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A CFD model for the frictional resistance predictionof
antifouling coatings
Yigit Kemal Demirel a,n, Mahdi Khorasanchi a, Osman Turan a,
Atilla Incecik a,Michael P. Schultz b
a Department of Naval Architecture, Ocean and Marine
Engineering, University of Strathclyde, 100 Montrose Street,
Glasgow G4 0LZ, UKb Department of Naval Architecture and Ocean
Engineering, United States Naval Academy, Annapolis, MD, USA
a r t i c l e i n f o
Article history:Received 27 February 2014Accepted 9 July
2014
Keywords:Antifouling coatingsFrictional resistanceComputational
Fluid DynamicsHull roughness
a b s t r a c t
The fuel consumption of a ship is strongly influenced by her
frictional resistance, which is directlyaffected by the roughness
of the hull's surface. Increased hull roughness leads to increased
frictionalresistance, causing higher fuel consumption and CO2
emissions. It would therefore be very beneficial tobe able to
accurately predict the effects of roughness on resistance. This
paper proposes a ComputationalFluid Dynamics (CFD) model which
enables the prediction of the effect of antifouling coatings
onfrictional resistance. It also outlines details of CFD
simulations of resistance tests on coated plates in atowing tank.
Initially, roughness functions and roughness Reynolds numbers for
several antifoulingcoatings were evaluated using an indirect
method. Following this, the most suitable roughness functionmodel
for the coatings was employed in the wall-function of the CFD
software. CFD simulations oftowing tests were then performed and
the results were validated against the experimental data given
inthe literature. Finally, the effects of antifouling coatings on
the frictional resistance of a tanker werepredicted using the
validated CFD model.
& 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Hull resistance is of paramount importance to ships since
itdirectly affects their speed, power requirements and fuel
con-sumption. For this reason, reducing a ship's resistance is
afundamental requirement for naval architects, in order to
benefitship owners.
Ship resistance can be classified into two types:
frictionalresistance and residuary resistance. Frictional
resistance canaccount for up to 8085% of a ship's total resistance,
particularlyfor merchant ships sailing at low speeds (van Manen and
vanOossanen, 1988). As 95% of the world's cargo is transported by
sea(RAEng, 2013), a means of reducing the frictional resistance
ofships would dramatically reduce their fuel consumption, leadingto
reduced carbon emissions worldwide. The best method toreduce
frictional resistance is to apply a treatment to a ship's hull,to
minimise its physical and biological roughness. Physical rough-ness
can be minimised by applying some preventative measures,but
biological roughness (fouling) is more difficult to control.Fouling
begins to occur immediately after a ship is immersed in
water, and will continue to occur throughout a ship's life at
seauntil a cleaning process is performed. The level of fouling
dependson several factors, including the length of time spent at
sea, thewater temperature, the geographical location of the ship,
surfaceconditions and the salinity of the sea. The longer the
ship'simmersion time, the greater the level of fouling. Such
fouling isresponsible for a dramatic increase in a ship's
frictional resistance.
Fouling causes surface roughness, resulting in an increase in
aship's frictional resistance and fuel consumption (Kempf,
1937).Milne (1990) stated that the fuel consumption may increase by
upto 40%, unless any precautions are taken to prevent fouling.
Accord-ing to Taylan (2010), the increase in resistance due to
microorganismfouling is around 12%, whereas an accumulation of hard
shelledorganisms may cause an increase in resistance of 40%.
Schultz (2007)investigated the effect of fouling on the required
shaft power for afrigate at a speed of 15 knots. He found that the
presence of slimealone required a 21% increase in shaft power,
compared to anotherwise identical slime-free frigate, whereas heavy
calcareousfouling led to an 86% increase in shaft power
requirements.
The use of marine antifouling coatings is a common method usedto
smooth hull surfaces to reduce the frictional resistance and
fuelconsumption of a ship. Additionally, the use of coatings with a
propercathodic protection system can offer effective corrosion
protection(Tezdogan and Demirel, 2014). However, such coatings will
have
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Ocean Engineering
http://dx.doi.org/10.1016/j.oceaneng.2014.07.0170029-8018/&
2014 Elsevier Ltd. All rights reserved.
n Corresponding author. Tel.: 44 1415484275.E-mail address:
[email protected] (Y.K. Demirel).
Ocean Engineering 89 (2014) 2131
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initial surface roughnesses which affect a ship's frictional
resistance.A means of assessing the effect of such a coating on
frictionalresistance would therefore be of great benefit. However,
at present,there is no accurate method available to predict the
effect of shiproughness due to the use of antifouling coatings
(ITTC, 2005, 2011a).
An early review of studies investigating the effect of roughness
onfrictional resistance was performed by Lackenby (1962).
Recently,Demirel et al. (2013b) demonstrated the importance of
antifoulingcoatings with regards to ship resistance and powering.
Differentcoatings result in different levels of fouling, meaning
varying levels ofhull roughness are seen for the same immersion
time. A variety ofcoatings were therefore evaluated with regards to
hull roughness aftera specific time, and predictions of the
increase in effective power for anLNG carrier were made. Schultz
(2004, 2007) investigated the effects ofseveral coatings' roughness
and fouling on ship resistance and power-ing, and Candries et al.
(2003) examined the effect of antifoulings oncylindrical surfaces
and flat plates. Candries (2001) compared the drag,boundary layer
and roughness characteristics of two coatings.
Khor and Xiao (2011) investigated the effects of fouling and
twoantifouling coatings on the drag of a foil and a submarine by
employ-ing a Computational Fluid Dynamics (CFD) method. They used
theequivalent sand grain roughness height and the built-in
wall-functionwhich considers the uniform sand-grain roughness
function modelproposed by Cebeci and Bradshaw (1977), based on
Nikuradse's data(1933). Currently, the ITTC (2011b) is still
questioning the validity ofthe roughness model and equivalent sand
grain roughness used inCFD applications for hull roughness, since
it is known that the built-inroughness function model is based on
uniform, closely packed sandroughness, whereas the roughness
functions of real engineeringsurfaces do not show this behaviour.
