rticle Engineering Thermohysics July 11 Vol.56 No.: 167 173 doi: 1.17/s11434-11-447-x SPECIL TOPICS: Oen-air traeling-wae thermoacoustic generator XIE XiuJuan 1*, GO Gang 1,, ZHOU Gang 1 & LI Qing 1 1 Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese cademy of Sciences, Beijing 119, China; Graduate Uniersity of Chinese cademy of Sciences, Beijing 149, China Receied Noember 19, 1; acceted February 15, 11 Taking the inut and reflected waes into account, the relationshi between the acoustic imedance at the end and the inut of a system were theoretically analyzed. Closed and oen acoustic configurations that influence the ressure, olumetric elocity, imedance and acoustic work were comared in detail. Based on the aboe inestigation, an oen-air traeling-wae thermoacoustic generator was designed and fabricated. It is comosed of a looed tube, a resonator oen at one end, a regenerator, and hot and cold heat exchangers. It is a small scale and simle configuration. The resonant frequency is 74 Hz at 1 bar in air. The maximum acoustic ressures at the oen end and.5 m far away from the oen end are 133.4 db and 11 db from a reference alue of μpa when the heating ower was 1 W, resectiely. coustic ressure is reasonable for ractical alication as a low-frequency acoustic source. In further work, we beliee that the acoustic ressure at the oen end can achiee 15 db, which could be a solution to roblems in existing acoustic generators. These roblems include low acoustic ressure and system comlexity. It can be used as a basic acoustic source for low frequency and long-range noise exeriments, and as a suly for high acoustic ressures necessary for industrial sources. oen-air, traeling-wae, thermoacoustic generator Citation: Xie X J, Gao G, Zhou G, et al. Oen-air traeling-wae thermoacoustic generator. Chinese Sci Bull, 11, 56: 167 173, doi: 1.17/s11434-11- 447-x The thermoacoustic rincile [1] is a thermodynamic effect that occurs between comressible gases (the first medium) and solids (the second medium) in an acoustic field. It results in a time-aeraged heat flow and a time-aeraged work flow along (against) the sound roagation direction at enetration deths that are far from the solid boundaries. The conersion of heat to work is called thermal to acoustic effect, and the oosing rocess is called the acoustic to thermal effect. Based on these two effects, thermoacoustic systems can be classified as thermoacoustic engines and thermoacoustic refrigerators. regenerator in an acoustic field can bring standing-waes [,3], traeling-waes [4 6] and standing traeling waes [7,8] into being. In the latest two decades, engineering alications in thermoacoustic refrigeration and thermoacoustic electricity hae been raidly deeloed. In 199, thermoacoustic engines first re- *Corresonding author (email: xiexiujuan@mail.ic.ac.cn) laced linear comressors to drie ulse tube refrigerators [9]. Researchers of China hae focused on large-scale thermoacoustic engines to drie ulse tube refrigerators and high-frequency thermoacoustic systems since [1 1]. Recently, a new lowest cooling temerature in liquid hydrogen, K, was achieed [13]. In 3, the thermoacoustic engine was alied in an electrical field to drie a linear C generator [14]. Luo s grous [15] inestigated thermoacoustic electricity rototyes and linear generators, which is caable of roducing electric owers in the hundreds of watts. For acoustic configurations, thermoacoustic comonents such as regenerators and heat exchangers can be inserted into a closed resonator to create many tyes of thermoacoustic engines. The closed configuration can be filled with gases at MPa mean ressures. The gas tyes that can be used are flexible, including nitrogen, helium, argon, and a He-r mixture. The highest mean ressure that has been The uthor(s) 11. This article is ublished with oen access at Sringerlink.com csb.scichina.com www.sringer.com/sc
