Asymptotic behavior of the mixed mass in Rayleigh–Taylor and Richtmyer–Meshkov instability induced flows

Zhou, Ye; Cabot, William H.; Thornber, Ben

doi:10.1063/1.4951018

Title: Asymptotic behavior of the mixed mass in Rayleigh–Taylor and Richtmyer–Meshkov instability induced flows

Journal Article · Mon May 23 00:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4951018· OSTI ID:1569166

Zhou, Ye ^[1]; Cabot, William H. ^[1];

^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
The Univ. of Sydney, Sydney (Australia)

Rayleigh–Taylor instability (RTI) and Richtmyer–Meshkov instability (RMI) are serious practical issues in inertial confinement fusion research, and also have relevance to many cases of astrophysical fluid dynamics. So far, much of the attention has been paid to the late-time scaling of the mixed width, which is used as a surrogate to how well the fluids have been mixed. Yet, the actual amount of mixed mass could be viewed as a more direct indicator on the evolution of the mixing layers due to hydrodynamic instabilities. Despite its importance, there is no systematic study as yet on the scaling of the mixed mass for either the RTI or the RMI induced flow. In this article, the normalized mixed mass (Ψ) is introduced for measuring the efficiency of the mixed mass. Six large numerical simulation databases have been employed: the RTI cases with heavy-to-light fluid density ratios of 1.5, 3, and 9; the single shock RMI cases with density ratios of 3 and 20; and a reshock RMI case with density ratio of 3. Using simulated flow fields, the normalized mixed mass Ψ is shown to be more sensitive in discriminating the variation with Atwood number for the RTI flows. Moreover, Ψ is demonstrated to provide more consistent results for both the RTI and RMI flows when compared with the traditional mixedness parameters, Ξ and Θ.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1569166

Alternate ID(s):: OSTI ID: 1254198

Report Number(s):: LLNL-JRNL-681886; PHPAEN; 806148; TRN: US2100253

Journal Information:: Physics of Plasmas, Vol. 23, Issue 5; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 48 works

Citation information provided by
Web of Science

References (50)