Izaguirre-Alza et al. (2010) alsoconducted experiments with plates
coated with two different coatings.They used the CFD software
package STAR-CCM to simulate theirexperiments and validate the
roughness feature of the software.Although the comparison shows a
very good agreement betweenthe experimental data and the evaluated
results, there is no evidenceof the use of a specific roughness
function model, rather than thebuilt-in roughness function.
Leer-Andersen and Larsson (2003), on theother hand, employed
roughness functions in a commercial CFD codeand predicted the skin
friction of full scale ships. However, they used aspecific module
of the software and the study does not include RANScalculations.
Date and Turnock (1999) demonstrated the requiredtechniques to
predict the skin friction of flat plates using RANS solversand also
showed that the effect of surface roughness on skin frictioncan be
predicted using CFD software.
To the best of our knowledge, no specific CFD model exists
topredict the effects of a marine antifouling coating's roughness
onflow and frictional resistance. The aim of the present study
istherefore to fill this gap by employing a modified wall-function
inthe CFD software. The proposed approach enables the predictionof
the frictional resistance coefficients of coated plates for
differentspeeds, using only roughness measurements of the surfaces.
Thismodel will also be a solid basis for a CFD model for the
predictionof the effect of fouling on frictional resistance.
In this study, the experimental data of Schultz (2004) wereused
to establish the most suitable roughness function model
forcoatings. The required quantities were evaluated from the
experi-mental data using an indirect method, and a roughness
functionmodel and roughness length scale were determined for
coatings.This roughness function model was then employed in the
wall-function of the CFD software package STAR-CCM .
Following this, a validation study was performed through
CFDsimulations of towing tests involving coated plates at
threeReynolds numbers (2.8106, 4.2106 and 5.5106), in a
similarmanner to the experiments of Schultz (2004), using STAR-CCM
.Frictional resistance coefficients and roughness Reynolds
numberswere computed and compared with the experimental data.
It
should also be borne in mind that CFD simulations performed
inthis study are similar in part to those performed by Demirel et
al.(2013a, 2014). However, these were exploratory studies and
thesimulations were performed at only one towing speed.
Addition-ally, within the present study, improvements were made to
thesimulations to ensure their reproducibility.
It is important to note that the investigation was carried
outusing flat plates, based on the major assumption of Froude,
whichproposes that the skin friction of a hull is equal to that of
a flatplate of the same length and area as the wetted surface of
the ship(Lackenby, 1962). It is therefore convenient to choose a
flat plate,as the surface roughness affects only the skin friction
of a ship.
After the validation study, the effect of antifouling coatings
onthe frictional resistance of a tanker was predicted using
thedeveloped CFD model. A flat plate of length 170 m was chosen
torepresent a handymax tanker. Different types of antifouling
coat-ings were considered at an operational ship speed of 13
knots.The plate was fully submerged since the surface roughness
doesnot affect the wave-making resistance. Frictional resistance
coeffi-cients of the plate were evaluated for each case.
This paper is organised as follows: in Section 2, brief
theoreticalinformation is given about the turbulent boundary layer
and aboutroughness effects on the velocity profile in the turbulent
boundarylayer. A determination of the appropriate roughness
functionmodel for antifouling coatings is presented in Section 3,
while anew wall-function formulation is proposed and details of the
CFDsimulations are covered in Section 4. In Section 5, the
numericalresults and the experimental data are compared, and
predictionsof the increase in the frictional resistance
coefficients of a tankercoated with different antifouling coatings
are demonstrated.Finally, the results of the study are discussed in
Section 6, alongwith recommendations for future avenues of
research.
2. Background
2.1. The turbulent boundary layer
The turbulent boundary layer concept is essential in order
tounderstand and assess the flow around a ship, since a
turbulentboundary layer occurs around a ship when she is in
motion.
If a flat plate is taken as an example, the flow is laminar at
thefirst portion of the plate. As the flow continues across the
plate, itbecomes more and more turbulent in the transition region,
untilit eventually becomes a turbulent flow. The length of the
transitionregion can vary due to several factors including surface
roughness,pressure and velocity fluctuations (Candries, 2001). Fig.
1 showsthe typical development of a turbulent boundary layer over a
flatsurface (Cortana, 2013).
The turbulent boundary layer is assumed to consist of two
mainregions: an inner region and an outer region. The flow in the
innerregion is affected by surface conditions, such as roughness,
whilstthe flow in the outer region is not affected by such
conditions.
The inner region is composed of a viscous sublayer and a log-law
region. The mean average velocity in this region depends uponwall
shear stress, the density of the fluid, kinematic viscosity andthe
distance from the wall.
The non-dimensional mean velocity profile can be expressed bythe
law of the wall, given by
U f y 1where U is the non-dimensional velocity in the boundary
layerand y is the non-dimensional normal distance from the
bound-ary. These terms are further defined as follows:
U UU
2
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 213122
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y yU
3
where U is the mean velocity, U is the friction velocity defined
asffiffiffiffiffiffiffiffiffiffiw=
p, y is the normal distance from the boundary, is the
kinematic viscosity, w is the shear stress magnitude and is
thedensity of the fluid.
The viscous sublayer consists of a linear sublayer and a
bufferlayer. As the name suggests, the velocity profile is linear
in thelinear sublayer, given by
U y 4
In the buffer layer, the velocity profile begins to deflect
fromlinearity. In the log-law region, a velocity profile for
smoothsurfaces was suggested as follows (Millikan, 1938):
U 1ln y B 5
where is the von Karman constant and B is the smooth wall
log-law intercept. The velocity profile in a typical turbulent
boundarylayer is shown in Fig. 2 (Schultz and Swain, 2000).
