On the piston and sloshing modes in moonpools

doi:10.1017/S0022112000002871

Home
/
Papers
/
On the piston and sloshing modes in moonpools

Journal Article•DOI•

On the piston and sloshing modes in moonpools

Bernard Molin¹•Institutions (1)

École Normale Supérieure¹

10 Mar 2001-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 430, Iss: 1, pp 27-50

TL;DR: In this article, the authors considered rectangular moonpools of large horizontal dimensions and determined the natural modes of oscillation of the inner free surfaces under the assumption of infinite water depth and infinite length and beam of the barges that contain the moonpool.

read less

Abstract: So-called ‘moonpools’ are vertical openings through the deck and hull of ships or barges, used for marine and offshore operations, such as pipe laying or recovery of divers. In the present study rectangular moonpools of large horizontal dimensions are considered. The natural modes of oscillation of the inner free surfaces are determined, under the assumption of infinite water depth and infinite length and beam of the barges that contain the moonpools. The problem is treated in two and three dimensions, via linearized potential flow theory. Results are given for the natural frequencies and the associated shapes of the free surface, for wide ranges of the geometric parameters. Simple quasi-analytical approximations are derived that yield the natural frequencies. The most striking result is that the natural frequencies of the longitudinal sloshing modes increase without bounds when both the draught and the width decrease to zero, the length of the moonpool being kept constant. As a corollary the problem of waves travelling in a channel through a rigid ice sheet is addressed and their dispersion equation is derived. The same behaviour is obtained: the waves travel increasingly faster as both the draught and the width of the channel are reduced.

...read moreread less

Citations

PDF

Open Access

More filters

Book•

Liquid Sloshing Dynamics

[...]

Raouf A. Ibrahim¹•Institutions (1)

Wayne State University¹

19 May 2005

TL;DR: In this article, the authors present a detailed review of liquid sloshing dynamics in rigid containers, including linear forced and non-linear interaction under external and parametric excitations.

...read moreread less

Abstract: Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

...read moreread less

920 citations

Journal Article•DOI•

Two-dimensional resonant piston-like sloshing in a moonpool

[...]

Odd M. Faltinsen¹, Olav F. Rognebakke¹, Alexander Timokha¹•Institutions (1)

Norwegian University of Science and Technology¹

25 Mar 2007-Journal of Fluid Mechanics

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).

...read moreread less

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.

...read moreread less

142 citations

Cites background or methods from "On the piston and sloshing modes in..."

...Thinking in terms of the lowest l and i and using estimates of the resonant sloshing frequencies by Molin (2001), we find that lσ/σi ≈ √ l/2i for Λ∗ in case 3....
[...]
...Treating this problem within the framework of the linearized theory of water waves (Molin 2001; McIver 2005; Kuznetsov, Maz’ya & Vainberg 2002), the fluid motions inside the moonpool demonstrate a resonance....
[...]
...In addition, the figure includes the predictions by Molin (2001), which can be written as Λ∗ = ( d + 1 π ( 3 2 + ln b∗ 2 ))−1 , (4.12) where b∗ b corresponds to the position of an artificial sink or source used in Molin’s method (in both graphs, we have simply assumed that b∗ = b; see figure 1 b)....
[...]
...A quasi-analytical approximation of the resonant frequencies and corresponding modes for a rectangular moonpool in a two-dimensional barge was analysed by Molin (2001) in a simple and ingenious way....
[...]
...To mimic the effect of the outer free surface, Molin (2001) located two sinks symmetrically on the horizontal axis (at keel level), at distances ±b∗/2 from the barge centre (b∗ is somewhat larger than the beam of the barge; speculative manipulations with these distances were described by Maisondieu…...
[...]

Journal Article•DOI•

First- and second-order analysis of resonant waves between adjacent barges

[...]

Liang Sun¹, R. Eatock Taylor¹, Paul H. Taylor¹•Institutions (1)

University of Oxford¹

01 Aug 2010-Journal of Fluids and Structures

TL;DR: Water wave diffraction by two parallel closely spaced rectangular barges is investigated in this article, to characterise the general problem of LNG offloading from a floating plant into a shuttle tanker.

