Flame Stretch and the Balance Equation for the Flame Area

Abstract

When a flame propagates in a nonuniform flow it experiences strain and curvature effects. The fractional rate of change of the flame area constitutes the flame stretch. This quantity is often used to describe the structure and extinction mechanisms of turbulent flames. It also occurs in many recent studies of premixed laminar flames. This article provides a unified view of this concept on the basis of a novel derivation of stretch in terms of strain rate and curvature. The flame stretch, the rate of change of the normal to the flame front and the rate of change of the curvature are deduced from a general transport theorem. As an illustration, the components of flame stretch are evaluated in the case of a direct numerical simulation of the interaction between a pair of vortices and a laminar flame. Another application of flame stretch concerns the determination of the available flame surface density. A balance equation is derived for this quantity and cast in various useful forms thus providing a basis for the turbulent combustion models which rely on a determination of the local density of flame area