Flapwise Mode Research Articles

In-situ monitoring of an offshore wind turbine blade using acceleration and strain measurements

One of the most critical components of wind turbines is the blades. As blades are constantly exposed to weather and high loads, they can wear and become damaged. Performing in-situ continuous monitoring can help detect sudden damages and prevent further degradation, which is imperative to avoid economic losses and fatal accidents. However, monitoring a rotating rotor blade presents some challenges. One challenge is the consideration of lightning protection. Hence, a non-conductor measurement system must be used. Another challenge is system identification and modal tracking considering environmental and operational conditions (EOCs). Furthermore, vibration-based monitoring results from actual and operational rotor blades are scarce in the existing literature. This study centres on operational modal analysis (OMA) using covariance- driven stochastic subspace identification (SSI-COV) of an offshore wind turbine blade in operation employing eight months of data from fibre optic accelerometers (FOA) and fibre Bragg grating (FBG) strain gauges. The identification focuses on the first two bending modes in flapwise and edgewise directions and the first torsional mode. The study aims to determine which fibre optic sensor delivers better results. Furthermore, it addresses the effect of EOCs on the modal parameters, where system identification and modal tracking are discussed. It was found that tracked modes showed similar trends with respect to time, and a high connection was observed between wind speed, rotor speed, and pitch angle with frequency and damping. Additionally, acceleration and strain measurements deliver the same frequency and damping values. FBG better identified the first flapwise mode. On the other hand, FOA was superior in almost all other modes. This study points towards employing FOA for vibration-based monitoring of wind turbine blades using modal parameters.

Continuum approach of nonlinear dynamic analysis of a rotating wind turbine blade considering hub motion

This paper reports the nonlinear dynamics of a large wind turbine blade considering the hub motion. The investigation is based on a continuum mathematical model, which is derived using the extended Hamilton principle. The proposed model is validated via comparison with both published results and numerical simulations obtained from open source software. The steady state amplitude curves as well as the dominating frequencies of the modal forces are compared and analyzed with discussions on the effects of the hub motion amplitude, yaw angle and rotational frequency of the blade. Comparison of dominant frequencies of modal forces shows that the skewed inflow can strengthen the periodic excitation whose frequency equals to the rotating frequency of the blade. The steady state amplitude curves show that vibration of the edge-wise mode is more significant than that of the flap-wise mode when under the hub motion excitation. Moreover, internal resonance between the first three modes is also observed. The skewed inflow has a significant effect on the first mode in terms of vibration amplitude and the most unfavorable direction of hub motion. Finally, recommendation on how to avoid the resonance and internal resonance of the blades under skewed inflow are given.

Wind Turbine Aeroelastic Stability in OpenFAST

Wind turbines are growing in size and increasingly suffer from aeroelastic instabilities. Unfortunately, numerical models often show inconsistent results during verification studies. We address this gap by first introducing novel linearization capabilities within the open-source aero-hydro-servo-elastic framework OpenFAST. Next, a code-to-code benchmark study is presented that compares modal parameters between OpenFAST and HAWCStab2 for a land-based version of the International Energy Agency 15-MW reference wind turbine modeled with quasi-steady aerodynamics. The two solvers are in strong agreement except for discrepancies in the second rotor flapwise modes. The differences are attributed to the torsional flexibility of the tower, which is assumed torsionally stiff in the OpenFAST model. Work is ongoing to close this modeling gap. The aeroelastic stability of a low-specific-power land-based wind turbine is also investigated. The impact of design choices is discussed, high-lighting how narrow the margins are between a stable design and an unstable design.

