Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session E5: Rayleigh-Benard Convection III: Turbulence |
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Chair: Katepalli Sreenivasan, New York University Room: 308 |
Sunday, November 20, 2011 4:40PM - 4:53PM |
E5.00001: Heat transport near the transition to the ultimate state of turbulent Rayleigh-B\'enard convection Guenter Ahlers, Xiaozhou He, Denis Funfschilling, Holger Nobach, Eberhard Bodenschatz Measurements of the Nusselt number $Nu$ for Rayleigh-B\'enard convection (RBC) of a cylindrical sample over the Rayleigh-number range $2\times 10^{12} \leq Ra \leq 2\times 10^{15}$ and the Prandtl-number range $0.79 \leq Pr \leq 0.86$ are presented. The aspect ratio $\Gamma \equiv D/L$ was 0.50 ($D= 1.12$ m was the diameter and $L = 2.24$ m was the height). For $Ra \leq 2\times 10^{13}$ the data yielded $Nu = Nu_0 Ra^{\gamma_{eff}}$ with $\gamma_{eff} = 0.312$, consistent with classical RBC.\footnote{G. Ahlers, S. Grossmann, and D. Lohse, Rev. Mod. Phys. {\bf 81}, 503 (2009)} For larger Ra $\gamma_{eff}$ increased, reaching approximately $\gamma_{eff} = 0.38$ near $Ra = 10^{15}$, consistent with predictions\footnote{R. H. Kraichnan, Phys. Fluids {\bf 5}, 1374 (1962)}$^,$\footnote{S. Grossmann and D. Lohse, Phys. Fluids {\bf 23}, 045108 (2011)} for an ultimate state with turbulent boundary layers. [Preview Abstract] |
Sunday, November 20, 2011 4:53PM - 5:06PM |
E5.00002: Ultimate State of Two-Dimensional Rayleigh-B\'enard Convection between Free-Slip Fixed-Temperature Boundaries Jared Whitehead, Charles Doering Rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-B\'enard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number $Nu$ is bounded in terms of the Rayleigh number $Ra$ according to $Nu \leq 0.2891 Ra^{5/12}$ uniformly in the Prandtl number $Pr$. This Nusselt number scaling challenges some theoretical arguments regarding the asymptotic high Rayleigh number heat transport by turbulent convection. [Preview Abstract] |
Sunday, November 20, 2011 5:06PM - 5:19PM |
E5.00003: The Reynolds number near the transition to the ultimate state of turbulent Rayleigh-B\'enard convection Xiaozhou He, Guenter Ahlers, Denis Funfschilling, Holger Nobach, Eberhard Bodenschatz Measurements of a Reynolds number $Re$ for Rayleigh-B\'enard convection (RBC) of a cylindrical sample over the Rayleigh-number range $2\times 10^{12} \leq Ra \leq 2\times 10^{15}$ and the Prandtl-number range $0.79 \leq Pr \leq 0.86$ are presented. The aspect ratio $\Gamma \equiv D/L$ was 0.50 ($D= 1.12$ m was the diameter and $L = 2.24$ m was the height). We used the elliptic approximation of He and Zhang\footnote{G.-W. He and J.-B. Zhang, Phys. Rev. {\bf 73}, 055303 (2006)}$^,$\footnote{X. He, G. He, and P. Tong, Phys. Rev. {\bf 81}, 065303 (2010)} to determine an effective Re. For $Ra \geq 3 \times 10^{14}$ the data yielded $Re = Re_0 Ra^{\alpha_{eff}}$ with $\alpha_{eff} \simeq 0.50$. This result is consistent with predictions for the ultimate state, where the boundary layers are turbulent.\footnote{R. H. Kraichnan, Phys. Fluids {\bf 5}, 1374 (1962)}$^,$\footnote{S. Grossmann and D. Lohse, Phys. Fluids {\bf 23}, 045108 (2011)} [Preview Abstract] |
Sunday, November 20, 2011 5:19PM - 5:32PM |
E5.00004: Ultimate Taylor-Couette turbulence Detlef Lohse, Sander Huisman, Dennis van Gils, Siegfried Grossmann, Chao Sun With the Twente turbulent Taylor-Couette (T$^3$C) facility we can achieve $Re_i = 2 \cdot 10^6$ for the inner cylinder and $Re_o = \pm 10^6$ for the independently rotating outer cylinder. {\it Global} torque measurements have revealed an effective scaling $Nu_\omega \sim Ta^{0.38}$ for the dimensionless angular velocity flux [1]. We now provide {\it local} angular velocity flux measurements from high-speed particle image velocimetry (PIV). Though the flux shows huge fluctuations, its spatial and temporal average nicely agrees with the result from the global measurements and in addition reveals the structure of the turbulent flow. From the PIV images we can also derive the scaling of the radial velocity fluctuations, giving $Re \sim Ta^{1/2}$. Both $Nu_\omega$ and $Re$ scaling relations exactly follow what had been predicted in ref.\ [2] for the ultimate regime. \\[4pt] [1] D. van Gils {\it et~al.}, Phys. Rev. Lett. {\bf 106}, 024502 (2011).\\[0pt] [2] S. Grossmann and D. Lohse, Phys. Fluids {\bf 23}, 045108 (2011). [Preview Abstract] |
