Energy transfer modelling of active thermoacoustic engines via Lagrangian thermoacoustic dynamics

• Resonant control on thermoacoustic engines to amplify power rating.
• Least-action principle of thermoacoustic dynamics to shape engine chamber.
• Spatiotemporal transfer function into feedback systems.
• Conservation law of thermoacoustic storage to figure out engine cycles.
• Robin boundary condition to identify flow leakage.

This paper develops energy-transfer modelling of active thermoacoustic engines resonantly controlled on boundary for amplification of power rating toward satisfaction of renewable industry. Therein the wave equation of thermoacoustic dynamics in resonators with non-uniform media and boundary actuations is derived and then turned into a least-action principle. With this least-action principle, we obtain the governing equation of longitudinal resonators with spatially variant cross-section areas to investigate how to shape the resonator for boosting piston stroke and power-transmission efficiency. It is followed by spatiotemporal transfer-function modelling that functionally represents the dynamics and interprets the boundary actuations into internal inputs. This helps formulate the overall dynamics into feedback-interconnection between the thermoacoustic dynamics in the resonator and the mechatronic dynamics of the alternative current generator, so that synthesis of feedback systems can be applied to design the entire engine. Transfer-function modelling following least-action principle leads to the conservation law of thermoacoustic storage, which figures out engine cycles, the most fundamental principle in designing active thermoacoustic engines. Based on such feedback realization, digital signal processing is programmed to numerically assess power ratings of active designs.

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