The Power of Sound

A reprint from American Scientist the magazine of Sigma Xi, The Scientific Research Society

This reprint is provided for personal and noncommercial use. For any other use, please send a request to Permissions, American Scientist, P.O. Box 13975, Research Triangle Park, NC, 27709, U.S.A., or by electronic mail to [email protected]. ©Sigma Xi, The Scientific Research Society and other rightsholders The Power of Sound

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

Steven L. Garrett and Scott Backhaus

ast February, a panel of the Nation- source into acoustic power while re- Such thermal effects also explain why Lal Academy of Engineering an- jecting waste heat to a low-temperature 19th-century glassblowers occasionally nounced the results of its effort to rank sink. A thermoacoustic refrigerator heard their heated vessels emit pure the greatest engineering achievements does the opposite, using acoustic pow- tones—a hint that thermoacoustics of the 20th century. Second and tenth er to pump heat from a cool source to a might have some interesting practical on that list were two very successful hot sink. These devices perform best consequences. Yet it took more than a heat engines: the automobile (and when they employ noble gases as their century for anyone to recognize the op- hence, the internal-combustion engine) thermodynamic working fluids. Unlike posite effect: Just as a temperature dif- and the refrigerator and air condition- the chemicals used in refrigeration ference could create sound, sound could er, heat engines operated in reverse. over the years, such gases are both produce a temperature difference—hot But these two pillars of modern tech- nontoxic and environmentally benign. to one side, cool to the other. How nology share another, less flattering Another appealing feature of thermoa- acoustic cooling can arise is, in retro- distinction: Both have inadvertently coustics is that one can easily flange an spect, rather easy to understand. damaged the environment—by cloud- engine onto a refrigerator, creating a Suppose an acoustic wave excites a ing skies with smog, spewing green- heat-powered cooler with no moving gas that was initially at some average house gases or leaking compounds parts at all. temperature and pressure. At any one that erode the earth’s protective blan- So far, most machines of this variety spot, the temperature will go up as the ket of stratospheric ozone. reside in laboratories. But prototype pressure increases, assuming the rise Over the past two decades, investiga- thermoacoustic refrigerators have op- happens rapidly enough that heat has tors like ourselves have worked to de- erated on the Space Shuttle and aboard no time to flow away. The change in velop an entirely new class of engines a Navy warship. And a powerful temperature that accompanies the and refrigerators that may help reduce thermoacoustic engine has recently acoustic compressions depends on the or eliminate such threats. These thermo- demonstrated its ability to liquefy nat- magnitude of the pressure fluctuations. acoustic devices produce or absorb ural gas on a commercial scale. For ordinary speech, the relative pres- sound power, rather than the “shaft That sound-powered equipment can sure changes are on the order of only power” characteristic of rotating ma- accomplish these tasks seems almost one part per million (equivalent to 74 chinery. Because of its inherent mechan- magical—and rightly so: Arthur C. decibels, or dB, in sound pressure lev- ical simplicity, such equipment may one Clarke once remarked that “any suffi- els), and the associated variation in day serve widely, perhaps generating ciently developed technology is indis- temperature is a mere ten-thousandth electricity at individual homes, while tinguishable from magic.” Below we of a degree Celsius. Even for sounds at producing domestic hot water and pro- attempt to reveal the legerdemain and the auditory threshold of pain (120 dB), viding space heating or cooling. explain the simple physics that makes temperature oscillates up and down by How do these machines work? In a thermoacoustic machines possible. only about 0.02 degree. nutshell, a thermoacoustic engine con- Figure 1. Glassblowers can sometimes hear verts heat from a high-temperature Speech and Hot Air their handiwork spontaneously emit sounds The interaction of heat and sound has when the application of heat to one end of a Steven L. Garrett received his Ph.D. in physics interested acousticians since 1816, vessel inadvertently transforms it into a from the University of California, Los Angeles in when Laplace corrected Newton’s ear- “thermoacoustic engine.” This phenomenon 1977 and is currently the United Technologies lier calculation of the speed of sound was first documented in the scientific litera- Professor in the Graduate Program in Acoustics in air. Newton had assumed that the ture in 1850, when the theoretical connection and a Senior Scientist with the Applied Research expansions and compressions of a between heat and sound was well recog- Laboratory, both at the Pennsylvania State sound wave in a gas happen without nized. But it was not until quite recently that University. Scott Backhaus earned his doctorate in affecting the temperature. Laplace ac- scientists realized that acoustic waves can physics from the University of California, Berkeley also produce cooling. The authors discuss the in 1997. He is currently the Reines Fellow at Los counted for the slight variations in fundamental physics behind thermoacoustic Alamos National Laboratory. Address for Garrett: temperature that in fact take place, and engines and refrigerators, and they describe Penn State, Applied Research Laboratory, P. O. by doing so he derived the correct how machines based on these principles are Box 30, State College, PA 16804. Internet: speed of sound in air, a value that is 18 now being engineered to operate reliably and [email protected] percent faster than Newton’s estimate. at high efficiency.

