A compromise between the temperature difference and performance in a standing wave thermoacoustic refrigerator
Summary (3 min read)
- 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 .
- 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.
- 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,.
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Cites background from "A compromise between the temperatur..."
...…the role of the stack geometric parameters on the thermoacoustic refrigerator performance (N Atiqah Alamir 2017, 2019; Alamir and Elamer 2018; Alcock, Tartibu, and Jen 2017; Elnegiry, Eltahan, and Alamir 2016; Ibrahim, Omar, and Abdel-Rahman 2011; Napolitano, Romano, and Dragonetti 2017;…...
"A compromise between the temperatur..." refers background in this paper
...This cooling technology is now in the research and development process, and it is expected for noticeable spread commercially ....
"A compromise between the temperatur..." refers background or methods in this paper
...DeltaEC  was used as a verification tool for this algorithm....
...For each segment, DeltaEC has a more complicated momentum and continuity equations that include additional effects such as the viscous and thermal losses resulting from the acoustic power dissipation at the sides of ducts; however, the general form is as following :...
...The four unknown guesses are the unknown hot heat exchanger power required for each DeltaEC trial, the resonance frequency (which varies with the operating conditions and geometric parameters in each trial [6,21]), volume flow rate and the mean temperature ( that are dependent on the power of the acoustic driver , which is variant in this study) at the beginning segment....
...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....
"A compromise between the temperatur..." refers background in this paper
...Wetzel and Herman  developed an algorithm for thermoacoustic refrigerators....
...The thermal penetration depth is the gas layer thickness where heat is transferring through during half a cycle of vibrations :...
...Viscous penetration depth is the layer thickness where viscosity effect is observable across the boundaries :...
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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.