168 Xie X J, et al. Chinese Sci Bull July (11) Vol.56 No. used is 5.5 MPa [14]. Howeer, only thermoacoustic comonents that can withstand these ressures can be used. Thermoacoustic owers generally scale with m a, which is a dimensionless reference. Hence, for a gien ressure ratio 1 / m, a high mean ressure and high acoustic seed of gases yield a high ower er unit olume of the system. Light gases also hae a high thermal conductiity, which leads to higher enetration deths and, consequently, larger regenerator and heat exchanger gas. This allows for easier heat exchanger fabrication, which is adantageous for closed thermoacoustic engine alications [16]. Howeer, the closed configuration is restrictie in the outut of acoustic waes in oen saces. Therefore, some researchers hae gien their attention to deeloing other alications. In 1, Slaton [17] constructed an oen-air standingwae thermoacoustic system. The maximum acoustic ressure radiated from the oen end of their resonator corresonded to 81 db Sound Pressure Leel (SPL) ref μpa (1 μpa 1 6 Pa) for an inut electric ower of 76 W. He concluded that a higher ower ersion of that deice may be used as a continuous source at low frequency. The standing-wae thermoacoustic system is a simle configuration and allows for easy oscillation, because of the relatiely low required onset temerature. Howeer, theoretically, the thermal efficiency of this system is lower than that of a traeling-wae thermoacoustic system because the standing-wae system has an irreersible thermal cycle [16]. Therefore, the erformance of this oen standing-wae system is limited. Comared with an oen standing-wae system, an oen traeling-wae thermoacoustic system has a higher onset temerature and is more difficult to design. Howeer, this system can be used to design as acoustic generator with higher ower outut, because of its Stirling thermal cycle. This can significantly increase the maximum acoustic ressure comared with Slaton s system. Inestigations into oen-air thermoacoustic systems are in their initial hases. In addition, a comarable closed system has not been reorted in the literature. Therefore, we roose an oen-air traeling-wae thermoacoustic generator. In this aer, taking the inut and reflected waes into account, a theoretical model on the acoustic imedance at the end and at the inut of the system were deried by soling the acoustic roagation equation. Comarisons of a closed acoustic configuration with an oen system while accounting for the influence of ressure, olumetric elocity, imedance and acoustic work were analyzed in detail. n oen-air traeling-wae thermoacoustic generator was designed and fabricated. Exerimental measurements of the ressure waeforms, and acoustic ressures at the oen end and at.1 m,.3 m and.5 m from the oen end at different heating owers were erformed. The acoustic ressures with and without a cone were comared. The maximum acoustic ressure at the oen end of the resonator was 133.4 db (ref μpa) for a heating ower of 1 W. 1 Oen-air traeling-wae thermoacoustic generator The acoustic configuration of the traditional traeling-wae thermoacoustic engine is comosed of a looed tube and a closed resonator. Thermoacoustic comonents such as regenerators and heat exchangers are inserted into the looed tube as shown in Figure 1(a). We adoted an oen resonator in our traeling-wae thermoacoustic generator. The acoustic wae roagates in the oen-air sace, which is shown in Figure 1(b). The essential difference between the closed and oen acoustic configurations is the end of resonator. closed thermoacoustic system has a stable boundary condition. Different mean ressures and gas tyes can be used and can be adjusted for erformance otimization according to the needs of the intended alication. n oen thermoacoustic system is oen to the atmoshere, meaning the oerating arameters are limited because the system must oerate at 1 bar in air. Therefore, in this aer, the differences between the closed and oen acoustic configurations are emhasized. Theoretical comarisons of closed and an oen acoustic configuration The thermoacoustics that occur in the regenerator of looed tube can be simlified and treated as an acoustic source to analyze the influence of the closed or an oen acoustic configuration in the system. These configurations are shown are in Figure 1(a) and (b). The continuity of the ressure and the elocity are assured at the surface of the looed tube that is connected to the resonator. This surface, namely the inut of the resonator, is set to be the origin of the x-coordinate. Here, the acoustic imedance is Z a. The length of resonator is l, and the acoustic imedance at the end of resonator is Z al. This simle acoustic configuration is shown in Figure. Figure 1 Schematic diagram of thermoacoustic system. (a) Closed traeling-wae thermoacoustic engine; (b) oen-air traeling-wae thermoacoustic generator.
