A Thermodynamically Consistent Methodology to Develop Predictive Simplified Kinetics for Detonation Simulations

The number of species and elementary reactions needed for describing the oxidation of fuels increases with the size of the molecule, and in turn, the complexity of detailed mechanisms. Although the kinetics for conventional fuels (H2, CH4, C3H8...) are somewhat well-established, chemical integration in detonation applications remains a major challenge. Significant efforts have been made to develop reduction techniques that aim to keep the predictive capabilities of detailed mechanisms intact while minimizing the number of species and reactions required. However, as their starting point of development is based on homogeneous reactors or ZND profiles, reduced mechanisms comprising a few species and reactions are not predictive. The methodology presented here relies on defining virtual chemical species such that the thermodynamic equilibrium of the ZND structure is properly recovered thereby circumventing the need to account for minor intermediate species. A classical asymptotic expression relating the ignition delay time with the reaction rate constant is then used to fit the Arrhenius coefficients targeting computations carried out with detailed kinetics. The methodology was extended to develop a three-step mechanism in which the Arrhenius coefficients were optimized to accurately reproduce the one-dimensional laminar ZND structure and the D−κ curves for slightly-curved quasi-steady detonation waves. Two-dimensional simulations performed with the three-step mechanism successfully reproduce the spectrum of length scales present in soot foils computed with detailed kinetics (i.e., cell regularity and size). Results attest for the robustness of the proposed methodology/approximation and its flexibility to be adapted to different configurations.