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Author: Ayse Sapmaz Publisher: ISBN: Category : Electronic dissertations Languages : en Pages : 133
Book Description
Understanding vibration of wind turbine blades is of fundamental importance. This study focuses on the effect of blade mistuning on the coupled blade-hub dynamics. Unavoidably, the set of blades are not precisely identical due to inhomogeneous materials, manufacturer tolerances, etc. This work is focused on the blade-hub dynamics of horizontal-axis wind turbines with mistuned blades. The reduced-order equations of motion are derived for the wind turbine blades and hub exposed to centrifugal effects and gravitational and cyclic aerodynamic forces. Although the blades and hub equations are coupled, they can be decoupled from the hub by changing the independent variable from time to rotor angle and by using a small parameter approximation. The resulting blade equations include parametric and direct excitation terms. The method of multiple scales is applied to examine response of the linearized 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. Besides illustrating the effects of damping and forcing level, the first-order perturbation solutions are verified withcomparisons to numerical simulations at superharmonic resonance of order two. The simulation point to speed-locking phenomenon, in which the superharmonic speed is locked in for an interval of applied mean loads. Additionally, the effect of rotor loading onthe rotor speed and blade amplitudes is investigated for different initial conditions and mistuning cases.Next, 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 is revealed. This resonance case is not captured by a first-order perturbation expansion. The relationship between response amplitude and frequency is studied. Resonances under constant loading are also analyzed. The effect of blade mistuning on the coupled blade-hub dynamics is taken into account. To better understand parametrically excited multi-degree-of-freedom behavior, approximate solutions to tuned and mistuned four-degree-of-freedom systems with parametric stiffness are studied. The solution and stability of a four-degree-of-freedom Mathieu-type system is investigated with and without broken symmetry. The analysis is done using Floquet theory with harmonic balance. A Floquet-type solution is composed of a periodic and an exponential part. The harmonic balance is applied when the Floquet solution is inserted into the original differential equation of motion. The analysis brings about an eigenvalue problem. By solving this, the Floquet characteristic exponents and the corresponding eigenvectors that give the Fourier coefficients are found in terms of the system parameters. The stability transition curve can be found by analyzing the real parts of the characteristic exponents. The frequency content can be determined by analyzing imaginary parts at the exponents. A response that involves a single Floquet exponent (and its complex conjugate) can be generated with a specific set of initial conditions, and can be regarded as a "modal response''. The method is applied to both tuned and detuned four-degree-of-freedom examples.
Author: Ayse Sapmaz Publisher: ISBN: Category : Electronic dissertations Languages : en Pages : 133
Book Description
Understanding vibration of wind turbine blades is of fundamental importance. This study focuses on the effect of blade mistuning on the coupled blade-hub dynamics. Unavoidably, the set of blades are not precisely identical due to inhomogeneous materials, manufacturer tolerances, etc. This work is focused on the blade-hub dynamics of horizontal-axis wind turbines with mistuned blades. The reduced-order equations of motion are derived for the wind turbine blades and hub exposed to centrifugal effects and gravitational and cyclic aerodynamic forces. Although the blades and hub equations are coupled, they can be decoupled from the hub by changing the independent variable from time to rotor angle and by using a small parameter approximation. The resulting blade equations include parametric and direct excitation terms. The method of multiple scales is applied to examine response of the linearized 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. Besides illustrating the effects of damping and forcing level, the first-order perturbation solutions are verified withcomparisons to numerical simulations at superharmonic resonance of order two. The simulation point to speed-locking phenomenon, in which the superharmonic speed is locked in for an interval of applied mean loads. Additionally, the effect of rotor loading onthe rotor speed and blade amplitudes is investigated for different initial conditions and mistuning cases.Next, 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 is revealed. This resonance case is not captured by a first-order perturbation expansion. The relationship between response amplitude and frequency is studied. Resonances under constant loading are also analyzed. The effect of blade mistuning on the coupled blade-hub dynamics is taken into account. To better understand parametrically excited multi-degree-of-freedom behavior, approximate solutions to tuned and mistuned four-degree-of-freedom systems with parametric stiffness are studied. The solution and stability of a four-degree-of-freedom Mathieu-type system is investigated with and without broken symmetry. The analysis is done using Floquet theory with harmonic balance. A Floquet-type solution is composed of a periodic and an exponential part. The harmonic balance is applied when the Floquet solution is inserted into the original differential equation of motion. The analysis brings about an eigenvalue problem. By solving this, the Floquet characteristic exponents and the corresponding eigenvectors that give the Fourier coefficients are found in terms of the system parameters. The stability transition curve can be found by analyzing the real parts of the characteristic exponents. The frequency content can be determined by analyzing imaginary parts at the exponents. A response that involves a single Floquet exponent (and its complex conjugate) can be generated with a specific set of initial conditions, and can be regarded as a "modal response''. The method is applied to both tuned and detuned four-degree-of-freedom examples.
