Body In Regular Waves Research Articles

Investigation of moonpools as pitch motion reducing device

Moonpools as a device for reducing pitch motion is investigated experimentally, numerically and by an approximate theory. A two-dimensional study is carried out of a rectangular body with two moonpools. Forced heave and pitch motion, as well as freely floating body in regular waves are studied. The body geometry is varied; two drafts and five different moonpool inlet configurations are considered; rounded and squared inlets, as well as vertical plates (appendages) extending below the inlet with three different depths. The outer corners of the body are square. There is a resonance as well as cancellation period in both pitch and heave, where the cancellation is the desired effect. By cancellation period we refer to a narrow period range where the pitch motion is nearly cancelled, due to the pressures induced by the moonpool piston-mode resonance. Our investigation reveals that the cases with rounded and square moonpool inlet geometries are most efficient in cancelling the pitch motions.

Two-dimensional numerical study of gap resonance coupling with motions of floating body moored close to a bottom-mounted wall

The piston mode fluid resonance in the narrow gap between a moored floating body and a bottom-mounted vertical wall is numerically investigated based on a two-dimensional potential flow model and viscous numerical simulations. This study focuses on understanding the effect of mooring stiffness on the coupling dynamics of the gap resonance and the sway or heave motion of the floating body in regular waves. Numerical studies show that the resonant wave amplitude in the gap is reduced by the sway and heave motions. The reduction is highly dependent on the mooring stiffness. Two resonant frequencies are confirmed, and both increase with the mooring stiffness. Different modes of motions are identified in terms of the phase difference between the oscillatory motions of the gap flow and the floating body. Higher harmonic components of responses are found for the specific mooring stiffness. The performance of potential flow models in predicting resonant responses is revisited based on the understanding that the overall damping effect consists of two parts: (1) radiation damping and (2) viscous dissipation. It is confirmed that a potential model is also able to produce reasonable predictions as radiation damping plays a dominant role, for example, at the second resonant frequencies of coupling the gap resonance with the sway motion. Otherwise, as viscous dissipation dominates radiation damping, noticeable over-predictions by a potential model occur as recognized before, for example, the present results at the second peak response of gap resonance with the heave motion. The relative viscous dissipation is quantified with the reflection coefficient of viscous numerical results, while the radiation damping is quantified based on a specially designed radiation potential model with inputs of viscous numerical solutions.

Mean Drift Forces on Vertical Cylindrical Bodies Placed in Front of a Breakwater

This paper presents a numerical and experimental investigation of the second-order steady horizontal and vertical drift forces acting on cylindrical bodies in regular waves. The examined bodies are either kept restrained in front of a vertical breakwater or are considered free- floating when alone in the wave field. Two principally different approaches for mean drift forces determination are described: the momentum conservation principle and the direct integration of all pressure contributions upon the instantaneous wetted surface of the bodies, whereas, for the solution of the associated diffraction and motion radiation problems, analytical and panel methodologies are applied. The hydrodynamic interaction phenomenon between the bodies and the adjacent breakwater are taken into account by using the method of images. Theoretical and numerical results, concerning the horizontal and the vertical drift forces, are presented and compared with each other. Furthermore, additional comparisons are made with experimental data obtained during an experimental campaign at French research institute for exploitation of the sea (IFREMER), in France.

Experimental Studies of Interaction Forces Affect the Position of Vertical Plates on Oscillating Heave Plates with Cylindrical Bodies in Regular Waves

This paper discusses an experimental study of a wave energy converter (WEC) without using reaction from the seabed. The WEC uses buoys and heave plates, which can react to their self-reacting. The interaction force between heave plates and buoys can absorb energy from ocean waves better. The heave plate model affects the output of energy produced. It is presented in this study with variations in the position of upright plates. The research aims to measure the influence of the place of the addition of vertical plates into heave plates on the WEC on the hydrodynamic performance (coefficient of mass increase, drag coefficient, and KC value) and the interaction of the force it produces with the buoy on regular waves. The conclusion is the vertical plate position makes the coefficient of mass added Ca increase with an increasing amount of KC, and an almost linear relationship was observed between them. As the frequency increases, the value of C increases slightly, but it is not clear. Thus, the oscillating frequency has little effect on the mass coefficient of added heave plates with vertical plates. Thus, the change in the vertical plate position has only a powerful effect on KC < 0.75. ©2020. CBIORE-IJRED. All rights reserved

A numerical simulation method for the flow around floating bodies in regular waves using a three-dimensional rectilinear grid system

The motion of a floating body and the free surface flow are the most important design considerations for ships and offshore platforms. In the present research, a numerical method is developed to simulate the motion of a floating body and the free surface using a fixed rectilinear grid system. The governing equations are the continuity equation and Navier–Stokes equations. The boundary of a moving body is defined by the interaction points of the body surface and the centerline of a grid. To simulate the free surface the Modified Marker-Density method is implemented. Ships advancing in regular waves, the interaction of waves by a fixed circular cylinder array and the response amplitude operators of an offshore platform are simulated and the results are compared with published research data to check the applicability. The numerical method developed in this research gives results good enough for application to the initial design stage.

