Alexandria Engineering Journal (2019) 58, 849–859
H O S T E D BY
Alexandria University
Alexandria Engineering Journal
www.elsevier.com/locate/aej
www.sciencedirect.com
ORIGINAL ARTICLE
Numerical study on the hydrodynamic drag force of
a container ship model
Ahmed G. Elkafas a,*, Mohamed M. Elgohary a, Akram E. Zeid b
a
Department of Naval Architecture and Marine Engineering, Faculty of Engineering, Alexandria University, 21544
Alexandria, Egypt
b
Department of Marine Engineering Technology, Faculty of Maritime Transport and Technology, Arab Academy for Science,
Technology & Maritime Transport, 21937 Alexandria, Egypt
Received 6 May 2019; revised 7 July 2019; accepted 28 July 2019
Available online 16 August 2019
KEYWORDS
Computational fluid dynamics;
ANSYS-CFX;
Ship resistance;
Holtrop method;
Container ship;
Hydrodynamic drag
Abstract In recent years, importance has been recognized increasingly for the reduction of fuel
consumption of ships in a seaway to reduce green-house gas emissions from shipping. From a ship
design viewpoint, it is of crucial importance to establish reliable prediction methods for ship’s resistance and propulsive power. The required power for the propulsion unit depends on the ship resistance and speed. There are three solutions for the prediction of ship resistance as follow analytical
methods, model tests in tanks and Computational Fluid Dynamics (CFD). The rapid developments
in computers and computational methods increased the opportunities of the CFD simulation to be
used in the ship design process. The present paper aims at simulating ship resistance using CFD
simulations method which is conducted using ANSYS-CFX software package. As a case study,
Container ship scale model is investigated. The results show the ship resistance which calculated
at various ship speeds and Froude number. Predicted results for resistance components at various
Froude numbers were compared against Resistance results computed by using Holtop method. It is
shown that the simulation results agree fairly well with the results computed from Holtrop method,
and that ANSYS-CFX code can predict ship resistance.
Ó 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria
University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/
licenses/by-nc-nd/4.0/).
1. Introduction
In recent years, importance has been recognized increasingly
for the reduction of fuel consumption of ships in a seaway to
* Corresponding author.
E-mail addresses: es-ahmed.gamal1217@alexu.edu.eg, marineengineer36@gmail.com (A.G. Elkafas).
Peer review under responsibility of Faculty of Engineering, Alexandria
University.
reduce green-house gas emissions from shipping. It is estimated that almost 90% of global trade is mobilized by shipping. In the process of carrying such an immense amount of
goods, ships produce roughly 3% of global CO2 emissions,
14–15% NOX emissions and 16% of SOX emissions [1].
Increasing environmental concerns and adoption of different
emission related regulations have motivated both shipbuilders
and owners to opt for more efficient and environment-friendly
vessels. From a ship design viewpoint, it is of crucial importance to establish reliable prediction methods for ship’s resis-
https://doi.org/10.1016/j.aej.2019.07.004
1110-0168 Ó 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
850
tance and propulsive power for a range of operational speeds.
With the development of power-driven vessels in the nineteenth century, Evaluation of ship hydrodynamic parameters
and components of ship resistance began to be important.
The resistance of a ship at a selected speed and displacement
is the fluid force acting on the ship in the opposite direction
of its forward motion [2]. It can be defined as the force
required to move the ship at a particular speed [3]. There are
three solutions for the prediction of ship resistance as follows
analytical methods, model tests in tanks and Computational
Fluid Dynamics (CFD).
Towing tank model testing has been since early times, the
most reliable method for power predictions, because of its high
cost and demand for a fixed and given geometry it can be used
only in the basic design stage when the design parameters
related to the vessel’s hull geometry are fixed and serves as a
final validation and benchmark to be used afterward in the
conclusion of the shipbuilding process during sea trials [4].
