Lock-in Phenomenon Research Articles

Numerical study of viscoelastic flow around an oscillating circular cylinder

The viscoelasticity-induced fluid–structure interaction studies have a significant influence on practical applications. To clarify the lock-in phenomenon and the wake topology of the vibrating cylinder placed in the viscoelastic flow, the Oldroyd-B fluid flows around an oscillating circular cylinder have been numerically investigated at Re = 10 and Re = 60, respectively. The governing equations are solved by the coupling of the square-root-conformation representation approach and the discontinuous Galerkin method in framework of the high-order dual splitting scheme. In addition, the arbitrary Lagrangian–Eulerian formulation is implemented in the coupling procedure in order to account for the interaction between the fluid and the oscillating body in the flow field. With this, complex boundary movements can be tackled simply and efficiently. In numerical simulation, the force coefficients and the wake structures of vortex and stress are discussed in some detail. At Re = 10, when the frequency of cylinder is small, it is obvious that the vortex shedding takes place in the wake. As the frequency increases, almost no obvious vortex shedding is observed. Also, the wake still oscillates at the same frequency of the cylinder for all cases, even for high Wi numbers. However, different wake modes of vortex and stress are found for various frequencies at Re = 60 and Wi = 0.1. In the lock-in region, the 2S mode of wake type are observed. Beyond the lock-in region, the wake type is no longer 2S, but the formation of vortex shedding and stress distribution in the far wake recovers to its natural mode. These numerical results open up a new field of study for viscoelastic fluids.

Sagnac Effect Compensations and Locked States in a Ring Laser Gyroscope.

Frequency lock-in-induced deadband phenomena are major problems of ring laser gyroscopes (RLGs), which deteriorate linear responses to changes in the applied rotation rate. In this work, the frequency lock-in phenomenon occurring in the RLG was successfully investigated by compensating for the Sagnac effect through frequency analysis using a newly defined error function. Integrative and generalized viewpoints from the analyzed results provide new possibilities for relevant performance improvements of optical gyroscopes, as well as a deeper understanding of locked states in principle aspects.

Numerical investigation of thermo-acoustic instability in a model afterburner with a simplified model for observed lock-in Phenomena

Thermoacoustic oscillations in a gas turbine afterburner are numerically investigated using CFD. A simplified 2-dimensional axisymmetric afterburner with bluff-body stabilized flame is considered in the investigation. Occurrences of both low and high-frequency thermo-acoustic oscillations in the afterburner chamber are observed at specific fuel flow rates. The flow field from the CFD shows the bluff-body vortex shedding frequency to lock-in with the acoustics of the chamber during the thermo-acoustic oscillations. The synchronization and lock-in of bluff-body wake with chamber acoustics happen with increase in fuel injection rates resulting in thermoacoustic coupling. The Proper Orthogonal Decomposition of the flow field revealed the presence of chamber acoustics in the pressure field confirming the coupling. Then a simplified mathematical model based on the van-der Pol oscillator is attempted to reproduce the observed lock-in behavior of the bluff-body wake. The chamber acoustic field is considered as the forcing term for the simplified oscillator. The oscillator model qualitatively captures the synchronization of the flame-holder wake oscillations with the chamber acoustics. This model could be extended to combustors with bluff-body wake in predicting the thermo-acoustic oscillations.

Theoretical model and numerical simulation of tower-wake-induced vibration of a flexible suspender

For a suspension bridge, suspenders in the wake of bridge tower interfered by the shedding vortices, would experience a large-amplitude vibration, named as tower-wake-induced vibration (TWIV). At specific wind speeds, the vibrating frequency of suspenders during TWIV would be captured by the shedding frequency of the tower wake, which is the lock-in of TWIV. The present research establishes the governing equations of flexible suspenders, considering the tension variations caused by the deformation, also adopts the aerodynamic model of TWIV, to study the lock-in phenomenon and the TWIV characteristics. To explore the variation trend of nonlinear frequency with amplitude of suspenders, the difference of dynamic parameters of suspenders in two vibrating motions are recognized through free vibration motions at first. Then, a formula for the equivalent amplitude-dependent (EAD) frequency of the suspender is raised. The lock-in phenomenon of TWIV is reproduced in these two motions as well. Eventually, TWIVs of four suspenders at various positions in the rear of bridge tower are simulated based on practical engineering, considering the variation of aerodynamic forces along the altitude due to the wind profile. The conclusions indicate that TWIV of suspenders is a low-frequency and low-order-mode vibration at high wind speeds.

