Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session AS: Buoyancy-Driven Flows I |
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Chair: Joseph Niemela, The Abdus Salam ICTP Room: 203B |
Sunday, November 23, 2008 8:00AM - 8:13AM |
AS.00001: Rotating turbulent Rayleigh-B\'enard convection: Effect of weak rotation on boundary layers and heat transfer Richard Stevens, Herman Clercx, Detlef Lohse The Grossmann-Lohse (GL) theory\footnote{Grossmann and Lohse, J. Fluid Mech. 407, 27 (2000)} for the heat transfer in turbulent Rayleigh-B\'enard (RB) convection heavily builds on the Prandtl-Blasius laminar boundary layer (BL) theory, according to which the thermal BL thickness $\lambda_\theta$ scales as $L Pr^{-1/2}$ in the low $Pr$ regime and with $L Pr^{- 1/3}$ in the high $Pr$ regime. In an attempt to extend the GL theory to the rotating RB case, we study the influence of rotation on the thermal BL thickness in flow above an infinite rotating disk. We show that with rotation $\lambda_\theta \propto Pr^{-1}$ in the low $Pr$ regime, whereas in the high $Pr$ regime the scaling remains unchanged. Furthermore, we obtain an analytic expression for the Nusselt number in the Ekman case (fluid at infinity rotates at almost the same speed as the disk). We moreover introduce a model to explain the experimentally\footnote{Rossby, {\emph{J. Fluid Mech.}} {\bf {36}}, 309 (1969)} and numerically\footnote{Oresta et al {\emph {Eur. J. Mech.}} {\bf{26}}, 1 (2007); Kunnen et al {\emph{Phys. Rev. E}} {\bf{74}}, 056306 (2006).} observed increased heat transfer (as compared to RB without rotation) at weak rotation. [Preview Abstract] |
Sunday, November 23, 2008 8:13AM - 8:26AM |
AS.00002: Interacting Stokes layers and wall modes in modulated rotating convection Antonio Rubio, Juan Lopez, Francisco Marques Thermal convection in a rotating cylinder near onset is investigated using direct numerical simulations of the Navier--Stokes equations with the Boussinesq approximation in a regime dominated by the Coriolis force. For thermal driving too small to support convection throughout the entire cell, convection sets in as alternating pairs of hot and cold plumes in the sidewall boundary layer, the so-called wall modes of rotating convection. We subject the wall modes to small amplitude harmonic modulations of the rotation rate over a wide range of frequencies. The modulations produce Stokes boundary layers which drive a time-periodic large-scale circulation that interacts with the wall-localized thermal plumes in a non-trivial manner. The resultant phenomena include a substantial shift in the onset of wall mode convection to higher temperature differences for a broad band of frequencies, as well as a significant alteration of the precession rate of the wall mode at very high modulation frequencies due to the mean azimuthal streaming flow resulting from the modulations. [Preview Abstract] |
Sunday, November 23, 2008 8:26AM - 8:39AM |
AS.00003: Rotating High Rayleigh Number Convection Joseph Niemela, Simone Babuin, Katepalli Sreenivasan Very high Rayleigh number convection with rotation is studied using cryogenic helium gas as the working fluid. Rayleigh and Taylor numbers were obtained up to maximum values of $Ra=4 \times 10^{15}$ and $Ta = 3 \times 10^{15}$ under Boussinesq conditions. For these experiments the Rossby number was in the range 0.4 $<$ Ro $<$ 1.6 and Prandtl number varied as 0.7 $<$ Pr $<$ 6. Under all conditions, the effect of added steady rotation was to diminish the heat transfer. However, a sinusoidal time- variation of the rotation rate provided periodic spin-up which led to significant enhancement of the Nusselt number, presumably due to Ekman pumping, in the case when the Taylor number based on the modulation amplitude surpassed a critical value, roughly $10^{14}$. Otherwise the periodic spin-up caused a reduction in the heat transfer as in the case when the rotation rate was held constant. The effect on heat transfer did not appear to be sensitive to the period of the modulation, which was nominally set to be comparable to the turn-over time of the large-scale mean wind. [Preview Abstract] |
Sunday, November 23, 2008 8:39AM - 8:52AM |
AS.00004: Double Diffusive Plumes Bruce Sutherland, Brace Lee Sour gas flares attempt to dispose of deadly $H_2S$ gas through combustion. What does not burn rises as a buoyant plume. But the gas is heavier than air at room temperature, so as the rising gas cools eventually it becomes negatively buoyant and descends back to the ground. Ultimately, our intent is to predict the concentrations of the gas at ground level in realistic atmospheric conditions. As a first step towards this goal we have performed laboratory experiments examining the structure of a steady state plume of hot and salty water that rises buoyantly near the source and descends as a fountain after it has cooled sufficiently. We call this a double-diffusive plume because its evolution is dictated by the different (turbulent) diffusivities of heat and salt. A temperature and conductivity probe measures both the salinity and temperature along the centreline of the plume. The supposed axisymmetric structure of the salinity concentration as it changes with height is determined by light-attenuation methods. To help interpret the results, a theory has been successfully adapted from the work of Bloomfield and Kerr (2000), who developed coupled equations describing the structure of fountains. Introducing a new empirical parameter for the relative rates of turbulent heat and salt diffusion, the predictions are found to agree favourably with experimental results. [Preview Abstract] |
Sunday, November 23, 2008 8:52AM - 9:05AM |
