Wave-body Interactions Research Articles

Focused wave interaction with a partially-immersed rectangular box using 2-D incompressible SPH on a GPU comparing with experiment and linear theory

Wave interaction with bodies spanning the water surface is a common problem. A basic rectangular box of small draft is considered in two dimensions and focused waves are used to minimise reflections. Overtopping occurs in some cases making the inherently mass conservative smoothed particle hydrodynamics (SPH) method appropriate. This is applied in incompressible (divergence-free) form with a 2-D graphics processing unit (GPU) version of the Chow et al. (2019) code with some improvements. A newly parallelised GPU algorithm for the population of a compressed sparse row matrix storage array for the pressure Poisson equation is presented and provides a 327–446 times function speedup and overall simulation time speedups of 1.45–1.78 times with over 5 million particles. The inclusion of the parallel function leads to a completely parallel ISPH algorithm. Peak pressures on the base and front face are compared with experiment and linear (potential-flow) theory. The experiments used periodic focused waves which showed some variation in form about a peak crest although crest elevations were repeatable, and these are reproduced in the model. Converged incompressible SPH (ISPH) values are in approximate agreement with both. Overtopping of the box shows qualitative agreement with experiment. While linear theory cannot account for overtopping or viscous (eddy-shedding) effects, submerged pressure prediction provides a useful approximation. The ISPH model is single phase and limited video evidence suggests that air entrapment can occur in the initial stages of overtopping near the front face. Quite complex vorticity generation and eddy shedding is predicted with free-surface interaction. The study shows the capability and limitations of single phase ISPH for complex wave-body interaction.

On optimal energy-extraction performance of arrays of wave-energy converters, with full consideration of wave and multi-body interactions

An array of ocean-wave energy converters, compared to a stand-alone device, provides lower energy-production costs but affects the aggregate power performance. Previous studies suggested that wave-interaction effects within the array could increase energy production by over 15% per device. However, no physical constraints on the WECs were considered in these studies; as a result, the devices can experience unrealistically large motions. A control strategy is thus desirable to coordinate individual WECs and maximize the energy extraction. We apply model-predictive control (MPC) to an array of point-absorber-type WECs by developing a formulation that accommodates hard constraints on the motion of each device and on the Power-takeoff (PTO) forces with excellent computational efficiency. Full multi-body wave-interaction effects are computed by a semi-analytical method within linear-wave theory. This framework enables us to demonstrate results of realistic maximal power production for arrays of two, three, and four devices operating under constraints in sea waves of various incident angles. It is observed that wave–body interactions have actually destructive effects on the array power production for the majority cases in irregular sea waves. Also discussed are effects of the reactive power produced by the PTO unit and the possibility of removing it within the MPC framework.

Time domain potential and source methods and their application to twin-hull high-speed crafts

ABSTRACT The numerical accuracy of time dependent potential and source methods is compared against analytical and other numerical results using an in-house transient wave-body interaction three-dimensional wave Green function computational tool of ITU-WAVE. The time dependent Impulse Response Functions (IRFs) are used to predict the behaviour of radiation forces, exciting forces, and response of floating bodies. For radiation force IRFs, the numerical results show that potential method converges with less numbers of panels compared to source method, while in the case of diffraction force IRFs, the convergence is achieved with the same number of elements for both potential and source methods. As potential method achieves convergence faster than source method for radiation force IRFs prediction, potential method is applied for the hydrodynamic and response parameters of a twin-hull high-speed craft. The present ITU-WAVE numerical results, which are compared with experimental, analytical, and other numerical results for validation purposes show satisfactory agreements.

Numerical investigation of the Fourier–Kochin theory for wave-induced response estimation of floating structures

The Fourier–Kochin theory—an indirect solution approach for the boundary integral representations of free-surface flows that rely on free-surface Green function—is investigated by considering effective computation and reliable prediction. The present study addresses wave–body interaction with zero forward speed by adopting a higher-order approximation. Three distinct hull forms, the DTMB 5415, a scaled model reproduced from it, and a barge are used for practical application. The scaled frigate and barge models are used for comparative analysis to assess the performance of different computation techniques, modeling elements, and solution methods and to find the best course; the purpose of studying DTMB 5415 is to provide a realistic application based on a full-scale hull form by using the findings of the earlier benchmark studies. The analyses that cover both the rigid-body and elastic responses indicate that an adaptive approach for the computation of Fourier components has the potential to eliminate the numerical drawbacks of the presented implementation the Fourier–Kochin theory, but also stringently needs parallelism, preferably using the Single Program Multiple Data model. Using discontinuous elements for free-surface discretization when applying the Extended Boundary Integral Equation Method, the featured technique for irregular frequency suppression, is also promoted.

