Test Case 3

--- Obliquely towed condition ---

KVLCC2M [Geometry ]

Conditions

• Obliquely towed condition in still water
• Fixed(even keel)
• Double model flow

Froude number ( Fn )	Reynolds number ( Rn )	Drift angle ( β )
0	3.945×106	β = 0, 3, 6, 9, 12 [deg] for integral variables β = 6, 12 [deg] for Fig. 3-7, Fig. 3-10, Fig. 3-11, and Fig. 3-12 β = 0, 6, 12 [deg] for others

Items and Remarks

Figure Number	Items	Remarks
	Integral variables: Coefficients of forces and moments, in x-direction: Total ( CX ) , split into pressure ( CXP ) and friction ( CXF ) components, and in y-direction: Total ( CY ) , split into pressure ( CYP ) and friction ( CYF ) components, Coefficient of yaw moment ( CN ) around the origin.
Fig. 3-1	Integral variables: Coefficients of forces and moments, CX, CY, CN, N / Y versus β	To be compared with experimental results download
Fig. 3-2	Uncertainty analysis of the above item	UD is not available.
Fig. 3-3	Axial velocity contours and cross flow vectors on the WAKE 1 plane	The WAKE 1 plane is shown in Figure 2.
Fig. 3-4	Velocity on the WAKE 1 plane at z/Lpp=-0.05	The WAKE 1 plane is shown in Figure 2. To be compared with experimental results download(β=0) download(β=6) download(β=12)
Fig. 3-5	Uncertainty analysis of the above item	UD = 0.5, 1.0, 1.0 for u, v. w [%U] along the entire cut (proceedings of CFD Wordshop 2000)
Fig. 3-6	Kinematic eddy viscosity ( νt ) and longitudinal component of vorticity ( ω x ) contours on the WAKE 1 plane
Fig. 3-7	Hull surface pressure contours( port, starboard and bottom side views )	β = 6 and 12 [deg]
Fig. 3-8	Hull surface pressure at x/Lpp = -0.4 and x/Lpp = 0.4	To be compared with experimental results download
Fig. 3-9	Uncertainty analysis of the above item ( USN, UV, E )
Fig. 3-10	Distribution of the side force component along the hull	To be compared with experimental results (02/Dec/2004 corrected) download ( β = 6 ) download ( β = 12 ) β = 6 and 12 [deg]
Fig. 3-11	Uncertainty analysis of the above item	UD = 14.1 [ % &Delta Yrange ] ( β = 6 ) UD = 8.66 [ % &Delta Yrange ] ( β = 12 ) β = 6 and 12 [deg]
Fig. 3-12	Limiting streamlines ( Port, Starboard, and bottom views )	β = 6 and 12 [deg]

• Coordinate system for comparisons is fixed to midship on the undisturbed waterplane. ( see Figure )
• All quantities are non-dimensionalized by density of water ( $\rho$ ), ship speed ( $U$ ), length between perpendiculars ( $L_{PP}$ ), and draft ( $d$ ):

  $$F_n = \dfrac{U}{\sqrt{g \cdot L_{PP}}}, \quad R_n = \dfrac{U \cdot L_{PP}}{\nu}$$

  
  
  where $g$ is the gravitational acceleration and $\nu$ is the kinematic viscosity.
• All CFD predicted force coefficients should be reported using the provided ( Geometry page ) $L_{PP}$ and $d$. Force coefficients are defined as follows:

  $$C_{X} = \dfrac{X}{\frac{1}{2} \rho U^2 L_{PP} d}, \quad C_{X_F} = \dfr... ...\rho U^2 L_{PP} d}, \quad C_{X_P} = \dfrac{X_P}{\frac{1}{2} \rho U^2 L_{PP} d}$$

  $$C_{Y} = \dfrac{Y}{\frac{1}{2} \rho U^2 L_{PP} d}, \quad C_{Y_F} = \dfr... ...\rho U^2 L_{PP} d}, \quad C_{Y_P} = \dfrac{Y_P}{\frac{1}{2} \rho U^2 L_{PP} d}$$

  $$C_{N} = \dfrac{N}{\frac{1}{2} \rho U^2 L_{PP}{}^2 d}$$

  
  
  where $C_N$ is around the origin of the coordinates.
• $\Delta Y$ is defined to satisfy following equation,

  $$C_Y = \int_{bow}^{stern} \!\!\! \Delta Y dx \qquad \qquad \qquad$$

  
  

Figure 1:  Coordinate system for hydrodynamic forces and moment

 

Figure 2:  Coordinate systems for velocity fields

 

Figure 3:  Coordinate system for hull surface pressure and lateral force distribution