Thermoacoustic refrigerators : experiments and scaling analysis

Thermoacoustics, as the word spelling indicates, is an interdisciplinary field in physics. Both acoustics and thermodynamics are involved in the description of this interesting phenomenon. When a solid wall is present in direction of the wave vector of an acoustic field, the interaction between the wall and the acoustic wave generates a transfer of heat from one location of the wall to another. This mechanism can be used to drive so called standing- or traveling-wave type of refrigerators and heat pumps. This is possible provided that instead of a solid wall a heat transfer medium which essentially is a porous plug, is applied to increase the effective surface area for the heat transport. Such a porous plug is known as stack for standing wave type of apparatus, and regenerator in the case of traveling wave type of apparatus. When the mechanism is used in the reverse way - an applied temperature gradient along a wall - , an acoustic wave is generated spontaneousley by the interaction between the sound wave and a solid. This is possible provided that the temperature gradient exceeds a certain critical value, and by properly designing a resonator and stack geometry to amplify one specific frequency. With a mechanic-electric converter a so called, prime mover power generator can be made. When a regenerator, which has a much smaller pore size than the stack, is employed in an acoustic network, the Stirling cycle can be realized. The so-called traveling-wave type refrigerators or engines are machines that use thermoacoustic effects to realize the Stirling cycle. The advantages of thermoacoustic machines over conventional refrigerators and engines, such as no moving parts, environment-friendly, and high reliability, make thermoacoustic apparatus of interest for future applications. Much work has been done on larger-scale (1 - 25 meter) thermoacoustic machines in the past decades. With the growing demand for small scale cooling devices in for instance laptop computers, mobile phones, and satellites, development of miniature refrigerators draws more and more attention. This PhD work is therefore dedicated to the analysis of miniaturization of thermoacoustic refrigerators. Both types: standing-wave and traveling-wave are investigated. An introduction and historical review on thermoacoustics is given in chapter 1. In chapter 2, the linear thermoacoustic theory is reviewed. The main content of chapter 3 is about modeling of standing-wave systems and validation of the modeling by investigation of a standing-wave type apparatus, which is similar to the so-called "TAC" (thermoacoustic couple). At the end of chapter 3, the measurements are analyzed and compared with computations based on proposed modeling. Chapter 4 is devoted to modeling traveling-wave systems and model validation by experiments. An analytical model for a complete traveling-wave system of refrigerator is developed. After that, the optimization of regenerator material is considered. Various regenerator materials: metal honeycomb and ceramic honeycomb with different channel shapes, stainless steel wire screens in different hydraulic radii and porosities, were applied in a coaxial traveling-wave engine to characterize their performance. The metal honeycombs gave partially because of their larger cell size a poor performance, the ceramic honeycoms have an improved performance, and the best performance was measured with the stainless steel wire screens. The measurements of ceramic honeycombs and stainless steel wire screens showed that there is an optimum value for the dimensionless hydraulic radius (the ratio of hydraulic radius to a reference thermal penetration depth), which is around 0.3 for stainless steel wire screen regenerators and 0.16-0.2 for square cell honeycombs. The efficiency goes up with increasing porosity, to a maximum value above which the heat capacity of the solid becomes the limiting factor. The conclusion for stainless steel wire screen regenerators is also in agreement with the theoretical prediction by using the proposed analytical model. A full traveling-wave refrigerator driven by a mechanical compressor was designed and built. This system is again aiming at the validation of the model with measurements. The theoretical computation showed an acceptable agreement with measurements. In chapter 5, the analytical models for standing-wave systems (developed in chapter 3) and traveling-wave systems (developed in chapter 4) are utilized to characterize the performance in scaling down. By inserting three different scaling factors: , , , into the analytical models, the cooling power and efficiency of scaling down systems are obtained. The results show that the scaling behaviour of a standing-wave system is the same as that of a traveling-wave system. The cooling power in the scaled-down system consists of two groups of energy flow scaling with different factors: one group of energy flow scales with a factor , whereas the conduction loss scales as . Apparently, the conduction loss term decreases less than the other one and results in a reduced cooling power. So the efficiency decreases rapidly in scaling down. The term, which is the product of the scaling factor and the original ratio of energy losses due to thermal conduction to acoustic work, causes the reduction of efficiency after scaling down. The unified scaling behaviour of standing-wave and traveling-wave systems points out that the thermal conduction loss will finally dominate the losses and becomes the limitation factor for scaling down. We hope that the future design of mini-thermoacoustic-machine will benefit from this finding to reduce the conduction loss, finally to develop smaller (<5 cm) and more powerful thermoacoustic refrigerators.