Engineering Acoustics/Thermoacoustics

Introduction

One ordinarily thinks of a sound wave as consisting only of coupled pressure and position oscillations. In fact, temperature oscillations accompany the pressure oscillations and when there are spatial gradients in the temperature oscillations, oscillating heat flow occurs. The combination of these oscillations produces a rich variety of “thermoacoustic” effects. In everyday life, the thermal effects of sound are too small to be easily noticed; for example, the amplitude of the temperature oscillation in conversational levels of sound is only about 0.0001°C. However, in an extremely intense sound wave in a pressurized gas, these thermoacoustic effects can be harnessed to create powerful heat engines and refrigerators. Whereas typical engines and refrigerators rely on crankshaft-coupled pistons or rotating turbines, thermoacoustic engines and refrigerators have no moving parts (or at most only flexing parts without the need for sliding seals). This simplicity, coupled with reliability and relatively low cost, has highlighted the potential of thermoacoustic devices for practical use. As a result, thermoacoustics is maturing quickly from a topic of basic scientific research through the stages of applied research and on to important practical applications[1]. Recently, thermoacoustic phenomena have been employed in the medical field for imaging of tissues.

History

The history of thermoacoustic engines is long but sparsely populated. A review of Putnam and Dennis[2] describes experiments of Byron Higgins[3] in 1777 in which acoustic oscillations in a large pipe were excited by suitable placement of a hydrogen flame inside. The Rijke tube[4], an early extension of Higgins' work, is well known to modern acousticians. Higgins' research eventually evolved into the modern science of pulse combustions[5] whose applications have included the German V-I rocket (the "buzz bomb") used in World War II and the residential pulse combustion furnace introduced by Lennox, Inc., in 1982. The Sondhaus tube is the earliest thermoacoustic engine that is a direct antecedent of the thermoacoustic prime movers. Over 100 years ago, glass blowers noticed that when a hot glass bulb was attached to a cool glass tubular stem, the stem tip sometimes emitted sound, and Sondhauss quantitatively investigated the relation between the pitch of the sound and the dimensions of the apparatus.

The English physicist, Lord Rayleigh explained the Sondhauss tube qualitatively in 1896: "In almost all cases where heat is communicated to a body, expansion ensues and this expansion may be made to do mechanical work. If the phases of the forces thus operative be favorable, a vibration may be maintained. For the sake of simplicity, a tube, hot at the closed end and getting gradually cooler towards the open end, may be considered. At a quarter of a period before the phase of greatest condensation, the air is moving inwards, i.e., towards the closed end, and therefore is passing from colder to hotter parts of the tube; but in fact the adjustment of temperature takes time, and thus the temperature of the air deviates from that of the neighboring parts of the tube, inclining towards the temperature of that part of the tube from which the air has just come. From this it follows that at the phase of greatest condensation heat is received by the air, and at the phase of greatest rarefaction heat is given up from it, and thus there is a tendency to maintain the vibrations."

The history of imposing acoustic oscillations on a gas to cause heat pumping and refrigeration effects is even briefer and more recent than the history of thermoacoustic prime movers. In a device called a pulse-tube refrigerator, Gifford and Longsworth produced significant refrigeration by applying a very low-frequency high-amplitude pressure oscillation to the gas in a tube. As they explained the phenomenon, "If any closed chamber is pressurized and depressurized by delivery and exhaustion of gas from one point on its surface and the flow is essentially smooth, heat pumping will occur away from the point on its surface," because of the temperature changes that accompany the pressure changes in the gas, and their time-phasing relative to the oscillatory gas flow.

Principle of operation

When a sound wave is sent down a half-wavelength tube with a vibrating diaphragm or a loudspeaker, the pressure pulsations make the gas inside slosh back and forth. This forms regions where compression and heating take place, plus other areas characterized by gas expansion and cooling.

A thermoacoustic refrigerator is a resonator cavity that contains a stack of thermal storage elements (connected to hot and cold heat exchangers) positioned so the back-and-forth gas motion occurs within the stack. The oscillating gas parcels pick up heat from the stack and deposit it to the stack at a different location. The device "acts like a bucket brigade" to remove heat from the cold heat exchanger and deposit it at the hot heat exchanger, thus forming the basis of a refrigeration unit. [1] The governing mathematical equations of the thermoacoustic phenomenon are given below.

Thermoacoustic machines

There are two basic kinds of thermoacoustic machines:

1. Thermoacoustic prime movers
2. Thermoacoustic refrigerator

Basic components of a thermoacoustic system

A thermoacoustic machine generally consists of:

1. Acoustic driver
2. Stack or regenerator
3. Heat exchanger
4. Resonator

Acoustic driver

Electrodynamic drivers are used in a class of electrically driven thermoacoustic refrigeration systems. The mechanical and electrical characteristics of the driver, in conjunction with the acoustic load impedance at the driver piston, determine the electroacoustic efficiency of the actuator. The electroacoustic efficiency is, of course, a key factor in the overall efficiency of the cooling system. For this reason, it is useful to develop models that allow the efficiency of any such driver to be predicted for varying operating conditions and loads. A detailed description of linear models of loudspeakers using equivalent electrical circuits is readily available.[2]

Equivalent electrical circuit of an electroacoustic driver

Several methods based on such linear models have been proposed in order to determine the model parameters experimentally.

Stack

In the thermoacoustic refrigerator the stack is the main component where the thermoacoustic phenomenon takes place. Below shown are two stacks of different materials used in a standing wave thermoacoustic refrigerator.

Heat exchanger

The heat exchangers employed in a thermoacoustic refrigerator influence the acoustic field created in the resonator. There are many design constraints such as porosity of the heat exchanger and high heat transfer coefficient for efficiency. Due to these constraints, special kind of heat exchangers are used. One typical micro channel aluminum heat exchanger is shown below.

Resonator

This the part of refrigerator which is only there for maintaining the acoustic wave. Because it is a dead volume which causes heat loss and adds bulk, quarter wavelength resonators are preferred over half wavelength.

References

1. Greg Swift et al.,"Thermoacoustics for Liquefaction of Natural Gas",LNG Technology.
2. L. L. Beranek, Acoustics, McGraw–Hill, New York.
3. R. W. Wakeland, ‘‘Use of electrodynamic drivers in thermoacoustic refrigerators,’’J. Acoust. Soc. Am. 107, 827–832,2000.