Stability analysis of confined V-flames. I. Analytical treatment of the high-velocity limit

TL;DR

This paper analytically investigates the linear stability of confined V-flames in high-velocity streams, revealing that such flames are universally unstable regardless of gas expansion, with detailed eigenfunctions and growth rates derived.

Contribution

It provides an analytical solution for the stability of V-flames in high-velocity channels, highlighting the universal instability and elucidating the role of vorticity and memory effects.

Findings

V-flames are unstable for all gas expansion coefficients.

Analytic expressions for eigenfunctions and growth rates are derived.

Memory effects due to vorticity influence disturbance dynamics.

Abstract

The problem of linear stability of confined V-flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames in high-velocity channel streams. It is demonstrated that dynamics of flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the curved front. The perturbation growth rate spectrum is determined, and explicit analytic expressions for the eigenfunctions are given. It is found that the piecewise linear V-structure is unstable for all values of the gas expansion coefficient.