Optimization design of spar cap layup for wind turbine blade

Abstract

Based on the aerodynamic shape and structural form of the blade are fixed, a mathematical model of optimization design for wind turbine blade is established. The model is pursued with respect to minimum the blade mass to reduce the cost of wind turbine production. The material layup numbers of the spar cap are chosen as the design variables; while the demands of strength, stiffness and stability of the blade are employed as the constraint conditions. The optimization design for a 1.5 MW wind turbine blade is carried out by combing above objective and constraint conditions at the action of ultimate flapwise loads with the finite element software ANSYS. Compared with the original design, the optimization design result achieves a reduction of 7.2% of the blade mass, the stress and strain distribution of the blade is more reasonable, and there is no occurrence of resonance, therefore its effectiveness is verified.

Keywords

wind turbine blade / spar cap layup / optimization design / blade mass

Introduction

As one of the most important parts of wind turbines, the blade is required to have a reasonable structural form, advanced materials and a scientific production technology to endure the bending moments and tension caused by different loads such as wind force, blade weight and centrifugal force [1]. Therefore, the design and manufacturing process have a decisive influence on the structural performance of the blade.

Because of the light-weight, high-strength, good corrosion resistance and designable characteristics, composite materials are broadly used in virtually every area of our life, from aerospace to medicine applications, and also in wind turbine industry [2]. The large-scale turbine blades made by composite materials have the advantages of high bearing capacity and reliable structural performance. However, these blades are high cost and the structural design analysis is very complex. Decreasing the use of the materials and minimizing the blade mass by optimizing the blade structure is one of the effective ways to reduce the cost, which means to improve the structural design and finally reach the economy and rationality of the blade structure by adjusting the layer numbers, layer shape, stacking sequence and layer orientations of the materials [3,4].

The spar cap is the chief structure to endure the force and bending moment in a blade, its size has a significant impact on the blade mass and the stiffness of the blade [3]. To ensure the security and stability of the blade under different load cases, the spar cap layup is generally thicker, thus the blade could not make full use of the materials. Hence, the material layup numbers of the spar cap can be properly decreased to reduce the cost of production. Based on the aerodynamic shape and structural form of the blade are fixed, the material layup numbers of the spar cap are chosen as the design variables and the minimum of the blade mass is selected as the objective function, the optimization design for a 1.5 MW wind turbine blade is carried out at the action of ultimate flapwise loads with the finite element software ANSYS.

Structure parameters of the blade

The blade is made of composite materials with a length of 37 m and a mass of 6543.6 kg. It comprises an imbedded stud root structure, a thickened spar cap, and two shear webs. The materials consist of a surface gel coat, reinforcing materials and UD-tapes for the skin and the spar cap. Balsa and PVC core materials are also used in the leading edge, the trailing edge and the shear webs. Figure 1 shows the blade planform and a typical structural cross section.

Mathematical model of optimization design

General expression of optimization design

The mathematical model for design variable X={\left[\begin{array}{llll}{x}_{\mathrm{1}},& x_{\mathrm{2}},& \cdots ,& x_n\end{array}\right]}^{\mathrm{T}} can be expressed as follows:

Objective function \min F(X)

(1)\begin{array}{lll}\mathrm{s}.\mathrm{t}.\hfill & h_j(X)=\mathrm{0}\hfill & j=\mathrm{1},\mathrm{2},\cdots ,k;\hfill \\ \hfill & G_i(X)\le \mathrm{0}\hfill & i=\mathrm{1},\mathrm{2},\cdots ,m;\hfill \\ \hfill & X\ge \mathrm{0},\hfill & \hfill \end{array}

where h_j(X) is the non-upper and non-lower limit equality constraint, k is the number of equality constraints, G_i(X) is the non-upper and non-lower limit inequality constraint, m is the number of inequality constraints.

Design variables

The blade mass changes with the change of the thickness of the spar cap. Therefore, the material layup numbers of the spar cap are chosen as the design variables. Due to the material layup numbers of the spar cap close to the root and in the middle areas of the blade are much more than that close to the tip, only the areas from 3.8 to 26.7 m of the spar cap along the span wise are selected to be optimized. For the sake of simplicity, the spar cap layup on two sides are defined the same. The selected areas are divided into 15 sections, each as a variable, so there are 15 design variables.

Objective function

Considering the cost, the minimum blade mass is selected as the optimization objection function. It is given as follows:

(2)F(X)={\displaystyle \sum _i{\rho }_i\times V_i},

where {\rho }_i is the material density, V_i is the volume of the material.

Constraint conditions

The blade optimization design is a multi-criteria constrained optimization problem [5,6]. In this paper, the demands of strength, stiffness and stability of the blade are taken into account.

The strength constraints: the stress and strain generated in the blade cannot exceed allowable value [™]. It is expressed as follows:

(3)\{\begin{array}{l}\sigma \le {\sigma }_{\max }\\ ϵ\le {ϵ}_{\max },\end{array}

where \sigma is the blade stress, {\sigma }_{\max } is the maximum allowable stress, ϵ is the blade strain, {ϵ}_{\max } is the maximum allowable strain.

The stiffness constraints: in order to avoid the risk of the blade and tower collisions, the maximum tip deflection should be less than the set value [8]. It is expressed as follows:

(4)d\le d_{\max },

where d is the tip deflection, d_{\max } is the maximum allowable tip deflection.

