Numerical modelling of wave-induced vertical ship motions at the Port of Richards Bay : calibration and computation of extreme values

Sebopa, Mogau (2020-03)

Thesis (MEng)--Stellenbosch University, 2020.

Thesis

ENGLISH ABSTRACT: The CSIR conducted extensive scale model studies of wave-induced hull motion response of ships in shallow water. The aim of these studies was to produce a solid database that will, in future, assist South African ports with channel depth optimization. Physical model tests of a fully laden 150kt deadweight bulk carrier were carried out at a scale of 1:100. Physical model test results used to calibrate the Wavescat model and involved exciting the ship with waves from 90°, 135° and 180° with relation to the ship’s bow at zero forward speed. Depth to draught ratio (d/D) varied from 1.5, 1.4, 1.3 and 1.2 with a wave spectrum of significant wave heights of 3 m, 4 m and 5 m and a peak period of 10 s. Sensitivity tests for beam waves (90°) were conducted using d/D of 1.1, significant wave heights from 1m until bottom touching occurred and peak periods of 10 s and 12 s. The sensitivity tests were conducted to study the effects of wave heights on the hull motion response. Both wave spectrums and the response amplitude operators (RAOs) data were processed using a time-domain analysis to determine significant hull motion response in relation to angles of wave incidence and depth to draught ratios. The findings of the studies were that: • The ratios of significant hull motion amplitudes to significant wave height (As/Hs) for 135° and 180° have the same magnitude and are not sensitive to a reduction of depth to draught ratios up to about d/D of 1.5, where As=Hs starts decreasing with a further reduction of d/D. As/Hs values for 90° have the highest magnitude out of all the tested angles which appear to be directly proportional to d/D ratios as tested. • The over-all pitch and heave significant hull motion amplitude (As) values for 135° and 180° were 0.2 to 0.3 times Hs, while As for 90° was 0.75 times Hs. • The Rayleigh probability distribution provided a good estimate of the most probable extreme motion amplitude in relation to the probability of occurrence of the numbers of motion amplitudes occurring in the given period of time. • The relationship between the maximum individual hull motion amplitude (Amax) and the significant hull motion amplitude (As) for motions larger than 1.5m deviate from the initial linearity of this relationship. • Significant hull motion increases linearly with an increase in wave height, from the wave height ranges tested for both physical and numerical models. The objectives of the present studies is to use the Wavescat numerical model to test if it can accurately compute vertical keel point motions of a fully laden 150 kt deadweight coal carrier ship model with a draught of 17 m by : • using results obtained from the fully laden 150 kt deadweight physical model, to calibrate the numerical model. Wave spectrums from Mike21BW and RAOs computed by the Wavescat model will be used to calculate vessel response spectrums, which will then help determine vertical keel point motions for different depths, wave heights and incident wave directions. • converting the vessel response spectrums to time domain to obtain timeseries for each selected depth, wave height and incident wave direction. Since the wave phase of the original timeseries is unknown, wave phases will randomly be chosen and • using the zero - crossing method to determine the ship motion amplitudes for each selected depth, wave height and incident wave direction. This excercise will be followed by grouping ship motion amplitudes of the same heights and incident wave direction which will then be fitted to non-linear probability distributions. • For the latter purpose, the Rayleigh distribution, the Generalized Extreme Value distribution, the Generalized Pareto distribution and the Weibull distribution will be applied to determine which distribution best represents the non-linear relationship of maximum individual hull motion amplitudes for ship motion amplitude more than 1.5 m. These probability distributions will be fitted to ship motion amplitudes greater than 1.5 m because their non-linearity were not well represented by the Rayleigh distribution in the research previously conducted by the CSIR. The calibrated Wavescat model will then be used to investigate the nonlinear factors that affect the vertical keel point motions. These non-linear factors are speed, centre of roll rotation, small underkeel clearance and squat. The ship model’s vertical keel point motions will be tested for storm conditions with wave heights of 3 m and 4 m and peak periods of 14 s 16 s and 18s.

