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Bifurcation analysis of index infinity DAE parabolic models describing reactors and reacting flows
Author(s) -
Ratnakar Ram R.,
Balakotaiah Vemuri
Publication year - 2017
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.15568
Subject(s) - mathematics , steady state (chemistry) , bifurcation , infinity , hopf bifurcation , domain (mathematical analysis) , flow (mathematics) , mathematical analysis , algebraic number , thermal conduction , mechanics , thermodynamics , physics , geometry , nonlinear system , chemistry , quantum mechanics
We show that most steady‐state models of chemical reactors and reacting flows in which convection effects are dominant and diffusion/conduction is neglected in the flow direction but included in the transverse directions, may change from parabolic type with a unique solution to index infinity differential‐algebraic equation (DAE) type with an infinite number of steady‐state solutions depending on the values of the reaction parameters. When a model is of index infinity, standard numerical methods may find only one of the solutions corresponding to latest possible ignition. We present complete bifurcation analysis of these models, a method for finding all solutions, determine the stability and, for some simpler cases, the domain of initial conditions attracted to these states. We also demonstrate that the various steady‐state solutions of the DAE systems are best found by integrating the transient hyperbolic versions of the models with appropriately selected capacitance terms and initial conditions. © 2016 American Institute of Chemical Engineers AIChE J , 63: 295–305, 2017