This document summarizes a study on predicting the form factor of a displacement type vessel (JBC hull) using computational fluid dynamics (CFD). Single-phase CFD simulations were performed for the JBC hull at various velocities within the Prohaska range. The form factor, which represents the ratio of viscous pressure force to frictional force, was calculated from the simulations and found to depend on Reynolds number, contrary to Prohaska's theory of independence. Frictional force results matched well with empirical ITTC formulas. The study aims to further investigate scale effects on form factor prediction.

1. Journal of Thermal Engineering
CONFERENCE ON ADVANCES IN MECHANICAL ENGINEERING ISTANBUL 2016 – ICAME2016
11-13 May 2016, Yildiz Technical University, Istanbul, Turkey
ON THE FORM FACTOR PREDICTION OF A DISPLACEMENT TYPE VESSEL: JBC
CASE
Uğur Can
Yildiz Technical University
Istanbul, Turkey
İsmail Hakkı Topal
Yildiz Technical University
Istanbul, Turkey
Ali Doğrul
Yildiz Technical University
Istanbul, Turkey
Taner Çoşgun
Yildiz Technical University
Istanbul, Turkey
Nurten Vardar
Yildiz Technical University
Istanbul, Turkey
Keywords: Form Factor, JBC, Prohaska, Computational Fluid Dynamics
* Corresponding author: Taner Çoşgun
E-mail address: tcosgun@yildiz.edu.tr
ABSTRACT
Ship hydromechanics has been a fascinating research area
for decades. Calculation of ship total resistance and resistance
components has been crucial in order to estimate the
hydrodynamic performance of the floating bodies. In this
manner, many approaches have been proposed in the literature.
To calculate the resistance components precisely, the form
factor of the ship hull has a significant importance. Form factor
is defined by the ratio of viscous pressure force to the frictional
force. This study focuses on the prediction of the form factor by
employing a commercial CFD code. The flow around JBC hull,
which is a well-known benchmark case, has been simulated for
various velocities by staying in Prohaska range. Single phase
analyses have been conducted by neglecting the free surface
effect. Mesh dependency study has been made and then form
factor has been calculated in order to show the effect of
Reynolds number on the form factor.
INTRODUCTION
Developments in computer technology has accelerated the
numerical studies in ship hydromechanics. Computational fluid
dynamics (CFD) analyses have a significant role in ship design
process. CFD codes have a wide range of application especially
in total ship resistance estimation and calculation of resistance
components. Total ship resistance is crucial in ship
hydrodynamic performance. In this manner, also the resistance
components have to be calculated precisely.
Resistance component representing the ship hull form
effect is crucial which may be called as viscous pressure
resistance [1]. In order to calculate the wave resistance
component, form factor of the ship has to be defined. Well-
known method to calculate the form factor is suggested in the
study of Prohaska [2]. In this work, Prohaska has mentioned
that the form factor is independent from the ship speed and the
form factor is same for model and full scale ship. Also it is
proposed that the wave resistance is related with Froude number
for low speeds.
Garcia [3] has studied the scale effect on the form factor
and stated that the form factor is not same for model and full
scale ship. Kouh et al. [4] has made some CFD analyses for
different ship geometries by using double body approach in
order to calculate the form factor. Degiuli [5] has investigated
the form factor for blunt ships with Prohaska method and
offered some coefficients. Min et al. [6] has made a study on
form factor with a method offered by ITTC 1978 [7] and
proposed a new calculation method.
In this paper, numerical analyses have been conducted in
order to simulate the single phase flow around Japanese Bulk
Carrier (JBC) model ship. During the analyses, free surface
effect has not been taken into account in order to neglect the
wave resistance. The analyses have been performed for Froude
numbers in Prohaska range (0.12<Fn<0.20). The frictional
forces have been compared with the ones calculated by the
ITTC formula [8]. At Fn=0.14, a grid dependency study has
been made. Double body method has been applied to the

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numerical results for prediction of the form factor and the effect
of Reynolds number on the form factor for one scale factor has
been shown.
MATHEMATICAL MODEL
To model the flow field, RANS (Reynolds Averaged Navier
- Stokes) equations are used as governing equations. Time
independent continuity and momentum equations in Cartesian
coordinates are,
0i
i
U
x



(1)
  1i j j i ji
j i j j i j
U U U u uUP
x x x x x x


      
      
         
(2)
Where Ui and u’
i expresses the mean and fluctuation
velocity components in the direction of the Cartesian coordinate
xi, P the mean pressure, ρ the density and ν the kinematic
viscosity.
The well-known k-𝜺 model has been used to simulate the
turbulent flows. The Reynolds stress tensor is then calculated by
the Boussinesq model;
2
3
ji
i j t ij
j i
UU
u u k
x x
 
       
   
(3)
2
C k /t  
, (4)
Where νt is the eddy viscosity and Cμ is an empirical
constant (Cμ=0.009), k is the turbulent kinetic energy and ε is
the dissipation rate of k. The turbulence quantities k and ε are
then computed from a k– ε model using two transport equations,
 j t
k
j j k j
kU k
P
x x x

 

    
     
     
(5)
  2
1 2c P c
j t
k
j j j
kU
x x x k k
 

   


    
     
