A Framework For Suppression Of Thermoacousitc Instability Using The Nyquist Criterion

To simulate complex multiphysics and multiscale phenomena, such as thermoacoustic combustion instabilities, a comprehensive model is often created by combining subsystems. This approach allows the contribution of acoustic terminations to be separated from the acoustic response of the flame, potentially providing a systematic approach to suppressing thermoacoustic instabilities. In this paper, we present a framework for developing terminations and silencers using the Nyquist criterion and winding number. Firstly, we determine the dispersion relation to establish the system's eigen-frequencies. Then, by distinguishing between the Nyquist diagram and the Nyquist criterion and using the argument (arg) of the dispersion relation, we propose two thermoacoustic stability criteria. This approach is similar to the theory used in microwave technology. Using this methodology, we can develop a systematic method for characterizing the quality of specific combustion devices and provide guidelines for designing stable acoustic embeddings in thermoacoustic systems. To validate this approach, we will perform an eigenvalue analysis on a classical duct-flame-duct test case, and the results will demonstrate the effectiveness of this analogy in solving thermoacoustic problems.