thermoacoustic refrigeration

THERMOACOUSTIC REFRIGERATION

INTRODUCTION

Refrigerators have become necessities in modern society. Most conventional

refrigerators operate using a vapor compression cycle, a process which involves

interaction between vapor and a refrigerant. While this method of chemical refrigeration

is extremely efficient, the refrigerants used [once chlorofluorocarbons (CFCs), now hydro

fluorocarbons (HFCs)] are ozone depleting chemicals, which is a major cause of concern.

From creating comfortable home environments to manufacturing fast and

efficient electronic devices, air conditioning and refrigeration remain expensive, yet

essential, services for both homes and industries. However, in an age of impending

energy and environmental crises, current cooling technologies continue to generate

greenhouse gases with high energy costs.

Thermoacoustic refrigeration is an innovative alternative for cooling that is

both clean and inexpensive. Through the construction of a functional model, we will

demonstrate the effectiveness of thermoacoustics for modern cooling. Refrigeration relies

on two major thermodynamic principles. First, a fluid’s temperature rises when

compressed and falls when expanded. Second, when two substances are placed in direct

contact, heat will flow from the hotter substance to the cooler one. While conventional

refrigerators use pumps to transfer heat on a macroscopic scale, thermoacoustic

refrigerators rely on sound to generate waves of pressure that alternately compress and

relax the gas particles within the tube. The model constructed for this research project

employed inexpensive, household materials. Although the model did not achieve the

original goal of refrigeration, the experiment suggests that thermoacoustic refrigerators

could one day be viable replacements for conventional refrigerators.

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CHAPTER 1: BASICS

The first and second laws of thermodynamics place an upper bound on the

efficiency of heat engines. If TH and TC are the hot and cold thermal reservoirs,

respectively, and QH and QC the associated heat flows with W the work flows as shown

in Figure 1.1, in the usual case of cyclic engines operation, QH and QC and W are time

averaged powers. The operation is assumed steady-state, so that the time-averaged state

of the engine itself does not change. The first law of thermodynamics states that

The second law states that the entropy generated by the system must be positive

or zero. Since the engine is in (time averaged) steady state, the net entropy increase in the

reservoirs is

For the prime mover, the efficiency of interest is H Q W = η . Combining

Equations (1) and (2) to eliminate Qc,

The temperature ratio in Equation (4) is called the Carnot efficiency,

c η . It is the highest efficiency that a prime mover can achieve. Meanwhile for a heat

pump, the efficiency is called the coefficient of performance, W Q COP C = , reflecting

the fact that QC is the desired output of the refrigerator. Combining Equation (1) and (3)

to eliminate QH,

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Thermoacoustic systems operate in a similar manner with the heat engine

generating acoustic power and the heat pump requiring acoustic power. The efficiency

and COP, however, are not derived similarly.

.

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CHAPTER 2: THERMOACOUSTIC THEORY

Thermoacoustic effects had been observed for a long time, with the two most

famous devices, the Sondhauss tube and Rijke tube being described in 1850 and 1859

respectively (Wheatley et.al., 1985). However, a theoretical explanation to the

thermoacoustical effects observed in these devices is only available through Lord

Rayleigh whose discussion is mostly qualitative. According to Rayleigh, heating and

cooling could create acoustic power “if heat be given at the moment of greatest

condensation, or be taken from it at the moment of greatest rarefaction” and the heating

and cooling could be created by an acoustic wave (Backhaus and Swift, 2002). A

quantitative theoretical explanation is available only by 1970s through the works of

Nikolaus Rott. These theories are later used in the development of a thermoacoustic heat

engine.

Thermoacoustic heat engines are able to function as a prime mover or a heat

pump owing to the nature of the thermoacoustical phenomena where acoustic power is

generated if oscillatory thermal expansion and contraction is created and oscillatory

thermal expansion and contraction could be caused by a temperature gradient. The

difference of the function of the heat engine is therefore dependant on whether thermal or

acoustic power is given. Acoustic power is provided through an acoustic driver while

thermal power or heat is provided through the heat exchangers.

