Adjoint methods and Bayesian data assimilation for modeling the thermoacoustic behaviour of premixed flames

The aviation industry heavily relies on combustion for long-haul air travel due to essential power-to-weight and energy-to-weight ratios. To address environmental concerns, research focuses on reducing carbon dioxide (CO2) and nitrous oxide (NOx) emissions through lean premixed combustion, sustainable fuels, and hydrogen fuel. Lean combustion, while promising for lowering NOx emissions at reduced temperatures, poses challenges related to thermoacoustic oscillations, necessitating ongoing research. Thermoacoustic instability occurs when flame perturbations synchronize with pressure oscillations, converting heat to work over an oscillation cycle—a fundamental thermoacoustic mechanism described by the Rayleigh criterion. These instabilities can severely affect performance, cause component damage, and even lead to catastrophic failures. Effective modelling of combustion instability remains challenging due to the extreme sensitivity of the thermoacoustic mechanism to minor system changes. Successful development requires comprehensive testing and modifications, emphasizing the need for quantitatively accurate models and adjoint methods to efficiently identify and implement necessary changes for mitigating combustion instability in engine designs. The literature offers numerous thermoacoustic models, making model selection challenging. An alternative approach involves Bayesian inference, leveraging extensive experimental data and prior beliefs to identify the most suitable model. This approach benefits from the sensitivity of measurable features in thermoacoustics to model parameters. This process results in quantitatively-accurate models that are interpretable and can be extrapolated. Moreover, the assimilation process is expedited when the model is differentiable, allowing efficient optimisation using gradient-descent methods based on the flame position gradient with respect to the model parameters. This research aims to enhance understanding of thermoacoustic instability by developing differentiable computational tools, allowing differentiation with respect to parameters and initial conditions. The study comprises four main research topics: firstly, an examination of triggering and non-normality in thermoacoustics, delving into minimal triggering thresholds in the Rijke tube while considering the influence of time delay on perturbations; secondly, the creation of a differentiable model for laminar premixed flames, with a focus on evaluating how influential parameters affect flame transfer function and studying the effects of flame base oscillations; thirdly, the application of Bayesian data assimilation to assimilate experimental flame images of acoustically forced laminar premixed conical flames into a quantitatively accurate reduced-order model to identify the most probable model parameters; and finally, an exploration of the impact of hydrogen enrichment on thermoacoustic instabilities in laminar conical premixed methane/air flames, shedding light on hydrogen fraction as a modifiable parameter to control thermoacoustic instabilities.