Effect of Spar Design Optimization on the Mass and Cost of a Large-Scale Composite Wind Turbine Blade

Abstract

Mass and cost tradeoffs by deploying three optimized spars, made of all-glass, hybrid and all-carbon composites, applied to a publicly available large-scale composite blade of 100 m in length for a 13.2 MW wind turbine, are explored. The blade mass and cost minimizations are calculated for two design load cases, generating the worst aerodynamic loads for parked and rotating rotor blades, while meeting the stiffness, strength, stability and resonance design requirements, as recommended by the wind turbine standards. The optimization cases are formulated as a single-objective, multi-constraint optimization problem, while taking into account the manufacturability of hybrid spars in particular, and it is solved using a genetic algorithm method. The blade mass lowers in the range of 8.1–13.3%, 18.5–20.7% and 25.7–26.4% for the optimized all-glass, hybrid and all-carbon spars, respectively, while the cost decreases for the optimized all-glass spars only. The cost increases in a range of 1.2–13.6% and 24.5–31.5% when the optimized hybrid and all-carbon spars are used. Further, the hybrid spar optimization using the blade mass and cost objective functions, as well as the effects of spar optimization on the blade’s structural performance in terms of tip deflection, strength, buckling resistance and first natural frequency, are discussed.

1. Introduction

The use of wind turbines for power generation is consistently on the rise as the world is gradually shifting its power generation to renewable energy technologies [1]. Large-scale wind turbines are popular as the output power increases squarely with the blade length and they are capable of harnessing wind energy effectively [2,3,4,5]. However, the size growth of turbines is hindered by the blade mass increasing cubically with the blade length [6].

Blade mass is lowered by using light-weight materials such as fiber reinforced plastics composites with enhanced mechanical properties. Glass fibers, particularly the variant E-glass, having high electrical resistance, are traditionally used by composite wind turbine blade manufacturers for reinforcement as it offers the essential properties at a low cost. For large-scale blades, however, the replacement of glass fibers with significantly lighter, stiffer and stronger, yet expensive carbon fibers is a viable option. Other alternatives such as aramid, basalt and natural fibers have also been demonstrated as promising reinforcements as aramid fibers are tough and damage tolerant, basalt fibers are lighter and stiffer than glass fibers and cheaper than carbon fibers, and natural fibers are light and environment friendly. However, the aramid and basalt fibers lack adhesion to polymer resins, while the natural fibers are thermally less stable and show a huge variation in their mechanical properties [7,8,9,10,11]. Speaking of the matrix materials, the polyester resins are typically used for composite blades due to their low cost, but the epoxy resins are now often used for large-scale blades due to their superior performance. Use of thermoplastic matrix materials has the recyclability advantage; however, the higher viscosity and the requirement of a high processing temperature results in costly fabrication [9,12]. Additional mass saving can be materialized by optimizing the layup of composite blades by fine tuning its stacking sequence, ply materials, ply angles and/or ply thicknesses. However, it is a challenging task to obtain an optimal design due to anisotropy of the composite materials, complexity of layup and the presence of a wide variety of loading conditions prevalent at on-shore and off-shore sites, as outlined by the wind turbine standards [13,14].

The literature reports various attempts at the mass saving of composite wind turbine blades of different sizes through layup optimization. A turbine blade model developed for Atlantic Orientation Corporation (AOC) 15/50 was studied by Monte et al. [15] to reduce its mass. They kept the ply material unchanged and optimized the stacking sequence and the ply angles, resulting in an 8.29% mass reduction. However, the blade had a small length, measuring 7.2 m only, and there was limited exposure to the complexity involved in the layup optimization of large turbine blades. For a 40 m long blade of a 2 MW wind turbine, a layup optimization study taking into account the ply materials, thicknesses and angles was carried out by Hu et al. [16]. They combined the glass-fiber reinforced plastic and carbon-fiber reinforced plastic materials to reach an optimal hybrid layup and reported mass and cost reductions of 22.8% and 23.8%. Their focus was on the development of a generalized optimization technique; however, they demonstrated it using a blade model with unrealistic layup.

On the other hand, the mass saving through optimization of the blade spars rather than its complete layup, seems to be of much higher practical value, as the spars account for almost 40% of the overall mass of a turbine blade. Some studies [17,18,19] have addressed this topic by reporting the mass saving in a range of 2.3–8.5% for a 1.5 MW composite blade via its spar optimization, using the number and location of layers in the spars, the spar width and the location of webs as design variables. Another piece of work [20] demonstrated a set of mass and cost trade-off solutions for the same blade using glass-fiber and carbon-fiber composites for the spars, while overlooking its manufacturability. Further, this work does not disclose details on the blade layup used due to commercial reasons, consequently limiting its worth for academia in particular. There have also been studies where researchers conducted integrated aerodynamic and structure optimization to reach low mass yet efficient blade designs [21,22,23,24]. However, such approaches involve the blade topology optimization to lower mass, and require high-end specialized tools and expensive computation equipment, as well as them being time and labor intensive. As a result, they are not typically practiced by the industry for preliminary layup design of composite blades.

The blade mass saving using optimized spars is promising from a practical perspective. The spars are made of unidirectional laminates with the thickness varying along the blade length, and they can withstand mainly the bending loads. Despite the reported work on this issue, gaps still exist: (a) The researchers investigated mainly the blade mass reduction through the optimization of its spars made of a glass-fiber composite (i.e., all-glass spars) and no comprehensive study has been carried out to investigate the usage of optimized all-carbon and hybrid composite spars while taking into account its manufacturability concern, and (b) there is a lack of well-documented work in the public domain on this subject that is motivating to explore it in a detailed and systematic manner. It should be noted that spars made of a lightweight, stiffer and stronger carbon-fiber composite (i.e., all-carbon spars) can significantly lower the blade mass and improve its structural performance; however, these are expensive. Thus, the hybrid spars made of glass-fiber and carbon-fiber composites can be considered to reduce both mass and cost.

