TY - JOUR
T1 - Forced synchronization of quasiperiodic oscillations in a thermoacoustic system
AU - Guan, Yu
AU - Gupta, Vikrant
AU - Wan, Minping
AU - Li, Larry K.B.
N1 - Funding Information:
This work was supported by the Research Grants Council of Hong Kong (Project nos 16235716, 26202815 and 16210418), the National Natural Science Foundation of China (grant nos 11672123 and 91752201) and the Shenzhen Science and Technology Program (grant no. JCYJ20170412151759222).
Publisher Copyright:
© 2019 The Author(s).
PY - 2019/11/25
Y1 - 2019/11/25
N2 - In self-excited combustion systems, the application of open-loop forcing is known to be an effective strategy for controlling periodic thermoacoustic oscillations, but it is not known whether and under what conditions such a strategy would work on thermoacoustic oscillations that are not simply periodic. In this study, we experimentally examine the effect of periodic acoustic forcing on a prototypical thermoacoustic system consisting of a ducted laminar premixed flame oscillating quasiperiodically on an ergodic torus at two incommensurate natural frequencies, and. Compared with that of a classical period-1 system, complete synchronization of this system is found to occur via a more intricate route involving three sequential steps: As the forcing amplitude, , increases at a fixed forcing frequency, , the system transitions first (i)to ergodic quasiperiodicity; then (ii)to resonant quasiperiodicity as the weaker of the two natural modes, , synchronizes first, leading to partial synchronization; and finally (iii)to a limit cycle as the remaining natural mode, , also synchronizes, leading to complete synchronization. The minimum required for partial and complete synchronization decreases as approaches either or , resulting in two primary Arnold tongues. However, when forced at an amplitude above that required for complete synchronization, the system can transition out of and into or . The optimal control strategy is to apply off-resonance forcing at a frequency around the weaker natural mode and at an amplitude just sufficient to cause , because this produces the largest reduction in thermoacoustic amplitude via asynchronous quenching. Analysis of the Rayleigh index shows that this reduction is physically caused by a disruption of the positive coupling between the unsteady heat release rate of the flame and the and acoustic modes. If the forcing is applied near the stronger natural mode , however, resonant amplification can occur. We then phenomenologically model this thermoacoustic system as two reactively coupled van der Pol oscillators subjected to external sinusoidal forcing, and find that many of its synchronization features-such as the three-step route to , the double Arnold tongues, asynchronous quenching and resonant amplification-can be qualitatively reproduced. This shows that these features are not limited to our particular system, but are universal features of forced self-excited oscillators. This study extends the applicability of open-loop control from classical period-1 systems with just a single time scale to ergodic quasiperiodic systems with two incommensurate time scales.
AB - In self-excited combustion systems, the application of open-loop forcing is known to be an effective strategy for controlling periodic thermoacoustic oscillations, but it is not known whether and under what conditions such a strategy would work on thermoacoustic oscillations that are not simply periodic. In this study, we experimentally examine the effect of periodic acoustic forcing on a prototypical thermoacoustic system consisting of a ducted laminar premixed flame oscillating quasiperiodically on an ergodic torus at two incommensurate natural frequencies, and. Compared with that of a classical period-1 system, complete synchronization of this system is found to occur via a more intricate route involving three sequential steps: As the forcing amplitude, , increases at a fixed forcing frequency, , the system transitions first (i)to ergodic quasiperiodicity; then (ii)to resonant quasiperiodicity as the weaker of the two natural modes, , synchronizes first, leading to partial synchronization; and finally (iii)to a limit cycle as the remaining natural mode, , also synchronizes, leading to complete synchronization. The minimum required for partial and complete synchronization decreases as approaches either or , resulting in two primary Arnold tongues. However, when forced at an amplitude above that required for complete synchronization, the system can transition out of and into or . The optimal control strategy is to apply off-resonance forcing at a frequency around the weaker natural mode and at an amplitude just sufficient to cause , because this produces the largest reduction in thermoacoustic amplitude via asynchronous quenching. Analysis of the Rayleigh index shows that this reduction is physically caused by a disruption of the positive coupling between the unsteady heat release rate of the flame and the and acoustic modes. If the forcing is applied near the stronger natural mode , however, resonant amplification can occur. We then phenomenologically model this thermoacoustic system as two reactively coupled van der Pol oscillators subjected to external sinusoidal forcing, and find that many of its synchronization features-such as the three-step route to , the double Arnold tongues, asynchronous quenching and resonant amplification-can be qualitatively reproduced. This shows that these features are not limited to our particular system, but are universal features of forced self-excited oscillators. This study extends the applicability of open-loop control from classical period-1 systems with just a single time scale to ergodic quasiperiodic systems with two incommensurate time scales.
KW - Instability control
KW - Nonlinear instability
UR - http://www.scopus.com/inward/record.url?scp=85072750443&partnerID=8YFLogxK
U2 - 10.1017/jfm.2019.680
DO - 10.1017/jfm.2019.680
M3 - Journal article
AN - SCOPUS:85072750443
SN - 0022-1120
VL - 879
SP - 390
EP - 421
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -