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Research Papers: Ocean Engineering

Amplitude Induced Nonlinearity in Piston Mode Resonant Flow: A Fully Viscous Numerical Analysis

[+] Author and Article Information
Luca Bonfiglio

Department of Mechanical Engineering,
MIT-Sea Grant College,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: bonfi@mit.edu

Stefano Brizzolara

Kevin T. Crofton Department of Aerospace and
Ocean Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: stebriz@vt.edu

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received April 8, 2016; final manuscript received July 13, 2017; published online September 29, 2017. Assoc. Editor: Muk Chen Ong.

J. Offshore Mech. Arct. Eng 140(1), 011101 (Sep 29, 2017) (11 pages) Paper No: OMAE-16-1038; doi: 10.1115/1.4037487 History: Received April 08, 2016; Revised July 13, 2017

Near field flow characteristics around catamarans close to resonant conditions involve violent viscous flow such as energetic vortex shedding and steep wave making. This paper presents a systematic and comprehensive numerical investigation of these phenomena at various oscillating frequencies and separation distances of twin sections. The numerical model is based on the solution of Navier–Stokes equations assuming laminar-flow conditions with a volume of fluid (VOF) approach which has proven to be particularly effective in predicting strongly nonlinear radiated waves which directly affect the magnitude of the hydrodynamic forces around resonant frequencies. Considered nonlinear effects include wave breaking, vortex shedding and wave-body wave-wave interactions. The method is first validated using available experiments on twin circular sections: the agreement in a very wide frequency range is improved over traditional linear potential flow based solutions. Particular attention is given to the prediction of added mass and damping coefficients at resonant conditions where linear potential flow methods fail, if empirical viscous corrections are not included. The results of the systematic investigation show for the first time how the so-called piston-mode motion characteristics are nonlinearly dependent on the gap width and motion amplitude. At low oscillation amplitudes, flow velocity reduces and so does the energy lost for viscous effects. On the other hand for higher oscillation amplitude, the internal free surface breaks dissipating energy hence reducing the piston mode amplitude. These effects cannot be numerically demonstrated without a computational technique able to capture free surface nonlinearity and viscous effects.

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Figures

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Fig. 1

Catamaran cross section and probes for wave elevation. The circular cross section center of each hull is placed at a distance b from the catamaran symmetry plane and is characterized by a radius a corresponding to the depth of the catamaran at rest. Dimensions indicated are expressed in meters.

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Fig. 2

Grid sensitivity study: coarsest-medium-finest meshes designed to be simulated at 6 rad/s. Three different mesh regions: structured around the free surface, body-fitted structured around the body and unstructured in the far field. Mesh size at cylinder wall d1=3e−4 m for M1 (coarse), d2=1e−4 m for M2 (medium) and d3=2e−5 m for M3 (fine).

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Fig. 3

Validation study: CFD results are presented through solid and dashed line for ξ=0.635 cm and ξ=1.27 cm, respectively. Dashed-dot line represents potential flow theory. Experiments have been represented through filled dots when stiffeners have been used during the experiments. (a) Nondimensional added mass coefficient: b=1.5a, (b) nondimensional damping coefficient: b=1.5a, (c) nondimensional added mass coefficient: b=2.0a, (d) nondimensional damping coefficient: b=2.0a, (e) nondimensional added mass coefficient: b=4.0a, and (f) nondimensional damping coefficient: b=4.0a.

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Fig. 4

Nondimensional vorticity contour for hull configuration b=1.5a at the piston mode frequency: (a) ξ=0.635 cm, (b) ξ=1.27 cm, (c) ξ=2.54 cm, and (d) ξ=3.81 cm

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Fig. 5

Nondimensional wave elevation at probes located at centerline y = 0 (A), y=b+2a (B), y=b+4a (C), and y=b+8a (D). Hull distance b=1.5a, heave amplitude ξ=0.635 cm, oscillation frequency ω=6.50 rad/s.

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Fig. 6

Nondimensional added mass, damping coefficients and inner wave amplitude (probeA). From left to right b=1.5a, b=2a and b=4a. From top to bottom ξ=0.635 cm, ξ=1.270 cm, ξ=2.540 cm and ξ=3.81 cm. Vertical lines correspond to undamped piston mode frequency resulting from Eq. (8) with λ = 1. Nondimensional added mass values are indicated on the left axis while nondimensional damping and inner wave amplitude values are indicated on the right axis.

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Fig. 7

Hydrodynamic coefficients resulting from a forced heave motion of amplitude ξ=1.27 cm. Symbols on the curves represent computed points: (a) nondimensional added mass coefficient and (b) nondimensional damping coefficient.

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Fig. 8

Nondimensional added mass (left axis), damping, inner (probe A) and outer wave amplitude (probe B, C, D) (right axis) for hull distance b=1.5a and motion amplitude ξ=1.27 cm. Damping experiences a relative minimum at nondimensional frequency of 0.903 corresponding to the trapping mode frequency presented in Fig. 9. (a) ω=6.25 rad/s : piston mode frequency, (b) ω=7.25 rad/s : zero damping frequency, and (c) wave elevation plot comparison (circles: piston mode frequency, crosses: zero damping frequency).

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Fig. 9

Volume of fluid contour and wave elevation plots for ω=6.25 rad/s and ω=7.25 rad/s. Hull distance b=1.5a and oscillation amplitude ξ=1.27 cm.

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Fig. 10

Free decay test of a column of water located at z = a (deck height) for an hull configuration b=1.5a: (a) inner wave elevation and (b) fast Fourier transform (FFT) of inner wave elevation

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Fig. 11

Nondimensional piston-mode frequency trend with respect to heave amplitude for three different gap widths

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Fig. 12

Nondimensional inner wave amplitude trend with respect to heave amplitude for three gap widths

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Fig. 13

Nondimensional inner wave amplitude trend with respect to gap width for four heave amplitudes

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