Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session G11: Rayleigh-Benard Convection I |
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Chair: Hessam Babaee, MIT Room: 111 |
Monday, November 23, 2015 8:00AM - 8:13AM |
G11.00001: Traveling Waves in Natural-convection Flow Around an Array of Heated Cylinders Hessam Babaee, FangFang Xie, Chryssostomos Chryssostomidis, George Karniadakis In this numerical study traveling waves formed around an array of heated cylinders are investigated. The cylinders with a heat source are confined vertically. The natural convection flow around the cylinders leads to horizontal and axial traveling waves. In this study the physical mechanisms leading to the formation of the traveling wave are characterized. The effect of traveling wave on Nusselt number around the cylinder is also investigated. We use Dynamically Orthogonal (DO) decomposition with stochastic perturbations to capture the coherent structures in the flow. [Preview Abstract] |
Monday, November 23, 2015 8:13AM - 8:26AM |
G11.00002: Main Modes of Heat Transport in Rayleigh-B\'enard Convection Analyzed by a POD approach Johannes Luelff Rayleigh-B\'enard convection, i.e. the buoyancy-induced movement of a fluid enclosed between two horizontal plates, is the definite setup to study thermal convection. We are interested in the heat transport of the main modes that are found in the convection cell. To this end, we apply the technique of proper orthogonal decomposition (POD) to obtain a set of empirical basis modes from simulation data. Usually the POD method results in modes that are optimal in describing the generalized energy, i.e. kinetic energy plus temperature variance. We extend the technique so that instead it gives the optimal modes with respect to the heat transport, measured in terms of the Nusselt number. We then demonstrate at numerical simulations of different RB setups and geometries that the proposed ansatz performs consistently better than the standard approach in describing the heat transport. Furthermore, the coherent structures that are connected to the biggest heat transport are examined. [Preview Abstract] |
Monday, November 23, 2015 8:26AM - 8:39AM |
G11.00003: Prandtl number dependence of heat and mass transfer in horizontal convection Olga Shishkina In a horizontal convection system heat and fluid flow occurs from a differential heating/cooling of the bottom surface of a fluid layer. In the present work we study how the convective heat transport, measured by the Nusselt number Nu, scales with the Rayleigh number Ra and Prandtl number Pr and derive multiple scaling regimes, one of which is the Rossby scaling (H.T. Rossby, Deep Sea Res., 12, 1965) for laminar horizontal convection flows. Our theoretical results are supported by direct numerical simulations for a wide range of Ra and Pr. [Preview Abstract] |
Monday, November 23, 2015 8:39AM - 8:52AM |
G11.00004: Global and local statistics in turbulent convection at low Prandtl numbers Janet Scheel, Joerg Schumacher Very high resolution direct numerical simulations (DNS) of turbulent Rayleigh-Benard Convection (RBC) for low Prandtl numbers which are typical for liquid metals such as mercury/gallium (0.021) or sodium (0.005) will be presented. The scaling of global momentum and heat transport is determined and compared to experimental and theoretical results. We also present mean profiles of root-mean-square velocity and vorticity as well as the thermal and kinetic energy dissipation rates. The velocity boundary layer is found to be much thinner than the thermal boundary layer, and the consequences of this for the heat transport as well as the nature of turbulence in RBC will also be discussed. Finally we investigate the skin friction coefficient and shear Reynolds numbers for these systems. Results will also be compared and contrasted with results from DNS for Prandtl numbers of 0.7 and 6.0 and similar Rayleigh numbers. [Preview Abstract] |
Monday, November 23, 2015 8:52AM - 9:05AM |
G11.00005: Turbulent structures in convection from a heated sidewall in a stratified fluid Keaton Burns, Andrew Wells, Glenn Flierl We present direct numerical simulations of 2D turbulent convection along a heated vertical wall in a fluid with a stable background stratification. Our model considers a Boussinesq fluid with a constant background temperature gradient in a horizontally bounded and vertically periodic domain. The temperature along one sidewall is increased by a constant amount, driving an upward convective flow along the wall and introducing a potential-rise length scale to the system. We examine the resulting turbulent structures and statistics at and above Reynolds numbers of $10^5$, which lies in the range of well-developed turbulent heat transfer for the unstratified case. We also discuss the applicability of this system as a model of melt water flows alongside icebergs and ice shelves, and the potential emergence of convective layers without double-diffusion in geophysical scale problems, in contrast to the double-diffusive layering in laboratory models. [Preview Abstract] |
Monday, November 23, 2015 9:05AM - 9:18AM |
G11.00006: Penetrative internally heated convection in two and three dimensions David Goluskin, Erwin van der Poel We carry out 2D and 3D direct numerical simulations of penetrative convection in a fluid layer. The convection is driven by uniform internal heating between top and bottom plates of equal temperature. The Prandtl number is varied between $0.1$ and $10$, and a Rayleigh number based on the heating rate is varied up to $5\times10^{10}$. The asymmetry between upward and downward heat transport is greatly affected by spatial dimension. The fraction of internally produced heat escaping across the bottom plate, as opposed to the top one, is 1/2 without flow and initially falls as convection strengthens. As convection becomes very strong, however, this fall continues in 3D but reverses in 2D. The mean fluid temperature is much less sensitive to dimension, growing with the heating rate ($H$) like $H^{4/5}$ in both 2D and 3D. We draw analogy between the inverse of this fluid temperature and the Nusselt number in ordinary Rayleigh-B\'enard convection. [Preview Abstract] |
Monday, November 23, 2015 9:18AM - 9:31AM |
G11.00007: Mixed insulating and conducting boundary conditions in Rayleigh-B\'enard convection Dennis Bakhuis, Rodolfo Ostilla M\'onico, Erwin van der Poel, Roberto Verzicco, Detlef Lohse We report the results of 3D direct numerical simulations of a rectangular doubly periodic Rayleigh-B\'enard system. These results are an extension of earlier 2D work by Ripesi et al. (Journal of Fluid Mechanics 742, 636, 2014). The Rayleigh number is between $10^7$ and $10^9$ and the Prandtl number is set to unity. The bottom plate is homogeneously heated and the cold top plate of this setup has been split into conducting and insulating regions. While keeping both areas equal the pattern has been varied and multiple characteristics like the Nusselt number and bulk temperature have been recorded. When the top plate was divided into one conducting and insulating halves, we see that the Nusselt number is about two thirds of the fully conducting case. However, when we now increase the number of divisions, the Nusselt number slowly approaches that of the fully conducting case. This is a surprising result, as even though only half of the effective area can conduct heat, the same heat transport as a fully conducting cold plate is achieved. [Preview Abstract] |
Monday, November 23, 2015 9:31AM - 9:44AM |
G11.00008: High Rayleigh number simulations in a slender laterally periodic domain Roberto Verzicco, Erwin van der Poel, Detlef Lohse The results of three-dimensional DNS simulations of Rayleigh-B\'enard convection with Ra up to $10^{13}$ in a laterally periodic geometry with progressively decreasing aspect-ratios are presented. We show global quantities such as the heat transport as well as local time-averages and vertical profiles. It is observed that the heat transport for laterally unconfined geometries can be computed at relatively small aspect-ratios whose value decreases with Rayleigh number. This is beneficial in terms of computational cost, as the total simulated domain gets smaller. The boundary layers profiles are studied and movies of horizontal cross-section of the bulk and the boundary layer are shown. [Preview Abstract] |
Monday, November 23, 2015 9:44AM - 9:57AM |
G11.00009: Thermal boundary layer profiles in turbulent Rayleigh-Benard convection Penger Tong, Yin Wang, Xiaozhou He We have studied the mean temperature boundary layer profile T(z) and root-mean-square (rms) temperature profile S(z) in turbulent Rayleigh-Benard convection along the central axis z of a convection cell, which has a thin vertical disk shape with an inner diameter D = 18 cm. The temperature measurements were made at fixed Prandtl numbers Pr = 4.3 and Pr = 7.6 and with the Rayleigh number Ra varied in the range between $1\times 10^9$ and $1\times 10^{10}$. The measured T(z) for different values of Pr and Ra can all be well described by the newly proposed boundary layer model [Shishkina et al., Phys. Rev. Lett. {\bf 114}, 114302 (2015)] with a parameter c varying from 1 to 2.1. The measured rms temperature profile S(z) is found to be a single-peaked function with the peak position located at $z\simeq 0.8 \delta$, where $\delta$ is the boundary layer thickness. The measured S(z) has two separate scaling lengths. Within the boundary layer, it scales with $\delta$ and can be fitted to a power law, $S(z)\sim (z/\delta)^{\alpha}$ with $\alpha\simeq 0.6$. Outside the boundary layer, it scales with the cell size D and follows a different power law, $S(z)\sim (z/D)^{\beta}$, with $\beta= -0.42$. *This work was supported by the Research Grants Council of Hong Kong SAR. [Preview Abstract] |
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