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Experimental study of the temperature variations in a standing wave loudspeaker driven thermoacoustic refrigerator
Accepted Manuscript Experimental Study of the Temperature Variations in a Standing Wave Loudspeaker Driven Thermoacoustic Refrigerator Mahmoud A. Alamir PII: DOI: Article Number: Reference:
S2451-9049(19)30135-0 https://doi.org/10.1016/j.tsep.2019.100361 100361 TSEP 100361
To appear in:
Thermal Science and Engineering Progress
Received Date: Revised Date: Accepted Date:
30 March 2019 27 May 2019 27 May 2019
Please cite this article as: M.A. Alamir, Experimental Study of the Temperature Variations in a Standing Wave Loudspeaker Driven Thermoacoustic Refrigerator, Thermal Science and Engineering Progress (2019), doi: https:// doi.org/10.1016/j.tsep.2019.100361
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Experimental Study of the Temperature Variations in a Standing Wave Loudspeaker Driven Thermoacoustic Refrigerator
Mahmoud A. Alamir * College of Science and Engineering, Flinders University, Clovelly Park, Adelaide, SA 5042, Australia. *
[email protected] ; [email protected] Tel.: +61 451052313
Highlights A standing wave loudspeaker driven thermoacoustic refrigerator is tested. Temperature variations through the resonator and its cross sections are studied. The temperature variations affect the performance of the refrigerator considerably. The effect of the stack parameters on the temperature difference is investigated.
1
Abstract The temperature difference across the stack is essential to the performance of thermoacoustic refrigerators. This paper experimentally investigates the effect of the stack geometric parameters on the temperature difference across the stack in a standing wave loudspeaker driven thermoacoustic refrigerator. In addition, it investigates the temperature variations through the resonator and its cross-sections. The effect of this variability on the performance of the refrigerator is also presented. Celcor Ceramic stacks are used at five normalised stack positions of 0.286, 0.764, 1.05, 1.43 and 1.72, four normalised stack lengths of 0.076, 0.114, 0.153 and 0.191, and two stack porosities of 0.8 and 0.85. Results show that the maximum and minimum temperatures through the resonator are across the stack, particularly at the centre point of each side of the stack. Moreover, at certain stack positions, hot and cold sides across the stack are altered. The coefficient of performance also increases at high-temperature difference positions. As a result, this study provides guidelines for increasing the performance of thermoacoustic refrigerators, which still lack competitiveness because of their relatively low performance. It also helps design some parts such as heat exchangers to consider the maximum and minimum temperature positions of thermoacoustic refrigerators.
Keywords: Thermoacoustic refrigeration, Temperature difference, Optimisation algorithms, Oscillatory heat transfer, Heat exchangers.
1. Introduction In many parts of the world, energy and environmental problems are rising considerably. Therefore, optimised performance of energy conversion systems is needed.
Moreover,
conventional vapour compression cycles can affect the ozone layer negatively due to the refrigerants used [1]. Recent years have seen an increasingly rapid interest in thermoacoustic refrigeration for its many advantages including the use of environment-friendly working fluids, the controlled cooling capacity, the simple design, and the quiet operation [2,3]. This technology is under research and development, and its commercial spread is expected [4]. 2
In thermoacoustic refrigerators, sound waves pump heat from a low-temperature source to a high-temperature sink. A schematic diagram of a simple standing wave thermoacoustic refrigerator driven by a loudspeaker is shown in Fig. 1. An acoustic driver (e.g. loudspeaker or linear motor) transmits the acoustic wave to the resonator with the desired frequency and power, produced from the function generator and the amplifier, respectively. Then, the acoustic wave produces hot and cold temperature areas through the resonator due to the high and lowpressure areas, respectively. Therefore, the stack in the resonator can keep a temperature gradient across its sides. Finally, two heat exchangers are positioned across the stack for the heat transfer. Insert Fig. 1 about here. The interest of improvements in thermoacoustic systems has rapidly increased. As a result, design and optimization algorithms for thermoacoustic devices have been developed [5]. For example, the algorithm developed by Wetzel and Herman [6] specified the total consumed power in this optimisation algorithm for the thermoacoustic refrigerator. Tijani [7] tested a loudspeaker driven thermoacoustic refrigerator. A flow-chart was also presented to optimise these refrigerators by following the normalised stack length and position effect on the performance. Babaei and Siddiqui [8] also investigated an optimisation algorithm for the thermoacoustic devices by balancing the energy and entropy in thermoacoustic devices. Other types of genetic algorithms were also used such as the General Algebraic Modelling Systems (GAMS) [9] and teaching-learning-based optimisation algorithm [10]. However, problems can be found with these optimisation algorithms. For example, they could disregard optimising important operating conditions such as the resonance frequency [11] and not compromise high temperature difference conditions and performance [12]. Other problems include the theoretical background used as the basic linear theory equations developed Rott and Swift [13] are used. They can be different from the equations of real systems with different components. Other problems could be incapability to track real temperature variations inside the refrigerator. This work contributes to identifying the variability of the temperature inside the refrigerator and its effect on the performance. 3
The stack affects the performance of thermoacoustic refrigerators substantially [11,14–20]. Zolpakar et al. [14] showed that the geometric parameters of the stack had a major role in determining the temperature difference across the stack. The effect of the stack parameters on the temperature difference and the cooling effect was experimentally investigated by Tartibu [15]. The stack positions close to the pressure antinode had the maximum performance. Yahya et al. [16] experimentally studied the thermal performance of some stack materials for developing low-cost materials of thermoacoustic refrigerators. The steel wool stacks gave the highest performance. Despite the importance of these studies, the studies of the stack geometric parameters, that show the temperature variations through the resonator and the effect of these variations on performance, still need further investigations. The studies about temperature variations have mainly focused on its change across the stack. However, the temperature distribution across the resonator and at the same cross-section of the resonator can also be helpful. This is because the performance can be optimised depending on the variability of the temperature. Also, a better understanding of the temperature distribution through the resonator can help develop the design of some components, such as heat exchangers, to give the maximum performance. Therefore, the present study shows the temperature variations through the resonator and at the cross sections of a standing wave loudspeaker driven thermoacoustic refrigerator. In addition, it investigates the change of the temperature difference across the stack with different geometric parameters. The effect of this variability on the performance is also presented. The current study provides some important insights into how the temperature varies through the resonator, at the cross sections, and with the stack geometric parameters and how this variability affects the performance of the thermoacoustic refrigerator.
