Effect of regenerator positioning on thermoacoustic effect in a looped tube traveling wave thermoacoustic engine

Energy Conversion and Management 95 (2015) 94–100

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Effect of regenerator positioning on thermoacoustic effect in a looped tube traveling wave thermoacoustic engine Konstantin Tourkov a,⇑, Laura Schaefer b a b

University of Pittsburgh, Department of Mechanical Engineering and Material Science, 225 Benedum Hall, Pittsburgh, PA 15261, United States University of Pittsburgh, Department of Mechanical Engineering and Material Science, 153 Benedum Hall, Pittsburgh, PA 15261, United States

a r t i c l e

i n f o

Article history: Received 13 December 2013 Accepted 9 February 2015

Keywords: Thermoacoustics Temperature distribution Regenerator positioning

a b s t r a c t This paper discusses the effect of regenerator positioning on the intensity of the thermoacoustic effect in a looped-tube traveling wave thermoacoustic engine (TAE). Traveling wave thermoacoustic engines work on the principle of the acoustic wave moving through the loop of the engine, across the regenerator, with the pressure and velocity curves in phase, amplifying the acoustic effect. Increasing the intensity of the effect, while keeping the energy input the same increases the efficiency of the TAE, and can be further applied in a thermoacoustic refrigeration system to increase the COP. The intensity of the effect in relation to the positioning of the regenerator, also called a stack in standing wave devices, is proven here to have an optimum positioning inside of the straight part of the loop. The increase in intensity under constant heat input proves an increase in efficiency. Ó 2015 Elsevier Ltd. All rights reserved.

1. Background

1.1. Thermoacoustic energy conversion

Thermoacoustic heat engines (TAEs) work on the principle of the Stirling cycle, developed by Robert Stirling in 1816 [1], shown schematically in Fig. 1 and on a pressure–volume diagram in Fig. 2. The first engine utilized two mechanical pistons and a heat exchanger, functioning as a constant volume regenerator. Each cycle was completed in four steps, beginning with the compression of the working gas at a constant temperature, while simultaneously transferring heat to a heat sink. The second step follows with the gas being heated at constant volume via a regenerative heat exchanger. The gas is further heated in the third step, while it expands, driving the power piston. The fourth step finishes the cycle with the gas transferring heat at a constant volume through the heat exchanger and returning to the displacement piston. Thermoacoustics began with the Byron Higgins experiment in 1777 [4,5], when he noticed that a flame heating a glass tube could produce sound. Other experimental investigations followed, but no accurate theory was proposed until Nikolaus Rott developed the general linear theory of thermoacoustics in 1969 [6]. Since then, many analytical and experimental investigations on TAEs and thermoacoustic refrigerators (TARs) have been conducted, improving performance of devices with the goal of developing competitive technologies for the market.

Ceperley was first to recognize that the pistons used for the compression and displacement steps of the Stirling cycle can be replaced with thermoacoustic waves that result in pressure and velocity oscillations [7]. While not all thermoacoustic engines are designed in the same way, the overwhelming majority are based on the principle of a temperature gradient applied across a porous medium. When subjected to an externally imposed temperature gradient (such as that produced by an electric heated coil) over the porous medium, commonly referred to as a stack, pressure disturbances present due to noise can be amplified at the frequency of the resonator and would subsequently be used to drive the thermal energy across the stack. The stack geometry was found to play an important role in the efficiency of the energy conversion [8]. A critical temperature gradient is required to initialize the oscillation amplification, which can be found using an equation initially developed by Swift [9]:

⇑ Corresponding author. E-mail address: [email protected] (K. Tourkov). http://dx.doi.org/10.1016/j.enconman.2015.02.027 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.

rT crit ¼

xp qm cp u

ð1Þ

The variables controlling the critical temperature gradient value are the standing wave pressure p and velocity u, as well as mean gas density qm , specific heat capacity cp , and the frequency x. The principle of using a thermal gradient to drive the oscillations can also be reversed to drive a temperature gradient using the oscillations, thus creating refrigeration. Typical design of a thermoacoustic

