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Mass and momentum transport in the Tilted Rocket Rig experiment

K. Ferguson*, K. M. Wang, and B. E. Morgan

  • Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, USA

  • *ferguson43@llnl.gov
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Phys. Rev. Fluids 8, 094502 – Published 27 September, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.094502

Abstract

High-fidelity large eddy simulations of the inclined Rayleigh-Taylor instability in the Tilted Rocket Rig experimental configuration [Smeeton and Youngs, AWE Report No. O 35/87 (1987)] are performed using a tenth-order compact finite difference code. These simulations are analyzed for spatial distributions of turbulent kinetic energy, turbulent mass flux velocity, species mass fraction flux, species mass fraction variance, and Favre-averaged Reynolds stresses at two time instances, t=37ms and t=52ms. Additionally, the vertical distribution of the components of the unclosed budget equations over the center of the domain for these quantities are examined. The dominant terms of these budget equations are further decomposed to examine the principal contributions to these terms in each axis. Notably, the principal contribution to the horizontal turbulent mass flux velocity budget is found to be from a term which is commonly neglected in many Reynolds-averaged Navier-Stokes models.

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References (39)

  1. V. S. Smeeton and D. L. Youngs, Experimental investigation of turbulent mixing by Rayleigh-Taylor instability III, AWE Report No. O 35/87, Atomic Weapons Establishment, 1987.
  2. D. L. Youngs, Modelling turbulent mixing by Rayleigh-Taylor instability, Physica D 37, 270 (1989).
  3. Lord Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, Proc. London Math. Soc. s1-14, 170 (1883).
  4. G. I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I, Proc. R. Soc. Lond. A 201, 192 (1950).
  5. Y. Zhou, Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. I, Phys. Rep. 720–722, 1 (2017).
  6. Y. Zhou, Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II, Phys. Rep. 723–725, 1 (2017).
  7. M. J. Andrews, D. L. Youngs, D. Livescu, and T. Wei, Computational studies of two-dimensional Rayleigh-Taylor driven mixing for a tilted-rig, J. Fluids Eng. 136, 091212 (2014).
  8. N. A. Denissen, B. Rollin, J. M. Reisner, and M. J. Andrews, The Tilted Rocket Rig: A Rayleigh-Taylor test case for RANS models, J. Fluids Eng. 136, 091301 (2014).
  9. I. W. Kokkinakis, D. Drikakis, and D. L. Youngs, Modeling of Rayleigh-Taylor mixing using single-fluid models, Phys. Rev. E 99, 013104 (2019).
  10. M. Xiao, Y. Zhang, and B. Tian, Modeling of turbulent mixing with an improved K-L model, Phys. Fluids 32, 092104 (2020).
  11. H.-s. Xie, M.-j. Xiao, and Y.-s. Zhang, Unified prediction of turbulent mixing induced by interfacial instabilities via Besnard-Harlow-Rauenzahn-2 model, Phys. Fluids 33, 105123 (2021).
  12. M. Xiao, Y. Zhang, and B. Tian, A K-L model with improved realizability for turbulent mixing, Phys. Fluids 33, 022104 (2021).
  13. A. W. Cook, Artificial fluid properties for large-eddy simulation of compressible turbulent mixing, Phys. Fluids 19, 055103 (2007).
  14. A. W. Cook, Enthalpy diffusion in multicomponent flows, Phys. Fluids 21, 055109 (2009).
  15. W. H. Cabot and A. W. Cook, Reynolds number effects on Rayleigh-Taylor instability with possible implications for type-Ia supernovae, Nat. Phys. 2, 562 (2006).
  16. B. E. Morgan, B. J. Olson, J. E. White, and J. A. McFarland, Self-similarity of a Rayleigh-Taylor mixing layer at low Atwood number with a multimode initial perturbation, J. Turbul. 18, 973 (2017).
  17. B. E. Morgan, B. J. Olson, W. J. Black, and J. A. McFarland, Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of a reacting Rayleigh-Taylor mixing layer in a spherical geometry, Phys. Rev. E 98, 033111 (2018).
