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 D2: Convection and Buoyancy-Driven Flows II: Rayleigh-BĂ©nard Convection |
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Chair: Bob Behringer, Duke University Room: 23A |
Sunday, November 18, 2012 2:15PM - 2:28PM |
D2.00001: Temperature fluctuations in turbulent Rayleigh- B\'enard convection for Ra up to $2\times 10^{14}$ and Pr $\simeq 0.8$ Xiaozhou He, Dennis P.M. van Gils, Eberhard Bodenschatz, Guenter Ahlers We report on measurements of temperature space-time cross-correlation functions $C_T(r,\tau)$ in Rayleigh-B\'enard convection (RBC) near the side wall of a cylindrical sample with aspect ratio $\Gamma \equiv D/L = 1.00$ ($D= 1.12$ m was the diameter and $L = 1.12$ m was the height). The results covered the Rayleigh-number range $4\times 10^{11} \leq Ra \leq 2\times 10^{14}$ and the Prandtl-number range $0.79 \leq Pr \leq 0.86$. Our results extend previous measurements for a lower Ra range\footnote{X. He, G. He, and P. Tong, Phys. Rev. E, {\bf 81}, 065303 (2010).} and confirmed the elliptic approximation (EA) of He and Zhang\footnote{G.-W. He and J.-B. Zhang, Phys. Rev. E, {\bf 73}, 055303 (2006).} up to $Ra \simeq 10^{14}$. Using the EA, we determined an effective Reynolds number near the transition to the ultimate state of turbulent RBC.\footnote{X. He, D. Funfschilling, H. Nobach, E. Bodenschatz and G. Ahlers, Phys. Rev. Lett., {\bf 108}, 024502 (2012).} [Preview Abstract] |
Sunday, November 18, 2012 2:28PM - 2:41PM |
D2.00002: Logarithmic temperature profiles in turbulent Rayleigh-B\'enard convection Guenter Ahlers, Xiaozhou He, Denis Funfschilling, Dennis van Gils, Eberhard Bodenschatz We report experimental results for the vertical profiles of the mean temperature $\langle T \rangle$ and the rms temperature fluctuation $\sigma$ for turbulent Rayleigh-B\'enard convection in the interior of a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 0.50$ ($D = 112$ cm and $L = 224$ cm are the diameter and height respectively) over the Rayleigh number range $4 \times 10^{12} \leq Ra \leq 10^{15}$ for a Prandtl number $Pr \simeq 0.8$. We found that $\langle T \rangle$ and $\sigma$ vary linearly with $ln(z/L)$ where $z$ is the distance from the bottom or top plate. Such a dependence had been predicted\footnote{S. Grossmann and D. Lohse, Phys. Fluids {\bf 23}, 045108 (2011).} for the ultimate state ($Ra > 5\times 10^{14}$), but was unexpected for the classical state ($Ra < 10^{13}$). The results for $\langle T \rangle$ and $\sigma$ suggest similarities to the logarithmic profiles found for the velocity in shear flows.\footnote{I. Marusic {\it et al.}, Phys. Fluids {\bf 22}, 065103 (2010).}$^,$\footnote{M. Hultmark {\it et al.}, Phys. Rev. Lett {\bf 108}, 094501 (2012).} [Preview Abstract] |
Sunday, November 18, 2012 2:41PM - 2:54PM |
D2.00003: Describing Chaotic Dynamics in Rayleigh-Benard Convection Using Persistent Homology Theory Jeffrey Tithof, Michael Schatz, Konstantin Mischaikow, Miroslav Kramar, Vidit Nanda, Mark Paul, Mu Xu We present a new technique for describing the dynamics of spatio-temporal chaos in Rayleigh-Benard convection (RBC). Developed as a tool in algebraic topology, persistent homology theory provides a powerful mathematical formalism for describing the time evolution of geometrical objects. This is done by encoding their topological characteristics in a so-called persistence diagram. When applied to shadowgraph images of spiral defect chaos in RBC, different flow structures correspond to unique features in the persistence diagram. Use of these diagrams helps us to understand the dynamical connections between RBC states, complementing the traditional techniques used in pattern recognition. [Preview Abstract] |
Sunday, November 18, 2012 2:54PM - 3:07PM |
D2.00004: Heat Transport Processes in Turbulent Rayleigh-B\'enard Convection described with PDF equations: Numerics and Models Johannes Luelff, Michael Wilczek, Richard Stevens, Rudolf Friedrich, Detlef Lohse Rayleigh-B\'enard convection, i.e. the convection of a fluid enclosed between two plates that is driven by a temperature gradient, is the idealized setup of a phenomenon ubiquitous in nature and technical applications. Of special interest for this system are the statistics of turbulent temperature fluctuations, which we are investigating for a fluid enclosed in a cylindrical vessel. To this end, we derive an exact evolution equation for the probability density function (PDF) of temperature from first principles. Appearing unclosed terms are expressed as conditional averages of velocities and heat diffusion, which are estimated from direct numerical simulations. Our theoretical framework allows to connect the statistical quantities to the dynamics of Rayleigh-B\'enard convection, giving deeper insights into the temperature statistics and transport mechanisms in different regions of the fluid volume, i.e. in the boundary layers, the bulk and the sidewall regions. Furthermore, a minimalistic model of the conditional averages that still incorporates the core features is developed by physical reasoning to highlight the overall character of the heat transport processes. [Preview Abstract] |
Sunday, November 18, 2012 3:07PM - 3:20PM |
