Thermoacoustic Refrigerators


A thermoacoustic refrigerator (TAR) is a refrigerator that uses sound waves in order to provide the cooling. In a TAR, the working fluid is a helium-argon mixture, and the compressor is replaced by a loudspeaker. The advantages of this kind of refrigeration cycle are two-fold.

  • The helium and argon are inert, environmentally friendly gases, unlike many of the common refrigerants.
  • The loudspeaker is a simple device that is more durable than a compressor and is the TAR’s only moving part.

The downside of the TAR is that as of yet these types of refrigerators have failed to achieve efficiencies as high as those as standard refrigeration units. Some researchers contend that the set-up of the TAR is such that it never will be able to attain efficiencies as high as standard refrigeration units. Others believe that there is no reason that a TAR can’t achieve efficiencies as high as standard refrigeration units. They attribute the currently lower efficiencies to the peculiar sensitivity of the TAR to input parameters and the relative youth of the field in general.

Different Types of TARs

There are two types of TARs. The first is known as a standing wave thermoacoustic refrigerator. The second is a traveling wave (or pulse tube) thermoacoustic refrigerator. The standing wave TAR uses a fixed number of oscillations with nodes that remain unchanged over time. In other words, the wave of as a whole does not move over time, remaining stationary. This is similar to a situation where you take a string and fixed two ends and then pluck it. Because of the fixed ends the wave of the string remains fixed in place.

The traveling wave TAR, as it sounds like, makes use of a wave of sound that travels across the TAR. This is analogous to the situation where you take the string and flick it forward like a whip. The disturbance of the whip creates a sound wave that sends the wave forward. Each type of TAR has specific advantages in certain situations, and research is being done into cascading combinations of standing wave and traveling wave TARS to try to take advantage of these varying advantages.

Standing Wave TAR

The standing wave TAR is similar to a Stirling cycle, which is dependent on pressure oscillations that occur out of phase with each other. The standing wave TAR is composed of 5 major components all incased in a tube of some kind. On one end is the loudspeaker. This then leads to a configuration of a stack with a hot heat exchanger on one side and a cold heat exchanger on the other side. The combination of these three components is called “the stack”. The stack is composed of a large number of thin, parallel plates with only small openings between them. Finally, on the other end of the stack is a bulb known as the resonator.

The purpose of the loudspeaker is to supply work to the system in the form of sound waves (this takes the place of the compressor in a standard refrigeration cycle). The purpose of the stack is to actually take advantage of the oscillating gas such as to cause heat transfer from the cold heat exchanger to the hot heat exchanger. The purpose of the resonator is to maintain a particular frequency as a standing wave. Each of these components is important to the TAR; however, resonators and loudspeakers are common devices in acoustics in general. It is the stack that is unique to the TAR and is also probably the most complex component.

The Stack

How Heat is Transferred

The stack is composed of many narrow passages separated by thin plates. It is oscillation of the gas within these plates that causes the heat transfer. To understand how this occurs, imagine a small parcel of gas that is starting on the cold side. This side corresponds to the low-pressure point in the sound wave. Assuming that this gas is an ideal gas, then a low pressure also means a low temperature. Thus, the cold side is able to transfer energy to the low temperature gas particle in the form of heat. The parcel then oscillates to its high pressure point on the hot side of the stack. As the gas pressurizes, its temperature also increases. Thus, when it hits the high temperature side, its temperature is higher than that of the hot sink, and it transfers energy into the hot sink in form of heat. The parcel then depressurizes as it moves back to the cold side where the cycle starts over again. Notice that this set up depends on many important factors. First, the points on the sound wave must correspond to the correct locations on the stack, which makes the TAR fairly sensitive to parameter changes. Second, the pressure changes must be large enough to be able to change the gas from a temperature lower than that of the cold sink to higher than that of the hot sink. Keep in mind that such oscillations are usually no more than 10% of the static pressure (i.e. the “average” pressure), so the TAR cannot generally work under extreme temperature conditions.

Distance Between Stack Plates

The distance between the plates in the stack is extremely important. If the gaps are too narrow, viscous effects will cause the gas to lose too much energy to friction, and the device will be too inefficient. If the gaps are too large, there won’t be enough contact between the gases and the plates to cause appreciable temperature oscillations. To assist in determining the gap between the plates we make use of two characteristic parameters of the gas. These parameters are dependent on a mixture of gas properties and the physical setup of the TAR. The thermal penetration depth squared is defined as twice the thermal conductivity divided by the angular frequency of the sound wave. The viscous penetration depth squared is defined as twice the kinematic viscosity divided by the angular frequency of the sound wave. The thermal penetration depth tells us approximately how far the heat transfer of the gas will penetrate over one oscillation of the gas. The viscous penetration tells us approximately how far away from the center of the gas the viscous effects are felt. Both the thermal and viscous effects are really asymptotic functions, so these values really just give an approximate value to these depths, not a definite cutoff. However, we want to have the gap between the plates of the stack on the same order of magnitude as these penetration depths in order to avoid the negative effects mentioned earlier. As luck has it, these two values are almost always close to each other, so we don’t run into problems where there’s no satisfactory area for both. To be more specific, most researchers are looking at gap sizes approximately 2-3 times these penetration depths.

Mathematically Modeling the Stack

Unfortunately, the functioning of the stack is very complex mathematically. It can be described through use of a real pressure, imaginary pressure, and temperature at any point in the stack. In reality, the temperature at any given points remains nearly constant in steady state, but the real and imaginary pressures really represent a sine function for pressure at the given point rather than a fixed value. With this in mind, the equations that govern the TAR’s stack are:


Fun Facts

  • When a person talks face to face with you, you actually experience thermoacoustic effects from the sound waves. However, the temperature change is on the order of magnitude of 1e-8 degrees Celsius, so you don’t notice it.
  • Ben & Jerry’s ice cream has had a thermoacoustic refrigerator fitted to one of their ice cream freezers.
  • The idea that sound waves could be used for refrigeration or engines came from the Stirling cycle. The Stirling cycle was based on two cylinders that oscillated 90 degrees out of phase with each other. It was noticed that sound waves actually had this same property, and the concept of the thermoacoustic refrigerator was born.

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