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American Scientistthe magazine of Sigma Xi, The Scientific Research Society

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Last February, a panel of the Nation-al Academy of Engineering an-

nounced the results of its effort to rankthe greatest engineering achievementsof the 20th century. Second and tenthon that list were two very successfulheat engines: the automobile (andhence, the internal-combustion engine)and the refrigerator and air condition-er, heat engines operated in reverse.But these two pillars of modern tech-nology share another, less flatteringdistinction: Both have inadvertentlydamaged the environment—by cloud-ing skies with smog, spewing green-house gases or leaking compoundsthat erode the earth’s protective blan-ket of stratospheric ozone.

Over the past two decades, investiga-tors like ourselves have worked to de-velop an entirely new class of enginesand refrigerators that may help reduceor eliminate such threats. These thermo-acoustic devices produce or absorbsound power, rather than the “shaftpower” characteristic of rotating ma-chinery. Because of its inherent mechan-ical simplicity, such equipment may oneday serve widely, perhaps generatingelectricity at individual homes, whileproducing domestic hot water and pro-viding space heating or cooling.

How do these machines work? In anutshell, a thermoacoustic engine con-verts heat from a high-temperature

source into acoustic power while re-jecting waste heat to a low-temperaturesink. A thermoacoustic refrigeratordoes the opposite, using acoustic pow-er to pump heat from a cool source to ahot sink. These devices perform bestwhen they employ noble gases as theirthermodynamic working fluids. Unlikethe chemicals used in refrigerationover the years, such gases are bothnontoxic and environmentally benign.Another appealing feature of thermoa-coustics is that one can easily flange anengine onto a refrigerator, creating aheat-powered cooler with no movingparts at all.

So far, most machines of this varietyreside in laboratories. But prototypethermoacoustic refrigerators have op-erated on the Space Shuttle and aboarda Navy warship. And a powerfulthermoacoustic engine has recentlydemonstrated its ability to liquefy nat-ural gas on a commercial scale.

That sound-powered equipment canaccomplish these tasks seems almostmagical—and rightly so: Arthur C.Clarke once remarked that “any suffi-ciently developed technology is indis-tinguishable from magic.” Below weattempt to reveal the legerdemain andexplain the simple physics that makesthermoacoustic machines possible.

Speech and Hot AirThe interaction of heat and sound hasinterested acousticians since 1816,when Laplace corrected Newton’s ear-lier calculation of the speed of soundin air. Newton had assumed that theexpansions and compressions of asound wave in a gas happen withoutaffecting the temperature. Laplace ac-counted for the slight variations intemperature that in fact take place, andby doing so he derived the correctspeed of sound in air, a value that is 18percent faster than Newton’s estimate.

Such thermal effects also explain why19th-century glassblowers occasionallyheard their heated vessels emit puretones—a hint that thermoacousticsmight have some interesting practicalconsequences. Yet it took more than acentury for anyone to recognize the op-posite effect: Just as a temperature dif-ference could create sound, sound couldproduce a temperature difference—hotto one side, cool to the other. Howacoustic cooling can arise is, in retro-spect, rather easy to understand.

Suppose an acoustic wave excites agas that was initially at some averagetemperature and pressure. At any onespot, the temperature will go up as thepressure increases, assuming the risehappens rapidly enough that heat hasno time to flow away. The change intemperature that accompanies theacoustic compressions depends on themagnitude of the pressure fluctuations.For ordinary speech, the relative pres-sure changes are on the order of onlyone part per million (equivalent to 74decibels, or dB, in sound pressure lev-els), and the associated variation intemperature is a mere ten-thousandthof a degree Celsius. Even for sounds atthe auditory threshold of pain (120 dB),temperature oscillates up and down byonly about 0.02 degree.

516 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproductionwith permission only. Contact [email protected].

