Development of parallel thermoacoustic engine: Evaluations of onset temperature ratio and thermal efficiency

Size: px

Start display at page:

Download "Development of parallel thermoacoustic engine: Evaluations of onset temperature ratio and thermal efficiency"

Melanie Johnson
5 years ago
Views:

1 Acoust. Sci. & Tech. 36, 2 (215) PAPER #215 The Acoustical Society of Japan Development of parallel thermoacoustic engine: Evaluations of onset temperature ratio and thermal efficiency Yosuke Nakano 1;, Shin-ichi Sakamoto 2, Aiko Kido 3 and Yoshiaki Watanabe 3 1 Faculty of Science and Engineering, Doshisha University, 1 3 Tataramiyakodani, Kyotanabe, Japan 2 Department of Electronic Systems Engineering, University of Shiga Prefecture, 25, Hassaka-cho, Hikone, Japan 3 Faculty of Life and Medical Sciences, Doshisha University, 1 3 Tataramiyakodani, Kyotanabe, Japan (Received 1 December 213, Accepted for publication 16 September 214) Abstract: For practical applications of a thermoacoustic system using factory exhaust heat or solar heat, it is necessary to decrease the onset temperature ratio. In a previous study, a cascade thermoacoustic system with a number of prime movers connected in series was examined. This system can be driven at a lower onset temperature ratio than a conventional thermoacoustic system with a single prime mover. However, there are some problems with this system: it cannot be driven continuously and its thermal efficiency is low. Therefore, a parallel thermoacoustic engine was proposed. In this study, we compared the onset temperature ratios and thermal efficiencies of three systems: a normal thermoacoustic engine with a single prime mover, a cascade thermoacoustic engine, and a parallel thermoacoustic engine with two prime movers. The results indicated the parallel thermoacoustic engine to be advantageous in terms of the onset temperature ratio and thermal efficiency. Keywords: Parallel thermoacoustic engine, Cascade thermoacoustic engine, Onset temperature ratio, Thermal efficiency PACS number: Ud [doi:1.125/ast ] 1. INTRODUCTION The high quality of life enjoyed by humans since ancient times has been supported by the natural environment. By using natural resources as fuel, we have acquired a high energy production capacity, which has enhanced the quality of life. Although this has allowed us to achieve rapid economic growth, adverse effects on the environment, such as ozone depletion, air pollution, and global warming caused by the mass consumption of fossil fuels has become serious problems at the beginning of the 21st century. New continuously utilizable energy systems that do not discharge detrimental materials to the environment are required to solve these environmental problems. Therefore, we have investigated a new next-generation energy system that exploits thermoacoustic effects, which is the key to solving energy problems in modern society. Thermoacoustic effects are observed when heat energy is converted into sound waves [1 6]. A system that dum331@mail4.doshisha.ac.jp converts heat energy into sound waves is called a thermoacoustic engine. For such an energy conversion device, the prime mover (PM) is composed of stacks of narrow tubes through which the sound waves propagate. In the PM, sound waves are generated when one side of the stack is heated to a high temperature. A thermoacoustic engine using sound waves can be used as a thermoacoustic refrigerator [7] and a thermoacoustic electric generator [8]. This thermoacoustic system presents many advantages. It utilize unused energy such as solar heat or industrial waste heat. The thermoacoustic refrigerator is not harmful to the environment because it requires no hazardous refrigerants. Moreover, it is inexpensive because it has a simple structure with no moving parts. However, it has not been applied because of its high driving temperature (over 3 C) and poor cooling performance. To enable further practical use of such thermoacoustic systems, low-temperature, high-efficiency drives are required. Some reports have described a cascade thermoacoustic system that can be driven at a low onset temperature ratio [9 13]. Biwa and Hasegawa achieved an onset temperature 149

