Frequency shifts during whistling occurs as transition between two phase synchronised limit cycles via a state of intermittency or abruptly

Abstract

Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained oscillations (limit cycle oscillations) are also referred to as aeroacoustic instabilities, which can be heard as a whistle. Understanding the change in dynamical state by altering the control parameter in an aeroacoustic system is critical in designing control strategies for aeroacoustic instabilities. In this study, as the control parameter Reynolds number ($Re$) is varied, we hear a change in the whistling frequency. We show that this change in frequency occurs via the state of intermittency, which has bursts of periodic fluctuations amidst the regime of the aperiodic fluctuations in acoustic pressure fluctuations. At a higher Reynolds number, we observe an abrupt transition from one limit cycle oscillation (LCO) to another limit cycle oscillation during the shift in whistling frequency. Further, we use synchronisation theory to investigate the coupled behaviour of the acoustic and the hydrodynamic fields. The acoustic pressure ($p'$) and hydrodynamic ($v'$) fluctuations during LCO exhibit phase synchronisation. Thus, we conclude that the shift in whistling frequency is a transition between the two phase synchronised limit cycle oscillations that occurs either through the state of intermittency or abruptly. The periodic bursts of intermittency correspond to the phase-synchronised periodic $p'$ and $v'$, and the aperiodic epochs correspond to the desynchronised aperiodic $p'$ and $v'$.