Analysis of Wind Turbine Blade Motion: Linear Formulation Including All Aeroelastic Load Couplings

2012 ◽  
Author(s):  
Fouad Mohammad ◽  
Emmanuel Ayorinde
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Cross Section ◽  
Equations Of Motion ◽  
Wind Turbine Blade ◽  
Lagrange Equations ◽  
Horizontal Axis Wind Turbine ◽  
External Work ◽  
Flow Angle ◽  
Pitch Moment

A wind turbine blade similar to a helicopter rotor blade has the structure of a pretwisted beam of a variable airfoil asymmetrical cross-section. A number of approximate theories have been developed by different researchers to study the dynamic behavior of the blade of a horizontal axis wind turbine. Some researchers include warping, but they do not include the blade’s pretwisting. Others include the axial and torsional loadings and the coupling among these loadings but they ignore the bending loading. The new contribution in this study is the consideration of all the extensional, torsional and flexural loadings with their couplings, variable airfoil cross sections with warping effects, shear deflection, rotary inertia and with or without blade’s pretwist to obtain a more accurate dynamic model. To the best knowledge of the authors the simultaneous inclusion of all these factors has not been done before. The aerodynamic loadings (lift, drag and pitch moment) were calculated at each time step for a 14m blade that has a linear decreasing NACA4415 airfoil cross section utilizing a time dependent set of parameters such as angle of attack, material and air density, wind and blade speed, flow angle, yaw, pitch angles. Assuming that deformation is small, the total strain energy and total kinetic energy and external work due to the aerodynamic loading acting on the blade were calculated and used in the Lagrange equations of motion where we obtained the stiffness, mass and damping matrices of the linear dynamic equations of motion. Then the unknown displacements and rotations u, v and w in the directions of x, y and z axes respectively, the bending rotations θ1, θ2 about the y and z axes respectively and the torsional rotation ϕ about the x axis, were solved using the Newmark implicit iteration scheme.

Simplified Procedure to Estimate the Wind Turbine Blade Aerodynamic Loadings Without Using CFD

2013 ◽  
Author(s):  
Fouad Mohammad ◽  
Emmanuel Ayorinde
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Equations Of Motion ◽  
Wind Turbine Blade ◽  
Aerodynamic Load ◽  
Horizontal Axis Wind Turbine ◽  
Cross Sectional ◽  
Flow Angle ◽  
Blade Length ◽  
The Right

The aerodynamic loadings that act on the blade of a horizontal axis wind turbine change as a function of time due to the instantaneous change of the wind speed, the wind direction and the blade position. The new contribution in this study is the introduction of a simplified non CFD based procedure for the calculation of all the aerodynamic loadings acting on a wind turbine blade. The premise of the current simplified model is that (a) the forces can be modeled by a set of point loads rather than distributed pressures, and (b) the magnitudes of these point loads can be estimated using the below load formulas, (c) an interpolation scheme needed to have all computed forces and moments as a function of the blade lengthwise x. Considering a 14m blade length and utilizing a time dependent set of parameters such as angle of attack, material and air density, wind and blade speed, flow angle, yaw, pitch angles, the centrifugal forces (along x-direction of the blade length), the cross-sectional forces (Fy and Fz) and the twisting moment of the blade (about the x-direction) were calculated for each of all the given time steps. After that the authors explain how to interpolate the calculated loadings (forces and twisting moment) and the right formulas to compute the aerodynamic load vector (the right side of the dynamic equations of motion).

Examination of Wind Turbine Blade Dynamics Considering Large Deformation and Including All Aeroelastic Load Couplings

2012 ◽  
Author(s):  
Fouad Mohammad ◽  
Emmanuel Ayorinde
Keyword(s):  
Wind Turbine ◽  
Large Deformation ◽  
Cross Sections ◽  
Equations Of Motion ◽  
Small Deformation ◽  
Iteration Scheme ◽  
Small Displacement ◽  
Lagrange Equations ◽  
Horizontal Axis Wind Turbine ◽  
External Work

Many researchers have studied the structural dynamics behavior of the blade of the horizontal axis wind turbine using different approximate theories where they considered some assumptions that other researchers ignored. In a previous study, the authors considered all the extensional, torsional and flexural loadings acting on the blade with their couplings, variable airfoil cross sections with warping effects, shear deflection, rotary inertia and with or without blade’s pretwist. That previous study was performed for the linear small displacement case. In the present study, the new contribution is considering all the inclusions of the previous study but for the nonlinear large deformation case instead of the small deformation case. To the best knowledge of the authors the simultaneous inclusion of all these factors has not been done so far. The external work that acts on the blade, the total strain energy and total kinetic energy for all the different load couplings were defined (all the important strain higher order terms are kept since large deformation is considered) and used to obtain the Lagrange equations of motion. Then the load vector R, mass and linear and nonlinear stiffness matrices were deduced from the derived Lagrange equations of motion to build the nonlinear dynamic equations of motion that was solved for the three unknown displacements in the directions of x, y and z axes and the three unknown rotations about the x, y and z axes at the required stations along the length of the given blade using the Newmark implicit iteration scheme for a 14m long pretwisted blade that has a linearly decreasing NACA4415 airfoil cross section from hub to tip.

scholarly journals Numerical simulation of icing effect on aerodynamic characteristics of a wind turbine blade

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4643-4650
Author(s):  
Yan Li ◽  
Lei Shi ◽  
Wen-Feng Guo ◽  
Kotaro Tagawa ◽  
Bin Zhao
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Aerodynamic Characteristics ◽  
Wind Turbine Blade ◽  
Horizontal Axis Wind Turbine ◽  
Ambient Temperatures ◽  
Research Findings ◽  
Simulation Results ◽  
Lift And Drag ◽  
Lift And Drag Coefficient

