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.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Ponta, F. L. , Otero, A. D. , Rajan, A. , and Lago, L. I. , 2014, “ The Adaptive-Blade Concept in Wind-Power Applications,” Energy Sustainable Develop., 22, pp. 3–12. [CrossRef]
Lin, J. , Luo, Z. , and Tong, L. , 2010, “ Design of Adaptive Cores of Sandwich Structures Using a Compliant Unit Cell Approach and Topology Optimization,” ASME J. Mech. Des., 132(8), p. 081012. [CrossRef]
Trease, B. , and Kota, S. , 2009, “ Design of Adaptive and Controllable Compliant Systems With Embedded Actuators and Sensors,” ASME J. Mech. Des., 131(11), p. 111001. [CrossRef]
Calkins, F. T. , and Mabe, J. H. , 2010, “ Shape Memory Alloy Based Morphing Aerostructures,” ASME J. Mech. Des., 132(11), p. 111012. [CrossRef]
Fasel, U. , Keidel, D. , Molinari, G. , and Ermanni, P. , 2017, “ Aerostructural Optimization of a Morphing Wing for Airborne Wind Energy Applications,” Smart Mater. Struct., 26(9), p. 095043. [CrossRef]
Molinari, G. , Quack, M. , Dmitriev, V. , Morari, M. , Jenny, P. , and Ermanni, P. , 2011, “ Aero-Structural Optimization of Morphing Airfoils for Adaptive Wings,” J. Intell. Mater. Syst. Struct., 22(10), pp. 1075–1089. [CrossRef]
Jenett, B. , Calisch, S. , Cellucci, D. , Cramer, N. , Gershenfeld, N. , Swei, S. , and Cheung, K. C. , 2016, “ Digital Morphing Wing: Active Wing Shaping Concept Using Composite Lattice-Based Cellular Structures,” Soft Rob., 4(1), pp. 33–48. [CrossRef]
Stephen, D. , and Paul, M. W. , 2012, “ A Morphing Trailing Edge Device for a Wind Turbine,” J. Intell. Mater. Syst. Struct., 23(6), pp. 691–701. [CrossRef]
Vasista, S. , Tong, L. , and Wong, K. C. , 2012, “ Realization of Morphing Wings: A Multidisciplinary Challenge,” J. Aircr., 49(1), pp. 11–28. [CrossRef]
U.S. DoE, 2015, “Wind Vision: A New Era for Wind Power in the United States,” U.S. Department of Energy, Washington, DC, Report No. DOE/GO-102015-4557. https://www.energy.gov/eere/wind/downloads/wind-vision-new-era-wind-power-united-states
IEA Wind, 2013, “ Long-Term Research and Development Needs for Wind Energy for the Time Frame 2012 to 2030,” IEA Wind, Paris, France, Report. https://nachhaltigwirtschaften.at/resources/iea_pdf/iea_wind_longterm_research_2012_2030.pdf
Philibert, C. , and Holttinen, H. , 2013, Technology Roadmap: Wind Energy, International Energy Agency, Paris, France.
Weisshaar, T. A. , 2013, “ Morphing Aircraft Systems: Historical Perspectives and Future Challenges,” J. Aircr., 50(2), pp. 337–353.
Castaignet, D. , Couchman, I. , Poulsen, N. K. , Buhl, T. , and Wedel-Heinen, J. J. , 2013, “ Frequency-Weighted Model Predictive Control of Trailing Edge Flaps on a Wind Turbine Blade,” IEEE Trans. Control Syst. Technol., 21(4), pp. 1105–1116. [CrossRef]
Pechlivanoglou, G. , Wagner, J. , Nayeri, C. , and Paschereit, C. , 2010, “ Active Aerodynamic Control of Wind Turbine Blades With High Deflection Flexible Flaps,” AIAA Paper No. 2010-644.
Wang, Y. , Sun, X. , Dong, X. , Zhu, B. , Huang, D. , and Zheng, Z. , 2016, “ Numerical Investigation on Aerodynamic Performance of a Novel Vertical Axis Wind Turbine With Adaptive Blades,” Energy Convers. Manage., 108, pp. 275–286. [CrossRef]
Alejandro Franco, J. , Carlos Jauregui, J. , and Toledano-Ayala, M. , 2015, “ Optimizing Wind Turbine Efficiency by Deformable Structures in Smart Blades,” ASME J. Energy Resour. Technol., 137(5), p. 051206. [CrossRef]
Alejandro Franco, J. , Carlos Jauregui, J. , Carbajal, A. , and Toledano-Ayala, M. , 2017, “ Shape Morphing Mechanism for Improving Wind Turbines Performance,” ASME J. Energy Resour. Technol., 139(5), p. 051214. [CrossRef]
Capuzzi, M. , Pirrera, A. , and Weaver, P. M. , 2014, “ A Novel Adaptive Blade Concept for Large-Scale Wind Turbines—Part I: Aeroelastic Behaviour,” Energy, 73, pp. 15–24. [CrossRef]
Capuzzi, M. , Pirrera, A. , and Weaver, P. M. , 2014, “ A Novel Adaptive Blade Concept for Large-Scale Wind Turbines—Part II: Structural Design and Power Performance,” Energy, 73, pp. 25–32. [CrossRef]
Barbarino, S. , Bilgen, O. , Ajaj, R. M. , Friswell, M. I. , and Inman, D. J. , 2011, “ A Review of Morphing Aircraft,” J. Intell. Mat. Syst. Struct., 22(9), pp. 823–877. [CrossRef]
Jae-Sang, P. , Seong-Hwan, K. , Sung Nam, J. , and Myeong-Kyu, L. , 2011, “ Design and Analysis of Variable-Twist Tiltrotor Blades Using Shape Memory Alloy Hybrid Composites,” Smart Mater. Struct., 20(1), p. 015001. [CrossRef]
