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Research Papers

Blade Load Unsteadiness and Turbulence Statistics in an Actuator-Line Computed Turbine–Turbine Interaction Problem

[+] Author and Article Information
Pankaj K. Jha

Department of Aerospace Engineering,
The Pennsylvania State University,
229 Hammond Building,
University Park, PA 16802
e-mail: pkj107@psu.edu

Sven Schmitz

Assistant Professor
Department of Aerospace Engineering,
The Pennsylvania State University,
229 Hammond Building,
University Park, PA 16802
e-mail: sus52@engr.psu.edu

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received February 7, 2015; final manuscript received January 18, 2016; published online February 23, 2016. Assoc. Editor: Yves Gagnon.

J. Sol. Energy Eng 138(3), 031002 (Feb 23, 2016) (13 pages) Paper No: SOL-15-1030; doi: 10.1115/1.4032545 History: Received February 07, 2015; Revised January 18, 2016

The objective of this study is to investigate how different volumetric projection techniques used in actuator-line modeling affect the unsteady blade loads and wake turbulence statistics. The two techniques for the body-force projection radius are based on either (i) the grid spacing or (ii) the combination of grid spacing and an equivalent elliptic blade planform. An array of two National Renewable Energy Laboratory 5-MW turbines separated by seven rotor diameters is simulated for 2000 s (about rotor 300 revolutions) within a large-eddy simulation (LES) solver of the neutral and moderately convective atmospheric boundary layer (ABL). The statistics of sectional angle of attack (AOA), blade loads, and turbine power histories are quantified. Moreover, the degree of unsteadiness of sectional blade loads in response to atmospheric and wake turbulence is computed via a reduced frequency based on the rate-of-change in sectional AOA. The goal of this work is to make the wind energy community aware of the uncertainties associated with actuator-line modeling approaches.

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Figures

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Fig. 1

OpenFOAM-LES computational setup and precursor data used for turbine–turbine interaction problem: (a) computational domain and (b) mean velocity profiles (Uhub = 8 m/s)

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Fig. 2

Instantaneous flow field in a horizontal plane at hub height (t = 2000 s, NBL inflow). The quantity shown is the component of vorticity normal to the plane: (a) ε/Δgrid = const. and (b) ε/c* = const.

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Fig. 3

Mean and standard deviation (error bar) of blade AOA: (a) turbine 1 (NBL), (b) turbine 2 (NBL), (c) turbine 1 (MCBL), and (d) turbine 2 (MCBL)

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Fig. 4

PDF of blade AOA: (a) turbine 1, r/R = 0.34, (b) turbine 1, r/R = 0.91, (c) turbine 2, r/R = 0.34, and (d) turbine 2, r/R = 0.91

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Fig. 5

PSD of AOA at selected spanwise stations: (a) turbine 1, r/R = 0.34 (NBL), (b) turbine 1, r/R = 0.91 (NBL), (c) turbine 1, r/R = 0.34 (MCBL), and (d) turbine 1, r/R = 0.91 (MCBL)

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Fig. 6

PSD of AOA at selected spanwise stations: (a) turbine 2, r/R = 0.34 (NBL), (b) turbine 2, r/R = 0.91 (NBL), (c) turbine 2, r/R = 0.34 (MCBL), and (d) turbine 2, r/R = 0.91 (MCBL)

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Fig. 7

Power histories for turbine–turbine interaction problem: (a) turbine 1 (NBL), (b) turbine 2 (NBL), (c) turbine 1 (MCBL), and (d) turbine 2 (MCBL)

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Fig. 8

PSD of turbine power: (a) turbine 1 (NBL), (b) turbine 2 (NBL), (c) turbine 1 (MCBL), and (d) turbine 2 (MCBL)

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Fig. 9

Mean and standard deviation of turbine power: (a) mean turbine power, (b) std. dev. in turbine power, and (c) std. dev. relative to mean power

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Fig. 10

Mean streamwise velocity distributions in the vertical direction: (a) 2D downstream of turbine 1, (b) 6D downstream of turbine 1, (c) 2D downstream of turbine 2, and (d) 6D downstream of turbine 2

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Fig. 11

PDF of reduced frequency: (a) turbine 1, r/R = 0.34, (b) turbine 1, r/R = 0.91, (c) turbine 2, r/R = 0.34, and (d) turbine 2, r/R = 0.91

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Fig. 12

Mean and standard deviation of reduced frequency: (a) mean, r/R = 0.34, (b) mean, r/R = 0.91, (c) std. dev., r/R = 0.34, and (d) std. dev., r/R = 0.91

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Fig. 13

Example of Cl response to dynamic stall model of Oye: (a) sample AOA(t) for turbine 1, r/R = 0.34 (MCBL), (b) dynamic Cl for turbine 1, r/R = 0.34 (MCBL), (c) sample AOA(t) for turbine 1, r/R = 0.91 (MCBL), and (d) dynamic Cl for turbine 1, r/R = 0.91 (MCBL)

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Fig. 14

Power response of NREL 5-MW turbine subject to uniform inflow: (a) power history and (b) power spectral density (PSD)

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