Experimental Study of a Strongly Shocked Gas Interface with Visualized Initial Conditions 8th International Workshop on the Physics of Compressible Turbulent Mixing California Institute of Technology, Pasadena, California, USA, Dec. 9-14, 2001 n i I s n n s o t Mark Anderson, i c t Jason Oakley, s u i W t Bhalchandra Puranik, e Riccardo Bonazza O s m f e N t u s c y l S e r Department of Engineering Physics a University of Wisconsin –Madison I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
2 Outline • University of Wisconsin Shock-Tube Laboratory (WiSTL) • Interface preparation • Shocked interfaces • Comparisons with non-linear theories • Conclusions I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
3 WiSTL (Wisconsin Shock Tube Laboratory) · Vertical Orientation Driver · Large Internal Square Cross-Section (25 cm square) Second Floor · Total Length=9.2 m Driven Length=6.8 m · Structural Capacity 20 Mpa Diaphragm · Modular Construction Section First Floor Interface Section 45.72 cm 25.4 cm T est Section B asement I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
4 Interface Preparation • Use of a retractable metal plate formed into a sinusoidal shape • Copper plate, 0.6 mm thick • Plastic deformation by rolling operation • Sine wave parameters: - Amplitude = 3.18 mm - Wavelength = 38.1 mm - η 0 / λ = 0.083 Rollers Formed plate I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
5 Study of initial conditions • P initial = 1 atm, T initial = 298 K • Ar-ion laser @ λ =514 and 488 nm, CW • Planar Mie scattering visualization • CCD camera: 256 x 256 pixel array, 8 bit/pixel • Two-stage retraction ( τ 1 ~ 250 ms, τ 2 ~ 80 ms) I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
6 RT Unstable Interface (CO 2 /Air) CO 2 Air seeded with smoke I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
7 Desired τ RT < 120 ms for RM Initial Condition CO 2 Air 0 ms 10 ms 20 ms 30 ms 40 ms 50 ms 60 ms 70 ms 80 ms 90 ms 100 ms 110 ms 120 ms 140 ms 160 ms 180 ms 200 ms 220 ms I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
8 R-M instability visualization results • CO 2 /Air, A post = 0.246, A pre = 0.206 •Very early interaction of the M=3.06 shock wave with the sinusoidal interface • Development of phase reversal (heavy/light configuration) CO 2 Air (a) (b) (c) (d) • (a): Pre-shocked interface (Note the location of peaks and troughs) • (b): Shocked interface ~ 5 µ s after initial shock acceleration • (c): Shocked interface ~ 36 µ s after initial shock acceleration • (d): Shocked interface ~ 39 µ s after initial shock acceleration I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
9 R-M instability visualization results (Cont’d) I.C. 0s 1.37 ms 1.08 ms 0.64 ms 1.80 ms 2.1 ms • Evolution of interface growth for the same nominal initial condition. • Each image was taken in a separate experiment with a M~3.06 shock. • Initial condition inferred from time of shock interaction and RT experiments. I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
10 Experiments: Image Analysis • Images – Initial condition: 3 peaks, 2 troughs – Shocked image: 1-4 peaks, 1-3 troughs – Median filter – Excess noise removed in driven and test gases manually – Convert to black and white, then apply Sobel operator to detect edge • Perturbation amplitude: ( ) 1 η = − − P V 1 P PIX PIX DIM 2 P = average pixel row number of perturbation peaks PIX V = average pixel row number of perturbation valleys PIX P = pixel dimension (mm/pixel) DIM • Error less than 2 pixels: 0.8 mm for initial condition, 0.4 mm for shocked interface I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
11 Analytic theories η = η ( t ) k [ u ] A t Richtmyer (1960) impulsive model: p 0 η η + d d 1 Bt Sadot et al. (1998) nonlinear theory: = + + 2 dt dt 1 Dt Et LIN η 2 d η d ( ) [ ] ( ( ) ( ) ) ′ = ± ′ ′ D 1 A k = ± + × π 2 E 1 A / 1 A 1 / 2 C k b / s b / s dt dt imp imp for low A ′ = π C 1 / 2 Zhang and Sohn (1997) nonlinear theory: η d η d dt = lin 2 dt η η d d total + η + η − + ' 2 ' 2 2 ' 2 2 2 1 k t max{ 0 , k A 1 / 2 } k t 0 0 dt dt lin lin I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
12 Comparison with Theories • Comparison with prediction from nonlinear theories shows qualitative agreement - - - Sadot et al . theory overpredicts at late times − ⋅ ⋅ ⋅ Zhang and Sohn theory underpredicts at all times I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
13 Experiment: Combined Imaging Setup Previously, the RM initial condition was inferred from a reference set of RT experiments. Dynamic imaging of the interface, prior to being shocked, provides interfacial initial condition data for each RM experiment. Provides the interface geometry of the initial condition which may be used in a numerical simulation. I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
14 Experimental conditions • Incident shock wave: M =2.90, in CO 2 • P initial = 1 atm, T initial = 300 K • Post-shock A ′ =0.245 ( A =0.206, A =( ρ 1 - ρ 2 )/( ρ 1 + ρ 2 )) • Planar Mie scattering visualization, smoke particles • Two-stage retraction ( τ 1 ~ 250 ms, τ 2 ~ 80 ms) • Interface section - Ar+ laser @ λ =488 nm, continuous wave - CCD camera, 256 x 256 pixel array, 8 bit/pixel, framing @ 100 fps • Test section - Nd:YAG laser @ λ =532 nm, 10 ns pulse - CCD camera: 1024 x 1024 pixel array, 16 bit/pixel, one shocked image per experiment I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
15 Experiment: CO 2 -air M =2.90 Experiment 322 Experiment 363 Experiment 351 x = 0.457 m x = 0.987 m x = 0.756 m η η = 4.64 mm η = 7.81 mm = 5.90 mm IC IC IC η η = 13.83 mm η = 28.0 mm = 12.3 mm RM RM RM τ τ = 0.70 ms τ = 1.57 ms = 1.13 ms RM RM RM • Initial condition well into nonlinear regime ( η 0 /λ > 0.2) • Phase inversion of shocked interface I s i n n n s o t c i t s Fusion Technology Institute WiSTL W i u t e Wisconsin Institute of Nuclear Systems UW- Madison Nuclear Engr & Engr Physics, University of Wisconsin - Madison O m s f N e t u s c S y l e a r
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