Investigation of the Hierarchical Structure of Kinetic Models in Ignition Problems

Abstract

In this paper a novel method for global analysis of chemical kinetic models is discussed and applied to auto ignition of high hydrocarbons. It is mainly based on the concept of decomposition of motions and follows major steps of the ILDM method. However, a very important difference of the suggested method is its ability of an explicit and global representation of the system decomposition as a standard singular perturbed system (SPS). The fact that the ILDM provides local information about the decomposition makes the ILDM quite accurate in description of the slow system dynamics, but for fast motions, which become very important in the context of ignition.extinction problems, there are up to now no reliable methods based on ILDM. Therefore, the current work is devoted to developing such a method which can be used efficiently for global analysis of the reaction mechanisms with subsequent formulation of explicit reduced models for unsteady combustion regimes like ignition processes. The suggested method is illustrated by a simple Lindemann kinetic model and then applied successfully to the auto ignition of a homogeneous n-heptane.air system.

Analysis of Kinetic Reaction Mechanisms

“…The efficiency of this approach was demonstrated on the wet carbon monoxide combustion system Bykov and Maas 2009a) and modelling the auto-ignition of a cyclohexaneÀair mixture . Using the method of global-quasi-linearisation (GQL) , the fast subsystem is solved by integration (which is less stiff compared to the original system), and the slow variables are assumed to be linear functions of time during the local time integration step.…”

On transformation to the singularly perturbed system

“…These properties will automatically guarantee the closeness of the solutions of ( 14) Ψ = Ψ (t) and of (18) through M : Ψ = Ψ (θ (t)). Therefore, there is a strong need in methods of construction of appropriate invariant manifolds in the system ( 14) state/phase space and in approaches that can be applied to study their properties.…”

Reaction-Diffusion Manifolds and Global Quasi-linearization: Two Complementary Methods for Mechanism Reduction~!2009-09-09~!2009-11-17~!2010-06-15~!

“…The method has been implemented in the ILDM code [29]. In order to verify the method and investigate its applicability limits it has been applied to the n-heptane autoignition problem [30]. 2D GQL slow manifold is presented in Fig.…”

“…5) they do not perform well in the context of ignition problems. However, in this particular case application of the GQL algorithm yields a 14 dimensional slow GQL manifold that can be successfully used to formulate the reduced model and reproduce the delay before the final thermal runaway within several percent of accuracy (see [30] for detailed comparison and analysis).…”

“…State space projection onto specific mole numbers with detailed system solution trajectory shown by the red line, 2D GQL slow manifold is the green mesh, cyan line with spheres is the reduced model solution trajectory. n-heptane auto-ignition problem[30].…”