On the other hand, the last decade has seen the exponential
growth of computational fluid dynamic solvers that solve Reynolds Averaged Navier Stokes equations over the hull form in
finite volume approaches [5]. Although originally the computational cost was penalizing its application in early design stages,
the advances in computing hardware and software allowed the
integration of Computational Fluid Dynamics (CFD) in the
early ship hull form design and optimization [6]. For the last
few decades computer technology has been exponentially
evolving in an unrestrained manner bringing massive Central
Processing Unit (CPU) power for acceptable price to the regular high-end users. Computational Fluid Dynamics (CFD)
is greatly dependent on CPU power since the basis in solving
a fluid flow of any kind is found in Navier-Stokes (NS) equations with extension. These require high computational effort
to acquire a satisfactory solution. So that Computational
Fluid Dynamic (CFD) approaches for studying the influence
of hydrodynamic forces on ships are increasingly used in the
marine field. CFD application is an easy and less time consuming application [7]. The accuracy of using CFD simulation is
proven to be high and most naval architects use this method
instead of towing tank experiment method which is tedious
and time consuming [2]. CFD application has advanced in
recent years and become one of the most important methods
used in ship building industries [8]. CFD methods can analyze
flow problems in resistance estimation. CFD techniques give
practical results with less effort in cost and time. Viscous flow
gives more accurate results of drag than potential flow [9,10].
Also, empirical or statistical methods are considered suited.
The most prominent of these is the approximate resistance and
power prediction method by Holtrop and Mennen together
with its revision [11]. Although this methodology provides sufficient accuracy, the statistical sample of the hull forms on
which it is based dates back to the 1970s and 1980s. Such hulls,
although roughly similar, have some distinct deviations from
modern commercial vessels. The Holtrop and Mennen method
is currently considered as one of the most accurate and efficient methods for the estimation of the resistance and propulsion power requirements of conventional monohull vessels at
the initial stages of design.
In this paper, example of CFD simulation of ship resistance
components is presented for Container ship model on calm
water. The software used for computations was ANSYS-
A.G. Elkafas et al.
CFX package which has implemented a RANS solver model.
In this paper, CFD simulations of the hull would be conducted
with the different velocities of flows. Predicted results for resistance components at various Froude numbers were compared
against resistance results computed by using Holtop method.
The study presented herein aims to assess the deviation of
the CFD simulation results when compared with the results
of Holtrop Method. The detail information about the geometry of the model, boundary layer, boundary domain, meshing
process, study conditions, testing installations would be presented on the following sections of the paper. Generally, it is
shown that the simulation results agree fairly well with the
results computed from Holtrop method, and that ANSYSCFX code can predict ship resistance
2. Theoretical background
2.1. Ship resistance and power
Ship Resistance is the total force that opposes the forward
motion of the ship at a corresponding speed in calm water.
Alternately, the force required to tow a ship in calm water at
a constant speed. In order to achieve a forward motion, vessel’s thrust must overcome the total resistance. The total resistance of ship consists of air and hydrodynamic resistances.
Hydrodynamic resistance is affected by the wetted surface area
of the ship hull. It can be divided into two main components
according to two approaches. It is composed of either the frictional and residual resistances or the viscous and wave resistances [2]. Particularly, frictional resistance component plays
an important role as it takes the largest portion of the total
ship resistance for the majority merchant ships. For example,
skin friction can account for up to 90% of the total resistance,
for a slow-speed ship [12]. The total resistance of a vessel can
be calculated by Eq. (1) [2].
