Sloshing is a violent resonent free surface flow in a container. The main objective of this thesis has been to study sloshing in rectangular and prismatic tanks. The tank may be excited by a harmonic motion or it may move with a ship in waves. In the latter case, the coupled ship motions and sloshing problem is investigated. A nonlinear analytically based sloshing model is used in the solshing calculations. Experiments have been conducedand collected data are utilized in the validation of the sloshing model and computations of interaction between sloshing and ship dynamics. Tank roof impacts are studied. Energy in the impact jet is dissipated and this leads to damping of the sloshing motion. An iterative procedure is applied to incorporate the effect of energy dissipation in the calculations. Damping of the soloshing motion is an important parameter around resonance for the coupled ship motion and sloshing system. The sloshing model is based on a nonlinear theory analysis of two-dimensional nonlinear sloshing of an imcompressible fluid with irrotational flow in a rectangular tank. Infinite tank roof height and no overtuning waves are assumed. The free surface is expressed as a Fourier series and the velocity potential is expanded in terms of the linear natural modes of the fluid motion. The infinite-dimensional modal system is approximated and the result is a finite set of ordinary differential equations in time for generalized coordinates (Fourier cofficients) of the free surface. This theory is not valid for small water depth or when water impacts heavily on the tank roof. The proposed method has a high computational efficiency, facilitates simulations of a coupled vehicle-fluid system and has been extensively validated for forced motions. Experiments with a smooth rectangular tank exited by forced harmonic horizontal oscillations have been performed and the results are used to validate the analytical sloshing model. Transients and associated nonlinear modulation of the waves, beating, are important due to the low level of damping of the fluid motion. The measured parameters are the motion of the tank and the free surface elevation at three positions. Pictures and video are used to study local flow details and the dynamics of the flow. At excitation periods in the vicinity of the first natural period for the fluid motion in the tank, even small motion amplitudes lead to violent sloshing and impacts between the rising water surface and the tank roof. Impacts cause high pressures and forces. The effect of slamming in the tank is included by a local anlysis interacting with the nonlinear sloshing model. A Wagner based mthod is used to find the flow induced by slamming. Hydroelastic effects are ignored. The hypothesis that the kinetic and potential energy in the jet flow coused by the impact is dissipated when the jet flow hits the free surface, enables a rational calculation of the damping effect of impacts on the slishing flow. The Wagner approach requires a small angle between the impacting free surface and the tank roof. A correction by a similarity solution, or alternatively, by a generalization of Wagner's theory valid for larger angles is applied when this is not the case. Since anslytically based methods are used, fluid impact load predictions are robust. A coupled ship motion and sloshing system is studied both experimentally and theoretically. Two-dimensional experiments on a box-shaped ship section excited by regular beam sea have been conducted. The section contains two tanks and can only move in sway. Fluid motion inside the tanks has a large effect on the sway motion response of the section. Simulatons of a corresponding system are performed by assuming a mainly linear external flow and applying the nonlinear sloshing model. The linear external hydrodynamic loads due to body motion are expressed in terms of a convoltion integral representing the history of the fluid motion. detailed numerical study of how to accuratly and numerical sway motion of the ship section is reported. The calculated cooupled motion is sensitive to the damping of the sloshing motion in a certain frequency range where the coupled sloshing and ship motions couse resonant ship motions. A quasi-linear frequency domain analysis is used to explain this by introducing the sloshing loads as a frequency dependent spring.

<p>The thesis addresses the hydrodynamic forces on cylinders where the angle between incoming flow and the cylinder axis, the angle of attack, is low. Measured results for a rigid cylinder with length to diameter ratio of 40 towed at both constant angle of attack and oscilllating in the transverse direction are used to discuss the applicability of suggested methods like the cross flow or the 2D+t principle. It is found that the longitudional flow do influence the transverse forces. The importance of the flow pattern initiated at the nose of the cylinder is clearly illustrated.</p><p>A combination of linear and quadratic dependence on the sine of the angle is used to model the response of a flexible cylinder with forced oscillation of the tow point. The result is compared to experimental result for a flexible cylinder with length to diameter ratio of 1100 and Reynolds numbers in and above the critical range. The cylinder is simulated in time domain with a Finite Element Method with second order elements. As an example of practical application of the model, the response of a part of a full scale streamer subject to irregular waves and a control device is investigated. In realistic sea states the response is found to be rather small, but not damped by the control device. </p>

