Nonlinear Potential Flow Research Articles

Two types of wave-current interactions and their effects on extreme waves in directional seas

The nonlinear wave-current interactions can influence and change extreme wave probability, spectral characteristics, and average shape of extreme waves significantly (Wang, J., Ma, Q. W., & Yan, S. (2021). On Extreme Waves in Directional Seas with Presence of Oblique Current. Applied Ocean Research, 112, pp. 102586). There are different scenarios of wave-wave interactions in reality. This study identifies two types of wave-current interactions: Type-I (waves propagating from current-negligible region to current-significant region) and Type-II (waves propagating from current-significant region to current-negligible region). The impacts of the two types of wave-current interactions on extreme wave probability and the spectral properties will be investigated by using fully nonlinear potential flow model. The numerical results reveal that the changes in extreme wave probability and spectral properties due to Type-I are more evident than those induced by Type-II. It is recommended that a proper type of wave-current interaction scenario should be selected in the design of the numerical modelling or laboratory experiments for wave-structure interactions to achieve more accurate representations of the local wave climate and flow conditions.

Effects of nonlinearity and viscous damping on the resonant responses in two-dimensional moonpools with a recess

In this study, the nonlinear and viscous damping effects on the resonant responses inside a two-dimensional moonpool with a recess are investigated. Based on a fully nonlinear potential flow (FNPF) model, the nonlinear moonpool responses excited by the forced heave motion of a structure are simulated in the time domain. To consider the vortex-shedding damping effects in the moonpool, induced by both piston-type motion (the first harmonic component) and sloshing-type motions (the higher harmonic components), a pressure drop model based on Faltinsen and Timokha (2015) is developed and applied to the FNPF model (FNPF-V for short). The response amplitude operators (RAOs) of the higher harmonics, by which the nonlinear effects are evaluated, are computed by the FNPF-V model. It is found that the higher harmonics are noticeable for the excitation frequencies ω n / ( n + 1 ) ( n is a positive integer, ω n denotes the natural frequency of the n th sloshing mode), where secondary resonances can be triggered. In addition, it is found that the strong nonlinear interactions between the first and higher harmonics can lead to a significant amplification of the moonpool responses. The nonlinear behaviour (the secondary resonance, as well as the sum- and difference-frequency effects) is substantially enhanced as the excitation amplitude increases. Moreover, it is found that the length of the recess influences the nonlinear response of the moonpool in two respects with opposite effects. On the one hand, for the same first harmonic response, moonpools with a longer recess are more apt to exhibit nonlinearity. On the other hand, for the same external excitation, as the length of the recess increases, the first harmonic responses at the excitation frequencies ω n / ( n + 1 ) decrease, suppressing the nonlinear behaviour. • This paper studies the secondary resonances triggered by the piston-mode response. • A pressure drop model is introduced to consider the vortex-shedding effects. • The nonlinear interactions between different harmonic components are investigated. • The effects of recess length on the nonlinear response are analysed and interpreted.

Experimental and numerical investigation of WEC-type floating breakwaters: A single-pontoon oscillating buoy and a dual-pontoon oscillating water column

Wave energy converters(WECs) integrated into floating breakwaters or, more generally, their designs also used as wave absorbers can provide a space- and cost-sharing solution to enhance the efficiency of coastal protection. In this study, the hydrodynamic performances of an oscillating buoy(OB)-type single-pontoon floating breakwater(SPFB) and an oscillating water column(OWC)-type dual-pontoon floating breakwaters(DPFB) are evaluated, respectively, and are comprehensively compared with each other. A series of physical experiments were conducted to investigate the effects of wave parameters, geometrical dimensions, gap distances and PTO damping coefficients. Numerical simulations based on the fully nonlinear potential flow theory cross-check the measured data, and help to further understand the contribution of higher-order waves. It is found that both the wave attenuation and energy conversion of the OWC-type DPFB with a non-uniform draft (i.e. shallow front-pontoon draft and deep back-pontoon draft) are better than those of the OB-type SPFB with the same displacement. Meanwhile, for an OWC-type DPFB, a larger ratio of the chamber width and the total pontoon width has a beneficial effect on the wave attenuation, but has an adverse effect on the maximum energy conversion efficiency. Under the premise of the same pontoon draft, the maximum conversion efficiency of the OWC for the optimal opening ratio is higher than that of the OB for the optimal PTO damping, but the effective frequency bandwidth is almost identical between two devices. Strong wave nonlinearity can generate more energy dissipation induced by the viscous effect and the vortices, resulting into the reduction of energy extraction. • The OB-type single-pontoon FB and the OWC-type dual-pontoon FB are compared. • Physical experiments are conducted and the corresponding numerical model is developed. • The OWC-type DPFB demonstrates better wave attenuation and energy extraction performance. • The ratio of the gap distance and the pontoon width is optimized for the OWC-type DPFB. • Wave nonlinearity reduce the energy conversion efficiency for both the two devices.

