Properties of the Turbulent Mixing Layer in a Spherical Implosion

[+] Author and Article Information
Ismael Boureima

Mechanical Engineering
and Engineering Science,
University of North Carolina at Charlotte,
Charlotte, NC 28223
e-mail: idjibril@uncc.edu

Praveen Ramaprabhu

Mechanical Engineering
and Engineering Science,
University of North Carolina at Charlotte,
Charlotte, NC 28223
e-mail: pramapra@uncc.edu

Nitesh Attal

Convergent Science, Inc.,
Madison, WI 53719
e-mail: nitesh.attal@convergecfd.com

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 15, 2016; final manuscript received May 18, 2017; published online December 22, 2017. Assoc. Editor: Ben Thornber.

J. Fluids Eng 140(5), 050905 (Dec 22, 2017) (8 pages) Paper No: FE-16-1831; doi: 10.1115/1.4038401 History: Received December 15, 2016; Revised May 18, 2017

We describe the behavior of a multimode interface that degenerates into a turbulent mixing layer when subjected to a spherical implosion. Results are presented from three-dimensional (3D) numerical simulations performed using the astrophysical flash code, while the underlying problem description is adopted from Youngs and Williams (YW). During the implosion, perturbations at the interface are subjected to growth due to the Richtmyer–Meshkov (RM) instability, the Rayleigh–Taylor (RT) instability, as well as the Bell–Plesset (BP) effects. We report on several quantities of interest to the turbulence modeling community, including the turbulent kinetic energy (TKE), components of the anisotropy tensor, density self-correlation, and atomic mixing, among others.

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Grahic Jump Location
Fig. 7

Time evolution of the turbulent mixing amplitude W in a spherical implosion. Results from flash are compared with turmoil data from Ref. [18].

Grahic Jump Location
Fig. 6

Radial profiles at different times of (a) <Yinner> and (b) <YinnerYshell>

Grahic Jump Location
Fig. 5

Isosurfaces of the mass fraction corresponding to the 50% level at (a) τ = 0.87, (b) τ = 1.00, (c) τ = 1.08, (d) τ = 1.22, and (e) τ = 1.44

Grahic Jump Location
Fig. 4

Radial trajectories of the 1% and 99% angular-averaged isosurfaces of the mass fraction, plotted from the 3D flash simulations with multimode initial perturbations. Results are compared with data from Ref. [18].

Grahic Jump Location
Fig. 3

Radial trajectories of the unperturbed interface, shocks and boundary from 1D, flash simulations. Results are compared with data from Ref. [18].

Grahic Jump Location
Fig. 1

Problem setup and geometry

Grahic Jump Location
Fig. 8

Time evolution of (a) the maximum molecular mixing thickness δ(t), (b) the total molecular mixing thickness (t), and (c) the atomic mix parameter Θ

Grahic Jump Location
Fig. 9

Cross-stream profiles of the TKE scaled by k0=1/2ρavgΔU2 from flash simulations at different mesh resolutions and plotted at τ = 1.44

Grahic Jump Location
Fig. 10

Cross-stream profiles of diagonal components of the anisotropy tensor at (a) τ = 1.2 (stagnation) and (b) τ = 1.44

Grahic Jump Location
Fig. 11

Cross-stream profiles of (a) the radial normalized turbulent mass flux ar and (b) the density-specific volume correlation b. Both quantities are plotted at τ = 1.44.

Grahic Jump Location
Fig. 2

Contours of the initial perturbation field

Grahic Jump Location
Fig. 12

Compensated kinetic energy spectra obtained from radial locations where Yinner = 50%: (a) τ = 0.77, (b) τ = 0.95, and (c) τ = 1.44



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