Spatial Dynamics of Steady Flames 1. Phase Space Structure and the Dynamics of Individual Trajectories
- 1 August 2008
- journal article
- Published by American Chemical Society (ACS) in The Journal of Physical Chemistry A
- Vol. 112 (34), 7768-7783
- https://doi.org/10.1021/jp801367x
Abstract
The spatial dynamics of steady, one-dimensional premixed H2/O2 flames are studied. The emphasis in this Article is the geometry of the phase space of the dynamical system describing the steady flames. It is shown that steady flames are described by trajectories on the stable manifolds of saddle fixed points. The saddle fixed points correspond to equilibrium points of time-dependent chemical-kinetic systems that are adiabatic and isobaric and whose constant enthalpy matches the asymptotic enthalpy of the flames. The dimensions of the stable manifolds match the dimensions of the chemical-kinetic systems under most conditions, although the dynamics on them are different. It is further shown that the stable manifolds have low-dimensional attractive submanifolds near the saddlepoint. An algorithm for generating trajectories over the spatial domain of these flames is proposed, and it is used to study individual trajectories and trajectory ensembles, whose collective behavior suggests that there are low-dimensional submanifolds away from the saddlepoint.Keywords
This publication has 44 references indexed in Scilit:
- Spatial Dynamics of Steady Flames 2. Low-Dimensional Manifolds and the Role of Transport ProcessesThe Journal of Physical Chemistry A, 2008
- Chemically Reacting FlowPublished by Wiley ,2003
- CombustionPublished by Springer Science and Business Media LLC ,2001
- Simplification of Mathematical Models of Chemical Reaction SystemsChemical Reviews, 1998
- Chapter 4 Mathematical tools for the construction, investigation and reduction of combustion mechanismsPublished by Elsevier BV ,1997
- Reduced kinetic models and their application to practical combustion systemsProgress in Energy and Combustion Science, 1995
- Accurate steady-state approximations: implications for kinetics experiments and mechanismThe Journal of Physical Chemistry, 1991
- On the geometry of transient relaxationThe Journal of Chemical Physics, 1991
- Geometry of the steady-state approximation: Perturbation and accelerated convergence methodsThe Journal of Chemical Physics, 1990
- The steady state and equilibrium approximations: A geometrical pictureThe Journal of Chemical Physics, 1988