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 D40: Flow Instability: Rayleigh-Taylor I |
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Chair: Andrew Cook, Lawrence Livermore National Laboratory Room: Sheraton Back Bay D |
Sunday, November 22, 2015 2:10PM - 2:23PM |
D40.00001: Lessons Learned from Numerical Simulations of Interfacial Instabilities Andrew Cook Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM) and Kelvin-Helmholtz (KH) instabilities serve as efficient mixing mechanisms in a wide variety of flows, from supernovae to jet engines. Over the past decade, we have used the Miranda code to temporally integrate the multi-component Navier-Stokes equations at spatial resolutions up to 29 billion grid points. The code employs 10th-order compact schemes for spatial derivatives, combined with 4th-order Runge-Kutta time advancement. Some of our major findings are as follows: The rate of growth of a mixing layer is equivalent to the net mass flux through the equi-molar plane. RT growth rates can be significantly reduced by adding shear. RT instability can produce shock waves. The growth rate of RM instability can be predicted from known interfacial perturbations. RM vortex projectiles can far outrun the mixing region. Thermal fluctuations in molecular dynamics simulations can seed instabilities along the braids in KH instability. And finally, enthalpy diffusion is essential in preserving the second law of thermodynamics. [Preview Abstract] |
Sunday, November 22, 2015 2:23PM - 2:36PM |
D40.00002: Exploring elastic and plastic regimes of Rayleigh-Taylor instability in solids Rinosh Polavarapu, Arindam Banerjee The elastic-plastic (EP) transition stage of Rayleigh-Taylor (RT) instability in an accelerated non-Newtonian material (soft solid) is investigated. The material exhibits both elastic and plastic behavior when the applied stress is less than yield stress. Different combinations of perturbation amplitude and wavelength are employed at the solid-gas interface. Plastic deformation of a stable interface under various acceleration profiles is analyzed. In addition, the evolution of single mode perturbations at various strain rates is examined by altering the angular acceleration of rotating disk on which the test section is mounted. These findings are used to characterize the effects of strain rate variation on the instability growth rate and the experimental results are compared to several analytical models on RTI in solids. The instability threshold for a perturbation of given amplitude and wavelength is observed to increase with an increase in angular acceleration. The perturbation velocities are measured and used to estimate values of growth-rate parameter in the unstable phase. [Preview Abstract] |
Sunday, November 22, 2015 2:36PM - 2:49PM |
D40.00003: Reynolds and Atwood Numbers Effects on Homogeneous Rayleigh Taylor Instability Denis Aslangil, Daniel Livescu, Arindam Banerjee The effects of Reynolds and Atwood numbers on turbulent mixing of a heterogeneous mixture of two incompressible, miscible fluids with different densities are investigated by using high-resolution Direct Numerical Simulations (DNS). The flow occurs in a triply periodic 3D domain, with the two fluids initially segregated in random patches, and turbulence is generated in response to buoyancy. In turn, stirring produced by turbulence breaks down the scalar structures, accelerating the molecular mixing. Statistically homogeneous variable-density (VD) mixing, with density variations due to compositional changes, is a basic mixing problem and aims to mimic the core of the mixing layer of acceleration driven Rayleigh Taylor Instability (RTI). We present results covering a large range of kinematic viscosity values for density contrasts including small (A$=$0.04), moderate (A$=$0.5), and high (A$=$0.75 and 0.9) Atwood numbers. Particular interest will be given to the structure of the turbulence and mixing process, including the alignment between various turbulence and scalar quantities, as well as providing fidelity data for verification and validation of mix models. [Preview Abstract] |
Sunday, November 22, 2015 2:49PM - 3:02PM |
D40.00004: Understanding the Rayleigh-Taylor instability through 1D and 3D simulations Mark Mikhaeil, Nicholas Denissen, Devesh Ranjan A series of Rayleigh-Taylor instability numerical simulations were completed using the Arbitrary Lagrangian-Eulerian hydrocode FLAG developed at Los Alamos National Laboratory. One-dimensional simulations employed a Reynolds-averaged Navier-Stokes approach with turbulence closure models selected from the Besnard-Harlow-Rauenzahn family of models. Growth rate parameters and turbulence statistics are derived from these simulations and compared between closure models. Variations from experimental results are explored and used to validate the models. The effect of density ratio on the bubble-spike growth rate asymmetry is also investigated. High resolution three-dimensional large eddy simulations (LES) are also completed and presented. LES were initialized using a multi-modal perturbation prescribed from experimental data collected at the Georgia Institute of Technology multi-layer Gas Tunnel facility. Turbulence statistics are gathered by averaging many simulations started with different initial conditions. Late time development is compared to Gas Tunnel experimental results and previous LES. [Preview Abstract] |
Sunday, November 22, 2015 3:02PM - 3:15PM |
D40.00005: Direct Numerical Simulations of Immiscible Rayleigh-Taylor Instability Zhaorui Li, Daniel Livescu Accurate simulations of multi-mode immiscible Rayleigh-Taylor instability (RTI) are presented with the recently developed generalized Cahn-Hilliard Navier-Stokes (GCHNS) equations method. In immiscible turbulent flows, besides the viscous cut-off scale, there are two additional characteristic length scales, which also affect the flow. One is the so-called ``cut-off'' length scale caused by the presence of surface tension and the other is the physical interface thickness. While in some practical applications the interface thickness can be large, in many other cases this thickness approaches the molecular scales. Accurate results can be obtained for these cases if the interface thickness is maintained smaller than all the cut-off scales of the flow, but still much larger than the molecular scales (e.g. mean free path). Our study shows that, as long as the scale-separation (e.g. the ratio of Kolmogorov scale to the interface thickness) is above a certain value (4 to 6 for the RTI problem considered in this study), the numerical results are fully converged with respect to the interface thickness. The results are used to study the physics of multi-mode immiscible RTI and contrasted to those obtained for the miscible case. [Preview Abstract] |
