Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session D2: Convection and Buoyancy-Driven Flows II: Heat Transfer |
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Chair: Daniel Maynes, Brigham Young University Room: 324 |
Sunday, November 24, 2013 2:15PM - 2:28PM |
D2.00001: Optimal aspect-ratio for heat transport in turbulent Rayleigh-B\'enard convection in Cartesian geometry Kai-Leong Chong, Matthias Kaczorowski, Ke-Qing Xia We present a three-dimensional direct numerical simulation study of the heat transfer efficiency, the Nusselt number $Nu$, as a function of the aspect ratio in turbulent Rayleigh-B\'enard convection with Cartesian geometry. The study spans a range of the Rayleigh number $Ra$ from $10^7$ to $3 \times 10^9$ but at a fixed Prandtl number $Pr=4.38$. A recent experimental and numerical study [1] has shown that the heat transfer efficiency increases significantly when the width of the convection cell is narrowed. In the present study, we carry out the simulations with even smaller aspect-ratio to further investigate the effect of cell confinement which is hard to achieve experimentally. It is found that there exists an optimal aspect ratio for heat transport at a given $Ra$. Furthermore we find an increase in the coherence of flow structures as the degree of confinement increases. \\[4pt] [1] S.-D. Huang, M. Kaczorowski, R. Ni, K.-Q. Xia. Confinement induced heat transport enhancement in turbulent thermal convection, submitted to Phys. Rev. Lett. [Preview Abstract] |
Sunday, November 24, 2013 2:28PM - 2:41PM |
D2.00002: Flow characteristics and heat transfer in wavy walled channels Zachary Mills, Tapan Shah, Vontravis Monts, Alok Warey, Sandro Balestrino, Alexander Alexeev Using lattice Boltzmann simulations, we investigated the effects of wavy channel geometry on the flow and heat transfer within a parallel plate heat exchanger. We observed three distinct flow regimes that include steady flow with and without recirculation and unsteady time-periodic flow. We determined the critical Reynolds numbers at which the flow transitions between different flow regimes. To validate our computational results, we compared the simulated flow structures with the structures observed in a flowing soap film. Furthermore, we examine the effects of the wavy channel geometry on the heat transfer. We find that the unsteady flow regime drastically enhances the rate of heat transfer and show that heat exchangers with wavy walls outperform currently used heat exchangers with similar volume and power characteristics. Results from our study point to a simple and efficient method for increasing performance in compact heat exchangers. [Preview Abstract] |
Sunday, November 24, 2013 2:41PM - 2:54PM |
D2.00003: Heat transfer and stability of horizontal convection with a moving forcing boundary Gregory Sheard, TzeKih Tsai, Wisam Hussam, Kean Yung Wong, Martin King Horizontal convection describes a buoyancy-driven flow driven by a non-uniform supply of buoyancy across a horizontal forcing boundary achieved by a combination of heating and cooling. Horizontal convection establishes a horizontal flow in a thin boundary layer adjacent to the forcing boundary, and an overturning circulation is completed by way of a diffuse slow-moving return flow outside of the forcing boundary layer. Horizontal convection bears some similarity to global ocean currents, and so this fundamental study considers a second driving mechanism in conjunction with buoyancy, horizontal movement of the forcing boundary, as a model for wind-driven forcing on the flow. We characterize the combinations of Rayleigh number for buoyancy forcing and Reynolds number for mechanical forcing that produce three distinct regimes of behaviour: a forced-convection regime at high Reynolds numbers and low Rayleigh numbers, a mixed regime, and a free-convection regime dominated by Rayleigh number. [Preview Abstract] |
Sunday, November 24, 2013 2:54PM - 3:07PM |
D2.00004: Local Wall Heat Flux Robert Kaiser, Ronald du Puits Thermal convection is an omnipresent mechanism in nature and industry whereas its complexity is still a great challenge for scientists. A common model system to study natural thermal convection is the Rayleigh-B\'enard setup. The flow inside a RB convection cell is driven by a temperature difference between top and bottom plate, while the heat loss throughout the sidewall is suppressed. A lot of effort has been taken to measure the global heat transport at high Ra spanning a wide Pr range. However, it is still unclear how it is locally distributed at the horizontal plates and how this distribution depends on the aspect ratio. We report local wall heat flux measurements using heat flux sensors at the surface of the heating plate. The measurements have been carried out in our large-scale RB experiment, called the ``Barrel of Ilmenau'' at $Ra=4\cdot 10^9$ varying $1<\Gamma<8$ and $Ra=10^8$ varying $4<\Gamma<20$. Own measurements in a small rectangular RB cell shows that the time-average of the local heat flux at the surface of the plates can vary with respect to the position at the plate by about 30\%. The locations of enhanced heat flux could be clearly associated with regions of strong plumeactivity like the area where plumes coming from the opposite plate and hit the plate surface. [Preview Abstract] |
