Untitled - Aerobib - Universidad Politécnica de Madrid

246 CHAPTER 10. AEROTHERMODYNAMIC FIELD OF A STABILIZED FLAME
ceding chapter, this flame front can be considered as a discontinuity surface between
unburnt and burnt gases.
The problem lies in determining:
a) The width of the flame as a function of the fraction of gas burnt.
b) The pressure drop along the chamber.
c) The velocity distribution in the different sections of the chamber.
d) The shape of the flame.
The following simplifying assumptions are introduced:
1) Combustion efficiency is the same at all points, that is, the heat released in the
combustion per unit mass of fuel is independent from the state of the gas before
the flame.
2) Heat capacity at constant pressure c p is independent from temperature, and has
the same value for the unburnt and burnt gases.
3) Unburnt and burnt gases behave as perfect gases. The constant R g of their state
equation has the same value for both gases
p
ρ = R gT. (10.1)
4) The flame propagation velocity is constant along the front and very small when
compared to the gas velocity.
5) Unburnt and burnt gases are ideal fluids, their viscosity and thermal conductivity
are negligible.
Furthermore, in this study only the case of stationary flow will be considered.
Thus stated, this problem has been studied by A.C. Scurlock [1] and [2], who introduced
further simplification by assuming both unburnt and burnt gases to be incompressible
fluids.
Since the flame speed is small compared to the gas speed, the angle between the
front and the streamlines is very small. Therefore, the streamlines are approximately
parallel to the chamber axis. Furthermore, due to the negligibility of the pressure drop
across the flame front, it can be assumed that pressure is constant at each cross section
of the chamber. Moreover, gas speed can be substituted by its component parallel
to the chamber axis. Therefore, from these assumptions an almost one-dimensional
theory can be worked out.
By using the aforementioned simplifying assumptions Scurlock obtained numerical
solutions for the equations of motion in some typical cases. In order to per-