     
(6)
P i
k i j
j
u
u u
x
  

(7)
where, Cε1=1.44, Cε2 =1.92 , Cμ=0.009, turbulent Prandtl
numbers for k and ε are σk=1.0 , and σε=1.3, respectively.
The use of standard k-𝜺 two equation turbulence model
formulation is reasonably robust, reliable near solid boundaries
and recirculation regions like ship boundary layers. The
pressure field is solved by using the well-known SIMPLE
algorithm.
GEOMETRY AND COMPUTATIONAL STRATEGY
Geometry and main dimensions of the JBC hull can be
found in fig.1. and table 1, respectively.
Fig 1. 3-D model of the ship hull below water line
Table 1. Main particulars
λ=57 Model Full Scale
Length LWL (m) 5 285
Draught T(m) 0,2895 16,5
Depth D (m) 0,4386 25
Wetted Surface S (m2
) 6,0191 19556,1
Boundaries of the virtual towing tank can be found in fig 2.
Distance from the inlet, outlet and bottom wall to the model is
4, 6 and 3 times of LWL (model length of water line),
respectively. To reduce the computational solution time, only
the half of the geometry is solved. To simulate the single phase
flow around the shipo hull, only the wetted surface of the ghull
is modeled.
Fig 2. Computational domain
Inflow to the solution domain is set as velocity inlet and at the
outlet, all gradient are set to zero. No slip boundary condition is
imposed to the ship hull and bottom and side walls which
ensures that the normal gradient of the velocity is zero. For the
reason of solving the half of the geometry, mid-section plane of
the hull is set as symmetry plane.

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Fig 3. Mesh distribution and refined regions
Mesh distribution around the hull is shown in fig.3. There
are three refinement regions are created around the hull in order
to increase the grid resolution at where the velocity gradients
are higher. The first refinement region enclose the whole hull.
Second and third refinement regions are at bow and stern of the
hull. Grid resolutions in the bow and stern regions are two times
higher than the refinement region 1.
Calculations are carried out for five different Froude
numbers ranging between 0.12 and 0.20 (representing Prohaska
range) which is defined as Fn=V/√(gL), where V is the bulk
velocity, g is the gravitational acceleration and L is the length of
the hull. The Reynolds number based on the bulk velocity and
the ship hull is 5.45x106
for the case of Fn=0.14. Simulations
are performed using commercial CFD tool (based on finite
volume method) CD-ADAPCO STAR CCM+.
NUMERICAL RESULTS
While generating the mesh structure, the crucial parameter
is wall y+
. Because of the flow is considered as single phase, the
frictional resistance should be calculated precisely. It is also
important for form factor prediction. During the analyses, wall
y+
is checked to keep its value between 30-300 as shown in fig.
4. Some regions in the ship stern show less than 30 due to local
stagnation points just before the ship wake.
Fig 4. Wall y+
distribution on the hull
The mesh dependency study is given in fig. 5. Optimum
mesh number has been found about 1.1 million by comparing
the non-dimensional friction coefficient with the empirical
ITTC formula. And all the analyses have been conducted using
the optimum mesh structure.
Fig 5. Mesh dependency study at Fn=0.14
With the help of CFD code based on finite volume method
(FVM), several single phase simulations are made to predict the
form factor and to show the effect of Reynolds number on the
form factor. The numerical results can be seen in fig. 6.
Fig 6. From factor prediction with respect to Rn
Fig. 7 represents the comparison of non-dimensional
friction coefficients with ITTC 57 results for various Reynolds
numbers. As can be seen below, there is an acceptable
agreement between numerical and empirical results.
Fig 7. Friction coefficient comparison via Rn

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CONCLUSION
This study focuses on the effect of ship velocity on the
form factor prediction for a model scale ship. JBC hull is
chosen as the floating platform for form factor calculation. As
proposed by Prohaska, the form factor is not dependent on ship
velocity. However this study shows that the form factor is a
dependent variable to the ship velocity. Also it is expected that
the form factor may change for different scale factors. A
research about scale effect on form factor is planned as a future
work.
ACKNOWLEDGEMENTS
The authors are grateful to Mr. Ahmet Yurtseven for his
valuable efforts during the numerical analyses using his custom
developed high performance bewulf cluster platform.
REFERENCES
[1] A. Dogrul, “Experimental and numerical investigation of
ship resistance and free surface deformations,” PhD
Thesis, Yildiz Technical University, Istanbul, 2015.
[2] C. W. Prohaska, “A simple method for the evolution of the
form factor and low speed wave resistance,” presented at
the Proceedings of 11th ITTC, Tokyo, Japan, 1966, pp. 65–
66.
[3] A. Garcı́a-Gómez, “On the form factor scale effect,”
Ocean Eng., vol. 27, no. 1, pp. 97–109, 2000.
[4] J.-S. Kouh, Y.-J. Chen, and S.-W. Chau, “Numerical study
on scale effect of form factor,” Ocean Eng., vol. 36, no. 5,
pp. 403–413, 2009.
[5] N. Degiuli, N. Hadžić, M. Pedišić Buča, and G. Semijalac,
“Form Factor Determination of the Full, Large Breadth and
Shallow Draught Ship Series,” Shipbuilding, vol. 58, no. 4,
pp. 380–388, 2007.
[6] K.-S. Min and S.-H. Kang, “Study on the form factor and
full-scale ship resistance prediction method,” J. Mar. Sci.
Technol., vol. 15, no. 2, pp. 108–118, 2010.
[7] ITTC, “Report of Performance Committee,” presented at
the Proceedings of 15th ITTC, Hague, 1978.
[8] ITTC, “Report of Resistance Committee,” presented at the
Proceedings of 8th ITTC, Madrid, 1957.