To address the shortcomings in the available research, the current work aims at exploring the mass and cost trade-off opportunities for a large-scale composite blade using the optimized spars. For this purpose, the “Sandia 100 m all-glass blade” of a 13.2 MW wind turbine developed by Sandia National Laboratories (SNL), USA [8], abbreviated as SNL blade, was chosen due to its publicly available details. The goal is (a) to investigate the blade mass saving potential along with the incurred cost by deploying the optimized all-glass, hybrid and all-carbon spars, while keeping the rest of layup unchanged, and (b) to conduct the not-yet-addressed spar optimization of the SNL blade to reduce its mass. To optimize the blade spars, single-objective multi-constraint problems are formulated, specifically addressing the manufacturability of the hybrid spars, and solved using the genetic algorithm method, while meeting the stiffness, strength, stability and resonance design requirements specified by wind turbine standards. The work will enable researchers in academia and industry to make other improvements to the SNL blade, built for the next generation of large-scale wind turbines.

2. Blade Model

The SNL blade used in this work is part of a three-bladed rotor of a large-scale horizontal-axis wind turbine, generating a rated output of 13.2 MW at a maximum speed of 7.44 rpm with variable speed and collective pitch controls. Each rotor blade, measuring 100 m in length, is made by combining two halves: a pressure-side facing the incident wind and a suction-side, as shown in the cross-sectional view A-A’ of Figure 1. Each half is constituted by four panel regions: a leading-edge panel, a spar, an aft panel and a trailing-edge reinforced panel. The pressure-side and suction-side spars and the leading-edge and aft webs form a box type beam structure bearing the bending loads, while the rest of blade structure preserves its aerodynamic shape, affecting the power output. Three webs transfer shear load between the blade pressure-side and suction-side halves and prevent buckling. The relative locations of the leading-edge, aft and trailing-edge webs are shown in Figure 1. The blade aerodynamic shape and composite layup are briefly discussed below and further details can be found in [8].

The blade aerodynamic shape is defined using the span-wise chord, twist and thickness distributions. The maximum chord of 7.63 m occurs at the blade length of 19.5 m, and the maximum twist of 13.3 degrees occurs at the root. The blade thickness is achieved by deploying different airfoils at various span-wise locations along the blade length.

The blade composite layup is made of E-glass/epoxy material. The unidirectional (UD) laminates ${\left[0\right]}_2$ (E-LT-500/EP-3) were used for the spar and trailing-edge reinforced panel regions. The tri-axial (TX) laminates ${\left[0\right]}_2 {\left[\pm 45\right]}_2$ (SNL Triax) were used for the root buildup. The TX laminates of 5 mm thickness were used as the external and internal skins. The foam core material along with the skins was used to build a sandwich construction for the leading-edge, aft and trailing-edge reinforced panel regions. Another sandwich construction made of the biaxial (BX) laminates ${\left[\pm 45\right]}_4$ (Saertex/EP-3) of 3 mm thickness and the foam of 80 mm thickness was used for the webs. The gelcoat of 0.6 mm thickness was used as a protection layer for the blade external surfaces and an extra resin layer of 5 mm thickness was added to the blade internal surfaces to attain accurate weight. The mechanical properties of various layup materials used are listed in

Table 1. Mechanical properties of the layup materials of an SNL blade.

Material Description	Density (kg/m3)	Stiffness				Strength
		${\mathbf{E}}_{\mathbf{L}} \left(\mathbf{GPa}\right)$	${\mathbf{E}}_{\mathbf{T}} \left(\mathbf{GPa}\right)$	${\mathbf{v}}_{\mathbf{L}\mathbf{T}} (-)$	${\mathbf{G}}_{\mathbf{L}\mathbf{T}} \left(\mathbf{GPa}\right)$	${\mathsf{ϵ}}_{\mathbf{U}\mathbf{L}\mathbf{T}}^{\mathbf{T}} (\%)$	${\mathsf{ϵ}}_{\mathbf{U}\mathbf{L}\mathbf{T}}^{\mathbf{C}} (\%)$
$\mathrm{UD} \mathrm{laminate} {\left[0\right]}_2$ (E-LT-500/EP-3)	1920	41.8	14.0	0.28	2.63	2.44	−1.53
$\mathrm{BX} \mathrm{laminate} {\left[\pm 45\right]}_4$ (Saertex/EP-3)	1780	13.6	13.3	0.51	11.8	2.16	−1.80
$\mathrm{TX} \mathrm{laminate} {\left[0\right]}_2{\left[\pm 45\right]}_2$ (SNL Triax)	1820	27.7	13.65	0.39	7.2
Gelcoat	1235	3.44	3.44	0.3	1.38
Resin (EP-3)	1100	3.5	3.5	0.3	1.4
Foam	200	0.256	0.256	0.3	0.022

, where ${ \mathrm{E}}_{\mathrm{L}}$, ${\mathrm{E}}_{\mathrm{T}}$, ${\mathrm{v}}_{\mathrm{LT}}$ and ${\mathrm{G}}_{\mathrm{LT}}$ represent the longitudinal stiffness, transverse stiffness, Poisson’s ratio and shear stiffness, respectively, while ${\mathsf{ϵ}}_{\mathrm{ULT}}^{\mathrm{T}}$ and ${\mathsf{ϵ}}_{\mathrm{ULT}}^{\mathrm{C}}$ represent the material strengths in terms of ultimate tensile and compressive strains.