Application of the generalized body-fixed coordinate system for the wave-body interaction problem of a small-depth elastic structure in head seas

Application of the generalized body-fixed coordinate system for the wave-body interaction problem of a small-depth elastic structure in head seas

Machine Learning to approximate free-surface Green's function and its application in wave-body interactions

Efficient and accurate evaluation of free-surface Green's function is the key to hydrodynamic problems solved by boundary element method (BEM). However, so far, there is still no unified numerical method that can accurately approximate all kinds of free-surface Green's functions. In theory, machine learning can be used to approximate any function with high accuracy. In the present study, neural networks are used for the numerical approximation of pulsating source Green's function, and the corresponding optimization algorithms for gradient descent are adopted. Regularization is used to prevent overfitting. Double-precision numerical results obtained by Romberg quadrature are used as training set and validation set. To improve the accuracy of present numerical approximation, the calculation domain of both Green's function and its gradient are divided into 4 zones, and various network structures are adopted in each zone. Finally, a machine model, called ZeroGF, is obtained by machine learning that can predict Green's function and its derivatives. The numerical results show that ZeroGF owns at least 4 digits of accuracy in above 99% area of all zones. BEM program incorporating with ZeroGF is validated in the hydrodynamic calculation of the hemisphere, Wigley III and the Barge. Good accuracy and reliability of ZeroGF is shown.

Flap-type wave energy converter arrays: Nonlinear dynamic analysis

The wave-body interaction of resonant oscillating wave energy converters (WECs) is complex and nonlinear. Rapid development of WECs needs a reliable simulation tool for analysis and design procedure with the ability to capture the instantaneous nonlinear behavior. This paper presents a methodology to study the behavior of a flap-type WEC utilizing hybrid physical and numerical simulation. Dynamic characteristics of the device as isolated and in an array are estimated and the time and oscillation amplitude-dependency of these parameters are explained. This methodology is developed for a device composed of a series of flaps placed on a vertical breakwater. However, the developed algorithm can be updated for any other WEC concept with special consideration on the consequent changes in the load transfer, surrounding hydrodynamic, and wave-structure interaction. This paper increases our understanding and knowledge of all involved phenomena and their direct effects on the natural period and the response and can be used for tunning dynamic characteristics of WEC device to incoming waves. Finally, the developed numerical model is used for the simulation of the WEC to different wave loads and the results are validated with the experimental tests.

A semi-analytical pulsating source incorporated with the panel method for wave-body interactions

ABSTRACT To deal with hydrodynamics, numerical integration of pulsating source Green’s function over a panel is very important. However, little research is focused on it. In the present paper, a semi-analytical integral expression of pulsating source over the panel is proposed. A coordinate transformation is performed and the panel is mapped into a unit rectangle. The space integral is carried out beforehand. Thus, the integral of Green’s function can be expressed as a θ-type single integral expression. Numerical results show that the present expression provides a new robust approach to obtain the integral of Green’s function over a panel in an accurate and stable manner. Based on the above method, radiation-diffraction problems of Wigley III and LNG carrier in waves are calculated, then ship motion responses versus various wave frequencies are computed. The calculated motions of ship acquired agree well with experimental data.

Numerical Investigation on Motion Responses of a Floating Hemisphere Over a Sloping Bottom

Abstract In the last several decades, some numerical approaches have been proposed to deal with three-dimensional wave-body interaction problems in sloping bottom environment. Most of them either adopt the finite depth Green function or add numerical damping terms into the free surface condition to treat far field radiation condition, which certainly give rise to numerical errors. The hybrid model (Belibassakis, “A Boundary Element Method for the Hydrodynamic Analysis of Floating Bodies in Variable Bathymetry Regions,” Eng. Anal. Boundary Elements 32, pp. 796–810) adopting the consistent coupled-mode system for incident wave propagation problem combining with the three-dimensional bottom-dependent Green function to treat the diffraction and radiation problem is a complete formulation, as the latter function appropriately characterize the far field radiation wave pattern over a smoothly sloping bottom. However, this model has not been validated after its publication. In this connection, comparisons with computational fluid dynamic (CFD) results are presented to verify its accuracy. Application of this hybrid model is also performed to investigate the effects on the floating hemisphere by the sloping bottom.

