Detonations structure

FIGURE 5.14 Effect of chemical reaction rates on detonation structures as viewed on Hugoniot... 

Detonation, Structure of Some Liquid Explosives in was discussed by T.P. Cotter in his Thesis, Cornell Univ, Ithaca, NY, Sept... 

Figure 30.6 Comparison of detonation structures with ethylene-oxygen (a) and ethylene-air (6) [16]...

In view of equations (5-34) and (15), the temperature must become relatively large in the detonation wave before x begins to change appreciably from its value (t = 0) at the cold boundary. Hence, the upstream portion of the detonation structure will lie very near the line t = 0 connecting the points (p + (0) and (p-.(0) in Figure 6.3, and the detonation structure will be represented by a curve similar to the one labeled c in Figure 6.3. The solution curve c is closely approximated by curve a followed by curve b in Figure 6.3. 

FIGURE 6.4. Schematic illustration of detonation structure in a pressure-volume plane. 

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. 

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. 

We have seen that considerations of detonation structure do not restrict the detonation propagation velocity (at least for strong and Chap-man-Jouguet waves). Therefore, wave speeds must depend on the experimental configuration and can be discussed only within the framework of a class of experiments. Here we shall first consider detonations produced by... 

A very convincing argument against the existence of weak detonations utilizes the results on detonation structure presented in Section 6.1.2.3. A ZND structure is not possible for weak detonations, and chemical reaction rates generally are not high enough to produce a direct transition to the end state. 

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 —... 

Instability analyses do not provide good indications of fully developed transverse structures of detonations because these structures correspond to highly nonlinear phenomena. A great deal of nonlinear evolution would occur between onset of instability and attainment of a mature multidimensional detonation structure. Intersections of oblique shocks are known to constitute a central element in transverse structures of detonations [69], [72]. Oblique-shock relations are therefore relevant to the nonplanar structure. 

In solid or liquid explosives, reactive molecules are continually interacting, and limitations on detonation structures associated with molecular mean free paths no longer apply. It becomes entirely possible for significant release of chemical energy to occur within the structure of the leading shock. This fact motivates new approaches to studies of detonation structure on the basis of molecular dynamics [189], [190]. Although the fundamental complexities that are encountered make the problem difficult, further pursuit of these lines of investigation seems desirable. 

Thermodynamics and statistical mechanics deal with systems in equilibrium and are therefore applicable to phenomena involving flow and irreversible chemical reactions only when departures from complete equilibrium are small Fortunately this is often true in combustion problems, but occasionally thermodynamical concepts yield useful results even when their validity is questionable [for example, in the analysis of detonation structure (see Section 6.1.5) and in transition-state theory (see Section B.3.4)]. The presentation is restricted to chemical systems appropriate independent thermodynamic coordinates are pressure, p, volume, V, and the total number of moles of a chemical species in a given phase, N-, Moreover, results related to combustion theory are emphasized. 

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