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This thesis is composed of theoretical, experimental, and numerical studies. In Part I, it discusses fundamental challenges of the discrete element method, provides a set of algorithms for addressing them, and presents performance gains of an improved algorithm on a target computer platform. A new contact detection and force resolution algorithm based upon (i) the fast common-plane (FCP) algorithm, (ii) using axisaligned bounding boxes (AABBs) to perform a proximity search, (iii) estimating the time of collision, and (iv) accurate resolution of contact points is presented. Benchmark simulations indicate an order of magnitude increase in performance is achievable for a relatively small number of elements. A new parallel discrete element algorithm is presented which combines the domain decomposition, object-oriented, and perfectly parallel strategies of parallelism to eliminate the drawbacks of parallel discrete element algorithms put forth by past studies. A significant speed-up is observed in comparison to past studies in trials conducted on a NUMA-based SMP computer. In Part II, various applications of the discrete element method are reviewed, with an emphasis on ice-structure interaction. The conical design of the Kulluk drillship is of particular interest due to its success in operating in the Beaufort Sea from 1975- 1993 and its subsequent purchase and recommission by Shell in 2006. Three previous experimental studies and a unique set of full-scale data measurements form the basis for comparison of a concurrent experimental and numerical investigation. The results of a model scale experiment at the NRC-IOT are analyzed and presented, followed by results of the numerical simulations. A 1:40 scale replica of the Kulluk platform in level ice produces results which are consistent with past experiments and confirm expected trends as well as different regimes of results dependent on the ductile/brittle behavior of ice. The numerical setup models the full-scale platform in three dimensions with a 24-sided rigid conical structure, ice as an elastic brittle material with plate-bending elements, and platform mooring through the implementation of a spread mooring algorithm. Numerical results are in agreement with past results for ice thickness of less than 1.2m, confirming that the initial design goal of the Kulluk was achieved while still overestimating the loads in comparison to the full-scale data set. Two explanations are presented for the non-conformity of the experimental and numerical predictions to the full-scale data results.

This thesis is composed of theoretical, experimental, and numerical studies. In Part I, it discusses fundamental challenges of the discrete element method, provides a set of algorithms for addressing them, and presents performance gains of an improved algorithm on a target computer platform. A new contact detection and force resolution algorithm based upon (i) the fast common-plane (FCP) algorithm, (ii) using axisaligned bounding boxes (AABBs) to perform a proximity search, (iii) estimating the time of collision, and (iv) accurate resolution of contact points is presented. Benchmark simulations indicate an order of magnitude increase in performance is achievable for a relatively small number of elements. A new parallel discrete element algorithm is presented which combines the domain decomposition, object-oriented, and perfectly parallel strategies of parallelism to eliminate the drawbacks of parallel discrete element algorithms put forth by past studies. A significant speed-up is observed in comparison to past studies in trials conducted on a NUMA-based SMP computer. In Part II, various applications of the discrete element method are reviewed, with an emphasis on ice-structure interaction. The conical design of the Kulluk drillship is of particular interest due to its success in operating in the Beaufort Sea from 1975- 1993 and its subsequent purchase and recommission by Shell in 2006. Three previous experimental studies and a unique set of full-scale data measurements form the basis for comparison of a concurrent experimental and numerical investigation. The results of a model scale experiment at the NRC-IOT are analyzed and presented, followed by results of the numerical simulations. A 1:40 scale replica of the Kulluk platform in level ice produces results which are consistent with past experiments and confirm expected trends as well as different regimes of results dependent on the ductile/brittle behavior of ice. The numerical setup models the full-scale platform in three dimensions with a 24-sided rigid conical structure, ice as an elastic brittle material with plate-bending elements, and platform mooring through the implementation of a spread mooring algorithm. Numerical results are in agreement with past results for ice thickness of less than 1.2m, confirming that the initial design goal of the Kulluk was achieved while still overestimating the loads in comparison to the full-scale data set. Two explanations are presented for the non-conformity of the experimental and numerical predictions to the full-scale data results.

