427
1
INTRODUCTION
Thepredictionofashipʹsself‐propulsionparameters
isachallengingtaskinshiphydrodynamicsingeneral
andintheshippowerestimationinparticulardueto
the accuracy in evaluating this parameter will effect
onaccuratepowerestimation.
Amongvariousmethodstoevaluatetheshipʹsself‐
propulsion,
the CFD method is the most commonly
usedduetoitsaccuracyandcomputationaltime[1‐4].
Therefore,thispaperaimstoevaluatetheshipʹsself‐
propulsionbasedontheCFDmethod.
Nowadays, according to CFD method, there are
two different approaches for predicting shipʹs self‐
propulsion point,
which consists of using the actual
propellerandusingvirtualdiskinsteadoftheactual
propeller,some previousresearchworksusingthese
approaches are reported in the literatures [3‐19].
Although, the advantage of virtual disk method is
simple and faster in predicting the shipʹs self‐
propulsion, it is unable
to provide detailed
information about flow around the propeller.
However,usingactualpropellermethodcanprovide
us all the information about flow field in the wake
regions efficiently and reliably. Therefore,this study
used actual propeller method to evaluate the shipʹs
self‐propulsionparameters.
Previous research has employed the
actual
propeller method to evaluate the self‐propulsion
characteristicsofaship.TuT.N.etal[3]utilizedthe
CFD method to investigate the interaction between
the hull of the ship and propeller, as well as the
propulsive coefficients for the actual propeller. The
simulation results showed good agreement with
measured
data. Castro, A.M., et al. [10] used actual
propeller method to evaluate the shipʹs self‐
propulsionparametersforcontainershipatfull‐scale.
Theobtainedsimulationresultsareagreedwellwith
the available data. In the research of Sun, W., et al.
[20]actualpropeller methodwas usedto performed
self‐propulsion simulation. The numerical results
obtained for ship self‐propulsion in full‐scale shows
good agreement with the measured data. The
previousstudieshaveplayedavitalroleinpredicting
Numerical Prediction of Ship's Sel
f
-Propulsion
Parameter by Using CFD Method
N.T.N.Hoa
HoChiMinhCityUniversityofTransport,HoChiMinh,Vietnam
ABSTRACT: This paper reports the results of numerical simulations of ship sel
f
‐propulsion using the
computationalfluiddynamics(CFD)method.Theslidingmeshmethodisutilizedtomodeltheactualpropeller
workingbehindtheship.Inaddition,thevolumeoffluidmethodwasappliedtoaccuratelytrackandsolvethe
free surface. Some severalimportant factorssuchas mesh generation, timestep,
turbulencemodel that can
affecttheaccuracyoftheobtainedsimulationresultsarediscussedinthisresearch.TheBenchmarkJapanese
BulkCarriervesselwasusedinthisstudyasthecasestudy.Thenumericalobtainedresultsarecomparedwith
measureddatatoverifyandvalidatethenumericalresults.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 18
Number 2
June 2024
DOI:10.12716/1001.18.02.22
428
propulsivecoefficients,andthisstudyusestheactual
propeller method to simulate the self‐propulsion of
theJBCshipinmodel‐scale.Theslidingmeshmethod
wasappliedtomodelactualpropellerlocatedbehind
theship.
2
MATERIALANDMETHOD
2.1
Flowmodel
The Reynolds‐Averaged Navier‐Stokes Equations
(RANSE) is amended with the force Fv. This
representsthepropelleractingonthefluidasgivenin
Equation1.
2
2
1
ij
ii
jv
jiij
uu
p
uF
xxx
x
(1)
whereρisthefluiddensit,μisthedynamicviscosity,
τ
ij is the Reynolds stress, p presents the mean
pressure,
i
u presents the averaged Cartesian
components.
TheRANSEaredefinedasfollows:
()
0
i
i
u
x
(2)
()
ij
i
ij ij
jij
u
p
uu uu
tx xx
(3)
wherex
iand
i
u arethepositionandvelocityvector,
ρ is the fluid density,
ij
uu is the Reynolds stress
tensor,
p
isthemeanpressure,tisthetimeand
ij
isthemeanviscousstresstensor.
ij
isdefinedasfollows:
j
i
ij
ji
u
u
x
x
(4)
whereμisthedynamicviscosity.
2.2
Turbulencemodel
TheRealizablek‐ε two‐layermodelisoneof the
turbulence models that calculates the eddy viscosity
by solving equations for k andε. This model is
designedtoaccuratelypredicttheturbulentflowina
widerangeofapplications.
t
CfkT
(4)
wheref
μisadampingfunction,Tisaturbulenttime
scaleandC
μisamodelcoefficient.
