Title: Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

Abstract

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number,$$A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$$, where$$\unicode[STIX]{x1D70C}_{2}$$and$$\unicode[STIX]{x1D70C}_{1}$$are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of$A=0.49$$,$$A=0.63$$,$$A=0.82$$and$$A=0.94$$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber,$$k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$$, experiments and simulations, where$$\unicode[STIX]{x1D706}$is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.

Authors:

Morgan, R. V.  ^[1];

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Cabot, W. H. ^[2]; Greenough, J. A. ^[2]; Jacobs, J. W. ^[1]

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+ Show Author Affiliations

1. Univ. of Arizona, Tucson, AZ (United States)
2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:

Fri Jan 12 00:00:00 EST 2018

Research Org.:

Univ. of Arizona, Tucson, AZ (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA)

Contributing Org.:

Lawrence Livermore National Laboratory

OSTI Identifier:

1419851

Alternate Identifier(s):

OSTI ID: 1568010

Report Number(s):

LLNL-JRNL-787438
Journal ID: ISSN 0022-1120; applab; PII: S002211201700893X; TRN: US1801403

Grant/Contract Number:  

NA0002929; AC52-07NA27344

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Fluid Mechanics

Additional Journal Information:

Journal Volume: 838; Journal ID: ISSN 0022-1120

Publisher:

Cambridge University Press

Country of Publication:

United States

Language:

English

Subject:

42 ENGINEERING; gas dynamics; nonlinear instability; turbulent mixing; Engineering - Mechanical and civil engineering