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TECHNICAL PAPERS

# Water Entry and Exit of a Horizontal Circular Cylinder

[+] Author and Article Information
Xinying Zhu

Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norwayxinying@ntnu.no

Odd M. Faltinsen

Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, Trondheim, NorwayOdd.Faltinsen@ntnu.no

Changhong Hu

Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japanhu@riam.kyushu-u.ac.jp

J. Offshore Mech. Arct. Eng 129(4), 253-264 (Dec 05, 2006) (12 pages) doi:10.1115/1.2199558 History: Received June 22, 2005; Revised December 05, 2006

## Abstract

In this paper we describe the fully nonlinear free-surface deformations of initially calm water caused by the water entry and water exit of a horizontal circular cylinder with both forced and free vertical motions. Two-dimensional flow conditions are assumed in the study. This has relevance for marine operations as well as for the ability to predict large amplitude motions of floating sea structures. A new numerical method called the CIP (Constrained Interpolation Profile) method is used to solve the problem. In this paper, the circular cylinder and free surface interaction is treated as a multiphase problem, which has liquid (water), gas (air), and solid (circular cylinder) phases. The flow is represented by one set of governing equations, which are solved numerically on a nonuniform, staggered Cartesian grid by a finite difference method. The free surface as well as the body boundary is immersed in the computational domain. The numerical results of the water entry and exit force, the free surface deformation and the vertical motion of the cylinder are compared with experimental results, and favorable agreement is obtained.

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## Figures

Figure 2

Averaged initial slamming coefficient Cs as a function of the nondimensional time step size dt∕T. Here Cs (0−0.02) denotes the slamming coefficient averaged from Vt∕R=0 to 0.02; Cs (0–0.03) is the slamming coefficient averaged from Vt∕R=0 to 0.03.

Figure 3

Grid distribution of part of the circular cross section with radius R and its close vicinity

Figure 6

Slamming coefficient Cs as a function of Vt∕R for the water entry test No. 3

Figure 9

Exit coefficient Ce as a function of Vt∕R for the water exit test No. 1

Figure 10

Exit coefficient Ce as a function of Vt∕R for the water exit test No. 2

Figure 11

Simplified calculations of the exit coefficient by Eq. 12 with and without the effect of viscous drag force as a function of Vt∕R for the two water exit tests

Figure 12

Comparisons between the simplified formula [Eq. 12] and the CIP calculations for the two water exit tests

Figure 13

Numerically predicted vorticity field for water exit test No. 1. OMG means the vorticity with dimension s−1.

Figure 16

Depth of penetration during water entry of a half-buoyant cylinder

Figure 17

Free surface deformation during water entry of a neutrally buoyant cylinder. CIP simulations (left) and experiments by Greenhow and Lin (right).

Figure 18

Depth of penetration during water entry of a neutrally buoyant cylinder

Figure 20

Predicted pressure distribution in Pascal at t=0.248s for the water exit described in Fig. 1. The atmospheric pressure has to be added to obtain the total pressure.

Figure 21

The distance from the cylinder top to mean free surface during water exit of a neutrally buoyant cylinder

Figure 1

Slamming coefficient Cs as a function of nondimensional submergence Vt∕R. Here: dt is the time step size used in the numerical integration; T=R∕V where R is cylinder radius and V is water entry velocity. The calculations are for the test condition No. 2 in Miao’s (7) experiments (see Table 1).

Figure 7

Slamming coefficient Cs as a function of Vt∕R for the water entry test No. 4

Figure 8

Slamming coefficient Cs as a function of Vt∕R for the water entry No. 5

Figure 14

Visualization of free surface deformation for water exit test No. 2. The pictures present the density function φ1, which is theoretically one for water and zero for the body and the air. Red=1. Blue=0.

Figure 15

Free surface deformation during water entry of a half-buoyant cylinder. CIP simulations (left) and experiments by Greenhow and Lin (right).

Figure 4

Slamming coefficient Cs as a function of Vt∕R for the water entry test No. 1

Figure 5

Slamming coefficient Cs as a function of Vt∕R for the water entry test No. 2

Figure 19

Free surface deformation during water exit of a neutrally buoyant cylinder. CIP simulations (left) and experiments by Greenhow and Lin (right).

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