Equivalence ratio vs mixture fraction

[Gavin]

Can someone clarify the difference between the `mixture_fraction` and `equivalence_ratio` properties in Cantera? The definitions given in the Cantera documentation (copied below) are very similar. I think the only difference is that Cantera's equivalence ratio considers the stoichiometric conditions while the mixture fraction is just the ratio of fuel to oxider. Is that correct?

The documentation for `property equivalence_ratio` states the following:

Get the equivalence ratio of the current mixture, which is a conserved quantity. Considers the oxidation of C to CO2, H to H2O and S to SO2. Other elements are assumed not to participate in oxidation (that is, N ends up as N2). If fuel and oxidizer are not specified, the equivalence ratio is computed from the available oxygen and the required oxygen for complete oxidation. The basis determines the composition of fuel and oxidizer: basis='mole' (default) means mole fractions, basis='mass' means mass fractions.

The documentation for `property mixture_fraction` states the following:

Get the mixture fraction of the current mixture (kg fuel / (kg oxidizer + kg fuel)). This is a quantity that is conserved after oxidation. Considers the oxidation of C to CO2, H to H2O and S to SO2. Other elements are assumed not to participate in oxidation (that is, N ends up as N2). The basis determines the composition of fuel and oxidizer: basis="mole" (default) means mole fractions, basis="mass" means mass fractions. The mixture fraction can be computed from a single element (for example, carbon with element="C") or from all elements, which is the Bilger mixture fraction (element="Bilger"). The Bilger mixture fraction is computed by default.

[Steven DeCaluwe]

Hi Gavin,

I think the key difference is in the “(kg fuel / (kg oxidizer + kg fuel)” for the mixture fraction description.

Whereas the equivalence ratio is, if I recall, “(moles of fuel / moles of fuel required for complete combustion of available oxidizer)”

Best,

Steven

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[Thorsten Zirwes]

Hi Gavin,

as Steven said, the mixture fraction is defined as the mass fraction of fuel in the mixture (see e.g. https://en.wikipedia.org/wiki/Mixture_fraction). The equivalence ratio is the ratio of (amount of fuel / amount of oxidizer) to (amount of fuel / amount of oxidizer oxidizer) at stoichiometry (see e.g. https://en.wikipedia.org/wiki/Air%E2%80%93fuel_ratio#Fuel%E2%80%93air_equivalence_ratio_(%CF%95) ).

There is a relation between the two quantities, as shown here: https://cantera.org/documentation/docs-2.5/doxygen/html/dc/d38/classCantera_1_1ThermoPhase.html#a692731bce4f8d60bc76cb33c913ca0af (Z is the mixture fraction and Z_st the mixture fraction at stoichiometric conditions).

 

You can find more examples including both quantities here: https://github.com/Cantera/cantera/blob/main/interfaces/cython/cantera/examples/thermo/equivalenceRatio.py