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5.6. DEFLAGRATIONS 123
mum temperature is reached shortly before the combustion ends (as is clearly shown
in Fig. 5.3), after which a slight temperature drop (100 to 200 ◦ C for typical cases)
takes place due to the fast expansion of the combustion products. For the very strong
detonations, like DE represented in Fig. 5.3, the maximum temperature is reached at
the end of the combustion. These results appear in Fig. 5.4, which shows the values
corresponding to a typical case for a Chapman-Jouguet detonation.
5.6 Deflagrations
We have said that the deflagrations, also known as flames, will be the subject of a
careful study in the following chapter. Consequently, herein we shall only include a
few brief considerations concerning their possible existence, structure and propagation
velocity.
In the preceding chapter we have seen that the propagation velocity of a deflagration
wave is always subsonic. Thereby it cannot be ascertained that in the deflagration
waves the condition α ≪ M 2 will be satisfied, and the system that must be used
for the study of its structure is B, at least within the region of the flame close to the
cold boundary. 14 Let us consider separately the weak and strong deflagrations, and let
us start by demonstrating that the latter cannot exist.
In the strong deflagration waves, the final velocity of the gases is supersonic.
Consequently, at least in the final zone of such waves, the condition M 2 ∼ 1 is satisfied,
and system A can be used. In particular in this zone, the variation law for the
velocity of the gases with respect to the wave is given in Fig. 5.1. However, due to
the influence of thermal conductivity and diffusion, this law can differ within the zone
close to the cold boundary. Hence, in a strong deflagration wave, the variation of the
velocity of the gases through the wave must follow a law as the one represented in
Fig. 5.5, where the curve in Fig. 5.1 representing the limiting solution of system A has
also been represented by a dash line. The velocity of the unburnt gases is represented
by point P . Starting from this point, the gases accelerate. When their Mach number
is such that condition α ≪ M 2 is satisfied, the curve overlaps the dash line of the
limiting solution (in the figure this happens at point B). If now one must reach point
D, corresponding to the final state where the velocity is supersonic, this can only be
achieved by passing through point C where the velocity is sonic. But the jump from C
14 It has been shown in the preceding chapter that the propagation velocity of a deflagration is always equal
to or smaller than that corresponding to the Chapman-Jouguet deflagration. In this case the Mach number
corresponding to the propagation velocity is always much smaller than unity. Thereby, the propagation
Mach number of the deflagrations observed is always much smaller than unity. In practice, of the order of
10 −3 .