Pressure waves rarefaction

Fig 2 Pressure in rarefaction wave behind Chapman-Jouguet point according to Taylor and to Langweilcr... 

If a reaction occurs in the rarefaction wave, a positive pressure wave eventually develops downstream and subsequently overtakes the front of the rarefaction wave... 

A feature of shock waves not yet considered is that there is inevitably a low pressure or rarefaction wave produced at the diaphragm at the same time as the shock wave. This moves initially in the opposite direction from the shock wave but is reflected by the back wall of the tube, and so eventually follows the main shock wave down the tube. Relative to laboratory coordinates this rarefaction wave travels with the local velocity of sound in the gas. This is considerably less than that of the shock wave because of the substantially lower temperature, but superimposed on it is the flow motion of the driver gas towards the low-pressure region. This has the result that the rarefaction wave tends to catch up with the shock wave. Because of the simplifications it allows, it is convenient to make the measurements on the shocked gas before the rarefaction arrives. This consideration is an important one in deciding on the relative positions of the diaphragm and observation points, and on the relative lengths of the high- and low-pressure areas . For a reason considered below, measurements are also sometimes made after the shock wave has been reflected from the front wall, but before the rarefaction wave has arrived. Such a situation is only used where absolutely necessary because it is now felt that the shock front is significantly distorted on reflection. 

Sound is propagated through any medium in waves that take the form of pressure peaks (compressions) and troughs (rarefactions) as illustrated in Figure 8.1. The pressure wave travels through the medium at the speed of sound. The auditory system in humans and most animals senses the impingement of these pressure waves... 

Sound waves in liquids are longitudinal density and pressure waves in which particle oscillations occur in the direction of the wave. The displacement around the rest position causes compression and rarefaction. The fundamental quantities of a sound wave are the time-dependent particle displacement the particle velocity v and the sound pressure p ... 

This phenomenon is based on the creation of cavities within the liquid caused by the propagation of a pressure wave through the Uquid [5]. During the rarefaction period, the microbubbles increase in size according to the gas compression law. Inside the bubble, the gas pressure tends to expand it On the other hand, the surface tension at the... 

Ultrasound passes through an elastic medium as a longitudinal wave, which is a series of alternating compressions and rarefactions. This means that hquid is displaced parallel to the direction of motion of the wave. Ultrasound comprises sound waves typically in the range of 20 kHz to approximately 500 MHz. The frequency (/) and the acoustic amplitude (PA,max) are the most important properties to characterize the pressure wave. The variation of the acoustic pressure (Pa) of an ultrasound wave as a function of time (t) at a fixed frequency is described by Eq. (2)... 

The rarefaction phase is a characteristic of slow combustion in unconfined and ventilated volumes. The rarefaction phase amplitude may be comparable with the compression phase amplitude. When the flame propagation velocity and the sound speed in the mixture are comparable, pressure waves are generated. The pressure wave amplitude depends on the mixture composition, initial conditions, the geometry and the combustion regime. Gas dynamics of the process must be taken into... 

The dependence of the pressure wave profile on the HAM volume (Fig. 9.7) and the unavoidable transition from the compression phase to the rarefaction phase attract attention. For defiagration, the pressure wave amplitude depends on the HAM cloud linear dimensions, in the near zone it is ten times less than for detonation (Fig. 9.8). The reduced impulse value is less than that of the detonation and it is practically the same for different volumes. Such a result is important for expert assessments of targets behavior depending on a HAM explosion type. Assessments of the effects based only on a pressure amplitude level might contain subjective errors. 

From Figs. 10.17 and 10.18 it follows that because of the significant duration of the rarefaction phase at F < 0.7, the rarefaction wave effect is more dangerous for some targets than the pressure wave effect. Figure 10.19 presents TNT equivalents based on the rarefaction phase pressure Kp (curves 1,2) and the compression phase pressure Kp+ (curves 3, 4) at various distances from the blast epicenter. Within the accuracy of the measured rarefaction wave parameters, the pressure TNT equivalent of the rarefaction phase does not depend on the distance and everywhere is not less than the TNT equivalent for the compression phase. 

Expansion waves are the mechanism by which a material returns to ambient pressure. In the same spirit as Fig. 2.2, a rarefaction is depicted for intuitive appeal in Fig. 2.7. In this case, the bull has a finite mass, and is free to be accelerated by the collision, leading to a free surface. Any finite body containing material at high pressure also has free surfaces, or zero-stress boundaries, which through wave motion must eventually come into equilibrium with the interior. Expansion waves are also known as rarefaction waves, unloading waves, decompression waves, relief waves, and release waves. Material flow is in the same direction as the pressure gradient, which is opposite to the direction of wave propagation. 

In materials that support shock waves, the sound speed increases with pressure. It is this same property that causes rarefactions to spread out as they progress. In Fig 2.6(b), an unloading wave is shown propagating into a stationary material with some initial pressure Pq. This time, we consider the evolution of two small decompressional disturbances. The first disturbance moves at the local sound speed of a, into its surroundings, which have begun... 

Another way of representing shock-wave profiles is in the form of F-t histories of the pressure or another variable at a series of points along its direction of propagation, as in Fig. 2.9. In the above example, the leading part of the shock front arrives first, effectively increasing the pressure instantaneously. The rarefaction arrives later and decreases the pressure over a time... 

For simplicity, we have shown an expansion wave in which the pressure is linearly decreasing with time. This, in general, is not the case. The release behavior depends on the equation of state of the material, and its structure can be quite complicated. There are even conditions under which a rarefaction shock can form (see Problems, Section 2.20 Barker and Hollenbach, 1970). In practice, there are many circumstances where the expansion wave does not propagate far enough to fan out significantly, and can be drawn as a single line in the x t diagram. 

Rarefaction wave A wave that reduces the normal stress (or pressure) inside a material as it propagates the mechanism by which a material returns to ambient pressure after being shocked (the state behind the wave is at lower stress than the state in front of it). Also known as unloading, expansion, release, relief, or decompression waves. 

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