina Shevtsova, Aliaksandr Mialdun, Denis Melnikov, Ilya Ryzhkov, Yuri Gaponenko An experimental evidence of convection caused by translational vibration of non-uniformly heated fluid in low gravity is reported. The theory of thermovibrational convection in weightlessness has been well developed but direct experimental proof of this type of motion was missing. An innovative point of the experiments is the observation of temperature field in front and side views of the cubic cell using digital optical interferometry. In addition, particle tracing is employed. The evolution of temperature field is studied systematically in a wide range of frequencies and amplitudes. The mean flow structures previously reported in theoretical studies are confirmed. The behavior of integral and local Nusselt numbers demonstrate strong enhancement of heat transfer during short periods of microgravity time, which is about 20s. The obtained results show, that mean vibrational flows can cause strong heat transport in the fluid. It was found that this transport becomes more intensive with increasing the vibrational impact. It opens the possibility of using vibrations as an alternative way of transferring heat and matter in space. The experimental results are supported by direct numerical simulations. [Preview Abstract] |
Tuesday, November 25, 2008 8:52AM - 9:05AM |
MS.00005: Exploring Extensive Chaos in Rayleigh-Benard Convection Alireza Karimi, Mark Paul For large spatially extended systems it is expected that the fractal dimension will scale linearly with system size yielding extensive chaos. The variation of the dimension for small changes in system size can yield fundamental insights into the nature of the underlying spatiotemporal chaos. Results from well known model equations of spatiotemporal chaos have yielded both deviations from extensivity as well as microextensivity. We explore this for experimentally accessible Rayleigh-Benard convection using large-scale numerical simulations for system parameters where convection has been shown to be extensive. We solve the full Boussinesq equations and compute the spectrum of Lyapunov exponents by simultaneously evolving many copies of the governing equations linearized about the full nonlinear driving solution. Using long-time numerical simulations we study the variation of the fractal dimension over a small range of system sizes chosen to introduce approximately two new chaotic degrees of freedom. [Preview Abstract] |
Tuesday, November 25, 2008 9:05AM - 9:18AM |
MS.00006: Asymptotic Solutions of the 2D Oberbeck--Boussinesq Equations in the Large Rayleigh Number, Moderate Prandtl Number Limit Greg Chini, Stephen Cox Boussinesq thermal convection in a horizontal layer between isothermal stress-free boundaries is the archetypal convection problem. In both natural and technological applications, the Rayleigh number $Ra$ generally exceeds the threshold for linear instability of the conduction state by orders of magnitude, so the high-$Ra$ limit of the governing equations is of particular interest. It is therefore remarkable that the structure of steady-state convection cells has not yet been established, except in the further limiting case of infinite Prandtl number ($Pr$). Here, we rectify this situation by presenting the first large-$Ra$ asymptotic analysis of the classical Rayleigh--B\'{e}nard convection problem with $Pr=\mathit{O}(1)$. We derive both details of the flow and a corresponding bulk heat transport coefficient, as a function of the cell aspect ratio. Predictions of our asymptotic theory are corroborated using full pseudospectral numerical simulations. [Preview Abstract] |
Tuesday, November 25, 2008 9:18AM - 9:31AM |
MS.00007: Experimental study of convection cell transition in internally heated layer Junpei Takahashi, Kanako Yano, Yuji Tasaka, Yuichi Murai, Yasushi Takeda, Takatoshi Yanagisawa, Yasuko Yamagishi Convection cell induced by internal heat sources in a shallow layer behaves characteristically with respect of internal Rayleigh number ($R_{I})$. For example, horizontal scale of the cell expands dramatically in proportion to $R_{I}$ and at higher $R_{I}$, another cell structure is formed; an additional cell appears in the cell or descending flow at the center of a cell expands to the edge of cell. These transitions of cell structure haven't been investigated well experimentally although it doesn't appear in ideal condition. We attempt to determine the flow structure in a cell by Particle Image Velocimetry to investigate transition mechanisms. The fluid layer has 210 times 210 mm of the cross section and is 7 mm in the height. Simultaneous multi-layer measurement is performed by color-striped light sheet and transitional state of convection cell is observed. Vertical velocity component is also obtained and we investigate how cell behaves with respect of $R_{I}$. $R_{I}$/$R_{Ic}$ was changed from 4 up to 25, where $R_{Ic}$ corresponds to the critical Rayleigh number at the onset of the convection. We confirmed cell transition is strongly related with development of descending flow at the center of a cell. Cell dilatation process is described as a consequence descending flow develops and strongly expands at the bottom of fluid layer. [Preview Abstract] |
Tuesday, November 25, 2008 9:31AM - 9:44AM |
MS.00008: Direct numerical simulation of turbulent mixed convection in heated vertical annulus Yong Joon Jun, Joong Hun Bae, Jung Yul Yoo Turbulent mixed convection in heated vertical annulus is investigated using Direct Numerical Simulation (DNS) technique. The objective of this study is to find out the effect of buoyancy on turbulent mixed convection in heated vertical annulus. Downward and upward flows have been simulated to investigate turbulent mixed convection by gradually increasing the inner wall heat flux. With increased heat flux, heat transfer coefficient first decreases and then increases in the upward flow due to the effect of buoyancy, but it gradually increases in downward flow. The skin friction increasingly rises in upward flow, while it slightly decreases in downward flow. All simulation results are in good agreement with existing numerical and experimental results. [Preview Abstract] |
Tuesday, November 25, 2008 9:44AM - 9:57AM |
MS.00009: Stability of steady thermal convection in a tilted rectangular cavity in low-mode approximation Albert Sharifulin, Rafil Sagitov The model system of ordinary differential equations governing the behavior of a non-uniformly heated fluid in a tilted cavity is used for studying the stability of steady regimes of thermal convection at arbitrary (not small) tilting of the rectangular cavity. The bifurcation curve is constructed, which separates the region of parameters (the Rayleigh number and the cavity tilting angle) into two regions: - the internal and external ones. In the external region, the system has one stable steady solution, and in the internal region, it has three steady solutions. One of them is always unstable in a monotone way, and two other may be both stable and unstable. The neutral curves are constructed, which determine the boundaries of the incipience of the oscillatory and monotone instabilities. [Preview Abstract] |
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