Computerized Method for Design of Propeller Blade

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13'o Congress of Intl. Maritime Assoc. of MediterraneaIMAM 2009, istanbul, Turkey, 12_15 Oct.20

Computerized method for propeller design of optimum diameter andrpmM.M. GAAFARY

AssociateProress"?r:,;!:::;";'#!g:j j'"*'::-:#:;TJ#""""Engineering;".:ABSTRACT: The process of marine propeller dosign, using theoretical or experimental charts of methodicaseries' consumes time and effort. This work proposes a computerized desigrr process for optimization opropeller diameter and number of revolutions for better characteristics and higher performance. In thirprocess, for known propeller rpm, thrust, and blad e area ratio, anoth.r *ol.ston of propeller thruslcoefficient is developed such that the unknown diameter is eliminated. Hence, a new developed curve olthrust coefficient can be plofted on any arbitrary propeller performance curyes such as ssp; ;;;;r-"1'rn*.0B-Series charts of prdpeller performance.

required optimum propeller diameter can beoptimum propeller number of revolutions o1using- Newton's divided differgnce method of, interpolation, thedetermined' A similar process has been appried to determine theknown propeller diameter.Flow charts and computer programs have been developed to represent the proposed procedure. Applicationshave been performed on the design of three different propellers of the existing ships. complete agreement isachieved between results of the present work and the real ships propeller diameters.

NOMENCLATI.IREblade area ratio,projected area,Wageningen series coefficient of Rntorque coefficient,thrust coefficient,propeller diameter,integers,advance ratio,thrust coefficient with eliminatednumber of revolutions,thrust coefficient with eliminated

diameter,torque coeffi cient of open propeller,tlirust coefficient of open propeller,static pressure at propeller CL, psiwater-vapor pressure, psiReynolds number,propeller number of revolutions persecond.propeller pitch/diameter ratiopropeller torque,propeller thrust,thrust deduction factor.propeller advance speed,service ship speed,

KaKrPoPvRnn

A^(*)^oAPCijt teffect,CqCrDi, j, k,lJKdK"

PIDaTtVuV.

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____.{,:9:.i.at,;,;:.w ship's wake fraction,Z number of blades,q propeller efficiency,p water density.

1. INTRODUCTIONTo perform a successful propeller design, a navalarchitect is faced with sorne irnportantrequirements, such as:

1- High efficiency,2- Sufficient thrust3- Proper strenglh,4- No cavitation erosion,5- Acceptable low vibration and habitablenoise excitation.

Generally, the most efficient propeller is thathaving the largest possible diameter and lowestrpm. Usually there are two ways to develop asuccessful propeller design, namely, the theoreticaland experimental methods. There are many moderrrtheoretical methods, such as lifting line and liftingsurface theories, Breslin, et aI (1994), Kerwin,(1981), Bahgat, (1966), Morgan, (1979, Andersen,et al (1919), Gaafary, 0987 and 1995), andCarlton, (1994). Also, there are many experimentalpropeller series test results, such as the NSMBWageningen A- and B-Series, Troost, (1951),SSPA-Series, Lindgren, (196I), and many others.The Wageningen B-Series is still up to nowapplicable, and it is very efficient method of 2.conventional propeller design, but the area ratiosare limited, and a designer usually interpolatesbetween chafts, which makes it a difficult process.Oosterveld, et al (1915) has developed amathematical polynomial to represent the propellerperformance curves of B-Series propeller type. Thisuseful and simple polynomial form is expressed byits multi-terms of arbttrary propeller's number ofblades, blade area ratio, pitch/diameter ratio,advance ratio and Reynolds number.Either theoretical or experimental method is appliedthe main task of propeller design is the optimizationprocess of propeller particulars, to achieve thehighest possible efficiency, Berlram, (2000), and

