Influence of scale-breaking phenomena on turbulent mixing rates

George, Erwin; Glimm, James; Li, Xin; Li, Yuanhua; Liu, Xinfeng

doi:10.1103/physreve.73.016304

Cited by 37 publications

(28 citation statements)

References 15 publications

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“…Using TSTT developed front tracking software, we cured the first problem [15,15,14,8], excess numerical mass diffusion, and by enhancements to this software, we also address the second problem, insufficient physics models for physical mass diffusion and/or physical surface tension, see [34]. The result is complete agreement or nearly so in the match of simulation to experiment for Rayleigh-Taylor mixing.…”

Section: Turbulent Mixingsupporting

confidence: 53%

Terascale Simulation Tools and Technologies

Li¹

2007

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Section: Turbulent Mixingsupporting

confidence: 53%

Terascale Simulation Tools and Technologies

Li¹

2007

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“…defined in terms of the simulation itself, as a measure of the time-dependent density contrast within the simulation bubble region [6,34,36]. We found that the untracked simulation reduced the density contrast, and A(t), by a factor of ∼2 relative to the nominal A = A(t = 0).…”

Section: (B) Front Tracking Rayleigh-taylor Simulationsmentioning

confidence: 84%

“…We consider the Rayleigh-Taylor (RT) mixing problem [1,2], in which a light fluid accelerates a heavy fluid. Numerical efforts to solve this problem date back more than 60 years, and only recently have systematic numerical solutions based on compressible fluid dynamics been found that address an experimental range of fluid parameters for both immiscible and miscible fluids, the latter over a range of Schmidt numbers [3][4][5][6]. The problem is to predict the growth rate α, defined in terms of the penetration distance h of the light fluid into the heavy fluid, via the equation…”

Section: Introductionmentioning

confidence: 99%

New directions for Rayleigh–Taylor mixing

Glimm

Sharp

Kaman

et al. 2013

Phil. Trans. R. Soc. A.

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We study the Rayleigh–Taylor (RT) mixing layer, presenting simulations in agreement with experimental data. This problem is an idealized subproblem of important scientific and engineering problems, such as gravitationally induced mixing in oceanography and performance assessment for inertial confinement fusion. Engineering codes commonly achieve correct simulations through the calibration of adjustable parameters. In this sense, they are interpolative and not predictive. As computational science moves from the interpolative to the predictive and reduces the reliance on experiment, the quality of decision making improves. The diagnosis of errors in a multi-parameter, multi-physics setting is daunting, so we address this issue in the proposed idealized setting. The validation tests presented are thus a test for engineering codes, when used for complex problems containing RT features. The RT growth rate, characterized by a dimensionless but non-universal parameter α , describes the outer edge of the mixing zone. Increasingly accurate front tracking/large eddy simulations reveal the non-universality of the growth rate and agreement with experimental data. Increased mesh resolution allows reduction in the role of key subgrid models. We study the effect of long-wavelength perturbations on the mixing growth rate. A self-similar power law for the initial perturbation amplitudes is here inferred from experimental data. We show a maximum ±5% effect on the growth rate. Large (factors of 2) effects, as predicted in some models and many simulations, are inconsistent with the experimental data of Youngs and co-authors. The inconsistency of the model lies in the treatment of the dynamics of bubbles, which are the shortest-wavelength modes for this problem. An alternative theory for this shortest wavelength, based on the bubble merger model, was previously shown to be consistent with experimental data.

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“…The authors and coworkers (7)(8)(9) observed the importance of minimizing numerical mass diffusion in Rayleigh-Taylor simulations. The above cited papers achieved values for α consistent with experiment using a special code (FronTier) based on front tracking and designed to eliminate numerical mass diffusion and to model correctly physical mass diffusion.…”

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confidence: 99%

Nonideal Rayleigh–Taylor mixing

Lim

Iwerks²,

Glimm³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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Rayleigh-Taylor mixing is a classical hydrodynamic instability that occurs when a light fluid pushes against a heavy fluid. The two main sources of nonideal behavior in Rayleigh-Taylor (RT) mixing are regularizations (physical and numerical), which produce deviations from a pure Euler equation, scale invariant formulation, and nonideal (i.e., experimental) initial conditions. The Kolmogorov theory of turbulence predicts stirring at all length scales for the Euler fluid equations without regularization. We interpret mathematical theories of existence and nonuniqueness in this context, and we provide numerical evidence for dependence of the RT mixing rate on nonideal regularizations; in other words, indeterminacy when modeled by Euler equations. Operationally, indeterminacy shows up as nonunique solutions for RT mixing, parametrized by Schmidt and Prandtl numbers, in the large Reynolds number (Euler equation) limit. Verification and validation evidence is presented for the large eddy simulation algorithm used here. Mesh convergence depends on breaking the nonuniqueness with explicit use of the laminar Schmidt and Prandtl numbers and their turbulent counterparts, defined in terms of subgrid scale models. The dependence of the mixing rate on the Schmidt and Prandtl numbers and other physical parameters will be illustrated. We demonstrate numerically the influence of initial conditions on the mixing rate. Both the dominant short wavelength initial conditions and long wavelength perturbations are observed to play a role. By examination of two classes of experiments, we observe the absence of a single universal explanation, with long and short wavelength initial conditions, and the various physical and numerical regularizations contributing in different proportions in these two different contexts.large eddy simulations | subgrid scale models | turbulence R ayleigh-Taylor (RT) instability is a classical hydrodynamic instability (1, 2) that occurs when a light fluid pushes against a heavy fluid. The density contrast is measured dimensionlessly by the Atwood number A ¼ ðρ 2 − ρ 1 Þ∕ðρ 2 þ ρ 1 Þ, with ρ i the density of fluid i. The mixing rate can be characterized by the dimensionless parameter α, defined through the equationwhere h is the penetration distance of the light fluid into the heavy and g is the acceleration. The mixing rapidly becomes turbulent, with Reynolds numbers Re ≈ 50;000 observed in typical experiments. For this reason, simulations based on compressible codes, with hyperbolic time step (CFL) restrictions, are unable to resolve the viscous length scales, and such codes are run in an under-resolved manner. Such simulations are called large eddy simulations (LES). LES require subgrid scale (SGS) models to describe the effect of the small (subgrid) scales on the large (grid-resolved) ones. Models for the Reynolds stress based on eddy viscosity are the most familiar of this type.Much of the work on RT mixing has been influenced by ideas of universality and self similarity. If α is to be a universal physical...

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Influence of scale-breaking phenomena on turbulent mixing rates

Cited by 37 publications

References 15 publications

Terascale Simulation Tools and Technologies

Terascale Simulation Tools and Technologies

New directions for Rayleigh–Taylor mixing

Nonideal Rayleigh–Taylor mixing

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