The C-equation and G-equation turbulent premixed combustion models require properties for temperature, density, unburnt density, unburnt thermal diffusivity and laminar flame speed, which are modeled as described in the sections that follow.
For more information, see the following sections:
The calculation method for temperature will depend on whether the model is adiabatic or non-adiabatic.
For the adiabatic premixed combustion model, the temperature
is assumed to be a linear function of reaction progress between the
lowest temperature of the unburnt mixture, 
, and the highest
adiabatic burnt temperature 
:
 | (8–97) |
For the non-adiabatic premixed combustion model, Ansys Fluent solves
an energy transport equation in order to account for any heat losses
or gains within the system. The energy equation in terms of sensible
enthalpy, 
, for the fully premixed fuel (see Equation 5–2) is as follows:
 | (8–98) |
represents
the heat losses due to radiation and 
represents the heat gains due to chemical reaction:
 | (8–99) |
| where | |
 = normalized average rate of
product formation ( ) | |
 = heat of combustion for burning 1 kg of fuel (J/kg) | |
 = fuel mass fraction of unburnt
mixture |
Ansys Fluent calculates the premixed density using the ideal gas law. For the adiabatic model, pressure variations are neglected and the mean molecular weight is assumed to be constant. The burnt gas density is then calculated from the following relation:
 | (8–100) |
where the subscript 
refers to the unburnt cold mixture, and the subscript 
refers to the burnt hot
mixture. The required inputs are the unburnt density (
),
the unburnt temperature (
), and the burnt adiabatic flame
temperature (
).
For the non-adiabatic model, you can choose to either include or exclude pressure variations in the ideal gas equation of state. If you choose to ignore pressure fluctuations, Ansys Fluent calculates the density from
 | (8–101) |
where 
is computed from the energy transport equation,
Equation 8–98. The required inputs are
the unburnt density (
) and the unburnt temperature
(
). Note that, from the incompressible
ideal gas equation, the expression 
may be considered to be the effective molecular
weight of the gas, where 
is the gas constant and 
is
the operating pressure.
If you want to include pressure fluctuations for a compressible gas, you will need to specify the effective molecular weight of the gas, and the density will be calculated from the ideal gas equation of state.
The laminar flame speed (
in Equation 8–71) can be specified as constant,
or as a user-defined function. A third option appears for non-adiabatic
premixed and partially-premixed flames and is based on the correlation
proposed by Metghalchi and Keck [437],
 | (8–102) |
In Equation 8–102, 
and 
are the unburnt
reactant temperature and pressure ahead of the flame, 
and 
.
The reference laminar flame speed, 
, is calculated from
 | (8–103) |
where 
is the equivalence ratio ahead of the flame
front, and 
, 
and 
are fuel-specific
constants. The exponents 
and 
are calculated from,
 | (8–104) |
The Metghalchi-Keck laminar flame speeds are available for fuel-air mixtures of methane, methanol, propane, iso-octane and indolene fuels.
The unburnt density (
in Equation 8–71) and unburnt thermal diffusivity
(
in Equation 8–77 and Equation 8–78) are specified constants
that are set in the Materials dialog box. However,
for compressible cases, such as in-cylinder combustion, these can
change significantly in time and/or space. When the ideal gas model
is selected for density, the unburnt density and thermal diffusivity
are calculated by evaluating the local cell at the unburnt state c=0.