RT ¼ RF þ RR Or RT ¼ RV þ RW
ð1Þ
where RT, RF, RR, RV and RW are the total resistance, friction
resistance, residual resistance, viscous and wave making resistance respectively. All above components of resistance are calculated using the generic form [2]:
1
R ¼ qCAV2
2
ð2Þ
where
C – The resistance coefficient
q – The density of the medium
A – Wetted Surface area
V – The vessel speed
For the current ship model, the total resistance in deep
water can be calculated using Holtrop-Mennen method. The
Holtrop method [11] is currently considered as one of the efficient methods for the estimation of the resistance and propulsion power requirements of conventional vessels. It is an
empirical method consisting of equations for the various resistance components that derive from the statistical analysis and
regression of a database with a large number of model test
results. The model developed by Holtrop is a numerical
Numerical study on the hydrodynamic drag force
851
description of the ship’s resistance, subdivided into components of different origin. Each component was expressed as a
function of the speed and hull form parameters. The application of Holltop’s method for the deep water resistance consist
many ship types, one of them is specified for our case as discussed in [11]. The Holtrop-Mennen Method has acquired
widespread recognition. Holtrop and Mennen tried to include
physical aspects in their formulas, but used the experimental
data for determining the coefficients. A summary of their
method which is based on test results from 334 models of tankers, cargo ships, trawlers, ferries, etc., is given below.
The resistance is split into viscous and wave resistance. For
the viscous resistance, the standard formula is used as presented in Eq. (3).
CV ¼ ð1 þ kÞCF
ð3Þ
where CF is obtained from the ITTC-57 formula. The form
factor k is determined from a formula obtained statistically
as follow.
B T L L3
k¼f
; ; CP ; c
ð4Þ
; ;
L L LR r
where c is a coefficient dependent on the shape of the after
body and LR is the length of the after body. If LR or S are
unknown, they may be obtained from other statistically
derived formulas. The appendage resistance is considered as
a correction to the form factor. For the wave resistance, Holtrop and Mennen use a theoretical expression attributed to
Havelock (1913), obtained by replacing the hull by two pressure disturbances separated by the wave making length of
the hull. The original expression is elaborated in the following
equation.
RW
d
¼ C1 C2 C3 emFn þ m2 cosðkFn2 Þ
W
ð5Þ
where W is the weight of the ship and C1, C2, C3, m, and m2 are
coefficients, which are functions of the form parameters of the
hull. Different coefficients are used for Fn = 0.40 and
Fn = 0.55. In the intermediate range, the residuary resistance
is obtained by an interpolation formula between the two limits.
Holtrop and Mennen also suggest a formula for the roughness
allowanceDCF and compute the total resistance as expressed in
Eq. (6).
1
RW
RT ¼ qV2 S½CF ð1 þ kÞ þ DCF þ
W
2
W
ð6Þ
After determining the resistances then the corresponding
effective power (PE) which help vessels moving through in
water with a determined speed can be calculated by Eq. (7).
PE ¼ RT V
ð7Þ
equations of mass, momentum can be written as follows in
Eqs. (8) and (9).
@q
þ r ðqUÞ ¼ 0
@t
ð8Þ
@ðqUÞ
þ r ðqU UÞ ¼ rp þ r s þ SM
@t
ð9Þ
where the stress tensor, s is related to the strain rate as
follow:
2
s ¼ lðrU þ ðrUÞT dr UÞ
3
ð10Þ
The Third governing equation of CFD is the total energy
equation which can be presented in the following form.
@ðqhhot Þ @q
þ r ðqUhhot Þ ¼ rðkrTÞ þ rðU sÞ þ U SM þ SE
@t
@t
ð11Þ
where htot is the total enthalby, related to the static enthalpy h
(T, p) by:
1
htot ¼ h þ U2
2
ð12Þ
The term rðU sÞ represents the work due to viscous stresses and is called the viscous work term. The term U SM represents the work due to external momentum sources and is
currently neglected.
Generally, the Navier-stokes equations describe both laminar and turbulent flows without the need for additional information. However, turbulent flows at realistic Reynolds
numbers span a large range of turbulent length and time scales.
In general, turbulence models seek to modify the original
unsteady Navier-stokes equations by the introduction of averaged and fluctuating quantities to produce the Reynolds Averaged Navier-Stokes (RANS) equations. Turbulence models
based on RANS equations are known as statistical Turbulence
models due to the statistical averaging procedure employed to
obtain the equations [14]. The Reynolds averaged equations
given below in Eqs. (13) and (14).
