INTRODUCTION OF AUCOSTIC REFRIGERATION

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CHAPTER 1
INTRODUCTION
1.1 HISTORY
Thermo acoustics, in its most general sense, is the study of the interaction between heat and
sound. The term has lately become narrower in its meaning so that it refers mostly to the field as
applied to heat engines and refrigerators. Thermo acoustics is by no means a new field, but many of
the major developments have happened fairly recently. As with many fields, thermo acoustics
began as an anecdotal curiosity, but after a fairly long period with little development, a resurgence
of interest has led to many advances in theory and experimental methods.
Evidence of thermo acoustic phenomena dates back centuries to when glass blowers first
noticed that a hot bulb at the end of a cool tube produced tonal sound. According to Putnam and
Dennis, studies in thermo acoustics began as early as 1777, when Byron Higgins placed a
hydrogen flame in a large pipe open at both ends, producing sound. Higgins noted that the acoustic
oscillations produce by the tube depended upon the position of the flame. Later, in 1859, Rijke, as
indicated by Feldman and Bisio and Rubatto, investigated acoustic oscillations in a similar
apparatus but with the hydrogen flame replaced by a mesh of heated metal wire (see Figure 1).
He found that sound was only produced while the tube was in a vertical orientation and the
heating element was in the lower half of the tube, indicating that the convective flow created by
heating air in the pipe was important to its sound production. Furthermore, Rijke concluded that the
sound produced was loudest when the mesh heater was a quarter of the tube length from the
bottom. These investigations eventually led to pulse combustion technology, which is only
somewhat related to the thermo acoustic device designed in this thesis.

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Figure1. Rijke tube.
A more closely related area of thermo acoustics branched off a few years earlier, in 1850.
According to Bisio and Rubatto, Sondhauss experimented with a closed-open tube, as pictured in
Figure 2, heating it by applying a flame to the bulb at the closed end to produce sound. Sondhauss
explored the connection between the geometry of the resonating tube and the frequency of the
sound produced. He noticed that the oscillation frequency was linked to the length of the tube and
the volume of the closed end bulb. Furthermore, Sondhauss found that the sound was more intense
when a hotter flame was applied. However, Sondhauss did not offer an explanation of the
observations. A review of Sondhauss’ work has been written by Feldman.
Figure2. Sondhauss tube.
In 1949, another form of Sondhauss vibration was observed by Taconis et al. In working with
liquid helium, a large temperature gradient was imposed on a glass tube. The temperature gradient,

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spanning from room temperature to cryogenic temperatures (~2°K), caused spontaneous
oscillations inside the glass tube. These oscillations were later studied by Yazaki et al. Although
Taconis provided an explanation of the oscillations, his qualitative theory was basically the same as
that which had already been proposed by Lord Rayleigh many years earlier to account for
observations of the Sondhauss tube. In 1896, Lord Rayleigh explained:
―For the sake of simplicity, a simple 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, ...and therefore is passing from colder to hotter parts of
the tube; but the heat received at this moment (of normal density) has no effect either in
encouraging or discouraging the vibration. The same would be true of the entire operation of the
heat, if the adjustment of temperature were instantaneous, so that there was never any sensible
difference between the temperatures of the air and of the neighboring parts of the tube. But in fact
the adjustment of temperature takes time, and thus 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.
Rayleigh’s criterion proved to be correct but did not include quantitative reasoning; however, he
did refer to the work of Kirchoff, who studied the propagation of sound including thermal
considerations.
The quantitative theory of thermo acoustics began with Kirchhoff in 1868. He derived equations
that accounted for thermal attenuation of sound as well as the normal viscous effects. Kirchhoff
then applied his results to the case of a tube with a large radius so that the viscous and thermal
effects due to the solid boundary could only be seen in a thin film of the fluid close to the wall.
Slightly extending this work, Rayleigh went on to consider narrow channels, but the theory was
still only in the context of sound absorption.
Partly relying on Kirchhoff’s work, Kramers attempted to further develop thermo acoustic theory.
In 1949, motivated by Taconis, Kramers derived a linear theory of thermo acoustics in an attempt
to explain the behavior of sound in a tube with a temperature gradient; however, the resulting

