The ZND structure of detonation waves

Zeldovich [9], von Neumann [10], and Doring [11] independently arrived at a theory for the structure of the detonation wave. The ZND theory states that the 

When the detonation velocity was calculated in the previous section, the conservation equations were used and no knowledge of the chemical reaction rate or structure was necessary. The wave was assumed to be a discontinuity. This assumption is satisfactory because these equations placed no restriction on the distance between a shock and the seat of the generating force. 

But to look somewhat more closely at the structure of the wave, one must deal with the kinetics of the chemical reaction. The kinetics and mechanism of reaction give the time and spatial separation of the front and the C-J plane. 

The distribution of pressure, temperature, and density behind the shock depends upon the fraction of material reacted. If the reaction rate is exponentially accelerating (i.e., follows an Arrhenius law and has a relatively large overall activation energy like that normally associated with hydrocarbon oxidation), the fraction reacted changes very little initially the pressure, density, and temperature profiles are very flat for a distance behind the shock front and then change sharply as the reaction goes to completion at a high rate. 

FIGURE 5.13 Variation of physical parameters through a typical detonation wave (see Table 5.5). 

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