Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session Q33: Convection and Buoyancy Driven Flows: Turbulent Rayleigh-BenardConvection
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Chair: Yulia Peet, Arizona State University Room: 106 |
Tuesday, November 21, 2017 12:50PM - 1:03PM |
Q33.00001: Organization and dynamics of the large-scale motions of turbulent Rayleigh-B\'{e}nard Convection in a cylindrical domain with a moderate aspect ratio. Yulia Peet, Philip Sakievich, Ronald Adrian At high Rayleigh numbers in moderate aspect-ratio cylindrical domains turbulent Rayleigh-B\'{e}enard convection (RBC) exhibits coherent large-scale motions that organize themselves into a collection of three-dimensional ``roll cells''. The current study presents a relatively long, on the order of 3000 free fall time units (or 100 eddy turnovers), Direct Numerical Simulation of the RBC in a cylindrical domain with a 6.3 aspect ratio and the Rayleigh number of 9.6x10$^{\mathrm{7}}$. The study shows that the spatial organization of the roll cells in the investigated domain can be well described by the azimuthal Fourier modes. A hub-and-spoke mode-3 pattern first emerges and dominates the flow for the first 20 eddy turnovers, which then transitions into a mode-2 pattern that persists for the remainder of the simulations. A spatial inhomogeneity of the observed mode-3 and mode-2 structures is investigated. A conclusion follows that the cylindrical geometry constraint applies a ``squeezing'' effect to the large-scale structures, which forces them to align with a strong azimuthal periodicity. [Preview Abstract] |
Tuesday, November 21, 2017 1:03PM - 1:16PM |
Q33.00002: Temperature boundary layer profiles in turbulent Rayleigh-Benard convection Emily S.C. Ching, Mohammad S. Emran, Susanne Horn, Olga Shishkina Classical boundary-layer theory for steady flows cannot adequately describe the boundary layer profiles in turbulent Rayleigh-Benard convection. We have developed a thermal boundary layer equation which takes into account fluctuations in terms of an eddy thermal diffusivity. Based on Prandtl's mixing length ideas, we relate the eddy thermal diffusivity to the stream function. With this proposed relation, we can solve the thermal boundary layer equation and obtain a closed-form expression for the dimensionless mean temperature profile in terms of two independent parameters: $\theta(\xi)= \frac{1}{b}\int_0^{b\,\xi}\,[1+\frac{3a^3}{b^3}(\eta-\arctan(\eta))]^{-c}\,d\eta, $ where $\xi$ is the similarity variable and the parameters $a$, $b$, and $c$ are related by the condition $\theta(\infty)=1$. With a proper choice of the parameters, our predictions of the temperature profile are in excellent agreement with the results of our direct numerical simulations for a wide range of Prandtl numbers (Pr), from Pr=0.01 to Pr=2547.9. [Preview Abstract] |
Tuesday, November 21, 2017 1:16PM - 1:29PM |
Q33.00003: Boundary layers in turbulent convection for air, liquid gallium and liquid sodium Janet Scheel, Joerg Schumacher The scaling of physical quantities that characterize the shape and dynamics of the viscous and thermal boundary layers with respect to the Rayleigh number will be presented for three series of three-dimensional high-resolution direct numerical simulations of Rayleigh-Benard convection (RBC) in a closed cylindrical cell of aspect ratio one. The simulations have been conducted for convection in air at a Prandtl number Pr = 0.7, in liquid gallium at Pr = 0.021 and in liquid sodium at Pr = 0.005. Then we discuss three statistical analysis methods which have been developed to predict the transition of turbulent RBC into the ultimate regime. The methods are based on the large-scale properties of the velocity profile. All three methods indicate that the range of critical Rayleigh numbers is shifted to smaller magnitudes as the Prandtl number becomes smaller. This work is supported by the Priority Programme SPP 1881 of the Deutsche Forschungsgemeinschaft. [Preview Abstract] |
Tuesday, November 21, 2017 1:29PM - 1:42PM |
Q33.00004: Direct numerical simulation of turbulent Rayleigh-B\'{e}nard convection in a vertical thin disk Wei Xu, Yin Wang, Xiao-Zhou He, Hiu-Fai Yik, Xiao-Ping Wang, Jorg Schumacher, Penger Tong We report a direct numerical simulation (DNS) of turbulent Rayleigh-B\'{e}nard convection in a thin vertical disk with a high-order spectral element method code NEK5000. An unstructured mesh is used to adapt the turbulent flow in the thin disk and to ensure that the mesh sizes satisfy the refined Groetzbach criterion and a new criterion for thin boundary layers proposed by Shishkina et al. The DNS results for the mean and variance temperature profiles in the thermal boundary layer region are found to be in good agreement with the predictions of the new boundary layer models proposed by Shishkina et al. [Phys. Rev. Lett. 114, 114302 (2015)] and Wang et al. [Phys. Rev. Fluids 1, 082301(R) (2016)]. Furthermore, we numerically calculate the five budget terms in the boundary layer equation, which are difficult to measure in experiment. The DNS results agree well with the theoretical predictions by Wang et al. Our numerical work thus provides a strong support for the development of a common framework for understanding the effect of boundary layer fluctuations. [Preview Abstract] |
