Shock wave energy

The research results clearly indicated that the smelt-water explosion yielded a localized, high-energy shock wave which moved at velocities of over 700 m/sec. The maximum pressure rise was achieved in about 1 msec. These facts were related to the results found in real boiler explosions in descriptive terms as there were 3-4 inch depressions 3 to 6 feet... 

Type of Strain Kinetic Energy Shock Wave... 

Note Currently, a German-built machine which uses high-energy shock waves to break up kidney stones from outside the body is being tested. The nonsuigical procedure is called extracorporeal shock wave lithotripsy, or stone exploding. 

Detonation. In a detonation, the flame front travels as a shock wave, followed closely by a combustion wave, which releases the energy to sustain the shock wave. The detonation front travels with a velocity greater than the speed of sound in the unreacted medium. 

Figure B3.3.13. Intersecting stacking faults in a fee crystal at the impact plane induced by collision with a momentum mirror for a square cross section of side 100 unit cells. The shock wave has advanced half way to the rear ( 250 planes). Atom shading indicates potential energy. Thanks are due to B Holian for tliis figure.

A laser beam is capable of putting so much energy into a substance in a very short space of time that the substance rapidly expands and volatilizes. The resulting explosive shock wave travels through the sample, subjecting it to high temperatures and pressures for short times. This process is also known as ablation. 

Explosives are commonly categorized as primary, secondary, or high explosives. Primary or initiator explosives are the most sensitive to heat, friction, impact, shock, and electrostatic energy. These have been studied in considerable detail because of the almost unique capabiUty, even when present in small quantities, to rapidly transform a low energy stimulus into a high intensity shock wave. 

Other. Because a foam consists of many small, trapped gas bubbles, it can be very effective as a thermal insulator. Usually soHd foams are used for insulation purposes, but there are some instances where Hquid foams also find uses for insulation (see Eoamed plastics Insulation, thermal). Eor example, it is possible to apply and remove the insulation simply by forming or coUapsing the foam, providing additional control of the insulation process. Another novel use that is being explored is the potential of absorbing much of the pressure produced by an explosion. The energy in the shock wave is first partially absorbed by breaking the bubbles into very small droplets, and then further absorbed as the droplets are evaporated (53). 

The equation that expresses conservation of energy can also be determined by considering Fig. 2.3. Since the piston moves a distance u At, the work done by the piston on the fluid during this time interval is Pu At. The mass of material accelerated by the shock wave to a velocity u is PqU At. The kinetic energy acquired by this mass element is therefore (pqUu ) At/2. If the specific internal energies of the undisturbed and shocked material are denoted by Eq and E, respectively, the increase in internal energy is ( — o)Po V At per unit mass. The work performed on the system is equal to the sum of kinetic and... 

To reiterate, the development of these relations, (2.1)-(2.3), expresses conservation of mass, momentum, and energy across a planar shock discontinuity between an initial and a final uniform state. They are frequently called the jump conditions" because the initial values jump to the final values as the idealized shock wave passes by. It should be pointed out that the assumption of a discontinuity was not required to derive them. They are equally valid for any steady compression wave, connecting two uniform states, whose profile does not change with time. It is important to note that the initial and final states achieved through the shock transition must be states of mechanical equilibrium for these relations to be valid. The time required to reach such equilibrium is arbitrary, providing the transition wave is steady. For a more rigorous discussion of steady compression waves, see Courant and Friedrichs (1948). 

For shock waves in solids, the shock pressure P is typically much greater than the initial pressure Pq, which is normally ambient atmospheric conditions, so that Pq is usually neglected. Eq can also be taken to be zero, sinee internal energy is a thermodynamie state funetion and ean be refereneed to any initial state. Removing Eq and Pq from the jump conditions results in their eommon form... 

The fact that shock waves continue to steepen until dissipative mechanisms take over means that entropy is generated by the conversion of mechanical energy to heat, so the process is irreversible. By contrast, in a fluid, rarefactions do not usually involve significant energy dissipation, so they can be regarded as reversible, or isentropic, processes. There are circumstances, however, such as in materials with elastic-plastic response, in which plastic deformation during the release process dissipates energy in an irreversible fashion, and the expansion wave is therefore not isentropic. 

Hugoniot curve A curve representing all possible final states that can be attained by a single shock wave passing into a given initial state. It may be expressed in terms of any two of the five variables shock velocity, particle velocity, density (or specific volume), normal stress (or pressure), and specific internal energy. This curve it not the loading path in thermodynamic space. 

The most common form of energy deposition used for planar shock wave research has been electrical resistance heating of a metal foil which vaporizes, driving a flyer plate to a high velocity before it impacts a specimen. In a hybrid system incorporation both resistance vaporization and an electromagnetic push, velocities to 18 km/s are reported for kapton flyer plates which are... 

The propagation of a shock wave from a detonating explosive or the shock wave induced upon impact of a flyer plate accelerated, via explosives or with a gun, result in nearly steady waves in materials. For steady waves a shock velocity U with respect to the laboratory frame can be defined. Conservation of mass, momentum, and energy across a shock front can then be expressed as... 

Figure 4.1. Profile of a steady shock wave, risetime imparting a particle velocity, e.g., Uj, pressure Pi, and internal energy density E, propagating with velocity U, into material that is at rest at density pQ and internal energy density Eq.

R.N. Orava and R.H. Wittman, Techniques for the Control and Application of Explosive Shock Waves, in Proc. 5th Int. Conf. on High Energy Fabrication, University of Denver, Denver, 1975, p. 1. 

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