Flexible Blades Research Articles

ANCF-based modelling of rigid-flexible coupling of helicopter flexible rotor blades

Abstract A high-precision rotor structure dynamic model applicable to a variety of helicopter blade hub structures is established considering rotor blade flexible deformation. The absolute nodal coordinate method is applied to the traditional rotor blade rigid-flexible coupling dynamics model, making the new model applicable to both fully articulated rotor blades and other advanced blade hub structures. No small-volume assumptions were made in the modelling process. Both Green’s strain expression under finite deformation and the geometrical relation of elastic deformation motion based on the absolute nodal coordinate method are used to derive the blade strain energy, kinetic energy, and the external load virtual work. The rotation angle at the articulation constraint at the root of the blade coupled with the elastic deformation degrees of freedom of the blade in three independent rigid body degrees of freedom, respectively. The rotor blade rigid-flexible coupling dynamics equations were established according to the Hamilton action principle. The time-domain simulation is carried out under a free single pendulum and fixed rotational speed/fixed torque for the established flexible blade model, which verifies the validity and high accuracy of the rigid-flexible coupling articulation model of the flexible rotor blade and the blade hub.

Разработка рекомендаций по применению трамвайных стрелочных переводов при различных условиях эксплуатации

Purpose: To consider the design features of single-blade and double-blade arrows, as well as double-blade arrows with flexible blades, the operating conditions of tram switches when placing tram nodes on the line and on the territory of tram parks. Methods: The analysis of the main operational and economic indicators of switches is carried out, taking into account the advantages and disadvantages of various types of arrow designs of the tram industry in St. Petersburg, including those requiring speed limits of tram cars when moving along the arrows. Results: Recommendations have been developed for the use of switches of various designs, depending on their operating conditions, load stress, speed of movement of rolling stock for safe passage along them, placement on the line on a combined, independent or separate track and in tram fleets, taking into account the complexity of replacing worn parts, as well as the need to ensure the required track development in the presence of cramped conditions. The proposed recommendations will allow the use of switches in accordance with modern requirements for tram crossings, which ensure comfortable movement of passengers. Practical importance: Considering the fact that economic indicators, along with the technical characteristics of switch designs and operational capabilities of track sections, are one of the main criteria for evaluating decision-making, it is proposed to use methodology for accounting for economic indicators based on determining the cost of the life cycle to justify the effectiveness of using a particular type of switch in the design and operation of tramways paths in specific conditions.

دراسة علمية حول العزم الزاوي وعلاقته بالخصائص الميكانيكية لشفرات التوربينات

The general trend now in all countries of the world and all sectors is to achieve sustainability. One of how this sustainability can be achieved is to develop and improve the properties of raw materials, and in the field of turbine-powered power plants, sustainability must be achieved in light of the global crisis facing the energy sector, in this study, which aims to study the effect of angular torque on Mechanical properties of turbine blades, so that we can develop and improve the properties of those blades Angular torque is very important in turbine blades because it drives the turbine to rotate. Angular torque results from a force acting on a rotating body. In the case of turbine blades, the force of the gas flow produces angular torque. Turbine blades typically consist of thin, curved metal sheets. When gas passes through the blades, it exerts a force on the blades. This force forces the blades to rotate around its axis the greater the angular torque it produces. The greater the angular torque, the faster the turbine rotates. This study provides a mathematical model to calculate the angular torque resulting from turbine blades. The model was used to study the effect of various factors on the angular torque, including the gas flow speed, the shape of the blades, and their mechanical properties. Then, a simulation was run using the ANSYS program to determine the relationship between the angular torque and the mechanical properties of the turbine blades. The results indicated a large deviation of the flexible blades and unstable rotation of the rotating blade systems, due to the coupling effect of rotation and vibration, where the mechanical properties of mass/inertia distributions, damping, and stiffness are related to changes in rotational speed and local deformation in rotor blade systems, thus, the harmonic balance must occur and the mechanical properties of the blades be improved. Keywords: Angular Torque, Mechanical Properties, Raw Materials, Turbine blades, mathematical model, flow speed, ANSYS, rotation and vibration, harmonic balance.

Bend-twist adaptive control for flexible wind turbine blades: Principles and experimental validation

This study proposes a new methodology for optimizing the power curve of a wind turbine at low wind speeds. The principles of bend-twist coupling and the mechanism of energy exchange between the structure and inflow are analyzed. For the blade’s geometric nonlinearity, the virtual displacements and strain fields are described using the Green-Lagrange strain theorem, retaining third-order terms in the energy expressions. The equations of motion are derived using Hamilton’s principle. The bend-twist coupling effects and large deformations of the blade are analyzed using the Updated Lagrange method. Notably, the angle of attack for a single blade section is influenced by bend-twist deformation, causing variations in the rotor’s maximum power coefficient from its optimal value. Additionally, the projection length of the blade, influenced by centrifugal forces, also affects the bend-twist deformation. Based on these findings, an aero-elastic coupling control strategy, termed “Bend-twist Adaptive Control”, is proposed and validated through experiments. The results demonstrate that the proposed control strategy could increase annual power production by 2.3 %. These conclusions offer a promising outlook for future wind turbine blade design and power optimization.

Experimental and computational investigations of flexible membrane nano rotors in hover

With reduced size, the flight Reynolds number of the nano rotor decreases, leading to a sharp drop in the aerodynamic efficiency of the nano rotor. Therefore, improving the aerodynamic performance of the nano rotor at low Reynolds numbers through flow control methods becomes imperative. In this study, from the perspective of bionics, flexible materials are employed in nano rotor design. Seven different layouts of flexible membrane rotor blades are designed and fabricated. The influence of leading and trailing edge flexibility, as well as membrane occupancy ratio on rotor blade propulsion characteristics, is explored through propulsion performance tests in hover.Results show that among several layouts proposed in this study, the layout with both reinforced leading and trailing edges of the flexible membrane nano rotor blade exhibits excellent propulsive performance. However, the propulsion performance of the flexible membrane rotors doesn't vary linearly with the ratio of membrane area to the whole rotor area. The appropriate ratio or flexibility can increase the propulsive performance of the rotor, especially at medium and high collective angles. At 7000 RPM and a 20° collective angle, the Figure of Merit of the flexible membrane nano rotor increases up to 4.2% when comparing with the nano rotor without membrane. This improvement becomes more significant with higher collective angles. The structural natural vibration characteristics of each flexible membrane with different layouts are analyzed through modal tests, ensuring the accuracy of the finite element model for flexible membrane rotors. Numerical analysis of the fluid-structure coupling of a flexible membrane rotor with different layouts indicates that rotor structural vibrations is highly consistent with fluctuation of aerodynamic parameters. The deformation of the flexible membrane under aerodynamic forces enhances local blade camber, but reduces angles of attack. This, subsequently, minimizes the size of laminar separation bubbles and the intensity of the blade tip vortices at high collective angles. Consequently, rotor power coefficients decrease, and overall aerodynamic performance improves.

Development of nonlinear flat shell element with nonlinear thickness variation for highly flexible wind turbine blade

Large deformation from continuously varied thicknesses on existing and wind turbine blade shell structures is investigated. Various structure models having complicated outer shapes and thickness variations are considered and validated in this paper. A co-rotational method is developed to analyze geometric nonlinearity with a triangular shell structure. The updated stiffness matrix from interpolated thickness function and integral formulation is suggested to consider complicated geometry and thickness variation. Moreover, the co-rotational flat shell element based on the updated stiffness matrix is developed to analyze various nonlinear shell structures, which are the main feature of this research. The numerical analysis for structure deformations show well matched trends in static load analysis. Furthermore, the deformation of a simplified flexible wind turbine blade having tapered geometry and various thickness cases is adopted as a practical case. Moreover, modal analysis for composite beam structure is performed to verify the dynamic problems. The structural behaviors of the nonlinear thickness shell are validated against the solid and the shell models in commercial software, ABAQUS.

