Untitled - Aerobib - Universidad Politécnica de Madrid

124 CHAPTER 5. STRUCTURE OF THE COMBUSTION WAVES
to D could only be attained through an endothermic reaction, and this kind of reaction
is impossible in a combustion process. As a consequence, the non-existence of the
strong deflagrations is concluded.
D
v
C
B
P
ε
Figure 5.5: Schematic diagram showing the variation of the velocity of gases in a deflagration.
On the other hand, since for a weak deflagration the final velocity is subsonic,
nothing is opposed to its existence.
In the weak deflagrations diffusion and heat conduction are important and the
system to be used is system B. Diffusion and heat conduction are responsible for
the propagation of the combustion to the unburnt gases, activating their reaction by
diffusion of the active centers (atoms, radicals, etc.) and by heating. As they heat, the
gases expand and accelerate, producing a slight pressure drop throughout the wave.
Fig. 5.6 shows qualitatively the structure of a deflagration wave bringing forth, by
comparison with Fig. 5.3, the difference in the mechanism that propagate the process
in each case. The system B of differential equations that must be integrated in order
to obtain the structure of the deflagration wave can be simplified by eliminating x, as
done in §4. Thus obtaining
p Dw
R m T m 2
dY
dε
= Y − ε, (5.49)
λw dT
m 2 dε = c pT − qε + e. (5.50)
In the deduction of this system, the state equation p = ρR m T has been used in order
to eliminate the density from the diffusion equation.