Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability

Thornber, B.; Griffond, J.; Bigdelou, P.; Boureima, I.; Ramaprabhu, P.; Schilling, O.; Williams, R. R.

doi:10.1063/1.5111681

Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability

Journal Article · Wed Sep 25 00:00:00 EDT 2019 · Physics of Fluids

DOI:https://doi.org/10.1063/1.5111681· OSTI ID:1806420

^[1]; Griffond, J. ^[2]; Bigdelou, P. ^[3]; ^[3]; ^[3]; ^[4]; ^[5]

Univ. of Sydney, NSW (Australia)
CEA, DAM, DIF, Arpajon (France)
Univ. of North Carolina, Charlotte, NC (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Atomic Weapons Research Establishment (AWRE), Aldermaston (United Kingdom)

The mean momentum and heavy mass fraction, turbulent kinetic energy, and heavy mass fraction variance fields, as well as the budgets of their transport equations are examined several times during the evolution of a narrowband Richtmyer-Meshkov instability initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3. The results are computed using the “quarter scale” data from four algorithms presented in the θ-group study of Thornber et al. [“Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer-Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)]. The present study is inspired by a previous similar study of Rayleigh-Taylor instability and mixing using direct numerical simulation data by Schilling and Mueschke [“Analysis of turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow using direct numerical simulation data,” Phys. Fluids 22, 105102 (2010)]. In addition to comparing the predictions of the data from four implicit large-eddy simulation codes, the budgets are used to quantify the relative importance of the terms in the transport equations, and the balance of the terms is employed to infer the numerical dissipation. Furthermore, terms arising from the compressibility of the flow are examined, in particular the pressure-dilatation. The results are useful for validation of large-eddy simulation and Reynolds-averaged modeling of Richtmyer-Meshkov instability.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: Australian Research Council (ARC); USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1806420

Alternate ID(s):: OSTI ID: 1566267

Report Number(s):: LLNL-JRNL--770657; 960167

Journal Information:: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 9 Vol. 31; ISSN 1070-6631

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

Country of Publication:: United States

Language:: English

References (55)

