Aerodynamic Damping Research Articles

Motion-amplitude-dependent nonlinear VIV model and maximum response over a full-bridge span

Nonlinear motion-amplitude $$(y_{T} )$$ -dependent energy-trapping properties of a bridge model undergoing vortex-induced vibration (VIV) are investigated. Energy-trapping properties of the model undergoing a full-process from still to a limit cycle oscillation (LCO) state are identified. A van der Pol-type model is adapted to describe the amplitude-dependent aerodynamic properties. Nonlinear parameter-amplitude relations, $$\varepsilon {-}y_{T}$$ and $$\xi_{\varepsilon } {-}y_{T}$$ , are established. Nonlinear aerodynamic damping is separated into two parts: the initial damping which varies with the reduced wind speed, and the $$\varepsilon $$ -related part which varies with both the reduced wind speed and the motion amplitude. The initial aerodynamic damping determines the threshold of VIV, while the $$\varepsilon $$ -related part dominates the evolution process and the LCO. The identified nonlinear analytical model is capable of predicting VIV responses at higher mechanical damping ratios. The energy-trapping properties of a section model in time are transformed into nonlinear properties distributed in space along an elongated 3-D elastic bridge span. According to this “time-space” transformation, the convection coefficient, which links the maximum response of a 3-D structure with that of a 2-D (1-DOF) sectional model, can be determined. Compared with a constant-parameter analytical model, an adapted nonlinear one brings to light significantly larger convection coefficients. Finally, parameter overflowing phenomena are revealed and discussed.

Closed-form derivation of aerodynamic damping matrix and pitch vector of an aero-servo-elastic wind turbine system

This paper develops closed-form expressions of aerodynamic damping matrix and pitch controller of an aero-servo-elastic wind turbine (WT) system. This facilitates establishing a linearized WT model completely analytically at an arbitrary operational point, without resorting to extensive numerical linearizations or fittings. The rotor blade flexibility and pitch controller are included in the model development, thus unfolding a full understanding of the aerodynamic coupling effects. The linearized WT model is verified by good agreement with results from the original nonlinear WT model. Based on the verified linearized model, it is seen that aerodynamic coupling between tower fore–aft and side–side vibrations is solely due to the tower top rotations, and the top rotations also significantly enlarge the diagonal aerodynamic damping coefficients. Both tower top rotations and flexible blade–tower interaction play important roles in tower aerodynamic damping ratios. The developed formulas of load coefficients are also readily applicable to a FE modeling framework of the tower–foundation system.

Aerodynamic damping functions in vortex-induced vibrations for structures with sharp edges

Ultimate limit state and fatigue analyses of slender structures in vortex-induced vibrations require knowledge of aerodynamic damping in the lock-in range. The aerodynamic damping depends primarily on the shape of the cross section. The paper provides an experimental database of aerodynamic damping functions for different shapes, with a focus on sharp-edged cross sections. The data are discussed with respect to existing results available for circular cross sections. The aerodynamic damping is measured directly through wind tunnel tests in forced vibrations. Wind tunnel tests in free vibrations are used to extend the functions in the range of large oscillations and to validate the model. This concept is implemented in a well-founded calculation method for vortex induced vibrations for the design of slender structures. This is suitable for code applications and is in line with the procedure described in the latest generation of Eurocode. The novelty with respect to previous models like the Vickery&Basu model consists in an aerodynamic damping parameter with positive curvature. This can be easily controlled for varying cross sections by changing the value of the function exponent.

