-
RECOMMENDED PRACTICEDNV-RP-C205
ENVIRONMENTAL CONDITIONS AND ENVIRONMENTAL LOADS
APRIL 2007
Since issued in print (April 2007), this booklet has been
amended, latest in October 2008. See the reference to Amendments
and Corrections on the next page. DET NORSKE VERITAS
-
FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and
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and RisersG) Asset OperationH) Marine OperationsJ) Wind
Turbines
Amendments and Corrections This document is valid until
superseded by a new revision. Minor amendments and corrections will
be published in a separatedocument normally updated twice per year
(April and October). For a complete listing of the changes, see the
Amendments and Corrections document located at:
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Recommended Practice DNV-RP-C205, April 2007 Introduction Page
3INTRODUCTION
BackgroundThis Recommended Practice (RP) is based on the
previousDNV Classification Notes 30.5 Environmental Conditions
andEnvironmental Loads and has been developed within a
JointIndustry Project (JIP), Phase I (2004-2005) and Phase
II(2006).
AcknowledgementThe following companies have provided funding for
this JIP:
Statoil, Norway Norsk Hydro, Norway BP, UK (Phase I).
In addition, the following companies and authorities
haveattended project meetings as observers, providing useful
com-ments to this new RP.
Aker Kvrner, Norway Moss Maritime, Norway Petroleum Safety
Authority, Norway Petroleum Geo-Services, Norway.
DNV is grateful for the valuable cooperation and discussionswith
these partners. Their individuals are hereby acknowl-edged for
their contribution.Marintek, Norway provided valuable input to the
developmentof Ch.10 Model Testing. Their contribution is highly
appreci-ated.DET NORSKE VERITAS
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Recommended Practice DNV-RP-C205, April 2007Page 4
IntroductionDET NORSKE VERITAS
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Recommended Practice DNV-RP-C205, April 2007 Contents Page
5CONTENTS
1. GENERAL
.............................................................. 91.1
Introduction
.............................................................91.2
Objective...................................................................91.3
Scope and application
.............................................91.3.1 Environmental
conditions...................................................
91.3.2 Environmental loads
........................................................... 91.4
Relationship to other
codes.....................................91.5 References
................................................................91.6
Abbreviations.........................................................101.7
Symbols...................................................................101.7.1
Latin
symbols....................................................................
101.7.2 Greek symbols
..................................................................
12
2. WIND CONDITIONS..........................................
142.1 Introduction to wind climate
...............................142.1.1
General..............................................................................
142.1.2 Wind
parameters...............................................................
142.2 Wind data
..............................................................142.2.1
Wind speed
statistics.........................................................
142.3 Wind modelling
.....................................................142.3.1 Mean
wind speed
..............................................................
142.3.2 Wind speed profiles
.......................................................... 152.3.3
Turbulence
........................................................................
172.3.4 Wind spectra
.....................................................................
192.3.5 Wind speed process and wind speed field
........................ 202.3.6 Wind profile and atmospheric
stability............................. 222.4 Transient wind
conditions ....................................232.4.1
General..............................................................................
232.4.2 Gusts
.................................................................................
232.4.3
Squalls...............................................................................
23
3. WAVE CONDITIONS.........................................
243.1 General
...................................................................243.1.1
Introduction.......................................................................
243.1.2 General characteristics of waves
...................................... 243.2 Regular wave theories
...........................................243.2.1 Applicability of
wave theories.......................................... 243.2.2
Linear wave theory
........................................................... 253.2.3
Stokes wave theory
........................................................... 263.2.4
Cnoidal wave theory
......................................................... 273.2.5
Solitary wave theory
......................................................... 273.2.6
Stream function wave theory
............................................ 273.3 Wave
kinematics....................................................273.3.1
Regular wave
kinematics..................................................
273.3.2 Modelling of irregular
waves............................................ 273.3.3
Kinematics in irregular waves
.......................................... 283.3.4 Wave kinematics
factor .................................................... 293.4
Wave transformation
............................................293.4.1
General..............................................................................
293.4.2 Shoaling
............................................................................
293.4.3 Refraction
.........................................................................
293.4.4 Wave
reflection.................................................................
303.4.5 Standing waves in shallow basin
...................................... 303.4.6 Maximum wave height
and breaking waves .................... 303.5 Short term wave
conditions ..................................313.5.1
General..............................................................................
313.5.2 Wave spectrum - general
.................................................. 313.5.3 Sea
state parameters
......................................................... 333.5.4
Steepness criteria
..............................................................
333.5.5 The Pierson-Moskowitz and JONSWAP spectra .............
333.5.6 TMA
spectrum..................................................................
343.5.7 Two-peak spectra
.............................................................
343.5.8 Directional distribution of wind sea and swell
................. 353.5.9 Short term distribution of wave height
............................. 353.5.10 Short term distribution of
wave crest
above still water level
....................................................... 36
stationary sea state
............................................................
363.5.12 Joint wave height and wave
period................................... 373.5.13 Freak waves
......................................................................
373.6 Long term wave statistics
..................................... 373.6.1 Analysis strategies
............................................................
373.6.2 Marginal distribution of significant wave height
............. 383.6.3 Joint distribution of significant wave height
and period .. 383.6.4 Joint distribution of significant wave
height
and wind speed
.................................................................
393.6.5 Directional
effects.............................................................
393.6.6 Joint statistics of wind sea and swell
................................ 393.6.7 Long term distribution of
individual wave height ............ 393.7 Extreme value
distribution .................................. 403.7.1 Design sea
state
................................................................
403.7.2 Environmental
contours....................................................
403.7.3 Extreme individual wave height
and extreme crest height
................................................... 403.7.4 Wave
period for extreme individual wave height ............ 413.7.5
Temporal evolution of
storms........................................... 41
4. CURRENT AND TIDE CONDITIONS............. 444.1 Current
conditions ................................................ 444.1.1
General..............................................................................
444.1.2 Types of
current................................................................
444.1.3 Current velocity
................................................................
444.1.4 Design current profiles
..................................................... 444.1.5
Stretching of current to wave surface
............................... 454.1.6 Numerical simulation of
current flows............................. 454.1.7 Current
measurements ......................................................
454.2 Tide conditions
...................................................... 464.2.1
Water
depth.......................................................................
464.2.2 Tidal levels
.......................................................................
464.2.3 Mean still water level
....................................................... 464.2.4
Storm
surge.......................................................................
464.2.5 Maximum still water level
................................................ 46
5. WIND
LOADS...................................................... 475.1
General
...................................................................
475.2 Wind pressure
....................................................... 475.2.1
Basic wind pressure
.......................................................... 475.2.2
Wind pressure coefficient
................................................. 475.3 Wind
forces............................................................
475.3.1 Wind force - general
......................................................... 475.3.2
Solidification effect
.......................................................... 475.3.3
Shielding effects
...............................................................
475.4 The shape
coefficient............................................. 485.4.1
Circular cylinders
.............................................................
485.4.2 Rectangular cross-section
................................................. 485.4.3 Finite
length effects
.......................................................... 485.4.4
Spherical and parabolical structures
................................. 485.4.5 Deck houses on horizontal
surface ................................... 485.4.6 Global wind
loads on ships and platforms........................ 495.4.7
Effective shape
coefficients.............................................. 495.5
Wind effects on helidecks .....................................
505.6 Dynamic analysis
.................................................. 505.6.1 Dynamic
wind analysis.....................................................
505.7 Model tests
............................................................. 515.8
Computational Fluid Dynamics........................... 51
6. WAVE AND CURRENT INDUCED LOADS ON SLENDER MEMBERS
................................ 52
6.1 General
...................................................................
526.1.1 Sectional force on slender
structure.................................. 526.1.2 Morisons load
formula ....................................................
526.1.3 Definition of force
coefficients......................................... 526.2 Normal
force ..........................................................
526.2.1 Fixed structure in waves and current
................................ 52DET NORSKE VERITAS
3.5.11 Maximum wave height and maximum crest height in a 6.2.2
Moving structure in still
water.......................................... 52
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Recommended Practice DNV-RP-C205, April 2007Page 6 Contents6.2.3
Moving structure in waves and
current.............................526.2.4 Relative velocity
formulation ...........................................536.2.5
Applicability of relative velocity formulation
..................536.2.6 Normal drag force on inclined cylinder
............................536.3 Tangential force on inclined
cylinder.................. 536.3.1 General
..............................................................................536.4
Lift
force.................................................................
546.4.1 General
..............................................................................546.5
Torsion moment ....................................................
