497
1 INTRODUCTION.
Tugboatspla y asignificantrolewhenshipsincapable
ofslowmanoeuvresarehandledinrestrictedwaters.
Shipsandtheirattendingtugsareexposedtodangers
such as collision, grounding, girting, and run‐overs
when operating in close proximity in restricted
waterways. Furthermore, the hydrodynamic
interaction forces and
moments can adversely affect
thehandlingandsafetyoftheattendingtugs. Hensen
(2012)showedthattheinteractioneffectschangewith
shiptype,widthoffairway,andthedriftanglesofthe
vessels; which can cause even experienced tug
masters difficulties in identifying safe operating
envelopesfortheirtugsduring
suchmanoeuvres.In
addition, Hensen (2012) stated that these effects
become prominent when the vessels were
significantly dissimilarin size and operatedin close
proximity during tight manoeuvres. Hensen,
Merkelbach, and Wijnen (2013) questioned 160 tug
masters with regard to their awareness of the
interaction effects during such manoeuvres. Around
30%
of the tug masters had faced critical situations
due to unexpected ship‐to‐ship interaction effects in
actualship‐assistmanoeuvres.
Shiphandlingsimulatorsuseempiricalandsemi‐
empirical methods, theoretical and numerical
methods, or potential flow methods to predict
interaction effects:(Sutulo & Soares, 2009).Withthe
exception of
the latter, the others require an
interaction effect coefficients database to solve
mathematicalmodelsfedintothesimulators,withthe
database developed and validated by empirical and
numerical techniques. For example Vantorre,
Verzhbitskaya,andLaforce(2002)conductedphysical
Accuracy of Potential Flow Methods to Solve Real-
time Ship-Tug Interaction Effects within Ship
Handling Simulators
B.N.Jayarathne,D.Ranmuthugala,S.Chai&J.Fei
A
ustralianMaritimeCollege,UniversityofTasmania,Newnham,Tasmania,Australia
ABSTRACT:Thehydrodynamicinteractioneffectsbetweentwovesselsthataresignificantlydifferentinsize
operatingincloseproximitycanadverselyaffectthesafetyandhandlingofthesevessels.Manyshiphandling
simulatordesignersimplementPotentialFlow(PF)solverstocalculatereal‐time
interactioneffects.However,
thesePFsolversstruggletoaccuratelypredictthecomplicatedflowregimesthatcanoccur,forexampleasthe
flowpassesawettransomhulloronewithadriftangle.Whenitcomestopredictingtheinteractioneffectsona
tugduringashipassist,itis
essentialtoconsidertherapidchangesofthetug’sdriftangle, asthehullacts
againsttheinflowcreatingacomplicatedflowregime.ThispaperinvestigatestheabilityofthecommercialPF
solver,Futureship®,topredicttheaccurateinteractioneffectsactingontugsoperatingatadriftangleduring
ship handling
operations through a case study. This includes a comparison against Computation Fluid
Dynamics (CFD) simulations and captive model tests to examine the suitability of the PF method for such
duties.AlthoughthePFsolvercanbetunedtosolvestreamlinebodies,itneeds furtherimprovementtodeal
withhullsat
driftangles.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 4
December 2014
DOI:10.12716/1001.08.04.03
498
modelteststodeterminetheshipinteractioneffectsin
head‐on and overtaking encounters of similar and
dissimilarships.Thetestresultswereusedtocreatea
new mathematical model to improve the quality of
the interaction effects within ship manoeuvring
simulators.
Researchers such as Sutulo and Soares (2009),
Sutulo,
Soares, and Otzen (2012) and Pinkster and
Bhawsinka (2013) employing Potential Flow (PF)
solvers to predict the interaction effects as an
alternative to the excessive work and high cost
involved in developing a coefficient based model.
Currentlyonlytherelativelysimple PFdouble‐body
panel method is utilised to provide
estimates of the
interaction forces and moments in real time within
simulators (Sutulo et al., 2012). Pinkster and
Bhawsinka(2013)developed acomputerprogramto
estimateandvalidatetheinteractioneffectsusingthe
simulatoroperatedbytheMaritimeResearchInstitute
Netherland (MARIN). The PF double‐body method
was employed within their
computer program for
multi‐bodycasesinvolvingshipsandportstructures.