2 Acoust. Sci. & Tech. 36, 2 (215) ratio of 1.19 using a cascade thermoacoustic engine with five regenerators [9]. However, some problems remain. The first problem is that its thermal efficiency is low because of the difficulty in setting up all stacks in positions where the acoustic impedance is high. When the stacks are set up in positions where the acoustic impedance is high, energy dissipation due to viscosity decreases because the volume velocity is minimized. In addition, stacks show high thermal efficiency depending on the phase of a progressive wave [14]. Here, the phase of the progressive wave is defined when the phase difference between the sound pressure and the volume velocity is zero. The second problem is that the high-temperature heat exchanger between the PM heats the low-temperature heat exchanger of the PM, which decreases its output over time. Here, we propose a parallel thermoacoustic engine, which is expected to be driven with high efficiency because two stacks can be set up in the high-impedance part. Furthermore, the system can heat two stacks with a single heat source. Therefore, this new system provides a solution to the above-mentioned problems. In this study, we evaluated the onset temperature ratio and thermal efficiency. 2. SOUND FIELD ANALYSIS METHODS A thermoacoustic engine consists of acoustic tubes, stacks, and heat exchangers. The sound pressure and volume velocity in acoustic tubes can be calculated by the following equations. 2 6C B x P ¼ C U i m 1 i P m f1 þð 1Þ g P ; ð1þ U ð Þ T m ð1 PrÞð1 ÞT m x Equation (1) is discretely integrated and it is rewritten as PðxÞ P ¼ M 1 ðx; x Þ ; ð2þ UðxÞ U ½M 1 ¼ðEþxC n 1 ÞðE þ xc n 2 ÞðE þ xc 1 ÞðE þ xc ÞŠ: Here, P is the sound pressure and U is the volume velocity,, m, P m, T m,, C p, and are the angular frequency, the mean density, the mean pressure, the mean absolute temperature, the ratio of specific heats, the isobaric specific heat, and the Prandtl number of the working gas, respectively. Here, the assumption that the heat capacity of the channel wall is considerably larger than that of the working gas is adopted. and are complex functions that allow us to describe the three-dimensional phenomena in the channel using the two one-dimensional equations. M 1 is the transfer matrix at dt m =dx 6¼, n is the partition number of the space considered, x is defined as ðx x Þ=n, T m is the temperature difference within a distance of x, and E represents the unit matrix. When dt m =dx ¼, Eq. (1) can be solved analytically because the cell in the second row and second column of the transfer matrix C becomes zero. The analytical solution of Eq. (2) can be given as PðxÞ P ¼ M 2 ðx; x Þ ; ð3þ UðxÞ U 2 i 13 m cos kðx x Þ kð1 Þ sin kðx x Þ 6M 2 ðx; x ÞB C7 kð1 Þ A5 ; sin kðx x Þ cos kðx x Þ ip m 13 C7 A5 : where the complex wave number k is given as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k ¼ 1 þð 1Þ ; ð4þ a 1 where a is the adiabatic sound speed in a gas, and M 2 is the transfer matrix when dtm=dx ¼. Firstly, two sound pressures ðpðxþ; P Þ and the phase difference at two points ðx; x Þ in the acoustic tube are measured by two pressure sensors. Secondly, when these values are assigned to Eq. (2), two volume velocities ðuðxþ; U Þ are calculated. Therefore, the sound pressure and volume velocity in each acoustic tube can be calculated when the default values ðp ; U Þ are assigned to Eqs. (2) and (3). The acoustic power intensity and acoustic impedance can be calculated using the sound pressure and volume velocity. 15