A CFD Study of Vortex-Induced Motions of a Semi-Submersible Floating Offshore Wind Turbine

Vortex-induced motion (VIM) is a critical issue for floating structures made of one or more columns, due to its significant impacts on their operational stability. Supported by column-type floating platforms, floating offshore wind turbines (FOWTs) may also experience large-amplitude VIM responses in current flow. Existing research on FOWTs has mostly focused on their wind/wave induced responses, yet less attention has been paid to their responses in current flow. In this paper, the VIM of the OC4 semi-submersible FOWT platform is studied numerically over a wide range of flow velocity. Three incidence angles, i.e., 0°, 90°, and 180°, are considered and the effect of current incidence on platform VIM is analysed. Results show that the so-called lock-in phenomenon is present and that a large transverse response amplitude of more than 0.3D persists until Vr = 30, with its maximum reaching over 0.8D at Vr = 8. Meanwhile, the transverse response amplitude for cases with the incidence angle of 180° is generally smaller, with a narrower lock-in regime, than those under the other two incidence scenarios. Flow field visualisation reveals that upstream vortices continuously interact with the downstream side column when the incidence angle turns to 180°, impacting the vortex shedding process and consequently fluid forces of the downstream column.

Hybrid Heat Transfer Augmentation from Oscillating Cylinder with Partial Superhydrophobic Janus Surfaces

Flow over an oscillating cylinder has been the subject of various studies as well as its heat transfer characteristics due to the lock-in phenomenon which occurs as a result of multiple frequencies being present in the system. The motivation was to investigate the effect of superhydrophobicity on heat transfer and wake dynamics of partially superhydrophobic oscillating cylinder. Applying the slip condition causes the drag and root-mean-square lift coefficients to reduce by 46 and 75% in comparison to the no-slip case, respectively. It also augments the average Nusselt number by 55% accompanied by a 21% increase of the natural shedding frequency compared to the no-slip cylinder. Considering the reduction of force coefficients, it is shown that the application of slip over a 135° segment of the surface is an optimum case, resulting in 47% and 85% decrease of the drag and root-mean-square lift coefficients, respectively. Application of slip over the surface of the cylinder also causes the average Nusselt number to become nearly 6 times greater than the no-slip oscillating cylinder at the lock-in condition. Further analysis based on thermal performance index (TPI) proves that a high value of TPI = 6 can be reached for the superhydrophobic cylinder.

Experimental investigation on vortex sound interaction in self-induced acoustic resonance

Acoustic resonance induced by vortex sound interaction in a confined space could cause both noise pollution and acoustic fatigue issues. The mechanism of vortex sound interaction, especially the acoustic feedback effect on vortex shedding, is a challenging question. External sound excitation method is commonly used in the existing studies, which is straightforward to show the modulate effect of sound on flow field, but would inevitably destroy the inherent coupling process between vortex and sound. In response to this problem, we perform experimental investigation based on a spontaneous resonance system consisting of a flow duct containing a plate. The acoustic feedback effect is evaluated by simultaneously monitoring the sound pressure on the duct wall and the vortex shedding fluctuation velocity behind the plate. By slowly increasing the incoming flow velocity, the frequency lock-in phenomenon is obviously detected. In accordance with our previous prediction, two sub-regions are observed in the lock-in region, which validates the rationality of the frequency competition mechanism during vortex sound interaction. Based on these findings, we propose an acoustic resonance suppression method based on the concept of duct wall treatment. Through introducing a non-locally reacting liner on the duct wall, the lock-in region disappears. Besides, the resonant amplitude of sound pressure and the corresponding fluctuation velocity are greatly reduced, which provides a potential effective control strategy for both the noise and structural vibration caused by acoustic resonance.

