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Research Papers: CFD and VIV

# Shape Effects on Viscous Damping and Motion of Heaving Cylinders1

[+] Author and Article Information
Ronald W. Yeung

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

Yichen Jiang

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

Normalized coefficients are defined by: $ω˜ = ωB/2g, X¯2 = X2/ρgB, μ¯22 = μ22/ρB2, λ¯22 = λ22B/2g/ρB2$.

1Paper presented at the 2011 ASME 30th International Conference on Ocean, Offshore, and Arctic Engineering (OMAE2011), Rotterdam, The Netherlands, June 19–25, 2011, Paper No. OMAE2011-50243. It is a pleasure and honor for the authors to contribute to the Jo Pinkster Symposium, held in his honor in OMAE-2011.

2Corresponding 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 May 12, 2011; final manuscript received May 3, 2014; published online July 29, 2014. Assoc. Editor: M. H. (Moo-Hyun) Kim.

J. Offshore Mech. Arct. Eng 136(4), 041801 (Jul 29, 2014) (9 pages) Paper No: OMAE-11-1042; doi: 10.1115/1.4027650 History: Received May 12, 2011; Revised May 03, 2014

## Abstract

Fluid viscosity is known to influence hydrodynamic forces on a floating body in motion, particularly when the motion amplitude is large and the body is of bluff shape. While traditionally these hydrodynamic force or force coefficients have been predicted by inviscid-fluid theory, much recent advances had taken place in the inclusion of viscous effects. Sophisticated Reynolds-Averaged Navier–Stokes (RANS) software are increasingly popular. However, they are often too elaborate for a systematic study of various parameters, geometry or frequency, where many runs with extensive data grid generation are needed. The Free-Surface Random-Vortex Method (FSRVM) developed at UC Berkeley in the early 2000 offers a middle-ground alternative, by which the viscous-fluid motion can be modeled by allowing vorticity generation be either turned on or turned off. The heavily validated FSRVM methodology is applied in this paper to examine how the draft-to-beam ratio and the shaping details of two-dimensional cylinders can alter the added inertia and viscous damping properties. A collection of four shapes is studied, varying from rectangles with sharp bilge corners to a reversed-curvature wedge shape. For these shapes, basic hydrodynamic properties are examined, with the effects of viscosity considered. With the use of these hydrodynamic coefficients, the motion response of the cylinders in waves is also investigated. The sources of viscous damping are clarified.

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## Figures

Fig. 1

Heaving cylinders of four different bottom shapes

Fig. 2

Definitions and computational domain D

Fig. 3

Comparison of hydrodynamic coefficients for four cylinders of different shapes, under two cases: D¯b=0.5. (a) Heave added-mass coefficient and (b) Heave damping coefficient.

Fig. 4

Comparison of hydrodynamic coefficients for four cylinders of different shapes, under two cases: D¯b=1.0. (a) Heave added-mass coefficient and (b) Heave damping coefficient.

Fig. 5

Hydrodynamic coefficients of base shape cylinders with three different drafts. (a) Base shape at y0 = 4 cm and (b) Base shape at y0 = 8 cm.

Fig. 6

Maximum heave force of base shape cylinders. (a) Base shape at y0 = 4 cm and (b) Base shape at y0 = 8 cm.

Fig. 7

Comparison of the time history of heave force for four cylinders of different bottom shapes, ω˜=0.6

Fig. 8

Comparison of the time history of heave force for four cylinders of different bottom shapes, ω˜=1.2

Fig. 9

Comparison of the maximum hydrodynamic heave forces on four cylinders with different shapes. (a) D¯b = 0.5 and (b) D¯b = 1.0.

Fig. 10

Visualization of vortex blobs at the case of D¯b=0.5 and ω˜=1.2, in the eighth period. The contour scale is based on a nondimensional vorticity defined by ζ/2g/B. (a) t /T = 7.25, (b) t /T = 7.50, (c) t /T = 7.75, and (d) t /T = 8.00.

Fig. 11

Heave RAO of four cylinders over a range of normalized frequency ω˜ . (a) D¯b = 0.5 and (b) D¯b = 1.0.

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