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Hydrodynamic Analysis of the Spherical Underwater Robot SUR-II

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This paper describes the development of the second-generation Spherical Underwater Robot (SUR-II). The new SUR-II has an improved propulsion system structure, resulting in better performance compared with the original design. This paper focuses on the characteristics of the water-jet thruster and the spherical hull of the SUR-II. To analyse its hydrodynamic characteristics, the main hydrodynamic parameters of the SUR-II were estimated based on two reasonable assumptions and a reasonable dynamic equation was proposed to describe the relationship between force and velocity. Drag coefficients were calculated separately for vertical and horizontal motions due to the fin on the robot's equator and the holes in the robot's hull. The holes had a particularly adverse effect on the horizontal drag coefficient. A hydrodynamic analysis using computational fluid dynamics was then carried out to verify the estimated parameters. The velocity vectors, pressure contours and drag coefficient for each state of motion were obtained. Finally, the propulsive force was determined experimentally to verify the theoretical calculations and simulation results.
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International Journal of Advanced Robotic Systems
Hydrodynamic Analysis of the
Spherical Underwater Robot SUR-II
Regular Paper
Chunfeng Yue1, Shuxiang Guo2,3 and Liwei Shi2,*
1 Graduate School of Engineering, Kagawa University, Takamatsu, Japan
2. Faculty of Engineering, Kagawa University, Takamatsu, Japan
3. School of Electrical Engineering, Tianjin University of Technology, Tianjin, China
* Corresponding author E-mail: s12d502@stmail.eng.kagawa-u.ac.jp
Received 3 Jul 2012; Accepted 9 Apr 2013
DOI: 10.5772/56524
© 2013 Yue et al.; licensee InTech. This is an open access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
AbstractThispaperdescribesthedevelopmentofthe
secondgenerationSphericalUnderwaterRobot(SURII).
ThenewSURIIhasanimprovedpropulsionsystem
structure,resultinginbetterperformancecomparedwith
theoriginaldesign.Thispaperfocusesonthe
characteristicsofthewaterjetthrusterandthespherical
hulloftheSURII.Toanalyseitshydrodynamic
characteristics,themainhydrodynamicparametersofthe
SURIIwereestimatedbasedontworeasonable
assumptionsandareasonabledynamicequationwas
proposedtodescribetherelationshipbetweenforceand
velocity.Dragcoefficientswerecalculatedseparatelyfor
verticalandhorizontalmotionsduetothefinonthe
robot’sequatorandtheholesintherobot’shull.The
holeshadaparticularlyadverseeffectonthehorizontal
dragcoefficient.Ahydrodynamicanalysisusing
computationalfluiddynamicswasthencarriedoutto
verifytheestimatedparameters.Thevelocityvectors,
pressurecontoursanddragcoefficientforeachstateof
motionwereobtained.Finally,thepropulsiveforcewas
determinedexperimentallytoverifythetheoretical
calculationsandsimulationresults.
KeywordsSphericalUnderwaterRobot,Hydrodynamic
Analysis,HydrodynamicCharacteristicsEstimation
1.Introduction
Theapplicationsofautonomousunderwatervehicles
(AUVs)havebeenexpandingandnowincludefields
suchasoceanresearch,scientificinvestigations,ocean
developmentandunderwaterprojects.Thedevelopment
ofautonomousunderwatervehicleshasreachedalevel
ofpracticaltechnologicalmaturity.Autonomous
underwatervehiclescanbedividedintotwocategories
basedonwhetherornottheirbodiesarestreamlined.The
vehicle’sshapeisdeterminedbytherequirementsofthe
application.Forexample,astreamlinedshapereduces
waterresistanceandispreferableifthevehiclemust
moveathighspeeds.However,ifunderwaterdetection
oroperationtasksaretheprimaryrolesofanunderwater
robot,anonstreamlinedshapeisoftenused.
Differenttasksrequireautonomousunderwaterrobotsto
beofdifferentshapesandsizes.Deepsearesearch
requireshighwaterpressureresistance,whilemonitoring
andobservationtasksrequiresmall,flexibleandstable
robots.Researchinfieldssuchashydrodynamics,
electronicsandmechanicsisnecessaryinordertobuilda
robotwithgoodmotioncontrolperformance.The
researchisofteninterdisciplinary;forexample,
1
Chunfeng Yue, Shuxiang Guo and Liwei Shi:
Hydrodynamic Analysis of the Spherical Underwater Robot SUR-II
www.intechopen.com
ARTICLE
www.intechopen.com Int J Adv Robotic Sy, 2013, Vol. 10, 247:2013
mechanicsandhydrodynamicsarebothusedin
designingmechanicalstructuresthatwillprovideoptimal
hydrodynamiccharacteristics.
Duetothegoodwaterpressureresistanceofspherical
objects,sphericalrobotscanperformarotationalmotion
witha0turnradius.Manytypesofspherical
underwaterrobotshavebeendeveloped.ODINIIIwasa
typicalprototyperobotdevelopedattheUniversityof
Hawaii[1,2].Ithadametalshell,adiameterof630mm
andaweightof150kg.Thissphericalunderwaterrobot
wasusedtomonitortheenvironmentandforunderwater
operations.ResearchersattheUniversityofManchester
andOxfordUniversitycodevelopedamicrospherical
underwaterrobot[3,4].Thisrobotusedsixpropellersin
itspropulsionsystemlocatedaroundtheequatorofits
sphericalhull.Thismicrorobotwasdevelopedto
monitornuclearstoragepondsandwastewatertreatment
facilitiestopreventleakage.Bothoftheserobotsused
propellersontheoutsideoftheirbodiesfortheir
propulsionsystems.Othersphericalunderwaterrobots
