Page 46 - Summer 2006

Echoes from Providence
Optimization of Miniature Thermoacoustic Coolers
Husam El-Gendy, Young Sang Kwon, Laurence Lyard and Orest G. Symko Department of Physics, University of Utah
Salt Lake City, Utah 84112
The ever increasing need for high-power density thermal management in various electronic devices and systems has motivated the development of miniature thermoacoustic coolers and heat pumps. A thermoacoustic approach is pre- sented here because it is relatively simple, it has very few mov- ing parts, it is quite efficient, and it can be applied to a wide range of systems needing thermal management; this work deals with the development of such a device.
Heat is pumped up a temperature gradient using an intense sound field inside a resonator. Cooling is produced because a sound field has inherent temperature oscillations which are caused by acoustic pressure variations; the temper- ature variations are thermally rectified using a stack of high surface area material, like cotton wool, placed in a resonator. A loud sound is produced by an acoustic driver which is cou- pled to the resonator. The stack is located inside the resonator at a position where the generated standing wave has a maxi- mum intensity. In order to have an operational cooler, a heat exchanger is thermally attached to each end of the stack. Thus heat will be absorbed from the cold heat exchanger and it will be pumped acoustically to the hot heat exchanger, where it is dissipated in air. In miniaturizing such a device the resonator length scales inversely with pumping frequency. It istypically~4cmfor4kHz,and7mmfor24kHz. Figure1 shows a schematic of a thermoacoustic refrigerator operating at approximately 4 kHz. Its cooling power density scales with the acoustic intensity produced by the driver in the resonator. Hence in the optimization of this device, it is essential to achieve high acoustic intensity. That is one of the goals of this project.
Figure 1 shows the acoustic driver coupled to a half-wave cylindrical resonator. The rate of heat extraction at the cold heat exchanger is QC and the rate of heat rejection at the hot heat exchanger is QH. The driver consists of a piezoelectric
element, in the bimorph configuration, which is impedance matched to the resonator by means of a light cone, firmly glued to a low impedance point of the piezo driver. Impedance matching can also be achieved by means of a Helmholtz resonator, tuned to the piezo driver. The stack, with a heat exchanger at each end, is located in the resonator at an axial position where sound intensity is maximum; it is approximately 3 mm long.
The cold heat exchanger, consisting of copper wire mesh, extends radially outside the resonator; thermal contact to the sample or device needing cooling is made there. The pumped heat and acoustic work are dissipated in the hot heat exchang- er, also made out of copper mesh. This heat exchanger is ther- mally anchored to copper or aluminum fins cooled convec- tively by air at ambient temperature. Since the hot heat exchanger can be a significant thermal bottleneck it is made out of two to four layers of copper mesh, soldered to the fin structure. The working gas in the cooler has usually been air, for convenience. Better performance can be achieved with helium gas or a gas mixture such as helium-argon.
Since the cooling power density of this device depends directly on the acoustic intensity inside the resonator, a special effort was taken to optimize this part of the cooler. An acoustic intensity of 160 dB can lead to a cooling power den- sity of 0.5 watt/cm2, using air at one atmosphere. In order to raise this level of cooling, as needed in many applications, the cooler was pressurized up to 15 atmospheres. This raises the cooling power accordingly. Increasing the working gas static pressure provides a better impedance match between the driv- er and working gas, thus raising the sound level for fixed elec- trical power input. In fact making the driver more efficient means that its power output can be reduced, thus extending its lifetime. Since the devices are small, the pressure of the work- ing gas can be raised to much higher levels than 15 atmos- pheres without exceeding the strength of materials.
Even though the piezoelectric driver is essentially a capacitor (but it is a lossy one), it does get heated up by two main mechanisms, electric hysteresis losses and mechanical straining on resonance, as well as Joule heating in input leads. This has two negative effects on the cooler in that there is a stray heat influx and that the sound level output saturates with electrical power input. The issue of impedance match- ing has been addressed again by coupling the piezo driver to a Helmholtz resonator which drives the cooler resonator. The advantages of such an arrangement are that the sound level is raised, the driver heating is contained within the hot part of the refrigerator, and there is a better defined standing wave inside the resonator. It is important to note that tuning to res- onance of all the elements in this unit is important for opti- mal performance.
Using a laser particle image velocimeter, streaming inside
44 Acoustics Today, July 2006