2.2. The effect of roughness on the turbulent boundary layer
Surface roughness leads to an increase in turbulence, whichmeans
that the turbulent stress and wall shear stress
increase.Ultimately, the velocity in the turbulent boundary layer
decreases.
Although roughness can be described using various para-meters,
the key parameter is thought to be the roughness height,k, or
equivalent sand roughness height, ks. The roughness heightcan be
normalised and termed the roughness Reynolds number,given by
k kU
6
The flow over a surface is generally classified with respect
tothe roughness Reynolds number, i.e. as a hydraulically
smoothregime, a transitionally rough regime or a fully rough
regime.However, it should be noted that different roughness types
maygenerate different flow regimes on surfaces even if the
sameroughness Reynolds number is recorded (Schultz, 2007).
The law of the wall in the inner region changes in the
presenceof surface roughness. The velocity in the inner region of
theturbulent boundary layer over a rough surface becomes a
functionof y and k , given as follows (Schubauer and Tchen,
1961):
U f y ; k 7
The effect of roughness on flow can also be observed on
thevelocity profile (Schultz and Swain, 2000). Roughness causes
adecrease in the log-law velocity profile (termed the
roughnessfunction) shown as U . The roughness function in the
velocityprofile due to roughness is depicted in Fig. 3 (Schultz and
Swain,2000). The log-law velocity profile for rough surfaces in
theturbulent boundary layer is given by
U 1ln y BU 8
in which U is the roughness function. It should also
beconsidered that the decrease in velocity profile manifests
itselfas an increase in the frictional resistance.
U values are typically obtained experimentally, since there isno
universal roughness function model for every kind of roughness.
3. Roughness functions
Schultz (2004) conducted towing tests of flat plates coated
withdifferent antifouling coatings in order to investigate the
initialdrag performances of the coatings. He used five antifouling
coatingsystems: Silicone 1, Silicone 2, Ablative Copper,
Self-Polishing
Fig. 2. Velocity profile in a turbulent boundary layer, adapted
from Schultz andSwain (2000).
Fig. 1. The development of a turbulent boundary layer over a
flat surface (Cortana, 2013).
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 2131 23
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Copolymer (SPC) Copper and SPC TBT (Tributyltin). Three
controlsurfaces were also tested: the plates covered with 60-grit
and 220-grit sandpapers (SP) and a smooth surface. The frictional
resistancecoefficients of each test surface were obtained for seven
differentReynolds numbers.
Roughness amplitude parameters of all test surfaces are shownin
Table 1. Ra is the average roughness height, Rq is the root
meansquare average of the roughness profile ordinates and Rt is
themaximum peak to trough roughness height.
k and U for the surfaces were obtained iteratively usingthe
following equations (Granville, 1987) using the
experimentaldata
k kL
ReLCF
2
ffiffiffiffiffiffi2CF
s !R
11
ffiffiffiffiffiffiCF2
r !R
1
32
U 0
CF2
R
" #
9
U ffiffiffiffiffiffi2CF
s !S
ffiffiffiffiffiffi2CF
s !R
19:7ffiffiffiffiffiffiCF2
r !S
ffiffiffiffiffiffiCF2
r !R
" #
1U
0ffiffiffiffiffiffiCF2
r !R
10
where L is the plate length, ReL is the plate Reynolds number,
CF isthe frictional drag coefficient, U
0is the roughness function
slope and the subscript S indicates a smooth condition
whereasthe subscript R indicates a rough condition.
The selection of the roughness height is critical to define
aroughness function model, though the selected roughness heightdoes
not affect the roughness function value it only affects theabscissa
of the profile of roughness functions against roughnessReynolds
numbers. For this reason, the roughness height can beselected such
that the roughness function values fall on a pre-defined roughness
function model, provided that the observedbehaviours are still
deemed appropriate relative to each other.
As per Schultz's (2004) suggestion, 0.17Ra is chosen as
theroughness height for antifouling surfaces, whereas the
roughnessheight for sandpapers is chosen as 0.75Rt. Fig. 4 depicts
theevaluated roughness functions and roughness Reynolds
numberstogether with the roughness function models.
It is evident from Fig. 4 that the roughness functions
forantifouling coatings are in good agreement with the
Colebrook-type roughness function of Grigson (1992) using k0.17Ra,
and theroughness functions for sandpapers show excellent
agreementwith Schlichting's (1979) uniform sand roughness function
usingk0.75Rt. It should be noted that these roughness heights
androughness function models were proposed by Schultz (2004).A
piece of future work may be the investigation of the range of
Table 1Roughness amplitude parameters for all test surfaces,
adapted from Schultz (2004).
Test surface Ra (m) Rq (m) Rt (m)
Silicone 1 1272 1472 6677Silicone 2 1472 1772 8578Ablative
Copper 1371 1671 8376SPC Copper 1571 1871 97710SPC TBT 2071 2472
1297960-Grit SP 12675 16077 983789220-Grit SP 3072 3872 275717
Fig. 3. The roughness effect on log-law velocity profile,
adapted from Schultz andSwain (2000).
Fig. 4. Roughness functions vs. roughness Reynolds number for
(a) coatings and (b) sandpapers.
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 213124
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applicability of the selected roughness height for
antifoulingcoatings.
As seen in Fig. 4, different types of surfaces, such as
antifoulingcoatings and sandpapers, show different roughness
functionbehaviours, meaning different pre-defined roughness
functionmodels are appropriate for each type. For this reason, the
selectedroughness length scales may vary accordingly in order for
them tofall on the corresponding model. This means that, the
roughnessfunction models and roughness heights selected in this
study maynot necessarily work for other surfaces and other
roughnessfunction models.
Although there are other roughness function models which
arethought to be suitable for real engineering surfaces and
fouling,such as the one described in Schultz and Flack (2007),
theColebrook-type roughness function of Grigson (1992) is
appro-priate when only antifouling coatings are taken into
account.
