Essay: Investigations in thermoacoustic refrigeration

In this paper the various investigations in thermoacoustic refrigeration system are reviewed. Thermo acoustic refrigerator is a new type of energy conversion device, which can convert acoustic power into heat energy based on the thermo acoustic effect. Thermoacoustic refrigeration is an emerging refrigeration technology which does not require any moving parts or any environmentally harmful refrigerants in its operation. Various optimization techniques, different stack & resonator tube designs, various gases and other parameters are reviewed.

Keywords ‘Thermoacoustic refrigerator, Working fluid, Operating conditions, Performance

1. Introduction:
Since modern refrigeration technologies were introduced in the early 19th century, their use has significantly increased. In fact it is now almost impossible imagine life without refrigeration and air conditioning. Currently, cooling is primarily achieved with vapor compression machines that use a specific refrigerant that can be tailored to any required temperature level. To achieve these properties, blends of hydrogen, carbon, fluorine and chlorine in various mixing ratios are utilized. Depending on those ratios, the refrigerant exhibits a specific set of properties in regard to refrigeration, but also a global warming potential and ozone depletion potential. Since the adverse effects of those substances have been discovered, the field of refrigeration is moving away from conventional refrigerants, constantly searching for better alternatives. Thermoacoustic refrigeration is such an alternative that can provide cooling to essentially any required temperature level without using any environmentally harmful substances.
Thermoacoustic refrigeration is an emerging refrigeration technology which does not require any moving parts or harmful refrigerants in its operation. Loudspeakers or electro-dynamic shakers convert electrical power into acoustic power. This technology uses acoustic waves to pump heat across a temperature gradient. This is relatively easy to implement and can be relatively inexpensive. Since there are no moving parts, the system can be much more extensive and may have robust operational lifetime. Heat can be produced from sound waves. The concept of ‘thermoacoustic’ forms naturally when thinking about sound and temperature. Both phenomena involve the oscillation of particles. Sound is a pressure wave that transfers kinetic energy from one air molecule to the next using compression and expansion of the medium. By manipulating sound waves, it is fairly simple, at least in principle, to produce heat.
A thermoacoustic device uses a fluid medium (gas) to do work within the stack. The stack is a chamber with numerous linear sub-chambers connected to both ends where there are heat exchangers, one for hot and one for cold thermal energy. The sub-chambers are divided by plates whose spatial distances determine the area of heat flux caused by the working fluid. The fluid itself undergoes compression and expansion as it moves about these tunnels as a result of the sound waves passing. Given the correct frequency and wavelength of sound waves, the hot heat energy will be transported to one side of the stack and the cold heat to another, which allows for a refrigeration process. Thermo acoustic refrigerator is a new type of energy conversion device, which can convert acoustic power into heat energy based on the thermo acoustic effect. With the advantages of simple construction, stable operation and no harm to environment, it attracts lots of researcher’s attention. The theory of thermo acoustic has a great progress in recent decades. In addition, thermo acoustic refrigerator / engine have been applied in waste heat recovery.
2. Literature Review:
Currently, thermoacoustic technology is not as advanced as the vapour compression refrigeration system, which has experienced significant improvement since its conception over a century ago. As a result, there is much room for discovery in the field of thermoacoustic. Optimization techniques as a design aid are severely under-utilized, and previous efforts in thermoacoustic optimization are rare. The idea of using sound waves for cooling gained interest in the 1960s. Even though the physical explanation of this refrigeration technique is simple, analysis of the phenomenon and the equations that describe it are not simple. The discovery of the thermoacoustic phenomenon goes back to more than a century ago; however, the significant work in this area was started about three decades ago at the Los Alamos National Laboratory. They have developed different types of thermoacoustic refrigerators and heat engines swift G. M. et. al. [66] A few other research groups are also working in this area. However, the development of such devices is still at preliminary stages. The present work is divided in four different parts, first part is related to theoretical, numerical, analytical, software, etc. methods of optimization, second part is related to stack & resonator tube design, third part is related to gases and fourth one is miscellaneous in which loudspeaker, amplifier etc. are include.
