|Home|Description |Geometry and Conditions | Instructions to participants|

Case 2.11

Conditions:

References:

Not yet available.

Requested computations:

Table/Figure# Items EFD Data Submission Instruction
Data file Image Image files Sample + Tecplot layout file
2.11-1 Comparison of:
    <in calm water>
  • total resistance coefficient (\(C_T \times 10^3\))
  • sinkage (\(z / L_{PP}\)) and trim (\(\theta\) [deg])

  • <in head waves>
  • total resistance coefficient (\(C_T \times 10^3\)), surge motion (\( x / \zeta_s \)), heave motion (\(z / \zeta_s\)), roll angle (\( \phi / k \zeta_s\)) and pitch angle (\(\theta / k \zeta_s\))
  • 0th, 1st, 2nd, 3rd and 4th harmonic amplitudes[-] and 1st, 2nd, 3rd and 4th harmonic phases [rad];
Refer to sample file for details Filename: [Identifier]_6conditions_2-11.xlsx (Excel file) [Identifier]_6conditions_2-11_20151112.xlsx
(updated on November, 13, 2015)
2.11-2-C1 Time histories of total resistance coefficient (\(C_T\)), surge motion (\(x/\zeta_s\)), heave motion (\(z/\zeta_s\)), roll motion(\(\phi/ k \zeta_s\)) and pitch angle (\(\theta/ k \zeta_s\)), which are reconstructed from the Fourier Series (not the raw signals)
(test condition 1)
Refer to sample file for details Filename:
[Identifier]_CT_T-his_C1_2-11.png ( for \(C_T\) )
[Identifier]_surge_T-his_C1_2-11.png ( for \(x/\zeta_s\) )
[Identifier]_heave_T-his_C1_2-11.png ( for \(z/\zeta_s\) )
[Identifier]_roll_T-his_C1_2-11.png ( for \(\phi/ k \zeta_s\) )
[Identifier]_pitch_T-his_C1_2-11.png ( for \(\theta/ k \zeta_s\) )
X-axis range:
\( 0.0 \le t / T_e \le 1.0 \)
Y-axis range:
\( 0.0066 \le C_T \le 0.0071 \)
\(-0.03 \le \displaystyle{\frac{x }{\zeta}} \le 0.12 \)
\(-1.0 \le \displaystyle{\frac{z }{\zeta}} \le 1.0 \)
\(-0.4 \le \displaystyle{\frac{\phi }{k \zeta}} \le 0.4 \)
\(-0.8 \le \displaystyle{\frac{\theta}{k \zeta}} \le 0.8 \)
Style:
CFD solid line
EFD open circles
Case2.11-2_20151112.zip
(updated on November, 13, 2015)
2.11-2-C2 Time histories of total resistance coefficient (\(C_T\)), surge motion (\(x/\zeta_s\)), heave motion (\(z/\zeta_s\)), roll motion(\(\phi/ k \zeta_s\)) and pitch angle (\(\theta/ k \zeta_s\)), which are reconstructed from the Fourier Series (not the raw signals)
(test condition 2)
Refer to sample file for details Filename:
[Identifier]_CT_T-his_C2_2-11.png ( for \(C_T\) )
[Identifier]_surge_T-his_C2_2-11.png ( for \(x/\zeta_s\) )
[Identifier]_heave_T-his_C2_2-11.png ( for \(z/\zeta_s\) )
[Identifier]_roll-his_C2_2-11.png ( for \(\phi/ k \zeta_s\) )
[Identifier]_pitch_T-his_C2_2-11.png ( for \(\theta/ k \zeta_s\) )
X-axis range:
\( 0.0 \le t / T_e \le 1.0 \)
Y-axis range:
\( 0.0058 \le C_T \le 0.0068 \)
\(-0.15 \le \displaystyle{\frac{x }{\zeta}} \le 0.20 \)
\(-1.5 \le \displaystyle{\frac{z }{\zeta}} \le 1.5 \)
\(-1.6 \le \displaystyle{\frac{\phi }{k \zeta}} \le 0.8 \)
\(-0.8 \le \displaystyle{\frac{\theta}{k \zeta}} \le 0.8 \)
Style:
CFD solid line
EFD open circles