Nonlinear dynamic analysis of parked large wind turbine blade considering parametric excitation

In this study, the nonlinear dynamics of parked large wind turbine blades are investigated, with a focus on the consideration of parametric excitations induced by the combined effect of wind and support motion. A continuum mathematical model for the blade is adopted. The time-varying damping terms that may induce parametric excitation are derived in this study. Nonlinear dynamic responses of NREL 5-MW wind turbine blade are numerically investigated using the multiple-scale method. Results show that the primary resonance of the first flapwise mode can induce the super-harmonic resonance of the first edgewise mode, with considering parametric excitation. Notably, when the ratio between the first flapwise to first edgewise modal eigenfrequencies is tuned to 1:2, the super-harmonic resonance leads to internal resonance between the two modes. In this case, the effects of incident wind speed, excitation direction and amplitude on the blade response are discussed. Quasi-periodic motions can also be induced because of the Neimark-Snack bifurcation in the case of large excitation amplitude.

A study on coupled edgewise and flapwise vibration modes of wind turbine blade

The coupled flapwise and edgewise vibrations of a horizontal axis wind turbine blade (HAWT) are discussed in this paper. Kinetic and potential energies of the blade are evaluated with consideration of the effects of gravity and aerodynamic forces. Hamilton’s principle is employed to develop the nonlinear coupled modal equations of the blade. The coupling between the first order edgewise and the first two order of flapwise modes is considered. This leads to three equations with nonlinear terms. Multiple-scales perturbation method is employed to solve these equations. Furthermore, the numerical values of structural specifications of National Renewable Energy Laboratory (NREL) 5-MW reference wind turbine blade are used, for example. It is shown that first edgewise and first flapwise vibrations are dominant, while second flapwise mode of vibration is less significant in the case of transient responses. Energy transfer between resonant modes is observed in both internal and combination resonances. The amplitude–frequency curves and phase diagrams during primary and combination resonances are obtained for the steady-state responses. Combination and primary resonances are further examined by considering various factors such as geometric nonlinearity and aerodynamic force.

Nonlinear Dynamics and Combination Resonance of a Flexible Turbine Blade with Contact and Friction of Shrouds

Flexible shrouded blades are commonly adopted in the last stages of steam turbines where complicated dynamical behavior can be induced by dry friction force generated on contacting interfaces between adjacent shrouds and the geometric nonlinearity due to the structural flexibility of the blades. In this paper, combination resonance caused by contact and friction forces generated on shroud interfaces is investigated, which is a concurrence of 1:3 internal resonance involving the first and second modes in the flapwise direction and the primary resonance of the first flapwise mode. The stiffness and damping at the contact interface are obtained by linearizing the contact and friction forces between shrouds through the harmonic balance method. The vibrating blade is modeled as a beam with a concentrated mass of which the responses under the combination resonance are solved through the multiple-scale method. Sensitivities of response with respect to the angle of shrouds, contact stiffness and rotation speed are illustrated, and the influences of these parameters on the periodicity and amplitudes of steady responses are demonstrated. The parametric regions where the combination resonance occurs are pointed out. Finally, parametric analyses are presented to show how the amplitude–frequency relation of the multiple-scale solutions under the combination resonance vary with detuning and design parameters. The present research provides a designing basis for improving the dynamic performance of flexible shrouded blades and suppressing vibrations of blades by adjusting structural parameters in practical engineering.

Experimental evidence of coupled-mode flutter in a two-meter-long non-rotating wind turbine blade

We have conducted a series of experiments on a 30:1 scale wind turbine blade and observed coupled-mode flutter. This observation validates the theoretical studies that predict larger wind turbine blades are susceptible to coupled-mode flutter. To conduct these experiments, we built a scaled-down model of the 61-meter NREL 5 MW blade. The blade was approximately 2 meters long and was built such that the ratios between its first torsional natural frequency and the flapwise natural frequencies were similar to those of the full-scale blade. This was important, because the theoretical predictions suggest that coupled-mode flutter occurs when one of the flapwise modes and the first torsional mode of the blade coalesce. In our experiments, as the wind speed was increased, turbulence induced vibrations were observed initially in the form of oscillations of the blade’s first flapwise mode, and then its second flapwise mode, with a region of multi-modal oscillations in between. It was observed that the first torsional natural frequency of the blade decreased with increasing wind speed and the second flapwise natural frequency increased slightly. Then at a critical wind speed, the second flapwise mode and the first torsional mode merged into a flutter mode, indicating coupled-mode flutter has occurred at this wind speed.