Turnock, et al (2006). It is the main target of thispaper to develop a direct computerized designprocedure for optimization of propeller diameterand rpm that guarantees the highest possiblepropeller performance. In this process, for knownpropeller rpm, thrust, and blade area ratio, anotherexpression of propeller thrust coefficient isdeveloped such that the unknown diameter iseliminated. Hence, a new developed curve of thrustcoefficient is plotted on Oosterveld's form ofWageningen B-Series charls of propellerperformance, (1975). Using Newton's divideddifference method of interpolation, Carnahan, et al,(1976), the required optimum propeller diameterhas been determined from the advance ratio of thehighest propeller efficiency. A similar process canbe applied to determine the optimum propellernumber of revolutions when the propeller diameteris known. Also, this proposed procedure is valid toapply when the propeller torque is known, insteadof the propeller thrust, hence, the optimum diameterand rpm can be determined.Flow charts and computer programs have beendeveloped to represent both of the Oosterveld'smathematical polynomial of Wageningen series andthe proposed procedure. Applications have beenperformed on three different propellers of existingships, where complete agreement has been achievedfor propeller particulars deduced by the proposedmethod and those of the real ship.FORMULATION OF THE METHODThis work presents a proposed procedure forpropeller design, where it deals with charts ofpropeller performance curves of (Kr, Kq, and q)versus (J). These curves are based on theoretical orexperimental results of methodical series of marinepropellers. Aside from the well known useful chartsof Bp - E, of propeller series of B-type of NSMB,Troost, (1951) and Lewis, (1989), the present workintroduces some kind of substitute of these designcharts. The main target of this work is to develop asimple computerized procedure of propeller designthat achieves optimum propeller diameter andnumber of revolutions. This is to develop the propertheory, then computerize that method, apply the

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computer program on existing ships of ih" ,u-"propeller t1'pe, and finaliy, eompare the resuits.This might be a direct verification of thiscomputerized method.2.1 Optimum Propeller DiameterConsider a specific systematic series ofconventional marine propellers with availableperformance curves, such as those of Troost,(1951), and Lindgren, (1961), the optimumpropeller diameter can be accomplished byeliminating the diameter between the relationsdefining thrust coefficient, (Kr) and advance ralio,(J). To reach there a naval architect need to knowthe following propeller particulars:

1. propeller rpm,2. speed ofadvance,3.. blade arearatio,4. required propeller thrust, and5. propeller number of blades.These particulars can be determined according tothe following:

o To avoid the harm of cavitation, the lowerpropeller rpm, the less chance of cavitationoccurrence could be,. Knowing the ship's wake, (w) at shipservice speed, the speed ofadvance is:Va: Vs (1 -w). As the blade area ratio increases, there willbe less chance of cavitation occwrence, andless propeller efficiency. However, to avoidcavitation or reduce it, an expression ofprojected blade area has been developed byNSMB, as in Lewis, (1989). When thisexpression is plotted, it gives a line justabove the upper limit of Burrill's cavitationdiagram for merchant ships, Lewis, (1989),this expression is,(Ar)' : L360(Po-Pv)I.sVowhere, according to Burrill,

Ap

Using this equation one can get the blad'' 'Area rario. ( + ), where,_^o(Ao: no, ).. The propeller thrust can be determined onbasis of accurate determination of the total

ship resistance, Rr, and the thrust deductionfactor, (t), as:P-. ! - "r(1-r)o For the number of propeller blades, (Z), as'it increases, the propeller efficiency andperf,ormance wi I I i ncrease.