4
2. Thermoacoustic refrigerator design The design parameters of the thermoacoustic refrigerator are nineteen parameters. Therefore, Wetzel et al. [6] developed a normalised analysis for the thermoacoustic design parameters to be used in thermoacoustic equations, as shown in Table 1. However, the stack porosity in Table 1 is for the parallel plate stack. The stack porosity for other stack types can be obtained by dividing the stack gas volume to the total stack volume as follows, 𝑉𝑔
𝐵=𝑉
𝑡𝑜𝑡
(3)
Insert Table 1 about here. The design presented in this paper is a standing wave loudspeaker driven thermoacoustic refrigerator. The refrigerator is designed based on the steps presented by Tijani [7]. The heat exchangers are not included in the current setup. Despite the importance of heat exchangers, the design of the current study is to investigate the temperature variability and its effect on the performance of the refrigerator. Considering the heat exchangers could block the flow and decrease the performance [17]. Therefore, a simplified design without heat exchangers is used.
5
3. Experimental set-up An experimental test rig of a standing wave loudspeaker driven thermoacoustic refrigerator is built as shown in Fig. 2. It consists of three main parts: the resonator, the stack, and the loudspeaker. Insert Fig. 2 about here. The resonator is a circular tube made from PVC (K = 0.19 W/m. K), has a diameter of 50 mm (2 inches) and a length of 850 mm. A PVC cap is used at one end of the resonator, while the other end has a cone with diameters of 2 and 6-inch made from stainless steel acting as an area reducer so that the resonator of 2-inch diameter can be connected to the 6-inch loudspeaker. The total length of the PVC resonator and the steel area reducer is one meter. A loudspeaker creates the thermoacoustic effect inside the resonator and has a diameter of 6 Inch. The air is the working gas, and it is at a mean pressure of 1 bar through the experiments. A rubber O-ring is used between the steel area reducer and the loudspeaker to prevent the leakage of air. Using a function generator from the type (MCP SG 1638N), the required frequency is transmitted to the resonator. An electrical amplifier receives the low voltage signal from the function generator to amplify it to the required loudspeaker input signal. A DC power supply from the type (Zhaoxin RXN-303D) is also used to feed an input voltage of 12 volts to the amplifier. For the estimation of the power delivered to the loudspeaker, a digital voltmeter (EZ DM–441B type) and an ammeter (Excel 9205A type) measure the input voltage and current, respectively. A Celcor Ceramic stack is used (K = 0.45 W/m. K, ρ = 1500 kg/m3, cp = 1060 J/kg. K). A schematic diagram and a photograph are shown in Fig. 3 for the cross-section of the stack used. The stack is at five normalised stack positions of 0.286, 0.764, 1.05, 1.43 and 1.72, four normalised stack lengths of 0.076, 0.114, 0.153 and 0.191, and two porosities of 0.8 and 0.85. Eight stacks are presented in these experiments, four with a porosity of 0.8 and the other four with a porosity of 0.85. Insert Fig. 3 about here. 6
The temperature is measured by K-type thermocouples which have an accuracy of ± 0.1 °C. They are connected to a temperature recorder (Yokogawa µR 180). Thermocouples at six positions of 150, 300, 450, 550, 700 and 850 mm from the loudspeaker are fitted into the resonator to show the temperature distribution through the resonator as shown in Fig. 4. The temperature inside the resonator is measured by eighteen thermocouples. Three thermocouples are divided at each position in the longitudinal direction, as shown in Fig. 5. Insert Fig. 4 and Fig. 5 about here. Microphones, from the type of LM 393, measure the amplitude pressure. The oscilloscope (Velleman type) receives the signal from the microphones and delivers it to a personal computer, which contains a program (PC lab 2000) to view the signal. An analysis of the error and relative errors for the quantities measured has been done as shown in table 2. In this analysis, the error and relative error of a measurement quantity (X) are calculated using Eqn. 4 and 5, where the measurement quantity depends on variables X1, X2, X3, ..., Xn. 𝜕𝑋
2
𝜕𝑋
2
𝜕𝑋
2
𝜕𝑋
2 1/2
𝐸𝑋 = [ (𝜕𝑥 𝐸1 ) + ( 𝜕𝑥 𝐸2 ) + ( 𝜕𝑥 𝐸3 ) … … … … + ( 𝜕𝑥 𝐸𝑛 ) ] 1
2
𝐸𝑋𝑟 =
𝐸𝑋 𝑋
3
× 100 %
Insert table. 2 about here.
7
𝑛
(4) (5)
4. Results and discussion 4.1.
Frequency effect
The thermoacoustic refrigerator should be working at the resonance frequency, which gives the maximum temperature difference across the stack. As indicated in Fig. 6, it is clear that for the current system and the shown geometric parameters, the resonance frequency is at 105 Hz. Recently, Alamir [11] showed that a fine step of the frequency should be changed to obtain an accurate resonance frequency. Fig. 6a supports these results and suggests that the temperature difference across the stack at 105 Hz is nearly 13.6 % higher than the temperature difference at 103 Hz and 107 Hz. The measurements of the coefficient of performance showed that it is 0.377 at 105 Hz; 9.3% higher than the performance at 103 Hz. An interesting result is obtained for the resonance frequency of the stack position, Xsn= 0.286 as shown in Fig. 6b. The resonance frequency occurs at 165 Hz, which is significantly different at the stack position, Xsn= 1.72. This may be related to the temperature field distribution, viscous and thermal losses near the loudspeaker and the length of the resonator in which the particles propagate. It can also be noted that a high-temperature difference is obtained at this resonance frequency as compared to other frequencies. Insert Fig. 6 about here.