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refrigerator is based on the use of a second stack positioned to receive the energy of the thermoacoustic wave and generate a temperature difference, thus withdrawing heat from one side of the stack and creating cooling. The most basic TAEs are standing wave engines, commonly designed with a straight resonator tube and a stack located close to a sealed end of the engine, as seen in Fig. 3. These engines operate with a stationary acoustic wave with a pressure node on the closed end of the tube, and a velocity node on the open end of the tube. 1.2. Traveling wave TAEs Traveling wave thermoacoustic engines have been the object of increased attention due to their potential for higher efficiencies, as compared to standing wave TAEs. While the general principle of the traveling wave engine is the same as that of the standing wave engine, the acoustic wave in the traveling wave engine, as the name suggests, travels through a loop built into the engine, as shown in Fig. 4. The increase in efficiency is caused by the difference in the phasing of the pressure and velocity curves between the two types [10]. While the standing wave engine operates on a phase angle of 90° between the two curves, the traveling wave engine operates exactly in phase between the two curves [11]. This allows for a more efficient transfer of the heat energy, thus increasing the potential overall efficiency of the engine. As in all thermal energy devices, parasitic losses occur in thermoacoustic engines and refrigerators in the form of streaming, or fluid vortices, and heat transfer. Gedeon streaming, defined as streaming around a torus, is specific to traveling wave engines, and has been shown to have a significant impact on performance [12,13]. Rayleigh streaming has also been identified as a contributor to losses in thermoacoustic devices, and can occur in both standing and traveling wave engines [14,15]. Heat transfer losses can occur in various forms and magnitudes, depending on the working temperatures. Conduction through the stack or regenerator, convection, and radiation losses to the working fluid have been examined and determined to have significant impact [16,17]. Due to the difficulty of separating the phenomena, they can be studied using CFD simulation with the goal of quantifying and reducing the sources of the largest losses [18].

Fig. 2. Pressure–volume diagram of a Stirling engine [3].

Stack Closed end

Hot side

Cold (Ambient) side

Resonator tube

Pressure

Open end

Velocity

Fig. 3. Schematic of standing wave engine with pressure and velocity magnitudes.

1.3. Application of thermoacoustics Thermoacoustic refrigeration has been implemented in several specialized cases where thermoacoustic engines prove to be a

Fig. 4. Schematic of a traveling wave TAE [3].

more advantageous solution than the more standard vapor compression refrigerators (VCRs). One of these examples is the use of TARs for cryogenic cooling, as was demonstrated in a collaborative effort between the National Institute of Standards and Technology (NIST) and Radebaugh, which resulted in an TAR capable of 5 W of cooling at 120 K and a no load temperature of 90 K [19]. Since several stages would be needed on a standard VCR to achieve this performance, the higher number of moving parts required would reduce its reliability, where a TAR, with absolutely no moving parts, has near zero maintenance required. Since heat, rather than a higher quality form of energy, such a electricity, is required to run a TAR, several applications can be found where waste heat produced by an existing process, such as an IC engine, can be used to drive a TAR [20,21]. 1.4. Current limitations of thermoacoustics

Fig. 1. Schematic of a Stirling engine [2].

As previously mentioned, traveling wave TAEs and TARs can achieve higher efficiencies than their standing wave counterparts.

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Therefore, traveling wave thermoacoustic devices, particularly those designed for refrigeration, have been receiving increasing attention. The technology, however, is not mainstream, due to the low coefficient of performance (COP), compared to that of VCRs, that the devices can achieve. While the COP of a standard VCR ranges between 2 and 6, depending on the working fluid [22], a TAR has a typical COP between 1 and 1.2 [23,24]. Efforts to improve the efficiency of traveling wave TARs can help make the technology more competitive, and bring thermoacoustic technology into a wider range of industrial applications, other than cryogenic cooling.

2. Experimental setup The goal of this study was to investigate the effect of the regenerator location on performance. First, the thermoacoustic behavior of a loop-tube engine was recorded and evaluated with the regenerator positioned in several spots inside the straight part of the device. The intensity of the thermoacoustic effect was then evaluated and a general relationship was identified that described how the intensity of the thermoacoustic effect changed with the change in the positioning of the regenerator. This relationship could then be used to determine an approximation for the optimal position of the regenerator in the loop-tube. The loop-tube was designed using 2 inch nominal diameter schedule 40 PVC and steel pipe, with the heating element positioned in the steel portion of the device, to prevent melting of the PVC. The straight portions of the pipe were approximately 34 inches long, with the turns approximately 12 inches in length. Standard 90° elbows were joined to the PVC pipe using PVC cement to create the 180° turns required for the loop. The PVC portion of the loop-tube was joined to the steel portion using 4-bolt flanges, with air tightness assured using full-face gaskets. A picture of the device can be seen in Fig. 5 and a closer view of the regenerator housing can be seen in Fig. 6. The regenerator, seen in Fig. 7, was comprised of a ceramic material (found in catalytic converters in automobile mufflers) with a hole density of approximately 20 holes per inch. The regenerator was machined down to fit into the pipe, and cut to approximately 3.5 inches in length. It was then modified to include an electric heating coil on one side. The heating portion of the coil was designed using 22 AWG wire with the lead wires built using 18 AWG wire to minimize heat dissipation through wire not directly in contact with the regenerator. Eight K-type thermocouples were used to record the hot and ambient side behavior of the regenerator. Four of the thermocouples were used to measure the hot side behavior. All four were mounted equidistant from each other and approximately 1/4 inch from the center of the regenerator, as shown in Fig. 8. Each was embedded approximately 1/16 inch from the surface of the hot side and the coil to help achieve a more uniform temperature reading. This would prevent major changes in the recorded tem-

