A compromise between the temperature difference and performance in a standing wave thermoacoustic refrigerator

TL;DR: The operating conditions and geometric parameters are important for the thermoacoustic refrigeration as mentioned in this paper, which is an evolving cooling technology in which the acoustic power is used to pump heat.

Abstract: Thermoacoustic refrigeration is an evolving cooling technology in which the acoustic power is used to pump heat. The operating conditions and geometric parameters are important for the thermoacoust...

Summary

1. Introduction

• Thermoacoustic refrigeration is a developing cooling technology.
• Following this, the wave through the resonator produces hot and cold temperature regions due to the high and low-pressure areas distribution across the resonator.
• Therefore, the operating conditions and the geometric parameters should be compromised to give a desired temperature difference across the stack with a high performance.

2. Thermoacoustic Refrigerator Design

• The thermoacoustic effect occurs inside the stack walls, so the thermal contact and viscous losses are presented at the stack surface.
• The stack geometric parameters influence the gained cooling load and the needed input power as demonstrated in Eqn. 4 and Eqn. 5 for the normalised cooling power ̇ and the normalised acoustic power ̇ respectively.
• The parallel plate stack from Mylar material is selected with porosity 0.75.
• The obtained results from the design steps are used in the DeltaEC model.

3. DeltaEC Model

• The effect of the operating conditions and geometric parameters change on the coefficient of performance of the thermoacoustic refrigerator and the temperature difference across the stack at different cooling loads will be presented numerically with the help of the free simulation software DeltaEC version 6.3b11 [8].
• DeltaEC solves the pressure and flow rate equations, which are concluded from the momentum equation and the continuity equations of fluid mechanics, respectively.
• A number of trials are then performed to form solutions for p1(x) and U1(x) that make guesses meet targets.
• The first boundary condition is to enforce the occurrence of resonance frequency [8,24] through the resonator, while the second boundary condition keeps pressure amplitude with known value independent of each trial of DeltaEC.
• Temperature of the hot heat exchanger is kept constant to show how the cold temperature is lower than this specific temperature.

4. Results and Discussion

• The effect of different operating conditions and geometric parameters on both the temperature difference across the stack and the performance of a thermoacoustic refrigerator is presented.
• After that, a compromise is held for maximizing both the temperature difference across the stack and the performance according to the criteria of acceptable range shown in Table 2.
• These criteria are considered reasonable for the required design parameters demonstrated in Section 2, which were primarily for small-size refrigerators.
• After that, the compromised values for the operating conditions and geometric parameters were chosen to achieve two factors.
• Second, the operating conditions and geometric parameters have values in between high performance and high temperature difference across the stack.

4.1 Mean Pressure

• Increasing the mean pressure decreases the temperature difference as shown in Fig. 4a, as the pressure amplitude would be insignificant relative to the mean pressure.
• The small thermal penetration depth decreases the temperature difference of the heat transfer between the gas parcels and the stack plates, as more gas parcels will be oscillating without interacting with the stack walls.
• Also, increasing cooling load will lead to a decrease of the temperature difference due to the cold side temperature rise.
• The acoustic energy is directly proportional to drive ratio, D, as the least wave amplitude from the input driver will lead to a good fluctuation.
• Then, a compromise is made to select the suitable mean pressure for their design considering the acceptable range in Table 2.

4.2 Amplitude Pressure

• The temperature difference starts at a low value in the first part of Fig. 6a due to the weakness of the pressure amplitude to make the change.
• After that, the increase of amplitude pressure increases the temperature difference, until it reaches a maximum value obtained near a drive ratio of 3 %.
• The input acoustic energy for a fixed mean pressure increases with the acoustic pressure increase, which means a lower performance as shown in Fig. 6b.
• The maximum temperature difference occurs at drive ratio equals 3%, but the performance is another key parameter and the authors considered factors shown in table 2.
• Therefore, a drive ratio equals 2 % is chosen to improve the performance and to account for the driver abilities to provide that drive ratio.

4.3 Stack Position

• The input acoustic signal changes with a sine wave, so the temperature distribution is also changed.
• The values of temperature differences at normalised stack positions from 0.25 to 0.3 do not change with a sensible change, so a normalised stack position equals 0.3 is chosen.

4.4 Stack Length

• Increasing the stack length means that larger number of the working fluid molecules will interact with the stack plates leading to the increase of temperature difference as shown in Fig. 8a.
• The stack is the place where the thermoacoustic effect and pumping heat takes place, so increasing the stack length will lead to more gas particles interact with the stack plates, and thus the acoustic power consumption will increase, and the performance will decrease as shown in Fig. 8b.
• Further increasing the stack length will result in a decrease in the temperature difference across the stack.
• This observed decrease in temperature difference across the stack could be attributed to the variability of the acoustic field inside the resonator.
• For different stack positions and cooling load of 5 W, the normalised stack length effect on the temperature difference and the coefficient of performance will be as shown in Fig.

4.5 Stack Spacing

• The thermal and viscous penetration depths parameters make a deep understanding of plate spacing change effect.
• Thus, increasing the spacing between the plates reduces the viscous penetration depth effect and the viscosity losses.
• After that, a weak thermal interaction with the plates is observed with the increase in the stack spacing, and the temperature difference is then considerably decreased.
• Increasing the plate spacing will increase the coefficient of performance in the studied range of normalized stack spacing, as the viscous losses are declined leading to a significant decrease in the consumed acoustic power and higher heat transfer rates between the gas particles and the cold heat exchanger according to the results obtained by DeltaEC.
• Until it reaches a region, where the change is less sensitive and the performance will remain constant as shown in Fig. 10b.

