Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session M18: Flow Instability: Rayleigh-Taylor II |
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Chair: Snezhana Abarzhi, Carnegie Mellon University Room: 206 |
Tuesday, November 24, 2015 8:00AM - 8:13AM |
M18.00001: Rayleigh-Taylor mixing with time-dependent acceleration Snezhana Abarzhi We extend the momentum model to describe Rayleigh-Taylor (RT) mixing driven by a time-dependent acceleration. The acceleration is a power-law function of time, similarly to astrophysical and plasma fusion applications. In RT flow the dynamics of a fluid parcel is driven by a balance per unit mass of the rates of momentum gain and loss. We find analytical solutions in the cases of balanced and imbalanced gains and losses, and identify their dependence on the acceleration exponent. The existence is shown of two typical regimes of self-similar RT mixing –acceleration-driven Rayleigh-Taylor-type and dissipation-driven Richtymer-Meshkov-type with the latter being in general non-universal. Possible scenarios are proposed for transitions from the balanced dynamics to the imbalanced self-similar dynamics. Scaling and correlations properties of RT mixing are studied on the basis of dimensional analysis. Departures are outlined of RT dynamics with time-dependent acceleration from canonical cases of homogeneous turbulence as well as blast waves with first and second kind self-similarity. [Preview Abstract] |
Tuesday, November 24, 2015 8:13AM - 8:26AM |
M18.00002: Stochastic model of Rayleigh-Taylor mixing with time-dependent acceleration Nora Swisher, Snezhana Abarzhi We report the stochastic model of Rayleigh-Taylor (RT) mixing with time-dependent acceleration. RT mixing is a statistically unsteady process, where the means values of the flow quantities as well as the fluctuations around these means are time-dependent. A set of nonlinear stochastic differential equations with multiplicative noise is derived on the basis of rigorous momentum model and group theory analyses to account for the randomness of RT mixing. A broad range of parameter regime is investigated; self-similar asymptotic solutions are found; new regimes of RT mixing dynamics are identified. We show that for power-law asymptotic solutions describing RT mixing the exponent is relatively insensitive and pre-factor is sensitive to the fluctuations, and find the statistic invariants of the dynamics in each of the new regimes. [Preview Abstract] |
Tuesday, November 24, 2015 8:26AM - 8:39AM |
M18.00003: The Evolution of the single-mode Rayleigh-Taylor instability under the influence of time-dependent accelerations Praveen Ramaprabhu, Varad Karkhanis, Rahul Banerjee, Hilda Varshochi, Manoranjan Khan, Andrew Lawrie From detailed numerical simulations of the single-mode Rayleigh-Taylor (RT) instability driven by time-varying acceleration histories, we report on several findings of relevance to the performance of Inertial Confinement Fusion capsules. The incompressible, Direct Numerical Simulations (DNS) were performed in two- and three-dimensions, and over a range of density ratios of the fluid combinations (characterized by the Atwood number). We have investigated several acceleration histories, including acceleration profiles g(t) of the general form $t^{n}$, with n $>$ -2. For the 2D flow, results from numerical simulations are compared with a potential flow model developed and reported as part of this work. When the simulations are extended to three dimensions, bubble and spike growth rates are in agreement with an extension to the drag buoyancy model with modifications for time-dependent acceleration histories. We have come up with simple analytic solutions to the Drag Buoyancy model for variable g flows, and compared the solution with the 2D and 3D DNS results. [Preview Abstract] |
(Author Not Attending)
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M18.00004: Simulations of mixing in Inertial Confinement Fusion with front tracking and sub-grid scale models Verinder Rana, Hyunkyung Lim, Jeremy Melvin, Baolian Cheng, James Glimm, David Sharp We present two related results. The first discusses the Richtmyer-Meshkov (RMI) and Rayleigh-Taylor instabilities (RTI) and their evolution in Inertial Confinement Fusion simulations. We show the evolution of the RMI to the late time RTI under transport effects and tracking. The role of the sub-grid scales helps capture the interaction of turbulence with diffusive processes. The second assesses the effects of concentration on the physics model and examines the mixing properties in the low Reynolds number hot spot. We discuss the effect of concentration on the Schmidt number. The simulation results are produced using the University of Chicago code FLASH and Stony Brook University's front tracking algorithm. [Preview Abstract] |
Tuesday, November 24, 2015 8:52AM - 9:05AM |
M18.00005: Rayleigh-Taylor instability (RTI) for a yield-stress fluid Ilham Maimouni, Julie Goyon, Etienne Lac, Nicolas Flamant, Thibault Pringuey, Philippe Coussot RTI is of great interest in several domains such as oil industry, geology and high-energy density physics. We experimentally study this instability for a yield-stress fluid, i.e. a fluid that is solid under a certain critical yield stress, and liquid above. For that, we superimpose, at rest, two rheologically - controlled immiscible fluids of different densities, a yield stress fluid under a heavier Newtonian one, and we observe the interface. For a given density difference, the instability occurs below a critical yield stress in the form of fingers of one fluid abruptly spreading through the other one. Above this critical yield stress, the interface remains undeformed. This set of data provides an empirical criterion for the instability. We find that this criterion is neither predicted by simple elastic material theory, nor by the assumption of yielding phenomena at sufficient initial perturbation amplitude. Instead, RTI occurs for a sufficiently larger density difference to yield stress ratio and the finger wavelength is independent of the sample size. Finally we show that the instability characteristics can be explained by the ability of a local perturbation beyond a critical size to penetrate the material. [Preview Abstract] |
