Development of an Analytical Unsteady Model for Wind Turbine Aerodynamic Response to Linear Pitch Changes

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Mohamed M. Hammam ◽  
David H. Wood ◽  
Curran Crawford
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Turbine Rotor ◽  
Speed Ratio ◽  
Element Analysis ◽  
Tip Speed Ratio ◽  
First Order ◽  
Vortex Model ◽  
Constant Pitch ◽  
Induced Velocity

A simple unsteady blade element analysis is used to account for the effect of the trailing wake on the induced velocity of a wind turbine rotor undergoing fast changes in pitch angle. At sufficiently high tip speed ratio, the equation describing the thrust of the element reduces to a first order, nonlinear Riccti's equation which is solved in a closed form for a ramp change in pitch followed by a constant pitch. Finite tip speed ratio results in a first order, nonlinear Abel's equation. The unsteady aerodynamic forces on the NREL VI wind turbine are analyzed at different pitch rates and tip speed ratio, and it is found that the overshoot in the forces increases as the tip speed ratio and/or the pitch angle increase. The analytical solution of the Riccati's equation and numerical solution of Abel's equation gave very similar results at high tip speed ratio but the solutions differ as the tip speed ratio reduces, partly because the Abel's equation was found to magnify the error of assuming linear lift at low tip speed ratio. The unsteady tangential induction factor is expressed in the form of first order differential equation with the time constant estimated using Jowkowsky's vortex model and it was found that it is negligible for large tip speed ratio operation.

The Rotor Speed Control of 5MW Wind Turbine under Rated Wind Speed Using Adaptive-PID Controller

2012 ◽  
Vol 229-231 ◽  
pp. 2323-2326
Author(s):  
Zong Qi Tan ◽  
Can Can Li ◽  
Hui Jun Ye ◽  
Yu Qiong Zhou ◽  
Hua Ling Zhu
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Pid Controller ◽  
Turbine Rotor ◽  
Speed Ratio ◽  
Rotor Speed ◽  
Rotating Speed ◽  
Tip Speed Ratio ◽  
Variable Wind ◽  
Wind Turbine Rotor

This paper designed the controller of the wind turbine rotor rotating speed. This model of adaptive-PID through control the tip-speed ratio and count the values of PID for variable wind speed. From the result of simulation, the wind speed can run in a good dynamic characteristic, and keep the rotor running in the best tip-speed ratio at the same time.

scholarly journals Numerical simulation and experimental study of blade pitch effect on Darrieus straight-bladed wind turbine with high solidity: A case study under realistic conditions

2020 ◽  
Author(s):  
Milad Babadi Soultanzadeh ◽  
Alireza Moradi
Keyword(s):  
Wind Turbine ◽  
Numerical Method ◽  
Pitch Angle ◽  
Numerical Results ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Regulation System ◽  
Lower Velocity ◽  
Realistic Condition ◽  
Tip Speed Ratio

Abstract Numerical and experimental studies were performed to examined the influence of pitch angle on the aerodynamic performance of a small Darrieus straight blade vertical axis wind turbine with high solidity and pitch regulation system under a realistic condition. By comparing experimental and numerical results, numerical results were validated. The power coefficient was measured and calculated at different tip speed ratios and for two pitch angles 0 and 5. The results revealed that 5 degrees increase in the pitch angle led to 25% elevation in the maximum value of the power coefficient (performance coefficient). Also, the numerical results showed higher accuracy at lower tip speed ratios for both pitch angles. After numerical method validation, numerical method employed to calculate the coefficient of performance and coefficient of torque function of Azimuth position as well as the flow field in the rotor affected zone and lateral distance. According to the numerical results, vorticity generation increased by the rise in the pitch angle at a constant tip speed ratio; the maximum performance coefficient occurred at a lower tip speed ratio with elevation in the pitch angle; finally, the increment in the pitch angle led to lower velocity profile in lateral distances of the rotor.

scholarly journals A case study on optimum tip speed ratio and pitch angle laws for wind turbine rotors operating in yawed conditions

2014 ◽  
Vol 555 ◽  
pp. 012022
Author(s):  
A Cuerva-Tejero ◽  
O Lopez-Garcia ◽  
D Marangoni ◽  
F González-Meruelo
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Speed Ratio ◽  
Tip Speed Ratio ◽  
Turbine Rotors

Including Swirl in the Actuator Disk Analysis of Wind Turbines

2007 ◽  
Vol 31 (5) ◽  
pp. 317-323 ◽  
Author(s):  
D.H. Wood
Keyword(s):  
Wind Turbine ◽  
Vortex Structure ◽  
General Model ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Core Radius ◽  
Simple Analysis ◽  
Tip Speed Ratio ◽  
Vortex Model ◽  
Actuator Disk

It is shown that the presence of swirl in the wake of a wind turbine complicates the simple actuator disk analysis that provides such basic results as the Lanchester-Betz limit on the power coefficient. The simple analysis remains valid at high tip speed ratio for a sufficiently small core radius of the hub vortex. As the tip speed ratio decreases, the present analysis eventually becomes invalid. It is, however, reasonable to conclude that including the effects of the hub vortex causes the maximum power coefficient to increase above the Lanchester-Betz limit with decreasing tip speed ratio. The extent to which this conclusion depends on the assumed vortex model was investigated briefly by considering a more general model for the hub vortex. The results strongly imply that some account of the vortex structure of the wake will be required to resolve fully the effects of swirl. Unfortunately there are no measurements currently available for the hub vortex.

