- Access by Xinjiang University
Turbulence at the edge of continuum
Phys. Rev. Fluids 6, 013401 – Published 11 January, 2021
DOI: https://doi.org/10.1103/PhysRevFluids.6.013401
Abstract
In typical turbulent flows, noncontinuum effects are extremely small and hence can be ignored. However, for some high-Mach-number flows, the Kolmogorov length scale is of the same order as the molecular mean free path, which could introduce noncontinuum molecular-level effects into the turbulent energy cascade. To investigate this, the compressible Taylor-Green vortex flow is simulated for near-continuum conditions using both noncontinuum molecular gas dynamics (direct simulation Monte Carlo method) and continuum computational fluid dynamics (direct numerical simulation of the Navier-Stokes equations). Although the energy-decay histories are basically the same, molecular-level fluctuations are observed to break the symmetries of the initial conditions and thereby produce different but statistically similar routes (based on velocity spectra) from the initial nonturbulent flow to the long-time turbulent flow.
Physics Subject Headings (PhySH)
Article Text
References (25)
- G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1953).
- K. R. Sreenivasan and R. A. Antonia, The phenomenology of small-scale turbulence, Annu. Rev. Fluid Mech. 29, 435 (1997).
- J. Schumacher, J. D. Scheel, D. Krasnov, D. A. Donzis, V. Yakhot, and K. R. Sreenivasan, Small-scale universality in fluid turbulence, Proc. Natl. Acad. Sci. USA 111, 10961 (2014).
- D. Buaria, A. Pumir, E. Bodenschatz, and P. K. Yeung, Extreme velocity gradients in turbulent flows, New J. Phys. 21, 043004 (2019).
- J. Schumacher, Sub-Kolmogorov-scale fluctuations in fluid turbulence, Europhys. Lett. 80, 54001 (2007).
- S. Stefanov, I. D. Boyd, and C.-P. Cai, Monte Carlo analysis of macroscopic fluctuations in a rarefied hypersonic flow around a cylinder, Phys. Fluids 12, 1226 (2000).
- E. R. Van Driest. Turbulent boundary layer compressible fluids, J. Aeronaut. Sci. 18, 145 (1951).
- E. R. Van Driest, Turbulent boundary layer on a cone in a supersonic flow at zero angle of attack, J. Aeronaut. Sci. 19, 55 (1952).
- H. Tennekes and J. L. Lumley, A First Course in Turbulence (The MIT Press, Cambridge, MA, 1972).
- U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1996).
- G. I. Taylor and A. E. Green, Mechanism of the production of small eddies from large ones, Proc. R. Soc London, Ser. A 158, 499 (1937).
- M. E. Brachet, D. I. Meiron, S. A. Orszag, B. G. Nickel, R. H. Morf, and U. Frisch, Small-scale structure of the Taylor-Green vortex, J. Fluid Mech. 130, 411 (1983).
- G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, 1998).
- A. L. Garcia, Nonequilibrium fluctuations studied by a rarefied gas simulation, Phys. Rev. A 34, 1454 (1986).
- 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).
- M. A. Gallis, T. P. Koehler, and S. J. Plimpton, sparta stochastic particle real time analyzer validation and verification test suite, Sandia Report No. SAND2014-19198 (2014).
- S. J. Plimpton, S. G. Moore, A. Borner, A. K. Stagg, T. P. Koehler, J. R. Torczynski, and M. A. Gallis, DSMC on petascale machines and beyond, Phys. Fluids 31, 086101 (2019).
- G. A. Bird, M. A. Gallis, J. R. Torczynski, and D. J. Rader, Accuracy and efficiency of the sophisticated direct simulation Monte Carlo algorithm for simulating noncontinuum gas flows, Phys. Fluids 21, 017103 (2009).
- M. Howard, A. M. Bradley, S. W. Bova, J. R. Overfelt, R. M. Wagnild, D. J. Dinzl, M. F. Hoemmen, and A. Klinvex, Towards a performance portable compressible CFD code, AIAA-2017-4407 (American Institute of Aeronautics and Astronautics, Reston, VA, 2017).
- J. B. Maeng, T. C. Fisher, and M. H. Carpenter, Generalized entropy stable weighted essentially non-oscillatory finite difference schemes in multi-block domains, AIAA-2019-3205 (American Institute of Aeronautics and Astronautics, Reston, VA, 2019).
- G. V. Candler, H. B. Johnson, I. Nompelis, P. K. Subbareddy, T. W. Drayna, V. Gidzak, and M. D. Barnhardt, Development of the us3d code for advanced compressible and reacting flow simulations, AIAA-2015-1893 (American Institute of Aeronautics and Astronautics, Reston, VA, 2015).
- R. W. MacCormack and G. V. Candler, The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation, Comput. Fluids 17, 135 (1989).
- P. K. Subbareddy and G. V. Candler, A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows, J. Comput. Phys. 228, 1347 (2009).
- 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).
- 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).
