Investigation of Wave-Structure Interaction Using State of the Art CFD Techniques

The suitability of computational fluid dynamics (CFD) for marine renewable energy research and development and in particular for simulating extreme wave interaction with a wave energy converter (WEC) is considered. Fully nonlinear time domain CFD is often considered to be an expensive and computationally intensive option for marine hydrodynamics and frequency-based methods are traditionally preferred by the industry. However, CFD models capture more of the physics of wave-structure interaction, and whereas traditional frequency domain approaches are restricted to linear motions, fully nonlinear CFD can simulate wave breaking and overtopping. Furthermore, with continuing advances in computing power and speed and the development of new algorithms for CFD, it is becoming a more popular option for design applications in the marine environment. In this work, different CFD approaches of increasing novelty are assessed: two commercial CFD packages incorporating recent advances in high resolution free surface flow simulation;a finite volume based Euler equation model with a shock capturing technique for the free surface;and meshless Smoothed Particle Hydrodynamics (SPH) method. These different approaches to fully nonlinear time domain simulation of free surface flow and wave structure interaction are applied to test cases of increasing complexity and the results compared with experimental data. Results are presented for regular wave interaction with a fixed horizontal cylinder, wave generation by a cone in driven vertical motion at the free surface and extreme wave interaction with a bobbing float (The Manchester Bobber WEC). The numerical results generally show good agreement with the physical experiments and simulate the wave-structure interaction and wave loading satisfactorily. The grid-based methods are shown to be generally less able than the meshless SPH to capture jet formation at the face of the cone, the resolution of the jet being grid dependent.

A Brief Summary of Finite Element Method Applications to Nonlinear Wave-structure Interactions

We review recent advances in the finite element method (FEM) simulations of interactions between waves and structures. Our focus is on the potential theory with the fully nonlinear or second-order boundary condition. The present paper has six sections. A review of previous work on interactions between waves and ocean structures is presented in Section one. Section two gives the mathematical formulation. In Section three, the finite element discretization, mesh generation and the finite element linear system solution methods are described. Section four presents numerical methods including time marching schemes, computation of velocity, remeshing and smoothing techniques and numerical radiation conditions. The application of the FEM to the wave-structure interactions are presented in Section five followed by the concluding remarks in Section six.

Nonlinear waves and wave-structure interactions in marine hydrodynamics——Recent progress

We briefly review the recent progress in marine hydrodynamics.Developments in wave-structure interaction,wave-current interaction,Rogue waves,sloshing in liquid tanks and their applications in ocean engineering,such as Floating Production Storage and Offloading facility(FPSO) and Very Large Floating Structure(VLFS),are presented.

波浪对垂直圆柱的冲击作用研究进展

Wave slamming is an important phenomenon due to its destructive power,and with the rapid development of offshore wind turbines,wave slamming on vertical cylinders has garnered lots of attention.However,the phenomenon of wave slamming on vertical cylinders is very complicated due to both the intrinsic complexity of breaking waves and that of slamming forces.The objective of this paper is to provide a general review of research related to this problem,including theoretical methods,experimental studies,numerical simulations,and full-scale measurements.Based on these approaches,the momentum theory/pressure impulse theory,spatial distribution characteristics of impacts to various breaking waves,wave generation methods,analysis methods for measured forces under structure response,scale effects in experiments,and in-situ measurements have been introduced and discussed.Results show that simplifications in existing models for wave impacting such as wave characteristics and structural response reduce its applicability and should be studied further both in theoretical,experimental and numerical researches.

极端海浪对LNG运输船影响的试验研究

This paper presents a comprehensive experimental study on the effect of extreme waves on a LNG carrier.The LNG carrier model was equipped with a variety of sensors to measure motions,green water height on deck as well as local and global loads.Experiments in transient wave packets provided the general performance in waves in terms of response amplitude operators and were accompanied by tests in regular waves with two different wave steepness.These tests allowed detailed insights into the nonlinear behavior of the vertical wave bending moment in steep waves showing that green water on deck can contribute to a decrease of vertical wave bending moment.Afterwards,systematic model tests in irregular waves were performed to provide the basis for statistical analysis.It is shown that the generalized extreme value distribution model is suitable for the estimation of the extreme peak values of motions and loads.Finally,model tests in tailored extreme wave sequences were conducted comparing the results with the statistical analysis.For this purpose,analytical breather solutions of the nonlinear Schrödinger equation were applied to generate tailored extreme waves of certain critical wave lengths in terms of ship response.Besides these design extreme waves,the LGN carrier was also investigated in the model scale reproduction of the real-world Draupner wave.By comparing the motions,vertical wave bending moment,green water column and slamming pressures it is concluded that the breather solutions are a powerful and efficient tool for the generation of design extreme waves of certain critical wave lengths for wave/structure investigations on different subjects.