haveusedwaterjetthrusters.ResearchersatHarbin
EngineeringUniversitydevelopedaspherical
underwaterrobotwiththreewaterjetthrusters[5,6].
However,thepropulsiveforceofthethrusterswas
considerablyreducedbecausethewaterinputpipeline
wascurved.ResearchersattheBeijingUniversityofPost
andTelecommunicationsdevelopedaspherical
underwaterrobotwithonetunnelpropeller[7].This
robotadjusteditsattitudebychangingitscentreofmass
byusingamovableweightbalancingblock.Thismadeit
possibletoadjustthedirectionofthetunnelpropeller
andtoachievesomelinearmotion,buttherobotcould
notcarryoutotherhybridmotionsbecauseitonlyhad
onepropeller.
Inourlaboratory,wedevelopedasphericalunderwater
robotthatusedthreevectoredwaterjetthrustersforits
propulsionsystem[8–11].Thepropulsionsystemwas
assembledinsidethesphericalhulltoreduceitseffectson
therobot’sflexibilityandtolimitdamagefrompossible
impacts.
1.1RelatedWork
Hydrodynamiccharacteristicsareimportantfactorsin
researchintounderwatervehicles.Theefficiencyand
accuracyofthecontrolalgorithmsandtheoptimum
structureoftherobotdependonhydrodynamicanalyses;
somanyresearchershavecarriedouthydrodynamic
analysesontheirunderwatervehicles.Uenoetal.
analysedtheSubmersibleSurfaceShip(SSS),anewtype
ofshipthatcanavoidroughseasbygoingunderwater
usingthedownwardliftofwingswhilemaintaining
residualbuoyancyforsafety[12].Theysetupatank
experimenttoanalyseitshydrodynamiccharacteristics
andthenproposedamathematicalmodeltodescribethe
interactioneffectsbasedontheresultingdata.Leroyeret
al.analysedtheDTMB5415barehullusinga
computationalfluidmechanics(CFD)methodand
proposedtwonumericalproceduresthatspedupthe
ReynoldsaveragedNavier–Stokes(RANS)solvers[13].
Theywereabletoobtainnumericalsolutionstorealistic
problemsuptofourtimesfasterusingthesetwo
procedures.MylonasandSayerpredictedtheforces
actingonayachtkeelbasedonlargeeddysimulation
(LES)anddetachededdysimulation(DES)solutions[14].
Propulsionsystemshavealsobeenamainresearch
subject.Weietal.predictedthepropellerexcitedacoustic
responseofasubmarinestructureusinganumerical
method[15].Chengetal.analysedthehydrodynamic
characteristicsofanunconventionalpropellerwithan
endplateeffectandcomparedtheresultstothoseofa
conventionalpropeller[16].Jietal.verifiedthat
accelerationduetochangesincavityvolumeisthemain
sourceofthepressurefluctuationsexcitedbypropeller
cavitation[17].Allofthesestudiesinvolvedpropellers
andresearchershaveusedmanydifferentmethodsto
analysevarioushydrodynamiccharacteristics.
1.2Motivation
TheSphericalUnderwaterRobot(SUR)hasauniquehull
andauniquepropulsionsystem.Therefore,
hydrodynamicanalysisisanimportantrequirementfor
themotioncontrolsystemoftherobot.Weconducted
hydrodynamicanalysestoobtainthemain
hydrodynamicparametersoftherobot,whichreflectits
performance.Waterresistanceandpressuredistribution
areimportantfeatureswheninvestigatinginteractions
betweenarobotandfluid,andthedragcoefficientisan
importantparameterwhenanalysingtheforceofwater
drag.
Thehydrodynamiccharacteristicsofanunderwaterrobot
differforeachmotion.Inpreviouswork,weassumed
thattherobotwasasphere,sothemotionfeatureswere
thesameforalldegreesoffreedom.However,our
previousanalysesdidnotyieldsufficientlyaccurate
results,becausewaterflowsthroughtheholesinthe
robot’shullduringhorizontalmotionandthemotionof
fluidisaffectedbythefinaroundtherobot’sequator.
Also,thepropulsiveforceinfluencestheflexibilityofthe
robot;therefore,weanalysedthepropulsiveforcebased
onsimulatedandtheoreticalcalculations.
1.3PaperOutline
Thispaperisstructuredasfollows.Section1provides
backgroundfortheresearch.Section2describesthe
secondgenerationSphericalUnderwaterRobot(SURII),
whichhasanimprovedwaterjetpropulsionsystem.This
sectionalsoprovidesthemotionstatesoftherobotto
eachdegreeoffreedom.Section3presentsthemain
2Int J Adv Robotic Sy, 2013, Vol. 10, 247:2013 www.intechopen.com
hydrodynamicparametersoftheSURIIandanalysesits
motionsindetail.Section4presentsahydrodynamic
analysisbasedonCFD.Section5describesanexperiment
usedtoverifythepropulsiveforceanalysisandSection6
summarizesourconclusions.
2.MechanicalStructureAnalysis
Wehavealreadyconductedextensiveresearchonthe
SURandobtainedsomeusefulresults.Lindesignedthe
firstgenerationSURandimplementeditsbasicmotion
control[18,19].
2.1AnalysisoftheVectoredWaterjetThruster
Thestaticanalysisisveryimportantforthisrobot.First,
unexpecteddeformationoccursinthepropulsionsystem.
Thedeformationofthepropulsionsystemofthefirst
generationrobothassomenegativeeffects[18,19].With
thevectoredwaterjetthruster,wecontrolthedirectionof
thethrusterinordertoimplementsomeunderwater
motions.However,thedeformationwillaffectthe
directionofthenozzle.Asaresult,thedirectionofthe
propulsiveforcecannotbecontrolledveryaccurately.In
addition,ifthepropulsionsystemisnotrigidenough,
vibrationswillalsobecausedveryeasily.Second,the
weightoftherobotistobereducedtoincreasetherobot’s
payloadcapacity.Therefore,astaticanalysisofthe
propulsionsystemwascarriedouttoimproveits
mechanicalfeatures.ANewtonpropulsiveforceactson
eachnozzleofthewaterjetthruster.Thethruster
operatesinthreeorientations:up,down,andhorizontal;
therefore,thestaticanalysiswasdividedintothreestates.
Whentheframeandtriangularsupportofthepropulsion
systemwasimproved,asshowninFigure1,itreduces
thedeformationofthevectoredwaterjetthrusterand
reducestheweightofthepropulsionsystemto1.08kg.

