Page 309 - Advanced thermodynamics for engineers

13.3 THE EFFECT OF DISSOCIATION ON PEAK PRESSURE 297

f is called the equivalence ratio: in this case f 1.0. For a rich mixture, f 1.0, if it is assumed that
the hydrogen has preferential use of the oxygen, then the equation becomes

2 4 3f 4f 4 7:52
CH 4 þ O 2 þ 3:76N 2 0 CO 2 þ CO þ 2H 2 O þ N 2 : (13.4)
f f f f
(note: Eqn (13.4) is only valid for 1.0 f 1.333 )
0
It will be assumed for the initial examples that the only dissociation is of the products, carbon
dioxide and water, which dissociate according to the equations
1
CO 2 5CO þ O 2 ; (13.5)
2
and
1
H 2 O5H 2 þ O 2 : (13.6)
2
These equations (Eqns (13.5) and (13.6)) have to be added into the basic equations to evaluate the
chemical equation with dissociation. The program does this automatically and evaluates the mole
fractions of the products. The approach adopted by the program is the same as that introduced in
Chapter 12, when the products of combustion are defined by a set of simultaneous equations. Later in
the chapter the dissociation of other compounds will be introduced to give a total of 11 species in the
products. The method of solving for these species is outlined by Baruah (Chapter 14) in Horlock and
Winterbone (1986).

13.3 THE EFFECT OF DISSOCIATION ON PEAK PRESSURE
In general, dissociation will tend to decrease the pressure achieved during the combustion process
(when it occurs in a closed system) because it reduces the temperature of the products. This reduction
in pressure is always evident with stoichiometric and lean mixtures, although an increase in pressure
over the equivalent situation without dissociation can occur in rich mixtures due to the increase in the
amount of substance in the products. Figures 13.2 and 13.3 show that the peak pressure is reduced by

140 FIGURE 13.2
120 Variation of pressure with equivalence
ratio for combustion of methane.
100 Weak Rich Initial pressure: 1 bar
Pressure / (bar) 80 Initial temperature: 300 K
Compression ratio, r:12
60
Compression index, k: 1.4
40
no dissociation
dissociation
20
0
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
Equivalence ratio, φ