Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session A2: Convection and Buoyancy-Driven Flows I: Numerical Simulations |
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Chair: Hans Johnston, University of Massachusetts - Amherst Room: 324 |
Sunday, November 24, 2013 8:00AM - 8:13AM |
A2.00001: High Rayleigh number simulations in a cylinderical cell with aspect-ratio 1/3 Erwin P. van der Poel, Roberto Verzicco, Detlef Lohse The results of DNS simulations of Rayleigh-B\'enard convection with Ra up to $10^{12}$ in a cylindrical geometry with aspect-ratio 1/3 are presented. The simulations were carried out on a PRACE tier 0 grant illustrating the size of the computational task, which required millions of CPU hours. With Pr $= 0.7$ these simulations match the new experimental setup build in the ``U-boat of G\"ottingen.'' We show global quantities such as the heat transport as well as local time-averages. The boundary layer profile and the strength of the large scale circulation are studied and movies of horizontal cross-section of the bulk and the boundary layer are shown. [Preview Abstract] |
Sunday, November 24, 2013 8:13AM - 8:26AM |
A2.00002: Numerical simulations of high Rayleigh, Prandtl and Schmidt number flows using multiple space/time resolutions Roberto Verzicco, Rodolfo Ostilla Monico, Erwin P. van der Poel, Detlef Lohse The numerical simulation of passive and active scalars in turbulence becomes more challenging as their diffusivity decreases. In fact, for large Prandtl or Schmidt numbers the Batchelor scale $\eta_T$ is smaller than the Kolmogorov scale $\eta$ and, being mesh size taylored to the smallest of the two, the momentum equation is integrated in space and time using unnecessary fine resolutions. This strongly penalizes the computation because, while the scalar dynamics is described by a single equation, the momentum evolves according to a vectorial equation and an elliptic equation for the pressure. Contrary to the intuition, it has observed that even in the case of a flow at Pr=0.7 the resolution needed for the scalar is larger than that of the momentum since the absence of pressure in the equation of the former keeps localized steep gradients. Motivated by the above observation here we show a novel numerical procedure that decouples the space and time resolutions of momentum and temperature and allows to use a refined mesh only for the quantities that need it. We show that, provided every quantity is adequately resolved, the conservation properties of the schemes are retained and at least an order of magnitude reduction of the computational effort is achieved. [Preview Abstract] |
Sunday, November 24, 2013 8:26AM - 8:39AM |
A2.00003: Effects of Velocity and Temperature Boundary Conditions in Turbulent Thermal Convection Hans Johnston, David Goluskin, Charles Doering, Glenn Flierl We report on 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 both temperature and velocity boundary conditions on the turbulent heat transport. In the first scenario, while imposing the no-slip velocity boundary condition, 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 findings are compared and contrasted with results of recent three-dimensional simulations and experiments. In the second scenario we consider the setup originally considered by Rayleigh for calculating conditions for the onset of thermal convection, fixed temperature boundary condition with free-slip velocity boundary conditions. Somewhat surprisingly, at high Rayleigh numbers a strong shear flow develops with periodic ``bursting'' of the thermal boundary layers. We'll discuss this phenomena and its impact on the heat transport. [Preview Abstract] |
Sunday, November 24, 2013 8:39AM - 8:52AM |
A2.00004: Solutions to inverse plume in a crosswind problem using a predictor -- corrector method Joseph VanderVeer, Yogesh Jaluria Investigation for minimalist solutions to the inverse convection problem of a plume in a crosswind has developed a predictor -- corrector method. The inverse problem is to predict the strength and location of the plume with respect to a select few downstream sampling points. This is accomplished with the help of two numerical simulations of the domain at differing source strengths, allowing the generation of two inverse interpolation functions. These functions in turn are utilized by the predictor step to acquire the plume strength. Finally, the same interpolation functions with the corrections from the plume strength are used to solve for the plume location. Through optimization of the relative location of the sampling points, the minimum number of samples for accurate predictions is reduced to two for the plume strength and three for the plume location. After the optimization, the predictor-corrector method demonstrates global uniqueness of the inverse solution for all test cases. The solution error is less than 1{\%} for both plume strength and plume location. The basic approach could be extended to other inverse convection transport problems, particularly those encountered in environmental flows. [Preview Abstract] |
Sunday, November 24, 2013 8:52AM - 9:05AM |
A2.00005: Time-dependent dynamics of fluid temperature driven by a constant temperature vertical wall in an insulated space Rachael Bonnebaigt, C.P. Caulfield, P.F. Linden We consider the time-dependent flow induced by heating at a vertical wall, held at constant temperature, in a sealed insulated box. Conservation of volume flux, momentum flux, and buoyancy flux give equations for the plume that rises up the wall and for return flow in the ambient fluid. We solve these equations numerically with three different assumptions: a) plume fluid spreading at the ceiling mixes ``perfectly'' throughout the box down to a first front, leading to two-layer stratification; b) plume fluid spreads at the ceiling with `zero' mixing into the evolving ambient fluid, leading to continuous ambient stratification; c) the heat transfer coefficient at the wall varies with height according to the classical model of F. J. Bayley (1955 {\it Proc. I. M. E.} {\bf 169} 361-370), i.e. that the Nusselt number is proportional to the one third power of an appropriate Rayleigh number. All schemes reach the same final state: the box reaches the wall temperature and the plume shuts down. We compare the three predictions for the time-dependent ambient temperature distribution with analogue laboratory experiments. [Preview Abstract] |
Sunday, November 24, 2013 9:05AM - 9:18AM |
A2.00006: Buoyancy-driven flow around $A + B \rightarrow C$ reaction fronts propagating in Hele-Shaw cells: Parabolic flights experiments and numerical simulations Laurence Rongy, Kerstin Eckert, Anne De Wit The dynamics of $A + B \rightarrow C$ reaction fronts is studied under modulated gravitational acceleration by means of a combination of parabolic flight experiments and numerical simulations. During modulated gravity the front position undergoes periodic modulation with an accelerated front propagation under hyper-gravity together with a slowing down under low gravity. The underlying reason for this is an amplification and a decay respectively, of the buoyancy-driven double vortex associated with the front propagation under standard gravitational acceleration, as explained by reaction-diffusion-convection simulations of an $A + B \rightarrow C$ front propagating in a thin layer. Deeper insights into the correlation between grey-value changes in the experimental shadowgraph images and characteristic changes in the concentration profiles are obtained by a numerical simulation of the imaging process. [Preview Abstract] |
Sunday, November 24, 2013 9:18AM - 9:31AM |
A2.00007: Non-Boussinesq exchange flow over topography Maziyar Jalaal, Boris Stoeber, Gregory A. Lawrence A series of numerical simulations are performed for the ``lock exchange'' problem in a two-dimensional duct, where the density ratio of the two phases is varied between 10 and 1000. A finite volume method based on an adaptive Cartesian grid is used with grid refinement in regions of high vorticity and/or density gradient. The physics of the problem is analyzed in detail, including wave formation, disturbance growth and the influence of the density ratio on flow features. The results are compared with laboratory experiments, DNS, and theoretical predictions (single and double -layer shallow water equations). The effects of introducing an obstacle are also investigated. [Preview Abstract] |
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