2.1 Methods of optimization
Various researchers did their research on thermoacoustic field by using linear theoretical method, numerical method, analytical method, software etc. to optimize the thermoacoustic refrigerator. Huelsz et al. [67] found expressions for the phase difference, ??, between the temperature and pressure waves by using a single-plate, linear theory for the thermoacoustic phenomenon at ideal conditions (zero Prandtl number and infinite heat capacity for the plate). Piccolo et al. [53] presented a methodology to investigate the origin of the deviations of the predictions of the linear theory and compared them with the measured performances of a thermoacoustic device. Tijani et al. [51] explained in detail the designing criteria for thermoacoustic refrigerator in order to achieve an optimal system. They used the linear thermoacoustic theory to describe the design criteria. They used dimensionless independent variables to decrease the number of parameters and to simplify the equations. They established a method to obtain the optimum design of the different parts of the thermoacoustic refrigerator. Daming Sun et al. [21] explained optimization on theoretical analysis based on linear thermoacoustic, a novel Helmholtz resonator was proposed to increase the transmission ability of a thermoacoustic engine, which makes full use of the interaction between inertance and compliance effects. With this configuration, the output pressure amplitude of a thermoacoustic engine was amplified and the maximal pressure amplitude can occur at the end of the Helmholtz resonator tube with a length much shorter than 1/4 wavelength. Bheemsha et al. [15] explain the design and optimization of a thermo acoustic refrigerator by using the general linear theory of thermo acoustics, as a basis for the design taking simplified assumptions into consideration of the design. Optimization was carried out using MATLAB.
Waxier [56] studied the acoustic disturbance theoretically. He solved a complete set of time-averaged second-order equations of fluid dynamics of a viscous, thermally conducting fluid between closely spaced parallel plates, when the derivative of the temperature in the absence of the acoustic disturbance with respect to x (the direction of plate length) is not equal to zero. Herman and Wetzel [63] presented a methodology for estimating and designing the thermoacoustic refrigerator components to obtain an optimized device.
Benson et al. [57] simulated a thermoacoustic device and numerically investigated the unsteady flow and the temperature field in the vicinity of an idealized thermoacoustic refrigerator. The numerical model simulates the unsteady mass, momentum, and energy equations in the thin-plate, and low Mach-number limits. They also analyzed the variations of the thermal performance of the device against the heat exchanger length and position. Tijani et al. [47] described an analytical model of the interaction between a sound wave and a solid surface. They found that the thermal-relaxation dissipation at the gas is minimal whenever the temperature oscillations in the wall follow the temperature oscillations in the gas. They concluded that a tube material with the smallest possible combination KpCs (where K, p, Cs are thermal conductivity, density, and specific heat of stack, respectively) and a gas with the largest possible combination KgpgCp could minimize the thermal-relaxation losses. Hadi Babaei et al. [26] illustrated a comprehensive design and optimization algorithm was developed for designing thermoacoustic devices. The unique feature of the algorithm was its ability to design thermo acoustically-driven thermoacoustic refrigerators that can serve as sustainable refrigeration systems.
K. Ghorbanian et al. [1] design and optimization of a heat driven thermoacoustic refrigerator. A simplified model was developed which enables to pinpoint and examine the most important physical characteristics of a compact traveling wave thermoacoustic refrigerator driven by a traveling wave thermoacoustic engine. The position, length and hydraulic radius of the refrigerator were optimized for the maximum total COP. The prime mover efficiency, refrigerator COP and dimensionless dissipation and their impacts on total COP are also investigated. N.M. HARIHARAN et al. [4] optimized the parameters like frequency, stack position, stack length, and plate spacing involving in designing TAR using the Response Surface Methodology (RSM). They also developed a mathematical model RSM based on the results obtained from DeltaEC software.
