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Title: Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity

Abstract

Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number (Rep) and Atwood number (A) on RTI’s late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when Rep is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei and Livescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high Rep, the bubble’s late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble [Wei and Livescu 2012]. A similar effect has also been observed in ablative RTI [Betti and Sanz 2006]. As the spike growth increases relative to that of the bubble at higher A, vorticity production shifts downward, away from the centerline and toward the spike tip. We modifymore » the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor η = 0.45 to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high A. However, we present evidence that if the large Rep limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller Rep thresholds.« less

Authors:
 [1];  [1];  [1];  [1]; ORCiD logo [2]
  1. Univ. of Rochester, NY (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1574757
Report Number(s):
LA-UR-19-26670
Journal ID: ISSN 0167-2789
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Physica. D, Nonlinear Phenomena
Additional Journal Information:
Journal Name: Physica. D, Nonlinear Phenomena; Journal ID: ISSN 0167-2789
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Bian, Xin, Aluie, Hussein, Zhao, Dongxiao, Zhang, Huasen, and Livescu, Daniel. Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity. United States: N. p., 2019. Web. doi:10.1016/j.physd.2019.132250.
Bian, Xin, Aluie, Hussein, Zhao, Dongxiao, Zhang, Huasen, & Livescu, Daniel. Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity. United States. doi:10.1016/j.physd.2019.132250.
Bian, Xin, Aluie, Hussein, Zhao, Dongxiao, Zhang, Huasen, and Livescu, Daniel. Mon . "Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity". United States. doi:10.1016/j.physd.2019.132250.
@article{osti_1574757,
title = {Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity},
author = {Bian, Xin and Aluie, Hussein and Zhao, Dongxiao and Zhang, Huasen and Livescu, Daniel},
abstractNote = {Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number (Rep) and Atwood number (A) on RTI’s late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when Rep is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei and Livescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high Rep, the bubble’s late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble [Wei and Livescu 2012]. A similar effect has also been observed in ablative RTI [Betti and Sanz 2006]. As the spike growth increases relative to that of the bubble at higher A, vorticity production shifts downward, away from the centerline and toward the spike tip. We modify the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor η = 0.45 to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high A. However, we present evidence that if the large Rep limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller Rep thresholds.},
doi = {10.1016/j.physd.2019.132250},
journal = {Physica. D, Nonlinear Phenomena},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {11}
}

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