Tuesday, November 21, 2017 1:42PM - 1:55PM |
Q33.00005: Rayleigh-B\'{e}nard convection with side wall heating Jun Zhang, Jinzi (Mac) Huang As an important mechanism of heat transfer in fluids, Rayleigh-B\'{e}nard convection (RBC) has been thoroughly studied in the past. In this talk, we examine the effect of heating from one vertical sidewall in an otherwise classical RBC in a cubic domain. With side heating introduced, experiment performed at high Rayleigh number shows a decrease of Nusselt number, while the speed of large scale circulation is enhanced due to the upwelling flow generated along the heated wall. Through the measurement of thermal boundary layers, we find that their thickness at both the top and bottom plates stay unaffected as long as the bottom heating power is fixed, while the bulk temperature increases with the side heating. Since we have now a non-isothermal boundary condition on the heated wall, we also discuss a modified definition of Nu that takes into account of the heat injection from the side. [Preview Abstract] |
Tuesday, November 21, 2017 1:55PM - 2:08PM |
Q33.00006: A new scaling law for temperature variance profile in the mixing zone of turbulent Rayleigh-B\'{e}nard convection Yin Wang, Wei Xu, Xiao-Zhou He, Hiu-Fai Yik, Xiao-Ping Wang, Jorg Schumacher, Penger Tong We report a combined experimental and numerical study of the scaling properties of the temperature variance profile $\eta $(z) along the central z axis of turbulent Rayleigh-B\'{e}nard convection in a thin disk cell and an upright cylinder of aspect ratio unity. In the mixing zone outside the thermal boundary layer region, the measured $\eta $(z) is found to scale with the cell height H in both cells and obey a power law, $\eta $(z)\textasciitilde (z/H)$^{\mathrm{\varepsilon }}$, with the obtained values of $\varepsilon $ being very close to -1. Based on the experimental and numerical findings, we derive a new equation for $\eta $(z) in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work thus provides a common framework for understanding the effect of boundary layer fluctuations on the scaling properties of the temperature variance profile in turbulent Rayleigh- B\'{e}nard convection. [Preview Abstract] |
Tuesday, November 21, 2017 2:08PM - 2:21PM |
Q33.00007: Heat Transport Enhancement of Turbulent Thermal Convection by Inserted Channels Ke-Qing Xia, Lu Zhang We report an experimental study on the heat transport properties of turbulent Rayleigh Benard Convection (RBC) in a rectangular cell with two types of 3D-printed structures inserted inside. The first one splits the original rectangular cell into 60 identical sub cells whose aspect ratio is 1:1:10 (length, width, height). The second one splits the cell into 30 sub cells, each with a 1:2:10 aspect ratio and a baffle in the center. We find that for large Rayleigh numbers (Ra), the Nusselt numbers (Nu) of both structures increase compared with that of the empty rectangular cell. An enhancement in Nu as much as 20\% is found for the second type of insertion at Rayleigh number $2\times10^9$. Moreover, the Nu-Ra scaling shows a transition with both geometries. The particle image velocimetry (PIV) measurement within a single sub unit indicates that the transition may be related to the laminar to turbulent transition in flow field. Direct numerical simulations (DNS) confirm the experimental results. Our results demonstrate the potential in using insertions to enhance passive heat transfer. [Preview Abstract] |
Tuesday, November 21, 2017 2:21PM - 2:34PM |
Q33.00008: Turbulent Superstructures in Rayleigh-B\'{e}nard convection at different Prandtl number J\"org Schumacher, Ambrish Pandey, Martin Ender, R\"udiger Westermann, Janet D. Scheel Large-scale patterns of the temperature and velocity field in horizontally extended cells can be considered as turbulent superstructures in Rayleigh-B\'{e}nard convection (RBC). These structures are obtained once the turbulent fluctuations are removed by a finite-time average. Their existence has been reported for example in Bailon-Cuba et al. (J. Fluid Mech., vol. 655, 152-173 (2010)). This large-scale order obeys a strong similarity with the well-studied patterns from the weakly nonlinear regime at lower Rayleigh number in RBC. In the present work we analyze the superstructures of RBC at different Prandtl number for Prandtl values between $Pr=0.005$ for liquid sodium and 7 for water. The characteristic evolution time scales, the typical spatial extension of the rolls and the properties of the defects of the resulting superstructure patterns are analyzed. Data are obtained from well-resolved spectral element direct numerical simulations. The work is supported by the Priority Programme SPP 1881 of the Deutsche Forschungsgemeinschaft. [Preview Abstract] |
Tuesday, November 21, 2017 2:34PM - 2:47PM |