Parametric studies have been utilized to estimate the effect of design parameters on device performance. Zoontjens et al. [46] illustrated the optimization of internal sections of thermoacoustic devices. Upon closer inspection, they used DeltaE to vary individual parameters to determine optimal designs. J. A. Lycklama a Nijeholt et al. [30] presented a two dimensional computational fluid dynamics (CFD) simulation study of a traveling wave thermoacoustic engine. Raspect et al. [62] used the finite difference method to solve the equations of thermoacoustic refrigerator, thermoacoustic engine and Stirling regimes. They assumed short stack and linear temperature gradient across the stack. They solved the equations for both standing and traveling wave and compared the results with the measured values. Bheemsha et al. [16] explained the design of a resonator and buffer volume for a Thermo Acoustic Refrigerator, modeling was done by using CATIA and optimization of the design was carried out using MATLAB.

2.2 Stack & Resonator tube
A long hollow tube is called as ‘resonance tube’ or simply ‘resonator’; a solid porous material is called stack. Tijani et al. [51] studied the effect of plate spacing and plate geometry in the stack on the performance of the device. Tijani et al. [30] attempted to optimize the stack spacing. They recommended a maximum pressure of 12 atms. Earlier, it was found that the refrigerator could sustain about 1.5 atms only. In order to maintain higher pressure and to obtain greater effectiveness, many aspects of the thermoacoustic refrigeration system, namely the construction materials used, different array for the stack, etc. would have to be altered.
N.M. Hariharan et al. [2] analysed the performance of thermoacoustic refrigerator (TAR) measured in terms of hot end temperature and temperature difference across refrigerator stack with two different spacing namely 0.4 mm and 0.8 mm and stack used in refrigerating section was made of low thermal conductivity materials namely Mylar sheet and photographic film & the experiments were carried out at 1 MPa pressure using helium as working fluid. High powered acoustic wave with frequency of 460 Hz and pressure amplitude of 0.07 MPa was obtained from twin thermoacoustic prime mover (TAPM) and this acoustic wave produced temperature difference of 160C across the Mylar sheet stack made of 0.4 mm spacing in refrigerator section N.M. Hariharan et al. [7] illustrates the influence of stack parameters such as plate thickness (PT) and plate spacing (PS) with resonator length on the performance of thermoacoustic engine, which measured in terms of onset temperature difference, resonance frequency and pressure amplitude using air as a working fluid.

Ishikawa and David [50] numerically investigated the influence of the stack plate length when the plate spacing is greater than the thermal penetration depth. They observed that there was a heat-pumping effect on the long and short plates compared with the particle displacement length of the acoustic standing wave. Further, the energy dissipation close to the plates increases quadratically with the particle displacement and they found no heat transfer when the plate spacing was equal to the thermal penetration depth. M.M. Bassem et al. [12] illustrated numerical optimization of regenerator radius and its position, and the performance of the optimized refrigerator was measured.
Ishakawa et al. [65] obtained a relationship between the size of the hot and cold exchangers and entropy generation rates in a thermoacoustic device and the temperature differences along the regenerator stack and their location in the resonator. They found that the heat transfer effect is more important than the viscous effect in the quick decrease of the entropy generation. In their study, they found that the size of the heat exchanger at the hot side of the regenerator stack should be smaller than that at the cold side. Biwa et al. [52] measured the phase angle dependence of the cooling power of a Gifford-McMahon refrigerator for the regenerator spherical particles with different diameters.
Wetzel and Herman [60] used a combination of holographic interferometry and high-speed cinematography to visualize and quantify the temperature fields in the vicinity of stack plate located between pressure and velocity nodes of an acoustic standing wave. They found that the heat is transferred either from the working fluid to the plate or vice versa. They measured the heat fluxes transferred from the colder fluid to the hot stack plate at the edge of a single stack plate and they investigated the difference between heat transfer in a steady forced convection and oscillatory flow. Pierrick Lotton et al. [24] used linear theory to calculate the thermal quantities inside the stack in the classical thermoacoustic refrigerators. Hadi Babaei et al. [17] illustrated the modified theoretical model of thermoacoustic couples to incorporate more realistic physical processes that are acoustic dissipation within the stack, and the heat exchange between the stack and its surroundings.
