EXTREME VERTICAL IMPACT ON THE DECK OF A GRAVITY-BASED STRUCTURE

Transcription

1 Rogue Waves 2004 Brest October 20 th 22 nd 2004 EXTREME VERTICAL IMPACT ON THE DECK OF A GRAVITY-BASED STRUCTURE Rolf Baarholm, Carl Trygve Stansberg, 1

2 Contents Background and objective for study Simplified model for wave-in-deck loads Case study: Statfjord A GBS Summary and conclusion 2

3 Background Subsidence of existing platforms yields need for re-examination with respect to wave-in-deck loads Air gap of floaters is an expensive parameter. Is it possible to allow for water impact loads in design condition? Today s practice to assess wave-in-deck loads is model testing Need for simple theoretical models for solving impact loads on decks of large-volume platforms Ekofisk Statfjord A (picture from Statoil) 3

4 Objective Develop a simple numerical method for solving wave-in-deck loads on largevolume offshore platforms. 4

5 WaveLand JIP: Designing for Wave Impact on Bow and Deck Structures 5

6 Air-Gap / Run up Photo example: Complex nonlinear wave disturbance under moored semisubmersible in year Norwegian Sea Storm 6

7 3D boundary value problem Potential theory? Fluid flow can be described in terms of a velocity potential, Φ Governing equation: in the fluid domain Boundary conditions: Initial conditions: + wavemaker + numerical beach Impact problem: need fine temporal and spatial discretization very computer expensive problem 7

8 Simplified 3D boundary value problem Write Φ = φ slam + φ wave φ slam =0 φ wave is known a priori φ slam =0 from diffraction analysis Set up BVP for φ slam FSC: φ slam =0 φ slam / z=v R φ slam / z=v R Apply FSC and BBC on horizontal plane z=0. Averaged impact velocity. Zhao and Faltinsen (1998): Analytical solution for axi-symmetric impact In general: Must be solved numerically (Green s 2 nd identity). 8

9 Force from conservation of fluid momentum Simplifications: Slamming force Added mass force Undisturbed wave force from φ wave 9

10 Further approximations Wetted area from by a von Karman approach, i.e. assume wave to be unaffected by the deck. Analytical expressions for the added mass by fitting wetted area to either Elliptical disk Rectangular plate Important when fitting wetted area to basic geometry Correct area Representative aspect ratio We can solve the force on the deck without solving the boundary value problem as such 10

11 Main steps in numerical solution A priori second order diffraction analysis (WAMIT). Establish RAOs and QTFs for: Wave elevation Fluid particle velocities Fluid pressure Determine if when impact occurs. Step solution in time. For each time step evaluate Wave elevation to second order at a finite number of locations underneath deck. (O(10 4 )) Wetted area from von Karman approach Added mass of wetted area by analytical expressions Impact velocity and acceleration to second order Force from impact and undisturbed wave 11

12 Case study: Statfjord A GBS Model of GBS built in scale 1:54 12

13 Model tests Extreme wave events Regular waves Two wave headings Measurements of Total vertical and horizontal loads Air gap at critical locations Local impact loads 13

14 Statfjord A GBS model: Test in high regular wave (H=40m, T=17s) (1) 14

15 Statfjord A GBS model: Test in high regular wave (H=40m, T=17s) (2) 15

16 Statfjord A GBS model: Example of test in extreme wave group 16

17 Numerical model NBDY= 5060 NFS = 6060 Panel model used in WAMIT computations 17

18 Test cases simulated 18

19 T=17s, H=40m, ß=270deg, η deck =21.7m Water entry phase Water exit phase 19

20 20

21 T=15.5s, H=37m, ß=270deg, η deck =21.7m 21

22 T=15.5s, H=37m, ß=240deg, η deck =21.7m 22

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24 Force 20 times smaller than in for the most severe case T=17s, H=34m, ß=270deg, η deck =21.7m 24

25 Hard impact: Relative error between exact and 2 nd order approximation for negative air-gap is small Soft impact: Relative error between exact and 2 nd order approximation for negative air-gap is large 25

26 Summary and conclusions A simple numerical method for evaluating wave-in-deck loads is developed The method is based on Potential theory Simplified boundary value problem Von Karman approach to evaluate wetted deck area Conservation of fluid momentum The entire wave-in-deck event is simulated Computer efficient Second order effects in wave elevation and kinematics crucial Satisfactory agreement for water entry force, water exit force and duration of wave-in-deck event Limitations: Integrated force only At present: regular waves only 26

27 Further work WaveLand JIP Phase III: Focus on use and validation of fullynonlinear numerical modelling. Wave amplification Kinematics in wave crest Deck impact High-speed photography pix CFD computations 0 Vector map: Masked vectors, vectors (1764), 943 rejected, 60 substituted Burst#; rec#: 1; 9 (9), Date: 17/09/2004, Time: 16:26:14:651 Analog inputs: 1 890; 0 957; 0 747; pix 1600 Particle Image Velocimetry (PIV) 27

28 Thanks for your attention! 28

29 = L A HK K F I I = E C / HA A M = JA H I = E A? / HA A M = JA H I = E A? - N JHA A M = L A A? I = E C * M I = E C 29

30 Wamit vs. Measurements, maximum surface elevation. T=15s, H=34m Measurements 1st order theory 2 nd order theory 30

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32 Validity of von Karman approach 32

33 Calibrated wave at (0.0,0.0) Measured vertcel force time series Time window used in comparisons (280s-330s) 33