Inertial Confinement Fusion Related Experimental Investigation of a Twice-Shocked Spherical Density
Inhomogeneity.
Nick Haehn, Chris Weber, Jason Oakley, Mark Anderson, Riccardo Bonazza
Department of Engineering Physics, University of Wisconsin-Madison
Visualization
Introduction
Argon bubble in ambient Nitrogen; M = 2.07
Shock-driven hydrodynamic instabilities limit the compression efficiency of fuels related
to Inertial Confinement Fusion. These instabilities increase turbulence and mixing
between the fuel and the capsule by magnifying non-uniformities between the density
interfaces. These non-uniformities create density gradients which are misaligned with
pressure gradients arising from shocks during the ablation of the fuel capsule.
Baroclinic vorticity ((ρ×p)/ρ2  0) is deposited as a result of these pressure and
density gradients, enhancing mixing processes and magnifying the density
perturbations through a phenomena known as Richtmyer-Meshkov Instabilities.
Radiative
heating
Ablation
Compression
Thermonuclear burn
ICF
Shock tube
L scale
10-6 m
10-2 m
T scale
10-9 s
10-6 s
 scale
103 kg/m3
100 kg/m3
M
~30
≤5
A
[-1,1]
[-1,1]
Shock-bubble interactions form a subset of the Richtmyer-Meshkov Instabilites. After
shock, the bubble develops into a vortex ring as a result of the deposited vorticity. After
the vortex ring has developed, it’s translational velocity differs from the shocked particle
velocity behind the shock wave due to the circulation of the ring1,2. After the shock wave
has reflected from the tube end-wall, it traverses the once-shocked vortex ring
(reshock) and deposits additional circulation onto the vortex ring. The present study
displays the diagnostical capabilities of the Wisconsin Shock Tube Laboratory (WiSTL),
including high speed planar imaging and Particle Image Velocimetry (PIV).
Experimental Setup
Wisconsin Shock Tube Laboratory:
• 9.13 m vertical tube
• Pneumatically retracting bubble injector
• 20 MPa impulsive load capability
• False bottom option
• 25.4 × 25.4 cm square internal cross section • Planar laser imaging (Nd:Yag or
• Wall mounted pressure transducers
Ar+ Laser)
-0.2 ms
0.0 ms
1.0 ms
1.2 ms
0.6 ms
0.4 ms
(V )
0.8 ms
Vorticity Field
( )
1.4 ms
1.8 ms
1.6 ms
Results
2.0 ms
Shown below are plots for 5 different Atwood (A) and Mach (M) number
combinations. Plots show a collapse of the data for early non-dimensional times.
Compared to results for once-shocked bubbles, an additional M and A dependence
shows up.
t
 
t
Image sequence for an Ar bubble in N2 impacted by an initial shock wave of strength of Mi = 2.07 and a reflected shock wave of strength
Mr = 1.74. The sequence was recorded at 10,000 fps. Reshock occurs at t = 0.0. The images correspond to a viewing area of 8.3 x 16.6 cm.
Once-Shocked vs. Twice Shocked Bubbles
Shock
Reshock
Do
2
i
2M Ac1
Mixing and
Turbulence
Translating Vortex
Ring
Diffuse Interfaces
Particle Velocity is
zero
Initial Circulation

After Shock
t 
Difference Between
Initial Conditions
Stationary Bubble
Well Defined
Interfaces
No Initial Circulation
Mi
Yre
0.2 ms
Vector Field
A
Particle Velocity is
non-zero
Y
Previous diagnostic methods allowed for geometrical measurements only (vortex
position, streamwise and spanwise dimensions, etc.). The application of PIV
methods allows additional information to be extracted about the flow field, such
as local velocity measurements, vorticity fields and circulations. These values are
critical for validating previously developed models and
 numerical simulations.
Raw Images
No Mixing or
Turbulence
Above Left: The initial shock is imaged with two high speed
cameras to capture the location, shape, size and position with
respect to the imaging laser sheet. The cameras are aligned 90º to
one another and are recorded at 250 fps to capture the time of the
incident shock. Above Right: The initial condition for the reshock
is imaged with planar Mie scattering. Shown left are two sample
initial condition images for separate experiments showing
repeatability. With the high speed imaging experiments, the initial
condition is seen as the shocked vortex ring enters from the top of
the video sequence. Left: After reshock, the particle velocity
behind the reflected shock wave is nearly zero, therefore, any
vortex motion should be primarily a result of circulation. The highspeed imaging offers an excellent way to measure the vortex
velocity and extract experimental circulation values using Kelvin’s
Circulation theorem.
A New Model for Shocked Bubbles
Mr
 Yv  Yre 

d 
Do 

*
Vv 
d
After Reshock
References
1
2
Ranjan, D., “Experimental investigation of primary
and secondary features in high-mach-number
shock-bubble interaction,” Phys. Rev. Lett. 98,
(2007).
Niederhaus, J.H., et al, “A computational parameter
study for the three-dimensional shock-bubble
interaction”, J. Fluid Mech. 594, 85 (2008).
Acknowldegments
Work Partially Supported by:
DOE Grant DE-FG52-06NA26196
NSF Award 0827285