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Title: Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry

Abstract

Tenth-order compact difference code Miranda is utilized to perform large-eddy simulation (LES) of a hydrogen gas–plastic mixing layer in a spherical geometry. Once the mixing layer has achieved self-similar growth, it is heated to 1 keV, and the second-order arbitrary Lagrangian-Eulerian (ALE) code Ares is used to simulate mixing layer evolution as it undergoes thermonuclear (TN) burn. Both premixed (in which deuterium and tritium are initially present in the gas) and nonpremixed (in which deuterium is initially present only in the plastic) variants are considered at Atwood numbers 0.05 and 0.50. The effect of turbulent mixing on mean TN reaction rate is examined, and a four-equation k – L – a – V Reynolds-averaged Navier-Stokes (RANS) model is presented. The k – L – a – V model, which represents an extension of the k – L – a model [Morgan and Wickett, Phys. Rev. E 91, 043002 (2015)] by the addition of a transport equation for the scalar mass fraction variance, is then applied in one-dimensional simulations of the reacting mixing layer under consideration. Excellent agreement is gained between LES and RANS in total TN neutron production when fluctuations in reaction cross-section can be neglected.

Authors:
 [1];  [1];  [2];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of Missouri, Columbia, MO (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1548329
Alternate Identifier(s):
OSTI ID: 1471160
Report Number(s):
LLNL-JRNL-750537
Journal ID: ISSN 2470-0045; PLEEE8; 934407
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 98; Journal Issue: 3; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Morgan, Brandon E., Olson, Britton J., Black, Wolfgang J., and McFarland, Jacob A. Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry. United States: N. p., 2018. Web. doi:10.1103/PhysRevE.98.033111.
Morgan, Brandon E., Olson, Britton J., Black, Wolfgang J., & McFarland, Jacob A. Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry. United States. https://doi.org/10.1103/PhysRevE.98.033111
Morgan, Brandon E., Olson, Britton J., Black, Wolfgang J., and McFarland, Jacob A. Mon . "Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry". United States. https://doi.org/10.1103/PhysRevE.98.033111. https://www.osti.gov/servlets/purl/1548329.
@article{osti_1548329,
title = {Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry},
author = {Morgan, Brandon E. and Olson, Britton J. and Black, Wolfgang J. and McFarland, Jacob A.},
abstractNote = {Tenth-order compact difference code Miranda is utilized to perform large-eddy simulation (LES) of a hydrogen gas–plastic mixing layer in a spherical geometry. Once the mixing layer has achieved self-similar growth, it is heated to 1 keV, and the second-order arbitrary Lagrangian-Eulerian (ALE) code Ares is used to simulate mixing layer evolution as it undergoes thermonuclear (TN) burn. Both premixed (in which deuterium and tritium are initially present in the gas) and nonpremixed (in which deuterium is initially present only in the plastic) variants are considered at Atwood numbers 0.05 and 0.50. The effect of turbulent mixing on mean TN reaction rate is examined, and a four-equation k – L – a – V Reynolds-averaged Navier-Stokes (RANS) model is presented. The k – L – a – V model, which represents an extension of the k – L – a model [Morgan and Wickett, Phys. Rev. E 91, 043002 (2015)] by the addition of a transport equation for the scalar mass fraction variance, is then applied in one-dimensional simulations of the reacting mixing layer under consideration. Excellent agreement is gained between LES and RANS in total TN neutron production when fluctuations in reaction cross-section can be neglected.},
doi = {10.1103/PhysRevE.98.033111},
journal = {Physical Review E},
number = 3,
volume = 98,
place = {United States},
year = {Mon Sep 17 00:00:00 EDT 2018},
month = {Mon Sep 17 00:00:00 EDT 2018}
}

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Cited by: 21 works
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Works referenced in this record:

Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density
journal, November 1882


The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I
journal, March 1950

  • Taylor, Geoffrey Ingram
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 201, Issue 1065, p. 192-196
  • DOI: 10.1098/rspa.1950.0052

Interaction of Rayleigh-Taylor Fingers and Circumstellar Cloudlets in Young Supernova Remnants
journal, September 1996

  • Jun, Byung-Il; Jones, T. W.; Norman, Michael L.
  • The Astrophysical Journal, Vol. 468, Issue 1
  • DOI: 10.1086/310224

Three-Dimensional Simulations of Rayleigh-Taylor Mixing in Core-Collapse Supernovae
journal, October 2010


Rayleigh-Taylor Instability and Laser-Pellet Fusion
journal, September 1974


Two-Dimensional Simulation of Fluid Instability in Laser-Fusion Pellets
journal, May 1975


Rayleigh–Taylor instability evolution in ablatively driven cylindrical implosions
journal, May 1997

