The Huygens entrainment phenomenon and thermoacoustic engines

Abstract

The earliest known reference to the mode-locking, or entrainment, of two maintained oscillators is Christiaan Huygens' description of two pendulum clocks "falling into synchrony" when hung on the same wall. We describe an analogous phenomenon in acoustics-the mode-locking of two thermoacoustic engines which have their cases rigidly welded together, but which are otherwise uncoupled. This "mass-coupling" might compete with acoustic coupling when the latter is used to enforce antiphase mode-locking in such engines, for vibration cancellation. A simple theory relating the phase difference between the engines in the locked state to the corresponding ratio of their pressure amplitudes is in excellent agreement with theory and numerical simulations. The theory's prediction relating the phase difference to the engines' natural frequency difference is qualitatively confirmed by experiment, despite larger experimental uncertainties. The mass coupling is relatively weak compared to the aforementioned acoustic coupling, and in general occurs in antiphase, so we conclude that mass coupling will not interfere with vibration cancellation by acoustic coupling in most circumstances.