Numerical simulation of ship maneuvring by a hybrid method with propulsive factors in waves taken into account

In this paper, based on the open-source code OpenFOAM, a hybrid method coupling the FNPT-based QALE-FEM and the viscous flow method is used to simulate the turn and zigzag maneuvers of the single-screw ship in waves. The external domain adopts the fully nonlinear potential flow theory to simulate the wave tank. The internal domain simulates the interaction between waves and ships by the viscous flow method. The 6DOF motion equations are combined with the propulsive factors in waves to simulate the ship maneuvering during the simulation. The KVLCC2 model is used for numerical simulation. The numerical method is validated by the comparison with the self-propelled maneuvering test. Then, the turning and zigzag maneuvers of the ship in different initial wave headings and wave parameters are simulated, and the influences of wave heading and wave parameters on ship maneuvering are discussed.

Numerical study of the effect of wind above irregular waves on the wave-induced load statistics

A wind-forcing model is implemented into a fully nonlinear potential flow solver for water wave propagation. The model is suited for simulations of a large number of waves and for generation of fully nonlinear wave kinematics. The direct effect of wind is achieved through Jeffreys sheltering mechanism, which models the form drag on steep waves by a varying surface pressure. We detail the implementation and examine the effect of the model parameters, which consist of a sheltering coefficient and a threshold of the spatial slope of the wave for activation of the wind model. Next, we present the calibration and application of the model for reproduction of a test campaign for the effect of wind over waves on the wave-induced loads on a vertical surface piercing cylinder. The experimental study has been reported in ( Kristoffersen et al., 2021 ) and consisted of four storm sea states, each run with a duration equivalent to 30 h (full scale), with and without a simultaneous scaled wind field above the waves in the flume. After calibration, the numerical model is able to reproduce many of the findings from the experimental study. When wind forcing is added and the significant wave height is kept fixed, the crest statistics are slightly suppressed in the tail by the presence of wind. The wind, however, leads to a pronounced increase in the wave steepness and to a larger number of breaking waves. Despite the increased number of breaking waves, the depth integrated inline force was only found to increase slightly for the most extreme events at small exceedance probabilities. In contrast, the local force in the vicinity of the free surface was found to increase significantly, at short term exceedance probabilities up to 10 −2 , which is consistent with the measured pressures. For the numerical force profile along the vertical direction of the pile, we found that the altitude of maximum wave force is lowered with the introduction of wind. All of these findings are consistent with the experimental observations. Further for the numerical wave-induced local force at short term exceedance probability of 10 −4 , an increase by a factor of 1.8 was found from the introduction of wind. Although the effect on the global inline force was less strong, this local effect is important for design. The present numerical approach offers a direct way to establish such design loads.

Fully nonlinear interfacial periodic waves in a two-layer fluid with a rigid upper boundary and their loads on a cylindrical pile

Based on the fully nonlinear potential flow theory, interfacial periodic gravity waves in a two-layer fluid with a rigid upper boundary are investigated quasi-analytically using the homotopy analysis method (HAM), and the corresponding wave loads on a cylindrical pile are estimated by Morison’s empirical formula. Because of the great freedom in the choices of auxiliary linear operators, initial guesses, and convergence-control parameter, convergent series solutions are obtained in the framework of the HAM. For Boussinesq wave loads on the cylinder in one wave period, there exists a phenomenon of peak–valley mismatch between the upper and lower layer inertial loads; the total drag, total inertial and global loads reach their own peaks almost at the same time when the upper layer load equals the lower layer load. As the wave height increases, the dominant load changes from inertial load to drag load. Previous theoretical studies about internal or interfacial periodic wave loads on a cylinder were mainly based on linear or weakly nonlinear wave models, which causes the lack of corresponding theoretical research in the frame of fully nonlinear wave theory. Compared with linear and weakly nonlinear wave models, the fully nonlinear wave model considered in this paper provides more accurate results for the maximal loads on a slender cylindrical pile exerted by Boussinesq interfacial periodic waves, especially for strongly nonlinear cases. All of these should enhance our understanding of internal periodic waves and their loads on a marine riser.