Author: Publisher: ISBN: Category : Aerodynamic load Languages : en Pages : 0
Book Description
Dynamic loads must be predicted accurately in order to estimate the fatigue life of wind turbines operating in turbulent environments. Dynamic stall contributes to increased dynamic loads during normal operation of all types of horizontal-axis wind turbines (HAWTs). This reports illustrates how dynamic stall varies throughout the blade span of a 10 m HAWT during yawed and unyawed operatingconditions. Lift, drag, and pitching moment coefficients during dynamic stall are discussed. Resulting dynamic loads are presented, and the effects of dynamic stall on yaw loads are demonstrated using a yaw loads dynamic analysis (YAWDYN).
Author: Publisher: ISBN: Category : Languages : en Pages : 7
Book Description
Surface pressure data from the National Renewable Energy Laboratory's ''Combined Experiment'' were analyzed to provide a statistical representation of dynamic stall occurrence on a downwind horizontal axis wind turbine (HAWT). Over twenty thousand blade rotational cycles were each characterized at four span locations by the maximum leading edge suction pressure and by the azimuth, velocity, and yaw at which it occurred. Peak suction values at least twice that seen in static wind tunnel tests were taken to be indicative of dynamic stall. The occurrence of dynamic stall at all but the inboard station (30% span) shows good quantitative agreement with the theoretical limits on inflow velocity and yaw that should yield dynamic stall. Two hypotheses were developed to explain the discrepancy at 30% span. Estimates are also given for the frequency of dynamic stall occurrence on upwind turbines. Operational regimes were identified which minimize the occurrence of dynamic stall events.
Author: Fatemeh Afzali Publisher: ISBN: Category : Electronic dissertations Languages : en Pages : 0
Book Description
Wind turbines are one of the fastest-growing energy sources. Based on their axis of rotation they fall into two basic categories: horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs). Darrieus VAWTs exploit aerodynamic lift. This study entails the vibration analysis of large vertical-axis Darrieus wind turbine blades. Very large wind turbines are becoming more abundant due to their ability to harvest greater wind power. VAWTs are less common than HAWTs for large wind applications, but have some favorable characteristics, for example in offshore applications, and so further development of large VAWTs is anticipated. However, VAWTs are known to have vibration issues. VAWT blade vibration is the focus of this work.The straight-bladed H-rotor/Giromill is the simplest type of VAWT. We first derive the equations of motion of a H-rotor blade modeled as a uniform straight elastic Euler-Bernoulli beam under transverse bending and twist deformation. The reduced-order model suggests the existence of periodic damping, periodic stiffness, and direct excitation generated by a cyclic aeroelastic load. The model also indicates spin softening, which could be detrimental as the turbines become large. Periodic damping and stiffness are examples of parametric excitation and are likely to carry over to other types of VAWT blades. Systems with parametric excitation have been studied with various methods. Floquet theory has been classically used to study the stability characteristics of linear systems with periodic coefficients, and has been commonly applied to Mathieu's equation, which represents a vibration system with periodic stiffness. We apply the Floquet theory combined with the harmonic-balance method to a linear vibration system with a periodic damping coefficient. Based on this theory, the approximated solution includes an exponential part, with an unknown exponent, and a periodic part. Our analysis investigates the initial conditions response, the boundaries of instability, and the characteristics of free response solution of the system. The coexistence phenomenon, in which some of the transition curves overlap so that the instability wedges disappear, is recovered in this approach, and is examined closely.An additional case of the parametric excitation is the combination of parametric damping and parametric stiffness. The Floquet-based analysis shows that the combined parametric excitation reshapes the stability characteristics, compared to the system with only parametric damping or stiffness and disrupts the coexistence which is observed in the parametric damping case.The aeroelastic forces encountered by the wind turbines can cause self-excitation in blades, the mechanism of which can be loosely modeled with van-der-Pol-type nonlinearity. We seek to understand the combined effect of parametric excitation and van der Pol nonlinearity, as both can induce instabilities and oscillations. The oscillator is studied under nonresonant conditions and secondary resonances, with and without external excitation. We analyze the system using the method of multiple scales and numerical solutions. For the case without external excitation, the analysis reveals nonresonant phase drift (quasi-periodic responses), and subharmonic resonance with possible phase drift or phase locking (periodic responses). Hard excitation is treated for nonresonant conditions and secondary resonances, and similar phenomena are uncovered.Some Darrieus VAWTs consist of curved blades. We lastly study the modal analysis of curved Darrieus wind-turbine blades and obtain the mode shapes and modal frequencies. The governing equations are derived using the fundamental deformation mechanics, and thin beam approximations are employed to express the strain and kinetic energies. The assumed-modes method is applied to the energies, and the Euler-Lagrange equation is used to discretize the equations of motion. Implementing these equations, mode shapes are calculated and mapped back onto the curved beam for visualization. This analysis is conducted for pinned-pinned and hinged-hinged blades. The results are compared with Finite element analysis using Abaqus and with the literature.
Author: Ayse Sapmaz
Author: Ayse Sapmaz
Author: Gizem Dilber Acar
Author: David Arthur Kendall
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Author: Norman John Siedschlag
Author: Rene H. Miller
Author: Fatemeh Afzali