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 517 with permission only. Contact [email protected]. Most refrigerators and air condition- swings that typical sound waves bring terial. Solids have much higher heat ca- ers must pump heat over considerably about are too small to be useful. To han- pacities per unit volume than gases, so greater temperature ranges, usually 20 dle larger temperature spans, the gas they can exchange a considerable degrees or more. So the temperature must be put in contact with a solid ma- amount of heat without changing in temperature by very much. If a gas car- rying a sound wave is placed near a solid surface, the solid will tend to absorb the heat of compression, keeping the temperature stable. The opposite is also true: The solid releases heat when the gas expands, preventing it from cooling down as much as it otherwise would. The distance over which the diffu- sion of heat to or from an adjacent solid can take place is called the thermal penetration depth. Its value depends on the frequency of the passing sound wave and the properties of the gas. In typical thermoacoustic devices, and for sound waves in air at audio frequencies, the thermal penetration depth is typically on the order of one-tenth of a millimeter. So to optimize the exchange of heat, the design of a thermoacoustic engine or refrigerator must include a solid with gaps that are about twice this di- mension in width, through which a high-amplitude sound wave propa- gates. The porous solid (frequently a jelly-roll of plastic for refrigerators or of stainless steel for engines), is called a “stack,” because it contains many lay- ers and thus resembles a stack of plates. When an acoustically driven gas moves through the stack, pressure, temperature and position all oscillate with time. If the gas is enclosed within a tube, sound bounces back and forth creating an acoustic standing wave. In that case, pressure will be in phase with displacement—that is, the pressure reaches its maximum or mini- mum value when the gas is at an extreme of its oscillatory motion. Consider how this simple relation can be put to use in a thermoacoustic refrigerator, which in its most rudi- mentary form amounts to a closed tube, a porous stack and a source of Figure 2. Thermoacoustic device consists, in essence, of a gas-filled tube containing a “stack” (top), acoustic energy. As a parcel of gas a porous solid with many open channels through which the gas can pass. Resonating sound moves to one side, say to the left, it waves (created, for example, by a loudspeaker) force gas to move back and forth through openings heats up as the pressure rises and then in the stack. If the temperature gradient along the stack is modest (middle), gas shifted to one side comes momentarily to rest before re- (a) will be compressed and warmed so that a parcel of gas with dimensions that are roughly equal versing direction. Near the end of its to the thermal penetration depth (δk) releases heat to the stack. When this same gas then shifts in motion, the hot gas deposits heat into the other direction (b), it expands and cools enough to absorb heat. Although an individual parcel the stack, which is somewhat cooler. carries heat just a small distance, the many parcels making up the gas form a “bucket brigade,” During the next half-cycle, the parcel which transfers heat from a cold region to a warm one and thus provides refrigeration. The same of gas moves to the right and expands. device can be turned into a thermoacoustic engine (bottom) if the temperature difference along the When it reaches its rightmost extreme, stack 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 side it will be colder than the adjacent por- and expands (d), it cools but stays hotter than the stack and thus releases heat. Hence, the parcel tion of the stack and will extract heat thermally expands at high pressure and contracts at low pressure, which amplifies the pressure os- from it. The result is that the parcel cillations of the reverberating sound waves, transforming heat energy into acoustic energy. pumps heat from right to left and can

