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 15.3-6 and 15.3-7 is as follows: , , , and are the th species mass fraction, temperature, density, and mixture fraction, respectively. and are the th species specific heat and mixture-averaged 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 15.3-2 to variable density is used [ 180]:
where is the density of the oxidizer stream.