Dynamic response of thermoacoustic oscillations and entropy waves generation within the Rijke tube subjected to open-loop control

Unsteady combustion generates entropy waves that, upon converted into entropy noise, can trigger thermoacoustic instability and amplify noise emissions. However, entropy waves are often overlooked in thermoacoustic systems, as they propagate silently with the mean flow within the combustion chamber. Therefore, this study introduces a quantitative approach to measuring and controlling entropy waves in a Rijke tube setup, utilizing the background oriented schlieren (BOS) method in combination with the multi-microphone method (MMM). As the amplitude of external acoustic excitation increases, nonlinear dynamics such as forced synchronization and modal coupling emerge in the spatial patterns of entropy waves. Moreover, the nonlinear response of the thermoacoustic system varies with the frequency of external acoustic excitation. This paper compares simultaneously measured thermoacoustic oscillations with entropy waves. In both low- and high-frequency ranges, the externally excited acoustic field induces forced synchronization of acoustic pressure and entropy waves, with the latter exhibiting a more pronounced nonlinear response, evidenced by harmonics of differential frequencies and amplitude saturation than the acoustic waves. In the moderate-frequency range, a strong entropy wave response is observed, accompanied by minimal nonlinear effects, with the acoustic field approximating a linear superposition. Here, the entropy waves display marked acoustic similarity, suggesting their generation may stem from the combined influence of velocity and pressure perturbations. These findings provide valuable insights into the mechanisms driving entropy wave generation. Novelty and significance statement This study explores the forced synchronization process of entropy waves, characterized by multi-mode coupling, and examines the nonlinear response characteristics of entropy waves under varying external excitation frequencies. A coherent response between acoustic waves and entropy waves is observed during the open-loop control process, suggesting that the generation of entropy waves downstream of the thermoacoustic system is likely influenced by the system's acoustic pressure. These findings highlight the intricate interplay between acoustic and entropy waves dynamics, offering new insights into their coupling and control in thermoacoustic systems.