Aeroelastic Model Research Articles

Study of aerodynamic damping of a crosswind-excited circular cylinder and its application to full-scale flexible structures

The accurate assessment of aerodynamic damping is essential when estimating the impact of aero-elastic effects on crosswind-excited line-like structures. This study aims to determine the crosswind aerodynamic damping of a circular cylinder by curve-fitting to the response probability density function. The generalized Van der Pol oscillator model is employed to depict the nonlinearity associated with amplitude-dependent aerodynamic damping. The initial section of this study presents the theoretical foundation of the identified approach used in this research. Subsequently, the efficacy of the identification methodology is validated by means of a stochastic simulation of the crosswind response of a circular cylinder. Moreover, identification of nonlinear aerodynamic damping is further accomplished by the utilization of an aero-elastic model wind tunnel test. The identified nonlinear aerodynamic damping is then utilized to determine the response statistical quantities for a total of 16 chimneys. The determined aerodynamic damping provides a satisfactory assessment of the peak response, which is crucial for design considerations.

Wind tunnel bench test of a pitch-and-plunge aeroelastic model undergoing nonlinear post-flutter oscillations

The nonlinear post-flutter aeroelastic behavior of a classical pitch-and-plunge airfoil model in low-speed wind tunnel bench tests is reported in this study for a range of airflow speeds where stable oscillations are observed. An experimental airfoil prototype is designed, characterized and evaluated. Time domain data of the airfoil motion as well as other pertinent frequency and bifurcation characteristics are presented for different values of airflow speed, starting at the critical linear flutter speed of the airfoil model and increasing up to the sudden manifestation of violent unstable oscillations (when the test is interrupted for the safety of the structural apparatus). Stable post-flutter nonlinear oscillations, mainly attributed to the dynamic stall phenomenon and in a lesser degree to hardening structural effects, are observed for a range of airflow speeds starting at the neutral stability boundary of the aeroelastic system. The amplitudes of oscillation increase with increasing airflow speed and settle onto a limit-cycle. The coupled frequency of oscillation is dominated by the plunge degree-of-freedom and also increases with increasing airflow speed. The observed critical airfoil cut-in speed of limit-cycle onset is about 8.1 m/s (reduced speed of 5.1), and the observed cut-out speed of unstable response is about 9.5 m/s (reduced speed of 6.0). This work contributes with the literature of Aeroelasticity by presenting the realization, evaluation, and wind tunnel test data of a pitch-and-plunge airfoil model undergoing nonlinear post-flutter oscillations that may be useful to support other studies for verification purposes of eventual numerical simulations of similar aeroelastic systems.

Wind field effects on crosswind displacement responses of square-section tall-slender structures with aspect ratio over 12

The crosswind responses of tall slender structures play an important role for the wind-resistant design, and they can be significantly influenced by the wind fields. There was a prevailing belief that the aeroelastic response of tall-slender structures was mostly observed under low-turbulent suburban flow. Nevertheless, aeroelastic response of tall-slender structures with substantially higher height and aspect ratio in high-turbulent urban flow may occur, remains unverified in the absence of empirical evidence. Moreover, the aeroelastic instability of vortex resonance and galloping of square-section tall-slender structures should be carefully addressed, especially the combined vortex resonance and galloping may occur. From these particular standpoints, this study aims to discuss the impacts of wind fields on the wind-induced vibrations in crosswind direction of square-sectioned tall-slender structures with aspect ratio 12, 16 and 20 through pivot model tests. The findings demonstrate the crosswind response of the model with λ = 12 is suppressed when it is in urban flow since the turbulence intensity profile is significantly large. Due to the sufficient height and slenderness, aeroelastic effects can occur for the aeroelastic models with λ = 16 and 20 in both suburban and urban flows. The combined vortex resonance and galloping effects are observed for the aeroelastic models with λ = 16 and 20 when they are low damped, even in urban flow. Thus, the attention should be paid to the crosswind response under urban flow for wind-resistant design of tall-slender structures with large aspect ratios and heights in practice.

Aeroelastic code comparison using the IEA 22MW reference turbine

Reference wind turbine designs and the associated aeroelastic models are widely used in both research and industry. Reference models representing future concepts are of particular interest. Current state of the art aeroelastic tools are relied upon to design the next generation of large wind turbines. However, modelling assumptions may be invalidated by upcoming very large turbines, and different aeroelastic tools may give inconsistent results. A 22MW turbine model has been defined as part of International Energy Agency (IEA) Wind Task 55 on Reference Wind Turbines and Farms to represent future turbines to be deployed in the 2030s. In this study, an aeroelastic model of this turbine has been created in four tools; Bladed, HAWC2, OpenFAST, and QBlade. Code comparisons are presented for steady state operation, linear stability analysis, and time domain power production simulations in steady and turbulent wind. Generally, the codes show a good agreement, but with some differences present in the linear stability analysis, periodic azimuthal variation, and time domain simulations. The models are a good basis for further study with the IEA 22MW turbine, and further code comparison exercises.

