Vortex simulation of three-dimensional reacting shear layers

The three-dimensional transport element method is extended to solve the conservation equations for reacting flow. The numerical scheme belongs to an adaptive, Lagrangian class of field methods in which the computational effort is concentrated in zones of finite vorticity and chemical reaction. The method is based on the accurate discretization of the vorticity and species concentrations among a number of spherically-symmetric transport elements, and the advection of these elements along particle trajectories. We use the low Mach number approximation of combustion in an open domain, and restrict our attention to the case of diffusion flames at low values of heat release. A single-step, second-order, infinite-rate kinetics chemical reaction model is employed. The scheme is applied to study the influence of flow induced by the primary and secondary instabilities on the reaction zone and product distribution in a temporal shear layer. Results are obtained in the high Peclet number regime for a wide range of Damkohler numbers. Changes in the reaction field can be related to either the entrainment or the strain field associated with the saturation of the instabilities. With increasing Damkohler number, the structure of the reaction region changes from a distributed zone embedded within spanwise and streamwise vortices, to a thin sheet surrounding their cores. However, the product concentration always exhibits strong similarity to the vorticity distribution, realizing its highest values in zones of high vorticity and falling rapidly in regions where the magnitude of the vorticity is small. Variation of the Peclet number yields minor changes in the shape of the product distribution and in the structure of the reaction zone, but strongly affects the product formation rates.