4.2.
Steady state operation
The experiments run until a steady state temperature across the stack ends is obtained as shown in Fig. 7. The steady state is achieved when the thermal losses are in an equilibrium state with the generating heat flux inside the resonator. Slower steady state at 600s is reached for the normalised stack position (Xsn = 1.72) which has a high-temperature difference than the normalised stack position (Xsn = 1.43) at 300s which has a low-temperature difference. Insert Fig. 7 about here.
4.3.
Input power effect
The input power is directly proportional to the input oscillating pressure, which is also directly proportional to the temperature difference as shown in Fig. 8. An electric power of 9 W (D = 8
0.0017 at f = 105 Hz) is used at a time of 600s for the whole of the following results to ensure the comparability between them.
4.4.
Temperature across the stack
The temperature distribution at positions shown in Fig. 5 at each stack side can be shown in Fig. 9. It is clear that the temperature varies across the same cross-section. In addition, the maximum and minimum temperatures are obtained at the centre points of the hot and cold sides of the stack (Positions 1 and 4), respectively. This may be explained because of the insulation losses near the resonator top ends. The coefficient of performance, at the centre points of the stack, is 0.299 which is 23.2% higher than the performance at the high ends of the stack (Positions 2 and 5) and 17.3% at the side ends of the stack (Positions 3 and 6). Accordingly, it is important to deal with this issue in many aspects, such as when designing the heat exchangers of thermoacoustic refrigerators. Insert Fig. 8 and Fig. 9 about here.
4.5.
Temperature through the resonator
The temperature can be varied through the hot and cold areas of the resonator. The effect of the temperature change is investigated through the hot and cold areas of the resonator to show the temperature change at different thermocouple positions through the resonator and at the same cross-section. Fig. 10 shows changes in the temperature across the six positions shown in Fig. 4. The maximum heating and cooling areas are across the stack at positions X3 and X4 for the hot and cold areas, respectively. This confirms that heat exchangers should be positioned across the stack positions. Also, a temperature gradient exists across the ends of the stack sides. This may be due to poor insulation of the PVC material used for the resonator. Further experimental studies can investigate the effect of the resonator material on this temperature gradient.
4.6.
Effect of the stack geometric parameters
The stack geometric parameters (i.e. stack porosity, normalised stack length, and normalised stack position) can affect the temperature difference across the stack as demonstrated in Fig. 11. 9
The thermal and viscous penetration depths can be significantly influenced by the stack porosity, and hence the temperature difference across the stack is changed [12]. In addition, the stack is the part where the gas particles interact with the stack surface. The temperature difference is therefore affected by the stack length. The pressure changes across the resonator in a sine wave, and consequently the temperature changes through the resonator length according to the pressure variations. In addition, the stack position near the resonator closed end, Xsn = 1.72, always gives a higher temperature difference across the stack. This may be because of the friction and viscous losses near the loudspeaker. The maximum temperature difference across the stack is 26.6 °C. This is obtained at a normalised stack length, Lsn = 0.191, and a porosity, B = 0.8. These conditions give the highest coefficient of performance in the current study of 0.377. Moreover, the temperature difference across the stack becomes with negative values at normalised stack positions varying from 0.25 to 0.5. The temperature difference is zero at these positions, after that the hot and cold sides across the stack are changed. This phenomenon may be explained that the distribution characteristics of the acoustic wave change through the resonator in a sine waveform. The coefficient of performance is high at the far ends from the loudspeakers, as shown in Fig. 12 for the normalised stack length, Lsn = 0.191. These results are in agreement with the results of Tartibu [15]. Insert Fig. 11 and Fig. 12 about here.
5. Conclusions An experimental study is presented to show the temperature variations in a standing wave loudspeaker driven thermoacoustic refrigerator. The temperature changes across the resonator and at the same cross-section of the resonator. Moreover, the maximum temperature difference occurs across the stack, particularly at the centre point of each stack side. Furthermore, the coefficient of performance is correlated with this temperature variability. In particular, the
10
increase in the temperature difference increases the performance. Therefore, the temperature variability should be considered for the high performance of thermoacoustic refrigerators. In this experiment, eight Celcor Ceramic stacks with different lengths, porosities and positions are used. For the current design of the thermoacoustic refrigerator, a normalised stack position of 1.72 gives the maximum temperature difference across the stack at a normalised stack length of 0.191, and a stack porosity of 0.8. In addition, normalised stack positions from 0.25 to 0.5 change the hot and cold side across the stack. The operating conditions affect the performance of thermoacoustic refrigerators. In this study, increasing the input electric power increases the temperature difference across the stack. A maximum temperature difference across the stack of 26.6 °C can be achieved. The operating frequency should also be adjusted finely to reach the resonance frequency at which a higher performance can be obtained. The present study has gone some way towards enhancing our understanding of the temperature distribution through the resonator of a standing wave loudspeaker driven thermoacoustic refrigerator. This can help increase the performance and develop parts of thermoacoustic refrigerators, such as heat exchangers, to take into account the maximum and minimum temperature positions. Careful consideration for the positions of high-temperature differences yields a high performance of the thermoacoustic refrigerator. Moreover, the stack geometric parameters and operating conditions can have a substantial effect on the temperature distribution through the resonator. A trade-off between the geometric parameters, operating conditions, and variability of the temperature difference across the stack is, therefore, highly recommended for optimised performance of thermoacoustic refrigerators.
Acknowledgements Generous advice given by Dr Ahmed Elamer, a senior lecturer at Brunel University London, has been a great help in this work. My special thanks are also extended to the staff of engineering workshops and electronic labs at Mansoura University for their help in setting up the experiments.