Corrosion fatigue analysis of NREL’s 15-MW offshore wind turbine with time-varying stress concentration factors

Over the last twenty years, significant development in wind turbine technologies has led to a dramatic increase in the scale of wind turbines with many now beginning to be installed in offshore locations. Consequently, modern multi-megawatt offshore wind turbines are exposed to increased cyclic loading in addition to an increased risk of corrosion attack. The combination of these two factors may result in wind turbine support structures becoming increasingly vulnerable to fatigue corrosion. The objective of this work is to investigate the impact of material thinning in fatigue-prone areas with respect to fatigue loading and ultimately to examine the potential repercussions on the lifespan of wind turbine support structures. To achieve this, a composite model is constructed coupling results from a multi-body structural dynamic model with time-varying Stress Concentration Factors (SCF) obtained from a finite element model (FEM) of NREL’s 15-MW monopile-based offshore wind turbine. The nonlinear aeroelastic multi-body dynamic model of the wind turbine is used to generate stress time histories for a set of environmental conditions based on the operational conditions of the wind turbine. The finite element model of the wind turbine is then used to identify fatigue-vulnerable regions in the wind turbine support structure and calculate SCFs for these specific areas. The integration of SCFs into the fatigue calculations reduced the lifespan of the turbine tower by a factor of 4, demonstrating the importance of precisely modelling such local stress concentrations for effective fatigue analysis. A novelty of this work arises in the ability of the finite element model to update the SCFs of the fatigue-prone areas over time as corrosion-induced wastage alters the substructure’s geometry, thereby inducing a global redistribution of stresses. A fatigue analysis is carried out availing of the SCFs which vary annually in addition to the stress-time histories produced by the multi-body dynamic model. The results illustrate that the phenomenon of corrosion thinning induced an 8.9% reduction in the fatigue life of the wind turbine tower, thus emphasising the significant importance of proactive maintenance strategies to mitigate the impact of corrosion.

An aeroelastic coupling of an actuator sector model with OpenFAST in atmospheric flows

This study presents an implementation of an aeroelastically coupled actuator sector model with OpenFAST in a neutral atmospheric boundary layer flow for a 15 MW reference turbine. Three structural cases with different levels of fidelity are considered. In addition, the results from an aeroelastic actuator line model are used for comparison. The results of the structural cases show the significance of including the torsional deflections and structural nonlinearities to accurately calculate the blade loads as it reduces the power and flapwise damage equivalent load values considerably. In terms of the wake flow, there are differences in the near wake between the considered structural cases. Despite this, further downstream the differences become non-significant. In addition, the results from the actuator sector model are in agreement with those obtained from the actuator line model while using the actuator sector model offers a reduction of around 55% to 80% in the computational time depending on the used structural solver.

Reduced-order modelling of floating offshore wind turbine: Aero-hydro-elastic stability analysis

A reduced-order aero-hydro-elastic analysis tool for performing the stability analysis on floating offshore wind turbines is presented. In this work, a high-order non-linear aero-elastic model initially developed for onshore wind turbines is extended by utilizing a super-element body, which models the floating platform, the mooring system and the hydrodynamic contributions. The turbine structure is modelled by a Finite beam Element Method, and the aerodynamic loads are modelled by the Blade Element Momentum method coupled with a Beddoes-Leishman type dynamic stall model in a state-space formulation. The linearization is performed around steady state equilibrium at any given mean wind speeds, rotor speeds and collective blade pitch angles utilizing Coleman transformation to remove the periodic terms. The order reduction is based on two projections to reduce the number of structural states and aerodynamic states separately using the structural modal project matrix and the aerodynamic shape functions. Concurrently, we investigate the effect of unsteady aerodynamic states on the stability analysis of a floating wind turbine. The results show the low-order aero-hydro-elastic model expands the scope of numerical tools available for conducting structural modal analysis and aero-hydro-elastic stability analysis on floating wind turbines.

