Development of an adaptive technique to reduce combustion thermochemistry
Résumé
The study of combustion requires description of the thermochemistry of elementary reactions. Modern detailed chemical kinetic description of hydrocarbon mixtures combustion with air involves hundreds of species, thousands of elementary reactions and timescales which vary up to nine orders of magnitude. Since each of these elementary reactions involve timescales which may span over several orders of magnitudes, the result- ing model is inherently stiff. These characteristics imply that the numer- ical integration of the detailed thermochemical evolution equations is the most expensive task when a detailed description of combustion chemistry is sought, for instance, in computational fluid dynamics models.
This work presents a technique, dubbed in situ adaptive tabulation (ISAT), which has been implemented in order to reduce the integration time of the system of equations governing the thermochemical evolution of reactive mixtures. The methodology consists in progressively creat- ing a table which stores solutions and initial conditions for the system of governing equations. A search is performed along this table whenever the integration of these equations is required and a tabulated solution is recovered. If the information recovered from the table is satisfactory, in a sense implicit to the technique, a linear interpolation gives an adequate approximate solution. This approximate solution has a local error which is second order accurate in time, thus ensuring that the global error is of first order. The technique was tested in a modification of the classical Partially Premixed Reactor (PaSR) called Pairwise Mixing Stirred Re- actor (PMSR) and the results obtained characterize the efficiency of the algorithm, demonstrating a reduction of up to two orders of magnitude in processing time when compared to the direct integration of the governing equations.