5. Conclusion

• Theoretical study using DeltaEC is presented to show the effect of changing the geometric parameters and operating conditions of a thermoacoustic refrigerator on both the coefficient of performance and the temperature difference across the stack.
• In addition, the physical phenomenon of the effect of the operating conditions and the geometric parameters is introduced.
• Moreover, depending on the designed thermoacoustic refrigerator, compromised values for the operating conditions and geometric parameters are collected as following: A drive ratio of 2 % will compromise the temperature difference and the coefficient of performance.
• A normalised stack position of 0.3 will compromise both the temperature difference across the stack and the performance.
• Nomenclature Latin Letters Resonator area, Sound velocity, Porosity, c Specific heat, ( ) Drive ratio, Frequency, Thermal conductivity, ( ) Length,.

Figures

Fig. 4. Mean pressure effect on (a) Temperature difference (b) Coefficient of performance.

Fig. 7. The normalised stack position effect (a) Temperature difference (b) Coefficient of performance.

Fig. 10. The stack spacing to thermal penetration depth effect on (a) Temperature difference (b) Coefficient of performance.

Fig. 9. Normalised stack length at different normalised stack positions effect on a) Temperature difference b) Coefficient of performance.

Full text

A compromise between the temperature
difference and performance in a standing
wave thermoacoustic refrigerator
Item Type Article
Authors Alamir, M.A.; Elamer, Ahmed A.
Citation Alamir MA and Elamer AA (2018) A compromise between the
temperature difference and performance in a standing wave
thermoacoustic refrigerator. International Journal of Ambient
Energy. Accepted for publication.
Rights © 2018 Taylor & Francis. The Version of Record of
this manuscript has been published and is available
in International Journal of Ambient Energy https://
doi.org/10.1080/01430750.2018.1517673.
Download date 09/08/2022 16:58:05
Link to Item http://hdl.handle.net/10454/16622

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International Journal of Ambient Energy
ISSN: 0143-0750 (Print) 2162-8246 (Online) Journal homepage: http://www.tandfonline.com/loi/taen20
A compromise between the Temperature
Difference and Performance in a Standing Wave
Thermoacoustic Refrigerator
Mahmoud Alamir & Ahmed A. Elamer
To cite this article: Mahmoud Alamir & Ahmed A. Elamer (2018): A compromise between the
Temperature Difference and Performance in a Standing Wave Thermoacoustic Refrigerator,
International Journal of Ambient Energy
To link to this article: https://doi.org/10.1080/01430750.2018.1517673
Accepted author version posted online: 29
Aug 2018.
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1
Publisher: Taylor & Francis & Informa UK Limited, trading as Taylor & Francis Group
Journal: International Journal of Ambient Energy
DOI: 10.1080/01430750.2018.1517673
A compromise between the Temperature Difference and
Performance in a Standing Wave Thermoacoustic Refrigerator
Keywords: DeltaEC; Performance; Refrigeration; Thermoacoustics; Temperature difference.
Highlights
 A theoretical DeltaEC model of a standing wave thermoacoustic refrigerator is built.
 Compromised values for the geometric parameters and operating conditions are
collected.
 The physical description of the performance and the temperature difference change
behavior is presented.

2
Abstract
Thermoacoustic refrigeration is an evolving cooling technology where the acoustic power is
used to pump heat. The operating conditions and geometric parameters are important for the
thermoacoustic refrigerator performance, as they affect both its performance and the
temperature difference across the stack. This paper investigates the effect of the stack
geometric parameters and operating conditions on the performance of a standing wave
thermoacoustic refrigerator and the temperature difference across the stack. DeltaEC software
is used to make the thermoacoustic refrigerator model. From the obtained results, normalised
values for the operating conditions and geometric parameters are collected to compromise
both the performance and the temperature difference across the stack.
1. Introduction
Thermoacoustic refrigeration is a developing cooling technology. It has many positives over
other alternative refrigeration technologies, as it uses environment friendly working gases, the
cooling capacity is continuously controlled, the design is simple, and it can operate quietly [1–
3]. This cooling technology is now in the research and development process, and it is expected
for noticeable spread commercially [4].

3
Thermoacoustic refrigeration uses the vibrational sound pressure waves. The heat is pumped
from low temperature source to high temperature sink by the sound waves. Fig. 1 shows a
typical standing wave thermoacoustic refrigerator. The function generator and the amplifier
feed the signal to the acoustic driver, and transmit the required frequency and power into the
resonator. Following this, the wave through the resonator produces hot and cold temperature
regions due to the high and low-pressure areas distribution across the resonator. The stack
which has low thermal conductivity separates the hot and cold areas inside the resonator, and
two heat exchangers are bounded the stack for heat transfer.
Insert Fig. 1 about here.
The temperature difference is a key parameter in refrigeration area, as a large temperature
difference may be required in some applications that need low temperatures. This can be on
the expense of the performance or even the obtained cooling loads. Further, the operating
conditions and geometric parameters of thermoacoustic refrigerators can have an influence on
both the temperature difference across the stack and the consumed acoustic power. Therefore,
the operating conditions and the geometric parameters should be compromised to give a
desired temperature difference across the stack with a high performance.
Recently, researchers have shown an increased interest in optimizing thermoacoustic
refrigerators. A number of researchers have reported design and optimization algorithms for
the thermoacoustic devices. Wetzel and Herman [5] developed an algorithm for
thermoacoustic refrigerators. The total acoustic power was introduced as follows,
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Frequently asked questions

Q1. What are the contributions mentioned in the paper "A compromise between the temperature difference and performance in a standing wave thermoacoustic refrigerator" ?

In this paper, the effect of different operating conditions on the thermo-acoustic performance of a standing wave thermoacoustic refrigerator was investigated.