  • Hsing, W. W.; Barnes, Cris W.; Beck, J. B.
  • Physics of Plasmas, Vol. 4, Issue 5
  • DOI: 10.1063/1.872326

On the Stability of Fluid Flows with Spherical Symmetry
journal, January 1954


Modified Bell–Plesset effect with compressibility: Application to double-shell ignition target designs
journal, March 2003

  • Amendt, Peter; Colvin, J. D.; Ramshaw, J. D.
  • Physics of Plasmas, Vol. 10, Issue 3
  • DOI: 10.1063/1.1543926

Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells
journal, September 2005


Hydrodynamic instability growth and mix experiments at the National Ignition Facility
journal, May 2014

  • Smalyuk, V. A.; Barrios, M.; Caggiano, J. A.
  • Physics of Plasmas, Vol. 21, Issue 5
  • DOI: 10.1063/1.4872026

Measurements of an Ablator-Gas Atomic Mix in Indirectly Driven Implosions at the National Ignition Facility
journal, January 2014


Development of the CD Symcap platform to study gas-shell mix in implosions at the National Ignition Facility
journal, September 2014

  • Casey, D. T.; Smalyuk, V. A.; Tipton, R. E.
  • Physics of Plasmas, Vol. 21, Issue 9
  • DOI: 10.1063/1.4894215

Indirect-drive noncryogenic double-shell ignition targets for the National Ignition Facility: Design and analysis
journal, May 2002

  • Amendt, Peter; Colvin, J. D.; Tipton, R. E.
  • Physics of Plasmas, Vol. 9, Issue 5
  • DOI: 10.1063/1.1459451

Role of shocks and mix caused by capsule defects
journal, September 2012

  • Bradley, P. A.; Cobble, J. A.; Tregillis, I. L.
  • Physics of Plasmas, Vol. 19, Issue 9
  • DOI: 10.1063/1.4752014

The effect of mix on capsule yields as a function of shell thickness and gas fill
journal, June 2014


Simulations of indirectly driven gas-filled capsules at the National Ignition Facility
journal, November 2014

  • Weber, S. V.; Casey, D. T.; Eder, D. C.
  • Physics of Plasmas, Vol. 21, Issue 11
  • DOI: 10.1063/1.4901598

K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities
journal, August 2006

  • Dimonte, Guy; Tipton, Robert
  • Physics of Fluids, Vol. 18, Issue 8
  • DOI: 10.1063/1.2219768

Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities
journal, April 2015


Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing
journal, January 2018


Development and validation of a turbulent-mix model for variable-density and compressible flows
journal, October 2010


A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing
journal, September 2015

  • Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R.
  • Flow, Turbulence and Combustion, Vol. 96, Issue 1
  • DOI: 10.1007/s10494-015-9643-z

Exact statistical results for binary mixing and reaction in variable density turbulence
journal, February 2017


Three-dimensional Rayleigh-Taylor instability of spherical systems
journal, July 1990


Turbulent mixing in spherical implosions
journal, January 2008

  • Youngs, David L.; Williams, Robin J. R.
  • International Journal for Numerical Methods in Fluids, Vol. 56, Issue 8
  • DOI: 10.1002/fld.1594

Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability
journal, November 2009

  • Lombardini, M.; Pullin, D. I.
  • Physics of Fluids, Vol. 21, Issue 11
  • DOI: 10.1063/1.3258668

Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth
journal, April 2014

  • Lombardini, M.; Pullin, D. I.; Meiron, D. I.
  • Journal of Fluid Mechanics, Vol. 748
  • DOI: 10.1017/jfm.2014.161

Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics
journal, April 2014

  • Lombardini, M.; Pullin, D. I.; Meiron, D. I.
  • Journal of Fluid Mechanics, Vol. 748
  • DOI: 10.1017/jfm.2014.163

Drive Asymmetry and the Origin of Turbulence in an ICF Implosion
journal, August 2012


Detailed implosion modeling of deuterium-tritium layered experiments on the National Ignition Facility
journal, May 2013

  • Clark, D. S.; Hinkel, D. E.; Eder, D. C.
  • Physics of Plasmas, Vol. 20, Issue 5
  • DOI: 10.1063/1.4802194

Inhibition of turbulence in inertial-confinement-fusion hot spots by viscous dissipation
journal, May 2014


Three-dimensional hydrodynamics of the deceleration stage in inertial confinement fusion
journal, March 2015

  • Weber, C. R.; Clark, D. S.; Cook, A. W.
  • Physics of Plasmas, Vol. 22, Issue 3
  • DOI: 10.1063/1.4914157

Three-dimensional simulations of low foot and high foot implosion experiments on the National Ignition Facility
journal, March 2016

