Vortex Lock-in Research Articles

Experimental comparison of a NACA0021 airfoil in large plunging and surging motions at 90 ◦ angle of attack

The topic of vortex-induced vibrations on a wind turbine blade has recently gained much attention due to its growing size and flexibility. To address this concern, a wind tunnel test was conducted to study the forced plunging and surging motion of a NACA0021 airfoil at 90° angle of attack. Results indicate that vortex lock-in occurred for a motion amplitude of one chord length even for a small frequency ratio (between motion frequency and static Strouhal frequency) of 0.39. Analysis of the drag coefficient, derived from the phase-averaged Particle Image Velocimetry (PIV) data, shows that a plunging airfoil experiences higher average loading than a surging airfoil, which is deemed to be more harmful considering the higher loading in the crossflow-direction due to the variation of effective angle of attack.

Component decomposition and spatial distribution of unsteady forces on a circular cylinder oscillated under various amplitudes at Re = 2.0×104

Vortex-induced vibrations (VIVs) are of practical significance in the design of engineering structures, and the dynamic loads responsible for VIVs are thus crucial. In this study, the force characteristics of a circular cylinder undergoing forced oscillations at vortex lock-in states are investigated by employing three-dimensional large eddy simulations (LES) at a moderate subcritical Reynolds number of 2.0 × 104. Simulations of the oscillating cylinder are performed under a series of normalized amplitudes ranging from 0.05 to 0.60 at a fixed reduced velocity of 6.0. Moreover, a force spectrum-based approach is proposed to decompose the overall force into motion-induced and vortex-shedding components. Alternative insights into the spatial distribution of the force are also obtained by analysing the spanwise correlation, pressure field, and flow feature. The numerical results show that the motion-induced lifts experience an abrupt jump in both magnitude and phase as the oscillation amplitude increases. Furthermore, the motion-induced forces are almost fully correlated except in the phase-jump regime, although the correlation of the overall forces is relatively weak. Finally, the identified force parameters are successfully applied to predict the VIV amplitudes of the cylinder under various mass-damping conditions.

Extraction of aerodynamic damping and prediction of vortex-induced vibration of bridge deck using CFD simulation of forced vibration

This study presents computational fluid dynamics (CFD) simulation of forced vibration of a bridge deck for extraction of amplitude-dependent aerodynamic damping in the vicinity of vortex lock-in region. The coordinate system fixed on the oscillating body is used to bypass the requirement of mesh updating. The three-dimensional flow around the vibrating deck is assumed to be homogeneous in spanwise direction and simulated using the efficient high-order spectral element/Fourier method. The aerodynamic damping is extracted from the simulated lift and then used to estimate the steady-state vortex-induced vibration (VIV) amplitude for given wind velocity and structural parameters. A good match of VIV amplitudes between simulations and wind tunnel tests validates the accuracy of simulation. The VIV mechanisms are discussed from the vortex shedding modes, distributions of dynamic pressure and energy transfer from flow to bridge deck. The leading-edge vortex shedding rather than Karman vortex shedding is identified to be responsible for the VIV. The hysteresis of VIV is observed which is related to the mode change of impinging leading-edge vortex and leading-edge vortex shedding. Finally, a novel forced vibration technique with a varying amplitude is proposed that permits extraction of aerodynamic damping by a single CFD run with improved efficiency.

Anisotropy of flux pinning properties in superconducting (Li,Fe)OHFeSe thin films

The electrical transport properties of (Li,Fe)OHFeSe films have been investigated in detail. The sharply textured films, prepared by matrix-assisted hydrothermal epitaxy (MHE) on LaAlO3, show a zero-resistance critical temperature T c of ∼42 K, J c values well above 1 MA cm−2 at low temperatures, and a maximum pinning force density F P of ∼100 GN m−3 at 4 K. The activation energy U 0 for thermal depinning of flux lines has been resolved for low magnetic fields, it agrees well with literature data. The coherence lengths and penetration depth were estimated via upper critical field B c2 and self-field J c, respectively, to be ξ ab ∼ 2.7 nm, ξ c = 0.24 nm, and λ ab ∼ 160–200 nm. The layered crystal structure leads to highly anisotropic and two-dimensional electrical properties, including trapping and lock-in of vortices.

Aerodynamic damping of inclined slender prisms

The aerodynamic damping of forward and backward inclined prisms has been identified through a series of forced vibration wind tunnel tests. The test results show that the amplitude of vibration and reduced wind velocity both have a significant effect on the aerodynamic damping of the inclined prisms, especially at reduced wind speeds where von Karman vortex lock-in occurs. The effect of forward and backward inclination on the characteristics of aerodynamic damping in inclined prisms is dissimilar to a vertical prism, and the characteristics have been discussed in terms of the unsteady aerodynamic force and Strouhal number in this study. This study not only advances our understanding on aerodynamic damping of inclined prisms, but also provides values that can be used to estimate aerodynamics and aeroelasticities of inclined prisms.

