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Title: Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation

Abstract

High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that mixing layer growth reaches a high degree of self-similarity after approximately 4.5 generations. Statistical convergence errors and boundary effects at late time, however, make it impossible to draw similar conclusions regarding the self-similar growth of more sensitive turbulence parameters. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k-L-a and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The k-L-a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.

Authors:
ORCiD logo [1];  [1];  [2];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of Missouri, Columbia, MO (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1430929
Report Number(s):
LLNL-JRNL-681041
Journal ID: ISSN 1468-5248
Grant/Contract Number:
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Turbulence (Online)
Additional Journal Information:
Journal Name: Journal of Turbulence (Online); Journal Volume: 18; Journal Issue: 10; Journal ID: ISSN 1468-5248
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 70 PLASMA PHYSICS AND FUSION

Citation Formats

Morgan, B. E., Olson, B. J., White, J. E., and McFarland, J. A. Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation. United States: N. p., 2017. Web. doi:10.1080/14685248.2017.1343477.
Morgan, B. E., Olson, B. J., White, J. E., & McFarland, J. A. Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation. United States. doi:10.1080/14685248.2017.1343477.
Morgan, B. E., Olson, B. J., White, J. E., and McFarland, J. A. Thu . "Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation". United States. doi:10.1080/14685248.2017.1343477.
@article{osti_1430929,
title = {Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation},
author = {Morgan, B. E. and Olson, B. J. and White, J. E. and McFarland, J. A.},
abstractNote = {High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that mixing layer growth reaches a high degree of self-similarity after approximately 4.5 generations. Statistical convergence errors and boundary effects at late time, however, make it impossible to draw similar conclusions regarding the self-similar growth of more sensitive turbulence parameters. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k-L-a and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The k-L-a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.},
doi = {10.1080/14685248.2017.1343477},
journal = {Journal of Turbulence (Online)},
number = 10,
volume = 18,
place = {United States},
year = {Thu Jun 29 00:00:00 EDT 2017},
month = {Thu Jun 29 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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  • The initial multi-mode interfacial velocity and density perturbations present at the onset of a small Atwood number, incompressible, miscible, Rayleigh-Taylor instability-driven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using high-resolution thermocouples and planar laser-induced fluorescence (PLIF), respectively. The initial multi-mode streamwise velocity perturbations at the two-fluid density interface were measured using particle-image velocimetry (PIV). It was found that the measured initial conditions describe an initially anisotropic state, in which the perturbations in the streamwise and spanwise directions are independent of one another. The evolution of various fluctuatingmore » velocity and density statistics, together with velocity and density variance spectra, were measured using PIV and high-resolution thermocouple data. The evolution of the velocity and density statistics is used to investigate the early-time evolution and the onset of strongly-nonlinear, transitional dynamics within the mixing layer. The early-time evolution of the density and vertical velocity variance spectra indicate that velocity fluctuations are the dominant mechanism driving the instability development. The implications of the present experimental measurements on the initialization of Reynolds-averaged turbulent transport and mixing models and of direct and large-eddy simulations of Rayleigh-Taylor instability-induced turbulence are discussed.« less
  • The initial multi-mode interfacial velocity and density perturbations present at the onset of a small Atwood number, incompressible, miscible, Rayleigh-Taylor instability-driven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using high-resolution thermocouples and planar laser-induced fluorescence (PLIF), respectively. The initial multi-mode streamwise velocity perturbations at the two-fluid density interface were measured using particle-image velocimetry (PIV). It was found that the measured initial conditions describe an initially anisotropic state, in which the perturbations in the streamwise and spanwise directions are independent of one another. The evolution of various fluctuatingmore » velocity and density statistics, together with velocity and density variance spectra, were measured using PIV and high-resolution thermocouple data. The evolution of the velocity and density statistics is used to investigate the early-time evolution and the onset of strongly-nonlinear, transitional dynamics within the mixing layer. The early-time evolution of the density and vertical velocity variance spectra indicate that velocity fluctuations are the dominant mechanism driving the instability development. The implications of the present experimental measurements on the initialization of Reynolds-averaged turbulent transport and mixing models and of direct and large-eddy simulations of Rayleigh-Taylor instability-induced turbulence are discussed.« less
  • Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radiusmore » of the interface (r{sub 0}) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r{sub 0}/λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r{sub 0}/λ is large enough (r{sub 0}≫λ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r{sub 0} can reduce the NSA of the second harmonic for arbitrary A at r{sub 0}≲2λ while increase it for A ≲ 0.6 at r{sub 0}≳2λ. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design.« less
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