Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session GH: Convection and Buoyancy Driven Flows IV |
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Chair: Andrew Duggleby, Texas A&M University Room: Long Beach Convention Center 103C |
Monday, November 22, 2010 8:00AM - 8:13AM |
GH.00001: Homogeneous purely buoyancy driven turbulent flow Jaywant Arakeri, Murali Cholemari, Shashikant Pawar An unstable density difference across a long vertical tube open at both ends leads to convection that is axially homogeneous with a linear density gradient. We report results from such tube convection experiments, with driving density caused by salt concentration difference or temperature difference. At high enough Rayleigh numbers (Ra) the convection is turbulent with zero mean flow and zero mean Reynolds shear stresses; thus turbulent production is purely by buoyancy. We observe different regimes of turbulent convection. At very high Ra the Nusselt number scales as the square root of the Rayleigh number, giving the so-called ``ultimate regime'' of convection predicted for Rayleigh-Benard convection in limit of infinite Ra. Turbulent convection at intermediate Ra, the Nusselt number scales as Ra$^{0.3}$. In both regimes, the flux and the Taylor scale Reynolds number are more than order of magnitude larger than those obtained in Rayleigh-Benard convection. Absence of a mean flow makes this an ideal flow to study shear free turbulence near a wall. [Preview Abstract] |
Monday, November 22, 2010 8:13AM - 8:26AM |
GH.00002: Viscous boundary layers in high Rayleigh number convection: A new insight from 3d velocity measurements Ronald du Puits, Ling Li, Andr\'e Thess The local transport inside the boundary layers in turbulent convection is one of the keys to understand the scaling of the global heat transport with respect to the temperature gradient and the vertical extent of a wall bounded fluid-mechanical system. We report highly resolved 3d-Laser Doppler Velocimetry measurements in a large-scale Rayleigh-B\'{e}nard experiment with air at Rayleigh numbers up to 10$^{12}$. The measurements were undertaken in the vicinity of the cooling plate in the central axis of the cylindrical sample. They differ from those reported in the paper du Puits et al [Phys. Rev. E 80, 036318 (2009)] in that all three velocity components have been measured simultaneously. In the present communication we will discuss the results of these measurements and compare them with previous ones as well as with theoretical predictions about the mean velocity profile and the fluctuations in non-isothermal shear layers. [Preview Abstract] |
Monday, November 22, 2010 8:26AM - 8:39AM |
GH.00003: Dependence of the Nusselt number on the Rayleigh number for Prandtl numbers near 0.7 James Hogg, Guenter Ahlers We report Nusselt-number measurements for a cylindrical Rayleigh-B\'enard sample of height $L = 49.6$ cm and aspect ratio $\Gamma = 0.497$ that were made using three pure gases: helium (Prandtl number Pr=0.67), nitrogen (Pr=0.73), and argon (Pr=0.67-0.70) at pressures up to 47 bars. They cover the Rayleigh number range $9\times10^{6} < Ra < 2\times10^{11}$. The uncorrected results are not well fit by the standard power law $Nu \propto Ra^{\gamma_{eff}}$ and the results for different gases disagree more than can be attributed to any expected Prandtl-number dependence. We find that a correction to the Nusselt number using a model for the non-linear temperature gradient in the side wall brings the results for different gases into agreement in their region of overlap. After the side-wall correction, the Nusselt number results are consistent with a power law, with $\gamma_{eff} \approx 0.32$ for relatively large $Ra$ and $\gamma_{eff} \approx 0.27$ for relatively small $Ra$. [Preview Abstract] |
Monday, November 22, 2010 8:39AM - 8:52AM |
GH.00004: Viscous and Thermal Boundary Layers in Simulated Turbulent Rayleigh-B\'enard Convection Janet Scheel, Elissa Kim We present the results from numerical simulations of three-dimensional, fully turbulent Rayleigh-B\'enard convection for cylindrical cells of aspect ratio 1 (diameter = depth). We use experimentally realistic boundary conditions, Prandtl numbers of 0.4 and 0.7, and Rayleigh numbers between $10^5$ and $10^9$. We focus on the thermal and viscous boundary layers, and compute profiles and boundary layer thicknesses in a variety of ways. We find that the different methods can effect the results. We also compare our results to experiments and theory. [Preview Abstract] |
Monday, November 22, 2010 8:52AM - 9:05AM |
GH.00005: Transient buoyancy-driven flow in a vertical cylindrical enclosure with wavy-sidewall due to thermal and concentration gradients Fausto Sanchez, Simon Martinez, Hugo Ramirez, Abraham Medina An axisymmetric transient convection flow, due to thermal and concentration gradients within a vertical cylindrical enclosure with adiabatic wavy sidewall, was studied. The two important cases of enclosure heated from below and heated from the top were studied. An analytical coordinate transformation was used to change the computation domain into a square. The heat and mass transfer were analyzed using non-dimensional parameters which include the cavity aspect ratio, the dimensionless wavelength and amplitude of the wavy-wall, Rayleigh and Prandtl numbers and the buoyancy ratio. For all cases the upper surface is consider as the one with high concentration, while the others are impermeable. Numerical results using a streamfunction formulation were developed. Heatlines and mass lines were used to illustrate the transport phenomena. Average Nusselt and Sherwood numbers were evaluated while the convection patterns arise within the cavity. The wavy-wall was found to promote thermal stratification and low velocity multiple cell patterns for low buoyancy ratio. [Preview Abstract] |
Monday, November 22, 2010 9:05AM - 9:18AM |
