Analysis of nonlinear harmonics and transient phenomena in a standing wave thermoacoustic engine

This study experimentally investigates development of nonlinear harmonics in a half-wavelength standing wave thermoacoustic engine, focusing on the influence of relative stack position and resonator length. Variational Mode Decomposition, Fast Fourier Transform, and spectrogram analysis are used to analyze the system. Results show that a drive ratio as low as 2.5 % can excite higher oscillation modes. The highest heat-to-acoustic energy conversion occurs when the stack is positioned at 6 % of resonator length, though at the cost of a significantly higher temperature difference at transient stage. An optimal resonator length (1070 mm) is identified, beyond which increased thermal penetration depth enhances boundary layer merging, leading to the development of a second oscillation mode. It is demonstrated that the engine operation at the transitional stage is linearly related to the onset conditions, allowing the output at transition to be interpreted similarly to onset behaviour. The dominancy of the second mode is notable in the region between the 1/3 and 2/3 of the resonator tube length, where the pressure amplitude is supposed to reach its maximum value. Utilizing the VMD method reveals a skewed peak in the longitudinal distribution of the pressure amplitude along the resonator tube for the second mode of oscillation.