Thermoacoustic heat engines are further divided into two categories, standing

wave engines and traveling-wave engines. The traveling wave engine is better known as a

Stirling engine (Backhaus and Swift, 2002), while thermoacoustic heat engines normally

refers to the standing wave heat engine. In standing-wave engines, a standing wave is

generated within the resonator and a stack with moderately spaced plates is introduced in

the resonator to ensure a poor but nonzero thermal contact. Fluid in traveling-wave

engine oscillates in a traveling wave and the plates in the stack are closely spaced to

ensure a perfect thermal contact between fluid and stack (Swift, 1988)

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CHAPTER 3: SOUND WAVES AND PRESSURE

Thermoacoustics 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 thermoacoustic 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

antinode 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 thermoacoustic effects.

All sound waves oscillate a specific amount of times per second, called the

wave’s frequency, and is measured in Hertz. For our thermoacoustic 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:

where f is frequency, v is velocity of the wave, and L is the length of the tube.

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The surroundings now do work on the system, adiabatically

compressing the gas and allowing the piston to fall back to its rest position.

However, because it is easier to compress the cooler gas than to add heat to the warm

gas, net work is done on the surroundings. To determine the efficiency of the cycle, the

total useful work done is compared to the total heat transferred. In Figure 3,

the total heat transferred equals the red area plus the white area. The work extracted

from the system is represented by the white area. Even the Carnot cycle, the ideal

thermodynamic process where each step is reversible and involves no change in entropy,

transfers more heat than it does work. However, the Carnot cycle has the best work

output with the given temperature difference and entropy difference, so it is

defined to be 100% efficient.

CHAPTER 4: EXPERIMENTAL DESIGN

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Device Construction In the construction of our thermoacoustic devices, we

followed the methods of Russell et al. Our materials included a boxed loudspeaker, a

Plexiglas tube, an aluminum stopper, film, and 15lb nylon fishing line.

A diagram of the thermoacoustic device

1. Stack A lot of time was spent making the most important feature of the device, the

stack. It was created by gluing fishing line at evenly spaced intervals along the roll of

film. To do this, we wound fishing line around a 1 meter long cardboard loom with slits

cut every 5mm along the edges. After the line was wound, a meter of photographic film

was secured to a stable surface and then sprayed with adhesive. The loom and line were

then pressed onto the film, weighted, and allowed to dry overnight. Once dry, the

cardboard and excess fishing line was removed. The film was rolled compactly and

placed inside a Plexiglass tube with a diameter of ¾ cm and a length of 23 cm. The stack

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was placed approximately 5 cm from the open end of the tube. Small holes were then

drilled above and below the stack to serve as entry points for the thermocouples.

2. Thermocouples

To construct the thermocouples, a high power small scale welder was to flash-

melt the chromel and alumel wires together on one end, while other ends were connected

to a K tap connector. The welded ends were then inserted into the previously drilled

holes.

3. Adhesives and Sealant

Another Plexiglas plate was cut so that it would cover the speaker entirely. A

hole was drilled in the center of this plate in order to allow the placement of the tube. To

secure an airtight seal between the tube and the plate, an epoxy was used, while a silicone

caulk was used on all the other areas which had potential for leakage (connection of plate

to loudspeaker, thermocouple holes).

4. Loudspeaker

These are selected as per requirement of frequency for wave generation (generally

400 Hz).

Fig- The final modified thermoacoustic device with heat sink.

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CHAPTER 5: THERMOACOUSTIC REFRIGERATION

The thermoacoustic effect occurs in the stack region and requires the presence

of two thermodynamics media i) Stack ii) working fluid (gases). This region also calls as

thermoacoustic core.

Figure: Thermoacoustic Refrigeration

While acoustics is primarily concerned with the macroscopic effects of sound

transfer like coupled pressure and motion oscillations, thermoacoustics focuses on the

microscopic temperature oscillations that accompany these pressure changes.

