Analysis of the extreme wave elevation due to second-order diffraction around a vertical cylinder

Statistical analysis of nonlinear random waves is important in coastal and ocean engineering. One approach for modeling nonlinear waves is second-order random wave theory, which involves sum- and difference-frequency interactions between wave components. The probability distribution of the non-Gaussian surface elevation can be solved using a technique developed by Kac and Siegert [21]. The wave field can be significantly modified by wave diffraction due to a structure, and the nonlinear diffracted wave elevation can be of interest in certain applications, such as the airgap prediction for an offshore structure. This paper investigates the wave statistics due to second-order diffraction, motivated by the scarcity of prior research. The crossing rate approach is used to evaluate the extreme wave elevation over a specified duration. The application is a bottom-supported cylindrical structure, for which semi-analytical solutions for the second-order transfer functions are available. A new efficient statistical method is developed to allow the distribution of the diffracted wave elevation to be obtained exactly, accounting for the statistical dependency between the linear, sum-frequency and difference-frequency components. Moreover, refinements are proposed to improve the efficiency for computing the free surface integral. The case study yields insights into the problem. In particular, the second-order nonlinearity is found to significantly amplify the extreme wave elevation, especially in the upstream region; conversely, the extreme elevation at an oblique location downstream is attenuated due to sheltering effects. The statistical dependency between the linear and sum-frequency components is also shown to be important for the extreme wave statistics.     

Wave run-up on bermed coastal structures

Reliable estimation of wave run-up is required for the effective and efficient design of coastal structures when flooding or wave overtopping volumes are an important consideration in the design process. In this study, a unified formula for the wave run-up on bermed structures has been developed using collected and existing data. As data on berm breakwaters was highly limited, physical model tests were conducted and the run-up was measured. Conventional governing parameters and influencing factors were then used to predict the dimensionless run-up level with 2% exceedance probability. The developed formula includes the effect of water depth which is required in understanding the influence of sea level rise and consequent changes of wave height to water depth ratio on the future hydraulic performance of the structures. The accuracy measures such as RMSE and Bias indicated that the developed formula is more accurate than the existing formulas. Additionally, the new formula was validated using field measurements and its superiority was observed when compared to the existing prediction formulas. Finally, the new design formula incorporating the partial safety factor was introduced as a design tool for engineers.     

Extracting energy while reducing hydroelastic responses of VLFS using a modular raft wec-type attachment

This paper presents the use of a modular raft Wave Energy Converter (WEC)-type attachment at the fore edge of a rectangular Very Large Floating Structure (VLFS) for extracting wave energy while reducing hydroelastic responses of the VLFS under wave action. The proposed modular attachment comprises multiple independent auxiliary pontoons (i.e. modules) that are connected to the fore edge of the VLFS with hinges and linear Power Take-Off (PTO) systems. For the hydroelastic analysis, the auxiliary pontoons and the VLFS are modelled by using the Mindlin plate theory while the linear wave theory is used for modelling the fluid motion. The analysis is performed in the frequency domain using the hybrid Finite Element-Boundary Element (FE-BE) method. Parametric studies are carried out to investigate the effects of pontoon length, PTO damping coefficient, gap between auxiliary pontoons, and incident wave angle on the power capture factor as well as reductions in the hydroelastic responses of the VLFS with the modular attachment. It is found that in oblique waves, the modular attachment comprising multiple narrow pontoons outperforms the corresponding rigid attachment that consists of a single wide pontoon with respect to the power capture factor and the reduction in the deflection of the VLFS. In addition, it is possible to have a considerable gap between pontoons without significantly compromising the effectiveness of the modular attachment.     