The Power of Sound

Sound waves in “thermoacoustic” engines and refrigerators can replacethe pistons and cranks that are typically built into such machinery

Steven L. Garrett and Scott Backhaus

Steven L. Garrett received his Ph.D. in physicsfrom the University of California, Los Angeles in1977 and is currently the United TechnologiesProfessor in the Graduate Program in Acousticsand a Senior Scientist with the Applied ResearchLaboratory, both at the Pennsylvania StateUniversity. Scott Backhaus earned his doctorate inphysics from the University of California, Berkeleyin 1997. He is currently the Reines Fellow at LosAlamos National Laboratory. Address for Garrett:Penn State, Applied Research Laboratory, P. O.Box 30, State College, PA 16804. Internet:[email protected]

Figure 1. Glassblowers can sometimes heartheir handiwork spontaneously emit soundswhen the application of heat to one end of avessel inadvertently transforms it into a“thermoacoustic engine.” This phenomenonwas first documented in the scientific litera-ture in 1850, when the theoretical connectionbetween heat and sound was well recog-nized. But it was not until quite recently thatscientists realized that acoustic waves canalso produce cooling. The authors discuss thefundamental physics behind thermoacousticengines and refrigerators, and they describehow machines based on these principles arenow being engineered to operate reliably andat high efficiency.

2000 November–December 517© 2000 Sigma Xi, The Scientific Research Society. Reproductionwith permission only. Contact [email protected].

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Most refrigerators and air condition-ers must pump heat over considerablygreater temperature ranges, usually 20degrees or more. So the temperature

swings that typical sound waves bringabout are too small to be useful. To han-dle larger temperature spans, the gasmust be put in contact with a solid ma-

terial. Solids have much higher heat ca-pacities per unit volume than gases, sothey can exchange a considerableamount of heat without changing intemperature by very much. If a gas car-rying a sound wave is placed near a sol-id surface, the solid will tend to absorbthe heat of compression, keeping thetemperature stable. The opposite is alsotrue: The solid releases heat when thegas expands, preventing it from coolingdown as much as it otherwise would.

The distance over which the diffu-sion of heat to or from an adjacent solidcan take place is called the thermal pene-tration depth. Its value depends on thefrequency of the passing sound waveand the properties of the gas. In typicalthermoacoustic devices, and for soundwaves in air at audio frequencies, thethermal penetration depth is typicallyon the order of one-tenth of a millime-ter. So to optimize the exchange of heat,the design of a thermoacoustic engineor refrigerator must include a solidwith gaps that are about twice this di-mension in width, through which ahigh-amplitude sound wave propa-gates. The porous solid (frequently ajelly-roll of plastic for refrigerators or ofstainless steel for engines), is called a“stack,” because it contains many lay-ers and thus resembles a stack of plates.

When an acoustically driven gasmoves through the stack, pressure,temperature and position all oscillatewith time. If the gas is enclosed withina tube, sound bounces back and forthcreating an acoustic standing wave. Inthat case, pressure will be in phasewith displacement—that is, the pres-sure reaches its maximum or mini-mum value when the gas is at an ex-treme of its oscillatory motion.

Consider how this simple relationcan be put to use in a thermoacousticrefrigerator, which in its most rudi-mentary form amounts to a closedtube, a porous stack and a source ofacoustic energy. As a parcel of gasmoves to one side, say to the left, itheats up as the pressure rises and thencomes momentarily to rest before re-versing direction. Near the end of itsmotion, the hot gas deposits heat intothe stack, which is somewhat cooler.During the next half-cycle, the parcelof gas moves to the right and expands.When it reaches its rightmost extreme,it will be colder than the adjacent por-tion of the stack and will extract heatfrom it. The result is that the parcelpumps heat from right to left and can


Figure 2. Thermoacoustic device consists, in essence, of a gas-filled tube containing a “stack” (top),a porous solid with many open channels through which the gas can pass. Resonating soundwaves (created, for example, by a loudspeaker) force gas to move back and forth through openingsin the stack. If the temperature gradient along the stack is modest (middle), gas shifted to one side(a) will be compressed and warmed so that a parcel of gas with dimensions that are roughly equalto the thermal penetration depth (δk) releases heat to the stack. When this same gas then shifts inthe other direction (b), it expands and cools enough to absorb heat. Although an individual parcelcarries heat just a small distance, the many parcels making up the gas form a “bucket brigade,”which transfers heat from a cold region to a warm one and thus provides refrigeration. The samedevice can be turned into a thermoacoustic engine (bottom) if the temperature difference along thestack is made sufficiently large. In that case, sound can also compress and warm a parcel of gas (c),but it remains cooler than the stack and thus absorbs heat. When this gas shifts to the other sideand expands (d), it cools but stays hotter than the stack and thus releases heat. Hence, the parcelthermally expands at high pressure and contracts at low pressure, which amplifies the pressure os-cillations of the reverberating sound waves, transforming heat energy into acoustic energy.

do so even when the left side of thestack is hotter than the right.