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calculations were not in good agreement with experimental results, differing by orders of
magnitude. Some of Kramers’ early simplifying assumptions were found to be invalid.
In 1969, a major breakthrough came with Rott’s investigation of thermo acoustics. Like, Kramers,
Rott was primarily concerned with explaining Taconis oscillations, but Rott’s efforts proved more
fruitful. Publishing many papers on the subject Rott developed a successful general linear theory of
thermo acoustics. With this theory, thermo acoustic devices including both refrigerators and
engines could be designed and investigated.
Although there are many categories of devices that apply thermo acoustic theory, thermo
acoustic refrigerators (TARs) and thermo acoustic engines (TAEs), which are closely related, are
particularly relevant to the present work. Investigation of TARs and TAEs began at Los Alamos
National Laboratory (LANL) in the early 1980s. Wheatley, Swift, and Hofler among others are
largely responsible for the new wave of advancements in practical thermo acoustic engines and
refrigerators. The first fully functioning thermo acoustic refrigerator was reported in Hofler’s
doctoral dissertation [22], where a standing-wave thermo acoustic refrigerator was built and
investigated. Much of the development in theory is summarized by Swift.
Since the early work at LANL, many thermo acoustic devices have been constructed—
some prototypes and a few for real applications; the following are a few notable examples.
Tijani designed and built a standing-wave TAR much like Hofler’s but devoted more attention
to the effects of varying certain parameters, such as working gas properties and stack size.
Garrett et al. developed a thermo acoustic refrigerator for cooling samples collected on space
missions. Swift designed a large thermo acoustic engine to drive an orifice pulse tube
refrigerator, another kind of thermo acoustic device, which liquefied natural gas. Ballister and
McKelvey created a thermo acoustic device for cooling shipboard electronics. Backhaus and
Swift as well as others have experimented with traveling-wave thermo acoustic refrigerators, but
such devices are not discussed in any detail here. As a last example, Adeff and Hofler designed a
TAR that was driven by a solar-powered thermo acoustic engine, creating a device containing no
moving parts and whose operation was perfectly benign to the environment; most TARs use
electrodynamics drivers, and electricity is mostly produced via fossil fuels. This thesis is
concerned with standing-wave TARs, such as those investigated by Hofler and Tijani.

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Current research in thermo acoustics focuses on the need to improve efficiency and
power density. Therefore, one objective of this thesis is to compare the effects of different
control schemes on TAR operation. While a few institutions are making progress, it is necessary
for a wider research base to become involved before TARs and TAEs can be made
commonplace. This thesis is one of the first in the field of thermo acoustics at the University of
Pittsburgh, so the second objective is to create a sound basic knowledge of thermo acoustic
refrigeration to aid future researchers at this institution.

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1.2:THERMOACOUSTICS
Thermo acoustics combines the branches of acoustics and thermodynamics together to
move heat by using sound. While acoustics is primarily concerned with the macroscopic effects
of sound transfer like coupled pressure and motion oscillations, thermo acoustics focuses on the
microscopic temperature oscillations that accompany these pressure changes. Thermo acoustics
takes advantage of these pressure oscillations to move heat on a macroscopic level. This results
in a large temperature difference between the hot and cold sides of the device and causes
refrigeration. The most important piece of a thermo acoustic device is the stack. The stack
consists of a large number of closely spaced surfaces that are aligned parallel to the to the
resonator tube. The purpose of the stack is to provide a medium for heat transfer as the sound
wave oscillates through the resonator tube. A functional cross section of the stack we used is
shown in figure 6. In typical standing wave devices, the temperature differences occur over too
small of an area to be noticeable. In a usual resonator tube, heat transfer occurs between the walls
of cylinder and the gas. However, since the vast majority of the molecules are far from the walls
of the chamber, the gas particles cannot exchange heat with the wall and just oscillate in place,
causing no net temperature difference. In a typical column, 99% of the air molecules are not near
enough to the wall for the temperature effects to be noticeable. The purpose of the stack is to
provide a medium where the walls are close enough so that each time a packet of gas moves, the
temperature differential is transferred to the wall of the stack. Most stacks consist of
honeycombed plastic spacers that do not conduct heat throughout the stack but rather absorb heat
locally. With this property, the stack can temporarily absorb the heat transferred by the sound
waves. The spacing of these designs is crucial: if the holes are too narrow, the stack will be
difficult to fabricate, and the viscous properties of the air will make it difficult to transmit sound
through the stack. If the walls are too far apart, then less air will be able to transfer heat to the
walls of the stack, resulting in lower efficiency.

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1.2.1. SOUND WAVES AND PRESSURE
Thermo acoustics is based on the principle that sound waves are pressure waves. These sound
waves propagate through the air via molecular collisions. The molecular collisions cause a
disturbance in the air, which in turn creates constructive and destructive interference. The
constructive interference makes the molecules compress, and the destructive interference makes
the molecules expand. This principle is the basis behind the thermo acoustic refrigerator.
One method to control these pressure disturbances is with standing waves. Standing waves are
natural phenomena exhibited by any wave, such as light, sound, or water waves. In a closed tube,
columns of air demonstrate these patterns as sound waves reflect back on themselves after
colliding with the end of the tube. When the incident and reflected waves overlap, they interfere
constructively, producing a single waveform. This wave appears to cause the medium to vibrate in
isolated sections as the traveling waves are masked by the interference. Therefore, these “standing
waves” seem to vibrate in constant position and orientation around stationary nodes. These nodes
are located where the two component sound waves interfere to create areas of zero net
displacement. The areas of maximum displacement are located halfway between two nodes and
are called antinodes. The maximum compression of the air also occurs at the antinodes. Due to
these node and antinodes properties, standing waves are useful because only a small input of
power is needed to create a large amplitude wave. This large amplitude wave then has enough
energy to cause visible thermo acoustic effects.
All sound waves oscillate a specific amount of times per second, called the wave’s frequency,
and is measured in Hertz. For our thermo acoustic refrigerator we had to calculate the optimal
resonant frequency in order to get the maximum heat transfer rate. The equation for the frequency
of a wave traveling through a closed tube is given by:
f =
𝑉
4𝐿

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Where,
f is frequency,
V is velocity of the wave,
L is the length of the tube.
Figure 1: Shows the relationship between the phase of the wave, the pressure, and the actual
arrangement of the molecules. The black line shows the phase of the sound wave, the red shows
the pressure and the dots below represent the actual molecules. From Reference 2

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1.2.2. EXPERIMENTAL WORK
Phase I:-Study and literature review:
We have done theoretical study and literature reviews on thermo acoustic refrigeration system
which were experimented by various experimenters.
We have selected the design criteria, material and constructed experimental set-up based on the
literature reviews.
Phase II:-Design.
1. Design of resonator tube and material consideration based on literature reviews:
i. Diameter of resonator tube.
ii. Length of resonator tube.
2. Design of stack by considering stack spacing, material and configuration based on literature
reviews.
3. Design of thermo acoustic driver (loud speaker) by:
i. Calculation and determination of resonance frequency.
ii. Input wattages of sound for optimum efficiency.
4. Design of cold and hot heat exchangers.
5. Design of constant frequency and power amplifier.
6. Fluid in the resonator tube. (Normal Air.)

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Phase III: - Construction:
1. Construction of resonator tube.
2. Construction of stacks with spiral configuration.
3. Construction of heat exchangers.
4. Construction of thermo acoustic driver and electronic circuit for constant frequency and
variable input wattages.
Phase IV:-Testing:
A).Testing by changing parameters:
1. Length of stack.
2. Diameter of resonator tube.
3. Length of resonator tube.
4. Frequency of sound.
B).Experimentation:-
Experimental Matrix for various input wattage of loudspeaker and response in terms of temperature
difference between hot and cold heat exchangers and minimum temperature achieved.

