Untitled - Aerobib - Universidad Politécnica de Madrid

9.5. ENTROPY JUMP ACROSS THE FLAME FRONT 239
PRODUCTS
FLAME FRONT
REACTANTS
Figure 9.6: Straight-line flame flow field according to Gross and Esch for ϕ/v 1 = 0.1 and
λ = 7.
2) Opposite to what occurs with fast flows, if the flow is slow pressure drop across
the flame front cannot be neglected.
In order to analyze the motion, the flame front can be considered as a surface with a
distribution of sources. For example, in the case of a plane motion, the strength of the
(λ − 1)ϕ
source per unit length of the front is . Now by expressing the condition that
2π
in the unburnt gases the velocity normal to the front must be ϕ, an integral equation
is obtained which must ϕ satisfied at the front. This integral equation determines the
flame shape which ”a priori” is unknown. Gross and Esch give approximate solutions
for certain cases. For example, for the case in which the flame front reduces to a
straight segment inclined to the incident flow. Fig. 9.6, taken from the said work,
shows the shape of the streamlines in this case.
9.5 Entropy jump across the flame front
The entropy of the unburnt gases is given by the expression 3
3 See chapter 1.
S 1 = S 01 + c p1 ln p1/γ 1
1
, (9.41)
ρ 1