MODELING OF WIND TURBINES USING HYBRID MODELS
I.K. Dobrev*, F. Massouh**
ENSAM bvd. L'Hôpital, 151, Paris, 75013, France +33 1 44246256/+33144246266 *ivan.dobrev@paris.ensam.fr; **fawaz.massouh@paris.ensam.fr
Received: 24 Sept 2007; accepted: 25 Oct 2007
A hybrid model of kind "actuator surface" has been developed to represent the flow past a wind turbine rotor. The model uses a Navier-Stokes solver and permits calculation of rotor power and wake if the aerodynamic properties of the blade sections are known. The rotor geometry is simplified; the blades are replaced by their mean surfaces and a "pressure jump" boundary condition is applied to these surfaces. Thus, the proposed model is economic compared to full geometry simulation, because it is not needed to have fine grid around the blade. The hybrid model couples the Navier-Stokes solver with a blade element method (BEM). The solving process is iterative: at the beginning of each iteration a BEM determines the pressure discontinuities on the blade by means of rotor inflow and blade section performances. Then the CFD solver applies this pressure discontinuity in order to model the blade forces and calculate the flow past the rotor. The obtained velocity field is compared with results of previous iterations and if the required precision is attained, the calculation stops. The proposed hybrid model is tested in the case of a horizontal axis wind turbine (HAWT). The obtained results for rotor power and axial trust are satisfactory. Thus, this model can be employed for simulation of aerodynamic interaction between the wind turbines installed in the wind farm.
Keywords: wind energy equipment
Organization(s): Ecole Nationale Supérieure d'Arts et Métiers, Researcher. Education: Tech. Univ.-Sofia, Faculty of Energetic Machines (1978-1983). Experience: Tech. Univ.- Sofia, assistant (1983-2003). ENSAM, researcher (2004 to now). Main range of scientific interests: wind turbine, aerodynamics. Publications: 2 papers in international scientific journals.
Ivan Dobrev
Organization(s): Ecole Nationale Supérieure d'Arts et Métiers, Researcher, Assoc. Prof. Education: PhD - Paris - VI University (1984). Experience: ENSAM (1979 to now).
Main range of scientific interests: fluid mechanics, wind energy. Publications: 7 papers in international scientific journals.
Fawaz Massouh
Introduction
The proximity between the wind turbines installed in wind farm creates problems of aerodynamic interactions. Generally the wind farm development is complex problem and multiplicity of factors comes in play when the wind turbines are positioned. To optimize the energy production and the operation costs, engineers use
software tools developed especially for wind farm design. These software tools take into account wind turbine data, wind speed and direction, site topography, etc. However, in all cases it is needed to avoid the negative effect of aerodynamic interference between the wind turbines.
The simplified aerodynamic models used for wind farm design are not well adapted and cannot describe correctly
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the behavior of wind turbine rotor. These models cannot obtain with sufficient precision the velocity field downstream the rotor and therefore they are not capable to evaluate the development of the wind turbine wake. To obtain numerical results with sufficient quality, a CFD simulation with an appropriate fine grid mesh is needed, but the solution is computationally very expensive. As result, modeling the interaction between more than two machines is impossible in practice. To reduce the computational cost, it is possible to use a simplified equivalent representation of the real rotor blades geometry that needs less grid points. This representation must be able to describe the behavior of the wind turbine rotor without modeling the exact blade geometry in the CFD computations. This kind of numerical modeling belongs to what is called hybrid modeling.
The hybrid models comprise two modules. In the first module a CFD solver computes the velocity field around the wind turbine rotor. Here, the presence of the rotor is modeled with source terms, pressure or velocity discontinuity. To prescribe these source terms or discontinuities, one second module uses a conventional method based usually on the blade element method (BEM). Here, the forces applied to the blades are calculated using the upstream velocity field and also the drag and lift coefficients of the blade sections. Thus, there is no need to model the flow around real blade geometry and the grid around the rotor may be coarsened. As results the need of computer power is reduced significantly.