3 Y. NAKANO et al.: DEVELOPMENT OF PARALLEL THERMOACOUSTIC ENGINE The acoustic power intensity I is written as I ¼ 1 2 Re½P ~UŠ; ð5þ where ~U is the volume velocity of the complex conjugate. The acoustic impedance Z is written as Z ¼ P U : ð6þ PM-Stack The heat flow is proportional to the entropy flow and is used when discussing the efficiency of a heat engine. The heat flow is written as the following equation under the condition that the enthalpy flow H is constant in a stack [14]. Q ¼ H I ¼ 1 2 Re ~ ð1 þ Þð1 ~ Þ P ~U þ mc p juj 2 dtm Im 2 ð1 2 Þj1 j 2 dx : ð7þ Here, is the thermal conductivity. The heat flow driven by fluid oscillation is divided into Q prog, Q stand, and Q dream. Q prog is the heat flow driven by a progressive wave. This heat flows in the reverse direction of sound propagation. The energy conversion by Q prog has no loss because of the reversible process. Q stand is the heat flow driven by a standing wave. Q dream is the heat flow driven by the dream pipe effect that depends on the temperature gradient. Q stand flows into the antinode from the node of the sound pressure. The energy conversions by Q stand and Q dream have loss owing to the irreversible process. Therefore, the rate of Q prog increases and the thermal efficiency becomes high. Q prog, Q stand, and Q dream are written as Q prog ¼ 1 2 RefP ~Ug Re ð1 Þð ~ Þ ð1 þ Þj1 j 2 ð8þ Q stand ¼ 1 2 RefP ~g Im ð1 Þð ~ Þ ð1 þ Þj1 j 2 ð9þ m C p juj 2 Q dream ¼ 2ð1 2 Þj1 j 2 Imf þ ~ g dt m dx ; ð1þ where represents the particle displacement. The total heat flow Q is equal to the sum of Q prog, Q stand, Q dream, and the heat flow independent of the fluid oscillation Q. The thermal efficiency in a stack is written as shown below using the input acoustic power intensity I in, the output acoustic power intensity I out, the generated acoustic power intensity I in the stack, and the absolute value of the heat flow Q H at the hot end of the stack [15,16]. ¼ I out I in jq H j ¼ I jq H j : ð11þ Fig. 1 Schematic illustration of a normal thermoacoustic engine. The thermal efficiency of a number of stacks is calculated by dividing the sum of the generated acoustic power intensities by the sum of the heat flows. The theoretical Carnot thermal efficiency, which gives the maximum efficiency of a heat engine, is defined as follows: Carnot ¼ ; ð12þ where is the temperature of the high-temperature heat exchanger and is the temperature of the low-temperature heat exchanger in a stack. The thermal efficiency relative to the Carnot thermal efficiency is defined as R ¼ : ð13þ Carnot 3. EXPERIMENTAL SYSTEMS AND METHOD When a temperature gradient is formed in a narrow tube, energy conversion from the heat flow to acoustic power occurs. When one side of a stack with a bundle of narrow tubes is heated to a high temperature, a temperature gradient is formed in the narrow tubes. Because of this temperature gradient, the gas in a stack spontaneously oscillates and acoustic power is generated. To induce this spontaneous gas oscillation, the temperature gradient along the walls of the narrow tubes must be higher than a critical value. When the gas in the system oscillates, the ratio of the temperature of the high-temperature heat exchanger ( )to that of the low-temperature heat exchanger ( ) in a stack is called the onset temperature ratio. However, the lowtemperature heat exchanger is not driven in this experiment in order to drive the thermoacoustic system without a moving part. The onset temperature ratios are compared among three experimental systems. Figures 1 3 show schematic illustrations of a normal thermoacoustic engine, a cascade thermoacoustic engine with two PM, and a 151

