Turbulent diffusion flames at low strain rates sustain a spatially continuous flame surface.However, at high strains, which may be localized in a flow or not, the flame can be quenched due to the increased heat loss away from the reaction zone.These quenched regions are sometimes called flame holes.Flame holes reduce the efficiency of combustion, can increase the production of certain pollutants (e.g. carbon monoxide, soot) as well as limit the overall stability of the flame. We present a numerical algorithm for the calculation of the dynamics of flame holes in diffusion flames. The key element is the solution of an evolution equation defined on a general moving surface. The low-dimensional manifold (the surface) can evolve in time and it is defined implicitly as an iso-level set of an associated Cartesian scalar field. An important property of the method described here is that the surface coordinates or parameterization does not need to be determined explicitly; instead, the numerical method employs an embedding technique where the evolution equation is extended to the Cartesian space, where well-known and efficient numerical methods can be used. In our application of this method, the field defined on the surface represents the chemical activity state of a turbulent diffusion flame. We present a formulation that describes the formation, propagation, and growth of flames holes using edge-flame modeling in laminar and turbulent diffusion flames. This problem is solved using a high-order finite-volume WENO method and a new extension algorithm defined in terms of propagation PDEs. The complete algorithm is demonstrated by tracking the dynamics of flame holes in a turbulent reacting shear layer.The method is also implemented in a generalized unstructured low-Mach number fluid solver (Sandia's SIERRA low Mach Module ``Nalu") and applied to simulate local extinction in a piloted jet diffusion flame configuration.
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