Figure1.Structureofthevectoredwaterjetthrusterafter
improvement
Thestaticanalysisresultsoftheimprovedpropulsion
system,showninFigure2(b)[20],indicatethatthe
largestdeformationwasabout2mmbeforethe
improvementandthedeformationwillcauseanangle
errorofabout1.5degrees.Aftertheimprovement,the
deformationisreducedto1mmandtheangularerroris
reducedto0.7degrees.Therefore,thedirectionofthe
propulsiveforceofthepropulsionsystemismore
accurate.ThesecondgenerationSphericalUnderwater
Robot(SURII)containstheimprovedvectoredwaterjet
thruster.

(a)previousdesign

(b)improved
Figure2.Deformationofthepropulsionsystemafter
improvement
Thevectoredwaterjetthrusteriscomposedmainlyof
fourcomponents:onewaterjetthruster,onewaterproof
box,twoservomotorsandonesupportframe.Thewater
3
Chunfeng Yue, Shuxiang Guo and Liwei Shi:
Hydrodynamic Analysis of the Spherical Underwater Robot SUR-II
www.intechopen.com
jetthrusterprovidesthepropulsiveforcefortheSURII.
Theservomotorsareemployedtochangethedirectionof
thewaterjetthruster.Thewaterproofboxprotectsthe
DCmotorofthewaterjetthrusterfromwater.The
supportframeisabasiccomponentofthewaterjet
thruster.
(a)frontview(b)topview
Figure3.Rangeofrotationinthehorizontalandverticalplanes
Eachvectoredwaterjetthrusterhastworotational
degreesoffreedom.Figure3(a)showstherangeof
rotationfrom90to+60degreesintheverticaldirection.
VerticalmotionoftheSURIIispossibleduetothe
rotationaldegreeoffreedomintheverticaldirection.
Figure3(b)showsthattherangeofrotationis60ointhe
horizontaldirection.Theservomotorsnotonlyadjustthe
thrusterorientation,butalsogenerateresistancetorqueto
ensurethatthethrusterorientationremainsinthecorrect
position.
2.2AnalysisoftheSURIIStructure
Figure4showstheconceptualdesignoftheSURII.The
waterproofboxcontainsallofthecontrolcircuitsand
severalsensors.Therobotcanbedividedintofour
systems:thepropulsionsystem,controlsystem,sensor
systemandmechanicalsystem.
Figure4.ConceptualdesignoftheSURII
Forthepropulsionsystem,threevectoredwaterjet
thrustersareassembledonatriangularsupport.The
systemisinstalledinsidethehullfortworeasons.
First,underwaterenvironmentsarecomplexanda
varietyofcreaturesliveinthewater.Havingthe
propulsionsysteminstalledinthehullcaneffectively
preventexternalimpacts.Second,thehulloftherobot
canthenbedesignedtoapproximateasphereandthe
influenceofthepropulsionsystemonthe
hydrodynamiccharacteristicsoftherobotwouldbe
reducedincomparedwithifitwereinstalledoutside
thehull.
DOFSurgeSwayHeaveRollPitch Yaw
Utilizationratio 100%31%96%33%7%100%
Table1.Theutilizationratioofeachdegreeoffreedomfor
underwatervehicles
Generally,anunderwatervehiclehassixdegreesof
freedom,butnotallofthesecanbeusedforactual
movements.Table1showsthetypicalutilizationratioof
eachdegreeoffreedominanunderwatervehicle[21]:
sway,pitchandrollareseldomused.TheSURIIhasfour
degreesoffreedom:surge,sway,heaveandyaw.Because
theSURIIissymmetricinitsgeometriccentreandhasa
0turnradius,swayhasthusfarnotbeenemployed.
Therefore,onlythreedegreesoffreedommustbe
consideredindetail:surge,heave,andyaw.
Figure5.Sphericalunderwaterrobot
2.3MotionStatesoftheSURII
Thethreemaindegreesoffreedomwereanalysedin
detail:surge,heave,andyaw.Ingeneral,twowaterjet
thrustersareemployedtoprovidepropulsiveforcefor
surgemotionandthethirdcanbeusedasabrake.If
highspeedsarerequired,theangleofthepropulsive
forcecanbeadjustedbyhorizontalservomotors,as
shownindetailinFigures6(a)and(b).Rotational
motionisshowninFigure6(c);therotationalanglecan
bemeasuredbyusingthefeedbackfromagyroscope.
Figures6(d),(e),and(f)presenttheup,downandhold
positions,respectively.
4Int J Adv Robotic Sy, 2013, Vol. 10, 247:2013 www.intechopen.com
(a)(b)
(c)

