Interaction of Linear Waves with Infinitely Long Horizontal Cylinders Studied by Boundary Element Method

The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation Method (BIEM). Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with those by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two-layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coefficients and energies are analyzed in detail, and some interesting physical phenomena are observed.     

Third-order theory for determining the hydrodynamic forces on axisymmetric floating or submerged bodies in oscillatory heaving motion

An investigation of the hydrodynamic behaviour of bodies in a large-amplitude oscillatory motion, for example in view of wave power absorption by floating bodies, not only requires the knowledge of added mass and damping coefficients, which can be calculated by means of a linear theory, but also of higher-order forces. Especially the third-order values will have to be calculated, because they contain a first-harmonic component.A computation procedure has been developed in order to calculate hydrodynamic forces up to the third order, acting on axisymmetric bodies in an oscillatory heaving motion. The method only requires the knowledge of first- and second-order potential functions, even for the calculation of third-order forces.Experiments have been carried out on floating conical and submerged cylindrical models, in order to evaluate the theoretical procedure.     

On diffraction and radiation problem for two cylinders in water of finite depth

The hydrodynamic problem arising form the interaction of linear water waves with a wave energy device consisting of two coaxial vertical cylinders of different radii is investigated. One cylinder is riding in waves, while another is submerged in fluid. By use of the method of separation of variables and the method of matched eigenfunction expansion, analytical expressions for the potentials are obtained. Using the expressions for the potentials, analytical expressions for the hydrodynamic coefficients and exciting forces/moments on the device are obtained. Numerical results of the hydrodynamic coefficients and exciting forces/moments are presented for some ratios of the radius of the submerged cylinder to that of the riding one. It is found that the radius of the submerged cylinder has a significant influence on the hydrodynamic coefficients and exciting forces/moments for relatively bigger radius of the submerged cylinder at low frequencies.     

On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.     

An extension of general identities for 3D water-wave diffraction with application to the Diffraction Transfer Matrix

Interaction theories are used in numerous branches of physics to efficiently evaluate wave scattering by multiple obstacles. An example of these interaction theories is the direct matrix method introduced by Kagemoto and Yue [1], which enables fast computation of three-dimensional water-wave multiple-scattering problems. The building block of interaction theories is a mathematical operator that encapsulates the mapping between incident and scattered waves. This operator is generally referred to as T-matrix and satisfies both reciprocity and energy identities. In some branches of physics, such as acoustics and electromagnetism, these identities are well established; in hydrodynamics, however, they have only been derived for a T-matrix that maps two-dimensional incident and scattered water waves. In three dimensions, water waves can be represented as a series expansion of cylindrical eigenfunctions. In this paper, we use this representation of water waves to derive the reciprocity and energy identities satisfied by the T-matrix of the direct matrix method, known as Diffraction Transfer Matrix (dtm). The identities derived herein represent an extension of existing general relations between two diffraction solutions. We show that this extension can be applied to verify the accuracy of the dtm entries, thereby increasing the reliability of existing schemes for computing the dtm. We present results for the dtm of two geometrically different isolated obstacles, as well as for the dtm of an asymmetric array. Finally, we demonstrate that the results presented herein can be extended to floating bodies found in a wide range of ocean engineering problems.     

Comparison of methods for computing hydrodynamic characteristics of arrays of wave power devices

A comparison of methods for the calculation of the hydrodynamic characteristics of arrays of wave power devices is presented. In particular, the plane-wave approximation and an exact multiple scattering formulation have been used to compute exciting wave forces, hydrodynamic coefficients and q factors for arrays of interacting wave power devices. The results obtained are compared with each other, and accuracy aspects of the computations are stressed and critically assessed.     

Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall

The radiation and the diffraction of linear water waves by an infinitely long floating rectangular structure submerged in water of finite depth with leeward boundary being a vertical wall are analyzed in this paper by using the method of separation of variables. Analytical expressions for the radiated and diffracted potentials are derived as infinite series with unknown coefficients determined by the eigenfunction expansion matching method. The expressions for wave forces and hydrodynamic coefficients are given. A comparison is made between the results obtained by the present analytical solution and those obtained by the boundary element method. By using the present analytical solution, the hydrodynamic influences of the submergence, the width, the thickness of the structure, and the distance between the structure and the wall on the wave forces and hydrodynamic coefficients are discussed in detail.     