4. Numerical modelling
4.1. Mathematical formulation
An Unsteady Reynolds-Averaged NavierStokes (URANS)method was
used to solve the governing equations in this study.These mass and
momentum conservation equations were solvedby the commercial CFD
software STAR-CCM . The averagedcontinuity and momentum equations
for incompressible flowsare given in tensor notation and Cartesian
coordinates by thefollowing (Ferziger and Peric, 2002):
uixi
0; 11
uit
xj
uiuju0iu0j pxi
ijxj
12
where is the density, ui is the averaged Cartesian components
ofthe velocity vector, u0iu
0j is the Reynolds stresses and p is the mean
pressure. ij are the mean viscous stress tensor components,
asfollows:
ij uixj
ujxi
13
in which is the dynamic viscosity.The solver uses a finite
volume method which discretises the
governing equations. A second order convection scheme was
usedfor the momentum equations and a first order temporal
discreti-sation was used. The flow equations were solved in a
segregatedmanner. The continuity and momentum equations were
linkedwith a predictorcorrector approach.
The Shear Stress Transport (SST) k turbulence model wasused in
order to complete the RANS equations, which blends thek model near
the wall and the k model in the far field.The Volume of Fluid (VOF)
method was used to model andposition the free surface, in cases
where a free surface was present.In this study, the
CourantFrederichLewis (CFL) number wasalways held at values less
than unity to ensure the numericalstability.
4.2. Wall-function approach for antifouling coatings
Wall functions are mathematical expressions which are used
tolink the viscosity affected region between the wall and
log-lawregion (ANSYS, 2011). This approach assumes that the near
wallcell lies within the logarithmic region of the boundary layer.
Thestandard wall functions used in this study impose standard
walllaws which have discontinuities between the laminar and
logarithmic regions. The velocity profiles of standard wall
lawsare given as follows (CD-ADAPCO, 2012):
U Ulam - y
rymUturb - y
4ym
(14
where U is the wall-parallel velocity normalised with respect
toU, ym is the intersection of the viscous and fully turbulent
regions,and the subscripts lam and turb indicate laminar and
turbulentproperties, respectively.
Given that roughness causes a downward shift in the
velocitydistribution in the log-law region, the mean velocity
distribution istaken to be equivalent to the turbulent velocity
profile from thispoint onward: U Uturb. The log-law velocity
profile is defined by
U 1lnE0y 15
where
E0 Ef
16
in which E is the wall function coefficient and f is the
roughnesscoefficient. is taken to be 0.42 as suggested by Cebeci
andBradshaw (1977). For smooth flows, f becomes unity, and E
waschosen such that Eq. (5) is satisfied for B5.2.
The coefficient f is directly related to the roughness
functionand its value depends on the flow regime. f is described by
Eqs.(17) and (18) (CD-ADAPCO, 2012). It is of note that the
coefficient fis an expanded version of the expression given by
Cebeci andBradshaw (1977)
f 1 - k o ksmA k
ksmkr ksm
Ck
h ia- ksmo k
okrACk - kr ok
8>>>>>:
17
where
a sin 2log k =ksmlog kr =ksm
" #18
ksm and kr designate the smooth and the rough roughness
Reynolds number limits, respectively, in which the flow is
hydrau-lically smooth for koksm and fully rough for k4k
r . The model
used by the software assumes that flow is occurring over
uniform,closely packed sand as proposed by Cebeci and Bradshaw
(1977),based on Nikuradse's data (1933), using the default values
ofksm2.25 and kr 90, and the coefficients A0 and C0.253.The
proposed model in this paper, on the other hand, suggests thatthe
wall law for antifouling coatings satisfies the mean
velocityprofile given by
U 1ln
y
1k
B 19
For this reason, only one roughness function model for
coatingsis proposed, since the roughness function behaviours of
coatingscan be represented by one simple model, as evidenced inFig.
4. ksm and k
r are therefore chosen such that it is almost
impossible for k to fall in the first two regimes k is
alwaysgreater than kr . The coefficients A and C are then chosen
such thatthe roughness function model matches the
Colebrook-typeroughness function of Grigson (1992). k0.17Ra is
chosen for thesurfaces coated with antifouling coatings.
4.3. Geometry and boundary conditions
It is necessary to select appropriate boundary conditions forCFD
problems, since these boundary conditions directly affect the
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 2131 25
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accurate flow solutions. Two sets of boundary conditions
aredefined in this study, one for the validation study and the
otherfor the full scale prediction study.
For the validation simulations, no-slip wall boundary
condi-tions were applied to the bottom and wall of the domain
becausethey represent the real bottom and wall of the towing tank
usedby Schultz (2004). Therefore the corresponding dimensions
werechosen accordingly. The plate was also modelled as a no-slip
roughwall in order to represent the roughness on the plate. The top
ofthe domain, which represents air, was modelled as a wall witha
slip condition applied to it. The two opposite faces at
thex-direction of the domain, i.e. the left-hand face and
right-handface of the domain in the top view, were modelled as a
velocityinlet and a pressure outlet, respectively. The symmetry
plane, asthe name implies, has a symmetry condition. Hence, only
half ofthe plate and control volume were taken into account. This
doesnot significantly affect the computations and it halves the
requiredcell numbers.
For the full scale prediction simulations, it is assumed that
theplate is completely submerged in an infinite ocean, since
surfaceroughness only affects skin friction. Therefore, it is only
necessaryto model a quarter of the plate. The total number of cells
and therequired computational time is decreased by quartering
theproblem by means of defining two symmetry planes, with
nocompromise in accuracy. For this reason, the lower faces, both
inthe top view and profile view, were modelled as symmetry
planes.The plate itself has a no-slip rough wall condition to
represent theroughness on the plate. The left-hand face and
right-hand face of
the domain in the top view were modelled as a velocity inlet and
apressure outlet, respectively. The rest was set up to be
symmetricalin order to eliminate wall effects to as great a degree
as possible.