Xie X J, et al. Chinese Sci Bull July (11) Vol.56 No. 169 Figure Simle model of acoustic configuration of the thermoacoustic system. The work roduced by the thermoacoustic effect in regenerator in the looed tube is transferred to the resonator. The ressure, 1, can be decomosed into the inut wae i and the reflected wae r, because of the endca of the resonator. i and r are exressed as i ai e i(ωt+kx) and r ai e i(ωt kx), resectiely. Here ar e i σ r r π, r is the ai reflected coefficient, σ π is the hase difference at the interface of the inut and reflected waes. Therefore, 1 is defined as ( + σπ) iωt ( ω + φ) ikx ikx i t 1 i + r ai e + r e e 1 e, (1) where ressure amlitude is 1 λ ai 1+ r + r cosk x+ σ 4, and φ is the constant hase. ccording to the definition of the elocity, 1 can be searated to i and r, where and r is gien by i t kx ar i t kx are e ρa i ( ω ) ( ω ) i t kx ai i t kx aie e ρa ( ω + ) ( ω + ). Therefore the elocity 1 + i r 1 i r. ρa ρa () Combining eqs. (1) and (), the secific acoustic imedance along the resonator is found to be ikx ikx 1 aie + are Zs ρa. (3) ikx ikx 1 aie are We can eliminate ai and ar by utting the secific acoustic imedances at x and xl into eq. (3). lso, the secific acoustic imedance at x can be exressed as one at x1. From this we find Z Zsl + iρa tan kl ρ a. ρ a + iz tan kl s sl Therefore, the acoustic imedance at x can be exressed as one at x1: ρa ρ al a Z + i tan kl Za, (5) ρa + izal tan kl where is the cross-sectional area, ρ and a are the density (4) and acoustic seed of the gas, resectiely. ( γ ) f ( ε ) ω 1+ 1 k / 1+ k a 1 f s is comlex wae number. ω and γ are the angular frequency and ratio of isobaric and ( 1+ i) δk isochoric secific heats, resectiely. Here, fk r ( 1+ i) δ and f. r is the radius of the resonator. The r k κ thermal enetration deth, δ k, ωρ c ω and the iscous enetration deth, μ ν δ ωρ ω, indicate how far heat and momentum can diffuse laterally during a time interal on the order of the eriod of the oscillation 1/ kρc diided by π. ε s, and k, κ, μ, ν and c are the ksρscs thermal conductiity, thermal diffusiity, dynamic diffusiity, kinematic iscosity, and isobaric heat caacity er unit mass of gas, resectiely. k s, ρ s and c s are the thermal conductiity, density and heat caacity er unit mass of solid, resectiely. (1) When the end has a closed endca, xl, Z al, eq. (5) simlifies to ρa Za i cot( kl). (6) Eq. (6) shows that the characteristics at the inut the resonator are related to the alue kl. The length of resonator is usually chosen to be in the range l(1/4 1/)λ in the thermoacoustic system. Then, kl l π 1+ ( γ 1 ) fk /( 1+ ε s) λ 1 f ( γ ) f ( ε ) 1+ 1 k / 1+ s ( π/ π), 1 f where λ is the waelength. The acoustic imedance is a function of the dimensions of the resonator, the mean ressure, the resonant frequency and the roerties of the gas. () When the end is oen to air, for the condition of low frequency kr<1, the acoustic imedance at the end of the resonator is similar to the acoustic radiation of a limitless baffle late. That is, Z al R al +ix al, where the real art 4 ρak πr is Ral, and the imaginary art is X al
17 Xie X J, et al. Chinese Sci Bull July (11) Vol.56 No. 8 3 akr. 3 ρ Eq. (5) can now be simlified to Z a ρ a ρa Ral + i Xal + tan kl. ρa X al tan kl + iral tan kl (7) Eqs. (6) and (7) show that the acoustic imedance at the inut of the resonator is correlated with the dimensions of the resonator, the mean ressure, the resonant frequency and the roerties of the gas. Therefore, for gien resonator dimensions and a fixed resonant frequency, the differences between a closed and an oen acoustic configuration can be quantitatiely analyzed based on the linear thermoacoustic model [16]. For a closed acoustic configuration, the resonator has two arts, one is L1 with a length of.53 m and the other is L with a length of 1 m, in which are filled with 1 bar and 5 bar of air, resectiely. For an oen acoustic configuration, a tube with a diameter of.5 m and a length of 1 m relaces L. It has the same olume and length as a room. Then the end of L1 can be aroximated as being oen to the atmoshere. The oerating arameters and roerties of the gas are listed in Table 1 for the closed and oen acoustic configurations. The frequency was maintained at 74 Hz, and the ariational range is about 3 Hz in the simulation. Therefore, the influence of frequency on the system can be ignored. From this, both the closed and oen acoustic configurations were ealuated. The influence of the ressure, olumetric elocity, imedance and acoustic work were considered and