Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session G2: Convection and Buoyancy-Driven Flows IV |
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Chair: Herman Clercx, Technical University Eindhoven Room: 23A |
Monday, November 19, 2012 8:00AM - 8:13AM |
G2.00001: Horizontal convection with mechanical stirring Ross Griffiths, Kial Stewart, Graham Hughes The effects of turbulent mixing on convective circulation forced by a horizontal gradient of buoyancy at the surface is examined using laboratory experiments in which a salt flux is introduced at the surface, at one end of a box, and a freshwater buoyancy condition is applied over the rest of the surface. Horizontal rods are oscillated and yo-yoed continuously through the water column, providing a diffusivity that can be calibrated. The convection reaches a stationary state having zero net salt flux. We find that for small stirring rates the small but finite volume flux from the dense source is significant and a virtual source correction is required to take this into account. The density stratification and overturning volume transport are consistent with a theoretical model for high Rayleigh numbers: the transport $\psi $ increases with diffusivity $\kappa $ ($\psi {\rm g}\sim {\rm g}\kappa ^{1/4})$. The results show that vertical mixing in the boundary layer is important, particularly in setting the density of the interior and the overturning rate. However, interior mixing is unimportant, which raises an interesting question over whether abyssal mixing rates in the ocean play any significant role in setting the abyssal ocean density or the transport in the Meridional Overturning Circulation. [Preview Abstract] |
Monday, November 19, 2012 8:13AM - 8:26AM |
G2.00002: The Effects of Surface Stress on Horizontal Convection Katarzyna E. Matusik, Stefan G. Llewellyn Smith Laboratory experiments have been designed to investigate the effects of a surface stress on horizontal convection. In the ocean, a zonal wind stress drives a meridional Ekman flow due to the effects of rotation. We explore features of horizontal convection in the presence of a surface stress that is imposed in opposition to the buoyancy-driven circulation. The buoyancy flux is achieved by injecting a plume of dense water into a fresh-water tank, while continuously maintaining a fresh-water surface boundary condition. The magnitude of the stress is varied by adjusting the flow rate of fresh water traversing along the surface; this stress is run in parallel to the north-south buoyancy gradient in order to simulate a 2D non-rotating system. We measure the steady-state density field using the synthetic schlieren technique, and the vertical and horizontal velocities are determined by PIV techniques. The boundary layer is resolved with conductivity probe measurements. The addition of a surface stress to horizontal convection may offer insight into the effects of wind on the ocean surface, namely the implications of a kinetic energy source on the overall energetics of the circulation. [Preview Abstract] |
Monday, November 19, 2012 8:26AM - 8:39AM |
G2.00003: Advection and buoyancy-induced turbulent diffusion in a narrow vertical tank Daan D.J.A. van Sommeren, C.P. Caulfield, Andrew W. Woods We describe experiments to examine the turbulent mixing due to a source with constant buoyancy flux $B_{s}$ at the top of a vertical tank (with dimensions $40d\times d\times d$) in which an upward flow with speed $u_{b}$ is present. Dense source fluid vigorously mixes with the less dense fluid of the upward flow. The mixed region of fluid is characterised by an unstable density gradient, which drives a turbulent flow which is dominated by eddies of the size of the width of the tank. These turbulent eddies are associated with the downward flux of dense fluid, which is modelled as a diffusive process. The upward flow with speed $u_{b}$ is associated with the advective upward flux of dense fluid. During the late-time steady mixing phase, the diffusive and advective flux of dense fluid are in balance. The mixed region then extends a distance $h_{st}=3d\lambda^{4/3}/\rm{Frn}$ from the top of the tank, where $\rm{Fr}$ is a Froude number defined by $\rm{Fr}=u_{b}/(B_{s}^{1/3}d^{-1/3})$, and $\lambda$ is an $O(1)$ constant relating the width of the tank to the characteristic mixing length of the turbulent eddies. We use a dye-attenuation technique to obtain vertical profiles of the horizontally-averaged reduced gravity, and show a good agreement between experiments and theory. [Preview Abstract] |
Monday, November 19, 2012 8:39AM - 8:52AM |