518 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. Figure 3. Simple thermoacoustic engine can be constructed from common components (left). A small test tube, a heater wire and a plug of porous ceramic (material used in automotive catalytic converters) properly arranged can produce about a watt of acoustic power. If one end of the ceramic plug is placed at the focus of a parabolic mirror (right), solar energy, too, can power this demonstration engine. (Courtesy of Reh-lin Chen.) do so even when the left side of the centrated sunlight or a flame—which The test tube amounts to an acoustic stack is hotter than the right. explains why glassblowers sometimes resonator, which, like a laser cavity, al- The span of movement for an indi- observe the spontaneous generation of lows a standing wave to build in am- vidual parcel is quite small, but the net sound when they heat the walls of a plitude as energy bounces back and effect is that of a bucket brigade: Each glass tube (serving as a stack) in such a forth. The open side of the test tube parcel of oscillating gas takes heat from way as to create a strong temperature serves the same function as the partial- the one behind and hands this heat off gradient, a phenomenon first docu- ly silvered mirror at the output side of to the next one ahead. The heat, plus mented in a scholarly journal in 1850. a laser. Both allow some of the energy the work done to move it thermo- Indeed, this “singing tube” effect stored within the resonant cavity to ra- acoustically, exits one end of the stack arises easily enough that Reh-lin Chen, diate into the surrounding environ- through a hot heat exchanger (similar a student in the Graduate Program in ment. Although Chen’s “acoustic laser” to a car radiator). A cold heat exchang- Acoustics at the Pennsylvania State produces only about a watt of sound er, located at the other end of the stack, University, was able to build a ther- power, a similar device heated by the provides useful cooling to some exter- moacoustic engine with only three burning of natural gas produces in ex- nal heat load. parts. The stack consists of a plug of cess of 10 kilowatts—a high-powered One can easily reverse this process porous ceramic (material that is nor- laser indeed! of refrigeration to make a thermo- mally used for automotive catalytic One of the most remarkable features acoustic engine. Just apply heat at the converters). Electrical current passing of such thermoacoustic engines is that hot end of the stack and remove it at through a heater wire attached at one they have no moving parts. They de- the cold end, creating a steep tempera- end of the plug imposes a temperature mand nothing beyond the basic physics ture gradient. Now when a parcel of gradient. A Pyrex test tube acts as a of the cavity and stack to force the com- gas moves to the left, its pressure and miniature organ pipe and sets up a pressions, expansions, displacements temperature rise as before, but the standing acoustic wave. Because the and heat transfers to happen at the stack at that point is hotter still. So heat cold end of the stack faces the mouth of right times. The internal-combustion flows from the stack into the gas, caus- the test tube, no cold heat exchanger is engines in our cars also depend on ing it to expand thermally just as pres- needed: Air streaming in and out of the proper timing—the intake, compres- sure reaches a maximum. Conversely, open end of the tube provides sufficient sion, expansion and exhaust stages of when the parcel shifts to the right, it cooling. Despite its simplicity, Chen’s the power cycle must take place in expands and cools, but the stack there engine is capable of producing sound smooth succession. But conventional is cooler still. So heat flows into the sol- at uncomfortable levels. automobile engines require at least two id from the gas, causing thermal con- valves per cylinder, each with a spring, traction just as pressure reaches a min- An Acoustic Laser rocker arm and a push rod (or an over- imum. In this way, the temperature The transparency of this device, literal head cam driven by a timing belt) to variation imposed on the stack drives and figurative, invites analogies with produce the required phasing. This dif- heat into and out of the gas, forcing it the laser. Borrowing some vocabulary ference makes thermoacoustic devices to do work on its surroundings and from optics, one would say that a non- much simpler and potentially much amplifying the acoustic oscillations. equilibrium condition (corresponding more reliable than conventional en- Maintenance of the steep thermal gra- to the population inversion of electron gines and refrigerators, because they dient requires an external source of energy levels in a laser material) is can avoid wear associated with valves, power, such as an electric heater, con- maintained across the heated stack. piston rings, crankshafts, connecting

