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Morgan BE. Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of three Rayleigh-Taylor mixing configurations with gravity reversal. Phys Rev E 2022; 106:025101. [PMID: 36109949 DOI: 10.1103/physreve.106.025101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 07/18/2022] [Indexed: 06/15/2023]
Abstract
High-fidelity large-eddy simulation (LES) is performed of Rayleigh-Taylor (RT) mixing in three different configurations involving gravity reversal. In each configuration, LES results are compared with one-dimensional Reynolds-averaged Navier-Stokes (RANS) results, and a deficiency in a commonly used transport equation for the mass-flux velocity, a_{j}, is identified. In the first configuration, a classical two-component RT mixing layer is allowed to develop before it is subjected to rapid acceleration reversal. In the second configuration, a three-component RT mixing layer with an intermediate density layer is allowed to develop before being subjected to rapid acceleration reversal. Finally, in the third configuration, a light layer is interposed between two heavy layers; in this configuration, only one interface is RT-unstable at a time as it undergoes rapid acceleration reversal. In all cases, a commonly used buoyancy production closure in the a_{j} transport equation is shown to lead to significant over-prediction of mixing layer growth after gravity reversal. An alternative formulation for this closure is then presented which is shown to more accurately capture the stabilization effect of gravity reversal.
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Affiliation(s)
- Brandon E Morgan
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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2
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Aslangil D, Lawrie AGW, Banerjee A. Effects of variable deceleration periods on Rayleigh-Taylor instability with acceleration reversals. Phys Rev E 2022; 105:065103. [PMID: 35854494 DOI: 10.1103/physreve.105.065103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Accepted: 05/17/2022] [Indexed: 06/15/2023]
Abstract
The dynamics of an interfacial flow that is initially Rayleigh-Taylor unstable but becomes statically stable for some intermediate period due to the reversal of the externally imposed acceleration field is studied. We discuss scenarios that consider both single and double-acceleration reversals. The accel-decel (AD) case consists of a single reversal imposed at an instant after the constant acceleration instability has entered a self-similar regime. The layer of mixed fluid ceases to grow upon acceleration reversal, and the dominant mechanics are due to internal wave oscillations. Variation of mass flux and the Reynolds stress anisotropy is observed due to the action of the internal waves. A second reversal of the AD case that is termed as accel-decel-accel, ADA is then explored; the response of the mixing layer is shown to depend strongly on the duration and the periodicity of the Reynolds stress anisotropy of the mixing layer during the deceleration period. We explore the effect of this variable deceleration period after the second acceleration reversal where the flow once again becomes Rayleigh-Taylor unstable based on metrics that include the integral mixing-layer width, bubble and spike amplitudes, mass flux, Reynolds stress anisotropy tensor, and the molecular mixing parameter.
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Affiliation(s)
- Denis Aslangil
- Department of Aerospace Engineering & Mechanics, The University of Alabama, Tuscaloosa, Alabama 35487, USA
| | - Andrew G W Lawrie
- Department of Mechanical Engineering, University of Bristol, Queen's Building, University Walk, Clifton BS8 1TR, United Kingdom
| | - Arindam Banerjee
- Department of Mechanical Engineering & Mechanics, Lehigh University, Bethlehem, Pennsylvania 18020, USA
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3
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Rigon G, Albertazzi B, Mabey P, Michel T, Falize E, Bouffetier V, Ceurvorst L, Masse L, Koenig M, Casner A. Exploring the Atwood-number dependence of the highly nonlinear Rayleigh-Taylor instability regime in high-energy-density conditions. Phys Rev E 2021; 104:045213. [PMID: 34781551 DOI: 10.1103/physreve.104.045213] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 09/19/2021] [Indexed: 11/07/2022]
Abstract
We experimentally study the late-time, highly nonlinear regime of the Rayleigh-Taylor instability in a decelerating phase. A series of laser-driven experiments is performed on the LULI2000 laser, in which the initial Atwood number is varied by adjusting the decelerating medium density. The high-power laser is used in a direct drive configuration to put into motion a solid target. Its rear side, which initially possesses a two-dimensional machined sinusoidal perturbations, expands and decelerates into a foam leading to a Rayleigh-Taylor unstable situation. The interface position and morphology are measured by time-resolved x-ray radiography. We develop a simple Atwood-dependent model describing the motion of the decelerating interface, from which its acceleration history is obtained. The measured amplitude of the instability, or mixing zone width, is then compared with late-time acceleration-dependent Rayleigh-Taylor instability models. The shortcomings of this classical model, when applied to high-energy-density conditions, are shown. This calls into question their uses for systems, where a shock wave is present, such as those found in laboratory astrophysics or in inertial confinement fusion.
