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# Chapter 1

### Detonation front structure

Standard practice of evaluation possible hazards, which can come from detonation precesses is usually based on the theory of sbased on the theory of stady state one-dimensinal detonation. The predictions of such theory are well-known and usually can have sufficient accuracy to provide necessary information for industrial designs.

Fig. 1. Detonation front structure.

However there are numerous examples demonstrating non-statinary and multi-dimensional nature structure of the detonations. These features can affect the maximum local pressures during detonation process and therefore can be important from the point of view of safety aspects for industrial applications.

Detonation waves in the mixtures, which are far enough from detonation limits, have internal multi-dimensional structures. Already classical works on structure of detonation waves, e.g. (Woitsekhovski, 1960, Strehlow, 1970a, 1970b, 1970c), allowed to discover different type of detonation waves:

• front structures, which have highly constant values of main characteristics averaged in time and regularly repeated structure;
• front structures, which have constant averaged characteristics but no regular structure;
• front structures, which exhibit really non-stationary behavior.

In case of lean or reach mixtures, which are close to their detonation limits, detonations occur usually exhibiting characteristics of the second or third types. Unfortunately, most of the experimental work was performed for the mixtures far from detonation limits, and detonations of marginal mixtures are not studied in full volume. Note that the role of front structure, as a rule, appears to be more significant in case of lean mixtures detonations, which are typical for industrial accidents.

Multi-dimensional structure of the detonation front includes leading shock wave and a number of transverse waves, which propagates perpendicular to the leading shock, reflecting from each other and from bounding walls. The surface of the leading shock consists of the sequence of convex parts, which start chemical reaction, and concave parts which are fast decaying waves. Additional reaction zones are located behind the transverse waves where the reaction completes.

### Detonation cell size

In Figure 1 (Gavrikov, 2000) a diamond-shaped form demonstrated a typical track of triple points intersecting shock waves. Such track is called detonation cell and can be easily obtained experimentally on sooted sur-faces located in detonating gases. These cells form a cellular structure observed experimentally, and are characterized by their two lengths: longitudinal size L and transverse size S. These two lengths are varying depending on type of burnable gase and intial conditions, however the relation S ≈ 0.6 · L or S \approx 0.6 \cdot L are kept usually constant.

$$S \approx 0.6 \cdot L$$

Fig. 2. Typical example of the soot \\ track for H2 cellular structure.

In Figure 2 (Kuznetsov, 2000, 2002) an example of soot track cellular structure produced by detonation of stoichiometric hydrogen-air mixture is shown. Average transverse cell size S ≈ 1 cm. For such mixture typically irregular detonation cellular structure is realized. The detonation cell size is kept constant for the given components for the same initial condition and depends only on the mixture composition, and therefore is often used as a mesure of mixture reactivity. Usually the detonation cell size reaches its minimum at the stoichiometry composition and grows for leaner and reacher mixtures.

### References

V. V. Voitsekhovski (1960) Front structure of detonation in gases (in Russian), Publ. AN SSSR.
R. A. Strehlow. (1970a) Multi-dimensional detonation wave structure, Acta Astronautica, 15, 345.
R. A. Strehlow, R. E. Maurer, S. Rajan. (1970b) Transverse waves in detonations. I. Spacing in the hydrogen – oxygen system, AIAAJ, 7, 323.
R. A. Strehlow, C. D. Engel. (1970c) Transverse waves in detonations. II. Structure and spacing in H2-O2, C2H2-O2, C2H4O2 and CH4-O2 systems, AIAAJ, 7, 492.
A. I. Gavrikov, A. A. Efimenko and S. B. Dorofeev, (2000), A model for detonation cell size prediction from chemical kinetics, Combustion and Flame, 20, Issues 1- 2, pp. 19-33
Kuznetsov M.S., Alekseev V. I., Dorofeev S. B. Comparison of critical conditions for DDT in regular and irregular cellular detonation systems. Shock Waves, 2000, v. 10, pp. 217-224
Kuznetsov M., Cicarelli G., Dorofeev S., Alekseev V., Yankin Yu., Kim T.H. DDT in Methane-Air Mixtures. Shock Waves, 2002, vol. 12, pp. 215-220
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