Offshore mooring towers are one of a number of single-point mooring (SPM) systems which provide a berthing point for tankers, enabling the transfer of crude oil to or from the moored vessel. The periodic slackening of the mooring hawser between the vessel and the tower gives rise to a discontinuously non-linear restoring function. Hence, the wave-induced motions of the tower can be highly complex, with the possibility of large amplitude, and potentially hazardous motions. A large amount of work has been carried out in studying single-point mooring systems. However, much of this work has focused on mooring forces and tanker motions. Few studies have looked in-depth at the motions of the mooring structure itself. In this thesis, mooring tower motions have been studied in detail using three techniques: numerical analysis, approximate analytical methods, and experimental modelling. Each of these approaches to the problem has demonstrated that large amplitude and hence potentially hazardous motions can occur. Numerical predictions of motion showed very good comparison with measured responses, particularly for synchronous motions. However, for more complex motions, such as subharmonic resonances, the agreement between measured and predicted results was seen to deteriorate. Approximate analytical methods did not perform so well. Useful results were obtained for the simplified single-degree-of-freedom symmetric model only, highlighting the need for a more sophisticated method. This research has been successful in providing insight into the complex non-linear motions of an offshore mooring tower. The fundamental mechanisms and features of the system have been presented. The methodology used in this study has been applied to the specific case of an offshore mooring tower. However, the general approach to investigating the non-linear motions of the structure is widely applicable in the field of offshore engineering.

The validation of the “interFoam” CFD model (part of the OpenFOAM) CFD library is described for a number of wave/structure interaction problems. The background to the research is described, including the reasons for the selection of a new, previously unvalidated CFD code for this purpose. The numerical aspects of the code are briefly reviewed as are some of its additional features including the simulation of porous media. The new wave-generating boundary condition, created as part of this project, is described. The model is validated for the propagation of waves, including violent, breaking waves, using the widely-known “Dingemans” test case as well as new data for wave and focussed wave group propagation over a bar. The model is validated for wave interaction with surface-piercing structures by examining a test case for focussed wave-group impact on a surface-piercing cylinder with one near-breaking wave and a second, breaking, wave. The model is shown to perform well in these cases without the need for calibration and can therefore be considered to be a valuable design tool. It is also shown that in these cases the model can run sufficiently fast to be practical and economic for use as a design tool. The model is validated for porous media with a case examining porepressure transmission through a porous breakwater. The model performs poorly without calibration, highlighting the high levels of uncertainty in the Darcy parameter, but once calibrated is found to produce accurate results in very reasonable time. A case study of a porous roundhead defence structure is also presented to further reinforce the practical usefulness of the model in design.

This paper presents analytic expressions for the wave structure function, frequency spread of the temporal frequency spectrum, and the temporal frequency spectrum of optical signals propagating through a random medium, specifically the Earth’s atmosphere. The results are believed to be valid for all optical turbulence conditions. These expressions are developed using the Rytov approximation method. Generally, the validity of statistical quantities obtained via this method is restricted to conditions of weak optical turbulence. However, in this work, by using a modification of the effective atmospheric spectral model presented by Andrews et al. for scintillation index, wave structure function expressions have been derived that are valid in all turbulence conditions as evidenced by comparison to experimental data. Analytic wave structure function results are developed for plane, spherical, and Gaussian-beam waves for one-way propagation. For the special case of a spherical wave, comparisons are made with experimental data. The double pass case is also considered. Analytic expressions for the wave structure function are given that incorporate reflection from a smooth target for an incident spherical wave. Additionally, analytic expressions for the frequency spread of the temporal frequency spectrum and the temporal frequency spectrum itself, after one-way propagation for horizontal and slant paths, are derived for plane and spherical waves. These results are also based on the Rytov perturbation method . Expressions that are believed to be valid in all turbulence conditions are also developed by use of the effective atmospheric spectral model used in the wave structure function development. Finally, double pass frequency spread expressions are also presented. As in the case of the wave structure function, reflection from a smooth target with an incident spherical wave is considered.

