^{1}

^{1}

^{2}

The Actuator Line/Navier-Stokes model is validated against wind tunnel measurements for flows past the yawed MEXICO rotor and past the yawed NREL Phase VI rotor. The MEXICO rotor is operated at a rotational speed of 424 rpm, a pitch angle of ?2.3^{。}, wind speeds of 10, 15, 24 m/s and yaw angles of 15^{。}, 30^{。} and 45^{。}. The computed loads as well as the velocity field behind the yawed MEXICO rotor are compared to the detailed pressure and PIV measurements which were carried out in the EU funded MEXICO project. For the NREL Phase VI rotor, computations were carried out at a rotational speed of 90.2 rpm, a pitch angle of 3^{。}, a wind speed of 5 m/s and yaw angles of 10^{。}and 30^{。}. The computed loads are compared to the loads measured from pressure measurement.

In order to precisely predict the performance of wind turbines in wind farms, it is required to have a detailed knowledge on the inflow conditions in front of the turbines which are usually created by the atmospheric turbulence, the ground and the upstream turbines. To compute such complex flows, using a standard CFD code, which solves both the boundary layer on the blades and the wake, is too expensive. In order to reduce computational costs, the Actuator Line/Navier-Stokes (AL/NS) technique [

An important check is whether the AL/NS technique can predict the loads on the blades and the wake behind the turbines correctly. In the first part of the MexNext project [

In this paper, the AL/NS technique is validated against wind tunnel measurements for wind turbine rotors in yaw. Both measurements for the MEXICO and NREL Phase VI rotors in yaw are used.

The numerical method used in the paper is the Actuator Line/Navier-Stokes model which was developed in [

The EllipSys3D code [

To determine the body forces on the rotor blades, we use a blade-element approach combined with airfoil characteristics. The computational domain is chosen to be fixed with the ground and three rotating blades are represented with a rotating body force. At each time step, the flow solver gives a Cartesian velocity field. The velocity at a given blade position is calculated by identifying the index of blade position and performing a tri-linear interpolation. In order to find the loading, the obtained Cartesian velocity (u, v, w) is transformed into the local velocity of the blades,

where (V_{n}, V_{t}) are the velocity in the normal and tangential directions of the rotor, respective, g is the yaw angle, q is the azimuth angle. Since the rotor is rotating with an angular velocity W, the flow angle is determined as

The angle of attack at each cross section is defined as

The force per spanwise unit length is

where

obtained directly from 2D measurements or computations need to be corrected for rotational effects caused by Coriolis and centrifugal forces, especially for cross-sections near the root. At the same time, airfoil cross-sec- tions near the blade tip are influenced from the fact of pressure equalization from the pressure and suction sides at the tip such that the tip flow is different from the corresponding 2D flow at the same angle of attack. To take into account tip effects, a function F_{1} is applied on the 2D airfoil data [

where B is number of blades, the function g is

and c is blade chord.

The g function adjusts the influence of the tip vortices on the pressure distribution in the blade tip region. The number of blades, B, determines the distance between the tip vortices at a fixed tip speed ratio whereas the tip speed ratio, WR/U_{∞}, determines both the distance between the tip vortices at a fixed number of blades, and the pitch of the vortex structure. Their influences on the pressure distribution on the blade are similar and thus are considered together in the g function. Finally, the obtained 2D force is put into a Cartesian regularized volume force.

To take into account the dynamic effects for yawed rotors, the Beddoes-Leishman type dynamic stall model [

AL/NS computations are carried for both yawed MEXICO and NREL Phase VI rotors. The obtained results are presented in the following two subsections.

Computations for flows past the MEXICO rotor at a rotational speed of 424 rpm, a pitch angle of −2.3˚, wind speeds of 10, 15, 24 m/s and yaw angle of 15˚, 30˚ and 45˚ were carried out by employing the AL/NS model on a Cartesian mesh consisting of 11.8 M mesh points in a domain of [−16R, 16R] × [−16R, 16R] × [−16R, 16R], with the finest mesh size of R/30 where R is the rotor radius. Two sets of airfoil data: original airfoil data (OAD) and modified airfoil data (MAD) are used for flows past the yawed MEXICO rotor. For more information about the airfoil data, the reader is referred to [

yaw angle of 45˚ is plotted. From the figure, good agreements for both normal and tangential force are seen between the computations and measurements.

The radial, tangential and axial velocity components in the rotor coordinates are also plotted. In

In order to show the structure behind a yawed rotor, iso-vorticity is plotted in

Computations for flows past the NREL Phase VI rotor [

The Actuator Line/Navier-Stokes model has been validated for both loading and velocity field against measurements for flows past the yawed MEXICO rotor, and for loading for the yawed NREL Phase VI rotor. In general, the model can predict correctly the force changes during a revolution. The velocity behind the rotor can also be predicted correctly in the near field. From the study we can conclude that the AL/NS model is ready to simulate flows past a wind turbine in yaw and to simulate complex flows in wind farms.

This work was supported by the Energy-Technological Development and Demonstration Program under the

project (J.nr. 64012-0146) and the Danish Council for Strategic Research under the project (Sags nr. 0603- 00506B). The authors wish to give thanks to the international partners for their collaborations in the Mex Next II project within the framework of IEA Wind Annex 29.

Wen Zhong Shen,Wei Jun Zhu,Hua Yang, (2015) Validation of the Actuator Line Model for Simulating Flows past Yawed Wind Turbine Rotors. Journal of Power and Energy Engineering,03,7-13. doi: 10.4236/jpee.2015.37002