Detonation Wave velocity

Since pj < p2 for a detonation and pj > p2 for a deflagration, the flow field becomes 0 < Up < Ui for detonation, and Up < 0 for deflagration. In the case of detonation, the velocity of the combustion products is less than the detonation wave velocity. In the case of deflagration, the combustion products are expelled in the opposite direction to the deflagration wave. 

ZhFizKhim 5, 1459(1934) (Detonation in gaseous mixtures. Variation of the detonation wave velocity with pressure) 6) M.A. Rivin A.S. Sokolik, ZhFizKhim 7, 571 (1936) (The explosion limits of gaseous mixtures. Expln limits of hydrogen-air mixtures) 7) Ibid, 8, 767(1936) (Expln limits in carbon monoxide-methane mixts)... 

An experimental arrangement is illustrated in Fig 1. on p 381 of Ref 93. A metal plate thickness , is bent thru an angle deton wave, velocity DQ travelling thru a layer of explosive. When the plate was deflected, it hit at an angle of incidence i a block of expl, density p.Q The thicknesses were sufficiently small compared to the other quantities so that the flow could be considered as plane two-dimensional and stationary. The reference system R had its origin at the point of impact I and was under uhiform linear motion. Theoretical and experimental studies of the flow were carried ont in the vicinity of the noinr nf impact... 

In a sound wave, the material merely vibrates and passes its energy on to the next layer. The detonation wave velocity is distinguished from the variable particle velocity involved in the to-and-fro vibration. The latter, in turn, is differentiated from the physical movement of material with its resulting finite displacement, in the direction of advance of the pulse, at velocity u. This movement is in response to a finite pressure differentiation, with consequent irreversibility and increase in entropy... 

An example of calculation of a shock tube flow with combustion and detonation were presented in Ref. 5. It was found that "/i>-layer aflfects dramatically transition to detonation of the Chapman-Jouguet type. This transition occurs after formation of the p-layer, and secondary local explosion in the re on of p-layer takes place. The space-time pressure diagrams and variation of the detonation wave velocity in time are presented schematically in Fig. 2. 

Fig. 2 Qualitative picture of variation with time pressure distribution and detonation wave velocity.

PREttCTED TRAJECTORY OF POINT OF INTERACTION OF REGULAR REFLECTION OF CYLINDRICAL WAVES 0 DETONATION WAVE VELOCITY... 

Further flame velocity growth may be caused by a change in the main mechanism of flame propagation, which occurs at DDT transition. The self-ignition of the compressed mixture behind the shock front becomes a key process continuing combustion wave propagation. The detonation wave velocity depends on the mixture composition and the initial conditions. Typical values of the detonation velocity are 1,000-2,000 m/s. 

Parameters of detonation waves have been calculated and found experimentally. Let us use the data presented in [1-3]. Figure 7.1 illustrates the dependence of the detonation wave velocity D and the gas velocity u on the equivalence ratio

dimensional detonation wave structure and indication of some parameters for HAM and HOM can be found in [4, 5] (Figs. 7.2, 7.3, 7.4, 7.5 and Tables 7.1, 7.2). 

Fig. 7.1 Detonation wave velocity D and gas velocity behind the wave u versus equivalence ratio (p for H2 + air at 0.1 MPa pressure and 298 K temperature...

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). 

The flux-corrected-transport technique was also used by Phillips (1980), who successfully simulated the process of propagation of a detonation wave by a very simple mechanism. The reactive mixture was modeled to release its complete heat of combustion instantaneously after some prescribed temperature was attained by compression. A spherical detonation wave, simulated in this way, showed a correct propagation velocity and Taylor wave shape. 

Figure 7-53. Detonation velocity, V, static pressure, Pg, and reflected pressure, Pp developed by detonation wave propagating through hydrogen-oxygen mixtures in a cylindrical tube at atmospheric pressure at 18°C. By permission, U.S. Bureau of Mines, Bulletin 627 [43].

If the outlet or discharge pressure is lowered further, the pressure upstream at the origin wtill not detect it because the pressure wave can only travel at sonic velocity. Therefore, the change in pressure downstream will not be detected upstream. The excess pressure drop obtained by lowering the outlet pressure after the maximum discharge has been reached takes place beyond the end of the pipe [3]. This pressure is lost in shock waves and turbulence of the jetting fluid. See References 12,13, 24, and 15 for further expansion of shock waves and detonation waves through compressible fluids. 

Stable detonation—a steady detonation wave with velocity and pressure close to CJ values. 

When a detonation wave passes through an explosive, the first effect is compression of the explosive to a high density. This is the shock wave itself. Then reaction occurs and the explosive is changed into gaseous products at high temperature. These reaction products act as a continuously generated piston which enables the shock wave to be propagated at a constant velocity. The probable structure of the detonation zone is illustrated in Fig. 2.3. 

It will be noted that asp2 is greater than pu v2 must be less than v and W2 (known as the streaming velocity) is positive, meaning that the explosion products travel in the same direction as the detonation wave. This positive streaming velocity is a characteristic and identifying property of a detonation wave. 

Tables 2.1 and 2.2 show that theory enables detonation velocities to be calculated in close agreement with those observed experimentally. This, unfortunately, is not a critical test of the theory as velocities when calculated are rather insensitive to the nature of the equation of state used. A better test would be to calculate the peak pressures, densities and temperatures encountered in detonation, and compare these with experimental results. The major difficulties here are experimental. Attempts to measure temperatures in the detonation zone have not been very successful, but better results have been obtained in the measurement of densities and pressures. Schall introduced density measurement by very short X-ray flash radiography and showed that TNT at an initial density of 1 -50 increased 22% in density in the detonation wave. More recently detonation pressures have been measured by Duff and Houston using a method (introduced by Goranson) in which the pressure is deduced from the velocity imparted to a metal plate placed at the end of the column of explosive. Using this method, for example, Deal obtains the detonation pressures for some military explosives recorded in Table 2.3. More...

Nonel fuse, invented by Nitro Nobel AB in Sweden, consists of a thick plastic tube of bore about 1 mm, the inside surface of which is dusted with a small amount of powdered high explosive. If a shock wave is formed at one end of the tube the explosive powder is raised to a dust and a stable detonation at velocity 2000 m s 1 proceeds indefinitely along the fuse. The plastic itself is unaffected and the only outside effect is a flash of light seen through the tube walls. This therefore is an extremely safe method of propagating a detonation from one place to another. 

Streaming velocity. The velocity of the products of detonation in the direction of travel of the detonation wave. 

A detonation wave is a very rapid wave of chemical reaction which, once it is initiated, travels at a stable supersonic speed, called the detonation velocity, in a high explosive. Typically, detonation velocities for pressed or cast high explosives range from... 

In general, detonation test apparatus consists of a steel tube that is filled with the substance under investigation. One end of the tube is provided with a booster charge consisting of an electric detonator covered by detonative material. The other end is either closed or provided with a witness plate. One type of steel tube apparatus is provided with a velocity probe to record the shock wave velocity as shown in Figure 2.28. 

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