2.11-2-C3 Time histories of total resistance coefficient (\(C_T\)), surge motion (\(x/\zeta_s\)), heave motion (\(z/\zeta_s\)), roll motion(\(\phi/ k \zeta_s\)) and pitch angle (\(\theta/ k \zeta_s\)), which are reconstructed from the Fourier Series (not the raw signals)
(test condition 3)
Refer to sample file for details Filename:
[Identifier]_CT_T-his_C3_2-11.png ( for \(C_T\) )
[Identifier]_surge_T-his_C3_2-11.png ( for \(x/\zeta_s\) )
[Identifier]_heave_T-his_C3_2-11.png ( for \(z/\zeta_s\) )
[Identifier]_roll_T-his_C3_2-11.png ( for \(\phi/ k \zeta_s\) )
[Identifier]_pitch_T-his_C3_2-11.png ( for \(\theta/ k \zeta_s\) )
X-axis range:
\( 0.0 \le t / T_e \le 1.0 \)
Y-axis range:
\( 0.0 \le C_T \le 0.008 \)
\(-0.1 \le \displaystyle{\frac{x }{\zeta}} \le 0.1 \)
\(-1.5 \le \displaystyle{\frac{z }{\zeta}} \le 1.5 \)
\(-1.2 \le \displaystyle{\frac{\phi }{k \zeta}} \le 1.2 \)
\(-0.15 \le \displaystyle{\frac{\theta}{k \zeta}} \le 0.15 \)
Style:
CFD solid line
EFD open circles
2.11-2-C4 Time histories of total resistance coefficient (\(C_T\)), surge motion (\(x/\zeta_s\)), heave motion (\(z/\zeta_s\)), roll motion(\(\phi/ k \zeta_s\)) and pitch angle (\(\theta/ k \zeta_s\)), which are reconstructed from the Fourier Series (not the raw signals)
(test condition 4)
Refer to sample file for details Filename:
[Identifier]_CT_T-his_C4_2-11.png ( for \(C_T\) )
[Identifier]_surge_T-his_C4_2-11.png ( for \(x/\zeta_s\) )
[Identifier]_heave_T-his_C4_2-11.png ( for \(z/\zeta_s\) )
[Identifier]_roll_T-his_C4_2-11.png ( for \(\phi/ k \zeta_s\) )
[Identifier]_pitch_T-his_C4_2-11.png ( for \(\theta/ k \zeta_s\) )
X-axis range:
\( 0.0 \le t / T_e \le 1.0 \)
Y-axis range:
\( 0.001 \le C_T \le 0.007 \)
\(-0.8 \le \displaystyle{\frac{x }{\zeta}} \le 0.8 \)
\(-0.8 \le \displaystyle{\frac{z }{\zeta}} \le 0.8 \)
\(-4.5 \le \displaystyle{\frac{\phi }{k \zeta}} \le 4.5 \)
\(-0.8 \le \displaystyle{\frac{\theta}{k \zeta}} \le 0.8 \)
Style:
CFD solid line
EFD open circles
2.11-2-C5 Time histories of total resistance coefficient (\(C_T\)), surge motion (\(x/\zeta_s\)), heave motion (\(z/\zeta_s\)), roll motion(\(\phi/ k \zeta_s\)) and pitch angle (\(\theta/ k \zeta_s\)), which are reconstructed from the Fourier Series (not the raw signals)
(test condition 5)
Refer to sample file for details Filename:
[Identifier]_CT_T-his_C5_2-11.png ( for \(C_T\) )
[Identifier]_surge_T-his_C5_2-11.png ( for \(x/\zeta_s\) )
[Identifier]_heave_T-his_C5_2-11.png ( for \(z/\zeta_s\) )
[Identifier]_roll_T-his_C5_2-11.png ( for \(\phi/ k \zeta_s\) )
[Identifier]_pitch_T-his_C5_2-11.png ( for \(\theta/ k \zeta_s\) )
X-axis range:
\( 0.0 \le t / T_e \le 1.0 \)
Y-axis range:
\( 0.0030 \le C_T \le 0.0055 \)
\(-0.4 \le \displaystyle{\frac{x }{\zeta}} \le 0.4 \)
\(-0.5 \le \displaystyle{\frac{z }{\zeta}} \le 0.3 \)
\(-0.4 \le \displaystyle{\frac{\phi }{k \zeta}} \le 0.2 \)
\(-0.5 \le \displaystyle{\frac{\theta}{k \zeta}} \le 0.5 \)
Style:
CFD solid line
EFD open circles

