Untitled - Aerobib - Universidad Politécnica de Madrid

5.5. DETONATIONS 117
waves. Such theories were initiated by the works of Taylor in England, von Neumann
[7] in the U.S.A., Zeldovich [8] in the U.R.S.S. and Döring [9] in Germany.
Within the combustion zone that follows the initial shock wave, the gases move
along the lower branch of the curve shown in Fig. 5.1, starting from point B. The point
ε = 1, at which the combustion ends and the thermodynamic equilibrium is reached
after the wave, cannot lie at the right hand side of D. Therefore, the three following
cases can occur:
1) The combustion ends at a point such as E of the lower branch, in which the
velocity is subsonic. This case represents a strong detonation.
2) The combustion ends at the point C that separates the subsonic from the supersonic
branch. In C the velocity of the burnt gases with respect to the detonation
wave is sonic. The corresponding detonation for this case is of the Chapman-
Jouguet type.
3) The representative point of the final state is point F in the supersonic branch.
Consequently, the final velocity is supersonic and the corresponding detonation
is weak.
We shall presently see that the last case cannot possibly occur. In fact, in order
to reach point F either one has to pass by point C, in which case the reaction between
C and F would be endothermic and therefore in contradiction with what happen in the
combustion, or else one must pass from B to D and from D to F by means of a jump
or expansion shock which is also impossible. Consequently, weak detonations are not
possible.
On the other hand, nothing opposes a strong detonation or a detonation of the
Chapman-Jouguet type. For a given case the occurrence of one or the other depends
on the boundary conditions after the wave. Let us see the influence of these conditions.
When the detonation is strong, the velocity of the burnt gases, with respect to
the wave is subsonic. Any perturbation produced in the burnt gases will propagate
throughout them with sound velocity and can therefore reach the wave and alter its
nature. For example, an expansion of the burnt gases will reach the wave, reducing
its strength down to the point where the velocity of the burnt gases with respect to the
wave equals the sound velocity. In such a case the wave becomes insensible to the
perturbations that occur in the burnt gases. Such is the situation that normally occurs
in practice; for example, when the detonation propagates along a tube, starting either
at an open or closed end. Thus the detonations normally observed in practice are of the
Chapman-Jouguet type, due to the fact that these are the only stable ones with respect
to perturbations coming from the burnt gases.