# Case 2.5

## Conditions:

• Same with G2010 case2.3a
• Self propelled at ship point in calm water
• Free (even keel)
• With propeller, without rudder
• $FR_{0}$
• $R_e = 1.40 \times 10^7$, $F_r = 0.26$$0$
• $L_{PP} = 7.27$$86$ [m], $U = 2.196$ [m/s]
• $\rho = 999.1$ [kg/m3], $\nu = 1.139 \times 10^{-6}$ [m2/s]
• $g = 9.81$ [m/s2]

## References:

Hino, T., (2005 ed.), “Proceedings of CFD Workshop Tokyo 2005”, NMRI report 2005

## Requested computations:

The self propulsion computation is to be carried out at the ship point following the experimental procedure. Thus, the rate of revolutions of the propeller $n$ is to be adjusted to obtain force equilibrium in the longitudinal direction considering the applied towing force (Skin Friction Correction, SFC): $T = R_{T(SP)}-SFC$
Where $T$ is the computed thrust, $R_{T(SP)}$ is the total resistance at self propulsion and SFC = 30.3[N] (from the test).
Report rate of revolutions $n$, thrust and torque coefficients $K_T$, $K_Q$ and resistance components $C_{T(SP)}$, $C_{P(SP)}$, $C_{F(SP)}$.
In case this procedure cannot be carried out, set $n$ to the measured value $9.5$[rps] and report towing force $(R_{T(SP)}-T)$, $K_{T}$, $K_{Q}$, $C_{T(SP)}$, $C_{P(SP)}$, $C_{F(SP)}$.

Table/Figure# Items EFD Data Submission Instruction
Data file Image Image files Sample + Tecplot layout file
2.5-1 V&V of $n$, $K_T$, $K_Q$ $C_{T(SP)}$, $C_{P(SP)}$, $C_{F(SP)}$
or (for given$n$)
$(R_{T(SP)}-T)$, $K_{T}$, $K_{Q}$, $C_{T(SP)}$, $C_{P(SP)}$, $C_{F(SP)}$
Refer to sample file for detail Filename:
[Identifier]_V&V_2.5.xls
(MS Excell file)
[Identifier]_V&V_2.5.xls

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 ( $S_0/{L_{PP}}^2=0.1781$ ) without 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 ($S_0$), propeller diameter ($D_P$), and propeller rate of revolution ($n$).

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*}