Investigation on a Thermoacoustically Driven Pulse Tube Cooler Working at 80 K

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Cryogenics 45 (2005) 380–385 www.elsevier.com/locate/cryogenics

Investigation on a thermoacoustically driven pulse tube cooler working at 80 K

L.M. Qiu *, D.M. Sun, W.L. Yan, P. Chen, Z.H. Gan, X.J. Zhang, G.B. Chen

Institute of Refrigeration and Cryogenic Engineering, Zhejiang University, Hangzhou 310027, China

Received 12 August 2004; received in revised form 25 December 2004; accepted 20 January 2005

Abstract

The pulse tube cooler (PTC) driven by a thermoacoustic engine can completely eliminate mechanical moving parts, and then achieves a simpler and more reliable device. A Stirling thermoacoustic heat engine has been constructed and tested. The heat engine can generate a maximal pressure ratio of 1.19, which makes it possible to drive a PTC and get good performance. Frequency is one of the key operating parameters, not only for the heat engine but also for the PTC. In order to adapt to the relatively low design frequency of the PTC, the operating frequency of the thermoacoustic heat engine was regulated by varying the length of the resonance tube. Driven by the thermoacoustic engine, a single stage double-inlet PTC obtained the lowest refrigeration temperature of 80.9 K with an operating frequency of 45 Hz, which is regarded as a new record for the reported thermoacoustically driven refrigerators. 2005 Elsevier Ltd. All rights reserved.

Keywords: Thermoacoustics (C); Pulse tube cooler (E); Frequency match (D)

1. Introduction Using a coaxial single-stage pulse tube cooler driven by a standing-wave thermoacoustic engine, one of the A thermoacoustically driven refrigeration system em- present authors, Chen obtained a refrigeration tempera- ploys a thermoacoustic engine converting thermal en- ture of 115 K in 2003 [2] and 88.6 K in 2004 [3]. All ergy into acoustic power, which can be in turn used to those above thermoacoustically driven refrigeration sys- drive a pulse tube cooler or other kinds of thermoacou- tems had employed standing-wave thermoacoustic en- stic refrigerator. With a simpler structure, such refriger- gines, in which the inherent irreversibility resulted in ation systems can operate by using environment-friendly low efficiency. It is suggested that a thermoacoustic en- working gases and make use of industrial waste heat as gine with higher efficiency should be employed to further well as solar energy. It is highly promising in many decrease the refrigeration temperature. The Stirling ther- applications, especially in natural gas liquefaction moacoustic engine experiences Stirling cycle in its regen- located in remote areas or coastal areas. erator, which has potentially higher efficiency [4] and Research in thermoacoustic field has been booming makes it possible to get a lower refrigeration tempera- in recent years. Swift and Radebaugh succeeded in con- ture by driving a PTC. For this purpose, Ueda et al. structing an orifice pulse tube cooler driven by a stand- tested a thermoacoustically driven refrigeration system ing-wave thermoacoustic engine and obtained a with a loop and a resonance tube. By simultaneous mea- refrigeration temperature around 91 K in 1990 [1]. surements of pressure p and velocity U, they put the second regenerator at a precise location in the loop and * Corresponding author. Tel./fax: +86 571 879 52793. refrigeration temperature as low as 25 C was obtained E-mail address: [email protected] (L.M. Qiu). without involving any moving parts [5]. Yazaki et al.

