In-Plane Blade-Hub Dynamics in Horizontal-Axis Wind-Turbines

2016 ◽  
Author(s):  
Gizem Acar ◽  
Mustafa A. Acar ◽  
Brian F. Feeny
Keyword(s):  
Multiple Scales ◽  
Horizontal Axis ◽  
Rotor Speed ◽  
Horizontal Axis Wind Turbine ◽  
Direct Excitation ◽  
Horizontal Axis Wind Turbines ◽  
Parametric Effects ◽  
Cyclic Variations ◽  
Independent Variable ◽  
Three Degree Of Freedom

Blade-hub dynamics of a horizontal-axis wind turbine is studied. Blade equations are coupled through the hub equation, and have parametric terms due to cyclic aerodynamic forces, centrifugal effects and gravitational forces. Blade inertia is usually small compared to the rotor inertia, which enables us to treat the effect of blade motion as a perturbation on the rotor motion. The rotor speed is not constant, and the cyclic variations cannot be expressed as explicit functions of time. Therefore, it is more convenient to use the rotor angle as the independent variable. By doing so, and assuming small variations in rotor speed, the blade equations are decoupled from the rotor equation. The inter-dependent blade equations constitute a three-degree-of-freedom system with periodic parametric and direct excitation. The response is analyzed by using method of multiple scales. The system has a superharmonic and a subharmonic resonances due to direct and parametric effects introduced by gravity. Amplitude frequency relations and stabilities of these resonances are studied.

Parametric Resonances of a Three-Blade-Rotor System With Reference to Wind Turbines

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Gizem D. Acar ◽  
Mustafa A. Acar ◽  
Brian F. Feeny
Keyword(s):  
Multiple Scales ◽  
Rotor System ◽  
Degree Of Freedom ◽  
Rotor Speed ◽  
Horizontal Axis Wind Turbine ◽  
Direct Excitation ◽  
Parametric Resonances ◽  
Parametric Effects ◽  
Rotor Angle ◽  
First Order Method

Abstract Coupled blade-hub dynamics of a coupled three-blade-rotor system with parametric stiffness, which is similar to a horizontal-axis wind turbine, is studied. Blade equations have parametric and direct excitation terms due to gravity and are coupled through the hub equation. For a single degree-of-freedom blade model with only in-plane transverse vibrations, the reduced-order model shows parametric resonances. A small parameter is established for large blades, which enables us to treat the effect of blade motion as a perturbation on the rotor motion. The rotor speed is not constant, and the cyclic variations cannot be expressed as explicit functions of time. Therefore, it is more convenient to use the rotor angle as the independent variable. By expressing the system dynamics in the rotor angle domain and assuming small variations in rotor speed, the blade equations are decoupled from the rotor equation. The interdependent blade equations constitute a three-degree-of-freedom system with periodic parametric and direct excitation. The response is analyzed by using a first-order method of multiple scales (MMS). The system has a superharmonic and a subharmonic resonances due to direct and parametric effects introduced by gravity. Amplitude-frequency relations and stabilities of these resonances are studied. The MMS solutions are compared with numerical simulations for verification.

In-Plane Blade-Hub Dynamics of Horizontal-Axis Wind Turbine With Mistuned Blades

2017 ◽  
Author(s):  
Ayse Sapmaz ◽  
Gizem D. Acar ◽  
Brian Feeny
Keyword(s):  
Wind Turbine ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Turbine Blades ◽  
Horizontal Axis ◽  
Wind Turbine Blades ◽  
Horizontal Axis Wind Turbine ◽  
Direct Excitation ◽  
Independent Variable ◽  
Rotor Angle

Understanding vibration of the wind turbine blades is of fundamental importance. This paper regards the effect of blade mistuning on the coupled blade-hub dynamics. Unavoidably, at any stage of the wind turbine, the set of blades will not be precisely identical due to the inhomogeneous material, manufacturer tolerances, etc. This paper is based on blade-hub dynamics of a horizontal-axis wind turbine with mistuned blade. The equations of motion are derived for the wind turbine blades and hub exposed to centrifugal effects and gravitational and cyclic aerodynamic forces. The equations are coupled. To decoupled them, the independent variable is changed from time to rotor angle. The resulting blade equations include parametric and direct excitation terms. The method of multiple scales is applied to examine response of the system. This analysis shows that superharmonic and primary resonances exist and are influenced by the mistuning. Resonance cases and the relations between response amplitude and frequency are studied.

