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 H13: Rayleigh-Taylor Instability I |
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Chair: Andrew Lawrie, University of Bristol Room: 27A |
Monday, November 19, 2012 10:30AM - 10:43AM |
H13.00001: Hydrodynamic instabilities and Boundary Value Problem Snezhana I. Abarzhi For the first time, on the basis of conservation principles and thermodynamics laws, we derive the generalized Rankine-Hugoniot conditions that can be applied for unsteady and curved fronts. The conditions describe the dynamics of the interface (front) in an explicit and covariant form and can be employed in convergent or Cartesian system of coordinates for three-dimensional systems. The theoretical framework is applied to the instabilities of Landau-Darrieus (LD), classical Rayleigh-Taylor (RT) and ablative Rayleigh-Taylor (ART). It is shown that in the case when if there is mass flux across the interface and no acceleration (LD), the front can be unstable only if the energy flux across the front is imbalanced. When acceleration is present (RT and ART), the dependence is obtained of the instability growth-rate on the mass flow and energy imbalance across the front. Connection between the ablative RTI and classical RTI is made. The stabilization mechanisms are discussed. The obtained results provide a theoretical framework for design of experiments under conditions relevant to inertial confinement fusion. [Preview Abstract] |
Monday, November 19, 2012 10:43AM - 10:56AM |
H13.00002: Direct Numerical Simulations of Rayleigh-Taylor instability with gravity reversal Daniel Livescu, Tie Wei In order to study the variable acceleration effects on the development of Rayleigh-Taylor instability (RTI), two unit problems are proposed: reversing the gravity and setting the gravity to zero in the turbulent stage of classical RTI. Data from high resolution Direct Numerical Simulations, covering the range of Atwood numbers from 0.04 to 0.9, are used to examine the modifications in the layer structure and turbulence properties following the change in gravity. After gravity reversal, the density inversion regions lead to new local RTI development, which efficiently mixes the large scales of the flow. This also introduces a strong directionality in the alignment of vorticity and strain rate eigenvectors. In addition, the turbulent transport reacts much faster to the change in gravity compared to the mean density. This renders the popular gradient diffusion hypothesis inappropriate for such flows, which pose significant challenges for engineering turbulence models. [Preview Abstract] |
Monday, November 19, 2012 10:56AM - 11:09AM |
H13.00003: Numerical investigations of Rayleigh-Taylor instability development from an initially isotropic turbulent velocity field Pooya Movahed, Bruce Fryxell, Eric Johnsen The Rayleigh-Taylor instability (RTI) is a process by which the misalignment of the pressure and the density gradient at unstably stratified interfaces generates baroclinic vorticity. This process can transition from laminar flow to a fully turbulent mixing region. Numerical simulations of RTI are traditionally initialized by either perturbing the density field at the interface or by transforming the density perturbations to velocity perturbations using linear theory. In this study, the initial interface separates the light and heavy fluids in an existing isotropic turbulent velocity field extending in the whole domain in each fluid. These initial conditions enable us to reach high Reynolds numbers rapidly during the simulation. First, we neglect gravity and quantify isotropy and intermittency of the decaying turbulent field in the mixing region. Second, the problem is revisited in the presence of a gravitational field. The initial fluctuating velocity field perturbs the interface and the baroclinic vorticity generated in the mixing region due to the instability provides energy for the initial decaying turbulent field. A comparison of relevant physical quantities regarding isotropy and mixing is made to the first case. The simulations are performed using a high-order accurate minimally dissipative kinetic-energy preserving and interface capturing scheme. This research was supported in part by the DOE NNSA under the Predictive Science Academic Alliance Program by grant DEFC52-08NA28616. [Preview Abstract] |
Monday, November 19, 2012 11:09AM - 11:22AM |
H13.00004: Efficient mixing in stratified flows: Rayleigh-Taylor instability within a stable stratification Megan Davies Wykes, Stuart Dalziel Turbulent mixing is generated at the Rayleigh-Taylor unstable interface between two stably stratified layers. Measurements of the density profile in a salt stratified laboratory experiment, before and after this process, show very high mixing efficiencies of 0.6 to 0.8. This is significantly higher than that seen in either shear flows or classical two-layer Rayleigh-Taylor instability. We discuss these startling results and present a simple turbulent diffusion model that captures the essential dynamics of the flow. [Preview Abstract] |
Monday, November 19, 2012 11:22AM - 11:35AM |
