Determination of Onset Frequency of Standing-Wave Thermoacoustic-Piezoelectric Energy Harvesters with General Impedance Boundaries

This chapter explores the intricate dynamics of standing-wave thermoacoustic-piezoelectric energy harvesters, focusing on the determination of their onset frequencies. By extending the smoothed Fourier series, the authors develop a model that can uniformly solve the dynamic behavior of these systems with general impedance boundaries, a critical factor in their performance. The chapter begins with a historical overview of thermoacoustic science, highlighting key contributions from Rayleigh, Rott, and Swift, and discusses the evolution of thermoacoustic energy harvesting technologies. It then presents a detailed model description and methodology, including the core thermoacoustic control equation and the impedance matching equation of the piezo-diaphragm. The authors introduce boundary complementary functions to address discontinuities at the boundaries, providing a more accurate representation of the system's behavior. The chapter also includes a thorough analysis of the effects of harvester length, working fluids, stack position, and impedance boundaries on the critical oscillation frequency. Through comparative studies and detailed graphs, the authors demonstrate the accuracy and applicability of their method, offering a significant contribution to the field of energy harvesting and thermoacoustics.