3. Design Requirements

Design of a composite blade has to meet the requirements specified by the wind turbine standards. For example, the International Electrotechnical Commission (IEC) standard 61400-1 and the Germanischer Lloyd (GL) standard for wind turbines state a set of design load conditions (DLCs) representing various combinations of incident winds, electrical faults in the turbine systems and other external situations for which the blade structural and functional integrity must be ensured by evaluating its stiffness, strength, stability, resonance and fatigue [13,14]. Stiffness is critical as it prevents collision of the blade with the tower, strength ensures that blade failure does not occur due to loads, stability is computed to avoid the blade buckling collapse, resonance is evaluated to avoid the blade failure due to excitation and fatigue predicts the blade design life.

For the SNL blade, the DLCs 6.2 and 1.4 drive its design [8]. The DLC 6.2 characterizes an inability of pitching the zero-degree pitched blades of a parked rotor out of a steady state 50-year extreme wind accompanied by an abnormal electric loss, while the DLC 1.4 is related to a spinning rotor producing normal power and experiencing an extreme coherent wind gust with direction change [13,14]. Both DLCs are responsible for generating high strains and tip deflections in the blade.

4. Modelling and Verification

The SNL blade can be modelled as a slender beam using the Euler–Bernoulli beam theory. Use of commercial finite element tools, despite their accuracy, becomes computationally expensive for optimization purpose. As a result, an open-source tool, Co-Blade [25], was used for modelling, as shown in Figure 2a. Co-Blade uses the Euler–Bernoulli theory of beams and classical laminate theory of composites, and includes the effects of cross-sectional shear flows caused by transverse and torsional loads necessary for the stiffness and strength analyses of thin-walled composite beam structures such as the SNL blade. In addition, it estimates buckling stability conservatively by assuming the blade anisotropic panels as pin-supported isotropic plates. The natural frequencies of the stationary and spinning blades were computed using BModes [26], a tool that solves coupled partial differential equations of a beam structure using finite element methods.

The turbine rotor blades are subjected to the aerodynamic thrust and torque loads caused by incident winds, the gravity load due to the blade weight and the centrifugal force due to the rotor rotation. The aerodynamic thrust load bends the blade in the flap-wise direction and generates tension and compression at the blade pressure-side and suction-side halves, and the aerodynamic torque load spins the rotor and generates tension and compression along the blade trailing- and leading-edges. The gravity load predominantly affects the leading- and trailing-edges of a rotating blade, while the centrifugal load causes the blade extension along its longitudinal direction. Since the blade extensional and edge-wise stiffness, in general, are much higher in magnitude that the flap-wise stiffness, the aerodynamic loads mainly responsible for the blade flap-wise bending are taken into account and the influences of gravity and centrifugal forces are ignored.

The aerodynamic loads were estimated from multibody dynamic analyses of a 13.2 MW wind turbine consisting of a three SNL-bladed rotor and other structural components, i.e., tower, hub and nacelle taken from [8]. The dynamic analyses were conducted for the DLCs 6.2 and 1.4 using tools developed by the National Renewable Energy Laboratory (NREL), USA, i.e., IECWind, Modes, AeroDyn and FAST [27,28,29,30]. IECWind was used to simulate the hub-height winds for DLCs 6.2 and 1.4 for a wind site of class IB. Modes was run to generate the blade mode shapes used in the dynamic analyses. AeroDyn subroutine linked with FAST (fatigue, aerodynamics, structures and turbulence), a multibody dynamic simulator, was used to compute the aerodynamic loads. The span-wise distributions of the instantaneous aerodynamic loads generating the highest blade deflections for DLC 6.2 and 1.4 are shown in Figure 2b,c. The flap-wise aerodynamic loads ${\mathrm{p}}_{\mathrm{y}}$, in general, were higher than the edge-wise loads ${ \mathrm{p}}_{\mathrm{x}}$ for both DLCs. A higher flap-wise load at the inboard of the stationary blade for DLC 6.2 is caused by the wind-induced drag forces, mainly influencing the vicinity of the blade root, as shown in Figure 2b. On the other hand, a higher flap-wise load at the outboard of the rotating blade for DLC 1.4 is caused by the wind-induced lift forces, predominantly acting at the vicinity of the blade tip, as shown in Figure 2c. It should be noted that the computed aerodynamic loads were used as the steady state loads for verification of the blade model as well as its spar optimization.

The blade model was verified before its spar optimization.

Table 2. Blade model verification for DLC 6.2.

Description	Computed	Reported [8]	Difference (%)
Mass (kg)	112,650	114,172	−1.3
Tip deflection (m)	12.04	12.3	−2.1
Max. peak strain (u)	3147	2662	18.2
Buckling load factor (-)	2.37	2.23	6.5
First mode frequency (Hz)	0.45	0.42	7.1

lists a comparison of computed and reported results for DLC 6.2. The computed values of blade mass, tip deflection, buckling load factor and first mode frequency of 112,650 kg, 12.04 m, 2.37 and 0.45 Hz, respectively, were in a good agreement with those reported. However, a noticeable difference in the peak strain results was observed. The peak strains represent the highest values of tensile and compressive longitudinal strains, computed span-wise at the outermost layer of the composite layup along the blade pressure-side and suction-side surfaces. The maximum peak strain then can be estimated by taking the maximum of a span-wise peak strain distribution. Consequently, the maximum value of peak tensile strain of 3147 u occurring at the maximum chord along the blade pressure-side was almost 18% higher. This difference could be due to different methods employed to estimate the peak strains. Similar findings were observed for DLC 1.4 but are not discussed for brevity.

5. Formulation of Optimization Problem

The pressure-side and suction-side spars of SNL blades are made of the stacked layers of UD E-glass/epoxy laminates (shortly named as reference all-glass spars). The span-wise thickness distribution of the reference spars is shown in Figure 3a. The thickness is zero at the root, increases almost linearly to the maximum value of 136 mm near a 19.5 m span, that remains constant up to a 24.9 m span, and then decreases almost linearly to zero again at the tip. It should be noted that the reference all-glass spars are not optimized.

Use of an all-glass composite for the reference spars for the SNL blade is due to its low material cost. A substantial reduction in the blade mass is possible if the spars built with light weight, stiffer and stronger UD carbon/epoxy laminates (named shortly as all-carbon spars) are used. All-carbon spars also improve the blade structural performance significantly but are an expensive alternative. It is therefore rational to use the hybrid spars made by mixing the UD glass-fiber and carbon-fiber composites to lower both the blade mass and cost, and further mass reduction can be materialized by deploying the optimized all-glass, hybrid and all-carbon spars.

To explore the blade mass potential along with the cost incurred using the optimized spars, a single-objective multi-constraint optimization strategy was adopted. Multi-objective optimization was avoided as it is computationally intensive and difficult to converge. Consequently, single-objective spar optimization problems for three cases listed in

Table 3. Spar optimization cases.

Description	Objective Function
Case 1 (all-glass)	Mass or cost
Case 2a (hybrid)	Mass
Case 2b (hybrid)	Cost
Case 3 (all-carbon)	Mass or cost

were solved. Case 1 refers to the optimization of all-glass spars using the blade mass or cost objective function, case 2a-b refers to the optimization of hybrid spars using the blade mass and cost objective functions and case 3 refers to the optimization of all-carbon spars using the blade mass or cost objective function. For cases 1 and 3, the blade mass or cost minimization leads to the same result because the spars are made of single material. However, the blade mass minimization for case 2a and the blade cost minimization for case 2b give different results as the glass-fiber and carbon-fiber composites in the hybrid spars contribute differently to the blade mass and cost. The mass minimization favors the light-weight carbon-fiber composite while the cost minimization favors the low cost glass-fiber composite.

To run the optimization cases, the material properties and costs of the UD glass-fiber and carbon-fiber composites are needed. The density and stiffness properties of the glass-fiber composite are listed in Table 1, and those of the carbon-fiber composite are listed in

Table 4. Mechanical properties of UD carbon/epoxy laminate.

Properties	Values
Density (kg/m3)	1220
${\mathrm{E}}_{\mathrm{L}}$ (GPa)	114.5
${\mathrm{E}}_{\mathrm{T}}$ (GPa)	8.39
${\mathrm{G}}_{\mathrm{LT}}$ (GPa)	5.99
${\mathrm{v}}_{\mathrm{LT}}$ (-)	0.27

, taken from [7]. The estimation of blade mass is straight forward using densities of the layup materials; however, the material cost data to estimate the blade cost are not available. Consequently, the cost of glass-fiber and carbon-fiber composites of 1$/kg and 10$/kg taken from [16,20] was used and a unit cost was assumed for the other materials in the rest of composite layup to simplify the cost estimation.

For the spar optimization, it is assumed that (a) the computed steady-state aerodynamic loads acting on the SNL blade for DLCs 6.2 and 1.4 do not change during optimization, (b) the E-glass/epoxy and carbon/epoxy composites and their hybrid forms are used in the spar layup, (c) the bonding between the mating edges of blades halves and between the blade halves and the webs is perfect, (d) the optimization of the pressure-side and suction-side spars is conducted simultaneously as both spars are symmetric in terms of geometry and material, and (e) the fatigue design requirement is not included as it increases the problem complexity because a whole spectrum of loading conditions covering the entire design life of a turbine is needed to be accounted for; besides, it does not drive the design of the SNL blade [8].

5.1. Objective Function

The blade mass and cost objective functions ${\mathrm{f}}^1\left({\mathrm{x}}_{\mathrm{i}}\right)$ and ${\mathrm{f}}^2\left({\mathrm{x}}_{\mathrm{i}}\right)$ used for the spar optimization cases listed in Table 3 are expressed by Equation (1). It should be noted that the blade mass (cost) comprises the spar mass (cost) and the mass (cost) of the rest of the layup materials.

$$\begin{gathered} {\mathrm{F}}^1\left({\mathrm{x}}_{\mathrm{i}}\right)= \mathrm{Blade} \mathrm{mass} ={\displaystyle \sum }_{\mathrm{j}}{\mathsf{\rho }}_{\mathrm{j}}{\mathrm{V}}_{\mathrm{j}} \\ {\mathrm{f}}^2\left({\mathrm{x}}_{\mathrm{i}}\right)= \mathrm{Blade} \cos \mathrm{t} ={\displaystyle \sum }_{\mathrm{j}}{\mathsf{\rho }}_{\mathrm{j}}{\mathrm{V}}_{\mathrm{j}}{\mathrm{C}}_{\mathrm{j}} \end{gathered}$$

(1)

where${ \mathrm{x}}_{\mathrm{i}}$ represents the design variables, and ${\mathsf{\rho }}_{\mathrm{j}}$, ${\mathrm{V}}_{\mathrm{j}}$ and ${\mathrm{C}}_{\mathrm{j}}$ represent the densities, volumes and costs of the layup materials.

5.2. Design Variables

The thickness distribution of the reference all-glass spars of the SNL blade spanning from 6.8 m to 78.5 m along the blade length, as shown in Figure 3b, is considered for optimization. The spars are discretized into 5 layers to take into account its manufacturability. The thickness and the location of each layer in the layered spar are represented by 15 design variables, as expressed by Equation (2).

$${\mathrm{x}}_{\mathrm{i}}={\left[{\mathrm{x}}_1,{ \mathrm{x}}_2,{\mathrm{x}}_3,\dots ,{\mathrm{x}}_{15}\right]}^{\mathrm{T}}$$

(2)

where design variables ${\mathrm{x}}_1$ to ${\mathrm{x}}_5$, ${\mathrm{x}}_6$ to ${\mathrm{x}}_{10}$ and ${\mathrm{x}}_{11}$ to ${\mathrm{x}}_{15}$ represent the thicknesses, the in-board and outboard locations of the layers of discretized spar. A thickness or location value between two design variables is linearly interpolated.

To address the manufacturability of hybrid spars, the layer materials were varied gradually from layer 1 to layer 5. Since the hybrid spars comprised a mix of the glass-fiber and carbon-fiber composites, all-glass material (100% glass-fiber composite and zero carbon-fiber composite) were used for layer 1. The proportion of glass-fiber composite then decreased, while that of the carbon-fiber composite increased for layer 2 and so on, until the last 5th layer with an all-carbon composite (zero glass-fiber composite and 100% carbon-fiber composite) was reached.

The density and stiffness properties of spar layers were controlled with a mixing ratio parameter ${\mathrm{mx}}_{\mathrm{p}}$ based on the rule of mixture approach. The ${\mathrm{mx}}_{\mathrm{p}}$ defines the properties of each pth layer in terms of the properties of glass-fiber reinforced plastic (GRP) and carbon-fiber reinforced plastic (CRP) composites, as expressed by Equation (3).

$${\mathrm{Properties} \mathrm{of} \mathrm{p}}^{\mathrm{th}} \mathrm{spar} \mathrm{layer} =\left(1-{\mathrm{mx}}_{\mathrm{p}}\right)\times \mathrm{GRP}+{\mathrm{mx}}_{\mathrm{p}}\times \mathrm{CRP} (\mathrm{p} =1,2,\dots ,5)$$

(3)

The ${\mathrm{mx}}_{\mathrm{p}}$ varied from 0 to 1, and the sets of ${\mathrm{mx}}_{\mathrm{p}}$ values used to model the all-glass, hybrid and all-carbon layered spars are listed in

Table 5. Values of mixing ratio parameter ${\mathrm{mx}}_{\mathrm{p}}$ used.

Spar Layer #	Case1 (All-Glass)	Case 2a-b (Hybrid)	Case 3 (All-Carbon)
1	0	0	1
2	0	0.25	1
3	0	0.50	1
4	0	0.75	1
5	0	1	1

.

5.3. Bounds and Constraints

Bounds and constraints were imposed on the design variables to get feasible solutions by taking into account the material continuity and fabrication considerations. The lower and upper bounds ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{L}}$ and ${ \mathrm{x}}_{\mathrm{i}}^{\mathrm{U}}$ are defined using Equation (4), while the thickness and location constraints ${\mathrm{x}}_{\mathrm{j}}$ and ${\mathrm{x}}_{\mathrm{k}}$ are defined using Equation (5).

$${\mathrm{x}}_{\mathrm{i}}^{\mathrm{L}} \le { \mathrm{x}}_{\mathrm{i}} \le { \mathrm{x}}_{\mathrm{i}}^{\mathrm{U}}, \left(\mathrm{i} =1, 2, \dots ,15\right)$$

(4)

$$\begin{gathered} {\mathrm{x}}_{\mathrm{j}}\ge 0, \left(\mathrm{j} =1, 2, \dots ,5\right) \\ {\mathrm{x}}_{\mathrm{k}+1}-{\mathrm{x}}_{\mathrm{k}}\ge 0, (\mathrm{k} =6,7,\dots ,14) \end{gathered}$$

(5)

5.3.1. Stiffness

This requirement prevents collision of the blade with the tower and is expressed as the blade tip deflection using Equation (6).

$$\mathsf{\delta }\le {\mathsf{\delta }}_{\mathrm{allow}}$$

(6)

where $\mathsf{\delta }$ and ${\mathsf{\delta }}_{\mathrm{allow}}$ represent the computed tip deflection caused by incident winds and the allowable clearance between the rotor blades and the tower. The $\mathsf{\delta }$ must be lower than that of ${\mathsf{\delta }}_{\mathrm{allow}}$ for a safe design. It should be noted that a total clearance of 19.54 m estimated by taking into account the rotor overhang, shaft tilt angle, pre-cone angle, tower radius and blade length of 8.16 m, 5.0 degrees, 2.5 degrees, and 2.0 m, and 100 m, respectively, exists between the rotor blades and the tower for the 13.2 MW wind turbine [8]. Consequently, the ${\mathsf{\delta }}_{\mathrm{allow}}$ values of 18.56 m and 13.68 m were estimated for DLCs 6.2 and 1.4 by applying a minimum allowable clearance requirement of 5% for a parked rotor and 30% for a rotating rotor, as recommended by the wind turbine standard [14].

5.3.2. Strength

This requires that the maximum strains generated in the layup materials due to loads must be lower or equal to corresponding allowable strains as expressed by Equation (7).

$${\mathsf{ϵ}}_{\max }\le {\mathsf{ϵ}}_{\mathrm{allow}}$$

(7)

where ${\mathsf{ϵ}}_{\max }$ and ${\mathsf{ϵ}}_{\mathrm{allow}}$ represent the maximum value of peak strains along the blade pressure- and suction-sides and the allowable strains. The ${\mathsf{ϵ}}_{\mathrm{allow}}$ values are computed by applying load and material reduction factors to the ultimate strains of the layup materials, as recommended by the wind turbine standard [14]. The reduction factors cover the load-related uncertainties and the effects of material aging, the environment and the method of manufacturing. Strength analysis of the UD and BX laminates are carried out only due to fact that the spars made of UD laminates and the sandwich constructed webs made of BX laminates and a foam core, form a box-beam mainly contributing to the blade bending stiffness. For case 1, the allowable tensile and compressive strains of 8196 u and −5139 u were computed after applying the load and material reduction factors of 1.35 and 2.205 for the UD all-glass laminates, and those of 7256 u and −6046 u were computed after applying the load and material reduction factors of 1.1 and 2.205 for the BX laminates, from corresponding ultimate strains listed in Table 1. The same allowable strains were also used for cases 2 and 3, as relevant strain data were neither available nor needed, as the strength requirement is not a key design driver for SNL blade [8].

5.3.3. Stability

This requires estimation of the blade buckling resistance to a catastrophic failure, and is expressed by Equation (8).

$$\mathsf{\lambda }\le 1$$

(8)

where λ represents the value of buckling criterion that must be less or equal to 1 for a safe design. For stability analysis, critical stresses in the pressure-side and suction-side panels and the web panels are computed considering the panel geometry and materials by applying a combined material partial factor of safety of 2.042 for the skin laminates and that of 1.856 for the foam core, as specified by the wind turbine standard [14]. Finally, the λ value for each panel is estimated by Equation (9) [31].

$$\mathsf{\lambda } ={\left(\frac{{\mathsf{\sigma }}_{\mathrm{c}}}{{\mathsf{\sigma }}_{\mathrm{c},\mathrm{crt}} }\right)}^{\mathrm{a}}+{\left(\frac{\mathsf{\tau }}{{\mathsf{\tau }}_{\mathrm{crt}} }\right)}^{\mathrm{b}}$$

(9)

where ${\mathsf{\sigma }}_{\mathrm{c}}$ and $\mathsf{\tau }$ represent the in-plane compressive normal and shear stresses caused by incident loads, and ${\mathsf{\sigma }}_{\mathrm{c},\mathrm{crt}}$ and ${\mathsf{\tau }}_{\mathrm{crt}}$represent the critical in-plane compressive normal and shear stresses causing buckling in the blade panels. The exponents a and b were set to be 1 and 1.5 for the pressure-side and suction-side panels, and 2 for the web panels.

5.3.4. Resonance

To avoid resonance, the blade natural frequency must not coincide with the turbine rotational speed and this requirement is imposed by Equation (10).

$$\left|{\mathrm{f}}_1-{\mathrm{f}}_{\mathrm{R}}\right|\ge \mathsf{\Delta }$$

(10)

where ${\mathrm{f}}_1$ and ${\mathrm{f}}_{\mathrm{R}}$ represent the blade first natural frequency and the turbine rotational frequency and $\mathsf{\Delta }$ represents the difference between ${\mathrm{f}}_1$ and ${\mathrm{f}}_{\mathrm{R}}$. The ${\mathrm{f}}_{\mathrm{R}}$ value of 0.124 Hz was estimated from the rated rotational speed of 7.44 rpm of the turbine and the $\mathsf{\Delta }$ value was set to 0.25 Hz to avoid resonance.

5.4. Data Normalization

In view of huge differences in the dimensions of design variables and objective functions, all data are normalized on a scale 0–1. Data normalization also speeds up the optimization. So, the normalized design variables ${\overline{\mathrm{x}}}_{\mathrm{i}}$ are computed from the lower and upper bounds ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{L}}$ and ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{U}}$ on design variables ${\mathrm{x}}_{\mathrm{i}}$ using Equation (11).

$${\overline{\mathrm{x}}}_{\mathrm{i}}=\frac{{\mathrm{x}}_{\mathrm{i}}-{ \mathrm{x}}_{\mathrm{i}}^{\mathrm{L}}}{{\mathrm{x}}_{\mathrm{i}}^{\mathrm{U}}-{ \mathrm{x}}_{\mathrm{i}}^{\mathrm{L}}}$$

(11)

Similarly, the mass and cost objective functions are also normalized on a scale 0–1 by the mass and cost of the SNL blades with the reference spars.

5.5. Genetic Algorithm Method

The optimization problem is solved using the genetic algorithm (GA) method, which is widely popular among the researchers working in the field of composites structures [32,33,34]. The method mimics the natural selection process observed in biological sciences. It is a population-based stochastic algorithm that attempts to achieve a global optimal solution by performing crossover and mutation operations among the population members.

A general view of the GA optimization method is shown in Figure 4. The process begins with an initial population consisting of individuals defining the blade spar. Each individual is evaluated using a fitness function. For fitness evaluation of each individual, blade stiffness, strength and stability analyses were carried out in Co-Blade and the resonance analysis was performed using the BModes program integrated to Co-Blade by means of MATLAB environment [35]. It should be noted that the aerodynamic loads previously computed from the dynamic simulations of a 13.2 MW wind turbine model were used for the blade structural analyses during optimization.

Based on the fitness value, the individuals are chosen to reproduce their offspring for next generation by applying the principles of natural selection, cross-over and mutation. Once the maximum number of generations is reached, the iterative process ends and an optimal solution is obtained.

For GA based optimization, a fitness function encompassing the objective function and the design constraints in terms of penalties is formulated, as expressed by Equation (12).

$$\begin{gathered} \min \mathrm{F}\left({\overline{\mathrm{x}}}_{\mathrm{i}}\right)={ \mathrm{f}}^{\mathrm{m}}\left({\overline{\mathrm{x}}}_{\mathrm{i}}\right)\times {\displaystyle \prod }_{\mathrm{n} =1}^4\max {\left(1,{\mathrm{p}}_{\mathrm{n}}\right)}^2 \\ {\mathrm{p}}_1=\frac{\mathsf{\delta }}{{\mathsf{\delta }}_{\mathrm{allow}}}, {\mathrm{p}}_2=\frac{{\mathsf{ϵ}}_{\max } }{{\mathsf{ϵ}}_{\mathrm{allow}}}, {\mathrm{p}}_3=\mathsf{\lambda }, {\mathrm{p}}_4=\frac{\mathsf{\Delta }}{\left|{\mathrm{f}}_1-{ \mathrm{f}}_{\mathrm{r}}\right|} \end{gathered}$$

(12)

where $\mathrm{F}\left({\overline{\mathrm{x}}}_{\mathrm{i}}\right)$ and ${\mathrm{f}}^{\mathrm{m}}\left({\overline{\mathrm{x}}}_{\mathrm{i}}\right)$ represent the fitness function and the m^th normalized objective function (i.e., set $\mathrm{m} =1$ for the blade mass objective function, or $\mathrm{m} =2$ for the blade cost objective function, as depicted by Equation (1)), and ${\mathrm{p}}_{\mathrm{n}}\left(\mathrm{n} =4\right)$ represents n penalties describing 4 design constraints, each having a value equal to 1 for a feasible solution, or otherwise higher to a value proportionate to the magnitude of a constraint violation.

The single-objective multi-constraint optimization problem was solved in MATLAB environment by setting the number of individuals and the number of generations to be 20 and 250, along with the crossover and mutation probabilities of 0.8 and 0.01. A summary of bounds and constraints on the design variables is listed in

Table 6. Summary of bounds and constraints.

Parameters	Lower Bound (LB)	Upper Bound (UB)	Units
${\mathrm{x}}_1-{\mathrm{x}}_5$	0	25	mm
${\mathrm{x}}_6-{\mathrm{x}}_{15}$	6.8	78.5	m
$\mathsf{\delta }$		18.56 (DLC 6.2) 13.68 (DLC 1.4)	m
${\mathsf{ϵ}}_{\max }$		8196, −5139 (UD laminate) 7256, −6046 (BX laminate)	$\mathrm{u}$
$\mathsf{\lambda }$		1
${\mathrm{f}}_1$	$\le {\mathrm{f}}_{\mathrm{r}}$$-$$0.25 \mathrm{or} \ge {\mathrm{f}}_{\mathrm{r}}$$+$ 0.25		Hz

.

6. Results and Discussion

Figure 5 shows convergence histories of the normalized mass objective function for DLC 6.2. For case 1, the minimization of the objective function ended after 250 complete iterations as no constraint or bound was violated. Additional mass reduction can be achieved by running more iterations but the result is considered satisfactory due to the narrow prospect of significant gain at an increased computational cost. For cases 2 and 3, the optimization stopped after 210 and 223 iterations as the buckling constraint was consumed, resulting in global optimal solutions. Similar observations were made for the optimization cases run for DLC 1.4, but are not discussed to avoid repetition.

Figure 6a–d shows a comparison of thickness distributions of the reference and the optimized spars. For all cases, the spar thickness in general decreases and the location of the highest thickness tended to shift towards the blade mid-span. For case 1, the optimized thickness distribution for DLC 1.4 fully covers that for DLC 6.2, indicating that the DLC 1.4 governs design optimization of the all-glass spars. The optimization for DLC 1.4 ended as the tip deflection constraint of 13.68 m was consumed, but no constraint or bound was violated for DLC 6.2. For the optimized all-glass spars, the highest thickness of 74.5 mm and 102.5 mm occurred at a 31–43 m and 36–48 m span for DLCs 6.2 and 1.4, as shown in Figure 6a. On the other hand, for cases 2a-b and 3, the thickness distributions for both DLCs are almost close to each other and tend to be flat, as is clearly noticeable for the optimized all-carbon spars in particular. This is caused by the presence of a stiffer and stronger carbon-fiber composite in the spars. For the optimized hybrid spars, using mass objective function (case 2a), the highest thickness achieved was 59.8–63.1 mm, occurring at a 36.5–45.2 m span, as shown in Figure 6b; for the optimized hybrid spars, using the cost objective function (case 2b), the highest thickness achieved was 57.63–64.3 mm, which occurred at a 40.3–53.7 m span, as shown in Figure 6c. Similarly, the highest thickness achieved was 36.5–43.2 mm, which occurred at a 30.5–42.2 m span for the optimized all-carbon spars (case 3), as shown Figure 6d.

Table 7. Summary of design constraints after optimization.

Description	Optimization	DLC	Tip Deflection (m)	Maximum Peak Strain (u)	Buckling Criterion (−)	First Natural Frequency (Hz)
Case 1	Mass or cost	6.2	16.28	5779	0.76	0.41
		1.4	13.68	4987	0.71	0.42
Case 2a	Mass	6.2	14.92	8095	1.0	0.45
		1.4	13.65	7508	1.0	0.45
Case 2b	Cost	6.2	14.06	7923	1.0	0.44
		1.4	13.53	7386	1.0	0.43
Case 3	Mass or cost	6.2	11.25	5638	1.0	0.51
		1.4	11.33	5425	1.0	0.49

shows a summary of the design constraints at end of optimization. The tip deflection constraint was violated for case 1 for DLC 1.4 as it governs the design optimization of the all-glass spars. The strength constraint remained always below the allowable limits. The buckling constraint was fully consumed for cases 2 and 3 as a substantial reduction in the spar thickness occurred due to carbon-fiber composite. The resonance constraint was never breached as the first mode frequency did not coincide with the turbine rotational frequency.

The blade tip deflection increased for case 1, the all-glass spars, due to thickness reduction. The deflection also increased for case 2a-b despite the presence of the stiffer carbon-fiber composite along with the glass-fiber composite in the hybrid spars. The carbon-fiber composite indeed improved the blade bending stiffness but this effect was overcome by the spar thinning and, as a result, the blade overall stiffness decreased and tip deflection increased. On the contrary, the tip deflection decreased for case 3, irrespective of the thickness reduction in the all-carbon spars. The lowest and highest tip deflections of 11.25 m and 16.28 m were observed for cases 3 and 1.

In case of the blade strength, the maximum peak strains were always tensile and appeared along the pressure-side spar for all cases. In comparison to the reference spars, the peak strains increased for all cases due to reduction in the spar thickness after optimization. The lowest and highest peak strains of 8095 u and 5425 u were observed for cases 3 and 2b.

The blade buckling resistance decreased for all cases as it was sensitive to the spar thickness. The buckling failure occurred along the suction-side spar under compression. For case 1, the value of buckling criterion was 0.71, which is well below the allowable limit; however, for cases 2 and 3, the allowable limits were reached as excessive thinning of the spars occurred due to the stiffer carbon-fiber composite. In fact, if the buckling margin of the current optimized hybrid and all-carbons spars is increased using the foam core material in between the UD spar layers to build the sandwiched construction resistant to buckling, then further saving in the blade overall mass and cost is possible via its spar optimization, but no such attempt was made due to the limited scope of this work.

The blade first natural frequency lowered for cases 1 and 2. The reduction in the spar thickness lowered both the blade mass and stiffness; however, the stiffness reduction was in a higher proportion than the mass reduction; consequently, the blade natural frequency lowered. On the contrary, the first natural frequency increased for case 3 due to the all-carbon spars. The lowest and highest frequencies of 0.41 Hz and 0.51 Hz were observed for cases 3 and 1.

Figure 7 shows the optimization results in comparison to the SNL blade, with the reference all-glass spars having mass and cost values of 112,650 kg and 112,650$. The blade mass decreased for all cases. The mass reduction occurred gradually from case 1 to case 3, as shown in Figure 7a, due to reduction in the spar thickness and incremental addition of a light weight carbon-fiber composite. A mass reduction of 8.1–13.3%, 18.5–20.7% and 25.1–26.4% occurred for cases 1, 2 and 3, respectively. On the other hand, the blade cost decreased for case 1 only, as shown in Figure 7b, due to thinning of the all-glass spars. The cost increased for cases 2 and 3 due to use of the expensive carbon-fiber composite in the hybrid and all-carbon spars. A cost increase of 1.2–13.6% and 24.5–31.5% occurred for cases 2 and 3, respectively.

The most promising results observed were for cases 1 and 2b. The blade mass and cost reductions for case 1 were in a range of 8.1–13.3%, demonstrating an improved adjustment of UD E-glass/epoxy laminates in the all-glass spars. For case 2b, referring to the hybrid spar optimization using the cost objective function, a substantial reduction in the blade mass (i.e., 18.5–19.9%) occurred, accompanied by a marginal cost increment (i.e., 1.2–3.5%) as compared to that of the SNL blade with the reference spars, showing the effective use of lightweight but expensive UD carbon/epoxy composite in the hybrid spars. It also indicates an opportunity to further fine-tune the hybrid spars in such a manner that the blade overall mass lowers but its cost does not exceed that of the original design.

7. Conclusions

Mass reduction opportunities along with reduction of the cost incurred for a publicly available SNL blade model were explored using the optimized spars subject to incident aerodynamic loads computed for DLCs 6.2 and 1.4. The DLCs were chosen as they generated the worst wind loads for parked and spinning rotor blades at a rated speed of 7.44 rpm. Three types of spars made of UD all-glass, hybrid and all-carbon composites, referred to as cases 1, 2 and 3, respectively, were optimized for the blade model, while keeping the remaining layup unaffected. The blade mass and cost objective functions, along with relevant design variables, bounds and constraints, taking into account the spar manufacturability, were formulated in the form of a single-objective multi-constraint optimization problem. The minimization of each objective function was conducted using a genetic algorithm method, while meeting the stiffness, strength, buckling and resonance requirements, as recommended in the wind turbine standards.

The results show that the blade mass lowers for all cases due to decrease in the spar thickness after optimization. The mass reduction achieved was in the range of 8.1–13.3%, 18.5–20.7% and 25.7–26.4% for cases 1, 2 and 3, respectively. On the other hand, the blade cost for case 1, describing the blade with optimized all-glass spars, decreased, and for cases 2 and 3, it increased in the range of 1.2–13.6% and 24.5–31.5%, involving the inclusion of expensive carbon-fiber composite in the hybrid and all-carbon spars. It is interesting to note that the hybrid spars with the blade cost minimization (case 2b) provided a substantial mass saving of 18.5–19.9% along with a marginally increased cost of 1.2–3.5%, suggesting effectiveness of the blade cost objective function over the mass objective function for optimization of the hybrid spars.

The blade stiffness and first natural frequency decreased for cases 1 and 2 due to the spar thinning, but increased for case 3, the all-carbon spars, for which the use of a stiffer carbon-fiber composite improved the blade stiffness in a higher proportion than the stiffness reduction caused by the spar thinning. The maximum peak strains were tensile and appeared along the blade pressure-side spar. Its values increased for all cases due to a reduction in the spar thickness but remained within the allowable limits. The blade buckling resistance also decreased for all cases as it is sensitive to the spar thickness reduction. In fact, for cases 2 and 3, the buckling criterion was fully consumed and terminated the optimization.

The current work examines the blade mass reduction through the optimized all-glass, hybrid and all-carbon spars, while taking into account the incurring cost. Further improvements can be made by including the remaining layup in the optimization process.