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 \((R_{T(SP)}-T)\), \(K_{T}\), \(K_{Q}\), \(C_{T(SP)}\), \(C_{P(SP)}\), \(C_{F(SP)}\).

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*}