Real time interaction forces and moments were fed
into the simulator using high speed computers to
solve the flow equations. However, the final results
were found to be highly sensitive to the initial
conditions,whichweretedioustosetup.
Sutulo et al. (2012) developed a PF double‐body
panelcodeonthebasisoftheclassicHessandSmith
methodtoestimateinteractioneffectsinrealtimeon
commonly used computer hardware. The results
obtained with the code were validated against
experimental data obtained in deep and shallow
watertowing
tanksforatugoperatingnearalarger
vessel.Theresults illustratedthepotential ofthe PF
double‐bodypanelmethodforpredictinginteraction
effects, while highlighting the lack of accuracy in
predicting the sway forces at small horizontal
clearances, which were expected to be more
pronounced in non‐parallel
operations, similar to
those encountered during tugs assisting ships.
Fonfach, Sutulo, and Soares (2011)didexperimental
and numerical investigations to explore the
contribution of various factors to interaction effects,
whichwerenotaccountedforbythePFmethod.They
revealed substantial influence of free‐surface effects
ontheaccuracyofpredicted
interactioneffects.
Manyresearchers(Doctors,2006;Doctors&Beck,
2005; Eliasson & Olsson, 2011; Mantzaris, 1998;
Mierlo, 2006; Pranzitelli, Nicola, & Miranda, 2011)
have investigated the capabilities of PF methods to
study various hull shapes, especially transom stern
hullswithfreesurface.Pranzitellietal.(2011)studied
the free‐surface
flow around a semi‐displacing
transomsternmotor‐yachtadvancingsteadilyincalm
water using both PF method and Computational
Fluid Dynamics (CFD), and comparing them to
Experimental Fluid Dynamics (EFD) results. It was
foundthattheresultsgeneratedfromthePFmethod
weresubstantiallydifferentbecauseoftheinabilityof
itspanelsto‘roll‐down’andintersectwitheachother
duringiterations.Theresearchersconcludedthatthe
presence of the free‐surface can make more
complicated discretisation, resulting in numerical
problemsforcomplexgeometries,suchasfortransom
sternhulls.
Consideringtheinteractioneffectsonatugduring
shipassist,
therapidchangesoftugdriftanglecauses
a large portion of the downstream wake due to the
hull to be characterised by a bluff body flow in a
similar manner to a wet transom flow, as shown in
Figure1.Thus,itisessentialtoselectaflowsolverthat
can
accuratelysolvesuchconditionsduringreal‐time
predictions.Therefore,thisstudyaimstoexaminethe
accuracy of the drag force prediction of the
commercialPF packageFutureship
®
,in wettransom
conditionsasacasestudytoinvestigateitssuitability
to use in complicated real‐time interaction effects
analysisoftugsoperatingatadriftangle.
Figure1. Tug operating parallel to the flow (top) and
operatingatadriftangle(bottom)
FS‐Flow
®
is the module used within Futureship
®
for Rankine‐Source panel code analysis (DNV GL
Maritime, 2014) and it solves the boundary value
problemofpotentialtheoryincludingnonlinearfree‐
surface.Thepotentialflowapproachassumesthatthe
fluidisinviscidandtheflowisirrotationalaroundthe
bodies.Hence,FS‐Flow
®
isequippedwithaseparate
module capable of calculating the viscousresistance
in terms of a friction line in combination with the
wavy wetted hull surface. Therefore, the dynamic
forces,static forces,andviscousforcesactingon the
bodiesareincludedinthefinalresults,althoughthe
fluidis considered
asinviscidwithinpotentialflow.
Thetotalresistanceanditscomponentsobtainedfrom
the PF solver was then compared against captive
modelexperimentsandCFDresultsgeneratedbythe
commercialCFDcode Star‐CCM+
®
toinvestigatethe
possibilityofusingthePFsoftwareforfutureanalysis
ofinteractioneffects.
2 NUMERICALANALYSIS
The setup and relevant features of the two
commercial software packages, FS‐Flow
®
and Star‐
CCM+
®
,areprovidedbelow.
499
2.1 HullFormandCoordinateSystem
A1:20scaled hullmodeloftheAustralianMaritime
College’s (AMC)35m trainingvesselTV Bluefin was
utilisedinthisstudy. Theparticularsofthefull and
model scalehulls aregiven in Table1. The twotest
conditions analysed to investigate the effects
of
transomgeneratedcomplexflowregimeswere:
drytransomwithamodeldraftof0.17m;and
wettransomwithamodeldraftof0.18m.
Table1.MainParticularsoftheHullForm
_______________________________________________
MainParticularsUnit FullScale ModelScale
_______________________________________________
LengthWaterline,L m 32.150 1.608
WettedSurfacearea,S m
2
384.15 0.96
DryTransomDraft m 3.480.17
WetTransomDraft m 3.600.18
_______________________________________________
A three‐dimensional model scale hull form was
developed using the commercial software
Rhinoceros
®
V5.0 and imported into the two
packages. The coordinate system for the analysis is
showninFigure2.Theflowvelocityvectorwasinthe
positive X direction while the horizontal plane
throughtheoriginwasconsideredasthefreesurface.
2.2 DomainandMeshinFS‐Flow
®
Flow velocities ranged from 0.34m/s to 1.04m/s in
model scale, acting along the positive X direction,
withthevesselallowedtotrimandheaveduringthe
analysis. The free surface had a rectangular shape,
with the inlet boundary at a distance equal to the
scaled model waterline length (L
m) upstream of the
origin,the outletboundaryat 3L
mdownstream from
the origin, and a total domain width of 1.1L
m. The
dimensionswereselectedtomatchthoseoftheAMC
towingtank,exceptforthelength,whichwasshorten
toreducethecomputationaleffortwithoutadversely
affectingwakeresolution. Themeshconfiguration is
illustrated in Figure 2, which was developed in FS‐
Flow
®
.
Figure2.CoordinatesandShipModelwithFreesurface in
FS‐Flow
®
The mesh independence study was conducted
through mesh refinements without affecting the
stability of the solver. The drag coefficient at a
forwardspeedof1.04m/swastestedfordrytransom
condition for the models with different panel
numbers to obtain an appropriate mesh. This
approachprovidedsufficientlyaccurateresultswhile
maintaining
low computational effort. The finest
mesh investigated had 4220 panels; while a 3490
panel mesh was selected as a suitable mesh for
steady‐statesimulationsasitspredictionswerewithin
1.5%ofthatforthefinestmesh(seeFigure3).
Figure3.Absolute%differenceofDragCoefficientagainst
finestpanelmeshfortheFS‐Flow
®
model
2.3 SetupandMeshinStar‐CCM+
®
Star‐CCM+
®
uses a finite volume technique to solve
the Reynolds Averaged Navier‐Stokes (RANS)
equations (CD‐Adapco, 2014). In order to directly
compare the CFD and EFD results, the width and
depthoftheAMCtowingtankwerereplicatedinthe
numerical fluid domain, although the length was
reduced to 10.0m
to decrease the mesh load while
ensuring the pressure andwakefields generated by
thehullweresufficientlyresolvedwithinthedomain.
In addition, since the flow around the hull is
symmetrical aboutthe centerline, onlythe starboard
half ofthe hull wasmodeledin ordertoreduce the
computational domain
and thus the associated
computational effort. The vessel was fixed in all
degreesof freedom,using particulartrim andheave
conditions obtained from the FS‐Flow
®
simulation
results. The computations were performed using
hexahedraltrimmedmeshgeneratedbyStar‐CCM+
®
.
Following a mesh independence study (Figure 4), a
mesh with approximately 3.5 million cells was
selected for the investigation as the percentage
difference reduced to below 0.5% beyond this size
mesh.
The near wall spacing on the vessel is defined
usingthedimensionlessdistance(y
+
)measuredfrom
the wall surface to the edge of the first layer. The
resolution of the boundary layer was estimated by
prescribingthenumberofinflationprismslayers,the
growthrate,andthefirstnodedistancefromthewall
(
y
)reflectedbythenon‐dimensionaldistancevalue
(y
+
)asdefinedinequation(1).
13
14
me
yL y 80R
(1)
Theminimumtotalthicknessoftheinflationlayers
around the hull was matched to 2 times Prandtl’s
1/7th power law of theoretical estimate of turbulent
boundarylayerthicknessoveraflatplate,i.e.2×0.16
L
m/Re
1/7
(White,2003).