Mathematical Modelling of Roll Motion for a Floating Body in Regular Waves Using Frequency Based Analysis with Speed

This paper deals with the mathematical modelling and frequency-based analysis for uncoupled roll motions of a floating body in regular waves with the variation of speed. First we compute hydrodynamic coefficients by using strip theory formulation. Considering sinusoidal wave with frequency (ω ) varying between 0.3 to 1.2 acts on beam to the floating body for zero and non-zero forward speed ( U =0 and 12 m/s) governing equation is obtained. Using the normalization procedure and frequency based analysis; group based equations are formulated for each case. Based on relative importance of the hydrodynamic coefficients, analytical solutions are derived for zero and non-zero forward speed. The sensitivity analysis with respect to the effect of damping is also investigated. This study could be useful to understand the effect of waves on roll motion due to the variation of speed for various frequencies.

Phase control through load control of oscillating-body wave energy converters with hydraulic PTO system

Oscillating bodies constitute an important class of wave energy converters, especially for offshore deployment. Phase control by latching has been proposed in the 1970s to enhance the wave energy absorption by oscillating bodies (especially the so-called point absorbers). Although this has been shown to be potentially capable of substantially increasing the amount of absorbed energy, the practical implementation in real irregular waves of optimum phase control has met with theoretical and practical difficulties that have not been satisfactorily overcome. The present paper addresses the case of oscillating-body converters equipped with a high-pressure hydraulic power take-off mechanism (PTO) that provides a natural way of achieving latching: the body remains stationary for as long as the hydrodynamic forces on its wetted surface are unable to overcome the resisting force (gas pressure difference times cross-sectional area of the ram) introduced by the hydraulic PTO system. A method of achieving sub-optimal phase-control is developed, based on the theoretical time-domain modelling of a single-degree of freedom oscillating body in regular and irregular waves, by adequately delaying the release of the body in order to approximately bring into phase the body velocity and the diffraction (or excitation) force on the body, and in this way get closer to the well-known optimal condition derived from frequency-domain analysis for an oscillating body in regular waves.

Determination of Roll Motion for a Floating Body in Regular Waves

This paper deals with the mathematical modelling of the roll motion of a floating body in regular waves in beam seas for non-restrained conditions. The hydrodynamic forces are computed with the application of strip theory, and frequency dependent sectional added mass moment of inertia and damping are integrated over the length of the body by using the Frank close fit method. The governing equation that arises after balancing the hydrodynamic and exciting forces is reduced to non-dimensional form prior to converting it into the frequency domain by applying the Laplace transform technique. Numerical experiments have been carried out for a vessel of 19 190 t displacement under the action of a small amplitude sinusoidal wave of 11.2 s periodicity to obtain the roll response. This has been done in order to check the roll response computed numerically by developing a numerical model, SHIPMOT-R, where the Runge-Kutta-Gill method is adopted. A good agreement has been achieved between the time histories of roll motions computed numerically and derived analytically for zero and nonzero forward speeds. It is observed that the roll amplitude increases with the increase of vessel speed. This modelling technique would be very useful for ascertaining a vessel's safety requirements in the early stages of design.

エアクッション支持浮体の規則波中応答特性と喫水影響に関する基礎的研究

エアクッション支持浮体の規則波中応答特性と喫水影響に関する基礎的研究

Mathematical model for coupled roll and yaw motions of a floating body in regular waves under resonant and non-resonant conditions

The prediction of resonance is very important with respect to the vessels stability in the early stages of design. In this paper, an efficient modeling approach is presented to determine coupled roll and yaw motions of a symmetric and slender floating body when the influences of small amplitude regular waves are dominant. The angular motions described in time domain by considering all internal and external forces are transformed into frequency domain to obtain motion characteristics. We adopt a semi-analytical treatment to obtain roll and yaw motions and derive system instability due to roll resonance. To compute hydrodynamic forces, we employ strip theory method where frequency dependent sectional added-mass, damping and restoring coefficients are derived from the Frank’s close-fit curve. Numerical experiments carried out for a vessel of mass 19,190 ton under the action of wave of frequencies 0.56 and 0.76 rad/s with zero and non-zero initial conditions are reported and the effect of various parameters on system stability is investigated. Model results indicate that damping factor ( ς) plays a pivotal role when wave encountering frequency ( ω) and undamped natural frequency ( β) are nearly equal. The essence of this study lies in the efficient modeling technique to evaluate damping factor and critical encountering frequency regime for a given ship particulars when experimentally derived resonance zone is absent.

