One-dimensional slow invariant manifolds for spatially homogenous reactive systems.
A reactive system's slow dynamic behavior is approximated well by evolution on manifolds of dimension lower than that of the full composition space. This work addresses the construction of one-dimensional slow invariant manifolds for dynamical systems arising from modeling unsteady spatially homogeneous closed reactive systems. Additionally, the relation between the systems' slow dynamics, described by the constructed manifolds, and thermodynamics is clarified. It is shown that other than identifying the equilibrium state, traditional equilibrium thermodynamic potentials provide no guidance in constructing the systems' actual slow invariant manifolds. The construction technique is based on analyzing the composition space of the reactive system. The system's finite and infinite equilibria are calculated using a homotopy continuation method. The slow invariant manifolds are constructed by calculating attractive heteroclinic orbits which connect appropriate equilibria to the unique stable physical equilibrium point. Application of the method to several realistic reactive systems, including a detailed hydrogen-air kinetics model, reveals that constructing the actual slow invariant manifolds can be computationally efficient and algorithmically easy.
Al-Khateeb
Ashraf N
AN
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556-5637, USA.
Powers
Joseph M
JM
Paolucci
Samuel
S
Sommese
Andrew J
AJ
Diller
Jeffrey A
JA
Hauenstein
Jonathan D
JD
Mengers
Joshua D
JD