Refraction of plane shock waves interacting with a layer of gas bubbles in a liquid

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.

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Effect of Thermal Radiation on the Propagation of Plane Shock Waves

The Physics of Fluids ◽

10.1063/1.1693145 ◽

1970 ◽

Vol 13 (7) ◽

pp. 1717 ◽

Cited By ~ 2

Author(s):

C. P. Wang

Keyword(s):

Shock Waves ◽

Thermal Radiation ◽

Plane Shock

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

Volume 2: Biomedical and Biotechnology Engineering ◽

10.1115/imece2008-68216 ◽

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.

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On the stability of plane shock waves

Journal of Fluid Mechanics ◽

10.1017/s0022112057000208 ◽

1957 ◽

Vol 2 (4) ◽

pp. 397-411 ◽

Cited By ~ 25

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.

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