Thermoacoustics - Wikiparency

# Thermoacoustics **Thermoacoustics** is the branch of [[Sound|acoustics]] concerned with the interaction between temperature, density and pressure variations of an acoustic wave and how that coupling can pump heat or, run the other way, generate sound from a temperature difference. A sound wave already compresses and rarefies the gas it moves through, and compression heats a gas while rarefaction cools it; thermoacoustics is what happens when that ordinary heating and cooling is deliberately coupled to a heat source, a heat sink, or a solid surface nearby. The coupling can either amplify a standing wave, as in the [[Rijke_tube|Rijke tube]], or use an externally imposed wave to pump heat from cold to hot, as in a thermoacoustic refrigerator. The article's microsim, *Thermoacoustics: the Rijke tube sings*, models the classic case: a vertical tube open at both ends with a heated wire gauze whose position along the tube decides whether the tube's standing wave grows or dies. The governing idea is Rayleigh's criterion, stated by Lord Rayleigh in 1878: a standing acoustic wave grows if heat is added to the gas at the moment of greatest compression and removed at the moment of greatest rarefaction, and it is damped if the timing is reversed.[^rayleigh1878] Everything in the field, from a singing gas flame to a modern thermoacoustic engine with no moving parts, is that criterion applied to a different geometry. *Try: in the microsim, drag the gauze position x/L past the quarter-length mark with the heater on and watch the gain readout cross zero — the tube sings only where the heat happens to land in phase with the pressure swing.* ## Historical review of thermoacoustics The phenomenon was first demonstrated, though not explained, well before Rayleigh's theory. In 1850 P. L. Rijke reported that a wire gauze heated by a flame and inserted a quarter of the way up a vertical glass tube open at both ends, with the flame then removed, would set the column of air singing loudly for several seconds while the gauze cooled — provided the gauze sat in the lower half of the tube.[^rijke1859] Rijke published the effect formally in 1859.[^rijke1859] Rayleigh supplied the general explanation in 1878: any process that deposits heat into the gas near a pressure maximum and removes it near a pressure minimum feeds energy into the standing wave, which is exactly what happens when a hot gauze sits in the region of an open tube's fundamental mode where the upward convective flow of heated air is in phase with the compressions.[^rayleigh1878] The twentieth century turned the demonstration into engineering: thermoacoustic engines and refrigerators with no moving parts other than the working gas itself were developed from the 1980s onward, notably by Gregory Swift and collaborators at Los Alamos National Laboratory, who built practical standing-wave and travelling-wave devices and worked out their thermodynamics in detail.[^swift1988] ## Sound A sound wave in a gas is a coupled oscillation of pressure, density, temperature and particle velocity, all varying together as the wave passes; where the wave compresses the gas, the local temperature rises adiabatically, and where it rarefies the gas, the temperature falls. In a tube open at both ends, the standing wave that fits the boundary conditions — an antinode of pressure at each closed obstruction and, for the fully open case, a displacement antinode with a pressure node at each open end — has its fundamental frequency set by the tube length L and the speed of sound c through f₁ = c / (2L), with overtones at integer multiples of f₁.[^up17-4] A 1.6 m tube in air at 343 m/s therefore sounds its fundamental near 107 Hz, the number the microsim's readout reproduces when the tube length control is set to 1.6 m. ## Penetration depths Heat and momentum do not diffuse instantly between the oscillating gas and a nearby solid surface; each diffuses only a finite distance during one cycle of the sound wave, a distance called the thermal or viscous penetration depth. The thermal penetration depth scales as the square root of the gas's thermal diffusivity divided by the angular frequency of the sound, and the viscous penetration depth scales the same way with kinematic viscosity in place of thermal diffusivity; both are largest at low frequency and shrink as frequency rises.[^swift1988] These depths set the natural pore size for the stacked plates or packed mesh — the "stack" or "regenerator" — used in a practical thermoacoustic engine: the gas in a pore narrower than a few penetration depths stays in close thermal contact with the solid, which is what lets the device exchange heat efficiently with the working gas each cycle. ## Thermoacoustic systems Practical thermoacoustic devices fall into two families depending on the phase relationship they set up between pressure and velocity in the working gas, which in turn decides how efficiently they can convert heat to acoustic power or acoustic power to a heat pump effect. Both families can run in either direction: fed a temperature difference across the stack or regenerator, the device is an engine that produces an acoustic wave (and, coupled to a linear alternator, electricity); fed an acoustic wave instead, driven by a loudspeaker-like element, the same geometry pumps heat from a cold heat exchanger to a hot one and works as a refrigerator or heat pump. Because the working fluid is an inert gas such as helium or a helium-argon mixture, and the only moving part in many designs is the gas itself (or, in some engines, a single free piston), thermoacoustic devices are attractive wherever long service life with no lubricated sliding seals matters, such as remote or long-duration cryocooling.