Reflection and Transmission of Regular Waves from/Through Single and Double Perforated Thin Walls

In this paper, reflection and transmission coefficients of regular waves from/through perforated thin walls are investigated. Small scale laboratory tests have been performed in a wave flume firstly with single perforated thin Plexiglas plates of various porosities. The plate is placed perpendicular to the flume with the height from the flume bottom to the position above water surface. With this thin wall in the flume wave overtopping is prohibited and incident waves are able to transmit. The porosities of the walls are achieved by perforating the plates with circular holes. Model settings with double perforated walls parallel to each other forming so called chamber system, have been also examined. Several parameters have been used for correlating the laboratory tests’ results. Experimental data are also compared with results from the numerical model by applying the multi-domain boundary element method （MDBEM） with linear wave theory. Wave energy dissipation due to the perforations of the thin wall has been represented by a simple yet effective porosity parameter in the model. The numerical model with the MDBEM has been further validated against the previously published data.

Nonlinear Dynamic Behaviors of A Floating Structure in Focused Waves

Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional（2-D） box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile（CIP）-based Cartesian grid model, in which a more accurate VOF（Volume of Fluid） method, the THINC/SW scheme（THINC： tangent of hyperbola for interface capturing; SW： Slope Weighting）, is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.

Hybrid Analysis Approach for Stochastic Response of Offshore Jacket Platforms

The dynamic response of offshore platforms is more serious in hostile sea environment than in shallow sea. In this paper, a hybrid solution combined with analytical and numerical method is proposed to compute the stochastic response of fixed offshore platforms to random waves, considering wave-structure interaction and non-linear drag force. The simulation program includes two steps: the first step is the eigenanalysis aspects associated the structure and the second step is response estimation based on spectral equations. The eigenanalysis could be done through conventional finite element method conveniently and its natural frequency and mode shapes obtained. In the second part of the process, the solution of the offshore structural response is obtained by iteration of a series of coupled spectral equations. Considering the third-order term in the drag force, the evaluation of the three-fold convolution should be demanded for nonlinear stochastic response analysis. To demonstrate this method, a numerical analysis is carried out for both linear and non-linear platform motions. The final response spectra have the typical two peaks in agreement with reality, indicating that the hybrid method is effective and can be applied to offshore engineering.

SECOND-ORDER INTERACTION OF IRREGULAR WAVES WITH A TRUNCATED COLUMN

A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.

A model for the scattering of long waves by slotted breakwaters in the presence of currents

Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwaters are investigated by using a simple model. The model is based on a long wave approximation. The effects of wave height, barrier geometry and current strength on the reflection and transmission coefficients are examined by the model. The model results are compared with recent experimental data. It is found that both the wave-following and wave-opposing currents can increase the reflection coefficient and reduce the transmission coefficient. The model can be used to study the interaction between long waves and slotted breakwaters in coastal waters.

Wave Dissipation Characteristics of A Mountain-Type Breakwater

One mountain-type breakwater consisting of two inclined plates and one vertical plate is proposed based on several types of traditional free surface breakwaters, including the horizontal plate, curtain wall, and trapezoidal barriers. The interaction between the regular waves and the fixed free surface mountain-type breakwater is measured in one wave flume(15.0 m×0.6 m×0.7 m). The wave propagation, reflection, and transmission process are simulated using the VOF method and the hybrid SAS/laminar method. The simulated wave profiles are consistent with the experimental observations. For waves with a length smaller than four times width of the mountain-type breakwater, the reflected wave amplitudes are slightly larger than those of the vertical-plate breakwater, while the wave transmission coefficients are all smaller than 0.5, and the wave loss coefficients are larger than 0.7. The wave energy is dissipated by wave breaking on the windward inclined plate, and turbulent flow around the vertical plate and the leeward inclined plate.