546.6 Hydrodynamic coefficients for normal flow....... 546.6.1
Governing parameters
.......................................................546.6.2 Wall
interaction effects
.....................................................556.7 Drag
coefficients for circular cylinders............... 556.7.1 Effect
of Reynolds number and roughness .......................556.7.2
Effect of Keulegan Carpenter number
..............................566.7.3 Wall interaction effects
....................................................566.7.4 Marine
growth...................................................................576.7.5
Drag amplification due to VIV
.........................................576.7.6 Drag coefficients
for non-circular cross-section...............576.8 Reduction factor
due to finite length................... 576.9 Added mass
coefficients........................................ 576.9.1 Effect
of KC-number and roughness .................................576.9.2
Wall interaction effects
.....................................................576.9.3 Effect
of free
surface.........................................................586.10
Shielding and amplification effects...................... 586.10.1
Wake
effects......................................................................586.10.2
Shielding from multiple cylinders
....................................596.10.3 Effects of large
volume structures ....................................596.11 Risers
with buoyancy elements ............................ 596.11.1
General
..............................................................................596.11.2
Morison load formula for riser section with buoyancy
elements
............................................................................596.11.3
Added mass of riser section with buoyancy element........596.11.4
Drag on riser section with buoyancy elements
.................606.12 Loads on jack-up leg chords
................................ 606.12.1 Split tube chords
...............................................................606.12.2
Triangular chords
..............................................................616.13
Small volume 3D objects.......................................
616.13.1 General
..............................................................................61
7. WAVE AND CURRENT INDUCED LOADS ON LARGE VOLUME
STRUCTURES............ 63
7.1 General
...................................................................
637.1.1
Introduction.......................................................................637.1.2
Motion time scales
............................................................637.1.3
Natural
periods..................................................................637.1.4
Coupled response of moored floaters
...............................647.1.5 Frequency domain
analysis...............................................647.1.6 Time
domain analysis
.......................................................647.1.7
Forward speed effects
.......................................................657.1.8
Numerical methods
...........................................................657.2
Hydrostatic and inertia loads...............................
657.2.1 General
..............................................................................657.3
Wave frequency loads ...........................................
667.3.1 General
..............................................................................667.3.2
Wave loads in a random
sea..............................................677.3.3 Equivalent
linearization
....................................................677.3.4
Frequency and panel mesh requirements
..........................677.3.5 Irregular frequencies
.........................................................687.3.6
Multi-body hydrodynamic interaction
..............................687.3.7 Generalized body
modes...................................................687.3.8
Shallow water and restricted
areas....................................687.3.9 Moonpool effects
..............................................................697.3.10
Fluid sloshing in tanks
......................................................697.4 Mean
and slowly varying loads............................ 707.4.1
Difference frequency QTFs
.............................................707.4.2 Mean drift
force
................................................................707.4.3
Newmans
approximation.................................................717.4.4
Viscous effect on drift forces
............................................717.4.5 Damping of low
frequency motions .................................71
7.5.1 General
..............................................................................737.5.2
Second order wave loads
..................................................737.5.3 Higher
order wave loads
...................................................737.6 Steady
current loads ............................................. 737.6.1
General
..............................................................................737.6.2
Column based structures
...................................................737.6.3 Ships
and
FPSOs...............................................................74
8. AIRGAP AND WAVE SLAMMING................. 768.1
General...................................................................
768.2 Airgap
...................................................................
768.2.1
Definitions.........................................................................768.2.2
Surface
elevation...............................................................768.2.3
Local run-up
.....................................................................768.2.4
Vertical
displacement........................................................768.2.5
Numerical free surface
prediction.....................................768.2.6 Simplified
analysis............................................................778.2.7
Wave current
interaction...................................................778.2.8
Airgap extreme
estimates..................................................778.3
Wave-in-deck.........................................................
778.3.1 Horizontal wave-in-deck force
.........................................778.3.2 Vertical
wave-in-deck
force..............................................778.3.3
Simplified approach for horizontal wave-in-deck force ...788.3.4
Momentum method for horizontal wave-in-deck force ....798.3.5
Simplified approach for vertical wave impact force.........798.3.6
Momentum method for vertical wave-in-deck force ........808.3.7
Diffraction effect from large volume structures
...............808.4 Wave-in-deck loads on floating
structure........... 818.4.1 General
..............................................................................818.5
Computational Fluid Dynamics........................... 818.5.1
General
..............................................................................818.6
Wave impact loads on slender structures........... 818.6.1
Simplified
method.............................................................818.6.2
Slamming on horizontal slender structure
........................818.6.3 Slamming on vertical slender
structure.............................828.7 Wave impact loads on
plates................................ 828.7.1 Slamming loads on a
rigid body .......................................828.7.2 Space
averaged slamming pressure
..................................828.7.3 Hydroelastic effects
..........................................................848.8
Breaking wave impact ..........................................
848.8.1 Shock
pressures.................................................................848.9
Fatigue damage due to wave impact ................... 848.9.1
General
..............................................................................84
9. VORTEX INDUCED OSCILLATIONS ........... 869.1 Basic concepts
and definitions ............................. 869.1.1 General
..............................................................................869.1.2
Reynolds number dependence
..........................................869.1.3 Vortex shedding
frequency ...............................................869.1.4
Lock-in..............................................................................889.1.5
Cross flow and in-line
motion...........................................889.1.6 Reduced
velocity...............................................................889.1.7
Mass
ratio..........................................................................889.1.8
Stability parameter
............................................................889.1.9
Structural
damping............................................................899.1.10
Hydrodynamic
damping....................................................899.1.11
Effective
mass...................................................................899.1.12
Added mass
variation........................................................899.2
Implications of VIV ..............................................
899.2.1 General
..............................................................................899.2.2
Drag amplification due to VIV
.........................................909.3 Principles for
prediction of VIV.......................... 909.3.1 General
..............................................................................909.3.2
Response based
models.....................................................909.3.3
Force based models
..........................................................909.3.4
Flow based
models............................................................919.4
Vortex induced hull motions................................ 919.4.1
General
..............................................................................919.5
Wind induced vortex shedding ............................ 929.5.1
General
..............................................................................92DET
NORSKE VERITAS
7.5 High frequency loads
............................................ 73 9.5.2 In-line
oscillations.............................................................92
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Recommended Practice DNV-RP-C205, April 2007 Contents Page
79.5.3 Cross flow
oscillations......................................................
929.6 Current induced vortex shedding
........................929.6.1
General..............................................................................
929.6.2 Multiple cylinders and pipe
bundles................................. 939.6.3 In-line VIV
response model..............................................
939.6.4 Cross flow VIV response
model....................................... 949.6.5 Multimode
response..........................................................
949.7 Wave induced vortex shedding
............................959.7.1
General..............................................................................
959.7.2 Regular and irregular wave motion
.................................. 959.7.3 Vortex shedding for KC
> 40............................................ 959.7.4
Response amplitude
.......................................................... 969.7.5
Vortex shedding for KC < 40
........................................... 969.8 Methods for
reducing VIO ...................................969.8.1
General..............................................................................
969.8.2 Spoiling
devices................................................................
979.8.3
Bumpers............................................................................
979.8.4 Guy
wires..........................................................................
97
10. HYDRODYNAMIC MODEL TESTING .......... 9910.1 Introduction
...........................................................9910.1.1
General..............................................................................
9910.1.2 Types and general purpose of model testing
................... 9910.1.3 Extreme loads and responses
............................................ 9910.1.4 Test methods
and procedures............................................ 9910.2
When is model testing recommended .................9910.2.1
General..............................................................................
9910.2.2 Hydrodynamic load characteristics
.................................. 9910.2.3 Global system concept
and design verification .............. 10010.2.4 Individual
structure component testing .......................... 10110.2.5
Marine operations, demonstration of functionality ........
10110.2.6 Validation of nonlinear numerical models
..................... 10110.2.7 Extreme loads and responses
.......................................... 10110.3 Modelling and
calibration of the environment .10110.3.1 General
...........................................................................
10110.3.2 Wave
modelling..............................................................
10110.3.3 Current
modelling...........................................................
10210.3.4 Wind modelling
..............................................................
10210.3.5 Combined wave, current and wind conditions
............... 10210.4 Restrictions and simplifications
in physical model
.................................................10310.4.1
General............................................................................
10310.4.2 Complete mooring modelling vs. simple springs ...........
10310.4.3 Equivalent riser models
.................................................. 10310.4.4
Truncation of ultra deepwater floating systems
in a limited
basin.............................................................
10310.4.5 Thruster modelling / DP
................................................. 10310.4.6 Topside
model
................................................................
10310.4.7 Weight
restrictions..........................................................
103
10.5 Calibration of physical model set-up.................
10310.5.1 Bottom-fixed models
...................................................... 10310.5.2
Floating models
..............................................................
10410.6 Measurements of physical parameters and
phenomena...........................................................
10410.6.1 Global wave forces and moments
.................................. 10410.6.2 Motion damping and
added mass ................................... 10410.6.3
Wave-induced motion response characteristics .............
10410.6.4 Wave-induced slow-drift forces and
damping................ 10410.6.5 Current drag forces
......................................................... 10410.6.6
Vortex-induced vibrations and motions (VIV; VIM)..... 10510.6.7
Relative waves; green water; air-gap..............................
10510.6.8 Slamming loads
..............................................................
10510.6.9 Particle Imaging Velocimetry
(PIV)............................... 10510.7 Nonlinear extreme
loads and responses ............ 10510.7.1 Extremes of a random
process........................................ 10510.7.2 Extreme
estimate from a given realisation ..................... 10610.7.3
Multiple realisations
....................................................... 10610.7.4
Testing in single wave groups
........................................ 10610.8 Data acquisition,
analysis and interpretation... 10610.8.1 Data acquisition
..............................................................
10610.8.2 Regular wave tests
..........................................................
10610.8.3 Irregular wave
tests.........................................................
10610.8.4 Accuracy level; repeatability
.......................................... 10610.8.5 Photo and
video
..............................................................
10610.9 Scaling effects
...................................................... 10710.9.1
General............................................................................
10710.9.2 Viscous problems
...........................................................
10710.9.3 Choice of
scale................................................................
10710.9.4 Scaling of slamming load measurements
....................... 10710.9.5 Other scaling effects
....................................................... 107
APP. A TORSETHAUGEN TWO-PEAK
SPECTRUM.............................................. 109
APP. B NAUTIC ZONES FOR ESTIMATION OF LONG-TERM WAVE
DISTRIBUTION PARAMETERS
..............................................................
111
APP. C SCATTER DIAGRAMS .................................
112
APP. D ADDED MASS COEFFICIENTS .................. 115
APP. E DRAG COEFFICIENTS ................................
119
APP. F PHYSICAL CONSTANTS.............................. 122DET
NORSKE VERITAS
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Recommended Practice DNV-RP-C205, April 2007Page 8 ContentsDET
NORSKE VERITAS
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Amended October 2008 Recommended Practice DNV-RP-C205, April
2007see note on front cover Page 91. General1.1 IntroductionThis
new Recommended Practice (RP) gives guidance formodelling, analysis
and prediction of environmental condi-tions as well guidance for
calculating environmental loads act-ing on structures. The loads
are limited to those due to wind,wave and current. The RP is based
on state of the art withinmodelling and analysis of environmental
conditions and loadsand technical developments in recent R&D
projects, as well asdesign experience from recent and ongoing
projects.The basic principles applied in this RP are in agreement
withthe most recognized rules and reflect industry practice and
lat-est research.Guidance on environmental conditions is given in
Ch.2, 3 and4, while guidance on the calculation of environmental
loads isgiven in Ch.5, 6, 7, 8 and 9. Hydrodynamic model testing
iscovered in Ch.10.
1.2 ObjectiveThe objective of this RP is to provide rational
design criteriaand guidance for assessment of loads on marine
structures sub-jected to wind, wave and current loading.
1.3 Scope and application
1.3.1 Environmental conditions
1.3.1.1 Environmental conditions cover natural phenomena,which
may contribute to structural damage, operation distur-bances or
navigation failures. The most important phenomenafor marine
structures are:
wind waves current tides.
These phenomena are covered in this RP.
1.3.1.2 Phenomena, which may be important in specific cases,but
not covered by this RP include:
ice earthquake soil conditions temperature fouling
visibility.
1.3.1.3 The environmental phenomena are usually describedby
physical variables of statistical nature. The
statisticaldescription should reveal the extreme conditions as well
as the
long- and short-term variations. If a reliable simultaneous
data-base exists, the environmental phenomena can be described
byjoint probabilities.
1.3.1.4 The environmental design data should be representa-tive
for the geographical areas where the structure will be situ-ated,
or where the operation will take place. For ships and othermobile
units which operate world-wide, environmental datafor particularly
hostile areas, such as the North Atlantic Ocean,may be
considered.
1.3.1.5 Empirical, statistical data used as a basis for
evalua-tion of operation and design must cover a sufficiently
longtime period. For operations of a limited duration, seasonal
var-iations must be taken into account. For meteorological
andoceanographical data 20 years of recordings should be
availa-ble. If the data record is shorter the climatic uncertainty
shouldbe included in the analysis.
1.3.2 Environmental loads
1.3.2.1 Environmental loads are loads caused by environmen-tal
phenomena.
1.3.2.2 Environmental loads to be used for design shall bebased
on environmental data for the specific location and oper-ation in
question, and are to be determined by use of relevantmethods
applicable for the location/operation taking intoaccount type of
structure, size, shape and response characteris-tics.
1.4 Relationship to other codesThis RP provides the basic
background for environmental con-ditions and environmental loads
applied in DNVs OffshoreCodes and is considered to be a supplement
to relevant national(i.e. NORSOK) and international (i.e. ISO)
rules and regula-tions.Other DNV Recommended Practices give
specific informationon environmental loading for specific marine
structures. Suchcodes include:
DNV-RP-C102 Structural Design of Offshore Ships Recommended
Practice DNV-RP-C103 Column Stabi-
lized Units DNV-RP-C206 Fatigue Methodology of Offshore Ships
DNV-RP-F105 Free Spanning Pipelines DNV-RP-F204 Riser Fatigue
DNV-RP-F205 Global Performance Analysis of Deep-
water Floating Structures.
1.5 ReferencesReferences are given at the end of each of Ch.2 to
Ch.10. Theseare referred to in the text.DET NORSKE VERITAS
-
Recommended Practice DNV-RP-C205, April 2007 Amended October
2008Page 10 see note on front cover1.6 Abbreviations
1.7 Symbols
1.7.1 Latin symbols
ALS Accidental Limit StateBEM Boundary Element MethodCF Cross
FlowCMA Conditional Modelling ApproachCQC Complete Quadratic
CombinationDVM Discrete Vortex MethodFD Finite DifferenceFEM Finite
Element MethodFLS Fatigue Limit StateFPSO Floating Production and
Storage and OffloadingFV Finite VolumeGBS Gravity Based
StructureHAT Highest Astronomical TideHF High FrequencyIL
In-lineLAT Lowest Astronomical TideLF Low FrequencyLNG Liquified
natural GasLS Least SquaresLTF Linear Transfer FunctionMHWN Mean
High Water NeapsMHWS Mean High Water SpringsMLE Maximum Likelihood
EstimationMLM Maximum Likelihood ModelMLWN Mean Low Water NeapsMLWS
Mean Low Water SpringsMOM Method Of MomentsPM Pierson-MoskowitzPOT
Peak Over ThresholdQTF Quadratic Transfer FunctionRAO Response
Amplitude OperatorSRSS Square Root of Sum of SquaresSWL Still Water
LevelTLP Tension Leg PlatformULS Ultimate Limit StateVIC Vortex In
CellVIM Vortex Induced MotionVIV Vortex Induced VibrationsWF Wave
Frequency
a0 Still water air gapa Instantaneous air gapA Dynamic
amplification factorA Cross-sectional areaA(z) Moonpool
cross-sectional areaA1 V/L, reference cross-sectional area for
riser with
buoyancy elementsAC Charnock's constantAC Wave crest heightACF
Cross flow VIV amplitudeAkj Added mass matrix elements
ar Relative accelerationAR Reference area for 2D added mass
coefficientAT Wave trough depthB Bowen ratioB1 Linear damping
coefficientBkj Wave damping matrix elementsBxx, Bxy Wave drift
damping coefficientsc Wetted length during slammingc Wave phase
velocityC Wind force shape coefficientCA Added mass coefficientCA0
Added mass coefficient for KC = 0CD Drag coefficientCd Hydrodynamic
damping coefficientCDn Normal drag coefficient for inclined
structural
memberCDS Drag coefficient for steady flowCDt Axial drag
coefficient for inclined structural
memberCe Wind force effective shape coefficientcg Wave group
velocityCh Horizontal wave-in-deck force coefficientCkj Hydrostatic
restoring elementsCL Lift coefficientCM Mass coefficientCoh(r,f)
Coherence spectrumCp Wind pressure coefficientCp Pressure
coefficientCpa Space average slamming pressure coefficientCv
Vertical wave-in-deck force coefficientd Water depthD Diameter or
typical cross-sectional dimensionD() Directionality functiond(z/r)
Instantaneous cross-sectional horizontal length
during slammingD(,) Directionality functionD[ ] Standard
deviationDb Diameter of buoyancy elementDC Diameter of clean
cylinder (without marine
growth)Di Diameter of element i in group of cylindersDp Width of
cluster of cylinderE Wave energy densitye Gap ratio (= H/D)E
Modulus of elasticityE(-) Quadratic free surface transfer
functionE(+) Quadratic free surface transfer functionE[ ] Mean
valueEI Bending stiffnessf Wave frequencyFc Current induced drag
force Fd() Mean drift forcefdrag Sectional drag force on slender
memberDET NORSKE VERITAS
-
Amended October 2008 Recommended Practice DNV-RP-C205, April
2007see note on front cover Page 11Fdx, Fdy Wave drift damping
forcesFh Horizontal wave-in-deck forceFH(h) Cumulative probability
function FHT(H,T) Joint probability distribution flift Sectional
lift force on slender memberfN Sectional normal drag force on
slender memberfn Natural frequencyFs Slamming forcefs Sectional
slamming forcefT Sectional axial drag force on slender memberFv
