An Improved Spalding-Stephenson Procedure for One-Dimensional Flame Calculations

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Abstract
–The Spalding-Stephenson transformation of the unsteady, flame conservation equations is one of the most widely used approaches to calculate the profiles of one-dimensional, laminar flames. This transformation takes full advantage of the time-dependent conservation equations under constant pressure conditions. Numerous procedures have been developed over the years to estimate the proper inlet, mass flow boundary conditions. In this paper the transformation is analyzed in depth and a formalism is developed for a generalized, mass flow boundary condition. The advantage of this generalized procedure for the mass flow is that it treats with no approximations the full range of flame conditions: from freely propagating, to burner stabilized, to transient. The capability to treat transient flames is demonstrated by calculations of a time-evolving hydrogen-air flame quenching at a wall and stabilizing (flashing back) onto a porous plug burner. Free flame profiles for methane-air and hydrogen-air flames that evolved to steady state were also calculated using the generalized (or instantaneous) mass flow procedure. Throughout these calculations the instantaneous flame speed is calculated directly from the species and enthalpy profiles.

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