Transformed-FNV:Wave forces on a vertical cylinder — A free-surface formulation

Existing force models for a vertical surface-piercing cylinder require water depth integration from the seabed to the free surface to determine the total inline force. However, acquiring the full wave kinematics profiles beneath the water surface presents a significant computational task. We revisit the finite water depth version of the well-known FNV theory (Kristiansen and Faltinsen, 2017) and propose a transformed version that expresses the total force solely in terms of the fully nonlinear wave properties at the free surface. This novel Transformed-FNV (T-FNV) formulation treats the Morison inertia term exactly and approximates the remaining two convective-derivative type terms with an assumption of slowly varying kinetic energy type terms. We evaluate the accuracy of this transformation against the original formulation, using wave kinematics obtained from fully nonlinear numerical simulations. Two T-FNV formulations are proposed with different input properties required. The first formulation uses the fully nonlinear wave kinematic properties at the free surface, whereas a fully approximated T-FNV formulation requires only the nonlinear free-surface elevation time history measured or calculated at the position of the column but in its absence. Both T-FNV formulations demonstrate good accuracy for wave forces for both deep and shallow-water cases against the original FNV model. The new T-FNV formulations also show the increased role of higher harmonics in the predicted force time histories when compared to those in the free-surface displacement, and the importance of using accurate higher order harmonic wave profiles in nonlinear force calculations

Transformed-FNV:Wave forces on a vertical cylinder — A free-surface formulation

Existing force models for a vertical surface-piercing cylinder require water depth integration from the seabed to the free surface to determine the total inline force. However, acquiring the full wave kinematics profiles beneath the water surface presents a significant computational task. We revisit the finite water depth version of the well-known FNV theory (Kristiansen and Faltinsen, 2017) and propose a transformed version that expresses the total force solely in terms of the fully nonlinear wave properties at the free surface. This novel Transformed-FNV (T-FNV) formulation treats the Morison inertia term exactly and approximates the remaining two convective-derivative type terms with an assumption of slowly varying kinetic energy type terms. We evaluate the accuracy of this transformation against the original formulation, using wave kinematics obtained from fully nonlinear numerical simulations. Two T-FNV formulations are proposed with different input properties required. The first formulation uses the fully nonlinear wave kinematic properties at the free surface, whereas a fully approximated T-FNV formulation requires only the nonlinear free-surface elevation time history measured or calculated at the position of the column but in its absence. Both T-FNV formulations demonstrate good accuracy for wave forces for both deep and shallow-water cases against the original FNV model. The new T-FNV formulations also show the increased role of higher harmonics in the predicted force time histories when compared to those in the free-surface displacement, and the importance of using accurate higher order harmonic wave profiles in nonlinear force calculations

Why rogue waves occur atop abrupt depth transitions

Abrupt depth transitions (ADTs) have recently been identified as potential causes of ‘rogue’ ocean waves. When stationary and (close-to) normally distributed waves travel into shallower water over an ADT, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show, by comparing to new experiments and numerical simulations, the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the ADT, and new second-order free waves generated due to the ADT

Data Informed Model Test Design With Machine Learning – An Example in Nonlinear Wave Load on a Vertical Cylinder

Model testing is common in coastal and offshore engineering. The design of such model tests is important such that the maximal information of the underlying physics can be extrapolated with a limited amount of test cases. The design of experiments also requires considering the previous similar experimental results and the typical sea-states of the ocean environments. In this study, we develop a model test design strategy based on Bayesian sampling for a classic problem in ocean engineering—nonlinear wave loading on a vertical cylinder. The new experimental design strategy is achieved through a GP-based surrogate model, which considers the previous experimental data as the prior information. The metocean data are further incorporated into the experimental design through a modified acquisition function. We perform a new experiment, which is mainly designed by data-driven methods, including several critical parameters such as the size of the cylinder and all the wave conditions. We examine the performance of such a method when compared to traditional experimental design based on manual decisions. This method is a step forward to a more systematic way of approaching test designs with marginally better performance in capturing the higher-order force coefficients. The current surrogate model also made several “interpretable” decisions which can be explained with physical insights

An investigation of high-order harmonics in the pressure field around a vertical cylinder in steep wave conditions

Offshore structures, encompassing foundations for offshore wind turbines, supports for marine renewable energy devices, bridge piers, and floating vessels, are consistently subjected to severe environmental loads. These loads often dictate the design criteria. Understanding the physics and statistics of wave-structure interaction, especially under non-linear loads experienced in extreme conditions, remains a complex and partially unresolved challenge. Notably, secondary load cycles significantly contribute to the ’ringing’ responses in cylindrical structures, as discussed in previous studies (e.g., Grue et al. (1993), Chaplin et al. (1997)). This paper focuses on analysing loads in focused wave groups, representing short-term extreme wave conditions, on bottom-mounted vertical cylinders relevant to fixed offshore wind turbines. Pressure contour plots over the cylinder’s surface were previously examined by Ghadirian & Bredmose (2020) while studying secondary load cycles. In this research, we adopt the phase-based harmonic separation method for wave forces (Fitzgerald et al. (2014)) to analyse the pressure contour plots. This method effectively isolates harmonic pressure components from the total pressures, enabling a novel exploration of the mechanisms behind secondary load cycles from the perspective of high-order harmonics on the cylinder surface

A new Gaussian Process based model for non-linear wave loading on vertical cylinders

We aim to establish a fast and accurate model for fast prediction of nonlinear loading on vertical cylinders such as are typically used for fixed offshore wind turbines. We follow a ‘Stokes-type’ force model and approximate the amplitude of the higher harmonics of force by relating these to the linear force time series raised to appropriate power through amplitude and phase coefficients. We reanalyse previous experimental data and perform new experiments to expand the parameter space and establish a force coefficients database for engineering applications. A machine learning model is used to interpolate the database and make predictions on the higher order force coefficients. The machine learning model also provides a cross-validated confidence interval to indicate the prediction uncertainty and reflect model reliability. We further extend the prediction capability to unidirectional random waves with a novel force segmentation method, which localised wave groups from the random background. The new Stokes-Gaussian Process (Stokes-GP) model developed can provide engineering predictions of nonlinear wave loading on a cylinder for individual wave groups and random seas, which are straightforward to apply and fast to compute and the important higher-order loading components are considered. This will significantly improve the accuracy of the loading prediction and the ease of application for force predictions.</p

On the arrangement of tidal turbines in rough and oscillatory channel flow

Fast tidal streams are a promising source of clean, predictable power, but the task of arranging tidal turbines for maximum power capture is complicated. Actuator disc models, such as the two-scale actuator disc theory, have proven useful in seeking optimal turbine arrangements, yet these models assume flows that are frictionless and steady, and thus quite unlike the channel flow conditions that actual tidal turbines experience. In this paper, we use numerical methods to relax these assumptions and explore how optimal turbine arrangements change as the flow transitions from frictionless and steady to rough and oscillatory. In so doing, we show that, under certain conditions, the assumption of quasi-steady flow in models of tidal turbines may neglect leading-order physics. When the ratio of drag to inertial forces in the unexploited channel is very low, for instance, the optimal turbine arrangements are found to be quite different, and the potential for enhanced power capture is found to be much greater than predicted by two-scale actuator disc theory

Foundations of offshore wind turbines: a review

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