Thermoacoustics 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

thermoacoustic 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 b. In typical

standing wave devices, the temperature differences occur over too small of an area to be

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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.

Working:-

Fig: Thermoacoustic Cycle

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Figure: Transport of heat along a stack plate

The cycle consists of two adiabatic steps (1 & 3) and tow isobaric steps (2 &

4). The acoustics standing wave moves the gas parcel forward, the gas parcel is

adiabatically compressed causing its temperature to rise, let’s say by tow arbitrary units

to reach the temperature T++, as indicated in figure 1.3, step (1). At this stage the gas

parcel is warmer than the stack plate and irreversible heat transfer from the working fluid

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towards the stack plate takes place. In step (2), the gas parcel cools down by one arbitrary

unit to the temperature T+. In the process of adiabatic expansion, the gas parcel moves

back to its initial location and cools down by two arbitrary units to reach the temperature

T-, as indicated in step (3). At this stage the gas parcel is colder than the stack plate and

irreversible heat transfer from the stack plate towards the gas parcel takes place in the

fourth step. During the described cycle, the gas parcel has returned to its initial position

and initial temperature T and therefore the cycle can start again. Since there are many

gas parcels moving along the stack plate, and heat that is dropped by one gas parcel, is

transported further by the adjacent parcel, a temperature gradient develops along the

stack plates.

Fig. Temperature variation above (Thot) and below (Tcold) the stack as afunction of time.

Figure shows typical results for the temperatures above the stack (Thot) and

below the stack (Tcold) as a function of time. The starting temperatures were normalized

to zero, so the plot shows the changes in temperature as measured by each thermocouple.

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To produce this plot the thermocouple leads were connected to a two-channel digital

oscilloscope with an 8 minute capture time. The plot shows that the temperature below

the stack (Tcold) begins decreasing immediately after the sound is turned on, dropping 4

°C in the first 15 seconds, with the rate of temperature change decreasing with time. After

4 minutes of operation the temperature below the stack has dropped by 10.5 °C and is

still decreasing. The temperature above the stack (Thot) increases, also more rapidly at

first, as the heat is being pumped through the stack. After approximately 2 minutes the

temperature above the stack has increased by 5 °C. After that it stops increasing as the

rate at which heat is moved through the stack equals the rate at which heat is conducted

through the aluminum cap into the surrounding room. After 4 minutes of operation, the

temperature difference between the top and bottom of the stack is about 15.5 °C, a

difference large enough to be detected by touching a finger along the outside of the

acrylic tube. The trends in Fig. are similar to those found in the literature.

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CHAPTER 6: POSSIBLE MODIFICATIONS

One possible way to dissipate more heat is to increase the surface

area of the cap by cutting grooves into each end of the aluminum plug. The

increased surface area gives air particles a larger area to collide into the aluminum plug

and transfer heat, allowing for there to be more collisions at a single time, thus

increasing the rate of heat conduction of the aluminum plug from the top end of the tube

into the surrounding air. The grooved aluminum plug will decrease the temperature in the

top end of the tube by dissipating heat faster than the flat aluminum plug could. This

will decrease the temperature difference between the top end and the bottom end,

allowing the bottom end to become colder than with the flat plug before the temperature

difference reaches the point that it exceeds the temperature gradient created by the

sound waves and heat can no longer be transferred.

Another possible method of dissipating the heat from the refrigerator would

involve heat absorption by water. Thin pipes could be run across the top end of the

stack. Liquid could flow through the stack, effectively transferring the excess

heat from the system. Water, with a relatively high heat capacity, would absorb the

heat quickly. The hot water could then be used for other applications, such as spinning a

turbine in a generator or an engine. This would be using the device as a heat pump to

power a device.

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Figure: The unmodified model data. The top red bar shows the readings of the warm

thermocouple. The bottom blue bar shows the readings for the cooler thermocouple.