L.M. Qiu et al. / Cryogenics 45 (2005) 380–385 381

directly embedded a second regenerator into the loop of the temperature of the outside wall of the heater, Tout. a traveling-wave thermoacoustic engine [6]. The high- To reflect the real temperature of thermal energy re- light of their setup is that traveling-wave thermoacoustic source and to give reference to practical applications, engine and cooler are directly coupled in a simple loop. temperature referred in this paper is Tin. Heating With helium–argon mixture as working gas, refrigera- power is adjusted by changing the charging voltage tion temperature reached 246 K with such simple to the heaters and is displayed by a digital dynamo- configuration. meter. In experiment, the working gas is helium of In 1999, Backhaus and Swift upgraded a thermal effi- high purity. ciency up to 30% by introducing a resonance tube into a Pressure data are acquired and analyzed by a real- looped tube [7]. But report on a PTC driven by such an time system. As shown in Fig. 1, pressure sensors la- engine has not been found so far. We designed and fab- beled as P1, P2 and P3 are located along the resonance ricated such a Stirling thermoacoustic engine to drive a tubes, in order to observe the pressure oscillation and single stage double inlet PTC [8]. Experimental results the acoustic power entering the resonance tubes. P4, show that the engine has the merits of large pressure P5, P6 and P7 are located at the three-way tube, iner- amplitude and good mono-frequency characteristic with tance tube, jet pump and main cooling heat exchanger, helium as working gas. As the design frequency of the respectively, in order to observe the distribution of PTC is about 15 Hz, we regulate the operating frequency acoustic field in the torus. Pressure data acquisition sys- of the thermoacoustic heat engine by varying the length tem comprises of pressure sensors, a data acquisition of resonance straight tube. Based on better frequency clip, a PII computer and a self-developed program match between the engine and the single stage double- based on Labview 6.1 by National Instruments (NI) inlet PTC, a minimum refrigeration temperature of Inc. The pressure sensors are of linear silicon piezo- 80.9 K is then obtained with working frequency of electric type (KPY 46R) and supplied by Infineon Tech- 45 Hz. nologies, Germany. The data acquisition clip is NI PC-1200, 12 bits in precision and 100 ks/s in sampling frequency. 2. Experimental apparatus A single stage double-inlet pulse tube cooler is adopted in this experiment. Table 1 gives the structure In this paper, the thermoacoustically driven PTC sys- parameters and material of its regenerator. The design tem consists of a traveling-wave thermoacoustic engine, frequency of the PTC is about 15 Hz. Driven by a a single-stage double-inlet PTC, vacuum system, as mechanical oil-free compressor, the PTC reached shown in Fig. 1, and measurement system. The structure 60 K with pressure ratio of 1.35. In addition, the joint of each part of the thermoacoustic heat engine was pre- tube between the engine and the cooler has the length viously introduced in Ref. [8]. and inner diameter of 0.6 m and 0.004 m, respectively. Two calibrated NiCr–NiSi thermocouples (with The joint tube is put in a water coat to cool the gas ±5 K accuracy) are arranged in the heater and their entering the PTC. A calibrated Rh–Fe resistance ther- locations are shown in Fig. 1. Deep in the heater, mometer (with 0.1 K accuracy) is applied to measure one shows the temperature of the cartridge heaters, the refrigeration temperature at the cold end of the Tin; while the other located on the outside wall shows PTC.

to 2 7 A P6 P7 8 1 A 2 3 to 4 PTC

to vacuum pump 4 Tout Tin

5 P5 A-A

P4 P3 P2 P1

Fig. 1. Schematic of the thermoacoustically driven pulse tube cooler system. 1: Main cooling heat-exchanger, 2: regenerator, 3: heater, 4: thermal buﬀer tube (TBT), 5: secondary cooling heat-exchanger, 6: feedback tubes, 7: compliance, 8: jet pump, 9: resonance tubes. 中国科技论文在线 http://www.paper.edu.cn

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Table 1 Structure parameters of the pulse tube cooler and regenerative material Pulse tube (mm) Regenerator (mm) Regenerative material Volume of reservoir (cm3) B10.1 · 0.35 · 119 B14.5 · 0.35 · 116 250 Mesh stainless-steel screen 400