[^swift1988] The two families differ chiefly in how the stack or regenerator sits relative to the resonator's pressure and velocity nodes, and in how strongly the heat exchangers pin the local gas temperature to the solid at each end. ### Standing-wave systems A standing-wave thermoacoustic engine or refrigerator places its stack near a pressure antinode of the resonator's standing wave, where pressure and velocity oscillate roughly 90 degrees out of phase; the Rijke tube is the simplest member of this family, with the heated gauze taking the place of the engineered stack. Standing-wave devices are mechanically simple — often no more than a closed or half-open tube with a heat exchanger inside — but the 90-degree phase mismatch between pressure and velocity limits how much of the available temperature difference can be converted to acoustic power, so standing-wave engines and refrigerators are typically less efficient than travelling-wave designs of comparable size.[^swift1988] ### Travelling-wave systems A travelling-wave thermoacoustic device instead arranges for pressure and velocity in the regenerator to be nearly in phase, the same relationship found in a travelling acoustic wave, which lets the working gas undergo something closer to the Stirling thermodynamic cycle at each element of the regenerator. Because the gas parcels near the regenerator are compressed and displaced almost together, travelling-wave engines and refrigerators can approach a substantially higher fraction of the Carnot efficiency limit than standing-wave devices, at the cost of a more elaborate acoustic network — typically a resonant loop rather than a simple tube — to set up the required phasing.[^swift1988] ## Minnesota *This section is specific to Wikitube.* No sourced Minnesota-specific thermoacoustics program is confirmed for this article; the closest documented Minnesota tie among acoustics articles on this site is the University of Minnesota's St. Anthony Falls Laboratory, whose turbulence research touches the same fluid-mechanics tools (see [[Hydrodynamic_stability]]), but that laboratory's published work is not thermoacoustic engines specifically. *Citation needed* if a Minnesota thermoacoustics research group or company should be named here. ## See also - [[Rijke_tube]] - [[Sound_amplification_by_stimulated_emission_of_radiation]] - [[Resonance]] - [[Standing_wave]] - [[Acoustic_resonance]] - [[Speed_of_sound]] ## References [^rayleigh1878]: Rayleigh, Lord (1878). "The explanation of certain acoustical phenomena." *Nature* 18, 319–321. https://doi.org/10.1038/018319a0 — heat given to the air at the moment of greatest condensation, or taken from it at the moment of greatest rarefaction, encourages the vibration; the reverse timing discourages it. [^rijke1859]: Rijke, P. L. (1859). "Notiz über eine neue Art, die in einer an beiden Enden offenen Röhre enthaltene Luft in Schwingungen zu versetzen" ["Notice of a new method of causing a vibration of the air contained in a tube open at both ends"]. *Annalen der Physik* 107, 339–343. https://doi.org/10.1002/andp.18591830616 — the heated gauze produces sound only when placed in the lower half of the tube, most strongly near a quarter of its length. [^swift1988]: Swift, Gregory W. (1988). "Thermoacoustic engines." *Journal of the Acoustical Society of America* 84 (4), 1145–1180. https://doi.org/10.1121/1.396617 — Rayleigh's criterion applied to standing-wave and travelling-wave devices, thermal and viscous penetration depths, and the practical engine and refrigerator designs built at Los Alamos National Laboratory. [^up17-4]: OpenStax, *University Physics Volume 1* (2016), ch. 17.4 "Normal Modes of a Standing Sound Wave" — a tube open at both ends has displacement antinodes and pressure nodes at each end, with resonant frequencies f_n = n v / (2L) for n = 1, 2, 3, ...; a tube open at both ends has a fundamental frequency twice that of the same length tube closed at one end.  **Microsim — three.js (Wikitube framework):** *Thermoacoustics* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/acoustics/Thermoacoustics.html" data-title="Thermoacoustics"></div> *Built from `MICROSIM_GUIDE/specs/acoustics/sims/Thermoacoustics.json`; part of the [[PORTAL_Acoustics|Acoustics portal]] spine (section sims and See-also variants).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Thermoacoustics) : [Wikitube](https://en.wikitube.io/wiki/Thermoacoustics) - skeleton pinned to revision 1372319098 (2026-09-11).