In the field of wind turbine aerodynamics, [1] presents a comprehensive review on wake aerodynamics of wind turbines and several hybrid models are discussed. It is shown that many hybrid models use an actuator disk with the application of pressure or source terms. In these axisymmetric models, the source terms are distributed uniformly in the azimuthal direction and as a result the individual presence of blades is lost. To overcome this limitation and to represent more realistically the flow field downstream the rotor, a three-dimensional representation of the rotor blades is developed in [2]. In this model named as "actuator line", the geometry of real blades is replaced in CFD by source terms distributed radially along the blade axis. Here, the blade forces are determined by means of two dimensional airfoil data and the results of CFD computations are used to obtain the relative velocity and angle of attack. Compared to actuator disk, this model permits to represent individually each blade with its tip and root vortices and thus to improve rotor wake representation. The comparison of the actuator line with experimental data reveals the effectiveness of this proposed model in case of yaw and non-yaw compared to actuator disk model [3].
This paper is intended to develop the model of "actuator surface" proposed by authors in [4] and [5]. Compared to actuator line model the actuator surface model goes further in the blade representation. Here, each blade is
replaced by a surface of pressure discontinuity. The distribution of this discontinuity varies along the span but also along the chord. Thus the actuator surface model improve the blade representation and therefore the initial conditions of wake development compared to active line. Finally, to validate the proposed model, the results of hybrid calculation in the case of wind turbine will be presented and will be compared with experimental data.
Hybrid modeling
Hybrid models like actuator disc and actuators line, are presented in details in [3] and therefore no additional explanations are required. However, the active surface model has some differences and this paper is intended to present them. Actuator surface model like other hybrid models also combines a blade element method with a Navier-Stokes solver. In the CFD domain, the rotor geometry is simplified and the blades are replaced by thin surfaces. The specified boundary condition on these surfaces is "pressure discontinuity". Hence, the imposed surface forces replace the rigid blade wall and the number of nodes is significantly reduced, as there is no need to model the blade boundary layer. In the beginning of each iteration from the upstream velocity, the blade geometry and the airfoil data, the BEM module calculates the pressure jump distribution on the surface replacing the blade. Then the CFD module computes the flow velocity field, using as boundary condition the pressure distribution previously obtained from the BEM module. The solution is carried out iteratively, exchanging data between the BEM and CFD modules; it stops after convergence is reached. The calculation of pressure discontinuity is based on the blade element approach. At the blade radius r, the elementary forces acting in the normal and tangential directions on a blade element with span dr and chord c are:
and
dFn = 2 pW 2Cn (a)cdr
dFt = - pW 2Ct (a)cdr.
(1)
(2)
In the above formulas the force coefficients Cn and Ct are determined using the aerodynamic blade sections performances Cn = Cn(a) and Ct = Ct(a). The angle of attack a may be expressed as:
a = ф - ß,
(3)
where p is the blade section pitch angle and 9 is the angle between the plane of rotation and the reference relative velocity W. In the vortex line methods or BEM the flow angle is easy to evaluate because the axial induced velocity wia and tangential velocity w it are known explicitly:
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9 = arctan
Vn
■ w,-
Qr-
(4)
where V0 is upstream velocity and Q is rotor angular velocity.
However, in actuator surface model the angle of attack a cannot be calculated explicitly because in the case of CFD modeling there is no means to separate the induced velocities in equation (4) from the rest of velocity field. Also the exact location, where flow angle must be calculated is not possible to define. Thus a different approach is needed to obtain the angle of attack. The flow around the wind turbine may be presented as the sum of a non-perturbed flow and another flow induced by the rotor blades. Then, the induced velocity field by the rotor also may be presented as a sum of two components:
- Local induced flow, created by the presence of the blade airfoils.
- Global induced flow, due to the presence of the rotor like an actuator that extracts kinetic energy from the wind and that slows down the velocity of the mass of air, which passes through the disk.
Upstream of the blades sections, at a distance of some chord lengths, the flow is slightly perturbed by the presence of local blade section. Therefore for the reference place, where the velocity and angle
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