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 519 with permission only. Contact [email protected]. that exactly one-half wavelength of sound fits inside), the piston would only have to move by something like 0.05 millimeter in a typical cavity (Q=30) to produce the same change in pressure. That tiny distance is only one two-hundredth as far as in the case of slow compression, yet it achieves exactly the same peak pressure. Clearly, an oscillating acoustic source that moves such small distances does not need a piston with sealing rings moving in a lubricated cylinder—elim- inating all sorts of pesky components found in conventional refrigeration compressors and internal-combustion engines. Flexible seals, such as metal bellows, would suffice. Such seals require no lubrication and do not de- mand the machining of close-tolerance parts to eliminate gas “blow-by” between a piston and its tight-fitting cylinder.

A Stereo Refrigerator The simplicity of the hardware in- volved in thermoacoustic machines is best appreciated by examining a con- crete example. In the mid-1990s, one of us (Garrett) and his colleagues at the Naval Postgraduate School in Mon- terey, California developed two thermoacoustic refrigerators for the Space Figure 4. Thermoacoustic engines are similar to optical lasers in that both types of apparatus Shuttle. The first was designed to cool amplify standing waves set up within resonant cavities. In a ruby laser (top), for example, en- electronic components, and the second ergy is added by means of a flash tube, which creates a “population inversion” of electron energy levels. In the thermoacoustic analogue (bottom), energy is injected into the cavity using was intended to replace the refrigera- the heated stack, which creates a nonequilibrium temperature distribution. tor-freezer unit used to preserve blood and urine samples from astronauts en- rods and so forth. Thus thermoacoustic one cycle, either by friction or by the gaged in biomedical experiments. devices require no lubrication. production of useful work. The ulti- This “thermoacoustic life sciences re- To the uninitiated, it may seem sur- mate value of the pressure variation frigerator,” as we called it, produced prising that pistonless engines can depends on the quality factor of the good results in the laboratory, yet achieve high power levels. Thermo- resonator, Q (which is equal to 2/π NASA sponsorship ended abruptly, os- acoustic devices manage this feat by times the ratio of the pressure the loud- tensibly for lack of funds. Because the exploiting acoustic resonance to pro- speaker produces in the resonator to project was progressing so well by that duce large pressure oscillations from that which the same loudspeaker time, we were quite puzzled. But six small gas motions. Consider a closed would have generated in an infinitely months later we discovered that the tube (an acoustic resonator) with a long tube, one in which there would be managers of our program at the NASA loudspeaker mounted at one end. The no reflected wave). Life Sciences Division were enmeshed oscillating movement of the loud- The result of this resonant Q amplifi- in a controversial FBI investigation of speaker pumps in acoustic energy, cation can be easily understood by con- kickbacks and bribery at the Johnson which travels down the tube at the sidering the motion of a piston com- Space Flight Center in Houston. Clear- speed of sound, reflects off the far end pressing some gas within a cylinder. If ly, they were preoccupied with some- and shoots back toward the source. If the initial length of the gas volume is, thing other than evaluating our techni- the frequency of the excitation is just say, 20 centimeters and the piston cal progress. Fortunately, the U.S. Navy right, the next increment of energy that moves slowly inward 1 centimeter, the was in need of a similar chiller and the loudspeaker injects will arrive in pressure of the gas would increase by 5 took over support of our efforts. step with the reflected portion of the percent, assuming no leakage around Because we had originally designed acoustic wave. the piston. If, however, it oscillated this refrigerator to operate in the rather The pressure swings in the resonat- back and forth rapidly at the resonant demanding environment of space, we ing wave will then grow until the ener- frequency of the cavity (860 cycles per chose a “stereo” configuration to pro- gy added during one cycle is exactly second, assuming that the cylinder is vide redundancy in case one of the equal to the energy dissipated during filled with air at room temperature so loudspeakers failed. The two loud-

