First and Second Order Wave-Current Interactions for Floating Bodies

2012 ◽  
Author(s):  
Charles Monroy ◽  
Yann Giorgiutti ◽  
Xiao-Bo Chen
Keyword(s):  
Field Method ◽  
Boundary Integral ◽  
Second Order ◽  
Boundary Integral Method ◽  
Diffraction Radiation ◽  
Floating Bodies ◽  
Order Problem ◽  
First Order ◽  
Wave Drift Damping ◽  
Order Quantities

The influence of current in sea-keeping problems is felt not only for first order quantities such as wave run-ups in front of the structure, but also mainly for second order quantities. In particular, the wave drift damping (which is expressed as the derivative of drift force with respect to the current) is of special interest for mooring systems. The interaction effects of a double-body steady flow on wave diffraction-radiation is studied through a decomposition of the time-harmonic potential into linear and interaction components. A boundary integral method is used to solve the first order problem. Ultimately, a far-field method is proposed to get access to second order drift forces.

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.

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.

Irregular Frequency Removal and Convergence in Higher-Order BEM for Wave Diffraction/Radiation Analysis

2019 ◽  
Author(s):  
Tomoaki Utsunomiya
Keyword(s):  
Free Surface ◽  
Wave Diffraction ◽  
Higher Order ◽  
The Body ◽  
Diffraction Radiation ◽  
First Order ◽  
Irregular Frequency ◽  
Intersection Line ◽  
Order Quantities ◽  
Drift Forces

Abstract Higher-order boundary element method (HOBEM) for wave diffraction/radiation analysis is a powerful tool for its applicability to a general (curved) geometry. Inspired by the paper which examined the convergence of BIE code with constant panels (Martic, et al., 2018; OMAE2018-77999), the convergence characteristics of HOBEM with quadrilateral panels have been examined. Here, the effect of removal of irregular frequencies is particularly focused as discussed by Martic, et al. (2018). The irregular frequency removal has been made by the rigid-lid method which is applicable to HOBEM, where the intersection line between the body-surface and the free-surface should be carefully handled. The results show that for first order quantities the convergence is quite good for both cases with/without irregular frequency removal (except where the irregular frequencies affect for the case without irregular frequency removal). For mean drift forces, the convergence becomes poor particularly for the case without irregular frequency removal. The convergence characteristics are examined and some discussions are made.

A Comparison of Different Approximations for Computation of Second Order Roll Motions for a FLNG

2013 ◽  
Author(s):  
Flavia C. Rezende ◽  
Allan C. de Oliveira ◽  
Xiao-bo Chen ◽  
Fabio Menezes
Keyword(s):  
Gas Production ◽  
Second Order ◽  
Plant Performance ◽  
Production Plant ◽  
Surface Boundary ◽  
Natural Period ◽  
Oil Companies ◽  
First Order ◽  
Exploration And Production ◽  
Order Quantities

The use of FLNG units for gas exploration and production offshore is a subject in study by some oil companies. More complex and sophisticated than a FPSO production plant, a gas production plant has strict motion criteria in order to have an optimal operational performance. Due to this, designers have been trying hull concepts with small initial stability and higher roll motion periods in order to reduce the unit motions and improve the plant performance. Indeed, the increase of roll natural period dramatically reduces the first order roll motions. However, the unit still responds at its resonance due to second order excitation. These kinds of loads are also more complex and require a great computational power to be evaluated. Due to its complexity, which would involve the solution of a non-homogeneous free surface boundary condition, some approximations are used in order to assess the second order loads and motions. In this paper, the different formulations for the first part of QTF, contributed by first order quantities, are revisited and the differences are highlighted. Furthermore the approximations for the computation of the second part of the QTF, contributed by the second order potential, are benchmarked for the case of a FLNG operating in deep water depth.

scholarly journals The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Alberto Cialdea ◽  
Vita Leonessa ◽  
Angelica Malaspina
Keyword(s):  
Dirichlet Problem ◽  
Differential Operators ◽  
Differential Forms ◽  
Variable Coefficients ◽  
Divergence Form ◽  
Boundary Integral ◽  
Second Order ◽  
Boundary Integral Method ◽  
Layer Potential ◽  
Partial Differential Operators

We investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains ofRm(m≥3) with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms.

Second-Order Diffraction Forces on an Array of Vertical Cylinders in Bichromatic Bidirectional Waves

1995 ◽  
Vol 117 (1) ◽  
pp. 12-18 ◽  
Author(s):  
J. H. Vazquez ◽  
A. N. Williams
Keyword(s):  
Cross Section ◽  
Finite Depth ◽  
Hydrodynamic Forces ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Order Problem ◽  
First Order ◽  
Wave Directionality ◽  
Vertical Cylinders ◽  
Green Function Approach

A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.

The Von Neumann-Mullins Theory of Grain Growth – Valid or Not?!

