Lagrangian Simulation of Diffusion Flames

Abstract

Abstract-We develop a new Lagrangian numerical technique to investigate the interaction between fluid mechanics and chemical reaction in diffusion flames through volumetric expansion and baroclinic vorticity production. We base our numerical method on the mixture-fraction variable formulation and the Burke-Schumann limit of an infinitely thin flame sheet, In this way. we do not attempt to resolve the flame structure in detail, but instead are in a position to simulate combustion in more complex flow fields. The method employs Lagrangian blobs that carry gradients of the mixture-fraction variable. Other blobs act as sources to account for thermal expansion, while vortex blobs are introduced to represent the baroclinic vorticity production. These blobs deform as a result of diffusion, strain, and thermal expansion. In its Lagrangian nature, our approach to diffusion flames corresponds to the technique recently developed by Ghoniem for premixed flames. In the incompressible flow limit, we demonstrate accuracy and convergence of our technique by comparison with available finite-difference results for the case of a flame sheet wrapping around a vortex. We then proceed to include the effects of volumetric expansion and baroclinic vorticity production. We find that the effect of thermal expansion is very strong in regions of temperature gradients in the circumferential direction, where fluid particles undergo rapid temperature changes. We furthermore observe the production of both co- and counterrotating vorticity that significantly affects the dynamics of the flow field. Two vorticity layers of opposite sign adjacent to the flame sheet transport additional fluid towards the burnt core, thus causing it to grow in an accelerated fashion.