Experimental investigation on a cabin-suspended catamaran in terms of motion reduction and wave energy harvesting by means of a semi-active motion control system

A novel concept catamaran equipped with a suspended cabin, named Wave Harmonizer Type 4 (WHzer-4), is proposed and evaluated. The mass-spring-mass system is constructed by mounting four sets of suspensions in-between the cabin and the twin-hull. Two sets of dual motor/generators (M/Gs) are attached on the center beam of the cabin's deck fore and aft. Each shaft-end of the dual M/Gs is connected to the twin-hull through a rack-pinion gear unit. In this way the vertical relative motion between the cabin and the twin-hull can be transferred into the rotational motion of the M/Gs, and vice versa. A semi-active motion control system, which contains a proportional-integral (PI) controller, is designed and applied to each of the dual M/Gs for the aim of absorbing wave energy under the condition of suppressing the local vertical velocity of the cabin as much as possible. A 1/5 scale model ship with a length of 1.6 m is built, and a forced-oscillation bench test is implemented to validate the performance of the control system. Then, a series of towing tank tests is carried out in regular head waves. The heave and pitch responses of the cabin, those of the twin-hull and the corresponding wave energy capture width ratio (CWR) at five control scenarios and two reference scenarios are investigated. Discussion on the results of the tank test shows that the motion reduction of the cabin and the wave energy harvesting can be achieved simultaneously at a few wave conditions. However, at other conditions, although noticeable amount of wave energy is harvested, motion reduction of the heave and pitch of the cabin could not be obtained at the same time. It is suggested that varying the gain settings of the PI controllers according to the location of the controllers may improve the effectiveness of the proposed control system.     

Wave tank and bench-top control testing of a wave energy converter

An increasing number of experiments are being conducted to study the design and performance of wave energy converters. Often in these tests, a real-time realization of prospective control algorithms is applied in order to assess and optimize energy absorption as well as other factors. This paper details the design and execution of an experiment for evaluating the capability of a model-scale WEC to execute basic control algorithms. Model-scale hardware, system, and experimental design are considered, with a focus on providing an experimental setup capable of meeting the dynamic requirements of a control system. To more efficiently execute such tests, a dry bench testing method is proposed and utilized to allow for controller tuning and to give an initial assessment of controller performance; this is followed by wave tank testing. The trends from the dry bench test and wave tank test results show good agreement with theory and confirm the ability of a relatively simple feedback controller to substantially improve energy absorption. Additionally, the dry bench testing approach is shown to be an effective and efficient means of designing and testing both controllers and actuator systems for wave energy converters.     

Hydrodynamic performance of a T-shaped floating breakwater

The comprehensive utilization of floating breakwaters, specially acting as a supporting structure for offshore marine renewable energy explorations, has received more and more attention recently. Based on linear water-wave theory, the hydrodynamic performance of a T-shaped floating breakwater is semi-analytically investigated through the matched eigenfunction expansion method (MEEM). Auxiliary functions, to speed up the convergence and improve the accuracy in the numerical computations, are introduced to represent the singular behavior of fluid field near the lower salient corners of the structure. The effects of the height and installation position of the vertical screen on the reflection and transmission coefficients, dynamic response and wave forces are examined. It is found that the presence of the screen shifts the resonance frequency of RAO for both surge and pitch modes to the low-frequency area, while has no effect on heave mode. The identical added masses, damping and transmission coefficients can be obtained in the cases where the screen holds the same distance away from the longitudinal central axis of the upper box-type structure. Moreover, a relatively small pitch response can be achieved in a wide wave–frequency range, when the breakwater is Γ-shaped.     

A modified numerical calculation method of collapse pressure for thick-walled offshore pipelines

Considering the shear deformation and thickness stretching of large deformation, a modified numerical calculation method based on the thick shell theory is established to determine the collapse pressure of thick-walled pipes. Verification experiments are conducted on ten pipe specimens in hyperbaric chambers. The good agreement between experimental results and numerical predictions shows the validity and reliability of the new numerical calculation method. Combining DNV specification, the characteristic collapse pressure is also calculated for comparison. The difference between experimental results and DNV calculations illustrates the latter one is much conservative in predicting collapse pressure for thick-walled pipes. Sensitivity analysis on manufacturing imperfections and material properties is investigated for pipes with different D/t ratios. Thick-walled pipes are easier to be affected by initial ovality, residual stress and hardening factor. Based on the stress distribution at the moment of collapse, a novel discovery is found that the collapse pressure of thick-walled pipes is dominated by material plastic behavior.     

