Activation energy asymptotic analysis and numerical modelling of a strained laminar corner flame

Abstract

A steady, two-dimensional corner flame is established when fuel and oxidizer enter the reaction zone in mutually perpendicular directions. A model problem in which the velocity fields are linear functions of spatial position is utilized to study the resulting flame. The flame structure is comprised of a diffusion flame surrounded on either side by fuel-rich and fuel-lean partially premixed laminar flames, similar to, but distinct from, triple flames. Using suitable coordinate transformations and change of variables, the governing equations in the thermodiffusive approximation are recast into a form akin to classical triple flames, with the strain rate appearing as the eigenvalue. A new exact integral representation of the solution to the mixture fraction equation is then utilized and high activation energy asymptotics are applied to solve approximately for the resulting flame shape, the imposed strain rate and, most significantly, the position of flame stabilization. This theoretically predicted flame is computed numerically, and comparisons are made between theory and computation.