Influence of resonator length on the performance of standing wave thermoacoustic prime mover Wahyu Nur Achmadin, Ikhsan Setiawan, Agung Bambang Setio Utomo, and Makoto Nohtomi Citation: AIP Conference Proceedings 1755, 110006 (2016); View online: https://doi.org/10.1063/1.4958540 View Table of Contents: http://aip.scitation.org/toc/apc/1755/1 Published by the American Institute of Physics Articles you may be interested in Thermoacoustic engines The Journal of the Acoustical Society of America 84, 1145 (1998); 10.1121/1.396617 Analysis and performance of a large thermoacoustic engine The Journal of the Acoustical Society of America 92, 1551 (1998); 10.1121/1.403896 Design, construction and evaluation of a standing wave thermoacoustic prime mover AIP Conference Proceedings 1717, 050007 (2016); 10.1063/1.4943482 Influence of Resonator Length on the Performance of Standing Wave Thermoacoustic Prime Mover Wahyu Nur Achmadin1, a), Ikhsan Setiawan1, Agung Bambang Setio Utomo1, and Makoto Nohtomi2 1 Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara BLS 21, Yogyakarta, 55281 Indonesia 2 Graduate School of Environment and Energy Engineering, Waseda University, Nishi-tomita 1101, Honjo City, Saitama pref., Japan. a) wahyu.achmadin@gmail.com Abstract. A research on the influence of resonator length on the performance of a standing wave thermoacoustic prime mover has been conducted. The thermoacoustic prime mover consists of an electric heater, a resonator tube filled with atmospheric air, and a stack. The stack was made of stainless steel wire mesh screens with mesh number of #14. The stack had a length of 5 cm and placed 13 cm from resonator hot-end. The resonator tube was made of stainless steel pipe with 6.8 cm inner diameter. The electric heater which has a maximum power capability of 299 W was attached to the hot side of the stack. We varied the resonator length from 105 cm until 205 cm. It was found that the thermoacoustic prime mover with a resonator length of 155 cm generated the sound with the smallest onset temperature difference and shortest time to reach the onset condition, those are 252 qC and 401 s, respectively. Also, the prime mover with a resonator length of 105 cm produced the highest frequency that is 174 Hz. On the other hand, by using resonator length of 180 cm, the prime mover generated the highest pressure amplitude of 0.0041 MPa, and the thermoacoustic device delivered the highest acoustic power of 2.8 W and efficiency of 0.9%. INTRODUCTION Thermoacoustics is a study concerned mainly with the interaction between heat and acoustic wave, namely with the conversion of thermal energy to acoustic energy and vice versa. Based on the heat flowing direction, the thermoacoustic device is divided into two categories; they are a thermoacoustic prime mover and thermoacoustic refrigerator. The thermoacoustic prime mover is transferring heat from a high-temperature reservoir to a lowtemperature reservoir to produce acoustic work, and conversely, thermoacoustic refrigerator is removing heat from a low-temperature reservoir to a high-temperature reservoir by absorbing acoustic work from an external agent. The simplicity and potentially offers low cost, and high reliability makes the thermoacoustic devices attractive for researchers. The thermoacoustic prime mover is environmentally friendly as they can utilize waste heat as heat sources for their operation and do not emit any exhaust gases[1-3]. Hariharan et al. have conducted research about the influences of stack geometry and resonator length on the performance of their thermoacoustic engine [4]. Other examples of the recent publications on standing-wave thermoacoustic prime mover were written by Hao et al. [5] and Setiawan et al. [6]. The former studied experimentally the influence of difference working gases on the performance of thermoacoustic prime mover while the latter made a numerical study on the effect various compositions of helium-based binary mixture working gases. This paper describes the influence of resonator length on the performance of thermoacoustic prime mover. In the next sections, it is presented the theory, experimental method, result, and discussion, and finally, some conclusions are provided. Advances of Science and Technology for Society AIP Conf. Proc. 1755, 110006-1–110006-7; doi: 10.1063/1.4958540 Published by AIP Publishing. 978-0-7354-1413-6/$30.00 110006-1 THEORY The hydraulic radius, porosity, and ZW parameter of the stack made of wire mesh screens are calculated as [7] rh d wire I 1 I 4(1 I ) Sndwire 4 §r Z W ¨¨ h ©Gk Where · ¸¸ ¹ (1) (2) 2 (3) rh is the hydraulic radius of the stacking channel, d wire is the diameter of the wire, I is porosity, n is the mesh number (number of meshes per inch), Gk the thermal penetration depth is roughly the distance that heat can diffuse through the medium during the time interval related to the period of the acoustic oscillation. The thermal penetration depth is given by: Gk k SfU m c p (4) Where k is the thermal conductivity, Um is the mean density, cp is the isobaric specific heat of the gas, f is the sound frequency. In this research, these equations have been calculated and shown in Table.1. EXPERIMENTAL METHOD Materials Materials that used in this research