<p>Large relative motions between the ship and the water may cause water shipping on the main deck. In this thesis, the fundamental features of water-on-deck phenomena are in vestigated, together with the "green" water loading on a deck house in the bow region. The studies are relevant for a stationary ship like a FPSO in head sea waves.</p><p>Potential flow theory is used to study numerically a nonlinear two-dimensional problem in a plane containing the ship's centerplane. The developed model is verified by various test cases, and validated by published as well as new experimental data.</p><p>The influence of wave parameters, ship motions and hull geometry is investigated. Relevance of three-dimensional effects is discussed.</p><p>Dedicated two-dimensional model tests have been performed, both to elucidate the fluid mechanics involved in the water shipping and to validate the numerical method. It is found that the water shipping starts in the form of a plunging wave hitting the deck. This could cause structural damages. Most often, the plunging is localized in the bow region and do not affect the main flow at a later stage. In a few cases, larger masses of water bluntly impacting with the deck have been observed. The latter is consistent with seldom observations reported in 3-D experiments, with large and steep waves plunging directly onto the deck. More often the water flow along the deck resembles the one subsequent to a dam breaking. Both types of events are investigated numerically. The impact pressures on a vertical wall in the bow area are measured and compare well with the boundary element method.</p><p>The reliability of a dam-breaking model and shallow-water approximation to study the propagation of water on the deck is examined. The former can only qualitatively describe the flow evolution.The latter can in principle be used but needs information from the exterior flow and, thus, the solution of the complete ship-waveinteraction problem.</p><p>Water impacts with a deck house in the bow area are studied in details. Use of a similarity solution for a water wedge hitting a rigid wall at 90º is compared with the fully numerical solution. The method predicts correctly the first stages of the impact with a smaller computational effort. Inuence of local flow conditions and wall slope on hydrodynamic loads is discussed. Importance of hydroelasticity is investigated in case of realistic structural parameters for the deck house. This shows a limited role of structural deformations in determining the maximum loads.</p>

<p>The objective of this thesis is to experimentally study different breaking waves cases. This is done by measuring in detail the free surface geometry and the internal kinematics of the waves as they approach breaking. Three principal wave cases were chosen for the study: A plunging breaker, a spilling breaker, and an intermediate breaker.</p><p>A major part of this work is the design, construction and building of a wave laboratory. The laboratory contains a glass wall waveflume which is 13.5m long, 1m deep and 0.6m wide, as well as equipment for measuring both the wave kinematics and geometry optically. The wave kinematics is measured using the Particle Image Velocimetry (PIV) method, while the wave profile geometry is measured using image analysis (space domain geometry), as well as standard wave gauges (time domain geometry).</p><p>The analysis of both the wave kinematics and geometry is done using parameters describing quantitatively important features in the wave evolution. The surface geometry is described using the commonly known zero-downcross parameters, and in addition, new parameters are suggested and used in the study, The kinematics are described by a set of four parameters suggested for the first time in this work. These parameters are: Velocity at the surface, velocity at the still water line (z = 0), mean velocity direction, and local wave number. The purpose of these parameters is to give a better understanding of the space and time domain development of the kinematics, and they appear to be a reasonable compromise between simplicity and accuracy.</p><p>The results presented here represents a thorough and detailed mapping of the breaking process. Much data is gathered and analysed, and throughout this thesis it is sought to present the data in the most intuitive way, so that other investigations may benefit from it. </p>

