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DNV GL © 2015 30 August 2017 SAFER, SMARTER, GREENERDNV GL © 2015
30 August 2017Arne Nestegård
OIL & GAS
Retningslinjer for lavfrekvent respons av flytere
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Konstruksjonsdagen, Ptil
DNV GL © 2015 30 August 2017
Background
Several line breakages on MODUs and floating production units may be attributed to overload during heavy weather.
Need to improve methods, procedures and standard industry practice in mooring line design predictions of nonlinear wave loads in large sea states.
In particular, the significant effect of low-frequency floater motions on extreme mooring loads needs attention.
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DNV GL © 2015 30 August 2017
Exwave JIP – Wave Forces on Floating Units in Extreme Seas
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MARINTEKNorwegian Marine Technology Research Institute
DNV GL © 2015 30 August 2017
Exwave JIP objectives
Identify, explore and describe technology gaps that can explain the occurrence of extreme wave-induced forces higher than expected, which may result in overload and line breakages in extreme seas.
Emphasis shall be on low-frequency (slowly varying) wave forces leading to slow drift vessel motions and deviations from classical 2nd order wave drift forces
Recommend improvements with guidelines in industry practice, taking into account proper modeling of low-frequency wave forces
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DNV GL © 2015 30 August 2017
Exwave - Handbook on low-frequency wave forces and response
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Contents• Introduction
• Main characteristics of moored floaters
• Wave and current loads
• Hydrostatic loads
• Steady current loads
• Wave frequency loads
• Slowly varying wave loads
• Simplified formulas
• Damping of low frequency motion
• Modelling alternatives
• Computational Fluid Dynamics
• De-coupled and coupled response analysis
• Validation and calibration of slowly varying forces and response
• General guidance on model testing
• Main findings in Exwave JIP
DNV GL © 2015 30 August 2017
Design equation and safety factors (DNVGL-OS-E301)
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The design equation for the ULS may be given by characteristic mean and dynamic tension and partial safety factors
TC-mean = characteristic mean line tension from mean environmental loads TC-dyn = characteristic dynamic line tension from LF and WF motions SC = characteristic mooring line capacity γ = partial safety factor
Class 1: Where mooring line failure is unlikely to lead to unacceptable consequences (loss of life, collision with adjacent platform, uncontrolled outflow of oil or gas, capsize or sinking)
Class 2: Where mooring line failure may well lead to unacceptable consequences of these types
0≥⋅−⋅− −− dyndynCmeanmeanCC TTS γγ
DNV GL © 2015 30 August 2017
Forces from waves, wind and currrent
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WF Mean LF
Waves 1st order wave frequency force
• 2nd order meanwave drift force
• 2nd order low frequency (slowly varying) force
• Wave drift damping
Wind • Mean wind force • LF force due to LF wind gusts
Current • Mean current force• Modifies mean wave
drift force
• Damping of LF motion• Modifies LF wave loads
DNV GL © 2015 30 August 2017
Floater excitation forces
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risermoorextWAWACUWIt qqqqqqqxx,q ++++++= )2()1(),(
Mean andLF windforce Mean
currentforce
WFwaveforce Mean and
LF wave force
Mooringforce
Riserforce
Other external force
DNV GL © 2015 30 August 2017
The challenge of mooring line tension predictions
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After calibrationModel test
Before calibrationModel test
Aksnes, V.Ø. (2014), "Correct" response in positioning analyses", Tekna Conference on DP and Mooring of Floating Structures Offshore, Trondheim, Norway, 12-13 February 2014
DNV GL © 2015 30 August 2017
Effect of sea state on wave drift force coefficient
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Comparing potential flow drift coefficient (WAMIT) with measured coefficient in 4 different sea states.
Verideep JIP – MARINTEK
Semi-submersible VISUND
Reported by Stansberg (ISOPE, 2001)
DNV GL © 2015 30 August 2017
DNVGL-OS-E301 Position mooring
3.4.2 The wave drift force coefficients calculated by standard wave diffraction analysis (potential theory) do not include viscous effects or current interaction effects. Current interaction effects on wave drift force shall be included together with viscous effects as relevant.
Viscous effects may be determined from experiments.
Current interaction effects can be extracted from model basin test with waves and current, or it can be calculated by an extended wave diffraction analysis. Such analysis shall be calibrated towards model basin results.
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DNV GL © 2015 30 August 2017
Simplified formula for current and viscous effects
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)()(~)( ωωω pdkB sum ⋅⋅=
))(95.0exp()( 30kDp −=ω
2)(1
)(~−+
=kLkk ω
OTC (2015)
( )
+−⋅⋅+⋅+=
ββ
αβωωβωsincos
)cos()()()cos1(),,( )(,, scepotidwccpscid HUGBfUCHUf
πNA
Nd WPsum
4=
DNV GL © 2015 30 August 2017
Validation of simplified formula
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Hs=11.5m – Tp = 12.5s – Uc = 0 m/s Hs=11.5m – Tp = 12.5s – Uc = 1.58 m/s – CollinearHs=11.5m – Tp = 12.5s – Uc = 0 m/s Hs=11.5m – Tp = 12.5s – Uc = 1.58 m/s – Non-collinear
Yang, Falkenberg, Nestegård & Birknes-Berg (2017) “Viscous Drift Force and Motion Analysis of Semi-Submersible in Storm Seastates compared with Model Tests” OMAE2017-62319
DNV GL © 2015 30 August 2017
Validation of response by simplified formula
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4040: Hs=11.5m – Tp = 12.5s – Uc = 0 m/s 4240: Hs=11.5m – Tp = 12.5s – Uc = 1.58 m/s – Collinear4320: Hs=11.5m – Tp = 12.5s – Uc = 0 m/s4350: Hs=11.5m – Tp = 12.5s – Uc = 1.58 m/s – Non-collinear
Mean
Std
Extreme
DNV GL © 2015 30 August 2017
Wave current interaction
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0
50
100
150
200
250
300
0.3 0.4 0.5 0.6 0.7 0.8 0.9
F 1(k
N/m
2 )
ω (rad/s)
U=0 m/s
U=0.4 m/s
U=0.8 m/s
DNV GL © 2015 30 August 2017
Wave current interaction
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Exwave semi-submersible. Collinear current Uc = 0.82 m/s.
