Experimental study of the interaction of a strong shock with a spherical density inhomogeneity H. F. Robey 1 , T. S. Perry 1 , R. I. Klein 1, 2 , J. A. Greenough 1 , H. Louis 1 , P. Davis 1 , J. O. Kane 1 , T. R. Boehly 3 1 Lawrence Livermore National Laboratory, Livermore, California 94550 2 U. C. Berkeley, Department of Astronomy 3 Laboratory for Laser Energetics, University of Rochester, Rochester, NY Presented at the 8 th 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 Incident Reflected Shock Shock air R22 Refracted Shock Shocked R22 Vortex ring From M = 1.2 shock tube experiments of Haas & Sturtevant, JFM 181, 41 (1987)
Once formed, a vortex ring is subject to a 3D azimuthal bending mode instability time Mode number, n vs. non-dimensional ~ ring translation velocity, V 15 Constant vorticity Distributed vorticity Experiment 10 n 5 from: Widnall, Bliss, & Tsai, JFM 66(1), 35 (1974). 2.0 2.5 3.0 3.5 4.0 ƒ = − Γ Γ V ln (8R/a) 1/4 Γ Γ The mode number is a function of the ring radius R and thickness a R 2a
Outline • Background / motivation • Omega Experimental Results • Numerical simulations • Conclusions
The Omega experiments are conducted in a very small Beryllium shock tube 2D slice through target 3D view of target Support stalk Au Grid Face-on backlighter Side-on Laser 800 µm CH backlighter Reference Alignment Beryllium tube grids fibers Beryllium (1500µm) shield Cu sphere (120 µm diameter)
Multiple beams of the Omega laser are used to both drive the strong shock and diagnose the interaction Side-on backlighter Target CAD drawing with beams Omega beam orientations Face-on backlighter beams Drive beams 10 beams @ 500J ~ 600 µm spot
Simultaneous side-on and face-on images of shock / sphere interaction with 120 µm diameter Cu sphere Shock # 19728 # 19736 # 19732 # 20637 # 20645 t = 13 ns t = 26 ns t = 39 ns t = 52 ns t = 78 ns Omega data of April, 2000 Omega data of Aug 2-3, 2000
Simultaneous side-on and face-on images of shock / sphere interaction with 240 µm diameter Cu sphere # 20627 # 20629 # 20643 # 20647 t = 27 ns t = 54 ns t = 78 ns t = 105 ns Omega data of Aug 2-3, 2000
Large-scale features appear repeatable from shot-to-shot, but small-scale details differ # 19731 # 19732 t= 39 ns t= 39 ns V-backlighter Fe-backlighter
The two orthogonal diagnostic views help to reveal the 3D morphology of this flow Illustration of 3D morphology Inner Outer 100 µm ring ring Inner ring ≈ 5 ≈ mode ≈ ≈ Outer ring ≈ ≈ 15 mode ≈ ≈
Analysis of Omega shock / sphere data quantifies the three-dimensional instability and breakup of the sphere inner outer inner ring Azimuthally averaged radial lineout outer ring 0 80 160 r (µm) Azimuthal lineout Azimuthal lineout through inner ring through outer ring 0 π 2π 0 π 2π 0 π 2π θ θ Spectrum of inner Spectrum of outer azimuthal lineout azimuthal lineout 1 10 100 1 10 100 Mode number Mode number From Robey et al., submitted to PRL (May, 2001)
Mode number spectra from face-on images of shock / sphere interaction reveal a dominant azimuthal mode Background line-outs # 19732 # 19732 Power spectrum of circular line-out Power spectrum of circular line-out through central feature (r=50 µm) through outer feature (r=127 µm) Inner line-out Outer line-out Background Background Mode number Mode number
The observed azimuthal mode number agrees well with the prediction from Widnall’s theory Mode number, n vs. non-dimensional ~ ring translation velocity, V Predicted Mode = 14-17 15 Constant vorticity Distributed vorticity 10 # 19732 n 5 Power spectrum of circular line-out through outer feature (r=127 µm) Observed peak at 15 2.0 2.5 3.0 3.5 4.0 ƒ V = ln (8R/a) − 1/4 ~ From azimuthal a = 20 µm Outer line-out V = 3.67 lineouts R = 127 µm Background Mode number
SNR should be greatly improved using a backlit pinhole due to greatly decreased pinhole-to-target distance 4 mm Pinhole-to-target, u = 64 mm Vanadium BL (6x magnification) Pinhole 8 mm 6 mm Pinhole-to-target u = 5.5 mm 2 mil Be # photons / resolution element ~ u -2 , and SNR = √ √ # photons √ √ filter Backlit pinhole increases SNR by factor of 11
We have begun investigating the ability to seed the azimuthal instability with machined initial perturbations Face-on view using point projection backlighting Machined Cu sphere With mode 16 perturbation Shocked sphere 120 µm Beryllium tube Shot #24527
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 Simulated radiograph of side-on view face-on view Inner ring Transparent Transparent Outer ring bubble bubble Simulations by J. A. Greenough
Mode number spectra of the experimental and the AMR face-on images are in good agreement Experiment AMR simulation # 19732 Power spectrum of circular line-out through outer portion of ring Outer line-out Background Mode number Mode number
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 orthogonal 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
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