The y
+
study was conducted between y
+
~1 to
y
+
~100 with the k‐ SST turbulence model, which
changefromthelowReynoldswalltreatmentmodel
to the empirical‐based wall function formulation
around y
+
=10. From Figure 5 it is seen that the %
variationofthedragcoefficientisaround5%atay
+
of
30.Thus, y
+
~30 was selected as a compromise
between accuracy and the solver time and effort.
However, it should be noted that this y
+
value is
500
acceptable for longitudinal flow, but too high for
oblique flow which would need a y
+
less than 1
(Leong et al., 2014). Customised anisotropic
refinement was applied to the free‐surface region
(Figure6)toresolvethewavefieldaroundthehull.
Figure4. CFD grid independent study: Absolute %
differenceofDragCoefficientagainstfinestmesh
Figure5. CFD near wall mesh (y
+
) study: % difference of
DragCoefficientagainsty
+
~1mesh
Figure6.HexahedralMeshusedinStar‐CCM+
®
Simulations were treated as implicit unsteady,
conducted for 25s durations with a 0.024s time step
and10inneriterations.Thefreesurfacewasmodelled
as an Euler Multiphase and the volume of fluid
technique,withtheinflowconsideredasaflatwave
having pa rticular velocity. The drag force acting on
the
vesselwascalculatedforsimilarspeedsanddrafts
asdoneforFS‐Flow
®
.
3 EXPERIMENTALSETUP
Captivescaledmodelexperimentswereperformedin
AMC’s100m(length)x3.55m(width)x1.5m(depth)
towingtank(Figure7).Thescaledhullmodel,which
wasallowed totrim andheave, wasattachedbelow
the towingcarriageusing onestraingauge and two
Linear Voltage Displacement Transducers
(LVDTs).
Experiments were conducted for the two different
draftsofthehullmodel.Atthelower0.17mdraftthe
transomwas inthedrycondition,whileatthehigher
0.18mdraftitwaswet.Bothconditionsweretestedat
speeds ranging from 0.34m/s to 1.04m/s in model
scale.
Figure7.ExperimentaltestinginAMCTowingTank;left‐
sternview,right–bowview
4 RESULTSANDDISCUSSION
4.1 DragCoefficientandFrictionCoefficient
The drag forces obtained from the numerical and
experimental work were non‐dimensionalised to
obtain the drag coefficient (C
T) as shown in Eq. (2).
Thefrictionalresistancecoefficients(C
F)giveninEq.
(3) obtained from the numerical results were
compared against the ITTC correlation line given in
Eq.(4)(ITTC,2011).
T
T
2
R
C
1
SV
2
(2)
F
F
2
R
C
1
SV
2
(3)
2
10 e
0.067
1 0.1194
log R 2
ITTCcorrelationline
(4)
withthedefinitionsgivenintheNomenclatureatthe
endofthispaper.
4.1.1 Drytransomwithamodeldraftof0.17m
Inthisconditionthetransomremaineddryabove
thewaterline, givinga streamlinedwater‐plane. The
non‐dimensionaliseddragforceresultsfromEFD,PF
codeFS‐Flow
®
(PF),andCFDareplottedagainstthe
LengthFroudenumber(F
n)inFigure8.
The numerical and EFD results have a similar
trendexceptatlowerF
n,wherethenumericalmodels
tend to over‐predict. This may be due to the non‐
accurate prediction of laminar to turbulent transient
region on the scaled experimental model. However,
thePFandCFDremainsimilarevenatlowF
n,with
the maximum difference between the PF and CFD
results being 15%, while the maximum difference
betweenthePFandEFDresultsis7.2%,exceptatthe
lowestF
nasdiscussedabove.
501
Figure8.CTcomparisonfordrytransomcondition
The results indicate that the viscous module
integrated within FS‐Flow
®
has good prediction
capability.Inordertoverifyitsaccuracy,thefrictional
coefficients (C
F) obtained from the PF and CFD
simulations were compared against the ITTC
correlationlineasshowninFigure9.TheC
Ffromthe
PFmethodcorrelateswellwith theITTClinewitha
maximumdifferenceof5%,whereastheCFDvalues
are slightly below the ITTC prediction with an
averagedifferenceof15%.Afinermeshwithdifferent
turbulencemodelsandasmallery
+
mayimprovethe
CFDresults.Thiswasnotcarriedoutsincetheaimof
the study was to investigate the accuracy of the PF
solver.Fromthe currentwork it isclear that thePF
solver in FS‐Flow
®
is suitable to solve flow around
wellstreamlinedhullgeometries.
Figure9.CFcomparisonfordrytransomcondition
4.1.2 Wettransomwithamodeldraftof0.18m
In order to test FS‐Flow
®
’s ability to solve wet
transom conditions, the model was tested at the
higherdraft.ThenondimensionalisedEFD,CFD,and
PFdragforcesinthisconditionareplottedagainstF
n
inFigure10.
Figure10.CTcomparisonforwettransomcondition
Itis evidentthatthe CFDand EFDresults arein
good agreement throughout the F
n range. However,
thePFresults,althoughisrelativelyclosetotheEFD
at low F
n, it significantly under predicts CT as Fn
increases. Interestingly, the direction of C
T changes
aroundF
nof0.2,causingthedragforceonthevessel
to act opposite to the flow direction, a physical
impossibility. Since the total drag is made up of
viscous,pressure,andwavemakingcomponents,itis
necessarytodecomposetheresistanceinthedifferent
components to identify the real cause for
this
discrepancy.
First considering the viscous drag force, a
comparisonwasmadebetweenthoseobtainedbythe
PF solver, the CFD shear force, and the ITTC
correlationline,presentedinFigure11.Itisapparent
thattheviscousforcegeneratedbyPFisinagreement
withtheITTCcorrelationline,which
issimilartothe
results obtained in the dry transom conditions as
discussedinsection4.1.1.
Figure11.CFcomparisonforWetTransomcondition
4.2 WavePatternandPressureContour
Since the results discrepancy was not related to the
viscous effects, the residuary components were next
investigated, especially as the error increased
significantly with F
n. Thus, the free surface wave
patternsgeneratedbythePFandCFDsimulationsas
well as photographs of the wave patterns from the
EFD work at a speed of 1.04m/s were compared to
identify the influence of wave making resistance.
Figure12provides thePFandCFDwavepatternsfor
wave heights between ±0.03m, with Figure 7
providingtheEFDpatterns.
Figure12.FreesurfacewavesheightsinPF&CFD
It is clearly seen from this plots that the waves
generated by PF are not in agreement with that
obtainedfromEFDandCFD.Notably,thesternwave
generatedbyPFhasthehighestmagnitude,whereas
CFD
PF
502
theCFDasexpectedhasitforthebowwave,similar
totheEFDasseeninthephotographsinFigure7.The
inaccurate wave pattern in PF will create a high
pressure region at the stern of the hull, which can
resultinanegativedragforce.Inorder
toverifythis,
the Dynamic Pressure Coefficient (C
P) generated by
PFwasexaminedasshownintheFigure13(a).
Figure13: a)DynamicPressureCoefficient andb) velocity
contourgeneratedbyPF
As suspected, the PF code has a high positive
pressure region at the stern due to the weakness in
predicting the horizontal velocity component within
thetransommesh.Thiscreatesaverylowhorizontal
velocity at the transom Figure 13 (b), and hence a
corresponding high pressure creating the negative
drag
forceon the vessel.Since this unrealisticresult
occurred due to the wet transom, it was decided to
check the drag force generated by the PF code
without the transom mesh (Figure 14) at a 0.18m
draft, with the results plotted against the F
n in
Figure15.
Figure14.PFhullwith(top)andwithout(bottom)transom
mesh
4.3 ResultswithoutTransomMesh
Itisinterestingtonotethatwhenthetransommeshis
omittedfromthehull,theaccuracyofthedragforce
predicted by the PF simulation is appreciably
improvedshowinggoodagreementwiththeEFDand
CFD results. Removing the transom mesh mitigated
the error attributed
to insufficient resolution of the
large pressure gradient on the hull and poor
numericalconditioningofthepressureintegration.
