Anders Ahlstr¨om Department of Mechanics
Royal Institute of Technology, Stockholm, Sweden e–mail: anders.ahlstrom@mech.kth.se
ABSTRACT
Summary A finite element model for simulation of the dynamic response of horizontal axis wind turbines has been developed. The aerodynamic model, used to transform the wind flow field to loads on the blades, is a Blade-Element/Momentum model. The model is rather general, and different configurations and wind conditions could easily be simulated. The model is primarily intended for use as a research tool when influences of specific dynamic effects are investigated.
Background
For a successful large-scale application of wind energy, the price of wind turbine energy must decrease in order to be competitive to the present alternatives. The behaviour of a wind turbine is made up of a complex interaction of components and sub-systems. The main elements are the rotor, tower, hub, nacelle, foundation, power train and control system, see figure 1. Understanding the interactive behaviour between the components provides the key to reliable design calculations, optimised machine configurations and lower costs for wind generated electricity. Consequently, there is a trend towards lighter and more flexible wind turbines, which makes design and dimen-sioning even more important [1].
Figure 1: Wind turbine layout.
The goal of this ongoing project is to produce a model with such accuracy and flexibility that different kind of dynamic phenomena can be investigated. The majority of the present aeroelastic models are based on a modal formulation and a time domain solution. The modal formulation models are computationally time efficient because of the effective way of reducing degrees of freedom, DOFs. However, these modal models are primarily suited for design purposes and will,
because of the reduced DOFs, not be suitable for research areas where phenomena such as in-stabilities may be investigated. This project has chosen the finite element method as a means to accurately predict the wind turbine loading and response.
The calculation model is based on three computer programs:
SOSIS-W for generation of the turbulent wind field [2].
AERFORCE package for the calculation of aerodynamic loads [3].
SOLVIA commercial finite element program for modelling of the structural dynamics [4].
Wind Field
It is very important for the wind industry to be able to describe the wind field properly. Turbine designers need the information to optimize the design of their turbines and turbine investors need the information to estimate their income from electricity generation.
SOSIS-W is an artificial wind data generator developed by Teknikgruppen AB [2]. The program is specially developed for providing time domain series with turbulent wind. SOSIS-W simulates three dimensional wind vectors, corresponding to gridpoints in a plane uniform cartesian grid, where the grid plane is perpendicular to the mean wind direction.
SOSIS-W creates three output files, one for each velocity component. The output data is arranged in rows and columns, where each row represents a time series and each element in a time series represents the velocity at a specific coordinate. Figure 2 shows an example of a grid net of size 4 x 4 and a rotor with its blades divided into 4 elements. However, in real simulations the resolution must be increased. Depending on the angle, phi, the time and the distance from the hub to the center of each blade element, the velocity will change in both space and time.
Figure 2: Example of a grid net of size 4 x 4 and a rotor with its blades divided into 4 elements.
Aerodynamics
Various methods may be used to calculate the aerodynamic forces acting on the blades of a wind turbine. The most advanced are numerical methods solving the Navier Stokes equations for the global as well as the flow near the blades. The two major approaches, for fast time simulations, to calculate the forces are the Actuator Disc Model and the Blade-Element Model.
The aerodynamic model used in this project is the Blade-Element/Momentum method which has been found very effective in comparative studies for wind turbine simulations. In spite of a number of limitations it is still the best tool available for getting good first order predictions of thrust, torque and efficiency for turbine blades under a large range of operating conditions.
The AERFORCE [3] package requires the input of airfoil aerodynamic data via tables as function of the angle of attack, the turbine blade and rotor geometry and wind and blade velocities. Cal-culation results are very dependent on the airfoil data, which is derived from experimental wind tunnel studies.
Extensions has been made to the BEM-method, in the AERFORCE package, to incorporate:
Dynamic inflow: Unsteady modelling of the inflow for cases with unsteady blade loading or unsteady wind.
Extensions to BEM-theory for inclined flow to the rotor disc (yaw model).
Unsteady blade aerodynamics: The inclusion of 2D attached flow unsteady aerodynamics and a semi-empirical model for 2D dynamic stall.
Figure 3: The aerodynamic forces acting on the rotor.
Structural Dynamics
As mentioned in the background to this paper a wind turbine is made up of a number of intercon-nected mechanical elements. The aerodynamics forces acting on the rotor will not only contribute
to the production of electrical power, they will also results in dynamic loads. To simulate the entire system, all motions must be taken into account.
The wind turbine is modelled using SOLVIA [4], which is a commercial finite element program for linear and nonlinear analysis of displacements, stresses and temperatures under static or dynamic conditions. The wind turbine is divided into three main parts, the tower, the nacelle and the rotor.
The parts are then coupled at nodes where important bearing and rotationally DOFs are restrained.
Figure 3 shows an example of the SOLVIA modelled rotor with the aerodynamic forces acting on each blade.
Conclusions
The combination of the three separate programs has produced a simulation package for wind turbine applications. Preliminary results indicate that the package is sufficiently accurate for the investigation of different kind of dynamic phenomena.
REFERENCES
[1] D. Eggleston and F. Stoddard. Wind Turbine Engineering Design. John Wiley & Sons, Chich-ester, (1997).
[2] I .Carlen. SOSIS-W Version 1.3., Teknikgruppen AB, Sollentuna, Sweden, (2000).
[3] A .Bj¨ork. AERFORCE: Subroutine Package for unsteady Blade-Element/Momentum Calcu-lations TN 2000-07. FFA, Bromma, Sweden, (2000).
[4] G. Larsson. SOLVIA, Finite Element System Version 99.0, Report SE 99-6, SOLVIA Engi-neering AB, V¨aster˚as, Sweden, (2000)