A study of nonlinear aeroelastic response of a long flexible blade for the horizontal axis wind turbine

As long flexible blades in large wind turbines are prone to excessive bending deformations, there are failures in dynamic analyses under linear (small deflection) conditions. Thus, a large deflection blade model is developed here to study the dynamic response. The updated Lagrangian equation is used to derive the large deflection blade model from the Euler–Bernoulli beam. Then, the nonlinear aeroelastic dynamics equations of the blade are established using blade element momentum (BEM) theory, and time-domain simulations are performed using the nonlinear Newmark and Newton–Raphson methods. The effects of structural vibrations and aerodynamic damping are considered throughout the process. Finally, the nonlinear model is applied to the DTU 10 MW wind turbine. The results show that under steady and below-rated wind speeds, the flapwise deflection of the nonlinear blade is smaller than that of the linear blade. However, this phenomenon is the opposite for above-rated wind speeds. Under a step wind, the model responds quickly to the blade’s flexible deformation. Under turbulence, the linear results are consistent with the DNVGL Bladed 4.3 results, indicating that the nonlinear blade based on the linear Euler–Bernoulli beam is reliable. Meanwhile, the flapwise deflection for both blades fluctuates slightly when turbulent speeds are lower than the rated speed (0–5 s and 41–50 s), which is distinct from the steady-state analysis. In the aeroelastic coupling analysis, responses that consider vibration feedback are significantly smaller than those without feedback, and a nonlinear blade is significantly more affected in the flapping direction than a linear blade. Finally, the aerodynamic performance of large wind turbines is negatively affected by certain turbulent wind speeds.

Frequency-dependent aerodynamic damping and its effects on dynamic responses of floating offshore wind turbines

This study investigates how the frequency-dependent characteristics of aerodynamic damping influence the dynamic responses of a floating offshore wind turbine (FOWT). To accomplish this, we established an aero-hydro-servo-structure coupled model for the OC4 DeepCWind wind turbine, and validated the aerodynamic and hydrodynamic models based on thrust force, mooring stiffness, hydrodynamic damping, and natural periods of platform motions. We identified and analyzed both the constant and frequency-dependent aerodynamic damping of the referenced wind turbine, and investigated their effects on platform motions, nacelle acceleration, and tower bending moment. Our findings highlight the close relationship between aerodynamic damping and the natural periods of platform motion in terms of suppression or amplification effects. We strongly recommend considering the contributions of frequency-dependent aerodynamic damping in a decoupled model.

Extreme structural response prediction and fatigue damage evaluation for large-scale monopile offshore wind turbines subject to typhoon conditions

Offshore wind is becoming the way forward for green energy harnessing worldwide. However, frequent typhoons are a major constraint for the development of offshore wind power for some regions in Asia and North America. Typhoons may pose a huge challenge to offshore wind farm development in southern China. In this paper, a fully-coupled analysis was carried out for a 10 MW large-scale monopile offshore wind turbine (OWT) using SIMO-Riflex-Aerodyn (SRA) code. The response characteristics of the OWTs in different typhoon regions are investigated based on the measured typhoon conditions in China. The effect of aerodynamic damping on the response and the load effect is analyzed in detail. Two different distribution methods are used to statistically extrapolate the response value and get the short-term extreme response. Cumulative linear fatigue damage is evaluated by the rain-flow counting method to explore the possible failure modes of large wind turbines during typhoons. The results show that aerodynamic loads play an important role in large monopile OWTs during high wind speeds in parked conditions. The extreme response and fatigue analyses from this study indicate that fatigue is a dominant failure mode for the large OWT tower during typhoons, while buckling is unlikely.

Research on the along-wind aerodynamic damping and its effect on vibration control of offshore wind turbine

The aerodynamic damping of the offshore wind turbine structure (OWT), which can be divided into along-wind aerodynamic damping and across-wind aerodynamic damping, is complex, changeable and closely related to the operation status of the wind turbine, the adopted control strategy and the wind speed. Further, the along-wind aerodynamic damping always plays a significant role in an operational OWT, which can effectively mitigate the dynamic response of the OWT structure. In this research, a new theoretical calculation method of the along-wind aerodynamic damping was firstly derived considering the contributions resulted from the changes in rotor speed with respect to wind speed. Then, this new proposed theoretical calculation process was verified by the simulation method in open-source software FAST and the parameters, which affect the along-wind aerodynamic damping such as wind speed, rotor speed and pitch angle, were also investigated. It is shown that the along-wind aerodynamic damping increases as the value of above influencing factors increases until the rotor speed approaches the rated rotor speed and the pitch angle is greater than the critical angle. Finally, the effect of aerodynamic damping on the performances of tuned mass damper (TMD) for an 5 MW OWT under operational condition was studied. The results demonstrate that the effectiveness of TMD is weakened with the increase of aerodynamic damping. Specifically, when the along-wind aerodynamic damping of the 5 MW OWT increases from 4.97% to 6.87%, the additional damping of the TMD decreases from 7.301% to 6.386%.