Characteristic Analysis of Three-Bladed Darrieus Wind Turbine Based on the Multiple Streamtube Model

2014 ◽  
Vol 651-653 ◽  
pp. 663-667 ◽  
Author(s):  
Jing Ru Chen ◽  
Zhen Zhou Zhao ◽  
Tao Li
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Characteristic Analysis ◽  
Negative Power ◽  
Tip Speed Ratio ◽  
Maximum Value ◽  
Blade Pitch Angle ◽  
Ratio Range

The paper analyzes the effect of airfoil thickness, camber and blade pitch angle on the performance of the three-bladed Darrieus wind turbines. The research results show that the increase of airfoil thickness, camber and pitch angle of blade, can improve power coefficient when the wind turbine tip speed ratio between zero and four. The increase of thickness and camber of the airfoil leads to running tip speed ratio range of wind turbine get narrowed, and reduces the power coefficient when wind turbine runs in high tip speed ratio range. When the pitch angle of blade is 1˚, power coefficient reaches the maximum value. Negative pitch angle has a bad impact on power coefficient and even creates negative power coefficients.

scholarly journals Development of a Computational System to Improve Wind Farm Layout, Part I: Model Validation and Near Wake Analysis

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 940 ◽  
Author(s):  
Rafael Rodrigues ◽  
Corinne Lengsfeld
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Wind Farm ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Speed Ratio ◽  
Stream Velocity ◽  
Near Wake ◽  
Tip Speed Ratio ◽  
Wind Farm Layout

The first part of this work describes the validation of a wind turbine farm Computational Fluid Dynamics (CFD) simulation using literature velocity wake data from the MEXICO (Model Experiments in Controlled Conditions) experiment. The work is intended to establish a computational framework from which to investigate wind farm layout, seeking to validate the simulation and identify parameters influencing the wake. A CFD model was designed to mimic the MEXICO rotor experimental conditions and simulate new operating conditions with regards to tip speed ratio and pitch angle. The validation showed that the computational results qualitatively agree with the experimental data. Considering the designed tip speed ratio (TSR) of 6.6, the deficit of velocity in the wake remains at rate of approximately 15% of the free-stream velocity per rotor diameter regardless of the free-stream velocity applied. Moreover, analysis of a radial traverse right behind the rotor showed an increase of 20% in the velocity deficit as the TSR varied from TSR = 6 to TSR = 10, corresponding to an increase ratio of approximately 5% m·s−1 per dimensionless unit of TSR. We conclude that the near wake characteristics of a wind turbine are strongly influenced by the TSR and the pitch angle.

scholarly journals Performance Analysis and Optimization of a Vertical-Axis Wind Turbine with a High Tip-Speed Ratio

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 996
Author(s):  
Liang Li ◽  
Inderjit Chopra ◽  
Weidong Zhu ◽  
Meilin Yu
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Angle Of Attack ◽  
Vertical Axis ◽  
Speed Ratio ◽  
Vertical Axis Wind Turbine ◽  
Aerodynamic Loads ◽  
Tip Speed Ratio ◽  
Aerodynamic Model ◽  
Lift And Drag

In this work, the aerodynamic performance and optimization of a vertical-axis wind turbine with a high tip-speed ratio are theoretically studied on the basis of the two-dimensional airfoil theory. By dividing the rotating plane of the airfoil into the upwind and downwind areas, the relationship among the angle of attack, azimuth, pitch angle, and tip-speed ratio is derived using the quasi-steady aerodynamic model, and aerodynamic loads on the airfoil are then obtained. By applying the polynomial approximation to functions of lift and drag coefficients with the angle of attack for symmetric and asymmetric airfoils, respectively, explicit expressions of aerodynamic loads as functions of the angle of attack are obtained. The performance of a fixed-pitch blade is studied by employing a NACA0012 model, and influences of the tip speed ratio, pitch angle, chord length, rotor radius, incoming wind speed and rotational speed on the performance of the blade are discussed. Furthermore, the optimization problem based on the dynamic-pitch method is investigated by considering the maximum value problem of the instantaneous torque as a function of the pitch angle. Dynamic-pitch laws for symmetric and asymmetric airfoils are derived.

