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Journal ArticleDOI

Acoustic matching of a traveling-wave thermoacoustic electric generator

05 Jun 2016-Applied Thermal Engineering (Pergamon)-Vol. 102, pp 272-282
TL;DR: In this paper, an effective approach for matching the acoustic impedances of the thermoacoustic engine and the linear alternators for maximizing the output electric power and thermal-to-electric efficiency was presented.
About: This article is published in Applied Thermal Engineering.The article was published on 2016-06-05 and is currently open access. It has received 36 citations till now. The article focuses on the topics: Thermoacoustics & Acoustic impedance.

Summary (4 min read)

1. Introduction

  • Traveling-wave thermoacoustic electric generator is capable of converting thermal energy into electric power with high reliability and efficiency with very simple structures.
  • After further optimizations, the system was able to achieve 473.6 W electric power and 14.5% thermal-to-electric efficiency [17].
  • Therefore, the match of the acoustic impedances between the thermoacoustic engine and the linear alternator is critical to the overall performance.
  • The effects of the acoustic impedance on the performance of the thermoacoustic system and whether the systems were acoustically well matched have not been studied by the above work.

2. Procedure of acoustic impedance match

  • Acoustic impedance denotes the ratio of pressure to volume flow rate in acoustic systems, such as thermoacoustic engines, pulse tube refrigerators, etc. Acoustic impedance Za is defined by, UpUpaaa U p j U p U p ZjZZ sincosImRe 1 1 1 1 1 1 (1) where, 1p and 1U denote the complex pressure amplitude and volume flow rate amplitude, respectively;.
  • Up is the phase difference between the pressure and volume flow rate.
  • When the acoustic impedance is matched in a thermoacoustic electric generator, it means that the thermoacoustic engine and the linear alternators can both work at or near their optimal working conditions simultaneously when they are connected.
  • Secondly, the required acoustic impedances to reach the optimal performances of the engine and the alternators should be matched.
  • In electrics, an effective way of realizing the electric impedance match in a power circuit is to introduce the concepts of input impedance of the electric load and the output impedance of the electric source, and design the load and electric source separately.

3. Experimental Setup

  • Figure 2 illustrates the schematic of the traveling-wave thermoacoustic engine [17].
  • The regenerator (REG) is the key component where thermoacoustic energy conversion happens, and is filled with stainless steel screens with a mesh number of 120.
  • The main ambient heat exchanger (MAHX) is of shell-tube type with working gas oscillating inside the stainless steel tubes with inner diameters of 2 mm and the chilling water flowing through the shell sides.
  • The schematic of the linear alternators, which are supplied by Lihan Thermoacoustic Technologies Co. Ltd, are depicted in Figure 3.
  • The generated electric power is therefore dissipated by the load resistance.

4. Output acoustic impedance of thermoacoustic engine

  • Requirements of acoustic impedances for coupling the engine and the load are different at different output positions.
  • Therefore, the output acoustic impedance characteristics can be simply modulated by changing the location for connecting the load.
  • A numerical model of the traveling-wave thermoacoustic engine is first built based on DeltaEC (Design Environment for Low-amplitude ThermoAcoustic Energy Conversion) [31].
  • The output acoustic power, thermoacoustic efficiency, pressure amplitude, volume flow rate, and frequency at different acoustic impedances can then be calculated by setting different values of the real and imaginary parts of the BRANCH component.
  • In the calculations, the hot and ambient heat exchangers are set at 650 °C and 13 °C, respectively.

4.1 Operating frequency

  • Figure 4 shows the variation of operating frequency of the thermoacoustic engine with the output impedance at the two output locations.
  • It is shown that the output acoustic impedance has weak effects on the operating frequency, especially at relatively high acoustic impedances.
  • In general, the operating frequencies of the engine are around 65.5 Hz.

4.2.1 Location A

  • Variations of the output acoustic power and thermoacoustic efficiency of the thermoacoustic engine with the acoustic impedance at location A are given in Figure 5(a) and Figure 6(a), respectively.
  • It is both beneficial for the power and the efficiency if the imaginary part Im[Za] of the output acoustic impedance approaches zero, which means the acoustic load is a pure acoustic resistance.
  • Increasing the magnitude of Im[Za] results in a decrease of the maximum output acoustic power and the thermoacoustic efficiency, especially the latter one.
  • The required output acoustic impedances of the engine for the maximum output acoustic power and thermoacoustic efficiency are not the same, and a compromise should be made when modulating the acoustic impedance of the load.

