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Journal ArticleDOI

Two-dimensional resonant piston-like sloshing in a moonpool

25 Mar 2007-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 575, pp 359-397
TL;DR: In this paper, the authors combined theoretical and experimental studies of the two-dimensional piston-like steady-state motions of a fluid in a moonpool formed by two rectangular hulls (e.g. a dual pontoon or catamaran).
Abstract: This paper presents combined theoretical and experimental studies of the two-dimensional piston-like steady-state motions of a fluid in a moonpool formed by two rectangular hulls (e.g. a dual pontoon or catamaran). Vertical harmonic excitation of the partly submerged structure in calm water is assumed. A high-precision analytically oriented linear-potential-flow method, which captures the singular behaviour of the velocity potential at the corner points of the rectangular structure, is developed. The linear steady-state results are compared with new experimental data and show generally satisfactory agreement. The influence of vortex shedding has been evaluated by using the local discrete-vortex method of Graham (1980). It was shown to be small. Thus, the discrepancy between the theory and experiment may be related to the free-surface nonlinearity.
Citations
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Book ChapterDOI
01 Jan 1991
Abstract: Part I. The Surface Vorticity Boundary Integral Method of Fluid Flow Analysis: 1. The basis of surface singularity modelling 2. Lifting bodies, two-dimensional aerofoils and cascades 3. Mixed-flow and radial cascades 4. Bodies of revolution, ducts and annuli 5. Ducted propellers and fans 6. Three-dimensional and meridional flows in turbo-machines 7. Free vorticity shear layers and inverse methods Part II. Vortex Dynamics and Vortex Cloud Analysis: 8. Vortex dynamics in inviscid flows 9. Simulation of viscous diffusion in discrete vortex modelling 10. Vortex cloud modelling by the boundary integral method 11. Further development and applications of vortex cloud modelling to lifting bodies and cascades 12. Use of grid systems in vortex dynamics and meridional flows Appendix.

218 citations

Journal ArticleDOI
TL;DR: In this article, the first and higher harmonic components of the resonant fluid response in the gap between two identical fixed rectangular boxes are experimentally investigated in a wave basin and it is shown that for an incident group with appropriate frequency content, the linear gap response may be substantially smaller than the second-harmonic component, which is strongly driven via quadratic coupling of the linear terms from the incident wave and occurs in gap resonant modes.
Abstract: The first- and higher-harmonic components of the resonant fluid response in the gap between two identical fixed rectangular boxes are experimentally investigated in a wave basin. Gap response is excited by transient wave groups (being based on scaled versions of the autocorrelation function of sea state spectra, representing NewWaves, the average shape of large waves in a sea state). Several different wave groups with different maximum surface elevations, spectral peak frequencies and bandwidths are used, while the bilge shape of the boxes and approach angle of the waves are also varied. Unlike a simple regular wave, it is complicated to separate the harmonic components for a transient wave group due to non-linear wave-wave and wave-structure interactions. A four-phase combination methodology is used to separate the first four harmonic components, and this also allows higher-harmonic components to be isolated with simple digital frequency filtering. Harmonic components up to 14th order in the incident wave amplitude have been extracted. It is shown that for an incident group with appropriate frequency content, the linear gap response may be substantially smaller than the second-harmonic component, which is strongly driven via quadratic coupling of the linear terms from the incident wave and occurs in the gap resonant modes. Double frequency excitation may have important practical implications for offshore operations. Fourth and zeroth (long wave) harmonics in the gap are further driven via quadratic coupling of the second-harmonic itself. Linear damping coefficients for the first few modes of the gap resonant response are derived from measured time series using a numerical fit and shown to be higher than those from linear diffraction calculations.

101 citations

Journal ArticleDOI
TL;DR: In this article, a numerical wavetank with a floating body based on a new domain-decomposition method is presented, which couples a Navier-Stokes solver (CFD) with potential theory.

84 citations

Journal ArticleDOI
TL;DR: In this article, the traditional potential flow theory to describe fully nonlinear waves is reformulated by separating the contributions from incident and scattered waves, in order to improve the computational efficiency.

76 citations

Journal ArticleDOI
TL;DR: In this paper, a fully nonlinear numerical wavetank based on Green's 2nd identity coupled with an inviscid vortex tracking method is applied to the moonpool problem, which is within the framework of potential theory.

