Heavy-alkane oxidation kinetic-mechanism reduction using dominant dynamic variables, self similarity and chemistry tabulation

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, n-decane and n-dodecane. Upon appropriate normalization, it is shown that the state vector for all four alkanes indeed obeys local full self similarity with respect to the dominant variable which is here a normalized temperature. Further, the vector of species mass fractions is partitioned into major species which are those of interest to calculate, and thus for which equations are solved, and minor species which are those of no interest to calculate and are therefore modeled. The goal of the chemical kinetic reduction is to provide a model which 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 is shown to lead to local full self similarity of the reaction rates between the modeled and calculated species; the local full self similarity also prevails for the energy of the modeled species and for the average heat capacity at constant volume of the heavy species. A methodology is developed to take advantage of this self similarity by considering the initial condition as a point in the three-dimensional space of the initial pressure, initial temperature and equivalence ratio, 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 interpolating from those known at the eight points. Once the modeled contributions are known, the conservation equations for the species and the energy, coupled with a real-gas equation of state, are solved. With a focus on the high-pressure conditions in automotive engines, extensive results are shown for the four alkanes over a wide range of initial temperatures (650–1000 K) and equivalence ratios (0.35–3.00) at 20 bar and 40 bar. The results consist of timewise profiles of the temperature and species, allowing the calculation of the ignition time and the equilibrium or maximum temperature. Comparisons between the reduced mechanism and the detailed mechanism show excellent to very good agreement for all alkanes when only 20 progress-variable light species are used in the reduced mechanism; the 20 species are the same for all fuels, and for n-decane and n-dodecane this represents a reduction in the species progress variables by factor of more than 100. As an example, calculations that excellently duplicate the elemental mechanism are also shown for n-dodecane using only 15 or 6 progress-variable light species, indicating the potential for further progress-variable reduction beyond the 20 species.