Free and encircled tip propeller blades design method for optimum efficiency

z? DEC. 1982

ÀRCHtEE

V SYMPOSIUM "THEORY AND PBACTICE IN SHIPBUILDING

-In inemoriam Prof. L. Sorta", May 1982, Split, YUGOSLAVIA

*FPE AND ENCIRCLED TIP PROPELLER BLADES DESIGN METHOD FOR OPTIMUM EFFICIENCY

Prof. dr Alice Vuini5, dipl.ing. Shipbuilding and Offshore

Engineering Department Technical faculty Rijeka

A free and encircled tip blades design method is

posed based on actuator disk - lifting line theory for

pro-pellers working with maximal possible efficiency.

Use is made of Sparenberg's linearized actuator disk theory and Klaren's coefficients.

Induced velocities are calculated by blade element momentum theory witri Betz's or van Manen and Eckardt-iiorgan

princip-les for homogeneous or inhomogeneous inflow.

Free tip blades design results are compared with those

cal-culated by induced factors method.

An analysis is worked out for four prototypes of optimum

pro-peller designs, that of a tanker and a container ship, then

of a trawler and a speed boat.

Note:

The author chose to denominate propeller blades with

endplates or rings attached to tips as "encircled tip

propeller blades".

* Research work sponsored by the Republic Community for Scientific Work of Croatia.

Lab. y. Scheepsbouwkunde

Technische Hogcschool

Deift

gets:

1+.112

-INTRODUCTION

Design methods are nowaday developed for propellers with free tip blades and for propellers rotating in nozzles.

In September 1980 the Astilleros Espaoles, S.A., Spain anno-unced to have developed a lifting line design method for prope-llers with endplates attached to blade tips, called Tip Vortex Free propellers (TVF) and, it was written both in the Shipping World and Shipbuilder and in the Marine Propulsion issue, that

the design method was also appropriate for heavy loaded propellers. There was also published an open water diagram of tests carried out at the Netherlands Ship Model Basin in Wageningen showing a great improvement of efficiency.

Till now, to the knowledge of the author of this paper, no de-sign method was published.

In Mart 1980, at the IV Symposium "Theory and Practice in Ship-building - In mexnoriam Prof. L. Sorta" in Opatija a paper (1) was presented where an analysis of quality factors and efficiency co-efficients was worked out by actuator disk - lifting line method.

Greater values of quality factors belonging to slow running - heavy loaded propellers seemed to support the idea, which was also pointed out by the Astilleros Espaíoles, S.A. that encircled blade tips will particularly improve the efficiency of such pro-pellers.

From calculations worked out in /1, Table 3/ it resulted that

quality factors of fast running propellers were much more impro-ved by tip rings than those of the slow running.

'.i1is fact was the reason why the author of this paper attempted to design propeller blades with free and encircled tips by the

application of the Sparenberg's theory and Klaren's coefficients.

RADIAL DISTRIBUTION 0F PROPELLER BLADE DYNAMICAL LIFT

Sparenberg's actuator disk theory /2/ presumes the water to be

inviscid, incompressible and unbounded and the propeller wake

without contraction.

Such linearized method is therefore a method of design more

appropriate to light loaded - shock free propeller blades.

The assumption of no existing induced drags in the twodimensio-nal approach means no induced velocities, or

c and c

=0

(1)

a t

which means, fig. 1:

=0.

(2)

These equalities being unreal for a working propeller here is proposed the application of blade element momentum theory to cal-culate the induced velocities with the Betz's principle of cons-tant efficiency along the radii or to the van Manen or

Eckardt-Mor-gan principle of water inhomogeneity.

2.1 Calculation of the hydrodynamical angle of attack including

induced velocities

- 14.113

-Fig. i Blade element forces and velocities

d T = p c dr y. _cax

d = p c dr vj _Ct r (4)

At each x = nR the blade element ideal efficiency coefficient

can be calculated by (3) and (4):

dT Va Ca Va

nix - dQ -'

The relation of the induced velocities at each blade element

is approximated by: Ca r w - c- /2

x_

X LX

- V

+

_Ca/2

Being Va rxw = tan (7) one gets

tane

tane

X X

tan and tan

= nix

For a given radial distribution of the blade elements

effici-encies the blade elements hydrodynamical angles of attack can be calculated at each radius.