Nonplanar multi-modal vibrations of fluid-conveying risers under shear cross flows

Risers/pipes conveying fluid are a typical kind of slender structures commonly used in marine engineering. It is of great academic significance and application value for us to evaluate and understand the vibration characteristics and nonlinear responses of these risers under the combined action of internal and external fluid flows. In this paper, the nonplanar vibrations and multi-modal responses of pinned-pinned risers in shear cross flow are numerically studied. With this objective in mind, the van der Pol wake oscillators are used to simulate the dynamical behavior of the vortex shedding in the wake. Two nonlinear equations of motion of the riser are proposed to govern the lateral responses of the riser structure. The nonplanar nonlinear equations for the riser and wake are then discretized by employing Galerkin's method and solved by using a fourth-order Runge–Kutta integration algorithm. Theoretical results show that the coupled frequencies for cross-flow (CF) and in-line (IL) motions and the corresponding coupled damping ratio could be influenced by the external and/or internal fluid velocities. Based on extensive calculations, the dynamical behavior of the riser with various internal and external flow velocities are presented in the form of bifurcation diagrams, time traces, phase portraits, oscillation trajectories and response spectrum curves. It is shown that some interesting dynamical phenomena, such as ‘lock-in’ state, ‘figure-of-eight’ trajectory and quasi-periodic oscillation, could occur in such a fluid-structure interaction system. Our results also demonstrate that the shear parameter can significantly affect the dynamic responses of the riser. When the shear parameter of the cross flow is large, multi-modal quasi-periodic responses of the riser can be excited, showing some new features undetected in the system of fluid-conveying risers in uniform cross flow.     

Characteristics of breaking irregular wave forces on a monopile

The substructures of offshore wind turbines are subjected to extreme breaking irregular wave forces. The present study is focused on investigating breaking irregular wave forces on a monopile using a computational fluid dynamics (CFD) based numerical model. The breaking irregular wave forces on a monopile mounted on a slope are investigated with a numerical wave tank. The experimental and numerical irregular free surface elevations are compared in the frequency-domain for the different locations in the vicinity of the cylinder. A numerical analysis is performed for different wave steepness cases to understand the influence of wave steepness on the breaking irregular wave loads. The wave height transformation and energy level evolution during the wave shoaling and wave breaking processes is investigated. The higher-frequency components generated during the wave breaking process are observed to play a significant role in initiating the secondary force peaks. The free surface elevation skewness and spectral bandwidth during the wave transformation process are analysed and an investigation is performed to establish a correlation of these parameters with the breaking irregular wave forces. The role of the horizontal wave-induced water particle velocity at the free surface and free surface pressure in determining the breaking wave loads is highlighted. The higher-frequency components in the velocity and pressure spectrum are observed to be significant in influencing the secondary peaks in the breaking wave force spectrum.     

Temporal variation of modulated-wave-train geometries and their influence on vertical bending moments of a container ship

A towing experiment was conducted using a modulated wave train to investigate the vertical bending responses of a hydro-structural container ship model. In the experiment, a spatially periodic modulated wave train, as a model of a freak wave in successive high waves mimicking the so-called three sisters, was generated by the recently established higher-order spectral method wave generation (HOSM-WG) method. HOSM-WG enables us to control the location and timing of the maximum crest height in a wave tank. With precise control of the towing carriage, an experiment was conducted in which the timing of the encounters between the ship model and the modulated wave train was accurately determined. The maximum sagging moment (SM) was found to increase in proportion with the encounter wave height. However, because of differences in the relative depth of the fore and aft troughs, the maximum SM is highly variable for a given wave height. The temporal wave-geometry evolution caused the relative trough-depth to vary significantly within a wave period in the vicinity of the maximum crest height. As a result, depending on the encounter timing, the SM varied considerably for a given wave height. The temporal variation of the wave geometry is a robust feature of a modulated wave train and is common between the spatially periodic and temporally periodic modulated wave trains.