4 Acoust. Sci. & Tech. 36, 2 (215) PM-Stack Temperature ratio / 1 Onset point 2 3 Time [sec] Normal_Stack Parallel_StackA Parallel_StackB Cascade_StackA Cascade_StackB 4 5 Normal_Stack Parallel_Stack Cascade_Stack Fig. 4 Temperature ratio of each stack ends in normal, cascade and parallel thermoacoustic engine. Fig. 2 PM-Stack Schematic illustration of a parallel thermoacoustic engine. PM-Stack PM-Stack tube and the upper tube. The thickness of each PM stack is 5 mm and the channel radius is.55 mm (6 cells/inch 2 ). In the cascade thermoacoustic engine, the distance between the two PM stacks is 15 mm in this experiment. The closer the two PM stacks, the greater the thermal efficiency, because the PM stacks are set up in high-impedance positions. The high-temperature heat exchanger of the PM stack is heated by an electric heater. In the cascade thermoacoustic engine, the two high-temperature heat exchangers of the PM stacks are heated by two electric heaters because there are two heat input parts in this system. However, in the parallel thermoacoustic engine, the two high-temperature heat exchangers of the PM stacks are heated by a single electric heater. The pressure fluctuation in the system is measured using pressure sensors (PCB Piezotronics Inc.). The acoustic power intensity is calculated by substituting the measured sound pressures into the wave equation while applying Rott s acoustic approximation [17 19]. Using a digital multimeter, the input power is measured when the system is driven. The temperatures of the PM stack ends are measured using K-type thermocouples. Fig. 3 Schematic illustration of a cascade thermoacoustic engine. parallel thermoacoustic engine with two PM, respectively. The arrows in each schematic illustration indicate the direction of the acoustic power flow. In the parallel thermoacoustic engine, it is assumed that the acoustic power flow of one PM does not flow back toward another PM. and are the temperatures of the high and lowtemperature heat exchangers, respectively. The high-temperature heat exchanger of the PM stack is defined as the origin. The total length of each system is 2.5 m to enable the tuning of the resonance frequency. The inner diameter of each system is 42 mm. In the parallel thermoacoustic engine, the length of the lower loop tube is 2.5 m and the length of the upper tube connected to the lower loop tube is 1.25 m. In this design, the antinode of the sound pressure is formed in the connecting part between the lower loop 4. EXPERIMENTAL RESULTS AND DISCUSSION Figure 4 shows the temperature of the high-temperature part in the PM stack after heat input for 5 s. The vertical axis shows the temperature ratio ( = ) between the high and low-temperature heat exchangers in the PM stack. The horizontal axis shows the time after first applying the heat. The arrows in the figure indicate the onset points of the systems. The onset times differ because the input heat is changed manually. The onset temperature ratio of the normal thermoacoustic engine is 2.23 (, 43 C;, 41 C). The onset temperature ratios of the cascade thermoacoustic engine are 1.73 (, 255 C;, 31 C) and 1.7 (, 252 C;,35 C). The onset temperature ratios of the parallel thermoacoustic engine are 1.85 (, 29 C;,29 C) and 1.85 (, 29 C;,29 C). The onset temperature ratios of the cascade and parallel 152