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
A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R. Flow, Turbulence and Combustion, Vol. 96, Issue 1 https://doi.org/10.1007/s10494-015-9643-z	journal	September 2015
Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow Van Leer, Bram Journal of Computational Physics, Vol. 23, Issue 3 https://doi.org/10.1016/0021-9991(77)90094-8	journal	March 1977
The Piecewise Parabolic Method (PPM) for gas-dynamical simulations Colella, Phillip; Woodward, Paul R. Journal of Computational Physics, Vol. 54, Issue 1 https://doi.org/10.1016/0021-9991(84)90143-8	journal	April 1984
Multicomponent Reynolds-averaged Navier–Stokes simulations of reshocked Richtmyer–Meshkov instability-induced mixing Morán-López, J. Tiberius; Schilling, Oleg High Energy Density Physics, Vol. 9, Issue 1 https://doi.org/10.1016/j.hedp.2012.11.001	journal	March 2013
Measurement of Richtmyer–Meshkov mode coupling under steady shock conditions and at high energy density Di Stefano, C. A.; Malamud, G.; Kuranz, C. C. High Energy Density Physics, Vol. 17 https://doi.org/10.1016/j.hedp.2015.09.001	journal	December 2015
High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations Daru, V.; Tenaud, C. Journal of Computational Physics, Vol. 193, Issue 2 https://doi.org/10.1016/j.jcp.2003.08.023	journal	January 2004
An improved reconstruction method for compressible flows with low Mach number features Thornber, B.; Mosedale, A.; Drikakis, D. Journal of Computational Physics, Vol. 227, Issue 10 https://doi.org/10.1016/j.jcp.2008.01.036	journal	May 2008
Sub-grid properties and artificial viscous stresses in staggered-mesh schemes Williams, R. J. R. Journal of Computational Physics, Vol. 374 https://doi.org/10.1016/j.jcp.2018.07.012	journal	December 2018
Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I Zhou, Ye Physics Reports, Vol. 720-722 https://doi.org/10.1016/j.physrep.2017.07.005	journal	December 2017
Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II Zhou, Ye Physics Reports, Vol. 723-725 https://doi.org/10.1016/j.physrep.2017.07.008	journal	December 2017
High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data Schilling, Oleg; Latini, Marco Acta Mathematica Scientia, Vol. 30, Issue 2 https://doi.org/10.1016/s0252-9602(10)60064-1	journal	March 2010
Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics Grinstein, Fernando F.; Margolin, Len G.; Rider, William J. https://doi.org/10.1017/CBO9780511618604	book	July 2007
Finite Volume Methods for Hyperbolic Problems LeVeque, Randall J. https://doi.org/10.1017/CBO9780511791253	book	January 2002
An experimental investigation of the turbulent mixing transition in the Richtmyer–Meshkov instability Weber, Christopher R.; Haehn, Nicholas S.; Oakley, Jason G. Journal of Fluid Mechanics, Vol. 748 https://doi.org/10.1017/jfm.2014.188	journal	May 2014
Simultaneous direct measurements of concentration and velocity in the Richtmyer–Meshkov instability Reese, Daniel T.; Ames, Alex M.; Noble, Chris D. Journal of Fluid Mechanics, Vol. 849 https://doi.org/10.1017/jfm.2018.419	journal	June 2018
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
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
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
A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence Ristorcelli, J. R. Journal of Fluid Mechanics, Vol. 347 https://doi.org/10.1017/s0022112097006083	journal	September 1997
Turbulent shear-layer mixing at high Reynolds numbers: effects of inflow conditions Slessor, M. D.; Bond, C. L.; Dimotakis, P. E. Journal of Fluid Mechanics, Vol. 376 https://doi.org/10.1017/s0022112098002857	journal	December 1998
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
A new turbulent two-field concept for modeling Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz mixing layers Llor, Antoine; Bailly, Pascal Laser and Particle Beams, Vol. 21, Issue 3 https://doi.org/10.1017/s0263034603213033	journal	July 2003
Supernova explosions in the Universe Burrows, Adam Nature, Vol. 403, Issue 6771 https://doi.org/10.1038/35001501	journal	February 2000
Effects of Diffusion on Interface Instability between Gases Duff, R. E.; Harlow, F. H.; Hirt, C. W. Physics of Fluids, Vol. 5, Issue 4 https://doi.org/10.1063/1.1706634	journal	January 1962
K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities Dimonte, Guy; Tipton, Robert Physics of Fluids, Vol. 18, Issue 8 https://doi.org/10.1063/1.2219768	journal	August 2006
Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data Schilling, Oleg; Mueschke, Nicholas J. Physics of Fluids, Vol. 22, Issue 10 https://doi.org/10.1063/1.3484247	journal	October 2010
Reshocked Richtmyer-Meshkov instability: Numerical study and modeling of random multi-mode experiments Malamud, G.; Leinov, E.; Sadot, O. Physics of Fluids, Vol. 26, Issue 8 https://doi.org/10.1063/1.4893678	journal	August 2014
Three-dimensional simulations of low foot and high foot implosion experiments on the National Ignition Facility Clark, D. S.; Weber, C. R.; Milovich, J. L. Physics of Plasmas, Vol. 23, Issue 5 https://doi.org/10.1063/1.4943527	journal	March 2016
Impact of domain size and statistical errors in simulations of homogeneous decaying turbulence and the Richtmyer-Meshkov instability Thornber, B. Physics of Fluids, Vol. 28, Issue 4 https://doi.org/10.1063/1.4944877	journal	April 2016
Turbulent mixing induced by Richtmyer-Meshkov instability Krivets, V. V.; Ferguson, K. J.; Jacobs, J. W. SHOCK COMPRESSION OF CONDENSED MATTER - 2015: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings https://doi.org/10.1063/1.4971732	conference	January 2017
A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the National Ignition Facility Nagel, S. R.; Raman, K. S.; Huntington, C. M. Physics of Plasmas, Vol. 24, Issue 7 https://doi.org/10.1063/1.4985312	journal	July 2017
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
Capsule physics comparison of National Ignition Facility implosion designs using plastic, high density carbon, and beryllium ablators Clark, D. S.; Kritcher, A. L.; Yi, S. A. Physics of Plasmas, Vol. 25, Issue 3 https://doi.org/10.1063/1.5016874	journal	March 2018
Modal model mean field self-similar solutions to the asymptotic evolution of Rayleigh-Taylor and Richtmyer-Meshkov instabilities and its dependence on the initial conditions Elbaz, Yonatan; Shvarts, Dov Physics of Plasmas, Vol. 25, Issue 6 https://doi.org/10.1063/1.5031922	journal	June 2018
A k ‐ε model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability Gauthier, Serge; Bonnet, Michel Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 9 https://doi.org/10.1063/1.857576	journal	September 1990
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 pressure–dilatation correlation in compressible flows Sarkar, S. Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 12 https://doi.org/10.1063/1.858454	journal	December 1992
Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories Dimonte, Guy; Schneider, Marilyn Physics of Fluids, Vol. 12, Issue 2 https://doi.org/10.1063/1.870309	journal	February 2000
A second-order turbulence model for gaseous mixtures induced by Richtmyer—Meshkov instability Grégoire, Olivier; Souffland, Denis; Gauthier, Serge Journal of Turbulence, Vol. 6 https://doi.org/10.1080/14685240500307413	journal	January 2005
Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids Schwarzkopf, John D.; Livescu, Daniel; Gore, Robert A. Journal of Turbulence, Vol. 12 https://doi.org/10.1080/14685248.2011.633084	journal	January 2011
Physics of the single-shocked and reshocked Richtmyer–Meshkov instability Thornber, B.; Drikakis, D.; Youngs, D. L. Journal of Turbulence, Vol. 13 https://doi.org/10.1080/14685248.2012.658916	journal	January 2012
FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes Fryxell, B.; Olson, K.; Ricker, P. The Astrophysical Journal Supplement Series, Vol. 131, Issue 1 https://doi.org/10.1086/317361	journal	November 2000
Rayleigh-Taylor and Richtmyer-Meshkov instabilities in multilayer fluids with surface tension Mikaelian, Karnig O. Physical Review A, Vol. 42, Issue 12 https://doi.org/10.1103/physreva.42.7211	journal	December 1990
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
Development and validation of a turbulent-mix model for variable-density and compressible flows Banerjee, Arindam; Gore, Robert A.; Andrews, Malcolm J. Physical Review E, Vol. 82, Issue 4 https://doi.org/10.1103/physreve.82.046309	journal	October 2010
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
Permanence of large eddies in Richtmyer-Meshkov turbulence with a small Atwood number Soulard, Olivier; Guillois, Florian; Griffond, Jérôme Physical Review Fluids, Vol. 3, Issue 10 https://doi.org/10.1103/physrevfluids.3.104603	journal	October 2018
Observation of Single-Mode, Kelvin-Helmholtz Instability in a Supersonic Flow Wan, W. C.; Malamud, G.; Shimony, A. Physical Review Letters, Vol. 115, Issue 14 https://doi.org/10.1103/physrevlett.115.145001	journal	October 2015
Late-Time Mixing Sensitivity to Initial Broadband Surface Roughness in High-Energy-Density Shear Layers Flippo, K. A.; Doss, F. W.; Kline, J. L. Physical Review Letters, Vol. 117, Issue 22 https://doi.org/10.1103/physrevlett.117.225001	journal	November 2016
Modeling of Reynolds Stress Models for Diffusion Fluxes Inside Shock Waves Souffland, D.; Soulard, O.; Griffond, J. Journal of Fluids Engineering, Vol. 136, Issue 9 https://doi.org/10.1115/1.4027381	journal	July 2014
Density Ratio and Entrainment Effects on Asymptotic Rayleigh–Taylor Instability Shimony, Assaf; Malamud, Guy; Shvarts, Dov Journal of Fluids Engineering, Vol. 140, Issue 5 https://doi.org/10.1115/1.4038400	journal	December 2017
Turbulence transport equations for variable-density turbulence and their relationship to two-field models Besnard, D.; Harlow, F. H.; Rauenzahn, R. M. https://doi.org/10.2172/7271399	report	June 1992
Steady Turbulent Flow Computations Using a Low Mach Fully Compressible Scheme Garcia-Uceda Juarez, A.; Raimo, A.; Shapiro, E. AIAA Journal, Vol. 52, Issue 11 https://doi.org/10.2514/1.j052948	journal	November 2014
Applications of shock-induced mixing to supersonic combustion Yang, Joseph; Kubota, Toshi; Zukoski, Edward E. AIAA Journal, Vol. 31, Issue 5 https://doi.org/10.2514/3.11696	journal	May 1993

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