Application of the Fourier–Kochin theory for the diffraction and radiation of free-surface waves about stationary floating bodies

The classical problem of time-harmonic diffraction and radiation of free-surface flows due to wave–body interaction is revisited based on the Fourier–Kochin theory for zero forward speed. The key idea of the Fourier–Kochin theory is reversing the order of the two fundamental tasks of the Green function based direct solutions of free-surface flows, i.e., evaluation of the Green function and its gradient, and their subsequent integration over the boundary surface. By implementing a higher-order numerical approximation along with the use of extended boundary integral equation method to suppress the irregular frequencies, three different bodies – a hemisphere, a vertical cylinder, and a frigate model – are studied. The Fourier–Kochin framework accurately captures the radiated and diffracted flow about oscillating bodies, in general, but slight irregularities are also observed at high frequencies for complicated body forms. Since the floating body is stationary here, the problem has a standard, unambiguous solution and the indirect approach introduced by the Fourier–Kochin theory may not seem worthwhile to adopt; however, its perspective becomes rewarding when the forward speed effects are considered. As a premise of this idea, the main goals here are to assess the practical application of the theory, to identify the challenges, and to investigate how to surmount them.

A potential flow method combining immersed boundaries and overlapping grids: Formulation, validation and verification

A fully nonlinear two-dimensional numerical method based on potential-flow theory for water waves and their interaction with surface-piercing rigid bodies is presented. The harmonic polynomial cell (HPC) method is used to solve the Laplace equation for the velocity potential and its time derivative. The HPC method, which is a high-order method using analytical expressions (harmonic polynomials) to represent the solution inside overlapping cells, has previously been shown accurate and efficient. Supplementary research has shown that, in order to maximally benefit from the method’s accuracy, it is a requirement that square or close-to-square cells are used. Here, we use an immersed boundary method to model non-stationary boundaries such as the free surface or the surface of a rigid body, and overlapping, body-fixed grids that are locally Cartesian to refine the solution near moving bodies. Combining these two modelling concepts with the HPC method represents the main novel contribution in the present work. With this combined method, denoted as an immersed-boundary overlapping grid method (IBOGM), the challenge of generating boundary-fitted grids for complex boundaries is avoided. Moreover, square cells can be used throughout the domain and the solution can be refined locally without increasing the number of unknowns unnecessarily. The method is systematically validated and verified against analytical, experimental and numerical reference results. The cases studied include propagation of steep waves, forced heave motions of a semi-submerged circular cylinder and a fixed and freely floating ship section in beam-sea waves. For the freely floating ship section, the present method is compared in detail with results from a dedicated study performed with a fully nonlinear boundary element method for cases with roll motions up to 30°. The present results are generally in good agreement with reference results, even for the most challenging wave–body interaction cases considered. Based on this, we later intend to use the method to examine in depth the importance of nonlinear effects in the interaction between waves and rigid bodies.

A novel numerical method for the hydrodynamic analysis of floating bodies over a sloping bottom

A novel numerical method combining Eigenfunction matching method (EMM) and 3D Rankine source method is developed to investigate wave-body interaction over a sloping bottom. The extended EMM is proposed to create an incident wave model over the sloping bottom, thereby obtaining the Froude-Krylov force and Neumann data on wet surfaces of the floating body for the diffraction problem. A 3D Rankine source method concerning the sloping bottom is developed, in which the free surface and seabed are both divided into the inner domain and outer domain. Source panels are placed in an exponential manner in the latter domain, by which the far field radiation condition is well satisfied. To verify the proposed method, comparisons with other mathematical models involving added mass and damping coefficients, wave exciting forces and motion RAOs by a floating hemisphere and a LNG carrier are carried out.

Numerical Simulation of Green Water on Deck with a Hybrid Eulerian-Lagrangian Method

Green water on the ship deck in rough sea conditions may induce extreme impulsive wave impacts on superstructures and result in severe structural damage. It is of great importance to consider green water loads in ship structure design. However, there are many challenges in predicting green water loads due to the strongly nonlinear wave–ship interactions and the multiphase, multi-scale nature of the wave impact phenomena. In this article, a three-dimensional hybrid Eulerian–Lagrangian approach is proposed for simulating green water loads on the ship deck. It is extended from an efficient and accurate two-dimensional method developed for fluid–structure interaction problems. In this method, the flow field is solved on a fixed regular Cartesian grid system in an Eulerian framework, whereas the solid body motion is tracked with a set of markers immersed in the fluid and solved in a Lagrangian framework. Two benchmark cases, green water on a fixed simplified Floating Production Storage and Offloading (FPSO) model and green water on ship, are simulated. Comparison between experimental data and numerical results shows that our method is a viable choice for predicting green water loads. Introduction In rough sea conditions, ships may undergo large-amplitude motions and suffer green water impacts due to the strongly nonlinear wave–body interaction. Large waves run up to the ship deck and impact on superstructures with huge volume of water impulsively. It can induce extreme impulsive wave impact loads on superstructures and result in severe structural damage. Thus, it is important to predict wave impact loads for ship structure design. However, there are still great challenges in predicting green water impact loads accurately because it is a flow phenomenon of high complexity and randomness due to its multiphase, highly turbulent nature with wave breaking, air entrainment, etc (Temarel et al. 2016).

A numerical solution of the wave–body interactions for a freely floating vertical cylinder in different water depths using OpenFOAM

In the present study, a finite volume method based on Reynolds-averaged Navier–Stokes equations is developed numerically in OpenFOAM to simulate two-phase flows around a freely floating cylinder in a numerical wave tank (NWT). All numerical computations are carried out using interDyMFoam solver, manipulating dynamic mesh. The left wall of NWT oscillates as a paddle wave-maker to produce desired waves. The accuracy of the current numerical method is confirmed by evaluating the results of some published experimental benchmarks, including the generation of regular waves in NWT and also the response of two fixed and floating objects in waves. Based on the current study findings, OpenFOAM is capable of predicting these cases of wave–structure interaction with good delicacy. Additionally, the moving wall of NWT as a flap-type wave-maker can produce waves with different attributes sufficiently. In the following, the influence of regular waves on a circular cylinder, operating freely in deep water, as well as the effect of the water depth on the cylinder’s movement and forces acting on it are assessed. The results indicated that the change in the water depth has a significant effect on the response of the freely floating cylinder in waves.

Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states.

Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g. pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulations offline, but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals (Chen & Chen, 1993. IEEE Trans. Neural Netw. 4, 910-918 (doi:10.1109/72.286886)), and it is the first implementation of such theory to realistic engineering problems.

The Performance of a Spectral Wave Model at Predicting Wave Farm Impacts

For renewable ocean wave energy to support global energy demands, wave energy converters (WECs) will likely be deployed in large numbers (farms), which will necessarily change the nearshore environment. Wave farm induced changes can be both helpful (e.g., beneficial habitat and coastal protection) and potentially harmful (e.g., degraded habitat, recreational, and commercial use) to existing users of the coastal environment. It is essential to estimate this impact through modeling prior to the development of a farm, and to that end, many researchers have used spectral wave models, such as Simulating WAves Nearshore (SWAN), to assess wave farm impacts. However, the validity of the approaches used within SWAN have not been thoroughly verified or validated. Herein, a version of SWAN, called Sandia National Laboratories (SNL)-SWAN, which has a specialized WEC implementation, is verified by comparing its wave field outputs to those of linear wave interaction theory (LWIT), where LWIT is theoretically more appropriate for modeling wave-body interactions and wave field effects. The focus is on medium-sized arrays of 27 WECs, wave periods, and directional spreading representative of likely conditions, as well as the impact on the nearshore. A quantitative metric, the Mean Squared Skill Score, is used. Results show that the performance of SNL-SWAN as compared to LWIT is “Good” to “Excellent”.

Advances on simulation of wave-body interactions under consideration of the nonlinear free water surface

ABSTRACT The paper refers to a boundary element method (BEM) in the time domain for the simulation of wave-body interactions considering the free water surface. The approach solves the boundary integral equations for the velocity and the acceleration potential. The model of the free water surface in this approach is based on the mixed-Eulerian-Lagrangian (MEL) method. Validation results are presented for two well-studied test cases. The first validation case is dedicated to the free water surface. Here, the nonlinear wave loads on a truncated cylinder are analysed and compared with a higher-order panel method and experimental data. Second, results of a Wigley hull moving with forward speed in head waves are shown and compared with experimental results published by Kashiwagi. The validation results in both test cases generally show good agreement with published data and demonstrate the ability of BEM to investigate different types of hydrodynamic problems related to wave-body interactions.

Finite difference solutions for nonlinear water waves using an immersed boundary method

AbstractIn this article, high‐order finite difference solutions of the exact potential‐flow problem for nonlinear water waves are developed which treat both the free surface and the uneven sea bottom boundary conditions using an immersed boundary method (IBM). The convergence, accuracy, and stability of this approach is first established for the linear problem, using various orders of scheme and different grid discretization strategies. The nonlinear wave problem on a flat bottom is then considered, and the solutions are compared with the highly accurate stream function theory solution. The convergence performance of the numerical solution for this nonlinear wave problem is established. Finally, linear wave shoaling and nonlinear wave propagation over a submerged bar are also tested. A preconditioned iterative solution strategy is also developed and shown to provide optimal scaling of the solution effort with increasing number of unknowns. Compared with existing free surface tracking methods, the IBM retains the same level of accuracy and stability when solving the linear problem. For the nonlinear problem, the IBM behaves reasonably in terms of accuracy, but generally with slightly higher computational effort. When it comes to the wave–body interaction problem, it is expected that the IBM will be advantageous compared with the σ‐transform method, since it removes the necessity of constructing an artificial continuous free‐surface inside the body.

The second-order interaction of monochromatic waves with three-dimensional bodies in a channel

A numerical model is developed to investigate the effect of the channel walls on the second-order hydrodynamic characteristics of three-dimensional bodies with arbitrary geometries in a wave channel based on the higher order boundary element method in the frequency domain. The second-order double-frequency radiation and diffraction potentials are obtained explicitly. In contrast to the second-order wave-body interaction problem in the open sea, the main difficulty stems from the boundary integral equation with the supplementary contribution of the up-wave and down-wave vertical surfaces of the channel in the second-order diffraction analysis. By exploiting the free-surface channel Green function and the known first-order scattering potential in eigenfunction expansion, the rapidly convergent integrals over the up-wave and down-wave vertical surfaces in the near fields can be evaluated analytically. Numerical results for the wave interaction with a bottom-mounted vertical circular cylinder, a fixed truncated vertical circular cylinder and a freely floating four-column structure are presented, and show that in comparison with the results in the open-sea condition, the second-order hydrodynamic properties of a body in a channel are affected more seriously than the linear ones due to the side-wall reflections.

Multibody Interactions of Floating Bodies with Time-Domain Predictions

The applications of the three-dimensional transient panel code ITU-WAVE based on potential theory is further extended to take into account the multibody interactions in an array system using linear and square arrays. The transient wave-body interactions of first-order radiation and diffraction hydrodynamic parameters are solved as the impulsive velocity potential to predict Impulse Response Functions (IRFs) for each mode of motion. It is shown that hydrodynamic interactions are stronger when the bodies in an array system are close proximity and these hydrodynamic interactions are reduced considerably and shifted to larger times when the separation distances are increased. The numerical predictions of radiation (added-mass and damping coefficients) and exciting (diffraction and Froude-Krylov) forces are presented on each floating bodies in an array system and on single structure considering array as single floating body. Furthermore, the numerical experiment shows the hydrodynamic interactions are more pronounced in the resonant frequency region which are of important for fluid forces over bodies, responses and designs of multibody floating systems. The present numerical results of ITU-WAVE are validated against analytical, other numerical and experimental results for single body, linear arrays (two, five and nine floating bodies) and square arrays of four truncated vertical cylinders.