Untitled - Aerobib - Universidad Politécnica de Madrid

210 CHAPTER 7. TURBULENT FLAMES
flame. In technical applications this ratio is generally very large, hence the main cause
for the activation of combustion would be in this case the distortion of the flame front.
Figure 7.1b seems to confirm this point of view. The major part of the later works on
the subject have attempted to estimate the importance of either one of these causes,
preserving Damköhler’s model. In 1952 von Kármán and Marble [12] proposed a different
model which considered the turbulent flame as a zone whose structure should
be defined by mean values of the characteristic variables (temperature, reaction rate,
etc.) to which were superimposed static oscillations of turbulent nature. Later, this
model was adopted and developed by Sommerfield and his collaborators [13], who
obtained some experimental evidence (not sufficient) that the approximation is correct.
The comparison between theoretical and experimental results is not conclusive
enough in any case to establish either one of the proposed theories, which are actually
in a preliminary phase.
Consequently the present study will only be a brief exposure of the basic principles
and fundamental results of these theories.
7.2 Turbulent combustion theories
So far, the only type of turbulence whose influence on combustion has been studied is
the isotropic. This turbulence is characterized by two magnitudes: its scale l and its
intensity v ′ . 1 Damköhler studies the influence of turbulence on the flame by comparing
l and v ′ with the corresponding magnitudes of the laminar combustion wave of the
mixture; these being thickness d l of the flame and the laminar propagation velocity
u l . When performing this comparison the following cases arise.
flame
1) The turbulence scale is small when compared to the thickness of the laminar
l
d l
≪ l (7.1)
In this case the action of turbulence is reduced to an activation of the transport coefficients
conductivity and diffusion at the flame). Let
x =
λ
ρc p
(7.2)
and
ε ∼ lv ′ , (7.3)
1 For an exposure of the principles of turbulence, see, i.e., H.L. Dryden: A review of the Statistical Theory
of Turbulence. Quart. Applied Math., Vol. 1, 1943, pp. 7-42.