520 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. speakers are similar to those used for sound reproduction, but they are much more powerful and operate over a lim- ited range of frequencies. They also dif- fer from normal speakers in that the cones are inverted, having their large diameter at the voice coil and small diameter where the sound is radiated. Figure 5. Gas pressure within a cylinder in- The moving parts of these speakers are creases in inverse proportion to the decrease joined to a stationary U-shaped reso- in volume when a piston is moved slowly in- nant cavity by small metal bellows. ward (top). For example, 1 centimeter of mo- The U-tube contains two separate tion in a 20-centimeter cylinder increases the stacks, each with two water-filled heat pressure by 5 percent. But the same peak exchangers, which resemble small car pressure will result if the piston shifts back and forth at the resonant frequency of the radiators, attached at the ends. Two of cavity by just 50 micrometers, movements these heat exchangers exhaust waste that are small enough for flexible bellows to heat, and two provide cooling. In this accommodate (middle). The standing wave incarnation, chilled water from our achieves its highest pressures at the two ends “life sciences refrigerator” circulated of the cylinder as gas sloshes back and forth, through racks of radar electronics on whereas the velocity of the gas is always zero the USS Deyo, a Navy destroyer. The at these points in a closed tube (bottom). maximum cooling capacity we achieved in our sea trials proved to be in excess frigerator itself reached 26 percent of flows between the gas and the stack. of 400 watts, using just over 200 watts the maximum, but inefficiencies of the But recently, one of us (Backhaus) and of acoustic power. At the lowest tem- heat exchangers reduced the useful his colleagues at Los Alamos National perature of operation we could com- cooling to the 17-percent value. That Laboratory demonstrated a technique fortably attain without risking the wa- level is little better than half of what that has enabled thermoacoustic en- ter freezing and blocking the pipes conventional chillers of similar size gines to break this seemingly insur- (about 4 degrees C), the refrigerator and cooling capacity can boast. mountable barrier by, strangely enough, performed at 17 percent of the efficien- Although we could have improved borrowing a technique that a Scottish cy that could, in principle, be coaxed the performance substantially with minister patented in 1816—the very from a perfect refrigerator operating some modest changes, thermoacoustic year Laplace first correctly calculated over the same temperature span—a refrigerators of this type will always the speed of sound. fundamental limit imposed by the Sec- have an intrinsic limit to their efficien- ond Law of Thermodynamics. The re- cy, which is imposed by the way heat Back to the Future

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

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 521 with permission only. Contact [email protected]. Figure 7. Stirling cycle contains four distinct steps—compression, heating, expansion and cooling—which produce a characteristic set of changes in pressure and volume (right). In a simple, two-piston Stirling engine (di- rectly below), the compression step (1) keeps one piston fixed as the other moves inward, the heat of compression being rejected into the adjacent cold reservoir. The next step (2) produces constant-volume regenerative heating, as both pistons move simultaneously, forcing cool gas through the porous regenerator, which was heated during the final step of the last cycle. Next (step 3), heat from the hot reservoir causes thermal expansion of the gas, which forces the adjacent piston to move outward. Finally (step 4), both pistons move together to create a constant-volume regenerative cooling of the heated gas. The changes in pressure and gas velocity within the regenerator of such a Stirling engine mimic the relationship seen in a traveling acoustic wave, where pressure and gas velocity move up and down in phase (bottom pair of panels).

