On the Formation of Nitrogen Oxides During the Combustion of ...

2.2 Theory of Exhaust Gas Formation
It is common practise to include the step of Equation (2.9) in the thermal
mechanism, even though the reacting species are both radicals, and thus the
concentration terms are typically very small in the chemical rate expression.
This combination of reactions (Eqs. (2.7) through (2.9)) is referred to as the
“extended Zeldovich mechanism” [149, 289, 443, 471, 472].
N+OH⇋NO+H (2.9)
As stated by Bowman [50], the formation of NO from atmospheric nitrogen
compares well for these three reactions and results extracted from detailed kinetics
calculations. However, it is essential that radical concentrations and
temperature are correctly evaluated during the combustion process. For fuelrich
mixtures, the extended reaction (Eq. (2.9)) is of particular importance.
Equation (2.7) represents the rate limiting step with the highest activation energy
of E a = 3.190×10 5 J mol −1 , coupled with its essential function of breaking
the strong N 2 triple bond [19, 443]. Consequently, the whole thermal
mechanism proceeds at a somewhat slower rate than the reactions of the
fuel constituents. Moreover, the production of atomic oxygen (O) required
in Equation (2.7) is also highly temperature sensitive. The local equivalence
ratio has a first-order effect on the available concentration of O, and the hightemperature
regime of the flame in combination with the hydrocarbon kinetics
of the fuel can boost the O concentration to several times its equilibrium
level [50, 391, 451].
Since the overall formation rate of NO due to the thermal mechanism is generally
slow compared to the fuel oxidation reactions, and following the suggestion
of Zel’dovich et al. [472], it is often assumed that the above reactions on
thermal NO can be decoupled from the fuel oxidation process. Equilibrium
is assumed for temperature and the concentrations of O 2 , N 2 , O, and OH. 11
The concentration of atomic nitrogen (N) is calculated from a steady-state approximation
applied to the reactions of Equations (2.7) through (2.9) [64, 289].
This approach was also chosen for the theoretical and numerical studies of
Bracco [54, 55], Altenkirch et al. [17], and Kesten [204] on NO generation in
single droplet flames conducted in the early 1970s. However, fuel oxidation
11 Even though this approach is more convenient than detailed chemistry modeling, its use has to be carefully
assessed. It may provide reasonable results if an extremely high temperature level and long residence times
are given, such as in automobile engines. A major shortcoming of the approach is that NO x formation is
underestimated in the reaction zone. Hence, this approach is not employed within the scope of this thesis.
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