Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session H19: Convection and Buoyancy-Driven Flows: Turbulence |
Hide Abstracts |
Chair: Rudie Kunnen, Technische Universiteit Eindhoven Room: 2006 |
Monday, November 24, 2014 10:30AM - 10:43AM |
H19.00001: An investigation of transitional Phenomena from Laminar to Turbulent Natural Convection using Compressible Direct Numerical Simulation ChungGang Li, Makoto Tsubokura The complete transition from laminar to turbulent natural convection in a long channel is investigated using compressible direct numerical simulation (DNS). Numerical methods of Roe scheme with precontioning and dual time stepping are used for addressing the flow field which is low speed but the density is variable. During the transient development, there are four stages which are laminar, unstable process, relaminarization and turbulence can be obviously identified. After reaching the quasi steady state, the laminar, transition and turbulence simultaneously coexist in the same flow field. Additionally, the comparisons of the statistics with the experimental data are also well consistent. [Preview Abstract] |
Monday, November 24, 2014 10:43AM - 10:56AM |
H19.00002: Covariant Lyapunov Vectors of Chaotic Rayleigh-B\'enard Convection Mu Xu, Mark Paul The complex dynamics of large spatially extended systems that are driven far-from-equilibrium are central to many important challenges. Much of the difficulty is rooted in the fact that the dynamics are extremely high dimensional. Progress has been made using Lyapunov exponents and vectors that have been computed using frequent Gram-Schmidt reorthonormalizations. However, a significant disadvantage of this approach is that the directions of all of the Lyapunov vectors, except the leading order vector, is lost due to the reorthonormalizations. However, it is well known that there exists a set of vectors intrinsic to the dynamics which satisfy the so-called Oseledec splitting and are called the covariant Lyapunov vectors. Recently, algorithms have become available to compute the spectrum of covariant Lyapunov vectors for large spatially extended systems. In this talk, we use the covariant Lyapunov vectors to explore the chaotic dynamics of Rayleigh-B\'enard convection in a large rectangular domain. Knowledge of the covariant Lyapunov vectors allows us to probe fundamental features of the dynamics such as the degree of hyperbolicity, the spatiotemporal features of the spectrum of Lyapunov vectors, and the possible splitting of the dynamics into physical and isolated modes. [Preview Abstract] |
Monday, November 24, 2014 10:56AM - 11:09AM |
H19.00003: Analysis of vortical structures in turbulent natural convection Sangro Park, Changhoon Lee Natural convection of fluid within two parallel walls, Rayleigh-B\'enard convection, is studied by direct numerical simulation using a spectral method. The flow is in soft turbulence regime with Rayleigh number $10^{6}$, $10^{7}$, $10^{8}$, Prandtl number $0.7$ and aspect ratio $4$. We investigate the relations between thermal plumes and vortical structures through manipulating the evolution equations of vorticity and velocity gradient tensor. According to simulation results, horizontal vorticity occurs near the wall and changes into vertical vorticity by vertical stretching of fluid element which is caused by vertical movement of the thermal plume. Additionally, eigenvalues, eigenvectors and invariants of velocity gradient tensor show the topologies of vortical structures, including how vortical structures are tilted or stretched. Difference of velocity gradient tensor between inside thermal plumes and background region is also investigated, and the result indicates that thermal plumes play an important role in changing the distribution of vortical structures. The results of this study are consistent with other researches which suggest that vertical vorticity is stronger in high Rayleigh number flows. Details will be presented in the meeting. [Preview Abstract] |
Monday, November 24, 2014 11:09AM - 11:22AM |
