The application of chemical reduction methods to a combustion system exhibiting complex dynamics

Abstract

A number of chemical model reduction techniques have been developed over recent years with a growing range of applications in combustion. The following work demonstrates the application of such reduction techniques for a combustion system describing the oxidation of carbon monoxide + hydrogen in a continuously stirred tank reactor (CSTR) at very low pressure. The system exhibits complex dynamics including oscillatory glow, oscillatory ignition and mixed mode oscillations. It is demonstrated that a range of local reduction methods can be applied to such complex systems, as long as sufficient coverage of the accessed regions of phase space are included in the reduction analysis. The methods include sensitivity analysis, the quasi-steady state approximation (QSSA) and repro-modelling based on the concept of an intrinsic low dimensional manifold (ILDM). The system is qualitatively different from some previous applications of ILDM methods where trajectories tend towards a fixed equilibrium. The underlying dimension of the system is seen to vary throughout selected trajectories with rapid increases occurring over very short time-scales during oscillatory ignition. Nevertheless, a final reduced model of only four variables is developed using fitted orthonormal polynomials describing the system dynamics on a slow manifold. The application serves to demonstrate that the relationship between local reduced model error and global errors can be complex for systems exhibiting complex dynamics, with regions of seemingly small local mapping gradients requiring tighter error control in order to control global errors. This feature may be common in cases where nearby trajectories are seen to diverge within the slow manifold over time.