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Space–time VMS computation of wind-turbine rotor and tower aerodynamics

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Abstract

We present the space–time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called “DSD/SST-VMST” method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this “ST/NURBS Mesh Update Method (STNMUM).” The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

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Acknowledgments

This work was supported in part by the Rice–Waseda research agreement (first author). Method analysis and evaluation components of this work were also supported in part by ARO Grant W911NF-12-1-0162 (second through sixth authors). The starting NURBS geometry for the turbine blade was provided by Yuri Bazilevs (UCSD). NURBS layers near the blade and the mesh on the blade surface were generated by Anthony Puntel.

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  1. Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Kenji Takizawa

  2. Mechanical Engineering, Rice University, MS 321, 6100 Main Street, Houston, TX, 77005, USA

    Tayfun E. Tezduyar, Spenser McIntyre, Nikolay Kostov, Ryan Kolesar & Casey Habluetzel

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  1. Kenji Takizawa
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Correspondence to Tayfun E. Tezduyar.

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Takizawa, K., Tezduyar, T.E., McIntyre, S. et al. Space–time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53, 1–15 (2014). https://doi.org/10.1007/s00466-013-0888-x

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