Thermo-acoustic instability is one of the most persistent and costly problems facing gas turbine manufacturers. It arises when heat release rate fluctuations from a flame lock into acoustic modes in a combustion chamber. This causes large amplitude oscillations even if the thermodynamic efficiency of the conversion from heat to work is small. Although the mechanism has been well understood for over a century and carefully studied through experiments and numerical simulations, engines that have been designed to be thermo-acoustically stable sometimes turn out to be unstable when tested. This is because thermo-acoustic behaviour is highly sensitive to the phase difference between heat release rate and pressure, which in turn is sensitive to small changes in the flame behaviour and the combustor1s shape. On the negative side, this sensitivity causes a modelling and practical challenge. On the positive side, it causes the model parameters to be highly observable from experimental data. This makes thermo-acoustic instability an ideal application for Bayesian inference because (i) the physics is well-known, (ii) model parameters are observable from data, (iii) data is available from laboratory to industrial scale rigs, (iv) we know from experience that thermo-acoustic instability can always been eliminated with small changes. The challenge is to design a quantitatively-accurate model that can predict those changes.

The overall aim of the Marie Curie Training Network HyNOISE is to optimize the design of hydrogen-fuelled gas turbine injectors so that the combustors are quiet and not susceptible to thermoacoustic instabilities. This requires a quantitatively accurate model of the thermoacoustic system, which is the combination of a hydrogen flame with an acoustic network. This model will be obtained by systematic assimilation of data from laboratory experiments (NTNU, Norway), large eddy simulations (TUB, Germany), and industrial experiments (RRD, Germany). This data will be assimilated into thermoacoustic models using Cambrige's adjoint-accelerated inference and optimization method (AXIOM).

The first objective is to extend AXIOM to typical hydrogen flame geometries using data from a laboratory scale combustor at NTNU. Bayesian model selection (a component of AXIOM) will be used to find the optimal component models for this simple system. The second objective is to extend AXIOM to industrial scale geometries using data from a real gas turbine fuel injector on an industrial test rig at RRD. Bayesian experimental design (another component of AXIOM) will be used to identify the experimental configurations that maximize the information that can be learned from a limited number of tests. The third objective is to develop and test several candidates mean field flame models with TUB and then to assimilate LES data into these models with AXIOM.

The result will be a Bayesian framework that transfers data from experiments and numerical simulations into low order models. These models will steadily accumulate data and become more quantitatively accurate over time. They can therefore be used for optimization and re-optimization, as more data become available in the future and as future designs change.