Test Case 2

--- Self-propelled condition ---

KCS [ Hull and propeller geometry ]

Conditions

• Self-propelled condition at ship point in still water
• Fixed(even keel)
• With propeller, without rudder

Froude number ( Fn )	Reynolds number ( Rn )
0.26	1.4×107

Propeller condition at the ship point

Open-water test: [Data file] [Performance Curve: eps | tif ]

In order to perform the self-propulsion computation, following three computations are required:

1) Double model flow without propeller effect to obtain the form factor $k$.

2) Towed condition at $Fn=0.26$ to obtain the total resistance $R_{T(Tow)}$ and the nominal wake $w_n$.

3)Self-propelled condition described below to obtain the propeller thrust $T$, the propeller torque $Q$ and other self-propulsion factors.

The self-propulsion computation is to be carried out at the ship point following the experimental procedure, i.e., the rate of propeller revolution $n$ is adjusted in such a way that the propeller thrust $T$ is balanced with the extrapolated full-scale resistance of the ship as follows:

$$T =R_{T(SP)}-SFC$$

$$R_{T(SP)} SFC$$

$$SFC = \left\{(1 + k)(C_{F0M}-C_{F0S}) - \Delta C_F \right\} \times \dfrac{1}{2}\rho U^2 S_0$$

$$k$$

$$C_{F0M} = 2.832 \times 10^{-3} \notag$$

$$R_{nM}=1.4\times 10^7$$

$$C_{F0S} = 1.378 \times 10^{-3}$$

$$R_{nS}=2.39\times 10^9$$

$$\Delta C_F$$

$$\Delta C_F =0.27 \times 10^{-3}$$

Note: In case the procedure above cannot be carried out, please set the propeller condition based on the measured values ($n=9.5$[rps], $K_T=0.170$, $K_Q=0.0288$ and $J=0.732$) and report only the available items( $C_{T(SP)}$, $C_{P(SP)}$, $C_{F(SP)}$, $K_T$, $K_Q$) and figures.

Items and Remarks

Figure Number	Items	Remarks
	Integral variables: <towed>  Form factor ( 1 + k ) at Fn = 0 Coefficients of  total resistance (CT(Tow)), split into    pressure (CP(Tow)) and    friction (CF(Tow)) components at Fn = 0.26,  Nominal wake coefficient ( 1 - w n ) <self-propelled> Coefficients of  total resistance (CT(SP)), split into    pressure (CP(SP)) and    friction (CF(SP)) components,  Propeller thrust coefficient ( KT ),  Propeller torque coefficient ( KQ ),  Thrust deduction coefficient ( 1 - t ),  Effective wake coefficient determined from thrust identity method ( 1 - wT ),  Propeller open water efficiency ( ηo ),  Relative rotative efficiency ( ηR ),  Advance ratio of propeller determined from thrust identity method ( J ),  Propeller rate of revolution ( n [rps] ),  Propulsive efficiency ( η )	Experimental results table
Fig. 2-1	Axial velocity contours and cross flow vectors downstream of propeller plane (x/Lpp=0.4911)	download
Fig. 2-2	Velocity downstream of propeller plane (x/Lpp=0.4911) at z/Lpp=-0.03	To be compared with the experimental results download
Fig. 2-3	Uncertainty analysis of the above item	UD = 5 % ( Proceedings of CFD Workship 2000 )
Fig. 2-4	Hull surface pressure contours ( port side view )	download

*: To be determined

• Coordinate system for comparisons is fixed to midship on the undisturbed waterplane.
• All quantities are non-dimensionalized by density of water ( $\rho$ ), ship speed ( $U$ ), and length between perpendiculars ( $L_{PP}$ ):

  $$F_n = \dfrac{U}{\sqrt{g \cdot L_{PP}}}, \quad R_n = \dfrac{U \cdot L_{PP}}{\nu}$$

  
  
  where $g$ is the gravitational acceleration and $\nu$ is the kinematic viscosity.
• All CFD predicted force coefficients should be reported using the provided ( Geometry page ) wetted surface area at rest ( $S_{0}$ ). Force coefficients are defined as follows:

  $$C_{T} = \dfrac{R_{T}}{\frac{1}{2} \rho U^2 S_{0}}, \quad C_{F} = \dfra... ...1}{2} \rho U^2 S_{0}}, \quad C_{P} = \dfrac{R_{P}}{\frac{1}{2} \rho U^2 S_{0}}$$

  $$1 + k = \frac{C_{T}}{C_{F0}}$$

  $$C_{F0} = \dfrac{0.075}{(\log_{10} R_{e} - 2 ){}^2}$$ (ITTC 1957 frictional coefficient line )

  
  

• Symbols:
  

  $\Delta C_F$	Roughness allowance
  $D$	Diameter of propeller
  $d_h$	Diameter of a propeller hub, $D \times \left( \text{Hub ratio} \right)$
  $J$	Advance ratio $\dfrac{v_a}{n D}$
  	By using the propeller thrust $K_T$ at the self propulsion test, the thrust identity method gives the corresponding advance ratio $J$ from the open water characteristics.
  $K_T$	Thrust coefficient, $\dfrac{T}{\rho n^2 D^4}$
  $K_Q$	Torque coefficient, $\dfrac{Q}{\rho n^2 D^5}$
  $K_{Q(O)}$	Torque coefficient in open water ( uniform flow )
  	By using the propeller thrust $K_T$ at the self propulsion test, the thrust identity method gives the corresponding open water torque $K_{Q(0)}$ from the open water characteristics.
  $n$	Propeller rate of revolution [rps]
  $Q$	Propeller torque
  $R_{T(Tow)}$	Total resistance in towed condition
  $R_{T(SP)}$	Total resistance in self-propelled condition
  $SFC$	Skin friction correction
  $T$	Propeller thrust
  $t$	Thrust deduction factor, $\dfrac{T-(R_{T(Tow)}-SFC)}{T}$
  $U$	Ship speed
  $v_a$	Propeller advance speed, determined by the thrust identity method, $v_a = J n D$
  $w_n$	nominal wake
  	$w_n = \dfrac{\displaystyle\int_0^{2 \pi} \int_{\frac{d_h}{2}}^{\frac{D}{2}} u r dr d\theta}{\dfrac{\pi}{4} \left( D{}^2 - d_h{}^2 \right)}$
  	where the origin is the center of propeller (see Figure)
  $w_T$	Taylor wake fraction, $\dfrac{U-v_a}{U}$
  $\eta$	Propulsive efficiency, $\dfrac{1-t}{1-w_t}\cdot \eta_o \cdot \eta_R$
  $\eta_o$	Propeller open water efficiency, $\dfrac{J K_T}{2 \pi K_{Q(0)}}$
  $\eta_R$	Relative rotative efficiency, $\dfrac{ K_{Q(0)}}{ K_Q}$

Figure :  Coordinate systems