Skeletal model reduction with forced optimally time dependent modes

Abstract

Skeletal model reduction based on local sensitivity analysis of time dependent systems is presented in which sensitivities are modeled by forced optimally time dependent (f-OTD) modes. The f-OTD factorizes the sensitivity coefficient matrix into a compressed format as the product of two skinny matrices, i.e. f-OTD modes and f-OTD coefficients. The modes create a low-dimensional, time dependent, orthonormal basis which capture the directions of the phase space associated with most dominant sensitivities. These directions highlight the instantaneous active species, and reaction paths. Evolution equations for the f-OTD modes and coefficients are derived, and the implementation of f-OTD for skeletal reduction is described. For demonstration, skeletal reduction is conducted of the constant pressure ethylene-air burning in a zero-dimensional reactor, and new reduced models are generated. The laminar flame speed, the ignition delay, and the extinction curve as predicted by the models are compared against some existing skeletal models in literature for the same detailed model. Finally, the results demonstrate the capability of f-OTD to eliminate unimportant reactions and species in a systematic, efficient and accurate manner.