scholarly journals MODEL TURBIN ANGIN AIRFOIL NACA 4418 TERHADAP VARIASI BUKAAN SUDUT SUDU PADA KECEPATAN ANGIN BERBEDA

2019 ◽  
Vol 11 (2) ◽  
pp. 97-102
Author(s):  
Yusuf Dewantoro Herlambang ◽  
Budhi Prasetiyo ◽  
Supriyo Supriyo ◽  
Wahyono Wahyono ◽  
Teguh Harijono Mulud
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Vertical Axis ◽  
Speed Ratio ◽  
Vertical Axis Wind Turbine ◽  
Tip Speed Ratio ◽  
Blade Pitch Angle

Penelitian ini mengkaji Turbin Angin Sumbu Vertikal (Vertical Axis Wind Turbine) Aerofoil NACA 4418 yang memiliki diameter rotor 560  mm, panjang sudu 800 mm, jumlah sudu 3 buah, serta bahan sudu terbuat dari fiberglass. Selanjutnya menganalis karakteristik turbin angin rotor vertikal 3-sudu tersebut pada kecepatan angin berbeda 5 m/s, 6 m/s, 7 m/s, 8 m/s, dan 9 m/s dengan 5 buah model turbin angin dengan bukaan sudut sudu (blade pitch angle) bervariasi yaitu 00, 100, 200, 300, dan 400. Hasil pengujian turbin angin diperoleh rasio kecepatan sudu (Tip Speed Ratio) yang optimum sebesar 1,7 pada sudut sudu 100 dengan putaran turbin 321 rpm dan kecepatan angin 5,42 m/s. Daya mekanik optimum yang diperoleh adalah 19,4 W pada bukaan sudut sudu sebesar 200 dengan putaran turbin 381 serta kecepatan angin 6,4 m/s. Turbin menghasilkan koesifien daya (Coefficient of Power) optimum yang dihasilkan sebesar 0,202 dengan bukaan sudut sudu sebesar 100 dan putaran turbin 198 rpm, dan daya mekanik yang dihasilkan 8,5 Watt pada variabel pengujian kecepatan sebesar 5,42 m/s.

scholarly journals Exergy and Energy Analysis of a CHP System with a Gas Turbine and a Horizontal Axis Wind Turbine

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Nima Norouzi
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Combustion Chamber ◽  
Gas Turbine ◽  
Pitch Angle ◽  
Speed Ratio ◽  
Horizontal Axis Wind Turbine ◽  
Tip Speed Ratio ◽  
Operational Costs ◽  
Chp System

The combined heating and power (CHP) system is among the most effective ways to increase energy and exergy efficiencies, reduce fuel consumption, and reduce operational costs. In this study, the combination of an electricity and heat CHP system with the prime movers of a gas turbine and a horizontal axis wind turbine under the strategy of providing electric charge has been investigated. This study aims to evaluate the effect of the wind turbine on the system. The Blade Element Momentum Theory (BEM) is used to model the wind turbine under different wind speeds, pitch angle, and tip speed ratios to show their effect on the gas turbine system under different combustion chamber temperatures and pressure ratios. The results show that the proposed CHP system has significant advantages over the separate production system. It is shown that the best operating condition for the wind turbine is at the wind speed of 12 m/s, the pitch angle of 5°, and the tip speed ratio of 3. Moreover, the wind speed and tip speed ratio effects become considerable at the high-pressure ratios of more than ten and the combustion chamber temperature below 1250°C on the total system's exergy efficiency. Also, compared to the separate production mode, operational costs and fuel consumption are reduced by about 55% and 60%, respectively. Finally, taking into account the interest rate, the payback period will be equal to 5.4 years.

scholarly journals Performance assessment and optimization of a helical Savonius wind turbine by modifying the Bach’s section

2021 ◽  
Vol 3 (8) ◽  
Author(s):  
M. Niyat Zadeh ◽  
M. Pourfallah ◽  
S. Safari Sabet ◽  
M. Gholinia ◽  
S. Mouloodi ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Performance Assessment ◽  
Turbulent Flows ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Tip Speed Ratio ◽  
Basic Model ◽  
Turbine Performance ◽  
Primary Model ◽  
Savonius Wind Turbine

AbstractIn this paper, we attempted to measure the effect of Bach’s section, which presents a high-power coefficient in the standard Savonius model, on the performance of the helical Savonius wind turbine, by observing the parameters affecting turbine performance. Assessment methods based on the tip speed ratio, torque variation, flow field characterizations, and the power coefficient are performed. The present issue was stimulated using the turbulence model SST (k- ω) at 6, 8, and 10 m/s wind flow velocities via COMSOL software. Numerical simulation was validated employing previous articles. Outputs demonstrate that Bach-primary and Bach-developed wind turbine models have less flow separation at the spoke-end than the simple helical Savonius model, ultimately improving wind turbines’ total performance and reducing spoke-dynamic loads. Compared with the basic model, the Bach-developed model shows an 18.3% performance improvement in the maximum power coefficient. Bach’s primary model also offers a 12.4% increase in power production than the initial model’s best performance. Furthermore, the results indicate that changing the geometric parameters of the Bach model at high velocities (in turbulent flows) does not significantly affect improving performance.

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