Nonuniform structural properties of wings confer sensing advantages.

Sensory feedback is essential to both animals and robotic systems for achieving coordinated, precise movements. Mechanosensory feedback, which provides information about body deformation, depends not only on the properties of sensors but also on the structure in which they are embedded. In insects, wing structure plays a particularly important role in flapping flight: in addition to generating aerodynamic forces, wings provide mechanosensory feedback necessary for guiding flight while undergoing dramatic deformations during each wingbeat. However, the role that wing structure plays in determining mechanosensory information is relatively unexplored. Insect wings exhibit characteristic stiffness gradients and are subject to both aerodynamic and structural damping. Here we examine how both of these properties impact sensory performance, using finite element analysis combined with sensor placement optimization approaches. We show that wings with nonuniform stiffness exhibit several advantages over uniform stiffness wings, resulting in higher accuracy of rotation detection and lower sensitivity to the placement of sensors on the wing. Moreover, we show that higher damping generally improves the accuracy with which body rotations can be detected. These results contribute to our understanding of the evolution of the nonuniform stiffness patterns in insect wings, as well as suggest design principles for robotic systems.

Estimation of wind-induced response of large membrane structures with nonlinear motion-induced aerodynamic force and nonlinear geometric stiffness

Wind-induced dynamic response for large membrane structures with consideration of the coupling influences of nonlinear motion-induced aerodynamic force and nonlinear geometric stiffness is analytically evaluated in this study. By utilizing the equivalent nonlinear system approach, the Fokker-Planck-Kolmogorov equation of the membrane structures is derived, and the analytical response solutions, including probability density function, root-mean-square value, kurtosis, peak response, and peak factor, are presented. The accuracy of the proposed analytical solutions is checked by the numerical results obtained with the fourth-order Runge-Kutta approach. The findings reveal that vortex-induced vibrations occur at high wind speed regions due to the effect of nonlinear negative aerodynamic damping. Additionally, the geometric stiffness nonlinearity caused by large deformation is found to be significant for reducing the dynamic response amplitude in membrane structures. This study proposed herein presents an effective analytical approach for predicting the aero-elastic response of such flexible structures subjected to wind loads.

Attitude Dynamics of Spinning Magnetic LEO/VLEO Satellites

With the growing popularity of small satellites, the interaction with the air in low and especially in very low Earth orbits becomes a significant resource for passive angular stabilisation. However, the possibility of spin motion remains a considerable challenge for missions involving aerodynamically stabilised satellites. The goal of this paper was to investigate the attitude motion of arbitrarily spinning satellites in LEO and VLEO under the action of aerodynamic, gravitational, and magnetic torques, taking into account the aerodynamic damping. Using an umbrella-shaped deployable satellite as an example, the study demonstrated that both regular and chaotic attitude regimes are possible in the attitude motion. The occurrence of chaos was verified by means of Poincaré sections. The results revealed that, to prevent chaotic motion, active attitude control and reliable deployment techniques for aerodynamically stabilised satellites are needed.

The Role of Vanes in the Damping of Bird Feathers

Bird feathers sustain bending and vibrations during flight. Such unwanted vibrations could potentially cause noise and flight instabilities. Damping could alter the system response, resulting in improving quiet flight, stability, and controllability. Vanes of feathers are known to be indispensable for supporting the aerodynamic function of the wings. The relationship between the hierarchical structures of vanes and the mechanical properties of the feather has been previously studied. However, still little is known about their relationship with feathers’ damping properties. Here, the role of vanes in feathers’ damping properties was quantified. The vibrations of the feathers with vanes and the bare shaft without vanes after step deflections in the plane of the vanes and perpendicular to it were measured using high-speed video recording. The presence of several main natural vibration modes was observed in the feathers with vanes. After trimming vanes, more vibration modes were observed, the fundamental frequencies increased by 51–70%, and the damping ratio decreased by 38–60%. Therefore, we suggest that vanes largely increase feather damping properties. Damping mechanisms based on the morphology of feather vanes are discussed. The aerodynamic damping is connected with the planar vane surface, the structural damping is related to the interlocking between barbules and barbs, and the material damping is caused by the foamy medulla inside barbs.

An efficient two-stage hybrid framework to evaluate vortex-induced vibration for bridge deck based on divergent vibration

High-fidelity CFD (computational fluid dynamics) numerical modeling offers an attractive alternative of VIV investigation for bridge deck. Conventional strategy to perform VIV prediction using CFD is to directly characterize the two-way coupled free vibration of structure and flow which could become dramatically expensive in computational cost. To bridge the gap, this study presents an efficient two-stage hybrid approach that combines a divergent vibration simulation for fast aerodynamic damping extraction and a nonlinear model to predict the VIV. A negative structural damping is imposed in the motion equation to intentionally create a divergent vibration which significantly accelerates the growth of motion and takes less than 1/3 of the elapsed time compared with a conventional VIV simulation whereas maintains reasonable accuracy in aerodynamic identification. A Π-shaped bridge deck is employed as a demonstration of the proposed approach. The modeled steady-state VIV performance is well validated against wind tunnel tests. The effect of negative damping on instantaneous flow field, surface pressure and amplitude prediction are discussed and the optimal damping ratio achieving balanced accuracy and efficiency is suggested. The proposed framework shows favorable efficiency while simultaneously retains satisfactory accuracy and is a potential numerical alternative of VIV investigation for bridge deck.

Aerodynamic vs. frictional damping in primary flight feathers of the pigeon Columba livia

During flight, vibrations potentially cause aerodynamic instability and noise. Besides muscle control, the intrinsic damping in bird feathers helps to reduce vibrations. The vanes of the feathers play a key role in flight, and they support feathers’ aerodynamic function through their interlocked barbules. However, the exact mechanisms that determine the damping properties of the vanes remain elusive. Our aim was to understand how the structure of the vanes on a microscopic level influences their damping properties. For this purpose, scanning electron microscopy (SEM) was used to explore the vane’s microstructure. High-speed videography (HSV) was used to record and analyze vibrations of feathers with zipped and unzipped vanes upon step deflections parallel or perpendicular to the vane plane. The results indicate that the zipped vanes have higher damping ratios. The planar surface of the barbs in zipped vanes is responsible for aerodynamic damping, contributing 20%–50% to the whole damping in a feather. To investigate other than aerodynamic damping mechanisms, the structural and material damping, experiments in vacuum were performed. High damping ratios were observed in the zipped vanes, even in vacuum, because of the structural damping. The following structural properties might be responsible for high damping in feathers: (i) the intact planar surface, (ii) the interlocking of barbules, and (iii) the foamy inner material of the barb’s medulla. Structural damping is another factor demonstrating 3.3 times (at vertical deflection) and 2.3 times (at horizontal deflection) difference in damping ratio between zipped and unzipped feathers in vacuum. The shaft and barbs filled with gradient foam are thought to increase the damping in the feather further.

