investigating optimal leg distance, using conceptual ... · dtu 10 mw: tower, turbine, and loads....
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12 January 2017
Investigating Optimal Leg Distance, using Conceptual Design Optimization
Kasper Sandal
Alexander Verbart
Mathias Stolpe
Technical University of Denmark,
Dept. of Wind Energy
1
Conceptualdesign
Basic design
Detaileddesign
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12 January 20172
minimize 𝑓(𝒙)
subject to 𝐊 𝒙 𝒖 − ∆𝑷 = 𝟎
𝝈 ≤ 𝝈 𝒙 ≤ 𝝈
𝝎 ≤ 𝝎 𝒙 ≤ 𝝎
Design considerations Optimal design problem
Design trends
This talk presents conceptual design optimization of jacket structures for offshore wind turbines
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12 January 20173
Photo: Iberdrola
A good jacket design has low mass to minimize material, transportation, and installation costs
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12 January 20174
Photo: W S van Zyl; G P A G van Zijl
To avoid resonance, the natural frequency must lie in the soft-stiff range between the 1p and 3p rotor frequencies
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12 January 20175
Reference jackets in the literature have very different leg distances
12 m
8 m
OC4 jacket
Designed for NREL 5 MW
34 m
14 m
INNWIND.EU jacket Designed for DTU 10 MW
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12 January 20176
Placing the same tower and turbine on two jackets allows us to compare them
JADOP models with DTU 10 MW tower & turbine
12 m
8 m
OC4 jacket
Designed for NREL 5 MW
34 m
14 m
INNWIND.EU jacket Designed for DTU 10 MW
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12 January 20177
When cross sections are equal, a slender jacket will have a lower mass and a lower frequency than a bulky jacket
Slender 1060 tons 0.20 Hz
Bulky 1510 tons 0.27 Hz
JADOP models with DTU 10 MW tower & turbine Diameters = 1 m Thicknesses = 50 mm
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12 January 20178
To satisfy the fatigue and ultimate limit states, the cross sections have to change when the slenderness change
Slender 1060 tons 0.20 Hz
Bulky 1510 tons 0.27 Hz
JADOP models with DTU 10 MW tower & turbine Diameters = 1 m Thicknesses = 50 mm
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12 January 20179
minimize 𝑓(𝒙)
subject to 𝐊 𝒙 𝒖 − 𝒇(𝒙) = 𝟎
𝝈 ≤ 𝝈 𝒙 ≤ 𝝈
𝝎 ≤ 𝝎 𝒙 ≤ 𝝎 Stress
Frequency
𝒙 = cross sections
The optimization problem for conceptual design is formulated with static loads, and constraints on stress, buckling, and frequency
Jacket mass
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12 January 201710
Damage equivalent loads are used to make an approximate fatigue constraint using static stress constraints
Rainflow counting: ∆𝜎𝑖 , 𝑛𝑖
𝐷 = 𝑖𝑛𝑖(∆𝜎𝑖)
𝑚
𝑎≤ 𝐷𝑚𝑎𝑥
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12 January 201711
Damage equivalent loads are used to make an approximate fatigue constraint using static stress constraints
Rainflow counting: ∆𝑃𝑖 , 𝑛𝑖
𝑛𝑇(∆𝑃1𝐻𝑧)𝑚 = 𝑖 𝑛𝑖(∆𝑃𝑖)
𝑚
⇒ ∆𝑃1𝐻𝑧=1
𝑛𝑇 𝑖 𝑛𝑖(∆𝑃𝑖)
𝑚
1
𝑚
∆𝜎1𝐻𝑧
Equal fatigue damage
𝐷 =𝑛𝑇 ∆𝜎1𝐻𝑧 𝑚
𝑎≤ 𝐷𝑚𝑎𝑥
∆𝜎1𝐻𝑧≤ ∆𝜎 =𝐷𝑚𝑎𝑥 𝑎
𝑇𝑙𝑖𝑓𝑒
1
𝑚
Quasi-static behaviour
1 degree of freedom load
High-cycle SN-curve
Rainflow counting: ∆𝜎𝑖 , 𝑛𝑖
𝐷 = 𝑖𝑛𝑖(∆𝜎𝑖)
𝑚
𝑎≤ 𝐷𝑚𝑎𝑥
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The problem is solved using the JAcket Design OPtimization tool JADOP and the open source optimization solver IPOPT
• Parametric input
• Analytic sensitivities
• Many types of constraints
DTU 10 MW: Tower, turbine, and loads
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12 January 201713
With leg distances from the INNWIND.EU jacket, the mass was minimized to 870 tons in 2 minutes on a laptop
Top leg distance = 14 m
Bottom leg distance = 34 m
Jacket mass = 870 tons
Natural frequency = 0,264 Hz
Computation time = 118 s
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12 January 201714
Optimization of 400 jackets indicate that an increased top leg distance reduces the jacket mass with about 20 percent
INNWIND.EU leg distances
Top leg distance = 14 m
Bottom leg distance = 34 m
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Since transition piece mass increases with larger top leg distance, the overall mass reduction is much less
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12 January 201716
Upper bound on soft-stiff range
High leg distances at both bottom and top increase the natural frequency
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Reducing the bottom leg distance of the INNWIND.EU jacket from 34 to 24 meters, reduces both overall mass and frequency
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In conclusion, the conceptual design optimization is a fast and useful tool for investigating key parameters such as leg distance
Bottom leg distance: 34 m 24 m
Mass: -6.7 percent
Frequency: -2.8 percent
Can also be used for pile stick-up, number of sections, height, etc.
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12 January 201719
In conclusion, the conceptual design optimization is a fast and useful tool for investigating key parameters such as leg distance
Bottom leg distance: 34 m 24 m
Mass: -6.7 percent
Frequency: -2.8 percent
Can also be used for pile stick-up, number of sections, height, etc.
Questions?
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EXTRA SLIDES
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Design according to DNVGL offshore standard and recommended practices
DNVGL-OS-C101 Design of offshore steel structures
DNVGL-RP-C203 Fatigue design of offshore steel structures
DNV-RP-C202 Buckling strength of shells
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Optimal design problem
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Load cases
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Shell buckling
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Column buckling
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SCF validity constraints
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Stress & SCF