@q
@ qUj ¼ 0
þ
@t @xj
ð13Þ
@ðqUÞ
@ @p
@
þ
qUi Uj ¼ þ
ðsij qui uj Þ þ SM
@t
@xj
@xj @xj
ð14Þ
where s is the molecular stress tensor (including both normal
and shear components of the stress).
The need of turbulence models for RANS simulation is to
determine the Reynolds stresses. This process can be conducted by three categories of RANS turbulence.
Linear eddy viscosity
2.2. Computational fluid dynamics theory
The proposed CFD model was developed based on the
Reynolds-averaged Navier-Stokes (RANS) method for three
dimensional unsteady viscous incompressible flow using
ANSYS-CFX software package. The averaged continuity
and momentum equations for incompressible flows may be
given as in the following two equations [13]. The instantaneous
This is a turbulence models which using Reynolds stress
that obtained from the Reynolds averaging from Navier stokes
equations. This involves the relation between Reynolds stresses
and mean strain. This models has disadvantages in flow situations, such as, over predict turbulence energy levels in stagnant
regions, Misinterpretation of normal stresses and does not
reproduce the asymmetry in the velocity profile
852
Nonlinear eddy viscosity models
This turbulence model is more accurate than linear eddy
viscosity model. It is due to the fact the turbulence is a highly
nonlinear phenomena
Reynolds stress model (RSM)
This turbulence model which is also referred as the second
moment closure model is most complete turbulence model. In
this turbulence model, the eddy viscosity is removed and Reynolds stress are directly computed.
Referring to ANSYS-CFX, there are three type of turbulence model, which are k-epsilon, k-omega, and shear stress
transport (SST) [15].
K-e Model
The k-e model consists of k, kinetic energy and e, balance of
dissipation along with the complete RANS equation. The k-e
model works well away from the wall around the boundary
layer edge and for fully turbulent flows in the high Reynolds
regime.
K-x Model
The k-x model consists of k, kinetic energy and x, specific
dissipation turbulent frequency. Works well within the low
Reynolds regime and should have been applied for the
transitional Reynolds for this simulation. The model predicts
separation early and requires a mesh inflation layer near the
wall.
SST Model
The shear stress transport SST model, which is applied in
this simulation, gives high accuracy modelling of the boundary
layer and is a combination of both k-e and k-x. The SST
model gives accurate predictions of the onset and the amount
of flow separation under opposing pressure gradients, where
turbulence is present. By applying both previous models, it
covers both regions of the boundary layer, close to the wall
and far away from the wall close to the boundary layer limit
and applies the Bradshaw relation for good separation prediction [16].
The shear stress transport (SST) model was used for this
simulation to gain the longitudinal forces, resistance forces,
acting on a container ship model, as it gives the best results
for maritime engineering applications.
3. Methodology and setup
3.1. Model details
The case study for this paper is selected to be a Container ship
model. The vessel is a twin-propeller container ship [17]. A
1:100 scale model of this vessel was built in software. The general parameters of the model are listed in Table 1.
The 3D model of the vessel is processed using Rhinoceros
5.0 and MAXSURF Modeler and Imported to Geometry
A.G. Elkafas et al.
Table 1
Vessel and model particulars.
Symbol
Full-scale
vessel
Scaled vessel
model (1:100)
Unit
Length between
perpendiculars (LPP)
Breadth (B)
Draught (D)
Displacement
Metacentric height (GM)
Vertical centre of
gravity (KG)
LCG length (from aft
perpendicular)
247
2.47
m
32
12
64,000 ton
–
–
0.32
0.12
63.4 kg
8.75
153
m
m
–
mm
mm
–
1160
mm
Module of ANSYS Workbench version 19. Fig. 1 shows the
bare hull of model built in Rhinoceros 5.
