### 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.

Original language | English |
---|---|

Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Computational Mechanics |

Volume | 53 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 Jan |

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### Keywords

- DSD/SST-VMST
- Mesh motion
- Remeshing
- Space-time VMS method
- ST/NURBS Mesh Update Method
- STNMUM
- Temporal NURBS functions
- Wind-turbine rotor and tower aerodynamics

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Mechanical Engineering
- Ocean Engineering
- Applied Mathematics
- Computational Mathematics

### Cite this

*Computational Mechanics*,

*53*(1), 1-15. https://doi.org/10.1007/s00466-013-0888-x

**Space-time VMS computation of wind-turbine rotor and tower aerodynamics.** / Takizawa, Kenji; Tezduyar, Tayfun E.; McIntyre, Spenser; Kostov, Nikolay; Kolesar, Ryan; Habluetzel, Casey.

Research output: Contribution to journal › Article

*Computational Mechanics*, vol. 53, no. 1, pp. 1-15. https://doi.org/10.1007/s00466-013-0888-x

}

TY - JOUR

T1 - Space-time VMS computation of wind-turbine rotor and tower aerodynamics

AU - Takizawa, Kenji

AU - Tezduyar, Tayfun E.

AU - McIntyre, Spenser

AU - Kostov, Nikolay

AU - Kolesar, Ryan

AU - Habluetzel, Casey

PY - 2014/1

Y1 - 2014/1

N2 - 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.

AB - 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.

KW - DSD/SST-VMST

KW - Mesh motion

KW - Remeshing

KW - Space-time VMS method

KW - ST/NURBS Mesh Update Method

KW - STNMUM

KW - Temporal NURBS functions

KW - Wind-turbine rotor and tower aerodynamics

UR - http://www.scopus.com/inward/record.url?scp=84892801325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892801325&partnerID=8YFLogxK

U2 - 10.1007/s00466-013-0888-x

DO - 10.1007/s00466-013-0888-x

M3 - Article

AN - SCOPUS:84892801325

VL - 53

SP - 1

EP - 15

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

IS - 1

ER -