Pressure and Shock Wave

The air-intake used to induce air from the flight-altitude atmosphere plays an important role in determining the overall efficiency of ducted rockets. The air pressure built up by the shock wave determines the pressure in the ramburner. The temperature of the compressed air is also increased by the heating effect of the shock wave. The fuel-rich gaseous products formed in the gas generator burn with the pressurized and shock-wave heated air in the ramburner. The nozzle attached to the rear-end of the ramburner increases the flow velocity of the combustion products through an adiabatic expansion process. This adiabatic expansion process is equivalent to the expansion process of a rocket nozzle described in Section 1.2. 

If the yield of a silent reaction is n% after a specific period of time while the yield of the corresponding sonochemical reaction is m%, the ratio min higher than 1 is described as the effect of ultrasound. Since its beginning, ultrasound effects have been considered to originate in the general phenomenon of cavitation, which generates high temperatures, pressures, and shock waves. 

It is evident from the above that, in order to establish the adial tic shock equation for a given medium, at least two shock wave parameters have to be determined experimentally. Modern experimental methods enable direct determination of the shock wave pressure and shock wave firont velocity with good accuracy. This proves to be sufficient for defining the adiabatic shock equation for a given medium. Once the adiabatic shock equation of a material is known, one may predict the behaviour of the material under cfynamic pressure action. 

Bauer, F., PVFj polymers ferroelectric polarization and piezoelectric properties under dynamic pressure and shock wave action, Ferroelectrics, 49, 231-240 (1983). 

Noise vibration Material failure, pressure and shock waves, valve/contact chattering Engineering control, use of antivibration materials/ isolation... 

The use of explosives in metalworking was initially employed in 1880 to make spittoons. Today, the missile and rocket industry use explosives to shape bulkheads, nosecones, and even large rocket sections. A small 50-g charge can do the work of a 1,000-t press shaping a thick metal plate 2-3 m in diameter. An example of a metal forming system is shown in Fig. 14.2. The dye is usually cheap material of concrete or plaster which can be evacuated. The sheet metal is held in place by a bed of water in which the explosive charge is detonated. The pressure and shock wave forces the metal into the evacuated mold in microseconds. 

F. Bauer, PVF] polymers Perroclcctiic polariaation and piezoelectric properties under dy> namic pressure and shock wave action. Ferroekethes 49 231 (1983). 

Generation of pressures and shock waves that can fail vessel support structures, leading to movement of the vessel and failure of containment piping penetrations,... 

An important application of the impedance match method is demonstrated by the pressure-particle velocity curves of Fig. 4.9 for various explosives. Using the above method, the pressure in shock waves in various explosives is inferred from the intersection of the explosive Hugoniot with the explosive product release isentropes and reflected shock-compression Hugoniots (Zel dovich and Kompaneets, 1960). The amplitudes of explosively induced shock waves which can be propagated into nonreacting materials are calculable using results such as those of Fig. 4.9. 

G.T. Gray III and C.E. Morris, Influence of Peak Pressure on the Substructure Evolution and Shock Wave Profiles of Ti-6A1-4V, in Sixth World Conference on Titanium (edited by P. Lacombe, R. Tricot, and G. Beranger), Les Editions de Physique, France, 1989, 269 pp. 

Employers, at a minimum, must have an emergency action plan that will facilitate the prompt evacuation of employees when there is an unwanted release of a highly hazardous chemical. This means that the employer s plan will be activated by an alarm system to alert employees when to evacuate, and that employees who are physically impaired will have the necessary support and assistance to get them to a safe zone. The intent of these requirements is to alert and move employees quickly to a safe zone. The use of process control centers or buildings as safe areas is discouraged. Recent catastrophes indicate that lives are lost in these structures because of their location and because they are not necessarily designed to withstand over-pressures from shock waves resulting from explosions in the process area. 

There are numerous early scientific works concerning the presence of shock waves and the influence of explosions, impacts, and shock waves on matter. The earliest work, however, did not lead to a delineation of the phenomenon as a distinct scientific enterprise. This distinction rests with a group of visionary scientists assembled at Los Alamos for the development of the atomic bomb during World War II. Having learned the methods and developed the technology to explosively load samples in a precise and reproducible manner, they realized that they had in their hands, for the first time, the ability to study matter in an entirely new range of pressure. After several precursor publications beginning in 1955, the existence of the new scientific field was reported to the world in the classic work by Melvin Rice, John Walsh, and... 