H19.00004: Multi-Scale Coherent Structure Interactions in Rayleigh-Benard Convection Philip Sakievich, Yulia Peet, Ronald Adrian Rayleigh-Benard convection (RBC) is characterized by a rich set of coherent structures. One of the most notable and widely recognized structures in RBC is the large scale circulations, or roll-cells. Roll-cells are identified by large circulatory currents that can span the boundaries of the domain. For domains with aspect ratios (AR) of less than two there is generally only one roll-cell present, but as the AR grows the number of roll-cells increase. Currently little is known about the physical dynamics of multiple roll-cell interactions and their effects on the smaller scale structures such as thermal plumes and waves. In the current presentation we present visualizations from a direct numerical simulation of turbulent RBC in a wide AR cell. We identify multiple roll-cells and track the evolution of smaller scale coherent structures as they develop inside the larger scale roll-cells. In this simulation a cylindrical domain with an AR of 6.3 is used with Prandtl and Rayleigh numbers of 6.3 and 9.6*10$^{\mathrm{7}}$ respectively. The spectral element code Nek5000 is used for simulation. [Preview Abstract] |
Monday, November 24, 2014 11:22AM - 11:35AM |
H19.00005: Anomalous scaling of temperature structure functions in turbulent thermal convection Penger Tong, Xiaozhou He, Xiaodong Shang The scaling properties of the temperature structure function (SF) are investigated in turbulent Rayleigh-Benard convection [1]. The measured SFs are found to exhibit good scaling in space and time and the resulting SF exponent is obtained both at the center of the convection cell and near the sidewall. It is found that the difference in the functional form of the measured SF exponents at the two locations in the cell is caused by the change of the geometry of the most dissipative structures in the (inhomogeneous) temperature field from being sheet-like at the cell center to filament-like near the sidewall. The experiment thus provides direct evidence showing that the universality features of turbulent cascade are linked to the degree of anisotropy and inhomogeneity of turbulent statistics. \\[4pt] [1] ``Test of the anomalous scaling of passive temperature fluctuations in turbulent Rayleigh-Benard convection with spatial inhomogeneity,'' Xiaozhou He, Xiao-dong Shang and Penger Tong, J. Fluid Mech. \textbf{753}, 104 (2014). [Preview Abstract] |
Monday, November 24, 2014 11:35AM - 11:48AM |
H19.00006: A New Parameterization of $Nu$-$Ra$ Relation in Turbulent Rayleigh-B\'{e}nard Convection J. Chen, Zi-Ping Che, Zhen-Su She Nusselt-Rayleigh relation is a key subject in the study of turbulent Rayleigh-B\'{e}nard convection (RBC). She et al. introduced Structural Ensemble Dynamics(SED) theory to study wall-bounded turbulence, which yields a multi-layer model of velocity and temperature profiles for RBC system. Here, we report a result of this study, i.e. a new parameterization of Nusselt number(Nu) as a function of Rayleigh number(Ra): $Nu=\alpha Ra^{1/7} \mathrm{exp}\left(\gamma Ra^\beta\right)$. The parameters ($\alpha$, $\beta$ and $\gamma$) are supposed to be slowly varying with Ra and other physical parameters, in particular Prandtl number(Pr). Analysis of a set of experimental data with $Ra=10^8\sim10^{12}$ and $Pr=0.7\sim7.0$ shows that this parameterization is efficient, yielding an accurate description of Nu-Ra with errors bounded within $1\%$. This parameterization surprisingly reveals two distinct states as $\alpha$ varies, with transition at $\alpha=1$. Then, an analytic model linking the variation of the three parameters is proposed, yielding a uniform description for the enormous empirical Nu-Ra data, significantly more accurate than the well-known Grossmann-Lohse (GL) model. In conclusion, the SED theory emphasizing the internal profiles provides a viable description of the RBC system. [Preview Abstract] |
Monday, November 24, 2014 11:48AM - 12:01PM |
H19.00007: Temperature power spectra of turbulent Rayleigh-B\'enard convection with a Prandtl number $Pr = 12.3$ $^*$ Guenter Ahlers, Ping Wei, Xiaozhou He We report on measurements of power spectra of temperature fluctuations in turbulent Rayleigh-B\'enard convection in a cylindrical sample with aspect ratio $\Gamma = D/L = 0.50$ (D is the diameter and L the height) as a function of the distance $z$ from the bottom or top plate. The working fluid was a fluorocarbon at a mean temperature $T_{m} = 25.00^{o}$C with a Prandtl number $Pr = 12.3$, and the Rayleigh number was $Ra \simeq 4 \times10^{11}$. Consistent with many previous investigations, there was a low-frequency range, spanning about a factor of twenty, where the spectra could be described by a power law $P(f) = P_0 f^{-\alpha}$. Contrary to the finding by He et al.