Hydrodynamics identities and wave-drift force of a porous body

In the present study, hydrodynamic interactions between water waves and porous bodies are investigated. Various hydrodynamic identities, such as the Haskind relation, Bessho-Newman relation etc., are systematically re-examined. Some of these identities, such as the symmetry of added mass and damping and the Haskind-Hanaoka relation, are still valid for porous bodies even without modification to the identities. However, when energy dissipation due to porosity is involved, appropriate supplementation is required to properly consider porous effects. In addition, the calculation of wave drift forces acting on a porous body is formulated either by pressure integration or using momentum conservation as basis. We conclude that porosity dissipation makes a more substantial contribution to wave drift forces than does conventional dissipation created by scattered and radiated waves.     

Wave interaction with a semi-porous cylindrical breakwater mounted on a storage tank

The interaction of linear water waves with a semi-porous cylindrical breakwater surrounding a rigid vertical circular cylinder mounted on a storage tank is investigated theoretically. The cylindrical breakwater structure is porous in the vicinity of the free-surface, while at some distance below the water surface it becomes impermeable. Under the assumptions of linearized potential flow, the coupled problem of flow in the interior and exterior fluid regions is solved by an eigenfunction expansion approach. Analytical expressions are obtained for the wave motion in both the interior and exterior flow regions. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the hydrodynamic loads and interior and exterior wave fields. It is found that for certain parameter combinations the semi-porous, cylindrical breakwater may result in a significant reduction in the wave field and hydrodynamic forces experienced by the interior structure.     

Hydrodynamic Interactions of Three Barges in Close Proximity in A Floatover Installation

The hydrodynamics of side-by-side barges are much more complex than those of a single barge in waves because of wave shielding, viscous effects and water resonance in the gap. In the present study, hydrodynamic coefficients in the frequency domain were calculated for both the system of multiple bodies and the isolated body using both low-order and higher-order boundary-element methods with different element numbers. In these calculations, the damping-lid method was used to modify the free-surface boundary conditions in the gap and to make the hydrodynamic results more reasonable. Then far-field, mid-field and near-field methods were used to calculate wave-drift forces for both the multi-body system and the isolated body. The results show that the higher-order method has faster convergence speed than the low-order method for the multi-body case. Comparison of different methods of computing drift force showed that mid-field and far-field methods have better convergence than the near-field method. In addition, corresponding model tests were performed in the Deepwater Offshore Basin at Shanghai Jiao Tong University. Comparison between numerical and experimental results showed good agreement.     

Hydrodynamic modeling of perforated structures

A hydrodynamic model of perforated or slotted structures is proposed. It is asymptotic in the sense that the openings are supposed to be infinitely small and numerous, and the wall thickness to be nil. At variance with other work, a quadratic, not linear, law, relating the pressure differential to the traversing velocity, is assumed. As a result the hydrodynamic coefficients (added mass and damping) become amplitude dependent. The model is applied to bodies of various shapes including cylinders, plates and disks, in forced motion or submitted to incoming waves. Good agreement with experimental data is generally observed.     

Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders

The interaction of water waves with arrays of bottom-mounted, surface-piercing circular cylinders is investigated theoretically. The sidewall of each cylinder is porous and thin. Under the assumptions of potential flow and linear wave theory, a semi-analytical solution is obtained by an eigenfunction expansion approach first proposed for impermeable cylinders by Spring and Monkmeyer (1974), and later simplified by Linton and Evans (1990). Analytical expressions are developed for the wave motion in the exterior and all interior fluid regions. Numerical results are presented which illustrate the effects of various wave and structural parameters on the hydrodynamic loads and the diffracted wave field. It is found that the porosity of the structures may result in a significant reduction in both the hydrodynamic loads experienced by the cylinders and the associated wave runup.     