71 citations

References
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Book
01 Jan 1947
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Abstract: Partial table of contents: THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS. Transformation to Principal Axes of Quadratic and Hermitian Forms. Minimum-Maximum Property of Eigenvalues. SERIES EXPANSION OF ARBITRARY FUNCTIONS. Orthogonal Systems of Functions. Measure of Independence and Dimension Number. Fourier Series. Legendre Polynomials. LINEAR INTEGRAL EQUATIONS. The Expansion Theorem and Its Applications. Neumann Series and the Reciprocal Kernel. The Fredholm Formulas. THE CALCULUS OF VARIATIONS. Direct Solutions. The Euler Equations. VIBRATION AND EIGENVALUE PROBLEMS. Systems of a Finite Number of Degrees of Freedom. The Vibrating String. The Vibrating Membrane. Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS. Completeness and Expansion Theorems. Nodes of Eigenfunctions. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS. Bessel Functions. Asymptotic Expansions. Additional Bibliography. Index.

7,426 citations

Book
01 Apr 1985
TL;DR: Second-order boundary value problems in polygons have been studied in this article for convex domains, where the second order boundary value problem can be solved in the Sobolev spaces of Holder functions.
Abstract: Foreword Preface 1. Sobolev spaces 2. Regular second-order elliptic boundary value problems 3. Second-order elliptic boundary value problems in convex domains 4. Second-order boundary value problems in polygons 5. More singular solutions 6. Results in spaces of Holder functions 7. A model fourth-order problem 8. Miscellaneous Bibliography Index.

5,248 citations


"Two-dimensional resonant piston-lik..." refers background in this paper

  • ...Conclusions on the asymptotic behaviour of the velocity potential ψ at the corner points may also be found in the book by Grisvard (1985)....

    [...]

  • ...Conclusions on the asymptotic behaviour of the velocity potential ψ at the corner points may also be found in the book by Grisvard (1985). By conducting direct analytical derivations, or by noting that summands in (3....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Abstract: Partial table of contents: THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS. Transformation to Principal Axes of Quadratic and Hermitian Forms. Minimum-Maximum Property of Eigenvalues. SERIES EXPANSION OF ARBITRARY FUNCTIONS. Orthogonal Systems of Functions. Measure of Independence and Dimension Number. Fourier Series. Legendre Polynomials. LINEAR INTEGRAL EQUATIONS. The Expansion Theorem and Its Applications. Neumann Series and the Reciprocal Kernel. The Fredholm Formulas. THE CALCULUS OF VARIATIONS. Direct Solutions. The Euler Equations. VIBRATION AND EIGENVALUE PROBLEMS. Systems of a Finite Number of Degrees of Freedom. The Vibrating String. The Vibrating Membrane. Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS. Completeness and Expansion Theorems. Nodes of Eigenfunctions. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS. Bessel Functions. Asymptotic Expansions. Additional Bibliography. Index.

4,525 citations

Book
25 Oct 1990
TL;DR: In this paper, linear-wave induced motions and loads on floating structures were modeled as Second-order nonlinear problems. But the authors did not consider the effects of the wind and current on the floating structures.
Abstract: 1. Introduction 2. Sea environment 3. Linear-wave induced motions and loads on floating structures 4. Numerical methods for linear-wave induced motions and loads 5. Second-order non-linear problems 6. Current and wind loads 7. Viscous wave loads and damping 8. Stationkeeping 9. Water impact and entry References Index.

1,976 citations


Additional excerpts

  • ...Energy-conservation rule and asymptotic behaviour as Λ → 0 According to Newman (1977) and Faltinsen (1990), the time derivative of the total dimensional energy of the entire moonpool can be written for our Oz-symmetric flows as dE dt̄ = 2 ∫ S̄B (p̄ − p̄0) ( −∂ψ̄ ∂z̄ ) dx̄ − 2ρ ∫ S̄−∞ ∂ψ̄ ∂t̄ ∂ψ̄…...

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Book
01 Jan 1981

1,210 citations


"Two-dimensional resonant piston-lik..." refers background in this paper

  • ...Comprehensive reviews of the literature may be found in Graham (1980) and Downie et al. (1988) as well as in the books by Lewis (1991) and Sarpkaya & Isaacson (1981)....

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