On the Definition of Reaction Progress Variable in Exhaust Gas Recirculation Type Turbulent MILD Combustion of Methane and n-Heptane

Three-dimensional Direct Numerical Simulations of Exhaust Gas Recirculation (EGR)-type Moderate or Intense Low Oxygen Dilution (MILD) combustion of homogeneous mixtures of methane- and n-heptane–air have been conducted with skeletal chemical mechanisms. The suitability of different choices of reaction progress variable (which is supposed to increase monotonically from zero in the unburned gas to one in fully burned products) based on the mass fractions of different major species and non-dimensional temperature have been analysed in detail. It has been found that reaction progress variable definitions based on oxygen mass fraction, and linear combination of CO, CO₂, H₂ and H₂O mass fractions (i.e. \({c}_{O2}\) $c_{O2}$ and \({c}_{c}\) $c_c$ ) capture all the extreme values of the major species in the range between zero and one under MILD conditions. A reaction progress variable based on fuel mass fraction is found to be unsuitable for heavy hydrocarbons, such as n-heptane, since the fuel breaks down to smaller molecules before the major reactants (products) are completely consumed (formed). Moreover, it has been found that the reaction rates of \({c}_{O2}\) $c_{O2}$ and \({c}_{c}\) $c_c$ exhibit approximate linear behaviours with the heat release rate in both methane and n-heptane MILD combustion. The interdependence of different mass fractions in the EGR-type homogeneous mixture combustion is considerably different from the corresponding 1D unstretched premixed flames. The current findings indicate that the tabulated chemistry approach based on premixed laminar flames may need to be modified to account for EGR-type MILD combustion. Furthermore, both the reaction rate and scalar dissipation rate of \({c}_{O2}\) $c_{O2}$ and \({c}_{c}\) $c_c$ are found to be non-linearly related in both methane and n-heptane MILD combustion cases but the qualitative nature of this correlation for n-heptane is different from that in methane. This suggests that the range of validity of SDR-based turbulent combustion models can be different for homogeneous MILD combustion of different fuels.