Darrieus Blade FEM for MCS Certification
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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.
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