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The Power of Sound


Steven Garrett, Scott Backhaus

Back to the Future

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 invention contained no potentially explosive 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 increased thermodynamic efficiency to impressive levels, but mechanical complexity was greater for Stirling's engine than for the high-pressure steam and internal-combustion varieties (which do not require two heat exchangers), restricting its widespread use.

Figure 7. Stirling cycleClick to Enlarge Image

The story of how one of the oldest ideas in the history of heat engines linked up with one of the newest is typical of the tortuous routes to discovery (or rediscovery) that many scientists experience. In this case, the journey began two decades ago, when Garrett had the pleasure of working with Gregory Swift, then a graduate student at the University of California, Berkeley. Swift eventually received his doctorate in physics and joined John Wheatley, who was just then preparing to move his low-temperature physics group to Los Alamos National Laboratory and focus his research efforts on the development of novel heat engines and refrigerators.

As a graduation present, Garrett gave Swift a copy of an intriguing article that Peter Ceperley, a physics professor at George Mason University, had published a few years earlier. It was entitled "A pistonless Stirling engine—The traveling wave heat engine." Ceperley cleverly recognized that the phasing between pressure and gas velocity within Stirling's regenerator was the same as the phasing in a traveling acoustic wave. He demonstrated that similarity by arranging a temperature gradient across a crude regenerator (a plug of fine steel wool) and sending a sound wave though it. Some thermal energy was converted to acoustic energy, though not enough to make up for the accompanying losses.

Swift brought Ceperley's article with him to Los Alamos, but he and his colleagues there decided that Ceperley's "engine" would never be able to amplify a sound wave and thereby produce useful power. The attenuation the sound suffered as it passed through the tiny pores in the regenerator would, it seemed, always overwhelm the modest gain that the temperature gradient created. So the Los Alamos physicists concentrated on using standing waves for acoustic engines and refrigerators, and, like several other research groups around the world, made considerable strides over the next decade and a half.

But in the past few years, the quest for improved efficiency led Swift, working with Backhaus, to reconsider Ceperley's approach. Looking again at the problem, we realized that the regenerator produces an amount of acoustic power that is proportional to the product of the oscillating pressure of the gas and the oscillating velocity of the gas. The power wasted in the regenerator is proportional to the square of the oscillating velocity. This loss is analogous to the power dissipated in an electrical resistor, which is proportional to the square of the current that flows through it.

Figure 8. Traveling-wave heat engineClick to Enlarge Image

Faced with such losses—say, from the resistance of the wires in a transmission line—electrical engineers long ago found an easy solution: Increase the voltage and diminish the current so that their product (which equals the power transferred) remains constant. So we reasoned that if the oscillatory pressure could be made very large and the flow velocity made very small, in a way that preserved their product, we could boost the efficiency of the regenerator without reducing the power it could produce.

These requirements led us back to acoustic standing waves used in more typical thermoacoustic engines as a way to obtain a high ratio of pressure to gas movement. Minimizing the flow velocity of the gas overcomes viscous losses inside the regenerator, whose tiny pores allow heat to move between gas and solid most efficiently. But using a regenerator instead of a normal stack changes the timing of heat transfer in a fundamental way: The oscillating gas has no time to shift position before the exchange of heat takes place. So it was not merely a matter of replacing a stack with a regenerator. The device that was needed had to reproduce some of the attributes of a standing wave (high pressure and small flow velocity) while also having some of the attributes of a traveling wave (pressure had to rise and fall in phase with velocity, not with displacement).

We were able to devise just such a hybrid by coupling a standing wave cavity (basically a long tube) with a dual-necked Helmholtz resonator. One neck is open to the flow of gas, and the other contains the regenerator and heat exchangers. The open passage acts much as a soda bottle does when one blows over its mouth. The mass of the air in the neck of the bottle and the springiness provided by the compressible gas trapped beneath it support oscillations—just as a solid mass and coiled spring do. Helmholtz developed this technique to amplify sounds in a narrow band of frequencies near the natural frequency of the resonator. The amount of amplification depends on how closely the frequency of the resonator matches the frequency of the sound that is incident on the neck.

Figure 9. Thermoacoustic Stirling engineClick to Enlarge Image

In our thermoacoustic Stirling engine, the natural frequency of the Helmholtz resonator is considerably higher than the frequency of operation. So the variation in pressure inside the Helmholtz resonator is only about 10 percent greater than inside the standing-wave resonator. Although modest, this difference is enough to drive some gas through the regenerator each time the pressure rises or falls—flow that is in phase with the changing pressure, just as in a traveling acoustic wave.

We thus neatly overcame the fundamental problem of Ceperley's traveling wave Stirling engine. But we were disappointed to discover that our engine performed rather inefficiently compared with our expectations. The problem turned out to be that the circular geometry of the two-necked Helmholtz resonator allowed gas to stream around the loop continuously, short circuiting the hot and cold ends of the regenerator and wasting large amounts of heat.

Once we realized what was happening, it was easy enough to correct the problem. One solution (which Ceperley 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 rivals what modern internal-combustion engines can offer.

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