243
1 INTRODUCTION
Thereductionoffuelcosthasalwaysbeenoneofthe
key strategic business goals for ship owners and
operators.Inthecurrentclimateofhighoilprices,the
reduction of fuel costs becomes essential; and
furthermore a variety of recent legislations require
ownersandoperatorstomovetowa
rdsthereduction
ofemissionsfromshipsofSOx,NOxandCO.
Hence the pressure on designers to achieve both
reduced fuel costs and reduced emissions by
optimising the hull and propeller has never been
higher.Inparalleltotheperformanceimprovementof
newbuiltvessels,therehasbeengreatinterestinthe
potentia
l to enhance the performance of existing
vesselsthroughretrofitofdevicestothehull.Awide
rangeofconceptshasbeenproposed,manyofwhich
involve modification or control of the flow in the
vicinity of the propeller.The interest in these
devicesariseswithincreasingoilprice.Thesedevices
are commonly called “energy saving devices (ESD)”
and sometimes “
retrofitting technologies” although
manycanbeconsideredfornewdesignsaswell.
Thesavingslookveryattractivetoshipoperators,
for instance a saving of 6‐7% from installation of a
wakeequalisingduct(Schneekluth,1986,Schneekluth
Numeric Wake Equalizing Duct Geometry
Optimization for a Given Ship
G.Martinas&O.S.Cupsa
M
aritimeUniversityofConstanta,Romania
ABSTRACT:Thereductionoffuelcosthasalwaysbeenoneofthekeystrategicbusinessgoalsforshipowners
and operators. In the current climate of high oil prices, the reduction of fuel costs becomes essential; and
furthermoreavarietyofrecentlegislationsrequire owners and operators to move towa
rds the reductionof
emissionsfromshipsofSOx,NOxandCO.
Hencethepressureondesignerstoachievebothreducedfuelcostsandreducedemissionsbyoptimisingthe
hullandpropellerhas never beenhigher.Inparallel to the performance improvement of new built vessels,
therehasbeengreatint
erestinthepotentialtoenhancetheperformanceofexistingvesselsthroughretrofitof
devicestothehull.InanycaseforinstancetheWEDdevicemustbecustomizedtofittotheafterbodyofthe
shipintermsofperformingitssupposedfunction. TheDesigneristhereforepla
cedinthe frontofmultiple
geometricsolutionsfrombetweenhehastomakeachoice.ThispaperisintendedtohelptheDesignerstohave
arationalchoosingapproachbyinvolvingthenumericoptimizationofthegeometryoftheWEDinorderto
select the best fitted WED to perform the best in order to achieve some predefined parameters. In thi
s
paperworkagivengeometryofaWEDdeviceistakenandviaDesignOptimizationthegeometryoftheduct
wasrefinedsothatbetterresultsareachievedwithasmallerandmorecompactWED.Indoingso,theDesigner
is assisted by numeric op
timization methods to choose from only three final candidates instead of several
thousandsinordertoprovidethebestfittedWEDgeometryforagivenshipafterbody.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 9
Number 2
June 2015
DOI:10.12716/1001.09.02.12
244
(WED) and Bertram, 1998) or 7‐9% from a
combination of wake equalising duct and pre‐swirl
fins (Mewis, 2008, Mewis, 2009). In general, the
negative aspects of the devices include the
considerablecostofinstallation,andalsothereported
reluctanceofmanufacturerstoguaranteetheclaimed
savings.
The claims
may not give details as to the
conditions under which the savings have been
achieved and/or how the savings have been
calculated and/or measured. Furthermore, the
magnitude of the savings may well be within the
rangeofuncertaintiesandmeasurementerrorsonthe
full‐scale vessel. Consequently, cautious operators
may
wellbeskepticalaboutthevalidityofthefigures
being presented to the market, and it is absolutely
reasonable and necessary for a buyer to verify
independently the amount of savings before any
investmentonanESDorESDs.