4.2.2 Location B

  • Variations of the output acoustic power and thermoacoustic efficiency of thermoacoustic engine with the acoustic impedance at location B are given in Figure 5(b) and Figure 6(b), respectively.
  • Similar to the trends with location A, both the output acoustic power and thermoacoustic efficiency are able to reach the higher maximum values when the imaginary part of the output acoustic impedance approaches zero.
  • When the imaginary output acoustic impedance Im[Za] is zero, the maximum output acoustic power of 837 W and highest thermoacoustic efficiency of 0.31 are achieved at the real output acoustic impedances Re[Za] of 1.8×107 Pa·s/m3 and 9×106 Pa·s/m3, respectively.
  • The ranges to achieve the relatively high acoustic power and efficiency are enlarged, which makes it easier for adjusting the acoustic impedance of the linear alternator to fall into the sweet spot range.
  • When Im[Za] is far away from zero, for example at the scale of 10 7 Pa·s/m3, the performances of the thermoacoustic engine are largely degraded.

4.3 Equivalent displacement

  • During the modulation of the acoustic impedance, the output acoustic power may exceed the maximum value that can be extracted by the linear alternators, and make the linear alternator be overloaded in displacements.
  • The volume flow rate |U1| at the output position is converted into the equivalent displacement |x1| of the linear alternators by using the relationship of |x1|=0.5|U1|/ωA.
  • Recalling the output performances given in Figure 5 and 6, though relatively good performances can still be obtained at these impedances, it is not appropriate to couple the linear alternators with the engine at these acoustic impedance ranges due to the overloaded displacements.

5.1 Effect of operating frequency

  • Figure 8 shows the dependences of input acoustic power and output electric power on operating frequency for one linear alternator at fixed pressure amplitude and load resistance.
  • The variations of the acoustic impedances of the linear alternator with the operating frequency are shown in Figure 9.
  • The imaginary part of the acoustic impedance reaches zero at the resonant frequency.
  • This is why the acoustic power extracted and the electric power generated at the resonant frequency reach the maximums.
  • When the operating frequency is far away from the resonant one, the acoustic power that can be extracted by the linear alternator is largely decreased due to the large acoustic reactance.

5.2 Effect of electric capacitance

  • Figure 10 and Figure 11 shows the effects of the connected electric capacitance on the input acoustic impedance and acoustoelectric efficiency of the two linear alternators when the load resistance is at 100 Ω and 180 Ω, respectively.
  • The above analysis shows that the linear alternators cannot be matched to the thermoacoustic engine at either location A or location B when the electric capacitance is either larger than 100 μF or smaller than 1 μF.
  • It denotes that the system is acoustically matched and the optimal performance can be obtained at the location B.

5.3 Effect of load resistance

  • Figure 12 and Figure 13 show the effects of the load resistance on the input acoustic impedance and acoustoelectric efficiency of the linear alternators when the electric capacitance is 9.6 μF, which is consistent with that used in the following experiments.
  • As shown in Figure 12, when no electric capacitance is connected in the circuit, both the real and imaginary parts of the acoustic impedance have very limited variation ranges when adjusting the load resistance.
  • It indicates that the load resistance has great effects on the real and imaginary parts of the input acoustic impedance of the linear alternator, which makes it possible to modulate the acoustic impedance in a large enough range to match with the thermoacoustic engine.
  • As shown in Figure 13, the acoustoelectric efficiency of the linear alternators first increases and then has a slightly decrease when increasing the load resistance.
  • The efficiency with the electric capacitance is higher than that without an electric capacitance at any load resistance, showing the importance of the electric capacitance.

6.1 Matching of operating frequency

  • The operating frequency is adjusted by using two different working gas, i.e. helium and nitrogen gases in the experiments.
  • When nitrogen is used as working fluid, the operating frequency of the whole system is about 23 Hz, which is much lower than the mechanical resonant frequency of the linear alternator.
  • It shows that both the electric power and the efficiency of the system with helium as the working fluid are much higher than those with nitrogen.
  • The optimal output acoustic power of the engine with nitrogen is about 260 W.
  • The results show that the match of the operating frequency is critical to the impedance match of the thermoacoustic electric generator.

6.2 Coupled at location A

  • Based on the above analysis about the match of the operating frequency, helium is used as the working fluid in the following experiments.
  • Figure 15 and Figure 16 shows the frequency, pressure amplitude, displacement, and electric current of the thermoacoustic electric generator when the engine and the alternator are coupled at location A.
  • All the four calculated parameters have good agreements with the experimental ones, showing the good accuracy of the numerical model.
  • The maximum electric power reaches 506.4 W in the experiments.
  • Tests are not conducted below 60 Ω for the safety concerns.