Gravity effects in two-dimensional and axisymmetric water impact models

The effect of gravity during the water entry of two-dimensional and axisymmetric bodies is investigated analytically and numerically. An extension to the Wagner model of water impact is proposed in order to take into account the effect of gravity. For this purpose, the free-surface condition is modified. The pressure is computed using the modified Logvinovich model of Korobkin (Eur. J. Appl. Maths, vol. 6, 2004, pp. 821–838). The model has been implemented and validated through comparisons with fully nonlinear potential flow simulations of different two-dimensional and axisymmetric water entry problems. Our investigation shows that it is equally important to account for gravity when computing the pressure distribution and to account for gravity when computing the size of the wetted surface in order to obtain accurate force results with the Wagner model. Simulations of wedges and cones with different values of deadrise angle ( $\beta$ ) entering water at constant speed ( $V$ ) demonstrate the accuracy of the semi-analytical model and show that the effect of gravity in such water impacts is governed by the effective Froude number defined as $Fr^*=V/(\sqrt {gh}\sqrt {\tan \beta })$ , with $g$ the acceleration due to gravity and $h$ the penetration depth. The accuracy of the semi-analytical model for decelerated water entries is also demonstrated by investigating the water entry of a wedge and a cone with a $15^\circ$ deadrise angle with deceleration until full stop. The semi-analytical model is able to accurately predict the effect of gravity during both two-dimensional and axisymmetric water entry problems with deceleration.

On the Nonlinear Response of a Tri-SWACH Vessel in Incident Waves

Abstract In this article, the nonlinear motion response of a Trimaran with SWATH-type center hull vessel (TriSWACH) is investigated and compared with the linear response using a hybrid method combining a regression analysis of the viscous damping generated by the hulls with a nonlinear potential flow simulation of rigid body motions. The TriSWACH is a hybrid trimaran hull form, developed using the SWATH (small waterplane area twin hull) technology, from which a single small waterplane area center hull is retained. It is designed to keep the magnitude of its motion response below its equivalent monohull counterpart while also benefiting from large intact transverse stability provided by its side hulls. Since a significant portion of the total damping generated by the submerged hull girder is viscous in nature, an accurate prediction of the steady-state motion response near natural frequency is highly dependent upon the correct modeling of the boundary layer flow. The total damping coefficients obtained experimentally from motion response transfer functions are used to augment the potential flow solution and improve the numerical prediction method at large angles of inclination, characteristic of operation in rough weather near the peak frequency of the motion response. Introduction SWATH1-type vessels exhibit ship motions less pronounced than a monohull of the same displacement. It has been reported that SWATHs have the potential to significantly reduce the impact of harsh environmental conditions on ship operability (Kennell et al. 1985). Although the interest in SWATH technology in ship design continued over the past few decades, it was recognized that this hull form required modifications in order to accommodate high-speed applications. An example of a TriSWACH concept is shown in Fig. 1, with the main distinguishing features compared to the SWATH-type vessel being the presence of the side hulls and one single main hull.

