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 LS: Convection I |
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Chair: John R. Saylor, Clemson University Room: 203B |
Monday, November 24, 2008 3:35PM - 3:48PM |
LS.00001: Convective Instabilities of Binary Mixtures in Annular Thermogravitational Columns Abdelfattah Zebib, Mounir Bou-Ali A theoretical and computational study of Soret separation of a binary mixture contained in a differentially heated infinite vertical annulus is presented. We first calculate the basic steady one-dimensional flow taking into account the vertical concentration gradient caused by thermodiffusion. Unstable (stable) stratification is induced at positive (negative) separation ratios. Linear stability of this basic state is performed and the critical Rayleigh number, wave number, frequency, and vertical concentration gradients are determined as functions of the separation ratio, Lewis and Parndtl numbers. It is shown that the preferred instability is axisymmetric when the induced vertical stratification is stable while it is azimuthal with unstable vertical stratification. Supercritical nonlinear computations are in agreement with linear theory and available experiments. Stability restrictions on the operation of the thermogravitational column will be discussed. [Preview Abstract] |
Monday, November 24, 2008 3:48PM - 4:01PM |
LS.00002: Two Dimensional Unsteady Convection in Pressure-Driven Nitrogen Flow in Long Microchannels with Uniform Heat Flux Input Zhanyu Sun, Yogesh Jaluria The transient features of pressure-driven Nitrogen flows in long microchannels under uniform heat flux input conditions are numerically studied. The two-dimensional momentum and energy equations are solved, where variable properties, rarefaction effects, including velocity slip, thermal creep, and temperature jump, as well as compressibility and viscous dissipation effects, are all taken into account. This paper focuses on two conditions: a sudden heat flux change at the channel wall and a sudden inlet pressure change. The thermal and fluid dynamics after these two changes are described and discussed in detail. The approach to steady-state conditions and the overall transient response are investigated. It is found that the overall transient response for the case with a sudden increase in the heat flux input is slower than that for the case with a sudden decrease in the heat flux input. The transient response for the case with a sudden increase in the inlet pressure is much faster than that for the case with sudden decrease in the inlet pressure. Based on the results obtained earlier, the difference in overall transient response is mainly caused by the energy taken up by the pressure work. Other physical results are obtained and discussed. [Preview Abstract] |
Monday, November 24, 2008 4:01PM - 4:14PM |
LS.00003: A study of the effect of surface conditions on free-surface evaporative convection S.M. Bower, J.R. Saylor An experimental study is presented of free-surface evaporative convection in both the presence and absence of a surfactant monolayer. The transfer of heat and the evaporation rate are quantified by parameterizing the Nusselt and Sherwood numbers in terms of the Rayleigh number. The goal of this study is to determine how these $Nu-Ra$ and $Sh-Ra$ relationships change when the hydrodynamic boundary condition is changed at the free surface. Specifically, two cases are presented: 1) a surface covered with a surfactant monolayer having a finite elasticity, and 2) a clean surface having zero elasticity. The resulting $Nu-Ra$ parameterization is also compared to investigations of the classical Rayleigh-B\'{e}nard experiment where the hydrodynamic boundary condition is of the no-slip type. [Preview Abstract] |
Monday, November 24, 2008 4:14PM - 4:27PM |