are lotted in Figures 3(a), 3(b), 4 and 5. The influences of the closed and oen acoustic configurations on the ressure amlitude, 1, and the olumetric elocity amlitude, U 1, along the length of the system are shown in Figure 3. When the end is closed, the minimum ressure amlitude occurs at x.53 m, not at the end of the resonator. The waeform of 1 is about 3/4 waelength. The ariational trend of U 1 is the oosite of 1 and has it maximum at x.53 m. lso, it reaches zero at the end of resonator. The closed system can be filled with high ressure gas. 1 is significantly enhanced at a mean ressure of 5 bar in air. Howeer, U 1 decreases, which shows that the imedance increases and iscous losses decrease with U 1. When the end is oen, the minimum alue of 1 is equal to zero and is at x.53 m. The waeform of 1 is 1/4 waelength. U 1 in the oen system is similar to that in the closed system. Comared with the closed acoustic configuration, the oen configuration at same mean ressure can achiee a higher 1 and U 1. Howeer, 1 is significantly lower and U 1 much greatly higher when the oen configuration is comared to the closed with 5 bar air. Note that the acoustic ressure at the end of the resonator should be high for alications, but it is at its minimum alue. This contradiction comes into being from two different mechanisms, and it is the key to allow the oen system to significantly imroe the acoustic ressure at the end of resonator. Figure 4 shows the imedance amlitude, Z 1, along the length in the closed and oen acoustic configurations. For the closed acoustic configuration, Z 1 reaches a maximum between 1 9 1 1 at the end of resonator. This is caused by the antinode of 1 and node of U 1. Z 1 initially decreases and then increases, after reaching a minimum at x.53 m. For the oen acoustic configuration, Z 1 has the maximum of 1 6 at the inut and the decreases to zero at the oen end. Table 1 Oerating arameters and gas roerties (ambient temerature 3 K) coustic configuration Gas tye Mean ressure (bar) Frequency (Hz) Thermal enetration deth (μm) Viscous enetration deth (μm) air 1 77.36 34. 55.8 Closed end air 5 76.65 136.7 115 Oen end air 1 74.1 334 84. Figure 3 Pressure amlitude and olumetric elocity amlitude along the length in the closed and oen acoustic configuration. (a) Pressure amlitude; (b) olumetric elocity amlitude.
Xie X J, et al. Chinese Sci Bull July (11) Vol.56 No. 171 Z 1 along the interal between.53 m is nearly equal for both closed and oen systems at a mean ressure of 1 bar air. It is helful to fill the resonator with to a high ressure to imroe Z 1. The acoustic work, Ė, done in the closed and oen acoustic configurations is shown in Figure 5. It was inferred 1 1 u1 ma from the relationshi: E ~ 1 U1 ~, and m a that a higher Ė can be acquired for higher alues of 1 and U 1. The total Ė roduced in the oen system is 5.6 W, and.38 W is transferred into the oen resonator. Howeer, Ė dissiates raidly to zero at the oen end. For the closed acoustic configuration, the total Ė is 14.86 W, and.94 W is transferred at 5 bar. t 1 bar, the total is.85 W, and the amount transferred is 1.4 W. In both of the closed configurations the Ė transorted into resonator dissiates gradually to zero at the closed end. We concluded from the aboe inestigations that the oen system has a higher 1, U 1 and Ė relatie to the closed system at the same ressure. 1 and Ė are lower in the 1 bar oen system comared with those in the 5 bar closed system. It is difficult to design an oen system, because of the raid losses in 1 and Ė at the oen end. Fortunately, acoustic radiation can be used for long-range roagation, which was not included in this model. Therefore, it is otimal for a 1/4 waelength system to use acoustic amlified comonents to imroe the erformance of the system. Based on linear thermoacoustic equations [16] and the aboe analysis, an oen-air traeling-wae thermoacoustic generator was designed and fabricated. 