Development of a FW-H tool coupled with CFD for infrasound noise emissions from wind turbines

Noise remains an obstacle to the advancement of onshore wind energy. Despite the ongoing debate on the effects of infrasound on human health, especially from wind turbines, there is consensus that the blade passing frequency (BPF) in the infrasound range modulates the audible higher-frequency sound and creates a rhythmic “swishing” sound at farther distances. This paper presents a simulation framework for assessing infrasound noise (<20 Hz) from wind turbines, which was designed to capture the relevant physics without incurring in overwhelming computational costs. The flow is modelled using large eddy simulation (LES) and is coupled through an actuator line method (ALM) to the aeroelastic model of a wind turbine. The use of an ALM significantly reduces the computation effort compared to blade-resolved CFD approaches. Moreover, the Ffowcs Williams-Hawkings (FW-H) acoustic analogy is applied on a permeable integration surface that surrounds the entire wind turbine, thereby capturing the coupled effects of rotor, tower, and the near-wake turbulence shed by the turbine. The present approach is shown to be capable of resolving rotor-tower interactions as tonal peaks at BPF and its harmonics, enabling the evaluation of design and control measures to mitigate infrasound noise emissions from wind turbines.

Effects of a Near Wake model on the performance of a Multi-Megawatt wind turbine with an active flap

The impact of including the near wake model in the aeroelastic models of an SWT-DD-120 wind turbine equipped with an active trailing edge flap system (ATEF) is studied. The ATEF installed on this turbine was tested in full scale in a series of campaigns between 2018 and 2022. Since standard BEM methods cannot accurately capture the induced velocities near the transition areas of the start and end of flap add-ons due to the strong interaction of the local trailed vorticity with the neighboring blade sections, this study aims to investigate if and how the near wake model is relevant in the aerodynamic and aeroelastic characterization of rotor blades with active flaps. It is shown that the Near Wake model, when combined with an active trailing edge flap system, has a marginal impact on the blades’ thrust-related loads, independently from the presence, actuation state, and actuation frequency of the flap. The impact on the torque-related loads is also marginal at the blade root, while it becomes more relevant in the blade area where the flaps are deployed.

Hierarchical sensitivity study on the aeroelastic stability of the IEA 15 MW reference wind turbine

Increased rotor size and blade flexibility are leading to new stability characteristics for current and future wind turbines. Numerical aeroelastic models are an essential tool to understand these new mechanisms and to design next-generation wind turbines suitably. A comprehensive understanding of how model input parameters influence the stability analysis will enhance the confidence in these simulations. This article presents a study on the sensitivity of uncertain parameters on aeroelastic stability predictions of the IEA 15 MW turbine model in HAWCStab2. It uses a hierarchical approach to handle the large number of investigated model parameters. Relevant uncertainties are identified through one-at-a-time and elementary effects analyses first. The remaining parameters are fed into a variance-based uncertainty quantification (UQ), that employs polynomial chaos expansion representations as surrogates for a full nonlinear description of the sensitivities. A robust post-processing of the stability analysis results is the main challenge of the presented methodology, but it is shown how the UQ process can still be used to explore the parameter space effectively. The presented study shows that the structural blade properties have the highest sensitivity and that a set of relatively small parameter variations can lead to unstable behavior of the reference model.

Multi-fidelity, steady-state aeroelastic modelling of a 22-megawatt wind turbine

In this work we present multi-fidelity steady-state aeroelastic framework that leverages the state-of-the-art simulation tool HAWC2 for the structural model, and a variety of aerodynamic models, comprising of the low fidelity blade element momentum (BEM) method, the medium fidelity blade element vortex cylinder (BEVC) method and the coupled near wake and vortex cylinder method, and finally the high-fidelity CFD solver EllipSys3D. The aeroelastic framework is part of AESOpt, an aerostructural framework for design of wind turbine blades. The different aerodynamic models are applied to compute the aeroelastic steady state of the newly designed IEA 22 MW Reference Wind Turbine. The results show a very good agreement between the medium- and high-fidelity aerodynamic models with a maximum of 2.7% difference between the high-fidelity aeroelastic response and that of the lower fidelities.

Validation of aeroelastic dynamic model of active trailing edge flap system tested on a 4.3 MW wind turbine

Validation of aeroelastic dynamic model of active trailing edge flap system tested on a 4.3 MW wind turbine

Flutter Characteristics of a Modified Z-Shaped Folding Wing Using a New Non-Intrusive Model

Unmanned aerial vehicles (UAVs) with folding wings can serve in multiple mission profiles, usually accompanied by sudden changes in flight speed. These bring great challenges to the aeroelastic design of UAVs, especially in the calculation of flutter characteristics. This paper developed a new non-intrusive aeroelastic model to quickly calculate the flutter characteristics of Z-shaped folding wings at different folding angles. First, the original Z-shaped folding wing was designed to be enhanced. Beams and ribs were arranged inside each wing segment to enhance the structural strength performance. Control surfaces were arranged in the middle-wing and outer-wing to enhance the aerodynamic control performance. Second, a parametric aeroelastic model at any folding angle was reconstructed based on the input file of Nastran software for the flutter calculation of the folding wing in the unfolded state. Finally, the effects of parameters such as folding angle, hinge stiffness between different wing segments, and hinge stiffness of the control surfaces on the flutter characteristics of the folding wing were investigated. The results show that the enhancement scheme could significantly increase the flutter speed and flutter frequency of the folding wing. The hinge stiffness between each wing segment had a significant impact on the flutter characteristics of the folding wing, but flutter at the control surface basically did not occur.

