On the closure of curvature in 2D flamelet theory

TL;DR

This paper introduces a method to relate flame curvature to flow gradients using a 2D composition space, enabling the elimination of curvature as an independent parameter in flamelet equations.

Contribution

It presents a novel approach to close curvature in flamelet theory by linking it to flow gradients within a 2D orthogonal composition space.

Findings

Curvature can be expressed as a function of flow gradients.

The method removes the need to treat curvature as an independent parameter.

Applicable to various orthogonal coordinate systems.

Abstract

So far, flamelet theory has treated curvature as an independent parameter requiring specific means for closure. In this work, it is shown how the adoption of a two-dimensional orthogonal composition space allows obtaining formal mathematical relations between the flame curvatures and the gradients of the conditioning scalars (also called flamelet coordinates). With these, both curvatures become a flame response to the underlying flow, which conveniently allows removing them from the corresponding set of flamelet equations. While the demonstration is performed in the context of partially premixed flames, the approach is general and applicable to any orthogonal coordinate system.