Fig. 6. Housing design used to insure air tightness.

Fig. 7. Regenerator used in the construction of the TAE.

perature if the heated coil slightly changed position due to expansion from heating. Ambient side thermocouples were positioned approximately 1/16 inch from the center of the regenerator and mounted at 1/8, 1/4, 3/8, and 1/2 inches from the surface of the ambient side, shown in Fig. 9, to help better evaluate the temperature behavior of the regenerator. Data were recorded using a several step voltage increase, starting with a base value at room temperature recorded for 60 s to identify any irregularities present in either the testing equipment

Electrodes

Regenerator Hot side

Ambient side

1

2 Thermocouple Posions

Heang Coil Heater electrodes

Regenerator

Fig. 5. Traveling wave engine used in experiment.

3

4

2 inches Fig. 8. Hot side thermocouple positioning.

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500

3.5 inches

Hot Side

Tcouple 1 Tcouple 2 Tcouple 3 Tcouple 4

1

Regenerator

2

3

4

Thermocouple Posions

Temperature (oC)

Ambient Side

Fig. 9. Ambient side thermocouple positioning.

3. Results 3.1. Patterns in thermoacoustic behavior Preliminary data were collected to study the behavior of the individual thermocouples in relation to the presence and the lack of oscillation for a fixed regenerator location at the 8.5 position. Figs. 11 and 12 show the behavior of the hot and ambient sides, respectively. The maximum temperature difference between the oscillation and no oscillation runs on the hot side was approximately 154 °C, while the maximum temperature difference for the ambient side was approximately 27 °C. While the thermocouples in the study have an accuracy of 2.2 °C [25], the hot side showed a greater variation in the recorded temperature. The error within the four thermocouples was calculated, as shown in Fig. 13,

No Oscillation

300 Oscillation

200 100 0

0

500

1000

1500

Time (sec) Fig. 11. Hot side individual runs.

Tcouple 1 Tcouple 2 Tcouple 3 Tcouple 4

70

Temperature (oC)

or the experimental setup. For a 4 min period, following the initial baseline recording, a 5 V voltage drop was applied across the heating coil. This was followed by three sequential 5 min periods of heating at 10 V, 15 V, and 20 V, respectively. After 20 min of recording, the current was shut off and a 5 min cool down was recorded. Preliminary data were collected with the ambient side of the regenerator mounted at 8.5 inches from the edge of the turn of the loop-tube. Following the initial data collection to validate the testing setup, the regenerator was moved to the 8.875, 7.25, 6.25, and 5.25 inch positions, as shown in Fig. 10. At each position, two separate trials were recorded, one of the performance with oscillation present, the other without the presence of oscillation. The presence of oscillation is expected to transfer heat to the ambient side from the hot side, decreasing hot side temperature, as compared to runs without the presence of oscillation, and increasing ambient side temperature, again, compared to runs without oscillation. A measure of the intensity of this effect can be inferred from the magnitude of the observed difference in temperature between the presence and absence of oscillation for both the hot and ambient sides of the regenerator. Thus, it can be said that the highest magnitude of the temperature difference induced by oscillations provides the point where the thermoacoustic intensity is strongest.

