Experimental and Numerical Study of the Depth Effect on the First Order and Slowly Varying Motions of a Floating Body in Bichromatic Waves

2010 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Numerical Study ◽  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Harmonic Waves ◽  
Depth Effect ◽  
Drift Motion ◽  
First Order

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and bi-harmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in bi-harmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

Experimental Investigation of the First and Second Order Wave Exciting Forces on a Restrained Body in Long Crested Irregular Waves

2011 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
Suresh Rajendran ◽  
C. Guedes Soares
Keyword(s):  
Experimental Investigation ◽  
Transfer Functions ◽  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Irregular Waves ◽  
Numerical Predictions ◽  
Exciting Forces ◽  
Wave Exciting Forces

The paper presents an experimental investigation of the first order and second order wave exciting forces acting on a body of simple geometry subjected to long crested irregular waves. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is restrained from moving. Second order spectral analysis is applied to obtain the linear spectra, coherence spectra and cross bi-spectra of both the incident wave elevation and of the horizontal and vertical wave exciting forces. Then the linear and quadratic transfer functions (QTF) of the exciting forces are obtained. The QTF obtained from the analysis of irregular wave measurements are compared with results from experiments in bi-chromatic waves and with numerical predictions from a second order potential flow code.

Analysis on the Performance of Deckwetness of Sandglass-type and Cylindrical Floating Bodies

2016 ◽  
Vol 60 (03) ◽  
pp. 145-155
Author(s):  
Ya-zhen Du ◽  
Wen-hua Wang ◽  
Lin-lin Wang ◽  
Yu-xin Yao ◽  
Hao Gao ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Linear Response Theory ◽  
Second Order ◽  
Irregular Waves ◽  
Wave Loads ◽  
Floating Bodies ◽  
Drift Motion ◽  
First Order ◽  
Series Of Experiments ◽  
Deck Wetness

In this paper, the influence of the second-order slowly varying loads on the estimation of deck wetness is studied. A series of experiments related to classic cylindrical and new sandglass-type Floating Production, Storage, and Offloading Unit (FPSO) models are conducted. Due to the distinctive configuration design, the sand glass type FPSO model exhibits more excellent deck wetness performance than the cylindrical one in irregular waves. Based on wave potential theory, the first-order wave loads and the full quadratic transfer functions of second-order slowly varying loads are obtained by the frequency-domain numerical boundary element method. On this basis, the traditional spectral analysis only accounting for the first-order wave loads and time-domain numerical simulation considering both the first-order wave loads and nonlinear second-order slowly varying wave loads are employed to predict the numbers of occurrence of deck wetness per hour of the two floating models, respectively. By comparing the results of the two methods with experimental data, the shortcomings of traditional method based on linear response theory emerge and it is of great significance to consider the second-order slowly drift motion response in the analysis of deck wetness of the new sandglass-type FPSO.

ORIENTATION OF SYMMETRIC BODIES FALLING IN A SECOND-ORDER LIQUID AT NONZERO REYNOLDS NUMBER

2002 ◽  
Vol 12 (11) ◽  
pp. 1653-1690 ◽  
Author(s):  
GIOVANNI P. GALDI ◽  
ASHWIN VAIDYA ◽  
MILAN POKORNÝ ◽  
DANIEL D. JOSEPH ◽  
JIMMY FENG
Keyword(s):  
Prolate Spheroid ◽  
Critical Value ◽  
Second Order ◽  
The Body ◽  
Body Of Revolution ◽  
Translational Velocity ◽  
Homogeneous Body ◽  
First Order ◽  
The Stability ◽  
Elasticity Number

We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value E c for the elasticity number E = We/Re , where E c depends only on the geometric properties of the body, such as size or shape, and on the quantity (Ψ1 + Ψ2)/Ψ1, where Ψ1 and Ψ2 are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

Second Order Difference Frequency Wave-Current Loading Using Kelvin-Newman Approximation

2020 ◽  
Author(s):  
Farid P. Bakti ◽  
Moo-Hyun Kim
Keyword(s):  
Second Order ◽  
The Body ◽  
Difference Frequency ◽  
Computational Time ◽  
Forward Speed ◽  
Frequency Wave ◽  
Order Difference ◽  
First Order ◽  
Current Interaction ◽  
Current Loading

Abstract Kelvin & Newman introduced a linearization method to include the current (or forward speed) effect into the diffraction & radiation wave field for large-slender floating bodies. The K-N method assumes a steady far-field current while disregarding the steady potential field due to the presence of the body. The method is proven to be reliable when the Froude number is relatively small, the body shape is relatively slender (∂∂x≪∂∂y,∂∂z), and the sea condition is mild. This requirement is fulfilled for typical FPSOs and ship-shaped vessels in a typical current (or forward speed) condition. Several studies suggested that the presence of the current might change the first order hydrodynamic coefficients such as the first order diffraction force, added mass, and radiation damping. Currents also contributed to a change in the second-order slowly-varying drift force. However, the effect of current in the second-order difference-frequency force is yet to be investigated. By expanding the Kelvin-Newman approximation up to the second order, and solving the problem in the frequency domain, we can save computational time while expanding the accuracy of the scheme. The second order quadratic force is the main focus of this study, since it is the main contributor to the total second order difference frequency forces especially near the diagonal. By implementing the Kelvin-Newman wave current interaction approach up to the wave’s second order, we can assess the performance of the Kelvin-Newman wave current interaction formulation in various sea conditions.