Large relative motions between the ship and the water may cause water shipping on the main deck. In this thesis, the fundamental features of water-on-deck phenomena are in vestigated, together with the "green" water loading on a deck house in the bow region. The studies are relevant for a stationary ship like a FPSO in head sea waves. Potential flow theory is used to study numerically a nonlinear two-dimensional problem in a plane containing the ship's centerplane. The developed model is verified by various test cases, and validated by published as well as new experimental data. The influence of wave parameters, ship motions and hull geometry is investigated. Relevance of three-dimensional effects is discussed. Dedicated two-dimensional model tests have been performed, both to elucidate the fluid mechanics involved in the water shipping and to validate the numerical method. It is found that the water shipping starts in the form of a plunging wave hitting the deck. This could cause structural damages. Most often, the plunging is localized in the bow region and do not affect the main flow at a later stage. In a few cases, larger masses of water bluntly impacting with the deck have been observed. The latter is consistent with seldom observations reported in 3-D experiments, with large and steep waves plunging directly onto the deck. More often the water flow along the deck resembles the one subsequent to a dam breaking. Both types of events are investigated numerically. The impact pressures on a vertical wall in the bow area are measured and compare well with the boundary element method. The reliability of a dam-breaking model and shallow-water approximation to study the propagation of water on the deck is examined. The former can only qualitatively describe the flow evolution.The latter can in principle be used but needs information from the exterior flow and, thus, the solution of the complete ship-waveinteraction problem. Water impacts with a deck house in the bow area are studied in details. Use of a similarity solution for a water wedge hitting a rigid wall at 90º is compared with the fully numerical solution. The method predicts correctly the first stages of the impact with a smaller computational effort. Inuence of local flow conditions and wall slope on hydrodynamic loads is discussed. Importance of hydroelasticity is investigated in case of realistic structural parameters for the deck house. This shows a limited role of structural deformations in determining the maximum loads.

The objective of this thesis is to experimentally study different breaking waves cases. This is done by measuring in detail the free surface geometry and the internal kinematics of the waves as they approach breaking. Three principal wave cases were chosen for the study: A plunging breaker, a spilling breaker, and an intermediate breaker. A major part of this work is the design, construction and building of a wave laboratory. The laboratory contains a glass wall waveflume which is 13.5m long, 1m deep and 0.6m wide, as well as equipment for measuring both the wave kinematics and geometry optically. The wave kinematics is measured using the Particle Image Velocimetry (PIV) method, while the wave profile geometry is measured using image analysis (space domain geometry), as well as standard wave gauges (time domain geometry). The analysis of both the wave kinematics and geometry is done using parameters describing quantitatively important features in the wave evolution. The surface geometry is described using the commonly known zero-downcross parameters, and in addition, new parameters are suggested and used in the study, The kinematics are described by a set of four parameters suggested for the first time in this work. These parameters are: Velocity at the surface, velocity at the still water line (z = 0), mean velocity direction, and local wave number. The purpose of these parameters is to give a better understanding of the space and time domain development of the kinematics, and they appear to be a reasonable compromise between simplicity and accuracy. The results presented here represents a thorough and detailed mapping of the breaking process. Much data is gathered and analysed, and throughout this thesis it is sought to present the data in the most intuitive way, so that other investigations may benefit from it.

The thesis addresses the hydrodynamic forces on cylinders where the angle between incoming flow and the cylinder axis, the angle of attack, is low. Measured results for a rigid cylinder with length to diameter ratio of 40 towed at both constant angle of attack and oscilllating in the transverse direction are used to discuss the applicability of suggested methods like the cross flow or the 2D+t principle. It is found that the longitudional flow do influence the transverse forces. The importance of the flow pattern initiated at the nose of the cylinder is clearly illustrated. A combination of linear and quadratic dependence on the sine of the angle is used to model the response of a flexible cylinder with forced oscillation of the tow point. The result is compared to experimental result for a flexible cylinder with length to diameter ratio of 1100 and Reynolds numbers in and above the critical range. The cylinder is simulated in time domain with a Finite Element Method with second order elements. As an example of practical application of the model, the response of a part of a full scale streamer subject to irregular waves and a control device is investigated. In realistic sea states the response is found to be rather small, but not damped by the control device.

