SNAME The Wageningen B-Screw Series.pdf

The Wageningen B-Screw Series By W . P. A. van L a m m e r e n ] and M. W . C. Oosterveld, 2

Member, J. D. van M a n e n / Member, Member

The Wageningen B-screw series have been extended gradually to 21 screw series having blade numbers ranging from 2 to 7 and blade-area ratios between 0.30 and 1.05. Recently, the existing screw series were correlated with the new screw series with an upto-date fairing technique. This correlation was made by means of a regression analysis. Further, the influence of the Reynolds number (scale effect) on the test results was taken into account. For ship maneuvering studies, it is necessary to know the propeller thrust and torque characteristics over a wider range of operating conditions. Therefore, openwater tests with B-series screws over the entire region of operation were: carried out. In order to obtain systematic knowledge on the cavitation characteristics of the B-screw series in a uniform flow, tests have been conducted. The curves for cavitation inception were established and the influence of cavitation on propeller thrust and torque was

determined.

Introduction AN IMPORTANT m e t h o d of screw design is t h a t b a s e d on t h e results of o p e n - w a t e r t e s t s w i t h s y s t e m a t i c a l l y v a r i e d series of screw models. T h e s e screw series c o m p r i s e m o d e l s whose c h a r a c teristic dimensions, such as p i t c h r a t i o P/D, n u m b e r of b l a d e s Z, b l a d e - a r e a r a t i o A u/Ao, b l a d e o u t line, s h a p e of b l a d e sections, a n d b l a d e t h i c k n e s s a r e s y s t e m a t i c a l l y varied. A m o n g t h e w e l l - k n o w n screw series as d e v e l o p e d b y Schaffran, T a y l o r , G a w n a n d others, t h e W a g e n i n g e n B-screw series of t h e N e t h e r l a n d s S h i p M o d e l B a s i n t a k e an i m p o r t a n t place. T h e B-series screw t y p e is f r e q u e n t l y used in p r a c t i c e a n d possesses s a t i s f a c t o r y efficiency as well as reasonable cavitation properties. T h e first t e s t s w i t h s y s t e m a t i c series of screw propellers were p e r f o r m e d a t t h e N e t h e r l a n d s S h i p M o d e l Basin in 1936. F r o m m o d e l experiDirectors, Netherlands Ship Model Basin, Wageningen, The Netherlands. =Head of Research Department, Netherlands Ship Model Basin, Wageningen, The Netherlands. Presented at the Annual Meeting, New York, N.Y., November 12-14, 1969, of THE SOCIETYOF NAVALARCHITECTS AND M A R I N E ]~NGINEERS.

merits c a r r i e d o u t b y B a k e r a n d R i d d l e [1]a a n d B a k e r [2] it h a d b e c o m e e v i d e n t t h a t screws used so far w h i c h h a d c i r c u l a r - b a c k b l a d e sections a n d elliptical b l a d e o u t l i n e ( T a y l o r a n d Sehaffran) were in m a n y cases inferior to screws w i t h airfoil sections. T e s t s p e r f o r m e d at t h e N e t h e r l a n d s S h i p M o d e l Basin confirmed t h e s e conclusions in m a n y cases. B a s e d on t h e s e results a series of f o u r - b l a d e d m o d e l screws of a s h a p e similar to B a k e r ' s was m a n u f a c t u r e d a n d t e s t e d in t h e open condition. T h i s series was called t h e A 4:-40 series (thus 4 - b l a d e d series w i t h 0.40 b l a d e a r e a r a t i o ) . T h e r e s u l t s of t h e o p e n - w a t e r tests w i t h this series were given b y T r o o s t [3]. L a t e r on it was f o u n d t h a t t h e A 4-40 series screws, owing to t h e n a r r o w b l a d e t i p s a n d t h e a i r f o i l - s h a p e d sections o v e r t h e whole blades, were o n l y s u i t a b l e for use in cases w h e r e no c a v i t a t i o n d a n g e r was present. I n a d d i t i o n , t h e A 4-40 series screw t y p e did h a v e t m f a v o r a b l e b a c k i n g c h a r a c t e r i s t i c s . T h e s e con,dderations led to t h e design of screws w i t h wider b l a d e tips, circularb a c k seetions n e a r t h e b l a d e tips, a n d airfoils h a p e d seetions n e a r t h e hub. Screws of t h i s t y p e a Numbers in brackets designate References at end of paper.

