Case 2.1

Conditions:

• Same with G2010 case2.2b
• With rudder
• Calm water condition
• \( FR_{Z \theta} \)
• \( L_{PP} = 7.2786 \) [m]
• \(g = 9.81\) [\(m/s^2\)]
• \(\rho = 999.5\) [\(kg/m^3\)]
• \(\nu = 1.27 \times 10^{-6}\) [\(m^2/s\)]
• Six speeds:

No.	1	2	3	4	5	6
Speeds [m/s]	\(0.915\)	\(1.281\)	\(1.647\)	\(1.922\)	\(2.196\)	\(2.379\)
Froude number (\(F_r\))	\(0.108\)	\(0.152\)	\(0.195\)	\(0.227\)	\(0.260\)	\(0.282\)
Reynolds number (\(R_e\))	\( 5.23 \times 10^6\)	\( 7.33 \times 10^6\)	\( 9.42 \times 10^6\)	\( 1.10 \times 10^7\)	\( 1.26 \times 10^7\)	\( 1.36 \times 10^7\)

References:

Not yet available.

Requested computations:

Note: a positive (+) sinkage value is defined upwards and a positive (+) trim value is defined bow up.

Submission Instructions:

• [Identifier] should be [Institute Name]-[Solver Name]. For example, if your institute is NMRI and solver is SURFv7, identifier should be NMRI-SURFv7.
• Identifier in the Figure should be [Institute Name]/[Solver Name]. For example, if your institute is NMRI and solver is SURFv7, identifier should be NMRI/SURFv7.
• All figures should be in black and white.
• Authors may change the contour levels for turbulence quantities for better qualitative comparison.
• V&V
  1. Resistance coefficients are based on wetted surface area ( \(S_0/{L_{PP}}^2=0.1803 \) ) with rudder for static orientation in calm water.
  2. Comparison Error, \( E\%D=(D-S)/D \times 100 \), where \( D \) is the EFD value, and \( S \) is the simulation value.
  3. Relataive change in solution: \( \varepsilon_{12} \% S_1 = |(S_1 - S_2 ) / S_1| \times 100 \), "1" refers to finest grid.
  4. Iterative uncertainty \( U_I \) is based on fine grid solution.
  5. \( p_{G,th} \) is the theoretical order of accuracy = order of convection scheme.
  6. \( U_G \) is grid uncertainty. To enable a comparison between different methods for uncertainty estimation, participants are strongly encouraged to deliver results for at least 3 systematic grids and if possible 4 or more.
     \( U_{SN} = \sqrt{{U_I}^2 + {U_G}^2} \) is the simulation numerical uncertainty.
  7. \( U_D \) is data uncertainty.
  8. \( U_{V} = \sqrt{{U_D}^2 + {U_{SN}}^2} \) is the validation numerical uncertainty.
  9. Brief details of the V&V method should be provided in the paper (including the determination of \(U_I\) ).

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} \end{align*} where \(g\) is the gravitational acceleration and \(\nu\) is the kinematic viscosity.

All CFD predicted force coefficients should be reported using the provided wetted surface area at rest (\(S_0\)).

Force coefficients are defined as follows: \begin{align*} C_T = \frac{R_T}{ \frac{1}{2} \rho U^2 S_0 }, \quad C_F = \frac{R_F}{ \frac{1}{2} \rho U^2 S_0 }, \quad C_P = \frac{R_P}{ \frac{1}{2} \rho U^2 S_0 }%, \quad %K_T = \frac{T}{ \rho n^2 {D_P}^4 }, \quad %K_Q = \frac{Q}{ \rho n^2 {D_P}^5 } \end{align*}