In an attempt to contribute the efforts for the robust and effective numerical tools concerning ship motions in astern seas, this thesis presents the development of a coupled non-linear 6-DOF model with frequency dependent coefficients, incorporating memory effects in random waves with a new axis system that allows straightforward combination between seakeeping and manoeuvring model whilst accounting for extreme motions. A combination of seakeeping and manoeuvring is achieved through the adoption of relatively new "horizontal body axis system" which accounts for large vertical motions as well. Furthermore, the frequency dependent terms are incorporated in order to improve the accuracy of the numerical model for non-zero encounter frequencies which are experienced especially when the ship has large heading angle. The effect of encounter frequency and so called "memory effects" are calculated in terms of radiation forces using convolution integrals. Equations of motions and external forces are described in terms of a new axis system. The wave forces are calculated through incident and diffraction wave forces. The incident wave forces are calculated using the instantaneous wave surface while low encounter frequency model is adopted for the calculation of diffraction forces. Finally, the whole numerical model is expressed in random sea environment including the convolution terms to carry out the simulations in more realistic sea environments. The validation of the numerical model with the results of benchmark tests commissioned by ITTC Specialist Group on Stability, showed reasonably satisfactory agreement while the inclusion of frequency dependent terms affected the accuracy of the numerical model. Parametrical studies were carried out to investigate the effect of different environmental and operational parameters to ship motions in extreme astern seas along with the effects of degrees of freedom and encounter frequency. In order to enhance the numerical model and to obtain further information about the coupling of the motions and the adequacy of the numerical model to carry out further simulations regarding dangerous situations during ship motions in random following and quartering seas, extensive captive and free running model tests were carried out. The numerical model provided good agreement with the experiments. The terms resulting from the coupling of vertical motions and large heeling angle to wave forces are obtained. It is believed that the numerical model has a good potential for providing a more rational basis for predicting the dangerous conditions which a ship could face in extreme astern seas, and for offering insights about the link of behaviour with the design parameters of a ship in the light of the validation with the experiment results and parametrical studies.

This thesis focuses on the effects of wave-induced motions on the airwake of a ship and on the operation of a helicopter in the airwake. While the topic is broad, efforts are concentrated on understanding fundamentals of the ship’s airwake structure at varying Reynolds (Re) numbers without motions, using available experimental data for validation of the computational fluid dynamics (CFD) methodology used, and on studying the effects of waves and motions on the airwake of a ship and a helicopter operating above a ship’s flight deck in full-scale. The static ONR Tumblehome (ONRT) ship geometry with a solid boundary representative of the free surface is simulated at three different Re numbers, 3.2x104, 1x106, and 1.3x108. Validation is performed against experimental measurements at model-scale Re=1x106. Full-scale simulations of the ONRT are carried out in head winds and regular waves approximately equivalent to conditions seen at sea states 3 and 6. Effects of waves and motions are isolated for both sea states using simulations with combinations of waves and motions, waves and no motions, no waves with motions, and no motions or waves. A triple velocity decomposition is conducted in order to quantify changes in the airwake due to motions and waves. The operation of rotorcraft in the ONRT airwake is analyzed using one-way and two-way coupling approaches. The one-way coupling approach uses the velocity field data from the full-scale ONRT simulations and disk actuator theory to calculate thrust fluctuations for three different rotor sizes. The results of the one-way coupling approach show that the smallest rotor is much more affected by small scale turbulence, while small scale fluctuations are filtered out by larger rotor diameters. In the two-way coupling approach, a helicopter based on the Sikorsky SH-60 hovering above the flight deck is simulated, including explicitly moving grids to discretize the main rotor, tail rotor, and fuselage. This method captures the effects of the interaction between the rotor downwash and the ONRT airwake. The study shows that for the mild conditions of sea state 3 the motions have little effect on the airwake behavior. At sea state 6 the airwake behavior is significantly altered, which is reflected in the resulting forces on the helicopter body operating in this condition.

We study the hydrodynamics of wedge,knuckle and box cross-sectional profiles undergoing transient extreme motions, in particular forced entry and exit at constant velocity or acceleration. Extensive data for the forces, pressures and free-surface profiles is generated by an extension of a fully-nonlinear boundary-integral method. The code is thoroughly checked by altering the time step and particle spacing on the bodies and Lagrangian free-surface markers, and, for the wedge,checking self-similarity for the infinite Froude number (gravity free) constant velocity entry. Difficulties with inviscid flow around sharp corners are discussed. Results for exit are of particular interest since no zero-gravity approximation is valid and this precludes application of existing slamming theories in reverse. Whilst entry generally gives larger free-surface motions (spray jets), pressures and hence forces, calculation of exit is needed for the velocity of subsequent slamming and so is of practical interest too. These results are compared with an approximate analytical model, based on Schwarz-Christoffel transformations to calculate the infinite-frequency added mass of the cross-section below the mean water line. For constant acceleration of both entry and exit, the analytical theory is good during the early stages of motion. Later, the assumption of an undisturbed mean water level is clearly violated; the exact calculations show a large amount of draw-down (up-rise), the free-surface making contact with the body well below (above) the mean water level. We therefore examine the effect of reducing (increasing) the submerged body volume to take account of this, which prolongs the agreement between the results considerably and therefore might be used to improve practical calculation of extreme ship motions using existing strip theory codes. Full sets of numerical data input/output are provided in the appendices, together with some mathematical details. We also speculate on the possible application of John's equation to wedge entry.

Ship roll motion has been the subject of many studies, because of the complexities associated with this mode of ship motion, and its impact on operability, safety, and survivability. Estimation and prediction of the energy transfer and dissipation of the hydrodynamic components, added inertia and damping, is essential to accurately describe the roll motions of a ship. This is especially true for ship operations in moderate to extreme sea conditions. In these conditions, a complex process of energy transfer occurs, which alters the physical behavior of the hydrodynamic components, and ultimately affects the amplitude of ship roll motion. Bilge keels have been used on ships for nearly two centuries, to increase damping and reduce the severity of roll motions experienced by a ship in waves. Because ship motions are more severe in extreme sea conditions, large roll angles may occur. With the possibility of crew injury, cargo damage, or even capsize, it is important to understand the behavior of the roll added inertia and damping for these conditions. Dead ship conditions, where ships may experience excitation from beam, or near beam, seas present a worst case scenario in heavy weather. The behavior of a ship in this condition should be considered in both the design and assessment of seakeeping performance. In this study, hydrodynamic component models of roll added inertia and roll damping were examined and assessed to be unsuitable for accurate prediction of ship motions in heavy weather. A series of model experiments and numerical studies were carried out and analyzed to provide improved understanding of the essential physical phenomena which affect the hydrodynamic components and occur during large amplitude roll motion. These observations served to confirm the hypothesis that the existing models for roll added inertia and damping in large amplitude motions are not sufficient. The change in added inertia and damping behavior for large roll motion is largely due to the effects of hull form geometry, including the bilge keels and topside geometry, and their interactions with the free surface. Therefore, the changes in added inertia and damping must be considered in models to describe and predict roll motions in severe wave environments. Based on the observations and analysis from both experimental and numerical methods, several time-domain model formulations were proposed and examined to model hydrodynamic components of large amplitude roll motions. These time-domain formulations included an analytical model with memory effects, a piecewise formulation, and several possibilities for a bilge keel force model. Although a piecewise model for roll damping was proposed, which can improve the applicability of traditional formulations for roll damping to heavy weather conditions, a further attempt was undertaken to develop a more detailed model specifically for the bilge keel force. This model was based on the consideration of large amplitude effects on the hydrodynamic components of the bilge keel force. Both the piecewise and bilge keel force models have the possibility to enable improved accuracy of potential flow-based numerical prediction of ship roll motion in heavy weather. However, additional development remains to address issues for further practical implementation. / Ph. D.

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.