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Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments
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10.1063/1.3555635
/content/aip/journal/pof2/23/3/10.1063/1.3555635
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/3/10.1063/1.3555635

Figures

Image of FIG. 1.
FIG. 1.

Top frame: Evolution of the scaled kinetic energy dissipation for the Taylor–Green vortex based on DNS data (Refs. 14 and 15). Middle frame: Comparative evolution of the scaled kinetic energy dissipation for the Taylor–Green vortex based on RAGE and DNS data (Refs. 14 and 15). Bottom frame: Comparative evolution of the mean enstrophy and scaled kinetic energy dissipation for the Taylor–Green vortex based on RAGE simulation data at various grid resolutions.

Image of FIG. 2.
FIG. 2.

Typical planar shock-tube computational domain; lengths in m.

Image of FIG. 3.
FIG. 3.

Visualization of the initial interface conditions tested in terms of distributions of the mass-fraction: (a) , (b) , (c) no IC perturbation, (d) weighted-short perturbation emulating the ICs in Ref. 6.

Image of FIG. 4.
FIG. 4.

Schematic describing the wavelength content of the tested IC perturbations (Table I); corresponds to the fundamental component of the egg-crate mode.

Image of FIG. 5.
FIG. 5.

Shock-interface diagram for a representative planar shock-tube simulation; the dark and light blue traces indicate the center and approximate edges of the mixing layer as specified in terms of by maximum and 1% value locations, respectively.

Image of FIG. 6.
FIG. 6.

Isosurfaces of the local mixedness function at , 4, 6, and 8 ms for the short, long, and no-perturbation cases at the 0.1 cm resolution.

Image of FIG. 7.
FIG. 7.

Volume renderings of the vorticity magnitude at for the short (top) and long (bottom) perturbation cases at the 0.1 cm resolution.

Image of FIG. 8.
FIG. 8.

Variation of the 3D mixing-layer thickness as a function of time vs IC perturbation spectral content for the baseline of 0.1 cm grid resolution vs laboratory (Ref. 10) results.

Image of FIG. 9.
FIG. 9.

Top frame: shows the 3D mixing zone width evolution before reshock for different IC spectral content. Lower frame: shows the 3D mixing zone width evolution after reshock for different IC spectral content.

Image of FIG. 10.
FIG. 10.

“Figure 4” from Ref. 11: computed shocked mixing-layer width with nonperturbed egg-crate mode vs grid resolution. The coarsest simulation in Ref. 11 used more than cells per characteristic scale —compared to in present and recent (Refs. 6 and 12) studies.

Image of FIG. 11.
FIG. 11.

Spectral characteristics of the egg-crate function : Frame on left: resolved (BEC) for the 0.1 cm grid, transverse stencil (left); frame on right: a similar analysis of a coarsened egg-crate mode (BCEC) definition is shown on the right, where the arrows indicate the cutoffs for the 0.1, 0.05, and 0.025 cm grids.

Image of FIG. 12.
FIG. 12.

Top frame shows 2D computed shocked mixing-layer width with nonperturbed BEC egg-crate mode vs grid resolution. Bottom frame shows 2D computed shocked mixing-layer width with nonperturbed BCEC egg-crate mode vs grid resolution.

Image of FIG. 13.
FIG. 13.

2D and 3D variation of mixing-layer thickness as a function of time vs resolution for the weighted-short perturbation case vs laboratory (Ref. 10) results.

Image of FIG. 14.
FIG. 14.

IC effects on time-series of mass-weighted enstrophy.

Image of FIG. 15.
FIG. 15.

IC effects on time-series of integrated turbulent kinetic energy.

Image of FIG. 16.
FIG. 16.

Top frame: Time dependent spectra of the turbulent kinetic energy vs resolution for the weighted-short case (left: 0.1 cm grid; right: 0.05 cm grid). Lower frame: Time dependent spectra of the variance of the mass-density vs resolution for the weighted-short case (left: 0.1 cm grid; right: 0.05 cm grid).

Image of FIG. 17.
FIG. 17.

PDFs of characteristic velocity functions for the short perturbed case: (a) longitudinal velocity derivatives, (b) transverse velocity derivatives, (c) vorticity magnitude, (d) PDFs of (air side), (e) PDFs of ( side); colors correspond to the same times as in Fig. 16; the time-dependent root-mean-square of the vorticity magnitude is used as scale in (a)–(c).

Image of FIG. 18.
FIG. 18.

Effects of grid resolution on late-time results for the short perturbation case : (a) PDFs of longitudinal velocity derivatives; (b) PDFs of transverse velocity derivatives ; (c) PDFs of the vorticity magnitude; (d) PDFs of for air side (solid) and side (dashed); the reference PDFs in (a)–(c) are based on the DNS data of incompressible isotropic turbulence (Ref. 25).

Image of FIG. 19.
FIG. 19.

Effects of grid resolution on late-time results for the short perturbation case (); comparative visualizations of local normalized mixedness function for 0.1 cm (top) and 0.05 cm (bottom) resolutions, as viewed from the air side (left) and side (right), respectively.

Image of FIG. 20.
FIG. 20.

Effects of grid resolution on late-time results for the short perturbation case ; comparative visualizations of vorticity magnitude for 0.1 cm (top) and 0.05 cm (bottom) resolutions.

Image of FIG. 21.
FIG. 21.

Total, solenoidal, and compressible velocity spectra for the short IC case at , based on and data slabs around the mixing layer, for the 0.1 cm (left) and 0.05 cm (right) resolutions, respectively; units of are in .

Image of FIG. 22.
FIG. 22.

Diagonal anisotropy tensor values at ; results corresponding to the short (top frame) and long (middle frame) perturbation cases are shown for the baseline of 0.1 cm resolution; results for the short perturbation case at 0.05 cm resolution are shown on (bottom frame). The corresponding cross-stream averaged mixedness is superimposed for reference in all cases.

Tables

Generic image for table
Table I.

Planar shock-tube simulations.

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/content/aip/journal/pof2/23/3/10.1063/1.3555635
2011-03-31
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/3/10.1063/1.3555635
10.1063/1.3555635
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