3.2. Fluid domain geometry
The boundary domain is the area where flows (Air and Water)
will influence the hull of the vessel. The boundaries of the fluid
domain are designed to be placed with a sufficient distance
from the area of investigation. This is to ensure the accuracy
of the solution. The fluid domain for container ship model’s
investigation was built based on the International Towing
Tank Conference (ITTC)’s recommendation in order to prevent flow reflections [18]. The inlet and the exterior boundary
such as top, bottom and side of wall whereby the flow is undisturbed usually occurred, they are required to be located
around one or two total length of the object of investigation
which in this case is the length between perpendiculars. As
the outlet of the fluid domain is normally where the fluid is
unsteady, it is required to be placed around three to five
perpendicular length away from the ship to prevent the
interference or reflection of the flow, where half of the body
is modelled to decrease the computational domain size and
time. The ship axis is located along the x-axis with the bow
located at x = LBP and the stern at x = 0. The still water level
lies at z = 0. The dimensions of the computational domain
satisfy the well-known ITTC procedure. Detailed information
about the principles of computational domain dimensions’
selection strategy can be found in [19] and [20]. Also a detailed
description of the boundary conditions is given in [21]. The
general view of the computational domain and the boundary
conditions are shown in Fig. 2. Table 2 shows the selected
dimension for the fluid domain which represented in
ANSYS-CFX.
3.3. Mesh
The meshing of the fluid domain and the model were conducted using ANSYS Meshing 19.0 with the CFD as the physic preference and the CFX as the solver. The size function for
the mesh is set as curvature, the mesh will not change the shape
of hull or resemblance the tendency of hull’s shape. While the
minimum size of the mesh is set to be 1 mm such that the mesh
is allowed to capture the curvature of the model [22]. Table 3
presents the finalized mesh criteria.
Numerical study on the hydrodynamic drag force
Fig. 1
Fig. 2
Table 2
853
Geometry of container ship model.
Boundary Domain Conditions.
Size of the fluid domain geometry.
Fluid domain entities
B.C
ITTC
Selected
Distance (m)
Rectangular
Inlet
Outlet
Top & Bottom wall
Side wall
1–2
3–5
1–2
1–2
1
3
1
1
2.5
7.5
2.5
2.5
Table 3
Mesh size and specification.
Criteria
Value
Nodes
Body sizing (m)
Face sizing (m)
Inflation layer
Growth rate
Maximum thickness boundary layer (m)
239,385
0.3
0.008
5
1.2
0.05
Fig. 3
LPP
LPP
LPP
LPP
In order to ensure that the mesh represents the actual body
for analysis, refinement were made on the body of the fluid
domain, face of Hull. The refinements were as below:
3.3.1. Body sizing
The body sizing is applied with unstructured tetrahedral element size of 0.3m. The aim of body sizing applied is such that
the mesh size for both side of interface for the Box are same.
This action allows the optimal interpolation between fluid
domains [14].
Meshing of hull and fluid domain.
854
A.G. Elkafas et al.
3.3.1.1. Face sizing. Further refinement is conducted on the
face of the Hull. The element size applied on the face of the
Hull was 0.008 m. The refinement is conducted so that the flow
behaviour around the Hull can be modelled with a higher mesh
resolution which hence increase the accuracy of the results.
Fig. 3 below shows Meshing and inflation layer around hull.
The analysis is conducted based on steady state approached
as RANS based CFD stimulation method is used.
3.4.2. Domain characteristic
Table 4 presents the domain characteristics that being applied
to the flow.
3.4. CFX pre solver
3.4.3. Boundary condition
The completed mesh in the previous module is then imported
to the CFX Pre Solver of ANSYS CFX to define its analysis
method, fluid flow characteristic and its boundary conditions.
The details of the setup are as below:
3.4.4. Output control
3.4.1. Analysis setting
The turbulence model that is selected for the analysis is
Shear Stress Transport (SST) Model.
Table 4
The main interested output of the analysis is the hydrodynamic
performance of the Hull in term of drag force. In order to
monitor the progress of the CFX-Solver, the hydrodynamic
characteristic is expressed in the following expression [force_x()@Hull].