Assessment of one-way coupling methods from a potential to a viscous flow solver based on domain- and functional-decomposition for fixed submerged bodies in nonlinear waves

To simulate the interaction of ocean waves with marine structures, coupling approaches between a potential flow model and a viscous model are investigated. The first model is a fully nonlinear potential flow (FNPF) model based on the Harmonic Polynomial Cell (HPC) method, which is highly accurate and best suited for representing long distance wave propagation. The second model is a CFD code, solving the Reynolds-Averaged Navier–Stokes (RANS) equations within the OpenFOAM® toolkit, more suited to represent viscous and turbulent effects at local scale in the body vicinity. Two one-way coupling strategies are developed and compared in two dimensions, considering fully submerged and fixed structures. A domain decomposition (DD) strategy is first considered, introducing a refined mesh in the body vicinity on which the RANS equations are solved. Boundary conditions and interpolation operators from the FNPF results are developed in order to enforce values at its outer boundary. The second coupling strategy considers a decomposition of variables (functional decomposition, FD) on the local grid. As the FNPF simulation provides fields of variables satisfying the irrotational Euler equations, complementary velocity and pressure components are introduced as the difference between the total flow variables and the potential ones. Those complementary variables are solutions of modified RANS equations. Extensive comparisons are presented for nonlinear waves interacting with a horizontal cylinder of rectangular cross-section. The loads exerted on the body computed from the four simulation methods (standalone FNPF, standalone CFD, DD and FD coupling schemes) are compared with experimental data. It is shown that both coupling approaches produce an accurate representation of the loads and associated hydrodynamic coefficients (inertia and drag) over a large range of incident wave steepness and Keulegan–Carpenter number, for a small fraction of the computational time needed by the complete CFD simulation.

Numerical simulation of turn and zigzag Maneuvres of trimaran in calm water and waves by a hybrid method

As one of the widely used high-performance ships, the hydrodynamic characteristics of the trimaran ships have been widely investigated in recent years. But, the study on the maneuverability and the skill of the maneuvering simulation are still limited. In this paper, a hybrid method coupling the FNPT-based (fully nonlinear potential flow theory) QALE-FEM (quasi arbitrary Lagrangian-Eulerian finite element method) with the viscous flow method is applied to simulate the turn and zigzag maneuvers of the trimaran in both calm water and waves. The environment of calm water and incident waves is simulated by the numerical tank of QALE-FEM. The maneuvering of the trimaran is carried out in the scope of the numerical tank by the viscous flow method. The grid convergence test is carried out first, and the computed results are compared with the experimental results. Then, the turn and zigzag maneuvers of a trimaran model in both calm water and waves are simulated to study the trimaran's maneuvering characteristics.

A flexible fully nonlinear potential flow model for wave propagation over the complex topography of the Norwegian coast

Coastal wave propagation and transformation are complicated due to the significant variations of water depth and irregular coastlines, which are typically present at the Norwegian fjords. A potential flow model provides phase-resolved solutions with low demands on computational resources. Many potential flow models are developed for offshore waves and lack of numerical treatments of coastal conditions. In the presented work, several modifications are introduced to a fully nonlinear potential flow model with a σ-grid for the purpose of coastal wave modelling: Shallow water breaking criteria are included in addition to deepwater breaking algorithms to approximate breaking waves over a complete range of water depth. A new coastline algorithm is introduced to detect complex coastlines and ensure robust simulations near the coast. The algorithm is compatible with structured grid arrangement in the horizontal plane and allows for high-order discretisation schemes for the free surface boundary conditions for an accurate representation of complex free surfaces. A parallelised solver for the Laplace equation is utilised to ensure fast simulations for large domains with multi-core infrastructures.The proposed model is validated against theories and experiments for various two- and three-dimensional nonlinear wave propagation and transformation cases that represent typical coastal conditions. The simulations show a good representation of nonlinear waves, and the results compare well with experiments. Furthermore, two large-scale engineering scenarios are simulated, where the applicability of the coastline algorithm and the parallel commutation capability of the model are demonstrated.

Hydrodynamic Coupling of Viscous and Nonviscous Numerical Wave Solutions Within the Open-Source Hydrodynamics Framework reef3d