Now, we might return to our main track of findingthe optimum propeller diameter, where

Kr: Pn2Pa (1)(2)developed by

(3)3) together to(4)

This relation of equation (4) can be graphed on aspecific Wageningen B-Series chart of marinepropellers performance curves of (Kr, Kq, and q)versus (J), of specific number of blades, and bladearea ratio, as shown and depicted on Figure (1). Apossible manual solution can be secured asfollows,1. Determine each intersection of (Kr; of (4),with those (Krt culves which are

dependent on varying (PiD) ratio,2. Determine the different values of (r1) foreach intersection. and then draw a curveconnecting them,Consider the point at which the curve o{(q) osculates the envelope of maximumefficiency curyes,The optimum diameter is secured at aspecific manually interpolated (P/D) ratio

I:vo nDIntroduce a new variable, K-" asBreslin, et al ( 1 994),n2TKn: frManipulating equations (1,2, andget: Kr: KnJn

aJ.-

A-I1F -

;sqft

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----|r--

that coresponds to the point where the fwocuryes of (n) osculate each other,5. The advance ratio at this osculation pointdetermines the optimum diameter,

Dopti.*u - # (5)Until now, this procedr,r" is performed manuallyfor propeller design according to on. of theavailable methodical series charts of propellerperformance curves.It is the target of .this paper to perform thisprocedure using a newly developed computerprogram. During the development of the program,some special steps are made to treat the differencesbefween applying the method numerically andmanually.Dffirences when the procedure ls apptiednttmerically rctther than manually :l. Not to find intersections between Kr-curveof (4), with (Kr; curves of varying (p/D)ratio, but to determine numerically, .byNewton's interpolation, the (P,4D) ratio ofKr- curve at every value of (J) with equal

small steps,2. At every specific value of (J) and (P/D),determine the (Kq) value, hence, determinethe propeller efficiency for each value of(J),3. Find the highest efficiency at every specific(J), and hence, the optimum diameter canbe determined.

The applied expression of Newton's divideddifference method of interpolation as given inCarnahan, et al (1976), is,F (xn, xn-1-, ... , xo: ILo -"P_, nttj=s\^i-xj)Hence, this is the formulation of the optimumdiameter, now we fum to the optimum rpmformulation.2.2 Optimum Propeller RPMIn a very similar fashion, a similar procedure isdeveloped to yield the optimum propeller rpm forgiven:

l. propeller diameter,2. speed ofadvance,3. blade area ratio,4. required propeller thrust, and5. propeller number of blades.In the same manner, these parameters can bedetermined as previously described.

Now, after eliminating the propeller number ofrevolutions, (n), between the expressions of (Kr)and (J). one may get,Kr : Ka 'J' Q)where,

Vr\d -and

wT- o.s p 1(1v]To determine the optimum propeller rpm for agiven diameter, one may apply a very similarprocedure to -that previously described. A newcurve of Kr, based on equation (7), canbe graphedon a specific Wageningen B-Series chart of marinepropellers performance curves of (Kr, Kq, and 11)versus (J), of specific number of blades, and bladearearatio, this process is depicted on Figure (1). Apossible manual solution can be secured whenfollowing the same first four steps mentioned inthe case of optimum diameter, while the fifth stepis given instead,5. The advance ratio at this osculation pointdetermines the optimum rpm,

RPMopumu* - # (10)The present developed computer program isapplicable to determine the optimum propellerrpm, just as in the case of optimum diameter.3. PROPOSED COMPUTEzuZED METHOD3.1 Computer Programfor Wageningen B-SeriesFor propeller design pulposes, the usefulexperimental test results of Wageningin methodicalseries of B-type propeller performance of NSMB,Troost, (1951), were plotted in charts form known

Tc.o (8)(e)

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as Bp - 6 diagrams. It is true that these B-typepropeller chafts are still applicable and yieldsaccurate propeller design. Howevet, aside from Bp-6 diagrams, it is the target of this work to apply thecurves of propeller performance of (Kr, Kq, and q)versus (J) at different (P/D) ratios. Oosterveld, et al(1975), has developed a mathematical polynomialto represent these propeller perfonnance curves ofB-Series propeller type. In the present wotk, a flowchart has been designed to represent the logicalsteps of processing numerically the Oosterveld'smathematical polynomial of Wageningen series, asshown on Figure (2). Based on that flow char1, acomputer program has been designed anddeveloped in this work. As an application of thedeveloped computer program to determine thepropeller performance values has been performedfor a specific propeller of the following particulars:t Z :5 ,. P/D :0.70 ,. ou :0.75 .noo Rn ':2 x1,06In this numerical approach, the mathematical

polynomial representation of Wageningen B-Series type of propellers, developed byOosterveld, et al (1975), is considered forapplications:

