Wake distributions

SKIBS -0G HAVTEKNIK

Department öf Ocean Engineering

WA}E: DISTRIBIFI IONS

IDANMARICS TEKNISKE HØJSKOLE

The Technical University of Denmark

LNGBY' Danmark

by

.Sv.Aa.Harvald. and Jan M.He

PREFACE

The paper

WAKE DISTRIBUTIONS was presented 1978.11.22 at the

International Symposium on Future Tasks and Problems

of Model Basins held on the occasion of

75 jAHRE, Versuchsansta].t für Wasserbau und Schiffbau, Berlin 1903-1978

In the introduction to the paper the following was mentioned:

It is always the desire of a propeller designer to design a propeller which would at a certain speed and a certain number

of revolutions absorb a minimum amount of power. Further, it

is necessary that the propeller is free from cavitation and that the pressure variation over the blades and the ship hull

is reasonable, thus avoiding noise and vibration.

In order to get these requirements fulfilled he must know

the velocities with which the water flows to the propeller disc.

In other words, he must know the wake distribution. One

can define wake as the numerical difference between the velo-city of the ship and the velovelo-city with which the water flows

to the propeller. By dividing this difference by the velocity

of the ship the wake fraction is obtained as:

V-V

_A

V

Primarily it is the effective wake fraction the designer would

like to know, that is the wake fraction determined by the

pro-peller acting as a wake measurer and a wake integrator. By

self propulsion model tests the effective wake fraction is

determined. It looks very simple, but nevertheless there are

torque identity respectively are different; secondly, it

should be noted that repeated experiments, with the same pro-peller or with other propro-pellers having the same diameter and

pitch, do not give same wake fraótions. A standard deviation

up to about 15 per cent can be detected.

Later when designing a propeller by use of the circulation theory it is of interest to know the radial variation of the

wake fraction. The radial distribution of the wake fraction

can be determined by means of blade wheels, resistance rings

or pitot tube measurements. The blade wheel method is the

simplest. The diagrams shown in Fig. i can also be used for

this estimation when taking into account the scale effect and

when a very high degree of accuracy is not required.

0,70

w

0,60 0,50 0h40 0,30 2O 0.2 0/. 0,6 0.8 _nR .0.10

w

o u-roRW FORP V-6:0.75 65 065 0.7 0.1O0 _0,2 Fig.

i.

0.70

w

0,60 0,40 0,30 FORM CORRECTION L = length of waterline B breadth on waterline D propeller diameter = block coefficient 04 06 08 /R 1.0

The radial variation of the wake fraction of

single screw ship models (L 7 m, R = tip

radius and r = distance from axis to section

in propeller blade). °/L WL:Qtl 0.06

IuuIu

I.'mII

Iiil'u'.

-uIiI'

_,.u-

r

) 02 04 0S 08 FI1i 'L 4.O.I3 0,04 6:075 0,65

w

wmc

(C)

MODEL SCALE 1:6 1:6

R0UGESS I R0UGHSS fl

Fig. ii. The wake distributions for Victory ship models.

SCALE 1:40 1:36

1:25 1:23

1:30

e(a)

Fig. iii. The modified wake distribution of the

scale A = 6 Victory ship model.

With regard to the wake distribution on the propeller disc a vast amount of data has been collected during recent years but

only a few relevant results have been published. 2mong the

pub-lished data there are some from the Dutch: experiments with

models of different scale ratios o the Victory ship. Fig. ii

shows the wake distribution for these models. It will be

no-ticed that the wake field changes from model to model The

very undulated curves are unrealistic and have been modified

later by the model basin (Fig. iii).

From the model experiments the designer had to establish

a picture of the wake field for the real ship.