Abstract A comprehensive understanding of the marine environment in the offshore area requires phase-resolved wave information. For far-field wave propagation, computational efficiency is crucial, as large spatial and temporal scales are involved. For the near-field extreme wave events and wave impacts, high resolution is required to resolve the flow details and turbulence. The combined use of a computationally efficient large-scale model and a high-resolution local-scale solver provides a solution that combines accuracy and efficiency. This article introduces a coupling strategy between the efficient fully nonlinear potential flow (FNPF) solver REEF3D::FNPF and the high-fidelity computational fluid dynamics (CFD) model REEF3D::CFD within the open-source hydrodynamics framework REEF3D. REEF3D::FNPF solves the Laplace equation together with the boundary conditions on a sigma-coordinate. The free surface boundary conditions are discretized using high-order finite difference methods. The Laplace equation for the velocity potential is solved with a conjugated gradient solver preconditioned with a geometric multigrid provided by the open-source library Hypre. The model is fully parallelized following the domain decomposition strategy and the message passing interface protocol. The waves calculated with the FNPF solver are used as wave generation boundary conditions for the CFD-based numerical wave tank REEF3D::CFD. The CFD model employs an interface capturing two-phase flow approach that can resolve complex wave structure interaction, including breaking wave kinematics and turbulent effects. The presented hydrodynamic coupling strategy is tested for various wave conditions and the accuracy is fully assessed.

Numerical Simulation of Liquid Sloshing Using a Fully Nonlinear Potential Flow Model in the Noninertial Coordinate System

Numerical Simulation of Liquid Sloshing Using a Fully Nonlinear Potential Flow Model in the Noninertial Coordinate System

Representation of 3-h Offshore Short-Crested Wave Field in the Fully Nonlinear Potential Flow Model REEF3D::FNPF

Abstract Stochastic wave properties are crucial for the design of offshore structures. Short-crested seas are commonly seen at the sites of offshore structures, especially during storm events. A long time duration is required in order to obtain the statistical properties, which is challenging for numerical simulations. In this scenario, a potential flow solver is ideal due to its computational efficiency. A procedure of reproducing accurate short-crested sea states using the open-source fully nonlinear potential flow model REEF3D::FNPF is presented in the paper. The procedure examines the sensitivity of the resolutions in space and time as well as the arrangements of wave gauge arrays. A narrow band power spectrum and a mildly spreading directional spreading function are simulated, and an equal energy method is used to generate input waves and avoid phase-locking. REEF3D::FNPF solves the Laplace equation together with the boundary conditions using a finite difference method. A sigma grid is used in the vertical direction and the vertical grid clustering follows the principle of constant truncation error. High-order discretization methods are implemented in space and time. Message passing interface is used for high performance computation using multiple processors. Three-hour simulations are performed in full-scale at a hypothetic offshore site with constant water depth. The significant wave height, peak period, kurtosis, skewness and ergodicity are examined in the numerically generated wave field. The stochastic wave properties in the numerical wave tank (NWT) using REEF3D::FNPF match the input wave conditions with high fidelity.

Investigation of ship responses in regular head waves through a Fully Nonlinear Potential Flow approach

In this study, the hydrodynamic performance of a ship in terms of motions and resistance responses in calm water and in regular head waves is investigated for two loading conditions using a Fully Nonlinear Potential Flow (FNPF) panel method. The main focus is understanding the ship responses in a broad range of operational conditions. Comprehensive analyses of the motions and their correlation with the wave making resistance including their harmonics in waves are presented and compared against experimental data. The predicted motions compare well with experimental data but the resistance prediction is not quite as good. The natural frequencies for heave and pitch are estimated from a set of free decay motion simulations in calm water to provide a better insight into the ship behavior near resonance conditions in waves. Interestingly, in addition to the well known peak in the added wave resistance coefficient around wave lengths close to one ship length, a secondary peak is detected in the vicinity of wave lengths with half the ship length.

THE INFLUENCE OF FORWARD SPEED AND NONLINEARITIES ON THE DYNAMIC BEHAVIOUR OF A CONTAINER SHIP IN REGULAR WAVES

The aim of this paper is to compare the heave and pitch motions for the S175 containership, travelling in head regular waves, obtained from frequency domain linear and time domain partly nonlinear potential flow analyses. The frequency domain methods comprise the pulsating and the translating, pulsating Green’s function methods, with the relevant source distribution over the mean wetted surface of the hull. The time domain method uses the radiation and diffraction potentials related to the mean wetted surface, implemented using Impulse Response Functions (IRF), whilst the incident wave and restoring actions are evaluated on the instantaneous wetted surface. The calculations are carried out for a range of Froude numbers, and in the case of the partly nonlinear method for different wave steepness values. Comparisons are made with available experimental measurements. The discussion focuses on the necessity for a nonlinear approach for predicting the radiation potential and the possible numerical methods for its formulation.

