In the axisymmetric problem, this is attributed to the intricate coupling between the flow deflection and the position of iso-mixture fraction surfaces relatively to iso-velocity surfaces.
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.
With this formulation, valid for arbitrary Lewis numbers, the flame lies on the stoichiometric mixture fraction level surface Z = Zs and its temperature can be easily calculated as Te′/T0="1+γ(1+Hs), where Zs = 1/(1 + S), γ is the non-dimensional heat release parameter, S is the air needed to burn the unit mass of fuel and Hs is the value of the excess enthalpy at the flame surface.
The goal of this paper is to investigate the effects of curvature of mixture fraction iso-surfaces on the transport of species in diffusion flames.
In cases where flame curvature is not uniform, the curvature-induced convective term generates gradients along mixture fraction iso-surfaces, which enhance tangential diffusion effects.
Upon formation on the rich side of the flame, soot is displaced relative to curved mixture fraction iso-surfaces due to differential diffusion effects between soot and the gas-phase.
Alternatively, a reaction progress variable based embedded flame model is developed using mixture fraction, total enthalpy and surface temperature.
Results are presented for Spalding B numbers and values of the mixture fraction at the droplet surface for the fast chemistry case and for the case where the droplet cannot sustain an envelope flame.
These curvature effects correspond to diffusion tangential to iso-surfaces of mixture fraction.
Following ignition, the high-temperature kernels expand and engulf the stoichiometric mixture-fraction iso-surface which in turn establish edge flames which propagate along the iso-surface.