InanycaseforinstancetheWED devicemust be
customizedto
fittotheafterbodyoftheshipinterms
ofperformingitssupposedfunction.TheDesigneris
therefore placed in the front of multiple geometric
solutionsfrombetweenhehastomakeachoice.This
paper is intended to help the Designers to have a
rationalchoosingapproachbyinvolving
thenumeric
optimizationofthegeometryoftheWEDinorderto
selectthebestfittedWEDtoperformthebestinorder
toachievesomepredefinedparameters.
2 CADANDFINITEVOLUMEANALISYS(FVA)
MODELOFTHESHIP
The goal of this paper is to calculate via software
Ansys 13
TM
the best geometric solution for a WED
device.ItisknownthatapoordesignoftheWEDis
notonlyimprovingtheoverallefficiencyofthevessel
butmayhaveanadverseimpactfailingtoachieveits
purpose.
The model has as departure point a real
portcontainer as seen below,
with the following
parameters(Fig.1):
LengthL‐[m]‐173
BreadthB‐[m]‐25
DraughtT‐[m]‐9.50
DiameterD‐[m]‐5
NumberofbladesZ‐6
PropellerRPM‐120
AverageSpeed‐16knots(7m/s)
Figure1.Port‐Container
Inordertohaveastartingpointforthesimulation,
first of all the afterbody was firstly CAD generated
withtheWEDdeviceattached,andalltheparameters
for fluid flow were calculated accordingly.From
thatpoint,theAnsysDesignExplorerwasinvolvedin
ordertooptimizethegeometry(Fig.2).
Figure2.CADgeometrywithWED
Inordertoprovidemoredetailsonthegeometry
of starting model of the WED device and the
optimization input parameters, the below figure is
shown,withdimensionsin[mm](Fig.3):
Figure3.WEDdevicegeometry
5 input geometric parameters were defined as
follows(Table1):
Table1.Inputgeometricparameters
_______________________________________________
Name TypeLowerlimit Upperlimit
_______________________________________________
P1 Angle Continuos 14[grade] 22[grade]
Minimize
P2 DuctLength Continuos 1980[mm] 2420[mm]
Minimize
P3 Smallradius Continuos 1600[mm] 2250[mm]
Minimize
P4 BiggerconeContinuos 2250[mm] 2750[mm]
radius
Minimize
P5 Distancefromthepropeller
Continuos 1800[mm] 2200[mm]
Minimize
_______________________________________________
245
The fluid domain was divided in two: the fluid
domain which is surrounding the afterbody having
the relative velocity on Oz axis of 7 m/s and the
Propeller fluid domain with CFX option of “frozen
Rotor” where the fluid is moving circularly around
OZaxiswith120RPM.Inbetween
thesetwodomains
interfaces were established. The other boundary
conditionswereinlet, outlet andopeningsasshown
below(Fig.4):
Figure4.BoudaryConditions
In order to make clear some important surfaces,
threecontrolplanesweredefinedasfollows(Fig.5):
Control plane number 1 (P1) placed at 1200 mm
abovethepropelleraxisandcoplanarwiththetwo
WEDdevicesaxis;
Control plane number 2 (P2) which is including
thepropelleraxis;
Control plane number 3 (P3) placed at 1500 mm
awayfromthepropellerdomain;
TargetPlanewhichisinfactoneof thepropeller
domaininterfacesasbelow:
Figure5.ControlPlanes
Taking into account the above defined control
planesasoutputparametersneedingtobeoptimized,
were defined as being the average fluid velocity
passing through the Target Plane (suspected to
improvethepropellerefficiency‐thebiggerthebetter)