Sunday, November 20, 2011 5:32PM - 5:45PM |
E5.00005: Mixing of a stable linear density stratification in Taylor-Couette flow R.L.F. Oglethorpe, C.P. Caulfield, Andrew W. Woods We consider mixing of an initially linear stable salt stratification in turbulent Taylor-Couette flow. The fluid is confined to a cylindrical annulus with a vertical axis. Mixing is caused by rotating the inner cylinder at a constant rate. The outer cylinder is fixed. Experimental measurements show that at high initial bulk Richardson number, defined as $Ri_{0} = N^{2}/\Omega^{2}$, where $N$ is the buoyancy frequency of the initial stratification and $\Omega$ is the rotation rate of the inner cylinder, an initially linear salt stratification develops a series of well mixed layers separated by sharp interfaces. The size of these layers appears to depend on $Ri_{0}$ and the gap width between the cylinders, $\Delta_{R}$. With time, the layers at the top and bottom of the tank evolve in salinity. This leads to entrainment from and eventual mixing with the adjacent layers as the salinity contrast across these interfaces decreases. As a result of successive merger events, eventually the system becomes well mixed. The salinity of the inner layers appears to remain constant, so that salt is transported from the bottom layer to the top layer without changing the structure of the interior. The salt flux through an interface appears to depend only on the rotation rate $\Omega$ of the inner cylinder, consistent with our previous study for an initial two-layer salt stratification (Woods {\it et al.} (2010) {\it J Fluid Mech.} {\bf 663}, 347-357). [Preview Abstract] |
Sunday, November 20, 2011 5:45PM - 5:58PM |
E5.00006: Side wall effects in turbulent thermal convection Richard J.A.M. Stevens, Detlef Lohse, Roberto Verzicco Research in thermally driven convective turbulence has always been trying to achieve the highest Rayleigh number ($Ra$) as various natural heat transfer phenomenon involve very high $Ra$. Since seemingly equivalent experiments with the same $Ra$ and Prandtl $Pr$ numbers and cell aspect--ratio ($\Gamma$) have not given the same heat transfers in the high--end of $Ra$, it has been conjectured that neglected details, like the finite conductivity of horizontal plates and sidewall, could play a role. It has indeed been shown that corrections for the heat leakage through the sidewall and for the finite thermal conductivity of the plates must be considered, although none of them could fully explain the differences among the experiments. Ahlers et al.\ recent experiments suggest that a factor that could trigger different heat transfers regimes is the temperature {\it outside} the cell. Indeed, in real experiments the sidewall is isothermal, but in most models it is assumed to be adiabatic. In our numerical simulations we now allow for an isothermal sidewall and assess the behavior of the system in presence of a conductive sidewall. We discuss the differences between an ideal set--up with perfectly adiabatic side walls and systems with an isothermal sidewall or a sidewall with finite thickness and heat conductivity. [Preview Abstract] |
Sunday, November 20, 2011 5:58PM - 6:11PM |