Molecular mixing in Rayleigh–Taylor instability Linden, P. F.; Redondo, J. M.; Youngs, D. L. Journal of Fluid Mechanics, Vol. 265 https://doi.org/10.1017/S0022112094000777	journal	April 1994
Spectral measurements of Rayleigh–Taylor mixing at small Atwood number Wilson, Peter N.; Andrews, Malcolm J. Physics of Fluids, Vol. 14, Issue 3 https://doi.org/10.1063/1.1445418	journal	March 2002
The definition and measurement of some characteristics of mixtures Danckwerts, P. V. Applied Scientific Research, Vol. 3, Issue 4 https://doi.org/10.1007/BF03184936	journal	July 1952
Estimating the effective Reynolds number in implicit large-eddy simulation Zhou, Ye; Grinstein, Fernando F.; Wachtor, Adam J. Physical Review E, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevE.89.013303	journal	January 2014
Non-spherical core collapse supernovae: III. Evolution towards homology and dependence on the numerical resolution Gawryszczak, A.; Guzman, J.; Plewa, T. Astronomy and Astrophysics, Vol. 521 https://doi.org/10.1051/0004-6361/200913431	journal	October 2010
Onset of Hydrodynamic Mix in High-Velocity, Highly Compressed Inertial Confinement Fusion Implosions Ma, T.; Patel, P. K.; Izumi, N. Physical Review Letters, Vol. 111, Issue 8 https://doi.org/10.1103/PhysRevLett.111.085004	journal	August 2013
Colloquium: Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas Zhou, Ye; Matthaeus, W.; Dmitruk, P. Reviews of Modern Physics, Vol. 76, Issue 4 https://doi.org/10.1103/RevModPhys.76.1015	journal	December 2004
Hot-spot mix in ignition-scale implosions on the NIF Regan, S. P.; Epstein, R.; Hammel, B. A. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3694057	journal	May 2012
Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations Zhou, Ye Physics of Plasmas, Vol. 14, Issue 8 https://doi.org/10.1063/1.2739439	journal	August 2007
Energy transfer in the Richtmyer-Meshkov instability Thornber, Ben; Zhou, Ye Physical Review E, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevE.86.056302	journal	November 2012
Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility Haan, S. W.; Lindl, J. D.; Callahan, D. A. Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3592169	journal	May 2011
Symmetric Inertial Confinement Fusion Implosions at Ultra-High Laser Energies Glenzer, S. H.; MacGowan, B. J.; Michel, P. Science, Vol. 327, Issue 5970 https://doi.org/10.1126/science.1185634	journal	January 2010
An in-flight radiography platform to measure hydrodynamic instability growth in inertial confinement fusion capsules at the National Ignition Facility Raman, K. S.; Smalyuk, V. A.; Casey, D. T. Physics of Plasmas, Vol. 21, Issue 7 https://doi.org/10.1063/1.4890570	journal	July 2014
The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability Thornber, B.; Drikakis, D.; Youngs, D. L. Journal of Fluid Mechanics, Vol. 654 https://doi.org/10.1017/S0022112010000492	journal	May 2010
On the computation of instabilities and symmetry-breaking in fluid mechanics Drikakis, Dimitris; Grinstein, Fernando; Youngs, David Progress in Aerospace Sciences, Vol. 41, Issue 8 https://doi.org/10.1016/j.paerosci.2005.10.001	journal	November 2005
Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh-Taylor instability Cabot, W.; Zhou, Ye Physics of Fluids, Vol. 25, Issue 1 https://doi.org/10.1063/1.4774338	journal	January 2013
First Measurements of Hydrodynamic Instability Growth in Indirectly Driven Implosions at Ignition-Relevant Conditions on the National Ignition Facility Smalyuk, V. A.; Casey, D. T.; Clark, D. S. Physical Review Letters, Vol. 112, Issue 18 https://doi.org/10.1103/PhysRevLett.112.185003	journal	May 2014
Advances in turbulent flow computations using high-resolution methods Drikakis, Dimitris Progress in Aerospace Sciences, Vol. 39, Issue 6-7 https://doi.org/10.1016/S0376-0421(03)00075-7	journal	August 2003
Numerical simulations of the two-dimensional multimode Richtmyer-Meshkov instability Thornber, B.; Zhou, Y. Physics of Plasmas, Vol. 22, Issue 3 https://doi.org/10.1063/1.4915517	journal	March 2015
Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics Balakumar, B. J.; Orlicz, G. C.; Ristorcelli, J. R. Journal of Fluid Mechanics, Vol. 696 https://doi.org/10.1017/jfm.2012.8	journal	March 2012
A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities Zhou, Ye Physics of Fluids, Vol. 13, Issue 2 https://doi.org/10.1063/1.1336151	journal	February 2001
Experimental study of initial condition dependence on Richtmyer-Meshkov instability in the presence of reshock Balasubramanian, S.; Orlicz, G. C.; Prestridge, K. P. Physics of Fluids, Vol. 24, Issue 3 https://doi.org/10.1063/1.3693152	journal	March 2012
The mixing transition in RayleighTaylor instability Cook, Andrew W.; Cabot, William; Miller, Paul L. Journal of Fluid Mechanics, Vol. 511 https://doi.org/10.1017/S0022112004009681	journal	January 1999
Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability Dalziel, S. B.; Linden, P. F.; Youngs, D. L. Journal of Fluid Mechanics, Vol. 399 https://doi.org/10.1017/S002211209900614X	journal	November 1999
The effect of mix on capsule yields as a function of shell thickness and gas fill Bradley, P. A. Physics of Plasmas, Vol. 21, Issue 6 https://doi.org/10.1063/1.4882247	journal	June 2014
