Abstract In the quest for a numerical method for surface waves and wave-induced effects applicable when linear or weakly nonlinear methods are insufficient, a three-dimensional numerical wave tank assuming fully-nonlinear potential-flow theory is proposed. When viscous-flow effects, breaking waves or other violent flow-phenomena are not of primary importance, potential-flow methods may have similar capability in capturing the involved physics as Navier-Stokes solvers while being potentially more accurate in handling wave-propagation mechanism and more computationally efficient. If made sufficiently accurate, efficient and numerically robust, fully-nonlinear potential flow models can therefore represent a powerful tool in the study of ocean waves and their interaction with marine structures, which is the main motivation behind the present work. The governing Laplace equation for the velocity potential is solved using the harmonic polynomial cell method, which is a field method giving high-order accuracy provided that the cells used to describe the water domain have no stretching or distortion. This can only be achieved in a grid with cubic cells, which leads to poor numerical efficiency unless measures are introduced to refine the grid locally. Here, to improve the efficiency using strictly cubic cells, an adaptive grid refinement technique is introduced. It is shown that this has the ability to improve the computational speed with a factor of up to 20 without sacrificing accuracy. Numerical results are shown to be in good agreement with highly accurate nonlinear reference solutions for regular and irregular waves of various steepness up to the limit of theoretical wave breaking. For long-crested irregular waves, significant discrepancies with a second-order theory for the crest-height distribution are identified, while the second-order theory appears to provide a better description of the crest height for the single short-crested irregular sea state simulated. Having demonstrated that the proposed numerical method accurately models nonlinear wave phenomena up to the limit of wave breaking, future work should seek to implement wave-body interaction capabilities. The adaptive grid refinement technique, which refines the grid dynamically depending on the position of boundaries of interest, is developed with this application in mind. Except from providing a robust way of dealing with wave-body intersection points, extending the method to account for wave-body interactions should therefore involve limited difficulty.
Results from Blind Test Series 1, part of the Collaborative Computational Project in Wave Structure Interaction (CCP-WSI), are presented. Participants, with a range of numerical methods, blindly simulate the interaction between a fixed structure and focused waves ranging in steepness and direction. Numerical results are compared against corresponding physical data. The predictive capability of each method is assessed based on pressure and run-up measurements. In general, all methods perform well in the cases considered, however, there is notable variation in the results (even between similar methods). Recommendations are made for appropriate considerations and analysis in future comparative studies.
For the design of the breakwater for the protection of Barra do Dande Ocean Terminal in Angola, a rock armor rubble mound structure was the obvious solution due to the proximity of a suitable quarry. For this type of breakwater there is a close relationship between damage resistance in terms of armor unit size and the required maintenance. Designing for small probability of damage generally infers high construction costs but lower maintenance costs. Breakwater roundheads are generally the most critical part of rubble mound breakwaters. In search of minimum lifetime costs, a stable low-cost solution for the breakwater head was investigated in terms of a three-layer rock armor solution applied in the most critical sectors of the roundhead. The aim was to avoid the production wise and construction wise costly large rock sizes while still maintaining a low probability of repairs. The three-layer rock armor solution applied in the critical roundhead sectors was studied in physical model tests at the Aalborg University Ocean and Coastal Engineering Laboratory, Denmark. This solution means that smaller rocks can be applied as failure occurs at significantly higher damage levels. The three-layer solution was a viable technical and economic solution for the port construction and operation.
This paper presents ISOPE's 2020 comparative study on the interaction between focused waves and a fixed cylinder. The paper discusses the qualitative and quantitative comparisons between 20 different numerical solvers from various universities across the world for a fixed cylinder. The moving cylinder cases are reported in a companion paper as part B (Agarwal, Saincher, et al., 2021). The numerical solvers presented in this paper are the recent state of the art in the field, mostly developed in-house by various academic institutes. The majority of the participants used hybrid modeling (ie, a combination of potential flow and Navier–Stokes solvers). The qualitative comparisons based on the wave probe and pressure probe time histories and spectral components between laminar, turbulent, and potential flow solvers are presented in this paper. Furthermore, the quantitative error analyzes based on the overall relative error in peak and phase shifts in the wave probe and pressure probe of all the 20 different solvers are reported. The quantitative errors with respect to different spectral component energy levels (ie, in primary, sub-, and superharmonic regions) capturing capability are reported. Thus, the paper discusses the maximum, minimum, and median relative errors present in recent solvers as regards application to industrial problems rather than attempting to find the best solver. Furthermore, recommendations are drawn based on the analysis.