Local and global loadings, which may cause the local damage and/or global failure and collapse of offshore structures and ships, are experimentally investigated in this study. The big research question is how the aeration of water and the elasticity of the structural section affect loading during severe environmental conditions. A further question is how the scattered waves from ships and offshore structures, the mooring line force and the structural response, which are known to affect local load and contribute to global load, will be affected by wave-structure interaction of a ship or offshore structure under non-breaking wave conditions. Three different experiments were undertaken in this study to try to answer these questions: (i) slamming impacts of a square flat rigid/elastic plate, which represents a plate section of the bottom or bow of ship structure, onto pure and aerated water surface with zero degree deadrise angle; (ii) wave impacts on a truncated vertical rigid/elastic wall in pure and aerated water, where the wall represents a plate section of a hull; and (iii) wave-structure interactions of different FPSO-shaped models, where the models were fixed or taut moored. The experiments were carried out at Plymouth University’s COAST Laboratory. Spatial impact pressure distributions on the square plate have been characterised under different impact velocities. It was found that the impact pressures and force in pure water were proportional to the square of impact velocity. There was a significant reduction in both the maximum impact pressure and force for slamming in aerated water compared to that in pure water. An exponential relationship of the maximum force and the void fraction is proposed and its coefficients are found from drop test in this study. There was also a significant reduction in the first phase of the pressure and force impulse for slamming into aerated water compared with pure water. On the truncated wall, aeration also significantly reduced peak wave loads (both pressure and force) but impulses were not reduced by very much. For the case considered here, elasticity of the impact plate has a significant effect on the impact loads, though only at high impact velocities; here the impact loads were considerably reduced with increasing elasticity. Wave loading on the truncated wall was found to reduce with increasing elasticity of the wall for all investigated breaking wave types: high aeration, flip-through and slightly breaking wave impacts. In particular, impact pressure decreases with increasing elasticity of the wall under flip-through wave impact. As elasticity increases, the impulse of the first positive phase of pressure and force decreases significantly. This significant effect of hydroelasticity is also found for the total force impulse on the vertical wall under wave impacts. Scattered waves were generated from the interaction of focused wave groups with an FPSO model. The results show that close to the bow of the FPSO model, the highest amplitude scattered waves are observed with the most compact model, and the third- and fourth-harmonics are significantly larger than the incident bound harmonic components. At the locations close to the stern, the linear harmonic was found to increase as the model length was decreased, although the nonlinear harmonics were similar for all three tested lengths, and the second- and third-harmonics were strongest with the medium length model. The nonlinear scattered waves increased with increasing wave steepness and a second pulse was evident in the higher-order scattered wave fields for the fixed and free floating models. In addition, the higher harmonics of the mooring line force, and the heave and pitch motions all increased with increasing wave steepness. Incident wave angles of 0 (head-on), 10 and 20 degrees were experimentally investigated in this study. As the incident wave angle between the waves and the long axis of the vessel was increased from 0 to 20 degrees, the third- and fourth-harmonic scattered waves reduced on the upstream side. These third- and fourth-harmonic diffracted waves are important in assessing wave run-up and loading for offshore structure design and ringing-type structural response in fixed and taut moored structures. The second-, third- and fourth-harmonics of the mooring line force, and the heave and pitch motions decreased as the incident wave angle increased from 0 to 20 degrees.

Today, more than forty percent of the world’s population lives within 100 kilometers of a coastal area, and population densities are only increasing. In recent years, extreme conditions have resulted in several failures of coastal protection structures around the world. During these failure events, the incurred cost of damages and loss of life has been nearly immeasurable. Rubble mound breakwaters have been used for millennia, and are critical even today for the protection of coastal areas. In the last several decades, the popularity of using concrete armour units in place of natural rock has risen greatly. However, the quantitative interaction between wave hydrodynamics and the armour layer is still not clearly understood. Due to highly complex, turbulent flow patterns that occur in the armour layer, direct assessment of forces acting on individual units has not been practical. This has prevented the coastal engineering field from applying a force-balance design approach that is commonplace in other civil engineering disciplines. Instead, a wealth of experimental testing and past case studies have resulted in a wide array of empirical formulae and design techniques. These approaches are often very idealized and do not account for all parameters that have been shown to affect armour unit stability. The current study aims to quantify the forces and pressures acting on units within an armour layer, using an experimental approach. This was achieved by developing an instrumented Core-Loc armour unit. This armour unit was outfitted with 6 pressure sensors, and the ability to be mounted on a force transducer. This unit was then put through a performance analysis and calibration procedure, before being extensively tested in a breakwater setting. Wide ranges of wave conditions were utilized, with the unit at three different locations along the breakwater slope. This was done to isolate both the effect of various sea state parameters, and the effect of unit location along a breakwater slope versus generated forces and pressures. In addition to the experimental study, an accompanying numerical study was performed in OpenFOAM. This had the intent of both developing general modeling rules of thumb for rubble mound breakwaters, and for replicating the experimental results. The results showed that using relatively low-tech, low-cost, and widely available instrumentation was capable of performing in a coastal engineering setting. The performance of the unit showed great promise for “smart-units” to usher in a new paradigm of experimental testing for rubble mound breakwaters. From the results of the performance analysis and calibration procedure, it was evident that the unit could record forces and pressures to a high degree of accuracy. From the breakwater testing program, notable relationships between unit location, surf similarity, and wave steepness emerged. It appeared that the largest hydrodynamic interaction with units occurs slightly below the SWL. As well, both decreased surf similarity, and increased wave steepness resulted in higher hydrodynamic interaction for all locations. General rules of thumb for modeling armour units, as well as wave conditions in a breakwater setting were developed for the numerical study in OpenFOAM. Additionally, the calibrated numerical model was capable of reproducing the experimental results with reasonable accuracy.