Figure 10: The modified model data. The top red bar shows the readings of the warm

thermocouple. The bottom blue bar shows the readings for the cooler thermocouple. As

shown in the diagram, the actual temperature difference was slightly greater in this

design, but not significantly different.

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CHAPTER 7: APPLICATIONS

1. In Telecommunications:

Thermal management has always been a concern for computer systems

and other electronics. Computational speeds will always be limited by the amount of

noise produced by computer chips. Since most noise is generated by waster heat,

computer components and other semiconductor devices operate faster and more

efficiently at lower temperatures. If thermoacoustic cooling devices could be scaled for

computer applications, the electronic industry would realize longer lifetimes for

microchips, increased speed and capacity for telecommunications, as well

as reduced energy costs.

2. In Freezers:

Ben and Jerry’s Ice Cream, in collaboration with Professor Garrett’s

research team, has begun production of thermoacoustic freezers to keep its ice cream

cold. Investing over $600,000 in Garrett’s program, Ben and Jerry’s has

already placed the freezers in many of its New York stores. The ice cream

company’s experiment has successfully demonstrated the viability of

thermoacoustic refrigeration.

3. In Automobiles:

Figure : Example arrangement of an ideal thermoacoustic heat engine driving an ideal

thermoacoustic heat pump in an automobile.

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Compared to current automotive refrigeration systems, thermoacoustic systems

are quite simple and inexpensive to construct, using steel, aluminium or even plastics

manufactured to low tolerances. These devices are expected to weigh no more than

equivalent vapour compression systems, and operate at lower pressures (usually less than

half the 2,000kPa of typical compressors). Although arguably only in development for

the last 25 years, thermoacoustic systems are highly capable devices with wide ranging

applications: from electricity generation to liquefaction of natural gas, and from cooling

of electronics racks in US Naval warships to onboard the Space Shuttle Discovery.

Figure: The recently completed thermoacoustic refrigerator (TAR).

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CONCLUSION

This device worked as a proof of concept device showing that a

thermoacoustic device is possible and is able to cool air, abet for only a short period of

time. If they were able to build the device with better materials, such has a more

insulating tube, we might have been able to get better results. In order to create a

working refrigerator we probably would have to attach a heat sink to the top of the

device, thus, allowing the excess heat to dissipate to the surroundings. However,

our device did demonstrate that thermoacoustic device have the ability to create and

maintain a large temperature gradient, more than 20 degrees Centigrade, which would be

useful as a heat pump.

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REFERENCES

1. “Standing Waves.” Rod Nave, Georgia State University.

Available: http://hyperphysics.phyastr.gsu.edu/hbase/waves/standw.html. 17 July 2006.

2. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.html

3. http://www.howstuffworks.com/stirling-engine.htm

4. http://en.wikipedia.org/wiki/Carnot_cycle

5. Daniel A. Russell and Pontus Weibull, “Tabletop thermoacoustic refrigerator for

demonstrations,” Am. J. Phys. 70 (12), December 2002.

6. G. W. Swift, “Thermoacoustic engines and refrigerators,” Phys. Today 48, 22-28

(1995)

7. http://www.rolexawards.com/laureates/laureate-36-lurie_garrett.html

8. “Thermal Management of Computer Systems Using Active Cooling of Pulse Tube

Refrigerators.” H.H. Jung and S.W.K Yuan.

Available: http://www.yutopian.net/Yuan/papers/Intel.PDF. 17 July 2006.

9. “Thermoacoustic Refrigeration for Electronic Devices: Project Outline.” Stephen Tse,

2006 Governor’s School of Engineering and Technology.

10. “Chilling at Ben & Jerry’s: Cleaner, Greener.” Ken Brown.

Available: http://www.thermoacousticscorp.com/news/index.cfm/ID/4.htm. 17 July 2006.

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http://www.thermoacousticscorp.com/news/index.cfm/ID/4.htm

http://www.howstuffworks.com/stirling-engine.htm

thermoacoustic refrigeration

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