and the average pressure on the inside of the WED
device(suspectedto
increasethedrag‐thesmallerthe
better)(Table2):
Table2.Outputparameters
_______________________________________________
ID ParameterNameStartingValue Unit
_______________________________________________
P6 VelocityTarget(maximize) 14.769ms^‐1
P7 PressureDuct(minimize) 89874Pa
_______________________________________________
3 CFASIMULATIONANDOPTIMIZATION
RESULTS
After reachingtheconvergenceof the given starting
modelsand goingthroughDesign ExplorerModule,
27designpoints(Table3)werecalculatedinorderto
definetheresponsesurfacesoftheproject:
Table3.DesignPoints
_______________________________________________
Name P1‐   P2– P3– P4– P5–
Angle Duct Small BiggerConeDistance
(degree) Lenght Radius RadiusPropeller
(mm) (mm) (mm) (mm)
_______________________________________________
1 182200 1925 2500 2000
2 142200 1925 2500 2000
3 222200 1925 2500 2000
4 181980 1925 2500 2000
5 182420 1925 2500 2000
6 182200 1600 2500 2000
7 182200 2250 2500 2000
8 182200 1925 2250 2000
9 182200
 1925 2750 2000
10  182200 1925 2500 1800
11  182200 1925 2500 2200
12  16.867 2137.7 1832.9 2429.2 2056.7
13  19.133 2137.7 1832.9 2429.2 1943.3
14  16.867 2262.3 1832.9 2429.2 1943.3
15  19.133 2262.3 1832.9 2429.2 2056.7
16  16.867 2137.7 2017.1 2429.2 1943.3
17  19.133 2137.7 2017.1 2429.2
2056.7
18  16.867 2262.3 2017.1 2429.2 2056.7
19  19.133 2262.3 2017.1 2429.2 1943.3
20  16.867 2137.7 1832.9 2570.8 1943.3
21  19.133 2137.7 1832.9 2570.8 2056.7
22  16.867 2262.3 1832.9 2570.8 2056.7
23  19.133 2262.3 1832.9 2570.8 1943.3
24  16.867 2137.7 2017.1 2570.8 2056.7
25  19.133 2137.7 2017.1 2570.8 1943.3
26  16.867
 2262.3 2017.1 2570.8 1943.3
27  19.133 2262.3 2017.1 2570.8 2056.7
_______________________________________________
Taking each and every design points to be
calculatedviaCFA(Table4),theoutputparametersto
beoptimizedareshownbelow:
246
Table4. Output calculated parameters for each design
points
_______________________________________________
Name P6–VelocityP7–Pressure
Target(ms^‐1) Duct(Pa)
_______________________________________________
114.5181.0123E+05
214.7599999
314.5141.0294E+05
414.5531.02E+05
514.4821.0077E+05
614.5271.033E+05
714.54197174
814.56197907
914.5811.0307E+05
1014.5561.0094E+05
1114.5711.0135E+05
1214.651.015E+05
1314.5961.0155E+05
1414.5741.008E+05
1514.5431.0136E+05
1614.698976
1714.53999788
1814.56398563
1914.57699455
2014.5951.0255E+05
2114.5531.0314E+05
2214.5471.0218E+05
2314.5141.0297E+05
2414.58898469
2514.5771.0143E+05
2614.571.0046E+05
2714.5581.0152E+05
_______________________________________________
The software is automatically selecting the
maximumandminimumcalculatedvaluesofoutput
parametersasbelow(Table5):
Table5.Minimumandmaximumoutputparameters
_______________________________________________
Minimum Maximum
_______________________________________________
P6‐VelocityTarget(ms^‐1) 14.478 14.784
P7‐PressureDuct(Pa)676481.4648E+05
_______________________________________________
By judging the above minimum and maximum
valueofthepressureinsidetheduct,thedifferenceis
20foldswhichisclearlymakingadifferencebetween
agoodandapoordesign.
