Nonlinear Numerical Wave Tank Research Articles

Hydrodynamic performance of a novel oscillating-water-column breakwater with a horizontal bottom-plate: Experimental and numerical study

Abstract In this study, the hydrodynamic characteristics of a novel oscillating water column (OWC) breakwater with a horizontal bottom-plate is numerically and experimentally investigated. A viscous fully nonlinear numerical wave tank (NWT) solved by the open source package OpenFOAM is established under laminar flow conditions. After comparing the numerical results with the experimental ones, the well-validated numerical model is further employed to investigate the effects of the length of horizontal bottom-plate (D), the immersion depth of back-plate ( d 2 ), the water depth (h) and the wave height (H) on the reflection ( C r ) and transmission ( C t ) coefficients, dissipation coefficient ( C d ) and column-confined energy coefficient ( C e ) of the breakwater. The results show that lengthening the bottom-plate can effectively increase the energy dissipation and then lead to lower reflection and transmission coefficients, and a smaller draught of the back-plate can also increase energy dissipation. The water depth has insignificant influence on the hydrodynamic coefficient of long waves, but influences the breakwater performance in short waves. The variation of wave height mainly contributes to the change of reflection coefficient.

Modeling of a Semisubmersible Floating Offshore Wind Platform in Severe Waves

Floating offshore wind platforms may be subjected to severe sea states, which include both steep and long waves. The hydrodynamic models used in the offshore industry are typically based on potential-flow theory and/or Morison’s equation. These methods are computationally efficient and can be applied in global dynamic analysis considering wind loads and mooring system dynamics. However, they may not capture important nonlinearities in extreme situations. The present work compares a fully nonlinear numerical wave tank (NWT), based on the viscous Navier–Stokes equations, and a second-order potential-flow model for such situations. A comparison of the NWT performance with the experimental data is first completed for a moored vertical floating cylinder. The OC5-semisubmersible floating platform is then modeled numerically both in this nonlinear NWT and using a second-order potential-flow based solver. To test both models, they are subjected to nonsteep waves and the response in heave and pitch is compared with the experimental data. More extreme conditions are examined with both models. Their comparison shows that if the structure is excited at its heave natural frequency, the dependence of the response in heave on the wave height and the viscous effects cannot be captured by the adjusted potential-flow based model. However, closer to the inertia dominated region, the two models yield similar responses in pitch and heave.

On the Assessment of Numerical Wave Makers in CFD Simulations

A fully non-linear numerical wave tank (NWT), based on Computational Fluid Dynamics (CFD), provides a useful tool for the analysis of coastal and offshore engineering problems. To generate and absorb free surface waves within a NWT, a variety of numerical wave maker (NWM) methodologies have been suggested in the literature. Therefore, when setting up a CFD-based NWT, the user is faced with the task of selecting the most appropriate NWM, which should be driven by a rigorous assessment of the available methods. To provide a consistent framework for the quantitative assessment of different NWMs, this paper presents a suite of metrics and methodologies, considering three key performance parameters: accuracy, computational requirements and available features. An illustrative example is presented to exemplify the proposed evaluation metrics, applied to the main NWMs available for the open source CFD software, OpenFOAM. The considered NWMs are found to reproduce waves with an accuracy comparable to real wave makers in physical wave tank experiments. However, the paper shows that significant differences are found between the various NWMs, and no single method performed best in all aspects of the assessment across the different test cases.

Nonlinear Wave Loads on High-rise Pile Cap Structures in the Donghai Bridge Wind Farm

A new type of bottom-fixed structure, the so-called high-rise pile cap foundation, has been proposed and used to support offshore wind turbines in the Donghai Bridge Wind Farm, China. Engineers are unaware of the wave load mechanisms for this new structure. Using the Navier-Stokes equations and volume of fluid technique, a fully nonlinear numerical wave tank is established to investigate free surface wave loads and moments for the new structure. The interaction between the cap and piles are discussed in detail. In the case of fully nonlinear waves, the maximum horizontal wave load on all the piles with the cap can increase by 30% compared with those without the cap, and the maximum horizontal wave load on a single pile is nearly doubled. The horizontal wave load on the cap with the piles can increase by about 15%, while the vertical wave load decreases slightly. The conventional Morison formula and diffraction theory generally underestimate the wave loads on the piles and the cap as well.

Numerical investigation of front-wall inclination effects on the hydrodynamic performance of a fixed oscillation water column wave energy converter

One of the main geometrical parameters of the fixed oscillating water column wave energy converters is the inclination angle of front wall. In this study, the effects of this parameter on the hydrodynamic performance of an oscillating water column is investigated using a fully nonlinear two-dimensional numerical wave tank, which is developed using the Ansys Fluent 15.0 commercial software. The accuracy of the developed wave tank is first examined by simulating an oscillating water column, having a front wall normal to the water-free surface, subjected to linear, small amplitude incident waves. The resultant absorption efficiencies are compared with available analytical data in the literature, where a good agreement was observed. Next, the simulations are performed for strongly nonlinear waves, up to the wave steepness of 0.069 ( H/L = 0.069), where H is the wave height and L is the wave length. Results show that the absorption efficiency of the oscillating water column decreases considerably as the wave height increases. Moreover, the maximum wave energy absorption efficiency for the highly nonlinear waves occurs at a pneumatic damping coefficient lower than that of the linear theory. Then, the absorption efficiency of the oscillating water column is determined for eight various front wall configurations at various incident wave periods. Results show that, the front walls that are slightly bent towards the inner region of the oscillating water column chamber are more efficient at some wave periods in comparison with the cases studied in this paper.

Validation and application of a fully nonlinear numerical wave tank for simulating floating offshore wind turbines

Numerical models are becoming a valid supplement, and even a substitute, to physical model testing for the investigation of fluid-structure interaction due to improved methods and a continuous increase in computational power. This research presents an extensive validation of a fully nonlinear numerical wave tank for the simulation of complex fluid-structure interaction of moored floating structures. The validation is carried out against laboratory measurements including recent and unpublished laboratory measurements of the OC5 floating offshore wind turbine subjected to waves. The numerical wave tank is based on the Navier-Stokes/6-DOF solver, interDyMFoam, provided by the open-source CFD-toolbox OpenFOAM, extended with the wave generation and absorption toolbox, waves2Foam, and an implementation for restraints of floating structures. Two methods are evaluated to address the instability issues of the partitioned Navier-Stokes/6-DOF solver, which are associated with artificial added mass. The model has been shown capable of computing detailed fluid-structure interactions, including dynamic motion response of a rigid structure in waves. However, instabilities due to numerical added mass is observed and discussed and it is concluded that further research is needed in order to establish a efficient yet stable scheme. Overall, good agreement is achieved between the numerical model and the physical model results.

Exact evaluation of hydrodynamic loads on ships using NURBS surfaces and acceleration potential

The development of an accurate surface intersecting methodology and adaptive acceleration potential scheme, in order to precisely compute pressure on the wet surface of ships hulls, is presented. Non-Uniform Rational B-Spline (NURBS) surfaces are used to describe the ships hulls and the free surface evolutions. The intersection of free surface with ship hull is found by solving the resultant system of equations yielded from surface intersecting scheme. The pressure distribution over the exact wet surface of ship hull surface is obtained based on acceleration potential in a time domain simulation. Hence, implicit body boundary condition is applied to evaluate the time derivative of velocity potential on the hull surface in a fully nonlinear numerical wave tank. On the other hand, tangential derivatives of the velocity potential on the wet surface are approximated by B-Spline surface. Wave propagation is considered to examine the accuracy and convergence of the present solution. Motions of a Wigley hulls in linear wave are compared with experimental measurements and prior numerical solutions to verify the present numerical procedure. Also, fully nonlinear motions of a Wigley hull in nonlinear wave is simulated.

Numerical and experimental investigation of hydrodynamic performance of a cylindrical dual pontoon-net floating breakwater

The use of a simple, inexpensive, and effective type of floating breakwater is increasingly becoming a necessity in shoreline and marine structure protection. This study concerns the hydrodynamic behavior of a dual pontoon floating breakwater (DPFB) when attached to one or more rows of plane net by using physical and numerical models. A two-dimensional (2D) fully nonlinear numerical wave tank (NWT) based on a time higher-order boundary element method (HOBEM) and mixed Eulerian-Lagrangian (MEL) approach is applied to obtain numerical solutions. In the model, Darcy's law is used to represent the porous media of the fluid-net interaction, and some auxiliary functions are introduced, instead of an iterative process using the acceleration potential method. Mesh regridding and interpolation combined with a double collocation node technique are implemented to tackle the mismatch between the meshes on the free surface and the wet body surface. In addition, the numerical model is verified with a series of corresponding experimental tests. Numerical solutions and measurement tests are executed to systematically examine the dependence of the reflection coefficient, transmission coefficient and motion responses on the design parameters, such as net number, net porosity, net height, wavelength and wave amplitude. It is found that the new floating breakwater exhibits a better performance with the optimal design parameters as compared with traditional DPFB, especially for long period and large amplitude waves.

Irregular wave transmission on bottom bumps using fully nonlinear NURBS numerical wave tank

In this study, a fully nonlinear three-dimensional numerical wave tank (NWT) is developed to simulate propagation of nonlinear random sea wave over the bottom ripple patches. Evolution of the free surface is performed by the non-uniform rational B-spline formulation (NURBS) and the mixed Eulerian–Lagrangian method (MEL). A high-order boundary integral equation is used to solve the Laplace equation in the Eulerian frame. The free surface is updated by the material node method and the fourth-order Runge–Kutta time integration scheme. Appropriate numerical solutions are obtained by deploying damping zones at the both tank end walls. Also, the NURBS approximation is applied to compute the kinematics of the free surface particles. Propagation of the irregular waves in an NWT is conducted and compared with the available experimental and numerical data. Bragg reflection of the random sea wave due to bottom ripple patches are compared with the prior numerical studies. The fully nonlinear free surface evolution of transmitted spectrum due to presence of the hemispherical bumps is modeled successfully. Also fifth-order Stokes wave is applied as a strong nonlinear incident wave to interact with the hemispherical bottom bumps.

A Numerical Study of a Submerged Horizontal Heaving Plate as a Breakwater

ABSTRACT Liu, C.; Huang, Z., and Chen, W., 2017. A numerical study of a submerged horizontal heaving plate as a breakwater. Using a nonlinear numerical wave tank (NWT) based on potential flow, a submerged horizontal plate heaving in regular waves was simulated, and its performance as a breakwater was examined. The NWT is based on a Mixed Eulerian-Lagrangian formulation and a de-singularized boundary integral equation method. The viscous effect on the motion of the plate is estimated by a linear damping coefficient, and the natural frequency of the heaving plate is controlled by the system stiffness. Compared with a fixed submerged horizontal plate, our results showed that the heaving motion of the plate with a critical stiffness could reduce the wave-transmission coefficient to almost zero and effectively suppress the free and locked waves on the leeside of the plate. The new type of breakwater can be an ideal alternative for small marinas and recreational harbors.

Improved HPC method for nonlinear wave tank

The recently developed Harmonic Polynomial Cell (HPC) method has been proved to be a promising choice for solving potential-flow Boundary Value Problem (BVP). In this paper, a flux method is proposed to consistently deal with the Neumann boundary condition of the original HPC method and enhance the accuracy. Moreover, fixed mesh algorithm with free surface immersed is developed to improve the computational efficiency. Finally, a two dimensional (2D) multi-block strategy coupling boundary-fitted mesh and fixed mesh is proposed. It limits the computational costs and preserves the accuracy. A fully nonlinear 2D numerical wave tank is developed using the improved HPC method as a verification.

Fully nonlinear numerical investigation on hydroelastic responses of floating elastic plate over variable depth sea-bottom

The time domain fully nonlinear analysis techniques are widely recognized as the unique approach to predict accurate transient behaviors and nonlinear characteristics of the VLFS (very large floating structure). However, these complex issues have not been perfectly solved due to some considerable factors, i.e. wave nonlinearity, displacement nonlinearity, and topography nonuniformity. In this paper, a 2D (two-dimensional) fully nonlinear NWT (numerical wave tank) is developed to investigate the interaction of a monochromatic wave with a floating elastic plate over the variable depth sea-bottom by using the HOBEM (higher order boundary element method). An Euler-Bernoulli-von Karman nonlinear beam model is applied to determine the fluid pressure imposed on the fluid-structure interface. Considering computational cost, the modal functions of a beam with free ends are introduced to approximate the plate displacement. The present model is validated against existing numerical and experimental results for elastic plate placed over flat sea-bottom and wave passing over a submerged object. Numerical calculations are conducted to obtain the hydroelastic higher harmonics and displacement nonlinearity of the elastic finite plate placed over various the trapezoid-shaped sea-bottoms with different shapes and arrangements. The effects of water depths, incident wave amplitudes and incident wave periods on the nonlinear responses of the plate are further emphatically examined.

Numerical and experimental investigation of nonlinear focused waves-current interaction with a submerged plate

This paper concerns the interaction of focused waves with uniform current and a submerged horizontal plate in the context of the two-dimensional nonlinear potential theory. A fully nonlinear NWT (numerical wave tank) based on a time domain HOBEM (higher-order boundary element method) is applied to the numerical solutions. In the model, the Goda's method is modified to discriminate incident and reflected waves, whereas the acceleration potential approach is introduced to determine the hydrodynamic forces on the structure. The corresponding experiments are also conducted in a two-dimensional glass-walled wave tank at Jiangsu University of Science and technology. The developed model is verified with published numerical results and validated with experimental test. Through a systematic parametric study, it is found that the maximum reflection or minimum transmission for different currents occur at the same plate width because of the compensating Doppler effects of current. The spectral analysis reveals that the energy dissipation occurs primarily in the fundamental waves when focused waves propagating over the plate. The current has a stronger influence on the wave forces than on wave surface elevation. Furthermore, the 'secondary loading cycle' phenomenon is also observed in the time series of the wave forces for a following current.

Wave interaction with a surface-piercing body in water of finite depth: a parametric study

ABSTRACTThe wave–body interactions for a surface-piercing body in water of finite depth are studied using a potential-theory-based, two-dimensional, fully nonlinear numerical wave tank. A parametric study was conducted in order to investigate the effects of the non-dimensional water depth, wave steepness, wave frequency, and beam–draft ratio on the wave-exciting forces acting on a fixed surface-piecing barge. It was found that a reduction of the water depth from deep to finite enhances all the wave-exciting forces. In all water depths, the second-order harmonics of the heave force and pitch moment are significantly large, although they can generally be neglected for the surge force. The barge was then allowed to move and the influence of the water depth on its wave forces is investigated. It was found that with the body motion involved, the surge force and the heave force reduce in the first-order harmonics while the pitch moment increases. In addition, a peak appears at finite water depth for the first-order harmonics of the heave force as well as for the heave displacement, indicating the great impact of water depth on the motions experienced by the floating barge.

Development of Multidirectional Nonlinear Numerical Wave Tank by Naoe-FOAM-SJTU Solver

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.

Comment on “A fully nonlinear implicit model for wave interactions with submerged structures in forced or free motion” by Guerber et al. (2012)

This paper reports a problem in the simulation of transient oscillation of a freely heaving cylinder appearing in Guerber et al. (2012)’s recent paper A fully nonlinear implicit model for wave interactions with submerged structures in forced or free motion. The problem is confirmed through a comparison study using an independent two-dimensional fully nonlinear numerical wave tank. The reason may come from the part solving the acceleration potential. In the end, the influence of this problem to the other results presented in the same paper is assessed.

Simulation of wave–body interaction: A desingularized method coupled with acceleration potential

A two-dimensional, potential-theory based, fully nonlinear numerical wave tank (NWT) is developed for the simulation of wave–body interaction. In this NWT, the concept of acceleration potential is adopted in addition to the velocity potential. Both potentials are solved using the desingularized boundary integral equation method (DBIEM). By tapping the strength of the DBIEM, a new acceleration-potential solving method is proposed, which turns the originally implicit kinematic boundary condition on the surface of a passively moving body into an explicit one. Unlike the other existing methods such as the mode decomposition method, the indirect method and the iterative method, the present method requires solving of only one boundary value problem to determine the acceleration potential, and hence significantly enhances the computational efficiency. Using this NWT, the nonlinear interaction between a freely floating barge and various incident waves is investigated. It is confirmed that the new acceleration potential solving method outperforms other existing methods, saving at least 45% of the computational time.

Wave propagation in a 3D fully nonlinear NWT based on MTF coupled with DZ method for the downstream boundary

Wave propagation in a three-dimensional (3D) fully nonlinear numerical wave tank (NWT) is studied based on velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied to eliminate the possible saw-tooth instabilities. The artificial wave speed employed in MTF (multi-transmitting formula) approach is investigated for fully nonlinear wave problem. The numerical results from incorporating the damping zone (DZ), MTF and MTF coupled DZ (MTF+DZ) methods as radiation condition are compared with analytical solution. An effective MTF+DZ method is finally adopted to simulate the 3D linear wave, second-order wave and irregular wave propagation. It is shown that the MTF+DZ method can be used for simulating fully nonlinear wave propagation very efficiently.

Development of Multidirectional Nonlinear Numerical Wave Tank by Naoe-FOAM-SJTU Solver

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.

Third-order effects in wave–body interaction

A review is presented of about 10 years research work on phenomena resulting from third-order interactions between an incoming wave system and the reflected wave system by a structure. The most striking manifestations are large run-ups that can be observed locally on the weather side. Two types of numerical potential flow models are described, one seeking for a steady-state solution in the frequency domain, and the other a fully nonlinear numerical wavetank based on extended Boussinesq equations. Numerous experimental investigations are described, with vertical walls and arrays of vertical cylinders. Computational results compare favorably with the measurements. Important issues such as the size of the interaction area and possible chaotic behavior are finally discussed.