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 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 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.

Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

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.

Extreme Response of Very Large Floating Structure Considering Second-Order Hydroelastic Effects in Multidirectional Irregular Waves

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Xujun Chen ◽  
Torgeir Moan ◽  
Shixiao Fu
Keyword(s):  
Second Order ◽  
Irregular Waves ◽  
Bending Moments ◽  
Floating Structure ◽  
First Order ◽  
Fluid Forces ◽  
Principal Coordinates ◽  
Vertical Displacements ◽  
Exciting Forces ◽  
Nonlinear Fluid

Hydroelasticity theory, considering the second-order fluid forces induced by the coupling of first-order wave potentials, is introduced briefly in this paper. Based on the numerical results of second-order principal coordinates induced by the difference-frequency and sum-frequency fluid forces in multidirectional irregular waves, the bending moments, as well as the vertical displacements of a floating plate used as a numerical example are obtained in an efficient manner. As the phase angle components of the multidirectional waves are random variables, the principal coordinates, the vertical displacements, and the bending moments are all random variables. Extreme values of bending moments are predicted on the basis of the theory of stationary stochastic processes. The predicted linear and nonlinear results of bending moments show that the influences of nonlinear fluid forces are different not only for the different wave phase angles, but also for the different incident wave angles. In the example very large floating structure (VLFS) considered in this paper, the influence of nonlinear fluid force on the predicted extreme bending moment may be as large as 22% of the linear wave exciting forces. For an elastic body with large rigidity, the influence of nonlinear fluid force on the responses may be larger than the first-order exciting forces and should be considered in the hydroelastic analysis.

The complete second-order diffraction solution for an axisymmetric body Part 2. Bichromatic incident waves and body motions

1990 ◽  
Vol 211 ◽  
pp. 557-593 ◽  
Author(s):  
Moo-Hyun Kim ◽  
Dick K. P. Yue
Keyword(s):  
Transfer Functions ◽  
Integral Equation Method ◽  
Axisymmetric Body ◽  
Second Order ◽  
Difference Frequency ◽  
Irregular Waves ◽  
Total Load ◽  
Frequency Wave ◽  
Order Diffraction ◽  
Incident Waves

In Part 1 (Kim & Yue 1989), we considered the second-order diffraction of a plane monochromatic incident wave by an axisymmetric body. A ring-source integral equation method in conjunction with a novel analytic free-surface integration in the entire local-wave-free domain was developed. To generalize the second-order theory to irregular waves, say described by a continuous spectrum, we consider in this paper the general second-order wave–body interactions in the presence of bichromatic incident waves and the resulting sum- and difference-frequency problems. For completeness, we also include the radiation problem and second-order motions of freely floating or elastically moored bodies. As in Part 1, the second-order sum- and difference-frequency potentials are obtained explicitly, revealing a number of interesting local behaviours of the second-order pressure. For illustration, the quadratic transfer functions (QTF's) for the sum- and difference-frequency wave excitation and body response obtained from the present complete theory are compared to those of existing approximation methods for a number of simple geometries. It is found that contributions from the second-order potentials, typically neglected, can dominate the total load in many cases.

scholarly journals Low Frequency Excitation and Damping of Four MODUs in Severe Seastates With Current

2018 ◽  
Author(s):  
Nuno Fonseca ◽  
Carl Trygve Stansberg ◽  
Kjell Larsen ◽  
Rune Bjørkli ◽  
Tjerand Vigesdal ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Low Frequency ◽  
Irregular Waves ◽  
Experimental Program ◽  
Peak Period ◽  
Numerical Predictions ◽  
Analysis Technique ◽  
Wave Drift Forces ◽  
Drift Forces

Model tests have been performed with four mobile offshore drilling units (MODUs) with the aim of identifying wave drift forces and low frequency damping. The MODUs configuration is different, namely on the number and diameter of columns, therefore the sample is representative of many of the existing concepts. The model scale is the same as well as the wave and current conditions. The experimental program includes irregular waves with systematic variations of the significant wave height, wave peak period, current velocity and vessel heading. The test data is post-processed to identify the surge and sway quadratic transfer functions (QTFs) of the slowly varying excitation, together with the linearized low frequency damping. The post-processing applies a nonlinear data analysis technique known as “cross-bi-spectral analysis” to estimate characteristics of second-order (quadratic) responses from the measured motions and undisturbed incident wave elevation. The empirical QTFs are then compared with numerical predictions to conclude on the role of viscous drift and the applicability of Newman’s approximation for calculation of drift forces in irregular waves. Finally, the empirical drift forces, empirical low frequency damping coefficients and low frequency motions statistics are compared for the three MODUs to conclude on the relation between the Semi configuration and the low frequency responses.

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