A Single Mooring System with Sag-Extensibility and Flexural Rigidity Applied to Offshore Platform

Floating platform system has been extensively used in ocean exploitation, particularly for a tension-leg platform （TLP） system in deep water. Most of the TLPs are multi-mooring systems, where multi-joints are connected to the tension-legs so that the platform is not allowed to twist freely and may subject to enormous force induced by large incident waves in the weak-direction of the structure. This study aims to exploit a single moored offshore platform system that may attract less force and can be operated with less effort. In our analysis, in addition to mechanical properties of the tether, two important properties are also taken into consideration for the single mooring tether with expanded cross sectional dimension and utilization of stronger material, namely, the sag-extensibility and the flexural rigidity. Finally, the dynamic structural behavior produced by the mechanical effects on the new system is investigated and compared with that of traditional design while the wave-structure interactions of large body are also accounted for. Our study finds that the neglect of sag-extensibility or the flexural rigidity of large, strong mooring cable may result in a conservative but not necessarily safe design.

Numerical Simulation of the Hydrodynamic Characteristics of the Porous I-type Composite Breakwater

Based on the three-dimensional Reynolds-averaged Navier-Stokes equation with the closure of renormalization group k-εturbulence model and volume of fluid method,a wave-breakwater interaction numerical flume was developed to examine the wave-structure interaction of the porous I-type composite(PITC)breakwater.The transmission and reflection coefficients of the breakwater at different wave steepness H/L are quantitatively analyzed,and the wave-dissipating performance of the breakwater is compared.By changing the submerged depth of the breakwater,the velocity field,and vorticity field in the wave propagation process are analyzed,and the optimal working water depth of the new breakwater is explored.The results show that the vertical wave force on the PITC breakwater is greater than the horizontal wave force.In addition,during the wave dissipation process,the transverse baffle provided by the new breakwater destroys the trajectory of the water particle.In the interior of the wave-breaking chamber,the water that enters from the gap of the permeable plate mixes with the water entering through the bottom hole.The turbulence created by this process further dissipates the wave energy.The relative submergence depth of h/d has a great influence on the hydrodynamic characteristics.When the relative depth is large,most of the wave energy enters the breakwater,the wave energy dissipation of the breakwater is large,and the wave-absorbing effect is good.These research results provide important referential data for the study of permeable plate breakwaters.

Will oscillating wave surge converters survive tsunamis?

With an increasing emphasis on renewable energy resources, wave power technology is becoming one of the realistic solutions. However, the 2011 tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed, creating large destructive waves. The question posed here is whether an oscillating wave surge converter （OWSC） could withstand the force of an incoming tsunami. Several tools are used to provide an answer： an analytical 3D model developed within the framework of linear theory, a numerical model based on the non-linear shallow water equations and empirical formulas. Numerical results show that run-up and draw-down can be amplified under some circumstances, leading to an OWSC lying on dry ground t

Wave uplift force on horizontal panels: a laboratory study

Accurate estimation of wave uplift force is essential to the designs of reliable coastal and marine structures.We presents a series of laboratory work here on the impact of regular waves on horizontal panels,from which an empirical formula to estimate accurately the wave uplift force on panels is established.The laboratory measurements show that the wave uplift force depends mainly on the incident wave height,the wave period,the wave length,the panel width,and the clearance between the subsurface of the panel and the still water level.Among these factors,the impact of the panel width on uplift forces is relatively complicated.Result shows that the relative panel width(i.e.,the ratio of panel width to wave length)plays a more important role in estimating the wave uplift force.Based on our comprehensive laboratory measurements,we further developed an empirical formula to compute wave uplift force on horizontal panels through dimensionless analysis.Compared with other empirical formulas,this formula uses dimensionless variables of clear physical meanings,thus can describe the interaction between waves and the panels in a better way.In addition,the efficiency of the formula to estimate wave uplift force on horizontal panels is verified against existing works.Therefore,the findings in this study shall be useful for understanding the mechanism of wave uplift force on horizontal panels and numerical model validation.

A new numerical framework for large-eddy simulation of waves generated by objects piercing water surface

A novel numerical framework is developed for large-eddy simulation(LES) of interactions among air, water, and solid bodies. The motions of air and water are solved on a fixed block-structured mesh, with the air–water interface captured using the volume-of-fluid method. A new sub-grid scale stress model based on the vortex identifier is used to improve the robustness and efficiency of the simulation flows with air–water interface. The new framework is tested in the context of bow waves and Kelvin waves generated by a water-surface vehicle. Wave breaking at the bow of the vehicle is captured in LES. The LES results of wave geometry approaches the measurements progressively as the grid resolution is refined. The simulation results indicate that LES is a useful tool for studying wave dynamics of water-surface vehicles.

Short-Crested Waves Interaction with A Concentric Porous Cylinder System with Partially Porous Outer Cylinder

In this paper, based on the linear wave theory, the interaction of short-crested waves with a concentric dual cylindrical system with a partially porous outer cylinder is studied by using the scaled boundary finite element method （SBFEM）, which is a novel semi-analytical method with the advantages of combining the finite element method （FEM） with the boundary element method （BEM）. The whole solution domain is divided into one unbounded sub-domain and one bounded sub-domain by the exterior cylinder. By weakening the governing differential equation in the circumferential direction, the SBFEM equations for both domains can be solved analytically in the radial direction. Only the boundary on the circumference of the exterior porous cylinder is discretized with curved surface finite elements. Meanwhile, by introducing a variable porous-effect parameter G, non-homogeneous materials caused by the complex configuration of the exterior cylinder are modeled without additional efforts. Comparisons clearly demonstrate the excellent accuracy and computational efficiency associated with the present SBFEM. The effects of the wide range wave parameters and the structure configuration are examined. This parametric study will help determine the various hydrodynamic effects of the concentric porous cylindrical structure.

Modelling of massive particulates for breakwater engineering using coupled FEMDEM and CFD

The seaward slope of many breakwaters consists of thousands of interlocking units of rock or concrete comprising a massive granular system of large elements each weighing tens of tonnes. The dumped quarry materials in the core are protected by progressively coarser particulates. The outer armour layer of freely placed units is intended to both dissipate wave energy and remain structurally stable as strong flows are drawn in and out of the particulate core. Design guidance on the mass and shape of these units is based on empirical equations derived from scaled physical model tests. The main failure mode for armour layers exposed to severe storms is hydraulic instability where the armour units of concrete or rock are subjected to uplift and drag forces which can in turn lead to rocking, displacement and collisions sufficient to cause breakage of units. Recently invented armour unit designs making up such granular layered system owe much of their success to the desirable emergent properties of interlock and porosity and how these combine with individual unit structural strength and inertial mass. Fundamental understanding of the forces governing such wave-structure interaction remains poor. We use discrete element and combined finite-discrete element methods to model the granular solid skeleton of randomly packed units coupled to a CFD code which resolves the wave dynamics through an interface tracking technique. The CFD code exploits several methods including a compressive advection scheme, node movement, and general mesh optimization. We provide the engineering context and report progress towards the numerical modelling of instability in these massive granular systems.

Hydrodynamic performance of combined cylinders structure with dual arc-shaped porous outer walls

This study examines the hydrodynamic performance of short-crested wave interaction with a new porous cylindrical structure by using the scaled boundary finite element method （SBFEM）, which is a semi-analytical technique combining the advantages of the finite element method and the boundary element method and with its own special features as well. The cylindrical structure consists of dual arc-shaped porous outer cylinders circumscribing an impermeable inner cylinder. A central feature of the newly extended method is that two virtual outer cylinders extending the arc-shaped porous outer cylinders with the same centre are introduced and variable porous-effect parameters are also introduced for the two virtual cylinders, so that the final SBFEM quation still can be handled in a closed-form analytical manner in the radial direction and by a finite element approximation in the circumferential direction. The entire computational domain is divided into two bounded and one unbounded domains, and a variational principle formulation is used to derive the SBFEM equation in each sub-domain. The velocity potential in bounded and unbounded domains is formulated using sets of Bessel and Hankel functions respectively, and the unknown coefficients are determined from the matching conditions. The results of numerical verification show that the approach discretises only the outermost virtual cylinder with surface finite-elements and fewer elements are required to obtain very accurate results.Influences of the incident wave parameters and structural configurations on the hydrodynamics are examined.

Hydrodynamic modelling of flow impact on structures under extreme flow conditions

Apart from the direct threat to human lives, the flood waves as a result of the rapid catchment response to intense rainfall, breaches of flood defences, tsunamis or storm surges may induce huge impact forces on structures, causing structural damage or even failures. Most existing design codes do not properly account for these impact forces due to the limited understanding of the underlying physical processes and the lack of reliable empirical formulae or numerical approaches to quantifying them. This paper presents laboratory experiments to better understand the interaction between the extreme flow hydrodynamics and the hydraulic structures and uses the measured data to validate a numerical model. The model solves the two-dimensional shallow water equations using a finite volume Godunov-type scheme for the reliable simulation of complex flow hydrodynamics. New model components are developed for estimating the hydrostatic and hydrodynamic pressure to quantify the flow impact on structures. The model is applied to reproduce two selected experiment tests with different settings and satisfactory numerical results are obtained, which confirms its predictive capability. The model will therefore provide a potential tool for wider and more flexible field-scale applications.