2.1.1 Approximation of the blade element efficiency

The resulting total ideal efficiency coefficient which

Spa-renberg calculated by actuator disk theory is

T

n

=(l+

) (9)

2

p9

V2(R2 - r2)

Assuming the hydrodynamical ideal thrust coefficient as

T

CT.₁ 1 (10)

1/2 p y2 (12 - rh)1T the equality (9) can be written as

= (1 +

4'

(5)

(8)

- Li.1114

-for a specific propeller working at a given advance coefficient. The application of Betz's principle gives for a homogeneous flow:

n. = n = const

lx

Inhomogeneity behind a ship implies according to van Manen:

lWa

3"

nix -

nl

_{- wa}

or to Eckardt - Morgan:

1 - Wa

= n

_{i - W}

(13)

2.2 Calculation of blade element specific lift

Cavitation and strength calculations on the twodimensional

approach needs the value (CLi c/D) to be known.

By dLj = I' vj dr (14) and dL1 _CLix p/2

v2

_c dr (la) is CLi C 2 r (12) D

Dvi

_X

The inflow water velocities can be approximated by

vj = y cos

-or cos

-v =V:l,

x X

sinS

X

which introduced in (16) gives:

CLi c

2 r

sin

D _{- D vax}

cos (j

2.2.1 Use of Klaren's coefficients for radial circulation

distribution

By actuator disk method Klaren calculates lifting-line

circulation distribution coefficient of the form:

2r

X = D vax or _{2 2} X X2 - D v

_T

which can be used in the equation (19).

2.3 strength and cavitation calculations

2.3.1 Blade strength calculations

The elementary beam strength method is here applied or

the blade is replaced by a beam which has sections equal to the

- +.115

-The blade element forces and moments are calculated as mean static values from the radial lift distribution working on a raked blade.

The characteristic thickness-chord value is gotten as M

tc-

2

(22)

w

K _{ctcos c}

2.3.2 Blade cavitation calculations

The calculation of cavitation conditions is worked out for Walchner-B thickness distribution and parabolic camber line.

The minimal allowed pressure coefficient at each radius is taken as Cpm* = f (CLj /(tx/cx) ; t,/c) (23) 1n x and Cpmi = . (24) with p - e - pg r o X cx -p/2

vj2

where is the cavitation safety coefficient.

2.3.3 Profile geometry and pitch angle

The profile camber is corrected by lifting surface

coeffi-cients of Morgan, i1ovi and Denny and by cascade correction

coe-fficients of Joosen.

The nominal pitcfl angle is calculated according to the NSMB

expression:

= -x

+ (0,04 Z - 0,06) CLix (26)

3. WORKED OUT ANALYSIS

3.1 Analysis aims

In order to get an insight into the results that could be

achieved by the application of this design method, computer

pro-grains were developed and applied to characteristical propeller de-signs.

The analysis was worked out aiming:

- to get an insight into the results this method is giving not

only for light loaded propellers but for a wide spectar of optimum

working conditions,

- to include the idea what big or small propeller dimensions,

high or light loading and slow and fast running conditions mean as regards the improving of blades efficiencies when the tips were encircled.

In order to achieve these aims variations of design input data have been made.

3.2 Input data

Four ships were chosen out among those previously analysed in

paper /1/, according to the following criterion:

one big and slow ship : a tanker,

one big and fast ship : a container ship,

one small and slow ship : a trawler and

one small and fast ship : a speed boat.

Table 2 - Input dota (part 11)

-

iJ16

-Table 1 - Input dota (port 1)

TANKER CONTAINER TRAWLER SPEEDBOAT 2961.790 N 1557563 N 1.51.20 N 62130 n

V 1.,746m1s I1,035m/s I,BOmJs 2O,76rn/s

n 1,50 l/s 2,0 11e 6,6 LIs 1S,833 Lis

D 8,760 m 6,605 rn 1,5 rn 1,1 rn z 5 5 3 3 E 80 0° 120 00

p-e

272790 P0 166493 P 111.1.42 P0 108796 P0 50000 MP0 50000 MP0 1.1000 MP0 50000 MP0 9 1025 kgim3 1025 kg/rn3 1000 kg/rn3 1000 kg/rn3 9m 7650 kg/rn3 7650 kg/rn3 1100 kg/rn3 7650 kg/rn3

