
The laminar counterflow diffusion flame equations can be transformed from physical space (with as the independent variable) to mixture fraction space (with as the independent variable) [ 286]. In FLUENT, a simplified set of the mixture fraction space equations are solved [ 285]. Here, equations are solved for the species mass fractions, ,
and one equation for temperature:
The notation in Equations 15.36 and 15.37 is as follows: , , , and are the th species mass fraction, temperature, density, and mixture fraction, respectively. and are the th species specific heat and mixtureaveraged specific heat, respectively. is the th species reaction rate, and is the specific enthalpy of the th species.
The scalar dissipation, , must be modeled across the flamelet. An extension of Equation 15.32 to variable density is used [ 180]:
where is the density of the oxidizer stream.