Maritime transport is the most energy-effective mode to move large amounts of goods around the world. Hauling cargo via waterway produces an enormous quantity of greenhouse gas emissions. Vessel fuel efficiency directly influences ship emissions by affecting the amount of burnt fuel. Optimizing ships operating in waves rather than in calm water conditions could decrease the fuel consumption of vessels. In particular, ship propellers are traditionally designed neglecting dynamic conditions such as time-varying wake distribution and propulsion factors, propeller speed fluctuations, ship motions, and speed loss. The effect of waves on the propeller performance can be evaluated using both a quasi-steady and a fully-unsteady approach. The former is a fast computational approximation method based on the assumption that the ratio of propeller angular frequency to wave encounter frequency is sufficiently large. The latter provides a complete representation of the propeller dynamics, but it is computationally expensive. The purpose of this paper is to compare the propeller performance in the presence of waves using the quasi-steady and the fully unsteady approach. This analysis is performed by observing the differences in unsteady propeller forces, cavitation volume, and hull pressure pulses between the two approaches. The full-scale KVLCC2 propeller is utilized for the investigation. Results show a good agreement between the quasi-steady and the fully-unsteady approach in the prediction of the temporal mean and the fluctuation amplitude of KT and KQ, the cavity volume variation, and the hull pressure pulses. Therefore, for the considered operating conditions, the quasi-steady approach can be used to compute the propeller performance in waves.
This article gives a review of techniques applied to make sea state estimation on the basis of measured responses on a ship. The general concept of the procedures is similar to that of a classical wave buoy, which exploits a linear assumption between waves and the associated motions. In the frequency domain, this assumption yields the mathematical relation between the measured motion spectra and the directional wave spectrum. The analogy between a buoy and a ship is clear, and the author has worked on this wave buoy analogy for about fifteen years. In the article, available techniques for shipboard sea state estimation are addressed, but with a focus on only the wave buoy analogy. Most of the existing work is based on methods established in the frequency domain but, to counteract disadvantages of the frequency-domain procedures, newer studies are working also on procedures formulated directly in the time domain. Sample results from several studies are included, and the main findings from these are mentioned.
This PhD thesis presents a numerical solution of the hydroelastic problems encountered especially by large flexible ships sailing in waves. The solution is implemented by extending an existing seakeeping tool (OceanWave3D-seakeeping) to allow for the efficient and accurate evaluation of the hydroelastic response of ships. OceanWave3D-seakeeping has been developed by the Maritime Group at DTU-Construct based on solving the linearized potential flow theory using high-order finite differences on overlapping curvilinear boundary-fitted grids. Modal superposition is employed to couple the hydrodynamic and structural analysis of ships at both zero and non-zero forward speed. The ship girder is approximated by an Euler-Bernoulli or a Timoshenko beam, and the vertical bending deformation is mainly considered in this work. The shear effects on the hydroelastic response are also investigated in the Timoshenko beam approximation. The solution has been validated against experimental measurements and reference numerical solutions for several test cases. The correct computation of the hydrostatic stiffness, structural stiffness and hydrodynamic forces is the key to the
accurate prediction of the hydroelastic response, and these three terms are discussed deeply in this thesis.
With respect to the hydrostatic stiffness model, some controversy has long existed in the literature about its correct form for elastic motion modes, with Newman [1] and Malenica [2] arriving at different forms which are respectively defined in earthand body-fixed reference systems. In this thesis a complete derivation of both forms including the buoyancy and gravitational terms is provided, and the equivalence of the two models associated with elastic motions is confirmed.