Ship Propeller Inflow Pr.*or, radial_distribution BlOdi tips C Ti A q

2011 hornog. tres 0.890

20111 inhomog. encircled (1D) 0.921

Ton ker const. 4.4389 0.1150

0.893 2011. homog. free

20141 inhornog. ,ncircled(JîD) 0.906

2021 free 0.697

Container homog. con st . 0.7588 0.2659

0.797

2021. encircLed(1D)

2031 free 0.928

Trawler homog. const. 16.5268 0.0579 _0.91.9

2034 encirc(ed(5t0)

201.1 free 0.1.74

201.2

TD

encircled(-Z- 1 0.557 Speed hornog. conet. 0.3794 0.3794 _0.627

boat 2043 ,ncircLed(---) 2044 encircled(STD) 0.681 2011 2014 20111 2011.1 2021 2021. 2031 2031. 2041 2042 2043 2044 X 0.2 .296 .285 .332 .32/. .090 .078 .123 .120 .61.7 .562 .509 .1.77 0.3 .322 .311 .360 .352 .108 .095 .126 .123 .739 .61.4 .585 551 0.1. .340 .329 .376 .368 .128 .113 .128 .125 .856 .751 .687 .652 0.5 .351 .339 .380 .372 .143 .126 .129 .126 .91.0 .834 .775 .71.1 0.6 .356 .31.1. .377 .369 .152 .135 .129 .126 .980 .886 .836 .813 0.7 .359 . 31.7 .365 .357 .155 . 11.2 .130 .127 .964 .901 . 877 .868 0.8 .358 . 350 .31.0 .335 .149 .146 .129 .127 .878 .883 .896 .908 0.85 .352 .3505 . 319 . 323 . 140 .1 h8 .128 .127 .800 .861 .899 .922 0.9 .323 .351 . 296 .313 . 12h . 149 .123 .127 .685 .832 .899 .933 0.95 .278 .3515 . 233 . 305 . 095 .149 .105 .127 .512 .800 . 898 .940 1 .000 .352 . 000 .301 .000 .150 .000 .127 .000 .800 .896 .943

1+.117

-The input design data are given in tables 1, 2 and 3.

The variations of design input data have been assumed as follows:

3.2.1 Free blade tips propellers working in homogeneous water

conditions designed by actuator disk method: Propellers No. 2011, 2021, 2031, 2041 and induction factors /4/ method: Propellers

No. 1011, 1021, 1031, 1041.

3.2.2 Encircled blade tip propellers working in homogeneous water

conditions designed by actuator disk method. (Total disk

circunì-ference encircled: Propellers No. 2014, 2024, 2034, 2044).

3.2.3 Encircled blade tip (light loaded, fast running) propellers

working in homogeneous water conditions designed by actuator disk

method. Speed boat propellers:

Propeller No. 2042 - a quarter of the disk circumference encircled,

Propeller No. 2043 - a half of the disk circumference encircled.

3.2.4 Encircled blade tip (heavy loaded, slow running) propellers

working in inhomogeneous flow of the tanker:

designed by induction factors method:

Propeller No. 10111 - free blade tips - van Manen principle,

designed by actuator disk method:

Propeller

No.

20111 - free blade tips _{Betz's principle}

Propeller No. 20141 - totaly encircled

Propeller No. 20111 (VM) - free blade tips } van Manen's principle

Propeller No. 20141 (VM) - totaly encircled

Propeller No. 20111 (EM) - free blade tips Eckardt-Morgan's

prin-Propeller No. 20141 (EM) - totaly encircled ciple.

It has to be remineci tnat constant raaial pressure distribution

was assumed all throughout the calculations.

4. PRESENTATION 0F RESULTS

Diagrams showing characteristic undimensional parameters were

prepared in order to get the idea about the differences resulting

from different methods and input data in accordance with the

gi-ven items under numbers 3.2.1 to 3.2.5 of the previous part.

4.1 The resulting radial distribution of the specific

lift

para-meters for free blade tip blades given in fig. 2, was calculated

by actuator disk method (AD) and in fig. 3, by induction factors

method (IF).