The span of movement for an indi-vidual parcel is quite small, but the neteffect is that of a bucket brigade: Eachparcel of oscillating gas takes heat fromthe one behind and hands this heat offto the next one ahead. The heat, plusthe work done to move it thermo-acoustically, exits one end of the stackthrough a hot heat exchanger (similarto a car radiator). A cold heat exchang-er, located at the other end of the stack,provides useful cooling to some exter-nal heat load.

One can easily reverse this processof refrigeration to make a thermo-acoustic engine. Just apply heat at thehot end of the stack and remove it atthe cold end, creating a steep tempera-ture gradient. Now when a parcel ofgas moves to the left, its pressure andtemperature rise as before, but thestack at that point is hotter still. So heatflows from the stack into the gas, caus-ing it to expand thermally just as pres-sure reaches a maximum. Conversely,when the parcel shifts to the right, itexpands and cools, but the stack thereis cooler still. So heat flows into the sol-id from the gas, causing thermal con-traction just as pressure reaches a min-imum. In this way, the temperaturevariation imposed on the stack drivesheat into and out of the gas, forcing itto do work on its surroundings andamplifying the acoustic oscillations.Maintenance of the steep thermal gra-dient requires an external source ofpower, such as an electric heater, con-

centrated sunlight or a flame—whichexplains why glassblowers sometimesobserve the spontaneous generation ofsound when they heat the walls of aglass tube (serving as a stack) in such away as to create a strong temperaturegradient, a phenomenon first docu-mented in a scholarly journal in 1850.

Indeed, this “singing tube” effectarises easily enough that Reh-lin Chen,a student in the Graduate Program inAcoustics at the Pennsylvania StateUniversity, was able to build a ther-moacoustic engine with only threeparts. The stack consists of a plug ofporous ceramic (material that is nor-mally used for automotive catalyticconverters). Electrical current passingthrough a heater wire attached at oneend of the plug imposes a temperaturegradient. A Pyrex test tube acts as aminiature organ pipe and sets up astanding acoustic wave. Because thecold end of the stack faces the mouth ofthe test tube, no cold heat exchanger isneeded: Air streaming in and out of theopen end of the tube provides sufficientcooling. Despite its simplicity, Chen’sengine is capable of producing soundat uncomfortable levels.

An Acoustic LaserThe transparency of this device, literaland figurative, invites analogies withthe laser. Borrowing some vocabularyfrom optics, one would say that a non-equilibrium condition (correspondingto the population inversion of electronenergy levels in a laser material) ismaintained across the heated stack.

The test tube amounts to an acousticresonator, which, like a laser cavity, al-lows a standing wave to build in am-plitude as energy bounces back andforth. The open side of the test tubeserves the same function as the partial-ly silvered mirror at the output side ofa laser. Both allow some of the energystored within the resonant cavity to ra-diate into the surrounding environ-ment. Although Chen’s “acoustic laser”produces only about a watt of soundpower, a similar device heated by theburning of natural gas produces in ex-cess of 10 kilowatts—a high-poweredlaser indeed!

One of the most remarkable featuresof such thermoacoustic engines is thatthey have no moving parts. They de-mand nothing beyond the basic physicsof the cavity and stack to force the com-pressions, expansions, displacementsand heat transfers to happen at theright times. The internal-combustionengines in our cars also depend onproper timing—the intake, compres-sion, expansion and exhaust stages ofthe power cycle must take place insmooth succession. But conventionalautomobile engines require at least twovalves per cylinder, each with a spring,rocker arm and a push rod (or an over-head cam driven by a timing belt) toproduce the required phasing. This dif-ference makes thermoacoustic devicesmuch simpler and potentially muchmore reliable than conventional en-gines and refrigerators, because theycan avoid wear associated with valves,piston rings, crankshafts, connecting


Figure 3. Simple thermoacoustic engine can be constructed from common components (left). A small test tube, a heater wire and a plug of porousceramic (material used in automotive catalytic converters) properly arranged can produce about a watt of acoustic power. If one end of the ceramicplug is placed at the focus of a parabolic mirror (right), solar energy, too, can power this demonstration engine. (Courtesy of Reh-lin Chen.)

rods and so forth. Thus thermoacousticdevices require no lubrication.