Tuesday, November 24, 2015 9:05AM - 9:18AM |
M18.00006: A 3D Bubble Merger Model for RTI Mixing Baolian Cheng In this work we present a model for the merger processes of bubbles at the edge of an unstable acceleration driven mixing layer. Steady acceleration defines a self-similar mixing process, with a time-dependent inverse cascade of structures of increasing size. The time evolution is itself a renormalization group evolution. The model predicts the growth rate of a Rayleigh-Taylor chaotic fluid-mixing layer. The 3-D model differs from the 2-D merger model in several important ways [1]. Beyond the extension of the model to three dimensions, the model contains one phenomenological parameter, the variance of the bubble radii at fixed time. The model also predicts several experimental numbers: the bubble mixing rate, the mean bubble radius, and the bubble height separation at the time of merger. From these we also obtain the bubble height to the radius aspect ratio, which is in good agreement with experiments. Applications to recent NIF and Omega experiments will be discussed. This work was performed under the auspices of the U.S. Department of Energy by the Los Alamos National Laboratory under Contract No. W-7405-ENG-36.\\[4pt] [1] B. Cheng, J. Glimm and D. Sharp, Chaos 12, 267 (2002). [Preview Abstract] |
Tuesday, November 24, 2015 9:18AM - 9:31AM |
M18.00007: The effect of an obstruction on the Rayleigh-Taylor instability Christopher Brown, Stuart Dalziel This talk discusses the effect of an obstruction on the evolution of the Rayleigh-Taylor instability in a confined geometry at low Atwood numbers. The introduction of an obstacle at the height of the initial interface results in dramatic changes to the dynamics of mixing, even when this obstacle is only a few percent of the domain width. Two situations are investigated using laboratory experiments and implicit large eddy simulations. In the first case, a single horizontal opening connects the upper and lower layers. A bidirectional flow exchanges fluid through the opening, this establishes a circulation cell in each layer. These cells exist quasi-steadily for long periods, increasing the time required for mixing compared with the classical case and resulting in a more uniformly mixed final stratification. The second case has two horizontal openings, one either side of the obstruction. This results in markedly different dynamics. The flow through each of the openings switches back and forth between being bidirectional (as with the single opening case) and unidirectional, with the direction of the unidirectional exchange reversing with a constant period. \\ \copyright British Crown Owned Copyright 2015/AWE [Preview Abstract] |
Tuesday, November 24, 2015 9:31AM - 9:44AM |
M18.00008: Dripping from a curved ceiling: a linear optimal transient growth analysis Gioele Balestra, Anna Lee, Joel Marthelot, Pierre-Thomas Brun, Pedro M. Reis, Francois Gallaire We investigate theoretically the stability of a thin viscous film on the underside of a curved cylindrical surface. Gravity acts both as a stabilizing force originating in the progressive drainage of the film and as a destabilizing force prone to form dripping droplets. The drainage solution, derived from lubrication equations, is found asymptotically stable with respect to infinitesimal perturbations. This result first reported by Trinh et al. when studying the region near the top of a coated cylinder is here generalized to the entire structure. The governing parameters, namely the Bond number, which prescribes the relative importance of gravity and surface tension forces, and the initial film thickness to cylinder radius ratio are found not to play a role in the long time stability of the film. However, the system displays a linear transient growth potential which increases exponentially with the Bond number. Depending on its value, there is a critical initial disturbance amplitude above which non-linear effects yield the formation of droplets, suggesting that the transition to dripping is noise and roughness dependent. [Preview Abstract] |
Tuesday, November 24, 2015 9:44AM - 9:57AM |
M18.00009: Validation of Nek5000 against low-Atwood, single-mode Rayleigh Taylor experiments Maxwell Hutchinson Experiments by Wilkinson and Jacobs [1] demonstrate the stagnation and reacceleration phases of the low-Atwood, single-mode Rayleigh Taylor instability between two water mixtures. We reproduce the experimental conditions of three runs in direct numerical simulations using the spectral element code Nek5000. The simulations required 17 billion grid points on 512 thousand cores of the Mira supercomputer to reach Rayleigh numbers up to 90 million. We extend the vertical dimension to reach higher bubble aspect ratios and demonstrate the limits of wall-bounded single-mode studies. Finally, exploration of the full-field results reveals spanwise secondary flows that enhance mixing at low to moderate Reynolds number. \\[4pt] [1] J. P. Wilkinson and J. W. Jacobs, Phys. Fluids 19, 124102 (2007). [Preview Abstract] |
Tuesday, November 24, 2015 9:57AM - 10:10AM |
M18.00010: Scale-coupling and Nonlinear Dynamics in Compressible Rayleigh-Taylor Instability Dongxiao Zhao, Hussein Aluie, Riccardo Betti The Rayleigh-Taylor instability (RTI) is a ubiquitous instability occurring in laser-accelerated targets and in many geophysical and astrophysical environments. Mass ablation or evaporation can significantly alter the RTI evolution in laser-driven plasmas as well as in molecular clouds and supernovae ejecta. We perform single and multimode simulations of 3D compressible RTI using a hybrid pseudospectral-compact finite difference scheme. We will present preliminary results on how different length scales are dynamically coupled at various stages of the instability, especially in the highly nonlinear regime. Our goal is to understand how ablation alters this scale-coupling and its effect on the overall growth of the mixed layer, which may have significant ramifications to modeling efforts in implosion physics. [Preview Abstract] |
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