Propagation velocities for detonations traveling in tubes

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 

FIGURE 6.6. Schematic illustration of the velocity profile behind a detonation wave propagating in a tube all velocities in the - x direction. 

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If it is accepted that a spinning mode of propagation exists, then an acoustic theory may be applied to predict the spin frequency, the slope of the helical path on the tube wall, and other characteristics of spinning detonations [75]-[76]. For a planar Chapman-Jouguet wave in an infinitely long tube and in a frame of reference in which the burnt gas is at rest, the circumferential velocity of a traveling tangential acoustic wave at the wall... 

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