Wave-structure Interaction Research Articles

Examination of the virtues of parametric energy coupling in wave energy conversion

Parametric resonance has been observed, both numerically and experimentally, in various studies of wave energy converters (WECs). Large heave motions induce a periodic variation in the metacentric height of a WEC body and, consequently, cause a harmonic variation in pitch/roll restoring coefficients, which can parametrically excite the pitch/roll modes. Current studies attempt to determine the onset conditions of parametric resonance, by detecting the boundaries between stable and unstable regions in the parameter space. In the literature, some studies aim to make use of parametric resonance for improving power capture. In contrast, some studies try to suppress the effect of parametric resonance, as it can reduce power capture efficiency in the primary degree of freedom. However, how energy transfers from one mode to another is not fully understood. This study aims to analyse energy transfer between heave and pitch/roll modes when parametric resonance occurs. A generic cylindrical point absorber is studied as a WEC floater to consider non-linear wave-structure interaction, including non-linear Froude-Krylov and viscous forces. A heave-pitch-roll three-degree-of-freedom model is derived for numerical study of the energy transfer between different operational modes.

Spatial-temporal measurement of waves in laboratory based on binocular stereo vision and image processing

Acquisition of wave field data is essential for hydrodynamics studies. Current studies show deficiencies in the spatial measurement of wave fields in the laboratory, and a more efficient method is urgently needed. A stereo imaging method was proposed for the spatial-temporal measurement of waves in the laboratory based on binocular stereo vision and digital image processing. Then, a series of regular and focused waves were simulated in a wave flume to examine the feasibility and reliability of the method by comparison with the measurements by wave probes. Floating particles were evenly sprinkled on the water surface as the representation of the water-air interface, providing texture features for wave surface images and allowing the realization of dense reconstruction. Synchronized cameras provided the synchronized stereo pairs sequence for each wave, and temporal reconstruction was achieved by processing frame by frame. The 4D spatial-temporal volume for every wave could be constructed. Subsequently, spatial slices of the volume obtained the instantaneous profiles of the wave field in different directions. Temporal slices obtained the wave time series at a fixed point, which were compared with the measurements of the standard resistive probe to verify the accuracy. The results showed that the proposed method was capable of measuring the spatial-temporal field of waves efficiently and precisely and offered the potential to measure more complex wave fields in nonlinear wave-structure interactions.

Linear analysis on the non-hydrostatic pressure field of depth-integrated models

In the development of depth-integrated models, certain assumptions are made on the vertical profile of the horizontal velocity, and the pressure field is eliminated through vertical integration of the vertical momentum equation. In this study, analytical forms of the approximated non-hydrostatic pressure field are derived from five most representative depth-integrated models, which include three Boussinesq-type models, a weighted residual type model and a non-hydrostatic model. A Stokes wave-type Fourier analysis is then conducted to examine their capability in reproducing the vertical profile of the non-hydrostatic pressure field, which is compared with linear wave theory. We found the Boussinesq-type models are able to reproduce the non-hydrostatic pressure field from shallower water up to the kd values similar to that of concerning linear wave phase velocity. Specifically, the two-layer Boussinesq model generally outperforms the higher-order (μ4) Boussinesq model, especially for higher kd values. The weighted residual type model can reasonably capture the non-hydrostatic pressure near to the free surface even at high kd values, but undulations appear in the lower part of the water column where non-hydrostatic pressure is close to zero. The non-hydrostatic model shows rapid convergence of linear wave phase velocity by using few vertical layers, however, its capability in reproducing the non-hydrostatic pressure field is limited, especially at the highest layer interface, where nonphysical phenomena of reversed pressure could appear. This suggests that it is necessary to employ more layers when detailed information on the pressure field is needed, e.g. wave–structure interaction problems.