Park, J.-S. , Kim, S.-H. , and Jung, S. N. , 2011, “ Optimal Design of a Variable-Twist Proprotor Incorporating Shape Memory Alloy Hybrid Composites,” Compos. Struct., 93(9), pp. 2288–2298. [CrossRef]
Lachenal, X. , Daynes, S. , and Weaver, P. M. , 2013, “ Review of Morphing Concepts and Materials for Wind Turbine Blade Applications,” Wind Energy, 16(2), pp. 283–307. [CrossRef]
Wang, W. , Caro, S. , Bennis, F. , and Salinas Mejia, O. R. , 2013, “ A Simplified Morphing Blade for Horizontal Axis Wind Turbines,” ASME J. Sol. Energy Eng., 136(1), p. 011018. [CrossRef]
Gili, P. , and Frulla, G. , 2016, “ A Variable Twist Blade Concept for More Effective Wind Generation: Design and Realization,” Smart Sci., 4(2), pp. 78–86. [CrossRef]
Barbarino, S. , Gandhi, F. , and Webster, S. D. , 2011, “ Design of Extendable Chord Sections for Morphing Helicopter Rotor Blades,” J. Intell. Mater. Syst. Struct., 22(9), pp. 891–905.
Wagg, D. , Bond, I. , Weaver, P. , and Friswell, M. , 2008, Adaptive Structures: Engineering Applications, Wiley, Hoboken, NJ.
Kudikala, R. , Kalyanmoy, D. , and Bhattacharya, B. , 2009, “ Multi-Objective Optimization of Piezoelectric Actuator Placement for Shape Control of Plates Using Genetic Algorithms,” ASME J. Mech. Des., 131(9), p. 091007. [CrossRef]
Loth, E. , Selig, M. , and Moriarty, P. , 2010, “ Morphing Segmented Wind Turbine Concept,” AIAA Paper No. 2010-4400.
Maheshwaraa Namasivayam, U. , and Conner Seepersad, C. , 2011, “ Topology Design and Freeform Fabrication of Deployable Structures With Lattice Skins,” Rapid Prototyping J., 17(1), pp. 5–16. [CrossRef]
Liu, S. , Li, Y. , and Li, N. , 2018, “ A Novel Free-Hanging 3D Printing Method for Continuous Carbon Fiber Reinforced Thermoplastic Lattice Truss Core Structures,” Mater. Des., 137(Suppl. C), pp. 235–244. [CrossRef]
Nejadkhaki, H. K. , and Hall, J. F. , 2018, “ Modeling and Design Method for an Adaptive Wind Turbine Blade With Out-of-Plane Twist,” ASME J. Sol. Energy Eng., 140(5), p. 051010. [CrossRef]
Nejadkhaki, H. K. , Hall, J. F. , Zheng, M. , and Wu, T. , 2018, “ Integrative Modeling Platform for Design and Control of an Adaptive Wind Turbine Blade,” ASME Paper No. DSCC2018-9235.
Gupta, A. K. , 2015, “ Efficient Wind Energy Conversion: Evolution to Modern Design,” ASME J. Energy Resour. Technol., 137(5), p. 051201. [CrossRef]
Johnson, K. E. , and Fingersh, L. J. , 2008, “ Adaptive Pitch Control of Variable-Speed Wind Turbines,” ASME J. Sol. Energy Eng., 130(3), p. 031012. [CrossRef]
Nejadkhaki, H. K. , and Hall, J. F. , 2017, “ A Design Methodology for a Flexible Wind Turbine Blade With an Actively Variable Twist Distribution to Increase Region 2 Efficiency,” ASME Paper No. V02AT03A025.
Moghaddam, N. S. , Skoracki, R. , Miller, M. , Elahinia, M. , and Dean, D. , 2016, “ Three Dimensional Printing of Stiffness-Tuned, Nitinol Skeletal Fixation Hardware With an Example of Mandibular Segmental Defect Repair,” Procedia CIRP, 49, pp. 45–50. [CrossRef]
Hau, E. , and Renouard, H. E. V. , 2014, Wind Turbines: Fundamentals, Technologies, Application, Economics, Springer, Berlin.
Gonzalez, A. , and Munduate, X. , 2008, “ Three-Dimensional and Rotational Aerodynamics on the NREL Phase VI Wind Turbine Blade,” ASME J. Sol. Energy Eng., 130(3), p. 031008. [CrossRef]
Carta, J. A. , Ramírez, P. , and Velázquez, S. , 2009, “ A Review of Wind Speed Probability Distributions Used in Wind Energy Analysis: Case Studies in the Canary Islands,” Renewable Sustainable Energy Rev., 13(5), pp. 933–955. [CrossRef]
Wais, P. , 2017, “ A Review of Weibull Functions in Wind Sector,” Renewable Sustainable Energy Rev., 70, pp. 1099–1107. [CrossRef]
Da Rosa, A. V. , 2012, Fundamentals of Renewable Energy Processes, Academic Press, Waltham, MA.


Grahic Jump Location
Fig. 1

Adaptively twisting blade concept

Grahic Jump Location
Fig. 2

Development environment for an aerodynamic adaptive structure

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

A modular blade with flexible sections composed of two stiffness regions

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
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).

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

Rayleigh distributions for different mean wind speeds, v¯

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
Fig. 13

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

Grahic Jump Location
Fig. 11

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

Grahic Jump Location
Fig. 12

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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In