Figure15.Comparisonforwettransomcondition,including
thePFmeshwithoutthetransommesh
Thus,itisnotedthatthePFcodeisunabletosolve
flowequationsontransversepanelswhichblockthe
flow streamlines creating breaking and spraying
waves. However,reasonable results can beobtained
for wet transom geometries if the transom mesh is
omitted.
Thus,itisimportanttoinvestigatethepossibility
ofutilisingthisfindingtoconductinteractioneffects
analysis during ship handling operations. During
such operations, tugs can dramatically change their
driftangletomaintainthecourseoftheship.IfthePF
codeisusedtosolvesuchcases,thepanelgeneration
hastobedoneasshownin
Figure16.
Figure16.ShipHandlingOperation:PanelgenerationinPF
As illustrated in Figure 16, when the tug drift
angle changes, a large portion of the downstream
wake due to the tug hull is characterised by a
stagnation pressure created due to a bluff body
similartoawettransom.Thisdownstreamareaisdue
to a large portion of the
vessel’s downstream side
hull. Thus, if the technique of omitting the
downstream transverse mesh panels to improve
resultsisutilised,asignificantpartofthe hullmesh
wouldbeomitted,unlikeintheinlineflowcondition
where the transom is a relatively small mesh panel.
This would result in accuracy
and stability issues
withinthePFsimulation.Thus,thedynamicpressure
prediction algorithm in FS‐Flow
®
is not capable of
handling non‐streamlined geometries and it needs
further improvements to solve complicated
interactioneffects.
b
)
a
)
503
5 CONCLUSION
Inthispaperthedragforcesactingonatransomstern
hulloperatingunderwetanddrytransomconditions
wereinvestigatedusingPF,CFD,andEFDmethods.
The aim was to identify the accuracy of the PF
method to determine real‐time interaction effects
acting on a tug
operating in close proximity to a
tanker within ship handling simulators. For the dry
transom flow, the PF solver showed very good
agreementwiththeEFDandCFDresults.However,it
failed to do so for the wet transom condition,
especially at higher F
n. Further investigations
revealed that these discrepancies were due to its
weaknessesinpredictingtheflowvelocityaroundthe
transompanelmesh, whichwasatnearrightangles
totheflowdirection.
Itwasidentifiedthat ifFS‐Flow
®
isusedtosolve
drag forces on wet transom hulls of tugs operating
paralleltotheflow,itisnecessarytoomitthetransom
stern mesh panel. Thus itissuitable to estimate the
forces acting on well streamlined bodies across the
length based F
n range, including the viscous effects.
However,thisisnotfeasiblewhenthetugisatadrift
angle, asthe mesh panel affectedwill represent one
full side of the vessel, thus adversely affecting the
mesh domain. Therefore, it was identified that the
investigated PF solver, FS‐Flow
®
, is limited in its
ability to predict real‐time interaction effects within
ship handling simulators, especially in manoeuvrers
suchastugassistoperations.
CurrentlytheauthorsareconductingCFDstudies
topredicttheofflineinteractioneffectsactingonatug
withvaryingdriftanglesoperatingincloseproximity
to a
large tanker, with validationthrough EFD. The
quantified results will be fed into AMC’s ship
handlingsimulatorviaadatabaseinordertopredict
real‐timeinteractioneffects.
NOMENCLATURE
AMC AustralianMaritimeCollege
CFD ComputationalFluidDynamics
C
F frictioncoefficient(dimensionless)
C
P dynamicpressurecoefficient(dimensionless),
p
CPP/q
C
T dragcoefficient(dimensionless)
DT drytransom
EFD ExperimentalFluidDynamics
F
n LengthFroudeNumber(dimensionless),
nm
FV/gL
g gravity(9.81m/s
2
)
ITTC InternationalTowingTankConference
Lm lengthoftheshipmodel(m)
P pressure(pa)
PFPotentialFlowcodeFS‐Flow
P
free‐streamreferencepressure(pa)
q dynamicpressure,
2
qV/2
(pa)
Re ReynoldsNumber(dimensionless),
em
RVL/v
R
F frictionalresistanceonshipmodel(N)
RT totalresistanceonshipmodel(N)
S wettedsurfaceareaofshipmodel(m
2
)
V velocityofshipmodel(0.34m/sto1.04m/s)
WT wettransom
y
+
nearwallmeshspacing(dimensionless)
y
firstnodewalldistanceofthenearwall
mesh
(m)
kinematicviscosityofwater(1.00x10
6
m
2
/s)
densityofwater(1000kg/m
3
)
ACKNOWLEDGEMENT
Theauthorswouldliketoacknowledgetheextensive
supportgivenbyAssociateProfessorJonathanBinns
andtheAMCtowingtankstaffduringthestudy.