(d)(e)
(f)
:thedirectionofmotion;:thedirectionofthepropulsiveforce.
Figure6.Basicmotionstates;(a)isregularmotioninsurge;(b)is
quickmotioninsurge;(c)isrotationinyaw;(d),(e),(f)are
verticalmotioninheave.
3.DynamicAnalysis
Hydrodynamiccharacteristicsplayadirectrolein
hydrodynamicanalysis,whichcanbeusedtoverifythe
accuracyoftheestimationofthemainhydrodynamic
parameters.Theestimationoftheparameterswasbased
onthefollowingassumptions:
1. Therobotisasphere;
2. Thefluidenvironmentisstaticwaterat20C.
3.1DynamicModeloftheSURII
ConsideringallofthefactorsthatinfluencetheSURII,a
sixdimensionaldynamicequationwasestablished:
RB add l q
RB A
(M M )v (D D (v))v
(C (v) C (v))v g( )
 
 
(1)
whereMRBdenotestherigidbodymassmatrix,Maddisthe
addedmassofthesphericalunderwaterrobot,CRB(v)is
therigidbodyCoriolismatrix,CA(v)isthehydrodynamic
Coriolismatrix,Dlvisthelineardampingterm,Dq(v)vis
thenonlineardampingterm,g()istherestoringforce
vectorand
isthecontrolvector,whichcontainsthe
propulsiveforceandthemoment.Thefollowing
simplificationscanbeproposedbasedonthediscussion
inSection2.First,therollandpitchmovementsare
passivelycontrolled,sotheyarenegligible.Second,the
surgeandswaymovementshavethesamedynamic
featuresduetothesphericalshape.Therefore,the
dimensionsofEquation1canbereducedtothree.
Coriolisforcesarecausedbytheearth’srotationandthe
speedofthemovingobject.ThespeedoftheSURIIrobot
islessthan0.3m/s,andmostofthefactorsintheCoriolis
matrixarerelatedtotherobot’svelocity,soCoriolis
forcescanbeignoredfortheselowspeedcases.In
hydrodynamicsterminology,gravitationalandbuoyancy
forcesarecalledrestoringforces,g().Thebuoyancy
forcesarealmostsolelydeterminedbythewaterproof
box.Thepositionofwaterproofboxcanbeadjusted
using4longscrews.Hence,thecentreofbuoyancyis
adjustable.Inrealsituations,therestoringforceexists.
However,ithasnoinfluenceonthemotionofsurge,
sway,heaveandyaw.Itsonlyeffectinthiscaseisto
adjusttherotationmotionofpitchandrollwhichwere
notconsideredinthispaperand,assuch,weignoredthe
g(Θ).Therefore,Equation1becomes:
RB add l q
(M M )v (D D (v))v
 
(2)
where
ismeasurableusingapropulsiveforce
experiment.TheparametersofEquation2mustbe
determinedaccuratelytoenhancetheaccuracyofthe
dynamicanalysis.
3.2RelatedParameterEstimation
Maddiscalculatedbasedonthesphericalshape:
3
add
2
M R
3

(3)
MRBcanbeobtainedwithmeasurementsandtheuseofa
3Dmodel:
RB
zz
m 0 0 6.3 0 0
M 0 m 0 0 6.3 0
0 0 I 0 0 0.1281
 