Growth of a Richtmyer-Meshkov turbulent layer after reshock Thornber, B.; Drikakis, D.; Youngs, D. L. Physics of Fluids, Vol. 23, Issue 9 https://doi.org/10.1063/1.3638616	journal	September 2011
Drive Asymmetry and the Origin of Turbulence in an ICF Implosion Thomas, V. A.; Kares, R. J. Physical Review Letters, Vol. 109, Issue 7 https://doi.org/10.1103/PhysRevLett.109.075004	journal	August 2012
Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities Youngs, D. L. Laser and Particle Beams, Vol. 12, Issue 4 https://doi.org/10.1017/S0263034600008557	journal	December 1994
Energy transfer in Rayleigh-Taylor instability Cook, Andrew W.; Zhou, Ye Physical Review E, Vol. 66, Issue 2 https://doi.org/10.1103/PhysRevE.66.026312	journal	August 2002
Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions Leinov, E.; Malamud, G.; Elbaz, Y. Journal of Fluid Mechanics, Vol. 626 https://doi.org/10.1017/S0022112009005904	journal	May 2009
Experiments on the Richtmyer–Meshkov instability with an imposed, random initial perturbation Jacobs, J. W.; Krivets, V. V.; Tsiklashvili, V. Shock Waves, Vol. 23, Issue 4 https://doi.org/10.1007/s00193-013-0436-9	journal	March 2013
X‐ray measurements of growth rates at a gas interface accelerated by shock waves Bonazza, R.; Sturtevant, B. Physics of Fluids, Vol. 8, Issue 9 https://doi.org/10.1063/1.869033	journal	September 1996
Experimental investigation of turbulent mixing by Rayleigh-Taylor instability Read, K. I. Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3 https://doi.org/10.1016/0167-2789(84)90513-X	journal	July 1984
Velocity measurements in turbulent gaseous mixtures induced by Richtmyer–Meshkov instability Poggi, Françoise; Thorembey, Marie-Hélène; Rodriguez, Gérard Physics of Fluids, Vol. 10, Issue 11 https://doi.org/10.1063/1.869794	journal	November 1998
Renormalization group theory for fluid and plasma turbulence Zhou, Ye Physics Reports, Vol. 488, Issue 1 https://doi.org/10.1016/j.physrep.2009.04.004	journal	March 2010
Onset of turbulence in accelerated high-Reynolds-number flow Zhou, Ye; Robey, Harry F.; Buckingham, Alfred C. Physical Review E, Vol. 67, Issue 5 https://doi.org/10.1103/PhysRevE.67.056305	journal	May 2003
Three‐dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability Youngs, David L. Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5 https://doi.org/10.1063/1.858059	journal	May 1991
The physics basis for ignition using indirect-drive targets on the National Ignition Facility Lindl, John D.; Amendt, Peter; Berger, Richard L. Physics of Plasmas, Vol. 11, Issue 2 https://doi.org/10.1063/1.1578638	journal	February 2004
Instability of the interface of two gases accelerated by a shock wave Meshkov, E. E. Fluid Dynamics, Vol. 4, Issue 5 https://doi.org/10.1007/BF01015969	journal	January 1972
Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae Cabot, William H.; Cook, Andrew W. Nature Physics, Vol. 2, Issue 8 https://doi.org/10.1038/nphys361	journal	July 2006
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I Taylor, Geoffrey Ingram Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 201, Issue 1065, p. 192-196 https://doi.org/10.1098/rspa.1950.0052	journal	March 1950
Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface Vetter, M.; Sturtevant, B. Shock Waves, Vol. 4, Issue 5 https://doi.org/10.1007/BF01416035	journal	March 1995
Measurements of an Ablator-Gas Atomic Mix in Indirectly Driven Implosions at the National Ignition Facility Smalyuk, V. A.; Tipton, R. E.; Pino, J. E. Physical Review Letters, Vol. 112, Issue 2 https://doi.org/10.1103/PhysRevLett.112.025002	journal	January 2014
Taylor instability in shock acceleration of compressible fluids Richtmyer, Robert D. Communications on Pure and Applied Mathematics, Vol. 13, Issue 2 https://doi.org/10.1002/cpa.3160130207	journal	May 1960
Non-spherical core collapse supernovae: II. The late-time evolution of globally anisotropic neutrino-driven explosions and their implications for SN 1987 A Kifonidis, K.; Plewa, T.; Scheck, L. Astronomy & Astrophysics, Vol. 453, Issue 2 https://doi.org/10.1051/0004-6361:20054512	journal	June 2006
Progress in understanding turbulent mixing induced by Rayleigh–Taylor and Richtmyer–Meshkov instabilities Zhou, Ye; Remington, B. A.; Robey, H. F. Physics of Plasmas, Vol. 10, Issue 5 https://doi.org/10.1063/1.1560923	journal	May 2003
The Definition and Measurement of Some Characteristics of Mixtures Danckwerts, P. V. Insights Into Chemical Engineering https://doi.org/10.1016/b978-0-08-026250-5.50050-2	book	January 1981
Non-spherical core collapse supernovae: I. Neutrino-driven convection, Rayleigh-Taylor instabilities, and the formation and propagation of metal clumps Kifonidis, K.; Plewa, T.; Janka, H. -Th. Astronomy & Astrophysics, Vol. 408, Issue 2 https://doi.org/10.1051/0004-6361:20030863	journal	September 2003
Non-spherical core collapse supernovae III. Evolution towards homology and dependence on the numerical resolution Gawryszczak, A.; Guzman, J.; Plewa, T. arXiv https://doi.org/10.48550/arxiv.1007.0463	text	January 2010
Non-Spherical Core-Collapse Supernovae II. Late-Time Evolution of Globally Anisotropic Neutrino-Driven Explosions and Implications for SN 1987A Kifonidis, K.; Plewa, T.; Scheck, L. arXiv https://doi.org/10.48550/arxiv.astro-ph/0511369	text	January 2005