Experimental study on effect factors of wind-induced response of flexible photovoltaic support structure

In recent years, the proportion of flexible photovoltaic (PV) support structures (FPSS) in PV power generation has gradually increased, and the wind-induced response of FPSS has gradually been noticed. In this study, the wind-induced responses of a FPSS with a single row and a single span were investigated by aeroelastic model wind tunnel tests. The effects of structural parameters of FPSS were systematically analyzed on 17 test cases (including inclinations, module spacings, initial tensions, spans and module sizes), and the variation of flutter critical wind velocities with structural parameters was obtained. The experimental results show that the most unfavorable wind direction is 180°. The static wind-induced response is mainly affected by the module inclination angle, module spacing and the structure span. The vortex-induced vibration (VIV) of the test models occurs in some specific test cases at low wind velocity, and it can be easily suppressed by changing the structural parameters. The flutter occurs at both directions of 0° and 180° when the wind velocity increases to a critical value. With the increase of module inclination angle, the flutter critical wind velocity of FPSS decreases first and then increases, and the most unfavorable module inclination is 25°. It is beneficial for suppressing the structure flutter by increasing the cable initial tension and the module spacing, and decreasing the span of the FPSS. Changing the module size will affect the aerodynamic characteristics and structural frequency of the structure, thereby affecting the wind-induced vibration of the structure.

Buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model

The aim of this study is to explore the buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model. The study includes the influence of turbulence integral length scale and wind yaw angle on the magnitude of buffeting force, spatial distribution of buffeting force, and buffeting displacement response. Under larger turbulence integral length scale, the buffeting force of the box beam and it’s spanwise correlation are larger, which verifies the three-dimensional effect of the buffeting force. It is worth mentioning that, unlike traditional section models, there are differences in the pressure values of the pressure strips in the aeroelastic model at the flow separation point, which may be influenced by the cables. The experimental results of different wind yaw angles show that there is little difference in the buffeting force of the box beam section under the condition of 0°∼15° wind yaw angle, indicating that the maximum buffeting response will occur in the range of 0°∼15° wind yaw angle, which is consistent with the displacement results measured by the aeroelastic model. In addition, by fixing the model with a steel wire, the static and vibration states of the model were achieved. However, due to the high stiffness of the model, it can only generate small buffeting displacement, and the self-excited force component can be almost ignored. There is no significant difference in the results between the static and vibration states.

Modal effects of span-layout types on coupled flutter of long-span suspension bridges

This study provides a theoretical explanation for a perplexing experimental phenomenon observed frequently in suspension bridge flutter testing, where the flutter critical wind speed (Ucr) predicted by two-dimensional (2D) section model testing is higher than that predicted by three-dimensional (3D) full aeroelastic model testing. Six long-span suspension bridges with either a single simply supported span or multiple continuously supported spans were taken as research examples, then the comparative studies on the flutter critical wind speeds, flutter frequencies, modal energy ratios and aerodynamic damping corresponding to 2D and 3D coupled flutter states were carried out to illustrate the flutter modal effects. The research findings indicate that the Ucr of 2D testing being higher than that of 3D testing is an inherent characteristic for single-span simply-supported suspension bridges, which can be attributed to the prominent aerodynamic negative damping associated with 2nd-order vertical bending mode. However, due to the aerodynamic positive damping associated with 3rd-order vertical bending mode, the Ucr of 2D testing is consistently lower than that of 3D testing in the cases of multi-spans continuously-supported suspension bridges. Additionally, to eliminate unsafe 2D evaluations, a reasonable modal matching principle is recommended for section model testing of single-span simply-supported suspension bridges.