\footnote{X. He, D.P.M. vanGils, E. Bodenschatz, and G.Ahlers, Phys. Rev. Lett. {\bf 112}, 174501 (2014).} for $Pr \simeq 0.8$ of a universal spectrum with $\alpha = 1.0$ in the near-wall range $z/L \leq 0.1$ and $\alpha \simeq 1.5$ for $z/L = 0.5$, we found that $\alpha$ varied with $z$ from about 0.6 near the plate ($z/L \simeq 0.01$) to about 1.1 at the cell center ($z/L = 0.5$). Along the sample center line and for $z/L \leq 0.1$ $\alpha$ could be described well by $\alpha =\alpha_0 \ln(z/L) + \alpha_1$ with $\alpha_0 \simeq 0.2$ and $\alpha_1 \simeq 1.5$. [Preview Abstract] |
Monday, November 24, 2014 12:01PM - 12:14PM |
H19.00008: Anisotropic turbulent temperature probability densities in high-Ra thermal convection Xiaozhou He, Dennis P. M. van Gils, Eberhard Bodenschatz, Guenter Ahlers We present systematic measurements of conditional diffusion $r(x) = \langle \ddot{X} \vert X=x\rangle$ and dissipation $q(x) = \langle (\dot{X})^2 \vert X=x \rangle$ of the normalized temperature fluctuations $X=(T-\bar{T})/\sigma$ in turbulent Rayleigh-B\'enard convection (RBC) at several radial positions where the flow is anisotropic. The data cover the Rayleigh-number range $10^{13} \leq Ra \leq 10^{15}$ for a Prandtl number $Pr \simeq 0.80$. The sample was a right-circular cylinder with aspect ratio $\Gamma \equiv D/L = 0.50$ ($D= 1.12$ m is the diameter and $L = 2.24$ m is the height). We compared experimental forms of $q(x)$ and $r(x)$ with previous investigations based on the ``fluctuation-dissipation'' relation for isotropic flow.\footnote{Emily S. C. Ching, Phys. Rev. Lett. {\bf 70}, 283 (1993)} We derived a general form for the temperature probability-density function (PDF). Similar analyses have also been extended to the study of the temperature time derivative, and to the temperature increment in the time domain. Good agreements are found between experimental temperature probability densities and predicted PDF forms. [Preview Abstract] |
Monday, November 24, 2014 12:14PM - 12:27PM |
H19.00009: Scale-by-scale energy budget in turbulent convection Rudie Kunnen, Herman Clercx Turbulent free convection is driven by buoyancy. A footprint of buoyancy is thus expected in the energy cascade. The existence of this so-called Bolgiano--Obukhov (BO) scaling is a long-standing open question. We use DNS of Rayleigh--B\'enard convection in a horizontally periodic domain to address this question. Moderate Rayleigh numbers $2.6\times 10^6$ and $2.5\times 10^7$ are applied, at three different Prandtl numbers $1$, $3$ and $10$. We show that the length scale bounding the convective scaling regime from below, the Bolgiano scale $L_B$, is typically large relative to the domain size. Scale-by-scale energy budgets are calculated based on Yakhot's equivalent of Kolmogorov's isotropic four-fifths law for convection. They reveal that buoyancy is active on many scales, obscuring the classical Kolmogorov scaling for scales smaller than $L_B$. Only at very large separations a buoyancy-dominated scaling range could exist. Close to the plates, where $L_B$ is smaller, anisotropy complicates the detection of scaling. [Preview Abstract] |
Monday, November 24, 2014 12:27PM - 12:40PM |
H19.00010: Turbulence production in low-Pr number convection flows Joerg Schumacher, Janet Scheel Convection at very low Prandtl numbers can be considered in some sense as Terra Incognita given the detailed investigations for $Pr\sim 1$ or $Pr>1$ and the challenges in studying these turbulent flows in simulation and experiment. Laboratory experiments for $Pr< 10^{-1}$ have to be conducted in liquid metals such as gallium at $Pr=0.021$ and sodium at $Pr=0.005$ both of which are opaque. High-resolution direct numerical simulations are therefore the only tool to unravel the detailed three-dimensional mechanisms of turbulence generation in low-Prandtl number flows and to compare to convection flows at $Pr\sim 1$. We therefore analyze flows for which Rayleigh and Prandtl numbers are chosen such that the same Grashof number results. Analysis on enstrophy production due to vortex stretching and temperature gradient are discussed together with statistics of local strain. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700