Open-loop forcing is known to be an effective strategy for controlling self-excited thermoacoustic oscillations, but the details of this synchronization process have yet to be comprehensively explored. In this study, we experimentally examine the synchronization dynamics of a laminar conical premixed flame in a tube combustor subjected to periodic acoustic forcing. We compare the response of this forced self-excited system with that of a forced Duffing–van der Pol oscillator, and find many similarities but also some differences. The similarities include (i) a torus-birth bifurcation from periodicity to quasiperiodicity at low forcing amplitudes, producing a stable ergodic ${\mathbb{T}}^2$ torus attractor in phase space; (ii) a transition from ${\mathbb{T}}^2$ quasiperiodicity to lock-in above a critical forcing amplitude, which increases linearly as the forcing frequency f_f deviates from the natural frequency f₁; (iii) two distinct routes to lock-in, one via a torus-death bifurcation if f_f is far from f₁ and one via a saddle-node bifurcation if f_f is close to f₁; and (iv) asynchronous quenching (AQ), which coincides with a torus-death bifurcation to lock-in and reduces the oscillation amplitude – by up to 90% in the combustor. There are, however, quantitative differences between the two systems, which pertain mainly to (i) the magnitude of the amplitude reduction achieved by AQ and (ii) the size of the AQ region in the f_f/f₁–forcing-amplitude plane.

This study has three main contributions. First, it shows that studying open-loop control from a synchronization perspective can provide valuable insight into the optimal forcing conditions. Second, it shows that the optimal forcing condition for weakening thermoacoustic oscillations is that which causes the onset of lock-in via a torus-death bifurcation, as this is where AQ occurs. Third, it shows that the synchronization dynamics of a real combustor can be qualitatively modelled with a low-order universal oscillator. This suggests that it may be possible to develop and test new control strategies by analyzing the solutions to such an oscillator.

已知开环强迫是控制自激热声振荡的有效策略，但是该同步过程的细节尚未全面探讨。在这项研究中，我们实验性地检查了层状锥形预混火焰在周期性燃烧声力作用下的管式燃烧器中的同步动力学。我们将这种强制自激系统的响应与强制Duffing-van der Pol振荡器的响应进行了比较，发现许多相似之处，但也有一些区别。相似之处包括（i）在低强迫振幅下从周期性到准周期性的环形出生分叉，产生稳定的遍历${\mathbb{Ť}}^{\mathrm{2个}}$相空间中的环面吸引子；（ii）从${\mathbb{Ť}}^{\mathrm{2个}}$准周期锁定在临界强迫幅度之上，该强迫幅度随着强迫频率f _f偏离固有频率f ₁线性增加；（iii）两种不同的锁定路径，如果f _f远离f ₁则通过环形死叉分叉，而如果f _f接近f ₁则通过鞍形节点分叉。; （iv）异步熄灭（AQ），它与环形死角分叉相吻合以锁定并减小振荡幅度–在燃烧室中最多可减少90％。但是，两个系统之间存在定量差异，这主要与（i）AQ所实现的幅度减小的幅度和（ii）f _f / f _1-强迫振幅平面中AQ区域的大小有关。

这项研究有三个主要贡献。首先，它表明从同步角度研究开环控制可以提供对最佳强制条件的有价值的见解。其次，它表明减弱热声振荡的最佳强迫条件是通过环形-死亡分叉而引起锁定开始的条件，因为这就是发生AQ的地方。第三，它表明可以用低阶通用振荡器定性地建模真实燃烧器的同步动力学。这表明可以通过分析此类振荡器的解决方案来开发和测试新的控制策略。