Kr:Ito If =o ZJ=oE?=o c,iur. ,t . (X)t . {f,)u 'l'....(11)

The propeller performance cur-ves of (Kr, Kq, andq) are plotted versus (J) as shown on Figure (3).Important Feature I: the propeller performancecurves shown on Figure (1) of Wageningen seriescan be reproduced by using this developedprogram. Almost for any arbitrary B-type propeller,the performance cur-ves can be developed at anyintermediate blade area ratio, any number of blades,(Z), and also at any pitch/diameter ratio, (P/D).

3.2 Computer Programfor Optimum DiameterConsidering the formulation steps of the optimumdiameter introduced in2.7, another flow chart hasbeen designed to describe the procedure's logic andits executing steps, as shown on Figure ( ) Thisinclude5 representation of the mathematicalpolynornial of Wageningen series of propellercharacteristics, calculation of (Kr) as shown inequation (4), interpolation fot (P/D) value at everystep of (J) which is done according to Newton'smethod of interpolat ion.When Newton's equation of interpolation, (6) isapplied numerically to determine the required(P/D), using the "pre-" and "post-" values of (Kr;and their corresponding (P/D) values, it yields,(P /D),"qurred : PD(j) + IPD(j + 1) -PD(i\1 * 1--!I:!IJi)-l (12)v / ' 'Kr(j+1)-Kr(j)'At that specific (P/D), calculations of (Kq and q)are performed. Repeating this process -is required atevery stepped (J). Hence, a decision must be takenby choosing the highest efficiency and itscorresponding advance ratio, (J), to determine theoptimum diameter as in equation (5).Based on that flow chart, a computer program hasbeen designed and developed specially to performthis proposed procedure numerically, which willsave time and effort as a contribution of thispresent work.3.3 Computer Programfor Optimum kPMIn a very similar manner, the formulation steps ofthe optimum rpm introduced in sub-section 2.2 areconsidered, and minor modifications on the flowchart of finding optimum diameter, shown onFigure (4), should be made to represent theprocedure's logic and its executing steps. Thisincludes representation of the mathematicalpolynomial of Wageningen series of propellercharacteristics, calculation of (Kr) as shown inequation (7), interpolation for (P/D) value at everystep of (J) which is done according to Newton'smethod. At that specific (P/D) of equation (12),calculations of (Kq and n) are performed.Repeating this process is required at every stepped

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---

(J). Hence, a decision must be taken by choosingthe highest efficiency and its correspondingadvance ratio, (J), to determine the optimum lpm,as in equation (10).Minor modifications need to be done to thecomputer program of finding the optimumdiameter numerically, which will save time andeffort in finding oplimum rpm.Important Feature II' A naval alchitect is notobligated to use charls such as Bp - 6 which hasfixed blade ratios and then interpolate betweenthem to get the optimum propeller particulars, aprocess which will consume time and effort. Thiswork provides a quick way to design a propellerwith optimum diameter and rpm.4. APPLICATIONS OF THE PROPOSEDMETHODFor the purpose of applying the presentcomputerized method on some existing ships,where each set of data has been prepared as aninput data to the developed computer program. Inthe following, there are three different examplesprovided herein together with the computerprogram output data.4.1 Optimum Propeller Diameter of SL-7 ContainerShipThe SL-7 container ship has the following data:Vs :33 knots; w : 0.125; t:0.098EHP : 81,028; Z :6; P/D: 1.13N : 134 tp*; (Yo) :0.65;D :7.0 mPresent Method Results:Doptimum :7.2 m and P/D : I.12.Comment: There is agreement between thediameters and PiD ratios.4.2 Optimum Propeller Diameter of a MerchantShipThis merchant ship has the following data:Vs : 19 knots; w :0.25;t- 0.25EHP :26,606; Z : 5: PID : 0.794N : 10s tp*; f#) :0.75;D : 8.2 mPresent Method Results:

Doptimum :8.26 m and P/D :0.792.Comment: There is agreement betw-een thediameters and P/D ratios.

