Oxidation chemical reactions of many practical fuels encompass thousands of species. When simulating complex turbulent reactive flows, it is impossible to account for the time and spatial evolution of all these species given current and foreseeable-future computer memory and time. This innovation reduces the number of necessary species to be tracked to only a few species, while still retaining faithfulness of the time and spatial evolution of the temperature and of the tracked species. The time evolution is currently the main focus.
Based on a demonstrated self-similarity of the detailed chemical mechanism, the number of computed species has been reduced by a factor of more than 100. The new model is valid for n-heptane, iso-octane, n-decane, and n-dodecane, and uses the same number and identity of species for each fuel, meaning that the mixtures of these fuels can be considered with the same model.
Specifically, a model of local and full or partial self-similarity is developed for situations in which a phenomenon exhibits a dominant variable, with the goal of applying the model to obtain reduced oxidation kinetics from detailed kinetics for n-heptane, iso-octane, ndecane, and n-dodecane. Upon normalization, it is shown that the state vector for all four alkanes obeys local full similarity with respect to the dominant variable, which in this case is the normalized temperature. Further, the vector of normalized species mass fractions is partitioned into major species, which are of interest for calculation and for which equations are solved, and minor species, which are of no interest for calculation and are therefore modeled. The goal of the chemical kinetic reduction is to provide a model that expresses the influence of the minor species on the major species. The identification of major species with the light species, and of the minor species with the heavy species, leads to partitioning the energetics into computed and modeled parts. This partition of the species set leads to local full similarity of the reaction rates between the modeled and the solved species, and for the average heat capacity at constant volume of the heavy species.
The methodology takes advantage of this self-similarity by considering the initial condition as a point in the three-dimensional space of the initial temperature, equivalence ratio, and initial pressure, choosing eight points surrounding the initial condition in this space, developing the self-similarity graphs at these eight points using the LLNL detailed mechanism in conjunction with CHEMKIN II, and calculating at each time step the modeled contributions at the surrounded point by interpolation from those known at the eight points. Once the modeled contributions are known, the governing equations solved are the conservation equations for the species and the energy coupled with a real-gas equation of state. It is shown over a wide range of equivalence ratios and thermodynamic initial conditions that the results obtained with each reduced mechanism duplicate with very high fidelity those obtained with the corresponding detailed mechanism.