Eqn. (6) determines the turbulent time scale as
follow:
e
TT
(6)
Thetransportequationsforkandtheεaregivenas
follows:
0
() (v)= ( )
t
kk
k
kk kP S
t
(7)
1
0
22
0
1
() (v)=
t
e
e
CP
tT
Cf S
TT
(8)
ProductiontermsP
kandPεaregivenbyEqn.(9)as
follow:
3
;
kckbM c b
P
fG G P fSk C G
(9)
The damping functions is given by Eqn. (10) as
follow:
2
*3
1
**3
;
1
1
46coscos 6 : :
3
:
k
f
k
f
Sk
CSSWW
SS
(10)
3
NUMERICALSIMULATION
3.1
Casestudy
The vesselused asa case studyin thisstudy isJBC
vessel. This vessel was developed by the Japanese
NationalMaritimeResearchInstitute.Thesimulation
isconductedatamodel‐scaleofλ=40,soitallowsus
to carry out a direct comparison with experimental
data.Thehull
formandpropellerspecificationsofthe
JBC vessel are listed in Tables 1 and 2. For further
visualization, Figures 1 and 2 provide views of the
shipanditspropeller.Thetowingtankmeasureddata
forJBC areavailablein [21,22],providinga reliable
sourceforcomparisonwiththe
simulationresults.
Table1.JBCshipparameters
________________________________________________
DescriptionsUnit Value
________________________________________________
ShiplengthL[m] 7.000
ShipbreadthB[m] 1.1250
Designshipdraft T[m] 0.4125
Volumedisplacement [m
3
] 2.787
FroudenumberFr [‐] 0.1420
________________________________________________
Figure1.ThegeometryofJBCvessel
Table2.Propellerparameters
________________________________________________
DescriptionsUnit Value
________________________________________________
Diameterofpropeller DP [m] 0.203
AngleofrakeΘ[deg.]5
ExpandedarearatioAE/A0 [‐] 0.500
BossratioDh/D
P [‐] 0.18
PitchratioP0.7/D
P [‐] 0.750
Numberofblades Z[‐] 5
Directionofrotation‐[‐] Clockwise
________________________________________________
429
Figure2.ViewsofJBCpropeller
The simulation setup for this test case study
replicatesthetowingtank testconditionsdetailedin
[21, 22]. The ship was tested without a rudder at a
designdraftof4125mandaFroudenumberof0.1420.
The shipʹs pitch and heave motions were kept free,
andtheenvironmentcondition
wascalmwater.
3.2
Numericalsetup
The simulation of shipʹs self‐propulsion using the
actual propeller method requires a computational
domain that is divided into two zones: a stationary
zone and a rotating sub‐zone. The stationary zone
encompasses the entire calculated domain and
contains the ship hull, while the cylindrical rotating
sub‐zone
containsthepropeller.Thestationaryregion
isbounded byan inletboundary located1.5L tothe
shipbow,anoutletboundarylocated2.5Lbehindthe
ship stern, and top and bottom boundaries located
1.5Land2.5Lfromtheship.Thesideboundariesare
positioned at 2.5L away from the ship
in lateral
direction.Thesizeofthecalculateddomainconforms
to the ITTC [3, 23]. A visual representation of the
calculateddomainisdepictedinFigure3.
Figure3. The calculated domain for self‐propulsion
prediction
The type of boundary condition was setup as
follows[3, 4]:The top,inlet,and bottomboundaries
are classified as velocity inlets, while the outlet is
subject to pressure conditions. The side boundaries
are set as symmetry planes. Additionally, the
boundaryconditionsaresetfortheshiphullsurface
andpropeller
areno‐slipwall.
Table‐3presentsthephysicsmodelsettingsusedin
thisstudy.TheVolumeofFluidmethodwasutilized
for tracking and solving the free surface, and the
Realizable k–ε turbulence model is chosen to close
RANSEduetoitsprovenaccuracyinpreviousstudies
[24]. The
vessel was permitted to move with heave
and pitch motions. The propellerʹs rotation was
introducedusingtheDFBImodel,whichenablesthe
propellertobeattachedtotheshipʹshull.Anessential
factoraffectingthelevelofaccuracyofthenumerical
resultsistheselectionofthetime‐step
size.Topredict
self‐propulsion, a time‐step size was chosen that
resultsinthepropellerrotatingapproximately0.5to
1.5degreespertimestep[23].
Table3.Setupforphysicsmodel
________________________________________________
ParametersSetting
________________________________________________
Solver3D,implicitunsteady
Turbulencemodel Realizablek–εtwolayer
Multiphasemodel Thevolumeoffluid
Temporaldiscretization First‐order
Walltreatmentallwally+treatment
________________________________________________
Thenumericalresultsaresignificantlyaffectedby
themeshgeneration.Inthisresearch,atrimmedcell
mesher was utilized to generate meshes for both
stationary and cylindrical rotating sub‐regions. The
grid was refined at the free surface to accurately
capturethe Kelvin wave. Additionally, local volume
grid refinements were implemented
around the
propeller, ship stern and ship bow regions, and the
rotating sub‐region to improve the resolution of the
simulations. To accurately capture the interactions
between the ship hull and the propeller, the trailing
andleadingedgesofthepropellerweresubjectedto
additionalrefinement.Prismlayerswerealso
applied
toresolvetheboundarylayer.Themeshconsistedofa
total of 8.7 million cells. Figure 4 displays the mesh
generationresults.
