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/m^{3}], \( \nu = 1.107 \times 10^{6}\) [m^{2}/s]
 \( g = 9.80 \) [m/s^{2}]
References:
Not yet available.
Requested computations:
Table/Figure#
 Items
 EFD Data
 Submission Instruction

Data file 
Image 
Image files 
Sample + Tecplot layout file 
1.2a1 
V&V of resistances, sinkage, and trim 
Refer to sample file for detail 
Filename: [Identifier]_V&V_1.2a.xls (MS Excell file) 
[Identifier]_V&V_1.2a.xls updated on July, 3, 2015 
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 NMRISURFv7.
 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
 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.
 Comparison Error, \( E\%D=(DS)/D \times 100 \), where \( D \) is the EFD value, and \( S \) is the simulation value.
 Relataive change in solution: \( \varepsilon_{12} \% S_1 = (S_1  S_2 ) / S_1 \times 100 \), "1" refers to finest grid.
 Iterative uncertainty \( U_I \) is based on fine grid solution.
 \( p_{G,th} \) is the theoretical order of accuracy = order of convection scheme.
 \( U_G \) 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.
 \( U_D \) is data uncertainty.
 \( U_{V} = \sqrt{{U_D}^2 + {U_{SN}}^2} \) is the validation numerical uncertainty.
 Brief details of the V&V method should be provided in the paper (including the determination of \(U_I\) ).
All quantities are nondimensionalized 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*}