Improved energy forecast for Offshore Wind farms Siri
Transcription
Improved energy forecast for Offshore Wind farms Siri
Cascade Analysis of a Floating Wind Turbine Lene Eliassen & Jasna B. Jakobsen, University of Stavanger Finn Gunnar Nielsen & Andreas Knauer, Statoil Mounting a wind turbine on a floating foundation introduces new challenges to the aerodynamic loading. The floater motion may contain a wide range of frequencies. To study some of the basic dynamic load effect on the blade due to these motions, a two-dimensional cascade approach combined with a potential vortex method is used. This is an alternative method to study the aeroelastic behaviour of wind turbines that is different to the traditional blade element momentum method. The analysis method demands little computational power, and can handle unsteady flows. ROTATION WIND MOTION OF WIND TURBIN Figure 1: An illustration of the wing, with the surface divided into panel elements Dynamics of a Floating Wind Turbine Figure 3: The two dimensional panel vortex method with three airfoils moving in the rotational direction Figure 2: One of the blades and the wind modelled in the program Discussion and Conclusion The floating wind turbines have in general six additional degrees of freedom compared to the bottom fixed wind turbines. These rigid body motions, if significant, will alter the angle of attack and the wind velocity. As a result the shape and strength of the wake behind the rotor will also vary. The aerodynamic loads are dependent on both the incoming wind and the wake shed behind, and therefore both wind and wake should be included in the simulation. The most common simulation tools for rotor loads, such as HAWC2 [1] and AeroDyn [2], are based on the blade element momentum theory, which does not directly include the wake strength and shape in the load estimations. In this work, the aerodynamic loading on a wind turbine in surge and pitch motion is studied, see Figure 4. The rotor loads on the oscillating wind turbine are investigated using a two-dimensional panel vortex method. This method includes the development of the wake, and calculates the aerodynamic loads based on the geometry of the airfoil. Method The nature of the investigated motion-dependent loads is such that there is a linear relationship between the velocity of the wind turbine and the associated force. The linear relationship has a negative slope, and the negative correlation between the axial rotor velocity and the associated loading corresponds to a positive aerodynamic damping, as expected according to the quasi-steady theory. We would further like to investigate analytically the aerodynamic 1 damping, based on the definition of the lift force; πΏ = ππ 2 πππΆπΏ . In the 2 equation, both the lift force coefficient, πΆπΏ , and the relative wind speed, U, will vary with the surge velocity. π is the air density, 1.225 kg/m3, c is the chord length and l is the unit length 1/m. A linearized approximation of the πΆπΏ curve about the mean angle of attack is used: πΆπΏ πΌ β πΆπΏ0 + Figure 4: Forced surge harmonic response of a wind turbine ππΆπΏ π₯ , ππΌ ππππ‘ relative wind velocity, U, is (ππ€πππ βπ₯)2 + (ππππ‘ )2 , where ππ€πππ is the wind velocity and ππππ‘ is the velocity of the blade rotation. The lift force can be rewritten as πΏ β πΏ1 + π2 π₯ , where: The two dimensional panel vortex method applied is based on the potential flow theory, and does therefore not consider boundary layer development and coupled viscous effects including stall. For higher angles of attack the method is invalid. The position and the strength of the vortex elements in the wake is included in the calculation of the aerodynamic forces. The method is coded in Matlab, and not optimized with regards to computational speed. Three blades are modelled in a cascade configuration, and it is assumed that there is no flow in the spanwise direction of the blade. As the blades are rotating along a repeating path of length 2*pi*R, the blades will be influenced by the wake of the upstream blade, see Figure 3. The aerofoils are modelled by using linear panel elements, see Figure 1. The panels have a constant distribution of source and doublet elements. The wake is modelled similarly, but using only doublet elements [3]. The position in the flow of the wake elements is part of the solution. To simulate the oscillation of a floating wind turbine, the incoming wind velocity is reduced to a harmonic component, representing the horizontal velocity of the rotor plane, see Figure 2. The harmonic rotor plane motion in axial direction is simulated with the amplitude of 1.5 m and the period of 12 sec, see Figure 4. The rotor used in the calculation is similar to the 5MW rotor used in the code comparison project OC3 [4]. The wind condition is set to 6 m/s, this is below rated speed and there is no pitching of the blades. The rotor has a constant speed of 7.96 rpm. where π₯ is the axial velocity of the wind turbine rotor. The πΏ1 = 1 2 πcπ(ππ€πππ 2 + ππππ‘2) πΆπΏ0 π2 = β1 2 πππ[ 2 ππ€πππ + and 2 ππΆπΏ 1 ππππ‘ ππΌ ππππ‘ + 2ππ€πππ πΆπΏ0 ]. The coefficient dependent on the rotor axial motion, π2 , is the aerodynamic damping coefficient. Using the information given in [4], as listed in Table 1, the first term of the lift force, πΏ1 , is 2.87 kN, and the aerodynamic damping, π2 , is -0.39 kN/(m/s). The two values based on the lift coefficient obtained by the vortex panel method, on a single blade, are πΏ1 = 2.88 kN and π2 =-0.46 kN/(m/s). Figure 5: Normal force on one airfoil, with respect to time. The red markers indicate each rotation of the rotor. The results from the vortex panel method, presented in Figure 5 and 6, show reasonable comparison with the theoretically based values. The mean normal load is 2.73 kN, and the aerodynamic damping coefficient is -0.44 kN/(m/s). In the further work we will extend these two-dimensional results to obtain damping force of a full rotor. [4] Table 1: The airfoil lift coefficient Figure 6: Normal force from one airfoil, with respect to the velocity of the wind turbine motion. Results The result for a node located at a radius of 44.55 m (0.7R) is presented in the following. A comparison between the lift coefficients as calculated with the vortex panel code, and the lift coefficient given in [4] are shown in Table 3. The force normal to the rotor plane is shown as a function of time in Figure 5. The trend is similar for the loading of all sections along the blade. The force is also plotted against the surge velocity of the wind turbine, see Figure 6. References [1] Larsen, Torben J. Welcome to HAWC2, DTU Risø Campus, Denmark. Accessed 13.09.2012. Available from http://www.hawc2.dk/HAWC2%20Info/Aerodynamic%20model.aspx [2] Laino, David J. NWTC Design Codes (AeroDyn), NREL, Boulder, Colorado, USA. Accessed 13.09.2012. Available from http://wind.nrel.gov/designcodes/simulators/aerodyn/ [3] Katz, J. Plotkin, A. (2008). Low-Speed Aerodynamics (2nd Edition). New York, USA: Cambridge University Press [4] Jonkman, J. Butterfield, S. Musial, W. Scott, G. Definition of a 5-MW Reference Wind Turbine for Offshore System Developement. (2009). NREL, Boulder, Colorado, USA. NREL/TP 500-38060. Corresponding author: Lene Eliassen, e-mail: [email protected]