Implementation of combustion chemistry by in situ adaptive tabulation of rate-controlled constrained equilibrium manifolds

A general methodology called in situ adaptive tabulation-rate-controlled constrained equilibrium (ISAT-RCCE) is developed to treat detailed chemistry in turbulent combustion calculations. This method combines dimension reduction and tabulation and can be implemented in a single computer program, which is independent of the detailed mechanism and of the level of reduction selected. The dimension reduction of a detailed mechanism is achieved by the RCCE approach, which is based on the maximum entropy principle of thermodynamics; and the tabulation is performed in situ during the combustion calculations and is made in the low-dimensional constraint subspace. This method is particularly attractive for very large kinetic mechanisms (e.g., including thousands of species) because the constrained equilibrium state depends on only a small number of constraints (or constraint potentials) which form the constraint subspace. Moreover, the unique and continuous maximum-entropy manifold determined by the RCCE assumption is well suited to the ISAT algorithm-an efficient computational technique for the implementation of combustion chemistry. Test calculations are performed for non-premixed methane/air combustion in a statistically homogeneous turbulent reactor, using a detailed kinetic mechanism with 31 species and 175 reactions. A direct approach of numerically integrating the full reaction equations (32-dimensional) is performed and the result is taken as the exact solution. The ISAT-RCCE calculations based on 10- to 16-dimensional constraint subspaces show good agreement with the accurate solution, and the accuracy of the results from the 16-dimensional ISAT-RCCE calculation is comparable to that of a reference calculation using ISAT and a 17-dimensional augmented reduced mechanism (derived from the same detailed mechanism). A speed-up factor of about 500 is obtained for the ISAT-RCCE calculation compared to the direct integration approach, which demonstrates the high efficiency of the now method.