Reid et al. [59] used a thermoacoustic refrigerator with a steady flow parallel to the thermoacoustic oscillations passing through the stack, in order to compare numerical studies with the experimental results for the stack temperature profile and the cooling power. Emmanuel C. Nsofor et al. [31] studied the oscillatory flow heat transfer at the heat exchanger of the thermoacoustic refrigeration system. The results from the experimental study were correlated in terms of Nusselt number, Prandtl number and Reynolds number to obtain a useful new correlation for the heat transfer at the heat exchangers. Results show that using straight flow heat transfer correlations for analyses and design of this system could result in significant errors. Results also show the relationship between the oscillatory heat transfer coefficient at the heat exchangers, the mean pressure and frequency of oscillation. Higher mean pressures result in greater heat transfer coefficients if the thermoacoustic refrigerating system operates at the corresponding resonant frequency.
A. Amjadi et al. [29] designed and constructed a simple thermoacoustic refrigerator with an adjustable mechanical resonator, coupled with the acoustic resonator. Their experimental data showed about 10 % increase in the efficiency of the refrigeration in comparison with a simple thermoacoustic refrigerator with no mechanical resonator. Emmanuel C. Nsofor et al. [23] did Experimental study on the performance of the thermoacoustic refrigerating system, the resonator was constructed from aluminum tubing but it had plastic tube lining on the inside to reduce heat loss by conduction. Significant factors that influence the performance of the system were identified. The cooling produced increases with the temperature difference between the two ends of the stack. High pressure in the system does not necessarily result in a higher cooling load. There exists an optimum pressure and an optimum frequency for which the system should be operated in order to obtain maximum cooling load.
Both Wetzel [60] and Besnoin [57] discussed optimization of thermoacoustic devices in their work. Wetzel targeted the optimal performance of a thermoacoustic refrigerator and Besnoin targeted the heat exchangers respectively. Pressure is one of the adjustable parameters. It has been proven that the temperature difference across stacks can be increased (to a certain extent) by increasing the internal average pressure for Helium. Wetzwl et al. considered geometric parameters and fluid properties of the system and a simplex algorithm to search for the optimal solution. However, in order to account for the thermoacoustic operating conditions, DeltaE was used extensively.
Insu Paek et al. [19] did experiment on a working prototype thermoacoustic refrigerator based on linear thermoacoustic theory which operated with and without water flow through the heat exchangers, their result showed that the coefficient of performance may be significantly reduced when the stack temperature profile becomes non-linear, i.e. when the system is operated for a temperature span smaller than the optimal value for a given stack length. N.M. Hariharan et al. [3] design and fabricate the twin thermoacoustic heat engine (TAHE) producing the acoustic waves with high resonance frequencies which were used to drive a thermoacoustic refrigerator efficiently by the influence of geometrical parameters and working fluids. Twin TAHE has gained significant attention due to the production of high intensity acoustic waves than single TAHE. Its performance was analyzed by varying the resonator length and working fluid. The performance was measured in terms of onset temperature difference, resonance frequency and pressure amplitude of the oscillations generated from twin TAHE. The simulation is performed using software DeltaE.
Florian Zink et al. [20] illustrates the optimization of stack by FEM method, while taking into account thermal losses to the surroundings. A. Piccolo [11] illustrated a simplified two-dimensional computational method for studying the entropy generation characteristics inside the core porous structures of a thermoacoustic refrigerator. The model integrates the equations of the standard linear thermoacoustic theory into an energy balance-based numerical calculus scheme. The numerically computed spatial distributions of the time-averaged entropy generation rate within a channel of the stack and adjoining heat exchangers evidence as the stack- heat exchangers junctions act as strong sources of thermal irreversibility. The study also shows as, for a fixed refrigerating output level and temperature span, minimum in entropy generation could be effectively used as a suitable design criterion for optimizing simultaneously the stack length, the stack position and the plates interspacing. The same method, when applied to the optimization of the heat exchangers, reveals that the length of the heat exchangers along the direction of the acoustic vibration should be comprised between x1 (the amplitude of the acoustic displacement) and 2×1, the optimal value resulting an increasing function of the fin interspacing and of the drive ratio.

