Rarefactiondriven 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. Singlemode twodimensional, and singlemode threedimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a nonconstant 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$$. Nominally twodimensional (2D) experiments (initiated with nearly 2D perturbations) and 2D simulations are observed to approach an intermediatetime velocity plateau that is in disagreement with the latetime velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2D bubbles in large wavenumber,$$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 latetime 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 freefall like behaviour. Finally, experiments initiated with threedimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.
 Authors:

 Univ. of Arizona, Tucson, AZ (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Univ. of Arizona, Tucson, AZ (United States); Lawrence Livermore National Lab. (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):
 LLNLJRNL787438
Journal ID: ISSN 00221120; applab; PII: S002211201700893X; TRN: US1801403
 Grant/Contract Number:
 NA0002929; AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluid Mechanics
 Additional Journal Information:
 Journal Volume: 838; Journal ID: ISSN 00221120
 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
Citation Formats
Morgan, R. V., Cabot, W. H., Greenough, J. A., and Jacobs, J. W. Rarefactiondriven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime. United States: N. p., 2018.
Web. doi:10.1017/jfm.2017.893.
Morgan, R. V., Cabot, W. H., Greenough, J. A., & Jacobs, J. W. Rarefactiondriven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime. United States. doi:10.1017/jfm.2017.893.
Morgan, R. V., Cabot, W. H., Greenough, J. A., and Jacobs, J. W. Fri .
"Rarefactiondriven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime". United States. doi:10.1017/jfm.2017.893. https://www.osti.gov/servlets/purl/1419851.
@article{osti_1419851,
title = {Rarefactiondriven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime},
author = {Morgan, R. V. and Cabot, W. H. and Greenough, J. A. and Jacobs, J. W.},
abstractNote = {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. Singlemode twodimensional, and singlemode threedimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a nonconstant 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 twodimensional (2D) experiments (initiated with nearly 2D perturbations) and 2D simulations are observed to approach an intermediatetime velocity plateau that is in disagreement with the latetime velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2D 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 latetime 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 freefall like behaviour. Finally, experiments initiated with threedimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.},
doi = {10.1017/jfm.2017.893},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 838,
place = {United States},
year = {2018},
month = {1}
}
Figures / Tables:
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