 
 
 
 
 
,
5
Chunfeng Yue, Shuxiang Guo and Liwei Shi:
Hydrodynamic Analysis of the Spherical Underwater Robot SUR-II
www.intechopen.com
add
16.75 0 0
M 0 16.75 0
0 0 0.3864
 
 
 
 
 
BasedonAssumption2andEquation4,Dlv=Cl
diag{u,v,w,p,q,r},whereCl=110–4isthelinearviscous
coefficientofthefluidat20C,anddiag{u,v,w,p,q,r}isthe
velocitymatrixoftherobot.Becausethevelocityisvery
small,Dlvcanalsobeneglected.ThissimplifiesEquation
2to:
RB add d
(M M )v F
 
(4)
Fdcanbecalculatedas:
2
q d d e
1
D (v)v F C (R ) V A
2
  (5)
whereCdisthedragcoefficient,ReistheReynolds
number,whichreflectstheflowcharacteristics,Visthe
velocityvectorandAisthecrosssectionalarea.
Whentherobotmovesinvertically,theringfinthatis
fixedonthesphericalhullequatorcannotbeignored.The
ringwidthisr=30mm,soA=
(R+r)2=0.1662m2.
Whentherobotmoveshorizontally,thefincanbe
ignored,soA=
R2=0.1256m2,whereR=200mmisthe
radiusoftherobot.
Forasphericalshape,CdisdeterminedbyRe:[22]
e
vD
R
(6)
where
isthekinematicviscosityofthefluid,and
=1
10–6at20C.Themaximumvelocityis0.3m/s,soRe=1.2
105>1103,whichindicatesthattheflowisturbulent
whentherobotmovesthroughthewater.BasedonTable
2,whenRe=1.2105,Cd=0.40.Forverticalmotion,FHd=
c2v2,wherec2=33.24.ThepropulsiveforceisequaltoFd.
Whentherobotmovesatmaximumvelocity,Fd=T,
whereTcanbeobtainedexperimentally.TheresultT=
2NwillbeverifiedinSection5.
ReRe<104104<Re<3×1053×105<Re<1×106
Cd24/Re+6.48×Re0.573+0.360.400.40
Cd30/Re+0.460.460.46
Cd24/Re+(1+0.0654Re2/3)3/20.400.40
Cd(0.352+(0.124+24/Re1/2)2 ‐ ‐
Cd(0.63+4.8×Re0.5)20.40 ‐
Table2.[23,24]RelationshipbetweenReandCdforaspherical
shape
Forverticalmotion,CdcannotbeobtainedfromTable2
becausetheholesinfluencethehydrodynamic
characteristics.Fluidflowsthroughtheholes,sotherobot
cannotbeclassifiedasclosed.However,athighspeeds
themaximumvelocityvmax=0.3m/sandpropulsiveforce
T 2 3N.BasedonEquation5,Cd=0.5
v2A/T=0.61.
Aftercomparingthetwovaluesofthedragcoefficient,
wefoundthattheholesinthesphericalhullincreased
waterresistance.
Fortherobot’srotationalmotion,thenonlineardamping
termiszerobecausetherobothasasymmetricalshape.
Afteranalysingandcalculatingtheparametersofthe
dynamicequation,weobtained:
z
23.05 0 0
0 23.05 0 v
0 0 0.5145
2T cos
39.25v 0 0 2
0 33.24v 0 v Tsin
0 0 0 M
 
 
 
 
 
 
 
 
 
 
 
 
 