Sunday, November 24, 2013 3:07PM - 3:20PM |
D2.00005: Optically induced natural convection in a cylinder using conducting metal oxide films Brian J. Roxworthy, Kimani C. Toussaint, Surya P. Vanka We present a computational study of light- driven natural convection in a cylinder. We solve the coupled electromagnetic, heat transfer, and fluid mechanics equations in an axi-symmetric geometry with heating and fluid flow induced by optical absorption in a conducting metal oxide film comprised of Indium-Tin-Oxide (ITO). Calculations are performed as a function of the relevant optical input parameters including the wavelength of the illumination source ($\lambda )$, the input power of the input light (P) which is assumed to have a Gaussian intensity distribution, and the numerical aperture of the focusing lens, defined as NA $= n$sin$\theta $, where $n $is the index of refraction of the local medium and $\theta $ is the half-angle of the focused light cone. Due to the localized, spatially non-uniform illumination, fluid flow is induced for any finite Rayleigh number Ra \textgreater\ 0 and the resulting flow closely resembles a toroidal Rayleigh-B\'{e}nard convection pattern. The maximum fluid velocity scales linearly with Pand increases with increasing AR up to AR $\sim$ 2; above this value, increasing $h_{fluid}$ has no effect on the peak velocity. The optical actuation enables dynamic reconfigurability of the heating and convection patterns, which benefit lab-on-a-chip fluid mixing and particle manipulation. [Preview Abstract] |
Sunday, November 24, 2013 3:20PM - 3:33PM |
D2.00006: Wall to Wall Optimal Transport Gregory P. Chini, Pedram Hassanzadeh, Charles R. Doering How much heat can be transported between impermeable fixed-temperature walls by incompressible flows with a given amount of kinetic energy or enstrophy? What do the optimal velocity fields look like? We employ variational calculus to address these questions in the context of steady 2D flows. The resulting nonlinear Euler--Lagrange equations are solved numerically, and in some cases analytically, to find the maximum possible Nusselt number $Nu$ as a function of the P\'eclect number $Pe$, a measure of the flow's energy or enstrophy. We find that in the fixed-energy problem $Nu\sim Pe$, while in the fixed-enstrophy problem $Nu\sim Pe^{10/17}$. In both cases, the optimal flow consists of an array of convection cells with aspect ratio $\Gamma(Pe)$. Interpreting our results in terms of the Rayleigh number $Ra$ for relevant buoyancy-driven problems, we find $Nu \leq 1+0.035 Ra$ and $\Gamma \sim Ra^{-1/2}$ for porous medium convection (which occurs with fixed energy), and $Nu \leq 1+0.115 Ra^{5/12}$ and $\Gamma \sim Ra^{-1/4}$ for Rayleigh--B\'enard convection (which occurs with fixed enstrophy and for free-slip walls). [Preview Abstract] |
Sunday, November 24, 2013 3:33PM - 3:46PM |
D2.00007: Solution breakdown due to natural convection of the boundary-layer radial flow on a constant temperature horizontal plate Ramon Fernandez-Feria, Carlos del Pino, Alberto Fern\'andez-Guti\'errez The boundary-layer flow of a cold horizontal current exiting radially from a cylindrical vertical surface with a constant velocity over a hotter horizontal wall with constant temperature is analyzed. The temperature and velocity fields are coupled by buoyancy through the pressure gradients, so that the boundary-layer equations are made dimensionless with a radial characteristic length in which natural and forced convection become of the same order of magnitude, being the Prandtl number the only nondimensional parameter governing the problem. A similarity solution valid for the leading edge boundary-layer flow is obtained, yielding as a first order correction the effect of natural convection on Blasius' thermal boundary layer. This solution is also used to start the numerical integration of the equations to find out the location where the boundary-layer flow blows up due to the termination of the solution in a singularity. The physical nature of this singularity is analyzed and its position is characterized numerically. The heat flux from the horizontal wall up to this singularity is also characterized and qualitatively compared with previous experimental results from a related experimental setup. [Preview Abstract] |