3.4.5. Solver control
Domain characteristics.
Criteria
Value
Fluid type
Fluid density (kg/m3)
Temperature (°C)
Kinematic viscosity (m2/s)
Morphology
Buoyancy model
Gravity Z component (m/s2)
Domain motion
Reference pressure (atm)
Turbulence model
Turbulent wall functions
Water
997
25
8.9E7
Continuous fluid
Buoyant
9.81
Stationary
1
SST
Standard
Table 5
Table 5 presents the type of boundary conditions that being
applied to the fluid domains and Fig. 4 shows the boundary
condition.
Solver control is used to increase the efficiency of the computer
resources and control the quality of the CFX solution; ensurTable 6
Solver control inputs.
Convergence control
Minimum iteration
Maximum iteration
Timescale control
200
1200
Auto
Convergence criteria
Residual type
Residual target
RMS
0.00001
Boundary condition setting specification.
Boundary type
Settings
Inlet
Inlet
Outlet
Top, Bottom and Side wall
Symmetry
Hull
Opening
Walls
Symmetry
Wall
Velocity Range = 1–2 [m/s]
Turbulence model: SST model
Mass and momentum: Entrainment Static Pressure: 0 [Pa]
Mass and momentum: Free slip wall
–
No Slip wall
Fig. 4
Boundary Condition on the Fluid Domain.
Numerical study on the hydrodynamic drag force
Fig. 5
855
Graph showing the convergence of the solution.
ing the result will converged to ensure the accuracy of the
results. The solver input and the convergence criteria were
defined in Table 6.
ing. As the residuals decrease further, the monitor values
change less and less between iterations. Once the monitor point
values have ‘‘flattened out”, so the solution is assumed to be
converged.
3.5. CFX solver
4. Independent study and results
The defined CFX-Pre files are imported into the CFX-Solver
for analysis. The run mode of the CFX solver was set to be
the Intel MPI Local Parallel with 2 partitions core and the
computations are made on 4 CPU with 2.50 GHz, on windows
Win10 system. Explanation of the numerical method can be
found in [23]. During the simulation progress, inspections on
the solution convergence is conducted and the results show a
converge trend. Figs. 5 and 6 show CFX Solver when simulate
the performance and reach the balance condition at results.
The residual monitors in Fig. 5 demonstrate monotonic convergence, indicating a well-posed problem and a tightly converged solution. Fig. 6 shows the change in the monitor
point(drag) values vs. iteration number. After approximately
100 iterations, the drag monitor point is within just a few percent of its final value. However, the drag value is still far from
its final value, so stopping the analysis here could be mislead-
4.1. Grid independence study
In order to reach the results with high accuracy in CFD simulation, the mesh must divide elements as much as possible.
However, the number of nodes of the simulated model directly
depends on three main factors (Technology, Time and Cost)
[24]. In this paper, Richardson’s extrapolation method for grid
convergence could be a proper choice for estimation of the
mesh error. To have a clear view of the method, the following
section have an illustration about calculation of the drag coefficient, which is based on the Richardson’s extrapolation
method [25] as shown in Fig. 7.
The grid convergence study was conducted based on the
ITTC, uncertainty analysis recommendation [4]. The convergence study was made based on three varying mesh resolution
856
A.G. Elkafas et al.
Fig. 6
Change of monitor point (drag) values vs. iteration number.
Fig. 7
Richardson Extrapolation method.
Numerical study on the hydrodynamic drag force
Table 7
857
The coarse, medium and fine mesh details.
Detail
Coarse
Medium
Fine
Body sizing (m)
Face sizing (m)
Number of nodes
Number of elements
Drag force (N)
Drag coefficient
0.3
0.008
248,863
781,248
5.13448
0.010107517
0.3
0.006
344,331
1,045,750
3
0.005905671
0.3
0.0046
503,421
1,496,670
2.334
0.004594612
Table 8
Results of meshing error estimation.
