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Research Papers: CFD and VIV

Bilge-Keel Influence on Free Decay of Roll Motion of a Realistic Hull1

[+] Author and Article Information
Yichen Jiang

Department of Mechanical Engineering,
University of California at Berkeley,
Berkeley, CA 94720-1740
e-mail: ycjiang@berkeley.edu

Ronald W. Yeung

American Bureau of Shipping
Endowed Chair in Ocean Engineering,
Director,
Berkeley Marine Mechanics Laboratory (BMML),
Department of Mechanical Engineering,
University of California at Berkeley,
Berkeley, CA 94720-1740
e-mail: rwyeung@berkeley.edu

1Paper presented at the 2014 ASME 33rd International Conference on Ocean, Offshore, and Arctic Engineering (OMAE 2014), San Francisco, CA, June 8-13, 2014, Paper No. OMAE2014-24542. It is a pleasure and honor for the authors to contribute to the J. Randolph Paulling Symposium, held in his honor in OMAE-2014. R. W. Yeung is grateful to many years of Collegialship with “Randy”.

2Present address: School of Naval Architecture, Dalian University of Technology, Dalian 116024, China.

3Corresponding 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 December 1, 2015; final manuscript received March 15, 2017; published online May 15, 2017. Assoc. Editor: Robert Seah.

J. Offshore Mech. Arct. Eng 139(4), 041801 (May 15, 2017) (12 pages) Paper No: OMAE-15-1123; doi: 10.1115/1.4036326 History: Received December 01, 2015; Revised March 15, 2017

The prediction of roll motion of a ship with bilge keels is particularly difficult because of the nonlinear characteristics of the viscous roll damping. Flow separation and vortex shedding caused by bilge keels significantly affect the roll damping and hence the magnitude of the roll response. To predict the ship motion, the Slender-Ship Free-Surface Random-Vortex Method (SSFSRVM) was employed. It is a fast discrete-vortex free-surface viscous-flow solver developed to run on a standard desktop computer. It features a quasi-three-dimensional formulation that allows the decomposition of the three-dimensional ship-hull problem into a series of two-dimensional computational planes, in which the two-dimensional free-surface Navier–Stokes solver Free-Surface Random-Vortex Method (FSRVM) can be applied. In this paper, the effectiveness of SSFSRVM modeling is examined by comparing the time histories of free roll-decay motion resulting from simulations and from experimental measurements. Furthermore, the detailed two-dimensional vorticity distribution near a bilge keel obtained from the numerical model will also be compared with the existing experimental Digital Particle Image Velocimetry (DPIV) images. Next, we will report, based on the time-domain simulation of the coupled hull and fluid motion, how the roll-decay coefficients and the flow field are altered by the span of the bilge keels. Plots of vorticity contour and vorticity isosurface along the three-dimensional hull will be presented to reveal the motion of fluid particles and vortex filaments near the keels.

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Figures

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Fig. 1

Underwater geometry of the INSEAN C2340 model

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Fig. 2

Computational planes along the longitudinal axis χ

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Fig. 3

Coordinate systems: the earth-fixed coordinates O¯x¯y¯χ¯, the body-fixed coordinates Ôx̂ŷχ̂, and the steadily translating coordinates Oxyχ

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Fig. 4

Illustration of the translating coordinate system Oχxy and its sub-systems spaced evenly on the χ axis

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Fig. 5

FSRVM model in a two-dimensional computational plane

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Fig. 6

Relation between global motion of Ô and sectional motion of Ôi, with positive yaw and pitch angles shown

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Fig. 7

Time history of the roll motion: comparison between the experimental measurement and the SSFSRVM simulation for Fr=0.0

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Fig. 8

Comparisons of vorticity evolution at the hull section χ/L=0.504 between experiments and simulations (t = 0.51 to 1.53 s and U = 0): (a) Experimental measurements and (b) SSFSRVM simulations

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Fig. 9

Comparisons of vorticity evolution at the hull section χ/L=0.504 between experiments and simulations (t = 2.03 to 3.05 s and U = 0): (a) Experimental measurements and (b) SSFSRVM simulations

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Fig. 10

Vorticity contours and vorticity iso-surfaces along the hull (Fr = 0): (a) t= 1.09 s, (b) t= 1.71 s, (c) t= 1.95 s, and (d) t= 2.27 s

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Fig. 11

Time history of the free decay motion in 4DOFs with an initial roll angle of 15 deg, at Fr = 0, as simulated by SSFSRVM

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Fig. 12

Time history of the roll motion: comparison between the experimental measurement and the SSFSRVM predictions for Fr=0.138

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Fig. 13

Comparisons of vorticity evolution at the hull sectionχ/L=−0.175 between experiments and simulations (Fr = 0.138): (a) Experimental measurements and (b) SSFSRVM simulations

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Fig. 14

Illustration of bilge keel geometry of different spans

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Fig. 15

Illustration of the configurations of bilge keels at the midship section, where B denotes the full beam of the hull

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Fig. 16

Comparison of the time histories of the roll decay motion between hulls with different bilge keel configurations

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Fig. 17

Comparison of the time histories of the hydrodynamic normal force on the port-side bilge keel between hulls with different bilge keel configurations

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Fig. 18

Illustration of the definition of consecutive double amplitude

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Fig. 19

Comparison of the roll decay coefficients versus mean roll angles between hulls with different bilge keel spans

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Fig. 20

Comparison of vorticity distributions of the midship section between hulls with different bilge keel configurations in the seventh oscillation. Each column represents one bilge keel configuration: (a) t = 15.47 s, (b) t = 15.73 s, (c) t = 15.98 s, and (d) t = 16.23 s.

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Fig. 21

Comparison of the time histories of the roll response in waves between hulls with different bilge keel configurations

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Fig. 22

Comparison of the time history of the roll motion between models with different boundary element sizes

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Fig. 23

Solution changes between the coarse/medium elements and the medium/fine elements

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Fig. 24

Comparison of the time history of the roll motion between different time step models

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