At present it is almost impossible to solve this problem

in a correct manner for three reasons. Firstly, one has to

evaluate the accuracy of the measurements at every point. It

is our impression that the standard deviation on such wake

measurements is about 0,05. Sometimes at the same point of

the propeller disc there may be differences in wake fraction

values as large as 0,25 for repeated model experiments. Secondly,

C,. -

--

---- /

,,

I

/

--I, Iy

'I*NTARY TESS C

I

,

,,

L,

j,

!I

I,

/}'

qs'

Q-s__)

WI

i i-!o

I,

----s-,. _v=,t:3mJg I

f

-.

,

-.

'.'-: -

/ -.

r'°

¡

ojo 60 50 040 30 J---.--i QO QiO SMOOTH MODEL

Fig. iiii. 'Computer rings' in the wake field

behind a single screw ship model.

during the experiments and then the curves for constant wake are

drawn by use of the computer. The contours for constant wake

fractión may take the shape of rings because of the particular interpolatión method used by the computer for plotting Let us call these rings as computer rings. Such rings are shown on Fig.

iiii and-

do not exist in

reality. Thirdly, one has to take into

account the scale effect on the wake. In the full-scale trial

condition the mean wake fraction is about 70 per cent of the model wake fraction while the mean wake fraction in the service

condition is nearly the same as that of the model experiment. Still we know very little about the wake field behind the real

ship in relation to the wake field of the model.

Over a number of years our institute has studied wake pro-blems and in the papr some of our latest investigations

re-garding wake diBtributions are reported.

Further, some remarks to the paper are stated in the Ap-pendix after the paper.

WAKE DISTRIBUTIONS

Stmmtary.

In order to get a better insight of the wake field behind a ship and especially to have a better knowledge of the influence of such factors as speed,roughness,stern form and rudder,a series of model experiments were car-ried out. The experience gained concerning these matters is discussed together

with an evaluation of the reliability of the five hole pitot tube measurements.

Introduction.

In the post-war period where the ships have grown bigger and bigger together with an ever increasing speed, there has been an increasing demand for a better knowledge of the wake field behind the ship It has been necessary to introduce a

better and more detailed description of the wake field in order to design more efficient propellers which also had a reasonable pressure variation over the blades and the ship hull thus

avoid-ing noise and vibration.

Today it is more or less a standard procedure to carry out wake measurements together with the more ordinary towing tank

tests when a new ship is being designed. Also a number of full

scale measurements have been taken during special trial trips.

In spite of this vast amount of data collected there is still a considerable lack of knowledge regarding the wake

dis-tribution and the factors influencing it. The object of the investigations.

The main object of the investigation carried out by the 15H was to look for some of the factors involved in shaping the wake field and how they influence. It is of great importance to know this in the search for a method which can predict the wake field for the real ship in a reasonably good and safe manner.

The factors investigated were: - Speed of vessel

- Friction due to roughness

- Form of the sterñ

- Rudder influence,

results the reliability of wake measurements was also

inve-stigated.

3. Description of the tests.

Becaùse the ISH has no test facilities it orders the tests

in a towing

tank in the same way as any shipyard or design

of-fice does Also the results are delivered to the ISH in the

same standard fashion as to any other customer.

The wooden model used has the following main particulars:

Lorgitudina1 center of buoyancy is 0,134 in forward of

ainidship. The model corresponds to a bulk carrier of approx.

50.000 t dead-weight. Fig. 1 shows the body plan and the

pro-file of the stern and stem.

Most of the test were carried out without rudder and with

a simplified stern form as shown in Fig. 1. In some of the

last tests series the stern was shaped as shown in Fig. 8. Most

of the tests were carried out with a smooth model. The

inve-stigation of the influence of the roughness was done in the

following way: Streamlines at model speed 1,3 rn/s and 2,0 rn/s

were determined by the wet paint method (Figs. 2, 3 and 4). A strip of coarse sand or rough gravel (granite of size between

4 nun and 8 mm) was glued between streamline 5 at velocity 2,0 rn/s

and a streamline located 60 mm outward from streamline 5 at

midship lection. At first the strip was fitted from midship

to the stern and later for the whole length of the vessel (see

Fig. 4).

At all the tests a row of cylindrical studs of 2,5 mm in diameter was fitted near the stem of the model for turbulence

stimulation.

Length on waterline L = L = 7,534 w

Length between perpendicular = 7,360 in

Breadth moulded B = 1,115 in Draught T = 0,432 w Wetted surface S = 12,087 w2 Displacement V = 2,742 in3 Block coefficient 6 = 0,755 6 = 0,773 pp

Midship section coefficient ß = 0,996

±

SICL ,1018-ID

Fig. 1. Body plan, profile of stern and Btem of model.

V

Fig. 2. Wave system and streamlines.

Fig. 3. Wave system and streamlines.

SCELO1S-IO V .2,mh

____

0

----,---- __p ¡

MOL 7O$-tO ¡

Fig. 4. Body plans With streamlines and strip of _{coarse sand.}

*0*-IC

I

14

fooeo 0 0 0 0 D -e 0 D 5C 0ODO

\ 0

_{0 0} D O 0 0 e e , _O O O O O

kt:r

1-c /°'

_{¿000 °}

T7---o

&sc

BL SL I IL 0 jA B IC

Fig. 6. Measuring points:

Model as single-screw ship. Model as 11twin-screw" ship.

Model with modified stern and with rudder.

The wake was measured with a five hole pitot tube as de-scribed in (51. The tests were performed with the model both as

a single- and as a twin-screw ship with the points of

measure-ments being located as shown in Fig. 6. The five holes in the

ball of the pitot tube were through plastic tube with boiled

water connected to five pressure transducers. The transducers

sent signals to a computer

which

calculated the mean value of

each of the five signals and which produced a paper tape with the recorded mean values for later calculation of the three

velocity components V, V and V, defined by:

= VA is the velocity in the fore-aft direction

V is the velocity in the port-starbord direction

is the velocity in the vertical direction.

The results were presented in a tabular form and as a

com-puter plot of equal Vs-curves and the velocity vectors in

the plane of the propeller disk.

v-v

The wake fration w is computed as: w = , where V

is the model speed.

For the sake of comparison the potential wake fraction

(wy) is calculated for a double body of the model using a

source/sink method. (The calculations have been done by Kristin Rasmussen in connection with his work for the master's degree

The results of the tests i.e. the wake measurements and the streamlines are presented here as they were delivered from the

towing tank. No reanalyzing, adjustment, fitting or fairing

have been made to the data. So the conclusions are drawn on

the basis of test data anyone would obtain from a commercial

towing tank.

4.2. Velocity dependance.

Most of the tests were done at two velocities: 1,3 rn/s and 2,0 m/s corresponding to approx. 6,5 rn/s and 10,0 rn/s (13 and 20 knots) for the full scale ship.

The axial wake distribution for the two velocities is

shown in Figs. lB and C, Figs. 7E and F, Figs. 7G and H and as cross curves in Fig. 10.

The picture is a little diffused. If, however, each

con-stant wake curve at one velocity is compared with the corre-sponding curve at the other velocity it will be found that the wake fraction at any particular point over most of the propeller

disc will be reduced with approx. 0,07 when the velocity is

in-creased from 1,3 rn/s to 2,0 rn/s. Only in part of the upper area

of the propeller disc this is not the case and therefore the volumetric mean wake fraction is only changed from 0,47 to 0,45

for the smooth ship and from 0,62 to 0,58 for the ship with

the gravel strip due to the change in the velocity.

As a comparison it can be mentioned that the volumetric wake fraction for a propeller behind a flat plate will only decrease by approx. 0,01 according to the von KärmAn's

empi-rical formulae ((1] p. 18). 4.3. Roughness dependance.