Investigation of blade flexibility effects on the loads and wake of a 15 MW wind turbine using a flexible actuator line method

Investigation of blade flexibility effects on the loads and wake of a 15 MW wind turbine using a flexible actuator line method

Acoustic emission monitoring of composite marine propellers in submerged conditions using embedded piezoelectric sensors

Flexible composite marine propellers can aid the marine industry in reducing carbon emissions and underwater radiated noise pollution. The structural integrity of the blades can be assessed using structural health monitoring. One of these methods is the measurement and analysis of damage-induced acoustic emission signals. This paper experimentally investigates the feasibility of using embedded piezoelectric sensors for the measurement of acoustic emissions throughout a submerged flexible composite marine propeller blade. A full-scale glass-fibre reinforced polymer blade has been manufactured with 24 embedded sensors. While suspended in artificial seawater, acoustic emissions were simulated on the blade. The measurements show that the embedded piezoelectric sensors can measure acoustic emissions while the blade is submerged. Further, the distance from source to sensor over which the acoustic emission is measurable was investigated. For a noise level of 40 dB and a source amplitude of 70 dB between 100 and 250 kHz, an average maximum measurable distance of 124 mm was obtained. For higher frequencies, the distance drops and for lower noise levels the distance increases.

Research on the Blades and Performance of Semi-Submersible Wind Turbines with Different Capacities

With the gradual increase in the maturity of wind energy technology, floating offshore wind turbines have progressively moved from small-capacity demonstrations to large-capacity commercial applications. As a direct component of wind turbines used to capture wind energy, an increase in the blade length directly leads to an increase in blade flexibility and a decrease in aerodynamic performance. Furthermore, if the floater has an additional six degrees of freedom, the movement and load of the blade under the combined action of wind and waves are more complicated. In this work, two types of semi-submersible wind turbines with different capacities are used as the research objects, and the load and motion characteristics of the blades of these floating offshore wind turbines are studied. Through the analysis of the simulation data, the following conclusions are drawn: with the increase in the capacity of the wind turbine, the flexible deformation of the blade increases, the movement range of the blade tip becomes larger, the blade root load increases, and the power fluctuation is more obvious. Compared with the bottom-fixed wind turbine, the flexible blade deformation of the floating offshore wind turbine is smaller; however, the blade root load is more dispersed, and the power output is more unstable and lower.

An Experimental Performance Assessment of a Passively Controlled Wind Turbine Blade Concept: Part A—Isotropic Materials

This paper is the first part of a two-part series, which presents preliminary findings on a novel flexible curved wind turbine blade designed for passive control, comparing its aerodynamic performance and behavior against a conventional straight blade. Characterized by its ability to twist around its longitudinal axis under bending loads, the flexible curved blade is engineered to self-regulate in response to varying wind speeds, optimizing power output and enhancing operational safety. This design utilizes inherent elasticity and specific geometric configurations to develop torsional loads, resulting in continuous adjustment of the blade’s pitch angle via twist–bend deformation. The study focuses on a comparative analysis conducted in a wind tunnel, testing both a small-scale model of the conventional blade and the flexible curved blade of equivalent diameter. Results indicate that the flexible curved blade concept successfully moderates its rotational speed and power output at higher wind speeds and demonstrates the capability to start generating power at lower wind speeds and stabilize power effectively, aligning with sustainability goals by potentially reducing reliance on active control systems. Despite promising outcomes, passive control mechanisms did not activate at the designed wind speeds, revealing a misalignment between expected and actual performance and underscoring the need for further refinements in blade design and control settings. Additionally, the power coefficient (Cp) versus tip speed ratio (TSR) comparison showed that flexible curved blades operate within a lower TSR range and exhibit controlled capping of power under high wind conditions, marked by a distinctive ‘hook-like’ feature in Cp behavior. This study confirms the feasibility of designing and manufacturing passively controlled wind turbine blades tailored to specific performance criteria and underscores the potential of such technology. Future work, to be detailed in a subsequent paper, will explore further optimizations and the use of Glass Fiber-Reinforced Polymer (GFPR) composite materials to enhance blade flexibility and performance.