Three-dimensional simulation of wave-structure interaction based on smoothed particle hydrodynamics

<p indent="0mm">Wave-structure interaction exists widely in the field of ocean engineering. Current numerical simulations on wave-structure interaction are usually limited to two dimensions. However, in many practical engineering problems, the three-dimensional effect is so significant that a two-dimensional simulation cannot accurately reflect the real hydrodynamic characteristics of offshore structures. On the basis of the smoothed particle hydrodynamics (SPH) method, three cases, i.e., double-submerged breakwaters, an oscillating wave surge converter, and a floating body, are simulated in this study in two-dimensional, quasi-two-dimensional, and three-dimensional conditions, respectively. The flume width effect on the hydrodynamic characteristics of the structure is discussed to explore the three-dimensional effect. Graphics processing unit (GPU) accelerated technology is applied in the present simulations to improve computational efficiency. The numerical results show that the three-dimensional effect of wave-structure interaction may cause a complex eddy current structure, which can reduce the effect of structures on wave propagation, enhance the effect of waves on structures, and strengthen the complexity of the structure motion.

Numerical modelling of breaking wave impact loads on a vertical seawall retrofitted with different geometrical configurations of recurve parapets

Abstract Experiments are the traditional techniques used in coastal engineering to study complex wave structure interactions. However, with the advent of high-performance computing, even performing 1:1 scale numerical simulations has become a reality. The progress aids in extending the parametric investigation or repeating the procedure for comparable structures. In this study, a numerical model in OpenFOAM® with waves2Foam wave boundary conditions is used to simulate wave structure interactions at seawalls with varied geometrical configurations of recurved parapets. The numerical model is validated by employing ForschungsZentrum Küste (FZK)'s large-scale (1:1) experiments. The validated model is then applied to the plain parapet and vertical wall to understand better overtopping behaviour, pressure distribution, and structural loads. Numerical modelling is used in this study to visualise and assess intrinsic parameters such as the velocity profile, vorticity, air entrapment, and entrainment better to understand the dissipation characteristics of seawalls with recurved parapets.

Three-dimensional coupling between Boussinesq (FEM) and Navier–Stokes (particle based) models for wave structure interaction

The paper presents coupling between a mesh-based finite-element model for Boussinesq equations (FEBOUSS Agarwal et al., 2022) with a meshless local Petrov–Galerkin model for the Navier–Stokes equations (MLPG_R Agarwal et al., 2021) in 3D. Boussinesq equation models are widely used for simulating wave-propagation over large domains with uneven topography using a 2D surface mesh. Mesh-less models inherently capture large free-surface deformations and have shown promise in simulating wave-structure interaction, run-up and breaking phenomenon. The hybrid approach in this paper assumes a 3D MLPG_R sub-domain surrounded by the 2D mesh of FEBOUSS. The coupling interface in MLPG_R consists of relaxation zones that can be placed along multiple boundaries of the sub-domain for exchanging particle velocity from FEBOUSS. This hybrid model is therefore capable of simulating directional waves, that has not been reported previously.The paper first presents the procedure for calculating the depth-resolved velocities in 3D from the Boussinesq model. The resultant velocities are compared against theory, experiments and other models. The following sections present the coupling algorithm along a single and multiple coupling interfaces in MLPG_R. Validation results for this hybrid model are provided using surface elevation and velocity measurements for regular waves, including directional cases. In general, the results from the hybrid model are reported to have marginal over-prediction of peaks compared to purely MLPG_R simulation. Finally, the interaction of a vertical cylinder with direction regular wave is simulated using the 3D hybrid model.

A generalized weak-scatterer approximation for nonlinear wave–structure interaction in marine hydrodynamics

In this paper, a generalized weak-scatterer (GWS) approximation is proposed for solving nonlinear wave–structure interaction problems. In contrast to the original weak-scatterer (OWS) theory, where the approximated free surface boundary conditions (FSBCs) are Taylor-expanded in the vertical direction from the incident wave surface, we apply Taylor series expansion in an arbitrary direction which, in particular, is tangential to the boundary of the floating structure close to the waterline. This leads to generalized kinematic and dynamic FSBCs for the radiated and scattered waves, along with corresponding expressions of the wave loads. Accordingly, an Arbitrary Lagrangian–Eulerian (ALE) approach is adopted to track the free-surface properties. The new GWS method is more consistent than the OWS model in that the wave markers do not separate from the body surface at the waterline for structures with flare. An Immersed-Boundary Adaptive Harmonic Polynomial Cell (IB-AHPC) method is implemented to solve the corresponding boundary value problems (BVPs) for both the velocity potential and the Lagrangian acceleration potential at each time step. The new formulation introduces additional convective terms in the FSBCs, making them similar to the seakeeping problems for ships with forward speed, and this requires special treatment to avoid instability in the time-domain simulations. Based on a matrix-based eigenvalue stability analysis, we illustrate that stable solutions can be achieved by introducing an upwind-biased scheme to discretize the convective terms in the kinematic FSBC. The proposed model is verified by three wave diffraction problems in regular waves, including a submerged circular cylinder, a rounded-corner rectangular ship section, and a trapezoidal section with a large flare angle.

Optical flow based measurement of flow field in wave-structure interaction

Accurate measurement of the flow field in the wave-structure interaction, which is fundamental to the study of flow mechanism, is still a challenging task to date. The widely used Particle Image Velocimetry (PIV) technique is a promising approach to measure the flow field. However, it requires having the laser sheet to highlight the artificial particles seeded in the water and is only suitable for the clear water condition. It is incapable for the scenario of wave impacting on the structure, since a large number of bubbles interfere the tracking of particles. In this study, a computer vision-based method, i.e. the Optical Flow (OF) based method, is proposed and adopted to measure the flow field, and further to explore the underlying flow mechanism in wave-structure interaction. Firstly, the OF method is validated by comparing with the direct numerical simulation (DNS) and PIV measured results, involving the simple case of open-channel flow and complicated case of vortex flow. It is shown that the OF method can reasonably capture the primary flow features, as well as obtain the velocity with comparable accuracy of PIV method. Then, the OF method is used to study the flow field in the process of wave impacting on a rectangular structure. From the OF measured flow field around the structure, it is found that some typical flow phenomena, e.g. wave splash, jet flow, air entrainment, and wake vortex, exist at different phases during the wave-structure interaction. It also demonstrates that the flow acceleration and kinetic energy of wave impacting on the structure are increased with the increase of wave height due to the increase of flow velocity. Therefore, the OF method could be a useful non-intrusive approach for flow measurement in the wave-structure interaction.

Extension of a coupled mooring–viscous flow solver to account for mooring–joint–multibody interaction in waves

To account for nonlinear wave–structure interaction, mooring dynamics and the associated viscous flow effects, a coupled mooring–viscous flow solver was formerly developed and validated (Jiang et al. in Mar Struct 72:783, 2020a, Validation of a dynamic mooring model coupled with a RANS solver). This paper presents an extension of the coupled mooring–viscous flow solver to solve mooring dynamics interacting with an articulated multibody offshore system. The presently extended solver is verified by comparing the predicted motions of and loads on a moored floating box to those obtained from the formerly validated solver, which was aimed for solving mooring dynamics interacting with a single floating body. The almost identical results obtained from both solvers verify the presently developed multi-module coupling technique for solving the mooring dynamics and articulated multibody dynamics in a coupled manner. Apart from the code comparison and verification, the numerical predictions are also validated against experimental tank measurements both for a single body and an articulated multibody. The good agreements between the numerical predictions and the experimental measurements validate the presently extended solver, where wave-induced body motions together with loads acting on mooring lines and joint connections were examined. Developed as an open-source tool, the extended solver shows a potential of the coupled methodology for analyzing an articulated multibody offshore system, moored with various mooring configurations in extreme sea states, which goes beyond the state of the art.

A Review on the Modelling of Wave-Structure Interactions Based on OpenFOAM

The modelling of wave-structure interaction (WSI) has significant applications in understanding natural processes as well as securing the safety and efficiency of marine engineering. Based on the technique of Computational Fluid Dynamics (CFD) and the open-source simulation framework - OpenFOAM, this paper provides a state-of-the-art review of WSI modelling methods. The review categorises WSI scenarios and suggests their suitable computational approaches, concerning a rigid, deformable or porous structure in regular, irregular, non-breaking or breaking waves. Extensions of WSI modelling for wave-structure-seabed interactions and various wave energy converters are also introduced. As a result, the present review aims to help understand the CFD modelling of WSI and guide the use of OpenFOAM for target WSI problems.

Development of a CFD-based numerical wave tank of a novel multipurpose wave energy converter

The development of new wave energy converters usually involves small-scale experiments in physical wave tanks. The jump to physical models at larger scales is an expensive and time-consuming process that can be supported by computational fluid dynamics (CFD) models. Using the CFD approach, it is possible to numerically simulate complex flows with high accuracy, once validation with experimental data has been carried out. This article describes an approach based on guidelines taken from the literature and adopted to develop and explore the capabilities of a CFD-based numerical wave tank for a novel multipurpose wave energy converter, REEFS. An incremental validation procedure, using experimental data collected with a piston-type wave tank, was adopted; the procedure began with wave-only tests which were followed by wave-structure interaction tests. Snapshots of numerical and experimental approaches were used to analyse fluid flow in the envelope of the REEFS converter. The results demonstrate that the CFD-based numerical wave tank model can adequately simulate the global wave surface profile, as well as local complex phenomena, such as the Venturi aspiration effect, that typically occur near the exterior stay vanes of the device. The results encourage the adoption of this model for future REEFS analysis.

Wave runup prediction for a semi-submersible based on temporal convolutional neural network

Nonlinear wave runup could result in serious wave impact on the local structures of offshore platforms in rough seas. The reliable and efficient wave runup prediction is beneficial to provide essential information for the design and operation of offshore platforms. This work aims to develop a novel data-driven method to achieve the nonlinear mapping underlying the wave-structure interactions. The Temporal Convolution Network (TCN) model was employed to predict the wave runup along the column of a semi-submersible in head seas. The incident wave and vertical motions including heave, roll, and pitch were fed into the TCN model to predict the wave runup. Experimental datasets were provided for training and test. Taking both temporal and spatial dependency into consideration, the input tensor space was optimized from the perspective of physical meaning and practicality. Sensitivity analyses were conducted to obtain the optimum length of time window and evaluate the relative importance of input variables to wave runup prediction. Moreover, the effects of characteristics and size of the training dataset on the model performance were investigated to provide guidelines for training dataset construction. Finally, upon validation, the generated TCN model showed a strong ability to provide stable and accurate wave runup results under various wave conditions, and it is a potential alternative tool to achieve efficient but low-cost wave runup prediction.

A model predictive control (MPC)-integrated multiphase immersed boundary (IB) framework for simulating wave energy converters (WECs)

In this work, we present a novel MPC-integrated multiphase IB framework that can compute the optimal energy-maximizing control force “on-the-fly” by dynamically interacting with a high-fidelity numerical wave tank (NWT). The computational model closely mimics the working setup of the device at its site of operation. Due to the requirement of solving a constrained optimization problem at each time step of the IB simulation, the MPC algorithm utilizes a low-dimensional dynamical model of the device that is based on the linear potential theory (LPT). The multiphase IB solver, on the other hand, is based on the high-dimensional fictitious domain Brinkman penalization (FD/BP) method, which fully-resolves the hydrodynamic non-linearities associated with the wave–structure interaction (WSI). A time-series forecasting auto-regressive model is implemented that predicts wave heights (from the past NWT data) to estimate the future wave excitation/Froude–Krylov forces for the MPC algorithm. Moreover, we also experiment with non-linear Froude–Krylov (NLFK) forces for the first time in an MPC formulation. The NLFK forces are computed efficiently using a static Cartesian grid, in which the WEC geometry is implicitly represented by a signed distance function. Under varying sea conditions, the predictions of the MPC-integrated multiphase IB solver are compared to the widely popular LPT-based solvers. In agitated sea conditions and/or under aggressive control, the LPT-based WSI solvers produce too optimistic (and misleading) power output values. Overall, six WSI/MPC solver combinations are compared for a heaving vertical cylinder to determine the reasons for discrepancies between high- and low-fidelity predictions. We also determine the pathway of energy transfer from the waves to the power take-off (PTO) system and verify the relationships using IB simulations. Additionally, three different sea states are simulated within the IB simulation to test the adaptive capability of MPC for WECs. MPC is demonstrated to adapt to changing sea conditions and find the optimal solution for each sea state.The interaction between the distributed-memory parallel multiphase IB solver (written in C++) and the serial MPC solver (written in MATLAB) is fully described to facilitate reproducibility. A bespoke communication layer between the two solvers is developed, which can be easily modified by the WEC community to experiment with other optimal controllers and computational fluid dynamics (CFD) solvers. All codes for this work are made open-source for pedagogical and research purposes.

Effect of floating substructure flexibility of large-volume 10 MW offshore wind turbine semi-submersible platforms on dynamic response

As the dimension of the floating substructures for ultra-large wind turbines increases, the flexibility of the large-volume floating substructures may increase to the extent that may significantly affect the dynamic responses of an ultra-large semi-submersible floating offshore wind turbine (FOWT), which introduces new challenges in capturing relevant physical effect in numerical simulation analysis. This paper describes a newly designed semi-submersible substructure for the Technical University of Denmark (DTU) 10 MW wind turbine, and the substructural flexibility is considered in aero-hydro-servo-elastic dynamic simulations by extending the simulation OpenFAST Code, including wave-structure interactions. A comprehensive comparison of flexible and rigid large-volume substructures models is presented to highlight the effect of substructural flexibility on the hydrodynamic loads and dynamic responses of the integrated FOWT system by implementing a fully coupled simulation analysis in the time domain. Additionally, the difference of flexible and rigid large-volume substructures models on the structural fatigue behavior of the novel semi-submersible FOWT is investigated and discussed by computing ultimate and damage-equivalent loads (DELs) for selected environmental conditions. The results show that the substructural flexibility has a significant impact on fatigue damage of the integrated FOWT system in operating sea states than that in extreme sea state.

Midfidelity model verification for a point-absorbing wave energy converter with linear power take-off

In the preliminary design stage of a waveenergy converter (WEC), researchers need fast and reliablesimulation tools. High-fidelity numerical models are usu-ally employed to study the wave-structure interaction, butthe computational cost is demanding. As an alternative,midfidelity models can provide simulations in the order ofreal time. In this study, we operate Uppsala University’sWEC in a relatively mild sea state and model it usingWEC-Sim. The model is verified based on OpenFOAMsimulations. To analyze the ability of the midfidelitymodel to capture WEC dynamics, we investigate the systemseparately with 1, 2, and 3 degrees of freedom. We examinethe contribution of viscous phenomena, and study bothlinear and weakly nonlinear solutions provided by WEC-Sim. Our results indicate that the viscous effects can beneglected in heave and surge motion, but not for pitch.We also find that the weakly nonlinear WEC-Sim solutionsuccessfully agrees with the computational fluid dynam-ics, whereas the linear solution could suggest misleadingresults.

Epistemic uncertainties on the estimation of minimum air gap for semi-submersible platforms

Different models are considered to estimate the minimum air gap of a semi-submersible accommodation unit in stormy conditions. The results are compared to quantify the epistemic uncertainties in the estimation of the minimum air gap. While both first- and second-order methods have been broadly considered in the literature to evaluate the air gap of semi-submersibles, the underlying hypotheses of these methods are considerably simplified, and conservative results depend on added margins of unknown degrees of confidence. Therefore, a systematic study is conducted to assess the uncertainties raised by some features of the state-of-the-art methods. First, the uncertainties resulting from the binned values of scatter diagrams and from the assumption that the highest significant wave height sea state is the critical sea state, are assessed. Then, the uncertainty implied in the finite set of control points is evaluated. The achievements are obtained considering First-Order Second-Moment methods, by performing searches over the environmental contours to find the actual critical sea states, and by performing Kriging interpolation over the whole underdeck of the platform. Moreover, the adopted uncertainty propagation tools allow characterising the minimum air gap in terms of its expected value and standard deviation. It is found that, before adding complexity to the wave-structure interaction model, air gap estimation is subject to large errors if rather few control points are assigned, or if a single critical sea state is assigned before performing any search for the actual critical sea state.

Generating Multistructured Ultrasound via Bioinspired Metaskin Patterning for Low‐Threshold and Contactless Control of Living Organisms

AbstractMetasurfaces of the subwavelength thicknesses provide a distinctive route for acoustic wave manipulation. Based on the advanced 3D printing, those judiciously designed 2D metamaterials enable intriguing effects such as abnormal reflection, transmission, and absorption. However, acoustic metasurfaces, with strong wave–structure interactions in subwavelength scales, have encountered a big challenge of being acoustically transparent due to the insufficient impedance mismatch underwater. Here, reconfigurable bioinspired metaskin patterning for generating multistructured waterborne ultrasound is proposed. The nanostructured metaskin exhibits the “lotus effect,” with the thickness of only 70 μm (≈1/20 wavelength at 1 MHz) and a tremendous impedance mismatch (≈0.0001 transmission) for ultrasound. By depositing the strippable metaskins via self‐assembly into different patterns, the focusing, the vortex, and the Talbot structured ultrasound beams are implemented, respectively. The multistructured ultrasound has the patterned intensity fields of energy redistribution, where even weak field enhancement at low frequencies can activate the living organisms directly without using microbubbles, which enables low‐threshold and contactless behavior control via the mechanical stimulus.

Coupled CFD-MBD numerical modeling of a mechanically coupled WEC array

The development of new wave energy devices (WECs) has continued unabated over the past decades. For large-scale applications, integrating individual WEC into an array system (WEC net) requires considerable expertise and research due to its highly complex and interrelated nature. Often for a WEC net, it contains main structures and multiple sub-structures. The WEC net response is defined as the total responses from all sub-structures, which is highly complex and closely interconnected with each other. This paper aims to develop a fully-coupled numerical modeling tool that can cope with the wave-structure interaction as well as the mechanical interaction among each sub-structure in a WEC net. The fluid field is solved by a Computational Fluid Dynamic (CFD) solver coupled with a Multi-body Dynamic structural solver. The hydrodynamic and power take-off performance of Albatern 12S Squid WEC net is studied and the results are validated against available laboratory testing data, and commercial mooring and hydrodynamics analysis software.It is found that the motion response of the CFD and experimental approach is in close agreement with each other. The interaction force among sub-structures can be well captured, and the results indicate that the mode response of individual float is strongly affected by the mechanical linking-arms as well as the incident wave conditions, which is hard to achieve without such integrated CFD tool. The power take-off (PTO) is modeled using a damping system. The predicted peak output power is found to increase with the decreasing of wave period and an optimal device's damping to reach a maximum power capture exists, which is dependent on the incoming wave period and height.

Time-Domain Implementation and Analyses of Multi-Motion Modes of Floating Structures

The study of wave-structure interactions involving nonlinear forces would often make use of the popular hybrid frequency–time domain method. In the hybrid method, the frequency-domain analysis could firstly provide the reliable and accurate dynamic parameters and responses; then these parameters and responses are transformed to the parameters to establishing the basic time-domain equation. Additionally, with the addition of the required linear and nonlinear forces, the time-domain analysis can be used to solve for the practical problems. However, the transformation from the frequency domain to the time domain is not straightforward, and the implementation of the time-domain equation could become increasingly complicated when different modes of motion are coupled. This research presents a systematic introduction on how to implement the time-domain analysis for floating structures, including the parameter transformations from the frequency domain to the time domain, and the methods for calculating and approximating the impulse functions and the fluid-memory effects, with special attention being paid to the coupling terms among the different motion modes, and the correctness of the time-domain-equation implementation. The main purpose of this article is to provide relevant information for those who wish to build their own time-domain analyses with the open-source hydrodynamic analysis packages, although commercial packages are available for time-domain analyses.

Higher-order gap resonance between two identical fixed barges: A study on the effect of water depth

Nonlinear piston-mode fluid resonance in the gap formed by two identical fixed barges in close proximity is investigated using a two-dimensional (2D) fully nonlinear numerical wave tank. To delve into the effect of water depth on higher-order resonances in the gap, consistent models are employed to describe the incident waves and wave-structure interactions for finite and shallow water depths. In contrast to previous studies, strong fourth- and fifth-order nonlinear gap resonances are observed under the action of shallow-water waves, resulting in significant higher-harmonic responses that are comparable to the corresponding first and second harmonics. For a given wave height, those waves are found to be more critical than the finite-depth waves, which are capable of evoking second- or third-order gap resonance. Highly oscillatory behavior is observed at the trough under the action of shallow-water waves. This is ascribed to the higher-harmonic diffraction effects, breaking the “perfect cancellation” between the incident-wave harmonics, which should, otherwise, produce smooth and flatter wave trough. Unlike what a linear diffraction theory will predict, the gap response does not behave completely in a quasi-static manner under long cnoidal waves, and the higher harmonics generally show larger phase differences to the corresponding incident-wave components until the resonance occurs. The present study suggests that the water-depth effect and higher harmonics should be consistently accounted for in the design and analysis of side-by-side marine operations in coastal environments involving piston-mode gap responses.