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: There are several ports around the world currently experiencing problems with moored vessel motions. Extreme vessel motions are mainly caused by long waves, which can become trapped inside a harbour basin. The extreme motions can cause downtime in port operations and in some instances cause mooring lines to break. Methods and procedures currently available to measure motions of moored vessels require vessel specific information as input. The implementation of these methods is seen as impractical to implement on every vessel visiting the port and require the physical measurement of some points on the vessel and/or the placement of some kind of measurement device on the vessel. A new Six Degree of Freedom (6DOF) motion measurement system for a moored vessel is presented in this document. The system analyses a video image sequence from one camera. The method estimates the 3D rigid motion for an object of known size by using a Pose from Orthography and Scaling with ITerations (POSIT) algorithm. The object for which the motion is estimated is located on the deck of the vessel and within the camera field of view. Geometric rigid body calculations allow for the calculation of camera perspective rotations and translation of an object on the vessel. Further geometric calculations allow for converting camera perspective motions to the 6DOF object motions. The primary objective of this study was to validate and verify the motions obtained from two proof-of-concept tracking systems. For evaluation purposes, the validation was done by using a small scale physical model set-up in a hydraulics laboratory and using a known method as reference. The Keoship system from the Council for Scientific and Industrial Research (CSIR) is currently one of the most accurate small scale vessel motion measurement systems and was used as reference. The first method tested was the tracking of a 2D LED rectangle mounted on the vessel. This method tracked a 2D object and was primarily used as a stepping stone to measure movement of a 3D object. The second method tracked a 3D object on the vessel. Each tracking method was tested for four different wave conditions with each condition additionally repeated twice as repeatability tests, resulting in a total of 12 tests for each tracking method. When comparing the 2D LED tracking and 3D Object tracking data to data measured with the Keoship system, results show that in general, the 3D Object tracking data compared better to the Keoship data. Tests under controlled conditions enabled a direct estimation of the absolute accuracy of the two developed methods. The verification and accuracy test results, indicated that the 2D LED tracking system should not be pursued further. The results also indicated that for prototype motions exceeding 0.6 m (i.e. storm events) the 3D Object tracking system would have an accuracy close to the maximum allowable accuracy criterion of 0.1 m. This makes the system viable at its current proof-of-concept stage for further development which would enable rapid deployment during a storm event in a prototype situation. / AFRIKAANSE OPSOMMING: Daar is verskeie hawens regoor die wêreld wat tans bewegings probleme op gemeerde skepe ervaar. Hierdie buitensporige bewegings word veroorsaak deur lang periode golwe wat binne die hawe bekkens vasgekeer word. Dit kan daartoe lei dat hawe bedrywighede tot stilstand kom en in ernstige gevalle ook veroorsaak dat meringslyne breek. Huidige metodes vir die meet van skeepsbewegings op vasgemeerde skepe, vereis skeep spesifieke inligting as inset. Die toepassing van hierdie metodes op elke skip wat die hawe besoek, word as onprakties beskou, aangesien dit die fisiese meting van sekere punte op die skip behels. In sekere gevalle is dit selfs nodig om meet toestelle op die skip te plaas. In hierdie dokument word ‘n nuwe metode aangebied om die ses grade van vryheid bewegings vir ‘n vasgemeerde skip te meet. Hierdie stelsel analiseer ‘n video beeld reeks van een kamera. Die metode bereken die 3D rigiede beweging van ‘n voorwerp, waarvan die grootte bekend is. ’n ‘Pose from Orthography and scaling with Iterations’ (POSIT) algoritme word hiervoor gebruik. Die voorwerp waarvoor beweging gemeet word is op die dek van die skip en in kamera sig. Rigiede geometriese voorwerp berekeninge word gebruik om die rotasie en translasie vanuit ‘n kamera perspektief te bereken. Verdere geometriese berekeninge maak dit moontlik om die bewegings vanuit die kamera perspektief te omskep in die ses grade van vryheid