Estimating nonlinear wind-induced response of roof cable nets by aeroelastic experiments and ML modeling

The paper examines the structural engineering challenges related to the assessment of the wind-induced vertical displacements of lightweight, hyperbolic-paraboloid cable-supported membrane roofs. Analysis and comparisons are conducted using three distinct methods for calculating the roof vertical, out-of-plane displacements. Finite element method (FEM) analysis is employed using: (i) estimated static nodal forces obtained from wind pressure coefficients determined by aerodynamic wind tunnel tests on a rigid building model, and (ii) loads found from wind pressure coefficients, estimated through machine learning (ML) methods, and (iii) measured roof response found from aeroelastic wind tunnel tests on a flexible model. The study examines three different roof geometries (square, rectangular and circular) and two distinct membrane curvatures for each geometry. Furthermore, wind directionality (three mean-wind incidence angles) and Reynolds number effects (seven mean wind velocities) are studied. Comparisons show that the non-linear FEM analysis, based on estimated static wind loads, underestimates the roof displacements at the roof center, compared to the direct measurements on the aeroelastic model. The main contribution of the study consists of a novel application of ML models, and Artificial Neural Networks (ANNs) in particular, which are employed to correct roof displacement estimations, found by simplified aerodynamic test pressure measurements on rigid roof models. The goal is to better describe the complex fluid-structure interaction of the roof membranes, which can only be achieved by direct aeroelastic tests that are difficult to design and execute. Finally, the study demonstrates that ANNs can be used not only for the preliminary design of the full-scale structure but also for construction of wind tunnel scale models.

Real-time time-varying economic nonlinear model predictive control for wind turbines

Economic nonlinear model predictive control is a great choice to tackle the control issues appearing in the current wind energy industry. In this paper, instead of generator power, aerodynamic power is employed in the economic cost function to establish the required conditions of stability and convergence of the economic performance, such as turnpike and problem convexity. However, since aerodynamic power depends on time-varying wind speed, conventional time-invariant economic nonlinear model predictive controllers cannot guarantee the stability and convergence of economic performance. This paper proposes a new time-varying economic nonlinear model predictive controller for wind turbine control that considers an economic trajectory, instead of a steady-state, in its optimization problem. The proposed time-varying economic cost function directly considers aerodynamic power, the activity of pitch angle and generator torque, and fatigue loads on the shaft and tower. Therefore, this controller can maximize power extraction and reduce fatigue load on the tower, drivetrain, and actuators. Furthermore, a fast-parallel Newton-type method is used to implement the proposed controller in actual wind turbines. An accurate aeroelastic model is used to validate the performance of the proposed control scheme. The proposed controller is also compared with two tracking nonlinear model predictive controllers, the baseline controller, and a newly developed method, under fatigue and extreme load scenarios in the presence and absence of uncertainty. The simulation results show the superior economic performance of the proposed approach. Moreover, the real-time results verify the computational speed that the proposed controller requires to deploy actual wind turbines.

Development of a low-cost flutter test bed with an EPS foam model for preliminary wing design

This paper discusses a novel, low-cost approach for the design and testing of a flutter test article made out of expanded polystyrene (EPS) foam. The low mass of this test article makes it especially suitable for serving as a test bed for similar low structure-to-fluid mass ratio wing configurations, though it could just as easily be used as the first step in the flutter testing of any structure with complex shape and mechanical properties. The material properties of EPS foam were tested using two different approaches: a 3-point bending test based on ASTM Standards for cellular materials and a new finite element model updating approach that used experimental data collected from simple ground vibration tests (GVT). It was found that the second approach provided material properties that were the most representative of the behavior of the specimen under flutter loads. That information was then used in a computational aeroelastic flutter model of the EPS foam wing. Wind tunnel flutter tests were performed for the EPS foam model. The computational frequency domain decomposition (CFDD) method was used to identify modal parameters and the damping trend extrapolating method was used to predict the critical flutter speed from pre-flutter experimental data. The flutter results from the aeroelastic model were in good agreement with the test data.

The Determination of Effective Modes of Wind-Bridge Coupling System Based on Stabilization Clustering Method

Modal identification is the core content of the full-bridge aeroelastic model wind tunnel test. Modal consistency is the most direct and effective basis to ensure that the model and the real bridge meet the similarity criteria. Accurate, simple and fast identification of modal parameters has very important practical significance for the evaluation and correction of aeroelastic models. In this paper, the eigensystem realization algorithm (ERA) and stochastic subspace identification (SSI) is improved, and the automatic identification theory of effective modes of bridge aeroelastic model based on stable clustering method is proposed. The stable diagram eliminates the unstable modes by comparing the results of different system orders, and the pedigree clustering further polarizes the stable modes to obtain multi-order and high-precision system modes. Numerical simulation examples and wind tunnel engineering examples show that the method has high accuracy and good adaptability, and can solve the problem of unstable damping identification results to a certain extent. In the wind tunnel test, the stable clustering method is one of the effective methods to identify the modal of the bridge aeroelastic model excited by the wind environment.