Untitled - Aerobib - Universidad Politécnica de Madrid

Chapter 9
Flows with combustion waves
9.1 Introduction
As previously seen in chapter 6, in a combustible mixture at ambient of higher pressure,
the thickness of the flame is of the order of a fraction of millimeter. This length
is generally “small” when compared to those of interest in aerothermodynamic problems.
Therefore, when studying these problems it is justified to assume that the flame
thickness is zero. In such a case the flame may be considered as a surface of discontinuity
of the pressure, temperature and velocity. The same idea is applied, for example,
in the study of gas dynamic problems involving shock waves. The problem has been
studied from this view point mainly by Emmons and his co-operators [1], [2], [3], [4].
In this chapter the general lines of Emmons’s work are followed. First the conditions
that must be satisfied across the flame are established and then some general properties
deduced. In the chapter that follows, the method is applied to the study of the
aerothermodynamic field originated by a flame stabilized in a combustion chamber.
This problem has been studied by Scurlock, Tsien, and Fabri-Siestrunck-Fouré.
9.2 Conditions that must be satisfied by the jump across
a flame front.
As aforesaid, the relations deduced herein are applicable only if the thickness of the
flame front is small when compared to a characteristic length of the phenomenon under
study. 1 The flame thickness must also be small compared to the radius of curvature
1 For instance, this does not occur in rarefied mixtures where the thickness of the flame can be large.
231