In the initial phase of the project, we made progress through the development and implementation of the proposed methodology. These activities laid the conceptual foundations required to pursue the broader objectives of the research. In particular, we focused on embedding the central project concept within a comprehensive theoretical structure. This effort was essential for the core idea into a formal framework capable to guide analytical and numerical investigations.
The primary scientific objective of this phase was to establish a theoretical basis for controlling thermoacoustic dynamics through the deliberate exploitation of defective eigenvalues of the system. Defective eigenvalues are closely related to the presence of exceptional points in the parameter space. Such spectral singularities can lead to unique physical behaviors, including enhanced sensitivity to parameter variations and modified stability properties. Recognizing these characteristics, the project explored how these spectral features could be harnessed as a design mechanism for control of thermoacoustic instabilities.
To systematically implement this concept, a theoretical framework was developed and designated as Exceptional Point–based Thermoacoustic Design (EPTD). The purpose of EPTD is to provide a structured methodology for identifying, analyzing, and utilizing exceptional points in thermoacoustic systems in order to define their stability. Following its formulation, the EPTD framework was applied to a sequence of three representative configurations. These case studies were selected to progressively increase the level of physical and modeling complexity, thereby allowing a systematic evaluation of the framework’s applicability across different thermoacoustic environments. The first configuration corresponded to a simplified academic setup chosen to isolate the essential mechanisms associated with exceptional-point dynamics. This initial step allowed the analytical aspects of the framework to be examined under controlled conditions and provided clear insight into the relationship between defective eigenvalues and thermoacoustic stability. The other configurations introduced additional physical parameters by incorporating more detailed system elements.
Overall, the investigations confirmed the robustness and adaptability of the EPTD framework. By successfully applying the methodology across configurations ranging from simplified academic systems to laboratory-scale setups, the project established a solid theoretical foundation for the subsequent phases of experimental validation.