Acoustic Response of a Vibrating Elongated Cylinder in a Hydrodynamic Turbulent Flow

The present paper contains the results of the numerical analysis of the interaction between a Newtonian incompressible turbulent flow and a linear elastic slender body, together with the influence of the fluid–structure interaction (FSI) on the noise generation and propagation. The purpose is to evaluate the differences in term of acoustic pressure between the case where the solid body is rigid (infinite stiffness) and the case where it is elastic (finite stiffness). A partitioned and implicit algorithm with the arbitrary Lagrangian–Eulerian method (ALE) is used for the interaction between the fluid and solid. For the evaluation of the turbulent fluid motion, we use a large eddy simulation (LES) with the Smagorinsky subgrid scale model. The equation for the solid is solved through the Lagrangian description of the momentum equation and the second Piola–Kirchoff stress tensor. In addition, the acoustic analogy of Lighthill is used to characterize the acoustic source (the slender body) by directly using the fluid dynamic fields. In particular, we use the Ffowcs Williams and Hawkings (FW-H) equation for the evaluation of the acoustic pressure in the fluid medium. As a first numerical experiment, we analyze a square cylinder immersed in a turbulent flow characterized by two different values of stiffness: one infinite (rigid case) and one finite (elastic case). In the latter case, the body stiffness and mean flow velocity are such that they induce the lock-in phenomenon. Finally, we evaluate the differences in terms of acoustic pressure between the two different cases.

Deep learning for predicting frequency lock-in of a freely vibrating sphere

In this paper, we present a deep learning-based reduced-order model (DL-ROM) for the stability prediction of unsteady three-dimensional fluid–structure interaction systems. The proposed DL-ROM has the format of a nonlinear state-space model and employs a recurrent neural network with long short-term memory (LSTM) cells. We consider a canonical fluid–structure system of an elastically mounted sphere coupled with the incompressible fluid flow in a state-space format. Specifically, we develop a nonlinear data-driven coupling for predicting the unsteady forces and the vortex-induced vibration (VIV) lock-in of the freely vibrating sphere in a transverse direction. We design an input–output relationship as a temporal sequence of force and displacement datasets for a low-dimensional approximation of the fluid–structure system. Based on the prior knowledge of the VIV lock-in process, the input function contains a range of frequencies and amplitudes, which significantly affects the system realization ability and enables an efficient DL-ROM without the need for a massive training dataset for the low-dimensional modeling. Once trained, the network provides a nonlinear mapping of input–output dynamics that can predict the coupled fluid–structure dynamics for a longer horizon via the feedback process. By integrating the LSTM network with the eigensystem realization algorithm (ERA), we construct a data-driven state-space model for the reduced-order stability analysis. We investigate the underlying mechanism and stability characteristics of VIV of a freely vibrating sphere via an eigenvalue selection process. Using the reduced-order eigenvalue analysis, we characterize the vibrating sphere-wake lock-in phenomenon and demonstrate that the lock-in responds at preferred vibration frequencies. To understand the frequency lock-in mechanism, we study the eigenvalue trajectories for a range of the reduced oscillation frequencies and the mass ratios. Consistent with the full-order simulations, the frequency lock-in branches are accurately captured by the combined LSTM-ERA procedure. The proposed DL-ROM aligns with the development of physics-based digital twin of engineering systems involving moving boundaries and fluid–structure interactions.

Effect of degrees of structural freedom on the flow-induced vibrations of isolated and tandem cylindrical structures

This study aims to numerically investigate the influence of degrees of structural freedom on the flow-induced vibration characteristics of an isolated and tandem cylindrical structures at low Reynolds number. Both the single and tandem cylinders underwent transverse-only (1-DoF) and combined streamwise and transverse (2-DoF) vibrations which are characterized by the mass–spring system. A fluid–structure interaction scheme is formulated using the split-forcing lattice Boltzmann equation for the fluid domain in combination with an immersed boundary solver and equations of rigid body motion for the structural part. The dynamic response of an isolated and tandem structures computed for 1- and 2-DoF cases are similar regarding the lock-in phenomenon and hydrodynamic forces at a relatively large mass ratio. The comparison of vorticity field suggests that an additional degree of freedom has no significant effect on the vortex shedding pattern. Furthermore, in the presence of another identical structure placed in the upstream direction, the downstream structure oscillates with higher amplitudes.