bewegings van die voorwerp. Die hoof doelwit van hierdie ondersoek was om die gemete bewegings van twee beweging stelsels te valideer en te verifieer. Die validasie en verifiëring was in ‘n hidrolise laboratorium met ‘n klein skaal model opstelling getoets. ‘n Meet metode van skeepsbeweging op klein skaal wat reeds bekend is, is gebruik as ‘n verwysingsraamwerk waarteen die metings vergelyk kan word. Die Keoship stelsel van die Wetenskaplike Nywerheids Navorsings Raad (WNNR) is tans een van die mees akkurate klein skaal skeepsbeweging meet stelsels, en was as verwysing gebruik. Die eerste bewegings metode is getoets op ‘n 2D reghoek vervaaridig uit ligstralede diodes. Hierdie metode het die 2D voorwerp gevolg en is hoofsaaklik gebruik as ‘n boublok om die beweging van ‘n 3D voorwerp te volg. Die tweede metode het die beweging van ‘n 3D voorwerp op ‘n skip gevolg. Vir elke meet metode was daar vier verskillende golf toestande. Elke golf toestand was ook ‘n verdere twee keer herhaal vir herhaalbaarheids doeleindes. Saam met die herhaalbaarheids toetse was daar in totaal, 12 toetse vir elkeen van die twee metodes gedoen. Met die Keoship metode as verwysing, bewys hierdie toetse dat die 3D metode beter resultate lewer as die 2D metode. Toetse onder beheerde toestande, het dit moontlik gemaak om die absolute akkuraatheid van albei sisteme wat ontwikkel was, te evalueer. Verifikasie en akuraatheids toetse het aangedui dat verdere ontwikkeling van die 2D metode gestuit moet word. Die resultate het ook aangedui dat die 3D metode ‘n akuraatheid baie na aan die maatstaf van 0.1 m sal hê wanneer prototipe bewegings 0.6 m oorskrei (b.v. gedurende ‘n storm). Dit sal die oplossing lewensvatbaar maak by die huidige bewys van konsep fase vir die verdere ontwikkeling wat vinnige ontplooiing gedurende ‘n storm sal moontlik maak.

O presente trabalho propõe um novo modelo hidrodinâmico para avaliação das forças oriundas da ação de correnteza marítima uniforme sobre o casco de navios petroleiros amarrados. A modelagem é válida para qualquer ângulo de incidência de correnteza e sua aplicação é voltada, especialmente, ao estudo dinâmico de sistemas FPSO (Floating Production Storage and Offloading systems), muito embora seu campo de aplicação possa facilmente ser estendido a problemas correlatos em engenharia naval. O modelo ora apresentado depende basicamente das dimensões principais do casco, necessitando de um conjunto bastante pequeno de parâmetros a serem determinados experimentalmente. Essa natureza quase-explícita da modelagem constitui sua principal vantagem face aos demais modelos usualmente empregados, e a mesma advém exatamente do contexto mais restrito para o qual foi formulado. O modelo heurístico estendido foi elaborado com base em um modelo estático previamente desenvolvido por Leite et al. (1998). Foram incorporados os efeitos provenientes do movimento de rotação do casco, tornando o modelo aplicável ao caso geral de movimentos do navio no plano horizontal. A determinação destes efeitos foi fundamentada em uma abordagem heurística, combinando-se estimativas semi-empíricas para as forças decorrentes de diferentes padrões de escoamento fluido no entorno do casco, padrões estes associados a faixas de ângulos de incidência distintas. As estimativas de força e momento em movimento combinado de translação e rotação do casco foram validadas a partir de resultados experimentais obtidos em ensaios de yaw-rotating, conduzidos com modelos de diferentes navios petroleiros, em duas condições de carregamento distintas. ) Posteriormente, a verificação experimental foi ampliada, analisando-se a adequação do modelo hidrodinâmico ao estudo de instabilidade dinâmica de navios atracados por intermédio de um cabo de amarração (hawser), fenômeno conhecido em engenharia naval como fishtailing. Em paralelo ao desenvolvimento do modelo hidrodinâmico e sua validação experimental, objetivos primeiros deste trabalho, procede-se a uma revisão crítica das diferentes abordagens teóricas comumente empregadas, baseada nos principais aspectos hidrodinâmicos envolvidos em aplicações práticas de navios amarrados em sistemas offshore. Assim, face à complexidade do problema em questão e dada a profusão de modelos teóricos existentes na literatura, mais do que a defesa de um ou outro método de análise, procura-se fornecer um orientação consistente para que o projetista de sistemas oceânicos possa escolher, com maior confiança, a abordagem mais apropriada para a aplicação em questão, ciente de suas vantagens e eventuais limitações. / A new hydrodynamic model