Global linear stability analysis of a slit flame subject to intrinsic thermoacoustic instability

TL;DR

This paper uses linear stability analysis with adjoint modes to investigate the intrinsic thermoacoustic feedback in a laminar slit flame, revealing the role of boundary layer vorticity and the transition to vortex shedding.

Contribution

It introduces a holistic linearized reactive flow model to analyze intrinsic thermoacoustic feedback, including finite rate chemistry and flow sensitivity.

Findings

The ITA feedback loop is closed by boundary layer vorticity.

Adjoint vorticity shows high flow sensitivity.

The ITA eigenmode transitions to vortex shedding in passive flames.

Abstract

The present study makes use of the adjoint modes of the Linearized Reactive Flow (LRF) equations to investigate the Intrinsic Thermoacoustic (ITA) feedback loop of a laminar premixed slit flame. The analysis shows that the ITA feedback loop is closed by vorticity generated in the boundary layer of the slit by impinging acoustic waves penetrating the slit. In this region, adjoint vorticity shows a high sensitivity of the flow. It is also hypothesised that the ITA eigenmode smoothly transitions to a purely hydrodynamic mode -- vortex shedding -- for a passive flame. The computational domain is chosen sufficiently short so as to isolate the ITA feedback loop from cavity modes. This analysis is made possible by the holistic character of the LRF model, i.e. a direct linearization of the non-linear reactive flow equations, including explicit finite rate chemistry and avoiding idealization of the flow.