Shock waves propagation

Figure 2.10. (a) An Eulerian x-t diagram of a shock wave propagating into a material in motion. The fluid particle travels a distance ut, and the shock travels a distance Uti in time ti. (b) A Lagrangian h-t diagram of the same sequence. The shock travels a distance Cti in this system. 

Example 2 (Shock Reflection from a Lower Z Interface). Figure 2.17 represents a shock wave propagation from left to right in material A. When the... 

We assume that in (4.38) and (4.39), all velocities are measured with respect to the same coordinate system (at rest in the laboratory) and the particle velocity is normal to the shock front. When a plane shock wave propagates from one material into another the pressure (stress) and particle velocity across the interface are continuous. Therefore, the pressure-particle velocity plane representation proves a convenient framework from which to describe the plane Impact of a gun- or explosive-accelerated flyer plate with a sample target. Also of importance (and discussed below) is the interaction of plane shock waves with a free surface or higher- or lower-impedance media. 

The physical state of the sample before and after impact is sketched in Fig. 4.6(a). Positive velocity, indicating mass motion to the right (in the laboratory), is plotted toward the positive, u, axis. Hence, in the initial state 0, the target B is at Up = 0 and P = 0, whereas the initial state in the flyer plate O is Up = Ufp and P = 0. Upon interaction of flyer plate A with target B, a shock wave propagates forward in the sample and rearward in the flyer plate. Because the pressure and particle velocity are continuous at the flyer-... 

J.N. Johnson, O.E. Jones, and T.E. Michaels, Dislocation Dynamics and Single-Crystal Constitutive Relations Shock-Wave Propagation and Precursor Decay, J. Appl. Phys. 41, 2330-2339 (1970). 

Andersen J.R. and Nestler, D.E., Shock Wave Propagation in Solids (A Survey of the Literature), University of Pennysivania Report, Philadelphia, PA, 71 pp., 1960. 

In the 1930s, Bone et al. [15] using rotating mirror camera observed the action of shock waves propagating into the unburnt mixture ahead of the accelerating flame, and postulated that the detonation wave was initiated as a result of preignition of the shock-compressed mixture. 

Seismic techniques, the reflection and refraction of sound or shock waves propagated through the earth, are also used to reveal details of the structure and interrelationship of various layers in the subsurface. The shock or sound waves record densities in the earth s surface that may indicate an oil or gas reservoir. Explosive charges or vibration devices are used to impart the required shock wave. 

Both deflagrations and detonations can produce what a lay observer might describe as an explosion . Nonetheless, a detonation is a special type of explosion with specific physical characteristics. It is initiated by the heat accompanying shock compression it liberates sufficient energy, before any expansion occurs, to sustain the shock wave. The shock wave propagates into the unreacted material at supersonic speed, typically 1500—9000 m/s. We discuss the practical differences between the effects of detonation and deflagration in Chapter 11 on post-blast issues. 

Shock Wave Propagation and Reflection in Solid Materials... 

When a shock wave propagates from one end (A) to the other end (B) of a solid body, a compression force is exerted in the wake of the shock wave that acts within the solid body. The shock wave is reflected at B and becomes an expansion wavethat propagates towards A. An expansion force is then exerted in the wake of the expansion wave that travels back from B. This process is shown schematically in Fig. 9.6. 

Fig. 9.6 Schematic representation of shock wave propagation and the generation of a reflected expansion wave within a solid wall.

When an explosive is detonated in water, a shock wave propagates through the water accompanied by a bubble. The chemical energy of the explosive is converted into shock wave energy and bubble energy. The volume of the bubble is increased by the expansion wave and decreased by the compression wave in an oscillatory fashion. The maximum size of the bubble is determined according toili i i... 

Shock Wave Propagation in a Two-Dimensional Flow Field... 

The shock wave propagation or expansion velocity was ealed from the expression ... 

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