Predictions of the environmental loading and induced motional and structural responses are among the most important aspects in the overall design process of offshore structures and ships. In this thesis, attention is focused on the wave loads and excited bodily motion responses of large offshore structures and special vessels. With the aim of improving the existing theoretical methods to provide techniques of theoretical effectiveness, computational efficiency, and engineering practicality in marine and offshore applications, the thesis concentrates upon describing fundamental and essential aspects in the physical phenomenon associated with wave-structure interactions and deriving new methods and techniques to analyse offshore structures and unconventional ships of practical interest. The total wave force arising from such a wave-structural interaction is assumed to be a simple superposition of the potential and the viscous flow force components. The linear potential forces are solved by the Green function integral equation whilst the viscous forces are estimated based on the Morison's damping formula. Forms of the Green function integral equation and the associated Green function are given systematically for various practical cases. The relevant two-dimensional versions are then derived by a transformation procedure. Techniques are developed to solve the integral equation numerically including the interior integral formulation and, in particular, to tackle the mathematical difficulties at irregular frequencies. In applying the integral equations to solve problems with various offshore structures and special vessels, some modified, improved or simplified methods are proposed. At first, simplified method is derived for predictions of the surge, sway and yaw motions of elongated bodies of full sectional geometry or structures with shallow draft. Then, a new shallow draft theory is described for both three- and two-dimensional cases with inclusion of the finite draft effect. Furthermore, a three-dimensional strip method is formulated where the end effects of the body are fully taken into account. Finally, an approximation to the horizontal mean drift forces of multi-column offshore structures are presented. Some new findings are also discussed including the multiple resonances occurring in the motions of multi-hulled marine structures due to the wave-body interaction, the mutual cancellation effect of the diffraction and the radiation forces arising from a full shaped slender body, and so on. Further to those verification studies for individual methods developed, more comprehensive example investigations are given related to two industrial applications. One is a derrick barge semi-submersible with zero forward speed; and the other, a SWATH ship with considerable speed. By correlation of all the proposed approaches with available analytical, numerical and experimental data, the thesis tries to demonstrate a principle that as long as principal physical aspects in the wave-structure interaction problem are properly treated, an appropriately modified or simplified method works, performs well and, sometimes, even better.

This thesis is concerned with the use of the open source computational fluid dynamics (CFD) software package, OpenFOAM® for predicting and analysing the behaviour of a near-shore oscillating wave surge converter (OWSC), when subject to various types of ocean wave conditions in a numerical wave tank (NWT). OpenFOAM® which utilises a Finite Volume Method (FVM) is used to solve the incompressible, Reynolds Averaged Navier-Stokes (RANS) equations for a two-phase fluid, based on a Volume of Fluid (VOF) phase-fraction approach to capture the interface between the air and water phases. Preliminary studies on classic wave-structure interaction benchmark cases, involving a fixed and a vertically oscillating semi-immersed horizontal cylinder are carried out. The gradual transition of the linear to non-linear behaviour of the horizontal and vertical forces induced on a fixed cylinder when subject to various regular waves, and the amplitude ratios of the surface waves elevations generated by the prescribed oscillatory motion of the cylinder, are shown to provide good overall agreement within the limitations of the relevant theory and the experimental data in the literature. The OWSC is modelled with the inclusion of a Power Take-Off (PTO) system, using a linear damping restraint, and simulated in two-dimensional (2D) and three-dimensional (3D) setups. The 2D and 3D numerical results, such as the surface wave elevations, flap angular velocity, PTO torque and flap angular displacement, compare well with one another and with the experimental data for operational regular head-on and oblique wave conditions. Small discrepancies between numerical results and experimental data are likely to be caused by non-linear behaviour of the PTO system. Pressure distributions on the flap surfaces and forces induced on the flap and hinge of the OWSC for various wave conditions are also presented. The effects between 2D and 3D wave-structure interactions become more significant when subject to large waves that break during impact. Comparison between the full scale and 1:24 scale numerical results of the OWSC shows no significant evidence of viscous and scaling effects. The validated 2D OWSC model is also subject to embedded focused waves, to predict the worse possible scenario of wave loading in extreme wave conditions. The delay of the focus event breaking is shown to affect the slamming behaviour for the larger focus event wave heights. Incorporation of a focused wave at different phase positions within a background of regular waves reveals that the focus event wave height has little effect on the peak tangential force on the flap during the slamming event, when a PTO cut-off mechanism is implemented to prevent excessive torque surges. In contrast, the peak radial force on the flap and the maximum resultant force on the hinge appear to respond more sensitively to the focus event wave height. It has been demonstrated that OpenFOAM® is able to provide a comprehensive understanding of the complex hydrodynamic analysis and prediction of highly non-linear wave-structure interactions for an OWSC, which give useful guidance and confidence to WEC developers on the design considerations relevant to the OWSC systems.

Aim and tasks of the work. The aim of this work is to investigate insufficiently analyzed variants of the electrodynamic super-wide-band slow-wave structures, create their models, improve methods of analysis, analyze properties of the systems and reveal potentiality of the traveling-wave cathode-ray tubes, slow-wave structures. In order to achieve the aim it is necessary: 1. To improve method for evaluation of non-linear distortions in the traveling-wave cathode-ray tubes and reveal possibilities of reduction of non-linear distortions. 2. To create models of the insufficiently analyzed variants of slow-wave structures and reveal properties of the slow-wave structures. 3. To reveal influence of periodical non-homogeneities on properties of slow-wave structures, simulate and reveal influence of transitions to properties of slow-wave structures and traveling-wav cathode-ray tubes. 4. To make investigation of potentiality of slow-wave structures and traveling-wave cathode-ray tubes and select variants of slow-wave structures that can guarantee wide band and high operating speed of the traveling-wave cathode-ray tubes. Scientific novelty and practical value. Models of insufficiently simulated slow-wave structures were created and their properties were analyzed. According to analysis and modeling results, variants of systems were selected that can guarantee the wide pass-band and high operating speed of the traveling-wave cathode-ray tubes. Using finite element method calculation... [to full text]

Aim and tasks of the work. The aim of this work is to investigate insufficiently analyzed variants of the electrodynamic super-wide-band slow-wave structures, create their models, improve methods of analysis, analyze properties of the systems and reveal potentiality of the traveling-wave cathode-ray tubes, slow-wave structures. In order to achieve the aim it is necessary: 1. To improve method for evaluation of non-linear distortions in the traveling-wave cathode-ray tubes and reveal possibilities of reduction of non-linear distortions. 2. To create models of the insufficiently analyzed variants of slow-wave structures and reveal properties of the slow-wave structures. 3. To reveal influence of periodical non-homogeneities on properties of slow-wave structures, simulate and reveal influence of transitions to properties of slow-wave structures and traveling-wav cathode-ray tubes. 4. To make investigation of potentiality of slow-wave structures and traveling-wave cathode-ray tubes and select variants of slow-wave structures that can guarantee wide band and high operating speed of the traveling-wave cathode-ray tubes. Scientific novelty and practical value. Models of insufficiently simulated slow-wave structures were created and their properties were analyzed. According to analysis and modeling results, variants of systems were selected that can guarantee the wide pass-band and high operating speed of the traveling-wave cathode-ray tubes. Using finite element method calculation... [to full text]

Yes / Stability and safety of offshore wind turbines with mono-pile foundations, affected by nonlinear wave effect and dynamic seabed response, are the primary concerns in offshore foundation design. In order to address these problems, the nonlinear wave effect on dynamic seabed response in the vicinity of mono-pile foundation is investigated using an integrated model, developed using OpenFOAM, which incorporates both wave model (waves2Foam) and Biot’s poro-elastic model. The present model was validated against several laboratory experiments and promising agreements were obtained. Special attention was paid to the systematic analysis of pore water pressure as well as the momentary liquefaction in the proximity of mono-pile induced by nonlinear wave effects. Various embedment depths of mono-pile relevant for practical engineering design were studied in order to attain the insights into nonlinear wave effect around and underneath the mono-pile foundation. By comparing time-series of water surface elevation, inline force, and wave-induced pore water pressure at the front, lateral, and lee side of mono-pile, the distinct nonlinear wave effect on pore water pressure was shown. Simulated results confirmed that the presence of mono-pile foundation in a porous seabed had evident blocking effect on the vertical and horizontal development of pore water pressure. Increasing embedment depth enhances the blockage of vertical pore pressure development and hence results in somewhat reduced momentary liquefaction depth of the soil around the mono-pile foundation. / Energy Technology Partnership (ETP), Wood Group Kenny, and University of Aberdeen; the National Science Fund for Distinguished Young Scholars (51425901) and the 111 project (B12032).