2004 ◽  
Vol 467-470 ◽  
pp. 1111-1116 ◽  
Author(s):  
Lasar S. Shvindlerman ◽  
Günter Gottstein ◽  
Anthony D. Rollett
Keyword(s):  
Relative Rate ◽  
Second Order ◽  
Rate Of Change ◽  
Recent Analysis ◽  
Order Problem ◽  
Von Neumann ◽  
First Order ◽  
Dimensional Network ◽  
The Stability ◽  
Grain Topology

We present a new analysis of the relative rate of growth or shrinkage of grains in a two-dimensional network, based on the classical Von Neumann-Mullins (VN-M) analysis. We find that an analysis of the stability of the grain shape during shrinkage or growth shows that any change in the regular 2D grain leads to changes in the shape. We also re-examine a recent analysis that claims to have invalidated the VN-M relationship, but find that it is still valid, and that the cited analysis, in fact, confused a second order correction with a first order problem, partly because their derivation was in error. The erroneous magnitude of the discrepancy led them to use unphysical issues to explain the discrepancy. The way in which the curvature is distributed along the perimeter of a grain only gives rise only to second order corrections to the rate of change of area as a function of grain topology (number of sides).

Performance Characteristics of a Tightly Moored Piston-Like Wave Energy Converter Under First- and Second-Order Wave Loads

2008 ◽  
Author(s):  
Spyros A. Mavrakos ◽  
George M. Katsaounis ◽  
Ioannis K. Chatjigeorgiou
Keyword(s):  
Wave Energy ◽  
Second Order ◽  
Wave Energy Converter ◽  
Performance Characteristics ◽  
Hydrodynamic Characteristics ◽  
Diffraction Radiation ◽  
Wave Loads ◽  
Energy Converter ◽  
Eigenfunction Expansions ◽  
First Order

The paper deals with the presentation of a model to predict performance characteristics of a tightly moored piston-like wave energy converter which is allowed to move in heave, pitch and sway modes of motion. The WEC’s piston-like arrangement consists of two floating concentric cylinders, the geometry of which allow the existence of a cylindrical moonpool between the external cylinder, the ‘torus’ and the inner cylinder, the ‘piston’. The first-order hydrodynamic characteristics of the floating device, i.e. exciting wave forces and hydrodynamic parameters, are evaluated using a linearized diffraction-radiation semi-analytical method of analysis that is suited for the type of bodies under consideration. According to the analysis method used, matched axisymmetric eigenfunction expansions of the velocity potentials in properly defined fluid regions around the body are introduced to solve the respective diffraction and radiation problems and to calculate the floats’ hydrodynamic characteristics in the frequency domain (Mavrakos et al. 2004, 2005). Based on these characteristics, the retardation forcing terms are calculated, which account for the memory effects of the motion. In this procedure, the coupling terms between the different modes of motion are properly formulated and taken into account (Cummins, 1962; Faltinsen, 1990). The floating WEC is connected to an underwater hydraulic cylinder that feeds a hydraulic system with pressurized oil. The performance of the system under the combined excitation of both first- and second order wave loads is here analyzed. To this end, the diffraction forces originated from the second order wave potentials are computed using a semi-analytical formulation which, by extension of the associated first-order solution, is based on matched axisymmetric eigenfunction expansions.

scholarly journals Second-order supercavitating hydrofoil theory

1962 ◽  
Vol 13 (3) ◽  
pp. 321-332 ◽  
Author(s):  
C. F. Chen
Keyword(s):  
Exact Solutions ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Lift Coefficient ◽  
Integral Form ◽  
Order Theory ◽  
Second Order ◽  
Order Problem ◽  
First Order ◽  
Lift And Drag

The second-order problem of Helmholtz flow past lifting hydrofoils and symmetric struts has been formulated and solved. The solution involves elementary operations on the known solutions of the first-order problem. The second-order lift and drag coefficients are given in integral form. Results obtained for a flat plate at incidence and a symmetric wedge agree with the exact solutions up to the second order. In terms of quantitative improvements, the present second-order theory predicts a lift coefficient for a flat plate at 45° incidence with an error of 8%, and a drag coefficient for a symmetric wedge of 50° included angle with an error of 5%; the corresponding angles at which the linear theory would predict force coefficients incurring the same errors are 5° and 15° respectively.

Study on 2nd-Order Wave Loads With Forward Speed Through Aranha’s Formula and Neumann-Kelvin Linearization

2020 ◽  
Author(s):  
Zhitian Xie ◽  
Jeffery Falzarano
Keyword(s):  
Current Velocity ◽  
Near Field ◽  
Field Method ◽  
Wave Loads ◽  
Forward Speed ◽  
Floating Bodies ◽  
Floating Structure ◽  
Sum Frequency ◽  
Wave Drift Damping ◽  
The Mean

Abstract The 2nd-order wave loads consist of difference frequency, sum frequency components and a steady drift component that is also called the mean drift load. The first two components are usually not of interest, because of their small amplitudes compared with the 1st-order wave loads. The remaining mean drift load should be taken into consideration due to its steady effect on floating bodies. In the previous research, the full derivation and expression of the 2nd-order wave loads applied to a floating structure was presented. Moreover, numerically estimated quadratic transfer function was also illustrated with both off-diagonal elements and diagonal elements called the mean drift coefficients. Most research topics in this scenario consider the wave only case. In this paper, the mean drift wave loads applied to a floating structure with forward speed or current velocity has been numerically estimated through Aranha’s formula, a far field method and Neumann-Kelvin linearization, a near field method. Therefore, the effect of the floating structure’s forward speed or current velocity on the 2nd-order mean drift loads that is also called the wave drift damping has been discussed through these two methods. This work will provide a meaningful reference and numerical basis for the ongoing projects of the floating structure’s seakeeping and maneuvering problems.

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