Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells

Mikaelian, Karnig O.

doi:10.1063/1.2046712

Cited by 115 publications

(118 citation statements)

References 46 publications

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“…The linear growth of a single mode perturbation due to a RT instability in the cylindrical geometry for incompressible fluids has been derived in Ref. [18]. The differential equation for this growth writes as:…”

Section: Theoretical Modelingmentioning

confidence: 99%

Nonlinear growth of the converging Richtmyer-Meshkov instability in a conventional shock tube

Vandenboomgaerde¹,

Rouzier²,

Souffland³

et al. 2018

Phys. Rev. Fluids

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Section: Theoretical Modelingmentioning

confidence: 99%

Nonlinear growth of the converging Richtmyer-Meshkov instability in a conventional shock tube

Vandenboomgaerde¹,

Rouzier²,

Souffland³

et al. 2018

Phys. Rev. Fluids

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“…The early-time growth of these instabilities has been investigated in cyli ndrical (Bell 1951 ;Mikaelian 2005;Yu & Livescu 2008;Lombardini & Pullin 2009) and spherical geometries (Bell 195 I ;Plesset I 95.+;Mikaelian 1990;Kumar, Hornung & Sturtevant 200 3;Mankbadi & Balachandar 201 2). The stability analysis by Krechetnikov (2009) actually unifies some of the work previously cited by uncovering the interrelation between the RT and RM instabilities and the general effect of interfacial curvature.…”

mentioning

confidence: 99%

Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth

2014

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We present large-eddy si mulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial s hock Mach number ~1.2, the density ratio (precisely IAol ~ 0.67) and the perturbation shape (dominant spherical wavenumber .f 0 = 40 and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy fluid or, inversely, from the heavy to the light fluid. After describing the computational problem we present results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. , vol. 748, 2014, pp. 113-142). A wave-diagram analysis of the radially symmetric flow highlights that the light-heavy mixing layer is processed by consecutive reshocks, and not by reverberating rarefaction waves as is usually observed in planar geometry. Less surprisingly, reshocks process the heavy-light mixing layer as in the planar case. In both configurations, the incident imploding shock and the reshocks induce Richtmyer-Meshkov (RM ) instabilities at the density layer. However, we observe differences in the mixing-layer growth because the RM instability occurrences, Rayleigh-Taylor (RT) unstable scenarios (due to the radially accelerated motion of the layer) and phase inversion events are different.A small-amplitude stability analysis along the lines of Be ll (Los Alamos Scientific Laboratory Report, LA-132 L, 1951 ) and Plesset (J. Appl. Phys., vol. 25, 1954, pp. 96-98) helps quantify the effects of the mean flow on the mixing-layer growth by decoupling the effects of RT/RM instabilities from Be ll-Plessel effects associated with geometric convergence and compressibility for arbitrary convergence ratios. The analysis indicates that baroclinic instabilities are the dominant effect, considering the low convergence ratio (~2) and rather high ce > 10) mode numbers considered.

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“…13 gave a secondorder theory in a cylindrical coordinate system for arbitrary Atwood numbers to study the cylindrical effect on RTI, namely, the effect of the initial radius of the interface known as Bell-Plessett effect 28,29 motivated by compression and geometrical convergence. As for the Bell-Plessett (BP) effect, its importance and relative investigations [30][31][32][33][34] in RTI, the detailed introduction can be found in Ref. 14, in which the evolution of the first four harmonics in the spherical RTI is analytically investigated just for the case of A ¼ 1, without assuming a source or a sink to exist at the spherical center to maintain a constant density of the region inside of the spherical interface.…”

Section: Introductionmentioning

confidence: 99%

Bell-Plessett effect on harmonic evolution of spherical Rayleigh-Taylor instability in weakly nonlinear scheme for arbitrary Atwood numbers

Liu

Hong-bin

et al. 2017

Physics of Plasmas

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Based on the harmonic analysis [Liu et al., Phys. Plasmas 22, 112112 (2015)], the analytical investigation on the harmonic evolution in Rayleigh-Taylor instability (RTI) at a spherical interface has been extended to the general case of arbitrary Atwood numbers by using the method of the formal perturbation up to the third order in a small parameter. Our results show that the radius of the initial interface [i.e., Bell-Plessett (BP) effect] dramatically influences the harmonic evolution for arbitrary Atwood numbers. When the initial radius approaches infinity compared against the initial perturbation wavelength, the amplitudes of the first four harmonics will recover those in planar RTI. The BP effect makes the amplitudes of the zeroth, second, and third harmonics increase faster for a larger Atwood number than smaller one. The BP effect reduces the third-order negative feedback to the fundamental mode for a smaller Atwood number, and strengthens it for a larger one. Hence, the BP effect helps the fundamental mode grow faster for a smaller Atwood number. Published by AIP Publishing. [http://dx

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Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells

Cited by 115 publications

References 46 publications

Nonlinear growth of the converging Richtmyer-Meshkov instability in a conventional shock tube

Nonlinear growth of the converging Richtmyer-Meshkov instability in a conventional shock tube

Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth

Bell-Plessett effect on harmonic evolution of spherical Rayleigh-Taylor instability in weakly nonlinear scheme for arbitrary Atwood numbers

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