An analytical study of the flame dynamics of a transversely forced asymmetric two-dimensional Bunsen flame

Abstract

Combustion instabilities in annular combustors are of great interest because of their industrial relevance. Azimuthal acoustic modes, which involve transverse acoustic forcing to flames, have become a key process related to annular combustor instabilities. Transverse mean flow may be a factor that affects azimuthal oscillations. This paper provides an analytical model for a transversely forced two-dimensional Bunsen flame under transverse mean flow. The model is established using a low-amplitude perturbation assumption applied to a G-equation formulation. Forced flame displacement and flame transfer functions (FTFs) are calculated. The results are verified based on numerical solutions of the G-equation. Effects of frequency, transverse mean flow velocity and vertical mean flow velocity on the FTFs are discussed. The symmetric flame without transverse mean flow has a vanishing response to transverse acoustic forcing, while asymmetric flames, which are formed with transverse mean flow, have a bandpass response to transverse forcing. The response at very low and high forcing frequencies is small, with higher transfer function gains only in a certain frequency range. This bandpass response, which is inherently linked to the asymmetry of the flame, is an important factor to account for when considering the flame dynamics related to transverse acoustic effects.

KEYWORDS:

• asymmetric two-dimensional Bunsen flame
• transverse forcing
• flame dynamics
• G-equation
• flame interaction

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51676110] as well as the Tsinghua Fudaoyuan Research Fund of Tsinghua University.