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.

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.

A comparative numerical study of four turbulence models for the prediction of horizontal axis wind turbine flow

2010 ◽  
Vol 224 (9) ◽  
pp. 1973-1979 ◽  
Author(s):  
N S Tachos ◽  
A E Filios ◽  
D P Margaris
Keyword(s):  
Wind Turbine ◽  
Turbulence Model ◽  
Numerical Study ◽  
Free Field ◽  
Turbulence Models ◽  
Horizontal Axis ◽  
Wind Condition ◽  
Computational Domain ◽  
Horizontal Axis Wind Turbine ◽  
Rans Equations

The analysis of the near and far flow fields of an experimental National Renewable Energy Laboratory (NREL) rotor, which has been used as the reference rotor for the Viscous and Aeroelastic Effects on Wind Turbine Blades (VISCEL) research program of the European Union, is described. The horizontal axis wind turbine (HAWT) flow is obtained by solving the steady-state Reynolds-averaged Navier—Stokes (RANS) equations, which are combined with one of four turbulence models (Spalart—Allmaras, k—∊, k—∊ renormalization group, and k—ω shear stress transport (SST)) aiming at validation of these models through a comparison of the predictions and the free field experimental measurements for the selected rotor. The computational domain is composed of 4.2×106 cells merged in a structured way, taking care of refinement of the grid near the rotor blade in order to enclose the boundary layer approach. The constant wind condition 7.2 m/s, which is the velocity of the selected experimental data, is considered in all calculations, and only the turbulence model is altered. It is confirmed that it is possible to analyse a HAWT rotor flow field with the RANS equations and that there is good agreement with experimental results, especially when they are combined with the k—ω SST turbulence model.

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 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.

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