GH.00006: Natural convection in a cylindrical cavity Jose Nunez, Miguel Lopez, Eduardo Ramos, Guillermo Hernandez, Sergio Cuevas, Minerva Vargas Natural convection in a vertical cylinder heated from below is studied experimentally and numerically. The aspect ratio (diameter/height) is 1.3 and we observe convective motions for a Prandtl number of 6.66 and a range of Rayleigh numbers from $1.0\times 10^5$ to $5.0\times 10^6$. This range of Rayleigh numbers includes steady and time-dependent flows. Experimental observations were made with a composed PIV system capable of simultaneously obtaining velocity distributions in two mutually perpendicular planes. The numerical model comprises the solution of the three-dimensional time-dependent Boussinesq equations in cylindrical coordinates. In all cases analyzed, the flows present complex three-dimensional structures and we use the \textit{vortex core} concept as a visualization technique to characterize the fluid motion. Experimental observations are compared with theoretical calculations and quantitative agreement is obtained for steady flow and averaged values in unsteady flow. [Preview Abstract] |
Monday, November 22, 2010 9:18AM - 9:31AM |
GH.00007: Axially periodic Rayleigh-B\'{e}nard convection in a cylindrical cell Laura Schmidt, Federico Toschi, Roberto Verzicco, Detlef Lohse Numerical simulations of Rayleigh-B\'{e}nard convection in an infinite cylindrical cell show that despite the restriction of velocity and temperature fluctuations due to the side walls, the system approaches the ultimate regime of thermal convection as the Rayleigh number (Ra) is increased. Here, Ra is defined based on the underlying linear temperature gradient which is driving the convection. This periodic system has exact solutions composed of modes of exponentially growing vertical velocity and temperature fields. In the low Ra regime these solutions dominate the dynamics and lead to very high and unsteady heat transfer. As Ra is increased, interaction between these modes stabilizes the system, evidenced by the increasing homogeneity and reduced fluctuations in the r.m.s. velocity and temperature fields. [Preview Abstract] |
Monday, November 22, 2010 9:31AM - 9:44AM |
GH.00008: The boundary layer structure in Rayleigh-B\'{e}nard convection in a cylindrical cell Nan Shi, Joerg Schumacher We report first results of our studies of the boundary layer structure in turbulent Rayleigh-B\'{e}nard convection in a cylindrical cell of aspect ratio one. They are based on three-dimensional direct numerical simulations (DNS) of the Boussinesq equations at $Ra=3\times 10^9$ and $Pr=0.7$. The study is motivated by two recent experiments: LDA measurements of the velocity boundary layer structure in the cylindrical Barrel of Ilmenau by du Puits et al. and PIV measurements in a slender rectangular convection cell by Xia et al. Both experiments detected deviations from the classical Blasius solution for time-averaged flow profiles. A rescaling by the instantaneous boundary layer thickness resulted however in a much better agreement with the Blasius profile in case of the rectangular cell. The DNS allow us to combine the analysis methods of both experiments. We confirm the significant deviation for the time-averaged profiles. Closer agreement with the Blasius solution is also reproduced for the fit with the instantaneous thickness. Our analysis is extended to the Pohlhausen solution in case of the thermal boundary layer. The flow profiles are also taken at different positions in the boundary layers. Further statistical properties in both boundary layers are reported. [Preview Abstract] |
Monday, November 22, 2010 9:44AM - 9:57AM |
GH.00009: 3D pattern flow in a right-angled triangular cavity Rafael Chavez, Francisco J. Solorio Most numerical studies in triangular cavities had been carried out considering the flow as two-dimensional. In the last years some numerical studies have been made to take in account the three-dimensional behavior, but there is a lack in experimental work in the field of right-angled triangular cavities. This work is an effort to fill this lack. Particle image velocimetry (PIV) is used to study the flow pattern into a cavity with the inclined wall cooled, the vertical wall adiabatic and the horizontal bottom wall heated. Four Rayleigh numbers are considered: 5$\times $104$^{3}$, 1$\times $10$^{4}$, 5$\times $10$^{4}$ and 1$\times $10$^{5}$, and glycerin is used as working fluid. For the smallest Rayleigh number (5$\times $104$^{3})$ the flow is two-dimensional. As the Rayleigh number is increased, the flow evolves into a more complex three-dimensional pattern, with an array of cells whose rotation axes are normal to the vertical adiabatic wall. It is found that the number of cells depends on the Rayleigh number. [Preview Abstract] |
Monday, November 22, 2010 9:57AM - 10:10AM |
GH.00010: Numerical simulation of the convective flow patterns within a rotating concentric annulus with radial gravity Ares Cabello, Ruben Avila The GEODYNAMO research requires the numerical study of the natural convection of the fluid confined in a rotating spherical shell. We present the flow patterns of a uniform-density Boussinesq fluid within a rotating spherical annulus with radial aspect ratio $\eta=0.35$. The convective flow is induced by a gravity field acting radially inwards towards the center of the spheres, and the temperature difference between the internal sphere at $T_i$ and the external sphere at $T_e$ (where $T_i>T_e$). We also show (i) the influence of the rotation on the heat transfer rate, and (ii) the influence of the differential rotation (the internal sphere rotates at a different angular velocity than the reference frame and the external sphere) on the heat transfer rate. The fluid equations are solved by using the spectral element method (SEM). In order to avoid the singularity at the poles of the spheres, the numerical mesh is generated by using the Cubed-Sphere algorithm. The flow patterns are obtained for subcritical and supercritical Rayleigh numbers and Taylor numbers in the range $10^3$ and $10^5$. The results are successfully compared with data previously reported in the literature. [Preview Abstract] |
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