Case 2.3a

Conditions:

• Self propelled at ship point in calm water

• Fixed (even keel)

• With propeller, without rudder

• FX₀

• Re = 1.4×10⁷, Fr = 0.26

References:

(2-4) 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), i.e.

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 tests)

Report rate of revolutions n, thrust and torque coefficients K_T, K_Q and resistance components CT_(SP), CP_(SP), CF_(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, CT_(SP), CP_(SP), CF_(SP).

Items and remarks

Table/ Figure #	Items	EFD Data		Submission Instruction
		Data file	Image	Table/Image file	Sample
2.3a-1	V&V of- Requested values: n, KT, KQ, CT(SP), CP(SP), CF(SP) or ( for given n ) ( RT(SP)-T ), KT, KQ, CT(SP), CP(SP), CF(SP)	Refer to sample file for details		Filename: [Identifier]_V&V_2-3a.xls (Excel file)	[Identifier]_V&V_2-3a.xls
2.3a-2	Axial velocity contours and cross flow vectors downstream of propeller plane (x/LPP=0.9911)	U_prop_EFD.dat	prop_contour_EFD.jpg prop_contour_EFD.lpk	Filename: [Identifier]_prop_contour_2-3a.jpg Axis: -0.04 ≤ y/LPP ≤ 0.04 -0.055 ≤ z/LPP ≤ 0.005 Contours level:    0 ≤ u/U ≤ 1.2,      ∆(u/U) = 0.1, #levels=13 Line style: solid lines	Refer to EFD image
			prop_vector_EFD.jpg prop_vector_EFD.lpk	Filename: [Identifier]_prop_vector_2-3a.jpg Axis: -0.04 ≤ y/LPP ≤ 0.04 -0.055 ≤ z/LPP ≤ 0.005 Reference vector: magnitude 0.2	Refer to EFD image
2.3a-3	Velocity downstream of propeller plane (x/LPP=0.9911) at z/LPP=-0.03	uvw_prop_EFD.dat	Refer to sample file for details	Filename:   [Identifier]_uvw_prop_2-3a.jpg Axis:     -0.03 ≤ y/LPP ≤ 0.03             -0.5 ≤ u/U, v/U, w/U ≤ 1.2 Line style: u/U: CFD solid line; EFD open squares v/U: CFD dashed line; EFD open triangles w/U: CFD dotted line; EFD open circles	[Identifier]_uvw_prop_2-3a.jpg
2.3a-4	Hull surface pressure contours ( port side view )	Not yet available	Cp_port_EFD.jpg	Filename: [Identifier]_Cp_port_2-3a.jpg Axis: 0.8 ≤ x/LPP ≤ 1.05 -0.05 ≤ z/LPP ≤ 0.01 Contours level: -1.0 ≤ Cp ≤ 1.0 ∆Cp=0.01, #levels=201 Contours style: Solid and dashed lines for positive (+) and negative (-) values, respectively.	Refer to EFD image

Submission Instructions:

· [Identifier] should be [Institute Name]-[Solver Name]. For example, if your institute is Chalmers and solver is SHIPFLOW4.2, identifier should be Chalmers-SHIPFLOW4.2

Identifier in the Figure should be [Institute Name]/[Solver Name]. For example, if your institute is Chalmers and solver is SHIPFLOW4.2, identifier should be Chalmers/SHIPFLOW4.2

· All figures should have aspect ratio of 1:1

· All figures should be in black and white

· Authors may change the contour levels for better qualitative comparison

V&V:

1.  Resistance coefficients are based on wetted surface area (S/L²) =0.1781 without rudder for static orientation in calm water.

2. Comparison Error, E%D=(D-S)/D×100, where D is the EFD value, and S is the simulation value. 

3. Relative change in solution: ε₁₂%S₁ = |(S₁-S₂)/S₁|×100, "1" refers to the finest grid.

4. Iterative uncertainty U_I is based on fine grid solution.

5. is the theoretical order of accuracy = order of convection scheme.

6. U_G is the grid uncertainty. is the simulation numerical uncertainty.

7. U_D is the data uncertainty.

8. is the validation 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 density of water (), ship speed (U), and length between perpendiculars (L_pp):

,

• where g is the gravitational acceleration and ν is the kinematic viscosity.

· All CFD predicted force coefficients should be reported using the provided wetted surface area at rest (S₀). Force coefficients are defined as follows:

Symbols:

D Diameter of propeller [m]

d_h Diameter of a propeller hub, D × (Hub ratio) [m]

K_T Thrust coefficient,

K_Q Torque coefficient,

n Propeller rate of revolution [rps]

Q Propeller torque [Nm]

R_T(SP) Total resistance in self-propelled condition [N]

SFC Skin friction correction [N]

T Propeller thrust [N]

U Ship speed [m/s]