Recently, there has been an increasing number of numerical studies on the gas delivery stage 161 163 324 325 496 608 and some experimental measurements in the near-nozzle region. 160 162 169 170 [177][327][608]-[6io] Extensive theoretical, 611 numerical, 161 and experi-mentah170 175 studies on high-speed gas jet flows in the near-nozzle region have been conducted to investigate velocity profiles, pressure distributions, shock waves and flow structures. 

The AI-H2O reaction increases the temperature and the number of moles of gas in the bubble by the production of H2 molecules. The pressure in the bubble is thereby increased. As a result, the bubble energy and shock wave energy are increased. It must be understood that the oxidation of aluminum powder is not like that of gaseous reactants. Reaction occurs at the surface of each aluminum particle and leads to the formahon of an aluminum oxide layer that coats the particle. The oxidized layer prevents the oxidation of the interior particle. The combustion efficiency of aluminum parhcles increases with decreasing particle size.l =l The shock wave energy and bubble energy are increased by the use of nano-sized aluminum powders. 

On the other hand, an over-expanded flow is formed at a nozzle exit when the pressure is lower than that of the ambient atmosphere and a shock wave is formed to increase the pressure. This shock wave is reflected at the interface between the flow stream and the ambient air and an expansion wave is formed. As in the case of the under-expanded flow, this process is repeated several times to form a diamond array, as shown in Fig. C-6 (b). 

Kistiakowsky (Ref 7) discusses spontaneous decay of gaseous shock waves and gives on p 951 three curves giving relationships between pressure of shock wave and distance from shock front (See Fig 2)... 

The detonation wave is a combination of a shock and combustion front, and has a constant width on the time-distance plot. Passage thru the intermediate state would require the attainment of extremely high peak pressure, and of wave-front velocities above the CJ value. Oppenheim quotes (Ref 3, p 476) some exptl evidence of these phenomena... 

In the book of Zel dovich Kompaneets (Ref 45a), the following subjects related to detonation pressure are discussed p 12-13 (Shock compression and isentropic compression) 14 (Static pressure) 27 (Pressure in weak shock waves) 31 (Pressure in shock wave of an ideal gas) 92-8 (Formation of an overcompressed detonation wsve on forcing the detonation in a gas to pass from a large pipe to a narrow one) ... 

Further in the book of Baum et al (Ref 20, pp 625-40) is given a mathematical treatment for determination of pressure of shock wave and of products of explosion at different distances from the center of the charge. The formulas derived on 15 pages of the book would take too much space if included here... 

Rarefaction waves were also considered by Kistiakowsky Wilson, and it. was shown that in the case of rarefaction no discontinuity can occur and the detonation wave is followed by an advancing rarefaction wave. Tables, constructed by them with.the aid of the eqs 11, 12 8t 13, of the peak values of the temp, pressure, density, and shock wave velocity as functions of the peak value of the particle velocity for shock waves in air. and water are given in Ref 29b... 

Booklet), pp 44- 8 (Detonation and shock waves) 20) E. Dubois, MAF 21, 369—93 (1947) (Investigation by means of a piezoelectric apparatus the forces of in stantaneous pressures produced when explosion waves meet an obstacle) 20a) R.H. Cole, "Underwater Explosions , Princeton UnivPress, Princeton, NJ (1948), Chapter 3 21) P. 

It shows and defines some of the parameters of particular interest in underwater expins, namely (1) shock wave peak pressure, (2) shock wave time constant, (3) shock wave impulse, and (4) shock wave energy flux dendty, which is often referred to simply as energy ... 

PA Tech Div Lecture, 29pp) 14) G. Taylor, PrRoySoc 201A, 159-74(1950) 15) H.G. Snay J.H. Rosenbaum, Shockwave Parameters in Fresh Water for Pressures up to 95 Kilobars, NAVORD Rpt 2383(1952) 16) Armament Engrg (1954), 185 97 17) Coll, Symposium on Blast and Shock Waves, HA, England (1955) 18) F. Berry et al, PrRoySoc 227A, 258-70(1955) ... 

The character of the solution is independent of the concrete form of the pressure decrease law at the piston it(t), described by the dimensionless function f(t/r), only if / decreases fast enough for large values of t/r. In particular, it is unimportant whether / increases continuously or discon-tinuously at t < r. Even for a continuous increase of the gas pressure, a shock wave will form with a pressure amplitude of the order of the maximum pressure P at the piston. The shock wave velocity here is of order D yjP/p0, so that some small mass of gas, of order Dp0r r is subjected to a shock compression of amplitude P. After the pressure at the piston goes to zero this gas, extending into the vacuum, attains a velocity of order u0 y/P/p0, and at the time t it will be located at a point x — u0t tyfP/p0. So, for example, if f(t/r) = 1 at 0 < t < t/r < 1 and... 

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