...read moreread less

107 citations

Cites background or methods from "On the piston and sloshing modes in..."

...B nm L B nnmm BL L mn mn dxdyygxf ydydxdxdygygxfxf R J (6) The above analysis is equivalent to that developed by Molin (2001) and applied to closed moonpool resonances....
[...]
...As pointed out by Molin (2001), it is easy to see that the velocity potential, , in the half space is...
[...]
...(2002), which itself is based on his earlier moonpool analysis (Molin 2001)....
[...]
...In the general case of arbitrary m and n, Molin shows that the quadruple integral in Eq. (6) may be reduced to a double integral. In the special case n = 0 he uses the residue theorem to obtain a simple single integral. For the gap problem, Molin et al. (2002) show that 0 n J can be written as:...
[...]
...This is based on some theory given by Molin et al. (2002), which itself is based on his earlier moonpool analysis (Molin 2001)....
[...]

Journal Article•DOI•

Gap resonance and higher harmonics driven by focused transient wave groups

[...]

Wenhua Zhao, Hugh Wolgamot, R. Eatock Taylor¹, Paul H. Taylor¹•Institutions (1)

University of Oxford¹

10 Feb 2017-Journal of Fluid Mechanics

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.

...read moreread less

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.

...read moreread less

101 citations

Cites background or methods from "On the piston and sloshing modes in..."

...To approximately predict the natural frequencies of the gap resonant modes, Molin (2001b) and Molin et al. (2002) extended the approach for the moonpool problem by modifying the boundary conditions at the ends....
[...]
...As suggested by Molin (2001a), it is worthwhile to check the WG data independently, particularly for the zeroth harmonic (difference frequency)....
[...]
...Gap resonance problems share some features with moonpool resonances, for which Molin (2001b) derived an analytical formula to estimate the natural frequencies and associated modal shapes of the resonant modes based on linear potential flow theory....
[...]
...(The depth variation is shown in figure 34(b), and is similar to that given by the analysis of Molin (2001b), although modified due to the presence of the rounded bilge.)...
[...]
...Without performing dedicated model tests, Faltinsen & Timokha (2015) estimated the damping coefficient for sharp cornered boxes by combining the approximation of Molin (2001b) and the pressure drop coefficient formula for a slatted screen....
[...]

Journal Article•DOI•

Gap resonance analyzed by a new domain-decomposition method combining potential and viscous flow DRAFT

[...]

Trygve Kristiansen¹, Odd M. Faltinsen¹•Institutions (1)

Norwegian University of Science and Technology¹

01 Jan 2012-Applied Ocean Research

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.

...read moreread less

84 citations

1
2
3
4
…
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54

Collapse

References

PDF

Open Access

More filters

Journal Article•DOI•

On the eigenvalue problem for fluid sloshing in a half-space

[...]

John W. Miles¹•Institutions (1)

University of California, San Diego¹

01 Nov 1972-Zeitschrift für Angewandte Mathematik und Physik

TL;DR: In this paper, the boundary value problem for free oscillations of a liquid in a half-space, which is bounded above by a rigid plane that contains a circular aperture, is transformed to a homogeneous, Fredholm integral equation for the velocity distribution in the aperture.

...read moreread less

Abstract: The boundary-value problem for free oscillations of a liquid in a half-space, which is bounded above by a rigid plane that contains a circular aperture, is transformed to a homogeneous, Fredholm integral equation for the velocity distribution in the aperture. Rayleigh-Ritz approximations to the eigenvalues are obtained by expanding the velocity distribution in appropriately weighted Jacobi polynomials. Numerical results demonstrate that the convergence of the approximations is much stronger than that of the approximations developed by Henrici, Troesch and Wuytack; for example, retaining twelve terms in the Rayleigh-Ritz expansion yields the dominant eigenvalue within one part in 10−8. A corresponding development is given for the two-dimensional problem, in which the aperture is an infinite strip.