Icing accretion on wind turbine will degrade its performance, resulting in reduction of output power and even leading to accidents. For solving this problem, it is necessary to predict the icing type and shape on wind turbine blade, and evaluate the variation of aerodynamic characteristics. In this paper the icing types and shapes in presence of airfoil, selected from blade of 1.5 MW horizontal-axis wind turbine, are simulated under different ambient temperatures and icing time lengths. Based on the icing simulation results, the aerodynamic characteristics of icing airfoils are simulated, including lift and drag coefficient, lift-drag ratio, etc. The simulation results show that the glaze ice with two horns presents on airfoil under high ambient temperature such as -5?C. When ambient temperatures are low, such as -10?C and -15?C, the rime ices with streamline profiles present on the airfoil. With increase in icing time the lift forces and coefficients decrease, and the drag ones increase. According to the variations of lift-drag ratios of icing airfoil, the aerodynamic performance of airfoil deteriorates in the presence of icing. The glaze ice has great effect on aerodynamic characteristics of airfoil. The research findings lay theoretical foundation for icing wind tunnel experiment.

scholarly journals Unsteady Flow and Vibration Analysis of the Horizontal-Axis Wind Turbine Blade under the Fluid-Structure Interaction

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Rui Zhu ◽  
Da-duo Chen ◽  
Shi-wei Wu
Keyword(s):  
Unsteady Flow ◽  
Wind Turbine ◽  
Turbine Blade ◽  
Wind Turbine Blade ◽  
Horizontal Axis ◽  
Leeward Side ◽  
Horizontal Axis Wind Turbine ◽  
Fluid Structure ◽  
Fluid Field ◽  
Stress Fluctuation

A 1.5 MW horizontal-axis wind turbine blade and fluid field model are established to study the difference in the unsteady flow field and structural vibration of the wind turbine blade under one- and two-way fluid-structure interactions. The governing equations in fluid field and the motion equations in structural were developed, and the corresponding equations were discretized with the Galerkin method. Based on ANSYS CFX fluid dynamics and mechanical structural dynamics calculation software, the effects of couplings on the aerodynamic and vibration characteristics of the blade are compared and analyzed in detail. Results show that pressure distributions at different sections of the blade are concentrated near the leading edge, and the leeward side of two-way coupling is slightly higher than that of one-way coupling. Deformation along the blade span shows a nonlinear change under the coupling effect. The degree of amplitude attenuation in two-way coupling is significantly greater than that in one-way coupling because of the existence of aerodynamic damping. However, the final amplitude is still higher than the one-way coupling. The Mises stress fluctuation in the windward and leeward sides is more obvious than one-way coupling, and the discrepancy must not be ignored.

Two-Step Optimization for Wind Turbine Blade With Probability Approach

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Ki-Hak Lee ◽  
Kyu-Hong Kim ◽  
Dong-Ho Lee ◽  
Kyung-Tae Lee ◽  
Jong-Po Park
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Design Space ◽  
Cost Model ◽  
Minimum Energy ◽  
Design Procedure ◽  
Wind Turbine Blade ◽  
Horizontal Axis Wind Turbine ◽  
Probability Approach ◽  
Strip Theory

A horizontal-axis wind turbine blade is designed using two step optimization procedures with probability approach. For the efficient management of the multiple design variables required for the blade design, the design procedure is divided into two optimization steps. In step 1, the diameter and rotating speed of a blade are determined and design points are extracted from the design space. In step 2-1, blade shapes are optimized by using the strip theory with the minimum energy loss method. The capacity factor and the cost model for each optimized blade shape are calculated in steps 2-2 and 2-3, respectively. To find the global optimum point in the design space, the space is modified into a highly possible region through the use of the probability approach.

A Preliminary Study on Small Thermoplastic Composite Wind Turbine Blade Design and Fabrication

2015 ◽  
Author(s):  
Juan Garate ◽  
Stephen A. Solovitz ◽  
Dave Kim
Keyword(s):  
Wind Turbine ◽  
Turbine Blade ◽  
Large Scale ◽  
Chord Length ◽  
Wind Turbine Blade ◽  
Thermoplastic Composite ◽  
Horizontal Axis Wind Turbine ◽  
Limit Condition ◽  
Glass Fiber Reinforced ◽  
Turbine Blade Design

Today a large-scale wind turbine blade can be 70 m long and 5 m in root chord length, and it is fabricated in a single piece. This feature leads to high initial costs, as transportation of a large blade requires special trucks, escorts, and road adaptations. These constraints can account for approximately 6–7% of the total investment for the blade. In addition, the manufacturing process commonly used is a hand lay-up configuration of thermoset composite sheets. These materials are not reusable after fabrication, which is a non-renewable feature of existing systems. The project consists of manufacturing thermoplastic composite blades in segments, which are joined before installation at the turbine site. This paper addresses the preliminary research results when conducting design and fabrication of a small blade with this innovative approach. Three segmented blades are manufactured for a horizontal-axis wind turbine, with each blade having a 50 cm span and a 4 cm tip chord length. The blade size and profile are designed based on the idealized Betz limit condition. The material used for manufacturing is a glass fiber reinforced thermoplastic composite system with a polypropylene matrix that melts at 200 °C. Each blade is fabricated in 4 independently manufactured pieces, consisting of top/bottom, and tip/root segments, via a vacuum assisted thermoforming technique. The parts will be assembled afterwards by a joining process, forming the final part for site testing.

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