Analytical treatment of 2D steady flames anchored in high-velocity streams

TL;DR

This paper provides an analytical framework for understanding 2D steady flames anchored in high-velocity streams, emphasizing the importance of transversal velocity in flame structure and deriving equations for flame front behavior.

Contribution

It introduces a consistent analytical approach using on-shell description to model steady anchored flames, including new equations for flame front position and gas velocity.

Findings

Derived a second-order differential equation for flame front position.

Numerical solutions confirm the validity of the analytical model.

Highlighted the crucial role of transversal velocity in flame structure.

Abstract

The problem of burning of high-velocity gas streams in channels is revisited. Previous treatments of this issue are found to be incomplete. It is shown that despite relative smallness of the transversal gas velocity, it plays crucial role in determining flame structure. In particular, it is necessary in formulating boundary conditions near the flame anchor, and for the proper account of the flame propagation law. Using the on-shell description of steady anchored flames, a consistent solution of the problem is given. Equations for the flame front position and gas-velocity at the front are obtained. It is demonstrated that they reduce to a second-order differential equation for the front position. Numerical solutions of the derived equations are found.