522 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. In his spare time, the Reverend Robert Stirling designed, built and demonstrated 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 depended on the expansion and displacement of air inside of a cylinder that was warmed by external combustion through a heat exchanger. Stirling also conceived the idea of a regenerator (a solid with many holes running through it, which he called the “economiser”) to store thermal energy during part of the cycle and return it later. This component in- creased thermodynamic efficiency to impressive levels, but mechanical com- Figure 8. Traveling-wave heat engine that Peter H. Ceperley envisioned more than two decades plexity was greater for Stirling’s engine ago amounts to a loop of gas-filled pipe with one or more porous regenerators inside. Heat ex- than for the high-pressure steam and changers attached to each regenerator supply heat or carry it away, setting up thermal gradients internal-combustion varieties (which (solid arrows). In this configuration (adapted from Ceperley’s 1979 patent), one regenerator is do not require two heat exchangers), meant to amplify the traveling acoustic wave (dashed arrow), while the second provides useful cooling. Although Ceperley was never able to construct a working traveling-wave engine, T. restricting its widespread use. Yazaki and three Japanese colleagues described in 1998 their success in building such a device The story of how one of the oldest to compare the properties of traveling- and standing-wave thermoacoustic engines. ideas in the history of heat engines linked up with one of the newest is “engine” would never be able to am- the flow velocity made very small, in a typical of the tortuous routes to discov- plify a sound wave and thereby pro- way that preserved their product, we ery (or rediscovery) that many scien- duce useful power. The attenuation the could boost the efficiency of the regen- tists experience. In this case, the jour- sound suffered as it passed through the erator without reducing the power it ney began two decades ago, when tiny pores in the regenerator would, it could produce. Garrett had the pleasure of working seemed, always overwhelm the mod- These requirements led us back to with Gregory Swift, then a graduate est gain that the temperature gradient acoustic standing waves used in more student at the University of California, created. So the Los Alamos physicists typical thermoacoustic engines as a Berkeley. Swift eventually received his concentrated on using standing waves way to obtain a high ratio of pressure doctorate in physics and joined John for acoustic engines and refrigerators, to gas movement. Minimizing the flow Wheatley, who was just then preparing and, like several other research groups velocity of the gas overcomes viscous to move his low-temperature physics around the world, made considerable losses inside the regenerator, whose group to Los Alamos National Labora- strides over the next decade and a half. tiny pores allow heat to move between tory and focus his research efforts on But in the past few years, the quest gas and solid most efficiently. But us- the development of novel heat engines for improved efficiency led Swift, ing a regenerator instead of a normal and refrigerators. working with Backhaus, to reconsider stack changes the timing of heat trans- As a graduation present, Garrett Ceperley’s approach. Looking again at fer in a fundamental way: The oscillat- gave Swift a copy of an intriguing arti- the problem, we realized that the re- ing gas has no time to shift position be- cle that Peter Ceperley, a physics pro- generator produces an amount of fore the exchange of heat takes place. fessor at George Mason University, had acoustic power that is proportional to So it was not merely a matter of replac- published a few years earlier. It was the product of the oscillating pressure ing a stack with a regenerator. The de- entitled “A pistonless Stirling engine— of the gas and the oscillating velocity of vice that was needed had to reproduce The traveling wave heat engine.” the gas. The power wasted in the re- some of the attributes of a standing Ceperley cleverly recognized that the generator is proportional to the square wave (high pressure and small flow phasing between pressure and gas ve- of the oscillating velocity. This loss is velocity) while also having some of the locity within Stirling’s regenerator was analogous to the power dissipated in attributes of a traveling wave (pressure the same as the phasing in a traveling an electrical resistor, which is propor- had to rise and fall in phase with ve- acoustic wave. He demonstrated that tional to the square of the current that locity, not with displacement). similarity by arranging a temperature flows through it. We were able to devise just such a gradient across a crude regenerator (a Faced with such losses—say, from hybrid by coupling a standing wave plug of fine steel wool) and sending a the resistance of the wires in a trans- cavity (basically a long tube) with a sound wave though it. Some thermal mission line—electrical engineers long dual-necked Helmholtz resonator. One energy was converted to acoustic ener- ago found an easy solution: Increase neck is open to the flow of gas, and the gy, though not enough to make up for the voltage and diminish the current so other contains the regenerator and heat the accompanying losses. that their product (which equals the exchangers. The open passage acts Swift brought Ceperley’s article with power transferred) remains constant. much as a soda bottle does when one him to Los Alamos, but he and his col- So we reasoned that if the oscillatory blows over its mouth. The mass of the leagues there decided that Ceperley’s pressure could be made very large and air in the neck of the bottle and the