400

60 50

Oscillation 40 No Oscillation

30 0

500

1000

1500

Time (sec) Fig. 12. Ambient side individual runs.

and normalized by the average of the four thermocouples at the instant of the recording, as shown in Fig. 14 as a percent value. The maximum temperature variation was recorded at 18.1 °C, corresponding to a normalized value of 3%. For values below 100 °C (ambient side operating range), the error was within thermocouple accuracy. While the presence of oscillation is clearly seen on the hot side in Fig. 11, the pattern of increasing temperature appears similar between oscillation and non-oscillation runs. This is not the case for the ambient side. Without the presence of oscillations, it was predicted that the regenerator would heat up evenly and a linear drop in temperature was expected as the distance from the hot coil

20

Ambient side

Hot side

Variation (K)

15

10

5

0

Regenerator

Regenerator posion (in)

Fig. 10. Diagram of regenerator placement.

0

500

1000

Time (sec) Fig. 13. Hot side thermocouple recorded error.

1500

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50

3.5 3

Temperature (oC)

Error (%)

2.5 2 1.5 1 0.5 0

30 20 10 0

0

500

1000

1500

−10

Time (sec)

increased. As seen in Fig. 12, the predicted behavior is displayed, proving the validity of the measurement. The presence of oscillations, however, distorts this pattern and it can be observed that the 3/8 inch position thermocouple displayed slightly higher temperatures than the 1/2 inch position. With the thermoacoustic effect providing an additional pathway for heat, it is expected that temperatures within the center of the regenerator would be closer, with the readings measured being within the margin of error. This behavior was also observed in the tests conducted while varying the regenerator placement. 3.2. Ambient side behavior The ambient side showed fairly uniform behavior across the different regenerator placements, as seen in Fig. 15. The runs with oscillations present show a similar pattern of a sharp increase at the points of increase in voltage, which decreases in slope with time. One placement position that shows deviation from the pattern is the 5.25 position where the slope seems to decrease at a faster rate than that of the other positions. The no oscillation runs showed slight deviation from a singular pattern, suggesting changing thermal conditions at each regenerator placement. In order to account for these conditions, Fig. 16 shows the temperature differences for each placement between the oscillation and no oscillation runs. The 6.25 position shows the largest difference, implying the highest intensity of the thermoacoustic effect. 3.3. Hot side behavior The behavior of the hot side showed a significant difference in temperature between runs with oscillation present and runs without oscillation. As predicted, there was a significant drop in

500

1000

1500

Fig. 16. Ambient side temperature difference induced by oscillation. Calculated by subtracting runs without from runs with oscillation.

temperature when oscillations were introduced. Fig. 17 shows the averaged temperatures of the oscillation and no oscillation runs. A tight grouping across the differing placements can be seen for the oscillation runs and the no oscillation runs. To quantify the effect of the placement of the regenerator on the thermoacoustic effect on the hot side, the differences between the oscillation and no oscillation readings were taken for each position and are displayed in Fig. 18. The 6.25 placement shows the largest average temperature difference, in agreement with the ambient side behavior. The 5.25 position shows a similarly high temperature difference. However, this high difference in temperature does not correspond to a high temperature difference on the ambient side. It can also be seen in Fig. 17 that the oscillation run for that position appears to be outside of the general grouping of the other positions, while the no oscillation run for that same position shows unusual behavior during the 20 V period. From this, it can be concluded that an unpredicted variable influenced the hot side readings for that particular position. It is hypothesized that local heat stresses affected thermal contact between the thermocouple and the regenerator, causing a variation in the readings. 3.4. Regenerator placement and intensity of the thermoacoustic effect To help evaluate the intensity of the thermoacoustic effect, the temperature differences for both the ambient and the hot sides were normalized to the highest difference at the 6.25 position and are displayed in Figs. 19 and 20, respectively. The hot side shows that during the 15 V and 20 V periods, the ratio between

500

100 8.875" 8.5" 7.25" 6.25" 5.25"

80 70 60

Oscillation

50 40

No Oscillation

30 0

500

8.875" 8.5" 7.25" 6.25" 5.25"

400

Temperature ( oC)

90

Temperature ( oC)

0

Time (sec)

Fig. 14. Hot side percent error.

20

8.875" 8.5" 7.25" 6.25" 5.25"

40

1000

1500

Time (sec) Fig. 15. Ambient side thermocouple averages for varying regenerator placement (runs shown with oscillation present and absent).

300

No Oscillation

Oscillation

200 100 0

0

500

1000

1500

Time (sec) Fig. 17. Hot side thermocouple averages for varying regenerator placement (runs shown with oscillation present and absent).

