Wave-body Interactions Research Articles

Modeling a solitary wave interaction with a fixed floating body using an integrated analytical–numerical approach

This paper presents the development of an integrated analytical–numerical model to simulate a solitary wave propagating past a fixed and partially immersed body. The velocity potentials of the inner fluid region beneath the structure are determined analytically with unknown coefficients evaluated from a system of newly formulated matching equations with the uses of continuous velocity and velocity potential as well as the orthogonal properties of the eigenfunctions. For the outer region, the propagation of an incident solitary wave and its subsequent wave reflection and transmission after the wave–body interaction are modeled by solving the generalized Boussinesq (gB) equations. Time variations of the wave profiles and hydrodynamic forces for various wave and structural conditions are computed. A series of experimental measurements of wave elevations were carried out for verification of the model performance. The wave elevations obtained from the model simulations are found to agree closely with the measured data. The parametric studies were performed to examine the effects of wave amplitude, structural submergence, and structural width on the transmitted and reflected waves. An increase of structural submergence results in a decrease of the transmitted wave amplitude. Also, with an increase in structural width, the transmitted wave amplitude decreases.

Global performances of a semi-submersible 5MW wind-turbine including second-order wave-diffraction effects

The global performance of the 5 MW OC4 semisubmersible floating wind turbine in random waves was numerically simulated by using the turbine-floater-mooring fully coupled and time-domain dynamic analysis program FAST-CHARM3D. There have been many papers regarding floating offshore wind turbines but the effects of second-order wave-body interactions on their global performance have rarely been studied. The second-order wave forces are actually small compared to the first-order wave forces, but its effect cannot be ignored when the natural frequencies of a floating system are outside the wave-frequency range. In the case of semi-submersible platform, second-order difference-frequency wave-diffraction forces and moments become important since surge/sway and pitch/roll natural frequencies are lower than those of typical incident waves. The computational effort related to the full second-order diffraction calculation is typically very heavy, so in many cases, the simplified approach called Newman\'s approximation or first-order-wave-force-only are used. However, it needs to be justified against more complete solutions with full QTF (quadratic transfer function), which is a main subject of the present study. The numerically simulated results for the 5 MW OC4 semisubmersible floating wind turbine by FAST-CHARM3D are also extensively compared with the DeepCWind model test results by Technip/NREL/UMaine. The predicted motions and mooring tensions for two white-noise input-wave spectra agree well against the measure values. In this paper, the numerical static-offset and free-decay tests are also conducted to verify the system stiffness, damping, and natural frequencies against the experimental results. They also agree well to verify that the dynamic system modeling is correct to the details. The performance of the simplified approaches instead of using the full QTF are also tested.

Simulation of Irregular Waves in a Numerical Wave Tank

Abstract The time domain boundary element method was utilized to simulate the propagation of the irregular waves in a numerical wave tank. The problem was solved in a time-marching scheme, upon the irregular waves being fed through the inflow boundary, in which the theoretical solution was obtained from the wave energy spectrum. The open boundary condition was modeled by the multi transmitting formula (MTF), in which the phase velocity was calculated according to the Sommerfeld’s condition. The velocity potential and wave elevation were directly obtained by integrating the free surface condition twice, with respect to time. The accuracy of the developed numerical scheme was verified by simulating the propagation of irregular waves. The numerical results show good agreements with the analytical solutions, which prove that the proposed scheme is a promising way to the simulation of wave-body interactions.

단파장 영역에서의 부가저항 해석

In this study, the added resistance of ships in short waves is systematically studied by using two different numerical methods - Rankine panel method and Cartesian grid method – and existing asymptotic and empirical formulae. Analysis of added resistance in short waves has been preconceived as a shortcoming of numerical computation. This study aims to observe such preconception by comparing the computational results, particularly based on two representative three-dimensional methods, and with the existing formulae and experimental data. In the Rankine panel method, a near-field method based on direct pressure integration is adopted. In the Cartesian grid method, the wave-body interaction problem is considered as a multiphase problem, and volume fraction functions are defined in order to identify each phase in a Cartesian grid. The computational results of added resistance in short waves using the two methods are systematically compared with experimental data for several ship models, including S175 containership, KVLCC2 and Series 60 hulls (C_B = 0.7, 0.8). The present study includes the comparison with the established asymptotic and empirical formulae in short waves.