AS.00005: Numerical experiments on salt finger type convection Satoko Komurasaki, Kunio Kuwahara Salt finger type convection is formed where hot, salty water overlying colder, less salty water. In the ocean, solar radiation may warm the surface layer of the sea but this may also give a high evaporation rate increasing the salt concentration. Therefore, salt fingers are often observed undersea. Double diffusive convection of salt finger type has been studied experimentally and numerically very much. However, some interesting problems remain. In the last our numerical study of salt finger type convection, it was simulated two dimensionally that under a condition, a large convective flow occurs which mixes fluid, and forms an uniform layer. In this study, we try to simulate this phenomenon three dimensionally, and carry out salt finger type convection under other conditions. In the computation, the governing incompressible Navier-Stokes equations are solved by the multidirectional finite-difference method. For high-Reynolds-number flows, the third-order upwind scheme is utilized for the convective terms to stabilize the computation. Results of the computation are visualized extensively. [Preview Abstract] |
Sunday, November 23, 2008 9:05AM - 9:18AM |
AS.00006: Thermal-hydraulic characterization of the natural circulation of air between two vertical cylinders enclosed in a rectangular cavity Luis Alfredo Payan-Rodriguez, Carlos Ivan Rivera-Solorio, Salvador Villarreal-Garcia, Alejadro Javier Garcia-Cuellar, Ramon Ramirez-Tijerina This work presents the results of an experimental analysis focused on the characterization of the natural circulation of air in the vicinity of two vertical cylinders. A three dimensional cavity encloses each cylinder, where one of them is a heat source and the other is a heat sink. A wall with two holes of variable diameter delimits and connects the two enclosures in order to restrict the air flow exchanged between them. The distance between the center lines of the cylinders was varied with the purpose of measuring the effect of the surrounding walls on the natural circulation. All configurations were tested for different heat generation rates. A Particle Image Velocimeter was used to obtain the flow patterns and a set of thermocouples was installed to measure the temperature field. The experimental results are analyzed and discussed. [Preview Abstract] |
Sunday, November 23, 2008 9:18AM - 9:31AM |
AS.00007: Three-dimensional measurement of temperature and velocity field in buoyancy driven flows Nobuyuki Fujisawa, Gen Sato, Youhei Ohkawa Three-dimensional measurements of temperature and velocity field in buoyancy driven flows are carried out using a background oriented Schlieren combined with tomographic reconstruction technique. This method is based on the refractive index measurement in the three-dimensional flow field, and the corresponding velocity field is evaluated from the displacement of the measured temperature field. The accuracy of this measurement is examined using the artificial images derived from the numerical simulation. [Preview Abstract] |
Sunday, November 23, 2008 9:31AM - 9:44AM |
AS.00008: Time dependent ventilation flows driven by opposing wind and buoyancy Imran Coomaraswamy, Colm Caulfield We consider flow in an enclosure containing an isolated heat source, ventilated by a windward high level opening and a leeward low level opening, so that prevailing wind acts to oppose buoyancy driven flow. Following the ``emptying filling box'' approach of Linden {\it et al.}\footnote{Linden, Lane-Serff \& Smeed, {\emph{J. Fluid Mech.}} {\bf{212}}, 309 (1990).}, Hunt \& Linden\footnote{Hunt \& Linden, {\emph{J. Fluid Mech.}} {\bf{527}}, 27 (2005).} demonstrate that multiple steady states can exist above a critical wind strength. We develop time dependent models for this system and apply them to an initial value problem - box filling with constant opposing wind. We identify the final state attained for any given heat load, wind strength and vent size. We note that the interface between the upper region of hot plume fluid and the lower region of cool ambient air can dramatically overshoot its final level before relaxing to equilibrium; in some cases, a fully mixed transient can occur before the stratified steady state is reached. Analogue laboratory experiments confirm the existence of these transient phenomena and elucidate the range of validity of our predictions. [Preview Abstract] |
Sunday, November 23, 2008 9:44AM - 9:57AM |
AS.00009: Buoyancy effects on added mass in density-stratified fluids Bruno Voisin In the presence of stable density stratification, owing to buoyancy, fluid motion gives rise to internal gravity waves which redistribute momentum and energy through the fluid. As a result, the added mass of moving bodies is modified and becomes anisotropic and frequency-dependent. The influence of these modifications on the definition itself of added mass and on its relation to hydrodynamic pressure, impulse, energy and to the dipole strength of the bodies is discussed. Coefficients of added mass are calculated explicitly for the small oscillations of spheres and circular cylinders. Implications for energy radiation and for the motion of floats are considered. In the first case the existence of a maximum at a frequency of oscillation equal to a fixed fraction 0.8 of the buoyancy frequency, practically independent of the direction of oscillation, is pointed out together with possible inferences for turbulent motion. In the second case classical results by Larsen on neutrally buoyant spheres and cylinders are recovered. [Preview Abstract] |
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