is a stack, which is made of a tight pile of stainless steel wire mesh screens with mesh number of #14 and arranged in stack length of 5 cm. Gasket carbon material with an outer diameter of 17.5 cm and width of 1.55 mm as to indicate the leakage. The resonator is made of stainless steel pipes with an inner diameter of 6.8 cm, whereas the total length is varied from 105 cm to 205 cm. Equipment The equipment used in this research is an electric heater system with maximum heat power of 299 W. Type-K thermocouples sensor produced by Sakaguchi E.H Voc Corp and dynamic pressure transducers of the PGM-10KH model from Kyowa Electronic Instruments Co., LTD, which connected the WE7000 Ethernet software with data logger types of Yokogawa models 707821. Then, the heat exchanger system consists of the cold heat exchanger and hot heat exchanger. Data retrieval The stack placed 13 cm from resonators closed-ends, between the cold heat exchanger and hot heat exchanger. The temperatures sensor and dynamic pressures were connected to the data logger and calibration constants on the pressure transducer are inserted. The operation of the thermoacoustic prime mover is done by providing the electrical input power to the heater. The data were recorded every second at temperature sensor and every 10 oC at dynamic pressure sensor. If the temperature difference has been constant, so we turn off the electric heater. This measurement repeated with variation of length tube resonator which was 105 cm, 130 cm, 255 cm, 180 cm, and 205 cm. 110006-2 Data processing The analysis of output data was done by interpreting the graph of the time history of temperature measurement and dynamic pressure measurement. The output data from dynamic pressure analyzed by fast Fourier transform to know the dominant frequency and amplitude for every measurement. This measurement is used to calculate the acoustic power and efficiency. The maximum results will be seen when it occurred at a difference temperature indicator of 350 oC in this research. The present experimental apparatus is schematically illustrated in Fig. 1. FIGURE 1. Schematic diagram of the standing wave TAPM. TH, TC, and TRHE are thermocouples. P1-P3 are dynamic pressures and TC, TH; TRHE is a thermocouple. The length unit is centimeter. About the measurement of acoustic power, Fusco et al. [8] and Swift [7] present a reliable method known as the two-microphone method, in which two sensors P1 and P3 of are placed with a known distance between them as shown in the following equation: E § ° G v º ¨ Im ª¬ P1 A P1B 1B ¼ ®1 °¯ 4rh A ¨ u¨ §Z · 2 Um a sin ¨ ¸ ¨ G v P 2 P 2 1B © 'x ¹ ¨ 8r 1 A h © Where A is the cross-sectional area, frequency, Gv Um is the mean gas density, a is the speed of sound, is the viscous penetration depth, Prandtl number, ª J 1 § J 1 · Z'x § Z'x · º ½° · ¨1 «1 ¸ a cot ¨ a ¸ » ¾ ¸ V © V ¹ © ¹ ¼ °¿ ¸ ¬ ¸ ª J 1 § J 1 · Z'x § Z'x · º ¸ ¨1 csc ¨ ¸» «1 ¸ V © V ¹ a © a ¹ ¼ ¸¹ ¬ Z (5) is the angular rh is the hydraulic radius, J is the specific heat ratio, V is the 'x is the distance between the two sensors. Moreover, the efficiency of the engine is defined as: E K u u100% 100% (6) Ein Where E is power output acoustic, Ein is electric power input. RESULT AND DISCUSSION Onset temperature difference is a minimum temperature difference between cold side and hot side of the stack that causes existence the sound wave the thermoacoustic prime mover. Determination of onset temperature difference can be done by observing the behavior of temperature like Fig.2. Figure 2 shows time history of temperatures measurement when prime mover heated by 299 W electric input power. We can see that temperature of the hot end of stack Th increases rapidly, likewise slow increases in the 110006-3 temperature of the resonators hot-end Trhe. The onset condition could be reached by increases the Trhe. Interpretation data like Fig. 2 with length resonator of 105 cm, 130 cm, 155 cm, 180 cm, and 205 cm is done too, that so obtain onset difference temperature as shown Fig.3. Based on the results obtained (Fig. 3), the tube resonator length of 155 cm has the lowest onset temperature difference at operation with electric input power 299 W. The onset temperature difference decrease at the tube resonator length of 105 to 155 cm, and then the onset increased with increasing of length tube resonator. This study proves that the ratio hydraulic radius with thermal penetration depth rh G k to the most appropriate onset temperature difference to generated the thermal contact is the tube resonator length of 155 cm. Setiawan had done the numerical calculate the effect of hydraulic radius to the onset of difference temperature which shown the value optimum ratio rh G k 2.1 to every tested gas [6]. While in this research, the tube resonator length of 155 cm had value optimum ratio 2.0, so it could be concluded that value of the ratio in this experiment approached the numerical and experimental value ratio rh G k as shown in Table 1. Figure 4 shows influence resonator length time to reach onset condition. From Fig. 4, the optimum value of time to reach onset condition and onset temperature difference is the resonator tube length of 155 cm, this condition caused by the influence of ratio rh G k to thermoacoustic