Vertical wave-in-deck forceg Acceleration of gravityg Wind response
peak factorGM Metacentric heightH Wind reference heightH Clearance
between structure and fixed boundaryH Wave heightH(1) First order
force transfer functionH(2-) Second order difference frequency
force transfer
functionH(2+) Second order sum frequency force transfer
functionh(z/r) Vertical reference height during slammingHb
Breaking wave heightHm0 Significant wave heightHs Significant wave
heightI Interaction factor for buoyancy elementsIkj Mass moments of
inertiaJn Bessel functionk Wave numberk Roughness heightka Von
Karman's constantKC Keulegan-Carpenter number = vmT/D
(KC = H/D in wave zone)Kkj Mooring stiffness elementsKn Modified
Bessel function of order Ks Shoaling coefficientKS Stability
parameter (Scrouton number) l Length of buoyancy elementL() Linear
structural operatorlc Correlation lengthLMO Monin-Obukhov lengthLu
Integral length scale in wind spectrumm Beach slopeM Mass of
structurem* Mass ratiom66 Added moment of inertia for
cross-sectionMa 3D added massma 2D added mass (per unit length)
Tangential added massMc Current induced moment due to dragMd()
Mean drift momentM Wave drift yaw moment
Tam
me Effective massMeq Equivalent moonpool massMkj Global mass
matrix elementsmn, Mn Spectral momentsmt Torsional moment on
slender structural membern Number of propeller revolutions per unit
timen Exponent for wave spreadingnx,ny,nz Components of normal
vectorP Wave energy fluxp Pressureps Space average slamming
pressureq Basic wind pressure
Sum frequency wave induced forceDifference frequency wave
induced force
R Richardson numberR Reflection coefficientr Ratio between modal
frequenciesr Displacement of structural memberr44 Roll radius of
gyrationr55 Pitch radius of gyrationRe Reynolds number = uD/S
Projected area of structural member normal to the
direction of forceS Wave steepnesss Exponent for wave spreadingS
Distance between buoyancy elementsS Waterplane areaS(f), S() Wave
spectrumS1 Average wave steepnessSi, i = 1,2 First moments of water
plane areaSij Second moments of water plane areaSm02 Estimate of
significant wave steepnessSmax Maximum wave steepnessSp Average
wave steepnessSR() Response spectrumSs Significant wave steepnessSt
Strouhal numberSU(f) Wind speed spectrumT Wave period T
Transmission coefficientt Thickness of marine growthT0 Propeller
thrust at zero speedT0 One-hour wind reference periodT1 Mean wave
periodT10 10-minute wind reference periodTc Mean crest periodTm01
Spectral estimate of mean wave periodTm02 Spectral estimate of
zero-up-crossing periodTm24 Spectral estimate of mean crest
periodTn Natural periodTp Peak periodTR Return period
)(2WAq
+
)(2WAq
DET NORSKE VERITAS
dz Tz Zero-up-crossing period
-
Recommended Practice DNV-RP-C205, April 2007 Amended October
2008Page 12 see note on front cover1.7.2 Greek symbols
U Forward speed of structure/vesselu(1) First order horizontal
velocityu(2-) Second-order difference-frequency horizontal
velocityu(2+) Second-order sum-frequency horizontal velocityu*
Friction velocityu,v,w Wave velocity components in
x,y,z-directionU0 One hour mean wind speedU10 10-minute mean wind
speedUG, AG Parameters of Gumbel distributionUR, Ur Ursell numbers
for regular waveUrs Ursell number for irregular waveUT,z Wind
velocity averaged over a time interval T at
a height z meterV Volume displacementvc Current velocityVc
Volume of air cushionvc() Far field currentvc,circ Circulational
current velocityvc,tide Tidal current velocityvc,wind Wind induced
current velocityvd Wake deficit velocityvm Maximum wave orbital
particle velocityvn Normal component of velocityvr Relative
velocityVR Reduced velocity = vT/D or v/(fD)VR Reference area for
3D added mass coefficientvs Significant velocityvt Normal component
of velocityW Projected diameter of split tube chordz(x,y,t)
Vertical displacement of the structure zB Vertical position of
centre of buoyancyzG Vertical position of centre of gravityzs
Stretched z-coordinate
Velocity of structural memberAcceleration of structural
member
Spacing ratio Angle between the direction of the wind and
the
axis of the exposed member or surface Asymmetry factor Angle
between wave ray and normal to the sea bed
depth contour Exponent in power law current profile Wave
attenuation coefficient Spectral band widthc Current flow velocity
ratio = vc/(vc+vm) H, c Scale parameters in Weibull distribution
Breaking wave parameter Wave direction of propagation Deadrise
angle during slamming Aerodynamic solidity ratio
r&r&&
Viscous frequency parameter = Re/KC = D2/T H, c Shape parameters
in Weibull distribution Logarithmic decrement (= 2) Spectral band
width Nondimensional roughness = k/DSS Spatial extent of slamming
pressure Local wave slope Shallow water non-linearity parameter
Spectral band widthk Random phase Velocity potential Solidity ratio
() Depth function in TMA spectrum Peak shape parameter (Jonswap)
Length scale of wind speed process Location parameter in
3-parameter Weibull distri-
bution Gas constant for air = 1.4( ) Gamma function Free surface
elevation Shielding factorh Height of moonpool1 Linear (first
order) free surface elevation2 Second order free surface elevationm
Local crest heightR,D Radiation and diffraction free surface
elevation Surface friction coefficient Finite length reduction
factor Moonpool geometry factor Wave length Shallow water parameter
Spectral band width Kinematic viscosity coefficienta Kinematic
viscosity coefficient for airij Irregular wave numbers Mass density
of water Autocorrelation for wind speed fielda Mass density of
airnm Cross-modal coefficients(f) Standard deviation of dynamic
structural responsea, b Spectral width parameters (Jonswap)b Stress
due to net buoyancy forceslam Stress in element due to slam loadU
Standard deviation of wind speedw Stress due to vertical wave
forces Wave angular frequencye Wave angular frequency of encounterp
Angular spectral peak frequencyi() Response transfer functionj
Rigid body motion in degree of freedom j Damping ratio Aspect ratio
= b/l Phase functionDET NORSKE VERITAS
-
Amended October 2008 Recommended Practice DNV-RP-C205, April
2007see note on front cover Page 13p Main wave direction Stability
function for wind profiles Wave amplification factor( ) Standard
Gaussian cumulative distribution
functionAngular acceleration of cross-section.&DET NORSKE
VERITAS
-
Recommended Practice DNV-RP-C205, April 2007 Amended October
2008Page 14 see note on front cover2. Wind Conditions2.1
Introduction to wind climate
2.1.1 GeneralWind speed varies with time. It also varies with
the heightabove the ground or the height above the sea surface. For
thesereasons, the averaging time for wind speeds and the
referenceheight must always be specified.A commonly used reference
height is H = 10 m. Commonlyused averaging times are 1 minute, 10
minutes and 1 hour.Wind speed averaged over 1 minute is often
referred to as sus-tained wind speed.
2.1.2 Wind parameters
2.1.2.1 The wind climate can be represented by the 10-minutemean
wind speed U10 at height 10 m and the standard deviationU of the
wind speed at height 10 m. In the short term, i.e. overa 10-minute
period, stationary wind conditions with constantU10 and constant U
can often be assumed to prevail. Thiswind climate representation is
not intended to cover wind con-ditions experienced in tropical
storms such as hurricanes,cyclones and typhoons. It is neither
intended to cover windconditions experienced during small-scale
events such as fastpropagating arctic low pressures of limited
extension. Theassumption of stationary conditions over 10-minute
periods isnot always valid. For example, front passages and
unstableconditions can lead to extreme wind conditions like
windgusts, which are transient in speed and direction, and for
whichthe assumption of stationarity does not hold. Examples of
suchnonstationary extreme wind conditions, which may be criticalfor
design, are given in DNV-OS-J101 and IEC61400-1.
2.1.2.2 The 10-minute mean wind speed U10 is a measure ofthe
intensity of the wind. The standard deviation U is a meas-ure of
the variability of the wind speed about the mean. Whenspecial
conditions are present, such as when hurricanes,cyclones and
typhoons occur, a representation of the wind cli-mate in terms of
U10 and U may be insufficient. The instanta-neous wind speed at an
arbitrary point in time during 10-minute stationary conditions
follows a probability distributionwith mean value U10 and standard
deviation U.
2.1.2.3 The turbulence intensity is defined as the ratio
U/U10.
2.1.2.4 The short term 10-minute stationary wind climate maybe
represented by a wind spectrum, i.e. the power spectral den-sity of
the wind speed process, SU(f). SU(f) is a function of U10and U and
expresses how the energy of the wind speed in aspecific point in
space is distributed between various frequen-cies.
2.2 Wind data
2.2.1 Wind speed statistics
2.2.1.1 Wind speed statistics are to be used as a basis for
rep-resentation of the long-term and short-term wind
conditions.Long-term wind conditions typically refer to 10 years or
more,short-term conditions to 10 minutes. The 10-minute meanwind
speed at 10 m height above the ground or the still waterlevel is to
be used as the basic wind parameter to describe thelong-term wind
climate and the short-term wind speed fluctu-ations. Empirical
statistical data used as a basis for design mustcover a
sufficiently long period of time.
2.2.1.2 Site-specific measured wind data over sufficientlylong
periods with minimum or no gaps are to be sought. Fordesign, the
wind climate data base should preferably cover a10-year period or
more of continuous data with a sufficient
2.2.1.3 Wind speed data are height-dependent. The meanwind speed
at 10 m height is often used as a reference. Whenwind speed data
for other heights than the reference height arenot available, the
wind speeds for the other heights can be cal-culated from the wind
speeds in the reference height in con-junction with a wind speed
profile above the ground or abovethe still water level.
2.2.1.4 The long-term distributions of U10 and U
shouldpreferably be based on statistical data for the same
averagingperiod for the wind speed as the averaging period which is
usedfor the determination of loads. If a different averaging
periodthan 10 minutes is used for the determination of loads, the
winddata may be converted by application of appropriate gust
fac-tors. The short-term distribution of the instantaneous
windspeed itself is conditional on U10 and U.
2.2.1.5 An appropriate gust factor to convert wind
statisticsfrom other averaging periods than 10 minutes depends on
thefrequency location of a spectral gap, when such a gap ispresent.
Application of a fixed gust factor, which is independ-ent of the
frequency location of a spectral gap, can lead to erro-neous
results. A spectral gap separates large-scale motionsfrom turbulent
scale motions and refers to those spatial andtemporal scales that
show little variation in wind speed.
2.2.1.6 The latest insights for wind profiles above watershould
be considered for conversion of wind speed databetween different
reference heights or different averaging peri-ods. Unless data
indicate otherwise, the conversions may becarried out by means of
the expressions given in 2.3.2.11.
2.2.1.7 The wind velocity climate at the location of the
struc-ture shall be established on the basis of previous
measurementsat the actual location and adjacent locations, hindcast
winddata as well as theoretical models and other
meteorologicalinformation. If the wind velocity is of significant
importance tothe design and existing wind data are scarce and
uncertain,wind velocity measurements should be carried out at the
loca-tion in question. Characteristic values of the wind
velocityshould be determined with due account of the inherent
uncer-tainties.
2.2.1.8 When the wind velocity climate is based on hindcastwind
data, it is recommended to use data based on reliable rec-ognised
hindcast models with specified accuracy. WMO(1983) specifies
minimum requirements to hindcast modelsand their accuracy. Hindcast
models and theoretical modelscan be validated by benchmarking to
measurement data.
2.3 Wind modelling
2.3.1 Mean wind speed
2.3.1.1 The long-term probability distributions for the wind
cli-mate parameters U10 and U that are derived from available
datacan be represented in terms of generic distributions or in
termsof scatter diagrams. An example of a generic distribution
repre-sentation consists of a Weibull distribution for the
arbitrary 10-minute mean wind speed U10 in conjunction with a
lognormaldistribution of U conditional on U10 (see 2.3.3.1). A
scatter dia-gram provides the frequency of occurrence of given
pairs (U10,U) in a given discretisation of the (U10, U) space.
2.3.1.2 Unless data indicate otherwise, a Weibull
distributioncan be assumed for the arbitrary 10-minute mean wind
speedU10 in a given height z above the ground or above the sea
waterlevel,
in which the scale parameter A and the shape parameter k are
))(exp(1)(10
kU A
uuF =DET NORSKE VERITAS
time resolution. site- and height-dependent.
-
Amended October 2008 Recommended Practice DNV-RP-C205, April
2007see note on front cover Page 152.3.1.3 In areas where
hurricanes occur, the Weibull distribu-tion as determined from
available 10-minute wind speedrecords may not provide an adequate
representation of theupper tail of the true distribution of U10. In
such areas, theupper tail of the distribution of U10 needs to be
determined onthe basis of hurricane data.
2.3.1.4 Data for U10 are usually obtained by measuring thewind
speed over 10 minutes and calculating the mean windspeed based on
the measurements from these 10 minutes. Var-ious sampling schemes
are being used. According to someschemes, U10 is observed from
every 10-minute period in aconsecutive series of 10-minute periods,
such that there are sixU10 observations every hour. According to
other schemes, U10is observed from only one 10-minute period every
hour orevery third hour, such that there are only 24 or 8 U10
observa-tions per day.
2.3.1.5 Regardless of whether U10 is sampled every 10 min-utes,
every hour or every third hour, the achieved samples usu-ally
obtained over a time span of several years form a data setof U10
values which are representative as a basis for estimationof the
cumulative distribution function FU10(u) for U10.
2.3.1.6 In areas where hurricanes do not occur, the
distribu-tion of the annual maximum 10-minute mean wind
speedU10,max can be approximated by
where N = 52 560 is the number of consecutive 10-minuteaveraging
periods in one year. Note that N = 52 595 when leapyears are taken
into account. The approximation is based on anassumption of
independent 10-minute events. The approxima-tion is a good
approximation in the upper tail of the distribu-tion, which is
typically used for prediction of rare mean windspeeds such as those
with return periods of 50 and 100 years.
2.3.1.7 Note that the value of N = 52 560 is determined on
thebasis of the chosen averaging period of 10 minutes and is
notinfluenced by the sampling procedure used to establish the
datafor U10 and the distribution FU10(u); i.e. it does not depend
onwhether U10 has been sampled every 10 minutes, every hour orevery
third hour. Extreme value estimates such as the 99%quantile in the
resulting distribution of the annual maximum10-minute mean wind
speed shall thus always come out asindependent of the sampling
frequency.
2.3.1.8 In areas where hurricanes occur, the distribution of
theannual maximum 10-minute mean wind speed U10,max shall bebased
on available hurricane data. This refers to hurricanes forwhich the
10-minute mean wind speed forms a sufficient rep-resentation of the
wind climate.
2.3.1.9 The quoted power-law approximation to the distribu-tion
of the annual maximum 10-minute mean wind speed is agood
approximation to the upper tail of this distribution. Usu-ally only
quantiles in the upper tail of the distribution are ofinterest,
viz. the 98% quantile which defines the 50-year meanwind speed or
the 99% quantile which defines the 100-yearmean wind speed. The
upper tail of the distribution can be wellapproximated by a Gumbel
distribution, whose expressionmay be more practical to use than the
quoted power-lawexpression.
2.3.1.10 The annual maximum of the 10-minute mean windspeed
U10,max can often be assumed to follow a Gumbel distri-bution,
in which a and b are site- and height-dependent
distributionparameters.
2.3.1.11 Experience shows that in many cases the Gumbel dis-
of the square of the annual maximum of the 10-minute meanwind
speed than of the distribution of the annual maximum ofthe mean
wind speed itself. Wind loads are formed by windpressures, which
are proportional to the square of the windspeed, so for estimation
of characteristic loads defined as the98% or 99% quantile in the
distribution of the annual maxi-mum wind load it is recommended to
work with the distribu-tion of the square of the annual maximum of
the 10-minutemean wind speed and extrapolate to 50- or 100-year
values ofthis distribution.
2.3.1.12 The 10-minute mean wind speed with return periodTR in
units of years is defined as the (11/TR) quantile in
thedistribution of the annual maximum 10-minute mean windspeed,
i.e. it is the 10-minute mean wind speed whose proba-bility of
exceedance in one year is 1/TR. It is denoted andis expressed
as
in which FU10,max,1 year denotes the cumulative
distributionfunction of the annual maximum of the 10-minute mean
windspeed.
2.3.1.13 The 10-minute mean wind speed with return periodone
year is defined as the mode of the distribution of the
annualmaximum 10-minute mean wind speed.
2.3.1.14 The 50-year 10-minute mean wind speed becomes
and the 100-year 10-minute mean wind speed becomes
Note that these values, calculated as specified, are to be
con-sidered as central estimates of the respective 10-minute
windspeeds when the underlying distribution function FU10,max
isdetermined from limited data and is encumbered with statisti-cal
uncertainty.
2.3.2 Wind speed profiles
2.3.2.1 The wind speed profile represents the variation of
themean wind speed with height above the ground or above thestill
water level, whichever is applicable. When terrain condi-tions and
atmospheric stability conditions are not complex, thewind speed
profile may be represented by an idealised modelprofile. The most
commonly applied wind profile models arethe logarithmic profile
model, the power law model and theFrya model, which are presented
in 2.3.2.4 through 2.3.2.12.
2.3.2.2 Complex wind profiles, which are caused by inversionand
which may not be well represented by any of the mostcommonly
applied wind profile models, may prevail over landin the vicinity
of ocean waters.
2.3.2.3 The friction velocity u* is defined as
where is the surface shear stress and a is the air density.The
friction velocity u* can be calculated from the 10-minutemean wind
speed U10 at the height H = 10 m as
where is a surface friction coefficient. The surface
frictioncoefficient is defined in 2.3.2.6. Some sources refer to as
asurface drag coefficient; however, it is important not to con-fuse
with the drag coefficient used for calculations of wind
NUU uFuF ))(()( 10max,10 year 1, =
[ ]{ })(expexp)(year 1,max,10 buauFU =
RTU ,10
)11(1year 1,,10 max,10R
UT TFU
R=
; TR > 1 year
)98.0(1year 1,50,10 max,10= UFU
)99.0(1year 1,100,10 max,10= UFU
au =*
10* Uu = DET NORSKE VERITAS
tribution will provide a better representation of the
distribution forces on structures.
-
Recommended Practice DNV-RP-C205, April 2007 Amended October
2008Page 16 see note on front cover2.3.2.4 A logarithmic wind speed
profile may be assumed forneutral atmospheric conditions and can be
expressed as
where ka = 0.4 is von Karmans constant, z is the height and z0is
a terrain roughness parameter, which is also known as theroughness
length. For locations on land, z0 depends on thetopography and the
nature of the ground. For offshore loca-tions z0 depends on the
wind speed, the upstream distance toland, the water depth and the
wave field. Table 2-1 gives typi-cal values for z0 for various
types of terrain.
Table 2-1 is based on Panofsky and Dutton (1984), Simiu
andScanlan (1978), JCSS (2001) and Dyrbye and Hansen (1997).
2.3.2.5 For offshore locations, the roughness parameter
z0typically varies between 0.0001 m in open sea without wavesand
0.01 m in coastal areas with onshore wind. The roughnessparameter
for offshore locations may be solved implicitly fromthe following
equation
where g is the acceleration of gravity and AC is Charnocks
con-stant. AC is usually higher for young developing and
rapidlygrowing waves than for old fully developed waves. For
opensea with fully developed waves, AC = 0.011-0.014 is
recom-mended. For near-coastal locations, AC is usually higher with
val-ues of 0.018 or more. Expressions for AC, which include
thedependency on the wave velocity and the available water
fetch,are available in the literature, see Astrup et al.
(1999).
2.3.2.6 An alternative formulation of the logarithmic
profile,expressed in terms of the 10-minute mean wind speed U(H)
inthe reference height H = 10 m, reads
in which
This implies that the logarithmic profile may be rewritten
as
2.3.2.7 The logarithmic wind speed profile implies that thescale
parameter A(z) at height z can be expressed in terms ofthe scale
parameter A(H) at height H as follows
The scale parameter is defined in 2.3.2.1.
2.3.2.8 As an alternative to the logarithmic wind profile,
apower law profile may be assumed,
where the exponent depends on the terrain roughness.
2.3.2.9 Note that if the logarithmic and power law wind
pro-files are combined, then a height-dependent expression for
theexponent results
2.3.2.10 Note also that the limiting value = 1/ln(z/z0) as
zapproaches the reference height H has an interpretation as
aturbulence intensity, cf. the definition given in 2.3.2.3. As
analternative to the quoted expression for , values for tabu-lated
in Table 2-1 may be used.
2.3.2.11 The following expression can be used for calculationof
the mean wind speed U with averaging period T at height zabove sea
level as
where H = 10 m and T10 = 10 minutes, and where U10 is
the10-minute mean wind speed at height H. This expression con-verts
mean wind speeds between different averaging periods.When T <
T10, the expression provides the most likely largestmean wind speed
over the specified averaging period T, giventhe original 10-minute
averaging period with stationary condi-tions and given the
specified 10-minute mean wind speed U10.The conversion does not
preserve the return period associatedwith U10.
2.3.2.12 For offshore locations, the Frya wind profile model
isrecommended unless data indicate otherwise. For extreme meanwind
speeds corresponding to specified return periods in excessof
approximately 50 years, the Frya model implies that the fol-lowing
expression can be used for conversion of the one-hourmean wind
speed U0 at height H above sea level to the mean windspeed U with
averaging period T at height z above sea level
Table 2-1 Terrain roughness parameter z0 and power-law exponent
Terrain type Roughness
parameter z0 (m)Power-law exponent
Plane ice 0.00001-0.0001Open sea without waves 0.0001Open sea
with waves 0.0001-0.01 0.12Coastal areas with onshore wind
0.001-0.01
Snow surface 0.001-0.006Open country withoutsignificant
buildings and vegetation
0.01
Mown grass 0.01Fallow field 0.02-0.03Long grass, rocky ground
0.05Cultivated land with scattered buildings
0.05 0.16
Pasture land 0.2Forests and suburbs 0.3 0.30City centres 1-10
0.40
0
ln*)(zz
kuzU
a
=
2
00 )/ln(
)(
=
zzzUk
gAz aC
)ln11()()(Hz
kHUzU
a
+=
2
0
2
)(lnzH
k a=
( ) ( )0
ln1
ln
zHU z U HHz
= +
0
0
ln
ln)()(
zHzz
HAzA =
=
HzHUzU )()(
=
HzzHzz
ln
ln
lnln
0
0
)ln047.0ln137.01(),(10
10 TT
HzUzTU +=
+= 0 ln)(41.01ln1),( TzIzCUzTU UDET NORSKE VERITAS
is the surface friction coefficient. 0TH
-
Amended October 2008 Recommended Practice DNV-RP-C205, April
2007see note on front cover Page 17where H = 10 m, T0 = 1 hour and
T < T0, where
and
and where U will have the same return period as U0.
2.3.2.13 Note that the Frya wind speed profile includes agust
factor which allows for conversion of mean wind speedsbetween
different averaging periods. The Frya wind speedprofile is a
special case of the logarithmic wind speed profilein 2.3.2.4. The
Frya wind speed profile is the best docu-mented wind speed profile
for offshore locations and maritimeconditions.
2.3.2.14 Over open sea, the coefficient C may tend to be
about10% smaller than the value that results from the quoted
expres-sion. In coastal zones, somewhat higher values for the
coeffi-cient C should be used, viz. 15% higher for U0 = 10 m/s
and30% higher for U0 = 40 m/s.
2.3.2.15 Both conversion expressions are based on winterstorm
data from a Norwegian Sea location and may not neces-sarily lend
themselves for use at other offshore locations. Theexpressions
should not be extrapolated for use beyond theheight range for which
they are calibrated, i.e. they should notbe used for heights above
approximately 100 m. Possible influ-ences from geostrophic winds
down to about 100 m heightemphasises the importance of observing
this restriction.
2.3.2.16 Both conversion expressions are based on the
appli-cation of a logarithmic wind profile. For locations where
anexponential wind profile is used or prescribed, the
expressionsshould be considered used only for conversions between
dif-ferent averaging periods at a height equal to the
referenceheight H = 10 m.
2.3.2.17 In the absence of information on tropical storm windsin
the region of interest, the conversion expressions may alsobe
applied to winds originating from tropical storms. Thisimplies in
particular that the expressions can be applied towinds in
hurricanes.
2.3.2.18 The conversion expressions are not valid for
repre-sentation of squall winds, in particular because the duration
ofsqualls is often less than one hour. The representation of
squallwind statistics is a topic for ongoing research.
2.3.2.19 Once a wind profile model is selected, it is
importantto use this model consistently throughout, i.e. the wind
profilemodel used to transform wind speed measurements at
someheight z to wind speeds at a reference height H has to
beapplied for any subsequent calculation of wind speeds, both atthe
height z and at other heights, on the basis of wind speeds atthe
reference height H.
2.3.2.20 The wind profile models presented in 2.3.2.4 and2.3.2.8
and used for conversion to wind speeds in heights with-out wind
observations are idealised characteristic model pro-files, which
are assumed to be representative mean profiles inthe short term.
There is model uncertainty associated with theprofiles and there is
natural variability around them: The truemean profile may take a
different form for some wind events,such as in the case of extreme
wind or in the case of non-neu-tral wind conditions. This implies
that conversion of wind datato heights without wind measurements
will be encumbered
racy which can be expected when conversions of wind speedsto
heights without wind data is carried out by means of windprofile
models. It is recommended to account for uncertainty insuch wind
speed conversions by adding a wind speed incre-ment to the wind
speeds that result from the conversions.
2.3.2.21 The expressions in 2.3.2.11 and 2.3.2.12 contain
gustfactors for conversion of wind speeds between different
aver-aging periods. As for conversion of wind speeds between
dif-ferent heights also conversion between different
averagingperiods is encumbered with uncertainty, e.g. owing to the
sim-plifications in the models used for the conversions. HSE(2002)
gives an indication of the accuracy which can beexpected when
conversions of wind speeds between differentaveraging periods is
carried out by means of gust factors. It isrecommended to account
for uncertainty in such wind speedconversions by adding a wind
speed increment to the windspeeds that result from the
conversions.
2.3.3 Turbulence
2.3.3.1 The natural variability of the wind speed about the
meanwind speed U10 in a 10-minute period is known as turbulenceand
is characterised by the standard deviation U. For givenvalue of
U10, the standard deviation U of the wind speed exhib-its a natural
variability from one 10-minute period to another.Measurements from
several locations show that U conditionedon U10 can often be well
represented by a lognormal distribution.
in which ( ) denotes the standard Gaussian cumulative
distri-bution function
The coefficients b0 and b1 are site-dependent
coefficientsdependent on U10.
2.3.3.2 The coefficient b0 can be interpreted as the mean
valueof lnU, and b1 as the standard deviation of lnU. The
follow-ing relationships can be used to calculate the mean value
E[U]and the standard deviation D[U] of U from the values of b0and
b1,
Reference is made to Guidelines for Design of Wind
Turbines(2001).
2.3.3.3 E[U] and D[U] will, in addition to their dependencyon
U10, also depend on local conditions, first of all the
terrainroughness z0, which is also known as the roughness
length.When different terrain roughnesses prevail in different
direc-tions, i.e. the terrain is not homogeneous, E[U] and D[U]may
vary with the direction. This will be the case for examplein the
vicinity of a large building. Buildings and other disturb-ing
elements will in general lead to more turbulence, i.e.,larger
values of E[U] and D[U], than will be found insmoother terrain.
Figure 2-1 and Figure 2-2 give examples ofthe variation of E[U] and
D[U] with U10 for an onshore andan offshore location, respectively.
The difference between thetwo figures mainly consists in a
different shape of the meancurve. This reflects the effect of the
increasing roughness
02 148.011073.5 UC +=
22.00 )()043.01(06.0
+=HzUIU
)ln
()(1
0| 10 b
bF UU
=
=x
dex
2/2
21)(
[ ] )21exp( 210 bbE U +=
[ ] [ ] 1)exp( 21 = bED UU DET NORSKE VERITAS
with uncertainty. HSE (2002) gives an indication of the accu-
length for increasing U10 on the offshore location.
-
Recommended Practice DNV-RP-C205, April 2007 Amended October
2008Page 18 see note on front coverFigure 2-1Example of mean value
and standard deviation of U as function of U10 onshore
location.
Figure 2-2Example of mean value and standard deviation of U as
function of U10 offshore location
2.3.3.4 In some cases, a lognormal distribution for U
condi-tioned on U10 will underestimate the higher values of U.
AFrechet distribution may form an attractive distribution modelfor
U in such cases, hence
The distribution parameter k can be solved implicitly from
and the distribution parameter 0 then results as
where denotes the gamma function
2.3.3.5 Caution should be exercised when fitting a
distributionmodel to data. Normally, the lognormal distribution
provides agood fit to data, but use of a normal distribution, a
Weibull dis-tribution or a Frechet distribution is also seen. The
choice ofthe distribution model may depend on the application,
i.e.,whether a good fit to data is required to the entire
distributionor only in the body or the upper tail of the
distribution. It isimportant to identify and remove data, which
belong to 10-minute series for which the stationarity assumption
for U10 isnot fulfilled. If this is not done, such data may confuse
thedetermination of an appropriate distribution model for U
con-ditioned on U10.
2.3.3.6 The following expression for the mean value of
thestandard deviation U, conditioned on U10, can be applied
for homogeneous terrain, in which
Measurements from a number of locations with uniform andflat
terrain indicate an average value of Ax equal to 2.4. In roll-ing
terrain, Ax tends to be somewhat larger. Unless data indi-cate
otherwise, the following approximation to Ax may be usedfor purely
mechanical turbulence (neutral conditions) over uni-form and flat
terrain
in which z0 is to be given in units of m. Reference is made
toPanofsky and Dutton (1984), Dyrbye and Hansen (1997), andLungu
and van Gelder (1997).
2.3.3.7 The 10-minute mean wind speed U10 and the
standarddeviation U of the wind speed refer to the longitudinal
windspeed, i.e. the wind speed in the constant direction of the
meanwind during a considered 10-minute period of stationary
con-ditions. During this period, in addition to the turbulence in
thedirection of the mean wind, there will be turbulence also
later-ally and vertically. The mean lateral wind speed will be
zero,while the lateral standard deviation of the wind speed Uy
canbe taken as a value between 0.75U and 0.80U. The meanvertical
wind speed will be zero, while the vertical standarddeviation of
the wind speed Uz can be taken as Uz = 0.5U.These values all refer
to homogeneous terrain. For complexterrain, the wind speed field
will be much more isotropic, andvalues for Uy and Uz very near the
value of U can beexpected.
2.3.3.8 When the wind climate at a location cannot be
docu-mented by site-specific measurements, the distribution of
U10can still, usually, be represented well, for example on the
basisof wind speed measurements from adjacent locations. How-ever,
the distribution of U will usually be harder to obtain,because it
will be very dependent on the particular local rough-ness
conditions, and it can thus not necessarily be inferredfrom known
wind speed conditions at adjacent locations. At alocation where
wind speed measurements are not available, thedetermination of the
distribution of the standard deviation Uof the wind speed is
therefore often encumbered with ambigu-ity. It is common practice
to account for this ambiguity by
0
0,5
1
1,5
2
2,5
3
0 5 10 15 20
U10 (m/sec)
D[
U]
E
[ U]
(m
/sec
) mean valuest. dev.
0
0,5
1
1,5
2
2,5
0 5 10 15 20 25
U 10 (m/sec)
D[
U]
E
[ U]
(m
/sec
) mean valuest. dev.
))(exp()( 0| 10k
UUF
=
[ ][ ] 1)11(
)21()(
2
2
=
k
kED
U
U
[ ])11(
0
k
E U
=
= 1)( dtetx tx
ka = 0.4 is von Karmans constantz = the height above terrainz0 =
the roughness parameterAx = constant which depends on z0
[ ] *ln
1
0
10 uA
zz
kAUE xaxU ==
0ln856.05.4 zAx =DET NORSKE VERITAS
using conservatively high values for U for design purposes.
0
-
Amended October 2008 Recommended Practice DNV-RP-C205, April
2007see note on front cover Page 192.3.4 Wind spectra
2.3.4.1 Short-term stationary wind conditions may bedescribed by
a wind spectrum, i.e. the power spectral densityof the wind speed.
Site-specific spectral densities of the windspeed process can be
determined from available measuredwind data.
2.3.4.2 When site-specific spectral densities based on meas-ured
data are used, the following requirement to the energycontent in
the high frequency range should be fulfilled, unlessdata indicate
otherwise: The spectral density SU(f) shallasymptotically approach
the following form as the frequency fin the high frequency range
increases
in which Lu is the integral length scale of the wind speed
process.
2.3.4.3 Unless data indicate otherwise, the spectral density
ofthe wind speed process may be represented by a model spec-trum.
Several model spectra exist. They generally agree in thehigh
frequency range, whereas large differences exist in thelow
frequency range. Most available model spectra are cali-brated to
wind data obtained over land. Only a few are cali-brated to wind
data obtained over water. Model spectra areoften expressed in terms
of the integral length scale of the windspeed process. The most
commonly used model spectra withlength scales are presented in
2.3.4.5 to 2.3.4.10.
2.3.4.4 Caution should be exercised when model spectra areused.
In particular, it is important to be aware that the true inte-gral
length scale of the wind speed process may deviate signif-icantly
from the integral length scale of the model spectrum.
2.3.4.5 The Davenport spectrum expresses the spectral den-sity
in terms of the 10-minute mean wind speed U10 irrespec-tive of the
elevation. The Davenport spectrum gives thefollowing expression for
the spectral density
in which f denotes the frequency and Lu is a length scale of
thewind speed process. The Davenport spectrum is
originallydeveloped for wind over land with Lu = 1200 m as the
proposedvalue.
2.3.4.6 The Davenport spectrum is not recommended for usein the
low frequency range, i.e. for f < 0.01 Hz. There is a gen-eral
difficulty in matching the Davenport spectrum to data inthis range
because of the sharp drop in the spectral densityvalue of the
Davenport spectrum near zero frequency.
2.3.4.7 The Kaimal spectrum gives the following expressionfor
the spectral density,
in which f denotes frequency and Lu is an integral length
scale.Unless data indicate otherwise, the integral length scale Lu
canbe calculated as
z denotes the height above the ground or above the sea
waterlevel, whichever is applicable, and z0 is the terrain
roughness.Both z and z0 need to be given in units of m.
2.3.4.8 An alternative specification of the integral length
scaleis given in IEC61400-1 for design of wind turbine
generatorsand is independent of the terrain roughness,
where z denotes the height above the ground or the sea
waterlevel, whichever is applicable.
2.3.4.9 The Harris spectrum expresses the spectral density
interms of the 10-minute mean wind speed U10 irrespective ofthe
elevation. The Harris spectrum gives the following expres-sion for
the spectral density
in which Lu is an integral length scale. The integral length
scaleLu is in the range 60-400 m with a mean value of 180 m.
