Liñán's diffusion flame theory


Liñán diffusion flame theory is a theory developed by Amable Liñán in 1974 to explain the diffusion flame structure using activation energy asymptotics and Damköhler number asymptotics. Liñán used counterflowing jets of fuel and oxidizer to study the diffusion flame structure, analyzing for the entire range of Damköhler number. His theory predicted four different type of flame structure as follows,
The theory is well explained in the simplest possible model. Thus, assuming a one-step irreversible Arrhenius law for the combustion chemistry with constant density and transport properties and with unity Lewis number reactants, the governing equation for the non-dimensional temperature field in the stagnation point flow reduces to
where is the mixture fraction, is the Damköhler number, is the activation temperature and the fuel mass fraction and oxidizer mass fraction are scaled with their respective feed stream values, given by
with boundary conditions. Here, is the unburnt temperature profile and is the stoichiometric parameter. The four regime are analyzed by trying to solve above equations using activation energy asymptotics and Damköhler number asymptotics. The solution to above problem is multi-valued. Treating mixture fraction as independent variable reduces the equation to
with boundary conditions and.

Extinction Damköhler number

The reduced Damköhler number is defined as follows
where and. The theory predicted an expression for the reduced Damköhler number at which the flame will extinguish, given by
where.