An updated empirical correlation formalism for laminar flame speeds: Application to a TRFE gasoline surrogate in highly diluted conditions

In order to comply with present and future stringent environmental policies, engine manufacturers have to improve engine design and control to achieve combustion with high dilution ratios. The use of CFD simulations with complex combustion chemistry remains prohibitive, and alternatives to assess quickly the laminar flame speeds at local grid cell conditions (temperature, pressure, equivalence ratio, and dilution ratio) are desired, such as empirical correlations. Whereas these correlations should ideally be obtained from experimental measurements, comprehensively validated kinetic models can help extend databases to conditions that cannot be achieved practically. Hence, the present study proposed a reduced kinetic mechanism, containing 593 species and 3698 reactions, for one gasoline surrogate, namely Toluene Reference Fuel with Ethanol addition (TRFE). It is obtained by first compiling sub-mechanisms from the literature for the four components (isooctane, n-heptane, toluene, and ethanol) with updates of some key rate constants, and then is reduced for 1-D flame speed computations. The model was first validated against recent experimental laminar flame speed measurements of TRFE/air/diluent mixtures for various temperatures, pressures, equivalence ratios, and dilution ratios and then employed to extend the experimental database for the TRFE surrogate to higher dilution ratios and temperatures. A new formalism, including new mathematical expressions for the reference and dilution terms, and the temperature exponent are proposed. This new formalism exhibits improved abilities in fitting the laminar flame speeds, especially at high dilution ratios and in very fuel-lean and fuel-rich conditions. A new mathematical correlation based on these formulas was developed, whose correlation parameters were obtained by fitting both experimental data and mechanism predictions. Regardless of the conditions, the present correlation is observed to show overall good agreements with available experimental data in the literature for laminar flame speeds and their dependence on equivalence ratio, temperature, pressure, and dilution. Results show that the effect of dilution in reducing flame speeds is not linear and depends on the equivalence ratio. A parameter μ is defined in the correlation formulas to evaluate the dilution effectiveness of the diluent, which is found to be composition-specific and possibly follows a linear mixing rule for diluent mixtures.