By setting the goals of maximization or
minimizationdefinedaboveforalltheparameters,at
the end of the
optimization process three best
candidateswillbegenerated(Table6):
Table6.Thethreebestcandidates
_______________________________________________
Candidate Candidate Candidate
Point1 Point2 Point3
_______________________________________________
P1‐Angle(degree)  
14.164≈ 14.644 15.284
14grade
P2‐DuctLength(mm)
 
2049≈  1997.4 1988.8
1050
P3–SmallRadius(mm)
 
2081.8≈ 2242.3 2028.3
2080
P4–BiggerCone(mm)
 
Radius2330.3≈ 2282.3 2295.1
2330
P5–DistanceFrom(mm)  
Thepropeller2159.4≈ 2005.4 2154.7
2160
P6–VelocityTarget
 
(ms^‐1)14.78 14.756 14.702
P7–PressureDuct(Pa)
 
98351 94591 1.0633E+05
_______________________________________________
HereonceagaintheDesigneriscalledtomake a
decision, we choose the first candidate having three
starstothemostoftheparameters.
Inordertohaveanoverallideaontheinfluenceof
each and any input parameter has on the output
parameter, the sensitivity charts
and response
surfaces are the best aids for judgment. Since the
possible combinations are many, only few response
surfacesaregivenbelow.
Duct Pressure‐Duct Angle and Duct Length
ResponseSurface(Fig.6)
Figure6. Duct Pressure‐Duct Angle and Duct Length
ResponseSurface
Fromtheabovechartonemayimplythattheduct
Angle hasa bigger influence than the Length of the
247
duct over the Pressure inside the duct, which is
somehow in line with a common sense hypothesis.
Thesmallertheangleisandthebiggerthelengthis
thenthesmallertheinsidepressurewillbe.
DuctPressure‐DuctAngleandDuctSmallRadius
ResponseSurface(Fig.7)
Figure7.DuctPressure‐DuctAngleandDuctSmallRadius
Responsesurface
Thepressureinsidetheductwillbesmallerasthe
angleissmallerandthesmallradiuswillbesmaller.
Velocity over the Target Surface‐Duct Angle and
DuctLengthResponseSurface(Fig.8)
ThesmallertheDuctangle(near14degrees)and
theLengthis, the biggerthevelocityof the
fluidon
thetargetsurfacewillbe.
Figure8.DuctPressure‐DuctAngleandDuctSmallRadius
Responsesurface
Inordertoplacealltheinfluencesonasinglechart
(Fig.9),thesensitivitychartisusedasbelow:
Figure9.Sensitivitychart
Finally if one wants to visualize the effect of the
optimized input parameters, we can recalculate the
model with these new optimized parameters for
geometry resulting for the output parameters the
followingfigures:
The influence of optimized parameters on the
velocitythroughthetargetsurface(Fig.10‐11)
Byanalyzingthe
figuresbelow,onemayseethat
theshapeofthevelocityfieldsontheupperzoneof
thepropellerismoreextended,sothattheoptimized
versionis“pushing”morefluidonthiszone.
Figure10.Thestartingmodelvelocities
248
Figure11.Theoptimizedmodelvelocities
The influence of optimized parameters on the
pressureinsidetheduct(Fig.12‐13)
The starting model has a bigger (red colored)
pressure fields on the inside the duct whereas the
optimisedversionhassmallerandplacedattheoutlet
zone of the duct pressure fields, which is an
indication that
the inside pressure and the drag is
thendiminishedfortheoptimizedversion.
Figure12.Thestartingmodelductpressures
Figure13.Themodelductpressures
4 CONCLUSIONS
Thewakeequalizing duct(WED)is one ofthemost
commonlyusedenergysavingdevicesforimproving
the propulsion performance of a ship; and reducing
thepropeller‐excitedvibrationsandviscousresistance
forces.
In this paperwork a given geometry of a WED
device is taken and via Design Optimization
the
geometryoftheductwasrefinedsothatbetterresults
areachievedwithasmallerandmorecompactWED.
In doing so, the Designer is assisted by numeric
optimizationmethodstochoosefromonlythreefinal
candidates instead of several thousands in order to
providethebestfittedWED
geometryforagivenship
afterbody.
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