Comparison of 25 MW downwind and upwind turbine designs with individual pitch control

As conventional upwind wind turbines grow larger, the increased mass and flexibility of the longer blades present challenges concerning costs, structural loads, and safety constraints such as tower clearance. At extreme scales, wind turbines in a downwind configuration may provide a feasible alternative to address these challenges by allowing lightweight, flexible blades that can reduce capital costs and blade loads while maintaining safety margins. Downwind turbine blades suffer from increased fatigue loading due to the tower shadow effect. In this study, novel downwind, three-bladed wind turbine designs at 25 MW rating with lightweight, flexible blades are evaluated and compared in terms of power production and structural loading. To obtain a baseline performance, a standard collective blade pitch wind turbine controller is implemented for the two downwind and one upwind turbine designs. Individual pitch control is then added for the downwind turbines to reduce structural fatigue on the turbine blades. In summary, the two downwind turbine designs that differ in rotor pre-coning and shaft tilt angles using collective and individual pitch control are compared against a conventional upwind turbine with collective pitch control at the same scale under turbulent wind conditions.

On the influence of rotor nacelle assembly modelling on the computed eigenfrequencies of offshore wind turbines

Motivated by the mismatch of measured and computed eigenfrequencies for the second tower mode of offshore wind turbines as well as previous studies examining the influence of including flexible blades in structural models, the need to extend the current integrated model to include flexible blades became apparent. A basic modelling approach which takes the blades as beam elements was implemented in an in-house finite element model of offshore wind turbines and benchmarked for the NREL 5 MW reference turbine with OpenFast. Moreover, the modelling approach was benchmarked with measurements that were obtained during the installation of a Belgian offshore wind turbine. The inclusion of flexible blades is shown to have a significant influence on the second tower mode and is able to reduce the mismatch between measurements and computations. Furthermore, the capability of the inclusion of flexible blades to model the effects of additional parameters is presented. Overall, the need to extend the rotor nacelle modelling in structural models of offshore wind turbines beyond a lumped mass approach is demonstrated.

Towards blade-resolved ice accretion simulations of flexible blades using mixed-fidelity models

We present a modular framework for blade-resolved fluid-structure interaction simulations of rotors. The framework is based on the coupling of the multi-body solver MBDyn with the fluid solver SU2 using the library preCICE. A preliminary validation is carried out against other open-source codes analysing the UAE Phase VI experiment. In the future, the framework will be used to study ice accretion on flexible blades. Indeed, blade flexibility has not been considered yet in the numerical modelling of ice accretion due to lacking computational tools and high computational costs. A first application on ice accretion is shown by analyzing the temporal evolution of the modal frequencies of an isolated blade during an icing event simulated numerically with a quasi-3D approach. The results provide insight into the nature of ice throw from wind turbines.

Towards vortex-based wind turbine design using GPUs and wake accommodation

Vortex methods are often cited as a promising alternative to the classical Blade Element Momentum (BEM) theory for wind turbine design, overcoming some of its limitations such as imposing steady-state, uniform, and aligned inflows. BEM assumptions are being questioned, especially for large rotors with very flexible blades or even floating wind turbines. However, vortex methods are not yet widespread due to their computational costs. The following work demonstrates how free vortex wake methods using filament discretizations can become an affordable and viable alternative to BEM. This is achieved by combining filament number reduction as well as graphical processing units (GPUs) computations. The efficiency and accuracy of the proposed approaches are demonstrated against simple test cases, including an elliptical wing and a rigid horizontal axis wind turbine (HAWT). Finally, the approaches are applied to the aero-hydro-servo-elastic simulation of floating horizontal axis wind turbines.

