Hydrodynamic and differential-diffusion effects on premixed flame propagation

Flame propagation in gaseous mixtures generally involve two length scales: one scale is associated with the diffusion processes and characterizes the flame thickness, and the other scale is associated with the underlying flow field. When the hydrodynamic length is larger than the nominal flame thickness, the flame can be viewed as a surface of density discontinuity, advected and distorted by the flow. The analysis of the internal structure of the flame provides expressions for the flame speed and temperature and jump conditions for the velocities and pressure across the flame. The resulting hydrodynamical model is valid for flames of arbitrary shape propagating in general fluid flows, being laminar or turbulent. The present work extends earlier studies by adopting a curvilinear coordinate system attached to the flame front, thus presenting a formulation in coordinate-free form, using a two-reactant scheme thus allowing for mixtures whose compositions vary from lean to rich including stoichiometric conditions, using non-unity and general reaction orders in an attempt to mimic a wider range of reaction mechanisms, allowing all transport coefficients to depend arbitrarily on temperature in order to better represent actual experimental conditions, and incorporating volumetric heat losses which may often lead to flame extinction.; When the hydrodynamic length is comparable to the diffusion length, there is a strong coupling between the fluid dynamical and transport processes within the flame zone. The structure of such thick flames has been studied in the context of a diffusive-thermal model. Specifically flame propagation in channels subjected to a prescribed flow either supporting or opposing the propagation has been investigated. Special attention has been given to the effects of conductive heat losses to the walls and differential diffusion. Explicit asymptotic expressions for the burning rate and flame shape are obtained for narrow and wide channels. These are complemented with numerical calculations spanning the remaining range of moderate channel widths. The results show that the structure of thick flames differs from the classical well-known structure of premixed flames in that transverse diffusion, normally negligible compared to axial diffusion, becomes significant with important consequences on burning rates. In the course of this investigation, it was found that when the Lewis number is large enough, a pulsating mode of propagation results. The present work thus extends earlier stability studies by examining the onset and mode of oscillations of two-dimensional curved flames and incorporating the effects of channel's width, conductive heat losses and convection.