Lock-on of vortex shedding to a pair of synthetic jets with phase difference
Yu, Simon C. M.
Date of Issue2017
School of Mechanical and Aerospace Engineering
This paper furthers our understanding of lock-on that is induced by periodic external forcing. The effect of forcing phase difference is investigated. An extended linear theory is proposed to predict the centers of various lock-on regimes, including harmonic, subharmonic, and superharmonic lock-on, in a parametric map spanned by the forcing frequency and phase difference. It reveals that when the forcing frequency is equal to the natural vortex shedding frequency or its integer multiple, harmonic or subharmonic lock-on occurs at particular forcing phase differences, whereas when the forcing frequency is a submultiple of the natural shedding frequency, superharmonic lock-on occurs. To confirm this theory and also further determine the shape and size of each lock-on regime, a series of numerical simulations is conducted on a circular-cylinder flow system with periodic external forcing being realized by a pair of synthetic jets (SJs). At a Reynolds number 100 and under moderate SJ forcing, five lock-on regimes are captured, including the primary, secondary, tertiary, and first- and second-superharmonic lock-on. It is found that these lock-on regimes are generally in a rhomboidal shape, and their size gradually reduces when the SJ frequency is away from the natural vortex shedding frequency. With these simulations, the aerodynamic forces and wake formation in each lock-on regime are analyzed and compared, with the discussion being focused on the effects of SJ frequency and phase difference. Furthermore, stability analysis is conducted to reveal more flow physics related to lock-on.
Physical Review Fluids
© 2017 American Physical Society (APS). This paper was published in Physical Review Fluids and is made available as an electronic reprint (preprint) with permission of American Physical Society (APS). The published version is available at: [http://dx.doi.org/10.1103/PhysRevFluids.2.104701]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.