  • Clark, D. S.; Weber, C. R.; Milovich, J. L.
  • Physics of Plasmas, Vol. 23, Issue 5
  • DOI: 10.1063/1.4943527

Detailed high-resolution three-dimensional simulations of OMEGA separated reactants inertial confinement fusion experiments
journal, July 2016

  • Haines, Brian M.; Grim, Gary P.; Fincke, James R.
  • Physics of Plasmas, Vol. 23, Issue 7
  • DOI: 10.1063/1.4959117

Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation
journal, June 2017


The mixing transition in RayleighTaylor instability
journal, January 1999


Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae
journal, July 2006

  • Cabot, William H.; Cook, Andrew W.
  • Nature Physics, Vol. 2, Issue 8
  • DOI: 10.1038/nphys361

Rayleigh–Taylor shock waves
journal, December 2007

  • Olson, Britton J.; Cook, Andrew W.
  • Physics of Fluids, Vol. 19, Issue 12
  • DOI: 10.1063/1.2821907

Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability
journal, November 2011

  • Olson, Britton J.; Larsson, Johan; Lele, Sanjiva K.
  • Physics of Fluids, Vol. 23, Issue 11
  • DOI: 10.1063/1.3660723

On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface
journal, August 2014

  • Tritschler, V. K.; Olson, B. J.; Lele, S. K.
  • Journal of Fluid Mechanics, Vol. 755
  • DOI: 10.1017/jfm.2014.436

Large eddy simulation requirements for the Richtmyer-Meshkov instability
journal, April 2014

  • Olson, Britton J.; Greenough, Jeff
  • Physics of Fluids, Vol. 26, Issue 4
  • DOI: 10.1063/1.4871396

Comparison of two- and three-dimensional simulations of miscible Richtmyer-Meshkov instability with multimode initial conditions
journal, October 2014

  • Olson, Britton J.; Greenough, Jeffrey A.
  • Physics of Fluids, Vol. 26, Issue 10
  • DOI: 10.1063/1.4898157

Artificial fluid properties for large-eddy simulation of compressible turbulent mixing
journal, May 2007


Enthalpy diffusion in multicomponent flows
journal, May 2009


A study of ALE simulations of Rayleigh–Taylor instability
journal, March 2001

  • Darlington, Rebecca M.; McAbee, Thomas L.; Rodrigue, Garry
  • Computer Physics Communications, Vol. 135, Issue 1
  • DOI: 10.1016/S0010-4655(00)00216-2

A tensor artificial viscosity using a finite element approach
journal, December 2009


Adaptive mesh refinement for hyperbolic partial differential equations
journal, March 1984


Local adaptive mesh refinement for shock hydrodynamics
journal, May 1989


Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder
journal, April 2015


Three-dimensional modeling and analysis of a high energy density Kelvin-Helmholtz experiment
journal, September 2012

  • Raman, K. S.; Hurricane, O. A.; Park, H. -S.
  • Physics of Plasmas, Vol. 19, Issue 9
  • DOI: 10.1063/1.4752018

Symmetry tuning of a near one-dimensional 2-shock platform for code validation at the National Ignition Facility
journal, April 2016

  • Khan, S. F.; MacLaren, S. A.; Salmonson, J. D.
  • Physics of Plasmas, Vol. 23, Issue 4
  • DOI: 10.1063/1.4947223

Development of an inertial confinement fusion platform to study charged-particle-producing nuclear reactions relevant to nuclear astrophysics
journal, April 2017

  • Gatu Johnson, M.; Zylstra, A. B.; Bacher, A.
  • Physics of Plasmas, Vol. 24, Issue 4
  • DOI: 10.1063/1.4979186

Multi-group diffusion of energetic charged particles
journal, June 1975


Electron-ion equilibration in a partially degenerate plasma
journal, October 1974


A new quotidian equation of state (QEOS) for hot dense matter
journal, January 1988

  • More, R. M.; Warren, K. H.; Young, D. A.
  • Physics of Fluids, Vol. 31, Issue 10
  • DOI: 10.1063/1.866963

A new global equation of state model for hot, dense matter
journal, September 1995

  • Young, David A.; Corey, Ellen M.
  • Journal of Applied Physics, Vol. 78, Issue 6
  • DOI: 10.1063/1.359955

Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations
journal, May 2004


Decay of Passive Scalar Fluctuations in Isotropic Homogeneous Turbulence
journal, January 1968


Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories
journal, February 2000

  • Dimonte, Guy; Schneider, Marilyn
  • Physics of Fluids, Vol. 12, Issue 2
  • DOI: 10.1063/1.870309

Experimental investigation of RayleighTaylor mixing at small Atwood numbers
journal, January 1999


Works referencing / citing this record:

Observation of persistent species temperature separation in inertial confinement fusion mixtures
journal, January 2020