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Shock propagation through multiphasemedia
R.J.R. Williams and D.L. Youngs
AWE plc, Aldermaston, UK
IWPCTM9
Cambridge, July 2004
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Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
Cambridge UK Edited by S B Dalziel
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Cambridge UK Edited by S B Dalziel
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Astrophysical multiphase flows
Starburst galaxy M82
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Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
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Astrophysical multiphase flows
Eagle nebula columns
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Astrophysical multiphase flows
Photoionized clumps in the Helix nebula
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Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
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Experimental multiphase flows
Reshock of Richtmyer-Meshkov fingers, e.g. in cylinder mix experi-
ments.
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Some previous numerical studies
Isolated clumps
2D Picone & Boris 88; Cowperthwaite 89; Klein et al 94
3D Stone & Norman 92; Robey et al 02
MHD: Mac Low et al 94 Small clusters: Jun et al 96; Steffen et al 97; Hazak et al 98;
Poludnenko, Frank & Blackman 02; Collins et al 03
Continuum approximations:
Mass loading Hartquist et al 86
Phase drag Youngs; Williams & Dyson 02
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Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
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Experimental comparisons
Shock tube experiments
Ranger & Nicholls 69
Haas & Sturtevant 87 Philpott et al 92
Laser driven experiments on loaded foam
With single sphere (Klein et al 00; Robey et al 02)
With plastic threads (Frank et al)
With dense particles (Foster et al)
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Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
Cambridge UK Edited by S B Dalziel P di f th 9th I t ti l W k h th Ph i f C ibl T b l t Mi i J l 2004
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Global dynamics
Simplified 2D model of M82No clouds Explicit Smoothed
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Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
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2D AMR simulations
Using Aqualung (Williams 99)
150 clumps with density 100 ambient, = 5/3
effective resolution up to 1024 4096
60 cells across each clump diameter.
a = 1 in upstream diffuse gas, Mach 10 or 2 incident shock.
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Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
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2D AMR simulations Mach 10
t = 0
t = 0.15
t = 0.3
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Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
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2D AMR simulations Mach 2
t = 0.5
t = 1.0
t = 1.5
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Structure of leading shock in 2D
Velocity vector and density for 2D flow, Mach 10 shock.Velocity field highly turbulent, flow nozzles between clumps, com-
paction at various angles.
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3D simulations
Using Turmoil3D (Youngs): mass fraction (upper), density (lower):-
t = 0.25
t = 0.5Mass fraction > 0.5 isosurface at t = 0.5:-
Clump gas is well mixed at this level, surfaces are strongly structured.
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3D simulations II
Column density in 3D simulation leading shock is closer to plane,
initial cloud crushing is more directed.
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g f p y f p g y
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1D characteristics Mach 10, 2D
Velocity: clump and diffuse gas, t = 0.1, ...,0.5:-
Leading diffuse shock weaker, broadened (but still supersonic) Clumps catch up. Peaks in early scatter are gaps in clump distri-
bution.
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g f p y f p g y
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1D characteristics Mach 2, 2D
Velocity: clump and diffuse gas, t = 1, ...,4:-
Leading shock spreads fully
Precursor wave escapes
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1D characteristics Mach 10, 2D
Density RMS:-
Significant density structure remains well after shock passage.
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1D characteristics Mach 10, 3D
Velocity: clump and diffuse gas, t = 0.4, 0.5, 0.6:-
Leading shock in diffuse gas weaker, still sharp
Clumps catch up in similar distance, with less scatter
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Multiphase flow model
Compare particulate model (adapted from Youngs 1994), with
Drag
Added mass terms Inter-phase pressure relaxation
Particle break up
heat exchange, surface tension/strength and viscosity effects are
neglected here.
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Developing the multiphase model I
t = 0.1
t = 0.15
t = 0.2
t = 0.3
t = 0.45
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Developing the multiphase model II
Break up speed from ram pressure balance not sound speed (cf.
Poludnenko et al)
Parameters defined using numerical and experimental results.
Gives vrel (1 t/tshred); tshred and combine break-up and drag.
Compare centre of mass motion for single shocked clump.
Mach 10 Mach 2
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Cambridge, UK Edited by S.B. Dalziel
Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004
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Multiphase flow model results
Mach 10 Mach 2
Velocities of clump and diffuse gas.
Initial particle size reduced to allow for initial anisotropic contraction.Diffuse overshoot similar to Mach 10 3D results.
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Conclusions
Multiphase structure is common in astrophysics
Broadens impinging shocks, drives diffuse flows to Mach 1
Turbulence driven by shock-surface interactions and shock colli-sions
Partial mixing occurs, but significant structure remains
...so may retain structure with detailed physics (e.g. cooling)
Experimental comparisons are being developed.
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