It is clear that the functions CL. C/D = f (nR) do follow the

same trend in all the cases. The va1us becoming zero at O.2R

(pressumed hub radius) in case of the IF-method, or having a value

in case of the AD-method, agree with the input of each method or

IF-method: CL

_hub

=0

AD - method : CLhub O

It can be observed that the value CLc/D is greater for smaller

diameters and for higher loadings.

4.2 The resulting radial distributions of ideal

blade thrust in

relation to the thrust value at O.7R are presented in fig. 4 and

5 by the AD and IF-method.

It can be observed that the AD-method is giving greater dif

f

eren-ces between the tip thrust loadings of light and heavy

loaded

'4.118

-4.3 The resulting radial distributions of the specific lift

para-meters calculated by AD-method for the case when the total disk circumference is encircled, are given in figs. 6.

It can be seen how the values of the specific lift parameters are nearly constant in case of light loaded-fast running propellers while heavy loaded-slow running propellers show obvious

diininis-hing of specific lift parameters values towards blade tips, and these trends hold both for big and for small diameters.

According to the AD-method the ideal thrust is nearly always line-any growing towards the blade tips when they are totally encirc-led.

4.4 The influence of the amount of disk circumference encircling

from f9.. O to D, being 9 the encircled length of the

circumfe-rence belonging to one blade, is presented in figs. 8 and 9.

It can be seen that the different thrust radial distributions, be-longing more or less to circumference encircling, do not sensibly influence the values and the trend of the hydrodynamical angles of attack including induced velocities.

4.5 The analysis of flow inhomogeneity influence has been

inclu-ded for the tanker ship propellers. The comparison of radial thru-st dithru-stributions for one free tip blade, from AD and IF-method, both for homogeneous and inhomogeneous flow, is presented in fig.

lo.

It follows that the AD-method gives in inhornogeneous flow greater thrust values towards the blade tip than in homogeneous flow, whi-le the opposite is recorded when using the IF-method.

From the AD-method results, as already found in paper /1/, encir-clec tips are not convenient when inhomogeneous flow is present. No remarkable differences in propeller real efficiency values re-sultec' when van Manen's or Eckardt-Morgan's radial ideal efficien-cy distributions were applied.

4.6 The comparison of hydrodynamical angles including induction

velocities, calculated for free tip blades working in homogeneous flow by AD and IF-methods, is presented in fig. 11.

It can be observed that the two methods agree about the trend of

this angle radial distributions, while the differences of angle

absolute values between propellers calculated by AD anu IF-method

are growing as the working condition is getting more and more that

of a heavy loaded slow running propeller, (no influence of

absolu-te diameabsolu-ter value).

The latter agrees with the principle of linearization present in

the AD-method, which is partly compensated in the IF-method.

4.7 Values of ideal and real efficiency coefficients were

calcu-lated for the free blade tip propellers working in homogeneous flow using both the AD and IF-method, while for the encircled tip

propellers just the AD-method could be applied.

From the diagram in fig. 12 it can be observed:

AD and IF-methods give equal ideal values of efficiency

coeffici-ents for free tip blades working at great coefficicoeffici-ents of advance.

The differences are growing for smaller values of this coefficient

when the loading is generally growing.

Encircled blades show an improvement in ideal coefficients of

effi-ciency at greater values of advance coefficients.

The real values of the efficiency coefficients follow the trends

the two methods are giving for the ideal values.

Almost no differences result in real efficiency valuesbetween

ii

LI. 1.2 1.0 OES 0.6 0.2 0.2 0.3 04 05 0.6 07 0.5

rg.2 -Comparison of lift coefficient radial dist-ribution for propellers with free tip blades

calculated by actuator diikmethod

0.2 03 04. 03 06 07 06 _0FR10

P19.4-Ctnrparson o rda ve thrust radial distribution for propellers with fred tip blades calculated by actuator disk method.

-

.119 -0.2 OIS 0_Io 0.03 0.2 03 0.4 03 06 0.1 0.1 0.9

Fig.)- Cerr,arisoi, e lift coefticien radial dist-ribution for propeller with freetip blades

calculated by induced factors method.