3. Experimental results 0.05

3.1. Performance of thermoacoustic engine Working Gas: He 0.04 Heating Power: 2050 W Working Pressure: 0.92 MPa We ﬁrst carried out non-load experiments on the P1 P2 thermoacoustic engine with 4 m long resonance tubes. 0.03 P3 P5 Fig. 2 shows the relationship between pressure ampli-

tude and heating power at different locations as shown 0.02 in Fig. 1. In experiment, the maximal heating tempera- Relative level ture and working pressure are 600 C and 2.08 MPa. Pressure amplitude is the direct driving force to the 0.01 PTC. It is apparent that the amplitude of pressure oscillation increases from P2 to P7 gradually and reaches the 0.00 maximum above the main cooler, which indicates a 50 60 70 80 90 100 110 120 130 140 150 160 standing-wave distribution along the engine. The largest Frequency (Hz) pressure amplitude occurs at P7 is 0.18 MPa (the corre- Fig. 3. Frequency analysis of pressure wave. sponding pressure ratio is 1.19), and the corresponding heating power and temperature (Tin) are 4360 W and 600 C, respectively. thermoacoustic refrigerators to achieve stable refrigera- Fig. 3 shows frequency spectra of pressure waves tion temperature. when the pressure oscillation gets the most intensive, with the filling pressure of 0.9 MPa. The heating power 3.2. Influence of total resonance tube length is 2050 W and the heating temperature is 600 C. The fundamental frequency is about 72 Hz and harmonic According to boundary conditions of acoustic field components are around 145 Hz. However, the harmonic and analysis of distribution of pressure amplitude along components at the locations of P5, P3 and P2 is consid- the engine, pressure amplitude distributes along the erably weak compared with the fundamental one and direction as shown in Fig. 4 as a 1/4 wavelength standing this contrast becomes more obvious at higher filling wave. The start point of the 1/4 wavelength standing- pressures. The stable mono-frequency characteristic wave distribution is at the upper surface of the main of the engine provides a good basis for driving cooler (P7, assumed as pressure antinode). Pressure ratio at P1 is very small and the phase difference between P1 and any other measurement point is about 180.So we assume that pressure node is between P1 and P2 and is 100 mm away from the entrance of the tapered 0.200 tube (see Fig. 1). The initial length of the resonance P2 straight tube is about 2 m, when the 1/4 wavelength is 0.175 P3 P5 3.6 m (including the part of the torus shown in Fig. 4 0.150 P6 from P7). To regulate the working frequency of the en- P7 gine, we lengthen the resonance tube. As long as there is 0.125 not frequency skip, pressure amplitude distribution along the heat engine is still 1/4 wavelength standing 0.100 wave and its frequency (f) can be calculated from Eq.

0.075 (1), even though the magnitude of pressure amplitude

Pressure amplitude (MPa) might change. 0.050 a a f ¼ ¼ ð1Þ k 4L 0.025 1000 1500 2000 2500 3000 3500 4000 4500 From Eq. (1), it is found that the frequency is inver- Heating power (W) sely proportional to the 1/4 standing wavelength (L), Fig. 2. Relationship between pressure amplitude and heating power. since the sound speed (a) nearly keeps constant. To 中国科技论文在线 http://www.paper.edu.cn

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P7 x=0

x torus

P5 resonance straight tube tapered tube

P2 P1

Fig. 4. Distribution of standing-wave acoustic ﬁeld along the heat engine.

predict the match state between the PTC and the ther- 85 moacoustic engine, we calculate the working frequency Working Gas: He 80 of the heat engine with different resonance tube lengths. Onset Working Pressure: 2.1 MPa The calculated and experimental results are shown in 75 Fig. 5. The tendency of predicted frequencies is in agreement with experimental results. However, the difference 70 4 m between predicted frequencies and experimental values 65 increases with an increase in the total resonance tube 60 length (including the length of the resonance straight 6 m tube and tapered tube). Up to now, it is difficult to quan- Frequency (Hz) 55 titatively explain the enlarged difference between the two 50 curves, although good agreement for a standing-wave 7 m thermoacousic engine has been obtained by using a sim- 45

