Trans RINA, Vol 157, Part A3, Intl J Maritime Eng, Jul-Sep 2015
ww w
y F x
tV uA vA wA Gf RSOR
11 xy z
zz zb F
V w w w
w z
w and s
Where V is the fractional volume open to flow, ρ and ν refer to
the density coefficients of the represent
turbulent diffusion term, and R is a mass source. V u,v,w
velocity x yz
horizontal and vertical directions. A is the fractional area open to flow in the x-direction, A and z
y
fluids respectively, R is a the instantaneous
components in the horizontal and vertical directions, (, , )
represent the respective coordinates in the x
A are
similar area fractions for flow in the y and z directions, respectively. P denotes the instantaneous
pressure.
These are maintained at set values without being influenced by other factors during the simulation process. (Gx, Gy, Gz) refer to the acceleration rate of the body, and (fx, fy, fz) are the viscous accelerations terms, Uw = (uw, vw, ww) are the velocity of the source component, which will generally be non-zero for a mass source at a general moving object, Us = (us, vs, ws) are the velocity vectors of the fluid at the surface of the source relative to the source itself.
2.2 COUPLED SHIP MOTION EQUATIONS This simulation
primarily solves the coupled ship
motion equations (Wei[12]). Two Cartesian coordinate systems were used to describe the body coordinate system and the space coordinate system, which are also called the
body-fixed and earth-fixed systems
(Baha[13]), respectively. In the following, the ship is defined as the body coordinate system. In contrast to numeric channel displacements, the (x, y, z) origin remained fixed in space and the coordinate axis sits parallel to the numeric channel axis when ship (x’, y’, z’) t = 0. Ship movements consist of 6 DOFs. The ship origin is set at the center of mass G. The G point remained fixed relative to the ship, meaning that uv w u v w 0
between ship movement
xR x
x
G
. The coordinate conversion (x’, y’, z’)
relative to the
numeric channel (x, y, z) is: sb
In the equation,
x and b
s
x
vectors of numeric channel and ship position; G
x
(5)
respectively represent the is the
positional vector of the numeric channel’s center of mass; and R represents the Cartesian conversion tensor.
According to kinematic theory, the general motions of rigid bodies
can be divided into translational and rotational motions. When rotating around the origin, the
P
z (4)
velocity of the center of mass:
kinematic viscosity
VV r
PG P/G In the equation, P/G
velocity of an arbitrary point on the rigid body is identical to that of the chosen point of origin; thus, the center of mass of the object can be chosen as the origin of the 6 DOF motions. Let P be a point on the object with a velocity relative to the velocity
V
G and angular (6)
r is the distance vector from G to P.
On the right side of equation (6), the first and second terms represent
center of mass, respectively. Note that is a property of
the translational and rotational motions of the
a moving object and an independent choice of origin. The equation of motion rules the two separate motions:
FmdU dt
TJ d G G (7)
dt
J
In the equations, G represents the center of mass, F
(8) is
the total force, m is the mass of the rigid body, GT is is the angular velocity of G, and [J] is the moment of
inertia tensor. 2.3 THREE-DIMENSIONAL SHIP MODELLING
Two 3D ship models were constructed in this study. Table 1 presents the geometric data of the two ship models. Ship 1 is a container ship and Ship 2 is a multipurpose ship. The ship models were drafted using the AutoCAD computer aided design (CAD) software. To construct the models, we established the ship type table: Table 1 presents
the
geometric parameters of the two types of ship models for inputting and drafting the ship models in AutoCAD. The origin (x = y = z = 0) was set at the node of the intersection line of the still water level and the midship cross-section and the vertical line of the ship stern. A total of 60 body plans were drafted from the ship stern toward the bow. Subsequently, we trimmed and converted the format of the model ship body: Ship models drafted by using AutoCAD, as shown in Figure 1, were exported to the numerical code-supported STereoLithography (STL) format. Then, the DA Design Expert meshing tool software was used to confirm the completeness of the STL object. Finally, the models were used to solve 3D Navier-Stokes equations.
3. RESULTS AND DISCUSSION
In the numerical simulated flow field computation example of this study, the fluid physical characteristic density
and dynamic viscosity coefficient in the computation of the bank effect ship analysis were
the total turning moment of G, U is the velocity of G,
©2015: The Royal Institution of Naval Architects
A-191
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