Largeeddy simulations of Richtmyer Meshkov instability in a converging geometry
Abstract
The RichtmyerMeshkov instability (RMI) refers to the baroclinic generation of vorticity at a perturbed density interface when impacted by a shock wave. It is often thought of as the impulsive limit of the RayleighTaylor instability. While the RMI has been widely covered in planar geometries, the present simulations investigate the mixing of materials resulting from the interaction of an imploding cylindrical shock wave with a concentric interface, perturbed in both axial and azimuthal directions, which separates outside air from SF{sub 6} (initially 5 times denser) confined in a 90{sup o} wedge. Two incident shocks of Mach numbers M{sub i} = 1.3 and 2.0 at initial impact are tested. These canonical simulations support recent work on understanding the compressible turbulent mixing in converging geometries relevant to both inertial confinement fusion and corecollapse supernova dynamics. Initial irregularities in the density interface form the misalignment between density and pressure gradients required to initiate a first RMI. A second RMI occurs after the initial shock has converged down the wedge, reflected off the axis and reshocks the distorted interface. Reshock interactions of decreasing intensity follow successively. Due to the converging geometry, the accelerated or decelerated motion of the interface also generates RayleighTaylor instabilities. Secondarymore »
 Authors:

 California Institute of Technology, Pasadena
 ORNL
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 989738
 DOE Contract Number:
 DEAC0500OR22725
 Resource Type:
 Journal Article
 Journal Name:
 Physics of Fluids
 Additional Journal Information:
 Journal Volume: 22; Journal Issue: 9; Journal ID: ISSN 10706631
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AIR; GEOMETRY; INERTIAL CONFINEMENT; INSTABILITY; MACH NUMBER; MIXTURES; NAVIERSTOKES EQUATIONS; PRESSURE GRADIENTS; RAYLEIGHTAYLOR INSTABILITY; SCALARS; SHOCK WAVES; SIMULATION; TRANSPORT; TURBULENT FLOW; WAVELENGTHS
Citation Formats
Lombardini, Manuel, and Deiterding, Ralf. Largeeddy simulations of Richtmyer Meshkov instability in a converging geometry. United States: N. p., 2010.
Web. doi:10.1063/1.3491373.
Lombardini, Manuel, & Deiterding, Ralf. Largeeddy simulations of Richtmyer Meshkov instability in a converging geometry. United States. doi:10.1063/1.3491373.
Lombardini, Manuel, and Deiterding, Ralf. Fri .
"Largeeddy simulations of Richtmyer Meshkov instability in a converging geometry". United States. doi:10.1063/1.3491373.
@article{osti_989738,
title = {Largeeddy simulations of Richtmyer Meshkov instability in a converging geometry},
author = {Lombardini, Manuel and Deiterding, Ralf},
abstractNote = {The RichtmyerMeshkov instability (RMI) refers to the baroclinic generation of vorticity at a perturbed density interface when impacted by a shock wave. It is often thought of as the impulsive limit of the RayleighTaylor instability. While the RMI has been widely covered in planar geometries, the present simulations investigate the mixing of materials resulting from the interaction of an imploding cylindrical shock wave with a concentric interface, perturbed in both axial and azimuthal directions, which separates outside air from SF{sub 6} (initially 5 times denser) confined in a 90{sup o} wedge. Two incident shocks of Mach numbers M{sub i} = 1.3 and 2.0 at initial impact are tested. These canonical simulations support recent work on understanding the compressible turbulent mixing in converging geometries relevant to both inertial confinement fusion and corecollapse supernova dynamics. Initial irregularities in the density interface form the misalignment between density and pressure gradients required to initiate a first RMI. A second RMI occurs after the initial shock has converged down the wedge, reflected off the axis and reshocks the distorted interface. Reshock interactions of decreasing intensity follow successively. Due to the converging geometry, the accelerated or decelerated motion of the interface also generates RayleighTaylor instabilities. Secondary KelvinHelmholtz instabilities develop along the sides of the interpenetrating fingering structures. The energetic reshock produces a large dynamical range of turbulent scales, requiring the utilization of largeeddy simulation (LES). We employed the stretchedvortex subgridscale model of turbulent and scalar transport based on an explicit structural modeling of smallscale dynamics. The imploding nature of the flow is particularly suitable for the use of adaptive mesh refinement (AMR) provided by the parallel blockstructured AMR framework AMROC. The Favrefiltered NavierStokes equations are solved on each Cartesian uniform subgrid of the mesh hierarchy. A weighted, essentially nonoscillatory scheme is used to capture discontinuities but reverts to a lownumerical dissipation, explicit, tuned centerdifference stencil in the smooth or turbulent flow regions, optimal for the functioning of our explicit LES. The computational domain is discretized with 95 x 95 x 64 cubic cells on the base grid (64 points in the periodic axial direction), with three additional levels of refinement based on the local density gradient, reducing the computational expenses compared to the equivalent finest unigrid 760 x 760 x 512 problem. The interpenetration of the two fluids after the reshock is clearly discernible in Fig. 1. The mixing is visualized by using isosurfaces of the heavyfluid mass fraction {psi}. The mixture is colored red as {psi} = 0.90, yellow as {psi} = 0.5, and green as {psi} = 0.1. To illustrate the multiscale nature of the turbulent mixing, we observe that the initial perturbation wavelength is 100 times larger than the finest grid size, which is itself about 100 times larger than the estimated smallest physical scale in the flow  the Kolmogorov scale  where the viscous dissipation of energy occurs. Incident shocks of higher Mach number (e.g., M{sub i} = 2.0) focus the flow further towards the axis, leading to a stronger turbulent mixing.},
doi = {10.1063/1.3491373},
journal = {Physics of Fluids},
issn = {10706631},
number = 9,
volume = 22,
place = {United States},
year = {2010},
month = {1}
}