DNV GL © 2015 30 August 2017
Aranha’s formula
)0,,(cos41),,,( redcwccd U
gU βωβωαβω FF
+=
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+= cwce U
gβωωω cos1
cw
cr g
Uβ
ωββ sin
2−=
= frequency of encounter
= frequency of encounter
αββ −=cw
DNV GL © 2015 30 August 2017
Slowly varying (LF) wave force - QTFs
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𝐹𝐹𝐿𝐿𝐹𝐹(𝑡𝑡) = 𝑅𝑅𝑅𝑅�𝑎𝑎𝑖𝑖𝑎𝑎𝑗𝑗𝐻𝐻(2)(𝜔𝜔𝑖𝑖 ,𝜔𝜔𝑗𝑗 )𝑅𝑅𝑖𝑖(𝜔𝜔𝑖𝑖−𝜔𝜔𝑗𝑗 )𝑡𝑡𝑁𝑁
𝑖𝑖 ,𝑗𝑗
Numerical prediction of QTFs
– Complete / simplified
Extracting QTFs from model tests
– Cross bi-spectral analysis
Newman’s approximation
Validity of Newman’s approximation
– Semis/FPSOs– Shallow/deep water
Unresolved: Effect of current and viscous effects on QTF.
DNV GL © 2015 30 August 2017
Damping of low frequency motion
Viscous hull damping
Wave drift damping
Mooring line damping
Thruster damping
Wind induced damping
Sea floor friction damping
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DNV GL © 2015 30 August 2017
Wave drift damping
Wave drift damping = rate of change of wave drift force wrt low frequency velocity of floater
Equivalence to wave current condition
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)()()0,(),( 2xOxBFxF dd +−= ωωω
0|)(
=∂∂
−=xx
FB d
ω
0
)(=
∂∂
=cUc
d
UF
B ω
𝐵𝐵 𝜔𝜔 ≈𝐹𝐹𝑑𝑑 𝜔𝜔,∆𝑈𝑈𝑐𝑐 − 𝐹𝐹𝑑𝑑 𝜔𝜔,−∆𝑈𝑈𝑐𝑐
2∆𝑈𝑈𝑐𝑐 0
50
100
150
200
250
300
0.3 0.4 0.5 0.6 0.7 0.8 0.9
F1
(kN
/m2)
ω (rad/s)
U=0 m/s
U=0.4 m/s
U=0.8 m/s
DNV GL © 2015 30 August 2017
Wave drift damping from Aranha’s formula
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dd F
gF
gB ω
ωωω 4)(
2
+∂∂
=
0
50
100
150
200
250
300
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7
F 1(k
N/m
2 )
ω (rad/s)
-200
-100
0
100
200
300
400
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7
B 11
(kN·
s/m
3 )
ω (rad/s )
Fd(ω)B(ω)
DNV GL © 2015 30 August 2017
Accuracy of Aranha’s formula
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DNV GL © 2015 30 August 2017
Modelling alternatives for LF wave excitation and damping
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DNV GL © 2015 30 August 2017
Morison modeling of viscous loads
Viscous drag excitation and damping from waves and current on hull is represented by the Morison drag model;
Relative velocity between floater and fluid particles is applied;
For the columns above the still water level (SWL), drag forces are integrated up to the actual free surface;
Both horizontal and vertical loads are accounted for.
Recommended drag coefficients from DNV-RP-C205.
Use asymmetry factor above SWL to account for enhanced wave kinematics relative to linear theory Yang et.al. (Exwave) OMAE2017-62319
DNV GL © 2015 30 August 2017
Statistics of surge motion comparison
DNV GL © 2015 30 August 2017
Computational Fluid Dynamics for wave drift force
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Modeling issues
– Vessel motions: Moving rigid mesh following the vessel motion
– Boundary condtions: Euler Overlay Method. Mass and momentum sources force CFD solution into undisturbed wave solution near boundaries
– Grid resolution
– Physical modelling: Euler solution vs NavierStokes
Drift force extracted from mooring line force
H=25.5 m, T=12.7 s
DNV GL © 2015 30 August 2017
Validation and calibration of slowly varying forces and response
Background and need for model testing
– Wave-current interaction
– Viscous effect on drift force
– Full second order modelling of LF wave force (QTFs)
– Higher order effects on wave drift force in high seastates
Types of tests
– Global design verification of complete floating system
– Taylor made model tests for estimation of wave forces on floater hull
Planning and execution of tests
Data processing, interpretation and documentation
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DNV GL © 2015 30 August 2017
Acknowledgements
Exwave JIP participants
Dr. Carl Trygve Stansberg, Advisor SINTEF Ocean
Dr. Nuno Fonseca, SINTEF Ocean
Dr. Jørn Birknes-Berg, DNV GL
Dr. Limin Yang, DNV GL
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DNV GL © 2015 30 August 2017
SAFER, SMARTER, GREENER
www.dnvgl.com
Thank you
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Arne Nestegå[email protected]+47 41419215