6.3 Coupled at location B

  • According to the output acoustic impedance of the thermoacoustic engine and the input acoustic impedance of the linear alternators, the engine and the alternators can be better matched at location B by adjusting the electric capacitance and the load resistance to be 9.6 μF and 100 Ω, respectively.
  • Therefore, the displacement increases when increasing the load resistance due to the reduced real acoustic impedance.
  • Figure 20 shows the relationship of output electric power of the coupled system with the real part of the acoustic impedance of the linear alternators.
  • When the heating temperature is fixed at 650 °C, the electric power reaches its maximums of 765.8 W in the simulations and 750.4.
  • The trends of the numerical results are similar to the experimental ones.

7. Conclusions

  • The general procedure for the impedance match is proposed systematically.
  • Two different coupling positions, including location A at the feedback loop and location B at the resonator, are investigated to modulate the output acoustic impedances of the engine.
  • This work was supported by National Natural Science Foundation of China under contract No. 51476136 and China Postdoctoral Science Foundation under contract No. 2013M541772.

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TL;DR: A review of the four main methods to convert the (thermo)acoustic power into electricity is provided in this article, focusing on possible configurations, operating characteristics, output performance, and analytical and numerical methods to study the devices.
Abstract: Thermoacoustic engines convert heat energy into high amplitude acoustic waves and subsequently into electric power. This article provides a review of the four main methods to convert the (thermo)acoustic power into electricity. First, loudspeakers and linear alternators are discussed in a section on electromagnetic devices. This is followed by sections on piezoelectric transducers, magnetohydrodynamic generators, and bidirectional turbines. Each segment provides a literature review of the given technology for the field of thermoacoustics, focusing on possible configurations, operating characteristics, output performance, and analytical and numerical methods to study the devices. This information is used as an input to discuss the performance and feasibility of each method, and to identify challenges that should be overcome for a more successful implementation in thermoacoustic engines. The work is concluded by a comparison of the four technologies, concentrating on the possible areas of application, the conversion efficiency, maximum electrical power output and more generally the suggested focus for future work in the field.

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Abstract: Latest developments in thermoacoustic devices have demonstrated comparable power output and efficiency, but higher reliability and lower cost when compared to conventional low-grade heat recovery technologies. A good coupling between multiple physical fields plays a pivotal role in realizing these potentials. This article provides a comprehensive review of the multi-physics coupling effects, namely, thermal-acoustic coupling, acoustic-mechanical coupling and mechanical-electric coupling, inside thermoacoustic devices including thermoacoustic engines, thermoacoustic electric generators, thermoacoustically-driven refrigerators, etc. The basic principles, operating characteristics, design strategies and future prospects are discussed individually for each coupling effect. System-level design techniques and synthetic optimization methodologies in consideration of the multi-physics coupling effects are presented. This review work gives insights into the underlying mechanisms of various coupling effects in thermoacoustic devices and provides guidelines for improvements of modern thermoacoustic technologies for low-grade thermal energy recovery, refrigeration and electric power generation purposes.

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Cites background from "Acoustic matching of a traveling-wa..."

  • ...49 Many efforts were recently devoted into employing the engine for power generation by using linear alternators 50 [19-25]....

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  • ...It indicates that the middle coupling position is a low acoustic impedance region, which also requires 190 a low load acoustic impedance for better output performances [19]....

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  • ...Previous work on thermoacoustic-linear alternator coupled systems 72 showed that the acoustic matching between them is critical for the overall performance [19]....

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Journal ArticleDOI
TL;DR: In this paper, a heat-driven multi-stage thermo-acoustic cooler is proposed to satisfy cooling requirements in the applications of natural gas liquefaction and high-temperature superconductivity.

23 citations

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Proceedings Article
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TL;DR: In this paper, an approximate analysis of energy flow and acoustical measurements of a thermoacoustic prime mover with arbitrary cross-sectional geometry is given. But this analysis is restricted to the case of TAEs with circular or parallel slit pore geometry.
Abstract: Thermoacoustic engines (TAEs) can be used to pump heat using a sound wave or pump a sound wave using a temperature gradient. The basic arrangement is a gas-filled acoustic resonator with appropriately positioned thermoacoustic elements. Two types of thermoacoustic elements are used in these engines: (1) heat exchangers used to communicate heat between the gas and external heat reservoirs; and (2) the TAE, also known as a stack. The TAEs are sections of porous media that support the temperature gradient, transport heat on the acoustic wave between the exchangers, and produce or absorb acoustic power. Previous results have been developed for TAEs with circular or parallel slit pore geometries. The theory is extended for gas-filled TAEs to include pores of arbitrary cross-sectional geometry. An approximate analysis of energy flow and acoustical measurements of a thermoacoustic prime mover are given. >

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"Acoustic matching of a traveling-wa..." refers background in this paper

  • ...596 [22] G.W. Swift, Thermoacoustic engines, The Journal of the Acoustical Society of America, 84 (1988) 597 1145-1180....

