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In the future, aircraft engines may utilize thermoacoustic heat engines which can convert recovered engine heat into acoustic power without the need for any moving parts. This acoustic power can then be transformed into useful mechanical or electrical energy, or be used to meet cooling requirements. Compared to traditional engines, thermoacoustic engines have a simpler design and exhibit stable functionality. A Stirling type thermoacoustic engine demonstrated 49% of Carnot efficiency in 2011 through subsequent design improvements. Recent research has shown that using looped resonators instead of standing wave types can lead to further efficiency gains. de Block et al proposed a configuration using two thermoacoustic stages and looped resonators, which was experimentally tested and published. However, there has been no further research on this type of thermoacoustic engine to explore its potential for higher efficiency or how it can be coupled with acoustic loads. This paper addresses these issues through a series of comprehensive numerical simulations based on established parameters and validated by published data. The simulation results indicate that the engine can achieve approximately 48% of the Carnot efficiency. Therefore, this new engine configuration has the potential to achieve high efficiency, as demonstrated by this research.