Generation of plane shock waves in a specially shaped chamber

1991 ◽  
Vol 56 (6) ◽  
pp. 2820-2821
Author(s):  
A. N. Chuprin
Keyword(s):  
Shock Waves ◽  
Plane Shock

Shock waves in an ultra-relativistic fluid

1964 ◽  
Vol 277 (1368) ◽  
pp. 24-31
Keyword(s):  
Equation Of State ◽  
Shock Waves ◽  
Mass Density ◽  
Special Theory ◽  
Plane Shock ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Conservation Equations ◽  
Relativistic Fluid ◽  
Density Relation

The special theory of relativity is used to analyze the motion of plane shock waves in a medium whose equation of state is u = 3 p , u being the mass density and p the pressure. The appropriate conservation equations together with this pressure-density relation provide a determinate set of equations for obtaining the downstream, in terms of the upstream, variables. The properties of normal and oblique shock waves in this gas are studied in the Lorentz frames in which the shocks are at rest.

Effects of Shock Waves on Acceleration of Cell Growth Rate by Shock Tube

2008 ◽  
Author(s):  
Masaaki Tamagawa ◽  
Norikazu Ishimatsu
Keyword(s):  
Shock Wave ◽  
Growth Rate ◽  
Endothelial Cells ◽  
Shock Waves ◽  
Shock Tube ◽  
Test Case ◽  
Plane Shock ◽  
Extracorporeal Shock Wave ◽  
Shock Wave Pressure

This paper describes effects of shock waves on cells to certificate the angiogenesis by shock wave (pressure wave) in the clinical application such as ESW (Extracorporeal Shock Wave). Especially, to investigate the effects of shock waves on the endothelial cells in vitro, the cells worked by plane shock waves using shock tube apparatus are observed and measured in the microscope. The peak pressure working on the endothelial cells at the test case is 0.4 MPa. After working shock waves on suspended cells, growth rate (area per one cell and population of cells) are measured by image processing. It is found that the growth rate of the shock-worked cells from 0 to 4h is clearly high compared with control one. It is concluded that once shock waves worked, the cells have capacity to increase growth rate in vitro. This preliminary result will be applied to fundamental investigations about shock wave stimulus on several kinds of cells in future.

On the stability of plane shock waves

1957 ◽  
Vol 2 (4) ◽  
pp. 397-411 ◽  
Author(s):  
N. C. Freeman
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Plane Shock ◽  
Two Dimensional ◽  
Small Perturbations ◽  
Diverging Channel ◽  
Maximum Stability ◽  
The Stability ◽  
Fourier Type

The decay of small perturbations on a plane shock wave propagating along a two-dimensional channel into a fluid at rest is investigated mathematically. The perturbations arise from small departures of the walls from uniform parallel shape or, physically, by placing small obstacles on the otherwise plane parallel walls. An expression for the pressure on a shock wave entering a uniformly, but slowly, diverging channel already exists (given by Chester 1953) as a deduction from the Lighthill (1949) linearized small disturbance theory of flow behind nearly plane shock waves. Using this result, an expression for the pressure distribution produced by the obstacles upon the shock wave is built up as an integral of Fourier type. From this, the shock shape, ξ, is deduced and the decay of the perturbations obtained from an expansion (valid after the disturbances have been reflected many times between the walls) for ξ in descending power of the distance, ζ, travelled by the shock wave. It is shown that the stability properties of the shock wave are qualitatively similar to those discussed in a previous paper (Freeman 1955); the perturbations dying out in an oscillatory manner like ζ−3/2. As before, a Mach number of maximum stability (1·15) exists, the disturbances to the shock wave decaying most rapidly at this Mach number. A modified, but more complicated, expansion for the perturbations, for use when the shock wave Mach number is large, is given in §4.In particular, the results are derived for the case of symmetrical ‘roof top’ obstacles. These predictions are compared with data obtained from experiments with similar obstacles on the walls of a shock tube.

Stability of Plane Shock Waves

1973 ◽  
Vol 30 (21) ◽  
pp. 1023-1025 ◽  
Author(s):  
G. R. Fowles ◽  
G. W. Swan
Keyword(s):  
Shock Waves ◽  
Plane Shock

scholarly journals MODELING THE INTERACTION OF A SHOCK WAVE WITH A DEFORMABLE PERMEABLE GRANULAR LAYER

2020 ◽  
Vol 82 (3) ◽  
pp. 353-363
Author(s):  
E.G. Glazova ◽  
I.A. Turygina ◽  
I.A. Modin
Keyword(s):  
Shock Waves ◽  
Granular Layer ◽  
Strong Shock ◽  
Solid Particles ◽  
Plane Shock ◽  
Friction Forces ◽  
Reflected Waves ◽  
Drag Forces ◽  
Dimensional Approximation ◽  
Granular Layers

This article presents a mathematical model that describes, in a one-dimensional approximation, the interconnected processes of unsteady deformation of flat permeable granular layers. The model consists of solid particles and wave processes in pore and surrounding gas. The model is based on nonlinear equations of dynamics of two interpenetrating continua. As interfacial forces, drag forces are taken into account when gas flows around ball particles and friction forces. The numerical solution of the equations is carried out according to the modified scheme of S.K. Godunov, adapted to the problems of the dynamics of interpenetrating media. The contact surfaces of pure gas with the porous granular layer and pore gas are the surface of the fracture of porosity and permeability. The numerical implementation of contact conditions is based on the solution of the problem of disintegration of a gap at a jump in porosity. Solutions are obtained for the effects of plane shock waves on a deformable granular layer. We study the transformation of waves passing through an elastoplastic granular layer with and without taking into account changes in the permeability of the layer. When solving problems, the dependence of the change in the permeability of a layer on its compression is used, which is also obtained numerically when modeling the compression of symmetric fragments of granular layers in a spatial setting. Numerical studies of the processes of nonlinear interaction of shock waves with deformable permeable granular layers have shown that the parameters of transmitted and reflected waves substantially depend on the degree of compression of the granular layers. Assessment of the protective properties of permeable barriers when exposed to strong shock waves should be carried out taking into account changes in their permeability due to deformation.

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