The Selection of Blade Sections

8/2/2019 The Selection of Blade Sections

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THESELECTIONOFBLADESECTIONS

Althoughthecirculationtheoryoffersasatisfactoryexplanationof

propelleractionandprovidesausefulmethodof calculatingpropeller

performance, it does not provide any means of selecting the mostdesirablebladeshapesforanyparticulardesign.Thetheoryleadsonlyto

theconclusion that, inorder fora section toproducea certain thrust,

theproductoftheliftcoefficientandsectionlengthmusthavethevalue

givenbyequationattheendofthetext.Presumablyanycombinationof

these factors could be used to produce the required product, but

practicalconsiderationgreatlyrestrictsthechoiceofthesefactors.

Sinceoneoftheprimaryobjectivesinthedesignofapropelleristo achieve the maximum possible efficiency, it is evident that each

section shouldbe selected tohave theminimumdrag. Ingeneral, the

dragof conventional sectionsdecreaseswithdecreasing thicknessand

decreasing angle of attack. Therefore, these values should be kept as

lowaspossible.Thedragalsodecreaseswithdecreasingsection length

but reduction of length requires a corresponding increase in the lift

coefficients to maintain a constant product and also an increase inthicknesstomaintainthestrength,bothofwhichareaccompaniedbyan

increase in the critical cavitation index, which, in turn, increases the

possibilityofcavitation.

Inthecaseoflowspeed,lightlyloadedpropellers,wherethereis

littlepossibilityof cavitation, theblades shouldbemadeasnarrowas

practicalandmeanwidthratiosas lowas0.20areusedfrequently.For

propellers which are designed to operate at high speeds, where thepossibilityofcavitationisgreater,thesectionlengthsmustbeincreased

with an accompanying loss of efficiency. It has been found most

convenient inpractice toassumeabladeoutlinebasedonexperience

with other propellers for similar applications. The critical cavitation

number of each section then can be compared with the cavitation

numberatwhicheachsectionoperates,basedontheresultantvelocity

andsubmergence,andthesection lengthsadjustedsothatallsectionshaveanequalmarginofsafety.

Thedeterminationofabladesectionshapetodevelopadesired

liftcoefficientcanbestbeaccomplishedby reference to theextensive

workdoneinthedevelopmentofairfoils.


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It has been shown that an airfoil can be considered as the

combinationofa symmetrical thicknessdistributionanda camber line

from which the offsets of the thickness distribution are plotted.

Theoretically, at zero angle of attack, the lift coefficient is a function,

primarily, of the camber, and, to a small degree, the thickness, but

experiments have shown that for all practical purposes the liftcoefficient canbe considered as a linear function of the camber ratio

alone. Theoretically, with an angle of attack the lift coefficient for

infiniteaspectratioincreasesattherateof2 perradianor0.1097per

degree,whichisconfirmedbyexperiment.

Since lift canbedevelopedeitherby camberorangleofattack,

thequestionarisesastowhichshouldbeusedorhowtheliftshouldbe

distributedbetweenthetwo.Experimentshaveshownthattheincreaseindragduetocamberinganairfoiltoprovideacertainliftcoefficientis

less than the increase in drag caused by obtaining the same lift

coefficient with an angle of attack. It can be shown also that,

theoretically,thereductioninpressureonthebackofanairfoilisless(or,

in other words, the critical cavitation index is lower) for a given lift

coefficientwhen the lift is provided by camber thanwhen the lift is

providedbyangleofattack.Onthisbasis, itwouldappearthattheuseofcamberalonewouldgivetheoptimumresults,but,inpractice,thisis

notthecase.

The characteristicsofmathematicallydefined camber lineshave

been determined by transformations of the potential flow around

cylindersinuniformflowinwhichtheviscosityhasbeenneglected.The

effectoftheviscosityinarealfluidisareductionofthecirculationthata

cambercurvewoulddeveloptheoreticallyinaperfectfluidand,hence,areduction of lift. For circular arc camber lines, the experimentally

determinedliftcoefficient isabout80percentofthetheoreticalvalue.

The reduction of circulation also results in the shift of the stagnation

pointfromtheendofthecamberlinetosomepointonthebackofthe

section.

It is possible, of course, to obtain a desired lift coefficientwith

circulararc camberby increasing the theoretically required camberbythefactor1/0.8.This isnotdesirable,however,fromthestandpointof

cavitation,since,withthestagnationpointontheback,thepressureon

the face near the leading edge is reduced greatly and danger of face

cavitation is increased as has been demonstratedwith tests of single

sections. It isconsideredmoredesirable, therefore, touseanangleof

attack to make up the difference between the theoretical and


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experimentalvalueoftheliftcoefficientassociatedwithagivencamber.