(7)
where
istheangleofthetwoworkingthrustersfor
horizontalmotionand
istheangleofthethrusterfor
verticalmotion.Therelationshipcurvesthatdescribe
howvelocityvarieswithtimewereobtainedusing
Equation7,basedonthemotionshowninFigure6and
=2
/3,
/3.TheresultsarepresentedinFigures7and8.
Table3demonstratesthatthemaximumspeedineach
directionofmotionisdifferent,basedontheresultsof
Figures7and8,andshowsthattheaccelerationtimeis
lessthan10seconds.
Figure7.Variationofspeedwithheaveintime
Figure8.Thecurvesthatshowthatspeedvarieswithtimein
surge
6Int J Adv Robotic Sy, 2013, Vol. 10, 247:2013 www.intechopen.com
MotionstateHeaveSurge
UpDownNormal
speed
High
speed
V
max
(m/s)0.2450.2280.2250.3
Timeconsumption(s)9997
Table3.Maximumvelocityinheaveandsurgemotion
4.HydrodynamicAnalysis
4.1HydrodynamicAnalysisoftheSURII
TheSURIIwasmodelledinacylindricalflowfieldwith
aradiusof1mandalengthof4m,asshowninFigure9.
Anunstructuredtetrahedronmeshwasadopted.The
meshdensitywasincreasedaroundtherobotandthree
boundarylayerswereusedtoobtainsatisfactoryresults
andreducetheamountoftimerequired.Figure9
presentsthemeshforhorizontalmotion.
Figure9.3Dmodelmesh
Thequalityofthemeshisadeterminingfactorinthe
accuracyofhydrodynamicanalysis.Therefore,themesh
wassmoothedbeforecarryingouttheanalysisandthe
3Dmodelwassimplifiedbeforemeshing.Forexample,
nutsandboltswereignoredtoreducethecomplexityof
themeshandenhancethemeshquality.Thevarious
robotcomponentswereestablishedasasinglebody.A
totalof1.5millionmeshelementswereused.
Aftercompletingthepreliminarywork,themeshfiles
wereoutputtothesolver.Thecommercialsoftware
packageFLUIDwasemployedtosimulatetheflow
aroundtheSURII.Threetypicalmodelswere
established:onefordownwardmotionwithaspeedof
0.228m/s,oneforsurgemotionwithaspeedof0.3m/s
andoneforrotationalmotionwithaspeedof3rad/s.
AccordingtoTable3andtheReynoldsnumbercriterion,
turbulentflowoccurredinallcases.Therefore,themain
parametersettingsforthehydrodynamicanalysiswereas
follows:inlet:velocityinlet;outlet:outflow;viscous
model:standardkepsilon;convergencecriterion:0.0001.
Therobotandfluidmoverelativetoeachother,sothe
robotwassetasastaticwallwhilethefluidwassetasa
constantvelocityflow.Figures10and11presenthow
boththevelocityandpressurewereaffectedbythefin
thatwasfixedontheequatoroftherobot.Thus,thefin
cannotbeignored.However,theeffectoftheholeswas
notobvious.Figure11showsacutawayviewoftherobot
duringverticalmotion.Thevelocityofthefluidinsidethe
robotwasthesameasthevelocityoftherobot.Therefore,
thefluidinsidetherobotcanbeassumedasbeingpartof
therobotandAssumption1isvalid.However,for
horizontalmotion(Figure12),thesimplificationsarethe
oppositeofthoseappropriateforverticalmotion:thefin
canbeignoredandtheholesmustbeconsidered,because
waterflowsintotherobotthroughthefrontholesand
thenoutoftherobotthroughthebackholes,asshownin
Figure13.Thus,therobotcannotbeassumedtobea
closedsphere.Insummary,thefinscannotbeignoredfor
verticalmotionandtheholescannotbeignoredfor
horizontalmotion.

(a)Velocityvectors
(b)Pressurecontours
Figure10.Influenceofrobotonthefluidduringdownward
motion
7
Chunfeng Yue, Shuxiang Guo and Liwei Shi:
Hydrodynamic Analysis of the Spherical Underwater Robot SUR-II
www.intechopen.com
Figure11.Cutawayviewofvelocityvectorsinverticalmotion

(a)Velocityvectors
(b)Pressurecontours
Figure12.Theinfluenceoftherobotonthefluidwhentherobot
ismovinghorizontally
C
d
wasobtainedfromthesimulations,asshowninFigure
14.Aftercalculatingabout100steps,thedragcoefficient
forverticalmotionconvergedtoaconstantC
d
=
0.40602667,similartothevaluecalculatedinSection3.
ForhorizontalmotionC
d
=0.58860832,whichindicatesa
3%errorcomparedtothecalculatedvalue.Therefore,the
resultsoftheCFDanalysisareacceptable.
Figure13.Cutawayviewofvelocityvectorsinhorizontalmotion

(a)
(b)
Figure14.Dragcoefficient:(a)verticalmotionand(b)horizontal
motion
Afterobtainingthedragcoefficient,Equation7canbe
modifiedasfollows:
z
23.05 0 0
0 23.05 0 v
0 0 0.5145
2T cos
36.99v 0 0 2
0 33.74v 0 v Tsin
0 0 0 M
 
 
 
 
 
 
 
 
 
 
 
 
 
(8)
Calculation steps
8Int J Adv Robotic Sy, 2013, Vol. 10, 247:2013 www.intechopen.com

(a)
(b)
Figure15.Yawmotion:(a)velocityvectors;(b)pressurecontours
Inadditiontoverticalandhorizontalmotion,rotational
motionwasalsosimulated.Thevelocityandpressure
resultsindicatedthattheeffectofrotationalmotionon
thefluidwasnegligible.Theinteractionbetweenthefluid
andtherobotwascausedbythepropulsionsystem,as
showninFigure15,andapressuresurfacewasgenerated
aroundthepropulsionsystem.
4.2HydrodynamicAnalysisoftheThruster
Thewaterjetthrustwasalsosimulatedtoanalysethe
propulsiveforceandthepropulsionsystemindetail.
Figure16(a)presentstherobotthruster.Becausethe
objectofstudywasonlyanozzleandblade,otherparts
wereomittedinthe3Dmodel,asshowninFigure16(b).
Inthesimulation,thebladewassetastherotatingpart
andtheinletwassetasavelocityinlet.Themaximum
velocityoccurredattheedgeoftheblade,asshownin
Figure16(b).Duetothefrictionofthenozzleandthe
waterresistance,theoutletvelocitywasabout2.5m/s.
Strongturbulenceoccurredinthenozzle.Thepropulsive
forceobtainedbypostprocessingwasT=2.18446.