LS.00004: Turbulent Thermal Convection with Polymer Additives Yves Dubief We study the effect of polymers in natural convection and test a new approach for the numerical resolution of the transport of low-diffusion scalars. Our natural convection incompressible flow takes place between two infinite parallel isothermal plates. We present simulations for Rayleigh numbers up to $5\times10^6$ for water alone and water with polymer additives. The behavior of polymer solutions, simulated using viscoelastic models, is analog to that observed in drag-reduced polymer wall flows. The polymers damp vortices (secondary instability, quasi streamwise vortices for wall flows) caused by thermal plumes, resulting in stronger and more coherent convection cells (primary instability, streaks). The overall heat transfer is significantly reduced. For some simulations, we have used a new numerical algorithm, the Adaptive Lagrangian Gradient Transport, to resolve sharp gradients of temperature and components of the polymer stress tensor. The algorithm calculates scalar gradients using a traditional finite-difference Eulerian approach in regions where the method is numerically stable. In the rest of the flow, determined by its local topology, the algorithm reconstructs gradients at computational nodes from particles that transport governing equations for the scalar gradients of interest. [Preview Abstract] |
Monday, November 24, 2008 4:27PM - 4:40PM |
LS.00005: Pattern formation in anticonvective systems Domnic Merkt Two-layer fluid systems with an undeformable interface heated from above in the presence of gravitational forces may show a rather paradox transition from conductive to convective states. This instability was found by {\sc Welander}[1] in 1964 and named anticonvection. Besides the applied temperature gradient various interactions at the interface play an essential role for anticonvection. I.e. this instability depends very sensitive on material parameters. Here we use the Boussinesq-approximation for incompressible fluids and classical boundary conditions of an undeformable interface. Starting from the basic hydrodynamic equations we derive the equations for the perturbed fields of the stationary state. A linear stability analysis for vertically infinitely extended systems can be done analytically. However, vertically bounded systems (in particular for experimental realization) require numerical investigations. We discuss the instability regime, influence of material parameters and show how vertical bounding effects this instability. Finally, numerical simulations of the fully nonlinear system show the resulting patterns for an anticonvective system and reveal velocity and temperature distributions in both fluids. \vspace*{1em} [1] P.Welander, Tellus {\bf 16}, 349 (1964) [Preview Abstract] |
Monday, November 24, 2008 4:40PM - 4:53PM |
LS.00006: Analysis of Stability of Channel Flow Subject to Distributed Heating Jerzy M. Floryan, Mohammed Hossain The linear stability of channel flow between two horizontal parallel walls in the presence of distributed wall-heating has been investigated. The case of periodic heating applied at the bottom wall has been considered in details. This heating results in the creation of zones of fluid with alternatively increased and decreased temperature. The mean flow and the linear stability equations have been solved using spectral methods. Two types of instability, i.e., vortex instability and traveling wave instability, have been examined. For the traveling wave instability two and three dimensional oblique waves have been considered. It has been found that from among various possible forms of disturbances the streamwise vortices appear at the lowest value of the Rayleigh number if the flow Reynolds number is sufficiently small, and two-dimensional Tollmien-Schlichting (TS) waves appear first if the flow Reynolds number is sufficiently large. The conditions when the two-dimensional waves dominate are similar to those found in the case of isothermal flow. [Preview Abstract] |
Monday, November 24, 2008 4:53PM - 5:06PM |
LS.00007: Buoyancy-driven convection around exothermic autocatalytic chemical fronts Laurence Rongy, Anne De Wit Spatiotemporal distributions of heat and mass across chemical fronts propagating in horizontal solutions can initiate buoyancy-driven convection. The goal of our work is to theoretically investigate the dynamics due to the coupling between exothermic autocatalytic reactions, diffusion, and buoyancy-driven flows. To do so, we numerically integrate the incompressible Stokes equations coupled through buoyancy terms to conservation equations for the concentration of the reaction product and for the temperature. A solutal and a thermal Rayleigh number measure the coupling between reaction-diffusion processes and buoyancy convection. The asymptotic dynamics in the case of an isothermal front is a steady vortex surrounding, deforming, and accelerating the front (L. Rongy, N. Goyal, E. Meiburg and A. De Wit, J. Chem. Phys. 127, 114710, 2007). We address here the influence of thermal effects on the dynamics of the system. We show that exothermic fronts can exhibit new types of dynamics in the presence of convection, particularly when the solutal and thermal effects are antagonistic, leading to temporal oscillations of the concentration, temperature, and velocity fields in a reference frame moving with the front. The influence of the Lewis number measuring the ratio between thermal and molecular diffusivity is investigated. [Preview Abstract] |
