Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session AW: Instability: Richtmyer-Meshkov/Rayleigh-Taylor I |
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Chair: Arindam Banerjee, Missouri University of Science & Technology Room: Hyatt Regency Long Beach Regency C |
Sunday, November 21, 2010 8:00AM - 8:13AM |
AW.00001: Richardson effects in turbulent buoyant flows Renaud Biggi, Guillaume Blanquart Rayleigh Taylor instabilities are found in a wide range of scientific fields from supernova explosions to underwater hot plumes. The turbulent flow is affected by the presence of buoyancy forces and may not follow the Kolmogorov theory anymore. The objective of the present work is to analyze the complex interactions between turbulence and buoyancy. Towards that goal, simulations have been performed with a high order, conservative, low Mach number code [Desjardins et. al. JCP 2010]. The configuration corresponds to a cubic box initially filled with homogeneous isotropic turbulence with heavy fluid on top and light gas at the bottom. The initial turbulent field was forced using linear forcing up to a Reynolds number of $Re_{\lambda}=55$ [Meneveau \& Rosales, POF 2005]. The Richardson number based on the rms velocity and the integral length scale was varied from 0.1 to 10 to investigate cases with weak and strong buoyancy. Cases with gravity as a stabilizer of turbulence (gravity pointing up) were also considered. The evolution of the turbulent kinetic energy and the total kinetic energy was analyzed and a simple phenomenological model was proposed. Finally, the energy spectra and the isotropy of the flow were also investigated. [Preview Abstract] |
Sunday, November 21, 2010 8:13AM - 8:26AM |
AW.00002: Wavelet-Based Simulations of Rayleigh-Taylor Instability Scott Reckinger, Daniel Livescu, Oleg Vasilyev The Rayleigh-Taylor instability is investigated using numerical simulations on an adaptive mesh, performed with the Adaptive Wavelet Collocation Method (AWCM). The wide range of scales present in the development of the instability are efficiently resolved with AWCM, due to the physics-based adaptivity and direct error control of the method. The problem is initialized consistent with the solutions from linear stability theory, where the base state is the diffusive mixing of incompressible variable density fluids. Of interest are the variable density and compressibility effects on the departure time from the linear growth, the onset of strong non-linear interactions, and the late- time behavior of the fluid structures. Simulations performed for a single-mode perturbation in the incompressible limit match the early time linear growth, the terminal bubble velocity, and a reacceleration region. In order to investigate the turbulent mixing rates of the pure heavy and light fluids within the Rayleigh-Taylor mixing layer, simulations of compressible homogeneous isotropic turbulent mixing in a triply-periodic domain are also performed. [Preview Abstract] |
Sunday, November 21, 2010 8:26AM - 8:39AM |
AW.00003: Statistical model for turbulent transition by variable-density pressure-gradient-driven mixing J. Bakosi, J.R. Ristorcelli A Monte-Carlo method for variable-density (VD) pressure-gradient-driven turbulence has been developed. VD effects due to non-uniform mass concentrations (e.g. mixing of different-density species) are considered. The model numerically computes the full time-evolution of the joint probability density function (PDF) of fluid density and velocity in a non-stationary Rayleigh-Taylor flow, that develops from quiescent state to a laminar stage, through transition to fully developed turbulence and dissipative decay. The coupled model for hydrodynamics and mixing is designed for arbitrary Atwood numbers. The main characteristics of the method are: (1) It eliminates the need for quasi-equilibrium assumptions, gradient diffusion hypotheses, modeling of the mass flux and of the density-specific-volume covariance; (2) The mixing state is represented by the density PDF; (3) It captures the density skewness, due to large differential accelerations of different-density species; and (4) It represents both small and large scale anisotropy. [Preview Abstract] |
Sunday, November 21, 2010 8:39AM - 8:52AM |