prime mover. The frequency at the closed resonator tube just influenced by air velocity at the tube resonator v and the tube resonator length. So the longer length of tube resonator the lower value of its frequency and the conversely, as shown in Fig. 5. In all the cases the experimental value is more than that of theoretical resonance frequency due to the variable cross-sectional area of the stack and non-uniform temperature distribution of gas in the system, which leads to lower values of sound velocity than assumed a value in the calculations [4]. FIGURE 2. Time history of temperature measurements for 299 W input electric power. Th and Tc are the temperatures of the hot and cold ends of the stacks. Trhe is the temperature of the resonator’s hot-end, Tr is the temperature in the room, and Tdiff is the temperature difference between both ends of the stack. FIGURE 3. Influence resonator length on the onset temperature difference with electric input power 299 W 110006-4 FIGURE 4. Influence resonator length on time to reach onset condition with electric input power 299 W TABLE 1. Stack parameter in thermoacoustic (mm) rh G k Resonator Length (cm) Frequency (Hz) (x10-4) 105 173 0.497 0.20 1.74 6.19 2.49 130 141 0.497 0.23 1.92 4.68 2.16 155 117 0.497 0.25 2.11 3.96 2.00 180 102 0.497 0.27 2.26 3.40 1.84 205 88 0.497 0.29 2.44 2.94 1.71 The pressure amplitude value decreased at resonator length of 205 cm as shown in Fig. 6. The decreasing possibility happened when thermal contact value with generated frequency less corresponding, so the pressure amplitude value is decreasing. Therefore, the optimum amplitude pressure on the thermoacoustic prime mover engine this research generated by the length of tube resonator 180 cm. The research result similar to the studies has been conducted by Biwa [9]. Biwa has conducted research to know energy conversion performance thermoacoustic with two types of the stack. Biwa used to stack with the value thermal contact ZW is 0.13 and 3.5. It was found that the value of the thermal contact stack ZW is 3.5 with the ratio hydraulic radius rh G k 1.87, It is the best stack because it could generate the large amplitude, the acoustic power, and the efficiency. In the following, stack with optimum amplitude ZW is 3.4, and the ratio is rh G k 1.84 (Table 1). FIGURE 5. Influence resonator length on the sound frequency at temperature difference 350 oC with electric input power 299 W 110006-5 FIGURE 6. Influence resonator length pressure amplitude at temperature difference 350 oC with electric input power 299 W FIGURE 7. Influence resonator length acoustic power at temperature difference 350 oC with electric input power 299 W FIGURE 8. Influence resonator length efficiency at temperature difference 350 oC with electric input power 299 Influence resonator length on the acoustic power and efficiency at temperature difference 350 oC as shown in Fig. 7 and Fig. 8. From Fig. 7 shows the best acoustic power is 2.78 W and from Fig. 8 shows the best efficiency is 0.93%. We can see that resonator length of 180 cm in Fig. 8 was decreased. In this case, the addition resonator length suspected would make the velocity of air gaseous in the stack decreases. The value of energy dissipation expands at work medium with high rate. The small dissipation value indicates that the thermal energy is used to move the thermal from a heat point to a cold point a bit wasted so the movement of heat will optimum. 110006-6 CONCLUSION This research has been carried out by varying the resonator length. The experimental results show that the resonator length affects the performance of the standing wave thermoacoustic prime mover. The best resonator length found in this research is 155 – 180 cm as it gives the lowest onset temperature difference, shortest the time to reach onset condition, and the highest pressure amplitude. We also found that the resonator length variation is altering the acoustic power and efficiency. The best acoustic power and efficiency in this research are 2.8 W and 0.9%, respectively. ACKNOWLEDGMENT A part of this work was supported by Department of Physics, Faculty of Mathematics and Natural Science Universitas Gadjah Mada. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. B. M. Chen, Y. A. Abakr, P. H. Riley, and D. B. Hann, AIP Conf. Proc. 1440, 532-540 (2012). J. A. Adeff and T. J. Hoffler, J. Acoust. Soc. Am. 107 (2000). D. L. Gardner and C. Q. Howard, “Waste-heat-driven thermoacoustic engine and refrigerator” in Proceedings of ACOUSTICS 2009, (Proceedings of ACOUSTICS, Adelaide, Australia, 2009). N. M. Hariharan, P. Sivashanmugam, and S. Kasthurirengan, Applied Acoustics 73, 1052-1058 (2012). X. H. Hao, Y.L. Ju, U. Behera, and S. Kasthurirengan, Cryogenics 51, 559-561 (2011). I. Setiawan, M. Nohtomi, and M. Katsuta, J. Phys.: Conf. Ser. 622 012010 (2015). G. W. Swift, Thermoacoustic: A Uniflying Perspective for Some Engine and Refrigerators, (Los Alamos National Laboratory, Los Alamos, New Mexico, Univetd States, 2001). A. M. Fusco, W. C. Ward, and G. W. Swift, The Journal of the Acoustical Society of America, 91 2229–2235 (1992). T. Biwa, Y. Tashiro, and U. Mizutani, Physical Review E 69, 066304 (2004). 110006-7

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