Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session M16: Convection and Buoyancy-Driven Flows: General II |
Hide Abstracts |
Chair: David Sondak, University of Wisconsin-Madison Room: 2000 |
Tuesday, November 25, 2014 8:00AM - 8:13AM |
M16.00001: An application of the unifying theory of thermal convection in vertical natural convection Chong Shen Ng, Andrew Ooi, Detlef Lohse, Daniel Chung Using direct numerical simulations of vertical natural convection (VNC) at Rayleigh numbers $1.0\times 10^5$--$1.0\times 10^9$ and Prandtl number $0.709$, we provide support for a generalised applicability of the Grossmann--Lohse (GL) theory, originally developed for horizontal natural (Rayleigh--B{\'e}nard) convection. In accordance with the theory, the boundary-layer thicknesses of the velocity and temperature fields in VNC obey laminar-like scaling, whereas away from the walls, the dissipation of the turbulent fluctuations obey the scaling for fully developed turbulence. In contrast to Rayleigh--B{\'e}nard convection, the direction of gravity in VNC is parallel to the mean flow. Thus, there no longer exists an exact relation linking the normalised global dissipations to the Nusselt, Rayleigh and Prandtl numbers. Nevertheless, we show that the unclosed term, namely the global-averaged buoyancy flux, also exhibits laminar and turbulent scaling, consistent with the GL theory. The findings suggest that, similar to Rayleigh--B{\'e}nard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for VNC and existing empirical power-law relationships should be recalibrated to better reflect the underlying physics. [Preview Abstract] |
Tuesday, November 25, 2014 8:13AM - 8:26AM |
M16.00002: Maximal transport in the Lorenz equations Charles R. Doering, Andre N. Souza We derive rigorous upper bounds on the transport $\langle XY \rangle$ where $\langle \cdot \rangle$ indicates time average, for solutions of the Lorenz equations without assuming statistical stationarity. The bounds are saturated by nontrivial steady (albeit often unstable) states, and hence they are sharp. Moreover, using an optimal control formulation we prove that no other flow protocol of the same strength, i.e., no other function of time $X(t)$ driving the $Y(t)$ and $Z(t)$ variables while satisfying the basic balance $\langle X^2 \rangle = \langle XY \rangle$, produces higher transport. [Preview Abstract] |
Tuesday, November 25, 2014 8:26AM - 8:39AM |
M16.00003: Optimal transport in truncated models of Rayleigh-B\'enard convection Andre N. Souza, Charles R. Doering We investigate absolute limits on heat transport in a truncated model of Rayleigh-B\'enard convection. Two complementary analyses are used to derive upper bounds in an eight model: a background method analysis and an optimal control approach. In the optimal control formulation the flow no longer obeys an equation of motion, but is instead a control variable. The background method and the optimal control approach produce the same estimate. However, in contrast to a simpler system (i.e., the Lorenz equations) the optimizing flow field---which is observed to be time independent---does not correspond to an exact solution of the equations of motion. [Preview Abstract] |
Tuesday, November 25, 2014 8:39AM - 8:52AM |
M16.00004: The oscillation modes of large-scale circulation in turbulent Rayleigh-B\'enard convection Dandan Ji, Kunlun Bai, Eric Brown We present measurement of the large-scale circulation (LSC) of turbulent Rayleigh-B\'enard convection of cubic cell. We found the reorientation events by rotation through the LSC orientation $\theta_0$ with a multi-peaked probability distribution $p(\theta_0)$, as predicted by the model presented by Brown and Ahlers (Phys. Fluids, 2008). In contrast to the results of oscillation modes in cylindrical cell, when the LSC was confined into one corner, the flow didn't exhibit the twisting and sloshing oscillation with a well-defined periodicity. The phase relation of $\theta_0$ at different heights in the cell was not fixed, so LSC was not in a plane. The sloshing displacement of the LSC from a center plane exhibited random switching between two states. [Preview Abstract] |
Tuesday, November 25, 2014 8:52AM - 9:05AM |
M16.00005: Path instability of a buoyancy-driven body: a sensitivity analysis to measure the fluid-object coupling Joel Tchoufag, Olivier Marquet, David Fabre, Jacques Magnaudet The dynamical path of buoyancy-driven bodies in a viscous fluid is investigated in a linear stability framework. The departure of falling/rising objects from a straight vertical path can be understood by examining the unstable linear global modes of the fully coupled fluid-solid system linearized around the falling/rising steady state. Although this approach offers a quantitative prediction of the various possible trajectories, it raises new questions about the physical interpretation of fully coupled fluid/solid modes. Are the observed trajectories driven by the fluid dynamics, the solid dynamics, or by their coupling? In which flow regions are those dynamics most active? To answer these questions, we present a straightforward adjoint-based-method that can be used to measure the coupling in any problem where reciprocal interactions between two sub-parts of a system take place. This method is exemplified on the case of a two-dimensional falling ellipse. In the particular case of large body-to-fluid inertia ratios, a clear distinction between body-related and wake-induced modes is observed, in line with results predicted by a quasi-static approach. [Preview Abstract] |
Tuesday, November 25, 2014 9:05AM - 9:18AM |