To the uninitiated, it may seem sur-prising that pistonless engines canachieve high power levels. Thermo-acoustic devices manage this feat byexploiting acoustic resonance to pro-duce large pressure oscillations fromsmall gas motions. Consider a closedtube (an acoustic resonator) with aloudspeaker mounted at one end. Theoscillating movement of the loud-speaker pumps in acoustic energy,which travels down the tube at thespeed of sound, reflects off the far endand shoots back toward the source. Ifthe frequency of the excitation is justright, the next increment of energy thatthe loudspeaker injects will arrive instep with the reflected portion of theacoustic wave.

The pressure swings in the resonat-ing wave will then grow until the ener-gy added during one cycle is exactlyequal to the energy dissipated during

one cycle, either by friction or by theproduction of useful work. The ulti-mate value of the pressure variationdepends on the quality factor of theresonator, Q (which is equal to 2/πtimes the ratio of the pressure the loud-speaker produces in the resonator tothat which the same loudspeakerwould have generated in an infinitelylong tube, one in which there would beno reflected wave).

The result of this resonant Q amplifi-cation can be easily understood by con-sidering the motion of a piston com-pressing some gas within a cylinder. Ifthe initial length of the gas volume is,say, 20 centimeters and the pistonmoves slowly inward 1 centimeter, thepressure of the gas would increase by 5percent, assuming no leakage aroundthe piston. If, however, it oscillatedback and forth rapidly at the resonantfrequency of the cavity (860 cycles persecond, assuming that the cylinder isfilled with air at room temperature so

that exactly one-half wavelength ofsound fits inside), the piston wouldonly have to move by something like0.05 millimeter in a typical cavity(Q=30) to produce the same change inpressure. That tiny distance is only onetwo-hundredth as far as in the case ofslow compression, yet it achieves ex-actly the same peak pressure.

Clearly, an oscillating acoustic sourcethat moves such small distances doesnot need a piston with sealing ringsmoving in a lubricated cylinder—elim-inating all sorts of pesky componentsfound in conventional refrigerationcompressors and internal-combustionengines. Flexible seals, such as metalbellows, would suffice. Such seals re-quire no lubrication and do not de-mand the machining of close-toleranceparts to eliminate gas “blow-by” be-tween a piston and its tight-fittingcylinder.

A Stereo RefrigeratorThe simplicity of the hardware in-volved in thermoacoustic machines isbest appreciated by examining a con-crete example. In the mid-1990s, one ofus (Garrett) and his colleagues at theNaval Postgraduate School in Mon-terey, California developed two thermo-acoustic refrigerators for the SpaceShuttle. The first was designed to coolelectronic components, and the secondwas intended to replace the refrigera-tor-freezer unit used to preserve bloodand urine samples from astronauts en-gaged in biomedical experiments.

This “thermoacoustic life sciences re-frigerator,” as we called it, producedgood results in the laboratory, yetNASA sponsorship ended abruptly, os-tensibly for lack of funds. Because theproject was progressing so well by thattime, we were quite puzzled. But sixmonths later we discovered that themanagers of our program at the NASALife Sciences Division were enmeshedin a controversial FBI investigation ofkickbacks and bribery at the JohnsonSpace Flight Center in Houston. Clear-ly, they were preoccupied with some-thing other than evaluating our techni-cal progress. Fortunately, the U.S. Navywas in need of a similar chiller andtook over support of our efforts.

Because we had originally designedthis refrigerator to operate in the ratherdemanding environment of space, wechose a “stereo” configuration to pro-vide redundancy in case one of theloudspeakers failed. The two loud-


Figure 4. Thermoacoustic engines are similar to optical lasers in that both types of apparatusamplify standing waves set up within resonant cavities. In a ruby laser (top), for example, en-ergy is added by means of a flash tube, which creates a “population inversion” of electron en-ergy levels. In the thermoacoustic analogue (bottom), energy is injected into the cavity usingthe heated stack, which creates a nonequilibrium temperature distribution.

speakers are similar to those used forsound reproduction, but they are muchmore powerful and operate over a lim-ited range of frequencies. They also dif-fer from normal speakers in that thecones are inverted, having their largediameter at the voice coil and small di-ameter where the sound is radiated.The moving parts of these speakers arejoined to a stationary U-shaped reso-nant cavity by small metal bellows.

