alexa A Review of in-situ Loading Conditions for Mathematical
ISSN: 2090-4541

Journal of Fundamentals of Renewable Energy and Applications
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Review Article

A Review of in-situ Loading Conditions for Mathematical Modeling of Asymmetric Wind Turbine Blades

Bardsley A*, Whitty JPM*, Howe J and Francis J

Energy and Power Management Research Group, School of Computing, Engineering and Physical Sciences, University of Central Lancashire, Preston, PR1 2HE, UK

Corresponding Authors:
Bardsley A
Energy and Power Management Research Group
School of Computing, Engineering and Physical Sciences
University of Central Lancashire,Preston, PR1 2HE, UK
Tel: +44 1772 201201
E-mail: [email protected]

Whitty JPM
Energy and Power Management Research Group
School of Computing, Engineering and Physical Sciences
University of Central Lancashire, Preston, PR1 2HE, UK
E-mail: [email protected]

Received date: December 09, 2014; Accepted date: January 26, 2015; Published date: February 04, 2015

Citation: Bardsley A, Whitty JPM, Howe J, Francis J (2015) A Review of in-situ Loading Conditions for MathematicalModeling of Asymmetric Wind Turbine Blades. J Fundam Renewable Energy Appl 5:153. doi:10.4172/2090-4541.1000153

Copyright: © 2015 Bardsley A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.



This paper reviews generalized solutions to the classical beam moment equation for solving the deflexion and strain fields of composite wind turbine blades. A generalized moment functional is presented to effectively model the moment at any point on a blade/beam utilizing in-situ load cases. Models assume that the components are constructed from inplane quasi-isotropic composite materials of an overall elastic modulus of 42 GPa. Exact solutions for the displacement and strains for an adjusted aerofoil to that presented in the literature and compared with another defined by the Joukowski transform. Models without stiffening ribs resulted in deflexions of the blades which exceeded the generally acceptable design code criteria. Each of the models developed were rigorously validated via numerical (Runge-Kutta) solutions of an identical differential equation used to derive the analytical models presented. The results obtained from the robust design codes, written in the open source Computer Aided Software (CAS) Maxima, are shown to be congruent with simulations using the ANSYS commercial finite element (FE) codes as well as experimental data. One major implication of the theoretical treatment is that these solutions can now be used in design codes to maximize the strength of analogues components, used in aerospace and most notably renewable energy sectors, while significantly reducing their weight and hence cost. The most realistic in-situ loading conditions for a dynamic blade and stationary blade are presented which are shown to be unique to the blade optimal tip speed ratio, blade dimensions and wind speed.

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