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Nomenclature Subscripts
Latin Letters A
Area, [m2 ]
B
Porosity, …
c
Specific heat, [kJ/ (kg. K)]
D
Drive ratio, …
f
Frequency, [Hz]
K
Thermal conductivity, [W/ (m. K)]
L
Length, [m]
l
The half plate thickness, [mm]
P
Pressure, [Pa]
T
Temperature, [K]
V
Volume, [m3 ]
X
Stack position, [m]
yo
Half stack spacing, [mm]
ambient Ambient or surrounding
Thermal penetration depth, [m]
δv
Viscous penetration depth, [m]
µ
Dynamic viscosity, [Pa. s]
ρ
Fluid density, [kg/m3 ]
ω
Angular frequency, [rad/s]
∆T
Temperature Difference, [K]
Cold
g
Gas
h
Hot
hex
Heat exchanger
k
Thermal
m
Mean
n
Normalised
o
Greek Letters δk
c
12
Oscillating
p
At constant pressure
s
Stack
v
Viscous
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[3]
Brown J, Domanski P. Review of alternative cooling technologies. Appl Therm Eng 2014;64:252–62.
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[6]
Wetzel M, Herman C. Design optimization of thermoacoustic refrigerators. Int J Refrig 1997;20:3–21.
[7]
Tijani M. Loudspeaker-driven thermo-acoustic refrigeration. 2001.
[8]
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[9]
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[10]
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[11]
Alamir MA. Experimental Study of the Stack Geometric Parameters Effect on the Resonance Frequency of a Standing Wave Thermoacoustic Refrigerator. Int J Green Energy 2019.
[12]
Alamir MA, Elamer AA. A compromise between the Temperature Difference and Performance in a Standing Wave Thermoacoustic Refrigerator. Int J Ambient Energy 13
2018;0750:1–13. doi:10.1080/01430750.2018.1517673. [13]
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[15]
Tartibu LK. Maximum cooling and maximum efficiency of thermoacoustic refrigerators. Heat Mass Transf Und Stoffuebertragung 2016;52:95–102. doi:10.1007/s00231-015-1599y.
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Yahya S, Mao X, Jaworski A. Experimental investigation of thermal performance of random stack materials for use in standing wave thermoacoustic refrigerators. Int J Refrig 2017;75:52–63.
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Elnegiry E, Eltahan H, Alamir M. Optimizing the performance of a standing wave loudspeaker driven thermoacoustic heat pump. Int J Sci Eng Res 2016;7:460–5.
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Table 1 Normalised parameters of the thermoacoustic refrigerator. Normalised design requirements
Geometric parameters 𝛿𝑘 2𝑦0
Normalised thermal penetration depth
𝛿𝑘𝑛 =
Normalised temperature difference
∆𝑇𝑚𝑛 =
Drive ratio
𝐷=
Normalised stack length
∆𝑇𝑚 𝑇𝑚
Normalised stack position
𝑃0 𝑃𝑚
Blockage ratio or porosity
𝐿𝑠 𝜆⁄ 2𝜋 𝑋𝑠 𝑋𝑠𝑛 = 𝜆⁄ 2𝜋 𝑦0 𝐵= 𝑦0 + 𝑙 𝐿𝑠𝑛 =
Table 2 Absolute and relative errors of the measured parameters. Parameter
Absolute Error
Relative Error
Temperature Difference
0.14142 °C
0.532 %
Amplitude Pressure
1 Pa
0.04 %
Frequency
0.1 Hz
0.1 %
Cooling Load
0.0018 W
0.0416 %
Power
0.1855 W
2.06 %
Performance
0.01
2.08 %
Function Generator
AC
Amplifier
Hot Heat Exchanger AC
Cold Heat Exchanger
Loudspeaker
Stack
Xs
Fig. 1. A schematic diagram of a simple standing wave thermoacoustic refrigerator.
15
1
AC
2
9
8
11
3
10
7 4
5
6
13
E
14
12
12
(a)
(b) 1. Function generator 5. Steel reducer 9. Temperature recorder 13. Microphone
2. Power supply 6. PVC resonator 10. PC Oscilloscope 14. Rubber O-ring
3. Power amplifier 4. Loudspeaker 7. R.M.S. measurement (type 1) 8. R.M.S. measurement (type 2) 11. Personal computer 12. Wooden holder
Fig. 2. The built thermoacoustic refrigerator (a) Schematic diagram (b) Photograph.
16
Plates Spacing
Plate thickness
50 mm
Ls
(a)
(b) Fig. 3. The cross-section of the stack (a) Diagram (b) Photograph.
100 cm 85 cm 70 cm
X1
X2
X3
X4
X5
15 cm 30 cm 45 cm
55 cm
Fig. 4. Thermocouples positions through the resonator.
17
X6
10 mm
TC2
TC3
TC5
TC6
TC1
TC4
50 mm
Fig. 5. Thermocouple positions at each cross-section of the stack end.
30 25 20 15
Temperature Difference, K
10 5 0 0
100
200
300
400
500
(a) 10 8 6 4 2 0 0
50
100
150
200
Frequency, Hz (b) Fig. 6. The frequency effect on the temperature difference across the stack at B = 0.8, Lsn = 0.191 and two normalized stack positions (a) Xsn = 1.72 (b) Xsn = 0.286.
18
40
35
30
25
Temperature, ◦C
20
15
(a) 40
35
30
25
20 0
200
400
600
800
1000
1200
Time, s (b) Fig. 7. Steady state operation at B = 0.8, Lsn = 0.191 and two normalized stack positions (a) Xsn = 1.72 (b) Xsn = 1.43.
19
30
B = 0.8, Lsn = 0.191, Xsn = 1.72, f = 105 Hz
Temperature Difference, K
25 20 15
10 5 0 0
1
2
3 4 5 6 7 Input Electric Power, W
8
9
10
Fig. 8. The temperature difference versus the power input. 40
Lsn = 0.191, Xsn = 0.96 , f = 105 Hz
Temperature, ◦C
36 32
T1 T3 T5
28
T2 T4 T6
24 20 0
200
400
600 Time, s
800
1000
1200
Fig. 9. The temperature changes at each side of the stack with time. 30
Lsn = 0.191, Xsn = 0.96, f = 90 Hz
Temperature, ◦C
29 28 27 TC1 TC2 TC3
26 25 24 0
100
200
300
400
500
600
700
800
900
Resonator Length, mm
Fig. 10. The temperature distribution through the resonator at a frequency, f = 90 Hz.