Unlessdata indicate otherwise, the integral length scale Lu can be
cal-culated as for the Kaimal spectrum, see 2.3.4.6. The
Harrisspectrum is originally developed for wind over land and is
notrecommended for use in the low frequency range, i.e. forf <
0.01 Hz.
2.3.4.10 For design of offshore structures, the empirical
Simiuand Leigh spectrum may be applied. This model spectrum
isdeveloped taking into account the wind energy over a seawayin the
low frequency range. The Simiu and Leigh spectrum S(f)can be
obtained from the following equations
where
f = frequencyz = height above the sea surfaceU10 = 10-minute
mean wind speed at height z
353
2
10
214.0)(
= fUL
fS uUU
3/42
10
2
102
))(1(
)(32
)(
UfL
fUL
fSu
u
UU
+
=
3/5
10
102
)32.101(
868.6)(
UfL
UL
fSu
u
UU
+
=
0ln074.046.0)300
(300 zuzL +=
+
0
Nights where temperature stratification severely >>0
)(ln*)(0
=
zzuzU
0
10
20
30
40
50
60
6 7 8 9 10 11 12 13
wind speed (m/s)
heig
ht (m
)
neutral
stable
unstable
20
0
)(dzdUdz
dg
R
=
RzLMO = in unstable air
RRzLMO
51= in stable air
)07.01()(
22 Bzv
zuTg
Rd
+
+
=
zu / zv /u v
)()(
12
12
qqTT
Lc
BMO
p
1T 2TDET NORSKE VERITAS
denoted 1 and 2, respectively, and and are the averagesuppresses
mechanical turbulence generation 1q 2q
-
Amended October 2008 Recommended Practice DNV-RP-C205, April
2007see note on front cover Page 23specific humidities at the same
two levels. The specific humid-ity q is in this context calculated
as the fraction of moisture bymass.
2.3.6.8 Application of the algorithm in 2.3.6.7 requires an
ini-tial assumption to be made for LMO. An iterative approach
isthen necessary for solution of the Richardson number R.
Con-vergence is achieved when the calculated Richardson numberR
leads to a Monin-Obukhov length LMO by the formulas in2.3.6.6 which
equals the value of LMO. Further details aboutatmospheric stability
and its representation can be found inPanofsky and Dutton
(1984).
2.3.6.9 Topographic features such as hills, ridges and
escarp-ments affect the wind speed. Certain layers of the flow
willaccelerate near such features, and the wind profiles willbecome
altered.
2.4 Transient wind conditions
2.4.1 General
2.4.1.1 When the wind speed changes or the direction of thewind
changes, transient wind conditions may occur. Transientwind
conditions are wind events which by nature fall outsideof what can
normally be represented by stationary wind condi-tions. Examples of
transient wind conditions are:
gusts squalls extremes of wind speed gradients, i.e. first of
all extremes
of rise times of gust strong wind shears extreme changes in wind
direction simultaneous changes in wind speed and wind direction
such as when fronts pass.
2.4.2 Gusts
2.4.2.1 Gusts are sudden brief increases in wind speed,
char-acterised by a duration of less than 20 seconds, and
followedby a lull or slackening in the wind speed. Gusts may be
char-acterised by their rise time, their magnitude and their
duration.
2.4.2.2 Gusts occurring as part of the natural fluctuations
ofthe wind speed within a 10-minute period of stationary
windconditions without implying a change in the mean windspeed
level are not necessarily to be considered as transientwind
conditions, but are rather just local maxima of the station-ary
wind speed process.
2.4.3 Squalls
2.4.3.1 Squalls are strong winds characterised by a suddenonset,
a duration of the order of 10-60 minutes, and then arather sudden
decrease in speed. Squalls imply a change in themean wind speed
level.
2.4.3.2 Squalls are caused by advancing cold air and are
asso-ciated with active weather such as thunderstorms. Their
forma-tion is related to atmospheric instability and is subject
toseasonality. Squalls are usually accompanied by shifts in
winddirection and drops in air temperature, and by rain and
lightning.Air temperature change can be a more reliable indicator
of pres-ence of a squall, as the wind may not always change
direction.
2.4.3.3 Large uncertainties are associated with squalls andtheir
vertical wind profile and lateral coherence. The verticalwind
profile may deviate significantly from the model profilesgiven in
2.3.2.4 and 2.3.2.8. Assuming a model profile such asthe Frya wind
speed profile for extreme mean wind speeds asgiven in 2.3.2.13 is a
possibility. However, such an assumptionwill affect the wind load
predictions and may or may not beconservative. References
1) Andersen, O.J., and J. Lvseth, The Maritime TurbulentWind
Field. Measurements and Models, Final Report forTask 4 of the
Statoil Joint Industry Project, Norwegian Insti-tute of Science and
Technology, Trondheim, Norway, 1992.
2) Andersen, O.J., and J. Lvseth, The Frya database andmaritime
boundary layer wind description, Marine Struc-tures, Vol. 19, pp.
173-192, 2006.
3) Astrup, P., S.E. Larsen, O. Rathmann, P.H. Madsen, and
J.Hjstrup, WASP Engineering Wind Flow Modellingover Land and Sea,
in Wind Engineering into the 21stCentury, eds. A.L.G.L. Larose and
F.M. Livesey,Balkema, Rotterdam, The Netherlands, 1999.
4) Det Norske Veritas and RIS, Guidelines for Design ofWind
Turbines, Copenhagen, Denmark, 2001.
5) Dyrbye, C., and S.O. Hansen, Wind Loads on Structures,John
Wiley and Sons, Chichester, England, 1997.
6) HSE (Health & Safety Executive), Environmental
consid-erations, Offshore Technology Report No. 2001/010, HSEBooks,
Sudbury, Suffolk, England, 2002.
7) IEC (International Electrotechnical Commission), WindTurbines
Part 1: Design Requirements, IEC61400-1, 3rdedition, 2005.
8) JCSS (Joint Committee on Structural Safety), Probabilis-tic
Model Code, Part 2: Loads, 2001.
9) Lungu, D., and Van Gelder, P., Characteristics of
WindTurbulence with Applications to Wind Codes, Proceed-ings of the
2nd European & African Conference on WindEngineering, pp.
1271-1277, Genova, Italy, 1997.
10) Mann, J., Wind field simulation, Journal of Prob.Engng.
Mech., Vol. 13, No. 4, pp. 269-282, Elsevier, 1998.
11) Panofsky, H.A., and J.A. Dutton, Atmospheric Turbu-lence,
Models and Methods for Engineering Applications,John Wiley and
Sons, New York, N.Y., 1984.
12) Saranyansoontorn, K., L. Manuel, and P.S. Veers, AComparison
of Standard Coherence Models for InflowTurbulence with Estimates
from Field Measurements,Journal of Solar Energy Engineering, ASME,
Vol. 126,pp. 1069-1082, 2004.
13) Simiu, E., and R.U. Scanlan, Wind Effects on Structures;An
Introduction to Wind Engineering, John Wiley, NewYork, N.Y.,
1978.
14) WMO (World Meteorological Organization), Guide
toMeteorological Instruments and Methods of Observation,Publication
No. 8, World Meteorological Organisation,Geneva, Switzerland,
1983.DET NORSKE VERITAS
-
Recommended Practice DNV-RP-C205, April 2007 Amended October
2008Page 24 see note on front cover3. Wave Conditions3.1
General
3.1.1 IntroductionOcean waves are irregular and random in shape,
height, lengthand speed of propagation. A real sea state is best
described bya random wave model.A linear random wave model is a sum
of many small linearwave components with different amplitude,
frequency anddirection. The phases are random with respect to each
other.A non-linear random wave model allows for sum- and
differ-ence frequency wave component caused by non-linear
interac-tion between the individual wave components.Wave conditions
which are to be considered for structuraldesign purposes, may be
described either by deterministicdesign wave methods or by
stochastic methods applying wavespectra.For quasi-static response
of structures, it is sufficient to usedeterministic regular waves
characterized by wave length andcorresponding wave period, wave
height and crest height. Thedeterministic wave parameters may be
predicted by statisticalmethods.Structures with significant dynamic
response require stochas-tic modelling of the sea surface and its
kinematics by timeseries. A sea state is specified by a wave
frequency spectrumwith a given significant wave height, a
representative fre-quency, a mean propagation direction and a
spreading func-tion. In applications the sea state is usually
assumed to be astationary random process. Three hours has been
introduced asa standard time between registrations of sea states
when meas-uring waves, but the period of stationarity can range
from 30minutes to 10 hours.The wave conditions in a sea state can
be divided into twoclasses: wind seas and swell. Wind seas are
generated by localwind, while swell have no relationship to the
local wind.Swells are waves that have travelled out of the areas
wherethey were generated. Note that several swell components maybe
present at a given location.
3.1.2 General characteristics of wavesA regular travelling wave
is propagating with permanent form.It has a distinct wave length,
wave period, wave height.Wave length: The wave length is the
distance between suc-cessive crests.Wave period: The wave period T
is the time interval betweensuccessive crests passing a particular
point. Phase velocity: The propagation velocity of the wave form
iscalled phase velocity, wave speed or wave celerity and isdenoted
by c = / T.Wave frequency is the inverse of wave period: f =
1/T.Wave angular