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

2 Combustion Theory
The results of the validation were analyzed utilizing statistical means. Normal
relative difference ǫ m,abs (Eq. (2.26)) and total relative difference ǫ m,tot
(Eq. (2.27)) were evaluated for each case consulting spatial profiles of the mass
fraction Y m of critical species m. The normal relative difference is a measure
for the degree of agreement of two curves, whereas the total relative difference
gives an idea of whether a mechanism overestimates or underestimates
the production of species m [298]:
ǫ m,abs =
ǫ m,tot =
∫∣ ∣Ym − Y m,ref
∣ ∣ dx
∫
Ym,ref dx
, (2.26)
∫
(Ym − Y m,ref ) dx
∫ . (2.27)
Ym,ref dx
A quantitative summary of the results is given in Tables 2.1 and 2.2 taking
into consideration laminar premixed flames of CH 4 , C 2 H 6 , CO, and H 2 . The
equivalence ratio φ was successively set to 0.8, 1.0, and 1.2 for each of these
flames. The Aachen C 10 H 22 mechanism together with the Leeds NO x kinetics
(“n-Decane (Aachen) + NO x (Leeds)”) exhibited poor convergence and stiff
Table 2.1: Mean Values of Normal Relative Difference of Mass Fraction of NO for Laminar
Premixed Flames. All values of the normal relative difference ǫ m,abs are given in %.
GRI 3.0 GRI 2.11 Leeds Princeton Princeton Aachen
+ Li + Leeds + Li
GRI 3.0 0.0 24.4 20.4 16.1 17.5 24.4
GRI 2.11 16.6 0.0 15.9 17.7 16.3 39.0
Leeds 21.2 20.9 0.0 24.3 23.4 40.3
Table 2.2: Mean Values of Total Relative Difference of Mass Fraction of NO for Laminar Premixed
Flames. All values of the total relative difference ǫ m,tot are given in %.
GRI 3.0 GRI 2.11 Leeds Princeton Princeton Aachen
+ Li + Leeds + Li
GRI 3.0 0.0 8.9 3.1 4.1 13.5 2.5
GRI 2.11 −5.3 0.0 −3.7 −1.8 6.4 1.7
Leeds 1.4 10.3 0.0 7.4 17.4 10.1
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