Toward a Flame Embedding Model for Turbulent Combustion Simulation

Combustion in turbulent flows may take the form of a thin flame wrapped around vortical structures. For this regime, the flame embedding approach seeks to decouple computations of the outer nonreacting flow and the combustion zone by discretizing the flame surface into a number of elemental flames, each incorporating the local impact of unsteady flow-flame interaction. An unsteady strained laminar flame solver, based on a boundary-layer approximation of combustion in a time-dependent stagnation-point potential flow, is proposed as an elemental flame model. To validate the concept, two-dimensional simulations of premixed flame-vortex interactions are performed for a matrix of vortex strengths and length scales, and a section of the flame is selected for comparison with the flame embedding model results. Results show that using the flame leading-edge strain rate gives reasonable agreement in the cases of low strain rate and weak strain rate gradient within the flame structure. This agreement deteriorates substantially when both are high. We propose two different schemes, both based on averaging the strain rate across the flame structure, and demonstrate that agreement between the one-dimensional model and the two-dimensional simulation greatly improves when the actual strain rate at the reaction zone of the one-dimensional flame is made to match that of the two-dimensional flame.