Radiation of water waves by a submerged nearly circular plate

A thin nearly circular plate is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the surface of the plate which is conformally mapped onto the unit disc. The solution is computed by a spectral method proved to be efficient for the case of a circular disc. Numerical results are presented for the heave added mass and damping coefficients for two types of nearly circular plates

Optimal control of the heave motion of marine cable subsea-unit systems

One of the key problems associated with subsea operations involving tethered subsea units is the motions of support vessels on the ocean surface which can be transmitted to the subsea unit through the cable and increase the tension. In this paper, a theoretical approach for heave compensation is developed. After proper modelling of each element of the system, which includes the cable/subsea-unit, the onboard winch, control theory is applied to design an optimal control law. Numerical simulations are carried out, and it is found that the proposed active control scheme appears to be a promising solution to the problem of heave compensation

Acoustic intensity calculations for axisymmetrically modeled fluid regions

An algorithm for calculating acoustic intensities from a time harmonic pressure field in an axisymmetric fluid region is presented. Acoustic pressures are computed in a mesh of NASTRAN triangular finite elements of revolution (TRIAAX) using an analogy between the scalar wave equation and elasticity equations. Acoustic intensities are then calculated from pressures and pressure derivatives taken over the mesh of TRIAAX elements. Intensities are displayed as vectors indicating the directions and magnitudes of energy flow at all mesh points in the acoustic field. A prolate spheroidal shell is modeled with axisymmetric shell elements (CONEAX) and submerged in a fluid region of TRIAAX elements. The model is analyzed to illustrate the acoustic intensity method and the usefulness of energy flow paths in the understanding of the response of fluid-structure interaction problems. The structural-acoustic analogy used is summarized for completeness. This study uncovered a NASTRAN limitation involving numerical precision issues in the CONEAX stiffness calculation causing large errors in the system matrices for nearly cylindrical cones

Wave scattering by circular arc shaped plates

This work investigates the reflection and transmission properties of a circular arc plate which is submerged in deep water. The purpose is to compare the reflective properties of a circular arc plate with those for a submerged, circular cylinder in order to assess the suitability of using circular arc plates when constructing a water wave lens. Linear theory is assumed and two separate techniques are used to determine the wave field. The first involves expanding the potential as a series of multipole potentials outside a circular region and a series of nonsingular solutions of Laplace's equation within the region and matching the expansions on the boundary. The second technique is based on a variational procedure and is used to derive an explicit, approximate expression for the reflection coefficient, under the assumption that the plate is short compared with the other length scales in the problem. Results are presented which compare the approximate solution with the full numerical method for a variety of plates. Finally, the full numerical calculations of the reflection and transmission coefficients for a plate are compared with those for a submerged, circular cylinder

Interaction of wave with a body submerged below an ice sheet with multiple arbitrarily spaced cracks

The problem of wave interaction with a body submerged below an ice sheet with multiple arbitrarily spaced cracks is considered, based on the linearized velocity potential theory together with the boundary element method. The ice sheet is modeled as a thin elastic plate with uniform properties, and zero bending moment and shear force conditions are enforced at the cracks. The Green function satisfying all the boundary conditions including those at cracks, apart from that on the body surface, is derived and is expressed in an explicit integral form. The boundary integral equation for the velocity potential is constructed with an unknown source distribution over the body surface only. The wave/crack interaction problem without the body is first solved directly without the need for source. The convergence and comparison studies are undertaken to show the accuracy and reliability of the solution procedure. Detailed numerical results through the hydrodynamic coefficients and wave exciting forces are provided for a body submerged below double cracks and an array of cracks. Some unique features are observed, and their mechanisms are analyzed

Numerical analysis of a horizontal pressure differential wave energy converter.

CFD modeling of an innovative wave energy device has been carried out in this study. OpenFoam wave modeling solver interFoam has been employed in order to investigate the energy extraction capability of the wave energy device. The innovative concept is based on utilizing the pressure differential under the crest and trough of a wave to drive flow through a pipe. The simulated surface elevation of a wave has been validated against the reported wave tank experimental data in order to provide confidence in the modeling outcome. Further, simulations have been carried out with the device placed near to the bottom of the numerical wave tank in order establish the energy extraction potential. The simulation results confirm that effective power can be generated from the wave energy device. The efficiency of the device decreases with the increase in wave height, although it increases with the wave period. Higher power-take off (PTO) damping is also beneficial in extracting increased energy from waves

Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances

In this joint theoretical, numerical and experimental study, we investigate the phenomenon of forced generation of nonlinear waves by disturbances moving steadily with a transcritical velocity through a layer of shallow water. The plane motion considered here is modelled by the generalized Boussinesq equations and the forced Korteweg-de Vries (fKdV) equation, both of which admit two types of forcing agencies in the form of an external surface pressure and a bottom topography. Numerical results are obtained using both theoretical models for the two types of forcings. These results illustrate that within a transcritical speed range, a succession of solitary waves are generated, periodically and indefinitely, to form a procession advancing upstream of the disturbance, while a train of weakly nonlinear and weakly dispersive waves develops downstream of an ever elongating stretch of a uniformly depressed water surface immediately behind the disturbance. This is a beautiful example showing that the response of a dynamic system to steady forcing need not asymptotically tend to a steady state, but can be conspicuously periodic, after an impulsive start, when the system is being forced at resonance. A series of laboratory experiments was conducted with a cambered bottom topography impulsively started from rest to a constant transcritical velocity U, the corresponding depth Froude number F = U/(gh[sub]0)^1/2 (g being the gravitational constant and h[sub]0 the original uniform water depth) being nearly the critical value of unity. For the two types of forcing, the generalized Boussinesq model indicates that the surface pressure can be more effective in generating the precursor solitary waves than the submerged topography of the same normalized spatial distribution. However, according to the fKdV model, these two types of forcing are entirely equivalent. Besides these and some other rather refined differences, a broad agreement is found between theory and experiment, both in respect of the amplitudes and phases of the waves generated, when the speed is nearly critical (0.9 F > 0.2, finally disappear at F ~= 0.2. In the other direction, as the Froude number is increased beyond F ~= 1.2, the precursor soliton phenomenon was found also to evanesce as no finite-amplitude solitary waves can outrun, nor can any two-dimensional waves continue to follow, the rapidly moving disturbance. In this supercritical range and for asymptotically large times, all the effects remain only local to the disturbance. Thus, the criterion of the fascinating phenomenon of the generation of precursor solitons is ascertained

Motion and wave load analyses of large offshore structures and special vessels in waves

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Predictions of the environmental loading and induced motional and structural responses are among the most important aspects in the overall design process of offshore structures and ships. In this thesis, attention is focused on the wave loads and excited bodily motion responses of large offshore structures and special vessels. With the aim of improving the existing theoretical methods to provide techniques of theoretical effectiveness, computational efficiency, and engineering practicality in marine and offshore applications, the thesis concentrates upon describing fundamental and essential aspects in the physical phenomenon associated with wave-structure interactions and deriving new methods and techniques to analyse offshore structures and unconventional ships of practical interest. The total wave force arising from such a wave-structural interaction is assumed to be a simple superposition of the potential and the viscous flow force components. The linear potential forces are solved by the Green function integral equation whilst the viscous forces are estimated based on the Morison's damping formula. Forms of the Green function integral equation and the associated Green function are given systematically for various practical cases. The relevant two-dimensional versions are then derived by a transformation procedure. Techniques are developed to solve the integral equation numerically including the interior integral formulation and, in particular, to tackle the mathematical difficulties at irregular frequencies. In applying the integral equations to solve problems with various offshore structures and special vessels, some modified, improved or simplified methods are proposed. At first, simplified method is derived for predictions of the surge, sway and yaw motions of elongated bodies of full sectional geometry or structures with shallow draft. Then, a new shallow draft theory is described for both three- and two-dimensional cases with inclusion of the finite draft effect. Furthermore, a three-dimensional strip method is formulated where the end effects of the body are fully taken into account. Finally, an approximation to the horizontal mean drift forces of multi-column offshore structures are presented. Some new findings are also discussed including the multiple resonances occurring in the motions of multi-hulled marine structures due to the wave-body interaction, the mutual cancellation effect of the diffraction and the radiation forces arising from a full shaped slender body, and so on. Further to those verification studies for individual methods developed, more comprehensive example investigations are given related to two industrial applications. One is a derrick barge semi-submersible with zero forward speed; and the other, a SWATH ship with considerable speed. By correlation of all the proposed approaches with available analytical, numerical and experimental data, the thesis tries to demonstrate a principle that as long as principal physical aspects in the wave-structure interaction problem are properly treated, an appropriately modified or simplified method works, performs well and, sometimes, even better.SERC (through the MTD Ltd), MoD, BPP Ltd and the Royal Society/BP Award