3 Exerimental setu Figure 4 Imedance amlitude along the length in the closed and oen acoustic configurations. Figure 5 coustic work along the length in the closed and oen acoustic configurations. The exerimental setu of the oen-air traeling-wae thermoacoustic generator is shown in Figure 6 and is comosed of three arts: a looed tube, a resonator and a cone. The looed tube is comosed of a comliance tube, inertance tube and some thermoacoustic comonents. These include a hot and cold heat exchangers and a regenerator. Eight iezoelectric ressure sensors for measuring the ressure amlitude are laced along the system, and are indicated as P 1 P 8 in Figure 6. In the looed tube, the ressure dro in heat exchanger, comared with that in the regenerator, was small and negligible. Therefore the ressure, which was measured using sensor P 1 as a reference, was distributed at the inut of cold heat exchanger. Sensor P was laced at the outut of the comliance tube to measure the ressure dro. Pressure sensors P 3 P 8 were used to measure ressure losses in the inertance tube, through regenerator, thermal buffer tube and resonator, resectiely. In addition, measured ressures could be analyzed using the acoustic field distribution and ressure waeform. Sensor P 9 was an acoustimeter with high sensitiity, which was used to acquire the acoustic ressure far away from the outut of the resonator. Thermocoules T 1 T 3 were laced in the middle of heater and at the two ends of regenerator. They were used to simultaneously measure the temerature at the two ends of regenerator and the onset temerature of system. T 1 and T were Ni Cr thermocoules, and T 3 was a Cu Cu thermocoule. The looed tube assured that the hase difference in ressure that generates the olumetric elocity near the regenerator is matched to the traeling-wae hase. The gas arcel initiates the Stirling thermal cycle within the enetration deth of the regenerator. The resonator stabilizes the resonant frequency, increases the acoustic imedance near the regenerator, and transfers the acoustic ower. The cone imroes the SPL at the outut of system. This generator is smaller than 1 m in length and.3 m in height. 4 Results and discussion The ressure amlitudes 1, which were measured using P 1 P 8, are shown in Figure 7. During these measurements, the heating ower was 1 W. In Figure 7, it can be seen that 1 was at its maximum near the cold heat exchanger. long counterclockwise direction in the looed tube, 1 steadily decreased from P to P 5, and in the resonator from P 6 to P 8. The eak-to-eak ressure amlitude (P-P ressure
17 Xie X J, et al. Chinese Sci Bull July (11) Vol.56 No. Figure 6 Exerimental setu of the oen-air traeling-wae thermoacoustic generator. amlitude) at P 1 was 4.6 kpa and the SPL was 161.6 db. e This was calculated by using SPL log1 db, where e was the measured ressure and equal to P-P ressure amlitude here, ref was the referenced ressure with the alue of 1 5 Pa in the air. The uer surface of cold heat exchanger was set at the origin of x-coordinate. Unfolding the looed tube in counterclockwise direction along the comliance tube, the inertance tube was at a negatie osition in x, and in the clockwise direction, the cold heat exchanger, regenerator, thermal buffer tube and resonator were at ositie ositions in x. The ressure amlitude along the length of the system was analyzed and shown in Figure 8 for arious heating owers. The P-P ressure amlitude increased as the heating ower increased. The resonant frequency was 74 Hz, and the acoustic seed was 347 m/s when the ambient air temerature was 3 K. Therefore the waelength of system was λa/f, Figure 7 Pressure amlitudes ersus time measured by ressure sensors P 1 P 8. ref Figure 8 Peak-to-eak ressure amlitude along the length of the system measured by ressure sensors P 1 P 8. which was 4.75 m. The waeform of the P-P ressure amlitude was nearly 1/4 waelength. The effect of the cone on the acoustic ressure exressed as SPL radiated from the oen end of the resonator was inestigated for arious heating owers Q h. The results are shown in Figure 9. Without the cone, the SPL attenuated linearly with distance toward the oen end of the resonator. The attenuation of the SPL could be reduced effectiely using the cone for identical heating owers. In Figure 9, the results are shown with and without the cone at a heating ower of 145 W. The SPL.5 m far away from the oen end of resonator was about 95 db, and increased nearly 15 db when the cone was added. The maximum acoustic ressure at the oen end and.5 m away from the oen end of the resonator were 133.4 db and 11 db (ref μpa) for a heating ower of 1 W, resectiely. The arameters, including onset temerature T onset, the temerature in the heater T heater, the hot temerature T h, the cold temerature T c and the acoustic ressure at the oen end of resonator, are