Hydrodynamic analysis of oscillating water column wave energy devices

A 40-chamber I-Beam attenuator-type, oscillating water column, wave energy converter is analyzed numerically based on linearized potential flow theory, and experimentally via model test experiments. The high-order panel method WAMIT by Newman and Lee (WAMIT; a radiation–diffraction panel program for wave-body interactions, 2014, http://www.wamit.com ) is used for the basic wave-structure interaction analysis. The damping applied to each chamber by the power take off is modeled in the experiment by forcing the air through a hole with an area of about 1 % of the chamber water surface area. In the numerical model, this damping is modeled by an equivalent linearized damping coefficient which extracts the same amount of energy over one cycle as the experimentally measured quadratic damping coefficient. The pressure in each chamber in regular waves of three different height-to-length ratios is measured in the experiments and compared to calculations. The model is considered in both fixed and freely floating, slack-moored conditions. Comparisons are also made to experimental measurements on a single fixed chamber. The capture width ratio in each case is predicted based on the pressures in the chambers. Good agreement is found between the calculations and the experiments.

A desingularized Rankine source method for nonlinear wave–body interaction problems

A two-dimensional nonlinear wave–body interaction problem is solved by a desingularized integral method in combination with a mixed Euler–Lagrange method. A special treatment of the intersection point singularity is introduced by employing an optimal technique to smooth the wave elevation around the intersection point and the utilization of a free surface control point distribution. By this means the nonlinear boundary effects arising from body surface and free surface are taken into consideration in addition to the development of a free surface Rankine source distribution method. A Lagrangian formulation is applied to capture the time-dependent motion of the control points and source points to describe the body and free surface nonlinear boundary conditions. The validation of the proposed method is demonstrated by comparing findings with a selection of existing numerical and experimental data.

A Continuous Desingularized Source Distribution Method Describing Wave–Body Interactions of a Large Amplitude Oscillatory Body

A Rankine source method with a continuous desingularized free surface source panel distribution is developed to solve numerically a wave–body interaction problem with nonlinear boundary conditions. A body undergoes forced oscillatory motion in a free water surface and the variation of wetted body surface is captured by a regridding process. Free surface sources are placed in continuous panels, rather than points in isolation, over the calm water surface, with free surface collocation points placed on the calm water surface. Nonlinear kinematic and dynamic free surface boundary conditions along the collocation points on the calm water surface are solved in a time domain simulation based on a Lagrange time dependent formulation. Compared with isolated desingularized source points distribution methods, a significantly reduced number of free surface collocation points with sparse distribution are utilized in the present numerical computation. The numerical scheme of study is shown to be computationally efficient and the accuracy of numerical solutions is compared with traditional numerical methods as well as measurements.

Wave-current impacts on surface-piercing structure based on a fully nonlinear numerical tank

Fully nonlinear wave-body interactions for a surface-piercing structure with combined wave-current flow in different water depths are studied by using a 2-D numerical tank. The model is based on Reynolds averaged Navier-Stokes (RANS) equations and renormalization group (RNG) k – ɛ model. The mean and maximum wave-current impacts, including forces in two directions and rotational moment, are calculated and discussed. The effects of U/C and water depth condition on forces and moment have been investigated and the results for combined irregular waves and currents are compared with those induced by combined regular waves and currents.

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.

Colour surface flow visualisation of interfering slender bodies at Mach 3

A study to understand the flow physics produced by two slender bodies in close proximity in high-speed airflow was undertaken. The interference flow field generated by the bodies is dominated by shock and expansion waves, and of particular significance is the complex interaction of the bow-shock wave emanating from the disturbance generator, striking the surface of the disturbance receiver. To gain insight into the shock wave-body interaction, the traditional surface oil flow visualisation technique was extended to include colour, which assists the eye in tracking the streak lines back to their separation and reattachment regions. In addition, the fine particle sizes of the colour pigment produced crisper and more definitive separation lines over the body, in comparison to the traditional monochrome pigments, such as lamp-black or titanium-dioxide. Subsequently, the dried surface pattern was lifted off the body using matte-acetate tape, digitised and then straightened using datum markings along the sting. This allowed the shock impingement location and shock diffraction path over the body to be established quantitatively, which was used to validate numerical simulations. The experimental and computational data showed good agreement for all configurations considered, providing complementary information about the disturbance-induced effects generated in the interference flow field, and provided detailed insight into the near-surface flow topology produced by the shock wave-slender body interaction.