(a)
(b)
Figure16.Yawmotion:(a)waterjetthruster;(b)velocityvectors
Weanalysedboththerobotandthethrusterusing
separatehydrodynamicanalyses.However,thetwoflow
fieldsinteractwhentherobotismoving,whilethe
hydrodynamicanalysesonlyfocusedonthebasic
motions.Ifahybridmotionisalsorequired,adynamic
meshmustbeemployedtodescribethefluidfield.
5.Experiment
5.1propulsiveforceexperiments
Thepropulsiveforcewasdeterminedexperimentallyto
verifythetheoreticalandsimulationresultsinSections3
and4.Inthisexperiment,asixdegreeoffreedomload
cellwasemployedtomeasurethepropulsiveforceofthe
thruster.Figure17illustratestheprincipleofthe
experiment.Whenthethrusterisworking,thepropulsive
forceactsonthenozzle.Thedifferenceofthemoment
actingontheXYplaneiscausedbythepropulsiveforce
andthearmofthepropulsiveforceismeasurable.
Therefore,thepropulsiveforcecanbecalculated;Figure
18presentstheresults.
9
Chunfeng Yue, Shuxiang Guo and Liwei Shi:
Hydrodynamic Analysis of the Spherical Underwater Robot SUR-II
www.intechopen.com
Figure17.Principleofpropulsiveforceexperiment
Figure18.Propulsiveforce
Intheexperiment,thethrusteroperatedforabout2
hours.AlthoughtheDCmotorcausedsomevibrations,
themeanvaluewas2N.
5.2Verticalmotionexperiment
Toevaluatetheimprovedpropulsionsystem,wecarried
outaverticalmotionexperimentinapool,whichwas
alsodoneusingthepreviousrobotSUR[8].Thesetwo
experimentswerecarriedoutinthesamepoolwiththe
samecontrolalgorithm.Thedepthofthepoolwas110
cm.First,therobotstayedintheinitialpositionwitha
depthof20cm.Thenitdivedfrom20cmto90cm.
Finally,therobotfloatedupwardto20cm.In[8],we
comparedtheexperimentalresultswiththesimulation
resultsandobtainedthepositionerrorsofthevertical
motion,asshowninFig.20(a),ofwhichthemaximum
errorisabout15cm.Fortheimprovedpropulsion
system,wealsorecordedthetrajectoryoftherobot’s
geometricalcentreduringthediving/floatingmotion.
Figure20(b)showstheexperimentalandsimulation
resultsoftheimprovedrobot,fromwhichwecanseethat
thepositionerrorforverticalmotionisgreatlyreduced
andthemaximumerrorisabout10cm.
Figure.19Theexperimenttestingverticalmotionwiththe
improvedpropulsionsystem

