In this study, a CFD-based linear dynamics model combined with the direct Computational Fluid Dynamics/Computational Structural Dynamics (CFD/CSD) simulation method is utilized to study the physical mechanisms underlying frequency lock-in in vortex-induced vibrations (VIVs). An identification method is employed to construct the reduced-order models (ROMs) of unsteady aerodynamics for the incompressible flow past a vibrating cylinder at low Reynolds numbers ( ). Reduced-order-model-based fluid–structure interaction models for VIV are also constructed by coupling ROMs and structural motion equations. The effects of the natural frequency of the cylinder, mass ratio and structural damping coefficient on the dynamics of the coupled system at are investigated. The results show that the frequency lock-in phenomenon at low Reynolds numbers can be divided into two patterns according to different induced mechanisms. The two patterns are ‘resonance-induced lock-in’ and ‘flutter-induced lock-in’. When the natural frequency of the cylinder is in the vicinity of the eigenfrequency of the uncoupled wake mode (WM), only the WM is unstable. The dynamics of the coupled system is dominated by resonance. Meanwhile, for relatively high natural frequencies (i.e. greater than the eigenfrequency of the uncoupled WM), the structure mode becomes unstable, and the coupling between the two unstable modes eventually leads to flutter. Flutter is the root cause of frequency lock-in and the higher vibration amplitude of the cylinder than that of the resonance region. This result provides evidence for the finding of De Langre (J. Fluids Struct., vol. 22, 2006, pp. 783–791) that frequency lock-in is caused by coupled-mode flutter. The linear model exactly predicts the onset reduced velocity of frequency lock-in compared with that of direct numerical simulations. In addition, the transition frequency predicted by the linear model is in close coincidence with the amplitude of the lift coefficient of a fixed cylinder for high mass ratios. Therefore, it confirms that linear models can capture a significant part of the inherent physics of the frequency lock-in phenomenon.

Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers

Frequency lock-in can occur on a spring suspended airfoil in transonic buffeting flow, in which the coupling frequency does not follow the buffet frequency but locks onto the natural frequency of the elastic airfoil. Most researchers have attributed this abnormal phenomenon to resonance. However, this interpretation failed to reveal the root cause. In this paper, the physical mechanism of frequency lock-in is studied by a linear dynamic model, combined with the coupled computational fluid dynamics/computational structural dynamics (CFD/CSD) simulation. We build a reduced-order model of the flow using the identification method and unsteady Reynolds-averaged Navier–Stokes computations in a post-buffet state. A linear aeroelastic model is then obtained by coupling this model with a degree-of-freedom equation for the pitching motion. Results from the complex eigenvalue analysis indicate that the coupling between the structural mode and the fluid mode leads to the instability of the structural mode. The instability range coincides with the lock-in region obtained by the coupled CFD/CSD simulation. Therefore, the physical mechanism underlying frequency lock-in is caused by the linear coupled-mode flutter – the coupling between one structural mode and one fluid mode. This is different from the classical single-degree-of-freedom flutter (e.g. transonic buzz), which occurs in stable flows; the present flutter is in the unstable buffet flow. The response of the airfoil system undergoes a conversion from forced vibration to self-sustained flutter. The coupling frequency certainly should lock onto the natural frequency of the elastic airfoil.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C26CDDCD34DE422BAE714029AFA0BE71/S0022112017001203a.pdf/div-class-title-mechanism-of-frequency-lock-in-in-transonic-buffeting-flow-div.pdf

Mechanism of frequency lock-in in transonic buffeting flow

Amplification/suppression of flow-induced motions of an elastically mounted circular cylinder by attaching tripping wires

Fluid flow and heat transfer around a confined semi-circular cylinder: Onset of vortex shedding and effects of Reynolds and Prandtl numbers

http://midra.uni-miskolc.hu/JaDoX_Portlets/displayContent?docId=19049&secId=12784

CFD analysis of power-law fluid flow and heat transfer around a confined semi-circular cylinder

Influence of mass and damping ratios on VIVs of a cylinder with a downstream counterpart in cruciform arrangement

VIVs of a circular cylinder with a downstream strip-plate in cruciform arrangement

Prospect of Micro Power Generation Utilizing VIV in Small Stream Based on Verification Experiments of Power Generation in Water Tunnel

Earlier wind tunnel experiments supported by visualization in water flow carried out by the present authors showed that two types of longitudinal vortices shed periodically from a cruciform two identical circular cylinder system in uniform flow. These longitudinal vortices induce resonance-like oscillations over a wide velocity range accompanied by the synchronization phenomenon. The specific aim of this work is to investigate the universality of the longitudinal vortex shedding by carrying out experiments in both water and air flows. In addition to the velocity, the alternating lift force loading on the upstream cylinder in water flow is measured by using load-cells. The two longitudinal vortices are confirmed to shed periodically for small size systems in water flow in spite of large difference in the experimental conditions. Relationships of the Strouhal number and the lift force coefficient for the vortex shedding against Reynolds number agree well with the previous data except for the peculiar vanishing of the necklace vortex when Re is larger than 22000. The cause of this phenomenon is left for further investigation.

/pdf/universality-of-longitudinal-vortices-shedding-from-a-15w2ob4tb0.pdf

Universality of Longitudinal Vortices Shedding from a Cruciform Two Circular Cylinder System in Uniform Flow

Three cylindrical bodies with different cross sectional configurations, i.e. a circular, semi-circular and triangular cylinder, are used as the test cylinders, in order to investigate the influence of movement of separation point on the Karman vortex excitation. The cylinders were supported elastically by plate springs. The synchronization of Karman vortex shedding occurs on all three cylinders over almost equal ranges of oscillation amplitude and frequency given by the mechanical oscillator. However, the Karman vortex excitation behavior differs drastically among the three cylinders in spite that the cylinders are supported elastically with virtually equal structure parameters.

Mizuyasu Koide

Papers

Influence of mass and damping ratios on VIVs of a cylinder with a downstream counterpart in cruciform arrangement

VIVs of a circular cylinder with a downstream strip-plate in cruciform arrangement

Prospect of Micro Power Generation Utilizing VIV in Small Stream Based on Verification Experiments of Power Generation in Water Tunnel

Universality of Longitudinal Vortices Shedding from a Cruciform Two Circular Cylinder System in Uniform Flow

Influence of Cross-Sectional Configuration on Karman Vortex Excitation