a cfd model for the frictional resistance prediction of ... · a cfd model for the frictional...

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

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/oceaneng

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

www.sciencedirect.com/science/journal/00298018www.elsevier.com/locate/oceanenghttp://dx.doi.org/10.1016/j.oceaneng.2014.07.017http://dx.doi.org/10.1016/j.oceaneng.2014.07.017http://dx.doi.org/10.1016/j.oceaneng.2014.07.017http://crossmark.crossref.org/dialog/?doi=10.1016/j.oceaneng.2014.07.017&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.oceaneng.2014.07.017&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.oceaneng.2014.07.017&domain=pdfmailto:[email protected]://dx.doi.org/10.1016/j.oceaneng.2014.07.017

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

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

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.


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


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.


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.


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


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







Fig. 12. k Distribution on the plates coated with SPC TBT at (a) Re2.8106, (b) Re4.2106, and (c) Re5.5106.


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


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.


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

a cfd model for the frictional resistance prediction of ... · a cfd model for the frictional...

Documents