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Approximate solutions to explosion kinetics
Author(s) -
Aiken R. C.
Publication year - 1982
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690280416
Subject(s) - computation , scaling , a priori and a posteriori , combustion , singular perturbation , isothermal process , statistical physics , mathematics , kinetic energy , steady state (chemistry) , perturbation (astronomy) , transient (computer programming) , thermodynamics , kinetics , mechanics , computer science , physics , mathematical analysis , chemistry , classical mechanics , algorithm , geometry , philosophy , epistemology , quantum mechanics , operating system
Abstract Stiffness in combustion models is quite different from that in more conventional kinetic descriptions. The steady‐state approximation, so useful in other contexts, cannot be applied in the usual ad hoc manner but can be applied with attention to its origins in singular perturbation analysis. The magnitude and time scaling on the equations representing the isothermal kinetics of hydrogen combustion reveal distinct regions of the transient to which this approximation may naturally and successfully be made to reduce computation time. The steady‐state approximation is found to apply to some free radicals, but not all, and these can change between regions. An analytical solution to an important section of the transient is found and illustrates dramatically the power of the approach. The analysis may be applied a priori and leads to a stagewise efficient numerical solution.