Xie X J, et al. Chinese Sci Bull July (11) Vol.56 No. 173 listed in Table for heating owers of 145 W and 1 W with and without the cone. Using the cone significantly decreased the onset temerature and the temerature in the heater. The absolute temerature ratio between the two ends of regenerator is defined as τt h /T c. The acoustic ower has a direct ratio with τ. lower temerature in the heater means that more heating ower can be added to the system, which is imortant for achieing a large τ. Therefore, more acoustic ower and a higher SPL can be acquired with the cone. With further inestigations into the configuration and the line tye of the cone, the SPL at the oen end of the resonator could be otimized. 5 Conclusions In this aer, we designed and fabricated an oen-air traeling-wae thermoacoustic generator. This design has the adantages of being small and haing a simle configuration. We comared the closed and oen acoustic configurations in detail. We modeled the effects on the ressure, olumetric elocity, imedance and acoustic work. We concluded that the oen system has a higher 1, U 1 and Ė relatie to the closed system for the same mean ressure (1 bar air). 1 and Ė are lower in the 1 bar oen system than in the 5 bar closed system. In the oen system the modeled waeform had a 1 of a 1/4 waelength system in which 1 and Ė dissiated raidly at the oen end. Based on the aboe analysis, we fabricated a 1 bar oen-air thermoacoustic Figure 9 coustic ressure ersus the distance to the oen end of the resonator. Table Cone Oerating arameters, temerature and acoustic ressure Heating ower Temerature ( C) (W) Onset T 1 T T 3 coustic ressure (db) Without 145 49.5 658.8 371.3 34.8 13. With 145 45 547.3 33.8 6.9 15.1 1 45 647.8 348.1 8. 133.4 generator. It had a maximum acoustic ressure of 161.6 db near sensor P 1 at the cold heat exchanger. The cone at the oen end of the resonator reduces the onset temerature and the temerature in the heater. This increased the absolute temerature ratio and acoustic ressure. The maximum acoustic ressures at the oen end and.5 m from the oen end of the resonator were 133.4 db and 11 db (ref μpa) for a heating ower of 1 W, resectiely. This is suitable for ractical use as a low-frequency acoustic source. In future work, we hoe to achiee an SPL of 15 db. t this leel, the deice could be a ossible solution for some of the roblems of existing acoustic generators, which include low acoustic ressures and system comlexity. We beliee this system can be used as a basic acoustic source for low frequency and long-range noise exeriments, and as a suly for high acoustic ressures for studying industrial sources and ibrations. This work was suorted by the National Natural Science Foundation of China (58681). 1 Swift G W. Thermoacoustic engines. J coust Soc m, 1988, 84: 1145 118 Feldman K T. Reiew of the literature on Sondhauss thermoacoustic henomena. J Sound Vib, 1968, 7: 71 8 3 Wheatley J C, Hofler T, Swift G W, et al. n intrinsically irreersible thermoacoustic heat engine. J coust Soc m, 1983, 74: 153 17 4 Ceerley P H. istonless Stirling engine-the traeling wae heat engine. J coust Soc m, 1979, 66: 158 1513 5 Yazaki T, Maekawa T, Tominaga, et al. Traeling wae thermoacoustic engine in a looed tube. Phys Re Lett, 1998, 81: 318 3131 6 Backhaus S, Swift G W. thermoacoustic Stirling heat engine. Nature, 1999, 399: 335 338 7 Gardner D L, Swift G W. cascade thermoacoustic engine. J coust Soc m, 3, 114: 195 1919 8 Hu Z J, Li Q, Li Q, et a1. high frequency cascade thermoacoustic engine. Cryogenics, 6, 46: 771 777 9 Radebaugh R. reiew of ulse tube refrigeration. d Cryo Eng B, 199, 35: 15 1191 1 Jin T, Chen G B, Shen Y. thermoacoustically drien ulse tube refrigerator caable of working below 1K. Cryogenics, 1, 41: 595 56 11 Sun D M, Marc D, Guenter T, et al. Inestigation on regenerator temerature inhomogeneity in Stirling-tye ulse tube cooler. Chinese Sci Bull, 9, 54: 986 991 1 Zhou G, Li Q, Li Z Y, et al. Influence of resonator diameter on a miniature thermoacoustic Stirling heat engine. Chinese Sci Bull, 8, 53: 145 154 13 Hu J Y, Luo E C, Li S F, et al. Heat-drien thermoacoustic cryocooler oerating at liquid hydrogen temerature with a unique couler. J l Phys, 8, 13: 1496 14 Backhaus S, Tward E, Petach M. Traeling-wae thermoacoustic electric generator. l Phys Lett, 4, 85: 15 17 15 Luo E C, Wu Z H, Dai W, et al. 1W-class traeling-wae thermoacoustic electricity generator. Chinese Sci Bull, 8, 53: 1453 1456 16 Swift G W. Thermoacoustics: Unifying Persectie for Some Engines and Refrigerators. Sewickley, P: coustical Society of merica Publishers, 17 Slaton W V. n oen-air infrasonic thermoacoustic engine. l coust, 1, 71: 36 4 Oen ccess This article is distributed under the terms of the Creatie Commons ttribution License which ermits any use, distribution, and reroduction in any medium, roided the original author(s) and source are credited.