# 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:

Table/Figure# Items EFD Data Submission Instruction
Data file Image Image files Sample + Tecplot layout file
2.1-1 V&V of resistances, sinkage($\sigma$),
and trim($\tau$)
Refer to sample file for detail Filename:
[Identifier]_6V&V_2-1.xls
(MS Excell file)
[Identifier]_6V&V_2.1.xls
2.1-2 Coefficients of total resistance ($C_T$) versus $F_r$
(results and uncertainties)
vary_Fr_2-1.xls Refer to sample file for detail Filename:
[Identifier]_CT_Fr_2-1.jpg
Axis:
$0.09 \le F_r \le 0.30$
$2.8 \le C_T \times 10^3 \le 5.2$
Line style:
$C_T \times 10^3$:
CFD solid line with open left-triangles;
EFD solid diamonds
Uncertainty bars:
$\pm U_D$ horizontal short bars
$\pm U_{SN}$ horizontal long bars
[Identifier]_CT_Fr_2-1.jpg
[Identifier]_CT_Fr_2-1.lpk
2.1-3 Sinkage ($\sigma$) versus $F_r$
(results and uncertainties)
vary_Fr_2-1.xls Refer to sample file for detail Filename:
[Identifier]_sinkage_Fr_2-1.jpg
Axis:
$0.09 \le F_r \le 0.30$
$-2.8 \le \sigma \times 10^2 \le 0.4$
Line style:
$\sigma \times 10^2$:
CFD solid line with open up-triangles;
EFD solid squares
Uncertainty bars:
$\pm U_D$ horizontal short bars
$\pm U_{SN}$ horizontal long bars
[Identifier]_sinkage_Fr_2-1.jpg
[Identifier]_sinkage_Fr_2-1.lpk
2.1-4 Trim ($\tau$) versus $F_r$
(results and uncertainties)
vary_Fr_2-1.xls Refer to sample file for detail Filename:
[Identifier]_trim_Fr_2-1.jpg
Axis:
$0.09 \le F_r \le 0.30$
$-0.28 \le \tau^\circ \le 0.04$
Line style:
$\tau^\circ$:
CFD solid line with open circles;
EFD solid down triangles
Uncertainty bars:
$\pm U_D$ horizontal short bars
$\pm U_{SN}$ horizontal long bars
[Identifier]_trim_Fr_2-1.jpg
[Identifier]_trim_Fr_2-1.lpk

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*}