AW.00004: Direct numerical simulations of Rayleigh-Taylor instability with gravity reversal Mark Petersen, Daniel Livescu, Robert Gore We have conducted high resolution, high Reynolds number Direct Numerical Simulations (DNS) of the Rayleigh-Taylor (RT) instability on the 0.5 petaflop, 150k compute cores BG/L Dawn supercomputer at Lawrence Livermore National Lab. This includes a suite of simulations with Atwood number ranging from 0.04 to 0.9 and grid size of $1024^2$ by 4096, and a high resolution simulation of grid size $4096^3$ and Atwood number of 0.75. After the layer width has developed substantially, additional branched simulations have been run under reverse gravity and zero gravity conditions. The simulations provide an extensive database to study Rayleigh-Taylor turbulence, including mixing layer growth rate and self-similar behavior, turbulence and mixing asymmetries, and spectral characteristics. Individual terms in the moments transport equations are recorded to develop and validate turbulence closure models. [Preview Abstract] |
Sunday, November 21, 2010 8:52AM - 9:05AM |
AW.00005: Turbulence characteristics in the variable-density Rayleigh-Taylor mixing layer Daniel Livescu, Mark Petersen, Rob Gore The turbulence generated in the Rayleigh-Taylor mixing layer is studied using data from Direct Numerical Simulations on up to $4096^3$ meshes. The simulations cover the range of Atwood numbers $A=0.04 - 0.9$ in order to study small departures from the Boussinesq approximation as well as large Atwood number effects. The results show that, although the layer width becomes self-similar relatively fast, the lower order terms in the self-similar expressions for turbulence moments have long-lasting effects and derived quantities, such as the turbulent Reynolds number, are slow to follow the self-similar predictions. This has important consequences for moment closures, which generally assume full, asymptotic self-similarity. The results also show that at large Atwood numbers, the turbulence structure changes qualitatively and various turbulence moments become asymmetric. These asymmetries, together with that of the mixing itself, have a profound influence on the shape of the mixing layer. [Preview Abstract] |
Sunday, November 21, 2010 9:05AM - 9:18AM |
AW.00006: Revised Froude number for Rayleigh-Taylor flow with secondary instabilities Karthik Mahadevan Muthuraman, Praveen Ramaprabhu, Guy Dimonte, Paul Woodward, Chris Fryer, Gabe Rockefeller, Yuan-Nan Young Recent simulations [1] and experiments [2] have shown the late-time Rayleigh-Taylor (RT) saturation velocity is sensitive to the appearance of secondary Kelvin-Helmholtz (KH) vortices. Specifically, RT bubbles experience a late surge due to the induced velocity of the KH vortices and saturate at a Froude number twice that predicted by potential flow models [3]. We describe this picture with a simple toy model that idealizes the KH rollups as a pair of counter-rotating point vortices. From classical linear theory, the KH growth rates depend on several parameters such as viscosity, surface tension, and density difference between the fluid streams. We have studied the influence of these parameters on the fundamental RT mode using high aspect ratio, single mode numerical simulations, and will discuss our findings. At very late time, turbulent mixing occurs due to further instabilities. The results are expected to be of relevance to turbulent mix models that are based on bubble growth and merger.[1] Ramaprabhu, P. et al. 2006, Physical Review E. 74, 066308. [2] Wilkinson, J.P. \& Jacobs, J.W. 2007, Phys. Fluids 19, 124102. [3] Goncharov, V.N. 2002 Physical Review Letters 88, 1345021. [Preview Abstract] |
Sunday, November 21, 2010 9:18AM - 9:31AM |
AW.00007: Non-linear effects in the combined Rayleigh-Taylor and Kelvin-Helmholtz Instabilities Britton Olson, Johan Larsson, Sanjiva Lele The combined Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) Instability has been studied extensively in the linear regime. We have performed studies outside the linear regime by means of Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) where relatively little attention has been devoted. Motivation for research in this area has traditionally been plasma physics applications such as Inertial Confinement Fusion (ICF) and Type-1a supernovae collapse. Results of linear stability analysis for a discontinuous interface which combines RT with KH show that for all parameters defining the instabilities, shear addition will increase the growth rate of the RT instability. Our results show that outside this linear regime, shear in fact does mitigate the spreading rate of the RT mixing region. We present a physical explanation of this phenomenon and simple scaling laws which provide a collapse of the data. We further provide a method for determining the optimal amount of velocity shear that will effectively minimize the early time peak mixing rate. [Preview Abstract] |