5 Y. NAKANO et al.: DEVELOPMENT OF PARALLEL THERMOACOUSTIC ENGINE Acoustic impedance [Pa s /m 3 ] PM-Stack A.5 PM-Stack B Distance [m] Acoustic impedance [Pa s/m 3 ] Upper tube Lower loop tube T R 1. PM-Stack B PM-Stack A 1.5 Lower loop tube Upper tube Fig. 5 Acoustic impedance of a cascade thermoacoustic engine. Distance [m] thermoacoustic engines are lower than that of the normal thermoacoustic engine. Because the total tube length of the parallel thermoacoustic system is greater than that of the cascade thermoacoustic engine, the energy dissipation of the parallel thermoacoustic engine is larger. Therefore, the onset temperature ratio of the parallel thermoacoustic engine is higher than that of the cascade thermoacoustic engine. Using Eqs. (5), (7), (11), and (12), the acoustic power intensity I, the heat value of the high-temperature heat exchanger Q H, the thermal efficiency, and the theoretical Carnot thermal efficiency Carnot were calculated. In the normal thermoacoustic engine, I is 5.81 W/m 2, Q H is 326 W/m 2, is 1.8%, and Carnot is 54.5%. The thermal efficiency relative to Carnot, R, is 3.3%. In the parallel thermoacoustic engine the R values of PM stacks A and B are 8.7 and 6.9%, respectively. The total R is 7.8%. In the cascade thermoacoustic engine, R for PM stack A is 17.8%. For PM stack B of the cascade thermoacoustic engine, R decreases because the acoustic power intensity dissipates. The total R is 3.%. The total R in the parallel thermoacoustic engine was the highest. Figures 5 and 6 show the acoustic impedance in the cascade thermoacoustic engine and parallel thermoacoustic engine, respectively. The acoustic impedances of PM stacks A (3. kpas/m 3 ) and B (3. kpas/m 3 ) in the parallel thermoacoustic engine are higher than those of PM stacks A (1.25 kpas/m 3 ) and B (.65 kpas/m 3 ) in the cascade thermoacoustic engine. When the stacks are set up in positions where the acoustic impedance is high, the energy dissipation due to the viscosity decreases. Therefore, the thermal efficiency in the parallel thermoacoustic engine is high. In the cascade thermoacoustic engine, not all the stacks can be located in high-impedance positions because of geometric limitations. PM stack B is located at a position with a lower acoustic impedance than PM stack A. Therefore, the thermal efficiency in the cascade thermoacoustic engine is low. In these engines, there are two high-impedance Fig. 6 Heat flow ratio (Q prog, Q stand, Q dream /Q) [%] Acoustic impedance of a parallel thermoacoustic engine PM-Stack A Q prog / Q Q stand / Q Q dream / Q PM-Stack B Q prog / Q Q stand / Q Q dream / Q (a) (b) Thickness of PM-Stack [m] Fig. 7 Heat flow ratios ðq prog ; Q stand ; Q dream =QÞ of stack in a cascade thermoacoustic engine (a) and a parallel thermoacoustic engine (b). is the high heat exchanger and is the low heat exchanger. positions. In this study, PM stacks are set up in only one high-impedance position, because the HP stack is set up in another high-impedance position when this system is driven as the thermoacoustic refrigerator in the future. Figure 7 shows the heat flow ratios ðq prog ; Q stand ; Q dream =QÞ in each stack [13]. The right side of Fig. 7 shows the heat flow ratios for the high-temperature heat exchanger in each stack. The left side of Fig. 7 shows those for the low-temperature heat exchanger in each stack. Here, 5x