© 2000 Sigma Xi, The Scientific Research Society. Reproduction 2000 November–December 523 with permission only. Contact [email protected]. the hot and cold ends of the regenerator and wasting large amounts of heat. Once we realized what was happen- ing, it was easy enough to correct the problem. One solution (which Ceper- ley had suggested years earlier for his circular design) would be to add a flexible membrane that passed acoustic waves yet blocked the continuous flow of gas. But prior experience with such membranes led us to believe that it would be hard to engineer something sufficiently robust to hold up over time. So instead we added a jet pump (asymmetric openings that allow flow to pass in one direction more easily than the other) to create a slight back- pressure in the loop, just enough to cancel the streaming. And we were pleased to find that the efficiency of the engine improved markedly. At best it ran at 42 percent of the maximum theoretical efficiency, which is about 40 percent better than earlier thermoacoustic devices had achieved and ri- vals what modern internal-combustion engines can offer.

Figure 9. Thermoacoustic Stirling engine designed at Los Alamos National Laboratory (top) The Next Competition weighs 200 kilograms and measures 3.5 meters long. The regenerator (middle, dark red) sits in Thermoacoustic engines and refrigera- one of two channels that connect the main helium-filled resonator with a “compliance volume” tors were already being considered a (dark blue); the other connection is through a narrow pipe, or “inertance tube” (dark green). The few years ago for specialized applica- inertance and compliance provided by these components act (respectively) like inductance and tions, where their simplicity, lack of lu- capacitance in an analogous electrical circuit (bottom), which introduce phase shifts (between brication and sliding seals, and their voltage and current in an electrical network and between gas pressure and velocity in an use of environmentally harmless work- acoustic network). Although pressure and gas velocity are 90 degrees out of phase within the ing fluids were adequate compensa- main standing-wave resonator, the phase shift created by the inertance-compliance network at tion for their lower efficiencies. This the left creates a small pressure difference across the regenerator, driving gas through it. This flow increases and decreases in phase with the rise and fall of pressure in the main resonator. latest breakthrough, coupled with oth- This configuration thus achieves the same phasing of pressure and gas velocity within the re- er developments in the design of high- generator as is found in a traveling wave. Yet the standing wave of the main resonator provides power, single-frequency loudspeakers for much larger pressure swings than those found in a traveling wave with a comparable and reciprocating electric generators, amount of gas motion. These conditions ensure that the regenerator provides more gain than suggests that thermoacoustics may loss, thus amplifying the acoustic oscillations within the engine. The thermal energy injected at soon emerge as an environmentally at- the hot end of the regenerator is transformed efficiently into acoustic energy, which can be used, tractive way to power hybrid electric for example, to drive a reciprocating electric generator or to power a refrigerator. One such de- vehicles, capture solar energy, refriger- vice under development for commercial application is intended to liquefy natural gas. ate food, air condition buildings, lique- springiness provided by the compress- percent greater than inside the stand- fy industrial gases and serve in other ible gas trapped beneath it support os- ing-wave resonator. Although modest, capacities that are yet to be imagined. cillations—just as a solid mass and this difference is enough to drive some In 2099, the National Academy of coiled spring do. Helmholtz developed gas through the regenerator each time Engineering probably will again con- this technique to amplify sounds in a the pressure rises or falls—flow that is vene an expert panel to select the out- narrow band of frequencies near the in phase with the changing pressure, standing technological achievements of natural frequency of the resonator. The just as in a traveling acoustic wave. the 21st century. We hope the machines amount of amplification depends on We thus neatly overcame the funda- that our unborn grandchildren see on how closely the frequency of the res- mental problem of Ceperley’s traveling that list will include thermoacoustic onator matches the frequency of the wave Stirling engine. But we were dis- devices, which promise to improve sound that is incident on the neck. appointed to discover that our engine everyone’s standard of living while In our thermoacoustic Stirling en- performed rather inefficiently com- helping to protect the planet. We and a gine, the natural frequency of the pared with our expectations. The prob- small band of interested physicists and Helmholtz resonator is considerably lem turned out to be that the circular engineers have been working hard higher than the frequency of operation. geometry of the two-necked Helmholtz over the past two decades to make So the variation in pressure inside the resonator allowed gas to stream around acoustic engines and refrigerators part Helmholtz resonator is only about 10 the loop continuously, short circuiting of that future. The latest achievements