Frequency Lock-In Phenomenon of Vortex Induced Vibration of a Rotating Blade Considering Bending-Torsion Coupling Effect

Abstract A rotating thin blade with bend-torsional coupling subjected to vortex induced vibration (VIV) is considered in this paper. It is necessary to study the motion coupled bending torsion due to the discordant centroid and shear center and the effect of centrifugal force at high-speed. The blade with a single axisymmetric section is regarded as a beam instead of an oscillator. The motion equation coupled bending-torsion of the blade is established by using the Euler–Lagrange equations, and the effect of centrifugal force is also employed. Vortex shedding is described by a nonlinear oscillator satisfying Van Der Pol (VDP) equation. Ritz–Galerkin method is employed to simplify the equations of the blade, and the interaction between the bending and torsion modes of blade and wake modes is discussed. The motion equation is simplified based on the contribution of the blade flutter mode. Furthermore, the single-mode approximation is used to investigate the effects of mass ratio, damping, and coupling coefficient on the locking phenomenon. It is also analyzed that the variation of flutter amplitude and locking region of the rotating blade considering bending-torsion coupling.

Unsteady cavitation dynamics and frequency lock-in of a freely vibrating hydrofoil at high Reynolds number

In this paper, we numerically investigate the influence of unsteady partial cavitation on the fluid–structure interaction of a freely vibrating hydrofoil section at high Reynolds numbers. We consider an elastically-mounted NACA66 hydrofoil section that is free to vibrate in the transverse flow direction. The fluid–structure interaction of this system is of interest in characterizing the cavitation-induced vibration and noise of marine propellers. The coupled cavitation dynamics and the fluid–structure system are solved using a body-fitted variational framework based on homogeneous mixture-based cavitation with a hybrid URANS-LES turbulence modeling. Specifically, we explore the occurrence of large-amplitude vibrations during unsteady partial cavitating conditions that are absent in the non-cavitating flow configuration. We examine a frequency lock-in phenomenon as the main source of sustained large-amplitude vibration whereby the unsteady lift force locks into a sub-harmonic of the hydrofoil’s natural frequency. We determine the origin of this flow unsteadiness in the vicinity of the trailing edge of the hydrofoil through the interplay between the growing cavity and the adverse pressure gradient. We systematically analyze the impact of flow-induced structural vibration on the combined vortex and cavity synchronization.

Numerical Simulation of Vortex-Induced Transverse Vibration of a Cylinder with Very Low Mass Ratio

Vortex-induced vibration (VIV) of flow past different types of cylinders is important in many engineering fields and has led to a large number of fundamental studies. Computational fluid dynamics (CFD) has become a powerful tool to investigate VIV problems. In this paper, the VIV of an elastically supported rigid-body circular cylinder was numerically studied by solving the Reynolds-averaged Navier–Stokes (RANS) equations with the shear stress transport (SST) k-ω turbulence model. The dynamic mesh approach was used to tackle the domain mesh change due to the cylinder motion. The characteristics of the amplitude response of the cylinder and the vortex shedding frequency at different reduced velocities were compared with the experimental data, and good agreement was found regarding the vibration amplitude and the frequency lock-in phenomenon. Results show the influence of added mass was perceptible in the free vibration and in the initial branch with small cylinder vibration amplitude, while it is fairly weak in the upper and lower branches considering the fact that the main response frequency of the cylinder is close to the natural frequency in a vacuum. Detailed vorticity distributions clearly indicate the 2P vortex modes at the upper and lower branches, and the 2S mode at the initial branch and their generation mechanisms are analyzed. The effects of the cylinder vibration on the lift and drag forces at different branches are discussed, and the frequencies of peak values in their Fourier spectra are examined. The phase difference between the lift force and the cylinder vibration shows an obvious jump from the initial branch to the upper branch with the vortex mode switching from 2S to 2P.