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1.02 8.875" 8.5" 7.25" 6.25" 5.25"

150

Ratio to Hottest Placement

Temperature (oC)

200

100

50

0

1.01 1 0.99 0.98 8.875" 8.5" 7.25" 6.25" 5.25"

0.97 0.96 0.95

0

500

1000

1500

0

Time (sec)

500

1000

1500

Time (sec)

Ambient side temperature difference

the highest temperature difference and each position stays relatively equal. Sharp decreases in the temperature ratio can also be seen at the times when voltage changes occur, implying the more intense presence of the thermoacoustic effect for the 6.25 position. The onset of the thermoacoustic effect can also be observed at approximately 400 s, marked by sudden sharp changes in the ratio behavior. The ambient side behavior does not show a linear ratio at each voltage, with only the 7.25 position appearing relatively linear for the 15 V and 20 V time periods. The intensity of the thermoacoustic effect can be observed to increase substantially for the 6.25 position with increases in voltage, when compared to other regenerator positions. The reason for this can be seen in the basic operation of a looped tube traveling wave engine. For a traveling wave, the pressure and velocity oscillations are in phase. This means that the regenerator of a traveling wave engine can be designed to be in ideal thermal contact with the gas, which leads to better heat transfer, and better overall performance. These effects have been detailed in [11,26,27]. To further illustrate this relationship, surface plots were generated for the ambient and hot sides, shown in Figs. 21 and 22, respectively. For the hot side, a gradual increase in the average temperature difference can be seen in the behavior across all voltages as the regenerator is moved closer to the edge. A peak appears to occur close to the 6.25 position (0.18 of the total straight tube length) after which a mild decrease can be observed. The ambient side behavior shows a substantially better defined pattern of gradual increase with the decrease of the distance to the edge. The 20 V averages show the clearest presence of a peak at the same position as the hot side. However, the subsequent drop is far more

Fig. 20. Hot side normalized temperature difference induced by oscillation.

60 40 20 0 −20 1500 1000

time (sec)

500 0

5

6

7

8

9

Position (inches)

Fig. 21. Ambient side temperature difference vs. positioning.

Hot side temperature difference

Fig. 18. Hot side temperature difference induced by oscillation. Calculated by subtracting runs with from runs without oscillation.

200 100 0 −100 1500 1000 500

time (sec)

0

5

6

7

8

9

Position (inches)

Fig. 22. Hot side temperature difference vs. positioning.

Ratio to Hottest Placement

1.005 1 0.995 0.99 0.985 8.875" 8.5" 7.25" 6.25" 5.25"

0.98 0.975 0.97

0

500

1000

1500

Time (sec) Fig. 19. Ambient side normalized temperature difference induced by oscillation.

significant for the ambient side than the hot side. Both figures agree on a peak close to the 6.25 position and show that positioning has a significant impact on the intensity of the thermoacoustic effect, and thus the efficiency of the TAE. The relationships on the hot and ambient sides can be combined to show a total temperature change when oscillations are present, as seen in Fig. 23. The peak can be more clearly seen in this plot than the hot side, and the overall impact of the presence of oscillations shows a large drop in the temperature gradient across the regenerator, as was expected. Additionally, the voltage input shows a large impact on the behavior (as expected), but does not lend itself to a direct measurement of efficiency in the transfer of thermal energy to acoustic energy. Further investigation would provide a quantitative assessment of the performance of a loop tube and potential for additional optimization of other parameters.

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Total temperature difference

100

300 200 100 0 −100 1500 1000

time (sec)

500 0

5

6

7

8

9

Position (inches)

Fig. 23. Combined hot and ambient difference vs. regenerator positioning.

4. Conclusion We have quantified the thermoacoustic effect in a traveling wave loop-tube design TAE and have shown the impact of regenerator positioning inside the loop-tube on its efficiency. Temperature was measured on the hot and ambient sides of the regenerator during inputs of heat incrementally increased every 5 min. Procedure was executed for the device operating, allowing acoustic oscillations, and the device turned off, preventing oscillations from occurring. Using the temperature difference between oscillation and no oscillation runs for each regenerator position, the effect was measured for the hot and ambient sides of the regenerator. A significant increase in efficiency can be seen when the regenerator is moved to approximately 0.18 of the total straight length from the edge, measured from the ambient side facing the edge. More effective conversion of thermal energy to thermoacoustic energy increases the amount of cooling produced by a given amount of heat and thus increases the COP. Increases in COP in TAEs can help make it more competitive with traditional vapor compression refrigeration, broadening the range of industries for its use. Acknowledgement This material is based upon work supported by the National Science Foundation under Grant No. CBET-0729905. References [1] Garrett Steven L. Reinventing the engine. Nature 1999;339:303–5. [2] Kaushik SC, Kumar S. Finite time thermodynamic analysis of endoreversible Stirling heat engine with regenerative losses. Energy 2000;25:989–1003.

