# Case 3.9

## Conditions:

• Free running at model point in calm water (mandatory)

• With propeller, With rudder
• With bilge keels
• $$FR_{all}$$
• $${R_{e}}^{*}=3.39 \times 10^6, {F_r}^{*}=0.20$$
• $$L_{WL} = 3.147$$ [m], approach speed $$V_A = 1.11$$ [m/s]
• Target Yaw angle: $$\psi_{C} = 0^{\circ}$$
• Rudder angle should be controlled in the following Computational Setup.

$${R_{e}}^{*}$$ : nominal Reynolds number, the Reynolds number when ship runs in calm water with constant propeller rate of revolution.
$${F_r}^{*}$$ : nominal Froude number, the Froude number when ship runs in calm water with constant propeller rate of revolution.

All quantities are non-dimensionalized by approach speed ($$V_A$$), and waterline length ($$L_{WL}$$):
\begin{align*}
F_r = \frac{V_A}{\sqrt{g \cdot L_{WL}}}, \quad R_e = \frac{V_A\ \cdot L_{WL}}{\nu}
\end{align*}
where $$g$$ is the gravitational acceleration and $$\nu$$ is the kinematic viscosity.

## Computational Setup:

1. All calculations are to be conducted for model scale conditions.
2. All simulations results should be provided in the format described in next section.
3. The propeller rate of revolution should correspond to the self propulsion point of the model (In case self-propulsion cannot be carried out, propeller rate of revolution should be set the measured value 8.97[rps]).
4. Similar to the experiment, the rudders should be controlled by following autopilot:
\begin{align*}
\delta (t) = K_P ( \psi (t) – \psi_C )
\end{align*}
where $$\delta (t)$$ is rudder angle, proportional gain $$K_P$$ is 1.0, $$\psi_C$$ is the target yaw angle and $$\psi(t)$$ is yaw angle. The maximum rudder rate should be assigned to $$35.0$$ [deg/s].

## General Format for Submissions:

1. Sinkage $$\sigma$$, trim $$\tau$$, velocity $$u$$, propeller thrust coefficient $$K_T$$ and torque coefficient $$K_Q$$, propeller rate of revolution $$n$$, resistance and its components $$C_{T(SP)}, C_{P(SP)}, C_{F(SP)}$$ should be submitted.
2. Sinkage $$\sigma$$ should be given in an Earth-fixed coordinate system with $$z$$ pointing downward as shown in Figure 1. Trim $$\tau$$ is positive for bow up position. Sinkage should be normalized by $$L_{WL}$$ and trim should be reported in degree.
3. The velocity $$u$$ should be reported in ship-fixed coordinate system with $$x$$ axis positive toward bow.
The reported velocities should be non-dimensionalized as $$u = \dot{x}\, / V_A$$ .
4. The propeller thrust $$T$$ and torque $$Q$$ should be reported in shaft coordinate system axis positive toward the engine. Values should be normalized by density of water$$\rho$$, propeller diameter ($$D_P$$), and $$n$$ as follows.
\begin{align*}
K_T = \frac{T}{ \rho n^2 {D_P}^4 }, \quad
K_Q = \frac{Q}{ \rho n^2 {D_P}^5 }
\end{align*}
5. Total resistance and its components $$C_{T(SP)}, C_{F(SP)}, C_{P(SP)}$$ should be reported in ship coordinate system. They should be non-dimensionalized using wetted surface area at rest $$S_0$$ and ship speed:
\begin{align*}
C_T = \frac{R_T}{ \frac{1}{2} \rho {V_A}^2 S_0 }, \quad
C_F = \frac{R_F}{ \frac{1}{2} \rho {V_A}^2 S_0 }, \quad
C_P = \frac{R_P}{ \frac{1}{2} \rho {V_A}^2 S_0 }, \quad
\end{align*}
6. In case self-propulsion cannot be carried out, propeller rate of revolution should be set the measured value 8.97[rps] and $$T_x-R_T$$ should be also reported where $$T_x$$ is the propeller thrust in ship-fixed coordinate system.
7. SI units should be used throughout (i.e. m, m/s, etc). Exceptions are angles in degrees.

Figure 1: Earth and ship-fixed coordinate system

## 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.

## References:

Not yet available.
Details of EFD procedures are shown here (IIHR_ONRT_DATA_06-12-2015.pdf).

Table/Figure# Items EFD Data Submission Instruction
Data file Image Image files Sample + Tecplot layout file
3.9-1 for $$\psi_C=0^{\circ}$$ Ship motions
$$u$$, sinkage and trim
Refer to sample file for detail N/A [Identifier]_Case3.9.xlsx
3.9-2 Propulsion coefficients
$$K_T$$, $$K_Q$$, $$n$$, $$C_{T(SP)}$$, $$C_{F(SP)}$$, $$C_{P(SP)}$$ (and $$T_x – R_{T(SP)}$$ (if $$n$$ is set to the measured value and self-propulsion is not conducted)
N/A N/A N/A