REFERENCES
CD‐Adapco.(2014).UserManualofStarCCM+Version08.
DNVGLMaritime.(2014).UserManualofFS‐FlowVersion
14.0228.
Doctors, L. J. (2006). A Numerical Study of the Resistance of
Transom Stern Monohulls. Paper presented at the 5th
International Conference on High Performance Marine
Vehicles,Australia.
Doctors,L.J.,
&Beck,R.F.(2005).TheSeparationoftheFlow
Past a Transom Stern. Paper presented at the First
International Conference on Marine Research and
Transportation(ICMRTʹ05),Ischia,Italy.
Eliasson, S., & Olsson, D. (2011). Barge Stern Optimization:
Analysis on a Straight Shaped Stern using CFD. (MSc
thesis), Chalmers
University of Technology,
Gothenburg,Sweden.(X‐11/266)
Fonfach, J. M. A., Sutulo, S., & Soares, C. G. (2011).
Numerical study of Ship to Ship Interaction Forces on the
BasisofVariousFlowModels.Paperpresentedat the2nd
International Conference on Ship Manoeuvring in
Shallow and Confined Water: Ship to
Ship Interaction,
Trondheim,Norway.
Hensen, H. (2012). Safe Tug Operation: Who Takes the
Lead? International Tug & OSV, 2012(July/August ), 70‐
76.
Hensen,H.,Merkelbach,D.,&Wijnen,F.V.(2013).Report
on Safe Tug Procedures (pp. 40). Netherlands: Dutch
SafetyBoard.
ITTC. (2011). Resistance Test (Vol. 7.5‐02‐02‐
01):
InternationalTowingTankConference.
Leong,Z.Q.,Ranmuthugala,D.,Penesis,I.,&Nguyen,H.
(2014). RANS‐Based CFD Prediction of the
Hydrodynamic Coefficients of DARPA SUBOFF
Geometry in Straight‐Line and Rotating Arm
Manoeuvres. Transactions RINA: Part A1‐ International
JournalMaritimeEngineering.
Mantzaris,D.A.(1998).ARankinePanel
MethodasaToolfor
the Hydrodynamic Design of Complex Marine Vehicles.
504
(Ph.D. thesis), Massachusetts Institute of Technology,
USA.
Mierlo,K.V.(2006).TrendValidationofSHIPFLOWbasedon
the Bare Hull Upright Resistance of the Delft Series. (MSc
thesis),DelftUniversityofTechnology,Netherlands.
Pinkster, J. A., & Bhawsinka, K. (2013). A Real‐time
Simulation Technique for Ship‐Ship and Ship‐Port
Interactions. Paper presented at the 28th International
Workshop on Water Waves and Floating Bodies
(IWWWFB2013),LʹIslesurlaSorgue,France.
Pranzitelli,A.,Nicola,C.,&Miranda,S.(2011).Steady‐state
calculations of Free Surface Flow around Ship Hulls and
ResistancePredictions.PaperpresentedattheHighSpeed
Marine
Vehicles(IXHSMV),Naples,Italy.
Sutulo, S., & Soares, C. G. (2009). Simulation of Close‐
Proximity Maneuvers using an Online 3D Potential Flow
Method.PaperpresentedattheInternationalConference
on Marine Simulation and Ship Maneuverability,
PanamaCity,Panama.
Sutulo,S.,Soares,C.G.,&Otzen,J.F.(2012).Validation
of
Potential‐Flow Estimation of Interaction Forces Acting
upon Ship Hulls in Parallel Motion. Journal of Ship
Research,56(3),129–145.
Vantorre,M.,Verzhbitskaya,E.,&Laforce,E.(2002).Model
TestBasedFormulationsofShip‐ShipInteractionForces.
ShipTechnologyResearch,49,124‐141.
White, F. M. (2003). Fluid Mechanics (5
ed.). New York:
McGraw‐Hill.