Numerical investigation on the effect of diameter ratio on wake induced vibrations of tandem cylinders

Numerical simulations of WIV (wake induced vibration) for tandem cylinders with different diameter ratio in the impingement regime are performed for a low Reynolds number of Re = 150 and low mass ratio of m* = 2.0. Five different diameter ratios of d/D = 1/2, 3/4, 1, 4/3, and 3/2 are examined, in order to identify the effects of diameter ratio on 2-DOF (two-degree-of-freedom) vibration responses of the cylinder in the range of 2≤Ur ≤ 14. The results show that the diameter ratio and vortex mode play important roles in the vibration amplitudes and frequencies of the downstream cylinder. The WIV can be further classified into WIEV (wake interference and enhancement vibration) and WCV (wake controlled vibration) according to two distinct mechanisms of the amplification of cross-flow vibration amplitude. As d/D ≤ 1, the vibration frequencies of the downstream cylinder are significantly pulled down and interfered by the small vortices shedding from the small upstream cylinder. Meanwhile, a wider range of lock-in and enhanced vibration amplitudes are the features for WIEV. The inline direction of the downstream cylinder have large response amplitudes in a wide range of Ur (reduced velocity) and reach to the maximum value at d/D = 1. As d/D > 1, the hydrodynamic characteristics of the downstream cylinder are mainly controlled by the larger vortices shedding from the upstream cylinder. The downstream cylinder vibrates as the vortex shedding frequency of the larger upstream cylinder and the lock-in phenomenon is absent. WCV significantly increases the risk of fatigue failure of the cylindrical structure.

Lock-in phenomenon in the wake flow past an oscillating circular nano-cylinder

In this paper, the lock-in/synchronization phenomenon in the wake flow around an oscillating nano-cylinder is studied with molecular dynamics simulation. The results show that the lock-in valley of the velocity fluctuation also occurs in nano-scale. Similar to those in normal scales (usually >1 mm), three regimes of lock-in, transition, and no-lock-in states are also obtained. Unlike in normal scales, the concurrence of the density and velocity fluctuation waves with different phase and the same frequency makes the fluctuation frequency of the lift force different from that of the velocity. The oscillation of the nano-cylinder can intensify the lift force fluctuation, especially in the lock-in state. The intensity of the lift force increases with the amplitude of the nano-cylinder vibration. The lock-in valley of the lift force usually covers a wider range of frequency than that of the velocity. Improving the inflow Reynolds number can reduce the coverage range of the lock-in valley in frequency. The lock-in valley does not vary apparently as the Jz number, which represents the interaction intensity between fluid molecules, increases until it approaches Jz ≈ 1.4. The rise of Kn number can promote the occurrence of the lock-in phenomenon.

Numerical Simulation of Acoustic Resonance in a Duct Containing a Flat Plate

This work is about numerical simulations of vortex induced acoustic resonance in a duct, experimentally investigated by Welsh et al. Vortex shedding of low-speed flow over a flat plate excites an acoustic duct mode, leading to a lock-in of shedding and acoustic resonance frequency over a wide range of flow velocities. This study shows that a state-of-the-art compressible Navier–Stokes flow solver is able to capture the lock-in phenomenon. The focus is on the numerical parameters required to precisely recover the experimental results in terms of lock-in range and acoustic pressure levels. Complete and reliable physical data are thereby obtained, which can aid in developing a systematic understanding of the complex flow interactions. Furthermore, hysteresis behavior is discovered and numerically explored.

