Hugoniot relations and the hydrodynamic theory of detonations

If one is to examine the approach to calculate the steady, planar, one-dimensional gaseous detonation velocity, one should consider a system configuration similar 

Actual laboratory velocities or velocities with respect to the tube 

FIGURE 5.1 Velocities used in analysis of detonation problem. 

In this type of representation, all combustion events are collapsed into a discontinuity (the wave). Thus, the unknowns are uu u2, p2, T2, and P2. Since there are four equations and five unknowns, an eigenvalue cannot be obtained. Experimentally it is found that the detonation velocity is uniquely constant for a given mixture. In order to determine all unknowns, one must know something about the internal structure (rate of reaction), or one must obtain another necessary condition, which is the case for the detonation velocity determination. 

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C. Hugoniot Relations and the Hydrodynamic Theory of Detonations are developed and substituted in... 

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