The impact of the wind attack angle on a typical bridge deck’s flutter behavior by the distributed aerodynamic characteristics method

To investigate the influence of the wind attack on a bridge deck’s flutter performance, the concept of “pressure flutter derivatives” was introduced as a part of the “distributed aerodynamic characteristics” method, which can be used to visualize the dominant fluctuations of the pressure field. The distributions of the aerodynamic damping and stiffness under different wind attack angles were visualized, instead of using an overall force perspective. The analysis was carried out through two-dimensional computational fluid dynamics simulations based on a typical box deck section. Necessary data were obtained through the forced vibrations of the deck. The dominant pressure fluctuations were demonstrated, around which the wind attack angles’ impact on the Scanlan flutter derivatives was discussed. For the deck section used in this study, the wind attack angle was found to most affect the windward parts of the deck. When wind attack angle ranged from − 1.5 ° to 3 ° , two regions contributed the most: one located behind the windward faring vertex and the other located behind the first vertex of the upper slab. When the wind attack angle decreased to − 3 ° , a new dominant region appeared behind the first vertex of the lower slab, which caused a sudden reduction of the flutter critical speed.

Aerodynamic Damping of the Tubed Vortex Reducer in an Axial Compressor Disk Cavity

The tubed vortex reducer in the axial compressor can destroy the vortex in the disk cavity, by a thin-walled tube, to reduce the total pressure loss. The tube may suffer from vibration problems, such as flutter and forced vibration, which are closely related to aerodynamic damping. In this paper, the energy method and the influence coefficient method are used to study the aerodynamic damping of the tube. Based on the modal characteristics, steady and unsteady flow characteristics of the tube, the first and second modes with lower frequencies and greater vibration risk are selected as the analysis objects. The energy method is used to calculate the aerodynamic damping of the tube with different amplitudes, which shows that the results approximately meet the linear assumption and are accurate. The results obtained by the influence coefficient method show that the aerodynamic influence between adjacent tubes is very small, and the effect of inter-tube phase angle on the aerodynamic damping can be ignored. Finally, it is found that the effect of structural coupling caused by the support ring on the aerodynamic damping of the tube is mainly reflected in two aspects: frequency reduction and tube mode coupling.

Effects of aerodynamic damping on freestanding bridge tower under the joint action of wind and wave loads

This study uses a time-domain simulation to investigate the effect of aerodynamic damping on a freestanding bridge tower under the joint action of wind and wave loads. The physical model of the bridge tower, which has been tested in laboratory, is numerically reconstituted considering structural nonlinearities obtained from free oscillation tests. Random wind fields are generated using the harmonic superposition method, and the wind flow characteristics, such as mean wind velocity and turbulence intensity, are identified based on the data collected in the laboratory. The wave loads measured at the bottom of the foundation during the experimental model tests are used for the simulation. The dynamic responses of the tower under the joints action of wind and wave loads are successfully simulated. A clear reduction in structural vibration in the wave-controlled region is confirmed by simulation results. Further numerical investigation indicates that an increase in the mean wave velocity produces additional aerodynamic damping in the structural motion system, which significantly dampens the responses of the wave-induced vibration. A simple method for determining the dynamic responses of a bridge tower under the joint action of wind and wave loads, using the data obtained from wind- and wave-only cases, is proposed.

Influences of Attack Angles on Aerodynamic Derivatives and Flutter Characteristics of Flat Box Girders

The flutter response of Nanjing Fourth Bridge flat box girder under different wind attack angles was tested in detail through sectional model test. The evolution of unsteady and steady critical amplitude with wind speed was discussed. Based on the amplitude envelope of the flutter response and the Hilbert transform, the amplitude- dependent modal damping of the system is identified, and the mechanism of the flutter mode change in the wind angle of attack is initially explained. Secondly, the modal parameters of the system under different wind attack angles were extracted. Based on the bimodal coupled flutter analysis method, the nonlinear flutter derivatives of the section under different wind attack angles were identified, and the change law of the amplitude dependence of the key flutter derivatives on the wind attack angle and the potential influence on the flutter morphology and characteristics of the section were studied. Finally, the effect of wind attack angle on uncoupled and coupled aerodynamic damping is analyzed by deconstructing the modal damping one by one, and the dynamic mechanism of the differential flutter performance caused by fractional damping is illustrated.