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1.3. RELEVANCE:-
Unconventional cooling technologies are currently being explored, or revisited, in response to
environmental concerns related to many refrigerants widely used in vapor response compression
cycles. Thermo acoustic cooling devices show promise as alternative cycles because they:
1) Utilize environmentally being working fluids,
2) Use energy in the form of either electricity or heat, such as from a natural gas burner,
3) Can achieve low temperatures with simple designs,
4) Have continuous capacity control,
5) Have no sliding seals and do not require the use of lubricants,
6) Could potentially be made quite and
7) Require small compression ratios, allowing the use of electro acoustic transducers such as
loudspeakers in place of mechanical compressors.

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1.4. LIMITATIONS
1. The downside of the TAR is that these failed to achieve efficiencies as high as those of standard
refrigeration units.
2. The coefficient of performance of most advanced TAR is only 1 when compared to 3-4 of
modern refrigerators.
3. Another major problem of TAR is that it is fully on or off.
4. These refrigerators were able to cool the air for a shirt amount of time before the cooled air
started raising its temperature.
5. Very much regenerator has failed to achieve efficiencies as high as those of standard
refrigeration units.

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1.5. APPLICATIONS:
Speaking of its practical applicability, prototype of thermo acoustic refrigerators have
operated on the Space Shuttle and abroad a Navy warship. And a powerful thermo acoustic engine
has recently demonstrated its ability to liquefy natural gas on a commercial scale.
In practice there is a large variety of applications possible for both thermo acoustic engines
and refrigerators and combination of these. Below, some concrete examples are given of possible
applications:
a. Liquefaction of natural gas:
Burning natural gas in a thermo acoustic engine generates acoustic energy.
This acoustic energy is used in a thermo acoustic heat pump to liquefy
natural gas.
b. Chip cooling:
In this case a piezoelectric element generates the sound wave. A thermo
acoustic heat pump cools the chip.
c. Electronic equipment cooling on naval ships:
In this application, a speaker generates sound waves. Again a thermo acoustic pump is used to
provide the cooling.

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d. Electricity from sunlight:
Concentrated thermal solar energy generates an acoustic wave in a heated
thermo acoustic engine. A linear motor generates electricity from this.
e. Cogeneration (combined heat and power):
A burner heats a thermo acoustic engine, therewith generating acoustic
energy. A linear motor converts this energy to electricity. Waste heat of
burner (flue gases) can be used to supply heat.
f. Upgrading industrial waste heat:
Acoustic energy is created by means of industrial waste heat in a thermo
acoustic engine. In a thermo acoustic heat pump this acoustic energy is used
to upgrade the same waste heat to a useful temperature level.
Though it probably won’t be useful for car air conditioning systems any time soon since
they are too bulky and heavy, it may prove useful for “niche applications”, such as cooling satellite
sensors or super fast computers. In addition to being useful on shipboard, this technology could be
adapted for soft drink machines, medicine storage, computer chips and food transport companies.
Chilled water from the refrigerator circulated through racks of radar electronics on the USS
Deyo, a Navy destroyer. Although we can improve the performance substantially with some
modest changes, thermo acoustic refrigerators of this type will always have an intrinsic limit to
their efficiency.

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1.6. OBJECTIVE & SCOPE:
Since the seventies, the research in the Low Temperature group focused on dilution refrigerators.
Such devices generate cooling by mixing 4He and 3He.Temperatures as low as 2K can be reached.
About a decade ago the group is attention shifted to other new cooling technologies and their
applications. Presently, the pulse- tube refrigerator is a successor of the Stirling-cycle refrigerator.
The Stirling refrigerator requires two moving parts, one of which is in contact with cold
temperature .In 1963, Gifford and Longs worth discovered a refrigeration type which eliminated
the cold moving part. The elimination of the moving part at the cold side is very important step
towards high reliability .Recently, Swift et al.eliminated the remaining piston at ambient
temperature, substituting for it a thermo acoustic heat engine since thermo acoustic technology can
also lead to device without moving parts, attention in Low Temperature group is also focused in
this direction for possible application.