Detonation wave

The structural model of a detonation wave proposed by Zeldovich, von Neumann, and Doring (ZND model) involves the pressure at the shock front increasing along the Hugoniot curve without chemical reaction until it attains the value at the point of intersection of the Rayleigh line and the Hugoniot curve. 

8) Repeat the procedure from (3) to (7) until the minimum value of Wj is determined. 

9) The minimum value of is the detonation velocity Up at point J (Chapman-Jouguet detonation velocity). 

Computations of the thermochemical values of various combinations of oxidizers and fuels can be found in the JANAF tables.FI Practical computations are carried out by the use of computer programs such as the cited NASA program.PI Table 3.2 shows an example of a computation comparing the detonation and deflagration characteristics of the gaseous mixture 2H2 -1- O2. 

Since the detonation velocity is equal to the speed of sound at the CJ point, Wp is determined by means of Eqs. (3.24) and (3.25). The temperature of detonation at the CJ point is higher than the temperature of deflagration because of the shock wave compression on the detonation wave. 

In general, the wave propagation velocity in the deflagration branch is termed the flame speed, and that in the detonation branch is termed the detonation velocity. 

Experimental observations indicate that the pressure of the detonation front is higher than the pressure at J, but less than the pressure at the point of the intersection of the Rayleigh line and the Hugoniot curve, and finally reaches the pressure at J shown in Fig. 3-6. 

Computations of the thermochemical values of various combinations of oxidizers and fuels are obtained from [7], and practical computations are done by the use of the computer programs described in [8]. A computational example of detonation characteristics of the gaseous mixture, 2 H2 + 02, is shown in Table 3-2 and compared with deflagration characteristics. 

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Fig. 3.2. Controlled, high pressure shoek loading ean be routinely earried out with large diameter plane wave explosive lenses whieh initiate Detonation in cylinders of high explosives with known, reproducible behavior. Detonation waves from the explosive are transmitted into metal plates which can serve as standards and on which samples to be studied are placed.

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). 

An improvement on the CJ model is the ZND (Zeldovich, von Neumann, and Doring) model, which takes the reaction rate into account (Nettleton 1987, Classman 1996, Lewis and von Elbe 1987). The ZND model describes the detonation wave as a shock wave, immediately fol-... 

Denisov, Yu. N., K. I. Shchelkin, and Ya. K. Troshin. 1962. Some questions of analogy between combustion in a thrust chamber and a detonation wave. 8th Symposium (International) on Combustion, pp. 1152-1159. Pittsburgh PA The Combustion Institute. 

Strehlow, R. A. 1970. Multi-dimensional detonation wave structure. Astronautica Acta 15 345-357. 

Such hot spots react instantaneously as localized, constant volume sub-explosions (Urtiew and Oppenheim 1966 Lee and Moen 1980). If the mixture around such a sub-explosion is preconditioned sufficiently to ignite on shock compression, a detonation wave will engulf the entire process of flame propagation. 

The preceding section described the state of transition expected in a deflagration process when the mixture in front of the flame is sufficiently preconditioned by a combination of compression effects and local quenching by turbulent mixing. However, additional factors determine whether the onset of detonation can actually occur and whether the onset of detonation will be followed by a self-sustaining detonation wave. 

The nature of the restrictive boundary conditions for detonation is closely related to the cellular stmcture of a detonation wave (Section 3.2.2). It was systematically investigated in a series of flame propagation experiments in obstacle-filled tubes by Lee et al. (1984). The most important results are summarized below ... 

As with a high explosive, a fuel-air mixture requires a minimum charge thickness to be able to sustain a detonation wave. Hence, a fully unconfined fuel-air charge should be at least 10 to 13 characteristic-cell sizes thick in order to be detonable. If the charge is bounded by a rigid plane (e.g., the earth s surface) the minimum charge thickness is equal to 5 to 6.5 characteristic-cell sizes (Lee 1983). 

A fuel-air mixture is detonable only if its composition is between the detonabil-ity limits. The detonation limits for fuel-air mixtures are substantially narrower than their range of flammability (Benedick et al. 1970). However, the question of whether a nonhomogeneous mixture can sustain a detonation wave is more relevant to the vapor cloud detonation problem because, as described in Section 3.1, the composition of a vapor cloud dispersing in the atmosphere is, in general, far from homogeneous. 

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. 

Examining the conditions for the formation and propagation of detonation waves is relevant to special applications of detonations to propulsion as well as safety. 

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].

Kirkwood, J. G. and Wood, W. W., Editor, Shock and Detonation Waves, Gordon and Breach, London and New York. 

A flame trap is employed where premixed air and gas is used in combustion equipment and prevents the flame passing upstream into the pipe system. Flame traps should be situated as near as possible to the gas burner. This is so that the flame does not have a long pipe mn in which it might accelerate to such a speed as to form a detonation wave and make the trap useless. 

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. 

The fact that gases have a simple equation of state makes possible the use of absorptiometry with polychromatic beams to give information about the state of a gas under conditions (in detonation waves,16 boundary layers,17 or supersonic flow18) transient or difficult of access. Temperature measurements19 have also been made. The technique is a unique method for studying the fluidization of a finely divided solid by a gas. Bed density profiles, which reveal the character and effectiveness of fluidization, have been readily determined20 without disturbing the system as probes would inevitably do. 

Detonation waves in gases studied by x-ray absorptiometry, 84 Deviation, standard, see Standard deviation... 

V.M. Bozomolov LM. Voskoboinikov, Calculation of Detonation Wave Parameters for Mixtures of Explosives with Inert Additives , FizGoreniyaVzryva 6(2) 183—6 (1970) 47)... 

Neumann s Classical Theory of the Plane Detonation Wave. See Detonation, Classical Theory of Plane Detonation Wave in Vol 4, D237-R... 

The superior shaped-charge performance of Octol, as indicated previously, is limited by perturbances of the detonation wave front that af-... 

Ref D. Venable and T.J. Boyd, Jr, PHERMEX Applications to Studies of Detonation Waves and Shock Waves , 4th ONRSympDeton (1965), 639-47 (29 refs are included)... 

Plane Detonation Waves with Finite.Reactions. 

See Detonation Waves Steady-state, One-Dimensional Reaction Waves with Finite Reaction Rate in Vo 4, D7Q3-R to D704-R. Ref S. Brinkley, Jr J.M. Richardson, 4th SympCombstn, Williams Wilkins, Baltimore (1952), 450-57 CA 49, 6608 (1955)... 

Lu, Vyn, Sandus and Slagg (Ref 17) conducted ignition delay time and initiation studies on solid fuel powder-air mixts in an attempt to determine the feasibility of solid-air detonations. The materials investigated included Al, Mg, Mg-Al alloy, C and PETN. Ignition delay time was used as a method of screening the candidate fuels for further work in initiation studies which determined detonation wave speed, detonation pressure, detonation limits, initiation requirements, and the effect of particle size and confinement. The testing showed the importance of large surface area per unit mass, since the most... 

Akulintsev et al, On the Possibility of Stimulated Emission of CO Molecula Behind Overdriven Detonation Waves in CS2+02 Mixtures , FizikaGoreniaiVziyva 12, No 5 (1976) 739—44... 

Salamandra, G.D., Bazhenova, T.V., and Naboko, I.M., Formation of detonation wave during combustion of gas in combustion tube. Seventh Symposium (International) on Combustion, Butterworths, London, pp. 851-855, 1959. 

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