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Meta-heuristic multidisciplinary design optimization of wind turbine blades obtained from circular pipes

  • Alessandro Ceruti
Original Article
  • 43 Downloads

Abstract

Aim of this paper is to present a methodology useful to optimize the geometry of the blades of a small-size wind turbine which are obtained from a circular pipe: an optimal chord distribution and airfoil sweep can be obtained with a proper cutting path. A strong reduction in manufacturing costs and time can be achieved for blades which are a critical element in wind turbine systems, especially in case of renewable plants in developing countries. An algorithm has been developed to obtain the shape of the blades and wind turbine performances are computed by the Blade-Element Method, due to its low computational simplicity; the XFoil tool has been used to compute the aerodynamic of the blades. Heuristic algorithms have been applied to obtain a feasible design solution assuring the best efficiency of the wind turbine. Also structural considerations are kept into account to provide a feasible configuration able to withstand the forces acting on the rotating blades. Results obtained suggest that an optimal design of such a kind of blades can be obtained thanks to this methodology. The mathematical framework developed for the optimization is efficient and the heuristics algorithms allow the convergence to feasible configurations. The computing time is compatible with a practical application of the method also in industries.

Keywords

Multidisciplinary optimization Particle swarm algorithm Wind turbine Design CAD 

Abbreviations

a

Axial induction factor (–)

ac

Critical axial induction factor (–)

a

Angular induction factor (–)

A1, A2

Coefficients for the lift Viterna model (–)

AR

Blade aspect ratio (–)

B1, B2

Coefficients for the drag Viterna model (–)

CD

Local drag coefficient (–)

CDmax

Maximum lift coefficient (–)

CL

Local lift coefficient (–)

CLstall

Local stall lift coefficient (–)

ch

Chord of the airfoil (m)

ch_a

Chord of the tip section (m)

ch_b

Chord of the intermediate section (m)

ch_c

Chord of the root section (m)

D

Pipe diameter (m)

dis_d

Position of the tip section chord (m)

dis_e

Position of the intermediate section chord (m)

dis_f

Position of the root section chord (m)

Fx

Axial force (N)

FS

Airfoil scale factor (–)

K

Correction factor in Glauert equation (–)

len_l

Blade span (m)

len_g

Distance tip/intermediate section (m)

len_h

Distance tip/rotation centre (m)

N

Number of blades (–)

r

Radius measured from wind turbine hub (m)

R

Radius of the wind turbine from rotation axis (m)

Q

Factor for tip loss (–)

s

Pipe thickness (m)

T

Torque (Nm)

t

Parameter along Bezier curve (0 ÷ 1)

V

Wind speed (m/s)

W

Speed of the flow impacting the airfoil (m/s)

XLE, ZLE

Coordinates of the airfoil leading edge (m)

XTE, ZTE

Coordinates of the airfoil trailing edge (m)

xi, yi

Chord points’ coordinates in the plane (m)

Xi, Yi, Zi

Chord points’ coordinates respect to blade longitudinal axis (m)

Xi_up, Yi_up, Zi_up

Coordinates of the airfoil upper surface (m)

Xi_down, Yi_down, Zi_down

Coordinates of the airfoil lower surface (m)

xi_rot, yi_rot

Rotated chord points’ coordinates in the plane (m)

xi_lean, yi_lean, zi_lean

Coordinates of the projection chord points on the pipe (m)

α

Blade angle of attack (rad)

αstall

Blade stall angle of attack (rad)

β

Relative flow angle on the blades (rad)

λr

Tip–speed ratio at radius r (–)

γ0

Airfoil settling angle (rad)

γrot

Blade geometry rotation angle (rad)

Ω

Blade rotational speed (rad/s)

ω

Wake rotational speed (rad/s)

ρ

Air density (kg/m3)

σ′

Local solidity (–)

τ

Airfoil inclination angle on the pipe (rad)

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.DIN, Department of Industrial EngineeringUniversity of BolognaBolognaItaly

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