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False bottoms revisited: computational study for KCS under pure yaw motion in shallow water (H/T = 1.2)

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Abstract

To investigate the effect of a false bottom on a ship in shallow water, viscous CFD simulations of the KRISO Container Ship (KCS) under pure yaw motion at H/T = 1.2 are carried out using the in-house flow solver “NAGISA” with the in-house overset grid assembler “UP_GRID”, both developed at NMRI. Validations of forces and moment over one yaw motion period show that inertial contributions are significant in the surge and sway forces, while they are almost negligible in the yaw moment. The sway force in the present study is dominated by the inertial force, and thus, it must be deducted when the effect of a false bottom is investigated. Yaw-related linear hydrodynamic coefficients for false bottoms show more than a 25% difference compared to the values for true bottoms yet changing the tank bottom configuration does not affect the course stability index for the ship used in the present study. Throughout the local flow analysis, negative pressure and its propagated region are more pronounced in the true bottom than in the false bottom, which strongly influences the pressure distribution on the hull surface. The hull with a true bottom is subjected to a larger suction force from the tank bottom on its fore to the side tangential region than that with a false bottom. Vortical structures around the hull are also affected by the tank bottom configuration.

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Data availability statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

A E /A 0 :

Expanded area ratio of a propeller

B(m):

Breadth of a ship

B towing tank(m):

Width of a towing tank

B false bottom(m):

Width of a false bottom

C :

Course stability index

C B :

Block coefficient of a ship

\({C}_{p}\left(t\right)\) :

Nondimensional pressure over time

D p(m):

Diameter of a propeller

Fn :

Froude number

\({F}_{z\_fb}\)(N):

Dimensional pressure force in vertical direction acting on a false bottom

g(m/s2):

Gravity acceleration

H towing tank(m):

Depth of a towing tank

H/T :

Depth-draught ratio

L pp(m):

Length between perpendiculars

m(kg):

Mass of a ship

\(\overline{m }\) :

Nondimensional mass of a ship

N’ :

Yaw moment coefficient in the ship fixed coordinate system

N’ cal :

Yaw moment coefficient in the ship fixed coordinate system from CFD simulation

N’ p :

Pressure component of N’cal

N r :

1St order hydrodynamic coefficient of the yaw moment with respect to r

N rrr :

3Rd order hydrodynamic coefficient of the yaw moment with respect to r

N v :

1St order hydrodynamic coefficient of the yaw moment with respect to v

N1c :

1St cosine harmonic amplitude of N’

N3c :

3Rd cosine harmonic amplitude of N’

\({n}_{y}\) :

Unit normal vector in the horizontal direction

P(m):

Unit normal vector in the horizontal direction

Q :

Nondimensional 2nd invariant of the velocity gradient tensor

R i :

Reynolds number

r(rad/s):

Yaw angular velocity of a ship

\(\dot{r}\)(rad/s2):

Yaw angular acceleration of a ship

\({r}_{i}\) :

Refinement ratio for a grid/time step study; i = G for a grid convergence study, and i = T for a time step convergence study

\({r}_{max}^{^{\prime}}\) :

Nondimensional maximum yaw rate

S i :

Solution from a fine (i = 1), medium (i = 2) and coarse (i = 3) grid/time step

T(m):

Designed draught of a ship

T c(s):

Characteristic time

T’ cal :

Thrust coefficient in the ship fixed coordinate system from CFD simulation

T m :

Nondimensional yaw motion period

\(\overline{U }\) :

Nondimensional ship speed

U i :

Grid (i = G) and time step (i = T) uncertainty

U 0(m/s):

Constant ship speed

u(m/s):

Axial velocity of a ship

v(m/s):

Lateral velocity of a ship

\(\dot{v}\)(m/s2):

Lateral acceleration of a ship

X’ :

Axial force coefficient in the ship fixed coordinate system

X’ cal :

Axial force coefficient in the ship fixed coordinate system from CFD simulation

X0c :

0Th cosine harmonic amplitude of X’

X2c :

2Nd cosine harmonic amplitude of X’

X4c :

4Th cosine harmonic amplitude of X’

x G(m):

Axial center of gravity of a ship

Y’ :

Lateral force coefficient in the ship fixed coordinate system

Y’ cal :

Pressure component of Y’cal

Y r :

1St-order hydrodynamic coefficient of the sway force with respect to r

Y rrr :

3Rd-order hydrodynamic coefficient of the sway force with respect to r

Y v :

1St-order hydrodynamic coefficient of the sway force with respect to v

Y1c :

1St cosine harmonic amplitude of Y’

Y3c :

3Rd cosine harmonic amplitude of Y’

y G(m):

Lateral center of gravity of a ship

Z :

Number of propeller blades

\(\beta\) (deg) :

Drift angle of a ship

\(\Delta t\) :

Nondimensional physical time step

\({\varepsilon }_{21}\) :

Solution change between a fine grid/time step to a medium grid/time step

\({\varepsilon }_{32}\) :

Solution change between a medium grid/time step to a coarse grid/time step

\(\upeta\) (mm):

Transverse displacement of a ship under pure yaw test

\({\eta }_{0}\) (mm):

Transverse displacement of a ship under pure yaw test

\(\psi\) (deg):

Heading angle of a ship under pure yaw test

\({\psi }_{0}\) (deg):

Heading angle of a ship under pure yaw test

\(\nu\)(m2/s):

Fluid kinematic viscosity

\(\omega\) (rad/s):

Frequency of the prescribed yaw motion

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Acknowledgements

The experimental data of the KCS under pure yaw motion in shallow water with a false bottom have been provided by the organizers of the SIMMAN2020 Workshop at the KRISO [9]. Their permission to use these data in the present study prior to the workshop is greatly appreciated. Constructive comments and suggestions to improve the manuscript from Professor Hironori Yasukawa at Hiroshima University and Professor Shigeru Nishio at Kobe University are also appreciated.

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Authors and Affiliations

  1. National Maritime Research Institute, 6-38-1 Shinkawa Mitakashi, Tokyo, 181-0004, Japan

    Nobuaki Sakamoto, Takuya Ohmori, Kunihide Ohashi & Hiroshi Kobayashi

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  1. Nobuaki Sakamoto
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Correspondence to Nobuaki Sakamoto.

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Sakamoto, N., Ohmori, T., Ohashi, K. et al. False bottoms revisited: computational study for KCS under pure yaw motion in shallow water (H/T = 1.2). J Mar Sci Technol 28, 117–135 (2023). https://doi.org/10.1007/s00773-022-00912-7

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