ilar method [9]. It is mostly due to the function of the 40 tapered damping tube. The flexible acoustic boundary 0 2000 4000 6000 8000 10000 12000 14000 leads to the error in our calculating the length of the Time (s) 1/4 wavelength, and causes the enlarged difference. Fig. 6. Frequency variation with time. Fig. 6 shows the variation of operating frequency with different resonance tube lengths during the whole operation. Each curve represents one particular length limit is set at 673 C. At the beginning, the operating fre- of resonance tube with the heating power increasing quency increases by a little because of the increase of gradually. In all experiments the heating temperature mean gas temperature, which causes the increase of sound speed. Once the engine reaches its steady state, the operating frequency nearly maintains the same value. Such a stable frequency characteristic will benefit 80 for driving a PTC to obtain a stable refrigeration 75 Working Pressure: 2.25 MPa temperature. Working Gas: He 70 experiments 3.3. Cool-down of the PTC 65 prediction

60 Fig. 7 shows the eﬀect of resonance tube length on 55 pressure amplitude PA at the pressure antinode of the 50 system. Pressure amplitude reﬂects the intensity of acoustic oscillation in a thermoacoustic system. The Frequency (Hz) 45 acoustic energy stored in the system can be written as 40 [10]: 35 1 P 2 30 E ¼ A pR2L ð2Þ st 4 q a2 25 m 467895 Here, a, qm,andR denote sound speed, mean gas Total length of resonanance tubes (m) density and resonator radius, respectively. It is shown Fig. 5. Frequency dependence on the total length of resonance tubes. in Eqs. (1) and (2) that increasing the length of the 中国科技论文在线 http://www.paper.edu.cn

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with operating frequency of 45 Hz. As shown in 0.18 Fig. 5, with the length of the resonance tubes increasing, operating frequency decreases, which is helpful for the

0.17 PTC to obtain better cooling performance. However, the pressure amplitude decreases simultaneously, which weakens the driving force to the PTC (see Fig. 7). The 0.16 (MPa)

A compromise between operating frequency and pressure P amplitude inﬂuences the performance of the PTC. Fig. 0.15 9 shows a typical cool-down process with the resonance tube of 7 m. With heating power and working pressure

0.14 of 2350 W and 2.73 MPa, respectively, the refrigeration temperature reached 83 K after about 3 h. By further valve setting optimization, the lowest refrigeration tem- 0.13 4685 7 perature obtained is 80.9 K, which is the new record of Total length of resonance tubes (m) PTC driven by a thermoacoustic engine. Based on the literatures on thermoacoustically driven Fig. 7. Effect of resonance tube length on pressure amplitude and thermoacoustic efficiency. refrigeration systems, a comparison among three thermoacoustically driven PTCs is made in Table 2. An orifice single stage PTC driven by the first standing-wave resonance tube influences the performance of thermoa- thermoacoustic engine obtains a refrigeration tempera- coustic engine in two aspects. One is to decrease the ture of 91 K with operating frequency and pressure operating frequency of the thermoacoustic engine. The amplitude of 28 Hz and 0.125 MPa, respectively [1]. other is to increase the volume of acoustic field. If the Although the traveling wave thermoacoustically driven acoustic energy keeps unchanged and only the length PTC system in this paper has lower working pressure of the resonance tubes changes, there exists a compro- and heating temperature, its pressure amplitude and mise between working frequency and pressure ampli- pressure ratio are still higher because of the high effi- tude. In fact, it is difficult to keep the stored energy ciency of the engine. Therefore, the traveling wave ther- unchanged by only changing the resonance tube length moacoustically driven PTC system obtains lower in experiments, because when we lengthen the resonance refrigeration temperature of 80.9 K. The same PTC tube the heating power (Q) absorbed by the engine de- has been also driven by a standing-wave thermoacoustic creases with the same heating temperature limit engine with the resonance tube of 4 m [2]. The minimum (673 C). As a result, pressure amplitude PA decreases temperature of the PTC is 124 K, while it is 110 K for with the increase of resonance tube length, as is shown the present engine under almost the same operating con- in Fig. 7. ditions (see Fig. 8). Recently, a coaxial single stage PTC Fig. 8 shows the refrigeration temperature depen- driven by the second standing-wave thermoacoustic dence on resonance tube lengths. A minimum refrigera- engine obtains a minimum refrigeration temperature tion temperature occurs when the total length is 7 m of 88.6 K by further optimization of the engine [3].

