Case 1.2a (NMRI)

Conditions:

• Towing in calm water condition
• Without rudder, without propeller
• With ESD
• \( FR_{Z \theta} \)
• \( R_{e}=7.46 \times 10^6, F_r=0.142 \)
• \( L_{PP} = 7.000 \) [m], \(U=1.179\) [m/s]
• \( \rho = 998.2\) [kg/m³], \( \nu = 1.107 \times 10^{-6}\) [m²/s]
• \( g = 9.80 \) [m/s²]

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 ( \(\frac{S_{0\_wESD}}{{L_{PP}}^2}=0.2504 \) ) with ESD 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.

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*}