Export citation

Export citation

Choose format for download:

Download Citation
  • Rapid Communication
  • Access by Xinjiang University

Gas-kinetic simulation of sustained turbulence in minimal Couette flow

M. A. Gallis1,*, J. R. Torczynski1, N. P. Bitter1, T. P. Koehler1, S. J. Plimpton2, and G. Papadakis3

  • 1Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185-0840, USA
  • 2Computing Research Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185-1316, USA
  • 3Department of Aeronautics, Imperial College, London SW7 2AZ, United Kingdom

  • *magalli@sandia.gov

Phys. Rev. Fluids 3, 071402(R) – Published 26 July, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.071402

Abstract

We provide a demonstration that gas-kinetic methods incorporating molecular chaos can simulate the sustained turbulence that occurs in wall-bounded turbulent shear flows. The direct simulation Monte Carlo method, a gas-kinetic molecular method that enforces molecular chaos for gas-molecule collisions, is used to simulate the minimal Couette flow at Re=500. The resulting law of the wall, the average wall shear stress, the average kinetic energy, and the continually regenerating coherent structures all agree closely with corresponding results from direct numerical simulation of the Navier-Stokes equations. These results indicate that molecular chaos for collisions in gas-kinetic methods does not prevent development of molecular-scale long-range correlations required to form hydrodynamic-scale turbulent coherent structures.

Physics Subject Headings (PhySH)

Article Text

References (30)

  1. T. E. Faber, Fluid Dynamics for Physicists (Cambridge University Press, Cambridge, UK, 1995).
  2. L. S. G. Kovasznay, Turbulence in supersonic flow, J. Aero. Sci. 20, 657 (1953).
  3. E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938).
  4. H. Grad, On molecular chaos and the Kirkwood superposition hypothesis, J. Chem. Phys. 33, 1342 (1960).
  5. W. G. Vincenti and C. H. Kruger Jr., Introduction to Physical Gas Dynamics (Wiley, New York, 1965).
  6. M. N. Kogan, Rarefied Gas Dynamics (Plenum, New York, 1969).
  7. G. A. Bird, Direct simulation and the Boltzmann equation, Phys. Fluids 13, 2676 (1970).
  8. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, UK, 1970).
  9. H. Grad, Singular limits of solutions of Boltzmann's equation, in Proceedings of the 8th International Symposium on Rarefied Gas Dynamics, edited by K. Karamcheti (Academic, New York, 1974).
  10. S. Tsugé, Approach to the origin of turbulence on the basis of two‐point kinetic theory, Phys. Fluids 17, 22 (1974).
  11. C. C. A. Sastri, Long-range correlations in kinetic theory, J. Stat. Phys. 13, 43 (1975).
  12. S. Tsugé and K. Sagara, Kinetic theory of turbulent compressible flows and comparison with classical theory, Phys. Fluids 19, 1478 (1976).
  13. S. S. Girimaji, Boltzmann Kinetic Equation for Filtered Fluid Turbulence, Phys. Rev. Lett. 99, 034501 (2007).
  14. B. J. Alder and T. E. Wainwright, Studies in molecular dynamics. I. General method, J. Chem. Phys. 31, 459 (1959).
  15. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1998).
  16. M. A. Gallis, T. P. Koehler, J. R. Torczynski, and S. J. Plimpton, Direct simulation Monte Carlo investigation of the Richtmyer-Meshkov instability, Phys. Fluids 27, 084105 (2015).
  17. M. A. Gallis, T. P. Koehler, J. R. Torczynski, and S. J. Plimpton, Direct simulation Monte Carlo investigation of the Rayleigh-Taylor instability, Phys. Rev. Fluids 1, 043403 (2016).
  18. M. A. Gallis, N. P. Bitter, T. P. Koehler, J. R. Torczynski, S. J. Plimpton, and G. Papadakis, Molecular-Level Simulations of Turbulence and Its Decay, Phys. Rev. Lett. 118, 064501 (2017).
  19. W. Wagner, A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation, J. Stat. Phys. 66, 1011 (1992).
  20. M. A. Gallis, J. R. Torczynski, and D. J. Rader, Molecular gas dynamics observations of Chapman-Enskog behavior and departures therefrom in nonequilibrium gases, Phys. Rev. E 69, 042201 (2004).
  21. M. A. Gallis, J. R. Torczynski, D. J. Rader, M. Tij, and A. Santos, Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow, Phys. Fluids 18, 017104 (2006).
  22. E. R. Smith, A molecular dynamics simulation of the turbulent Couette minimal flow unit, Phys. Fluids 27, 115105 (2015).
  23. J. Jimenez and P. Moin, The minimal flow unit in near-wall turbulence, J. Fluid Mech. 225, 213 (1991).
  24. J. M. Hamilton, J. Kim, and F. Waleffe, Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech. 287, 317 (1995).
  25. F. Waleffe, On a self-sustaining process in shear flows, Phys. Fluids 9, 883 (1997).
  26. A. J. Smits, A Physical Introduction to Fluid Mechanics (Wiley, New York, 1999).
  27. D. J. Rader, M. A. Gallis, J. R. Torczynski, and W. Wagner, DSMC convergence behavior of the hard-sphere-gas thermal conductivity for Fourier heat flow, Phys. Fluids 18, 077102 (2006).
  28. M. A. Gallis, J. R. Torczynski, S. J. Plimpton, D. J. Rader, and T. Koehler, DSMC: The quest for speed, in Proceedings of the 29th International Symposium Rarefied Gas Dynamics, edited by J. Fan, AIP Conf. Proc. No. 1628 (AIP, Melville, NY, 2014), p. 27.
  29. S. J. Plimpton and M. A. Gallis, SPARTA direct simulation Monte Carlo (DSMC) simulator, http://sparta.sandia.gov, 2015.
  30. P. F. Fischer and J. W. Lottes, Hybrid Schwarz-multigrid methods for the spectral element method: Extensions to Navier-Stokes, in Domain Decomposition Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering Vol. 40, edited by T. J. Barth et al. (Springer, Berlin, Heidelberg, 2005).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation