OTG-13 Prediction of air gap for column stabilised units Won Ho Lee 1 SAFER, SMARTER, GREENER
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 2
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 3
Offshore Technical Guidance DNVGL-OTG-13 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. 4
Use of OTG-13 and OTG-14 Unit satisfies air gap requirement Apply procedure in OTG-13 for estimating airgap a in design sea state a > 0 a < 0 Unit satisfies air gap requirements a > 0 Carry out more advanced numerical analysis or perform model tests a < 0 Apply OTG-14 to estimate wave impact design loads or derive design loads from model tests 5
Airgap Vertical distance between underside of deck and wave surface. Source: Statoil, Marintek 6
Definitions z z p p a z p = amplitude of vertical displacement at location p(x,y) η a 0 SWL η = wave surface elevation a 0 = still water air gap (freeboard) a = air gap χ = η z p = upwell Air gap: a( x, y, t) = = ( a ( x, y) + z ( x, y, t) ) a 0 0 ( x, y) χ( x, y, t) p η( x, y, t) Negative air gap (freeboard exceedance): a( x, y, t) < 0 7
Contributions to upwell Contributions to upwell: Wave frequency (WF) upwell χ WF Low frequency (LF) upwell χ LF Mean upwell due to mean inclination of floater χ mean Vertical displacement of floater z ( x, y, t) = z ( x, y) + z ( x, y, t) z ( x, y, t) p mean WF + LF Wave surface elevation η ( x, y, t) =η ( x, y, t) WF No mean- or low-frequency contributions to wave surface elevation 8
Linear radiation-diffraction analysis Wave frequency response (floater motion and wave surface elevation) is usually calculated by a linear frequency domain radiation-diffraction analysis. Geometric modelling principles Selection of frequencies Ensuring accurate structural mass properties Modelling of external stiffness (mooring properties) Modelling of viscous damping 9
Wave Frequency Response - RAOs Wave surface and vessel motion have different phase angles: Wavesurface Vesselmotion Upwell η ( χ( t) = η ( L) z p L) ( ( t) = η ( t) = z p L) cos cos cos( ωt + φ) z ( ωt + φ( ω) ) ( ωt + ψ ( ω) ) p cos( ωt + ψ ) 10
Wave Frequency Response - RAOs 11
Response T = 10 sec 2.0 1.5 1.0 0.5 χ = 1.50 RAO 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 ωt Wave Vessel motion Upwell T = 10 sec 12
Response T = 16 sec 1.5 1.0 0.5 RAO 0.0-0.5-1.0-1.5 χ = 0.37 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 ωt Wave Vessel motion Upwell T = 16 sec 13
Wave surface elevation Wave surface elevation η = η + η WF ( L) ( NL) The linear wave surface elevation is obtained by a linear radiation/diffraction analysis (e.g. SESAM: Hydro-D) Simplified analysis η η = η + η + η WF ( L) ( L) ( L) ( L) I D R = η + η αη ( L) ( NL) ( L) I : Incident, undisturbed wave surface D: Contribution to wave surface due to wave diffraction R: Contribution to wave surface due to motion of semi (wave radiation) Asymmetry factor 14
Asymmetry Factor 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 Non-linear Linear 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. 15
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 η 90 from the model test and the extreme linear surface elevation from the numerical analysis, also taken as the 90% percentile. η α = η The extreme value can be obtained by assuming Gumbel distributed maxima 90 ( L) 90 16
Asymmetry Factor from Model Tests Asymmetry factor varies with horizontal position and wave direction 1.26 1.28 1.20 1.06 1.22 1.16 1.30 With permission from Statoil 17
Asymmetry Factor 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. 18
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 cos n θ where n = 6 for H s < 8 m and n = 10 for H s > 8 m. 19
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. 20
Design Sea State H s,max =17.3 m DNV GL Steepness criterion 10-4 Design for unrestricted operation 10-2 Steepness criterion NCS site specific design 21
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 z = z + LF z 2 2 LF, wave LF, wind 22
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. 23
Combination of Extremes Wave frequency upwell χ WF = αη ( L) z WF 90% percentile in design sea state Low frequency upwell Mean upwell χ LF = z LF χ mean = z mean Wave frequency and low-frequency upwell can be assumed to be uncorrelated Total upwell: χ = χ + χ + χ mean 2 WF 2 LF 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. 24
Some special effects to consider for air gap predictions Effect of current should be considered if τ = z 2 πu c / gt > 0.1 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 25
Heave and Pitch Coupling Response Pitch out of phase with wave Pitch in phase with wave 26
Wave amplification close to columns Runup αη (L) α η (L) η (L) 2 ( 1 ( 0.5k ) ) 2 * s α ( s) = α + 1.5k p η c 1 pd D Stansberg (2014) 2 2 k p = 4π /( gt p ) = wave number [m -1 ] T p = sea state peak period [s] η c = linear crest elevation [m] s = distance from column [m] D = column diameter [m] 27
Wave Amplification Hs=16.3m, Tp=14.0s Stansberg, C.T. (2014) Non-linear wave amplification around column-based platforms in steep waves. Proc. OMAE. 28
Airgap z z p a η a 0 SWL Linear analysis of large event Upwell defined by: χ = η-z p Negative airgap when: χ > a 0 Simplified airgap analysis: χ = αη (1) -z p CFD Analysis gives Impact
Non-linear analysis tools for air gap calculations Non-linear time domain radiation-diffraction analysis (potential flow) Computational Fluid Dynamics (Navier-Stokes) Wave excitation force on semi H=23m, T=12.7s 30
CFD simulation of semi in steep waves H=23m, T=12.7s 31
Thank you Won Ho Lee Won.ho.lee@dnvgl.com 832 470 5422 www.dnvgl.com SAFER, SMARTER, GREENER 32