Numerical Study of Superharmonic Resonances in a Mistuned Horizontal-Axis Wind-Turbine Blade-Rotor Set

2019 ◽  
Author(s):  
Ayse Sapmaz ◽  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Wind Turbine ◽  
Initial Conditions ◽  
Numerical Study ◽  
Horizontal Axis ◽  
Rotor Speed ◽  
Horizontal Axis Wind Turbine ◽  
First Order ◽  
Direct Excitation ◽  
Rotor Angle ◽  
Perturbation Solutions

Abstract This paper is on a simplified model of an in-plane blade-hub dynamics of a horizontal-axis wind turbine with a mistuned blade. The model has cyclic parametric and direct excitation due to gravity and aerodynamics. This work follows up a previous perturbation study applied to the blade equations written in the rotor-angle domain and decoupled from the hub, in which superharmonic and primary resonances were analyzed. In this work, the effects of mistuning, damping, and forcing level are illustrated. The first-order perturbation solutions are verified with comparisons to numerical simulations at superharmonic resonance of order two. Additionally, the effect of rotor loading on the rotor speed and blade amplitudes is investigated for different initial conditions and mistuning cases.

scholarly journals Study and Design of a Horizontal Axis Wind Turbine (0.5 kW) Using Software Solid Works

2021 ◽  
pp. 1-17
Author(s):  
Hagninou E. V. Donnou ◽  
Drissa Boro ◽  
Jean Noé Fabiyi ◽  
Marius Tovoeho ◽  
Aristide B. Akpo
Keyword(s):  
Wind Energy ◽  
Wind Turbine ◽  
Wedge Angle ◽  
Three Dimensional ◽  
Synchronous Generator ◽  
Horizontal Axis ◽  
Geometrical Shape ◽  
Horizontal Axis Wind Turbine ◽  
Horizontal Axis Wind Turbines ◽  
Lift And Drag

In the present work, the study and design of a horizontal axis wind turbine suitable for the Cotonou site were investigated on the coast of Benin. A statistical study using the Weibull distribution was carried out on the hourly wind data measured at 10 m from the ground by the Agency for Air Navigation Safety in Africa and Madagascar (ASECNA) over the period from January 1981 to December 2014. Then, the models, techniques, tools and approaches used to design horizontal axis wind turbines were presented and the wind turbine components characteristics were determined. The numerical design and assembly of these components were carried out using SolidWorks software. The results revealed that the designed wind turbine has a power of 571W. It is equipped with a permanent magnet synchronous generator and has three aluminum blades with NACA 4412 biconvex asymmetrical profile. The values obtained for the optimum coefficient of lift and drag are estimated at 1.196 and 0.0189 respectively. The blades are characterised by an attack optimum angle estimated at 6° and the wedge angle at 5°. Their length is 2.50 m and the maximum thickness is estimated at 0.032 m for a rope length of 0.27 m. The wind turbine efficiency is 44%. The computer program designed on SolidWorks gives three-dimensional views of the geometrical shape of the wind turbine components and their assembly has allowed to visualize the compact shape of the wind turbine after export via its graphical interface. The energy quantity that can be obtained from the wind turbine was estimated at 2712,718 kWh/year. This wind turbine design study is the first of its kind for the study area. In order to reduce the technological dependence and the import of wind energy systems, the results of this study could be used to produce lower cost wind energy available on our study site.

scholarly journals New airfoils for micro horizontal-axis wind turbines

2021 ◽  
Author(s):  
Manoj Kumar Chaudhary ◽  
◽  
S. Prakash ◽  
Keyword(s):  
Reynolds Number ◽  
Wind Turbines ◽  
Low Reynolds Number ◽  
Horizontal Axis ◽  
Speed Ratio ◽  
Maximum Output ◽  
Horizontal Axis Wind Turbine ◽  
Horizontal Axis Wind Turbines ◽  
Low Reynolds ◽  
Bem Theory

