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On the Axisymmetric Counterflow Flame Simulations: Is There an Optimal Nozzle Diameter and Separation Distance to Apply Quasi One-Dimensional Theory?

Two-dimensional axisymmetric numerical analysis of counterflow flames was employed to better understand the applicability of the quasi one-dimensional theory of Seshadri and Williams to flames produced by small diameter convergent nozzles. The computational domain considered included the convergent sections of two opposed nozzles as well as the surrounding inert annular co-flows. For computational efficiency, the fuel-oxidizer system of diluted hydrogen versus air in non-premixed flame mode, with a detailed chemical kinetic model and mixture-averaged transport property description, was considered. With an increase of nozzle diameter from 6.5 mm to larger values (with plug flow velocity profiles at the nozzle exit), the influence of the radial terms on eigenvalue and scalar variables has been compared. Error metric on nozzle diameter effects is presented with comparison to typical experimental measurement uncertainties. The analysis also showed that, for nozzle separation distances below the free-floating limit, the self-similar function in quasi one-dimensional formulation can be preserved by specifying radial velocity boundary conditions, as long as the radial gradients are negligible.