Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session G2: Convection and Buoyancy-Driven Flows IV: Rayleigh-Benard Convection |
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Chair: Richard Stevens, Johns Hopkins University Room: 324 |
Monday, November 25, 2013 8:00AM - 8:13AM |
G2.00001: Kinetic energy transport in Rayleigh-B\'enard convection Klaus Petschel, Stephan Stellmach, Michael Wilczek, Johannes L\"ulff, Ulrich Hansen Convective systems are often characterized by scaling laws for the heat transport. Several studies have indicated that these scaling laws are inextricably linked to the viscous dissipation rate and therefore to the kinetic energy balance. In the present study, direct numerical simulations of turbulent Rayleigh-B\'enard convection are analyzed with respect to the horizontally averaged kinetic energy balance. Based on this budget equation, distinct regions where energy is produced, dissipated and transported by several flux processes are identified. These regions depend strongly on the Prandtl number, which gives new insights into the flow dynamics in the different Prandtl number regimes. [Preview Abstract] |
Monday, November 25, 2013 8:13AM - 8:26AM |
G2.00002: Statistical description of Rayleigh-B\'enard convection yields limit cycle behavior Johannes Luelff, Michael Wilczek, Rudolf Friedrich, Richard Stevens, Detlef Lohse Rayleigh-B\'enard convection describes the buoyancy-induced movement of a fluid enclosed between two horizontal plates, and serves as an idealized setup of phenomena occuring in nature and technical applications. The temperature fluctuations that occur in the fully turbulent case are of special interest, yet they can't be directly described from first principles due to the chaoticity of the system. Therefore we describe the statistics of temperature fluctuations by investigating the probability density function (PDF) of temperature, for the case of a cylindrical vessel and for periodic horizontal boundary conditions. Our ansatz is to derive exact evolution equations that describe the shape and deformation of the PDF; unclosed terms appearing in the form of conditional averages are estimated from direct numerical simulations of the two turbulent Rayleigh-B\'enard systems. Following these steps, for both cases a limit cycle behavior appears in the phase space of the temperature PDF, highlighting the connection between the statistics and the dynamics of the system that our ansatz permits. The properties, interpretations and implications of this limit cycle are discussed; also, it is shown that the limit cycle can be connected to coherent structures formed by the convecting fluid. [Preview Abstract] |
Monday, November 25, 2013 8:26AM - 8:39AM |
G2.00003: Resolving the fine-scale structure in turbulent Rayleigh-Benard convection Janet Scheel, Mohammad Emran, Joerg Schumacher Results from high-resolution direct numerical simulations of turbulent Rayleigh-Benard convection in a cylindrical cell with an aspect ratio of one will be presented. We focus 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. These dissipation rates as well as the local dissipation scales are compared for different Rayleigh and Prandtl numbers. We also have investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We also demonstrate that global transport properties, such as the Nusselt number and the energy balances, are partly insensitive to insufficient resolution and yield consistent 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. [Preview Abstract] |
Monday, November 25, 2013 8:39AM - 8:52AM |
G2.00004: Mixed convection in a Rayleigh-B\'{e}nard cell with an imposed mean wind Lahcen Bouhlali, Andrea Scagliarini, Halld\'or Einarsson, \'Armann Gylfason, Federico Toschi Turbulent convection is present in a variety of natural occurring flows and engineering applications. In the most studied situation, the Rayleigh-B\'{e}nard (RB) setup, a fluid is confined between two differentially heated parallel plates under gravity. However, in many real-life situations, the picture can be complicated by flows interplaying/competing with the ``natural'' convection. In the atmosphere, for instance, thermal convection often coexists with currents due to pressure gradients. Buoyant and forced convection are also active in industrial flows (as in, e.g., heat exchangers). In this work we report a numerical study of a mixed convecting system. We consider a fully developed turbulent RB cell and at a given time we apply a constant pressure gradient, orthogonal to gravity. We will discuss the scaling properties of the heat flux with Rayleigh and friction Reynolds numbers as well as the statistics of small scale fluctuations of hydrodynamic fields. We will show that, depending on the relative ratio between buoyancy and pressure, the heat flux can be much depleted and the conductive profile for the temperature recovered. Such behaviour can be captured with simple phenomenological arguments. Comparisons with experimental results will be also presented. [Preview Abstract] |
