A Jacobian-based framework for the derivation of comprehensive thermoacoustic jump conditions

Low-order network models are an efficient framework to describe and predict thermoacoustic phenomena in confined combustion systems. These models are based on the interconnection of compact and non-compact elements representing the main components of the system. Assumptions such as small Mach numbers or constant gas properties are typically applied in the derivation of these elements. This work proposes a Jacobian-based framework for the derivation of comprehensive thermoacoustic jump conditions (compact elements) accounting for acoustic, entropic, and compositional perturbations. The modularity provided by the Jacobian-based formulation renders the framework easily applicable for the derivation of a variety of compact elements and provides a straightforward implementation guideline. Application-specific assumptions to increase computational efficiency or, conversely, to ease the implementation may be included a posteriori, enabling easy switching between accurate and efficient formulations without rederivation. The capabilities of this framework are demonstrated by deriving a novel, highly accurate lean premixed flame model. This novel flame model is validated for the case of a lean premixed H₂ autoignition flame. Novelty and Significance This study proposes a novel framework for developing jump conditions for compact elements of thermoacoustic network models. Unlike the established approach of deriving case-specific jump conditions by hand, our Jacobian-based method generates jump conditions valid for a wide range of application cases with a modularity that eases implementation and the possibility of straightforward a posteriori customization for specific application cases. For the first time, jump conditions for acoustic, entropic and compositional perturbations across a lean premixed flame that allow for arbitrary Mach numbers, realistic gas properties as well as flame movement are developed, showcasing the capabilities of the proposed framework. The proposed framework adds flexibility to thermoacoustic network models that enable a quick adjustment to vary application-specific requirements concerning accuracy and efficiency.