The dimensions of the plate and the control volume, and
theboundary conditions used, are shown in Fig. 5 for the
validationstudy and in Fig. 6 for the full scale prediction study.
The validationsimulations are reproductions of the experiments
given by Schultz(2004).
Another critical selection is the positioning of the
boundaries,especially the downstream outlet boundary and the
upstream inletboundary. The inlet is placed at one plate length
upstream and theoutlet boundary is placed at two plate lengths
downstream for thefull scale predictions, to ensure the boundary
independent solu-tions as per the findings of Date and Turnock
(1999). The positionsof the inlet and outlet boundaries are doubled
for the validationstudy since there is a free surface in this
case.
4.4. Mesh generation
A cut-cell grid with prism layer mesh on the walls wasgenerated
using the automatic mesh generator in STAR-CCM .The plate was
meshed separately to give a much finer grid, withadditional
refinement at the free surface. Refined meshes weregenerated in the
area around the plate, as well as in the wakeregion, in order to
accurately capture the flow properties for thevalidation study. A
special near-wall mesh resolution was appliedto all surfaces with
the no-slip boundary condition. Details of thenear-wall mesh
generation are given in the following section.
A convergence test was carried out in order to obtain
gridindependent solutions, since the cell numbers are influential
on
Fig. 5. (a) The plate, (b) profile view of the domain and (c)
top view of the domain,showing the dimensions and boundary
conditions used for the validation study.
Fig. 6. (a) The plate, (b) profile view of the domain and (c)
top view of the domain,showing the dimensions and boundary
conditions used for the full scaleprediction study.
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 213126
-
the solution. It is of note that once the mesh independent
solutionis achieved, further refinement of the mesh does not affect
thefinal solution, though it does affect the solution time. The
fulldetails and a discussion of the grid dependence tests are given
inSection 5.1. As a result of the tests, in total, ca. 4 million
cells weregenerated for both the validation and prediction
studies.
Fig. 7 shows cross-sections of the meshed domain whereasFig. 8
shows a view of mesh configurations of the plate and thefree
surface. Fig. 9 shows cross-sections of the meshed domain ofthe
full scale prediction simulations. It is of note that the
figuresshow the whole sections as if there is no symmetrical
boundaryowing to the visual transform feature of the software.
4.4.1. Near-wall mesh generationAn important point is the
selection of the prism layer
thickness and the number of prism layers, since this repre-sents
the boundary layer of the wall. The prism layer thick-ness and the
prism layer number determine the normaldistance from the centroid
to the wall in wall-adjacent cells.This distance is crucial to
capture the gradients in theboundary layer and it should be
selected with regards tothe roughness height and required y
values.
The prism layer thickness on all no-slip walls was set to
thecorresponding turbulent boundary layer thickness along the
flatplate in question for each Reynolds number. Prism layer
numberswere selected to ensure that the y value on the plate
ismaintained at a value greater than 30 in order to use
standardwall laws for all Reynolds numbers. It is of note that the
sameprism layer numbers were used for all Reynolds numbers. In
theprism layer mesh generation, a geometric progression with
ratio1.5 was used in all directions. A near wall mesh dependence
studywas carried out and the details and a discussion of the study
aregiven in Section 5.1. The final y distribution on the
smoothsurfaces is shown in Fig. 10 for the validation study and in
Fig. 11for the full scale prediction study. Only a small portion of
the plateis shown in Fig. 11, as it is 170 m long in total.
5. Results
5.1. Grid dependence tests
Systematic studies were performed using the surfaces coatedwith
SPC TBT in order to obtain grid independent solutions forboth
validation and full scale prediction studies.
Fig. 7. (a) Profile view cross-section and (b) top view
cross-section of the domain.
Fig. 8. Mesh for the plate and free surface.
Fig. 9. (a) Profile view cross-section and (b) top view
cross-section of the domain.
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 2131 27
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Firstly, a near-wall grid dependence study was carried out
todetermine the effect of y on the calculated CF values of both
theplate operating at Re2.8106, and the plate which representsthe
tanker operating at 13 knots. To generate each mesh, thedistance of
the first grid from the rough wall was graduallychanged, whilst
keeping all other parameters the same. The resultsfrom different
simulations, each with a different y value, areshown in Table 2 for
the validation study and in Table 3 for the fullscale prediction
study. The y values listed represent the modes ofthe y distribution
histograms.
As demonstrated in Table 2, the solution with the y value of7.5
deviates significantly from the experimental data, as
expected,since standard wall laws can be used only if y values are
greaterthan 30. The results presented in Table 2 demonstrate that
thesolution with the y value of 50 was converged fairly well.This
resolution was therefore used throughout all cases of thevalidation
study.
It can be seen from Table 3 that the solutions with the y
values of 110 and 75 converged well, with little variation in
the CFvalue when using y values of either 110 or 75. On the other
hand,the difference in the total number of cells is half a million
betweenthese two resolutions. Therefore, the resolution with the y
value
of 110 was chosen and used throughout all cases of the full
scaleprediction study.
Having determined the near-wall mesh resolutions, a
griddependence test for the rest of the domain, including the
plateitself, was carried out. The rest of the domain was
discretised infour different resolutions; coarse, medium, fine and
very fine. Thefrictional resistance coefficients for each mesh
configuration werecomputed and are given in Tables 4 and 5.
The solution for the coarse mesh configuration in the
valida-tion study did not converge, and showed very large
oscillations.This may be due to the weak resolution of the plate
geometry,as well as the free surface and wake. From Tables 4 and 5
it is
Fig. 10. y Values on the smooth plates at (a) Re2.8106, (b)
Re4.2106, and (c) Re5.5106.
Fig. 11. y Values on the smooth plate at 13 knots.
