Formulation reproducing the ignition delays simulated by a detailed mechanism: Application to n-heptane combustion

This article is part of the project to model the kinetics of high-temperature combustions, occurring behind shock waves and in detonation waves. The "conventional" semi-empirical correlations of ignition delays have been reformulated, by keeping the Arrhenius equation form. It is shown how a polynomial with 3^N coefficients (where N ∈ [1, 4] is the number of adjustable kinetic parameters, likely to be simultaneously chosen among the temperature T, the pressure P, the inert fraction X_Ar, and the equivalence ratio Φ) can reproduce the delays predicted by the Curran et al. [H.J. Curran, P. Gaffuri, W.J. Pitz, C.K. Westbrook, Combust. Flame 129 (2002) 253-280] detailed mechanism (565 species and 2538 reactions), over a wide range of conditions (comparable with the validity domain). The deviations between the simulated times and their fits (typically 1%) are definitely lower than the uncertainties related to the mechanism (at least 25%). In addition, using this new formalism to evaluate these durations is about 10⁶ times faster than simulating them with Senkin (Chemkin III package) and only 10 times slower than using the classical correlations. The adaptation of the traditional method for predicting delays is interesting for modeling, because those performances are difficult to obtain simultaneously with other reduction methods (either purely mathematical, chemical, or even mixed). After a physical and mathematical justification of the proposed formalism, some of its potentialities for n-heptane combustion are presented. In particular, the trends of simulated delays and activation energies are shown for T ∈ [1500 K, 1900 K], P ∈ [10 kPa, 1 MPa], X_Ar ∈ [0, 0.7], and Φ ∈ [0.25, 4.0].