20
Fig. 11. The effect of the normalised stack position on the temperature difference at different normalised stack lengths. 0.4
Coefficient of performance
0.35 0.3 0.25 0.2 0.15 B=0.8
0.1
B=0.85
0.05 0
0
0.5
1
1.5
2
Normalised stack position, Xsn
Fig. 12. The coefficient of performance at different normalised stack positions at normalised stack length, Lsn = 0.191.
21
Conflict of Interest The author declares no conflicts of interests.
22
S2451-9049(19)30135-0 https://doi.org/10.1016/j.tsep.2019.100361 100361 TSEP 100361
To appear in:
Thermal Science and Engineering Progress
Received Date: Revised Date: Accepted Date:
30 March 2019 27 May 2019 27 May 2019
Please cite this article as: M.A. Alamir, Experimental Study of the Temperature Variations in a Standing Wave Loudspeaker Driven Thermoacoustic Refrigerator, Thermal Science and Engineering Progress (2019), doi: https:// doi.org/10.1016/j.tsep.2019.100361
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental Study of the Temperature Variations in a Standing Wave Loudspeaker Driven Thermoacoustic Refrigerator
Mahmoud A. Alamir * College of Science and Engineering, Flinders University, Clovelly Park, Adelaide, SA 5042, Australia. *
[email protected] ; [email protected] Tel.: +61 451052313
Highlights A standing wave loudspeaker driven thermoacoustic refrigerator is tested. Temperature variations through the resonator and its cross sections are studied. The temperature variations affect the performance of the refrigerator considerably. The effect of the stack parameters on the temperature difference is investigated.
1
Abstract The temperature difference across the stack is essential to the performance of thermoacoustic refrigerators. This paper experimentally investigates the effect of the stack geometric parameters on the temperature difference across the stack in a standing wave loudspeaker driven thermoacoustic refrigerator. In addition, it investigates the temperature variations through the resonator and its cross-sections. The effect of this variability on the performance of the refrigerator is also presented. Celcor Ceramic stacks are used at five normalised stack positions of 0.286, 0.764, 1.05, 1.43 and 1.72, four normalised stack lengths of 0.076, 0.114, 0.153 and 0.191, and two stack porosities of 0.8 and 0.85. Results show that the maximum and minimum temperatures through the resonator are across the stack, particularly at the centre point of each side of the stack. Moreover, at certain stack positions, hot and cold sides across the stack are altered. The coefficient of performance also increases at high-temperature difference positions. As a result, this study provides guidelines for increasing the performance of thermoacoustic refrigerators, which still lack competitiveness because of their relatively low performance. It also helps design some parts such as heat exchangers to consider the maximum and minimum temperature positions of thermoacoustic refrigerators.
Keywords: Thermoacoustic refrigeration, Temperature difference, Optimisation algorithms, Oscillatory heat transfer, Heat exchangers.
1. Introduction In many parts of the world, energy and environmental problems are rising considerably. Therefore, optimised performance of energy conversion systems is needed.
Moreover,
conventional vapour compression cycles can affect the ozone layer negatively due to the refrigerants used [1]. Recent years have seen an increasingly rapid interest in thermoacoustic refrigeration for its many advantages including the use of environment-friendly working fluids, the controlled cooling capacity, the simple design, and the quiet operation [2,3]. This technology is under research and development, and its commercial spread is expected [4]. 2
In thermoacoustic refrigerators, sound waves pump heat from a low-temperature source to a high-temperature sink. A schematic diagram of a simple standing wave thermoacoustic refrigerator driven by a loudspeaker is shown in Fig. 1. An acoustic driver (e.g. loudspeaker or linear motor) transmits the acoustic wave to the resonator with the desired frequency and power, produced from the function generator and the amplifier, respectively. Then, the acoustic wave produces hot and cold temperature areas through the resonator due to the high and lowpressure areas, respectively. Therefore, the stack in the resonator can keep a temperature gradient across its sides. Finally, two heat exchangers are positioned across the stack for the heat transfer. Insert Fig. 1 about here. The interest of improvements in thermoacoustic systems has rapidly increased. As a result, design and optimization algorithms for thermoacoustic devices have been developed [5]. For example, the algorithm developed by Wetzel and Herman [6] specified the total consumed power in this optimisation algorithm for the thermoacoustic refrigerator. Tijani [7] tested a loudspeaker driven thermoacoustic refrigerator. A flow-chart was also presented to optimise these refrigerators by following the normalised stack length and position effect on the performance. Babaei and Siddiqui [8] also investigated an optimisation algorithm for the thermoacoustic devices by balancing the energy and entropy in thermoacoustic devices. Other types of genetic algorithms were also used such as the General Algebraic Modelling Systems (GAMS) [9] and teaching-learning-based optimisation algorithm [10]. However, problems can be found with these optimisation algorithms. For example, they could disregard optimising important operating conditions such as the resonance frequency [11] and not compromise high temperature difference conditions and performance [12]. Other problems include the theoretical background used as the basic linear theory equations developed Rott and Swift [13] are used. They can be different from the equations of real systems with different components. Other problems could be incapability to track real temperature variations inside the refrigerator. This work contributes to identifying the variability of the temperature inside the refrigerator and its effect on the performance. 3
The stack affects the performance of thermoacoustic refrigerators substantially [11,14–20]. Zolpakar et al. [14] showed that the geometric parameters of the stack had a major role in determining the temperature difference across the stack. The effect of the stack parameters on the temperature difference and the cooling effect was experimentally investigated by Tartibu [15]. The stack positions close to the pressure antinode had the maximum performance. Yahya et al. [16] experimentally studied the thermal performance of some stack materials for developing low-cost materials of thermoacoustic refrigerators. The steel wool stacks gave the highest performance. Despite the importance of these studies, the studies of the stack geometric parameters, that show the temperature variations through the resonator and the effect of these variations on performance, still need further investigations. The studies about temperature variations have mainly focused on its change across the stack. However, the temperature distribution across the resonator and at the same cross-section of the resonator can also be helpful. This is because the performance can be optimised depending on the variability of the temperature. Also, a better understanding of the temperature distribution through the resonator can help develop the design of some components, such as heat exchangers, to give the maximum performance. Therefore, the present study shows the temperature variations through the resonator and at the cross sections of a standing wave loudspeaker driven thermoacoustic refrigerator. In addition, it investigates the change of the temperature difference across the stack with different geometric parameters. The effect of this variability on the performance is also presented. The current study provides some important insights into how the temperature varies through the resonator, at the cross sections, and with the stack geometric parameters and how this variability affects the performance of the thermoacoustic refrigerator.