Dynamic inflow and unsteady aerodynamics models for modal and stability analyses in OpenFAST

This work presents two aerodynamic models that are used to perform modal and stability analyses of wind turbines. Including aerodynamic effects in stability analyses is important to capture aerodynamic inertia, stiffness, and damping. The two models consist of a dynamic inflow model based on Øye’s model and an unsteady aerodynamics model based on a simplified Beddoes-Leishman dynamic stall model. Both models are written in a continuous-time state-space form, which is the form needed to perform linearizations within OpenFAST. In this article, we present the new models, perform some simple verifications against HAWC2 results, and then perform stability analyses. We investigate the contribution of the aerodynamic effects on the turbine modes, particularly the flapwise modes, which are the most affected. Because of the development presented in this work, Campbell diagrams accounting for dynamic stall and dynamic wake effects were generated for the first time using OpenFAST.

Free vibration analysis of a rotating single edge cracked axially functionally graded beam for flap-wise and chord-wise modes

This study concerns with the free vibration analyses for centrifugally stiffened cracked beams modelled as functionally graded material in the axial direction. The variation of material properties along the cracked beam is expressed in terms of the power law distribution. Analyses are carried out by the Rayleigh–Ritz method that uses shape functions and energy expressions written for centrifugally stiffened Euler-Bernoulli beams. The influence of the hub radius, angular velocity, crack location to beam length ratio and crack depth to thickness ratio and cross-section size ratio and inhomogeneity on natural frequencies are examined for the beams with the clamped-free boundary condition. The results are verified by using the data available in the open literature and/or the outputs of finite element analyses performed for an axially functionally graded solid beam. The results show that the fundamental frequency parameters reduce with the increasing the ratio of crack depth to thickness. The highest natural frequency droop exists close to the root of the beam for flap-wise and chord-wise vibrations. Another important finding is that reduction of natural frequency parameters in chord-wise modes is larger than that in flap-wise modes when the crack location is varied. This new research should help to improve predictions of the impact of the crack on free vibrations for the rotating cracked axially functionally graded beams.

Offshore Wind Turbine Loads and Motions in Unstable Atmospheric Conditions

Even though it is widely known that unstable atmospheric stability conditions can lead to higher turbulence, the use of proper turbulent wind models considering unstable conditions are not often used in the simulation of loads and motions of offshore wind turbines. For this reason, the Højstrup model, which was specifically developed for unstable conditions, is used to simulate a spar-buoy offshore wind turbine (OWT) and investigate the importance of unstable conditions in the design of floating offshore wind turbines. It is found that fatigue damage of a spar-buoy OWT is strongly influenced by unstable conditions, where very unstable condition gives 65% higher fatigue damage than neutral conditions for the tower top torsion, followed by 37% higher for tower base side-side bending and 24% higher for blade root flap-wise mode.

Wind-induced instabilities and monitoring of wind turbine

This paper presents real-time monitoring data and analysis results of the non-stationary vibrations of an operational wind turbine. The advanced time-frequency spectrum analysis reveals varied non-stationary vibrations with timevarying frequencies, which are correlated with certain system natural modes characterized by finite element analysis. Under the effects of strong wind load, the wind turbine system exhibits certain resonances due to blade passing excitations. The system also exhibits certain instabilities due to the coupling of the tower bending modes and blade flapwise mode with blade passing excitations under the variation of wind speed. An analytical model is used to elaborate the non-stationary and instability phenomena observed in experimental results. The properties of the nonlinear instabilities are evaluated by using Lyapunov exponent estimation.

Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory

Free vibration behavior of bidirectional-functionally graded, double-tapered rotating micro-beam is investigated. An improved mathematical model based on Timoshenko beam theory and modified couple stress theory is developed that includes the effects of geometric non-linearity, spin-softening, Coriolis acceleration and high operating temperature. The problem is formulated in two steps. In the first step, the problem involving time-invariant inertia force due to rotation of the beam with constant angular speed is formulated using minimum potential energy principle and the governing non-linear equations are solved employing an iterative algorithm. In the next step, the free vibration problem is formulated employing Hamilton’s principle and using the tangent stiffness of the deformed configuration induced due to time-invariant inertial loading. The governing equations for free vibration are transformed to state-space to formulate an eigenvalue problem. The governing equations are solved by approximating the displacement fields following Ritz method. The model is successfully validated with the available results. Extensive sets of results are presented for the first two chord-wise and flap-wise modes of vibration in non-dimensional speed versus frequency plane. The effects of different parameters such as size-dependent thickness, axial and thickness gradation indices, taperness parameters, hub parameter, length-thickness ratio, operating temperature and FGM composition are reported.

Analysis of the coupled aeroelastic wake behavior of wind turbine

With the development of wind energy in recent years, the aeroelastic performances and the wake characteristics of a wind turbine and their effect on the downstream wind turbine have become research priorities. However, traditional aeroelastic analysis tools based on the Blade Element Momentum theory (BEM) cannot calculate the wake characteristics of a wind turbine. This study focuses on the coupled aeroelastic wake behavior of the wind turbine and developed a new tool called ALFBM, which combines the Actuator Line Method (ALM) and the nonlinear finite element Beam theory. The coupled aeroelastic wake behavior of a single NREL 5 MW wind turbine under the inlet velocity of 8 m/s and 11.4 m/s are studied. The aerodynamic and structural results such as power, thrust, natural frequencies, and tip deflections are compared with the results of former researches to verify this new analysis tool. Also, these results show that the stress stiffening effect and the nonlinear bending effect significantly decrease the frequency of flapwise mode by 12.7% and the tip deflection by 31%. It is found that the modal shape of every asymmetry flapwise mode varies periodically during the wind turbine rotation. The wake results demonstrate that the recovery of the velocity and vorticity in the far wake region (>5D) are underestimated when the deformation of the wind turbine blades are neglected.

Benefits of subcomponent over full-scale blade testing elaborated on a trailing-edge bond line design validation

Abstract. Wind turbine rotor blades are designed and certified according to the current IEC (2012) (International Electrotechnical Commission) and DNV GL AS (2015) (Det Norske Veritas Germanischer Lloyd Aksjeselskap) standards, which include the final full-scale experiment. The experiment is used to validate the assumptions made in the design models. In this work the drawbacks of traditional static and fatigue full-scale testing are elaborated, i.e., the replication of realistic loading and structural response. Subcomponent testing is proposed as a potential method to mitigate some of the drawbacks. Compared to the actual loading that a rotor blade is subjected to under field conditions, the full-scale test loading is subjected to the following simplifications and constraints: first, the full-scale fatigue test is conducted as a cyclic test, wherein the load time series obtained from aeroservoelastic simulations are simplified to a damage-equivalent load range. Second, the load directions are typically applied solely in two directions, often pure lead–lag and flapwise directions which are not necessarily the most critical load directions for a particular blade segment. Third, parts of the blade are overloaded by up to 20 % to achieve the target load along the whole span. Fourth, parts of the blade are not tested due to load introduction via load frames. Finally, another downside of a state-of-the-art, uni-axial, resonant, full-scale testing method is that dynamic testing at the eigenfrequencies of today's blades with respect to the first flapwise mode between 0.4 and 1.0 Hz results in long test times. Testing usually takes several months. In contrast, the subcomponent fatigue testing time can be substantially shorter than the full-scale blade test since (a) the load can be introduced with higher frequencies which are not constrained by the blade's eigenfrequency, and (b) the stress ratio between the minimum and the maximum stress exposure to which the structure is subjected can be increased to more realistic values. Furthermore, subcomponent testing could increase the structural reliability by focusing on the critical areas and replicating the design loads more accurately in the most critical directions. In this work, the comparison of the two testing methods is elaborated by way of example on a trailing-edge bond line design.