01 03 01. 05 04 0.7 05 09 RLO

Flg.3 -Comparison of relative thrust radial distribuWon for

propellers with free tip blades calculated by

induced factor method.

Ship Propellec(lF) TOnker 1011 Container C 1011 Trawler 1031 Speed boot X 101.1

r

r / -r-

1+

-.

-.--\

\

t Ship Tanker ContaIner Trawler Speed boat Propeller s S 4 X 2011 2021 2031 20/.1 (AD) Ship Tanker ContaIner Trawler speed boat s s X Propellei(1F) loll 1021 1031 1041

/41

51lp Propeller (AO) Tanker 2011 Contaìrwr 2021 Trawler + 2031 Speed boat X 201.1

/

/

0.20 0.1 S CLI. C o 0.10 0.0; 1.1 I.' I. 1.2 to 01 0.6 04 o_2

02 03 01. OES 06 0.7 0.9 0.9 lO

Flg.$ Comparison of itt coefttflt rOd.t. drstributó'

for propel ter with encircled tipi calculated by

actuator disk method.

E;'

so IC 4C IO 2 0.3 0.4 0.5 0.6 0.7 0.1 Q3I

P,S Propeller radial diittlbut Ioni of idiOt thrust by actuator diak method.

-di1 dT11071 2.0 1.8 1.6 l.A 1.2 io o,, 0.6 OEA 0.2 02 0.3 0.4 OS 0k 07 05 o9,lO

Pi9.7 Comparison of elative thrust rcdial distributions of propellers with encircled blade tips

calcula-td by actuator disk mithod

0.2 02 0.4 05 0.6 0.7 0$

r/R1'°

Pig. 9 propeller radial distributIons of hydrodynamal

angle fi calculated by actuator disk method.

Ship Propeller (AD) Tankir s 2014

\

Container 5 2024 Trawler 2034. boct 2 04h

\

\S\\

\\

1111111

Ship Propeller (AO) Tanker 2011.

ContaIner 2024

Trawler 2031.

Speed boat 2041.

il

Speed boat propellers _f

z s 3 Di llOOm;Y: 20,760m11n:l5,1335

Propeller (AZ)

- 2041 s free blade tips (I 1:0 i

201.2 4 _{imclrcl.d tlpa(I Is !D14)}

2043 s encircled tipi(2 I 12) 204'. * encircled tipiCI I:IID

-/e

//

z Speed 3 D: 2041 2042 2043 20.64. Propeller(AD) boat free l,l0mV: encircled 5 encIrcled . encircled propellers blade 20,76 mts:ns 15833s tips( :0 tips(Il:flDIA lips(I l:íD12) tips(I lrrTD CL C D 0.10 005 (radI 1.0 05 01 0.7 0k OES 0h Q3 02 Ql

400 Eìq 200 dr 100

2 03

04 05 06 03 09 (19 1.0 fiR

Jig.iO tanker shIp propellers with Irre lip blades.

Actuator disk- lifting lIne method (A D)

Induction factor- lifting line methodliF)

Results corrected for induced drag influence

free-tips encircled

LO (AD) (IF) (AD) Ideal V U real i 08 0.6 0.2 * i; D s $76 m; Vs 9498 mie; n Propeller(AD) Propeller(IF HomogeneousIlow 5 2011 5 tOit Inhomogerreous flow + 201fl lotit

Comparison ol radiai thrust distribution for one blade(ideal)

0 0.5 .0 LS

Fig. 12 Propellers with free and encircled sips ha-ving equal diameters calculated to give

equal ideal thruit(induced drag excluded)

in homogeneous flow.

4.121

-0.2 03 01. 0.5 06 07 OS

Fig. ii Comparison ot hydrodynamical angle (Il cal-culated for propeliera with Ire. tip bladee

by actuator diik and induced facter rrrthods.

PropeIlerlAD) Ship Prop.11.c(IF) 2011 Tanker n toit

. 2031 Trawler 1031

e 201.1 Speedboat s 1041

i

2021 ContaIner n 1031

'

,

uuii

SpeedAl Obeet

L

' - / AAl conlaIni

il

N

\+

Lilitrawl. Lili tanker (l Er adj 1.0 0.9 0.8 0,7 0.6 0.5 0-L 03 0.2 0.1

f4.122

-CONCLUSIONS

The results of this analysis indicate that the presented

me-thod agrees qualitatively in case of free tip blades with the

induction factors method throughout the analysed range of advance coefficients.