Plunging Oscillations of Airfoils and Wings: Progress, Opportunities, and Challenges

The vortex dynamics of thrust and lift generation for periodically plunging airfoils and finite wings at low Reynolds numbers is reviewed. Effects of vortex lock-in phenomenon, leading-edge vortex, vortex merging and pairing, vortex–wing interactions, leading-edge geometry, wake deflection, and chordwise and spanwise flexibility on lift and thrust are discussed. Mean lift force of the oscillating airfoil at post-stall angles of attack becomes maximum at optimal frequencies due to the vortex lock-in at the fundamental frequency, subharmonic, and first harmonic of the natural shedding frequency. Bifurcations of wakes of plunging airfoils, which depend on the mean angle of attack and the initial conditions and can produce large mean lift coefficients, are not observed for finite wings. One or two arch-type vortical structures may develop from the leading-edge vortices shed on low-aspect-ratio wings. Significant spanwise flows can develop on finite wings due to the dynamics of tip vortices or leading-edge vortices. Chordwise and spanwise flexibility of plunging airfoils and wings are known to enhance the mean thrust and lift; however, the physical mechanism of the optimal conditions is not well understood. Various flow control opportunities to exploit the flow physics as well as remaining challenges and unresolved issues are summarized.

Crosswind response of tall buildings with nonlinear aerodynamic damping and hysteretic restoring force character

This study deals with analysis of stochastic crosswind response of tall buildings with bilinear hysteretic restoring force character at the vicinity of vortex lock-in speed where nonlinear negative aerodynamic damping is significant. The nonlinear aerodynamic damping at a given wind speed and the hysteretic damping resulted from hysteretic restoring force are modelled as polynomial functions of amplitude of narrow-band building response. It permits analytical estimations of response statistics by using equivalent nonlinear equation (ENEL) approach, which include root-mean-square value, kurtosis, extreme value distribution and fatigue damage. Response history analysis is also performed to prove the accuracy of this analytical framework. A comprehensive parameter study is carried out to shed insights on the characteristics of inelastic crosswind response. This study also illustrates the advantage of the ENLE approach over the statistical linearization approach with assumption of Gaussian response distribution when applied to estimate inelastic crosswind response at wind speed region with negligible aerodynamic damping. This study not only presents an effective analytical approach but also sheds new insights towards improved understanding of inelastic crosswind response of tall buildings, contributing to a safer and more economical design of tall buildings against strong winds.

鉄系超伝導体における次元交差

Since the discovery of Fe-based superconductors (FBS), great progress in the growth of single crystals and thin films of these materials have been made. Now high-quality FBS thin films are available, which spurs progress in fundamental and application research. In this paper, we report on the transport properties of epitaxial SmFeAs(O,F) and Fe(Se,Te) thin films. We found vortex trapping and lock-in caused by the Sm(O,F) blocking layer in SmFeAs(O,F) when the magnetic field is close to the ab-plane. The vortex trapping is hallmarked by a drop of the exponent n in E~J n (E and J are electric field and current density), whereas a local peak within the dip of n is a sign of the vortex lock-in. Interestingly, vortex trapping and lock-in were also observed in Fe(Se,Te), albeit Fe(Se,Te) shows a low superconducting transition temperature and low anisotropy.

Analysis of crosswind fatigue of wind-excited structures with nonlinear aerodynamic damping

This study addresses crosswind fatigue analysis of wind-excited flexible structures at the vicinity of vortex lock-in speed where the nonlinear aerodynamic damping effect is significant. The nonlinear aerodynamic damping is modeled as a polynomial function of time-varying displacement or velocity of vibration. The crosswind response is a narrow-band hardening non-Gaussian process with a reduced peak factor and having a distribution of vibration amplitude different from Rayleigh distribution. Analytical solutions of cycle number and fatigue damage are derived and their accuracy is validated through comparison with rainflow cycle counting method using simulated response time histories. A correction factor as a function of response kurtosis is also introduced that facilitates the calculation of non-Gaussian fatigue damage from the Gaussian fatigue prediction. The effectiveness and accuracy of the proposed framework are illustrated by crosswind responses of a squared tall building and a two-dimensional structural section model, and by full-scale vibration measurement data of a traffic-signal-support-structure. This study provides an improved estimation of crosswind fatigue of wind-excited flexible structures with a consideration of hardening non-Gaussian response character.

