The onset of detonation

Depending upon various conditions, an explosive medium may support either a deflagration or a detonation wave. The most obvious conditions are confinement, mixture ratio, and ignition source. 

Original studies of gaseous detonations have shown no single sequence of events due primarily to what is now known as the complex cellular structure of a detonation wave. The primary result of an ordinary thermal initiation always appears to be a flame that propagates with subsonic speed. When conditions are such that the flame causes adiabatic compression of the still unreacted mixture ahead of it, the flame velocity increases. According to some early observations, 

TABLE 5.1 Qualitative Deflagration in Gases Differences Between Detonations and 

When an explosive gas mixture is placed in a tube having one or both ends open, a combustion wave can propagate when the tube is ignited at an open end. This wave attains a steady velocity and does not accelerate to a detonation wave. 

The reaction zone in a detonation wave is no different from that in other flames, in that it supplies the sustaining energy. A difference does exist in that the detonation front initiates chemical reaction by compression, by diffusion of both heat and species, and thus inherently maintains itself. A further, but not essential, difference worth noting is that the reaction takes place with extreme rapidity in highly compressed and preheated gases. 

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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. 

In a smooth tube, the onset of detonation will take place only if the internal tube diameter is larger than about one characteristic-detonation-cell size. 

Yatsufusa,T., Ghao, J.G., and Lee, J.H.S., The effect of perturbation on the onset of detonation. Proceedings of the 21st International Colloguium on the Dynamics of Explosions and Reactive Systems on GD, Poitiers, 2007. 

Figure 6-21 Explosion data for propane showing peaks indicative of the onset of detonation. Data from W. Bartknecht, Explosions (New York Springer-Verlag, 1981).

Addition of 3% wax to 470 micron Tetryl at 66.5% TMD increased from about 70mm (no wax) to about 240mm. This is a much greater increase than observed for waxed and unwaxed RDX. Furthermore, addition of wax apparently changes the initial low temp decompn behavior, observed in pure Tetryl, into behavior typical of other expls, in that accelerated burning in waxed Tetryl starts sooner (further away from the onset of detonation) than in pure Tetryl... 

The chapter contains the results of theoretical and experimental investigations of control of the deflagration-to-detonation transition (DDT) processes in hydrocarbon-air gaseous mixtures relative to propulsion applications. The influence of geometrical characteristics of the ignition chambers and flow turbulization on the onset of detonation and the influence of temperature and fuel concentration in the unburned mixture are discussed. 

The operation mode of the pulsed detonation-wave generator has been shown to be closely related to periodical onset and degeneration of a detonation wave. Those unsteady-state regimes should be self-sustained to guarantee reliable operation of such devices. Thus, DDT processes are of major importance. Minimizing the predetonation length and ensuring stability of the onset of detonation enables an increased effectiveness of pulsed detonation devices. 

The mathematical models for simulating turbulent flame acceleration and the onset of detonation in chemically reacting flows were described in detail in [1-3]. The system of equations for the gaseous mixture was obtained by Favre averaging. The standard k e model was modified an equation was added that determined the mean squared deviate of temperature in order to model the temperature fluctuations. 

The results of numerical experiments showed that increasing the number of turbulizing chambers did not promote DDT for the present configuration, but did just the opposite — it prevented the onset of detonation and brought to establish the galloping combustion mode. The effect is due to very sharp variations in the cross-section area in the chambers and periodic flame slowing down due to its expansion. 

To investigate the influence of the expansion ratio on the onset of detonation, a set of numerical experiments was carried out on the DDT in tubes with diameters of... 

The presence of turbulizing chambers makes the onset of detonation more stable and fixed to a definite place depending on chamber geometry, mixture composition, and initial temperature ... 

Fast turbulent deflagrations often transit spontaneously to detonations. For fully developed self-sustained detonation, boundary conditions and confinement play minor roles. The Chapman-Jouguet velocity and overpressure are based on the energetics of the mixture and can be evaluated from equilibrium thermodynamic computations. During the onset of detonation, the transient peak overpressures developed can be much higher than the equilibrium detonation pressures. Transition from deflagration to detonation is to be avoided whenever possible because of this extremely high pressure transient at the onset of detonation. 

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