4.3 Optimum Propeller Diameter of 250,000 TonDwt TankerThis tanker has the following data:Vs : 16 knots; w : 0.37; t: 0.22EHP :23,200; Z :5: P/D:0.74N :85'p*; (ff) :0.733;D :8.8mPresent Method Results:Doptimum :8.92 m and P,1D :0.74.Comment: There is agreement befween the'diameters and P/D ratios.Important Feature III: The computer program givesaccurate output results that almost agree with thereal ship propeller diameters.5. ANALYSIS OF THE RESULTSFrom the present work,.the following remarks andcomments can be drawn:l- The proposed computerized method has

been developed to be applied almost on anypropeller performance curves, such asWageningen B-series propellers, as shownand depicted on Figure (1).2- Figure (2) shows a flow chart that has beendeveloped in this present work, it gives thelogical sequence of executing steps, inorder to determine the propellerperformance curyes for almost anypropeller methodical series.3- A computer program has been developedby following the designed flow chart. As anapplication of the program, theperformance curves of one of theWageningen B-series propellers, as shownon Figure (3).4- Figure (4) shows another flow charl thathas been developed to represent theproposed computerized method that mightdetermine the optimum propeller diameterand rym for almost any propellermethodical series.5- Applications of the present method on threedifferent existing ship propellers, yields

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almost a complete agreement of the resultswith those of reai ships.

6. CONCLUSIONSA proposed computerized method of propellerdesign has been developed and checked forapplications on Wageningen B-series ofconventional marine propellers. The followingconclusions can be drawn from the present work:- 1- For known propeller rpm, blade area ratio,

ship required thrust, and number of blades,the optimum propeller diameter can bedetermined2- On the curve of required KT, the Newton'sdivided difference method of interpolationhas been applied to determine intermediatevalues of pitch/diameter ratios at differentadvance coelflcients.3- A computer program has been designed torepresent l"he developed method.4- Optimizing the different values of Kr andKq for the highest efficiency, yields thedetermination of optimum propellerdiameter at specific (J), and (P/D).5- The method could be considered as a quickalternative tool that saves time and effortthat are consumed in propeller design bythe available charts.6- Applications of the present method on threedifferent existing ship propellers, yieldsalmost a complete agreement of the resultswith those of real ships.

7- The method is also applicable to determinethe optimum propeller rpm.8- This computerized method is also valid tobe applied when the propeller torque isknown instead of propeller thrust, byfollowing the same procedure to determinethe optimum propeller diameter andoptimum rpm.

Future Work:The presentdevelopment for method might have morethe application on other

methodical series, such as Gawn-Burrill series, K-type propeller series ofducted propellers.REFERENCESAndersen, P. and Boil, P., Nov. 1979. Propeller Designby Lifting Line Theory,ISH Design Basic Program,Yol.2" Institute Skibs-og Havteknik, DTH,Denrnark.Bahgat. F.. 19b6. Marine Propellets. Al-MaarefEstablishment, Alexandria, Egypt.Bertram, V., 2000. Practical Ship Hydrodynamics,

Buttelwofth - Heineman-r.r, New York.Breslin, J. P., and AnderserrP., 1994. Hydrodynamics ofShip Propellers, First Edirion, CambridgeUniversify Press.Carlton, J.S., 1994. Marine Propellers & Propuluon,Butterworth and Heinemann, Oxford.

Carnahan, B., Luther, H.A., and Wiikes, J.O., 1916.Applied Numerical Methods. John Wiley, NewYork. N.Y..

