Onset of Oscillations in Traveling Wave Thermo-Acoustic-Piezo-Electric Harvesters Using Circuit Analogy and SPICE Modeling

Abstract

Equations governing different physical fields such as mechanical, acoustical, and electrical are inherently similar. This enables mechanical, thermal, and acoustical networks to be fully described with analogous electric networks. For thermo-acoustic-piezo-electric (TAP) harvesters, such a modeling approach allows the whole system to be characterized in the electrical domain and facilitates the understanding of the underlying physics. In this paper, a traveling wave thermo-acoustic-piezoelectric (TWTAP) energy harvester is considered which converts thermal energy, such as solar or waste heat energy, directly into electrical energy without the need for any moving components. The input thermal energy generates a steep temperature gradient along a porous regenerator. At a critical threshold of the temperature gradient, self-sustained acoustic waves are developed inside an acoustic resonator. The associated pressure fluctuations impinge on a piezo-electric diaphragm, placed at the end of the resonator, to generate electricity. The acoustic pressure oscillations are amplified by a specially designed acoustic feedback loop that introduces appropriate phasing to make the pulsations take the form of traveling waves. The behavior of this TWTAP is modeled using electrical circuit analogy. The developed model combines the descriptions of the acoustic resonator, feedback loop, and the regenerator with the characteristics of the piezo-electric diaphragm. With the help of a simulation program with integrated circuit emphasis (SPICE) code, the developed electric circuit is used to analyze the system’s stability with regard to the input heat and hence predict the necessary temperature ratio required to establish the onset of self-sustained oscillations inside the harvester’s resonator. The predictions are compared with published results obtained using root locus and numerical methods and validated against experiments. This approach provides a very practical approach to the design of TAP energy harvesters both in the time and frequency domain. Such capabilities do not exist presently in the well-known design tool design environment for low-amplitude thermo-acoustic energy conversion (DeltaEC) developed at Los Almos National Laboratory which is limited to steady-state analysis. This is in contrast to the present approach which can be applicable to both steady as well as transient analysis.