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Chapter 4
Combustion Waves
4.1 Detonation and deflagration
When an explosive mixture is ignited, a wave or reaction front originates which propagates
the combustion throughout the mixture. The wave thickness is normally very
small. By assuming this thickness to be zero, that is, assuming that gases burn instantaneously
as they cross the wave, the state of the mixture and the state of the burn
gases can be compared, in a way similar to that used when studying shock waves; 1
that is, by applying the laws of the conservation mass, momentum and energy across
the front, without taking into consideration the intermediate transformations between
the initial and final states Thus, the following system of three equations is obtained
ρ 1 v 1 = ρ 2 v 2 , (4.1)
ρ 1 v1 2 + p 1 = ρ 2 v2 2 + p 2 , (4.2)
1
2 v2 1 + h 1 = 1 2 v2 2 + h 2 , (4.3)
where ρ, p and h are the density, pressure and total enthalpy per unit mass and v the
normal velocity relative to the reaction front. Subscripts 1 and 2 refer to the unburnt
gases and to the combustion products respectively. In particular, v 1 is the propagation
velocity of the wave, that is, the velocity at which the wave moves through the unburnt
gases, Fig. 4.1.
For a given composition, the specific enthalpy h 1 of the unburnt gases is a
function of the pressure p 1 and the density ρ 1 of the mixture
h 1 = h 1 (p 1 , ρ 1 ) . (4.4)
1 See i.e. Courant-Friedrichs: Supersonic Flow and Shock Waves. Intersciences Pub. Inc., New York,
1948, pp. 121 and following.
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