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Affiliation(s)
- G Rigon
- LULI, CNRS, CEA, Ecole Polytechnique, UPMC, Univ Paris 06, Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France.,JSPS International Research Fellow, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
| | - B Albertazzi
- LULI, CNRS, CEA, Ecole Polytechnique, UPMC, Univ Paris 06, Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France
| | - P Mabey
- LULI, CNRS, CEA, Ecole Polytechnique, UPMC, Univ Paris 06, Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France.,Freie Universität Berlin, Department of Physics, Arnimallee 14, 14195 Berlin, Germany
| | - Th Michel
- LULI, CNRS, CEA, Ecole Polytechnique, UPMC, Univ Paris 06, Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France
| | - E Falize
- CEA-DAM, DIF, F-91297 Arpajon, France
| | - V Bouffetier
- Université de Bordeaux-CNRS-CEA, CELIA, UMR 5107, F-33405 Talence, France
| | - L Ceurvorst
- Université de Bordeaux-CNRS-CEA, CELIA, UMR 5107, F-33405 Talence, France
| | - L Masse
- CEA-DAM, DIF, F-91297 Arpajon, France
| | - M Koenig
- LULI, CNRS, CEA, Ecole Polytechnique, UPMC, Univ Paris 06, Sorbonne Universités, Institut Polytechnique de Paris, F-91128 Palaiseau cedex, France.,Graduate School of Engineering, Osaka University, Osaka, 565-0871, Japan
| | - A Casner
- Université de Bordeaux-CNRS-CEA, CELIA, UMR 5107, F-33405 Talence, France.,CEA-CESTA, 15 avenue des Sablires, CS 60001, 33116 Le Barp Cedex, France
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4
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Pal N, Boureima I, Braun N, Kurien S, Ramaprabhu P, Lawrie A. Local wave-number model for inhomogeneous two-fluid mixing. Phys Rev E 2021; 104:025105. [PMID: 34525630 DOI: 10.1103/physreve.104.025105] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Accepted: 07/28/2021] [Indexed: 11/07/2022]
Abstract
We analyze the local wave-number (LWN) model, a two-point spectral closure model for turbulence, as applied to the Rayleigh-Taylor (RT) instability, the flow induced by the relaxation of a statically-unstable density stratification. Model outcomes are validated against data from 3D simulations of the RT instability. In the first part of the study we consider the minimal model terms required to capture inhomogeneous mixing and show that this version, with suitable model coefficients, is sufficient to capture the evolution of important mean global quantities including mix-width, turbulent mass flux velocity, and Reynolds stress, if the start time is chosen such that the earliest transitions are avoided. However, this simple model does not permit the expected finite asymptote of the density-specific-volume covariance b. In the second part of the study, we investigate two forms for a source term for the evolution of the spectrum of density-specific-volume covariance for the LWN model. The first includes an empirically motivated calibration of the source to achieve the final asymptotic state of constant b. The second form does not require calibration but, in conjunction with enhanced diffusion and drag captures the full evolution of all the dynamical quantities, namely, the mix-layer growth, turbulent mass-flux velocity, Reynolds stress, as well as the desired behavior of b.