Sunday, November 21, 2010 9:31AM - 9:44AM |
AW.00008: Self-Similar Solutions of Reynolds-Averaged Navier-Stokes Models for Rayleigh-Taylor Instability-Induced Turbulence and Mixing Oleg Schilling Many applications in which modeling the effects of mixing induced by interfacial hydrodynamic instabilities is important, such as inertial confinement fusion and astrophysics, require a Reynolds-averaged Navier-Stokes (RANS) description due to the prohibitively large range of scales present. In appropriate limits, the RANS equations typically admit self-similar solutions that are useful for developing insights into the late- time behavior of turbulence and mixing. In addition, these solutions provide constraints on model coefficients through large-scale observables, other constraints through coefficient relationships, expressions for closures of the transport equations, and checks on numerical solutions of the full RANS equations. Analytical and semi-analytical solutions of two- equation, and recently proposed three- and four-equation RANS models that include descriptions of scalar turbulence, are derived in various limits for Rayleigh-Taylor instability. The implications of the coefficient constraints on closure modeling of terms in the RANS model are discussed. The results of this study are also related to state-of-the-art simulations and experiments. [Preview Abstract] |
Sunday, November 21, 2010 9:44AM - 9:57AM |
AW.00009: A Posteriori Tests of a Three- and Four-Equation Advanced Reynolds--Averaged Navier--Stokes Model for Rayleigh--Taylor Turbulent Mixing Gregory Burton, Oleg Schilling A high-order, multicomponent implementation of a three- and four- equation, variable-density incompressible Reynolds-averaged Navier-Stokes model incorporating both mechanical and scalar turbulence is used to simulate Rayleigh-Taylor turbulent mixing with an Atwood number equal to one-half. The closures in this model were previously tested a priori against the large Reynolds number $3072^3$ Cabot-Cook direct numerical simulation (DNS) data over the entire evolution of the flow into the late-time self-similar regime. Using both Reynolds number-dependent and late-time coefficients obtained by minimizing the $L^2$ norm between the model and DNS data, the predicted mixing layer evolution is compared with both the averaged DNS data and analytical self-similar solutions of the transport equations. The terms in the transport equation budgets are compared in detail to their profiles across the mixing layer predicted by the DNS. The implications of these results for advanced modeling of Rayleigh-Taylor turbulent mixing are discussed. [Preview Abstract] |
Sunday, November 21, 2010 9:57AM - 10:10AM |
AW.00010: Comparisons of a Reynolds-Averaged Navier--Stokes Model with Self-Similar Solutions for Large Atwood Number Rayleigh--Taylor Mixing Rhys Ulerich, Oleg Schilling A new high-order, multicomponent, weighted essentially nonoscillatory (WENO) implementation of a three- and four- equation Reynolds-averaged Navier-Stokes (RANS) model incorporating both mechanical and scalar turbulence is used to simulate intermediate-to-large Atwood number Rayleigh-Taylor turbulent mixing. The predicted RANS mixing layer evolution is compared with the analytical self-similar solutions of the transport equations. The terms in the transport equation budgets are compared in detail to their self-similar profiles across the mixing layer. Additionally, the sensitivity of the RANS solutions to variations in the initial conditions and in the model coefficients is explored. The implications of these results for advanced modeling of Rayleigh-Taylor turbulent mixing are discussed. [Preview Abstract] |
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