Alison S. Tomlin

Chapter 4 Mathematical tools for the construction, investigation and reduction of combustion mechanisms

Publisher Summary Chemical mechanisms have been employed in hydrocarbon combustion as a means of understanding the underlying phenomenology of the combustion process in terms of the elementary reactions of individual species. This chapter provides an introduction to most of the mathematical methods that have been used for the construction, investigation, and reduction of combustion mechanisms. The use of algebraic manipulation in techniques, such as the quasi-steady-state approximation (QSSA) and lumping, make the production of a reduced mechanism essential and make subsequent calculations as simple as possible. Computational singular perturbation (CSP) is an alternative to the rate-of-production and sensitivity methods for mechanism reduction and provides an automatic selection of the important reactions as well as time-scale analysis. The simplest and most widely used technique involving the separation of time scales is the QSSA; however, a possible limitation is that it may not provide the minimum low-order system. Chemical lumping can prove very useful in areas, such as the combustion of hydrocarbon mixtures or soot formation. Several programs are available for the investigation and reduction of combustion mechanisms, including MECHMOD, a code for the automatic modification of CHEMKIN format combustion mechanisms, and KINALC, which is an almost automatic program for the investigation and reduction of gas-phase reaction mechanisms. KINALC is a postprocessor to CHEMKIN-based simulation packages SENKIN, PREMIX, OPPDIF, RUN1DL, PSR, SHOCK and EQLIB. Because models in combustion are expected to cover a wide range of conditions, it is natural to expect that a different approach might be used for different cases.

Mechanism reduction for the oscillatory oxidation of hydrogen; Sensitivity and quasi-steady-state analyses

In this paper, a strategy for reducing complex chemical reaction mechanisms is developed and illustrated with reference to the oscillatory H[sub 2] + O[sub 2] system in a CSTR in the region of the second explosion limit. The approach involves the identification of redundant species via rate sensitivity analysis and of redundant reactions by the principal component analysis of the rate sensitivity matrix. Temperature sensitivity analysis is also employed and the application of the quasi-steady-state approximation is discussed briefly and used n the final stages of the reduction. The above procedures are shown to assist the understanding of the underlying mechanisms of the reaction for the chosen conditions and the competition between branching steps during oscillatory ignitions is discussed. The reduced mechanism is compared with models discussed elsewhere.

Analysis of Kinetic Reaction Mechanisms

Chemical processes in many fields of science and technology, including combustion, atmospheric chemistry, environmental modelling, process engineering, and systems biology, can be described by detailed reaction mechanisms consisting of numerous reaction steps. This book describes methods for the analysis of reaction mechanisms that are applicable in all these fields. Topics addressed include: how sensitivity and uncertainty analyses allow the calculation of the overall uncertainty of simulation results and the identification of the most important input parameters, the ways in which mechanisms can be reduced without losing important kinetic and dynamic detail, and the application of reduced models for more accurate engineering optimizations. This monograph is invaluable for researchers and engineers dealing with detailed reaction mechanisms, but is also useful for graduate students of related courses in chemistry, mechanical engineering, energy and environmental science and biology.

The effect of lumping and expanding on kinetic differential equations

Let us consider the differential equation

DISPERSION EXPERIMENTS IN CENTRAL LONDON The 2007 Dapple Project

\dot{\bf y}(t)={\bf f}({\bf y}(t))

On the use of adaptive gridding methods for modelling chemical transport from multi-scale sources

with an

Theoretical Validation of Chemical Kinetic Mechanisms: Combustion of Methanol

\bf f

A general analysis of approximate nonlinear lumping in chemical kinetics. II. Constrained lumping

from

Improvement of the modeling of the low-temperature oxidation of n-butane: study of the primary reactions.

{\bf R}^N

An investigation of important gas-phase reactions of nitrogenous species from the simulation of experimental measurements in combustion systems

to