The U-tube contains two separatestacks, each with two water-filled heatexchangers, which resemble small carradiators, attached at the ends. Two ofthese heat exchangers exhaust wasteheat, and two provide cooling. In thisincarnation, chilled water from our“life sciences refrigerator” circulatedthrough racks of radar electronics onthe USS Deyo, a Navy destroyer. Themaximum cooling capacity we achievedin our sea trials proved to be in excessof 400 watts, using just over 200 wattsof acoustic power. At the lowest tem-perature of operation we could com-fortably attain without risking the wa-ter freezing and blocking the pipes(about 4 degrees C), the refrigeratorperformed at 17 percent of the efficien-cy that could, in principle, be coaxedfrom a perfect refrigerator operatingover the same temperature span—afundamental limit imposed by the Sec-ond Law of Thermodynamics. The re-

frigerator itself reached 26 percent ofthe maximum, but inefficiencies of theheat exchangers reduced the usefulcooling to the 17-percent value. Thatlevel is little better than half of whatconventional chillers of similar sizeand cooling capacity can boast.

Although we could have improvedthe performance substantially withsome modest changes, thermoacousticrefrigerators of this type will alwayshave an intrinsic limit to their efficien-cy, which is imposed by the way heat

flows between the gas and the stack.But recently, one of us (Backhaus) andhis colleagues at Los Alamos NationalLaboratory demonstrated a techniquethat has enabled thermoacoustic en-gines to break this seemingly insur-mountable barrier by, strangely enough,borrowing a technique that a Scottishminister patented in 1816—the veryyear Laplace first correctly calculatedthe speed of sound.

Back to the Future


Figure 5. Gas pressure within a cylinder in-creases in inverse proportion to the decreasein volume when a piston is moved slowly in-ward (top). For example, 1 centimeter of mo-tion in a 20-centimeter cylinder increases thepressure by 5 percent. But the same peakpressure will result if the piston shifts backand forth at the resonant frequency of thecavity by just 50 micrometers, movementsthat are small enough for flexible bellows toaccommodate (middle). The standing waveachieves its highest pressures at the two endsof the cylinder as gas sloshes back and forth,whereas the velocity of the gas is always zeroat these points in a closed tube (bottom).

Figure 6. Inner workings of the thermoacoustic refrigerator used to cool radar electronics (left) are comparatively simple: A pair of loudspeak-ers drives gas through two porous stacks attached to heat exchangers through which water circulates. Conventional refrigerators require manymore components, including mechanical compressors (right), which contain moving parts that are prone to wear.


Figure 7. Stirling cycle contains four distinct steps—compression, heating,expansion and cooling—which produce a characteristic set of changes inpressure and volume (right). In a simple, two-piston Stirling engine (di-rectly below), the compression step (1) keeps one piston fixed as the othermoves inward, the heat of compression being rejected into the adjacentcold reservoir. The next step (2) produces constant-volume regenerativeheating, as both pistons move simultaneously, forcing cool gas throughthe porous regenerator, which was heated during the final step of the lastcycle. Next (step 3), heat from the hot reservoir causes thermal expansionof the gas, which forces the adjacent piston to move outward. Finally(step 4), both pistons move together to create a constant-volume regenera-tive cooling of the heated gas. The changes in pressure and gas velocitywithin the regenerator of such a Stirling engine mimic the relationshipseen in a traveling acoustic wave, where pressure and gas velocity moveup and down in phase (bottom pair of panels).

In his spare time, the Reverend RobertStirling designed, built and demon-strated a rather remarkable type of hot-air engine, one that still bears his name.Unlike steam engines of the era, his in-vention contained no potentially explo-sive boiler. Stirling’s engine dependedon the expansion and displacement ofair inside of a cylinder that was warmedby external combustion through a heatexchanger. Stirling also conceived theidea of a regenerator (a solid with manyholes running through it, which hecalled the “economiser”) to store ther-mal energy during part of the cycleand return it later. This component in-creased thermodynamic efficiency toimpressive levels, but mechanical com-plexity was greater for Stirling’s enginethan for the high-pressure steam andinternal-combustion varieties (whichdo not require two heat exchangers),restricting its widespread use.

The story of how one of the oldestideas in the history of heat engineslinked up with one of the newest istypical of the tortuous routes to discov-ery (or rediscovery) that many scien-tists experience. In this case, the jour-ney began two decades ago, whenGarrett had the pleasure of workingwith Gregory Swift, then a graduatestudent at the University of California,Berkeley. Swift eventually received hisdoctorate in physics and joined JohnWheatley, who was just then preparingto move his low-temperature physicsgroup to Los Alamos National Labora-tory and focus his research efforts onthe development of novel heat enginesand refrigerators.

As a graduation present, Garrettgave Swift a copy of an intriguing arti-cle that Peter Ceperley, a physics pro-fessor at George Mason University, hadpublished a few years earlier. It wasentitled “A pistonless Stirling engine—The traveling wave heat engine.”Ceperley cleverly recognized that thephasing between pressure and gas ve-locity within Stirling’s regenerator wasthe same as the phasing in a travelingacoustic wave. He demonstrated thatsimilarity by arranging a temperaturegradient across a crude regenerator (aplug of fine steel wool) and sending asound wave though it. Some thermalenergy was converted to acoustic ener-gy, though not enough to make up forthe accompanying losses.

Swift brought Ceperley’s article withhim to Los Alamos, but he and his col-leagues there decided that Ceperley’s

“engine” would never be able to am-plify a sound wave and thereby pro-duce useful power. The attenuation thesound suffered as it passed through thetiny pores in the regenerator would, itseemed, always overwhelm the mod-est gain that the temperature gradientcreated. So the Los Alamos physicistsconcentrated on using standing wavesfor acoustic engines and refrigerators,and, like several other research groupsaround the world, made considerablestrides over the next decade and a half.

But in the past few years, the questfor improved efficiency led Swift,working with Backhaus, to reconsiderCeperley’s approach. Looking again atthe problem, we realized that the re-generator produces an amount ofacoustic power that is proportional tothe product of the oscillating pressureof the gas and the oscillating velocity ofthe gas. The power wasted in the re-generator is proportional to the squareof the oscillating velocity. This loss isanalogous to the power dissipated inan electrical resistor, which is propor-tional to the square of the current thatflows through it.

Faced with such losses—say, fromthe resistance of the wires in a trans-mission line—electrical engineers longago found an easy solution: Increasethe voltage and diminish the current sothat their product (which equals thepower transferred) remains constant.So we reasoned that if the oscillatorypressure could be made very large and

the flow velocity made very small, in away that preserved their product, wecould boost the efficiency of the regen-erator without reducing the power itcould produce.

These requirements led us back toacoustic standing waves used in moretypical thermoacoustic engines as away to obtain a high ratio of pressureto gas movement. Minimizing the flowvelocity of the gas overcomes viscouslosses inside the regenerator, whosetiny pores allow heat to move betweengas and solid most efficiently. But us-ing a regenerator instead of a normalstack changes the timing of heat trans-fer in a fundamental way: The oscillat-ing gas has no time to shift position be-fore the exchange of heat takes place.So it was not merely a matter of replac-ing a stack with a regenerator. The de-vice that was needed had to reproducesome of the attributes of a standingwave (high pressure and small flowvelocity) while also having some of theattributes of a traveling wave (pressurehad to rise and fall in phase with ve-locity, not with displacement).

We were able to devise just such ahybrid by coupling a standing wavecavity (basically a long tube) with adual-necked Helmholtz resonator. Oneneck is open to the flow of gas, and theother contains the regenerator and heatexchangers. The open passage actsmuch as a soda bottle does when oneblows over its mouth. The mass of theair in the neck of the bottle and the


Figure 8. Traveling-wave heat engine that Peter H. Ceperley envisioned more than two decadesago amounts to a loop of gas-filled pipe with one or more porous regenerators inside. Heat ex-changers attached to each regenerator supply heat or carry it away, setting up thermal gradients(solid arrows). In this configuration (adapted from Ceperley’s 1979 patent), one regenerator ismeant to amplify the traveling acoustic wave (dashed arrow), while the second provides usefulcooling. Although Ceperley was never able to construct a working traveling-wave engine, T.Yazaki and three Japanese colleagues described in 1998 their success in building such a deviceto compare the properties of traveling- and standing-wave thermoacoustic engines.

springiness provided by the compress-ible gas trapped beneath it support os-cillations—just as a solid mass andcoiled spring do. Helmholtz developedthis technique to amplify sounds in anarrow band of frequencies near thenatural frequency of the resonator. Theamount of amplification depends onhow closely the frequency of the res-onator matches the frequency of thesound that is incident on the neck.

In our thermoacoustic Stirling en-gine, the natural frequency of theHelmholtz resonator is considerablyhigher than the frequency of operation.So the variation in pressure inside theHelmholtz resonator is only about 10

percent greater than inside the stand-ing-wave resonator. Although modest,this difference is enough to drive somegas through the regenerator each timethe pressure rises or falls—flow that isin phase with the changing pressure,just as in a traveling acoustic wave.

We thus neatly overcame the funda-mental problem of Ceperley’s travelingwave Stirling engine. But we were dis-appointed to discover that our engineperformed rather inefficiently com-pared with our expectations. The prob-lem turned out to be that the circulargeometry of the two-necked Helmholtzresonator allowed gas to stream aroundthe loop continuously, short circuiting

the hot and cold ends of the regeneratorand wasting large amounts of heat.

Once we realized what was happen-ing, it was easy enough to correct theproblem. One solution (which Ceper-ley had suggested years earlier for hiscircular design) would be to add a flex-ible membrane that passed acousticwaves yet blocked the continuous flowof gas. But prior experience with suchmembranes led us to believe that itwould be hard to engineer somethingsufficiently robust to hold up overtime. So instead we added a jet pump(asymmetric openings that allow flowto pass in one direction more easilythan the other) to create a slight back-pressure in the loop, just enough tocancel the streaming. And we werepleased to find that the efficiency of theengine improved markedly. At best itran at 42 percent of the maximum the-oretical efficiency, which is about 40percent better than earlier thermo-acoustic devices had achieved and ri-vals what modern internal-combustionengines can offer.

The Next CompetitionThermoacoustic engines and refrigera-tors were already being considered afew years ago for specialized applica-tions, where their simplicity, lack of lu-brication and sliding seals, and theiruse of environmentally harmless work-ing fluids were adequate compensa-tion for their lower efficiencies. Thislatest breakthrough, coupled with oth-er developments in the design of high-power, single-frequency loudspeakersand reciprocating electric generators,suggests that thermoacoustics maysoon emerge as an environmentally at-tractive way to power hybrid electricvehicles, capture solar energy, refriger-ate food, air condition buildings, lique-fy industrial gases and serve in othercapacities that are yet to be imagined.

In 2099, the National Academy ofEngineering probably will again con-vene an expert panel to select the out-standing technological achievements ofthe 21st century. We hope the machinesthat our unborn grandchildren see onthat list will include thermoacousticdevices, which promise to improveeveryone’s standard of living whilehelping to protect the planet. We and asmall band of interested physicists andengineers have been working hardover the past two decades to makeacoustic engines and refrigerators partof that future. The latest achievements


Figure 9. Thermoacoustic Stirling engine designed at Los Alamos National Laboratory (top)weighs 200 kilograms and measures 3.5 meters long. The regenerator (middle, dark red) sits inone of two channels that connect the main helium-filled resonator with a “compliance volume”(dark blue); the other connection is through a narrow pipe, or “inertance tube” (dark green). Theinertance and compliance provided by these components act (respectively) like inductance andcapacitance in an analogous electrical circuit (bottom), which introduce phase shifts (betweenvoltage and current in an electrical network and between gas pressure and velocity in anacoustic network). Although pressure and gas velocity are 90 degrees out of phase within themain standing-wave resonator, the phase shift created by the inertance-compliance network atthe left creates a small pressure difference across the regenerator, driving gas through it. Thisflow increases and decreases in phase with the rise and fall of pressure in the main resonator.This configuration thus achieves the same phasing of pressure and gas velocity within the re-generator as is found in a traveling wave. Yet the standing wave of the main resonator providesfor much larger pressure swings than those found in a traveling wave with a comparableamount of gas motion. These conditions ensure that the regenerator provides more gain thanloss, thus amplifying the acoustic oscillations within the engine. The thermal energy injected atthe hot end of the regenerator is transformed efficiently into acoustic energy, which can be used,for example, to drive a reciprocating electric generator or to power a refrigerator. One such de-vice under development for commercial application is intended to liquefy natural gas.

are certainly encouraging, but there isstill much left to be done.

AcknowledgmentsThe authors gratefully acknowledge thegenerosity with which Greg Swift hasshared his theoretical insights and techno-logical innovations during the past 20years with the world-wide community ofthermoacousticians.

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