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

A.2 Concepts of Kinetics Reduction
δ l B = {
1 if the l-th elementary reaction involves species B,
0 otherwise.
(A.9)
Taking into account only the direct influence of B on A, interaction coefficients
of the “first generation” are defined as
r prod,1st
AB
=
P AB
max(P A ,C A ) ,
C
r con,1st
AB
AB
=
max(P A ,C A ) .
(A.10)
(A.11)
If the influence of intermediate species has to be captured as well, reaction
coefficients of a higher generation are employed. For instance, B affects the
conversion of S o , and S o in turn is involved in the conversion of A. This particular
case represents the “second generation” with the additional coefficients:
N∑
r prod,2nd
AB
=
(r prod,1st
AS o
S o ≠A,B
N∑
r con,2nd
AB
=
(r con,1st
AS o
S o ≠A,B
)
r prod,1st
S o B
, (A.12)
)
r con,1st
S o B
. (A.13)
The overall reaction coefficient r AB is defined as the sum of Equations (A.10)
through (A.13) and is finally used to determine the relevance of species B to
species A in the reacting system:
r AB = r prod,1st
AB
+ r con,1st
AB
+ r prod,2nd
AB
+ r con,2nd
AB
. (A.14)
In combination with the user-defined threshold ε, the calculated value of r AB
delivers a criterion for the reduction of the reaction mechanism. If r AB ≥ ε,
species B is selected for the reduced mechanism. However, if r AB < ε, species
B can be neglected and is removed. Furthermore, reactions including removed
species are no more relevant either, and thus are removed from the
original mechanism as well.
Hence, extent and quality of the reduction are determined by the threshold ε
of the interaction coefficient, the input set of the production rates ˙ω Al , and the
preselected species A. For the set of production rates, values should represent
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