Untitled - Aerobib - Universidad Politécnica de Madrid

Chapter 6
Laminar flames
6.1 Introduction
It was demonstrated in chapter 4 that through a combustible mixture of gases two
types of combustion waves may propagate: detonation waves and deflagration waves
or flames. Chapter 5 includes the analysis of the nature of such waves, their structure
and the conditions which determine their propagation velocity. This analysis proved
that while in detonation waves the propagation velocity is determined only by a condition
of mechanical stability within the zone of burnt gases, which simplifies extremely
its determination, when dealing with flames their propagation velocity is determined
by an internal equilibrium between the processes of chemical reaction, heat transfer
(conductivity) and transport of the chemical species (diffusion), which makes the
study specially difficult.
The initial attempt to establish a theory on these bases, and in particular the
deduction of the first formula for the computation of the propagation velocity of a
flame through a given mixture, which is the fundamental problem of combustion, is
own to Mallard and Le Chatelier [1]. Their theory is purely thermal and it establishes
a primitive balance between the heat received by the gases through conduction, when
an assumed ignition temperature is reached, and the heat content of these gases. The
concept of reaction velocity is not applied in this theory.
The work by Mallard and Le Chatelier was the starting point for the development
of the “thermal theories of the flame”, so called because they did not include the
diffusion of species.
The idea of chemical reaction velocity, incorporated by Crussard [2] to this
thermal model, was a definite step forward in the progress of the theory. From there
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