A Comparison of Three Approaches to Compute the Effective Reynolds Number of the Implicit Large-Eddy Simulations

The Implicit large-eddy simulations (ILES) have been utilized as an effective approach for calculating many complex flows at high Reynolds number flows. Richtmyer–Meshkov (RM) instability induced flow can be viewed as a homogeneous decaying turbulence (HDT) after the passage of the shock. In this article, a critical evaluation of three methods for estimating the effective Reynolds number and the effective kinematic viscosity is undertaken utilizing high resolution ILES data. Effective Reynolds numbers based on the vorticity and kinetic energy decay rate, or the integral length and dissipation scale are found to be the most self-consistent when compared to the expected phenomenology and wind tunnel experiments.

[1]  S. Oughton,et al.  Nonlocality and the critical Reynolds numbers of the minimum state magnetohydrodynamic turbulence , 2011 .

[2]  Non-spherical core collapse supernovae - II. The late-time evolution of globally anisotropic neutrino-driven explosions and their implications for SN 1987 A , 2005, astro-ph/0511369.

[3]  M. Hussaini,et al.  Eddy viscosity and diffusivity modeling , 2005 .

[4]  Ben Thornber,et al.  Steady Turbulent Flow Computations Using a Low Mach Fully Compressible Scheme , 2014 .

[5]  F. Grinstein,et al.  Monotonically integrated large eddy simulation of free shear flows , 1999 .

[6]  Ye Zhou,et al.  A scaling analysis of turbulent flows driven by Rayleigh–Taylor and Richtmyer–Meshkov instabilities , 2001 .

[7]  R. D. Richtmyer.  Taylor instability in shock acceleration of compressible fluids , 1960 .

[8]  Katepalli R. Sreenivasan,et al.  An update on the energy dissipation rate in isotropic turbulence , 1998 .

[9]  J. Domaradzki,et al.  Effective eddy viscosities in implicit modeling of decaying high Reynolds number turbulence with and without rotation , 2005 .

[10]  P. Dmitruk,et al.  Colloquium: Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas , 2004 .

[11]  C. Meneveau,et al.  Decay of homogeneous, nearly isotropic turbulence behind active fractal grids , 2012 .

[12]  Ben Thornber,et al.  Energy transfer in the Richtmyer-Meshkov instability. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  P. Sagaut.  Large Eddy Simulation for Incompressible Flows , 2001 .

[14]  J. Lindl,et al.  Inertial Confinement Fusion: The Quest for Ignition and Energy Gain Using Indirect Drive , 1998 .

[15]  Seyed G. Saddoughi,et al.  Local isotropy in turbulent boundary layers at high Reynolds number , 1994, Journal of Fluid Mechanics.

[16]  P. Woodward,et al.  Three-dimensional simulation of a Richtmyer-Meshkov instability with a two-scale initial perturbation , 2002 .

[17]  R. A. Antonia,et al.  THE PHENOMENOLOGY OF SMALL-SCALE TURBULENCE , 1997 .

[18]  D. Meiron,et al.  Transition to turbulence in shock-driven mixing: a Mach number study , 2011, Journal of Fluid Mechanics.

[19]  Y. Kaneda,et al.  Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation , 2009 .

[20]  Dimitris Drikakis,et al.  On the implicit large eddy simulations of homogeneous decaying turbulence , 2007, J. Comput. Phys..

[21]  Ye Zhou.  Degrees of locality of energy transfer in the inertial range. [Kolmogoroff notion in turbulence theory] , 1993 .

[22]  B. Olson,et al.  Large eddy simulation requirements for the Richtmyer-Meshkov instability , 2013, 1402.2665.

[23]  Ye Zhou,et al.  Renormalization group theory for fluid and plasma turbulence , 2009 .

[24]  Timothy T. Clark,et al.  Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers , 2004 .

[25]  F. Grinstein,et al.  Estimating the effective Reynolds number in implicit large-eddy simulation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Nikos Nikiforakis,et al.  ANALYSIS OF IMPLICIT LES METHODS , 2008 .

[27]  Martin Oberlack.  On the decay exponent of isotropic turbulence , 2002 .

[28]  Mitsuo Yokokawa,et al.  Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box , 2003 .

[29]  D. Drikakis,et al.  The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability† , 2010, Journal of Fluid Mechanics.

[30]  P. Dimotakis.  The mixing transition in turbulent flows , 2000, Journal of Fluid Mechanics.

[31]  Ben Thornber,et al.  Growth of a Richtmyer-Meshkov turbulent layer after reshock , 2011 .

[32]  Giacomo Castiglioni,et al.  A numerical dissipation rate and viscosity in flow simulations with realistic geometry using low-order compressible Navier–Stokes solvers , 2015 .

[33]  A. S. Monin,et al.  Statistical Fluid Mechanics: The Mechanics of Turbulence , 1998 .

[34]  P. Smolarkiewicz,et al.  Effective eddy viscosities in implicit large eddy simulations of turbulent flows , 2003 .

[35]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .

[36]  L. J. Atherton,et al.  Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility , 2010 .

[37]  Gregory Falkovich,et al.  Bottleneck phenomenon in developed turbulence , 1994 .

[38]  Andris M. Dimits,et al.  Progress in understanding turbulent mixing induced by Rayleigh–Taylor and Richtmyer–Meshkov instabilities , 2003 .

[39]  Ben Thornber,et al.  Accuracy of high‐order density‐based compressible methods in low Mach vortical flows , 2014 .

[40]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[41]  C. G. Speziale,et al.  Advances in the Fundamental Aspects of Turbulence: Energy Transfer, Interacting Scales, and Self-Preservation in Isotropic Decay , 1998 .

[42]  P. Saffman.  The large-scale structure of homogeneous turbulence , 1967, Journal of Fluid Mechanics.

[43]  Y. Zhou,et al.  Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations , 2006 .

[44]  Ye Zhou.  A PHENOMENOLOGICAL TREATMENT OF ROTATING TURBULENCE , 1995 .

[45]  G. Batchelor,et al.  The theory of homogeneous turbulence , 1954 .

[46]  G. Batchelor,et al.  The large-scale structure of homogenous turbulence , 1956, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[47]  Nikolaus A. Adams,et al.  Assessing the numerical dissipation rate and viscosity in numerical simulations of fluid flows , 2015 .

[48]  Daniel Livescu,et al.  Computational Studies of Two-Dimensional Rayleigh-Taylor Driven Mixing for a Tilted-Rig , 2014 .

[49]  B. Fryxell,et al.  Instability and clumping in SN 1987A , 1991 .

[50]  E. Meshkov.  Instability of the interface of two gases accelerated by a shock wave , 1969 .

[51]  Ben Thornber,et al.  An Investigation Into Nonlinear Growth Rate of Two-Dimensional and Three-Dimensional Single-Mode Richtmyer–Meshkov Instability Using an Arbitrary-Lagrangian–Eulerian Algorithm , 2014 .

[52]  S Hickel,et al.  Evolution of length scales and statistics of Richtmyer-Meshkov instability from direct numerical simulations. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Ye Zhou.  Interacting scales and energy transfer in isotropic turbulence , 1993 .

[54]  R. J. R. Williams,et al.  An improved reconstruction method for compressible flows with low Mach number features , 2008, J. Comput. Phys..

[55]  H. Robey,et al.  Onset of turbulence in accelerated high-Reynolds-number flow. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.