Monday, November 25, 2013 8:52AM - 9:05AM |
G2.00005: Statistical classification of flow morphology in rapidly rotating Rayleigh-B\'{e}nard convection: A numerical and experimental synthesis David Nieves, Antonio Rubio, Keith Julien We use experimentally accessible statistical measures to distinguish between flow morphologies in rapidly rotating Rayleigh-B\'{e}nard convection (RRBC). Transitions between different flow regimes are identified for the fixed non-dimensional Prandtl number $\sigma = 7$ in terms of the reduced Rayleigh number $\widetilde{Ra}=RaE^{4/3}$, where $E$ is the non-dimensional Ekman number. Using cross-correlations of synthetic thermistor time signals we find that the flow transitions from the cellular regime to the convective Taylor column (CTC) regime at $\widetilde{Ra} \approx 20$, and from the CTC regime to the plume regime at $\widetilde{Ra} \approx 57$. Additionally, the horizontal flow structure is elucidated via spatial cross-correlations of vertically separated thermal fluctuations. Length, time, and velocity scales are produced for coherent columnar structures via spatial and temporal cross-correlations. Length, time and velocity scale data is seen to fit power-laws of the form $\alpha(\widetilde{Ra} - \widetilde{Ra}_{c})^{\beta}$, where $\widetilde{Ra}_c$ is the critical Rayleigh number for the onset of stationary convection. Through direct numerical simulation of non-hydrostatic quasi-geostrophic equations, a detailed examination of the flow morphology in RRBC is carried out. [Preview Abstract] |
Monday, November 25, 2013 9:05AM - 9:18AM |
G2.00006: Active transport in chaotic Rayleigh-B\'{e}nard convection Christopher Mehrvarzi, Mark Paul The active transport of a scalar species is studied numerically in a spatiotemporally chaotic flow field of Rayleigh-B\'{e}nard convection. There has been significant progress both theoretically and experimentally in understanding characteristics of active transport in steady periodic-flows such as a ring of vortices and other two-dimensional flows. In this work we are interested in the reaction-advection-diffusion of a scalar species in a three-dimensional chaotic flow field that is accessible to the laboratory. We study the transport using a highly efficient and parallel spectral element approach to simultaneously evolve the Boussinesq and reaction-advection-diffusion equations in large aspect-ratio cylindrical domains with experimentally relevant boundary conditions. We choose the system parameters to yield advection, reaction, and diffusion time scales that are comparable and investigate their interactions. We explore the effect of the chaotic convection patterns on the transport characteristics and quantify the reaction front speed and front geometry for a range of parameters. [Preview Abstract] |
Monday, November 25, 2013 9:18AM - 9:31AM |
G2.00007: Size-Dependent Rayleigh--B\'{e}nard Problem Arezoo Hajesfandiari, Ali Hadjesfandiari, Gary Dargush Problems of thermoviscous flows are of prime importance for many physical processes. Here the classical Boussinesq equations are modified by including couple stresses, which account for size-dependency. This size-dependency is specified by a material length scale $l$, which becomes increasingly important as the characteristic geometric dimension of the problem decreases. The modified two-dimensional linear momentum equations become \[ \rho \left( {\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}} \right)=-\frac{\partial p}{\partial x}+\mu \nabla^{2}u-\mu l^{2}\nabla^{2}\nabla^{2}u \] \[ \rho \left( {\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}} \right)=-\frac{\partial p}{\partial y}+\mu \nabla^{2}v-\mu l^{2}\nabla^{2}\nabla^{2}v-\rho \alpha \left( {T-T_{0} } \right) \] The stability of natural convection for the Rayleigh--B\'{e}nard problem is studied numerically and we consider the onset of convective instability and multiple stable steady states arising within specific ranges of Rayleigh and Prandtl numbers and $l$. [Preview Abstract] |
Monday, November 25, 2013 9:31AM - 9:44AM |
G2.00008: Boiling Rayleigh-Benard flow Daniela Narezo, Yanbo Xie, Guenter Ahlers, Chao Sun, Detlef Lohse We report on heat transport due to boiling of Novec7000 (1-methoxyheptafluoropropane) at the bottom plate of a turbulent Rayleigh-Benard sample which was filled with liquid (except for small vapor bubbles when boiling took place). The top surface of the bottom plate was a silicone wafer covered by a triangular lattice of 30 $\mu$m diameter and 100 $\mu$m deep cavities (the lattice spacing was 100 $\mu$m). The plate diameter and sample height both were 10 cm, but only a central bottom-plate area of 2.5 cm diameter was heated. When the cavities were activated (deactivated) by assuring that they were filled by vapor (liquid), then they nucleated (did not nucleate) bubble formation for bottom-plate temperatures $T_b$ larger than the boiling point $T_{BP}$. Results of the heat transport and of the mid height temperature at the side wall of the sample as a function of $T_b$ with a fixed applied temperature difference $\Delta T = T_b - T_t = 20$K ($T_t$ is the top plate temperature) will be reported. When $T_b > T_{BP}$, the effective conductivity of the 2-phase flow was enhanced relative to the supersaturated 1-phase system by up to 40 percent. The sidewall temperature $T_s$ was reduced in the presence of bubbles by up to 3 percent relative to the 1-phase case. [Preview Abstract] |
Monday, November 25, 2013 9:44AM - 9:57AM |
G2.00009: Periodic mode competition in Rayleigh-Benard convections with a horizontal magnetic field Yuji Tasaka, Kazuto Igaki, Takatoshi Yanagisawa, Sven Eckert Recent experimental studies (Yanagisawa, {\it et al.}, 2011) indicated that appearance of random flow reversals in Rayleigh-Benard convection with a horizontal magnetic field. Time intervals of the flow reversals obey Poisson process and this indicates that this event is memoryless. Bi-stable nature of this system under a condition of non-dimensional parameters, Rayleigh number $Ra$ and Chandrasekhar number $Q$, may induce this event with influences of external random noise. This even appears around $Ra = 10 Q$ in a range, $5 \times 10^2 < Q < 10^3$, where the upper limit is determined by the maximum intensity of magnetic field. The present study investigates extrapolability of this relation in a higher range of $Q$ up to $Q = 10^4$. The test fluid container has dimension of square of 200 mm in the horizontal plane and 40 mm in height. The container was filled with GaInSn and ultrasonic velocity profiling achieved quantitative flow pattern visualization. The visualization confirmed the extrapolability of the relation on flow reversals, but the observed flow reversals were not random but periodic. Proper orthogonal decomposition on the space-time velocity map elucidated periodic competitions between two convection modes with different wavenumbers in the periodic flow reversals. [Preview Abstract] |
Monday, November 25, 2013 9:57AM - 10:10AM |
G2.00010: Torsional oscillation of the large-scale circulation in turbulent Rayleigh-B\'enard convection at large Rayleigh numbers Dennis P.M. van Gils, Xiaozhou He, Guenter Ahlers, Eberhard Bodenschatz We present temperature measurements in turbulent Rayleigh--B\'enard convection (RBC) over the Rayleigh number range $3.0\times10^{13} \le Ra \le 1.3\times10^{14}$ and at constant Prandtl number $\Pr \approx 0.8$. The RBC sample, known as the High-Pressure Convection Facility (HPCF) of G\"ottingen [1], is an upright cylinder of aspect ratio $\Gamma = 1.00$. Using three horizontal rows of thermistors at different heights in the sample, we determined the orientation angle of the large-scale circulation (LSC) plane, similar to [2]. Results identify a well established single-roll LSC with a periodic ``torsional'' mode with a frequency $f_C$. The values of $f_C$ are consistent with the frequencies $f_L$ obtained from power spectra $P(f)$ of temperature time series taken at mid-height of the sample. The non-dimensionalized frequencies $\tilde{f}_C$ are well described by a power law: $\tilde{f}_C \propto Ra ^{\zeta_f}$ with ${\zeta_f} = 0.427 \pm0.001$.\\[4pt] [1] He, Funfschilling, Bodenschatz and Ahlers, New J.\ Phys.\ {\bf 14}, 063030 (2012).\\[0pt] [2] Weiss and Ahlers, J.\ Fluid Mech.\ {\bf 688}, 461 (2011). [Preview Abstract] |
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