Numerical Study of the Influence of Waving Bottom on the Fluid Surface Wave

2013 ◽  
Vol 275-277 ◽  
pp. 442-445
Author(s):  
Zheng Ren Wu ◽  
Chong Yuan Mo ◽  
Yong Xin Zhu
Keyword(s):  
Surface Wave ◽  
Multiple Scales ◽  
Numerical Study ◽  
Order Approximation ◽  
Approximate Equation ◽  
Second Order ◽  
First Order ◽  
Fluid Surface ◽  
Basic Equations ◽  
Multiple Scales Perturbation Method

The effect of waving bottom on the fluid surface wave was investigated. Starting from the basic equations of potential flow theory and boundary conditions, we used the multiple scales perturbation method to deduce fluid surface waves satisfy the first-order approximate equation and second-order approximate equation. Under the second-order approximation, the fluid surface waveform was simulated with the Matlab in the presence of different waving bottom form. The results show that there are three solitary waves on the surface of the fluid. With the development of time, the amplitude of each solitary wave has not changed. It seems that they are not affected each other and propagate independently. So it suggests that the waving bottom is effective for maintaining surface wave energy balance income and expenditure in spreading process.

Second Order Wave Loads on TLP-TAD Multi-Body System

2017 ◽  
Author(s):  
Miguel A. M. Ramirez ◽  
Antonio Carlos Fernandes
Keyword(s):  
Wave Amplitude ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Direct Method ◽  
Second Order ◽  
Order Effects ◽  
Wave Loads ◽  
Body System ◽  
First Order ◽  
Multi Body

The motions of floating moored structures are affected by first order wave loads which are proportional to the wave amplitude and associated with the wave frequency. On the other hand, second order wave loads are proportional to the square of the wave amplitude and related to the sum or difference of a pair of frequencies of the irregular sea. Although the second order loads are usually smaller compared to the first order loads, these loads can excite resonance motions in frequencies that the system has very low damping. Therefore, second order wave loads have particular importance in the design of mooring systems. The multi-body system composed by Tension Leg Platform (TLP) and Tender Assisted Drilling (TAD) is particularly susceptible to the second order effects, due to the very low natural frequencies of their horizontal modes and the very high natural frequencies of the vertical modes of the TLP. This work presents a numerical study of second order wave loads on the TLP-TAD multi-body system. An extensive hydrodynamic analysis focus on the hydrodynamic interactions between the floaters and how these effects modify the second order loads on the platforms was performed. The second order quadratic transform functions (QTFs) were evaluated using the indirect and the direct method. Moreover, the importance of the free surface integral was checked. Finally, the accuracy of Newman approximation for the low-frequency QTF was evaluated.

Second-order horizontal steady forces and moment on a floating body with small forward speed

1996 ◽  
Vol 313 ◽  
pp. 39-54 ◽  
Author(s):  
J. A. P. Aranha
Keyword(s):  
Three Dimensional ◽  
Vertical Axis ◽  
Second Order ◽  
Floating Body ◽  
Forward Speed ◽  
Damping Matrix ◽  
Wave Drift ◽  
Wave Drift Damping ◽  
Yaw Moment ◽  
Small Angular Velocity

In a recent work, a simple formula was derived for the ‘wave drift damping’ in a two-dimensional floating body and the obtained expression is exact within the context of the related theory, where only leading-order terms in the forward speed are retained. This formula is now generalized for a three-dimensional problem and the coefficients of the ‘wave drift damping matrix’ are given explicitly in terms of the standard second-order steady forces and moment in the horizontal plane; Munk's yaw moment, related with the steady second-order potential and discussed in Grue & Palm (1993), is not analysed in this paper and the effect of an eventual small angular velocity around the vertical axis is also not considered.Numerical results agree in general with the proposed formula although in a specific case a consistent disagreement has been observed, as discussed in §5.

Drift Motion of Floating Bodies Under the Action of Green Water

2021 ◽  
Author(s):  
Sasan Tavakoli ◽  
Luofeng Huang ◽  
Alexander V. Babanin
Keyword(s):  
Numerical Simulations ◽  
Water Waves ◽  
The Body ◽  
Green Water ◽  
Floating Body ◽  
Floating Bodies ◽  
Drift Motion ◽  
Upper Deck ◽  
Steep Waves ◽  
The Impact

Abstract Numerical simulations are peformed to model the dynamic motions of a free floating body exposed to water waves. The solid body has low freeboard and draft, and its upper deck can be washed by the steep waves. Thus, the green water phenomenon occurs as large waves interact with the floating body. The aim of the research is to improve the understanding of the green water emerging above the upper deck of a floating plate. A thin floating body with barriers is also modeled. For the case of the body equipped with barriers, no green water occurs. Green water has been seen to affect the wave field and the dynamic motions of the plate. It is observed that when water can wash the upper surface of the floating object, drift speed is slightly decreased as a proportion of the energy of waves is dissipated above the body. Water waves are seen to impact the upper surface of the thin floating body as the green water flows over its upper deck. Furthermore, water is seen to impact the plate as its front edge re-enters the water. The first water impact only occurs when the floating body is not equipped with any barrier. By sampling the numerical simulations, it is observed that the non-dimensional value of the impact pressure, resulting from the green water, is larger for the case of smaller wavelength.

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