September 5, 2019

Design and shape optimization of a wind turbine blade

Industry: Wind Power | Software: pSeven | Company: Flypoint Software


This paper is devoted to optimization investigations in the field of wind power industry, namely design and 3D shape optimization of a wind turbine blade with a rated power of 3 MW.

As an input data, the Customer offered a rated power of the wind turbine. For the creation of the initial geometry the parameters distributions of pitch, chord length, thickness, skew and rake of the blade were found. Moreover, the description of the blade airfoils was gained. Based on this data, the 3D parametric model of the wind turbine rotor was designed in Flypoint Parametrica software. You can see the shape of this model in the picture 1 and the geometrical characteristics are presented in the table 1.


Pic.1 – Geometrical model of the wind turbine rotor

Table 1 – Geometrical characteristics of the wind turbine

Characteristic Definition
Model diameter 90 m
Blade length 44 m
Blades number 3
Airfoils DU, NACA
Rated power 3 MW
Rated speed of the wind 16 m/c
Revolutions per minute on the rated mode 16,1 rpm

Note that the power of the wind turbine is calculated by formula:

\(P = Q * ω\)

where \(Q\) – is a torque, \(kN*m\), \(ω\) – is a radial speed, rad/s.


  • Lack of initial data for the wind turbine rotor design
  • A wind turbine blade consists of 2 different airfoils and has a lot of controlled parameters
  • High requirements for quality of a 3D model, which are necessary for production


Numerical simulation of the flow around the wind turbine rotor

The viscous gas flow around mathematical model of the rotor blades was calculated using the Reynolds-averaged Navier-Stokes equations closed by the k-ω SST Menter turbulence model.

Visualization of the vortex structure coming from the blades is presented in the picture 2.


Pic.2 Visualization of the vortex structure coming from the blades

Formulation of an optimization task

For a successful outcome, it is necessary to develop a full technology of shape optimization, comprising the CFD calculation and effective search of objective function extremum based on the rapid surrogate-based optimization algorithms.

Let`s consider conditions for shape optimization of the wind turbine blade (table 2):

Table 2. Conditions for shape optimization of the wind turbine blade

Objective function Increase of torque on the rated mode
Optimization algorithm Surrogate-based optimization
Controlled parameters Angle of rotation (deg)

The optimization task was solved with the help of pSeven 6.14, which controlled and launched Flypoint Parametrica and a CFD-calculation program. The optimization technology in pSeven is fully automated. It allows us to minimize manual working process and find a best solution in a reasonable time.

Optimization results

Optimization results of the blade shape are presented in the table 3.

Table 3. Optimization results

  Initial values Optimization results Comparison
Torque 1667 kN*m 2281 kN*m 36%
Power 2827 kW 3846 kW 36%

As we can see, the wind power of a wind turbine blade is increased by 36% and only the parameters of the angle of rotation were changed. Such a significant increase of the wind turbine power is due to the fact that the optimal distribution of the angle of attack along the blade length was found as a result of optimization. In addition, this result is reached thanks to the work with three-dimensional geometrical model, not just with a 2D airfoil.

Let’s note that optimal values significantly exceed the maximum power for a fix rotor speed. To overcome this issue the rotation speed was decreased with saving of the optimal value of the angle of attack on the top of the blade. This approach made it possible to obtain the required power of 3 MW at lower rotor speed. This undoubtedly leads to reducing loads of the turbine constructions and positively affects the work of the moving mechanisms of the object.

The optimum value of the angle of attack on the top of the blade was saved in all working range by varying number of rotor revolutions. Thus, we managed to choose the rotation speed for providing a power growth in a range wind speeds from 3 m/c to 20 m/c.


Nowadays a full-scaled wind turbine blade is at the production stage. However, a model-scaled wind turbine blade 6 meters long was designed for the Customer. It was necessary for the company to participate in an international exhibition. The image of the exhibition sample is presented in the picture 3.


Pic. 3 – Wind turbine blade at the international exhibition in St.Petersburg


The shape of a wind turbine blade with the rated power 3 MW was designed. Also, the CFD calculation of the viscous gas flow around the wind turbine rotor was provided and the problem of shape optimization in a given mode was solved. As a result of the optimization in pSeven, the power of the wind turbine was increased by 36%. Thanks to the effective collaboration between pSeven and Flypoint Parametrica a finished project was put into production only 3 months after the work started.

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