One-dimensional moving window atomistic framework to model long-time shock wave propagation

Shock wave propagation arising from steady one-dimensional motion of a piston in a granular gas composed of inelastically colliding particles is treated theoretically. A self-similar long-time solution is obtained in the strong shock wave approximation for all values of the upstream gas volumetric concentration v0. Closed form expressions for the long-time shock wave speed and the granular pressure on the piston are obtained. These quantities are shown to be independent of the particle collisional properties, provided their impacts are accompanied by kinetic energy losses. The shock wave speed of such non-conservative gases is shown to be less than that for molecular gases by a factor of about 2.The effect of particle kinetic energy dissipation is to form a stagnant layer (solid block), on the surface of the moving piston, with density equal to the maximal packing density, vM. The thickness of this densely packed layer increases indefinitely with time. The layer is separated from the shock front by a fluidized region of agitated (chaotically moving) particles. The (long-time, constant) thickness of this layer, as well as the kinetic energy (granular temperature) distribution within it are calculated for various values of particle restitution and surface roughness coefficients. The asymptotic cases of dilute (v0 [Lt ] 1) and dense (v0 ∼ vM) granular gases are treated analytically, using the corresponding expressions for the equilibrium radial distribution functions and the pertinent equations of state. The thickness of the fluidized region is shown to be independent of the piston velocity.The calculated results are discussed in relation to the problem of vibrofluidized granular layers, wherein shock and expansion waves were registered. The average granular kinetic energy in the fluidized region behind the shock front calculated here compared favourably with that measured and calculated (Goldshtein et al. 1995) for vibrofluidized layers of spherical granules.

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Study of laser-driven shock wave propagation in Plexiglas targets

Laser and Particle Beams ◽

10.1017/s0263034600004328 ◽

1992 ◽

Vol 10 (1) ◽

pp. 201-211 ◽

Cited By ~ 7

Author(s):

L. J. Dhareshwar ◽

P. A. Naik ◽

T. C. Kaushik ◽

H. C. Pant

Keyword(s):

Shock Wave ◽

Wave Propagation ◽

High Speed ◽

Second Harmonic ◽

Optical Probe ◽

Shock Wave Propagation ◽

Hydrodynamic Simulation ◽

One Dimensional ◽

Laser Beam Irradiation ◽

Shock Fronts

An experimental study of laser-driven shock wave propagation in a transparent material such as Plexiglas using a high-speed optical shadowgraphy technique is presented in this paper. A Nd:glass laser was used to produce laser intensity in the range 1012-1014 W/cm2 on the target. Optical shadowgrams of the propagating shock front were recorded with a second-harmonic (0.53-μm) optical probe beam. Shock pressures were measured at various laser intensities, and the scaling was found to agree with the theoretically predicted value. Shock pressure values have also been obtained from a one-dimensional Lagrangian hydrodynamic simulation, and they match well with experimental results. Shadowgrams of shock fronts produced by nonuniform spatial laser beam irradiation profiles have shown complete smoothing when targets with a thin coating of a material of high atomic number such as gold were used. Shock pressures in such coated targets are also found to be considerably higher compared with those in uncoated targets.

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