Case 1.7a (NMRI)

Conditions:

• Self propelled at ship point in calm water
• With propeller, without rudder
• Without 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:

The self propulsion computation is to be carried out at the ship point following the experimental procedure. Propeller open test data is provided HERE.
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 = 18.2[N] (from the test).
In case this procedure cannot be carried out, set \(n\) to the measured value \(7.8\)[rps].

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.

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*}

Difinition of blade angle for test case 1.7a and 1.8a of CFD workshop 2015 Tokyo is as follows.

<Coordinate system in this definition>

Origin	:	propeller center
X-axis	:	the longitudinal axis pointing from bow to stern
Y-axis	:	the horizontal axis pointing from port to starboard
Z-axis	:	positive upward

\(L_{tip}\) is a line passing through the propeller center and blade tip. An offset angle of \(L_{tip}\) (\(\Delta \theta\) in the figure) from Generator Line(Datum Line) in YZ-plane is 4.034[deg] in anti-clockwise direction. Here, in the workshop, blade angle is defined as the angle between \(L_{tip}\) and Z-axis in YZ-plane (positive clockwise).

Figure: Offset angle of \(L_{tip}\) from Generator Line and each blade positions at

Blade angle = 0 [deg] : Red

Blade angle = 24 [deg] : Green

Blade angle = 48 [deg] : Blue

(Only one blade is drawn for visibility.)