Parametric Hull Form Optimization of Containerships for Minimum Resistance in Calm Water and in Waves

This paper described the process of generating the optimal parametric hull shape with a fully parametric modeling method for three containerships of different sizes. The newly created parametric ship hull was applied to another ship with a similar shape, which greatly saved time cost. A process of selecting design variables was developed, and during this process, the influence of these variables on calm water resistance was analyzed. After we obtained the optimal hulls, the wave added resistance and motions of original hulls and optimal hulls in regular head waves were analyzed and compared with experimental results. Computations of the flow around the hulls were obtained from a validated nonlinear potential flow boundary element method. Using the multi-objective optimization algorithm, surrogate-based global optimization (SBGO) reduced the computational effort. Compared with the original hull, wave resistance of the optimal hulls was significantly reduced for the two larger ships at Froude numbers corresponding to their design speeds. Optimizing the hull of the containerships slightly reduced their wave added resistance and total resistance in regular head waves, while optimization of their hulls hardly affected wave-induced motions.

Numerical Simulation for the Evolution of Internal Solitary Waves Propagating over Slope Topography

In this study, the propagation and evolution characteristics of internal solitary waves on slope topography in stratified fluids were investigated. A numerical model of internal solitary wave propagation based on the nonlinear potential flow theory using the multi-domain boundary element method was developed and validated. The numerical model was used to calculate the propagation process of internal solitary waves on the topography with different slope parameters, including height and angle, and the influence of slope parameters, initial amplitude, and densities jump of two-layer fluid on the evolution of internal solitary waves is discussed. It was found that the wave amplitude first increased while climbing the slope and then decreased after passing over the slope shoulder based on the calculation results, and the wave amplitude reached a maximum at the shoulder of the slope. A larger height and angle of the slope can induce larger maximum wave amplitude and more obvious tail wave characteristics. The wave amplitude gradually decreased, and a periodic tail wave was generated when propagating on the plateau after passing the slope. Both frequency and height of the tail wave were affected by the geometric parameters of the slope bottom; however, the initial amplitude of the internal solitary wave only affects the tail wave height, but not the frequency of the tail wave.

On the importance of nonlinear hydrodynamics and resonance frequencies on power production in multi-mode WECs

Multi-mode Wave Energy Converters (WECs) are able to harvest energy from multiple Degrees-of-Freedom (DOFs) simultaneously, which increases the power that can be absorbed from the incident wave compared to single-DOF WECs. However, nonlinear coupling between hydrodynamic modes, which occurs when the WEC oscillates simultaneously in multiple directions, means that simply applying the typical control strategies used for single-DOF WECs can lead to sub-optimal performance. This study investigates the multi-DOF dynamic control of a submerged, flat cylindrical WEC subjected to hydrodynamic coupling effects modelled under the weakly nonlinear potential flow theory based on the weak-scatterer approximation. Results show that, at low incident wave frequencies, tuning the surge, heave and pitch modes of the WEC to the same natural frequency can result in power losses of up to 30% in the weakly nonlinear model compared to results obtained from a fully linear model. These discrepancies are attributed to the pitching motions of the WEC, which changes the projected surface area of the device relative to the equilibrium position and hence violates the assumptions of the linear theory. From these findings, a suggested design strategy where the surge, heave and pitch DOFs were all decoupled and tuned to different natural frequencies was therefore proposed. In the presence of weakly nonlinear hydrodynamic coupling, it was found that this design may result in significant improvements in power absorbed for the multi-mode WEC, compared to a case where all DOFs are simply tuned to match the peak frequency of a given sea state.

The role of bandwidth in setting the breaking slope threshold of deep-water focusing wave packets

We examine the role of wave packet bandwidth in modulating the breaking slope threshold for focusing deep-water surface gravity wave packets. Using a fully nonlinear potential flow solver and laboratory experiments, we show that the slope threshold may be strongly modulated by the wave packet bandwidth. We propose a new breaking threshold parameterization that shows that the slope threshold may be modulated by more than a factor of two by changes in the bandwidth. This has implications for parameterizations of the properties of the breaking induced flow (e.g., the energy dissipation) as they do not currently account for these effects.