269

Table 1 Btade

number Z

Btade

Summary of the Wageningen B-Screw Series ratio

area

A~/Ao

o.3o

2 3

0.55

#

0.140

1 . oo 0.45

_

0.55

o.6o

0.70

0.75

5

1.05

0.80

6

7

were called B-series screws. In this way the B 4 - 4 0 s c r e w s e r i e s w a s d e s i g n e d a n d g r a d u a l l y extended to further series with larger blade-area ratios and various blade numbers. These extensions were partly (mainly concerning the higher n u m b e r of b l a d e s a n d t h e l a r g e r b l a d e - a r e a r a t i o s ) s p o n s o r e d b y t h e ( f o r m e r ) B u r e a u of S h i p s of t h e United States Navy. T h e r e s u l t s of t h e o p e n w a t e r t e s t s w e r e g i v e n i n a n u m b e r of p u b l i c a t i o n s b y T r o o s t [3], a n d o t h e r s [4], [5], a n d [6]. A t p r e s e n t , a b o u t 120 s c r e w m o d e l s of t h e B series screw type have been tested at the Netherlands Ship Model Basin. Table 1 gives a summ a r y of t h e series. I n g e n e r a l , t h e r e s u l t s of t h e t e s t s w e r e g i v e n i n t h e f o r m of K T a n d K o coeffic i e n t s e x p r e s s e d a s a f u n c t i o n of t h e a d v a n c e c o e f f i c i e n t dr f o r a n a l y t i c a l w o r k , a n d in t h e f o r m of B p - 6 a n d B u - 6 d i a g r a m s f o r d e s i g n p u r p o s e s . From a correlation between the available diag r a m s of t h e B - s c r e w s e r i e s i t a p p e a r s t h a t s m a l l

differences exist. However, during the last years the B-series have been extended considerably and a c r o s s - f a i r i n g of t h e B - s c r e w s e r i e s d i a g r a m s f o r d i f f e r e n t b l a d e - a r e a r a t i o s a n d p r o b a b l y f o r diff e r e n t n u m b e r s of b l a d e s m u s t b e p o s s i b l e n o w . R e c e n t l y w e h a v e s t a r t e d t h e f a i r i n g of t h e B s c r e w s e r i e s t e s t r e s u l t s b y m e a n s of a r e g r e s s i o n a n a l y s i s . A s a r e s u l t of t h i s a n a l y s i s , t h e t h r u s t a n d t o r q u e c o e f f i c i e n t s K T a n d K o of t h e B - s e r i e s will b e e x p r e s s e d a s p o l y n o m i a l s of t h e a d v a n c e ratio J, the pitch ratio P/D, the blade area ratio A R / A o , a n d t h e n u m b e r of b l a d e s Z . I n a d d i t i o n , t h e e f f e c t of R e y n o l d s n u m b e r o n the test results was taken into account by using t h e m e t h o d d e r i v e d b y L e r b s [7] f r o m s i m i l a r m e t h o d s u s e d f o r t h e c a l c u l a t i n g of t h e p e r f o r m a n t e c h a r a c t e r i s t i c s of a i r s c r e w s f r o m t h e c h a r a c t e r i s t i c s of e q u i v a l e n t b l a d e s e c t i o n s . In the f u t u r e , t h e e f f e c t of R e y n o l d s n u m b e r m a y b e t a k e n i n t o a c c o u n t i n t h e p o l y n o m i a l s as well.

Nomendature By = loading coefficient, B,c CD Cf CL CT

= = = = =

N P ~/~ VA %

chord length of blade section drag coefficient skin-friction drag coefficient lift coefficient t h r u s t coefficient, T CT -711 / 2 p V A 2 --4 O

Cr* = t h r u s t coefficient, CT* = T 7r

~/2p[Va 2 -t- (0.77rnD) 2] ~ D 2 Co* = torque coefficient,

Q C o * = V..p[VA 2 + (0.77rnD)q -~ D~D 4

270

d = hub diameter D = propeller diameter J = advance coefficient, J -

VA nD

K~, = t h r u s t coefficient, KT--

T on2D ~

K o = torque coefficient,

O Ko = -pn2D - 5

n,N

= number

p = pv = p~ = _P O r R Re

= = = = =

of revolutions per second and per minute pressure vapor pressure static pressure of undisturbed streanl power torque radius propeller radius Reynolds number

The Wageningen B-Screw Series

t = maximum thickness of blade section T = thrust V,I = undisturbed stream velocity Z = number of screw blades AE/Ao = blade area ratio of screw .P/D = pitch ratio of screw d / D = hub diameter ratio = angle of attack of blade section /3 = hydrodynamic pitch angle a t 0.7 R, /3 = aretan VA/O.7rrnD = speed ratio, ~ = 101.27/J p = specific mass of water ao = cavitation number, p -- pv 170 - -

~/2. VA2

no = open-water efficiency, J Kr 2~ KQ = kinematic viscosity of water

,

~R

1__--~-4x ! o~

\

!

_

\

!

~

Pitch dlstibution °Ji

L __

"',

~ 4 =

I

__

\

02R

,,~

--t--n----

~.¢_--4---~------./

, - -B 4',- 7 0"

,~'--B zr- 5 "= - 1

s~-~o

Fig. 1

-7

'~ _-- ----J-- - - T - - - - ' ~ . /

T - - ~~ =4 --6-5~ - - ¢ ~ : ; , - . , , o

\ ....