SummaryThis Master&#146;s Thesis goal is to present fundamental physical aspects of Vortex Induced Vibrations (VIV) of marine risers, and outline methods for suppression of VIV. Main emphasis has been given to the use of strakes, and relevant theories connected to strakes&#146; influence on excitation of riser, riser response and drag is presented. Variation of outer diameter of the riser is also studied.The theory has been put to test through case studies of two Aker Solutions in-marine workover systems of 321 and 1300 m water depth. The computer program VIVANA has been used. Several analyses have been performed for various different riser configurations. For the 321 m water system, the following configurations have been studied:-Base configuration, i.e. no use of strakes-Staggered configuration, staggered bare and buoyant joints-Bottom strakes configuration, bottom section of riser covered with strakes-Middle strakes configuration, middle section of riser covered with strakes-Top strakes configuration, top section of riser covered with strakesFor the 1300 m water depth system, the following configurations have been evaluated:-Base configuration, i.e. no use of strakes-Staggered configuration, staggered bare and buoyant joints-Middle strakes configuration, middle section of riser covered with strakes-Top 50_150 strakes configuration, top 150 m of riser bare, then coverage of strakes-Top stakes configuration, top section of riser covered with strakesFor each water depth a total of 4 different current profiles have been applied. The current profiles include both measured current profiles from the relevant oil fields, as well as several other more &#147;theoretical&#148; current models.The main findings from the 321 m analyses were:-Staggered configuration gives generally lower VIV amplitudes of the dominating frequency compared to base configuration.-Staggered configuration gives generally lower maximum stress amplitudes compared to base configuration.-No clear trends when comparing fatigue life of staggered and base configuration are found, however significantly better fatigue results found for the staggered configuration in measured current.-Maximum accumulated damage is located at the WH/XMT interface.-Top and middle strakes configurations give best VIV suppression results.-Applying strakes to the top section of the riser gives significantly lower VIV amplitudes, stress amplitudes and higher fatigue lives across all current profiles.-Top strakes configuration supress VIV completely for the sheared current profile.-Very small riser deflections and corresponding low flex joint angles are found; thus no operational consequences for the 321 m water depth.&amp;#8195;The main findings from the 1300 m analyses were:-A significant increase in active response frequencies compared to the 321 m water depth, more than 30 active frequencies calculated.-No clear trends in VIV amplitudes of the dominating frequency when comparing staggered and base configuration.-Highest stress amplitudes found for the base configuration in all current profiles.-No clear trends in calculated fatigue life when comparing the staggered and base configurations. Maximum accumulated damage found in the WH/BOP interface.-Top 50_150 strakes configuration the most efficient in suppressing VIV.-Significantly lower VIV amplitudes of the dominating response frequency for the top 50_150 strakes configuration. Same result found for the maximum stress amplitudes.-Compared to the base configuration significantly better fatigue lives found for the top 50_150 strakes configuration, however for the measured current profile an increase of only 1 decade was found.-Staggered configuration gives lowest static riser deflection for all current profiles, also after drag amplification from VIV.-Percentage increase in riser deflection from VIV reduced by roughly 80% when comparing the top 50_150 base configuration to the base configuration.-LFJ angles exceeded lower limits for certain drilling and workover operations, however applying the top 50_150 strakes configuration will generally give a larger operational window compared to the base configuration.Some of the results from the 1300 m analyses revealed certain discrepancies linked to the dominating frequencies and frequencies inducing maximum stress amplitudes. These inconsistencies are probably related to the convergence limit given as input in the VIVANA module.