Outcome
Equation
Value
Change in solution (e32)
Changes in solution (e21)
Convergence ratio
Order of convergence
e32 = C(h3) C(h2)
e21 = C(h2) C(h1)
Ri = e21/e32
q = ln(e32/e21)/ln
(ri)
d = e21/rpi 1
CR = C1 – d
0.004201
0.001311
0.312019
3.461470
Error of the finest grid
Richardson extrapolated
solution
Relative error estimate (er)
0.000594
0.004000
er = Ci CR/CR
which were categorized into coarse, medium and fine mesh.
The mesh were varied by the modification of the face sizing
while keeping the body sizing with a constant element size.
The inflation layer was kept constant throughout the analysis
as the mesh resolution was based on the standard wall
calculation. It should be noted that there is a constant
refinement ratio exists between the nodes count on every mesh
that being conducted. Table 7 shows the details of the meshes
used for the convergence studies and drag force calculated at
each case at 1 m/s.
Based on formulas at the used equation section, outcomes
have been calculated and presented at Table 8.
Figs. 8 and 9 show the Richardson Extrapolation convergence studies and the relative error estimation that conducted
on the Hull to determine the mesh performance. It is expected
that the simulations which have the higher number of nodes
will be more accurate. The relative error estimation study is
conducted on the convergence result to determine is the error
between the results vary with number of nodes.
The drag coefficient was converged based on the graphs
which prove that the mesh is converged with different fineness
of mesh. However, the fine mesh is still chosen for analysis as it
provides a higher accuracy to the stimulation which hence minimizes the error of investigation.
4.2. Resistance results
0.012
Drag Coefficient
0.01
Drag Coefficient
CR
0.008
0.006
0.004
0.002
0
200
250
300
350
400
450
500
550
Number of Nodes(×1000)
Fig. 8
Number of nodes against Drag Coefficient.
Relave Error
10
1
100000
1000000
0.1
Number of Nodes
Fig. 9
nodes.
Drag’s Relative Error Estimation against the number of
After installation of simulation for the hull and boundary
domain in CFX-Pre, then simulations will run and export output data under tested conditions. It is the fact that this simulation only tests a half of the ship hull. Therefore, in order
to obtain the full resistance of the whole hull, the generated
result are doubled. Simulations presented in this study were
performed for 8 selected test conditions for different Froude
Number (Fn) and also different ship speeds as presented in
Table 9 which show the selected test conditions. The resistance
components resulted from CFD simulation are divided to skin
friction resistance and pressure resistance component. The
simulation results show that the skin friction resistance
account up to 90% of the total resistance as shown in Fig. 10.
In order to examine the accuracy of resistance results of the
simulated ship model by using ANSYS-CFX solver, the simulation results for the tested Froude numbers are thoroughly
validated by comparing directly with the resistance results
from the Holtrop prediction method [11] in MAXSURF software. The comparison determines the accuracy of the programming and the computational implementation of the
conceptual model in which it examines the mathematical
errors. CFD simulation and Holtrop method are investigated
similar test condition and Froude numbers to calculate the difference between both resistance components results.
Fig. 11 shows the comparison of skin friction resistance
results from CFD simulations to Holtrop skin friction resistance results. The comparison between two results is very good
for the whole simulated conditions. Within the simulated range
of Froude Number, the maximum error is 5.15% at Fn = 0.4.
The model results from CFD simulation indicate that the computations predicted 3.125% lower skin friction resistance at
Fn = 0.24 and 0.28, 4.2% lower skin friction resistance at
Fn = 0.35 compared to the results from Holtrop. Generally,
it is shown that the CFD simulation results agree fairly well
858
A.G. Elkafas et al.
Table 9
The selected test conditions (Speed-Froude Number).