H13.00005: Estimates of molecular mixing in confined Rayleigh-Taylor instability Andrew Lawrie, Stuart Dalziel We examine the behaviour of a system in which a RT unstable interface is confined between stable continuous stratifications. Recent experiments with linear stratifications (Lawrie \& Dalziel 2011, JFM) indicate an intrinsic limit to a fluid's ability to mix, which here can be measured robustly between quiescent initial and final states. Standard incompressible ILES does not match well because it cannot respect the balance of energy conversions observed in experiment. ILES operates with Sc=O(1), whereas Sc=700 in our experiments. Lawrie \& Dalziel detailed the relation between the p.d.f. of the density field and the availability of energy in the system. Here we extract the evolution of the p.d.f. over the life-cycle of the instability, and thus quantify the ILES mixing estimates in both 2D and 3D RT cases. In 3D, energy cascades to small scales, so the stretching of material surfaces that it induces tends to occur at comparable scales and this is the optimal condition for doing mixing. In 2D, however, energy accumulates at large scales and thus material surfaces do not become so rapidly stretched. We view the 2D case as an analogue for high Schmidt number behaviour, and this helps us understand the modelling approximations in 3D cases. [Preview Abstract] |
Monday, November 19, 2012 11:35AM - 11:48AM |
H13.00006: Evaluation of the Predictions of a Four-Equation Reynolds-Averaged Navier-Stokes Model Applied to Rayleigh-Taylor Instability-Induced Mixing Kyle K. Mackay, Oleg Schilling An implicit-in-time multicomponent, weighted essentially nonoscillatory implementation of a four-equation $K$-$\epsilon$ based Reynolds-averaged Navier--Stokes model is used to simulate Rayleigh--Taylor turbulent mixing at Atwood numbers ranging from $0.05$--$0.9$. The mechanical turbulence equations are coupled to modeled transport equations for the scalar variance and its dissipation rate. The predicted evolution of the mixing layer, molecular mixing and other quantities are compared to available experimental data, as well as to analytical self-similar solutions. The predictive capability of the model is evaluated, and several parametric studies are also presented. [Preview Abstract] |
Monday, November 19, 2012 11:48AM - 12:01PM |
H13.00007: Large Eddy Simulations of the Tilted Rig Experiment: A Two-dimensional Rayleigh-Taylor Instability Case Bertrand Rollin, Nicholas A. Denissen, Jon M. Reisner, Malcolm J. Andrews The tilted rig experiment is a derivative of the rocket rig experiment designed to investigate turbulent mixing induced by the Rayleigh-Taylor (RT) instability. A tank containing two fluids of different densities is accelerated downwards between two parallel guiding rods by rocket motors. The acceleration is such that the pressure and density gradients face opposite directions at the fluids interface, creating a Rayleigh-Taylor unstable configuration. The rig is tilted such that the tank is initially at an angle and the acceleration is not perpendicular to the fluids interface when the rockets fire. This results in a two dimensional Rayleigh-Taylor instability case where the fluids experience RT mixing and a bulk overturning motion. The tilted rig is therefore a valuable experiment to help calibrating two-dimensional mixing models. Large Eddy Simulations of the tilted rig experiments will be compared to available experimental results. A study of the behavior of turbulence variables relevant to turbulence modeling will be presented. LA-UR 12-23829. [Preview Abstract] |
Monday, November 19, 2012 12:01PM - 12:14PM |
H13.00008: RANS Simulations of the Tilted Rig Experiment:A Two-dimensional Rayleigh-Taylor Instability Case Nicholas Denissen, Bertran Rollin, Jon Reisner, Malcolm Andrews Modeling turbulent mixing due to unstable density stratification is of fundamental interest in many multiphysics applications. RANS models remain the tool of choice for efficient estimates of the effects of turbulence on complex problems. While many RANS models have been validated for canonical Rayleigh--Taylor turbulence, applications of interest often have non-planar/dynamic interfaces. This presentation will address the ability of a multispecies, compressible, turbulence model to compute RT mixing on a moving interface. The simulations are based on the tilted rocket-rig experiments designed to study mixing of fluids by the Rayleigh-Taylor instability. In this experiment, a tank containing two fluids of different densities is accelerated downward with the rig inclined by a few degrees off vertical. The RANS simulations are be compared to experiments, direct numerical simulations and large eddy simulations to analyze the model's ability to capture 2D flow features. [Preview Abstract] |
Monday, November 19, 2012 12:14PM - 12:27PM |
H13.00009: The Dynamics of Rayleigh-Taylor Stable and Unstable Contact Discontinuities with Anisotropic Thermal Conduction Daniel Lecoanet, Ian Parrish, Eliot Quataert We study the effects of anisotropic thermal conduction along magnetic field lines on an accelerated contact discontinuity in a weakly collisional plasma. Anisotropic conduction can result in doubly-diffusive instabilities, including the magnetothermal instability (MTI) and the heat flux driven buoyancy instability (HBI). We run fully non-linear numerical simulations of a contact discontinuity with anisotropic conduction. The non-linear evolution can be described as a superposition of three physical effects: temperature diffusion due to vertical conduction, the Rayleigh-Taylor instability (RTI) and the HBI. In simulations with RTI-stable contact discontinuities, the temperature discontinuity spreads due to vertical heat conduction. The HBI slows this temperature diffusion by reorienting initially vertical magnetic field lines to a more horizontal geometry, eventually stopping vertical temperature diffusion. In simulations with RTI-unstable contact discontinuities, the dynamics are initially governed by temperature diffusion, but the RTI becomes increasingly important at late times. These results could be important in various astrophysical contexts including supernova remnants, solar prominences and cold fronts in galaxy clusters. [Preview Abstract] |
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