Thermoacoustic engine with linear alternator

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.01 × C.03 · Temperature gradient × Thermoacousticfamily: ThermoacousticD.01 × C.14 · Temperature gradient × Electromagnetic inductionfamily: Electromagnetic induction

Measured or reported performance

1. thermal-to-electrical conversion efficiency at the maximum-efficiency point19.8%laboratory2014
   1 kW-class travelling-wave thermoacoustic electrical generator with a linear alternator; 4.0 MPa mean pressure; 64 Hz after 4.5 % mole fraction argon; electric output 970 W at this point; heating 650 °C, cooling 15 °C
   refs [3]
2. maximum electric power1043 Wlaboratory2014
   the same generator; 17.7 % thermal-to-electrical efficiency at this point, not the maximum efficiency
   refs [3]
3. thermal-to-electric conversion efficiency at the maximum-efficiency point18.4%laboratory2017
   three-stage travelling-wave thermoacoustic electric generator, units joined end-to-end by slim resonance tubes with a linear alternator as a bypass at the end of each; 6 MPa pressurised helium; electric output 3.46 kW at this point; heating 650 °C, cooling 25 °C
   refs [4]
4. maximum electric power4.69 kWlaboratory2017
   the same three-stage generator; 15.6 % thermal-to-electric efficiency at this point, not the maximum efficiency
   refs [4]

best recorded efficiency (derived)

19.8% — thermal-to-electrical conversion efficiency at the maximum-efficiency point, laboratory, 2014; derived from the structured data above, not a stored number

Typed bounds on this route

Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).

• Carnot limit · formula-bound · hard, applies to this route
  η ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c

Steps

1. 01
   Temperature gradient —drives→ Thermoacoustic effectestablishedclaim record

   thermal → acoustic · loss to thermal

   |∇T_crit| = β T_m ω |p₁| / (ρ_m c_p |u₁|); prime-mover onset requires |∇T| > |∇T_crit| · critical-gradient factor β T_m ω/(ρ_m c_p u₁) [K/(Pa·m)]

   p₁ and u₁ are the local first-order acoustic pressure and particle-velocity amplitudes; β is the volumetric thermal expansion coefficient (β T_m ≈ 1 for an ideal gas); this is the linear short-stack / standing-wave criterion of Swift 1988 — above the critical gradient the stack amplifies the wave, below it the same interaction pumps heat — not a closed-form performance law for every travelling-wave regenerator.

   • temperature gradient along the stack steeper than the critical gradient set by the acoustic pressure and displacement amplitudes
   • a resonant gas column

   gas · temperature gradient required

   refs [1]
2. 02
   Thermoacoustic effect —produces→ Acoustic waveestablishedclaim record

   acoustic → acoustic

   gas

   refs [1]
3. 03
   Acoustic wave —drives→ Linear alternator actiondemonstratedclaim record

   acoustic → electrical · loss to thermal

   • an acoustic pressure oscillation driving a piston attached to a magnet or coil

   conductor required · magnetic field required

   refs [1]
4. 04
   Linear alternator action —produces→ Charge carriersestablishedclaim record

   electrical → electrical

   refs [1]
5. 05
   Charge carriers —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • carriers driven through an external load at the potential difference the source maintains

   refs [2]

Evidence for the complete composition · 3

1. [1]
   G. W. Swift. Thermoacoustic engines (1988)

   Journal of the Acoustical Society of America 84, 1145–1180 · doi:10.1121/1.396617 · crossref ✓ 2026-09-19 · record
2. [3]
   Zhanghua Wu et al.. Investigation on a 1 kW traveling-wave thermoacoustic electrical generator (2014)

   Applied Energy 124, 140–147 · doi:10.1016/j.apenergy.2014.02.063 · record
3. [4]
   Tianjiao Bi et al.. Development of a 5 kW traveling-wave thermoacoustic electric generator (2017)

   Applied Energy 185, 1355–1361 (online December 2015) · doi:10.1016/j.apenergy.2015.12.034 · record

Evidence for the constituent relations · 2

1. [1]
   G. W. Swift. Thermoacoustic engines (1988)

   Journal of the Acoustical Society of America 84, 1145–1180 · doi:10.1121/1.396617 · crossref ✓ 2026-09-19 · record
2. [2]
   N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)

   Holt, Rinehart and Winston · book, no DOI · record