(a)ExperimentalresultsforSUR[8]
(b)ExperimentalresultsforSURII
Figure.20Theexperimentalresultsforverticalmotion
6.Conclusions
Thispaperpresentedahydrodynamicanalysisofthe
secondgenerationSphericalUnderwaterRobot(SURII).
Astaticanalysiswascarriedouttoimprovetherigidity
andflexibilityoftheoriginaldesignintermsofthe
structureofthevectoredwaterjetthruster.Theweightof
thepropulsionsystemwasreducedto1.08kg.Then,a
moreefficientpropulsionsystemwasdevelopedand
mountedontherobot.Therobotwasdescribedindetail
andthethreemostimportantdegreesoffreedom(surge,
heave,andyaw)wereselectedforfurtheranalysis.Based
ontheimprovedpropulsionsystem,wealsocarriedouta
verticalmotionexperimenttoverifytheperformanceof
theSURII.Comparingtheexperimentalresultswithour
Time /s
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15
Depth /cm
Time /s
Simulation Results
Experimen tal Results
10 Int J Adv Robotic Sy, 2013, Vol. 10, 247:2013 www.intechopen.com
previousworkswefoundthattheimprovedpropulsion
systemwashelpfulinenhancingtheaccuracyofmotion.
Therelatedhydrodynamicparameterswereestimated
beforethehydrodynamicanalysistoobtainmore
accurateresults.SincetheReynoldsnumberwasashigh
as1.2105,theflowwasturbulentwhentherobotwas
moving.Thedragcoefficientwasestimatedforhorizontal
andverticalmotion.Duetotheholesinthehull,Cd,when
movinghorizontally,wasashighas0.61.Then,the
maximumvelocityineachdirectionwasobtained.Allof
theseparameterswereusedtoestablishtheappropriate
dynamicequationfortherobot.
Ahydrodynamicanalysiswascarriedoutafterthemain
parameterestimation;therobotandwaterjetthruster
wereanalysed.Fortherobot,threemainbasicmotions
wereanalysedtoverifytheresultsoftheparameter
estimation;thedragcoefficientconvergedto0.41forthe
verticaldirectionand0.59forthehorizontaldirection.
Theseresultswereveryclosetotheparameterestimation
values.Thevelocityvectorandpressurecontours
clarifiedthehydrodynamicfeaturesandprovided
importantevidencetoconfirmtheassumptionsmade
duringthehydrodynamicparameterestimation.
Furthermore,thedynamicequationwasmodifiedbased
onthehydrodynamicanalysisresults.Thepropulsive
forcewascalculatedafterpostprocessingtheCFDdata.
Finally,apropulsiveforceexperimentwasusedtoverify
thetheoreticalandsimulationresults.
Theresultsofthehydrodynamicparameterestimation
andanalysisimprovedtheaccuracyofthedynamic
equations.Theseresultscanbeusedtoimprovethe
controlaccuracyofsphericalunderwaterrobots.
7.Acknowledgements
ThisresearchwassupportedbyKagawaUniversity
CharacteristicPriorResearchFund2011.
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12 Int J Adv Robotic Sy, 2013, Vol. 10, 247:2013 www.intechopen.com
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The work presented in this paper focuses on the CFD application of large eddy simulation (LES) and detached eddy simulation (DES) to the prediction of the forces acting on an International America's Cup Class yacht keel model exposed to uniform incident flow at turbulent Reynolds number regime. The simulations were performed using both methods on adapted unstructured grids. The model keel used in the current study was developed by Chalmers University for experimental purposes, and is used for validation of CFD codes in yacht hydrodynamics. Initial results obtained are compared and validated against existing experimental data from wind tunnels in terms of lift and drag coefficients measurements and wake flow observations behind the keel. Two sub-grid scale models for LES and two turbulence models for DES are investigated and compared. Sensitivity to numerical parameters is also addressed. Overall, qualitative results and predictions are satisfactory and quantitative findings agree and fit well with the experimental values although error in forces prediction is high in some cases.
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Research on underwater robots is attracting increased attention around the world. Various kinds of underwater robots have been developed, using an assortment of shapes, sizes, weights, and propulsion methods. In this paper, we propose a novel underwater robot, employing a spherical hull and equipped with multiple vectored water-jet-based thrusters. The overall design of the robot is first introduced, and the mechanical structure and electrical system are then individually described. Two important mechanical components are the spherical hull and the waterproof box, and these are discussed in detail. Detailed descriptions of the two-level architecture of the electrical system and the design of the water-jet thrusters are also given. The multiple vectored water-jet-based propulsion system is the key feature of the robot, and the experimental mechanism of this system is briefly explained. The three main principles behind the propulsion system are also presented. Finally, evaluation experiments are presented to verify the basic motions of a prototype robot. The experimental results demonstrate that the motion characteristics of this type of underwater robot are acceptable, and the design is worthy of further research.
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A mesh-less Refined Integral Algorithm (RIA) of Boundary Element Method (BEM) is proposed to accurately solve the Helmholtz Integral Equation (HIE). The convergence behavior and the practicability of the method are validated. Computational Fluid Dynamics (CFD), Finite Element Method (FEM) and RIA are used to predict the propeller excited underwater noise of the submarine hull structure. Firstly the propeller and submarine's flows are independently validated, then the self propulsion of the “submarine+propeller” system is simulated via CFD and the balanced point of the system is determined as well as the self propulsion factors. Secondly, the transient response of the “submarine + propeller” system is analyzed at the balanced point, and the propeller thrust and torque excitations are calculated. Thirdly the thrust and the torque excitations of the propeller are loaded on the submarine, respectively, to calculate the acoustic response, and the sound power and the main peak frequencies are obtained. Results show that: (1) the thrust mainly excites the submarine axial mode and the high frequency area appears at the two conical-type ends, while the torque mainly excites the circumferential mode and the high frequency area appears at the broadside of the cylindrical section, but with rather smaller sound power and radiation efficiency than the former, (2) the main sound source appears at BPF and 2BPF and comes from the harmonic propeller excitations. So, the main attention should be paid on the thrust excitation control for the sound reduction of the propeller excited submarine structure.
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In this paper we present the underwater experi- ments for spherical underwater robot which is developed in our laboratory. First, we give a brief illustration for the dynamics modeling of single water-jet propeller. Then, the coordination of multiple water-jet propellers is introduced. Based on the coordination, we discuss the transforms of three basic motions, surge, heave and yaw. To evaluate the characteristics of these basic motions, we carry out different experiments for each basic motions. And finally, we give the experimental results and analysis for the results. Index Terms—Water-jet, Dynamics modeling, Incoming an- gle, Basic motions, Hydrodynamic forces.
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This paper presents a spherical underwater robot which uses three vectored water-jet propellers as its propulsion system. In this paper we introduced the conceptual design of the spherical underwater robot including the hull, waterproof chamber , propulsion system. Then we develop a prototype of this spherical underwater robot. Finally, we carry out confirmatory experiments to verify the availability of the design of the spherical underwater robot.