for the analysis of current forces acting on moored tanker ships is proposed. The theoretical model is valid for any angle of attack of the current and is intended, primarily, for the analysis of FPSO (Floating Production Storage and Offloading) systems, although its application may be easily extended to other correlated problems in ocean engineering. The model depends basically on the ship main dimensions and requires few external parameters to be derived. This quasi-explicit nature certainly constitutes the model main advantage and it was only possible due to the more restricted context it was derived for. The extended heuristic model, as it is called, was based on a previous static version presented by Leite et al. (1998). The hydrodynamic effects arising from the ship yaw motion were now incorporated, making the model able to cope with the problem of combined drift-yaw motions. Yaw velocity influence was determined by means of a heuristic combination of semi-empirical formulations of force and moment components, resultant from distinct fluid flow patterns, each one related to a different range of angles of attack. Force predictions were validated through confrontation with yaw-rotating experimental results, obtained for different tanker models in distinct loading conditions. It was also verified experimentally that the model is capable of predicting the hydrodynamic forces involved in the unstable dynamic behavior of asingle-point moored tanker, when subjected to a steady ocean current, known as fisthailing phenomenon. A critical revision of the different theoretical models at hand represents a supplementary purpose of this work. This revision was performed based on the main hydrodynamic aspects involved in common offshore applications of moored tanker ships. ) Therefore, instead of a passionate defense of any particular theoretical procedure, the work aims to provide a consistent orientation in order to help the offshore system designer to choose, between the various hydrodynamic models, the one that is more suitable for the analysis of a specific project, confident on its advantages and aware of its eventual limitations.

O presente trabalho propõe um novo modelo hidrodinâmico para avaliação das forças oriundas da ação de correnteza marítima uniforme sobre o casco de navios petroleiros amarrados. A modelagem é válida para qualquer ângulo de incidência de correnteza e sua aplicação é voltada, especialmente, ao estudo dinâmico de sistemas FPSO (Floating Production Storage and Offloading systems), muito embora seu campo de aplicação possa facilmente ser estendido a problemas correlatos em engenharia naval. O modelo ora apresentado depende basicamente das dimensões principais do casco, necessitando de um conjunto bastante pequeno de parâmetros a serem determinados experimentalmente. Essa natureza quase-explícita da modelagem constitui sua principal vantagem face aos demais modelos usualmente empregados, e a mesma advém exatamente do contexto mais restrito para o qual foi formulado. O modelo heurístico estendido foi elaborado com base em um modelo estático previamente desenvolvido por Leite et al. (1998). Foram incorporados os efeitos provenientes do movimento de rotação do casco, tornando o modelo aplicável ao caso geral de movimentos do navio no plano horizontal. A determinação destes efeitos foi fundamentada em uma abordagem heurística, combinando-se estimativas semi-empíricas para as forças decorrentes de diferentes padrões de escoamento fluido no entorno do casco, padrões estes associados a faixas de ângulos de incidência distintas. As estimativas de força e momento em movimento combinado de translação e rotação do casco foram validadas a partir de resultados experimentais obtidos em ensaios de yaw-rotating, conduzidos com modelos de diferentes navios petroleiros, em duas condições de carregamento distintas. ) Posteriormente, a verificação experimental foi ampliada, analisando-se a adequação do modelo hidrodinâmico ao estudo de instabilidade dinâmica de navios atracados por intermédio de um cabo de amarração (hawser), fenômeno conhecido em engenharia naval como fishtailing. Em paralelo ao desenvolvimento do modelo hidrodinâmico e sua validação experimental, objetivos primeiros deste trabalho, procede-se a uma revisão crítica das diferentes abordagens teóricas comumente empregadas, baseada nos principais aspectos hidrodinâmicos envolvidos em aplicações práticas de navios amarrados em sistemas offshore. Assim, face à complexidade do problema em questão e dada a profusão de modelos teóricos existentes na literatura, mais do que a defesa de um ou outro método de análise, procura-se fornecer um orientação consistente para que o projetista de sistemas oceânicos possa escolher, com maior confiança, a abordagem mais apropriada para a aplicação em questão, ciente de suas vantagens e eventuais limitações. / A new hydrodynamic model for the analysis of current forces acting on moored tanker ships is proposed. The theoretical model is valid for any angle of attack of the current and is intended, primarily, for the analysis of FPSO (Floating Production Storage and Offloading) systems, although its application may be easily extended to other correlated problems in ocean engineering. The model depends basically on the ship main dimensions and requires few external parameters to be derived. This quasi-explicit nature certainly constitutes the model main advantage and it was only possible due to the more restricted context it was derived for. The extended heuristic model, as it is called, was based on a previous static version presented by Leite et al. (1998). The hydrodynamic effects arising from the ship yaw motion were now incorporated, making the model able to cope with the problem of combined drift-yaw motions. Yaw velocity influence was determined by means of a heuristic combination of semi-empirical formulations of force and moment components, resultant from distinct fluid flow patterns, each one related to a different range of angles of attack. Force predictions were validated through confrontation with yaw-rotating experimental results, obtained for different tanker models in distinct loading conditions. It was also verified experimentally that the model is capable of predicting the hydrodynamic forces involved in the unstable dynamic behavior of asingle-point moored tanker, when subjected to a steady ocean current, known as fisthailing phenomenon. A critical revision of the different theoretical models at hand represents a supplementary purpose of this work. This revision was performed based on the main hydrodynamic aspects involved in common offshore applications of moored tanker ships. ) Therefore, instead of a passionate defense of any particular theoretical procedure, the work aims to provide a consistent orientation in order to help the offshore system designer to choose, between the various hydrodynamic models, the one that is more suitable for the analysis of a specific project, confident on its advantages and aware of its eventual limitations.

Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: When a sailing ship passes a moored ship the moored ship experiences forces and moments. These forces and moments cause the moored ship to move. The resulting ship motions due to the passing ship can sometimes be more severe than the ship motions due to ocean waves and can cause serious accidents at moorings such as the failing of mooring lines or even the total break away of the ship from the berth. Since bulk carriers and tankers were traditionally the largest seafaring ships, passing ship studies have focused mainly on these vessels, but recently container ships have grown to a comparable size. In this study an existing numerical model “Passcat” is validated with physical model measurements for a Post Panamax container ship passing a Panamax bulk carrier. Other existing mathematical formulae are also evaluated by comparison with these model tests. In the physical model tests the passing speed (V), passing distance (G), depth draft ratio (d/D) and the presence of walls and channels were varied. It was found that the passing ship forces are proportional to the passing speed to the power of 2.32. This is slightly higher than the generally accepted quadratic relationship for passing ship induced forces. Similar relationships were found for the other variables. The numerical model results were compared to the physical model measurements by determining agreement ratios. A perfect agreement between the numerical and physical models would result in an agreement ratio of 1. Agreement ratio boundaries, wherein agreement would be regarded as good, were drawn between 0.7 and 1.3. The numerical model, Passcat, was found to under predict the passing ship forces. It was found that Passcat is valid for a wide range of sensitivities and remains within the agreement ratio limits as long as passing speed is limited to 10 knots (kt), depth draft ratio to more than 1.164, passing distance to less than four times the moored ship beam (Bm) for surge and sway estimation and passing distance to less than three times the moored ship beam for yaw estimations. These limits are true for no structures in the water. For structures in the water only the passing speed limits are different. When quay walls are present, the surge and sway forces will only provide acceptable answers at passing speeds below 9kt. When 9Bm or 12Bm channels are present, the sway force will only provide acceptable answers at passing speeds below 7kt. When a 6Bm channel is present, the yaw moments will only provide acceptable answers at passing speeds below 6kt. From the mathematical model evaluation study it was found that empirical or semi empirical methods can not provide answers with good agreement to the physical model when walls or channels are present. For the open water case, it is only the Flory method that can provide answers with good agreement to the physical model for surge, sway and yaw forces. The Flory method can provide answers with acceptable agreement within narrow boundaries of passing distance (1 to 2 times the beam of the moored ship), passing speed (4 kt to 14 kt) and depth draft ratio (less than 1.7). The numerical model, Passcat can be used with little effort to provide answers with better agreement to the physical model for a larger range of variables. / AFRIKAANSE OPSOMMING: Wanneer ’n skip verby ‘n vasgemeerde skip vaar, ondervind die vasgemeerde skip kragte en momente. Hierdie kragte induseer beweging van die vasgemeerde skip. Die beweging kan soms groter wees as die effek van wind of golwe. Indien die bewegings groot genoeg is kan dit van die vasmeer lyne van die skip laat breek, of al die lyne laat breek sodat die skip vry in die hawe ronddryf. Aangesien erts skepe en tenk skepe vir jare die grootste skepe in the wêreld was, het die meeste van die skip interaksie studies op daardie skepe gefokus. Die grootte van behouering skepe het egter in die onlangse tye gegroei om dimensies soortgelyk aan die van erts en tenk skepe te hê. In hierdie studie word ’n bestaande numeriese model “Passcat” gestaaf met fisiese model metings op ’n Post Panamax behoueringskip wat verby ‘n Panamax erts skip vaar. Bestaande wiskundige formules is ook getoets deur dit met dieselfde fisiese model metings te vergelyk. In die fisiese model studie is die spoed van die skip (V), tussenafstand (G), diepte diepgang verhouding (d/D) en die teenwoordigheid van kaai mure en kanale in die water getoets. Daar is gevind dat die kragte op die vasgemeerde skip direk eweredig is aan die spoed van die skip tot die mag 2.32. Dit is effens meer as die algemeen aanvaarde kwadratiese verhouding tussen vloeistof sleurkrag en vloeisnelheid asook tussen skip interaksie kragte en vaar snelheid. Soortgelyke verhoudings is vir al die veranderlikes bereken. Numeriese model resultate is vergelyk met die fisiese model om die verhouding van ooreenstemming te bepaal. ’n Perfekte ooreenstemming word voorgestel deur ’n verhouding van ooreenstemming van 1. Grense waarbinne die verhouding van ooreenstemming as goed beskou word is getrek tussen 0.7 en 1.3. Daar is gevind dat die numeriese model, Passcat, kragte oor die algemeen onderskat. Passcat is geldig vir 'n breë reeks van veranderlikes en sal geldig bly solank die skip spoed tot 10 knope, diepte diepgang verhouding tot meer as 1.164, tussenafstand tot minder as vier skipwydtes (Bm) vir 'surge' en 'sway' kragte en tot minder as drie skipwydtes vir 'yaw' momente beperk word. Hierdie grense is opgestel vir geen strukture in die water. Vir strukture in die water word slegs die skip spoed aangepas. Wanneer daar mure in die water is sal 'surge' en 'sway' slegs geskikte antwoorde gee as die skip spoed tot 9 knope beperk word. Vir 9Bm of 12Bm kanale sal geskikte antwoorde vir 'sway' kragte slegs voorkom met 'n skip spoed minder as 7 knope. Vir 6Bm kanale sal geskikte antwoorde vir 'yaw' momente slegs voorkom met 'n skip spoed van minder as 6 knope. Van die wiskundige model evaluasie studie is gevind dat empiriese of semi empiriese metodes nie resultate met goeie ooreenstemming tot the fisiese model metings kan gee, wanneer daar kaai of kanaal mure in die water is nie. Vir die oopwater geval is dit slegs die Flory metode wat antwoorde kan voorsien wat goed ooreenstem met die fisiese model vir 'surge', 'sway', en 'yaw' kragte. Die Flory metode voorsien hierdie resultate binne noue grense vir tussenafstand (1 tot 2 wydtes van die vasgemeerde skip), verbyvaar spoed (4 knope tot 14 knope) en diepte diepgang verhouding (minder as 1.7). Die numeriese model, Passcat, kan met min moeite antwoorde bereken wat beter ooreenstemming vir 'n groter reeks veranderlikes gee.