Table 2CF results at different y values for the validation
study.
y Total no. cells CF (CFD) % Experiment
230 3.2106 0.004026 6.42130 3.5106 0.003937 4.0850 4106 0.003776
0.197.5 4.5106 0.003494 7.65
Table 3CF results at different y values for the full scale
prediction study.
y Total no. cells CF (CFD)
1350 2.8106 0.001619250 3.6106 0.001595110 4106 0.00158475
4.5106 0.001580
Table 4CF results at different mesh configurations for the
validation study.
Mesh configuration Total no. cells CF (CFD) % Experiment
Coarse 1.5106 [ ] [ ]Medium 2.5106 0.003805 0.60Fine 4106
0.003776 0.19Very fine 6106 0.003785 0.07
Table 5CF results at different mesh configurations for the full
scale prediction study.
Mesh configuration Total no. cells CF (CFD)
Coarse 1.8106 0.001574Medium 2.5106 0.001576Fine 4106
0.001584Very fine 5.5106 0.001584
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 213128
-
evident that the solutions of the fine and very fine
meshesconverged very well in both the validation and prediction
study.Therefore, the fine mesh configuration was selected in
allsubsequent computations.
5.2. Validation study
5.2.1. Frictional resistance coefficientsTables 68 demonstrate
the frictional resistance coefficients
computed by CFD and obtained by experiments for five
differentcoatings, as well as a smooth surface, at
Re2.8106,Re4.2106 and Re5.5106, respectively.
As can be seen from Tables 68, the computed CF values of
thesmooth and coated surfaces are in fair agreement with
theexperimental data. The differences are slightly higher
atRe5.5106, though the differences at all of the Reynoldsnumbers
can be considered to be negligible since the
experimentaluncertainty in CF is given as 75% for Re2.8106 and 72%
forRe5.5106 (Schultz, 2004).
The computed CF values of the silicone coatings have
relativelyhigher differences from the experimental data at
Re2.8106,which is thought to be due to the slight deviation of the
roughnessfunctions from the proposed roughness function model at
thisReynolds number, as shown in Fig. 4.
The best agreement between the computed values and
theexperimental data is achieved at Re4.2106. In this case,
theroughness functions at the corresponding Reynolds number
cor-relate remarkably well with the roughness function model given
inFig. 4.
Although the differences in the roughness amplitude para-meters
of the coatings are very small, the proposed wall law andCFD model
is able to accurately take this effect into account. Asexpected,
the computed CF values increase with increases in theroughness
amplitude parameters, and the frictional resistancecoefficients
decrease with increasing speed.
It should be noted that Table 6 includes four sets of
resultspreviously determined by and discussed in, Demirel et al.
(2014)using the same methodology as in this study.
5.2.2. Roughness Reynolds numbersConsidering Eq. (6), the value
of k depends on the friction
velocity U. For this reason, the roughness Reynolds numbers
arenot uniform within the surface, instead varying depending on
the
Table 6The comparison of CF values at Re2.8106.
Surface CF (CFD) CF (experiment) Difference (%)
Smooth 0.003632 0.003605 0.74Silicone 1 0.003715 0.003666
1.35Silicone 2 0.003729 0.003663 1.81Ablative Copper 0.003722
0.003701 0.58SPC Copper 0.003736 0.003723 0.35SPC TBT 0.003776
0.003783 0.19
Table 7The comparison of CF values at Re4.2106.
Surface CF (CFD) CF (experiment) Difference (%)
Smooth 0.003411 0.003418 0.21Silicone 1 0.003528 0.003499
0.82Silicone 2 0.003545 0.003540 0.14Ablative Copper 0.003536
0.003507 0.84SPC Copper 0.003553 0.003526 0.78SPC TBT 0.003603
0.003611 0.23
Table 8The comparison of CF values at Re5.5106.
Surface CF (CFD) CF (experiment) Difference (%)
Smooth 0.003185 0.003226 1.26Silicone 1 0.003460 0.003374
2.54Silicone 2 0.003481 0.003426 1.60Ablative Copper 0.003470
0.003401 2.04SPC Copper 0.003491 0.003438 1.55SPC TBT 0.003551
0.003500 1.45
Fig. 12. k Distribution on the plates coated with SPC TBT at (a)
Re2.8106, (b) Re4.2106, and (c) Re5.5106.
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 2131 29
-
location on the plate. Due to the fact that the software is able
toobtain the U distribution on the plate in question, a user
definedvariable, k , can be created, and so the distribution of k
wasevaluated on the plates for each particular case. Histograms
werethen created using the distribution data. Fig. 12 shows the
k
distributions on the plates coated with SPC TBT at three
differentReynolds numbers as an example.
The most frequently occurring roughness Reynolds numberswere
obtained from the software and compared with thosecalculated with
Eq. (9) using the experimental data. The resultingcomparisons are
shown in Fig. 13.
The computed roughness Reynolds numbers showed reason-able
agreement with those obtained from the experimental data.The
average differences are 0.3%, 0.35% and 2.5% at Re2.8106,
Re4.2106 and Re5.5106, respectively. These results provethat the
roughness Reynolds numbers can be computed accuratelyby means of a
CFD approach for a given roughness height.
Accurate computation of k values is of paramount
importancebecause the imposed roughness function model provides
therequired U based on the computed k value, shown in Fig.
4,leading to the accurate computation of CF values. The computedk
values have relatively higher differences from the experimentaldata
at Re5.5106. This may be one of the reasons for the
slightdifferences between the computed and experimentally obtained
CFvalues at this speed shown in Table 8.
5.3. Prediction of CF values at full scale
Table 9 shows the predicted frictional resistance coefficients
ofa handymax tanker coated with several antifouling coatings at
anoperational speed of 13 knots. It also gives the percentage
increasein frictional resistance coefficients with respect to the
smoothcondition.
