VIOLENT WAVE TRAPPING - SOME RESULTS ON WATER PROJECTION AROUND SEMI-SUBs AND TLPs

Transcription

1 VIOLENT WAVE TRAPPING - SOME RESULTS ON WATER PROJECTION AROUND SEMI-SUBs AND TLPs Paul H. Taylor James Grice Rodney Eatock Taylor Department of Engineering Science University of Oxford

2 Contents Introduction Sea-states of interest First-order diffraction Second-order diffraction Second-order statistics Moving model vs. Fixed model Conclusions

3 Large floating offshore structures with multiple closely spaced columns

4 Large production semi-submersibles but geometry is not too dissimilar to a TLP Thunder Horse GoM Troll B North Sea (concrete)

5 Project background Strong interaction effects in groups of closely spaced columns can lead to violent wave structure interaction water projection to high level Usually considered by model testing Aim for a design tools for a screening process based on numerical modelling Build on past research to address areas of uncertainty Analyse a large existing semi-submersible rig as an example

6 Software used DIFFRACT Developed over 25 years first at UCL and then in Oxford Analyses single- and multibodied structures up to 2 nd order for forces, body movements and surface elevation Gambit A commercial mesh generator used in pro-processing 8 noded quadrilateral elements Simplified symmetric version of structure with 4 columns connected by pontoons in deep water

7 Finding Near-Trapping frequencies

8 Near-trapping modes A near-trapping mode is a local standing wave pattern within the obstacle array which is excited by incoming waves but slowly leaks energy outwards away from the array. They occur at wavelengths dependent on the structure geometry. See Evans & Porter, Near-trapping of waves by circular arrays of vertical cylinders (1997)

9 Surface elevation amplification for unit-amplitude regular incident waves at Near-Trapping frequencies Incident angle varies T=6.4 seconds Max η/a =2.79 T=5.2 seconds

10 Investigating the effect of column shape on diffraction

11 Single column surface interaction Maximum value: 1.87x Maximum value: 2.17x T=5.2 seconds

12 Single column surface interaction Maximum value: 1.87x Maximum value: 1.79x T=5.2 seconds

13 Surface interaction around a pair of columns Maximum value: 2.05x Maximum value: 2.39x T=5.2 seconds

14 Surface interaction around a square array of four columns Maximum value: 2.1x7 Maximum value: 2.49x T=5.2 seconds

15 So typical large 4-column structures can trap waves at periods < 7 sec But severe storms have wave periods > 12 sec So no problem? No Nonlinear effects can produce frequency doubling: 12 sec incoming wave drives large response at 6 sec [And even frequency tripling 15 sec wave gives large response at 5 sec.. etc.]

16 Column shape in arrays affects details of local response ( here, second-order potential sum diffraction) T I = 12.8 seconds (T I /2= 6.4 seconds) Circular columns Intermediate columns (most similar to many semi-subs) Square columns Max η P (2+) = Max η P (2+) = Max η P (2+) =

17 Mode shapes to first- and second-order - low freq. mode shapes match well inside the array T R = 7.6 seconds T R = 5.9 seconds T R = 5.2 seconds T R = 4.4 seconds

18 Second-order statistics - in random waves in a severe storm Realistic severe conditions T p = 15.2 seconds, H S = 12m

19 Collection of crest elevation statistics to second-order T p = 15.2 seconds, H S = 12m As little as 5 minutes computation time for a sea-state calc ~1million waves (Hard part is finding DIFFRACT or WAMIT coeffs)

20 Collection of trough depth statistics to second-order T p = 15.2 seconds, H S = 12m

21 Collection of crest elevation statistics to second-order confidence boundaries Collection of crest statistics from 10 different random realisations of the same sea-state T p = 15.2 seconds, H S = 12m Mean crest height distribution for all 10 random realisations and the 95% confidence boundaries

22 Collection of crest elevation statistics to second-order T p = 15.2 seconds, H S = 12m

23 Designer waves averaged over 500 crests Probability of occurrence, P = 10-4 Average response surface elevation Average incident wave giving response T p = 15.2 seconds, H S = 12m

24 Designer response waves - crests P = 10-4 P = 10-3 P = 10-2 P = 10-1

25 Wave diffraction by a moving body Semi-sub now freely floating only slow drift restrained Realistic severe conditions T p = 15.2 seconds, H S = 12m

26 Large semi-sub heave response Only radiation damping is modelled therefore large response at resonant period Zero net force corresponds with change in phase of heave response

27 An example of a random surface elevation time history at the centre of 4-column semi-sub T p = 15.2 seconds, H S = 12m, β=45 η Move is relative to MWL η Move R z is relative to deck height (17.5m)

28 Statistics of response surface elevation for a moving model

29 Collection of crest elevation statistics to second-order for fixed and moving models T p = 15.2 seconds, H S = 12m

30 Average expected surface elevation for a 1-in-1500 wave crest to second-order with fixed and freely floating bodies T p = 15.2 seconds, H S = 12m, β=45 Fixed model Moving model Harmonic components to second-order for each model

31 Average expected surface elevation for a 1-in-1500 wave trough to second-order for fixed and freely floating models Fixed model Near the centre of the model at (12m,12m) Moving model T p = 15.2 sec, H S = 12m, β=45

32 Conclusions practical results Significant 2 nd order as well as linear wave near-trapping around large 4-column structures Column cross-sectional shape has some effect, but proximity to other columns is dominant effect on wave-structure interactions A vertically restrained 4-column structure can have fairly regular water-deck impacts The freely heaving model has far fewer water-deck impacts than the fixed model Efficient Monte Carlo type simulations can model 10 6 waves in ~5 minutes (for a given platform geometry and wave direction) An average extreme event identified and could be used as a designer wave for further analysis and targeted wave-tank model testing

33 Many thanks to EPSRC and BP for funding the CASE award. Dr Dan Walker and Dr Richard Gibson for their continuing support. Thank you for listening