M16.00006: B\'enard-Marangoni instability driven by moisture absorption Sangwoo Shin, Ian Jacobi, Jason Wexler, Howard Stone We describe experiments that exhibit B\'enard-Marangoni convection cells in hygroscopic fluids without external heating. B\'enard-Marangoni convection cells are classically driven by a heat source beneath a thin layer of fluid with a free-surface. External heating provides a reservoir of hot fluid to amplify the free-surface temperature perturbations which drive Marangoni flow; without the heat source, the system naturally damps the temperature fluctuations and stabilizes itself. By drawing water vapor from ambient air, certain hygroscopic fluids can generate their own internal heat source by exploiting an exothermic enthalpy of solution with water. We verify the origin of the instability by using different hygroscopic fluids. The dynamics of this unusual instability are measured as a function of the fluid and air properties of the system, and a mathematical model is developed to rationalize the results quantitatively. [Preview Abstract] |
Tuesday, November 25, 2014 9:18AM - 9:31AM |
M16.00007: Oscillatory magnetoconvective instability in a ferrofluid layer placed in an oblique external magnetic field Sergey A. Suslov, Habibur Rahman, Aleksandra A. Bozhko Magnetite-based ferrofluids are manufactured magneto-polarisable nanofluids that magnetize in an external magnetic field in a similar way to natural paramagnetic fluids(e.g. oxygen), however to a much higher degree. Paramagnetic and ferrofluid flows are described by similar equations and it is expected that they would exhibit a similar behaviour. Indeed we show that in both type of fluids the most prominent instability structures align with the in-layer field component and the onset of magnetoconvection is delayed by the field inclination. However we find that in contrast to paramagnetic fluids the instabilities arising in differentially heated ferrofluids placed in a uniform external oblique magnetic field are oscillatory. This is traced back to the nonlinearity of the magnetic field distribution induced inside the ferrofluid layer that arises whenever the direction of the applied magnetic field is not normal. Given that the magnetic field inclination with respect to the plane of the layer is inevitable near its edges the obtained stability results shed light on the possible reasons for the existnce of unsteady patterns that have been detected in the normal field experiments we reported previously. [Preview Abstract] |
Tuesday, November 25, 2014 9:31AM - 9:44AM |
M16.00008: Stratified shear flow in an inclined square duct Colin Meyer, Paul Linden We present results of experiments on stratified shear flow in an inclined duct. The duct connects two reservoirs of fluid with different densities, which drives a counterflow with a dense layer flowing beneath a less-dense layer moving in the opposite direction. Depending on the dimensionless Atwood number $A$ and duct angle $\theta$, we identify four flow states: a laminar $\mathsf{L}$ state, a Holmboe wavemode $\mathsf{H}$ state, a spatio-temporally intermittent $\mathsf{I}$ state, and a fully developed turbulent $\mathsf{T}$ state. We map a state diagram of these flows in the Atwood number -- $\theta$ plane and examine the force balances that determine each of these states. We find the $\mathsf{L}$ and $\mathsf{H}$ states to be hydraulically controlled at the ends of the duct and the flow is determined by the pressure difference associated with the density difference between the reservoirs. The $\mathsf{I}$ and $\mathsf{T}$ states are associated with increasing dissipation within the duct. We replot the state-space in the Grashof number -- $\theta$ phase plane and find the transition to the $\mathsf{T}$-state is governed by a critical Grashof number. We then evaluate the level of turbulence by examining scalings for the thickness of interfacial region between the two layers. [Preview Abstract] |
Tuesday, November 25, 2014 9:44AM - 9:57AM |
M16.00009: Stratified shear flow in an inclined duct: equations and scalings Simon Vincent, Pierre Augier, Colin Meyer, Paul Linden We present a theoretical approach to model the behaviour of a stratified shear flow in an inclined duct, and relate the scalings emerging from these equations to the experimental work realized on this problem. We consider a system composed of two reservoirs, filled with fluids of different densities, connected by a square duct inclined from the horizontal. We observe from the experiments that a counterflow is established inside the duct with the denser fluid flowing beneath the less dense fluid, exhibiting a wide range of different regimes as the density difference and the inclination angle are increased. Our model shows that the velocities of the flow scale differently depending on the type of regime the system is in. We compare those scalings to the experimental data and show that the transition from the laminar regimes to the more turbulent ones can be described by different non dimensional numbers depending on the inclination angle and the Reynolds number. [Preview Abstract] |
Tuesday, November 25, 2014 9:57AM - 10:10AM |
M16.00010: Stratified shear flow in an inclined duct: measurements of velocity and scalar fields Paul Linden, Simon Vincent, Stuart Dalziel The effect of stable stratification on turbulent shear flow is a fundamental problem in turbulence. We present quantitative experimental results on the flow and density fields in a duct, inclined slightly from the horizontal, connecting two reservoirs containing fluids of different densities and. A counterflow is established in the duct with the denser fluid flowing beneath the less dense fluid. This flow exhibits a range of different flow regimes, from wavelike to intermittent to turbulent, depending on the angle of inclination of the duct, and the relative density difference between the two reservoir fluids. We use two-dimensional PIV and PLIF to measure and compare the velocity and density fields for each of the different regimes. We examine the mean signals to determine governing features such as the average gradient Richardson numbers for each regime. We also determine the characteristic features of the fluctuating fields in the different flow regimes and relate these to the structures observed in visualisations of the flow. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700