Numerical study of vortex-induced vibrations of a circular cylinder at different incidence angles

The effects of four different incidence angles (α) on the vortex-induced vibration (VIV) response of a two degrees-of-freedom cylinder were studied using the two-dimensional unsteady Reynolds-averaged Navier-Stokes equation and shear stress transport k-ω model, combined with the fourth-order Runge-Kutta method. The VIV characteristics, including the structural vibration amplitude, vibration frequency, lock-in regime, the pattern of vortex shedding, Strouhal number, hydrodynamic coefficient, and power conversion efficiency were systematically researched. The numerical results showed that a change of the incidence angle made the VIV response of the cylinder display multifrequency characteristics. As the incidence angle increased, the amplitude in the y direction gradually decreased; comparatively, the amplitude in the x direction gradually increased. The VIV responses for different incidence angles all presented an obvious lock-in phenomenon; however, the width of lock-in region changed slightly with variation of the incidence angle. As the incidence angle increased, the root-mean-square value of the hydrodynamic force coefficient in the y direction and the mean value of the hydrodynamic force coefficient in the x direction both had a decreasing tendency.

Mode-based energy transfer analysis of flow-induced vibration of two rigidly coupled tandem cylinders

Two rigidly coupled cylinders are commonly available in engineering practices, which are always subjected to flow-induced vibration (FIV) with large oscillating amplitude due to the complex gap flow. However, their FIV features and the underlying mechanism have not been clearly understanded. In this study, the FIV of two rigidly coupled square cylinders in a tandem arrangement was numerically investigated for Reynolds numbers 100 and 200 and gap L/D = 2.0 and 6.0 in a two-dimensional framework. The dynamic response and flow structures are first studied. Mode-based energy transfer analysis was developed based on proper orthogonal decomposition. The energy transfer between the cylinders and the coherence modes was then analyzed to uncover the underlying mechanism of the FIV. The results reveal that the soft lock-in phenomenon was observed for all cases. When the gap L/D = 2.0, the dynamic response is always smaller than a stationary cylinder and all the wake structures show “2S” modes, which results from the stabilized effects of the upstream cylinder. At L/D = 6.0, the oscillating amplitude is much higher than that of a single square cylinder, due to the vigorous interaction between gap flow and the cylinders. As Reynolds number increased from 100 to 200, both vortex-induced vibration (VIV) and galloping co-exist, while the VIV response was reduced. Concerning the energy transfer, for L/D = 2.0, the first mode pair induced by Karman vortex shedding dominated the wake flow. The primary mode governed by UC stabilized the vibration, while the second mode tended to excite the FIV. For L/D = 6.0 in the galloping branch, the first two modes belonged to the vortex-induced modes, and the third mode represented the galloping mode. The galloping mode tended to excite the flow-induced vibration, while it was contrary for the vortex-induced modes.

Frequency and phase lock-in behind circular cylinder in the presence of random irregular waves

The effect of random waves and steady current on the wake of an elastically mounted cylinder is studied in a series of experiments. The relation between the vortex shedding frequency and waves' nonlinearities is discussed. A phase-based method is proposed in order to detect the presence of a subharmonic phase lock-in phenomenon.

Mitigation of laminar separation flutter using active oscillation of local surface

This work explores the mitigation effect of laminar separation flutter (LSF) using active oscillation of a local surface at Re = 77 000. Aerodynamic forces and flow field of a National Advisory Committee for Aeronautics (NACA) 0012 airfoil are obtained by numerical simulations using the γ−Reθ transition model. The local oscillation is considered as a harmonic motion of a single mode varying both in temporal and spatial domains. The control effects of oscillation positions, amplitudes, and frequencies on the pitch instability are investigated. The work done by aerodynamic moment per motion cycle when the airfoil undergoes prescribed harmonic pitch motion is defined to evaluate the control performance. The mitigation effect of LSF is demonstrated by a fluid–structure interaction (FSI) method. The results show that the oscillation region should be placed on 0.2c for small oscillation amplitude while the optimal oscillation position is 0.6c for large oscillation amplitude. The flow control mechanism is analyzed in terms of the flow structure. A series of vortices are formed and moved downstream under the effect of active oscillation of the local surface. These vortices suppress the formation of a large-scale laminar separation phenomenon, which improves the pitch stability. The frequency lock-in phenomenon occurs in a certain oscillation frequency range, and it can improve the control performance on the pitch instability. The results of FSI show that the active oscillation of the local surface can completely eliminate the LSF.