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.

A correction model for the effect of spanwise flow on the viscous force contribution in BEM and Lifting Line methods

Design optimization and aeroelastic load evaluation for wind turbines are still infeasible for CFD due to computational cost. These tasks are carried out using 3D engineering aerodynamic methods, where the local aerodynamic loads are obtained from tabulated 2D aerodynamic polars, which makes the models fast. With recent developments such as highly flexible blades, coned/prebent/swept blades, the relative inflow direction to the “inner” 2D airfoil section systems can have a significant component in the spanwise direction. The Crossflow Principle (CP) is used to treat the effects of this in a physically consistent manner. Cases dominated by pressure forces are described well with the CP method, but it is shown in the paper that CP fails to describe the part of the forces stemming from the friction forces correctly. It is shown in the paper that the power loss due to friction forces will be underestimated with the crossflow principle for rotors with significantly swept blades or other designs with a significant amount of local crossflow on the blades. The present work presents a simple model to correct the baseline crossflow principle method to take into account also the friction force part in a consistent manner. The model is validated with 3D CFD results on a 2D airfoil section. It is shown that the new model successfully corrects for the addition of the viscous forces due to spanwise flow component. The paper includes examples of the effect of using the model on rotor designs with different amounts of blade sweep simulated using a blade element momentum (BEM) and blade element vortex cylinder (BEVC) methods.

Assessing the impact of vortex generators on the dynamic stall behaviour of a thick airfoil

Modern slender wind turbine blades use thick inboard airfoils and thicker trailing edges prone to flow separation. The increasing size of these flexible blades amplifies the importance of considering unsteady aerodynamics during the design phase. Environmental conditions result in Leading Edge Erosion (LER), further complicating the sectional unsteady aerodynamic behaviour. Although vortex generators are a well-studied method for passive separation control under steady conditions, their influence on unsteady aerodynamics for clean and rough blade sections is an area that requires further exploration. While some numerical studies exist, reliable experimental data is lacking in the literature. This work presents experimental results on the dynamic stall behaviour of a DU97W300 airfoil, a typical thick root section. The investigation covers both clean and rough conditions, both with and without VGs, to create an understanding of how VGs impact dynamic stall. Moreover, various VG array configurations are used to study the parametric dependence of dynamic stall phenomena on the VG array parameters.

Validating low- and high-fidelity simulations of a yawed 8 MW wind turbine against measurements

This paper presents a comparison study of the aerodynamic behavior of an 8 MW wind turbine operating under yawed conditions using field measurements, Blade Element Momentum (BEM) theory and Computational Fluid Dynamics (CFD). Turbulent inflow wind field measurements are used to generate an IEC-compliant turbulence box upstream of the wind turbine that is used within the BEM tool MoWiT and the CFD tool chain by IWES in OpenFOAM. Both simulation approaches take into account blade flexibility using modal reduced, anisotropic beam elements in BEM and Geometrically Exact Beam Therory (GEBT) in CFD. While the focus is being set towards the CFD approach, turbine power output, blade root bending moments and blade tip deflections are analyzed. It is shown that both modeling approaches react differently towards the generated wind field.