320 300 On set 110 280 Working Pressure: 2.73 MPa 260 Heating Power: 2350 W 105 Working Gas: He 240 Resonance Tube Length: 7 m 100 220 200 95 180 160 90 140 120 85 Refrigeration temperature (K) Refrigeration temperature (K) 100 80.9 K

80 80 60 3894 5 6 7 0 50 100 150 200 250 300 350 Total length of resonance tubes (m) Time (min)

Fig. 8. Eﬀect of resonance tube length on refrigeration temperature. Fig. 9. Cool-down curve with a 7 m long resonance tube. 中国科技论文在线 http://www.paper.edu.cn

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Table 2 Comparison of two standing wave and a traveling wave thermoacoustically driven PTCs Type of thermoacoustic engine Standing-wave engine [1] Standing-wave engine [3] Stirling engine Working gas Helium Helium Helium Filing pressure, MPa – 2.1 2.61 Heating power, W 3000 2200 2350 Heating temperature, K 950 770* 933 Mean working pressure, MPa 3.136 2.641 2.727 Pressure amplitude, MPa 0.125 0.159 0.160 Pressure ratio 1.0918 1.128 1.125 Frequency, Hz 28 44.7 45.8 Refrigeration temperature of PTC, K 91.0 88.6 80.9 * Heating temperature here is Tout, which is the temperature of the outer wall of the heater.

4. Conclusion References

The frequency matching between a thermoacoustic [1] Radebaugh R, et al. Development of a thermoacoustically driven engine and a PTC is of great importance to obtain better orifice pulse tube refrigerator. In: Proceedings of 4th Interagency Meeting on Cryocoolers, Plymouth, MA, David Taylor Research cooling performance. It is simple and efficient to adjust Center, 1990, Navy Report DTRC91/003. p. 205. the operating frequency by varying the length of the res- [2] Tang K, Chen GB, Kong B, et al. A 115 K thermoacoustically onance straight tube. A single stage double-inlet PTC driven pulse tube refrigerator with low onset temperature. driven by a thermoacoustic Stirling engine with a 7 m Cryogenics 2004;44:287–91. long resonance tube has succeeded in reaching the min- [3] Tang K, Chen GB, Jin T, Bao R. Thermoacoustically driven pulse tube refrigeration below 90 K. Accepted by ICEC20. imum refrigeration temperature of 80.9 K at 45 Hz, [4] Ceperley PH. A pistonless Stirling engine—The traveling wave which is a new record for thermoacoustially driven heat engine. J Acoust Soc Am 1979;66(5):1508–13. refrigerators. [5] Ueda Y, Biwa T, et al. Experimental studies of a thermoacoustic Stirling prime mover and its application to a cooler. J Acoust Soc Am 2004;115(3):1134–41. [6] Yazaki T, Biwa T, Tominaga A. A pistonless Stirling cooler. Appl Acknowledgments Phys Lett 2002;80(1):157–9. [7] Backhaus S, Swift GW. A thermoacoustic Stirling heat engine. The research is financially supported by the National Nature 1999;399:335–8. Science Foundation of China under contract No. [8] Sun D, Qiu L, Zhang W, et al. Investigation on a traveling-wave 50006011 and the Foundation of the Author of National thermoacoustic heat engine with high pressure amplitude. Energy Convers Manage 2004;46(2):281–91. Excellent Doctoral Dissertation of PR China under con- [9] Zhou S, Yoichi M. Experimental research of thermoacoustic tract No. 200033. Alexander von Humboldt Foundation prime mover. Cryogenics 1998;38(8):813–22. and DAAD Foundation of Germany donated some [10] Swift GW. Thermoacoustic engines. J Acoust Soc Am advanced measurement equipments. 1988;84(4):1145–80.