A Rankine source computation for three dimensional wave–body interactions adopting a nonlinear body boundary condition

A three-dimensional wave–body interaction problem is numerically simulated by a Rankine source scheme in combination with a mixed Euler–Lagrange method. Singular free surface source points are placed exterior to the free surface, which is known as a desingularized method, and free surface boundary conditions are satisfied along control points on the computational domain. A new source distribution algorithm incorporating vertical desingularized distance and horizontal free surface source arrangements is developed and the method connects body panel size to free surface panel size. The nonlinear or exact body boundary condition is captured by regridding the wetted body surface at each time step. A Lagrangian frame of reference is used to capture the motion of singularities during the regridding process. The nonlinear effects caused by the variation of the wetted body surface are evaluated based on this method. The numerical scheme of study is shown to be computationally efficient and computation time is significantly reduced in comparison with earlier numerical investigations using the desingularized method.

Numerical analysis of added resistance on ships in short waves

In the present study, a Rankine panel method, which is based on the potential theory and a Cartesian-grid method, which solves the Euler equation directly, are applied to calculate ship motion and added resistance. In the Rankine panel method, a near-field method which calculates added resistance by integrating the second-order pressure on a body surface is adopted. In the Cartesian grid method, the wave–body interaction problem is considered as a multiphase problem, and volume fraction functions are defined in order to distinguish each phase in a Cartesian grid system. The added resistance is calculated by subtracting the steady surge force from the mean surge force measured in motion problems. This study focuses on added resistance under short wave conditions. Calculation capacities of the Rankine panel method and Cartesian grid method in short wavelength are systematically analyzed for several models, including Series 60 hulls (CB=0.7, 0.8), S175 containerships and KVLCC2 hulls. In addition, established asymptotic methods in short wavelength are examined.

A CIP-based numerical simulation of freak wave impact on a floating body

The purpose of this work is to develop advanced numerical tools for modeling freak waves impact on a floating body undergoing large amplitude motions. An improved model governed by the Navier–Stokes equations with free surface boundary conditions is presented for nonlinear wave-body interactions, in which a more accurate Volume of Fluid (VOF)-type scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) is adopted for interface capturing. The model is solved by a Constrained Interpolation Profile (CIP)-based high order finite-difference method on a fixed Cartesian grid system. A focusing wave theory is used for freak wave generation. Newly designed physical experiments in a two-dimensional glass-wall wave tank are performed for benchmark validation. Fairly good agreements are obtained from the qualitative and quantitative comparisons between numerical results and laboratory data regarding to distorted free surfaces and large amplitude body motions. Some discrepancies are found for the predicted peak pressure. The effects of grid resolution on body motions and impact pressure are performed for error analysis. The comparison of the numerical results and measured data reveals that the proposed model is capable of reproducing the nonlinear dynamics of the floating body for applications.

Time series prediction of nonlinear ship structural responses in irregular seaways using a third-order Volterra model

To predict the nonlinear structural responses of a ship traveling through irregular waves, a third-order Volterra model was applied based on the given irregular data. A nonlinear wave–body interaction system was identified using the nonlinear autoregressive with exogenous input (NARX) technique, which is one of the most commonly used nonlinear system identification schemes. The harmonic probing method was applied to extract the first-, second- and third-order frequency response functions of the system. To achieve this, a given set of time history data of both the irregular wave excitation and the corresponding midship vertical bending moment for a certain sea state was fed into the three-layer perceptron neural network. The network parameters are determined based on the supervised training. Next, the harmonic probing method was applied to the identified system to extract the frequency response function of each order. While applying the harmonic probing method, the nonlinear activation function (i.e., the hyperbolic tangent function) was expanded into a Taylor series for harmonic component matching. After the frequency response functions were obtained, the structural responses of the ship under an arbitrary random wave excitation were easily calculated with rapidity using a third-order Volterra series. Additionally, the methodology was validated through the in-depth analysis of a nonlinear oscillator model for a weak quadratic and cubic stiffness term, whose analytic solutions are known. It was confirmed that the current method effectively predicts the nonlinear structural response of a large container carrier under arbitrary random wave excitation.

Fully-Nonlinear Wave-Current-Body Interaction Analysis by a Harmonic Polynomial Cell Method

A new numerical 2D cell method has been proposed by the authors, based on representing the velocity potential in each cell by harmonic polynomials. The method was named the harmonic polynomial cell (HPC) method. The method was later extended to 3D to study potential-flow problems in marine hydrodynamics. With the considered number of unknowns that are typical in marine hydrodynamics, the comparisons with some existing boundary element- based methods, including the fast multipole accelerated boundary element methods, showed that the HPC method is very competitive in terms of both accuracy and efficiency. The HPC method has also been applied to study fully-nonlinear wave-body interactions; for example, sloshing in tanks, nonlinear waves over different sea-bottom topographies, and nonlinear wave diffraction by a bottom-mounted vertical circular cylinder. However, no current effects were considered. In this paper, we study the fully-nonlinear time-domain wave-body interaction considering the current effects. In order to validate and verify the method, a bottom-mounted vertical circular cylinder, which has been studied extensively in the literature, will first be examined. Comparisons are made with the published numerical results and experimental results. As a further application, the HPC method will be used to study multiple bottom-mounted cylinders. An example of the wave diffraction of two bottom-mounted cylinders is also presented.

