actuator disk

FINE TM /Marine note Note on the Body Force Propeller implementation Theory In FINE TM /Marine, the momentum equations include a body-force term f b , used to model the effects of a propeller without modeling the real propeller. There are numerous approaches for calculating f b including simple prescribed distributions, which recover the total thrust T and torque Q, to more sophisticated methods which use a propeller performance code in an interactive way with the RANS solver to capture propeller-hull interaction and to distribute f b according to the actual blade loading. For the latter, special interface should be developed to extract effective wake from RANS solution and to produce f b calculated by a propeller performance code. FINE TM /Marine does, however, include a prescribed body force with axial and tangential components. The radial distribution of forces, with components f bx (axial), f br (radial)=0 and f b (tangential), is based on non-iterative calculation of Stern et al. (1) , the Hough and Ordway (2) circulation distribution with optimum type from Goldstein (3) , and without any loading at the root and tip: f bx = A x r ∗ 1−r ∗ , f b = A r ∗ 1 −r ∗ r ∗ 1−r h ' r h ' They represent body forces per unit volume normalized by U² / L where U is the reference velocity, L is a reference length, and the fluid density. Coefficients are expressed as: r ∗ = r ' −r h ' 1−r h ' ,r h ' = R H / R P ,r ' =r / R P r = y −Y PC 2 z− Z PC 2 A x = C T 105 16 4 3r h ' 1−r h ' A = K Q J 2 105 43r h ' 1 −r h ' J = 2 U D P = U nD P , D P =2 R P ,n=/ 2 C T = 2 T U 2 R P 2 ,K T = T n 2 D P 4 , K Q = Q n 2 D P 5 and where C T and K Q are the thrust and torque coefficients, J is the advance coefficient, n is the number of rotations per second (rps), is the rotation speed, R P is the propeller radius, R H is the hub radius, is the mean chord length projected into the x-z plane (or actuator disk thickness), and Y PC and Z PC define the propeller center coordinates. As derived, these forces are defined over an "actuator cylinder" with volume defined by R P , R H , and . 1

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Actuator Disk

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FINETM/Marinenote

NoteontheBodyForcePropellerimplementation

Theory

InFINETM/Marine,themomentumequationsincludeabodyforcetermfb,usedtomodeltheeffectsofapropellerwithoutmodelingtherealpropeller.Therearenumerousapproachesforcalculatingfbincludingsimpleprescribeddistributions,whichrecoverthetotalthrust T andtorque Q,tomoresophisticatedmethodswhichuseapropellerperformancecodeinaninteractivewaywiththeRANSsolvertocapturepropellerhullinteractionandtodistributefbaccordingtotheactualbladeloading.Forthelatter,specialinterfaceshouldbedevelopedtoextracteffectivewakefromRANSsolutionandtoproducefbcalculatedbyapropellerperformancecode.FINETM/Marinedoes,however,includeaprescribedbodyforcewithaxialandtangentialcomponents.Theradialdistributionofforces,withcomponentsfbx(axial),fbr(radial)=0andfb (tangential),isbasedonnoniterativecalculationofSternetal.(1),theHoughandOrdway(2) circulationdistributionwithoptimumtypefromGoldstein(3),andwithoutanyloadingattherootandtip:

f bx=Axr1r , f b=A r1r

r1rh' rh'

Theyrepresentbodyforcesperunitvolumenormalizedby U/L whereUisthereferencevelocity,Lisareferencelength,andthefluiddensity.Coefficientsareexpressedas:

r= r'rh'

1rh', r h'=RH /RP , r '=r /RP

r=yY PC2zZPC2

Ax=CT

1051643rh' 1rh'

A=KQ J2

10543rh' 1rh'

J=2UDP

= UnDP, DP=2RP , n=/2

CT=2T

U2RP2 , KT=

Tn2DP

4 , KQ=Q

n2DP5

andwhereCTandKQarethethrustandtorquecoefficients,Jistheadvancecoefficient,nisthenumberofrotationspersecond(rps),istherotationspeed,RPisthepropellerradius,RHisthehubradius,isthemeanchordlengthprojectedintothexzplane(oractuatordiskthickness),andYPCandZPCdefinethepropellercentercoordinates.Asderived,theseforcesaredefinedoveran"actuatorcylinder"withvolumedefinedbyRP,RH,and.

1
FINETM/Marinenote

IntegrationofthebodyforcesoverthisanalyticalvolumeexactlyrecoverstheprescribedthrustTandtorqueQ:

T=L2U2Af bxdA

Q=L3U2Ar f bdA

dA=2rdr

Practice

InFINETM/Marine,userdoesnotexplicitlyneedtospecifyCT,KQandJ,butprescribesthethrustTandthetorqueQ.AxandAcoefficientsarethencomputedusingtheaboverelations.

Asanexample,afictitiouspropellerregionismaterializedbelowwherebodyforcemethodmustbeactivated:

IfthepropellertorqueQisnotknown,itishoweverpossibletoestimateitsmagnitudefromopenwatertestofthepropeller,ifavailable.SuchopenwatertestusuallyprovidestheperformancecurveasillustratedforthepropelleroftheKRISOContainerShip(KCS)fromthetestcase2oftheTokyoWorkshop2005:

2
FINETM/Marinenote

Foraprescribedthrustand/oranadvanceratioparameterknowingtheadvancespeedUandratioJfromthepropellerrotationspeed(nor),KQisobtainedformtheperformancecurveandthepropellertorqueQcanbededucedfromthepropellerthrustTas:

Q=T DPKQKT

Asanexample,forthiscase,thepropellerconditionwasDP=0.25mandJ=0.732.Fromtheperformancecurve,wehaveKT=0.170andKQ=0.029sothepreviousrelationwritesQ~1.47T.

References

(1) Stern,F.,Kim,H.T.,Patel,V.C.,andChen,H.C.,"AViscousFlowApproachtotheComputationofPropellerHullInteraction,"JournalofShipResearch,Vol.32,No.4,December1988,pp.246262.

(2) Hough,G.andOrdway,D.,TheGeneralizedActuatorDisk,TechnicalReportTARTR6401,ThermAdvancedResearch,Inc.,1964.

(3) Goldstein,S.,"OntheVortexTheoryofScrewPropellers",Proc.oftheRoyalSociety(A)123,440,1929.

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TheoryPracticeReferences