Second order diffraction forces on a ship in irregular waves

1987 ◽  
Vol 9 (2) ◽  
pp. 96-103 ◽  
Author(s):  
A. Benschop ◽  
A.J. Hermans ◽  
R.H.M. Huijsmans
Keyword(s):  
Second Order ◽  
Irregular Waves ◽  
Order Diffraction

Second-Order Difference-Frequency Loads on FPSOs by Full QTF and Relevant Approximations

2020 ◽  
Author(s):  
Espen Engebretsen ◽  
Zhiyuan Pan ◽  
Nuno Fonseca
Keyword(s):  
Near Field ◽  
Time Domain Analysis ◽  
Second Order ◽  
Difference Frequency ◽  
Irregular Waves ◽  
Mooring Line ◽  
Diffraction Radiation ◽  
Surface Integral ◽  
Order Difference ◽  
Order Diffraction

Abstract This paper investigates three different approximations of the full Quadratic Transfer Function (QTF) for calculating horizontal plane second-order difference-frequency loads on FPSOs, namely Newman’s approximation, full QTF without free surface integral and the white-noise approximation. Second-order excitation loads obtained from approximated QTFs are compared in frequency-domain with those obtained by the full QTFs computed from second-order diffraction/radiation analysis in WADAM. The comparison is performed for a new-build FPSO in a range of water depths and environmental combinations. The full QTFs from second-order diffraction/radiation analysis are further compared to empirical QTFs as identified from cross bi-spectral analysis of model test results in irregular waves. A mesh convergence study is presented for calculating full QTFs by the near-field approach in a second-order diffraction/radiation analysis. The importance of including viscous damping in heave, roll and pitch is illustrated for the mean wave-drift force in surge and sway. FPSO motions and mooring line tensions from fully-coupled time-domain analysis in OrcaFlex is compared when using approximated QTFs and full QTFs from second-order diffraction/radiation 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.

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.

Nonlinear Wave Disturbance Around a Vertical Circular Column

2002 ◽  
Author(s):  
C. T. Stansberg ◽  
H. Braaten
Keyword(s):  
Linear Prediction ◽  
Harmonic Component ◽  
Nonlinear Effects ◽  
Second Order ◽  
Wave Disturbance ◽  
Difference Frequency ◽  
Irregular Waves ◽  
Order Effects ◽  
Sum Frequency ◽  
Circular Column

The wave disturbance close to vertical columns is analysed. In particular, the deviations from linear predictions are investigated, by experimental as well as by numerical methods. Thus a second-order numerical diffraction model is established by means of a diffraction analysis code (WAMIT) and compared to model tests with a single, fixed column with diameter 16m. Tests in regular, bi-chromatic as well as irregular waves are run. Significant nonlinear effects are observed, especially in steep waves, with the maximum elevation in front of the column increasing from 11.5m in a linear prediction to around 19m, in a 12s regular wave with 22m wave height. The main nonlinear effects in front of the column are identified as second-order sum-frequency and difference-frequency terms, plus a significant nonlinear increase in the first harmonic component. The WAMIT prediction of the second-order effects agrees fairly well with the measurements, although with some overprediction and underprediction, respectively, of the sum-frequency and difference-frequency (LF and mean set-up) terms in the steepest waves. For the underprediction of the first harmonic, however, a theory beyond second order is required.

Influence of Multidirectional Irregular Wave Sampling to Second-Order Hydroelastic Responses of VLFS

2009 ◽  
Author(s):  
Xujun Chen ◽  
Torgeir Moan ◽  
Xuefeng Tang
Keyword(s):  
Computer Time ◽  
Second Order ◽  
Irregular Waves ◽  
Floating Structure ◽  
First Order ◽  
Fluid Forces ◽  
Irregular Wave ◽  
Very Large Floating Structure ◽  
Principal Coordinates ◽  
Hydroelastic Response

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 this theory, four types of multidirectional irregular wave samplings are introduced, the frequency steps Δω of the four samplings are 0.04, 0.04, 0.02 and 0.01 rad/s, and the corresponding numbers of wave components N are 17, 75, 147 and 285 respectively. The result of principal coordinates and displacements of a very large floating structure (VLFS) for the four types of sampling are presented and discussed. The influence of the sampling is analyzed. The conclusions show that the sampling of the multidirectional irregular waves influence the second-order hydroelastic response of the VLFS. The accuracy and the computer time of the calculating with sampling of frequency step Δω = 0.02 rad/s are acceptable.

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