Estimation of stochastic crosswind response of wind-excited tall buildings with nonlinear aerodynamic damping

This study addresses the analysis of crosswind response of tall buildings and flexible structures at wind speed region higher than the vortex lock-in speed, where nonlinear negative aerodynamic damping effect is significant. The modeling of nonlinear aerodynamic damping as a function of time-varying velocity and/or displacement of vibration is established based on motion-induced aerodynamic force information obtained from forced-vibration model testing in wind tunnel, referred to as harmonic balance. Response time history simulations are performed by solving the nonlinear equation of motion to explore the unique hardening non-Gaussian characteristics of crosswind response and its extreme value distribution with reduced peak factor. The response time history simulations also provide a bases for assessing the performance of analytical predictions of root-mean-square (RMS) response using crosswind loading spectrum and equivalent aerodynamic damping models. The limitations of the equivalent aerodynamic damping models as functions of RMS response derived from harmonic balance and statistical linearization with an assumption of Gaussian response are revealed. This study, at the first time, by using the method of equivalent nonlinear equation, presents complete analytical solutions of crosswind response statistics, including not only the RMS response, but also response kurtosis, response probability distribution, peak factor and extreme value distribution. The comparison of the analytical predictions with response simulation results illustrates that the method of equivalent nonlinear equation is very accurate in predicting crosswind response statistics that are influenced by the nonlinear aerodynamic damping. The narrow band feature of response is further considered in this study in the calculation of crossing rate using amplitude process, which leads to even better predictions of extreme statistics. This general framework can also be readily adopted in design codes and standards for calculating vortex-induced vibration of towers and chimneys.

Vortex lock-in transition and evidence for transitions among commensurate kinked vortex configurations in single-layered Fe arsenides

We report an angle-dependent study of the magnetic torque $\tau(\theta)$ within the vortex state of single-crystalline LaO$_{0.9}$F$_{0.1}$FeAs and SmO$_{0.9}$F$_{0.1}$FeAs as a function of both temperature $T$ and magnetic field $H$. Sharp peaks are observed at a critical angle $\theta_c$ at either side of $\theta=90^{\circ}$, where $\theta$ is the angle between $H$ and the inter-planar \emph{c}-axis. $\theta_c$ is interpreted as the critical depinning angle where the vortex lattice, pinned and locked by the intrinsic planar structure, unlocks and acquires a component perpendicular to the planes. We observe a series of smaller replica peaks as a function of $\theta$ and as $\theta$ is swept away from the planar direction. These suggest commensurability effects between the period of the vortex lattice and the inter-planar distance leading to additional kinked vortex configurations.

Periodically plunging foil near a free surface

Experiments were performed to investigate the effects of amplitude and depth on the drag reduction of a NACA 0012 airfoil plunging near a free surface for a range of frequencies. Beyond the effect of the free surface, at low Strouhal numbers based on amplitude, Sr A, the drag reduction follows a parabolic trend with greater effect for greater amplitude, similar to the Garrick predictions. At Sr A ≈ 0.08, larger amplitudes break from this trend due to leading-edge vortex formation. As a result, smaller amplitudes become preferable for Sr A > 0.12. In addition, for the first time, vortex lock-in is documented experimentally. The effect of depth is twofold; firstly with decreasing depth, there is a general departure from the Garrick trends. Secondly, a reduction in thrust is observed around a constant unsteady parameter of τ = U ∞ 2πf/g ≈ 0.25; around this value significant free-surface waves form that detract from thrust creation. For depths greater than two chord lengths, there is negligible free-surface effect.

Vortex lock-in transition coinciding with the 3D to 2D crossover in YBa2Cu3O7

A vortex lock-in transition was directly detected by torque magnetometry in an overdoped YBa2Cu3O7 single crystal of low anisotropy (\approx 7). The locked-in state was observed below the 3D to 2D crossover temperature Tcr = 76 K, independently of extrinsic pinning effects thanks to a high quality clean crystal and the use of a vortex shaking technique. The shape of the torque signal as a function of the angle between the applied magnetic field and the crystallographic c-axis is in very good agreement with the model developped by Feinberg and Ettouhami [Int. J. Mod. Phys. B 7, 2085 (1993)] for quasi-2D superconductors, despite the low anisotropy of the material.

Geometry dependent resistivity behavior in mesoscopic Bi2Sr2CaCu2O8+δ single crystals

In order to investigate the interaction between Josephson vortices and pancake vortices in a layered Bi2Sr2CaCu2O8+δ superconductor, c-axis resistivity measurements were carried out on fabricated mesoscopic single crystals for two experimental geometries, when an applied high magnetic field of 14 T is perpendicular (Bex⊥L) and parallel (Bex∥L) to the width of sample. In the first case, the angular dependence of the resistance obtained near the ab-plane at T=30K exhibited hysteretic non-monotonic behavior with local maxima at θ=0.6° away from the ab-plane and dips and spikes at θ=0.2° marking a vortex lock-in transition. In the second geometry (Bex∥L), instead of a local maximum, peculiar resistance shoulders were observed. At higher temperatures, hysteresis is reduced, while the vortex lock-in transition becomes considerably broader indicating the interaction of pancake and Josephson vortices.