Speed (m/s)
1
1.2
1.4
1.6
1.7
1.8
1.9
2
Fn ¼ pVffiffiffiffiffiffi
0.20315
0.24378
0.28441
0.32504
0.345355
0.36567
0.385985
0.4063
gL
with the results computed from Holtrop method, and that
ANSYS-CFX code can predict ship resistance.
Fig. 12 shows the comparison of pressure resistance
results from CFD simulations to Holtrop form component
results. Within the simulated range of Froude Number, the
model results from CFD simulation indicate that the computations predicted greater results than those from Holtrop
method.
18
Total Resistance
16
Skin Fricon Resistance
Resistance (N)
14
Pressure Resistance
12
10
8
6
5. Conclusion and recommendation
4
2
0
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Froude Number (Fn)
Fig. 10 Resistance components values calculated by CFD
simulation Versus Froude Number.
Skin Fricon Resistance (N)
16
CFD Simulaon
14
Holtrop Method
12
10
8
6
4
2
0
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Froude Number(Fn)
Fig. 11 Comparison of Skin friction resistance between CFD
simulation and Holtrop Method.
1.6
Resistance(N)
1.4
1.2
CFD pressure component
1
Holtrop Form component
0.8
0.6
0.4
0.2
0
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Froude Number (Fn)
Fig. 12 Comparison between CFD simulation’s pressure component and Holtrop’s form component.
In this paper, a Reynolds averaged Navier Stokes (RANS)
method is presented to predict the resistance components
results for a container ship model. The software used for computations was ANSYS-CFX package which has implemented a
RANS solver model. The turbulence model that is selected for
the analysis is Shear Stress Transport (SST) Model which gives
high accuracy modelling of the boundary layer and is a combination of both k-e and k-x. To predict the resistance of ship
with different running attitudes conveniently, a plenty of
numerical simulations of ship advancing at different speeds
and Froude numbers are carried out. After installation of simulation for the hull and boundary domain in CFX-Pre, then
simulations will run and export output data under tested conditions. The resistance components resulted from CFD simulation are divided to skin friction resistance and pressure
resistance component. The simulation results show that the
skin friction resistance account up to 90% of the total
resistance.
Accuracy of the computations is evaluated by comparing
with the results from Holtrop Method in MAXSURF software. First, computed skin friction resistance results from
CFD simulation are compared with Holtrop skin friction resistance results. The comparison between two Results is very
good for the whole simulated conditions. Within the simulated
range of Froude Number, the maximum error is 5.15% at
Fn = 0.4. Then, the comparison of pressure resistance results
from CFD simulations to Holtrop form component results is
presented. Within the simulated range of Froude Number,
the model results from CFD simulation indicate that the computations predicted greater than results from Holtrop method.
Generally, it is shown that the degree of agreement with Holtrop prediction method is satisfactory for resistance components. The present simulation seems to indicate the
availability of ANSYS-CFX as a tool for the prediction of ship
resistance and its application to the development of ship
design.
A grid convergence study has been conducted to determine
the accuracy of the mesh and hence increase the accuracy
of the predicted result. The grid convergence study done and
the analysis conducted with Low Reynolds Wall Treatment,
the stimulation result seem to be acceptable and further
investigation can be conducted.
Numerical study on the hydrodynamic drag force
In general, the CFD simulations by computer software,
which would give us the results with high accuracy, timesaving and presented in visual images must be highly used.
So that more and more CFD simulations would be applied
on the whole fields simply because of its efficiency and
reliability.
The recommendations for a better future of this work can
be concluded, the verification of the accuracy of CFD simulation results based on the results from Holtrop method. It is not
really objectivity when evaluates the results of a software by
another one’s. However, due to limitations of research which
have led to not carry out simulations by the experimental
model in towing tank in order to get data for validation purposes. Therefore, one of the future recommendations, the
Results of CFD simulation must be compared with Experimental data generated from Towing tank or using another
software in order to be more validated.
For further investigation, it is necessary to solve the problem of nodes number limitation. The higher use of nodes number will increase the accuracy of result even though the
simulation time will be longer.
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