[3] Yu Z, Jaworski A. Impact of acoustic impedance and flow resistance on the power output capacity of the regenerators in travelling-wave thermoacoustic engines. Energy Convers Manage 2010;51:350–9. [4] Putnam AA, Dennis WR. Survey of organ-pipe oscillations in combustion systems. J Acoust Soc Am 1956;28:246–59. [5] Higgins B. Nicholson’s Journal; 1802: p. 130. [6] Rott N. Damped and thermally driven acoustic oscillations in wide and narrow tubes. Z Angew Math Phys 1969;20:230–43. [7] Ceperley Peter H. Gain and efficiency of a short traveling wave heat engine. J Acoust Soc Am 1985;77(3):1239–44. [8] Pat Arnott W, Bass Henry E, Raspet Richard. General formulation of thermoacoustics for stacks having arbitrarily shaped pore cross sections. J Acoust Soc Am 1991;60(6):3228–37. [9] Swift Greg W. Thermoacoustics: a unifying perspective for some engines and refrigerators. Melville,NY: Acoustical Society of America; 2002. [10] Rossing TD. Springer handbook of acoustics. Springer Van Godewijckstraat; 2007. [11] Yazaki T, Iwata A, Maekawa T, Tominaga A. Traveling wave thermoacoustic engine in a looped tube. Phys Rev Lett 1998;81(15). [12] Olson JR, Swift Gregory. Acoustic streaming in pulse tube refrigerators: tapered pulse tubes. Cryogenics 1997;37(12):769–76. [13] Gusev Vitalyi, Job Stephane, Bailliet Helene, Lotton Pierrick, Bruneau Michel. Acoustic streaming in annular thermoacoustic prime-movers. J Acoust Soc Am 2000;108(3):934–45. [14] Gaitan DF, Gopinath A, Atchley AA. Experimental study of acoustic turbulence and streaming in a thermoacoustic stack. J Acoust Soc Am 1994;96:3220. [15] Yazaki T, Tominaga A. Measurement of sound generation in thermoacoustic oscillations. In: Proceedings of the royal society – mathematical, physical and engineering sciences (series A); 1998. [16] Organ Allen J. The regenerator and the Stirling engine. Mechanial Engineering Publications Limited; 1997. [17] Zink Florian, Vipperman Jeffrey S, Schaefer Laura A. Influence of the thermal properties of the driving components on the performance of a thermoacoustic engine. In: Proceedings of the international mechanical engineering congress and exhibition (IMECE); 2009. [18] Zink Florian, Vipperman Jeffrey S, Schaefer Laura A. Heat transfer analysis in thermoacoustic regenerators using CFD simulation. In: Proceedings of the ASME summer heat transfer conference; 2009. [19] Kagawa Noboru. Regenerative thermal machines. Paris: International Institute for Refrigeration; 2000. [20] Poese Matthew E, Smith Robert WM, Garrett Steven L, van Gerwen Rene, Gosselin Pete. Thermoacoustic refrigeration for ice cream sales. In: Proceedings of 6th IIR Gustav Lorentzen conference; 2004. [21] Babaei H, Siddiqui K. Design and optimization of thermoacoustic devices. Energy Convers. Manage. 2008;49:3585–98. [22] Phelan PE, Swanson J, Chiriac F, Chiriac V. Designing a mesoscale vaporcompression refrigerator for cooling high-power microelectronics. In: Thermal and thermomechanical phenomena in electronic systems (ITHERM’04); 2004. [23] Herman Cila, Travnicek Z. Cool sound: the future of refrigeration? thermodynamic and heat transfer issues in thermoacoustic refrigeration. Heat Mass Transf 2006;42:492–500. [24] Tijani MEH, Zeegers JCH, de Waele ATAM. The optimal stack spacing for thermoacoustic refrigeration. J Acoust Soc Am 2002;112:128–33. [25] OMEGA . [26] Wetzel Martin, Herman Cila. Experimental study of thermoacoustic effects on a single plate Part I: Temperature fields. Heat Mass Transf 2000;36:720. [27] Zink Florian, Waterer Hamish, Archer Rosalind, Schaefer Laura. Geometric optimization of a thermoacoustic regenerator. Int J Therm Sci 2009;48(12):2309–22.