Numerical study on two-degree-of-freedom vortex induced vibrations suppression of a circular cylinder via synthetic jets at different excitation frequencies

Highlights

• In-phase synthetic jets have the best performance on 2DOF VIVs suppression.

• Lock-in phenomena in low $f_{sj}^{*}$ range may discount the 2DOF VIVs suppression.

• When $f_{sj}^{*}$ ≥ 3.2, δ_Cd decreases with Δφ increasing, δ_Cl shows reverse changing trend.

• Vortex patterns are significantly different in two SJ phases when $f_{sj}^{*}$ is very low.

Abstract

In this work, a pair of synthetic jets are investigated for control of vortex induced vibration (VIV) of a circular cylinder in uniform flow in the low Reynolds number regime. In particular, the study focuses on three representative phase differences (0, π/2, and π) between the pair of synthetic jets to study the influence of synthetic jet excitation frequency ratio $f_{sj}^{*}$ ($f_{sj}^{*}$ = f_sj/f_n,water) on 2DOF VIVs control by two-dimensional numerical simulation. The Reynolds number is fixed at 150, the mass ratio m* (m* = m_osc/m_d) of the circular cylinder is 2.0, and the natural oscillation frequencies in the in-flow and cross-flow directions are equal. The amplitude response, frequency response, hydrodynamic forces, and wake patterns are analyzed. The results show that both in-flow and cross-flow oscillations of the circular cylinder can be significantly suppressed by synthetic jets with various phase differences, and the wake becomes symmetric when $f_{sj}^{*}$ ≥ 4.0. When $f_{sj}^{*}$ < 4.0, many fluctuations can be observed from the changing curves of in-flow and cross-flow oscillation amplitudes, and the oscillation may be enhanced by the occurrence of lock-in between the oscillation frequencies and the synthetic jet excitation frequencies. Besides, vortex shedding modes of the controlled cases are significantly different in blowing and suction phases of the synthetic jet, when the excitation frequency is very low, such as $f_{sj}^{*}$ = 0.2.

Introduction

As a novel flow control method, synthetic jets (SJs) have gained a lot of attention over the last two decades. Synthetic jets are generated using an actuator that consists of a cavity with an orifice, backed with a diaphragm that is driven sinusoidally. This causes periodic expulsion and ingestion of fluid through the orifice (Jeyalingam and Jabbal, 2018), and a quasi-steady jet can be formed some distance from the orfice. This is called the syntheic jet as it is synthesised from the surrounding fluid. Compared with passive control technology (Ding et al., 2016; J. Wang et al., 2019; Zhu et al., 2019; Hu et al., 2019; Ding et al., 2020; L.J. Wang et al., 2019; Chen et al., 2017), synthetic jets can cause local and global modification by imparting momentum and vorticity to the external flow. Therefore, synthetic jets have been adopted in a variety of fields, such as delaying the flow separation (Monir et al., 2014; Choi et al., 2018), enhancing heat transfer (Paolillo et al., 2019), decreasing vibration and noise (Nelson et al., 2017), and so on.

In recent years, some scholars have tried to use this novel strategy to control the vortex formation and evolution in the wake of the circular cylinder (DeMauro et al., 2013; Feng and Wang, 2014; C.L. Wang et al., 2017). The alternating vortex shedding in the wake of the circular cylinder is responsible for the occurrence of vortex induced vibration (VIV) (Baek et al., 2001), especially when the phenomenon of “VIV lock-in” or “synchronization” occurs, causing strong oscillations to be excited (Yan et al., 2019; Feng et al., 2019). Feng and Wang (Feng and Wang, 2010) experimentally studied the flow around a circular cylinder controlled by a synthetic jet positioned at the rear stagnation point, at a Reynolds number of 950. They found that the synthetic jet vortex pair can induce a symmetric vortex shedding mode, and the synchronization between the wake vortex and the synthetic jet at a certain range of excitation frequency was also observed. Feng and Wang (Feng and Wang, 2012) further investigated the influence of the suction duty cycle factor of a synthetic jet generated by a non-sinusoidal waveform, on controlling the flow around a circular cylinder at Re = 950. The results showed that the flow separation around the circular cylinder can be well controlled by the synthetic jet during both suction and blowing cycles, and the blowing process had better control effect when the blowing and suction velocities were the same. In addition, the control efficiency on drag reduction was found to decrease with decreasing suction cycle factor. However, Wang et al. (Wang et al., 2016), using a pair of symmetric synthetic jets at Re = 100, found that the synthetic jets operational range for suppressing VIV of a circular cylinder was much narrower than that for the fixed circular cylinder in which the lift oscillation can be completely suppressed. This was attributed to the cylinder oscillation inducing large relative flow speeds around the cylinder, resulting in shear layers with larger vorticity.

While a number of studies have been carried out, on the influence of synthetic jets for VIV control of circular cylinders, only very limited number and range of parameters, of importance to the problem, have been investigated so far. When utilizing a pair of synthetic jets, their phase difference, location around the cylinder, orientation angle, actuation frequency relative to the natural frequencies, and momentum coefficient among others, could have a strong influence of on the flow around the cylinder, and therefore on VIV control. Therefore, in order to realize optimal synthetic jet based VIV flow control solutions for real world applications, it is necessary to fill the knowledge gaps though further studies on the influence of these crucial parameters. This is especially so, for two-degree-of-freedom (2DOF) vortex induced vibrations control. In our previous work (H.B. Wang et al., 2019), the effects of synthetic jet position angle α and momentum coefficient Cu on 2DOF VIVs have been revealed. Furthermore, we have shown that symmetric synthetic jets issued in the streamwise direction can effectively mitigate 2DOF VIVs of the circular cylinder when positioned at the leeward side of the cylinder, and when Cu ≥ 2.0. Synthetic jet (SJ) excitation frequency is another important parameter for SJ-based control. According to the work of Wang et al. (C.L. Wang et al., 2017), synthetic jets pairs with various phase differences, over a wide frequency range, can cause the appearance of various lock-in phenomena, which are not always helpful for one-degree-of-freedom VIV suppression.

In the present work, the study is extended to two-degree-of-freedom VIVs and the influence of synthetic excitation frequency and phase difference between the pair of synthetic jets, on VIV control, are systematically studied. The Reynolds number is fixed at 150 (Re = 150) in the present work, and the flow in the wake of the circular cylinder is two-dimensional (W.L. Chen et al., 2018; Shaaban and Mohany, 2018; Zou et al., 2019). Therefore, two-dimensional numerical simulations are conducted in the study.

The paper is arranged as follows. In Section 2, the physical model under study, the numerical method and details are described. In Section 3, the details of the findings obtained in this work are discussed. The conclusions are finally drawn in Section 4.