Untitled - Aerobib - Universidad Politécnica de Madrid

9.4. INCLINED FLAME FRONT 237
60
50
40
λ = 12
8
6
5
4
δ ( o )
30
3
20
λ = 2
10
δ max
0
10 30 50 70 90
α 1
( o )
Figure 9.4: Velocity deviation across the flame front as a function of α 1.
Its value is given by
tan δ max = 1 2
( )
√λ 1 − √λ . (9.32)
Even though the normal velocity is always “small”, the tangential velocity v t , which
by virtue of equation (9.3) is the same at both sides of the front, can be “large”. Therefore,
it must be taken into account when writing the energy equation. As a result, the
temperature at each side of the front can differ, considerably, from the corresponding
stagnation temperature. This is exactly the opposite to what occurs in the case of a
normal front.
Therefore, two different cases are to be considered, either
v t ≃ O(v n ), (9.33)
in which case
or
in which case
T 1 ≃ T s1 , T 2 ≃ T s2 , λ ≃ n, (9.34)
v t ≫ v n , (9.35)
v 2 1 ≃ v 2 2 ≃ v 2 t , (9.36)
and equation (9.13) reduces to
c p1 T 1 + q = c p2 T 2 . (9.37)