Cluster-based control of thermoacoustic instabilities in a turbulent hydrogen combustor

We apply a data-driven feedback control strategy, termed cluster-based control (CBC), to suppress self-excited thermoacoustic instabilities in a turbulent combustor with a lean-premixed hydrogen-enriched flame. From a single pressure sensor, we construct a two-dimensional delay-embedded feature space that encapsulates the thermoacoustic dynamics of the system. This space is then partitioned via k-means clustering, and each cluster is assigned an optimized actuation amplitude using a Nelder-Mead simplex algorithm that balances instability attenuation against actuation cost. In under 100 optimization iterations (around 1 hour), CBC achieves an 83% reduction in thermoacoustic amplitude, outperforming both brute-force open-loop mapping and some machine-learning controllers. Phase-space trajectories confirm that CBC steers the system toward low-amplitude clusters, while spectral analysis and Rayleigh index calculations reveal that CBC suppresses thermoacoustic instabilities by disrupting the phase locking between pressure and heat-release-rate fluctuations. These results demonstrate that CBC provides an efficient, low-dimensional framework for real-time suppression of thermoacoustic instabilities, paving the way for its integration into sustainable combustion systems.