As seen in Table 9, the percentage increase in
frictionalresistance coefficients due to the antifouling coatings'
roughnessvaries between 3.77% and 6.10%. SPC TBT leads to the
highestincrease in CF values as expected due to its relatively
higherroughness amplitude parameters. However, the reader
shouldnote that the evaluated CF values and the percentage
increases
Fig. 13. Roughness heights vs. roughness Reynolds numbers at (a)
Re2.8106, (b) Re4.2106 and (c) Re5.5106.
Table 9The comparison of CF values at full scale at 13
knots.
Surface CF (CFD) Increase in CF (%)
Smooth 0.001494 Silicone 1 0.001550 3.77Silicone 2 0.001558
4.32Ablative Copper 0.001554 4.05SPC Copper 0.001562 4.59SPC TBT
0.001585 6.10
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 213130
-
are due to the initial roughness of the coatings, and the
increase inCF over time varies depending on the time-dependent
dragperformance of each coating.
6. Conclusions
A CFD model for the prediction of the effect of
antifoulingcoatings on frictional resistance has been proposed. The
Colebrook-type roughness function of Grigson (1992) was employed in
thewall-function of the solver and a validation study was carried
outto examine the validity of the proposed model. The
frictionalresistance coefficients and roughness Reynolds numbers
for fiveantifouling coatings and a smooth surface were computed
usingCFD simulations. The results of the validation study were in
fairlygood agreement with the experimental data, with the
differencesbetween CFD and the experiment ranging from 0.14% to
2.54% forCF and from 0.3% to 2.5% for k . It has been shown that
surfaceroughness can be modelled by employing modified wall
lawswithin the wall functions. It may be concluded that the
proposedapproach is capable of predicting the roughness effects of
antifoul-ing coatings on frictional resistance. Hence, the
increases in the CFvalues of a ship due to different types of
antifouling coatings werepredicted using the proposed CFD
model.
It should be borne in mind that this study's aim was to proposea
robust CFD model, rather than a case-based model, to predict
thefrictional resistance of antifouling coatings. For this reason,
anappropriate representative roughness function model wasemployed
in spite of the slight discrepancies between the indivi-dual
roughness function values and the model. The
insignificantdifferences between the computed CF values and the
experimentaldata are therefore thought to be due to the
aforementionedinsignificant scatter.
The main advantage of the proposed model is that it enables
theuse of a simple roughness length scale, according to the
surfaceroughness measurements, rather than equivalent sand-grain
rough-ness height, which is a hydrodynamically obtained
parameter.
Additionally, the critical points of the numerical modelling
ofroughness effects on flow have been highlighted in this paper.It
has also been demonstrated that the existing roughness
functionmodel of the CFD software can be modified according to
theexperimental data and that the effects of different types
ofroughness on flow can be predicted in this way.
Future plans are to utilise this approach and employ a new
walllaw to simulate fouling and to predict the effect of fouling
onfrictional resistance. A piece of future work may be the
investiga-tion of the validity of the wall function approach to
simulate thesurface roughness on ship hulls, rather than on flat
plates, sincethe pressure gradient varies significantly along ship
hulls.
A final point to note is that while CFD provides accurate
resultsin order to model roughness effects on frictional
resistance,experimental data and further study into the correlation
betweenroughness and drag are a necessity for the development
ofaccurate CFD prediction methods.
Acknowledgements
The authors gratefully acknowledge that the research pre-sented
in this paper was partially generated as part of the EUfunded FP7
project FOUL-X-SPEL (Environmentally Friendly Anti-fouling
Technology to Optimise the Energy Efficiency of Ships,Project no.
285552, FP7-SST-2011-RTD-1).
It should be noted that the results were obtained using theEPSRC
funded ARCHIE-WeSt High Performance Computer
(www.archie-west.ac.uk). EPSRC Grant no. EP/K000586/1.
References
ANSYS, 2011. FLUENT Theory Guide. Release 14.Candries, M., 2001.
Drag, Boundary-layer and Roughness Characteristics of Marine
Surfaces Coated with Antifoulings (Ph.D. thesis). Department of
MarineTechnology, University of Newcastle-upon-Tyne, UK.
Candries, M., Atlar, M., Mesbahi, E., Pazouki, K., 2003. The
measurement of the dragcharacteristics of tin-free self-polishing
co-polymers and fouling release coat-ings using a rotor apparatus.
Biofouling1029-245419 (Suppl. 1), S27S36.
Cortana, 2013. Description of Drag. Available from:
http:/www.cortana.com/Drag_Description.htm (accessed 24.11.13)
(online).
CD-ADAPCO, 2012. User Guide STAR-CCM . Version 7.02.011.Cebeci,
T., Bradshaw, P., 1977. Momentum Transfer in Boundary Layers.
Washington,
DC, Hemisphere Publishing Corp., New York, McGraw-Hill Book
Co.Date, J.C., Turnock, S.R., 1999. (62pp.). A Study into the
Techniques Needed to
Accurately Predict Skin Friction Using RANS Solvers with
Validation AgainstFroude's Historical Flat Plate Experimental
DataUniversity of Southampton,Southampton, UK (Ship Science
Reports, (114).
Demirel, Y.K., Khorasanchi, M., Turan, O., Incecik, A., 2013a. A
parametric study: hullroughness effect on ship frictional
resistance. In: Proceedings of the Interna-tional Conference on
Marine Coatings. 18th April 2013. London, UK, pp. 2128.
Demirel, Y.K., Khorasanchi, M., Turan, O., Incecik, A., 2013b.
On the importance ofantifouling coatings regarding ship resistance
and powering. In: Proceedings ofthe 3rd International Conference on
Technologies, Operations, Logistics andModelling for Low Carbon
Shipping. 910 September 2013. London, UK.
Demirel, Y.K., Khorasanchi, M., Turan, O., Incecik, A., 2014.
CFD approach toresistance prediction as a function of roughness.
In: Proceedings of theTransport Research Arena Conference 2014.
1417 April 2014. Paris La Dfense,France.
Ferziger, J.H., Peric, M., 2002. Computational Methods for Fluid
Dynamics3rd ed.Springer, Berlin, Germany.
