Flame speed in diffusion dominated premixed flames

Development of a premixed flame theory that includes the effects of flame stretch and curvature has been at the forefront of combustion research. Diffusion dominated flames such as highly curved flame balls present a challenging flame structure that has not been included in current flame stretch theory so far. In such flames, the relationship between consumption speed and negative displacement speed usually marks the boundary of what flame stretch theory can predict. In this work, our objective is to derive a general formulation which naturally includes this relationship. We use flamelet equations derived using a mass based stretch rate and show that if the diffusion flux at the unburnt side is not ignored, as is normally done in flame stretch theory, a formulation that can describe the propagation of different types of premixed flames can be derived. Based on the thin reaction zone assumption, solutions from theory are verified against numerical results for 1D ideal flame balls. Further verification is done for multi-dimensional ball-like flames, where both convection and diffusion dominated regions are present for highly curved flames. It is shown that the extended theory is able to predict the flame kinematics in a better way by describing the diffusion dominated flame propagation as well.