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Research Papers

Reduced-Order Modeling of Torque on a Vertical-Axis Wind Turbine at Varying Tip Speed Ratios

[+] Author and Article Information
Muhammad Saif Ullah Khalid, Tariq Rabbani, M. Salman Siddiqui

Department of Mechanical Engineering,
NUST College of Electrical
& Mechanical Engineering,
National University of Sciences & Technology,
Islamabad 44000, Pakistan

Imran Akhtar

Assistant Professor
Department of Mechanical Engineering,
NUST College of Electrical
& Mechanical Engineering,
National University of Sciences & Technology,
Islamabad 44000, Pakistan
e-mails: imran.akhtar@ceme.nust.edu.pk; akhtar@vt.edu

Naveed Durrani

Adjunct Faculty
Institute of Space Technology,
Islamabad 44000, Pakistan

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 24, 2014; final manuscript received July 12, 2014; published online April 2, 2015. Assoc. Editor: Carlo L. Bottasso.

J. Comput. Nonlinear Dynam 10(4), 041012 (Jul 01, 2015) (9 pages) Paper No: CND-14-1055; doi: 10.1115/1.4028064 History: Received February 24, 2014; Revised July 12, 2014; Online April 02, 2015

Vertical-axis wind turbine (VAWT) has received significant attention due to its application in urban environment. Torque produced by VAWT determines its efficiency and power output. In this paper, we develop a reduced-order model of torque VAWT at different tip speed ratios (TSR). We numerically simulate both 2D and 3D flows past a three-bladed Darrieus H-type VAWT and compute overall torque acting on the turbine. We then perform higher-order spectral analysis to identify dominant frequencies and nonlinear couplings. We propose a reduced-order model of torque in the form of modified van der Pol equation with additional quadratic term to allow for even harmonics in addition to odd harmonics present in the system. Using, a perturbation approach of method of multiple scales, we solve the proposed model and compute the coefficients at different TSR. The model not only predicts torque accurately in time domain but also in spectral domain. These reduced-order models provide an accurate and computationally efficient means to predict overall performance and output of the turbine with varying free-stream conditions even in predictive setting.

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Figures

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Fig. 2

Mesh over the turbine–(a) complete domain, (b) close-up of rotor, and (c) close-up of airfoil

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Fig. 3

Mesh over the turbine for case II (left) and case III (right)

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Fig. 4

Instantaneous spanwise vorticity in case I (left) and case III (right)

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Fig. 5

Time histories of torque for case I: (a) TSR = 2.50, (b) TSR = 3.0, (c) TSR = 3.50, and (d) TSR = 4.50

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Fig. 6

Amplitude spectra of torque for case I: (a) TSR = 2.50, (b) TSR = 3.0, (c) TSR = 3.50, and (d) TSR = 4.50

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Fig. 7

Auto-bispectrum of torque data for case I: (a) TSR = 2.5 and (b) TSR = 3.5

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Fig. 8

Auto-trispectrum of torque data for case I: (a) TSR = 2.5 and (b) TSR = 3.5

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Fig. 9

Temporal and spectral matching at TSR = 3.5 in case I; (a) time history obtained from CFD (solid) and read-only memory (ROM) (circle) and (b) frequency spectra obtained from CFD (solid) and ROM (dashed)

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Fig. 10

Temporal and spectral matching at TSR = 3.5 in case II; (a) time history obtained from CFD (solid) and ROM (circle) and (b) frequency spectra obtained from CFD (solid) and ROM (dashed)

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Fig. 11

Temporal and spectral matching at TSR = 3.5 in case III; (a) time history obtained from CFD (solid) and ROM (circle) and (b) frequency spectra obtained from CFD (solid) and ROM (dashed)

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Fig. 12

Variation of model coefficients with TSR for all cases: case I (), case II (), and case III (○); (a) μ versus TSR; (b) α versus TSR; and (c) γ versus TSR

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Fig. 13

Comparison of reduced-order model results with CFD data in predictive setting; (a) time history obtained from CFD (solid) and ROM (circle) and (b) frequency spectra obtained from CFD (solid) and ROM (dashed)

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