A scalar variable representing the progress of reaction from unburnt to burnt is denoted by c. The transport equation for c describes the spatial and temporal evolution of the reaction progress in a turbulent flow field. Ahead of the flame, c is defined as zero in the unburnt reactants, and behind the flame c is unity in the burnt products. Within the flame brush c varies between zero and one. The flame brush propagates upstream at a modeled turbulent flame speed. Fluent offers two models for the turbulent flame speed, namely the Zimont model [735], [736], [738] and the Peters model [514], as detailed in Peters Flame Speed Model.
For more information, see the following section:
In many industrial premixed systems, combustion takes place in a thin flame sheet. As the flame front moves, combustion of unburnt reactants occurs, converting unburnt premixed reactants to burnt products. The premixed combustion model therefore considers the reacting flow field to be divided into regions of burnt and unburnt species, separated by the flame sheet. Note that the c-equation model assumes that the laminar flame is thin in comparison to the turbulent flame brush, so a value of reaction progress between 0 and 1 implies that the fluctuating flame spends some time at the unburnt state and the remainder at the burnt state; it does not represent an intermediate reaction state between unburnt and burnt.
The flame front propagation is modeled by solving a transport
equation for the density-weighted mean reaction progress variable,
denoted by 
:
 | (8–70) |
| where | |
 = mean reaction progress variable | |
 = turbulent
Schmidt number = 0.7 | |
 = reaction progress source
term ( ) | |
 = laminar thermal conductivity of the mixture | |
 = mixture specific heat |
The progress variable is defined as a normalized sum of the product species mass fractions,
Based on this definition, 
where the mixture is unburnt and 
where the mixture is burnt:
- : unburnt mixture
- : burnt mixture
The value of 
is defined as a boundary condition
at all flow inlets. It is usually specified as either 0 (unburnt)
or 1 (burnt).
The mean reaction rate in Equation 8–70 is modeled as [736]:
 | (8–71) |
| where | |
 = density of unburnt
mixture | |
 = turbulent flame speed |
Ansys Fluent provides two models for the turbulent flame speed.
Many other models for 
exist [77] and can be specified using user-defined functions. More information
about user-defined functions can be found in the Fluent Customization Manual.