Cited By (6)

The transition to turbulence in shock-driven mixing: effects of Mach number and initial conditions Mohaghar, Mohammad; Carter, John; Pathikonda, Gokul Journal of Fluid Mechanics, Vol. 871 https://doi.org/10.1017/jfm.2019.330	journal	May 2019
Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ -group collaboration Thornber, B.; Griffond, J.; Poujade, O. Physics of Fluids, Vol. 29, Issue 10 https://doi.org/10.1063/1.4993464	journal	October 2017
Turbulent mixing and energy transfer of reshocked heavy gas curtain Zeng, Wei-Gang; Pan, Jian-Hua; Sun, Yu-Tao Physics of Fluids, Vol. 30, Issue 6 https://doi.org/10.1063/1.5032275	journal	June 2018
Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities Zhou, Ye; Clark, Timothy T.; Clark, Daniel S. Physics of Plasmas, Vol. 26, Issue 8 https://doi.org/10.1063/1.5088745	journal	August 2019
Time-dependent study of anisotropy in Rayleigh-Taylor instability induced turbulent flows with a variety of density ratios Zhou, Ye; Cabot, William H. Physics of Fluids, Vol. 31, Issue 8 https://doi.org/10.1063/1.5110914	journal	August 2019
Mixed mass of classical Rayleigh-Taylor mixing at arbitrary density ratios Zhang, You-sheng; Ruan, Yu-cang; Xie, Han-song Physics of Fluids, Vol. 32, Issue 1 https://doi.org/10.1063/1.5131495	journal	January 2020

Figures / Tables (4)

Similar Records

Asymptotic behavior of the mixed mass in Rayleigh–Taylor and Richtmyer–Meshkov instability induced flows

Journal Article · Sun May 15 00:00:00 EDT 2016 · Physics of Plasmas · OSTI ID:1569166

Zhou, Ye; Cabot, William H.; Thornber, Ben

A Comparison of Interface Growth Models Applied to Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

Journal Article · Thu Oct 29 00:00:00 EDT 2020 · Journal of Fluids Engineering · OSTI ID:1569166

Canfield, J.; Denissen, N.; Francois, M.; +4 more

A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

Journal Article · Wed Jan 01 00:00:00 EST 2020 · Physica. D, Nonlinear Phenomena · OSTI ID:1569166

Schilling, Oleg

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY