Analysis of the spatio-temporal scales of laminar premixed flames near equilibrium

Abstract

The interplay between chemistry and transport is addressed by exploring the coupling between the spatial and temporal scales of one-dimensional laminar premixed combustion in reactive mixtures described by detailed chemical kinetics and multicomponent transport. System dynamics are investigated in the neighbourhood of the equilibrium state; in so doing, the time scales associated with modes of varying wavelength for the complete unsteady, spatially inhomogeneous system are obtained. The results reveal that short wavelength modes are dominated by diffusion-based time scales, and long wavelength modes are dominated by reaction-based time scales. The analysis further identifies critical wavelengths where the effects of reaction and diffusion are balanced, and it is seen that the critical wavelengths are well estimated by classical diffusion theory.

Keywords:

• laminar flames
• stability
• length and time scales
• detailed kinetics
• reaction–diffusion

Acknowledgements

The authors recognise the support of the National Science Foundation (NSF) under CBET-0650843, and the Center for Applied Mathematics at University of Notre Dame.