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01 February 2017 SAFER, SMARTER, GREENERDNV GL © 2017

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01 February 2017Won Ho Lee

OTG-13

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Prediction of air gap for column stabilised units

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Contents

Air gap design requirements

Purpose of OTG-13

OTG-13 vs. OTG-14

Contributions to air gap

Linear analysis for wave frequency response

Asymmetry factor

Low-frequency and mean contributions to air gap

Combination of extremes

Special effects to consider

Non-linear analysis

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Design requirements

DNVGL-OS-C101 Design of offshore steel structures, general – LFRD Method - April 2016

DNVGL-OS-C103 Structural design of column stabilised units – LFRD Method - July 2015

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Offshore Technical Guidance DNVGL-OTG-13

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The purpose of OTG-13 is to define a recommended procedure for estimating air gap for column stabilized units.

The procedure can be applied to predict air gap for a given annual probability of exceedance.

Classification rules (DNVGL-OS-C103) require documentation of load effects at an annual probability 10-2 due to possible wave impact.

For negative air gap wave impact loads can be estimated by applying DNVGL-OTG-14.

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Use of OTG-13 and OTG-14

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Apply procedure in OTG-13 for

estimating airgap ain design sea state

Unit satisfies

air gap requirement

a > 0 a < 0Carry out more

advanced numerical analysis or perform model

tests

Apply OTG-14 to estimate wave impact design loads or derive

design loads from model tests

Unit satisfies air gap

requirements

a > 0

a < 0

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Airgap

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Source: Statoil, Marintek

Vertical distance between underside of deck and wave surface.

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Definitions

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( )),,(),(

),,(),,(),(),,(

0

0

tyxyxatyxtyxzyxatyxa p

χ

η

−=

−+=Air gap:

zp

SWL

a0

η

a

z

zp = amplitude of vertical displacementat location p(x,y)

η = wave surface elevation

a0 = still water air gap (freeboard)

a = air gap

χ = η – zp = upwell

Negative air gap (freeboard exceedance): 0),,( <tyxa

p

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Contributions to upwell

Contributions to upwell:

– Wave frequency (WF) upwell

– Low frequency (LF) upwell

– Mean upwell due to mean inclination of floater

Vertical displacement of floater

Wave surface elevation

– No mean- or low-frequency contributions to wave surface elevation

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WFχ

LFχ

meanχ

),,(),,(),(),,( tyxztyxzyxztyxz LFWFmeanp ++=

),,(),,( tyxtyx WFηη =

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Linear radiation-diffraction analysis

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Geometric modelling principles

Selection of frequencies

Ensuring accurate structural mass properties

Modelling of external stiffness (mooring properties)

Modelling of viscous damping

Wave frequency response (floater motion and wave surface elevation) is usually calculated by a ”linear frequency domain radiation-diffraction” analysis.

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Wave Frequency Response - RAOs

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( )( )

)cos()cos()(

)(cos)(

)(cos)(

)(

)()(

ψωφωηχ

ωψω

ωφωηη

+−+=

+=

+=

tztt

tztz

tt

pL

pp

LL

Upwell

motionVessel

surfaceWaveWave surface and vessel motion have different phase angles:

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Wave Frequency Response - RAOs

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Response T = 10 sec

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-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

RAO

ωtWave Vessel motion Upwell T = 10 sec

|χ| = 1.50

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Response T = 16 sec

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-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

RAO

ωtWave Vessel motion Upwell T = 16 sec

|χ| = 0.37

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Wave surface elevation

Wave surface elevation

The linear wave surface elevation is obtained by a linear radiation/diffraction analysis (e.g. SESAM: Hydro-D)

Simplified analysis

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)()( NLLWF ηηη +=

)()()()( LR

LD

LI

L ηηηη ++=

)()()( LNLLWF αηηηη ≈+=

I : Incident, undisturbed wave surfaceD: Contribution to wave surface due to

wave diffractionR: Contribution to wave surface due to

motion of semi (wave radiation)

Asymmetry factor

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Asymmetry Factor

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Steep (non-linear) waves are asymmetric. For a given wave height H:

− Crests are higher than for a linear sinusoidal wave

− Troughs are shallower than for a linear sinusoidal wave

The amplification of steep asymmetric waves due to diffraction may be larger than for linear sinusoidal waves.

The asymmetry factor accounts for both effects above.

Non-linear

Linear

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Asymmetry Factor from Model Tests

Asymmetry factors derived from model tests shall be extracted at the 90% percentile level in the governing sea state.

The asymmetry factor for each position (x,y) is defined as the ratio between the extreme value η90 from the model test and the extreme linear surface elevation from the numerical analysis, also taken as the 90% percentile.

The extreme value can be obtained by assuming Gumbel distributed maxima

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)(90

90Lη

ηα =

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Asymmetry Factor from Model Tests

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Asymmetry factor varies with horizontal position and wave direction

1.061.20

1.26

1.281.161.22

1.30

With permission from Statoil

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Asymmetry Factor

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In lack of available model tests for the unit or a geometrically similar unit, an asymmetry factor α = 1.2 may be applied for all horizontal positions underneath the deck box excluding run-up areas close to columns. An enhanced asymmetry factor of α = 1.3 is recommended along the outer edge of the deck box in the up-wave direction.

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Design Sea States – Short Term Conditions

For unrestricted operation based on North Atlantic wave conditions the short term wave conditions shall be modelled by the Jonswap wave spectrum.

For restricted operation at a specific site the actual wave spectrum given in metocean design criteria for the site should be applied.

The sea state can be taken as short-crested with a directional spectrum cosn θwhere n = 6 for Hs < 8 m and n = 10 for Hs > 8 m.

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Design Sea States – Long Term Conditions

Extreme values for upwell may be estimated by the contour line method where the steepness criterion given in DNV-RP-C205 can be used to limit the steepness of the sea states.

For unrestricted operation, the North Atlantic wave conditions as described in DNV-RP-C205 shall be applied.

For restricted operation site specific conditions may be used. The design sea state may be selected as the less steep sea state either along the steepness criterion curve or the 10-2 annual probability contour which is the most critical wrt air gap.

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Design Sea State

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Design for unrestricted operation

NCS site specific design

Hs,max=17.3 m

10-2

10-4

DNV GL Steepness criterion

Steepness criterion

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Contributions from Low Frequency Motions

Low frequency (LF) contributions from resonant roll and pitch motions

LF motions are excited by wind and waves

Both contributions may be estimated in frequency domain (wind moment spectrum & difference frequency wave induced moment spectrum (from QTFs))

The maximum low frequency roll and pitch angles are taken

Contributions from wind and waves may be assumed to be uncorrelated

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2,

2, windLFwaveLFLF zzz +=

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Contributions from Low Frequency Motions (cont.)

In lack of available model tests or numerical prediction of LF motions, each of the maximum LF roll and LF pitch angle can be taken as 5 deg.

The maximum angles shall be applied separately for predominantly beam and head sea wave conditions respectively.

For oblique sea the rotation can be assumed to be in-line with wave direction (rotation about axis normal to wave direction), also with amplitude 5 deg.

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Combination of Extremes

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Wave frequency upwell 90% percentile in design sea state

Low frequency upwell

Mean upwell

Wave frequency and low-frequency upwell can be assumed to be “uncorrelated”

Total upwell:

WFL

WF z−= )(αηχ

LFLF z=χ

meanmean z−=χ

22LFWFmean χχχχ ++=

If the accuracy of ballasting to even keel in design sea state cannot be documented, it is recommended to add a mean contribution to upwell corresponding to 1 degree inclination (unintentional) in the most critical wave direction.

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Some special effects to consider for air gap predictions

Effect of current should be considered if

Resonance and non-linear effects

– Trapped waves / enhanced upwell of water in basin between columns

– Shallow pontoons

– Non-linear motion effects

– Wave run-up along columns

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1.0/2 >= zc gTUπτ

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Heave and Pitch Coupling Response

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Pitch in phase with wave

Pitch out of phase with wave

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Wave amplification close to columns

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( )( )22

* 5.0115.1)( DkDsks pcp −

−+= ηαα

η(L)

αη(L) α∗η(L)

Run- up

pk = )/(4 22pgTπ = wave number [m-1]

Tp = sea state peak period [s]

cη = linear crest elevation [m] s = distance from column [m] D = column diameter [m]

Stansberg (2014)

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Wave Amplification

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Stansberg, C.T. (2014) “Non-linear wave amplification around column-based platforms in steep waves”. Proc. OMAE.

Hs=16.3m, Tp=14.0s

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Airgap

Upwell defined by: χ = η-zp

Negative airgap when: χ > a0

Simplified airgap analysis: χ = αη(1)-zp

zp

SWL

a0

η

a

z

CFD Analysis gives Impact

Linear analysis of large event

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Non-linear analysis tools for air gap calculations

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Wave excitation force on semi H=23m, T=12.7s

Non-linear time domain radiation-diffraction analysis (potential flow)

Computational Fluid Dynamics (Navier-Stokes)

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CFD simulation of semi in steep waves

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H=23m, T=12.7s

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Thank you

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Won Ho LeeWon.ho.lee@dnvgl.com832 470 5422