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Thermoacoustic instabilities, caused by the coupling between unsteady heat release and acoustic waves, are a major challenge for the safe and efficient operation of gas turbines. Since these self-sustained oscillations can lead to severe structural damage, developing fast and reliable simulation tools is crucial.

This thesis presents the extension of STORM (State-space Thermoacoustic Reduced Order Model), a reduced-order solver originally developed by C. Laurent, and designed to study thermoacoustic instabilities in realistic gas turbine configurations. STORM is based on a modal decomposition of the acoustic field and a state-space formulation that couples acoustics, flame response (via Flame Transfer Functions), and boundary conditions. This work builds on a comprehensive understanding of existing modeling strategies, emphasizing the synergy between experimental and numerical approaches. In this thesis, the STORM methodology has been significantly strengthened: boundary conditions are handled more robustly, and a major numerical conditioning issue—responsible for spurious non-physical modes—has been resolved. Moreover, a key contribution is a new formulation for modeling jump conditions at interfaces, where the discontinuity is treated as a source term directly within the Helmholtz equation. This approach avoids domain splitting and the associated numerical instabilities, and has been successfully validated on academic 1D test cases. The last chapter illustrates the application of STORM to several experimental and industrially relevant configurations.

• MIRADAS, an academic burner from IMFT, serves as a benchmark for validation, with experimental Flame Transfer Functions and outlet impedance data. STORM accurately reproduces the observed instability.
• Safran post-combustor: STORM is used for a parametric study by varying FTF parameters. Around 100 full thermoacoustic computations (∼ 1000 modes on a 2-million-node mesh) were completed in under 2 hours. With conventional finite element solvers, a single mode typically takes ∼ 30 minutes, making this scale of analysis practically impossible. STORM thus enables the construction of complete multi-mode stability maps within feasible time.
• HYLON, an academic case with a two-velocity inlet flame, shows STORM's flexibility. While frequencies match experiments well, growth rates are less accurate, likely due to missing injector impedance data or limitations in the double-input FTF model.
• MICCA, a 16-injector annular combustor (EM2C), was also modeled. Thanks to STORM's flexibility, injector impedances have been incorporated via transfer matrix models, an essential factor to accurately predict the thermoacoustic modes. STORM successfully reproduced the experimental parametric study involving two injector types arranged in various configurations, correctly capturing the evolution of thermoacoustic modes with injector placement.

In conclusion, this work delivers a complete and efficient tool for thermoacoustic stability analysis based on reduced-order modeling. Its main achievements include a robust and modular solver applicable to complex geometries, direct integration of experimental flame and impedance data, the ability to conduct fast parametric studies and design analyses, and validation on several academic and industrial configurations. Future work will focus on applying STORM to increasingly complex systems to identify its current limitations and guide future developments. The aim is to progressively broaden the range of configurations the solver can handle.