  18. B. E. Morgan, Simulation and Reynolds-averaged Navier-Stokes modeling of a three-component Rayleigh-Taylor mixing problem with thermonuclear burn, Phys. Rev. E 105, 045104 (2022).
  19. A. W. Cook, W. H. Cabot, and P. L. Miller, The mixing transition in Rayleigh-Taylor instability, J. Fluid Mech. 511, 333 (2004).
  20. B. J. Olson and A. W. Cook, Rayleigh–Taylor shock waves, Phys. Fluids 19, 128108 (2007).
  21. B. J. Olson, J. Larsson, S. K. Lele, and A. W. Cook, Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability, Phys. Fluids 23, 114107 (2011).
  22. V. K. Tritschler, B. J. Olson, S. K. Lele, S. Hickel, X. Y. Hu, and N. A. Adams, On the Richtmyer-Meshkov instability evolving from a deterministic multimode planar interface, J. Fluid Mech. 755, 429 (2014).
  23. B. J. Olson and J. Greenough, Large eddy simulation requirements for the Richtmyer-Meshkov instability, Phys. Fluids 26, 044103 (2014).
  24. B. J. Olson and J. A. Greenough, Comparison of two- and three-dimensional simulations of miscible Richtmyer-Meshkov instability with multimode initial conditions, Phys. Fluids 26, 101702 (2014).
  25. A. Campos and B. E. Morgan, Direct numerical simulation and Reynolds-averaged Navier-Stokes modeling of the sudden viscous dissipation for multicomponent turbulence, Phys. Rev. E 99, 063103 (2019).
  26. B. E. Morgan, Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of three Rayleigh-Taylor mixing configurations with gravity reversal, Phys. Rev. E 106, 025101 (2022).
  27. D. Livescu, T. Wei, and M. R. Petersen, Direct Numerical Simulations of Rayleigh-Taylor instability, J. Phys.: Conf. Ser. 318, 082007 (2011).
  28. G. Dimonte, D. L. Youngs, A. Dimits, S. Weber, M. Marinak, S. Wunsch, C. Garasi, A. Robinson, M. J. Andrews, P. Ramaprabhu et al., A comparative study of the turbulent Rayleigh-Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration, Phys. Fluids 16, 1668 (2004).
  29. P. Ramaprabhu, G. Dimonte, and M. J. Andrews, A numerical study of the influence of initial perturbations on the turbulent Rayleigh-Taylor instability, J. Fluid Mech. 536, 285 (2005).
  30. D. Layzer, On the instability of superposed fluids in a gravitational field, Astrophys. J. 122, 1 (1955).
  31. V. N. Goncharov, Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers, Phys. Rev. Lett. 88, 134502 (2002).
  32. M. J. Andrews and D. B. Spalding, A simple experiment to investigate two-dimensional mixing by Rayleigh–Taylor instability, Phys. Fluids 2, 922 (1990).
  33. D. Besnard, F. H. Harlow, R. M. Rauenzahn, and C. Zemach, Turbulence transport equations for variable-density turbulence and their relationship to two-field models, Los Alamos Tech. Rep. No. LA-12303-MS, Los Alamos National Lab. (LANL), Los Alamos, USA, 1992.
  34. M. L. Wong, J. R. Baltzer, D. Livescu, and S. K. Lele, Analysis of second moments and their budgets for Richtmyer-Meshkov instability and variable-density turbulence induced by reshock, Phys. Rev. Fluids 7, 044602 (2022).
  35. B. E. Morgan and M. E. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities, Phys. Rev. E 91, 043002 (2015).
  36. N. O. Braun and R. A. Gore, A multispecies turbulence model for the mixing and de-mixing of miscible fluids, J. Turbul. 22, 784 (2021).
  37. T. Poinsot and D. Veynante, Theoretical and Numerical Combustion, 2nd ed. (Edwards, Philadelphia, PA, 2005).
  38. C. G. Speziale, S. Sarkar, and T. B. Gatski, Modelling the pressure-strain correlation of turbulence: An invariant dynamical systems approach, J. Fluid Mech. 227, 245 (1991).
  39. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).

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Phys. Rev. Fluids 8, 094502– Published 27 September, 2023
  • Received 4 April 2023
  • Accepted 7 September 2023
Article part of CHORUS
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