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Research Papers: Flows in Complex Systems

A Nonlinear Computational Model of Floating Wind Turbines

[+] Author and Article Information
Ali Nematbakhsh

Graduate Research Assistant
Student Mem. ASME
e-mail: ali.nb@wpi.edu

David J. Olinger

Associate Professor
Mem. ASME
e-mail: olinger@wpi.edu

Department of Mechanical Engineering,
Worcester Polytechnic Institute,
Worcester, MA 01609

Gretar Tryggvason

Professor
Fellow ASME
Department of Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556-5684
e-mail: gtryggva@nd.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 4, 2012; final manuscript received July 24, 2013; published online September 12, 2013. Assoc. Editor: Zvi Rusak.

J. Fluids Eng 135(12), 121103 (Sep 12, 2013) (13 pages) Paper No: FE-12-1605; doi: 10.1115/1.4025074 History: Received December 04, 2012; Revised July 24, 2013

The dynamic motion of floating wind turbines is studied using numerical simulations. The full three-dimensional Navier–Stokes equations are solved on a regular structured grid using a level set method for the free surface and an immersed boundary method for the turbine platform. The tethers, the tower, the nacelle, and the rotor weight are included using reduced-order dynamic models, resulting in an efficient numerical approach that can handle nearly all the nonlinear hydrodynamic forces on the platform, while imposing no limitation on the platform motion. Wind speed is assumed constant, and rotor gyroscopic effects are accounted for. Other aerodynamic loadings and aeroelastic effects are not considered. Several tests, including comparison with other numerical, experimental, and grid study tests, have been done to validate and verify the numerical approach. The response of a tension leg platform (TLP) to different amplitude waves is examined, and for large waves, a nonlinear trend is seen. The nonlinearity limits the motion and shows that the linear assumption will lead to overprediction of the TLP response. Studying the flow field behind the TLP for moderate amplitude waves shows vortices during the transient response of the platform but not at the steady state, probably due to the small Keulegan–Carpenter number. The effects of changing the platform shape are considered, and finally, the nonlinear response of the platform to a large amplitude wave leading to slacking of the tethers is simulated.

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Figures

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Fig. 1

The baseline tension leg platform with a 5-MW wind turbine. Notation: 1-rotor, 2-nacelle, 3-tower, 4-platform tank, 5-tank ballast section, 6-spoke, 7-tether.

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Fig. 2

Three different views of the upstream part of the computational grid. The grid consists of straight lines that are unevenly spaced to give a fine resolution around the platform.

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Fig. 3

A flow chart of the algorithm for numerical modeling of a floating wind turbine, based on the Navier–Stokes equations. xsi: points required for tracking the wind turbine; ϕ: distance function for tracking the free surface.

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Fig. 4

Comparison of the numerical results with the analytical solution [22] for the amplitude of a decaying wave in a closed flume

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Fig. 5

Vortex shedding behind a two-dimensional cylinder for Reynolds number equal to 150. Dashed and solid lines represent negative and positive vorticity.

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Fig. 6

(a) Results from the grid resolution study for the pitch motion of a block. (b) A comparison of the pitch motion results from the finest grid with the experimental results of Ref. [48].

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Fig. 7

Comparison of the response amplitude operators (RAO) given by current developed numerical model with the experimental and theoretical results of Ref. [48]

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Fig. 8

Two frames showing the motion of the floating platform (a) at t = 213 s and (b) at 218 s (when the wave has propagated half its wavelength) for the baseline run

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Fig. 9

(a) The wave height, measured half a wavelength upstream of tension leg platform; (b) the surge and heave response; (c) the pitch response; (d) the upstream and downstream tether forces

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Fig. 10

Top view of the velocity vectors at the midsection of the floating wind turbine tank in the very beginning of the transient region (t = 23 s). The solid line shows the floating wind turbine tank border. Note that slight deviation of the velocity field on the solid border grids with respect to the inside solid is due to transition region from solid to fluid.

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Fig. 11

(a) Surge response of the TLP to different incoming wave heights. At a wave period of 10 s, a linear trend is observed for low and moderate amplitude waves but not for very large waves. (b) Wind turbine interacting with a 13.5 -m wave. Waves radiated from the floater tank can be seen around the platform.

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Fig. 12

A comparison of the peak-to-peak pitch responses and the tether forces at steady state for different designs of the floating wind turbine tank. R shows the radius of three different platform tanks, which is normalized based on the radius of the standard tank.

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Fig. 13

The response of the TLP to a large nonlinear wave. (a) The very beginning of the simulation; (b) after 6.25 s. Splashing of the water can be seen behind the tank.

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Fig. 14

(a) The pitch and surge response of the TLP for large nonlinear wave versus time; (b) the tether forces versus time

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