r.j.r. williams and d.l. youngs- shock propagation through multiphase media

8/3/2019 R.J.R. Williams and D.L. Youngs- Shock propagation through multiphase media

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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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Astrophysical multiphase flows

Starburst galaxy M82

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Eagle nebula columns

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Photoionized clumps in the Helix nebula

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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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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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Global dynamics

Simplified 2D model of M82No clouds Explicit Smoothed

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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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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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2D AMR simulations Mach 10

t = 0

t = 0.15

t = 0.3

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2D AMR simulations Mach 2

t = 0.5

t = 1.0

t = 1.5

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Cambridge UK Edited by S B Dal iel Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004


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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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Velocity: clump and diffuse gas, t = 1, ...,4:-

Leading shock spreads fully

Precursor wave escapes

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Density RMS:-

Significant density structure remains well after shock passage.

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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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C b id UK Edi d b S B D l i l Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing July 2004


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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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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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r.j.r. williams and d.l. youngs- shock propagation through multiphase media

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