E5.00007: Boussinesq and non-Boussinesq plumes - universal solutions Ton S. van den Bremer, Gary R. Hunt Closed-form solutions describing the behaviour of rising buoyant axisymmetric turbulent plumes, emitted vertically from area sources in unconfined quiescent environments of uniform density, are proposed in a form that is universally applicable to Boussinesq and non-Boussinesq plumes. This work [1] thereby generalizes and consolidates results obtained separately for Boussinesq and non-Boussinesq plumes both based on the seminal plume model of Morton et al~(1956) [2]. The universality we identify crucially relies on expressing the plume equations in terms of the vertical variation of the plume Richardson number and the dimensionless radius, the introduction of an effective entrainment radius, and the classical entrainment model for which the horizontal entrainment velocity is proportional to the local vertical velocity; this velocity being modified in the non-Boussinesq case by a factor of $\sqrt{\rho/\rho_{a}}$, where $\rho$ and $\rho_{a}$ are the densities of the plume and the ambient fluids, respectively. Using the solutions developed, three characteristic heights are identified.\\[0pt] [1] Van den Bremer, T.S. \& Hunt, G.R., 2010. Universal solutions for Boussinesq and non-Boussinesq plumes. {\em J. Fluid Mech.} \textbf{644}, pp. 165 - 192.\\[0pt] [2] Morton, B.R., Taylor, G.I. \& Turner, J.S., 1956. Turbulent gravitational convection from maintained and instantaneous sources. {\em Proc. Roy. Soc. Lond. A} \textbf{234}, pp. 1 - 23. [Preview Abstract] |
Sunday, November 20, 2011 6:11PM - 6:24PM |
E5.00008: Quantifying near-wall coherent structures in turbulent convection G.S. Gunasegarane, Baburaj A Puthenveettil, Yogesh K Agrawal, Daniel Schmeling, Johannes Bosbach, Jaywant H. Arakeri We present planforms of line plumes formed on horizontal
surfaces in turbulent convection, along with the length of near-
wall line plumes measured from these planforms, in a six decade
range of Rayleigh numbers ($10^5 |
Sunday, November 20, 2011 6:24PM - 6:37PM |
E5.00009: Plume Statistics in Turbulent Rayleigh-B\'enard Convection James Hogg, Johannes Bosbach, Stephan Weiss, Guenter Ahlers We report spatial statistics of thermal plumes based on an analysis of shadowgraph images for a cylindrical Rayleigh-B\'enard sample of height $L = 9.5$ mm and aspect ratio $\Gamma = 10.6$. The fluids consisted of pure gases with Prandtl- numbers $Pr\approx0.7$ and gas mixtures with $0.17 \leq Pr < 0.7$. The Rayleigh-number range was $3\times10^{5} \leq Ra \leq 5\times10^{6}$. We found the plume-length probability-density functions to be well fit by lognormal distributions with fit parameters which revealed a sharp transition from patterns to turbulence. In the turbulent range the mean spacing between plumes was found to scale as $Ra^{-0.33}$, suggesting that the Kolmogorov length $\eta_K$ is the relevant length scale, rather than the thermal boundary-layer thickness. [Preview Abstract] |
Sunday, November 20, 2011 6:37PM - 6:50PM |
E5.00010: Experimental Measurement of the Local Energy Dissipation Rate and its Balance with the Local Heat Flux in Turbulent Thermal Convection Shi-Di Huang, Rui Ni, Ke-Qing Xia The local energy dissipation rate $\epsilon_{u,c}$ in Rayleigh- B\'enard convection cell was measured experimentally using the particle tracking velocimetry method, with varying Rayleigh number Ra, Prandtl number Pr, and system size $H$. It is found that $\epsilon_{u,c}/(\kappa^3H^{-4})=1.05\times10^{-4}Ra^{1.55 \pm0.02}Pr^{1.15\pm0.38}$. The Ra- and H-dependency of the measured result are found to be consistent with the assumption made for the bulk energy dissipation rate $\epsilon_{u,bulk}$ in the Grossmann-Lohse model, while the Pr-dependency is not. A remarkable finding of the study is that $\epsilon_{u,c}$ balances the directly measured local Nusselt number Nu$_{c}$ in the cell center, not only scaling-wise but also in magnitude. [Preview Abstract] |
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