Detonation shock, pressure, velocity

Figure 4.9. Shock pressure versus particle velocity for engineering materials, geological material, and explosive detonation products. Intersection of detonation product curves with nonreactive media predicts shock pressure and particle velocity at an explosive sample interface. (After Jones (1972).)...

A detonation shock wave is an abrupt gas dynamic discontinuity across which properties such as gas pressure, density, temperature, and local flow velocities change discontinnonsly. Shockwaves are always characterized by the observation that the wave travels with a velocity that is faster than the local speed of sound in the undisturbed mixtnre ahead of the wave front. The ratio of the wave velocity to the speed of sound is called the Mach number. 

The Chapman-Jongnet (CJ) theory is a one-dimensional model that treats the detonation shock wave as a discontinnity with infinite reaction rate. The conservation equations for mass, momentum, and energy across the one-dimensional wave gives a unique solution for the detonation velocity (CJ velocity) and the state of combustion products immediately behind the detonation wave. Based on the CJ theory it is possible to calculate detonation velocity, detonation pressure, etc. if the gas mixtnre composition is known. The CJ theory does not require any information about the chemical reaction rate (i.e., chemical kinetics). 

Explosive Chge Prepn Loading Density Chapman-J ouguet Detonation Ve locity D in km/sec Chapman -J ouguet Particle Velocity km/ sec UCJ Product Po-dD D Po Shock Velocity in Shock Pressure in H2O Chapman-J ouguet Pressure, P j. kbar Poly- tropic Expo- nent, Term M Tempetatute of Detonation T°K ... 

Detonation, Shock Impedance and Acoustic Impedance in. Acoustic impedance is the ratio between sound pressure and particle velocity. A sound wave, on reaching a boundary between two media, has part of its energy reflected at the boundary and part transmitted into the 2nd medium. The relationships depend on the values of the acoustic impedance in the two media. Swenson (Ref 2) showed that ... 

Jaffe et al (Ref 3), in the course of determination of the shock pressure required to initiate detonation of an acceptor in the shock sensitivity test, found that the velocity of the front as sensed by the pressure probe method, falls behind the true velocity of the shock front as the shock is attenuated. It has also been found that the maximum transmitted shock velocity generated by the two Tetryl pellets and measured in Lucite is 4.6mm/frsec. Shock velocities determined by optical method, shown in Table 3, p 25, run between 2.701... 

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... 

Detonation, Water Plexiglos Induced Shock Wove Velocity in. Cook et al (Ref 2) applied the "aquarium technique in the exptl detn of the equation of state for water Lucire. The results for water are compared with similar results by other methods. Measurements of the peak pressures in the deton wave are presented for RDX, RDX/salt, TNT HBX-1. Peak pressures were found to be the CJ or deton pressures of the thermohydro-dynamic theory. There was no evidence whatever for the "spike of the Zel dovich-von Neumann model even though conditions were such that this spike would have been detected by the method employed if it were present, at lease in the large diam, nonideal expls of max reaction zone length Refs.T) C. Fauquignon, CR 251, 38 (I960) 2) M, A. Cook et al, JAppl... 

In the preceding paragraphs we presented available shock and bubble data at distances relatively far from the detonating underwater charge. Hantel and Davis (Ref 9) obtained velocity and shock pressure data right up to the expl/water interface. We quote their summary Calibration data are presented for the shock... 

As discussed in the next section, there are several techniques for measuring particle velocity, which is usually designated as u or sometimes as Up. Consequently, since U, the shock velocity (or D if the shock is a detonation, ie, a chemically supported shock) is readily measurable, most measurements of shock pressure P are based on measurements of particle velocity and the relation ... 

Fig, XIV.7. Pressure profile of a one-dimensional detonation wave. = the velocity of the shock front relative to the unburned gases Vb(burned gases relative to the unburncd gases 5/ = thickness of combustion zone. 

The development of combustion in PETN by shock was studied by Dubnpv et al (Ref 93). Unfortunately, the original article is unavailable to us, but it appears that the effects of incident shock velocity, reflected shock pressure and temp, surrounding gas, and surface roughness of the PETN were examined Deflagration-to-Detonation Transition (DDT)... 

The transit time is mainly a function of the particular detonator design, that is, the type, density, and length of the explosives loaded into the detonator. The transit time is equal to the length of each explosive element or pressing, divided by the detonation velocity of that element, plus the excess transit time due to the buildup of run distance to steady-state detonation. Recall that the run distance, and hence excess transit time, is a function of the initiating shock pressure. Also, the initiating shock pressure from an EBW is a function of the burst current. Therefore, the transit time of an EBW detonator is not independent of the system. 

Clearly, the pressure oscillations in Figure 9 are associated with the spin, for, when the frequency of the oscillations is divided into the shock wave velocity, the wave length so obtained is just equal to the pitch of the helix as measured from the photograph (Figure 8). Subsequently, vibrations of this type have been observed in pressure records from many detonations (14)-... 

The detonation velocity refers to the velocity of the shock front relative to the unreacted material. Peak shock pressure needed to initiate RDX and other secondary explosives as a function of density and particle size have been measured by the small scale gap test [48]. For RDX, which is commonly used in detonators, peak pressure for initiation is found to range from 9 to 16 kbar. Since even under nonideal conditions lead azide produces over 100 kbar, as shown in Table VI, if enough azide is present, it readily initiates RDX, and other secondary explosives, as shown in Table VII. 

Fig. 6. Detonation in a slab of energetic material, (a) The detonation shock front runs at a constant velocity, driven by fast expansion of chemical reaction products. The highest pressure is in the von Neuman spike region just behind the front. At the Chapman Jouguet (C-J) plane the reaction is Just complete, (b) Shock compression follows the indicated Rayleigh line to where it intersects the unreacted Hugoniot at the von Neumann spike. The point where this Rayleigh line is tangent to the reacted Hugoniot is the C-J state of stable detonation velocity.

Shot No Brass Thick (cm) Initial Shock Velocity (m/sec) Initial Particle Velocity (m/sec) Initial Shock Pressure (kb) Initial Compression (V/Vo) dor po fe/cm ) Deton Vel, D (Final) (m/sec)... 

Figure 2.14 shows that the detonation with propagation velocity D = D starts from the crosspoint N of the Hugoniot curve and shock adiabatic curve. Only after passing point P is under pressure detonation point (or weak detonation point) is reached. Von Neumann named the detonation velocity as eigenvalue detonation... 

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