Untitled - Aerobib - Universidad Politécnica de Madrid

10.1. INTRODUCTION 247
form numerical computations, Scurlock substitutes the differential equations for finite
differences.
Some of the results, taken from Ref. [1], are given in Figs. 10.2 to 10.5. These
results correspond to the case where the density ratio of the unburnt gases to the burnt
gases is 6, and the ratio of the flame speed to the gas velocity at the chamber’s inlet is
λ = 0.10.
y/h
A B C
1
0
x/h
−1
0
1
2
3
4
5
6
7
8
9
10
11
∆ P / ∆ P t
1
0 1 2 3 4 5 6 7 8 9 10 11 x/h
Figure 10.2: Streamlines of flow through a flame front in a two-dimensional chamber and
pressure drop along it.
Fig. 10.2 shows the shape of the flame front and of the streamlines, as well
as the pressure drop ∆p along the chamber referred to the total pressure drop ∆p t ,
between the inlet and outlet sections.
Fig. 10.3 shows the velocity distribution for the cross-sections A, B and C
indicated in Fig. 10.2. These sections correspond to the point at which combustion
starts (section A), to the point where the burnt fraction is 0.25 (section B) and to the
point where this fraction is 0.75 (section C). In this figure all velocities are referred to
the velocity u 0 of the gas at the inlet of the chamber. Fig. 10.3 shows that:
1) While the velocity of the unburnt gases is constant at each cross section, the
velocity of the burnt gases increases from the flame front towards the chamber
axis where it is maximum.