Research Papers: Alternative Energy Sources

Weighted Least Squares Approach for an Adaptive Aerodynamic Engineered Structure With Twist Transformation

[+] Author and Article Information
Fuzhao Mou

Department of Mechanical and
Aerospace Engineering,
University at Buffalo—SUNY,
Buffalo, NY 14260

Hamid Khakpour Nejadkhaki, Aaron Estes

Department of Mechanical and
Aerospace Engineering,
University at Buffalo—SUNY,
Buffalo, NY 14260

John F. Hall

Department of Mechanical and
Aerospace Engineering,
University at Buffalo—SUNY,
Buffalo, NY 14260
e-mail: johnhall@buffalo.edu

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received July 6, 2018; final manuscript received January 15, 2019; published online February 18, 2019. Assoc. Editor: Christopher Niezrecki.

J. Energy Resour. Technol 141(5), 051207 (Feb 18, 2019) (11 pages) Paper No: JERT-18-1502; doi: 10.1115/1.4042642 History: Received July 06, 2018; Revised January 15, 2019

A design concept for a wind turbine blade with an adaptive twist transformation is presented. The design improves partial-load wind capture by adapting the twist distribution in relation to wind speed. Structural adaptability is enabled by actuating a series of compliant sections that are mounted on a relatively rigid spar. The sections are assumed to have a unique stiffness that is achievable through additive manufacturing technology. The authors' prior work employed an aerodynamic model to establish the theoretical blade twist distribution as a function of wind speed. The work in this paper focuses on a method to optimize the stiffness of each blade section that has been previously defined. A mathematical model is proposed to support design optimization. The model is parameterized in terms of actuator locations and the torsional stiffness ratios of each blade section. These parameters are optimized to allow the blade to adapt its twist distribution to match the prescribed configurations. The optimization is completed using a weighted-least squares approach that minimizes the error between the theoretical and practical design. The selected solution is based upon the configuration that maximizes production. Weights are assigned to bias the performance of the blade toward different operating regimes. Our results indicate that quadratically penalizing twist angle errors toward the blade tip increases power capture. A Rayleigh distribution is used to create three sets of wind data, which vary in average speed. These sets of data are used to evaluate the performance of the proposed blade and design technique.

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Fig. 1

Adaptively twisting blade concept

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Fig. 5

Two blade segments with torsional stiffness k1 and k2, connected in series. An actuator provides a torque, T, to twist the segments.

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Fig. 4

A modular blade with flexible sections composed of two stiffness regions

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Fig. 3

Definition of the absolute twist angle, φa, at distance, r, from the blade root

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Fig. 2

Development environment for an aerodynamic adaptive structure

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Fig. 6

Variation of twist within blade section. By varying the stiffness ratio, R, the actual twist angle (dotted line) can be optimized to approach the ideal twist angle (solid curve).

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Fig. 9

Ideal twist angle distributions, measured with respect to the rotor plane

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Fig. 11

Squared twist angle error, summed over all wind speeds, as a function of distance from the blade root

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Fig. 8

Rayleigh distributions for different mean wind speeds, v¯

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Fig. 7

Flowchart for optimization of actuator locations, P, and stiffness ratios, R

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Fig. 12

Percent improvement in cp as a function of wind speed, for all weighting schemes, compared to pitch control of NREL S809 blade

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Fig. 13

Cumulative twist angle error as a function of wind speed, using the Rayleigh distribution to assign different wind-speed optimization weights

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Fig. 10

Ideal and actual twist angle distributions using different weighting schemes. Optimal actuator locations are specified by markers.

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Fig. 14

Relative cumulative twist angle error, generated by subtracting the unweighted error from the weighted cases



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