Deployment of a large box structure in many sea states has been investigated. Two deployment methods are compared; crane installation over the side and through moonpool installation. The structure is 12 [m] long, 6 [m] wide and 12 [m] high with a mass of 250 [t]. Normand Subsea is used as installation vessel. Both JONSWAP and Torsethaugen wave spectra are used for crane lowering while only JONSWAP is used for moonpool installation.Splash zone lowering is seen as the most critical stage of the installation because hydrodynamic forces are largest at the surface. Hydrodynamic uplift is assumed limiting for the deployment, i.e &#147;slack slings&#148;. Slings are the lower part of the lift rigging. The operation limit is that dynamic uplift should not exceed 90 % of the modules static weight. Forces in z-direction are hence most interesting. Minimum wire tension for the lowering is therefore calculated at two time instances; when the module bottom end is at mean water level and when the module is fully submerged with its top end 0.5 [m] below mean water level. These time instances are referred to as time instance 1 and 2 in the report respectively. Design significant wave heights, Hs, are taken from plots of minimum wire tension for different wave peak periods Tp and wave headings. Based on these design Hs values, which equals the operation limits, operability rosettes are plotted. It is seen that wave headings 90&amp;#8304; and 120&amp;#8304; are most critical with lowest operability for crane installation while wave heading 90&amp;#8304; is worst for moonpool deployment.The lowest design Hs for all Tp values considering wave headings 0&amp;#8304; &#177;30&amp;#8304; is used as overall operation limit for deployment when weather window statistics are computed. Time instance 1 is worst for crane deployment with resulting forecasted weather operational criterion Hs=2.8 [m]. Time instance 2 is worst for moonpool deployment with forecasted operational criterion Hs=2.5 [m] and Tp &amp;#8805; 13.0 [s]. Reference time for deployment, hence the time needed from the weather forecast is issued to the module is landed on the seabed, is 6 hours. Based on reference time and forecasted operation limits weather window statistics are estimated.Moonpool deployment annual operability is 7.24 days, hence 2.0 % of the year, and can naturally not be used. Crane deployment annual operability is 213.22 days, 58.4 % of the year. This is much better but still not very good as it is theoretically desirable to be able to install the module any day year round.

The age of the easy accessible hydrocarbon goes towards the end and new more challenging fields is the future of the oil industry. This is often synonymous with large depths where sea bed mounted platforms are highly uneconomical options. Floating platforms are therefore commonly chosen solutions.In this thesis two types of deep foating platforms are investigated; The spar buoy, a well known, well documented concept and the Octabuoy, a newly developed concept. Both platforms are analysed in two DNV programs, Wasim and Waqum. Wasim is a non linear time domain hydrodynamic program and Waqum is an impulse response function operator with the possibility of adding non linear eects. The spar bouy concept is used as a pilot test in the softwares. A recreation of the experimental results from H.A. Haslum&apos;s doctoral thesis from 2000 is attempted. The impact of non linear effects and mooring on both platforms is discussed. The subject of viscous damping is also approached.As has previously been confirmed by many researchers, the spar buoy is susceptible to non linear eects. The triggering of the Mathieu effect is shown in the Wasim analyses. Discussion is also made as to whether the spar might also be susceptible to large excitations due to second order difference frequency interactions between surface waves and body motions. Both these effects happen at low frequencies where radiation damping is low. Viscous damping is therefore of importance. From previous research mooring is found to be important to avoid the Mathieu effect by increasing the damping and moving pitch periods out of the danger zones.After analysing the spar buoy, the Octabuoy&apos;s motion characteristics are tested in mild to severe sea states in both softwares. Non linear effects are found to be significant in the vertical rotational degrees of freedom. The heave motion however seems relatively unaffected by non linear effects. Since Wasim models the free surface linearly, what makes the pitch/roll motion affected by non linearities is found to be either non linear hydro statics or non linear Froude-Krylov forces. The Octabuoy is designed to avoid the variation on hydrostatic stiffness. However, the deadrise angle is 10 degrees larger than the ideal angle. Whether this is what leads to non linear pitch/roll motion is not known at this stage.Two softwares are used in the thesis. Wasim has very long CPU time but calculates accurately and detailed information is easily accessed with for instance the Wasim application ForceInspector. Waqum is very quick, with CPU time in the order of minutes. The program requires an experienced user who knows what must be included for a complete analysis. There are uncertainties about the results from Waqum analysis and more verication is needed for the author to feel confident about the software.To conclude, the programs might work well together. Much can be tested quickly in Waqum, and then final configurations can be run more thoroughly in Wasim. It is the experience of the author that at least until the new version of HydroD is finished, running time domain analysis in Wasim should be done through scripting. This gives a larger control over the actual input and might decrease the chance for error.Keywords: Octabuoy, Spar Buoy, Non Linear Effects, Mooring, Wasim, Waqum.