Sunday, November 22, 2015 3:15PM - 3:28PM |
D40.00006: DSMC Simulations of the Rayleigh-Taylor Instability in Gases Michael Gallis, Timothy Koehler, John Torczynski, Steven Plimpton The Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics is applied to simulate the Rayleigh-Taylor instability (RTI) in atmospheric-pressure monatomic gases (e.g., argon and helium). The computational domain is a 1~mm $\times$ 4~mm rectangle divided into 50-nm square cells. Each cell is populated with 1000 computational molecules, and time steps of 0.1~ns are used. Simulations are performed to quantify the growth of a single-mode perturbation on the interface as a function of the Atwood number and the gravitational acceleration. The DSMC results qualitatively reproduce all observed features of the RTI and are in reasonable quantitative agreement with existing theoretical and empirical models. Consistent with previous work in this field, the DSMC simulations indicate that the growth of the RTI follows a universal behavior. For cases with multiple-mode perturbations, the numbers of bubble-spike pairs that eventually appear are found to be in agreement with theoretical results for the most unstable wavelength. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Sunday, November 22, 2015 3:28PM - 3:41PM |
D40.00007: Evolution of Rayleigh-Taylor growth following an initial Richtmyer-Meshkov instability Jeremy Melvin, Baolian Cheng, James Glimm, David H. Sharp We investigate the evolution of a Rayleigh-Taylor (RT) growth on top of an already developing Richtmyer-Meshkov (RM) instability. Using numerical simulations utilizing a front tracking algorithm and theoretical analysis through a buoyancy-drag equation, an initially perturbed density discontinuity is subjected to a shock wave and then after a delay, a gravitational field is applied. The early time growth of the RM/RT instability is compared with a pure RT instability and asymptotic growth rate predictions for the RT evolution. A dependence on the RM seeding is shown to produce a meaningful change in the perturbation growth at early times. The implications of this to Inertial Confinement Fusion analysis, which largely focuses on the RT instability, is discussed. [Preview Abstract] |
Sunday, November 22, 2015 3:41PM - 3:54PM |
D40.00008: The Compressible Rayleigh-Taylor Instability and Vortex Dynamics in Stratified Media Scott A. Wieland, Daniel Livescu, Oleg V. Vasilyev, Scott J. Reckinger Fully resolved adaptive wavelet-based direct numerical simulations (WDNS) of the single-mode, compressible, and miscible Rayleigh-Taylor instability (RTI) have been performed at Reynolds numbers significantly larger than those previously attained. To ensure that WDNS properly captures the full extent of the length and time scales, an exhaustive resolution study was completed. The ensuing results explore the effects of compressibility and background stratification on the vortex generation and interaction that serves as the driver behind the RTI development beyond the early stages. To better understand the eventual suppression that arises at large background stratification, the simplified cases of a pair of counter rotating vortices (2D) and a vortex ring (3D) in stratified media are also presented for the purpose of isolating and explaining the physics behind these effects on RTI growth. [Preview Abstract] |
Sunday, November 22, 2015 3:54PM - 4:07PM |
D40.00009: Rayleigh-Taylor Instability in non-premixed reacting flames. Nitesh Attal, Praveen Ramaprabhu The Rayleigh-Taylor instability (RTI) occurs at a perturbed interface between fluids of different densities when a light fluid pushes a heavier fluid. The mixing driven by RTI affects several physical phenomena, such as Inertial Confinement Fusion, Supernovae detonation, centrifugal combustors and liquid rocket engines. The RTI in such flows is often coupled with chemical/nuclear reactions that may form complex density stratifications in the form of flames or ablative layers. We investigate such a non-premixed fuel-air interface subject to a constant acceleration and developing under the influence of chemical reactions using high-resolution, Navier-Stokes simulations [1]. The H$_{2}$ fuel is diluted with N$_{2}$ to vary the density difference across the interface in thermal equilibrium (at 1000K). The intervening layer between fuel and air is subject to exothermic combustion reactions to form a flame. Following combustion, initially unstable fuel-air interfaces at an Atwood number (A$_{t})$ \textless 0.5, transform into stable (fuel-flame) and unstable (flame-air) interfaces. We report on interfaces (A$_{t}=$ 0.2 and 0.6) with single wavelength, sinusoidal perturbations and a broadband spectrum of multimode perturbations. [1] Attal, N., et al. Comput. Fluids 107 (2015): 59-76. [Preview Abstract] |
Sunday, November 22, 2015 4:07PM - 4:20PM |
D40.00010: RANS Simulations of Rocket Rig Experiments: Capturing the Effects of the Rayleigh- Taylor Instability Subject to a Changing Body Force Rebecca Bertsch, Robert Gore Modeling turbulent mixing in variable density (VD) fluid flows is a key topic of interest in multi-physics applications due to the complex instability characteristics they exhibit. RANS models continue to be accurate and efficient tools to investigate the evolution of turbulence in these complex flow problems. Many RANS models are well validated for prototypical variable density flows such as Rayleigh-Taylor (RT) and Richtmeyer-Meshkov (RM). However, most lack the ability to accurately capture mix features in VD flows with changing body forces, like those seen in rocket rig experiments that undergo phases of acceleration and deceleration. This talk will present some simulations of an improved RANS model which substitutes the molecular diffusion term in the species equation with a demix term that is dependent on the turbulent mass flux and species micro-densities. Results from these simulations will be compared with previous RANS models, DNS, and experimental data to validate the new modelâ€™s ability to capture the mixing physics in RT flow subject to a changing body force. [Preview Abstract] |
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