Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session LR: Convection II |
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Chair: Charles Doering, University of Michigan Room: 200F |
Monday, November 23, 2009 3:35PM - 3:48PM |
LR.00001: A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux: Simulation Methods Hans Johnston, Charlie Doering We report the results of high resolution direct numerical simulations of two-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to $Ra=10^{10}$ in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we consider the extreme cases of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law $\nu \approx 0.138 \times Ra^{.285}$ with a scaling exponent indistinguishable from $2/7 = 0.2857\dots$ above $Ra = 10^{7}$. The overall flow dynamics for both scenarios, in particular the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers. The findings are compared and contrasted with results of recent three-dimensional simulations. [Preview Abstract] |
Monday, November 23, 2009 3:48PM - 4:01PM |
LR.00002: A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux: Simulation Results Charles R. Doering, Hans Johnston We report the results of high resolution direct numerical simulations of two-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to $Ra=10^{10}$ in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we considered the extremes of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law $\nu \approx 0.138 \times Ra^{.285}$ with a scaling exponent indistinguishable from $2/7 = .2857$\dots above $Ra = 10^{7}$. The overall flow dynamics for both scenarios, in particular the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers. [Preview Abstract] |
Monday, November 23, 2009 4:01PM - 4:14PM |
LR.00003: Effects of Shear on Unstably Stratified Convection Curtis Hamman, Parviz Moin Direct numerical simulations of plane channel flow heated from below are examined. At Richardson numbers of order unity ($|Ri| = Ra/PrRe^2$, $10^6 \leq Ra \leq 10^9$, $180 \leq Re_\tau \leq 590$ and $Pr = 1$), the production of wall-normal baroclinic vorticity is shown to have a substantial effect upon the mean momentum balance that leads to enhanced turbulent mixing, asymmetry, and turbulent heat transfer. These effects are neglected by traditional Boussinesq formulations, which generate zero baroclinic vorticity in the direction of gravity, accelerate negative and positive density fluctuations identically, and make no direct contribution to the streamwise mean momentum balance. Motivated by the work of Shirgaonkar and Lele (\emph{Physics of Fluids}, 2006), a computationally efficient extension to the Boussinesq approximation is developed and shown to accurately capture these essentially incompressible interactions between shear and buoyancy as observed in variable-density turbulence. Applications to heat exchangers and other advanced energy systems, in which the effects of shear and buoyancy are comparable, are highlighted. [Preview Abstract] |
Monday, November 23, 2009 4:14PM - 4:27PM |
LR.00004: ABSTRACT WITHDRAWN |
Monday, November 23, 2009 4:27PM - 4:40PM |
LR.00005: Large-scale flows in free and mixed convection Jorge Bailon-Cuba, Mohammad Emran, Joerg Schumacher Convective turbulence in closed volumes is associated with large-scale circulations of the flow (LSC). They depend sensitively on the geometry and the physical parameters, such as Rayleigh and Prandtl numbers. Here, we consider two systems: free convection in cylindrical cells and mixed convection in a complex rectangular setting with local heat sources. The LSC and the amount of heat transferred is determined by the so-called proper orthogonal decomposition (POD) of the turbulent fields. We apply the so-called snapshot method to extract the modes from DNS data. The most energetic POD modes give us insight into the dynamic dominance of coherent flow and temperature patterns, and how well the original inhomogeneous flow can be modeled with a reduced number of modes in a low-dimensional model. For example, in case of the cylindrical cell the primary POD mode transfers about one half of the total amount of heat through the vessel. For the mixed convection case, the influence of the geometry and the inflow conditions on these LSC structures is also addressed. [Preview Abstract] |
Monday, November 23, 2009 4:40PM - 4:53PM |
LR.00006: The development of a buoyant vortex (thermal) in stationary and plane stagnation flows Gali Alon, Jimmy Philip, Jacob Cohen The evolution of a buoyant vortex (thermal) in stagnant and irrotational plane stagnation flows is studied using both computational and theoretical tools. The relative effect of external shear is explored through the ratio between the two relevant time scales associated with the shear and buoyancy (viscous and diffusive effects, although included, are considered to be relatively small). An important effect of the stagnation base-flow is the earlier penetration of the ambient fluid into the buoyant mass, causing the formation of a buoyant vortex ring. Consequently, the growth of circulation ceases earlier resulting in a lower value of the maximum circulation. The initial growth rate of the circulation is theoretically predicted to be proportional to the density difference and the vertical extension along the structure's symmetry line. In an attempt to describe the time development of the circulation, a simple Lagrangian model is proposed, and its results agree with the numerical ones. Finally, theoretical analysis verified numerically, shows that the fluid impulse grows linearly or exponentially in stationary fluid or in plane stagnation flow, respectively. [Preview Abstract] |
Monday, November 23, 2009 4:53PM - 5:06PM |
LR.00007: Convectons in periodic and bounded domains Edgar Knobloch, Isabel Mercader, Oriol Batiste, Arantxa Alonso Numerical continuation is used to compute spatially localized convection in a binary fluid with no-slip laterally insulating boundary conditions and the results compared with the corresponding ones for periodic boundary conditions. The change in the boundary conditions produces a dramatic change in the snaking bifurcation diagram that describes the organization of localized states with periodic boundary conditions: the snaking branches turn continuously into a large amplitude state that resembles periodic convection with defects at the sidewalls. Odd parity convectons are more affected by the boundary conditions since the sidewalls suppress the horizontal pumping action that accompanies these states in spatially periodic domains [O. Batiste et al., J. Fluid Mech. 560, 149 (2006)]. [Preview Abstract] |
Monday, November 23, 2009 5:06PM - 5:19PM |
LR.00008: Bounds on the Nusselt Number for Marangoni Convection George Hagstrom, Charlie R. Doering We use the background method to prove rigorous upper bounds on the Nusselt number in terms of the Marangoni number in Marangoni convection. When the Prandtl number is infinite $Nu \leq .84 Ma^{2/7}$. For finite Prandtl number we proved that $Nu \la Ma^{1/2}$. We compare these to numerical simulations by Boeck and Thess that suggest that for real flows $Nu\la Ma^{2/9}$. We also use the background method and non-variational techniques to improve the lower bound for the critical Marangoni number for energy stability of the conduction solution in the infinite Prandtl number case. [Preview Abstract] |
Monday, November 23, 2009 5:19PM - 5:32PM |
LR.00009: A Model of Convective Taylor Columns in Rotating Rayleigh Benard Convection Ian Grooms, Keith Julien, Jeffrey Weiss, Edgar Knobloch Many real fluid flows are nearly incompressible and are influenced by both rotation and thermal forcing. Rotation tends to suppress variation along the axis of rotation, while strong thermal forcing often gives rise to thermal plumes that travel vertically (in the direction of gravity). When the axis of rotation and gravity are aligned, or nearly so, these effects can combine to produce long lived columnar structures which have been observed in laboratory and numerical experiments; these ``Convective Taylor Columns" can be interpreted as the effective particles ``convectons" of the flow, accounting for a significant proportion of the vertical heat and momentum flux in the fluid and for the enhanced lateral mixing otherwise absent in non-rotating flows. However, due to the experimental challenges of 3-D data acquisition and the numerical challenges of simulation at low Rossby number, these structures remain poorly understood. We here present a nonlinear model for these columnar structures in the context of rotating Rayleigh-B\'enard convection; our model makes use of multiscale asymptotics, complex variables, and special functions. [Preview Abstract] |
Monday, November 23, 2009 5:32PM - 5:45PM |
LR.00010: ABSTRACT WITHDRAWN |
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