# Combustion Chemistry

Thus for example, the reaction mechanism for the combustion of methane consists of 34 different chemical species, which react with each other in 302 elementary reactions. If one considers the combustion of complex hydrocarbons, the number of chemical species can increase to several hundreds, that of elementary reactions to several thousands.

Accurate knowledge of these detailed reaction mechanisms is of great importance for a correct description of kinetically controlled processes such as pollutant formation, ignition and flame extinction. The development of low-temperature kinetics (T < 1000 K) is particularly significant, since unlike high-temperature kinetics they have not been extensively investigated but are of great importance for the understanding of self-ignition processes (e.g. engine knock). Such detailed reaction mechanisms are being investigated at ITT.

The available experimental equipment includes a Rapid Compression Machine (RCM).

Detailed reaction mechanisms for various fuels can be developed with the help of the program KUCRS (Knowledge-basing Utilities for Complex Reaction Systems (http://www.frad.t.u-tokyo.ac.jp/~miyoshi/KUCRS/, 2005)). Sensitivity analyses and reaction flow analyses allow the velocity-determining reactions of these mechanisms to be identified. These reactions can then be investigated in further detail and the relevant reaction parameters adjusted.

Comparison of the ignition delays or of the concentration course of individual species, obtained from numerical simulations with the help of detailed reaction mechanisms and experimental investigations using the RCM, help in the validation of the reaction mechanisms.

The use of detailed reaction mechanisms with their large number of species and elementary reactions, is easily possible today in the simulation of spatially homogeneous reaction systems. If, however, real three-dimensional turbulent flows are considered, in which large temperature and concentration fluctuations occur (examples include flows in engines and gas turbines), the use of detailed reaction mechanisms involves massive computing times which can be difficult if not impossible to implement. This is the result of the complex interaction between chemical and physical processes during combustion, but also the properties of the equations that need to be solved for the chemistry, such as large dimension (one conservation equation for each species) and high stiffness. Therefore, there is great interest in simplified reaction mechanisms, which describe the system’s chemical dynamics as a function of only a few variables.

One method for computing such reduced mechanisms is the one of intrinsic low-dimensional manifolds (ILDM). It exploits the fact that over time, the dynamics of the chemical system are restricted to spaces of ever smaller dimensions. Once the system has reached such a space of a particular dimension, it no longer leaves it; therefore one speaks also of an attractive manifold.

The following illustration shows schematically this process of relaxation to low-dimensional spaces. The blue arrows indicate rapid processes, which to begin with relax to a two-dimensional ILDM (red grid). The remaining slow processes (black lines) move along the 2d-ILDM and finally concentrate on a line, a one-dimensional ILDM. Ultimately this leads to chemical equilibrium (green), which corresponds to a zero-dimensional ILDM.

*Fig. 1: Relaxation of rapid processes to a 2d-ILDM (red grid), movement to a 2d-ILDM and transition to a 1d-ILDM (black trajectories), and chemical equilibrium (green).*

In conjunction with eigenvector analysis of the Jacobi matrix of the chemical source terms, the ILDM method is able to determine the low-dimensional spaces of various dimensions. ITT has appropriate program code available, which just like the underlying methodology of ILDM is the subject of constant further development.

REDIM is another method for the reduction of chemical reactions. This method is the next generation of the ILDM technique, eliminating problems in the definition and application of the reduced models and covering not only the effect of reactive processes but also that of transport processes. This makes the method more stable and more powerful compared with the reduction methods, which either use only a local analysis of the chemical source term or rely on numerical analysis of the detailed system to identify the so-called skeletal mechanism.

The key-ideas of the REDIM method are decomposition of the movements and relaxation to a slow, invariant manifold. The relaxation process is determined by a multidimensional, parabolic system of partial differential equations, for whose solution an extended ILDM is used as a starting solution. The final relaxed manifold fulfils an invariance condition, therefore the manifold of the reduced system dynamics is reproduced accurately and follows the stationary solution of the detailed system. This method improves the performance of the ILDM concept significantly, and extends it in terms of the possibility of reducing the system in those regions of the state space (at low temperatures) where manifolds, which rely solely on the analysis of the chemical source term, do not exist. The following illustration shows an example of an REDIM.

*Fig. 2: Extended 2d-ILDM (red / blue grid), REDIM (green grid) and a stationary solution of the detailed system.*

Both in ILDM and in REDIM, the computed manifolds of a specified dimension are stored in tabulated form and can then be made available to a CFD code as a library. Therefore, during flow computation the CFD code no longer draws on a detailed reaction mechanism and solves equations for all the species that occur in it, but instead solves only a few conservation equations for the tabulation coordinates of the ILDM and then interpolates the species values from the stored table.

Research Assistant: