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Research Papers: Fundamental Issues and Canonical Flows

Turbulent Transport at High Reynolds Numbers in an Inertial Confinement Fusion Context

[+] Author and Article Information
J. Melvin, R. Kaufman, H. Lim, Y. Yu

Department of Applied
Mathematics and Statistics,
Stony Brook University,
Stony Brook, NY 11794

P. Rao

Department of Applied
Mathematics and Statistics,
Stony Brook University,
Stony Brook, NY 11794
e-mail: prao@ams.sunysb.edu

J. Glimm

Department of Applied
Mathematics and Statistics,
Stony Brook University,
Stony Brook, NY 11794
e-mail: glimm@ams.sunysb.edu

D. H. Sharp

Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: dcso@lanl.gov

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 16, 2013; final manuscript received April 6, 2014; published online July 9, 2014. Assoc. Editor: Stuart Dalziel.

J. Fluids Eng 136(9), 091206 (Jul 09, 2014) (6 pages) Paper No: FE-13-1087; doi: 10.1115/1.4027382 History: Received February 16, 2013; Revised April 06, 2014

Mix is a critical input to hydro simulations used in modeling chemical or nuclear reaction processes in fluids. It has been identified as a possible cause of performance degradation in inertial confinement fusion (ICF) targets. Mix contributes to numerical solution uncertainty through its dependence on turbulent transport coefficients, themselves uncertain and even controversial quantities. These coefficients are a central object of study in this paper, carried out in an Richtmyer–Meshkov unstable circular two-dimensional (2D) geometry suggested by an ICF design. We study a pre-turbulent regime and a fully developed regime. The former, at times between the first shock passage and reshock, is characterized by mixing in the form of interpenetrating but coherent fingers and the latter, at times after reshock, has fully developed turbulent structures. This paper focuses on the scaling of spatial averages of turbulence coefficients under mesh refinement and under variation of molecular viscosity [i.e., Reynolds number (Re)]. We find that the coefficients scale under mesh refinement with a power of spatial grid spacing derived from the Kolmogorov 2/3 law, especially after reshock. We document the dominance of turbulent over molecular transport and convergence of the turbulent transport coefficients in the infinite Re limit. The transport coefficients do not coincide for the pre- and post-reshock flow regimes, with significantly stronger transport coefficients after reshock.

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Figures

Grahic Jump Location
Fig. 2

Fractional mesh error for dimensionless turbulent transport coefficients, comparing coarse to fine (I–III) and medium to fine (II–III) grids, plotted versus Re. Left: Before reshock. Right: After reshock. Curves labeled 1, 2, 3 denote inverse isotropic viscosity, Schmidt number, and Prandtl number, respectively. The dashed-dotted line denotes the error in the comparison I–III and the solid line denotes the error in the comparison II–III.

Grahic Jump Location
Fig. 3

Re dependence of mean turbulent transport coefficients for a Richtmyer–Meshkov instability. Fractional variation for each of the four-dimensional transport coefficients, plotted as χturb(Re)/χturb(Re≈∞) versus Re, using the finest grid level. Left: Before reshock. Right: After reshock. Curves labeled 0, 1, 2, 3 denote anisotropic viscosity, isotropic viscosity, species diffusivity, and thermal diffusivity shown as a fraction of the values of these parameters at Re≈∞ and plotted versus the Reynolds number.

Grahic Jump Location
Fig. 4

Turbulent transport as a fraction of total transport plotted versus Re for each of four mean transport coefficients, with data taken at the fine grid level. Left: Before reshock. Right: After reshock. Curves labeled 0, 1, 2, 3 denote anisotropic viscosity, isotropic viscosity, species diffusivity, and thermal diffusivity, respectively, as a fraction of total transport.

Grahic Jump Location
Fig. 1

Log-log energy spectrum plots versus wave number. The reference lines have slopes k-5/3 (dashed) and k-3 (dashed-dotted). Left: Pre-reshock. Right: Post-reshock.

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