On the similarity of the sensitivity functions of methane combustion models

It is widely known that detailed kinetic mechanisms with identical reaction steps but with very different rate parameters may provide similar simulation results in combustion calculations. This phenomenon is related to the similarity of sensitivity functions, which arises if low-dimensional manifolds in the space of variables, and autocatalytic processes are present. We demonstrated the similarity of sensitivity functions for adiabatic explosions and burner-stabilized laminar flames of stoichiometric methane–air mixtures. The cause of similarities was investigated by calculating the dimension of the corresponding manifolds, and the pseudo-homogeneous property of the sensitivity ordinary differential equation (ODE). The methane explosion model showed global similarity, which means that different parameter sets could provide the same simulation results. This was demonstrated by numerical experiments, in which two significantly different parameter sets resulted in identical concentration profiles for all species. This phenomenon is important from a practical point of view in the fields of ‘validation’ of complex reaction mechanisms and parameter estimation of chemical kinetic systems.

Keywords:

• Methane combustion
• Sensitivity analysis
• Manifold
• Global similarity

Acknowledgements

The authors acknowledge the helpful discussions with Dr János Tóth and Professor Ulrich Maas, and the support of OTKA (grant number T043770 and instrumental grant M042110).