Motions Of Floating Bodies In Time HarmonicWaves

A numerical scheme based on the boundaryintegral equation method is developed to obtain the motion of floating bodies in time harmonic waves. It is assumed that the fluid is homogeneous, inviscid and incompressible, the flow is irrotational and the motionsare small. Theapproachhas been to formulatetheassociated problems with the motion of floating bodies in time harmonic waves as integral equations, modify the kernels of the integral equations to make them non-singular, discretize the integral equations using the Gaussian quadratureformula, solve the systems of linear complex algebraic equations for the velocity potentials and find the hydrodynamic characteristics regarding the motion of the body. The computations were performed on a hemisphere, two semi-spheroids, and a circular cylinder. The nondimensional parameters of each mode of motion of the floating bodies in regular waves were calculated and presented in graphical form.

Determination of coupled sway, roll, and yaw motions of a floating body in regular waves

This paper investigates the motion response of a floating body in time domain under the influence of small amplitude regular waves. The governing equations of motion describing the balance of wave‐exciting force with the inertial, damping, and restoring forces are transformed into frequency domain by applying Laplace transform technique. Assuming the floating body is initially at rest and the waves act perpendicular to the vessel of lateral symmetry, hydrodynamic coefficients were obtained in terms of integrated sectional added‐mass, damping, and restoring coefficients, derived from Frank′s close‐fit curve. A numerical experiment on a vessel of 19190 ton displaced mass was carried out for three different wave frequencies, namely, 0.56 rad/s, 0.74 rad/s, and 1.24 rad/s. The damping parameters (ςi) reveal the system stability criteria, derived from the quartic analysis, corresponding to the undamped frequencies (βi). It is observed that the sway and yaw motions become maximum for frequency 0.56 rad/s, whereas roll motion is maximum for frequency 0.74 rad/s. All three motions show harmonic behavior and attain dynamic equilibrium for time t > 100 seconds. The mathematical approach presented here will be useful to determine seaworthiness characteristics of any vessel when wave amplitudes are small and also to validate complex numerical models.

The Second-Order Diffraction Loads and Associated Motions of a Freely Floating Cylindrical Body in Regular Waves: An Eigenfunction Expansion Approach

A solution, exact to the second-order in wave steepness, is presented for the hydrodynamic loads and associated wave-induced motions of a freely floating circular cylindrical body in regular waves. Due to the circular cylindrical geometry considered, a computationally efficient eigenfunction expansion technique may be utilized to obtain the linearized solution. Furthermore, the present geometry allows the complex free-surface integral which appears in the second-order loading formulation to be integrated analytically in the angular coordinate. An accurate and efficient methods is developed to evaluate the remaining integral in the radial direction. In the near field this integral is evaluated numerically, while in the far field an analytical solution based upon the asymptotic forms of the linearized potential components is utilized. Numerical results are presented which illustrate the first- and second-order hydrodynamic loads on and associated wave-induced motions an several example cylindrical structures.As well as providing information on the second-order hydrodynamics of a freely floating cylindrical body, the present solution serves as an important, independent benchmark for the numerical solution for the second-order hydrodynamic loads and associated motions of arbitrary floating structures in waves currently under development at the University of Houston and elsewhere.

The slow-drift motion of arrays of vertical cylinders

The large-amplitude rectilinear ‘slow-drift’ oscillation of a floating body constrained by a weak restoring force in random waves is considered. The free-surface flow is approximated by a perturbation series expansion for a small slow-drift velocity and wave steepness. A model slow-drift equation of motion is derived, the time-dependent slow-drift excitation force and wave damping coefficient are defined and the complete series of free-surface problems governing their magnitude are formulated. The free-surface problem governing the wave-drift damping coefficient in monochromatic waves is studied and an explicit solution is obtained for a vertical circular cylinder of infinite draught. This solution is extended for arrays of vertical circular cylinders by employing an exact interaction theory. The wave-drift damping coefficient is evaluated for configurations of interest in practice and an expression is derived for the steady drifting velocity of an unconstrained body in regular waves.

The vertical drift force and pitch moment on axisymmetric bodies in regular waves

This paper deals with the evaluation of the second-order steady vertical force and pitching moment exerted by regular surface waves on floating or submerged vertical axisymmetric bodies in water of finite depth. Some new expressions valid for bodies of arbitrary shape are first obtained, based on momentum considerations. The derived relations are then implemented in the special case of vertical bodies of revolution, for which series representations of the required first-order diffraction and forced-oscillation velocity potentials can be established through matched eigenfunction expansions. Numerical results concerning the mean vertical drift force and pitch moment for various axisymmetric bodies are presented and compared with those of other authors and pertinent experimental data.