2.3 Gases
The Ozone-depleting Substances Regulations were made under the Environmental Protection Act (EPA). It is in line with The Montreal Protocol, which is an international agreement, signed by 165 countries to control the production and exchange of certain ozone-depleting substances. The Regulations control the import, export, transit shipment, manufacture, use, sale and offer for sale of any HCFCs or products that contain or are intended to contain HCFCs. Under these Regulations, the manufacturing and import of many products that contain HCFCs have been prohibited since July 1, 1999, and the offers for sale and sale of many products that contain HCFCs have been restricted since January 1, 2000. No environmentally hazardous refrigerants are needed and only inert gases that are environmentally safe and suitable are used. The international restriction on the use of CFC (chlorofluorocarbon) and skepticism over the replacements of CFC, gives thermoacoustic devices a considerable advantage over traditional refrigerators. The gases used in these devices are (e.g. helium, xenon, air) harmless to the ozone and have no greenhouse effect. It is expected that in the near future, regulations will be tougher on the greenhouse gases. The awareness about the destructive effects of CFC on the ozone depletion and the banning of the CFC’s production, lead the researchers to find an alternative solution to this problem.
Garret et al. [68] developed a new spacecraft cryocooler, which uses resonant high-amplitude sound waves in inert gases to pump heat, which was used in the space shuttle Discovery. Tijani et al. [54] achieved temperature as low as -65 ??C in their thermoacoustic device. They used it to study the effect of some important thermoacoustic parameters, such as the Prandtl number by using binary gas mixture. Jin et al. [48] studied thermoacoustic phenomenon in a pulse tube refrigerator. They used a thermoacoustic prime mover to create an acoustic wave to drive the refrigerator. They studied the characteristics of the thermoacoustic prime mover and the effect of working fluid i.e. helium and different percentage of helium- argon mixture, on the thermoacoustic refrigerator. They achieved a cryogenic temperature of 120 K in their experiments. Sakamoto et al. [46] conducted experiments on a thermoacoustic cooler consisting of acoustic loop-tube with two stacks inside. Stack 1 was employed as a prime mover and stack 2 as a heat pump. They used the mixture of air and helium gas at the atmospheric pressure as the working fluid. They observed a temperature drop of approximately 16 ??C. They also found that the self-sustained sound had higher harmonics which lowered the efficiency of the system.
R. C. Dhuley and M. D. Atrey [14] investigated the effect of two operating parameters, the resonant frequency and charging pressure on the dynamic pressure inside a thermoacoustic refrigerator, because the dynamic pressure inside a Thermoacoustic Refrigerator (TAR) is an important parameter which governs the cold temperature and the cooling power. S. H. Tasnim et al. [9] did the study on a numerical investigation of the effects of variation in working fluids and operating conditions on the performance of a thermoacoustic refrigerator. The performance of a thermoacoustic refrigerator was evaluated based on the cooling power, coefficient of performance (COP), and the entropy generation rate within the device. The effect of the variation of the working fluid was observed by changing the Prandtl number.

2.4 loud speaker, microphone, amplifier etc
Bailliet et al. [58] measured the acoustic power flow in the resonator of a thermoacoustic refrigerator by using Laser Doppler Anemometry (L.D.A) together with microphone acoustic pressure measurement. They found good agreement between the experimental and theoretical results Symko et al. [44] used thermoacoustic refrigerator and prime mover to remove heat from an electronic circuit. They drove the thermoacoustic devices at frequencies between 4-24 kHz and investigated the performance of the devices. Jebali et al. [42] analyzed experimentally the performance of a thermoacoustic refrigerator subjected to variable loading and compared the experimental data with the computed data. In their experiments, the hot heat exchanger was maintained at ambient temperature and the temperature of the cold heat exchanger was varied to achieve temperature differences of 0.5 and 10 K along the stack. They measured and calculated cooling load for these temperature differences while varying the driving frequency between 30 and 65 Hz.