The stability constraints: to prevent the occurrence of resonance, the first natural frequency of the blade should be separated from the harmonic vibration associated with rotor rotation [6]. It is expressed in the inequality form:

(5)\left|F_{\mathrm{b}\mathrm{l}\mathrm{a}\mathrm{d}\mathrm{e}}-F_{\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{r}}\right|\ge \mathrm{\Delta },

where F_{\mathrm{b}\mathrm{l}\mathrm{a}\mathrm{d}\mathrm{e}} is the first natural frequency of the blade, F_{\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{r}} is the frequency of the rotor rotation and \mathrm{\Delta } is the associated allowable tolerance.

Considering the manufacturing maneuverability and the continuity of the materials layup, the design variables should be satisfied with the following inequality form:

(6)\{\begin{array}{ll}{x}_i^L\le x_i\le x_i^U,\hfill & i=\mathrm{1},\mathrm{2},\cdots ,\mathrm{15}\hfill \\ x_j-x_{j+\mathrm{1}}\le \mathrm{0},\hfill & j=\mathrm{1},\mathrm{2},\cdots ,\mathrm{7}\hfill \\ x_{k+\mathrm{1}}-x_k\le \mathrm{0},\hfill & k=\mathrm{8},\mathrm{9},\cdots ,\mathrm{14},\hfill \end{array}

where x^L is the lower bound variables, x^U is the upper bound variables.

The detail range values of the constraint conditions are in Table 1.

The analysis and calculation model of the blade

According to the geometrical parameters, the airfoil data and the actual layup design, the finite element model of the blade is created using SHELL91 element and SHELL99 element in ANSYS. SHELL91 element is a layered composite shell element with shear deformation and linear capability, while SHELL99 element is a layered composite shell element with shear deformation and nonlinear capability. The created model consists of 27453 elements, 80687 nodes, as shown in Fig. 2.

The blade is treated as a cantilever beam [9], and the calculated 4429.3 kN·m ultimate flapwise loads are reduced to several concentrated loads. Figure 3 shows the distribution of the loads.

Results and analysis

The optimization design is carried out by combing above objective and constraint conditions with the APDL language and the First-Order optimization method in ANSYS. The process converges in 20 steps.

Figure 4 shows the changing process of material layup numbers of the spar cap, which all decrease after optimization. The material layup numbers decrease obviously from 11 to 20 m and from 22 to 23.5 m along span wise, while the numbers decrease slightly at the other areas between the final optimization design and the original design. As the design variables are not constrained to change linearly, the shapes of the optimized spar cap layup are irregular.

Table 2 lists the structural performance of the blade before and after optimization. The mass of the blade finally reduces 473.4 kg (or 7.2%) after optimization. The maximum stress, strain and tip deflection all increases, and the maximum strain reaches the allowable value, but they still satisfy the constraint conditions set in the procedure. The stress and strain distribution of the blade is more reasonable after optimization, which means the optimization design result has a better use of the materials. Both of the structural stiffness of the blade and the blade mass reduces with the decrease of the material layup numbers of the spar cap. Meanwhile, the reduced ratio of the stiffness is greater than that of the blade mass. Therefore, the first natural frequency decreases, but there is no occurrence of resonance. In general, the blade mass reduces and the structural performance improves after optimization, the result achieves the purpose of the optimization design.

Conclusions

First, the result to reduce the blade mass is obtained after optimization. The reduction of the blade mass cannot only decrease the brake torque and the periodic vibration bending moment of the blade, but also reduce the use of materials and the cost of the whole wind turbine system.

Secondly, compared with the original design, the optimization result has obvious advantages. It verifies the rationality and effectiveness of the optimization design model and can be a reference for the engineering design of the wind turbine blade.

References

[1] Fei J F. Structural analysis of the composite wind blade using finite element method. M. E. Dissertation. Wuhan: Wuhan University of Technology, 2009 (in Chinese)

[2] Li C L, Wang J H, Xue Z M. Application and development of materials of large-scale wind turbine blades. FRP/CM, 2008(4): 49-52 (in Chinese)

[3] Liao C C, Zhao X L, Wang J L, . Optimization design of the frequency based on wind turbine blade layers. Journal of Engineering Thermophysics, 2011, 32(2): 1311-1314 (in Chinese)

[4] Li C L, Chen C. Structure analysis and lamination optimum design of wind turbine rotor blade. FRP/CM, 2009(9): 50-53 (in Chinese)

[5] Fuglsang P, Madsen H A. Optimization method for wind turbine rotors. Journal of Wind Engineering and Industrial Aerodynamics, 1999, 80(1-2): 191-206

[6] Jureczko M, Pawlak M, Mezyk A. Optimisation of wind turbine blades. Journal of Materials Processing Technology, 2005, 167(2-3): 463-471

[7] JB/T10194-2000. Rotor Blades of Wind Turbine. Machinery Industry Standard of PRC, 2000 (in Chinese)

[8] Burton T, Sharpe D, Jenkins N, . Wind Energy Handbook. Chichester: John Wiley & Sons Ltd, 2001

[9] Hansen M. Aerodynamics of Wind Turbines. London: James & James (Science Publishers) Ltd, 2000

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg