Darrieus Blade FEM for MCS Certification

4.1. Load cases (from IEC 61400-2 plus other identified cases) Ten load cases that comprising the SLM are tabulated in Table 4-. For each load case, the appropriate

type of analysis is stated (i.e. fatigue or ultimate loads). Note only Case A is a fatigue load.

Table 4-8: Design load cases

Design situation Load

case

Description Wind inflow Type of

analysis

Comment for

DS1500 VAWT

Power

production

A Normal operation Vdesign = 1.4 Vave Fatigue

B Yawing Ultimate Not needed,

no yawing for

VAWT

C Yaw error Ultimate Not needed,

no yawing for

VAWT

D Maximum thrust 2.5 Vave Ultimate

Power

production plus

occurrence of

fault

E Maximum

rotational speed

- Ultimate

F Short at load

connection

Vdesign Ultimate

Shutdown G Braking Vdesign Ultimate

Parked (idling or

stand still)

H Parked wind

loading

Ve50 = 1.4 Vref Ultimate

Parked at fault

conditions

I Parked wind

loading (maximum

exposure)

Ultimate Not needed,

turbine standing

still when parked

Transport,

assembly,

maintenance and

repair

J Crane lifting - Ultimate Defined by

manufacturer for

extreme case

Each of the necessary load cases are described in the Section 4.1. The intention of the description is to

create a general understanding of the background for the equations.

5.1. Darrieus blade

5.1.1. Material description

Darrieus blades are made from extruded A6063-T5 aluminum alloy. The shell manufactured to follow

NACA 0015 with chord length of 180 mm.

5.1.2. Mechanical properties for structural analysis

Characteristic values for key mechanical properties of A6063-T5 are listed in Table .

Table 5-4 Mechanical properties of A6063-T5

Properties Value

Density, ρ (kg/m3) 2700

Modulus of elasticity, E (GPa) 68.90

Poisson’s ratio, ν 0.330

Material fatigue limit strength (MPa) 68.90

Material ultimate limit strength (MPa) 56.36

5.1.3. Description of finite element model

Finite element modeling makes it possible to take into account previously described material properties,

enabling structural analysis. The analyses are carried out using SolidWorks Simulation.

The general computational model used for all load cases is described below.

Model information

Figure 5-3 Darrieus blade model

Figure 5-4 Darrieus blade mesh

The basis mesh for Darrieus blade analysis is created using high quality tetrahedral elements. The mesh

details are tabulated below:

Table 5-5 Mesh/ element property for Darrieus blade analysis

Mesh / element property Value

Total nodes 1102084

Total elements 589982

Max element size 5 mm

Min element size 3.5 mm

Maximum aspect ratio 11.832

Elements with aspect ratio < 3 96.8%

Restraints

The Darrieus blade is fixed on both of its end to the upper connector and lower connector. The fixture sets

all translational degrees of freedom to zero.

Table 5-6 Restraint for structural analysis of Darrieus blade

Fixture name Fixture Image Fixture Details

Fixed

represents

bolted

connection to

connector

Entities: 6 face(s) Type: Fixed Geometry

Fixed

represents

bolted

connection to

connector

Entities: 6 face(s) Type: Fixed Geometry

On flat faces

represents

contact surface

to connector

Entities: 1 face(s) Type: On Flat Faces

Translation: ---, ---, 0 Units: mm

Fixture name Fixture Image Fixture Details

On flat faces

represents

contact surface

to connector

Entities: 1 face(s) Type: On Flat Faces

Translation: ---, ---, 0 Units: mm

Loads

The blade loads are defined in section 4.1. They are repeated in table below for easy reference.

Table 5-7 Loads for fatigue analysis of Darrieus blade

Load case Loading type Scale factor Maximum

loading

Value Loading ratio

A Centrifugal 1.25 ωz-max,B -293 rpm 0.454

Gravity g -9.81 m/s2 1

Table 5-8 Loads for ultimate analysis of Darrieus blade

Load case Loading type Loading Value

E Centrifugal ωz,B -293 rpm

Gravity g -9.81 m/s2

F Short circuit Mz,B 40.35 N.m

Gravity g -9.81 m/s2

G Braking Mz,B 253.86 N.m

Gravity g -9.81 m/s2

H Wind Fx,B -1248.93 N

Gravity g -9.81 m/s2

The load models consider the loads to be acting on the whole Darrieus blade. The centrifugal loads are

applied with reference to the rotor axis.

Figure 5-5 Loads for load case A and E

Figure 5-6 Loads for load case F and G

Figure 5-7 Loads for load case H

5.1.4. Fatigue analysis

This section shows analysis plots of the fatigue load case. The first figure shows the equivalent von Mises

stress plot, while the second figure shows the damage occurred for the assumed load modeling.

Load case A

Figure 5-8 Equivalent von Mises stress for load case A

Figure 5-9 Damage after 2x109 cycles for load case A

Table 5-9 Summary of results of fatigue analysis, comparison to fatigue limit strength and damage

percentage

Equivalent von Mises

Stress (MPa)

Material Fatigue Limit

Strength (MPa)

Damage

Load Case A 20.82 68.90 4%

5.1.5. Ultimate analysis

This section shows analysis plots of the ultimate load cases. The figures show the equivalent von Mises

stress plot for each load assumption from load case E to load case H.

Load case E

Figure 5-10 Equivalent von Mises stress for load case E

Load case F

Figure 5-11 Equivalent von Mises stress for load case F

Load case G

Figure 5-12 Equivalent von Mises stress for load case G

Load Case H

Figure 5-13 Equivalent von Mises stress for load case H

Table 5-10 Summary of results of ultimate analysis and comparison to material ultimate limit strength

Equivalent von Mises Stress

(MPa)

Material Ultimate Limit Strength

(MPa)

Load Case E 20.82 56.36

Load Case F 3.61 56.36

Load Case G 5.86 56.36

Load Case H 8.19 56.36

5.1.8. Summary of Darrieus blade analysis

Through stress analysis, the structural integrity of the Darrieus blade was verified in all load cases. The

limit states were not exceeded in all of the load cases.

Through deflection analysis it was verified that the maximum Darrieus blade deflection does not cause

mechanical interference between the blade and the tower.

Modal characteristics of the Darrieus blade were investigated and it was found that the possible excitation

frequencies of the turbine do not coincide with the natural frequencies of the blade.