524 American Scientist, Volume 88 © 2000 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. of the 16th International Congress on Acoustics refrigerators. Physics Today 48(7):22–28. are certainly encouraging, but there is 2:813–814, eds. P. K. Kuhl and L. A. Crum. Swift, G. W. 1997. Thermoacoustic natural gas still much left to be done. Woodbury, New York: Acoustical Society of liquefier. Proceedings of the DOE Natural Gas America. Conference, Morgantown, West Virginia: Acknowledgments Garrett, S. L. 1997. High-power thermoacoustic Federal Energy Technology Center. The authors gratefully acknowledge the refrigerator. US Patent 5,647,216. Swift, G. W. 1997. Thermoacoustic engines and Garrett, S. L. 1999. Reinventing the engine. refrigerators. In Encyclopedia of Applied Physics generosity with which Greg Swift has Nature 399:303–305. 21:245–264, ed. G. L. Trigg. New York: Wi- shared his theoretical insights and techno- Garrett, S. L., J. A. Adeff and T. J. Hofler. 1993. ley-VCH. logical innovations during the past 20 Thermoacoustic refrigerator for space appli- Swift, G. W., D. L. Gardner and S. Backhaus. years with the world-wide community of cations. Journal of Thermophysics and Heat 1999. Acoustic recovery of lost power in thermoacousticians. Transfer 7:595–599. pulse tube refrigerators. Journal of the Gifford, W. E., and R. C. Longsworth. 1966. Sur- Acoustical Society of America 105:711–724. Bibliography face heat pumping. Advances in Cryogenic Wheatley, J. C., G. W. Swift and A. Migliori. Armstrong, N. 1999. The Engineered Century, Engineering 11:171–179. 1983. Acoustical heat pumping engine. US The Bridge 30(1):14–18. Migliori, A., and G. W. Swift. 1988. A liquid- Patent 4,398,398. Backhaus, S., and G. W. Swift. 1999. A thermo- sodium thermoacoustic engine. Applied Wheatley, J. C., G. W. Swift and A. Migliori. acoustic-Stirling heat engine. Nature Physics Letters 53:355–357. 1986. The natural heat engine. Los Alamos 399:335–338. Reid, R. S., W. C. Ward and G. W. Swift. 1998. Science 14:2–33. Backhaus, S., and G. W. Swift. 2000. A thermo- Cyclic thermodynamics with open flow. acoustic Stirling heat engine. Journal of the Physical Review Letters 80:4617–4620. Acoustical Society of America 107:3148–3166. Rott, N. 1980. Thermoacoustics. Advances in Benedict, R. E. 1991. Ozone Diplomacy: New Di- Applied Mechanics 20:135–175. rections in Safeguarding the Planet. Cambridge, Sondhaus, C. 1850. Ueber dei Schallschwingun- Mass.: Harvard University Press. gen der Luft in erhitzten Glasröhren und in Ceperley, P. H. 1979. A pistonless Stirling en- gedeckten Pfeifen von ungleicher Weite. gine—The traveling wave heat engine. Annalen der Physik und Chemie 79:1–34. Journal of the Acoustical Society of America Swift, G. W. 1988. Thermoacoustic engines. 66:1508–1513. Journal of the Acoustical Society of America Chen, R-L., and S. L. Garrett. 1998. Solar/heat 88:1145–1180. driven thermoacoustic engine. In Proceedings Swift, G. W. 1995. Thermoacoustic engines and