Trans RINA, Vol 157, Part A3, Intl J Maritime Eng, Jul-Sep 2015
draft ratios were below 1.5 (h/T < 1.5). Li et al. [6] used three types of ship models to conduct bank effect experiments, and the results indicated that the critical h/T ratio was approximately 1.10. When the h/T was nearly or below 1.10, the sway force changed from bank suction to bank cushion,
and sway were adopted from several crucial methods developed by Dr. C. W. Hirt force and yaw moment
substantially increased as a result of water depth reduction. This phenomenon conforms to Bernoulli’s principle, which states that when a fluid flows from broad to narrow zones, velocity increases and pressure decreases, and vice versa. Pedersen[7] conducted review and application of ship collision and grounding analysis procedures. Lo et al.[2] used the bank effects on a simulated ship navigating along a vertical bank as a basis for extending this effect on the study of two ships during fronting and passing (Lo[8]). Parameters such as
ship speed, ship distance, and
navigation time were investigated. Ship speed and distance were demonstrated to influence the sway force and yaw moment of the ships. Zhou et al. [9] performs a series of simulations using computational fluid dynamics (CFD) software to examine the effects of a ship sailing along a bank in restricted waters. Ma et al. [10] discussed the vessel speed and distance to bank on the magnitude and time-based variation of the hydrodynamic interaction among hull, rudder and bank for a ship sailing along a bank in restricted waters.
Along with the enhancement of the computational power of computers, computational fluid dynamics (CFD) has reached incredible precision and reliability in numerical simulations of fluid structure-coupled problem bodies. Regarding ship towing tests, CFD technology can directly perform numerical simulation and visualization postprocessing, present coupled motion of the hull with 6 degrees of freedom (DOFs), compute physical values such as velocity field vectors, pressures, and vorticity distributions in the computation zone. Thus, ship–bank interactions can
be observed, and the physical
phenomena of the flow field can be further analyzed. To save time and financial costs necessary for conducting tank experiments, and to visualize physical values such as velocity and pressure field distributions around a ship on a computer (values that are difficult to obtain in physical
experiments), this study applied CFD for simulating the influences of bank effects on ships.
2. THEORETICAL AND NUMERICAL MODELS
This study adopted numerical methods to simulate the navigation of ships along banks and the bank effects produced. The simulation comprised vertical and sloped banks and how these influenced two types of ships. Computations
were performed to solve the
Navier–Stokes equations formula of the 3D viscous flow field to construct and analyze the models in this study. Regarding numerical methods, this study adopted the Finite
difference method (FDM) for solving the
time-dependent variation of flow field velocities and pressures. The techniques implemented in this study
vv v y
F x
tV uA vA wA
11 xy z
v z
Gf RSOR v w
P y
yy yb VF
v v s (3) Momentum equations
uu u tV x
F
y
11 xy z
u z
VF
P uA vA wA
x Gx
fb R u u u
(2)
xx w s SOR
fluid dynamic from the Los
Alamos National Laboratory in 1963, such as orthogonal grid systems for processing uneven boundaries and the original creation of the volume of fluid (VOF) free surface tracking technology. Dr. Hirt established Flow Science Inc. in 1980, published the VOF method for the dynamics of free boundaries with Hirt and Nichols[11] in 1981, and released the numerical analysis software for engineering and
casting and mold flow analyses, in 1985. The unique fractional volume computation technology can provide extremely realistic and detailed free surface capture such as wave–structural object interactions and breaking wave simulations. A new-generation,
high-precision
fluid dynamic model was also developed and widely applied in the field of science and engineering for mold casting, reservoir hydrography, ocean outfall, and pollution dispersion analyses. Regarding maritime transport, the swaying of cargo in oil tankers, ship-wave coupled motions, bank effects, and interactions during ship fronting and passing can be analyzed.
Hull motion has 6 DOFs, comprising surging
(displacement along the x-axis), broadsiding (displacement along the y-axis), heaving (displacement along the z-axis), rolling (rotation around the x-axis), pitching (rotation around the y-axis), and yawing (rotation around the z-axis) of the ship model’s center of mass.
2.1 GOVERNING EQUATIONS
The partial differential equations governing the viscous and incompressible flow for the fluid medium are given by the Navier-Stokes equations. The corresponding dimensional
form of the governing equations
Continuity equation F xy z
VuA
tx y
vA z for
conservation of mass and momentum can be expressed in x-, y- and z- axis coordinate system as:
wA RDIF RSOR (1)
science simulations and industrial
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©2015: The Royal Institution of Naval Architects
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