17.3. Normalization of Sensitivity Coefficients

Ansys Chemkin further manipulates the raw sensitivity coefficients to make them more useful. First, we compute normalized sensitivity coefficients in the form of logarithmic derivatives, that is,

(17–6)

or

(17–7)

Second, although the gas-phase species solution variables are mass fractions, the sensitivity coefficients are computed in terms of mole fractions, as follows:

(17–8)

where are the gas-phase mole fractions, are the species molecular weights, and is the mean molecular weight of the gas-phase mixture.

Normalized sensitivity coefficients for the surface-site fractions and bulk-phase mole fractions are computed as:

(17–9)

and

(17–10)

where is the site fraction of surface species , and is the mole fraction of the bulk species .

In some cases, it can be argued that sensitivity coefficients are more useful when they are normalized by the maximum value of each dependent variable (for example, the maximum value over the solution time or the maximum value over a spatial profile). For such cases, Ansys Chemkin allows the option for users to obtain sensitivity coefficients normalized as:

(17–11)

where is the maximum mole fraction of the species in the relevant domain. This normalization avoids artificially high sensitivity coefficients in regions where the mole fractions are approaching zero, and thus subject to numerical errors. The implementation of this "maximum" normalization option is performed during post-processing as a "units" option in Ansys Chemkin Graphical Post-Processor.