Page 285 - Advanced Thermodynamics for Engineers, Second Edition

274 CHAPTER 12 CHEMICAL EQUILIBRIUM AND DISSOCIATION

A numerical method for solving these equations is given in Horlock and Winterbone (1986), based
on the original paper by Lavoie et al. (1970).
Figure 12.7 shows the results of performing such calculations using a simple computer program.
The coefficients in the program were evaluated using the data presented in Table 9.3 in Chapter 9, but
with the addition of OH and N. The three diagrams are based on combustion of octane in air at a
constant pressure of 30 bar, and show the effect of varying equivalence ratio, f, at different tem-
peratures. The conditions are the same as quoted in Heywood (1988). Figure 12.7(a) shows the
results for the lowest temperature of 1750 K, and it can be seen that the graph contains no atomic
4
nitrogen (N) or atomic oxygen (O) because these are at very low concentrations (<10 ). When the
mixture is weak some OH is produced. It is apparent from this diagram that there is not much
dissociation of the carbon dioxide or water because the concentration of oxygen drops to very low
values above f ¼ 1. Some nitric oxide is formed in the weak region (x NO ¼ 3 10 3 at the weakest
mixture), but this rapidly reduces to a very low value at stoichiometric simply because there is no
oxygen available to combine with the nitrogen. Figure 12.7(b) shows similar graphs for a
temperature of 2250 K, and it can be seen that the NO level has increased by almost a factor of 10.
ThereisalsosomeNOformedbycombustionwith rich mixtures;thisisbecause,by this
temperature, the carbon dioxide and water are dissociating, as is indicated by the increase in the
CO and the OH radical in the weak mixture region. By the time 2750 K is reached, shown in
Fig. 12.7(c), there is a further tripling of the NO production and CO is prevalent throughout the weak
mixture zone. There are also significant amounts of OH and oxygen over the whole range of
equivalence ratio.
The diagrams shown in Fig. 12.7 are relatively contrived because they do not depict real com-
bustion situations. However, they do allow the parameters which control the production of the products
of combustion to be decoupled to show the effects of changing the parameters independently of each
other. The equilibrium concentrations depicted in Fig. 12.7 are the values which drive the formation of
the exhaust constituents through the chemical kinetics equations.

12.11 DISSOCIATION PROBLEMS WITH TWO, OR MORE, DEGREES
OF DISSOCIATION
The previous example, Example 3, which considered the dissociation of carbon monoxide, shows the
fundamental techniques involved in calculating dissociation but it is an unrealistic example because
rarely are single component fuels burned. Even if a single component fuel such as hydrogen was
burned in an engine, it would be necessary to consider other ‘dissociation’ reactions because it is likely
that nitric oxide will be formed from the combination of the oxygen and nitrogen in the combustion
chamber. These more complex examples will be considered here.

12.11.1 EXAMPLE 4: COMBUSTION OF A TYPICAL HYDROCARBON FUEL

A weak mixture of octane ðC 8 H 18 Þ and air, with an equivalence ratio of 0.9, is ignited at 10 bar and
500 K and burns at constant volume. Assuming the combustion is adiabatic, calculate the conditions at