# Study of Standing-Wave Thermoacoustic Electricity Generators for Low-Power Applications
## 1 Introduction  
Thermoacoustic (TA) engines are energy conversion devices (prime movers, refrigerators and heat pumps) whose operation relies on the interaction between heat and sound near solid surfaces, a phenomenon identified as the \"thermoacoustic effect\" [1]. Since in these devices the phasing of the transformations which build up the underlying thermodynamic cycle is naturally accomplished by an acoustic wave (rather than by pistons, valves and displacers), there are a number of technological benefits. First of all, there is the complete absence of moving mechanical parts, which leads to engineering simplicity, reliability, longevity, and low maintenance costs. Secondly, they are intrinsically low cost, being constituted basically by a small number of standard components made of inexpensive and common materials, namely pressure vessels (acoustic networks/ resonators), solid porous materials (stack/regenerators), heat exchangers (generally of the fined-tube or shell-and-tube type), and electroacoustic transducers. Furthermore, they use environment friendly working fluids, can be employed in a large variety of applications (those involving heating, cooling or power generation), and can be driven by different power sources (gas/biomass combustion, solar energy, etc.) allowing, in particular, the exploitation of waste heat and renewable energy sources, since they are potentially configurable to operate with low temperature differentials [2]. These characteristics make TA technology a discipline of relevant interest for the energy industry, giving it a primary position among emerging renewable energy technologies.  
A great body of research in TA technology is being developed, specifically with respect to TA electricity generators (TAEGs). A TAEG is essentially a TA engine coupled to an electroacoustic transducer (linear alternator, loudspeaker, etc.) to convert a fraction of the useful acoustic power (generated from heat) into electrical output energy. Flexure-bearing supported linear alternators (LAs) characterized by low friction losses are generally applied for acoustic-to-electric transduction in TAEGs since they are capable of achieving transduction efficiencies of up to 90%. Relevant examples of this new class of electricity generators integrating LAs in TA engines are, among others, the demonstrators developed by [PERSON] et al. [3], [PERSON] et al. [4], and [PERSON] et al. [5], all working at thermal-to-electric efficiencies (\(\eta_{he}\)) near 18%. Standard electrodynamic loudspeakers (LSs) operated in reverse mode can be also used in lieu of LAs, but in low-power applications (a few hundred watts). This is due to the fact that an LS, generally designed for high-fidelity applications, is characterized by a weak and fragile cone, a short stroke, low power handling, and a low acoustic-to-electric efficiency (\(\eta_{ae}\)). In any case, when a particular application requires low power levels, low cost for generated kW\({}_{e}\), and not very high transduction efficiencies (~50%) the use of LSs could be justified. Relevant examples of this new class of electricity generators integrating LSs in TA engines are the prototypes developed by [PERSON] et al. [6] and [PERSON] et al. [7] working at thermal-to-electric efficiencies (\(\eta_{he}\)) below 5%.  
This work is specifically concerned with the study/development of low-cost TAEGs of the standing wave-type using standard LSs as LAs. Throughout the work, a theoretical analysis of LAs is firstly outlined. Three different configurations are then considered for coupling the LA to the TA engine which, in order to respect cost and technological simplicity requirements, is conceived to work with air at atmospheric pressure. Finally, the prototypes' behavior is simulated by standard codes based on the linear theory of thermoacoustics and their performance is compared.