Development and validation of a framework to predict the linear stability of transverse thermoacoustic modes of a reheat combustor

To achieve fully carbon-neutral, fuel-flexible and on-demand grid power delivery, gas turbines featuring constant pressure sequential combustion architecture show great potential. A sequential combustor is comprised of two axially-staged combustion chambers with the first stage typically being a swirl-stabilised propagating flame. Post first stage combustion, the exhaust stream is first diluted with air and later enriched with additional fuel in the second stage resulting in a vitiated product mixture at high temperatures leading to auto-ignition. Thermoacoustically-stable combustion stages are critical to ensure low emissions, high reliability and ensure mechanical integrity. The second stage firing under auto-ignition conditions can be subject to transversal instabilities. This article presents a finite element coupled method to model the thermoacoustic behaviour of a second stage reheat flame in an efficient, cost-effective approach. To do so, prior techniques to model the response of autoignition-stabilised flames to longitudinal acoustic perturbations is leveraged to quantify the auto-ignition flame's heat release rate response to transverse acoustic waves. Subsequently, the framework is used to compute the stability of transverse eigenmodes for an atmospheric reheat combustor. Validation is performed by comparison to experimentally obtained pressure sensor measurements and chemiluminescence imaging of the flame. It is observed that the framework can correctly predict the combustor's unstable first transverse mode and also capture the dynamic flame response qualitatively. Consequently, the framework presented in this work can be leveraged to get reliable and time-efficient stability estimates of the transverse thermoacoustic modes in experimental reheat burners.