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Affiliation(s)
- Nairita Pal
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Ismael Boureima
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Noah Braun
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Susan Kurien
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Praveen Ramaprabhu
- Mechanical Engineering and Engineering Science, University of North Carolina-Charlotte, Charlotte, North Carolina 28223, USA
| | - Andrew Lawrie
- Hele-Shaw Laboratory, Queen's Building, University of Bristol, University Walk, Clifton BS8 1TR, United Kingdom
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5
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Li H, Tian B, He Z, Zhang Y. Growth mechanism of interfacial fluid-mixing width induced by successive nonlinear wave interactions. Phys Rev E 2021; 103:053109. [PMID: 34134196 DOI: 10.1103/physreve.103.053109] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 04/28/2021] [Indexed: 11/07/2022]
Abstract
Interfacial fluid mixing induced by successive waves, such as shock, rarefaction, and compression waves, plays a fundamental role in engineering applications, e.g., inertial confinement fusion, and in natural phenomena, e.g., supernova explosion. These waves bring nonuniform, unsteady external forces into the mixing zone, which leads to a complex mixing process. The growth rate of the mixing width is analyzed by decomposing the turbulent flow field into the averaged field and the fluctuating counterpart. The growth rate is thus divided into three parts: (i) the stretching or compression (S(C)) effect induced by the averaged-velocity difference between two ends of the mixing zone, (ii) the penetration effect induced by the fluctuations which represent the penetration of the two species into each other, and (iii) the diffusive effect, which is induced by the molecular diffusion and is negligible in high-Reynolds-number flows at Schmidt number of order unity. The penetration effect is further divided into the Richtmyer-Meshkov (RM) effect, which is induced by fluctuations that were deposited by earlier wave interactions, and the Rayleigh-Taylor (RT) effect, which is caused by the fluctuations that arise in an overall acceleration of the mixing zone. During the passage of the rarefaction waves, the mixing zone is stretched, while during the passage of the compression waves or shock waves, the mixing zone is compressed. To illustrate these effects, a physical model of RM mixing with reshock is used. By combining the S(C), RM, and RT effects, the entire evolution of mixing width is restructured, which agrees well with numerical simulations for problems with a wide range of density ratios.
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Affiliation(s)
- Haifeng Li
- Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
| | - Baolin Tian
- Institute of Applied Physics and Computational Mathematics, Beijing 100094, China.,HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China
| | - Zhiwei He
- Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
| | - Yousheng Zhang
- Institute of Applied Physics and Computational Mathematics, Beijing 100094, China.,HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China
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6
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Boffetta G, Magnani M, Musacchio S. Suppression of Rayleigh-Taylor turbulence by time-periodic acceleration. Phys Rev E 2019; 99:033110. [PMID: 30999487 DOI: 10.1103/physreve.99.033110] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2018] [Indexed: 06/09/2023]
Abstract
The dynamics of Rayleigh-Taylor turbulence convection in the presence of an alternating, time-periodic acceleration is studied by means of extensive direct numerical simulations of the Boussinesq equations. Within this framework, we discover a mechanism of relaminarization of turbulence: the alternating acceleration, which initially produces a growing turbulent mixing layer, at longer times suppresses turbulent fluctuation and drives the system toward an asymptotic stationary configuration. Dimensional arguments and linear stability theory are used to predict the width of the mixing layer in the asymptotic state as a function of the period of the acceleration.
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Affiliation(s)
- G Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - M Magnani
- Dipartimento di Fisica, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - S Musacchio
- Université Côte d'Azur, CNRS, LJAD, Nice 06108, France
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7
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Yu CX, Xue C, Liu J, Hu XY, Liu YY, Ye WH, Wang LF, Wu JF, Fan ZF. Multiple eigenmodes of the Rayleigh-Taylor instability observed for a fluid interface with smoothly varying density. Phys Rev E 2018; 97:013102. [PMID: 29448344 DOI: 10.1103/physreve.97.013102] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2017] [Indexed: 11/07/2022]
Abstract
In this article, multiple eigen-systems including linear growth rates and eigen-functions have been discovered for the Rayleigh-Taylor instability (RTI) by numerically solving the Sturm-Liouville eigen-value problem in the case of two-dimensional plane geometry. The system called the first mode has the maximal linear growth rate and is just extensively studied in literature. Higher modes have smaller eigen-values, but possess multi-peak eigen-functions which bring on multiple pairs of vortices in the vorticity field. A general fitting expression for the first four eigen-modes is presented. Direct numerical simulations show that high modes lead to appearances of multi-layered spike-bubble pairs, and lots of secondary spikes and bubbles are also generated due to the interactions between internal spikes and bubbles. The present work has potential applications in many research and engineering areas, e.g., in reducing the RTI growth during capsule implosions in inertial confinement fusion.
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Affiliation(s)
- C X Yu
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - C Xue
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - J Liu
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China.,Center for Applied Physics and Technology, Peking University, Beijing 100871, China
| | - X Y Hu
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - Y Y Liu
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - W H Ye
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - L F Wang
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - J F Wu
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - Z F Fan
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
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