Diffusion edge-flame: approximation of the flame tip Damköhler number

A relation is provided to approximate the Damköhler number at the tip of an edge-flame. The reaction zone extremity is modeled as a one-dimensional diffusion flame to which additional transverse fluxes are added. The Damköhler number at the flame tip is then characterized by a relation that involves the quenching Damköhler number of a one-dimensional diffusion flamelet. In this expression, a linear relation appears between the edge-flame Damköhler number and the amount of heat diffusing away from the flame tip, along the iso-mixture fraction surfaces. Numerical simulations are performed to estimate the validity of these analytical results. The behavior of the Damköhler number is well reproduced for a large range of two-dimensional and planar edge-flames, including weakly varying partially premixed fronts, triple-flames and edge-flames close to full quenching. The approximation is also verified in axi-symmetric lifted flames.