### 7.14.5. Equivalence Ratio and Conditional Fresh/Residual Mixtures

The `Equivalence Ratio` variable in the results file and in CEL is conditioned to the ‘fresh’ mixture. It is calculated for the fuel and oxidizer with the residual material removed from the mixture:

| (7–94)

| (7–95)

Without loss of generality the residual material is assumed to be stoichiometric. Mixture fraction and equivalence ratio conditional to the residual fraction are by definition

and

, respectively. Fuel-rich or fuel-lean residual material can be modeled as a combination of stoichiometric residuals with either excess fuel or excess oxidizer in the fresh mixture. For the purpose of specifying boundary conditions or initial values, the primitive variables can be calculated from the generalized conditional mixture fractions, enabling

according to:

| (7–96)

| (7–97)

where denotes the mass fraction of non-stoichiometric residual material, and

and

are the conditional mixture fractions for the fresh and the residual mixture. Note that

if, and only if,

. Conditional equivalence ratios can be transformed into conditional mixture fractions and vice versa according to:

| (7–98)

| (7–99)

| (7–100)

| (7–101)

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