Note:
a positive (+) surge(x) value is defined forward and a positive (+) heave (z) value is defined upwards.
a positive (+) roll(\(\phi\)) value is portside up and positive (+) pitch (\(\theta\)) value is defined bow up.

Submission Instructions:

All quantities are non-dimensionalized by denstiy of water (\(\rho\)), ship speed (\(U\)), and length between parpendiculars (\(L_{PP}\)): \begin{align*} F_r = \frac{U}{\sqrt{g \cdot L_{PP}}}, \quad R_e = \frac{U \cdot L_{PP}}{\nu} \tag{1} \end{align*} where \(g\) is the gravitational acceleration and \(\nu\) is the kinematic viscosity.


Figure 1: Relationship between ship heading and wave encounter angle. (Arrow shows ship heading)

Remarks:

Fourier Series Instructions:

As a time reference, incident wave height at FP of the ship is defined as \begin{align*} \zeta_T (t) = \frac{\zeta_s}{L_{PP}} \cos ( 2 \pi f_e t + \gamma_I ) \tag{3} \end{align*} \(\gamma_I\) is the initial phase and is equal to be zero from the present definition of \(t=0\) below.
Fourier series for time history \(X\) (\(X=C_T\), \(x\), \(z\), \(\phi\), \(\theta\), and \(\zeta_T\)) are determined as follows: \begin{align*} X_F (t) &= \frac{X_0}{2} + \sum_{n=1}^N X_n \cos ( 2 n \pi f_e t + \Delta \gamma_n ) \tag{4} \\ \Delta \gamma_n &= \gamma_n - \gamma_I \tag{5}\\ a_n &= \frac{2}{T_e} \int_0^{T_e} X(t) \cos ( 2 n \pi f_e t ) dt \quad ( n = 0, 1, 2, \cdots ) \tag{6} \\ b_n &= \frac{2}{T_e} \int_0^{T_e} X(t) \sin ( 2 n \pi f_e t ) dt \quad ( n = 1, 2, \cdots ) \tag{7} \\ X_n &= \sqrt{ {a_n}^2 + {b_n}^2 } \tag{8} \\ \gamma_n &= tan^{-1} \left( - \frac{b_n}{a_n} \right) \tag{9} \end{align*} \(X_n\) is n-th harmonic amplitude and \(\gamma_I\) is the corresponding phase.

Symbols:

\(\zeta_s\) - Wave amplitude \(= \displaystyle{\frac{H_s}{2}} \)
\(f_e\) - Wave encounter frequency \(= f_w + \displaystyle{\frac{U}{\lambda} \cos \left(\frac{\pi}{180}\chi \right) }\)
\(f_w\) - Frequency of the incident wave \(=\sqrt{\displaystyle{\frac{g}{2 \pi \lambda}}} \)
\(t\) - Time, when\(t=0\), a crest of the incident wave is coincident at FP
\(T_e\) - Wave encounter period \(= \displaystyle{\frac{1}{f_e}} \)