Adapting Methods For Bed Level Assessment In And Around Submerged Vegetation

Coastal vegetation has the capacity to reduce flow and orbital velocities near the bed and stabilize the sediment with its root network. As a result it has an effect on sediment dynamics which gains increasing attention as ecosystem service in coastal protection. To quantify and predict this ecosystem service, laboratory experiments with live or artificial vegetation are often conducted. During these experiments the assessment of bed level change is challenged by the presence of the vegetation. Standard optical and acoustic measurement techniques cannot obtain data below vegetation canopies. Especially for submerged flexible vegetation like seagrass, this challenge is aggravated for airborne methods that require flume drainage (e.g. terrestrial laser scanning) (Follett and Nepf, 2012). Flexible blades will spread on the ground during drainage, potentially covering meadow edges and thus excluding areas of interest from the bed level analysis. Moreover, live aquatic vegetation may be stressed by air exposure, if the facility is drained for bed level measurements. This potentially leads to different, non-natural behaviour in consecutive experiments. And finally, draining and refilling the facility is time consuming, especially as it needs to be done very carefully as not to disturb any generated bedforms. This time aspect hampers the collection of time series and thus the assessment of the development of bed level changes with airborne methods. Underwater technology like sonar and echo sounder avoid shading of areas by spread-out vegetation, but are equally not capable of obtaining data below vegetation canopies. Moreover, instruments that can obtain spatially resolved data underwater often require a minimum water depth which may exceed the water depth relevant for experiments with vegetation. In intertidal areas (e.g. salt marshes) the challenge of obtaining bed level data below vegetation canopies is overcome by the use of a sediment-erosion-bar (SEB) (Cahoon et al., 2002). For this method a horizontal bar is installed at a fixed height above the ground and the distance between this bar and the ground is measured at defined locations along the bar and set time intervals to obtain information on the bed level change. SEBs have successfully been adapted to laboratory settings in the past (Spencer et al., 2016), but still required flume drainage. We applied this method in an undrained flume to assess sediment dynamics in and around an artificial seagrass meadow. Additionally, we tested underwater photogrammetry to obtain 3D-spatial information (e.g., 3D models) on bed level and bedforms at and near the vegetation edges. Photogrammetry has been successfully applied to obtain bedform information in the presence of seagrass stands, but to date still required the drainage of the facility (Meysick et al., 2022).

Analyzing the Effects of Atmospheric Turbulent Fluctuations on the Wake Structure of Wind Turbines and Their Blade Vibrational Dynamics

In recent trends, a rising demand for renewable energy has driven wind turbines to larger proportions, where lighter blade designs are often adopted to reduce the costs associated with logistics and production. This causes modern utility-scale wind turbine blades to be inherently more flexible, and their amplified aeroelastic sensitivity results in complex multi-physics reactions to variant atmospheric conditions, including dynamic patterns of aerodynamic loading at the rotor and vortex structure evolutions within the wake. In this paper, we analyze the influence of inflow variance for wind turbines with large, flexible rotors through simulations of the National Rotor Testbed (NRT) turbine, located at Sandia National Labs’ Scaled Wind Farm Technology (SWiFT) facility in Lubbock, Texas. The Common Ordinary Differential Equation Framework (CODEF) modeling suite is used to simulate wind turbine aeroelastic oscillatory behavior and wind farm vortex wake interactions for a range of flexible NRT blade variations, operating in differing conditions of variant atmospheric flow. CODEF solutions of turbine operation in Steady-In-The-Average (SITA) wind conditions are compared to SITA wind conditions featuring a controlled gust-like pulse overimposed, to isolate the effects of typical wind fluctuations. Finally, simulations of realistic time-varying wind conditions from SWiFT meteorological tower measurements are compared to the solutions of SITA wind conditions. These increasingly complex atmospheric inflow variations are tested to show the differing effects evoked by various patterns of spatiotemporal atmospheric flow fluctuations. An analysis is presented for solutions of wind turbine aeroelastic response and vortex wake evolution, to elucidate the consequences of variant inflow, which pertain to wind turbine dynamics at an individual and farm-collective scale. The comparisons of simulated farm flow for SITA and measured fluctuating wind conditions show that certain regions of the wake contain up to a 12% difference in normalized axial velocity, due to the introduction of wind fluctuations. The findings of this study prove valuable for practical applications in wind farm control and optimization strategies, with particular significance for modern utility-scale wind power plants operating in variant atmospheric conditions.