Vortex phases in magnetic fields near ab-plane in Bi2Sr2CaCu2O8+δ single crystal

Vortex matter of the layered superconductors in very high magnetic fields near the ab-plane was studied by using the c-axis resistivity measurements on the mesoscopic Bi2Sr2CaCu2O8+δ single crystals. While the angular dependence of resistance exhibits the sharp lock-in features in low magnetic field region, it was found that the vortex lock-in transition becomes considerably broad in high magnetic fields, showing anomalous shoulders at 0.3° away from the ab-plane. The appearance of the resistance shoulder is followed with the stronger current level dependence, indicating possible different phases due to interplay of Josephson vortices and pancake vortices near ab-plane.

Vortex states in mesoscopic single crystals Bi 2Sr 2CaCu 2O 8+δ in high magnetic fields

The c-axis resistivity measurements were performed in the vicinity of the ab-plane in order to investigate the interaction between Josephson vortices and pancake vortices in Bi 2Sr 2CaCu 2O 8+ δ mesoscopic single crystals. It was found that the angular dependence of the c-axis resistivity drastically changes in high magnetic field regime. The vortex lock-in transition becomes considerably broad in high magnetic fields, while the angular dependence of resistance exhibits the sharp lock-in features in low magnetic field region.

Vortex Lock-In Phenomenon in the Wake of a Plunging Airfoil

The flow over a NACA0012 airfoil, oscillated sinusoidally in plunge, is simulated numerically using a two-dimensional Navier-Stokes solver at a Reynolds number of 20,000. The wake of the airfoil is visualized using a numerical particle tracing method for high reduced frequencies (1.0 <k< <10.0) and small nondimensional amplitudes (h < 0.1). Anomalous vortex shedding modes (involving multiple vortices shed per half-cycle of airfoil motion) observed experimentally in the literature are reproduced numerically and are shown to be the result of interaction between the plunging frequency and a natural bluff-body shedding frequency. This results in a vortex lock-in phenomenon analogous to that seen for oscillating cylinders. However, the lock-in boundary is not symmetric about the natural shedding frequency, due to the sharp trailing edge forcing the flow to separate at the trailing edge on the windward side of the airfoil for the majority of the plunge cycle at higher frequencies and amplitudes.

A moving frame of reference algorithm for fluid/structure interaction of rotating and translating bodies

AbstractA mathematical and numerical formulation is derived for fluid/structure interaction problems involving arbitrary geometries relevant to the simulation of bridge deck instabilities due to cross winds. A translating and rotating moving frame of reference is attached to the body to utilize an efficient fixed mesh spectral/hp element solver. The formulation is validated against experiments with flow simulations of circular cylinders at Reynolds numbers of 100–400 undergoing free and forced motion in the transverse and in‐line directions. The well‐documented phenomena of vortex lock‐in is captured. The formulation is then applied a rectangular body at Re=250 under forced and free motion the latter of which demonstrates torsional galloping. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Irreversible magnetization under rotating fields and lock-in effect on a ErBa2Cu3O7-δ single crystal with columnar defects

We have measured the irreversible magnetization M_i of an ErBa_2Cu_3O_7 single crystal with columnar defects (CD), using a technique based on sample rotation under a fixed magnetic field H. This method is valid for samples whose magnetization vector remains perpendicular to the sample surface over a wide angle range - which is the case for platelets and thin films - and presents several advantages over measurements of M_L(H) loops at fixed angles. The resulting M_i(\Theta) curves for several temperatures show a peak in the CD direction at high fields. At lower fields, a very well defined plateau indicative of the vortex lock-in to the CD develops. The H dependence of the lock-in angle \phi_L follows the H^{-1} theoretical prediction, while the temperature dependence is in agreement with entropic smearing effects corresponding to short range vortex-defects interactions.

Superconducting anisotropy in Nd 1.85Ce 0.15CuO 4 single crystals

The magnetic torque of the Nd 1.85Ce 0.15CuO 4 crystal consists of three contributions in the superconducting state, i.e., (1) a torque of the anisotropic magnetic moment of the Nd 3+ ions, (2) a torque coming from the mass difference between m ab and m c and (3) a torque of the vortex lock-in states appeared when the field is applied parallel to the CuO 2 planes. We analyze a torque component arising from the mass anisotropy by using the anisotropic London model and obtain an anisotropy parameter γ c =28±3. The irreversibility line of Nd 1.85Ce 0.15CuO 4 is in excellent accordance with that of the La-based cuprate.