Diffraction–radiation of multiple floating structures in directional waves

The dynamics of multiple floating structures have been studied using the finite element method. The emphasis is on the hydrodynamic behaviour of multiple bodies under a multi-directional wave field. A two-dimensional numerical model has been adopted to evaluate hydrodynamic coefficients and forces in an oblique wave field. The responses in sway, heave and roll modes are reported. The linear filter technique is then used to extrapolate the responses under directional waves. The effect of mean wave direction and directional homogeneity on the hydrodynamic behaviour of the structure is studied. Based on the present study, it is found that the two-dimensional model is applicable to investigate the wave-structure interaction problems of the type herein considered.     

Hydrodynamic loads during the deployment of ROVs

Offshore operators understandably seek to operate remotely operated vehicles (ROVs) for as long as possible and in the widest range of sea conditions. Accurate predictions of the hydrodynamic loads are important at the design stage as well as in operation, particularly during the launch and recovery phases when snatching of the tether may occur. There is some speculation that calculation methods currently advocated in guidelines lead to an over-estimation of the hydrodynamic forces and consequently to unduly restrictive operability constraints. The present paper has measured wave forces on a 1/8 scale model of a widely used ‘workclass’ ROV, as well as on a solid box of similar envelope dimensions, and compared these against Morison's equation using coefficients derived from three methods. It is concluded that simple linear theory using total (substantive) derivatives, together with a Morison coefficient C_m≈1.5, can provide good estimates of the loading even in waves of quite high steepness, perhaps for height-to-wavelength ratios up to 0.08; i.e., in practice, up to wave breaking.     

The effect of sub-optimal control and the spectral wave climate on the performance of wave energy converter arrays

A linear hydrodynamic model is used to assess the sensitivity of the performance of a wave energy converter (WEC) array to control parameters. It is found that WEC arrays have a much smaller tolerance to imprecision of the control parameters than isolated WECs and that the increase in power capture of WEC arrays is only achieved with larger amplitudes of motion of the individual WECs. The WEC array radiation pattern is found to provide useful insight into the array hydrodynamics. The linear hydrodynamic model is used, together with the wave climate at the European Marine Energy Centre (EMEC), to assess the maximum annual average power capture of a WEC array. It is found that the maximum annual average power capture is significantly reduced compared to the maximum power capture for regular waves and that the optimum array configuration is also significantly modified. It is concluded that the optimum configuration of a WEC array will be as much influenced by factors such as mooring layout, device access and power smoothing as it is by the theoretical optimum hydrodynamic configuration.     

A comparison of complete and approximate solutions for second-order diffraction loads on arrays of vertical ci cular cylinders

This paper presents a comparison between two theoretical methods for computing the second-order diffraction loads on arrays of bottom-mounted, surface-piercing vertical circular cylinders in regular waves. One method presents a complete solution for the second-order hydrodynamic loads on the cylinder array via a numerical integration over the mean fluid free-surface. The other method is based on a large spacing approximation between the array members and involves the solution of a set of equivalent isolated body problems to obtain estimates for the second-order hydrodynamic loads. Numerical results for a pair of cylinders indicate very good agreement between the two methods at center-to-center spacing of both three and five radii, indicating that the approximate method may be sufficient to compute hydrodynamic interference effects to the second-order in many practical engineering situations.     

A general method for calculating hydrodynamic forces

This paper presents the derivation of a general method for calculating wave forces on the cylindrical members of offshore structures. By means of the proposed method one can calculate the wave loading on cylindrical members of fixed or floating offshore structures orientated randomly in waves. This method of calculating wave forces is based on the linear Airy wave theory. Calculation procedure of wave force components is presented in great detail on the basis of wave particle kinematic properties obtained from the linear Airy wave theory. In the procedure of calculating wave forces presented, definitions of the wave reference system for propagating wave, the structure reference system for the platform and the member reference system for the tubular members of the structure are first established, and then the calculation of wave forces is given in terms of its components, which are pressure, acceleration and velocity forces, including current forces. At the end of the paper, expressions of total heave, sway and surge forces and total roll, pitch and yaw moments acting on the platform are given as a sum of these forces acting on each member of the platform. The calculation procedure derived in this paper provides a very efficient means of calculating wave forces and moments during the time-domain simulations of a floating platform experiencing large amplitude motion in intact, progressive flooding and damaged conditions. Comparisons of the predictions with the measurements which will be presented elsewhere reveal that the calculation procedure developed can predict large amplitude oscillatory and steady motion characteristics of an intact and damaged platform in waves with an acceptable degree of accuracy.     

