A Reduced-order Model for Lock-on via Vortex-combustion-acoustic Closed-loop Coupling in A Step Combustor

ABSTRACT

The lock-on of the frequency of acoustic oscillations to the frequency of the vortex shedding in a reacting flow in a backward-facing step combustor is demonstrated using a reduced-order model. Individual models for the flow, flame and acoustic models are developed. A two-dimensional flow field with growth and shedding of vortices is modeled using a potential flow model derived via a conformal mapping of the step geometry. Combustion and acoustic models are derived using thermo-diffusive equations and the one-dimensional Galerkin method, respectively. A modulation of heat release rate fluctuations is thus enabled by vortices advecting past the flame, overcoming the time and space-localized assumptions in vortex kicked oscillator models. Comparisons with results from kicked oscillator models show a better prediction of the dominant frequencies during stable and unstable operations. A Reynolds number sweep is performed to reveal the transition from stable to unstable operation and thus the onset of instability. A shift in the dominant frequency of pressure fluctuations from the natural duct acoustic mode to the natural vortex shedding mode is observed, indicative of a lock-on. The results compare well with past experimental and computational data for similar geometry and flow conditions.

KEYWORDS:

• Vortex-acoustic lock-on
• combustion instability
• reduced-order modeling

Acknowledgments

The National Centre for Combustion R&D was supported by the Science and Engineering Research Board, Government of India.

Declaration of Interests

The authors report no conflict of interest.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the Science and Engineering Research Board.