D2.00005: Logarithmic temperature profiles in DNS of turbulent convection Roberto Verzicco, Richard Stevens, Detlef Lohse, Sigfried Grossmann We report numerical results for vertical profiles of mean and rms temperature fluctuations for confined turbulent thermal convection in a cylindrical sample of aspect ratio $\Gamma = 0.5$ and $1$ (diameter over height ratio) over a Rayleigh number range $2\times 10^{10} \leq Ra \leq 2\times 10^{12}$ and for a Prandtl number $Pr=0.7$. We found that both quantities vary linearly in $\ln (z)$ with $z$ the distance from the horizontal plates. This behaviour had been predicted for the ultimate regime but it was not expected for the classical state ($Ra \leq 10^{13}$). Similar findings have recently been obtained also experimentally\footnote{Ahlers G. et al. ``Logarithmic temperature profiles in turbulent Rayleigh-B\'enard convection'' To appear in Phys. Rev. Lett. 2012.} and an excellent agreement with the numerical results has been observed for the mean temperature profiles. The rms fluctuations, in contrast, present relevant differences with respect to the experiments and several explanations are possible. [Preview Abstract] |
Sunday, November 18, 2012 3:20PM - 3:33PM |
D2.00006: Three-dimensional instability of cylindrical Rayleigh-Benard convection De-Jun Sun, Bo-Fu Wang, Dong-Jun Ma The instabilities and transitions of flow in a vertical cylindrical cavity with heated bottom, cooled top and insulated side wall are investigated. The fluid is quiescent at small Rayleigh number and becomes axisymmetric or three dimensional flow when the Rayleigh number is increased. We mainly concerned on the transition of the axisymmetric flow to three dimensional flow through a secondary bifurcation. The steady axisymmetric base flow is obtained by direct numerical simulation and Jacobian-Free Newton-Krylov method, and the stability modes are obtained using the global instability analysis technique. The stability boundaries for the axisymmetric flow are derived for Prandtl numbers from 0.02 to 1 for aspect ratio A (=height/radius) equals 1, 0.9, 0.8, 0.7, respectively. Stable axisymmetric flow beyond the second bifurcation was found in certain ranges of Prandtl number for A=1, 0.9 and 0.8, exclusive of the case for A=0.7. There is no new axisymmetric flow after the second bifurcation for A=0.7 case, but there are multiplicity critical modes as Prandtl number changes., where five kinds of steady modes m=1, 2, 8, 9, 10 and three kinds of oscillatory modes m=3, 4, 6 are presented. [Preview Abstract] |
Sunday, November 18, 2012 3:33PM - 3:46PM |
D2.00007: An experimental study of flow reversals in turbulent Rayleigh-B\'{e}nard convection in rectangular cells Shi-Di Huang, Rui Ni, Ke-Qing Xia We present an experimental study of reversals of the large-scale circulation (LSC) in turbulent Rayleigh-B\'{e}nard convection. The experiment was conducted in two rectangular cells with the heights and lengths being equal and fixed at 12.6 cm while the widths being 3.84 cm and 2.56 cm, corresponding to lateral aspect ratios $\Gamma$ being 0.3 and 0.2, respectively. It is found that reversals of the LSC occur more frequently in the $\Gamma=0.2$ cell than they do in the $\Gamma=0.3$ cell. The increased temperature fluctuations in the bulk indicates that there are more plumes going through the bulk flow due to the shear effects from the sidewall, which results in a less stable LSC thus more frequent flow reversals. [Preview Abstract] |
Sunday, November 18, 2012 3:46PM - 3:59PM |
D2.00008: Natural convection inside a cylindrical container with a free upper surface Guillermo Ram\'Irez-Z\'u\~niga, Guillermo N. Hern\'adez, Guillermo Hern\'andez-Cruz, Jos\'e N\'u\~nez, Eduardo Ramos This work reports experimental observations and numerical calculations of the natural convective flow inside a cylindrical container (height/diameter= 1.25) with a free upper surface. The bottom and top walls are at high and low temperatures respectively. The Rayleigh number range explored is $10^5$ $< Ra <$ $5 \times 10^6$ which includes steady-state and time dependent flows. The working fluid considered is water (Pr=6.67). The observations were made with a stereoscopic PIV system that rotates around the container. With this device, the three component velocity field in the whole volume of the container can be recorded and full three dimensional flow patterns can be reconstructed. The numerical calculation was made with a hybrid finite volume-spectral method considering a free stress boundary for the upper surface. Flow patterns and stability properties are described in the context of potential applications to crystal growth technology. [Preview Abstract] |
Sunday, November 18, 2012 3:59PM - 4:12PM |
D2.00009: Non- Oberbeck- Boussinesq effects in Poiseuille- Rayleigh- B{\'e}nard turbulent channel flow Alfredo Soldati, Francesco Zonta The importance of the Oberbeck-Boussinesq (OB) approximation in turbulent Poiseuille-Rayleigh-B{\'e}nard (PRB) flow is established via Direct numerical Simulation (DNS) of water flows with viscosity ($\mu$) and thermal expansion coefficient ($\beta$) purely varying with temperature (non-Oberbeck-Boussinesq conditions, NOB). In PRB flows, the combination of buoyancy driven/pressure driven effects produce a complex flow structure, which depends on the relative intensity of the flow parameters (i.e. the Grashof number, $Gr$, and the shear Reynolds number, $Re_{\tau}$). In liquids, however, temperature variations induce local changes of fluid properties which influence the macroscopic flow field. We present results for different shear Richardson numbers ($Ri_{\tau}=Gr/Re_{\tau}^2$) under constant temperature boundary conditions. As the Richardson number is increased, buoyant thermal plumes are generated. Rising and falling thermal plumes induce large scale thermal convection which increases momentum and heat transport efficiency. Analysis of friction factor ($C_f$) and Nusselt number ($Nu$) for NOB conditions shows that the effect of $\mu(T)$ is negligible, whereas the effect of $\beta(T)$ is critical. [Preview Abstract] |
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