In this study, small horizontal-axis wind turbine blades operating at low wind speeds were optimized. An optimized blade design method based on blade element momentum (BEM) theory was used. The rotor radius of 0.2 m, 0.4 m and 0.6 m and blade geometry with single (W1 & W2) and multistage rotor (W3) was examined. MATLAB and XFoil programs were used to implement to BEM theory and devise a six novel airfoil (NAF-Series) suitable for application of small horizontal axis wind turbines at low Reynolds number. The experimental blades were developed using the 3D printing additive manufacturing technique. The new airfoils such as NAF3929, NAF4420, NAF4423, NAF4923, NAF4924, and NAF5024 were investigated using XFoil software at Reynolds numbers of 100,000. The investigation range included tip speed ratios from 3 to 10 and angle of attacks from 2° to 20°. These parameters were varied in MATLAB and XFoil software for optimization and investigation of the power coefficient, lift coefficient, drag coefficient and lift-to-drag ratio. The cut-in wind velocity of the single and multistage rotors was approximately 2.5 & 3 m/s respectively. The optimized tip speed ratio, axial displacement and angle of attack were 5.5, 0.08m & 6° respectively. The proposed NAF-Series airfoil blades exhibited higher aerodynamic performances and maximum output power than those with the base SG6043 and NACA4415 airfoil at low Reynolds number.

Second-Order Perturbation Analysis of In-Plane Blade-Hub Dynamics of Horizontal-Axis Wind Turbines

2018 ◽  
Author(s):  
Ayse Sapmaz ◽  
Brian F. Feeny
Keyword(s):  
Perturbation Analysis ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Second Order ◽  
Horizontal Axis ◽  
Dynamic Responses ◽  
Order Perturbation ◽  
Resonance Case ◽  
Horizontal Axis Wind Turbine ◽  
Rotor Angle

This paper deals with a second-order perturbation analysis of the in-plane dynamic responses of both tuned and mistuned three-blade-hub horizontal-axis wind-turbine equations. The blades are under effect of gravitational and cyclic aerodynamics forces and centrifugal forces. Although the blades and hub equations are coupled, they can be decoupled by changing the independent variable from time to rotor angle and by using a small parameter approximation. A second-order method of multiple scales is applied in the rotor-angle domain to analyze in-plane blade-hub dynamics. A superharmonic resonance case at one third the natural frequency was revealed. This resonance case was not captured by a first-order perturbation expansion. The relationship between response amplitude and frequency is studied. The effect of blade mistuning on the coupled blade-hub dynamics are taken into account.

scholarly journals Designing a Tapperless Blade with an S-4320 Airfoil on a Micro-Scale Horizontal Axis Wind Turbine (Case Studies at PT Lentera Bumi Nusantara)

2021 ◽  
Vol 3 (1) ◽  
pp. 27-34
Author(s):  
Reza Simatupang ◽  
Deddy Supriatna
Keyword(s):  
Wind Turbine ◽  
Quantitative Research ◽  
Horizontal Axis ◽  
Blade Design ◽  
Horizontal Axis Wind Turbine ◽  
Microsoft Excel ◽  
Quantitative Research Methods ◽  
Micro Scale ◽  
Wind Speeds ◽  
Horizontal Axis Wind Turbines