Modal properties and stability of bend–twist coupled wind turbine blades

Abstract. Coupling between bending and twist has a significant influence on the aeroelastic response of wind turbine blades. The coupling can arise from the blade geometry (e.g. sweep, prebending, or deflection under load) or from the anisotropic properties of the blade material. Bend–twist coupling can be utilized to reduce the fatigue loads of wind turbine blades. In this study the effects of material-based coupling on the aeroelastic modal properties and stability limits of the DTU 10 MW Reference Wind Turbine are investigated. The modal properties are determined by means of eigenvalue analysis around a steady-state equilibrium using the aero-servo-elastic tool HAWCStab2 which has been extended by a beam element that allows for fully coupled cross-sectional properties. Bend–twist coupling is introduced in the cross-sectional stiffness matrix by means of coupling coefficients that introduce twist for flapwise (flap–twist coupling) or edgewise (edge–twist coupling) bending. Edge–twist coupling can increase or decrease the damping of the edgewise mode relative to the reference blade, depending on the operational condition of the turbine. Edge–twist to feather coupling for edgewise deflection towards the leading edge reduces the inflow speed at which the blade becomes unstable. Flap–twist to feather coupling for flapwise deflections towards the suction side increase the frequency and reduce damping of the flapwise mode. Flap–twist to stall reduces frequency and increases damping. The reduction of blade root flapwise and tower bottom fore–aft moments due to variations in mean wind speed of a flap–twist to feather blade are confirmed by frequency response functions.

Measurement of rotating beam vibration using optical (DIC) techniques

In this paper, an experimental study is presented to validate a dynamic model of a rotating beam. The majority of existing vibration instrumentation is typically wired to an acquisition system through a connection using slip rings. An issue is the inherent signal to noise and the reliability of slip ring electrical connections. Herein, an experimental test rig is designed to overcome these issues. In addition, the rig is conceived to incorporate capabilities such as applying variable rotational speed using a variable frequency driver and provide vertical base excitation input to the centre of the rotation using a linear bearing. The tests are performed using random excitation on the fixed end of the rotating cantilever beam to excite the flapwise modes of the beam. The responses are then measured optically using a single high-speed camera, and the images are post-processed using a digital image correlation (DIC) method. This non-contacting optical method is used to extract the deflection of the beam as a function of time. The frequency response functions are then obtained from the measured responses. The modal frequencies are estimated and compared with numerical simulations to validate a Rayleigh-Ritz and FE numerical model for different rotational speeds.

Fundamental aeroelastic properties of a bend–twist coupled blade section

The effects of bend–twist coupling on the aeroelastic modal properties and stability limits of a two-dimensional blade section in attached flow are investigated. Bend–twist coupling is introduced in the stiffness matrix of the structural blade section model. The structural model is coupled with an unsteady aerodynamic model in a linearised state–space formulation. A numerical study is performed using structural and aerodynamic parameters representative for wind turbine blades. It is shown that damping of the edgewise mode is primarily influenced by the work of the lift which is close to antiphase, making the stability of the mode sensitive to changes in the stiffness matrix. The aerodynamic forces increase the stiffness of the flapwise mode for flap–twist coupling to feather for downwind deflections. The stiffness reduces and damping increases for flap–twist to stall. Edge–twist coupling is prone to an edgetwist flutter instability at much lower inflow speeds than the uncoupled blade section. Flap–twist coupling results in a moderate reduction of the flutter speed for twist to feather and divergence for twist to stall.

