Equivalence ratio in partially premixed flame system

[fyyfifowffums]

Hi, I'm learning the basics of plasma assisted combustion so I've been reading up on a few articles related to it.
My question is regarding this article http://enu.kz/repository/2011/AIAA-2011-971.pdf

Using a setup consisting of a pair of counterflow burners, the composition of the oxidizer stream was fixed at O₂/Ar/He/CH₄(0.26:0.32:0.4:0.02) while the fuel stream was CH₄ diluted by Ar (fuel mole fraction varied from 0.2 to 0.4). In this experiment, both oxidation and fuel reforming occurs. How do I find the equivalence ratio for both cases?

Oxidation: CH₄ + 2O₂→ CO₂ + 2H₂O
Fuel reforming: 2CH₄ + O₂→ 4H₂ + 2CO

The equivalence ratio is defined as (fuel-to-oxidizer ratio)/ (fuel-to-oxidizer ratio)_st and usually methane will be the fuel and oxygen as oxidizer, but in this case the oxidizer itself is premixed with methane so how do I calculate the equivalence ratio? Please help. I get so confused.

 

[bigfooted]

The equivalence ratio is different everywhere in your flame. In partially premixed cases, it is more useful to use the Takeno flame index as a measure for the combustion regime, or use the mixture fraction together with the equivalence ratio to characterize the flame.

 

[fyyfifowffums]

The equivalence ratio is different everywhere in your flame. In partially premixed cases, it is more useful to use the Takeno flame index as a measure for the combustion regime, or use the mixture fraction together with the equivalence ratio to characterize the flame.

I see! I never thought about different parts having different equivalence ratios before. No wonder I couldn't get a constant value. It makes more sense now. Thank you so much!