Alkane Kinetics Reduction Consistent with Turbulence Modeling using Large Eddy Simulation

Abstract

A methodology for deriving a reduced kinetic mechanism for alkane oxidation is de- scribed, inspired by n-heptane oxidation. The model is based on partitioning the species of the skeletal kinetic mechanism into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement of the species ensemble. For mod- eling purposes, the heavy species are mathematically decomposed into constituents, which are similar but not identical to groups in the group additivity theory. From analysis of the n-heptane LLNL skeletal mechanism in conjunction with CHEMKIN II, it is shown that a similarity variable can be formed such that the appropriately non-dimensionalized global constituent molar density exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures that is of interest for predict- ing n-heptane oxidation. Furthermore, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable. The light species en- semble is partitioned into quasi-steady and unsteady species. The reduced model is based on concepts consistent with those of Large Eddy Simulation in which functional forms are used to replace the small scales eliminated through filtering of the governing equations; these small scales are unimportant as far as dynamic energy is concerned. Here, we remove the scales deemed unimportant for recovering the thermodynamic energy. The concept is tested by using tabular information from the n-heptane LLNL skeletal mechanism in con- junction with CHEMKIN II utilized as surrogate ideal functions replacing the necessary functional forms. The test reveals that the similarity concept is indeed justified and that the combustion temperature is well predicted, but that the ignition time is overpredicted, which is traced to neglecting a detailed description of the processes leading to the heavies chemical decomposition. To palliate this deficiency, functional modeling is incorporated into our conceptual reduction. This functional modeling includes the global constituent molar density, the enthalpy evolution of the heavies, the contribution to the reaction rate of the unsteady lights from other light species and from the heavies, the molar density evolution of oxygen and water, and the mole fractions of the quasi-steady light species. The model is compact in that there are only nine species-related progress variables. Re- sults are presented showing the performance of the model for predicting the temperature and species evolution for n-heptane. The model reproduces the ignition time over a wide range of equivalence ratios, initial pressure and initial temperature. Preliminary results for iso-octane using the full mechanism are also presented, showing encouragingly that the concept may be generalized to other alkanes. The utility of the model and possible improvements are discussed.