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2. Thermoacoustic refrigerator design The design parameters of the thermoacoustic refrigerator are nineteen parameters. Therefore, Wetzel et al. [6] developed a normalised analysis for the thermoacoustic design parameters to be used in thermoacoustic equations, as shown in Table 1. However, the stack porosity in Table 1 is for the parallel plate stack. The stack porosity for other stack types can be obtained by dividing the stack gas volume to the total stack volume as follows, 𝑉𝑔
𝐵=𝑉
𝑡𝑜𝑡
(3)
Insert Table 1 about here. The design presented in this paper is a standing wave loudspeaker driven thermoacoustic refrigerator. The refrigerator is designed based on the steps presented by Tijani [7]. The heat exchangers are not included in the current setup. Despite the importance of heat exchangers, the design of the current study is to investigate the temperature variability and its effect on the performance of the refrigerator. Considering the heat exchangers could block the flow and decrease the performance [17]. Therefore, a simplified design without heat exchangers is used.
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3. Experimental set-up An experimental test rig of a standing wave loudspeaker driven thermoacoustic refrigerator is built as shown in Fig. 2. It consists of three main parts: the resonator, the stack, and the loudspeaker. Insert Fig. 2 about here. The resonator is a circular tube made from PVC (K = 0.19 W/m. K), has a diameter of 50 mm (2 inches) and a length of 850 mm. A PVC cap is used at one end of the resonator, while the other end has a cone with diameters of 2 and 6-inch made from stainless steel acting as an area reducer so that the resonator of 2-inch diameter can be connected to the 6-inch loudspeaker. The total length of the PVC resonator and the steel area reducer is one meter. A loudspeaker creates the thermoacoustic effect inside the resonator and has a diameter of 6 Inch. The air is the working gas, and it is at a mean pressure of 1 bar through the experiments. A rubber O-ring is used between the steel area reducer and the loudspeaker to prevent the leakage of air. Using a function generator from the type (MCP SG 1638N), the required frequency is transmitted to the resonator. An electrical amplifier receives the low voltage signal from the function generator to amplify it to the required loudspeaker input signal. A DC power supply from the type (Zhaoxin RXN-303D) is also used to feed an input voltage of 12 volts to the amplifier. For the estimation of the power delivered to the loudspeaker, a digital voltmeter (EZ DM–441B type) and an ammeter (Excel 9205A type) measure the input voltage and current, respectively. A Celcor Ceramic stack is used (K = 0.45 W/m. K, ρ = 1500 kg/m3, cp = 1060 J/kg. K). A schematic diagram and a photograph are shown in Fig. 3 for the cross-section of the stack used. The stack is at five normalised stack positions of 0.286, 0.764, 1.05, 1.43 and 1.72, four normalised stack lengths of 0.076, 0.114, 0.153 and 0.191, and two porosities of 0.8 and 0.85. Eight stacks are presented in these experiments, four with a porosity of 0.8 and the other four with a porosity of 0.85. Insert Fig. 3 about here. 6
The temperature is measured by K-type thermocouples which have an accuracy of ± 0.1 °C. They are connected to a temperature recorder (Yokogawa µR 180). Thermocouples at six positions of 150, 300, 450, 550, 700 and 850 mm from the loudspeaker are fitted into the resonator to show the temperature distribution through the resonator as shown in Fig. 4. The temperature inside the resonator is measured by eighteen thermocouples. Three thermocouples are divided at each position in the longitudinal direction, as shown in Fig. 5. Insert Fig. 4 and Fig. 5 about here. Microphones, from the type of LM 393, measure the amplitude pressure. The oscilloscope (Velleman type) receives the signal from the microphones and delivers it to a personal computer, which contains a program (PC lab 2000) to view the signal. An analysis of the error and relative errors for the quantities measured has been done as shown in table 2. In this analysis, the error and relative error of a measurement quantity (X) are calculated using Eqn. 4 and 5, where the measurement quantity depends on variables X1, X2, X3, ..., Xn. 𝜕𝑋
2
𝜕𝑋
2
𝜕𝑋
2
𝜕𝑋
2 1/2
𝐸𝑋 = [ (𝜕𝑥 𝐸1 ) + ( 𝜕𝑥 𝐸2 ) + ( 𝜕𝑥 𝐸3 ) … … … … + ( 𝜕𝑥 𝐸𝑛 ) ] 1
2
𝐸𝑋𝑟 =
𝐸𝑋 𝑋
3
× 100 %
Insert table. 2 about here.