Forexample,a liftcoefficientof1.0theoreticallyrequiresacirculararc

camber ratio of 0.08. Actually this camber ratiowould produce a lift

coefficientofonly0.8, so thatanangleofattackof0.2/0.1097=1.82

degrees must be used in conjunction with the 0.08 camber ratio to

develop the lift coefficientof1.0.This incursa slight increase indrag,which is considered less objectionable than the possibility of face

cavitation.

There are a considerable number of mathematically defined

camber lines forwhich theoretical lift andpressure characteristics are

available.Sofaras isknown,thesuitabilityofallofthesecamber lines

forpropellershasnotbeeninvestigated,butone,inparticular,seemsto

haveverydesirablecharacteristics.ThisistheNACAa=1camberwhichtheoretically produces a uniform chordwise distribution of load and

pressureand,hence,foragivenliftcoefficientthereductionofpressure

onthebackofasectionistheminimumthatcanbeobtained.

Turningnowtotheconsiderationofsectionthickness, it isfound

thatmostinvestigationsofairfoilshavebeenmadewithsectionshaving

thicknessratiosof0.06orgreaterand,therefore,areapplicableonlyto

theinnersectionsofwidebladedpropellersand,toasomewhatgreaterextent,tonarrowbladedpropellers.Theconclusionsthatcanbedrawn

fromtheseinvestigationsare:

1. The drag increases with increasing thickness ratio above athicknessratioof0.06atwhichitissomewhatlessthanthedrag

ofaflatplate,whichhasnotbeenexplained;hence,forsections

thinnerthan0.06,thedragprobablyincreasesagain.

2.

Thedragincreaseswithincreasingcamberandangleofattack.3. Thedrag increasesasthepositionofmaximumcamber ismovedtowardthetrailingedge,althoughtheincreaseissmalluntilafter

the position of maximum camber passes the midpoint of the

chord.

Thedrag coefficient isalsoa functionofReynoldsnumber,and,

although there is little variationbetweenaReynoldsnumberof6x105

and6x10

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,belowthisrangethedragcoefficientincreasesrapidly.AboveaReynoldsnumberof6x106 thedrag coefficient curvesarepractically

paralleltothefrictionline.

Recentaeronauticalresearchhasresulted inthedevelopmentof

severalthicknessdistributions.Incarefullyconductedwindtunneltests,

thesectionshaveshownvery lowdragcoefficients (of theorderof50

percentofthefrictiondragofaflatplateatthesameReynoldsnumber)


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overasmallangularrangeandasmallrangeofReynoldsnumber.Such

thicknessdistributionshavebeenusedforpropellersbuthaveresulted

inlittleifanygaininefficiencyprobablybecauseofthehighturbulence

inthewake.Itisbelievedthatforagiventhicknessratioanyreasonably

wellshaped thickness distribution will have approximately the same

drag. Figure12 shows the variationof drag coefficientof airfoilswiththicknessandangleofattackderivedfromtheexperimentsofGutsche.

The Reynolds number at which the experiments were conducted is

within the range (2.5x105 to 7.0x10

5) at which model propellers are

ordinarily tested, but ship propellers run at higher Reynolds numbers

and,therefore,thesedragcoefficientsaresomewhathigherthanwould

be obtained for smooth fullscale propellers. The drag coefficient of

ogivalsectionsisappreciablylargerthanthevaluesshownhere.The pressure distributions around the newer type laminar flow

sectionsbasedupontestsintwodimensionalflowarebelievedtooffer

definite advantages over the older type sections, due to the lower

pressurevariation foragiven thickness ratioand to theshiftingof the

minimumpressurepointfartherfromtheleadingedgewhereitisnotso

much affected by an angle of attack. A comparison of the pressure

distribution on the back of two sections is shown in Figure 11, fromwhichtheeffectofthicknessdistributioncanbeseen.Itisapparentalso

that, with the new type sections, it is particularly desirable to use

camber in preference to angle of attack. It must be remembered,

however, that forasectionofapropeller inagreatlyvaryingwakean

angleofattackcannotbeavoidedoverpartof thecircumferenceand,

hence,under these conditions, themaximum thickness shouldbewell

forwardofthemidpointandtheleadingedgewellrounded.Itshouldbenotedthatthetrailingedgeofmostairfoilsistoothin

forpropellerwork.Theedge thickness canbe increased toapractical

value,withoutappreciablyaffectingtheperformanceofthesections,by

adding an additional thickness distribution over the after portion on

bothsidesofthecamberline.


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Where:

CL=Liftcoefficient.

c=Chordlength.

D=Diameter.

Z=Numberofblades.

x=Ratiooflocalradiustotipradius. =Goldsteinfactor.

=Advanceangle.

i=Hydrodynamicpitchangle.


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The Selection of Blade Sections

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