Florian Zink et al. [20] suggested more powerful speaker to obtain more acoustic power and the worked on operating frequency to run the device. Kamran Siddiqui et al. [28] investigated the velocity fields of an acoustic standing wave in a rectangular channel, also determined the effect of variation of certain refrigerator parameters on pressure amplitudes. K. Tang et al. [22] explained the Influence of acoustic pressure amplifier dimensions on the performance of a standing-wave thermoacoustic system. Kang Huifang et al. [25] investigated the synthetical optimization of hydraulic radius and acoustic field which is characterized by the ratio of the traveling wave component to the standing wave component. They also discussed the heat flux, cooling power, temperature gradient and coefficient of performance of thermoacoustic cooler with different combinations of hydraulic radiuses and acoustic fields.
Andrew C. Trapp [13] illustrates the mathematical programming model to optimize the performance of a simple Thermoacoustic heat engines. Wongee Chun et al. [8] were analyzed and studied Sound waves and acoustic energy generated by two identical TA (Thermo Acoustic) lasers. SPL (Sound Pressure Level) meters and microphones were employed to measure and study the sound waves at different distances from the openings of the TA laser pair for different laser position arrangements. The sound waves of the two TA lasers at or near the focusing point were found to be almost 1800 out of phase when the distance between the openings of the two lasers was within about two tube diameters and the angle between the laser axes did not exceed 1350. As the distance increased, it became difficult to control the two TA lasers in synchronized operation. For separation distances greater than three times tube diameter, the sound wave amplitudes and the phase difference between the two laser outputs varied periodically with time. With the openings of the two TA lasers touching each other, the frequency of the sound waves increased when the angle between the laser axes was very close to 1800. In this case, the glass tube opening was no longer a pressure anti-node and the wavelength of the fundamental mode reduced to approximately twice the tube length.
Na Pan et al. [5] did experiment on forced oscillation driven by loudspeaker and compared with self-excited oscillation. Also Impacts of driving frequency and power on onset temperature were discussed. And their results show that forced oscillation has a higher selectivity for driving frequency. The self-excited oscillation frequency (fundamental frequency) was the optimal choice to drive thermoacoustic engine in practical application. The lowest onset temperature was gradually achieved with the increase of driving power. Pressure amplitude was mainly affected by the onset temperature. The lower the onset temperature was, the smaller the pressure amplitude. Their work provided a guide for the selection of driving signal in practical application.
Na Pan and Chao Shen [6] illustrated the interaction between thermal convection and acoustic oscillation with different driving powers. The temperature and velocity distributions of thermoacoustic core between the hot and cooling heat exchangers were measured by Thermal Infrared Imager and Particle Image Velocimetry (PIV) at 205 Hz, which is the resonance frequency of thermoacoustic engine. And also suggested that the acoustic oscillation has a significant effect on the thermal convection and the heat transfer is enhanced with the perturbation of acoustic streaming.
Florian Zink et al. [18] illustrates the benefits of thermoacoustic technology with a consideration of its Total Equivalent Warming Impact (TEWI) compared to conventional cooling in vehicles, which was shown to be a potential target application. Also, additional target applications are suggested.
Thermoacoustic refrigerator is a device that operates efficiently by using sound waves, environmentally friendly and non-flammable gases, and is suitable for handling residential refrigeration needs. The thermoacoustic refrigerator has only no moving part, and is relatively simple and inexpensive to construct and operate. Thermoacoustic refrigerators tend to be compact and lightweight, and contain no harmful refrigerants, which make them environmentally friendly. This aspect will make it a very appealing option in the future.
This is by no means complete list of the optimization of thermoacoustic refrigeration system components, but it is an overview of optimization targets. Each work is undoubtedly a valuable addition to the thermoacoustic community, but these should not be considered optimizations in the classical sense, but are rather parametric studies. In all likelihood, each optimal design is a local optimum as the optimization performed by each group can be considered with one variable only while maintaining other parameters the same.

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