6 Acoust. Sci. & Tech. 36, 2 (215) Table 1 Heat flow ratios ðq prog ; Q stand ; Q dream =QÞ of a high heat exchanger (the high heat exchanger is set up in the right side of PM Stack). Q prog =Q [%] Q stand =Q [%] Q dream =Q [%] Normal Cascade A Cascade B Parallel A Parallel B the flow in the axial direction has a positive value and the flow in the opposite direction has a negative value. Table 1 shows the heat flow ratios in the high-temperature heat exchanger. The total heat ratio in Table 1 is not 1% because the heat ratio unrelated to the fluid oscillation is not included in it. In the cascade thermoacoustic engine, the Q dream =Q values of PM stacks A and B were 53 and 72%, respectively. In the parallel thermoacoustic engine, the Q dream =Q values of PM stacks A and B were 9 and 1%, respectively. The Q dream =Q values of the parallel thermoacoustic engine were lower than those of the cascade thermoacoustic engine. Because Q dream has an irreversible process, Q dream is one factor that reduces the thermal efficiency. In the cascade thermoacoustic engine, the Q prog =Q values of PM stacks A and B were 2 and 6%, respectively. In the parallel thermoacoustic engine, the Q prog =Q values of PM stacks A and B were 9% and 1%, respectively. The Q prog =Q values of the parallel thermoacoustic engine were higher than that of the cascade thermoacoustic engine. Because Q prog has a reversible process, Q prog is one factor that raises the thermal efficiency. Because of these factors, the parallel thermoacoustic engine has a higher thermal efficiency, suggesting its advantageousness. In the future, thermoacoustic refrigerators and thermoacoustic electric generators using a parallel thermoacoustic engine driven at a high thermal efficiency are expected to be realized. 5. SUMMARY The onset temperature ratio and thermal efficiency were compared among a normal thermoacoustic engine, a parallel thermoacoustic engine, and a cascade thermoacoustic engine. The results suggest that in the parallel thermoacoustic engine, it is possible to realize a lower onset temperature ratio than that in the normal thermoacoustic engine. Moreover, it appears to be possible to realize a higher thermal efficiency (7.8%) than that of the cascade thermoacoustic engine. This is because it is possible to set up the two PM stacks of the parallel thermoacoustic engine in a position with a higher acoustic impedance. In the future, we will design a thermoacoustic refrigerator or thermoacoustic electric generator with high thermal efficiency using the parallel thermoacoustic engine. ACKNOWLEDGMENTS This research was partially supported by Japan Society for the Promotion of Science, a Grant-in-Aid for Young Scientists (A), (B), a Grant-in-Aid for Exploratory Research, and the Program for Fostering Regional Innovation. REFERENCES [1] P. H. Ceperley, A pistonless stirling engine The traveling wave heat engine, J. Acoust. Soc. Am., 66, (1979). [2] G. W. Swift, Thermoacoustic engines, J. Acoust. Soc. Am., 84, (1998). [3] T. Yazaki, A. Iwata, T. Maekawa and A. Tominaga, Traveling wave thermoacoustic engine in a looped tube, Phys. Rev. Lett., 81, (1998). [4] S. Backhaus and G. W. Swift, A thermoacoustic-stirling heat engine: Detailed study, Nature, 399, (1999). [5] T. Biwa, Y. Tashiro, U. Mizutani, M. Kozuka and T. Yazaki, Experimental demonstration of thermoacoustic energy conversion in a resonator, Phys. Rev. (E), 69, (24). [6] Y. Ueda and C. Kato, Stability analysis of thermally induced spontaneous gas oscillations in straight and looped tubes, J. Acoust. Soc. Am., 124, (28). [7] S. Sakamoto and Y. Watanabe, Improvement in performance of stack as heat pump of thermoacoustic cooling system: Effect of thickness of heat boundary layer upon cooling effect, Jpn. J. Appl. Phys., 45, 9257 (26). [8] S. Backhaus, E. Tward and M. Petach, Traveling-wave thermoacoustic electric generator, Appl. Phys. Lett., 85, 185 (24). [9] T. Biwa and D. Hasegawa, Thermoacoustic engine with multiple regenerators, Proc. 14th Nat. Symp. Power and Energy Systems, No. 9-17, pp (29). [1] D. L. Gardner and G. W. Swift, A cascade thermoacoustic engine, J. Acoust. Soc. Am., 114, (23). [11] S. Hatori, Y. Ueda and A. Akisawa, Numerical design of a cascade thermoacoustic engine, Trans. Jpn. Soc. Mech. Eng. (B), 76(763), (21). [12] S. Hasegawa, T. Yamaguchi and Y. Oshinoya, Temperature of thermoacoustic refrigerator driven by a cascade thermoacoustic engine (Basic Study Using the Atmospheric Pressure Air), Trans. Jpn. Soc. Mech. Eng., 78(787), (212). [13] S. Hasegawa, T. Yamaguchi and Y. Oshinoya, Study on a high-efficiency multistage thermoacoustic engine with a controlled acoustic field that realizing traveling waves within all resonators, Teion Kogaku, 47, (212). [14] T. Biwa, New acoustic devices based on thermoacoustic energy conversion, JSME TED Newsl., No. 41, (23). [15] K. Kuroda, S. Sakamoto, K. Shibata, Y. Nakano, T. Tsuchiya and Y. Watanabe, Fundamental study for the solution of thermoacoustic phenomenon using numerical calculation, Jpn. J. Appl. Phys., 51, 7GE1 (212). [16] P. H. Ceperley, Gain and efficiency of a short traveling wave heat engine, J. Acoust. Soc. Am., 77, (1985). [17] N. Rott, Damped and thermally driven acoustic oscillations, Z. Angew. Math. Phys., 2, (1969). [18] N. Rott, Thermally driven acoustic oscillations. Part 2: Stability limit for helium, Z. Angew. Math. Phys., 24, (1973). [19] N. Rott and G. Zouzoulas, Thermally driven acoustic oscillations, Z. Angew. Math. Phys., 27, (1976). 154

Effect of Sub-Loop Tube on Energy Conversion Efficiency of Loop-Tube-Type Thermoacoustic System

Proceedings of 2 th International Congress on Acoustics, ICA 21 23-27 August 21, Sydney, Australia Effect of Sub-Loop Tube on Energy Conversion Efficiency of Loop-Tube-Type Thermoacoustic System Shin-ichi