AFRIKAANSE OPSOMMING: Die WNNR het uitgebreide skaalmodelstudies van golfgeïnduseerde rompbeweging van skepe in vlak water gedoen. Die doel van die studies was om ’n omvattende databasis te produseer wat in die toekoms Suid-Afrikaanse hawens sal help met die optimalisering van kanaaldieptes. Fisiese modeltoetse van ’n volgelaaide 150 kt dooiegewig grootmaatskip is op ’n skaal van 1: 100 uitgevoer. Die fisiese modelresultate is gebruik om die Wavescat-model te yk vir skeepsbeweging as gevolg van golwe van 90 , 135 en 180 teen geen voorwaartse spoed. Diepte tot diepgangverhouding (d/D) wissel van 1.2 tot 1.5 met ’n golfspektrum van maatgewende golfhoogtes van 3 m, 4 m, 5 m met ’n spitsperiode van 10 s. Sensitiwiteitstoetse is onderneem met ’n d/D van 1.1, maatgewende golfhoogtes vanaf 1 m totdat die bodem geraak word en vir spitsperiodes van 10 s en 12 s. Die sensitiwiteitstoetse is onderneem om die effek van golfhoogtes op die rompbeweging te bestudeer. Die data is toe verwerk met behulp van ’n tyddomein-ontleding om maatgewende rompbeweging te bepaal met betrekking tot golfinvalhoeke en d /D-verhoudings. Die bevindings van die studies is soos volg: • Die verhoudings van maatgewende rompbewegings tot maatgewende golfhoogte (As=Hs) vir 135° en 180° is dieselfde grootte en is nie sensitief vir ’n vermindering van d/D tot ongeveer 1.5 nie. Daarna begin As=Hs afneem met ’n vermindering van d/D. As=Hs-waardes vir 90° is die grootste vir al die getoetste hoeke. Dit kom voor dat As=Hs toeneem soos d/D toeneem. • Die amplitude van die maatgewende rompbewegings (As) vir stamp en dein se waardes vir 135° en 180° is tussen 0.2 en 0.3 keer Hs, terwyl dit 0.75 keer Hs vir 90° is. • Die Rayleigh-waarskynlikheidsverdeling verskaf n goeie skatting van die mees waarskynlike uiterste bewegingsamplitude in verhouding met die waarskynlikheid van voorkoms van die grootste waardes van die bewegingsamplitude in die gegewe tydperk. • Die verband tussen die maksimum individuele rompbewegingsamplitude (Amax) en die maatgewende rompbewegingsamplitude (As) vir bewegings groter as 1.5 m wyk af van die aanvanklike lineêre verband. • Maatgewende rompbeweging styg lineêr met ’n toename in golfhoogte vir die getoetste bereik vir beide fisiese en numeriese modelle. Die doelwit van hierdie studie is om te toets of die wiskundige skeepsbewegingsmodel Wavescat vertikale kielpunte se bewegings akkuraat kan voorspel vir ’n volgelaaide 150 kt-dooiegewig grootmaatsteenkoolskip met n diepgang van 17 m. Dit word gedoen deur: • Resultate wat in ’n fisiese modelstudie verkry is, vir yking van die wiskundige model te gebruik. Golfspektrums van Mike21BW en die berekende RAO’s van die Wavescat-model is benut om die skeepsbewegingspektrums te bereken. Op sy beurt word hierdie spektrums dan gebruik om die vertikale kielpuntbewegings vir verskillende dieptes, golfhoogtes, en invallende golfrigtings te bepaal. • Om die skeepsbewegingspektrums na die tyddomein oor te sit ten einde tydreekse vir elke gekose diepte, golfhoogte en invallende golfrigting te verkry. Omdat die golffase van die oorspronklike tydreeks onbekend is, word lukrake golffases tussen + en - gekies. • Deur die nulkruismetode te gebruik om die skeepsbewegingsamplitudes vir elke diepte, golfhoogte en invallende golfrigting te bepaal. Hierdie oefening word gevolg deur die groepering van skeepsbewegingsamplitudes vir dieselfde hoogtes en invallende golfrigting, wat dan teen nie-lineêre waarskynlikheidsverdelings gepas word. • Vir laasgenoemde doelwit, is die Rayleigh-, Veralgemeende Uiterste waarde (GEV)-, die Algemene Pareto en die Weibullverdelings toegepas. Sodoende kon bepaal word watter verdeling die nie-lineêre verwantskap van die maksium indiwiduele rompbeweging se amplitudes vir skeepsbeweging van meer as 1.5 m die beste weergee. Hierdie waarskynlikheidsverdelings is vir skeepsbeweging van meer as 1.5 m gepas omdat die nie-lineêre aard nie goed deur die Rayleigh-verdeling in die WNNR se vorige toetse weergegee is nie. Die geykte Wavescat-model is toe gebruik om die nie-lineêre faktore wat die vertikale kielpuntbewegings beïnvloed, te ondersoek. Hierdie nie-lineêre faktore is spoed, swaartepuntrotasie tydens skeepsrol, klein kielvryhoogtes en hurk. Die skeepsmodel se vertikale kielpuntbewegings is getoets vir stormtoestande met golfhoogtes van 3 m en 4 m, met spitsperiodes van 14 s, 16 s en 18 s.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/107812
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