Planar detonation structure

In the following section we shall discuss the structure of steady, plane, one-dimensional, gaseous detonations. Factors influencing detonation propagation velocities are considered in Section 6.2. Important unsteady and nonplanar aspects of detonation phenomena are treated in Section 6.3. Detonations in media that are not purely gaseous will be discussed in Section 6.4. Since the material on detonations is too extensive to be developed fully here, the reader is directed to the literature cited above for further details. 

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On the basis of numerical calculations of steady, planar detonation structure (for example, [33]) and of good experimental measurements performed mainly in the 1950s (for example, [34]-[37] see review in [38]), it was widely believed that the ZND structure was representative of most real detonations. This structure excludes weak detonations, which require special consideration (see Section 6.2.2). It is likely to apply to sufficiently strong detonations (over-driven waves, see Sections 6.2.6 and 6.3.3). However, for the most common—Chapman-Jouguet waves—more recent studies. 

We have inferred that for planar detonations, curve c in Figure 6.3 represents the most reasonable structure. The relationship between pressure and volume along this curve is illustrated in Figure 6.4 (the labels a through /identify corresponding curves in Figures 6.3 and 6.4). Since curve c lies close to curve a followed by curve fo, we concluded that these two curves afford a good approximation to the structure of most planar detonations. Since... 

For purposes of further analyses of detonation structure, the shock wave may be treated as a discontinuity. Both the viscous interaction between the shock and the reaction region and the molecular transport within the reaction region are small perturbations that do not appear to exert qualitatively significant influences on the wave structure. This conclusion appears to apply not only to steady, planar waves but also to unsteady, three-dimensional structures it affords one helpful simplification in the complicated analyses of transverse wave structures. It also alters the interpretation of a detonation as a deflagration-supported shock the support provided by the chemical reactions is of a nonplanar compressible gasdynamic character with negligible molecular transport. 

To obtain a rough physical understanding of the mechanism of the instability, attention may be focused first on a planar detonation subjected to a one-dimensional, time-dependent perturbation. Since the instability depends on the wave structure, a model for the steady detonation structure is needed to proceed with a stability analysis. As the simplest structure model, assume that properties remain constant at their Neumann-spike values for an induction distance after which all of the heat of combustion is released instantaneously. If v is the gas velocity with respect to the shock at the Neumann condition, then may be expressed approximately in terms of the explosion time given by equation (B-57) as Z = vt. From normal-shock relations for an ideal gas with constant specific heats in the strong-shock limit, the Neumann-state conditions are expressible by v/vq = po/p —... 

Reasonable models for the detonation wave structure have been presented by Zeldovich [9], von Neumann [10], and Doring [11], Essentially, they constructed the detonation wave to be a planar shock followed by a reaction zone initiated after an induction delay. This structure, which is generally referred to as the ZND model, will be discussed further in a later section. 

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