G2.00004: Simulation of highly-unsteady hydrothermal convection above the critical temperature in the deep sea Satoko Komurasaki Eruption of geothermally heated water from the hydrothermal vent in deep oceans of depth over 2,000 meters is numerically simulated. The hydrostatic pressure of water is assumed to be over 200 atmospheres, and temperature of heated water occasionally more than $300^{\circ}$C. Under these conditions, a part of heated water can be in the supercritical state, and the physical properties can change significantly by the temperature. The compressible Navier-Stokes equations are solved using a method for the incompressible equations under the assumption that the pressure is almost constant at the hydrostatic pressure and the density is a function of the temperature. The equations are approximated by the multidirectional finite difference method, and for the highly-unsteady-flow computation, KK scheme and a hybrid upwind scheme are used to stabilize the high-accuracy computation. Computational results show that complexity and the unsteadiness of the flow are significantly influenced by whether the issuing high temperature water is in the supercritical state or not. [Preview Abstract] |
Monday, November 19, 2012 8:52AM - 9:05AM |
G2.00005: A Computational Investigation of Mixed Convection in Microscale Flows Rustem Bilyalov, John Baker In order to study mixed convective heat transfer associated with flow in a vertical microscale channel, a two-dimensional computational model was used. A temperature difference was established in the direction normal to the flow by assuming that each of the channel walls is at a constant, but different temperature. The microscale geometry resulted in finite Knudsen number flows in the so-called slip flow regime. The Maxwell velocity-slip and temperature-jump boundary conditions were applied at the channel walls. The flow structure was visualized using contour plots of temperature and pressure as well as velocity vector plots. Flows corresponding to Knudsen numbers in the range of 0.01 through 0.1 and an Archimedes number in the range of 0.1 to 10 were considered. Mixed convective heat transfer, for both assisting and opposing conditions, was characterized using the Nusselt number. [Preview Abstract] |
Monday, November 19, 2012 9:05AM - 9:18AM |
G2.00006: Buoyancy-driven instability of a miscible horizontal displacement in a Hele-Shaw cell F. Haudin, L.A. Riolfo, B. Knaepen, A. De Wit In Hele-Shaw cells, viscous fingers are forming when a fluid is injected into a more viscous one. If the two fluids are reversed, with the less mobile fluid injected into the low viscosity one, the situation is expected to be stable from a viscous point of view. Nevertheless, a destabilization of the interface can be observed due to a buoyancy-driven effect if a density difference exists between the two miscible fluids. As a result, the Poiseuille profile established in the gap of the cell locally destabilizes and convection rolls are forming. In a view from above, a striped pattern is observed at the miscible interface between the two fluids. To characterize the development of this instability, we have performed an experimental study of viscously stable miscible displacements in a Hele-Shaw cell with radial injection. The displacing fluids are aqueous solutions of glycerol and the displaced ones are either dyed water or dyed glycerol solutions. The way the relative properties of the two fluids is influencing the onset time of the instability and the characteristic size of the pattern is studied. The influence of the gap width and of the flow rate on the buoyantly unstable dynamics is also characterized. [Preview Abstract] |
Monday, November 19, 2012 9:18AM - 9:31AM |
G2.00007: Thermal convection in a nonlinear non-Newtonian magnetic fluid Harald Pleiner, David Laroze We report theoretical and numerical results on the convection of a magnetic fluid in a viscoelastic carrier liquid. The non-Newtonian material properties are taken care of by a general hydrodynamic nonlinear viscoelastic model [1] that contains, but is more general than the standard Oldroyd and Giesekus phenomenological rheological equation for the stress tensor. We calculate the linear threshold for both idealized and rigid boundary conditions and make the comparison with the linear Oldroyd magnetic fluid [2]. In order to explore the nonlinear behavior we perform a truncated Galerkin expansion obtaining a generalized Lorenz system. We find numerically the system's stationary, periodic and chaotic regimes by investigating power spectra and Lyapunov exponents. Finally, we give a phase diagram depicting the various types of dynamical behavior as a function of the Rayleigh number and the viscoelastic material parameters. \\[4pt] [1] H. Pleiner, M. Liu, H.R. Brand, Rheol. Acta. 43, 502 (2004).\\[0pt] [2] L.M. P\'erez, J. Bragard, D. Laroze, J. Martinez-Mardones, H. Pleiner, J. Mag. Mag. Mat. 323, 691 (2011). [Preview Abstract] |
