Edge flames are fundamental flame structures essential to the description of flame hole dynamics in turbulent combustion and the stabilization of lifted jet flames. In this thesis we concentrate on the role of boundary conditions and how they, in turn, can induce an undesirable streamwise pressure gradient in the trailing diffusion flame that affects the edge flame speed. A novel numerical scheme is designed to solve the nonlinear eigenvalue problem based on the variable-density zero Mach number reactive Navier-Stokes equations. It employs a homotopy method to gradually map the solutions from the constant-density edge flame to the more challenging variable-density edge flame. The flow and the combustion fields are segregated within an outer Picard iteration embedded in a Newton method, which is solved sequentially using GMRES with proper multigrid preconditioners.This efficient algorithm enables the parametric study of the effects of differential diffusion and strain rate on edge flame structure and propagation velocity for variable-density flows. Previous studies observe that the ratio of the edge flame speed to the premixed stoichiometric laminar flame velocity scales approximately as the square root of the ratio of the cold stream density to the stoichiometric density. In our simulations, where no pressure gradient is present, it is found that the speedup of the normalized edge flame velocity might be superlinear on the density ratio. This result is new and complements previous results, for different boundary conditions, which suggests that the edge flame speed is a strong function of the particular hydrodynamic boundary conditions employed in the simulations.
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Solution of strained edge flames by a boundary value method
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