Unsteady Flow Transition Effects on a Pitching Transonic Laminar Airfoil

This paper presents a computational study of unsteady transonic effects on a pitching supercritical laminar airfoil using high-order implicit large-eddy simulation. A CAST10-2 airfoil operating at a chord-based Reynolds number of , a transonic freestream Mach number of , and a small nominal angle of attack of deg was subjected to forced pitching oscillations about the quarter-chord with a small amplitude of deg and reduced frequencies of , 0.23, and 0.285. Complex interactions between flow separation, the motion of multiple shocks, and excursions of transitional flow were elucidated and compared against inviscid simulations. The boundary layer was found to be highly sensitive to pitch frequency, due in large part to the effects of frequency on shock motion. was found to be indirectly affected by the impact of shock motion on the boundary-layer state. Aerodynamic damping diminished with increasing oscillation frequency until becoming negative at , indicating potential for aeroelastic instability.

Effect of System Mode and Structural Damping Perturbation on the Mistuned Forced Response and Aerodynamic Damping of Embedded Compressor Rotors

Abstract This paper is a continuation of previous papers by the authors that focuses on predicting the mistuned embedded rotor blade forced response. The compressor under consideration is a part of a 3.5stage rig located at Purdue University. Previously, the current authors have discussed the impact of sideband traveling wave forcing functions on the mistuned response and pinned down the reason for a constant underprediction in the amplification factor. This prompted further research to determine the sensitivity of the response to a known change in the system mode. In the first section of the current paper, the authors perturb the system modes frequencies in a probabilistic manner and compute the influence of the system mode on the mistuning amplification factor. The second part of this study involves determining the impact of a perturbation in the structural damping on the mistuned response. The study is also extended to an aerodynamic dynamic analysis wherein the impact of a perturbation in system mode frequency and structural damping is determined both individually and as a combined influence. Finally, a brief investigation of system eigenvalues and eigenvectors is conducted to understand the impact of mistuning on aerodynamic damping suppression. This analysis is joined with a broad examination of the relationship between damping and the extent of mistuning. The key conclusions from this paper are (1) the mistuned forced response was highly sensitive to the system mode input, i.e., although the input was probabilistic, the output was deterministic, (2) since the aerodynamic damping dominates in the case study, a change in the structural damping parameter has minimal effect on the mistuned response, particularly the mistuning amplification factor, (3) the results of the flutter analysis show that a perturbation in the system mode frequency stabilizes the system much faster than a perturbation in the structural damping, and the latter has minimal influence on the eigenvalues of the solution, (4) under the application of mistuning, compression of the damping components of the complex eigenvalues is dominant over the expansion of the frequency components and is amplified when the structural coupling is not considered, and (5) in cases of both random and near alternate blade mistuning, the relationship between mistuning and damping is positive up to a point, after which further increasing mistuning begins to reduce system damping.

The Numerical and Experimental Evaluation of a Coupled Blade Dynamic Limit Response With Friction Contacts

Abstract Increasing demand for turbine power and efficiency requires larger and higher loaded turbine blades, which in turn requires the consideration of aeromechanical interactions. Whilst CFD tools can reliably predict stability using aerodynamic damping as an indicator, the component of mechanical damping also needs consideration. An understanding of the mechanical damping in the system becomes key to a robust blade design. Mechanical damping for such a part comes predominantly from friction occurring at the coupling contact faces. It is well established and published that such contact forces are nonlinear in relation to the relative movement at the contact interface. Moreover, contact area, the rigidity in the contact, friction coefficient, and normal contact force must also be considered and included as parameters that influence the result. Consequently, the level of system damping is not a constant and depends highly on the system response itself, as well as the other aforementioned parameters. In the case of self-excited vibrations such as flutter, the evaluation of the damped limit response is a part of the blade design process. A tool has been developed to numerically simulate contact friction forces with the intention of parametrically evaluating the limit response and relating this to the mechanical integrity of the part. This paper presents the modeling of a coupled blade system with friction contact forces, results coming from this evaluation, and a comparison with test data.