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.

A Source Point Distribution Scheme for Wave-Body Interaction Problem

A two-dimensional linear wave-body interaction problem can be solved using a desingularized integral method by placing free surface Rankine sources over calm water surface and satisfying boundary conditions at prescribed collocation points on the calm water surface. A new free-surface Rankine source distribution scheme, determined by the intersection points of free surface and body surface, is developed to reduce numerical computation cost. Associated with this, a new treatment is given to the intersection point. The present scheme results are in good agreement with traditional numerical results and measurements. Keywords—Source point distribution, panel method, Rankine source, desingularized algorithm

Numerical simulation of a submerged cylindrical wave energy converter

In this study, a numerical model based on the complete solution of the Navier–Stokes equations is proposed to predict the behavior of the submerged circular cylinder wave energy converter (WEC) subjected to highly nonlinear incident waves. The solution is obtained using a control volume approach in conjunction with the fast-fictitious-domain-method for treating the solid objects. To validate the model, the numerical results are compared with the available analytical and experimental data in various scenarios where good agreements are observed. First, the free vibrations of a solid object in different non-dimensional damping ratios and the free decay of a heaving circular cylinder on the free surface of a still water are simulated. Next, the wave energy absorption efficiency of a circular cylinder WEC calculated from the model is compared with that of the available experiments in similar conditions. The results show that tuning the converter based on the linear theory is not satisfactory when subjected to steep incident waves while the numerical wave tank (NWT) developed in the current study can be effectively employed in order to tune the converter in such conditions. The current NWT is able to predict the wave-body interactions as long as the turbulence phenomena are not important which covers a wide range of Reynolds and Keulegan-Carpenter numbers.

Analysis of deepwater offshore structures: Issues and challenges

A brief overview of analysis of deepwater offshore structures with reference to modeling issues is presented. Floaters with moorings and risers exhibit nonlinear response under environmental loads. The modeling of such structures poses many challenges because of the flexibility of the riser/mooring system, fluid–structure interaction and random nature of wave loads. Tensioned beam finite elements can be used for structural modeling of line elements. Computational fluid dynamic modeling may be used to firm up hydrodynamic coefficients required in the Morison equation for the estimation of fluid loads on structural elements, as well as to evolve simplified models to represent vortex-induced motions. While wave-body interaction of large-volume structures may be modeled using computational fluid dynamic tools, the use of numerical models employing the fully nonlinear potential flow theory is worth exploring. Simpler analytical models for use in design analysis may be developed by employing coupled models based on nonlinear structural finite element methods and computational fluid dynamic tools. Simpler methods of evaluating stress-range statistics required for fatigue damage estimation need to be developed for the case of nonlinear stochastic response of deepwater systems.

Incompressible smoothed particle hydrodynamics (SPH) with reduced temporal noise and generalised Fickian smoothing applied to body–water slam and efficient wave–body interaction

Incompressible smoothed particle hydrodynamics generally requires particle distribution smoothing to give stable and accurate simulations with noise-free pressures. The diffusion-based smoothing algorithm of Lind et al. (J. Comp. Phys. 231 (2012) 1499–1523) has proved effective for a range of impulsive flows and propagating waves. Here we apply this to body–water slam and wave–body impact problems and discover that temporal pressure noise can occur for these applications (while spatial noise is effectively eliminated). This is due to the free-surface treatment as a discontinuous boundary. Treating this as a continuous very thin boundary within the pressure solver is shown to effectively cure this problem. The particle smoothing algorithm is further generalised so that a non-dimensional diffusion coefficient is applied which suits a given time step and particle spacing.We model the particular problems of cylinder and wedge slam into still water. We also model wave-body impact by setting up undisturbed wave propagation within a periodic domain several wavelengths long and inserting the body. In this case, the loads become cyclic after one wave period and are in good agreement with experiment. This approach is more efficient than the conventional wave flume approach with a wavemaker which requires many wavelengths and a beach absorber.Results are accurate and virtually noise-free, spatially and temporally. Convergence is demonstrated. Although these test cases are two-dimensional with simple geometries, the approach is quite general and may be readily extended to three dimensions.