7
𝑛
(4) (5)
4. Results and discussion 4.1.
Frequency effect
The thermoacoustic refrigerator should be working at the resonance frequency, which gives the maximum temperature difference across the stack. As indicated in Fig. 6, it is clear that for the current system and the shown geometric parameters, the resonance frequency is at 105 Hz. Recently, Alamir [11] showed that a fine step of the frequency should be changed to obtain an accurate resonance frequency. Fig. 6a supports these results and suggests that the temperature difference across the stack at 105 Hz is nearly 13.6 % higher than the temperature difference at 103 Hz and 107 Hz. The measurements of the coefficient of performance showed that it is 0.377 at 105 Hz; 9.3% higher than the performance at 103 Hz. An interesting result is obtained for the resonance frequency of the stack position, Xsn= 0.286 as shown in Fig. 6b. The resonance frequency occurs at 165 Hz, which is significantly different at the stack position, Xsn= 1.72. This may be related to the temperature field distribution, viscous and thermal losses near the loudspeaker and the length of the resonator in which the particles propagate. It can also be noted that a high-temperature difference is obtained at this resonance frequency as compared to other frequencies. Insert Fig. 6 about here.
4.2.
Steady state operation
The experiments run until a steady state temperature across the stack ends is obtained as shown in Fig. 7. The steady state is achieved when the thermal losses are in an equilibrium state with the generating heat flux inside the resonator. Slower steady state at 600s is reached for the normalised stack position (Xsn = 1.72) which has a high-temperature difference than the normalised stack position (Xsn = 1.43) at 300s which has a low-temperature difference. Insert Fig. 7 about here.
4.3.
Input power effect
The input power is directly proportional to the input oscillating pressure, which is also directly proportional to the temperature difference as shown in Fig. 8. An electric power of 9 W (D = 8
0.0017 at f = 105 Hz) is used at a time of 600s for the whole of the following results to ensure the comparability between them.
4.4.
Temperature across the stack
The temperature distribution at positions shown in Fig. 5 at each stack side can be shown in Fig. 9. It is clear that the temperature varies across the same cross-section. In addition, the maximum and minimum temperatures are obtained at the centre points of the hot and cold sides of the stack (Positions 1 and 4), respectively. This may be explained because of the insulation losses near the resonator top ends. The coefficient of performance, at the centre points of the stack, is 0.299 which is 23.2% higher than the performance at the high ends of the stack (Positions 2 and 5) and 17.3% at the side ends of the stack (Positions 3 and 6). Accordingly, it is important to deal with this issue in many aspects, such as when designing the heat exchangers of thermoacoustic refrigerators. Insert Fig. 8 and Fig. 9 about here.
4.5.
Temperature through the resonator
The temperature can be varied through the hot and cold areas of the resonator. The effect of the temperature change is investigated through the hot and cold areas of the resonator to show the temperature change at different thermocouple positions through the resonator and at the same cross-section. Fig. 10 shows changes in the temperature across the six positions shown in Fig. 4. The maximum heating and cooling areas are across the stack at positions X3 and X4 for the hot and cold areas, respectively. This confirms that heat exchangers should be positioned across the stack positions. Also, a temperature gradient exists across the ends of the stack sides. This may be due to poor insulation of the PVC material used for the resonator. Further experimental studies can investigate the effect of the resonator material on this temperature gradient.
4.6.
Effect of the stack geometric parameters
The stack geometric parameters (i.e. stack porosity, normalised stack length, and normalised stack position) can affect the temperature difference across the stack as demonstrated in Fig. 11. 9
The thermal and viscous penetration depths can be significantly influenced by the stack porosity, and hence the temperature difference across the stack is changed [12]. In addition, the stack is the part where the gas particles interact with the stack surface. The temperature difference is therefore affected by the stack length. The pressure changes across the resonator in a sine wave, and consequently the temperature changes through the resonator length according to the pressure variations. In addition, the stack position near the resonator closed end, Xsn = 1.72, always gives a higher temperature difference across the stack. This may be because of the friction and viscous losses near the loudspeaker. The maximum temperature difference across the stack is 26.6 °C. This is obtained at a normalised stack length, Lsn = 0.191, and a porosity, B = 0.8. These conditions give the highest coefficient of performance in the current study of 0.377. Moreover, the temperature difference across the stack becomes with negative values at normalised stack positions varying from 0.25 to 0.5. The temperature difference is zero at these positions, after that the hot and cold sides across the stack are changed. This phenomenon may be explained that the distribution characteristics of the acoustic wave change through the resonator in a sine waveform. The coefficient of performance is high at the far ends from the loudspeakers, as shown in Fig. 12 for the normalised stack length, Lsn = 0.191. These results are in agreement with the results of Tartibu [15]. Insert Fig. 11 and Fig. 12 about here.
5. Conclusions An experimental study is presented to show the temperature variations in a standing wave loudspeaker driven thermoacoustic refrigerator. The temperature changes across the resonator and at the same cross-section of the resonator. Moreover, the maximum temperature difference occurs across the stack, particularly at the centre point of each stack side. Furthermore, the coefficient of performance is correlated with this temperature variability. In particular, the
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increase in the temperature difference increases the performance. Therefore, the temperature variability should be considered for the high performance of thermoacoustic refrigerators. In this experiment, eight Celcor Ceramic stacks with different lengths, porosities and positions are used. For the current design of the thermoacoustic refrigerator, a normalised stack position of 1.72 gives the maximum temperature difference across the stack at a normalised stack length of 0.191, and a stack porosity of 0.8. In addition, normalised stack positions from 0.25 to 0.5 change the hot and cold side across the stack. The operating conditions affect the performance of thermoacoustic refrigerators. In this study, increasing the input electric power increases the temperature difference across the stack. A maximum temperature difference across the stack of 26.6 °C can be achieved. The operating frequency should also be adjusted finely to reach the resonance frequency at which a higher performance can be obtained. The present study has gone some way towards enhancing our understanding of the temperature distribution through the resonator of a standing wave loudspeaker driven thermoacoustic refrigerator. This can help increase the performance and develop parts of thermoacoustic refrigerators, such as heat exchangers, to take into account the maximum and minimum temperature positions. Careful consideration for the positions of high-temperature differences yields a high performance of the thermoacoustic refrigerator. Moreover, the stack geometric parameters and operating conditions can have a substantial effect on the temperature distribution through the resonator. A trade-off between the geometric parameters, operating conditions, and variability of the temperature difference across the stack is, therefore, highly recommended for optimised performance of thermoacoustic refrigerators.
