Experimental study of the interaction of a strong shock with a - - PowerPoint PPT Presentation

Experimental study of the interaction of a strong shock with a spherical density inhomogeneity

• H. F. Robey1, T. S. Perry1, R. I. Klein1, 2, J. A. Greenough1,
• H. Louis1, P. Davis1, J. O. Kane1, T. R. Boehly3

1Lawrence Livermore National Laboratory, Livermore, California 94550

• 2U. C. Berkeley, Department of Astronomy

3Laboratory for Laser Energetics, University of Rochester, Rochester, NY

Presented at the 8th Meeting of the International Workshop on the Physics of Compressible Turbulent Mixing Pasadena, CA December 9-14, 2001

This work was performed under the auspices of the U. S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.

Summary

• Experiments have been conducted on the Omega Laser to

study the interaction of a strong shock (M>10) with a spatially localized density inhomogeneity (Cu sphere)

• The interaction is diagnosed with x-ray radiography

simultaneously from two orthogonal directions

• The evolution of the shocked sphere is observed to proceed

as an initial roll-up into a double vortex ring structure followed by the appearance of an azimuthal instability which ultimately results in the three-dimensional breakup of the sphere.

• Numerical simulations are performed in both two and three-

dimensions, and results are in good agreement with experiment.

Outline

• Background / motivation
• Omega Experimental Results
• Numerical simulations
• Conclusions

These experiments recreate in a controlled setting the interaction of a strong shock with a dense molecular cloud

From Fesen el al., Ap.J. 262, 171 (1982): “The Cygnus Loop is the classic example of a moderately old supernova remnant (SNR). its structure and physical properties are the result of a supernova-generated shock wave interacting with the surrounding interstellar medium.” “Comparisons with published shock models indicate significant differences between the models and observations …”

The interaction of a shock with a dense spherical inhomogeneity has previously been studied only at low mach number

From M = 1.2 shock tube experiments of Haas & Sturtevant, JFM 181, 41 (1987) Vortex ring Incident Shock Reflected Shock Refracted Shock

air R22

Shocked R22

Once formed, a vortex ring is subject to a 3D azimuthal bending mode instability

time

2a R

2.0 2.5 3.0 3.5 4.0 5 10 15 ƒ V (8R/a) 1/4 = − ln n Constant vorticity Distributed vorticity Experiment

Mode number, n vs. non-dimensional ring translation velocity, V

~

from: Widnall, Bliss, & Tsai, JFM 66(1), 35 (1974).

The mode number is a function of the ring radius R and thickness a Γ Γ Γ Γ

Outline

• Background / motivation
• Omega Experimental Results
• Numerical simulations
• Conclusions

The Omega experiments are conducted in a very small Beryllium shock tube

Laser Beryllium shield Beryllium tube (1500µm) Au Grid Cu sphere (120 µm diameter) CH Side-on backlighter Face-on backlighter Alignment fibers Reference grids Support stalk

3D view of target 2D slice through target

800 µm

Multiple beams of the Omega laser are used to both drive the strong shock and diagnose the interaction

Drive beams 10 beams @ 500J ~ 600 µm spot Side-on backlighter beams Face-on backlighter beams Target CAD drawing with Omega beam orientations

Simultaneous side-on and face-on images of shock / sphere interaction with 120 µm diameter Cu sphere

t = 52 ns t = 39 ns t = 26 ns t = 78 ns Omega data of April, 2000

# 19736 # 19732 # 20637 # 20645

Omega data of Aug 2-3, 2000 t = 13 ns

# 19728 Shock

Simultaneous side-on and face-on images of shock / sphere interaction with 240 µm diameter Cu sphere

t = 78 ns t = 54 ns t = 27 ns t = 105 ns Omega data of Aug 2-3, 2000

# 20627 # 20629 # 20643 # 20647

Large-scale features appear repeatable from shot-to-shot, but small-scale details differ

t= 39 ns V-backlighter # 19731 t= 39 ns Fe-backlighter # 19732

The two orthogonal diagnostic views help to reveal the 3D morphology of this flow

100 µm

Illustration of 3D morphology

Inner ring Outer ring Inner ring mode ≈ ≈ ≈ ≈ 5 Outer ring mode ≈ ≈ ≈ ≈ 15

θ Mode number Mode number 0 π 2π 0 π 2π 1 10 100 1 10 100 0 80 160 0 π 2π θ r (µm)

Analysis of Omega shock / sphere data quantifies the three-dimensional instability and breakup of the sphere

Azimuthally averaged radial lineout From Robey et al., submitted to PRL (May, 2001) Azimuthal lineout through outer ring Spectrum of outer azimuthal lineout Azimuthal lineout through inner ring Spectrum of inner azimuthal lineout inner ring

• uter ring

inner

• uter

Mode number spectra from face-on images of shock / sphere interaction reveal a dominant azimuthal mode

# 19732 # 19732 Power spectrum of circular line-out through central feature (r=50 µm) Power spectrum of circular line-out through outer feature (r=127 µm) Mode number Mode number Inner line-out Background Background line-outs Outer line-out Background

The observed azimuthal mode number agrees well with the prediction from Widnall’s theory

# 19732 Power spectrum of circular line-out through outer feature (r=127 µm) Mode number Outer line-out Background

2.0 2.5 3.0 3.5 4.0 5 10 15 ƒ V (8R/a) 1/4 = − ln n Constant vorticity Distributed vorticity

Mode number, n vs. non-dimensional ring translation velocity, V

~

a = 20 µm R = 127 µm V = 3.67

~

From azimuthal lineouts Predicted Mode = 14-17 Observed peak at 15

SNR should be greatly improved using a backlit pinhole due to greatly decreased pinhole-to-target distance

4 mm 6 mm 8 mm Pinhole-to-target, u = 64 mm (6x magnification) Pinhole-to-target u = 5.5 mm # photons / resolution element ~ u -2, and SNR = √ √ √ √ # photons Backlit pinhole increases SNR by factor of 11 Vanadium BL Pinhole 2 mil Be filter

We have begun investigating the ability to seed the azimuthal instability with machined initial perturbations

Face-on view using point projection backlighting Shot #24527

Machined Cu sphere With mode 16 perturbation

120 µm Shocked sphere Beryllium tube

Outline

• Background / motivation
• Omega Experimental Results
• Numerical simulations
• Conclusions

2D simulations of the experiment performed with CALE predict the basic evolution of the sphere into a vortex ring

t= 10 ns t= 20 ns t= 30 ns t= 40 ns t= 50 ns t= 60 ns

Simulations by J. O. Kane

3D simulations of the experiment have been performed with an AMR code

Simulated radiograph of side-on view Transparent bubble Outer ring Simulated radiograph of face-on view Inner ring Transparent bubble

Simulations by J. A. Greenough

Mode number spectra of the experimental and the AMR face-on images are in good agreement

# 19732 Power spectrum of circular line-out through outer portion of ring Mode number Outer line-out Background Mode number

AMR simulation Experiment

Conclusion

• Experiments have been conducted on the Omega laser to explore

the interaction of a strong shock with a dense sphere

• The experiment has been diagnosed simultaneously from two
• rthogonal directions
• The experimentally observed azimuthal mode number is in good

agreement with both incompressible theory of Widnall and 3D numerical simulations.

• Future work will focus on shock interaction with less-dense objects

and interactions with multiple objects