Figure4.Somescreenshotsofthemeshsystem
4 RESULTANDDISCUSSION
Inthisstudy,theself‐propulsionpointwasdefinedas
thepointatwhichthepropellerthrustisequaltothe
resistance of the ship. However, in model scale
simulations, it is necessary to take into account the
SkinFrictionCorrectionForce(SFC)thataccountsfor
430
thevariationinskinfrictioncoefficientsbetweenthe
model scale and the full‐scale ship. Ignoring this
correctioncanleadtoinaccurateresults[25]
()
TSP
TR SFC
(11)
TheSFCvalueusedinthisstudywas18.2Nbased
on measured data [21, 22]. Since it is challenging to
determinetheself‐propulsioninonerun,sonormally,
two constant speed runs were carried out with two
propeller revolution rates (n = 7.80 and n=8.00 rps).
The
linear interpolation method was used to
determine the self‐propulsion point. The time step
wassetat3.5.10‐4s.
TheTable‐4inthisstudydisplaystheresultsofthe
resistance and thrust as a function of the propellerʹs
rotationrate.Theself‐propulsionpointwasidentified
at a rotation
rate of 7.85 revolutions per second, as
depicted in Figure 5. The comparison between the
numericalresults(CFD)andthemeasureddata(EFD)
is presented in Table 7. The results show a good
agreement between the two datasets. The difference
betweenthenumericalresultsandthemeasureddata
wasfound
tobe1.57%,2.84%and0.64%forresistance
of the ship, thrust of propeller and self‐propulsion
point,respectively.Figure6presentsatimehistoryof
resistanceoftheshipandpropellerthrustatarotation
rateof7.8revolutionspersecond.Theoscillationsof
propellerthrustarefivetimesthe
rotationalfrequency
duetotheeffectofshiphullform.
Table4.Numericalobtainedresults
________________________________________________
n[rps]RT(SP)‐SFC[N] T[N]
________________________________________________
7.8022.8522.55
8.0023.8524.75
________________________________________________
Figure5.Definingtheself‐propulsionpointprocedure
Detailedflowcharacteristicsaround theshiphull
andpropeller in theself‐propulsionsimulation were
also investigated. The figures illustrating these flow
characteristicsarepresentedinFiguresfrom7to 12,
respectively.
Table5.ComputedSelf‐propulsionpointincomparison
withmeasureddata
________________________________________________
ParametersEFD[22] CFD E%D
________________________________________________
RT(SP),[N]RT(SP) 40.760 41.39 1.57
T,[N]T 22.560 23.19 2.84
Self‐propulsionpoint n 7.800 7.85 0.64
________________________________________________
Figure6.Timehistoriesofresistanceoftheshipandthrust
atn=7.8rps.
Figure7.Wave‐elevationatn=7.8rps.
Figure8.Waterfreesurfaceatn=7.8rps.
Figure9. Velocity distribution in symmetry plane at n=7.8
rps.
Figure‐10. Dynamic pressure distribution on the blades
surfaceofpropelleratn=7.8rps.
431
Figure11. Dynamic pressure distribution on ship stern at
n=7.8rps.
Figure12.ComparionofvelocityfieldinAPbetweenCFD
andEFDatn=7.8rps.
The influence of propulsion models on the wake
distribution at the aft perpendicular of the ship is
depicted in Figure 11. It can be clearly observed in
Figure12,thewakecanbeclassifiedintotwozones,
i.e.thezoneinsidethepropellerandthezoneoutside
thepropeller.Thefirst
regionshowedanasymmetric
form due to the propeller, while the other region is
almostsymmetricform.
Propeller working behind the ship will introduce
pressurepulses onthe ship hull above thepropeller
region,whichmayeffectonnoiseandshipstructure
vibration.Figure11showstheinfluenceofpropeller
ondynamicpressuredistributionattheshipstern.As
can be seen from Figure 13 the asymmetry in the
dynamic pressure contours between the port and
starboard side at the region of the hull above
propeller.
5
CONCLUSIONS
Thepaperhassuccessfullyachieveditsobjectives.The
study utilized the CFD method to evaluate the ship
self‐propulsionparameters.Theslidingmeshmethod
was applied to model the actual propeller located
behindtheship.Shipisallowedtomovewithheave
andpitchmotion.Additionally,thepaperdealtwith
variousfactorsthatimpacttheaccuracyofsimulation
obtained results, such as choosing time step size,
turbulencemodelandgridgenerationtechnique.The
simulation results agreed well with the measured
data, with differences between simulation and
experimental results of 1.57%, 2.84% and 0.64% for
resistance of the ship, thrust and
self‐propulsion
point, respectively. Subsequent investigations will
focusonenhancingtheaccuracyofthesimulationsby
exploring various alternatives such as adjusting the
gridgenerationprocess,increasingthemeshsize,and
usingdifferentturbulencemodels.
ACKNOWLEDGMENT
I acknowledge the support of time and facilities form Ho
ChiMinhCityUniversityofTransportforthisstudy.
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