This article aims to design a taperless blade in a micro-scale wind turbine in medium wind speed, a case study at PT Lentera Bumi Nusantara. The methodology used in this research is quantitative research methods. Based on the test results in calculating the data using Microsoft Excel software and the blade airfoil design simulation using Qblade software, the use of the S-4320 airfoil in the application of the taperless blade design has research results that show that the airfoil design of the blade produces mechanical power at moderate wind speeds. It can be concluded that this blade design shows that the taperless blade with S-4320 airfoil can be applied to medium wind speeds in micro-scale horizontal axis wind turbines. Artikel ini bertujuan untuk merancang bilah jenis taperless pada turbin angin skala mikro dalam kecepatan angin sedang, studi kasus pada PT Lentera Bumi Nusantara. Metodologi yang digunakan dalam penelitian ini adalah dengan metode penelitian kuantitatif. Berdasarkan hasil pengujian dalam perhitungan data menggunakan software Microsoft Excel dan simulasi perancangan desain airfoil  bilah menggunakan software Qblade, penggunaan airfoil S-4320 dalam pengaplikasian desain bilah jenis taperless memiliki hasil penelitian yang menunjukan bahwa desain airfoil bilah tersebut menghasilkan tenaga mekanik pada kecepatan angin sedang. Dapat disimpulkan dalam desain bilah ini menunjukan bahwa bilah jenis taperless dengan airfoil S-4320 dapat diterapkan pada kecepatan angin sedang pada turbin angin sumbu horizontal skala mikro.

scholarly journals Experimental and Numerical Analysis of the Dynamical Behavior of a Small Horizontal-Axis Wind Turbine under Unsteady Conditions: Part I

Machines ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 52 ◽  
Author(s):  
Francesco Castellani ◽  
Davide Astolfi ◽  
Matteo Becchetti ◽  
Francesco Berno
Keyword(s):  
Control System ◽  
Wind Turbine ◽  
Dynamical Behavior ◽  
Urban Environments ◽  
Horizontal Axis ◽  
Test Case ◽  
Complex Flow ◽  
Horizontal Axis Wind Turbine ◽  
Horizontal Axis Wind Turbines ◽  
Unsteady Conditions

An efficient and reliable exploitation of small horizontal-axis wind turbines (HAWT) is a complex task: these kinds of devices actually modulate strongly variable loads with rotational speeds of the order of hundreds of revolutions per minute. The complex flow conditions to which small HAWTs are subjected in urban environments (sudden wind direction changes, considerable turbulence intensity, gusts) make it very difficult for the wind turbine control system to optimally balance the power and the load. For these reasons, it is important to comprehend and characterize the behavior of small HAWTs under unsteady conditions. On these grounds, this work is devoted to the formulation and realization of controlled unsteady test conditions for small HAWTs in the wind tunnel. The selected test case is a HAWT having 3 kW of maximum power and 2 m of rotor diameter: in this work, this device is subjected to oscillating wind time series, with a custom period. The experimental analysis allows therefore to characterize how unsteadiness is amplified moving from the primary resource (the wind) through the rotor revolutions per minute to final output (the power), in terms of delay and amplitude magnification. This work also includes a numerical characterization of the problem, by means of aeroelastic simulations performed with the FAST software. The comparison between experiments and numerical model supports the fact that the fast transitions are mainly governed by the aerodynamic and mechanical parameters: therefore, the aeroelastic modeling of a small HAWT can be useful in the developing phase to select appropriately the design and the control system set up.

Analysis on Aerodynamic Performance of Horizontal Axis Wind Turbine Based on Nonlinear Wake Model

2013 ◽  
Vol 448-453 ◽  
pp. 1716-1720
Author(s):  
Rui Yang ◽  
Jiu Xin Wang ◽  
Sheng Long Zhang
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Optimization Design ◽  
Aerodynamic Performance ◽  
Horizontal Axis ◽  
Wake Vortex ◽  
Horizontal Axis Wind Turbine ◽  
Horizontal Axis Wind Turbines ◽  
Wake Model ◽  
Induced Velocity

A computational method based on nonlinear wake model was established for horizontal axis wind turbines aerodynamic performance prediction. This method makes use of finite difference method to solve the integral differential equation of the model, the induced velocity of wake vortex can be calculated from equations and compared with the induced velocity of wake vortex in linear model. The comparison between the calculated results of wind turbine under axis flow condition, including tip vortex geometry and aerodynamic performance, and available experimental data shows that this method is suitable for wind turbine aerodynamic performance analysis. Finally, a series of numerical calculations were made to investigate the change of wake geometry and aerodynamic performance of the wind turbine when yawing and pitch angle increasing, which provide foundations for aerodynamic optimization design of horizontal axis wind turbines.

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