Lock-on of vortex shedding to a pair of synthetic jets with phase difference

Abstract

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.

Active Control of Bluff-Body Flows Using Plasma Actuators

“…For instance, it is now well acknowledged that with the increasing amplitude of global symmetric perturbations, these will eventually dominate over a large portion of the flow domain around a circular cylinder, thereby suppressing lift fluctuations [27,43,46,118,119]. Similar effects have also been observed with symmetric local forcing by a single synthetic jet located at either the front or back stagnation point, or a pair of symmetrically placed synthetic jet operated in-phase [89,108,112,[120][121][122][123]. Similarly, locking-on of antisymmetric vortex shedding at the subharmonic of the excitation frequency, which is well known for global perturbations [19,43,44,51,107], has also been observed for symmetric in-phase excitation by plasma actuators.…”

“…The forcing amplitude as quantified by C F did not have a marked effect although clearly a minimum level of 0.045% was necessary to incite the symmetric (or no shedding) mode and a lower level of 0.02% was necessary to incite vortex lock-on. The subharmonic, harmonic, and superharmonic lock-on regimes found by Jukes and Choi can be predicted on the basis of extended linear theory using simple rules of spatio-temporal symmetry [112]. On the basis of the theory, it may be anticipated that further lock-on regimes can be attained by changing the phase between actuators on the bottom and top sides of the cylinder as discussed in the following subsection.…”

Investigation of the influence of low-frequency forcing on the 3-D turbulent wake of a cantilevered triangular prism

“…(2016 a ) and for a cylinder wake by Wang et al. (2017). In both studies, primary lock-on required two-sided actuation with jets on the opposing sides pulsed out-of-phase.…”

“…Subharmonic or superharmonic lock-on (Baek, Lee & Sung 2001; Wang et al. 2017) occurs when is an integer multiple or submultiple of , which generally differs from . The lock-on phenomenon for cantilevered triangular geometries has not been studied previously.…”

“…The conditions on the actuation frequency and phase difference for synchronization of antisymmetric Kármán shedding have been discussed by Wang et al. (2017) for two-sided actuation using synthetic jets placed symmetrically about the leeward stagnation point of a 2-D cylinder. Using a low-order model based on extended linear theory, it was found that subharmonic lock-on regimes ( and ) are possible with two-sided in-phase actuation, while lock-on regimes at and are possible for antisymmetric actuation.…”