A finite element method (FEM) is a common way to compute the structural stiffness of ship hulls. However, for large modern ships, a FEM calculation based on a full structure is inevitably time-consuming since distinguished differences between the longitudinal and the cross-sectional scales of ship hulls usually exist, and the sectional configurations are generally complex, bringing difficulties to numerical modeling. Considering that the structure of modern ships (for example container ships), is usually nearly periodic in the longitudinal direction, in this thesis the ship hull is approximated as a periodic beam and a new implementation of asymptotic homogenization (NIAH) is introduced to efficiently calculate the structural stiffness. This can greatly improve the computational efficiency compared with a full FEM model. Several test cases with both solid and thin-walled sections are given to validate the proposed technique. A range of representative mid-ship sections for a container ship are also considered to investigate the influence of stiffeners on the hydroelastic response.
In the hydrodynamic part, zero-speed and forward-speed radiation and diffraction problems including the well-known m−terms in the body boundary conditions, have both been solved. For generalized modes, the boundary conditions using the corresponding generalized m−terms are applied in the calculation. Neumann-Kelvin (NK) and double-body (DB) linearization models are applied as the steady base flow, and their performance is investigated by comparison with experimental measurements. In head seas, the influence of increasing forward speed on the resonant response of the flexible modes is also studied.
Through the integration of hydroelastic analysis using potential flow theory, and advanced numerical techniques, this thesis contributes to a deeper understanding of the complex interaction between flexible ship hulls and ocean waves, offering valuable insights for the maritime industry.
Linear potential flow (LPF) models remain the tools-of-the-trade in marine and ocean engineering despite their well-known assumptions of small amplitude waves and motions. As of now, nonlinear simulation tools are still too computationally demanding to be used in the entire design loop, especially when it comes to the evaluation of numerous irregular sea states. In this paper we aim to enhance the performance of the LPF models by introducing a hybrid LPF-ML (machine learning) approach, based on identification of nonlinear force corrections. The corrections are defined as the difference in hydrodynamic force (viscous and pressure-based) between high-fidelity CFD and LPF models. Using prescribed chirp motions with different amplitudes, we train a long short-term memory (LSTM) network to predict the corrections. The LSTM network is then linked to the MoodyMarine LPF model to provide the nonlinear correction force at every time-step, based on the dynamic state of the body and the corresponding forces from the LPF model. The method is illustrated for the case of a heaving sphere in decay, regular and irregular waves – including passive control. The hybrid LPF model is shown to give significant improvements compared to the baseline LPF model, even though the training is quite generic.
We present computations of cavitating flow over a NACA0015 hydrofoil. The simulations are performed by a finite volume compressible Euler model with dynamic mesh adaptation. The adaptive mesh refinement (AMR) is driven by a generic, simple and efficient error estimator based on the jump in value between cell faces for a given variable. It is shown that AMR based on vapour fraction provide unsatisfactory results both for (quasi-) steady and unsteady cavitation, as the major flow features are not captured. Instead, adaptivity driven by the Q-value proved successful even for resolving the cavity interface.
We present a high-order nodal spectral element method for the two-dimensional simulation of nonlinear water waves. The model is based on the mixed Eulerian–Lagrangian (MEL) method. Wave interaction with fixed truncated structures is handled using unstructured meshes consisting of high-order iso-parametric quadrilateral/triangular elements to represent the body surfaces as well as the free surface elevation. A numerical eigenvalue analysis highlights that using a thin top layer of quadrilateral elements circumvents the general instability problem associated with the use of asymmetric mesh topology.We demonstrate how to obtain a robust MEL scheme for highly nonlinear waves using an efficient combination of (i) global L2 projection without quadrature errors, (ii) mild modal filtering and (iii) a combination of local and global re-meshing techniques. Numerical experiments for strongly nonlinear waves are presented. The experiments demonstrate that the spectral element model provides excellent accuracy in prediction of nonlinear and dispersive wave propagation. The model is also shown to accurately capture the interaction between solitary waves and fixed submerged and surface-piercing bodies. The wave motion and the wave-induced loads compare well to experimental and computational results from the literature.