Monday, November 19, 2012 9:31AM - 9:44AM |
G2.00008: Simulation of the flow and heat exchange in a cylindrical solar chemical reactor Manuel Ram\'Irez-Cabrera, Eduardo Ramos In this work, we present the simulation of the flow inside a cylindrical container filled with an optically participating medium. The motion is generated by the combined effect of the forced convection due to an axial pressure gradient and a natural convective flow induced by a beam of heat radiation that enters into the container though a transparent window located on one of the plane surfaces. The bouyancy force is considered perpendicular to the cylinder axis. The simulation is based on the simultaneous solution of the mass, momentum and energy conservation equations, coupled with the radiation intensity transfer equation. The flow patterns and temperature distributions as functions of the pressure gradient are described to identify the parameters required to maximize the heat absorbed and to obtain a specific temperature field for potential applications. The physical conditions considered are similar to those found in a cylindrical Solar-driven water-splitting thermochemical reactor and it is expected that the results will be useful to determine optimum design parameters. [Preview Abstract] |
Monday, November 19, 2012 9:44AM - 9:57AM |
G2.00009: New type of thermal waves in a vertical layer of magneto-polarizable nano-suspension: theory and experiment Sergey A. Suslov, Alexandra A. Bozhko, Gennady F. Putin, Alexander S. Sidorov Study of Boussinesq convection in a vertical differentially heated fluid layer is one of classical problems in hydrodynamics. It is well known that as the value of fluid's Grashof number increases the basic flow velocity profile becomes unstable with respect to stationary shear-driven disturbances (at Prandtl numbers Pr $<$ 12.5) or thermogravitational waves propagating vertically (at larger values of Prandtl number). However linear stability studies of a similar flow of magnetopolarizable nanosuspensions (ferrofluids) placed in a uniform magnetic field perpendicular to a fluid layer predicted the existence of a new type of instability, oblique waves, that arise due to the differential local magnetisation of a non-uniformly heated fluid. The existence of such (thermomagnetic) waves has now been confirmed experimentally using a kerosene-based ferrofluid with magnetite particles of the average size of 10 nm stabilized with oleic acid. The heat transfer rate measurements using thermocouples and flow visualization using a thermosensitive film and an infrared camera have been performed. Perturbation energy analysis has been used to determine the physical nature of various observed instability patterns and quantitatively distinguish between thermogravitational and thermomagnetic waves. [Preview Abstract] |
Monday, November 19, 2012 9:57AM - 10:10AM |
G2.00010: DEP thermal convection in annular geometry under microgravity conditions Harunori Yoshikawa, Olivier Crumeyrolle, Innocent Mutabazi Thermal convection driven by the dielectrophoretic force is investigated in annular geometry in microgravity environments. A radial heating and a radial alternating electric field are imposed on a dielectric fluid layer filling the gap of two concentric infinite-length cylinders. The resulting dielectric force field is regarded as spatially varying radial gravity that can develop thermal convection. The linear stability problem of a purely conductive basic state is solved by a spectral-collocation method for both axisymmetric and non-axisymmetric disturbances. A stationary non-axisymmetric mode becomes first unstable at a critical Rayleigh number to develop convection. The stability boundary shows asymmetry with respect to heating direction. For an outward heating the critical value approaches that of the Rayleigh-B\'{e}nard problem (1708) as the gap size decreases, while it converges to larger values in the narrow gap limit. For an inward heating the instability occurs only when the gap is narrower than a certain value. The critical number diverges with increasing the gap size. Instability mechanism is examined from energetic viewpoints. The feedback of electric field to temperature disturbances is found to stabilize the conductive state for narrow gaps. [Preview Abstract] |
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