A flamelet description of premixed laminar flames and the relation with flame stretch

Abstract

A laminar flamelet description is derived for premixed laminar flames. The full set of 3D instationary combustion equations is decomposed in three parts: (1) a flow and mixing system without chemical reactions, described by the momentum, enthalpy, and element conservation equations, (2) the G-equation for the flame motion, and (3) a flamelet system describing the inner flame structure and the local mass burning rate. Local fields for the flame curvature and the flame stretch couple the flamelet system with the flow and flame motion. To derive an efficient model, the flamelet equations are analyzed in depth, using the Integral Analysis, first introduced by Chung and Law [1]. It appears that the flamelet response is governed by algebraic equations describing the influence of flame stretch on the local mass burning rate, the enthalpy variation, and element composition. Known expressions for the mass burning rate, found by Joulin, Clavin, and Williams are recovered in some special cases. Furthermore, the validity of the expressions has been shown for weak and strong stretch by comparing the results with numerical results of lean stretched premixed methane/air flames, computed with skeletal chemistry. Finally, the theory is illustrated for the tip of a 2D stationary Bunsen flame.