Monday, November 24, 2008 5:06PM - 5:19PM |
LS.00008: Buoyancy-driven instabilities induced by chemical reactions in vertical porous media C. Almarcha, P.M.J. Trevelyan, A. De Wit Classical Rayleigh-Taylor or double diffusive instabilities can be triggered by a simple A+B$\rightarrow $C chemical reaction when two miscible solutions each containing one reactant are put in contact in the gravity field. A linear stability analysis of the evolving base state profiles is performed using a quasi-steady state approximation. This allows one to classify the various sources of instabilities as a function of the parameters which are the Rayleigh numbers and the ratio of diffusion coefficients of the chemical species. The resulting nonlinear dynamics due to this chemo-hydrodynamic feedback are then systematically analyzed to highlight how the chemical reaction can trigger or modify the hydrodynamical instabilities. It is also shown to what extent the~resulting buoyancy-driven instabilities enhance the total reaction rate. Finally, related experiments are also performed in a vertical Hele-Shaw cell with an acid-base reaction. [Preview Abstract] |
Monday, November 24, 2008 5:19PM - 5:32PM |
LS.00009: ABSTRACT WITHDRAWN |
Monday, November 24, 2008 5:32PM - 5:45PM |
LS.00010: Experimental investigation on coupling flows between liquid and liquid metal layers Kanako Yano, Yuji Tasaka, Yuichi Murai, Yasushi Takeda, Takatoshi Yanagisawa This study aims to clarify coupling of flows between liquid metal and other usual liquids, e.g. water or oil, in fluid dynamical systems. In past studies for two-layer Rayleigh-B\'enard system where the immiscible two liquids are layered, two types of coupling were observed; these are called as ``mechanical coupling'' and ``thermal coupling.'' As a typical character of low \textit{Pr} fluid, large-scale structure in the liquid metal layer has oscillating motion. In this study we investigate ``thermal coupling'' especially how the oscillation of cells in the liquid metal layer propagates to the upper liquid layer and vice versa by changing a ratio of the height of the layers and viscosity of the upper layer fluid. Visualization of the liquid metal motion was conducted by means of ultrasonic velocity profiling, and then the oscillating motion is expressed on the space-time velocity map. PIV measurement of the upper, transparent fluid layer shows the modulation of the convective motion due to the oscillation in the liquid metal layer. Point-wise measurement of temperature at several positions in the fluid layer represents the modulation quantitatively. [Preview Abstract] |
Monday, November 24, 2008 5:45PM - 5:58PM |
LS.00011: Plume shot noise in convection: evidence of a boundary layer instability consistent with the triggering of the Ultimate regime of convection Julien Salort A sudden enhancement of the heat transfer for Rayleigh numbers Ra$>$1e12 was reported in a Rayleigh B\'{e}nard cell in 1997 (Chavanne et al. PRL).This observation was interpreted as the occurrence of Kraichnan's ``Ultimate'' regime of convection, which is characterized by turbulent boundary layers. This interpretation has been indirectly supported by the outcome a test experiment, using a cell with corrugated surfaces. A more direct test would consist in probing fluctuations within the boundary layer, but its thinness (order 100 microns) causes instrumentation challenges. To overcome this difficulty, we recorded the shot noise induced by the thermal plumes leaving the bottom plate. We find that the heat transfer enhancement at Ra$\sim $1e12, is accompanied by a significant increase of shot noise. This observation is interpreted as the signature of a boundary layer instability, in agreement with the Ultime regime scenario. [ Gauthier F. and Roche P.-E et al., EPL 83:24005 (2008) ] \\[3pt] In collaboration with Fr\'ed\'eric Gauthier and Philippe-E. Roche, Institut NEEL, CNRS. [Preview Abstract] |
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