...read moreread less

37 citations

"On the piston and sloshing modes in..." refers background or result in this paper

...For h = 0 Miles (1972) obtains 2.006119....
[...]
...We take a very shallow draught case h/b = 0.0001, so we expect to get results in close agreement with the ones given by Miles (1972), who treats the zero draught case....
[...]
...It is also a problem for which there is abundant literature in the zero draught limit (Henrici, Troesch & Wuytack 1970; Miles 1972; Troesch & Troesch 1972; Troesch 1973; see also Fox & Kuttler 1983)....
[...]

Journal Article•DOI•

Sloshing frequencies for a half-space with circular or strip-like aperture

[...]

Peter Henrici¹, B. Andrew Troesch², Luc Wuytack³•Institutions (3)

ETH Zurich¹, University of Southern California², Katholieke Universiteit Leuven³

01 May 1970-Zeitschrift für Angewandte Mathematik und Physik

TL;DR: In der vorliegenden Arbeit werden Naherungswerte (mit stengen Fehlerschranken) hergeleitet fur die Eigenfrequenzen der Schlingerbewegungen einer einen Halbraum with kreis- or streifenformiger Offnung aus fullenden idealen Flussigkeit as mentioned in this paper.

...read moreread less

Abstract: In der vorliegenden Arbeit werden Naherungswerte (mit stengen Fehlerschranken) hergeleitet fur die Eigenfrequenzen der Schlingerbewegungen einer einen Halbraum mit kreis- oder streifenformiger Offnung ausfullenden idealen Flussigkeit. Das mathematische Modell kann als Grenzfall des klassischen Modells fur endliche Behalter betrachtet werden. Wegen der bekannten Gebietsmonotonie der Eigenwerte sind die Werte fur den Halbraum universelle obere Schranken fur die entsprechenden Eigenwerte beliebiger beschrankter oder unbeschrankter Behalter mit gleichartigen Offnungen.

...read moreread less

35 citations

Journal Article•DOI•

A remark on the sloshing frequencies for a half-space

[...]

B. Andreas Troesch¹, R. Troesch²•Institutions (2)

University of Southern California¹, University of Michigan²

01 Jul 1972-Zeitschrift für Angewandte Mathematik und Physik

TL;DR: In this article, the known sloshing frequencies of an incompressible and inviscid fluid in a half-space with circular or strip-like aperture are investigated in some detail, based on previous results.

...read moreread less

Abstract: The known sloshing frequencies of an incompressible and inviscid fluid in a half-space with circular or strip-like aperture are investigated in some detail, based on previous results [4]. The first two terms in the asymptotic expansion for large eigenvalues are determined and a conjecture is enunciated for the general structure of the next term. The asymptotic results are listed in Table 1 and compared with the known frequencies.

...read moreread less

27 citations

"On the piston and sloshing modes in..." refers background in this paper

...It is also a problem for which there is abundant literature in the zero draught limit (Henrici, Troesch & Wuytack 1970; Miles 1972; Troesch & Troesch 1972; Troesch 1973; see also Fox & Kuttler 1983)....
[...]

Journal Article•DOI•

Resonance interactions of waves in an ice channel

[...]

Aleksey Marchenko

01 Jan 1997-Journal of Applied Mathematics and Mechanics

TL;DR: In this paper, it is shown that an ice channel is a waveguide for surface waves and the dispersive properties of the natural oscillations of the liquid in the channel are investigated.

...read moreread less

11 citations

"On the piston and sloshing modes in..." refers background in this paper

...It looks as though this problem had never been studied before in infinite water-depth (there is some literature for shallow water, e.g. see Marchenko 1997)....
[...]

Journal Article•DOI•

Sloshing frequencies in a half-space by Kelvin inversion.

[...]

B. Andreas Troesch

01 Aug 1973-Pacific Journal of Mathematics

9 citations

"On the piston and sloshing modes in..." refers background in this paper

...It is also a problem for which there is abundant literature in the zero draught limit (Henrici, Troesch & Wuytack 1970; Miles 1972; Troesch & Troesch 1972; Troesch 1973; see also Fox & Kuttler 1983)....
[...]