Acknowledgements Generous advice given by Dr Ahmed Elamer, a senior lecturer at Brunel University London, has been a great help in this work. My special thanks are also extended to the staff of engineering workshops and electronic labs at Mansoura University for their help in setting up the experiments.
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Nomenclature Subscripts
Latin Letters A
Area, [m2 ]
B
Porosity, …
c
Specific heat, [kJ/ (kg. K)]
D
Drive ratio, …
f
Frequency, [Hz]
K
Thermal conductivity, [W/ (m. K)]
L
Length, [m]
l
The half plate thickness, [mm]
P
Pressure, [Pa]
T
Temperature, [K]
V
Volume, [m3 ]
X
Stack position, [m]
yo
Half stack spacing, [mm]
ambient Ambient or surrounding
Thermal penetration depth, [m]
δv
Viscous penetration depth, [m]
µ
Dynamic viscosity, [Pa. s]
ρ
Fluid density, [kg/m3 ]
ω
Angular frequency, [rad/s]
∆T
Temperature Difference, [K]
Cold
g
Gas
h
Hot
hex
Heat exchanger
k
Thermal
m
Mean
n
Normalised
o
Greek Letters δk
c
12
Oscillating
p
At constant pressure
s
Stack
v
Viscous
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Table 1 Normalised parameters of the thermoacoustic refrigerator. Normalised design requirements
Geometric parameters 𝛿𝑘 2𝑦0
Normalised thermal penetration depth
𝛿𝑘𝑛 =
Normalised temperature difference
∆𝑇𝑚𝑛 =
Drive ratio
𝐷=
Normalised stack length
∆𝑇𝑚 𝑇𝑚
Normalised stack position
𝑃0 𝑃𝑚
Blockage ratio or porosity
𝐿𝑠 𝜆⁄ 2𝜋 𝑋𝑠 𝑋𝑠𝑛 = 𝜆⁄ 2𝜋 𝑦0 𝐵= 𝑦0 + 𝑙 𝐿𝑠𝑛 =
Table 2 Absolute and relative errors of the measured parameters. Parameter
Absolute Error
Relative Error
Temperature Difference
0.14142 °C
0.532 %
Amplitude Pressure
1 Pa
0.04 %
Frequency
0.1 Hz
0.1 %
Cooling Load
0.0018 W
0.0416 %
Power
0.1855 W
2.06 %
Performance
0.01
2.08 %
Function Generator
AC
Amplifier
Hot Heat Exchanger AC
Cold Heat Exchanger
Loudspeaker
Stack
Xs
Fig. 1. A schematic diagram of a simple standing wave thermoacoustic refrigerator.
15
1
AC
2
9
8
11
3
10
7 4
5
6
13
E
14
12
12
(a)
(b) 1. Function generator 5. Steel reducer 9. Temperature recorder 13. Microphone
2. Power supply 6. PVC resonator 10. PC Oscilloscope 14. Rubber O-ring
3. Power amplifier 4. Loudspeaker 7. R.M.S. measurement (type 1) 8. R.M.S. measurement (type 2) 11. Personal computer 12. Wooden holder
Fig. 2. The built thermoacoustic refrigerator (a) Schematic diagram (b) Photograph.
16
Plates Spacing
Plate thickness
50 mm
Ls
(a)
(b) Fig. 3. The cross-section of the stack (a) Diagram (b) Photograph.
100 cm 85 cm 70 cm
X1
X2
X3
X4
X5
15 cm 30 cm 45 cm
55 cm
Fig. 4. Thermocouples positions through the resonator.
17
X6
10 mm
TC2
TC3
TC5
TC6
TC1
TC4
50 mm
Fig. 5. Thermocouple positions at each cross-section of the stack end.
30 25 20 15
Temperature Difference, K
10 5 0 0
100
200
300
400
500
(a) 10 8 6 4 2 0 0
50
100
150
200
Frequency, Hz (b) Fig. 6. The frequency effect on the temperature difference across the stack at B = 0.8, Lsn = 0.191 and two normalized stack positions (a) Xsn = 1.72 (b) Xsn = 0.286.
18
40
35
30
25
Temperature, ◦C
20
15
(a) 40
35
30
25
20 0
200
400
600
800
1000
1200
Time, s (b) Fig. 7. Steady state operation at B = 0.8, Lsn = 0.191 and two normalized stack positions (a) Xsn = 1.72 (b) Xsn = 1.43.
19
30
B = 0.8, Lsn = 0.191, Xsn = 1.72, f = 105 Hz
Temperature Difference, K
25 20 15
10 5 0 0
1
2
3 4 5 6 7 Input Electric Power, W
8
9
10
Fig. 8. The temperature difference versus the power input. 40
Lsn = 0.191, Xsn = 0.96 , f = 105 Hz
Temperature, ◦C
36 32
T1 T3 T5
28
T2 T4 T6
24 20 0
200
400
600 Time, s
800
1000
1200
Fig. 9. The temperature changes at each side of the stack with time. 30
Lsn = 0.191, Xsn = 0.96, f = 90 Hz
Temperature, ◦C
29 28 27 TC1 TC2 TC3
26 25 24 0
100
200
300
400
500
600
700
800
900
Resonator Length, mm
Fig. 10. The temperature distribution through the resonator at a frequency, f = 90 Hz.
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Fig. 11. The effect of the normalised stack position on the temperature difference at different normalised stack lengths. 0.4
Coefficient of performance
0.35 0.3 0.25 0.2 0.15 B=0.8
0.1
B=0.85
0.05 0
0
0.5
1
1.5
2
Normalised stack position, Xsn
Fig. 12. The coefficient of performance at different normalised stack positions at normalised stack length, Lsn = 0.191.
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Conflict of Interest The author declares no conflicts of interests.
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