Preferential Diffusion and the Initiation of Lean Flames of Light Fuels

Source abstract

As an attempt to better understand the problem of flame initiation, we study spherical flame kernels whose evolutions are triggered by a time-dependent, localized source of energy in a lean mixture of a light fuel, a heavier oxidizer, and a diluent in large excess. Assuming a chemical rate of the Arrhenius type, we investigate the influence of preferential diffusion on the flame dynamics by employing asymptotic techniques in the formal limit $\beta \to \infty$ of large Zel’dovich numbers ($\beta \sim$ activation to thermal energy ratio). We evidence a critical value $\phi _c < 1$ of the initial fuel-to-oxidizer mole number ratio $\phi$, beyond which the reaction may proceed under locally rich conditions, owing to the preferential diffusion of the reactants. For near-critical compositions $( \beta ( \phi - \phi _c ) = O( 1 ) )$ we obtain a nonlinear equation, with memory effects, to describe the flame radius growth and/or decay around its equilibrium values. It displays the influence of the energy source, of the chemistry, of the initial composition, and of the different mobilities of the two reactants. Upon analytical investigations, we obtain the early flame evolution, and we describe the long-time behavior of flame radius trajectories for total energy inputs that are close to the initiation energies. Finally, we identify circumstances in which the present theory fails, and discuss possible consequences on the flame initiation problem.