The results are equal in case of the calculated light loaded, fast

running propeller of the speed boat. This is the nearest case to

the optimum shock free working condition.

The trends of the functions for the radial distributions of all

the analysed parameters clearly show that they do comply with the up to date knowhow.

In this work the result is that the real losses eliminate the

gain in efficiencies achieved by potential theory when encircled tips are assumed. It has been noted that here no end plates forces were included.

As the tests carried on at the NSMB, The Netherlands, by the

Astilleros Espanoles, S.A., gave tangible improvements of the real

efficiencies resulting from application of end plates, further

de-velopment of the design method has to be done.

It seems resonable to extend the work in order to find out how - to include the induction drag instead of using the Betzs

principle into the actuator disk lifting line theory,

- an inconstant pressure distribution along the radii would alter the results,

- to include the forces of the encircling body.

ACKNOWLEDGEMENTS

The author would like once more to express her grateful thanks

to prof. dr J.A. Sparenberg and to his assistent L. Klaren of the

University of Groningen, The Netherlands, for their previous

wor-ked out calculations of the actuator disk data, looking forward to

a successful continuation of the than started collaboration.

The authors appreciation also goes to her sun, Dean, student

of Naval architecture at the Technical faculty Rijeka for his

in-valuable contribution for this research - the successful work

per-formed on the computer softwork. Her sincere thanks are also due

to Mrs. Mira Bobanovi for her skilled typewriting and to Mrs.

Jo-sipa Grinï for her skilled

drawingwork. SYMBOLS

c - profile expanded chord length

Ca , Ct - induced axial and tangential velocity

cLj - ideal lift coefficient

CTi - ideal thrust coefficient

Cpjn

- coefficient of minimal allowed pressure

D - propeller diameter

Dj - induced drag

e - water evapDration pressure

f - cavitation safety factor

'xi, x2 - Klaren's coefficient of radial

circulation distribu-t ion

- .123

-K

-

strength safety coefficient

J - advance coefficient

- length of encircled disk circumference

L - ideal hydrodynamica]. lift

M - blade bending moment

n - propeller revs per sec

Po - hydrostatic pressure at propeller axis

- nominal pitch

q - propeller quality factor

Q1 Q[, Q

-

real and ideal turning moment without and with

indu-ced velocities

r , R - radius of each profile, disk radius

- hub radius

t - blade element thickness

T, T, T

- real and ideal thrust without and with induced drag

y , v - total blade element inflow velocity without and with

induced velocities

Va , Vt - inflow axial and tangential velocities

Wa - axial wake coefficient

Z - number of blades

x - nR, also index of profile location

ciw - coefficient of profile momentum of resistance

,

- hydrodynamical angle without and with induced drag

- efficiency coefficient (real and ideal)

4N - nominal pitch angle

r - circulation

A - advance coefficient, (va/Ir nD)

w - rotational velocity, (2 im)

E

-

blade rake angle

p - water density

- blade material density

a - cavitation coefficient

- allowed material stress

Note: "Ideal" means "working in potential flow"..

REFERENCES:

Ill

Klaren,L., Sparenberg, J.A. and Vuini, A., "Screw blade tip

vortices: an attempt of control", IV Symposium Theory and

Prac-tice in Shipbuilding - In memoriam Prof. L.Sorta,Opatija, mart

19 80.

121 Sparenberg,J.A., "Principles of propulsion and its optimization

in incompressible and inviscid mflow", University of Groningen,

The Netherlands, 1977.

131

Vuini,A., Mra,Z., "Proraáun vrstoe i

kavitacije propelera

projektiranih Po metodi uzgonske linije", V Sympozijuin, Teorija

i praksa brodogradnje - In memoriam prof. L. Sorta, Split, mai

1982.

¿4! Lerbs,H.W., "Moderately loaded propellers with a finite number

of blades and an arbitrary distribution of circulation", Trans.

of Society of Naval Architects and Marine Engineers, Vol'. 60,