Sunday, November 24, 2013 3:46PM - 3:59PM |
D2.00008: Convection to Sessile Droplets on Superhydrophobic Surfaces Daniel Maynes, Robb Hays, Julie Crockett We report results from an investigation of the thermal convection to liquid droplets on heated horizontal superhydrophobic (SH) surfaces. We consider the transient response to droplets, initially at ambient temperature, as they are placed on heated SH surfaces at constant temperature. For comparative purpose we also consider the same scenario with smooth hydrophobic surfaces. The temporally varying droplet and surface temperatures were measured with an IR camera and a thermocouple, respectively. The droplets were also imaged with two CCD cameras and the time for the droplet to completely evaporate was monitored. For surface temperatures greater than the saturation temperature, high-speed video of the droplets was also acquired. Experiments were conducted over a range of surface temperatures varying from 40 to 215 C. The results show radically different behavior in the convection for the surface types considered. At all temperatures the total droplet evaporation time on the SH surfaces was significantly greater than on the smooth hydrophobic surface. At temperatures elevated above the saturation temperature the droplets on the SH surfaces remained at bulk temperatures significantly lower than the saturation temperature. Further, the droplets on the SH surfaces exhibited Leidenfrost-like behavior at surface temperatures far below the typical Leidenfrost point. Analysis of the data reveals overall heat transfer coefficients that decrease as the degree of superhydrophobicity increases. [Preview Abstract] |
Sunday, November 24, 2013 3:59PM - 4:12PM |
D2.00009: Anomalous convective heat transport and rain formation in cryogenic helium K.R. Sreenivasan, P. Urban, P. Hanzelka, D. Schmoranzer, L. Skrbek When a hot body A is thermally connected to a cold body B, the conventional wisdom is that heat flows from A to B. Here we describe the opposite case in which \emph{heat flows from a colder but constantly heated body B to a hotter but constantly cooled body A through the thermal link of two-phase cryogenic helium}. Specifically, we provide experimental evidence that heat flows through liquid and gaseous layers of cryogenic helium from constantly heated but cooler bottom plate of the Rayleigh-B\'{e}nard convection cell to its hotter top plate that is constantly cooled. The bottom plate is heated uniformly and the top plate is cooled by heat exchange with liquid helium maintained at 4.2 K. Additionally, for certain experimental conditions, a rain of helium droplets is detected by small sensors placed in the cell interior at about half of its height. These results are expected to be of some consequence to laboratory studies of phase change in atmospheric clouds. [Preview Abstract] |
Sunday, November 24, 2013 4:12PM - 4:25PM |
D2.00010: An air curtain in the doorway of a ventilated space Daria Frank, Paul Linden Air curtains are used to reduce the heat and the mass exchange between the indoor environment and the ambient. Their sealing ability is assessed in terms of the effectiveness $E$, the fraction of the exchange flow prevented by the air curtain compared to the open-door situation. Previous work studied the air curtain effectiveness when the doorway is the only means of ventilating a space. In this talk we examine effects of an additional displacement ventilation pathway on the effectiveness. The main controlling parameter is the deflection modulus $D_{m}$ which is the ratio between the momentum flux of the air curtain and the transverse forces due to the displacement ventilation. For small values of $D_{m}$ the air curtain is drawn inside the space by the ventilation flow. For high values of $D_{m}$ the flow is controlled by the air curtain. A smooth transition occurs between these two regimes and we estimate the $D_{m}$ value for the onset of this transition. Our model makes a quantitative prediction of $E(D_m)$ in the ventilation-driven regime, and explains qualitatively the shape of the curve in the other two regimes. Laboratory experiments were conducted to test the proposed model. The experimental data were compared to theoretical predictions and good agreement was found. [Preview Abstract] |
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