7 - - - - q -- - - - - ~ / u ~.-nxu

'

2'

~so'~.:

~

822 °/

G e n e r a l plan o f B 4 s c r e w series Pitch distribution

o ~ l

02R

:____&~

~_k [ I

c31!x

I

I

'~

' I

"m 85-45

B5-60

85-105 L

~ 2 2 ~-2N~u-

General plan of B 5 s c r e w series

T h e p o l y n o m i a l s a n d the corrected design diag r a m s of t h e four- a n d five-bladed B-series screws are g i v e n in this paper. I n order to o b t a i n d a t a for a n a l y z i n g the m a n e n v e r s of ships, submersibles, drilling vessels, a n d so on, o p e n - w a t e r tests with a p a r t of the Bscrew series were c o n d u c t e d over a wider r a n g e of a d v a n c e coefficients. T h i s e x p e r i m e n t a l p r o g r a m covered t h e following i t e m s : ahead, ahead, astern, astern,

rpm rpm rpm rpm

ahead astern astern ahead

=:~

>/

85-75

Fig. 2

speed speed speed speed

(

",

!

(lst quadrant) (2nd q u a d r a n t ) (3rd q u a d r a n t ) (4th q u a d r a n t )

T h e effect of p i t c h ratio P / D , blade area ratio A E / A o, a n d n u m b e r of blades Z on the characteristics of the B-screw series in the four q u a d r a n t s h a v e been d e t e r m i n e d . I n addition, t h e results of the f o u r - q u a d r a n t m e a s u r e m e n t s are a n a l y z e d in the form of a F o u r i e r series a n d the F o u r i e r coefficients are given. T o o b t a i n s y s t e m a t i c knowledge of the c a v i t a tion characteristics of the B-screw series in a uniform flow, tests were carried o u t in t h e large N S M B c a v i t a t i o n t u n n e l with a p a r t of the Bscrew series. T h e influence of c a v i t a t i o n on propeller t h r u s t a n d t o r q u e was measured. I n addition, i n c e p t i o n curves were established for tip vortex cavity, sheet c a v i t a t i o n a t suction a n d pressure sides, a n d b u b b l e c a v i t a t i o n a t back a t midchord. T h e results of all these i n v e s t i g a t i o n s concern-

Table

2

Dimensions of Four B-Screw Series

c~ Z D Az/Ao 1.662 1.882 2.050 2. 152 2.187 2. 144 1.970 1,582 ...

Y~

R 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

ar c~ 0.617 0.613 0.601 O. 586 0.56t O. 524 0.463 O. 351 0

and

Five-Bladed

tr D 0.0366 0,0324 0.0282 O, 0240 0,0198 O. 0156 0.0114 O, 0072 0.0030

b~ c~ 0.350 0.350 0.350 O. 350 0.389 O. 443 0.479 O. 500 ...

distance between leading edge and centerline at radius r b r = distance between leading edge and maximum thickness of blade profile at radius r chord length of blade profile at radius r Cr D = screw diameter r radius R = tip radius AL./Ao = expanded blade area ratio Z = number of blades t r = maxinmm thickness o1' blade profile at radius r a r

ing the W a g e n i n g e n B-screw series are given a n d discussed in this paper. G e o m e t r y of B-Series Screws

A s y s t e m a t i c screw series is formed b y a n u m b e r of screw models of which o n l y the pitch ratio J P / D is varied. All other characteristic screw d i m e n sions, such as d i a m e t e r D, n u m b e r of blades Z , blade area ratio A e / A o , blade outline, shape of b l a d e sections, b l a d e thicknesses, a n d h u b - d i a m eter ratio d / D are the same. T h e results of tests

The Wageningen B-Screw Series

271

[

/

[dynamometer --7

IRPM t---~(propetter thrust[

/a"d torque) J

Fig. 3

Measuring equipment for performing open-water test

with the four-bladed B-screw series with bladearea ratios of 0.40, 0.55, 0.70, 0.85, and 1.00 and the five-bladed series with blade area ratios of 0.45, 0.60, 0.75, and 1.05 are given in this paper. Figs. 1 and 2 show the general plans of the fourand five-bladed screw propellers respectively. The dimensions of these screws are given in Table 2. The diagrams show clearly that the B-series screws have relatively wide blade tips, circularback blade sections near the tip, and airfoil sections near the hub. The four-bladed screws have a decrease in pitch at the hub of 20 percent in order to adapt the screw better to the velocity distribution behind a ship. A large number of experiments has shown, however, that the difference in efficiency due to this decrease in pitch in comparison with a screw with constant pitch is insignificant. The five-bladed screws have a constant pitch. The hub-diameter ratio of the fourand five-bladed B-series screws was d / D = 0.167.

00~

/

CD 0.03

0.02

" ~ - ~ O rnln t x p ~ "X~O min t h e 0 r

0.01

0

025

0

0.025

0 050 0