Q33.00009: Kinetic thermal structure in turbulent Rayleigh-B\'{e}nard convection Jun Chen, Ze-Xia Yin, Zhen-Su She, Yun Bao Plumes are believed to be the most important heat carrier in turbulent Rayleigh--B\'{e}nard convection (RBC). However, a physically sound and clear definition of plume is still absent. We report here the investigation of a definition of plume called kinetic thermal structure (KTS), based on the analysis of vertical velocity gradient ($\Lambda = \partial w/\partial z$), using direct numerical simulation (DNS) data of the three-dimensional RBC in a rectangular cell for $Pr=0.7$ and $Ra=1\times10^8\sim5\times10^9$. It is shown that the conditional average of temperature on $\Lambda$ exhibits such a behavior that when $\Lambda$ is larger than a threshold, the volume carries a constant temperature of fluid, hence defines an unambiguous thermal structure, KTS. The DNS show that the KTS behaves in a sheet-like shape near the conducting plate, and becomes slender and smaller with increasing $Ra$. The heat flux carried by KTS displays a scaling law, with an exponent larger than the global-$Nu$--$Ra$ scaling, indicating stronger heat transport than the turbulent background. An advantage of the KTS is its connection to the balance equation allowing, for the first time, a prediction of the $Ra$-dependence of its vertical velocity and the characteristic $\Lambda$ threshold, validated by DNS. [Preview Abstract] |
Tuesday, November 21, 2017 2:47PM - 3:00PM |
Q33.00010: Effect of wall roughness on the large scale circulation in turbulent convection with cubic confinement Najmeh Foroozani, Joseph Niemela, vincenzo Armenio, Katepalli Sreenivasan Large-eddy simulations of turbulent Rayleigh-Bernard convection were conducted for a fluid of Prandtl number Pr=0.7 confined within a cubic box with rough top and bottom walls and Rayleigh number Ra=$10^8$. Two cases were considered, in which the roughness elements were formed by 1) 8 grooves aligned parallel to one set of the lateral walls and 2) 64 pyramidal structures uniformly distributed without a preferred orientation. For case (1), we observe that the large scale circulation (LSC) is unstable: on average it is aligned parallel to one set of lateral walls-- along the direction of the grooves-- but oscillates between the two adjacent diagonal planes with a well-defined frequency. For case (2), the LSC is oriented along one diagonal plane or the other, with occasional switching between them, consistent with observations made by Foroozani, et al. PRE 95, 033107 (2017) for the case of mechanically smooth walls in the same cubic geometry. Finally, when the roughness height for case (1) is reduced so that the horizontal boundaries are hydrodynamically smooth, the LSC reverts to this same diagonal orientation with occasional switching. [Preview Abstract] |
Tuesday, November 21, 2017 3:00PM - 3:13PM |
Q33.00011: Temperature oscillation and the sloshing motion of the large-scale circulation in turbulent Rayleigh-B{\'e}nard convection Heng-Dong Xi, Xin Chen, Ke-Qing Xia We report an experimental study of the temperature oscillation and the sloshing motion of the large-scale circulation (LSC) in turbulent Rayleigh-B{\'e}nard convection in water. Temperature measurements were made in aspect ratio one cylindrical cell by probes put in fluid and embedded in the sidewall simultaneously, and located at the 1/4, 1/2 and 3/4 heights of the convection cell. The results show that the temperature measured in fluid contains information of both the LSC and the signature of the hot and cold plumes, while the temperature measured in sidewall only contains information of the LSC. It is found that the sloshing motion of the LSC can be measured by both the temperatures in fluid and in sidewall. We also studies the effect of cell tilting on the temperature oscillation and sloshing motion of the LSC. It is found that both the amplitude and the frequency of the temperature oscillation (and the sloshing motion) increase when the tilt angle increases, while the off-center distance of the sloshing motion of the LSC remains unchanged. [Preview Abstract] |
Tuesday, November 21, 2017 3:13PM - 3:26PM |
Q33.00012: A similarity model solution for corner-roll in turbulent Rayleigh-B\'{e}nard convection Wen-Feng Zhou, Jun Chen, Zhen-Su She, Yun Bao The corner-roll (CR) is the coherent structure in Rayleigh-B\'{e}nard convection (RBC), playing an important role in determining convection dynamics and heat transport. By inspecting the streamlines of the average flow field of direct numerical simulation (DNS) of RBC for Rayleigh number, $10^8\le Ra\le5\times10^9$, we propose a similarity model of statistically steady CR, based on an invariant geometrical form for the central role connected to a multi-layer description near the wall. It is shown that the model predicts the right characteristics of the mean velocity scaling $u_{cr}/U_f\sim Ra^{-0.165}$ and global Reynolds number's scaling $Re_{cr}\sim Ra^{0.25}$, compared to DNS. Furthermore, the model allows to extract, from DNS, a characteristic velocity scaling and a Reynolds number's scaling for the CR. More interestingly, we find that the CR possesses a Nusselt number scaling, $Nu_{cr}\sim Ra^{0.33}$, higher than the wind-shearing region $Nu_{sh}\sim Ra^{0.285}$. This is explained by a model considering the mechanical balance of plume emission in CR, respectively predicting $Nu_{cr\_mod}\sim Ra^{1/3}$, $Re_{cr\_mod}\sim Nu*\frac{r}{H}\sim Ra^{1/3-0.085}$, and $u_{cr\_mod}/U_{f} \sim Ra^{-1/6}$. In conclusion, a similarity model for CR is proposed and validated by DNS. [Preview Abstract] |
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