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.

Acoustic energy output and coupling effect of a pair of thermoacoustic lasers

“…On the contrary, in their study of TA engine arrays McDonald and Symko [27] found the engines in a two-engine array entrained at a common frequency with approximately zero phase difference. The present result is also different from the TA engine pair studied by Spoor and Swift [29,30] for which the two engine outlets were connected through a half-wavelength tube. If vibration was completely cancelled in the coupled TA engines they studied, the half-wavelength tube must yield a 1801 phase difference between the two engines.…”

“…The Huygens mode-locking phenomenon [30] predicts two or more self-maintained oscillators would lock in frequency and phase. In the present investigation of TA laser pairs, the frequencies of the TA lasers were determined primarily by the lengths of the glass tubes, and the phase difference between the two laser outputs was never locked when the laser openings were far apart.…”

Timing and coordination in tone and intonation—An articulatory-functional perspective

“…Entrainment refers to a process whereby two nearby oscillating systems, such as clocks, having similar periods, fall into synchrony (Huygens, 1666 as cited by Spoor and Swift, 2000). Many synchronization phenomena in motor movements, including those of speech, have been likened to this process (Haken et al, 1985;Kelso et al, 1986).…”

Hysteretic behavior induced by an electroacoustic feedback loop in a thermo-acousto-electric generator

“…Some studies have focused on the description of the variety of nonlinear dynamics behavior observed in experiments (synchronization [24,25], route to chaos [26],...). Other studies [27,28,29,30,31] have focused on the forcing of acoustic oscillations in the context of thermoacoustic engines. In particular, a proof-of-concept study provided by Desjouy et al [28] in an annular engine has demonstrated that the addition of two auxiliary sources, appropriately tuned, can significantly improve the overall efficiency.…”