A linearized error propagation method for skeletal mechanism reduction

Abstract

A method of linearized error propagation (LEP) based on Jacobian analysis is developed for systematic skeletal mechanism reduction. Jacobian analysis is performed in LEP to estimate the reduction error in selected target species induced by the elimination of other species. Skeletal mechanisms are obtained by eliminating species that induce negligible worst-case errors to the target species. LEP is compared with the methods of directed relation graph (DRG) and DRG with error propagation (DRGEP) on the accuracy of reduction error estimation. It is shown that DRG can effectively control the worst-case error of every species retained in the skeletal mechanism by assuming that error may not decay in the worst cases along the graph-search paths, while it tends to overestimate the errors in the starting species, such that the skeletal mechanism can typically be further reduced if only the starting species are of interest. In contrast, DRGEP assumes geometric error decay along graph-search paths, and may overestimate the error decay and subsequently underestimate the reduction errors in species many steps away from the starting species, resulting in potential unsafe species-eliminations. Compared with DRG and DRGEP, LEP can overall more accurately estimate the errors in the target species such that smaller mechanisms can be obtained compared with DRG, while unsafe species eliminations are less likely compared with DRGEP. To demonstrate the performance of the LEP method, skeletal mechanisms are derived based on perfectly stirred reactor (PSR) solutions sampled along the S-curves, including both the ignition and the extinction states. A 35-species skeletal mechanism is obtained for ethylene−air based on the 111-species USC-Mech II, and a 146-species skeletal mechanism for n-heptane−air is obtained based on a 188-species skeletal mechanism previously developed using DRG. Validation of global flame behaviors, including PSR ignition and extinction residence time, auto-ignition delay, and laminar flame speed, shows that no significant errors are further induced by LEP.