Granville, P.S., 1987. Three indirect methods for the drag
characterization ofarbitrarily rough surfaces on flat plates. J.
Ship Res. 31, 7077.
Grigson, C.W.B., 1992. Drag losses of new ships caused by hull
finish. J. Ship Res. 36,182196.
ITTC, 2005. ITTC Recommended Procedures and Guidelines: Testing
and Extra-polation Methods, Propulsion, Performance, Predicting
Powering Margins. ITTC.
ITTC, 2011a. Specialist Committee on Surface Treatment Final
Report andRecommendations to the 26th ITTC.
ITTC, 2011b. ITTC Recommended Procedures and Guidelines:
Practical Guidelinesfor Ship CFD Application. ITTC.
Izaguirre-Alza, P., Prez-Rojas, L., Nez-Basez, J.F., 2010. Drag
reduction throughspecial paints coated on the hull. In: Proceedings
of the International Con-ference on Ship Drag Reduction
SMOOTH-SHIPS. 2021 May 2010. Istanbul,Turkey.
Kempf, G., 1937. On the effect of roughness on the resistance of
ships. Trans. Inst.Naval Archit. 79, 109119.
Khor, Y.S., Xiao, Q., 2011. CFD simulations of the effects of
fouling and antifouling.Ocean Eng. 38, 10651079.
Lackenby, H., 1962. Resistance of ships, with special reference
to skin friction andhull surface condition. Proc. Inst. Mech. Eng.
176, 9811014.
Leer-Andersen, M., Larsson, L., 2003. An experimental/numerical
approach forevaluating skin friction on full-scale ships with
surface roughness. J. Mar. Sci.Technol. 8, 2636.
Millikan, C.M., 1938. A critical discussion of turbulent flows
in channels and circulartubes. In: Proceedings of the International
Congress for Applied Mechanics.Cambridge, MA, pp. 386392.
Milne, A., 1990. Roughness and Drag from the Marine Paint
Chemist's View-pointMarine Roughness and Drag Workshop, London.
Nikuradse, J., 1933. Laws of Flow in Rough Pipes. NACA Technical
Memorandum1292.
RAEng, 2013. Future Ship Powering Options. Available from:
https:/www.raeng.org.uk/news/publications/list/reports/Future_ship_powering_options_report.pdf.
(accessed 01.12.13) (online).
Schlichting, H., 1979. Boundary-Layer Theory7th ed. McGraw-Hill,
New York.Schubauer, G.B., Tchen, C.M., 1961. Turbulent
FlowPrinceton University Press,
New Jersey, USA.Schultz, M.P., 2004. Frictional resistance of
antifouling coating systems. ASME J.
Fluids Eng. 126, 10391047.Schultz, M.P., 2007. Effects of
coating roughness and biofouling on ship resistance
and powering. Biofouling 23 (5), 331341.Schultz, M.P., Swain,
G.W., 2000. The influence of biofilms on skin friction drag.
Biofouling 15, 129139.Schultz, M.P., Flack, K.A., 2007. The
rough-wall turbulent boundary layer from the
hydraulically smooth to the fully rough regime. J Fluid Mech
580, 381405.Taylan, M., 2010. An overview: effect of roughness and
coatings on ship resistance.
In: Proceedings of the International Conference on Ship Drag
ReductionSMOOTH-SHIPS. Istanbul, Turkey.
Tezdogan, T., Demirel, Y.K., 2014. An overview of marine
corrosion protection with afocus on cathodic protection and
coatings. Brodogradnja/Shipbuilding 65 (2),4959.
van Manen, J.D., van Oossanen, P., 1988. Resistance. In: Lewis,
E.V. (Ed.), Principlesof Naval Architecture. Second Revision.
Volume II: Resistance, Propulsion andVibration. The Society of
Naval Architects and Marine Engineers, Jersey City, NJ.
Y.K. Demirel et al. / Ocean Engineering 89 (2014) 2131 31
http://www.archie-west.ac.ukhttp://www.archie-west.ac.ukhttp://refhub.elsevier.com/S0029-8018(14)00280-7/sbref1http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref1http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref1http://www.cortana.com/Drag_Description.htmhttp://www.cortana.com/Drag_Description.htmhttp://refhub.elsevier.com/S0029-8018(14)00280-7/sbref3http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref3http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref3http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref3http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref4http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref4http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref5http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref5http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref6http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref6http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref7http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref7http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref8http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref8http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref9http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref9http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref10http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref10http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref10http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref11http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref11https:/www.raeng.org.uk/news/publications/list/reports/Future_ship_powering_options_report.pdfhttps:/www.raeng.org.uk/news/publications/list/reports/Future_ship_powering_options_report.pdfhttps:/www.raeng.org.uk/news/publications/list/reports/Future_ship_powering_options_report.pdfhttp://refhub.elsevier.com/S0029-8018(14)00280-7/sbref12http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref13http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref13http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref14http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref14http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref15http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref15http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref16http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref16http://refhub.elsevier.com/S0029-8018(14)00280-7/ssbib1001http://refhub.elsevier.com/S0029-8018(14)00280-7/ssbib1001http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref915http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref915http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref915http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref18http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref18http://refhub.elsevier.com/S0029-8018(14)00280-7/sbref18
A CFD model for the frictional resistance prediction of
antifouling coatingsIntroductionBackgroundThe turbulent boundary
layerThe effect of roughness on the turbulent boundary layer
Roughness functionsNumerical modellingMathematical
formulationWall-function approach for antifouling coatingsGeometry
and boundary conditionsMesh generationNear-wall mesh generation
ResultsGrid dependence testsValidation studyFrictional
resistance coefficientsRoughness Reynolds numbers
Prediction of CF values at full scale
ConclusionsAcknowledgementsReferences