Numerical Investigation on the Selection of the System Outputs for Feedback Vibration Control of a Smart Blade Section

This study presents the possible and effective output signals for the feedback vibration control of the smart blade section undergoing different aerodynamic conditions. Equations of motions of the smart blade section are described by a typical wing section model, leading to three vibration modes (flapwise mode, edgewise mode, and torsional mode). The aerodynamics is described by an unsteady aerodynamic model and aerodynamic effects of the microtab installed on the trailing-edge of the blade section. The equations of the aeroservoelastic model are summarized into state-space equation for analysis of output choice in the feedback system. All vibration modes are proved to be fully controllable with the microtab actuation. The numerical results show that the most effective output signal is the combination of flapwise velocity and torsional velocity for the system undergoing the attached flow and the combination of all three-mode velocities for the system undergoing the stall flow. In addition, the output choice for different microtab configurations is also analyzed. The effectiveness of the proposed output signals in vibration control is confirmed by the simulation results.

Flapwise non-linear dynamics of wind turbine blades with both external and internal resonances

An investigation on the non-linear aeroelastic behavior of a wind turbine blade with both external and internal resonances is presented. The external resonance is a primary resonance that appears at the first flapwise mode; it can cause severe damage to blade. The internal resonance happens at the first two flapwise modes; it can enhance the energy transfer between two modes, and change blade dynamics in primary resonance. Three aspects including blade behavior in pure primary resonance (abbr. PPR; only considering external resonance), blade behavior in combination resonance (abbr. CR; including both external and internal resonances), and the influence of internal resonance (i.e. modal interaction) on external resonance are examined. A simple Bernoulli–Euler beam model, in which geometric non-linearity and unsteady aerodynamic force are considered, is used to describe the flapwise motion of blade. The perturbation method is applied to the infinite-degree-of-freedom discrete system, which is obtained from the original continuous system via Galerkin׳s method, to get dynamic responses. Amplitude–frequency curves of resonance modes in CR and PPR are derived, and the stability of the steady state motion of blade is judged. The strongest modal interaction between two resonance modes is taken into account, and then effects of modal interaction, excitation amplitude, damping and non-linearity on non-linear vibration properties of blade are analyzed. Also, influences of three designing parameters (inflow ratio, setting angle and coning angle) and two detuning on the non-linear behavior of blade are discussed for a concrete downwind turbine.

Parameter Sensitivities Affecting the Flutter Speed of a MW-Sized Blade

With the current trend toward larger and larger horizontal axis wind turbines, classical flutter is becoming a more critical issue. Recent studies have indicated that for a single blade turning in still air the flutter speed for a modern 35 m blade occurs at approximately twice its operating speed (2 per rev), whereas for smaller blades (5–9 m), both modern and early designs, the flutter speeds are in the range of 3.5–6 per rev. Scaling studies demonstrate that the per rev flutter speed should not change with scale. Thus, design requirements that change with increasing blade size are producing the concurrent reduction in per rev flutter speeds. In comparison with an early small blade design (5 m blade), flutter computations indicate that the non rotating modes which combine to create the flutter mode change as the blade becomes larger (i.e., for the larger blade the second flapwise mode, as opposed to the first flapwise mode for the smaller blade, combines with the first torsional mode to produce the flutter mode). For the more modern smaller blade design (9 m blade), results show that the non rotating modes that couple are similar to those of the larger blade. For the wings of fixed-wing aircraft, it is common knowledge that judicious selection of certain design parameters can increase the airspeed associated with the onset of flutter. Two parameters, the chordwise location of the center of mass and the ratio of the flapwise natural frequency to the torsional natural frequency, are especially significant. In this paper studies are performed to determine the sensitivity of the per rev flutter speed to these parameters for a 35 m wind turbine blade. Additional studies are performed to determine which structural characteristics of the blade are most significant in explaining the previously mentioned per rev flutter speed differences. As a point of interest, flutter results are also reported for two recently designed 9 m twist/coupled blades.