Transverse and axial forcing of a globally unstable axisymmetric jet

Abstract

Open jet flows are central to many natural and technological processes. They are susceptible to hydrodynamic instability and can be dominated by large-scale coherent structures in their near field. Under some conditions, such jets are convectively unstable and act as spatial amplifiers. As a result, they exhibit strong sensitivity to external perturbations and can be easily controlled by applying external forcing. However, under certain conditions, such jets can transition from a spatial amplifier to a self-excited oscillator, exhibiting limit cycle oscillations at a discrete natural frequency. Such oscillations can be detrimental in some applications as they can couple with structural, acoustics or other hydrodynamic modes of the system at nearby frequencies. It is, therefore, important to be able to control the self-excited dynamics of globally unstable jets. Previous experiments have shown that a marked reduction in the overall response amplitude of a globally unstable low-density axisymmetric jet can be achieved via asynchronous quenching when the jet is forced axially. However, a major limitation of this open-loop control strategy is that it requires the forcing frequency (f_f ) to be sufficiently far from the natural frequency of the jet (f_n). In this thesis, a more robust control strategy is proposed, one that has the potential to substantially attenuate the overall response amplitude of a self-excited jet (often to less than 10% of the unforced case). Specifically, we investigate the temporal and spatiotemporal dynamics of a globally unstable axisymmetric self-excited jet when it is forced with different combinations of transverse and axial forcing, produced by moving the jet within a standing acoustic waveform for a range of forcing frequencies and amplitudes. We find that, as an open-loop control strategy, transverse forcing is more effective than axial forcing in quenching the self-excited oscillations of the globally unstable jet. We show that this oscillation quenching occurs via asynchronous quenching regardless of the frequency detuning. Using spectral power analysis, we show that transverse forcing does not favor intermodal power transfer, resulting in the quenching of the self-excited oscillations. By contrast, axial forcing promotes power transfer from one mode to another. As a result, energy is continuously fed into the global mode, thus, hindering its suppression. We also examine the spatiotemporal dynamics of the jet by performing time-resolved stereoscopic particle image velocimetry. This enables us to investigate the dynamical evolution of the vortex structures in the near-field region of the jet. We find that maximum reduction in the oscillation amplitude coincides with the jet locking into transverse forcing. When the jet locks into transverse forcing, the vortex structures on both sides of the jet centerline are out-of-phase, indicating symmetry breaking. This is in stark contrast to the axisymmetric arrangement of vortex structures observed for the axially forced jet at the lock-in. We also find that the strength of vortex structures, measured in terms of the vortex ring circulation, is insensitive to the forcing frequency and amplitude. We phenomenologically model the temporal dynamics of the jet with two coupled van der Pol oscillators subjected to external forcing. We model the spatiotemporal dynamics of the jet with two complex Ginzburg-Landau (CGL) oscillators, forced externally to simulate axial and transverse forcing. We find that, despite their simplicity, both the CGL and VDP models can qualitatively reproduce many, but not all, of the salient synchronization features, observed in the forced jet. This study shows that there are subtle, but important, differences between the effects of transverse forcing and axial forcing on the synchronization dynamics of a globally unstable jet. This study provides new insight into the way transverse acoustic oscillations interact with axisymmetric hydrodynamic oscillations, opening up new pathways for the development of alternative open-loop flow-control strategies based on transverse forcing.

Date of Award	2021
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Larry LI (Supervisor)