New model to determine forces at on-bottom slender pipelines

The present paper proposes a numerical model to determine horizontal and vertical components of the hydrodynamic forces on a slender submarine pipeline lying at the sea bed and exposed to non-linear waves plus a current. The new model is an extension of the Wake II type model, originally proposed for sinusoidal waves (Soedigdo et al., 1999) and for combined sinusoidal waves and currents (Sabag et al., 2000), to the case of periodic or random waves, even with a superimposed current. The Wake II type model takes into account the wake effects on the kinematic field and the time variation of drag and lift hydrodynamic coefficients. The proposed extension is based on an evolutional analysis carried out for each half period of the free stream horizontal velocity at the pipeline. An analytical expression of the wake velocity is developed starting from the Navier–Stokes and the boundary layer equations. The time variation of the drag and lift hydrodynamic coefficients is obtained using a Gaussian integration of the start-up function. A reduced scale laboratory investigation in a large wave flume has been conducted in order to calibrate the empirical parameters involved in the proposed model. Different wave and current conditions have been considered and measurements of free stream horizontal velocities and dynamic pressures on a bottom-mounted pipeline have been conducted. The comparison between experimental and numerical hydrodynamic forces shows the accuracy of the new model in evaluating the time variation of peaks and phase shifts of the horizontal and vertical wave and current induced forces.     

Hydrodynamic coefficients of a submerged pulsating sphere in finite depth

By extending the work of Linton (Linton, C.M., 1991. Radiation and diffraction of waver waves by a submerged sphere in finite depth. Ocean Engineering 18 (1/2), 61–74), the problem of radiation of water waves by a submerged pulsating sphere in finite depth is formulated using the multipole method. As in Linton (1991), this leads to an infinite system of linear equations, which are easily solved numerically. Simple expressions are derived for the hydrodynamic characteristics of such a body. Results showing the effect of varying both the immersion depth and the water depth on the hydrodynamic coefficients of the pulsating sphere are given. The paper resumes the work presented in Lopes (Lopes, D.B.S., 1999. On the study of the Archimedes wave swing device for wave energy utilization (in Portuguese). MSc on the Management and Modelling of the Marine Environment, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa.).     

Hydrodynamic interactions and relative motions of two floating platforms with mooring lines in side-by-side offloading operation

The hydrodynamic interaction and mechanical coupling effects of two floating platforms connected by elastic lines are investigated by using a time-domain multi-hull/mooring/riser coupled dynamics analysis program. Particular attention is paid to the contribution of off-diagonal hydrodynamic interaction terms on the relative motions during side-by-side offloading operation. In this regard, the exact method (CMM: combined matrix method) including all the vessel and line dynamics, and the 12×12 hydrodynamic coefficients in a combined matrix is developed. The performance of two typical approximation methods (NHI/No Hydrodynamic Interaction: iteration method between two vessels without considering hydrodynamic interaction effects; SMM/Separated Matrix Method: iteration method between two vessels with partially considering hydrodynamic interaction effects, i.e. ignoring off-diagonal cross-coupling terms in the 12×12 hydrodynamic coefficient matrix) is also tested for the same side-by-side offloading operation in two different environmental conditions. The numerical examples show that there exists significant discrepancy at sway and roll modes between the exact and the approximation methods, which means that the cross-coupling (off-diagonal block) terms of the full hydrodynamic coefficient matrix play an important role in the case of side-by-side offloading operation. Therefore, such approximation methods should be used with care. The fender reaction forces, which exhibit large force with contact but no force without contact, are also numerically modeled in the present time-domain simulation study.