Multi-layered Richtmyer-Meshkov Instability

1
Multi-layered Richtmyer-Meshkov Instability
Pooya Movahed, Prof. Eric Johnsen Department of
Mechanical Engineering, University of Michigan,
Ann Arbor

• Motivation
• The physics of inertial confinement fusion (ICF)
  combine hydrodynamics, plasma physics and
  radiation. One of the important hydrodynamic
  processes in ICF is the Richtmyer-Meshkov
  instability (RMI), which occurs when a shock wave
  interacts with an interface separating different
  fluids1. The RMI reduces the yield of the
  reaction by mixing the ablator with the fuel.
  Through numerical simulations of the
  multi-layered RMI in a shock tube configuration,
  a basic understanding of the role of the RMI and
  mixing in ICF can be achieved.

Single-mode Multi-layered RMI

• Numerical Framework
• The 2D inviscid Euler equations are solved
  numerically.
• Base scheme second-order accurate
  MUSCL-Hancock.
• Interface-capturing scheme Roes approximate
  solver for the conservative variables with a
  ?-based model for the transport equation to
  prevent spurious pressure oscillations2.
• Programming language FORTRAN with MPI for
  intra-node communication (using up to 96 CPUs).

Density
Shock
SF6
Air
Air
Initial conditions A M 1.3 shock wave in air
moves right toward perturbed layer of SF6.
Schlieren
Single-mode RMI
Density

• Objectives
• The goals of the present work are to
• Develop a parallel code capable of simulating
  multi-component flows in a robust and accurate
  fashion.
• Investigate the role of reshock in the
  multi-layered RMI,
• Analyze the accuracy of available analytical
  solutions for the RMI at late times, and
• Investigate vorticity generation at early and
  late times.

Shock
Vorticity
Air
SF6
Before reshock The baroclinic vorticity has
different signs along the top/bottom parts of
the interface and the second interface has gone
through a phase change.
Schlieren
Terminology
Vorticity
The bubble and spike amplitudes ab(t) and as(t)
are the distances from the shocked and
unperturbed interface to the bubble and spike
tips. The spikes penetrate into the lighter fluid
and roll up while bubbles rise into the heavier
fluid.
Comparison of the present numerical results with
different analytical models and experiments by
Jacobs. Normalized growth of the amplitude as a
function of normalized time.
After reshock Mushroom shape structures develop.
Schlieren
The mixing layer amplitude a(t) is the average of
the bubble and spike amplitudes. The
dimenisionless time is ?kv0t, where k is the
wave number of the initial perturbation and v0
is the post-shock Richtmyer velocity.
Vorticity
Vorticity Evolution
Long time after reshock secondary baroclinic
vorticity is produced3.
Density
Circulation versus time for the single-mode RMI
with reshock(t1.8msec).

• Conclusions and Future Work
• Baroclinic vorticity basic mechanism
  determining the growth rate of the bubble and
  spike amplitudes.
• Sharp rise in circulation just after the passage
  of the shock
• - Circulation increases afterwards due to
  secondary vorticity.
• The flow exhibits turbulent characteristics and
  leads to significant mixing at late times.
• To capture the detailed turbulent mixing at late
  time
• Diffusive terms must be included,
• High-order accurate schemes (e.g., WENO) should
  be used to minimize the numerical dissipation.

Baroclinic term
Very late time mixing and turbulence regions
develop.

• References
• M. Brouillette, Annu. Rev. Fluid Mech. 34, 445
  (2002).
• R. Abgrall, J. Comput. Phys. 125, 150 (1996).
• N. J. Zabusky, Annu. Rev. Fluid Mech. 31, 495
  (1999).

1st Annual MPISE Graduate Student Symposium
Conference Ann Arbor, MI, September 29, 2010
Circulation versus time for the single-mode RMI
without resock
Computational Flow Physics
Laboratory