Gaafary, M. M., l.4ay 1987. Forces on Ship PropellerBlades of Low Aspect-Ratio, Ph.D. Dissertation,Department of Ocean Engineering, Stevens Institutof Tech., Hoboken, N.J., USA.Gaafary, M. M., Younis, G. M., Mosaad, M. A., andHamdi, T. A., 1995. Hydrodynamics of High SpeedMarine Propellers -- New Approach, IMAM'95,Dubrovnik, Croatia.Kerwin, J.E., Feb. 1981. Hydrodynamic T'heoryforPropeller Design and Analysls, Cambridge, Mass.,MIT Deparlment of Ocean Engineering.Lewis, Edward V., 1989. Principles of NavalArchitecture, Volume Ii, The Sociefy of NavalArchitects and Marine Engineers, SNAME.

Lindgren, H., 1961 . Model Test with a Family of Threeand Five Bladed Propel/ers, SSPA, the SwedishState Shipbuilding Experimental Tank, Nr. 47.Morgan, W"B., Silovic, V., and Denny, S.8., 1979.Propeller Lifting Surface Corrections, Trans.,SNAME, Vol. 86.Oosterueld, M.W.C., and Oossanen, P.V., July 1975.Further Computer-Analyzed Data of theWageningen B-Screw Series, IntemationalShipbuilding Progress, Y o1. 22,No. 25 1.Troost, L., 1951. Open Water Test Series with ModernPropeller Fornts, NSMB, Wageningen, Part II, andPart III.Tumock, S.R., Pashias, C. and Rogers,E.,2006. Flow.feattrre identi.fcation for capture of propeller tipvortex evolution, Proceedings of the 26thSymposium on Naval Hydrodynamics. Rome, Italy,INSEAN Italian Ship Model Basin / Office of NavalResearch.

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Krto Ko

rl

***0.7KT at PD=-{-0.7KQ at PD= 10- 0.7ETA at PD=

\,\ \K- lor \,dlch/diem=r.4 / \-to*o=p,/oL \/-i , -: EHVLOPE

xo ro, nit.r,/arJ),\ {

Ha q q il !ryigl_]i:Pf qqgg$lpdc.rrcJ RaLioJO,65

Nr: 2 !'FclEs

Figure (l): A scheme for the procedure of finding an optimum propeller diameter using Wageningen8-6-65 performance curves at a *.nge of (p/D) values, breslin, et al (1994\.

Ftuodct:aoFlF:z

= t.Lt l^*.--:(-l.o

Wageningen B-series of Z=5,Ae/Ad=O.75 at PID=O.70,70,60,50,4n?0,20,1

0 0 0,1 0,2 0,3 0.4 0.5 0,6 0,7 0,8Advance Ratio, J

Figure (3); Present proposed method computer program output of wageningen 8-5-75propeller perfofinance curves.

II

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lnput Data : Blade Area Ratio,Number of blades, n, P/D

Do k= 1.86Read : Coefficients of WageningenSdries oolvnomials. C{k).s(k)- t{k}. u{kl.

EKT{I) =0.

Do K= 1,39Estimate : thrust coeff. (KT)

EKT(l)=

Estimate : Torque coeff. (KQ)EKQ(t) =EKQ(t)+Ka(t)

Estimate : Propeller Efficiency (ETA)

J{l)=111;+0.02

OUtput Data : KT, KQ,',i:.I.1::

Figure (2): Flowchart to determine the propeller performance curves of Wageningen B-series.

i,!;l''l. :i, tq!-.::!:, .,,; ,-:i-l:..r r'::'iit,,j. r:.'t:i,:''.'"i'j,..' -,:1'.;iLif',i:*ii,, 219


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dg

-,@9!.q()o6'tskr69l +.o9EoaOF5Yaxoq()F?t{c)dNNOHp.6

O t;9ooogoAH\JHo\f,

vo9=boo

Input Data : Blade Area Ratio, Number ofblades, n, P/D

Read : Coefficients of Wageningen .series polynomials,ctk). slk). tlk). ufk). vfk)

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Computerized Method for Design of Propeller Blade

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