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  • ...69 Swift [22] pointed out that the best position for placing an acoustoelectric transducer in a 70 standing-wave resonator depends on the acoustic impedance of the transducer itself....

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TL;DR: In this paper, a traveling-wave thermo-acoustic electric generator was designed for use with an electrodynamic linear alternator, which can convert high-temperature heat to acoustic power with high efficiency.
Abstract: Traveling-wave thermoacoustic heat engines have been demonstrated to convert high-temperature heat to acoustic power with high efficiency without using moving parts Electrodynamic linear alternators and compressors have demonstrated high acoustic-to-electric transduction efficiency as well as long maintenance-free lifetimes By optimizing a small-scale traveling-wave thermoacoustic engine for use with an electrodynamic linear alternator, we have created a traveling-wave thermoacoustic electric generator; a power conversion system suitable for demanding applications such as electricity generation aboard spacecraft

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"Acoustic matching of a traveling-wa..." refers background in this paper

  • ...93 [10] pointed out that the moving mass of the linear alternators should be in a resonance state 94 under the combined actions of the forces from the gas spring, the flexure bearing and the 95...

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  • ...[10] in 2004, which achieved 40 an electric power of tens of watts....

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Journal ArticleDOI
TL;DR: The Los Alamos thermoacoustics code, available at www.lanl.gov/thermoACoustics/, has undergone extensive revision this year, and a Python-based graphical user interface wrapped around that core provides improved usability as discussed by the authors.
Abstract: The Los Alamos thermoacoustics code, available at www.lanl.gov/thermoacoustics/, has undergone extensive revision this year. New calculation features have been added to the original Fortran computational core, and a Python‐based graphical user interface wrapped around that core provides improved usability. A plotter routinely displays thermoacoustic wave properties as a function of x or tracks results when a user‐specified input variable, such as frequency or amplitude, is varied. The Windows‐like user interface provides mouse‐based control, scrolling, and simultaneous displays of plots and of several categories of numerical values, in which color indicates important features. Thermoacoustic phenomena can be calculated with superimposed steady flow, and time‐averaged pressure gradients are calculated. In thermoacoustic systems with toroidal topology, this allows modeling of steady flow caused by gas diodes (with or without time‐averaged heat transfer) and Gedeon streaming. Thermoacoustic mixture separation is included, also with superimposed steady flow. The volume integral of the complex gas momentum is available, so vibrations of thermoacoustic systems can be analyzed.

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"Acoustic matching of a traveling-wa..." refers methods in this paper

  • ...197 A numerical model of the traveling-wave thermoacoustic engine is first built based on 198 DeltaEC (Design Environment for Low-amplitude ThermoAcoustic Energy Conversion) [31]....

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Journal ArticleDOI
TL;DR: In this article, the authors proposed a traveling-wave thermoacoustic electricity generator, which employs a looped-tube travelling-wave engine to convert thermal energy into acoustic power, an ultra-compliant alternator within the engine loop to extract and convert the engine acoustic power to electricity, and an acoustic stub matching technique to match the alternator to the engine.

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"Acoustic matching of a traveling-wa..." refers background in this paper

  • ...Several other research groups adopted low-cost loudspeakers as the electric convertors 59 in traveling-wave thermoacoustic electric generators [18-21]....

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Journal ArticleDOI
Tianjiao Bi1, Zhanghua Wu1, Limin Zhang1, Guoyao Yu1, Ercang Luo1, Wei Dai1 
TL;DR: In this paper, a traveling-wave thermoacoustic electric generator is proposed, which consists of a multi-stage traveling wave thermo-acoustic heat engine and linear alternators, which is capable of converting thermal energy to acoustic power with advantage of heat source flexibility, reliability and efficiency.

96 citations


"Acoustic matching of a traveling-wa..." refers background in this paper

  • ...4 resonant thermoacoustic electric generator capable of generating about 5 kW electric power 52 was developed [9]....

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  • ...[9, 13-15] have 46 conducted a series of research work on traveling-wave thermoacoustic electric generators....

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  • ...It 32 is typically composed of a traveling-wave thermoacoustic engine [1-7] or several 33 traveling-wave thermoacoustic conversion units [8, 9] that consist of a hot heat exchanger, a 34 regenerator and a cold heat exchanger, and several linear alternators....

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