It is a coimiion knowledge that the friction belt for the

full scale ship is relatively thinner than for the model at corresponding velocities. If one operates in model scale it is very difficult to realïse how the contraction of the friction belt can occv. It is much easier to study an increase in the

thickness of the friction belt by increasing the roughness of

the model thus allowing an investigation of the Influence

V,t'3mJs 'x_1

w

CiL

w

// 1

V2m/s

('I

)J/I

-' 10 vo vo vo. ¶0 il o,io

!Jj)FULLSTPE

e.. _E . F

t

i I -- ---. 1

.

f, ¡/,

I _-TISI'

(

...J

_¡/

- - , -L ! ¡/ _,i

_{Q*._}

_W.

_CL.

_/11/

,/ t

c_._ / SMOOTH MODEL. BL. _C V2pm/s

SMOOTH ¡ (io

(

7'

SMOOTH

i

/ /

_MODEL

'J

\.

/'

_MODEL

10

N.," /

G

L.---'

H

i

. ftL

Fig. 7. Wake distributions for the model:

Calculated potential wake (Kristin Rasmussen, ISH, 1978). Smooth model, V = 1,3 rn/s.

Smooth model, V = 2,0 ut/s.

Strip of coarse sand from stein to amidships, V = 2,0 in/s. Strip of coarse sand from stem to stern, V = 1,3 rn/s. Strip of coarse sand from stem to stern, V = 2,0 nI/s.

Wake measured as for a twin-screw ship

without bossings (smooth model), V = 1,3 rn/s.

Wake measured as for a twin-screw ship

by means of this extra roughness an increase of _{the thickness}

of the friction belt was locally obtained.

In order to investigate where the friction _{is most} impor-tant for the wake distribution the gravel strip was introduced

first

theforward

_{partand next also on the aft partof the}

.

rnodel.

The resultS of the test. are

shownin

Figs. 7D, E and F

and as cross curves in Fig. 10.

The forward 1/2 strip was found to have

_none

or little

influence on the wake distribution. _{The curves for constant}

axial wake with and without gravels fitted _{cross each other} rather casually and it is more or less just the level which is

lifted. _{The disturbance from the gravel in the forward part}

of the model spread in a _{fan-shaped manner all over the}

sur-face. _{As a result of this the volumetric mean wake fraction}

was ±ncreased from. 0,46 to 0,48.

The results of the teste with the fore to aft gravel strip

were somewhat different. _{In an area of the top part of the}

propeller disc and. approx.. half propeller radius (R/2) _away

from the centerplane an increase of axial wake fraction _{up to} 0,25 was recorded _{There was a gradual change of the wake}

in-crease from.thjs area to the bottoni area of the propeller disc

from 0,25 to approx. zero. _{At the velocity of 1,3 rn/s the}

volumetric mean wake fraction was increased from 0,47 to 0,62

and at 2,0 rn/s it was changed from 0,46 to 0,58.

The wake fields at all the investigated conditions was very inhomogeneous and with quite a lot of rather casually distributed

t1islands".' These irregularities _{are much bigger than those}

found in the investigations made in Japan with "Yagoi Maru" and

her. models (61.. _{Looking closer to the constant wake curves in}

the area where the largest changes. occur because of the gravel

strip, one finds that the curves have moved _{in a direction of}

approx. 550 _{to horizontal (see Figs. 7B and E and also 7C and}

F),. The wake field was apparently altered in a very complicated

way when the böundary layer was changed. On the whole it _seems that the contour for constant wake for the model is displaced at a right angle to its original position when the _{roughness of}

Fig. 8. Profile of model with modified stern and rudder..

the surface is varied.. This indicates that the contour for constant axial wake for the full scale ship probably will be displaced in the same way when they are derived from the model

results. If so, the correction theory, proposed by Sasajima

in 1966 (4] is probably not absolutely correct. The method

proposed by Hoekstra in 1974 (2] seems to come close although the mathematical formulations given in connection with the

theory is too complicated if the not so accurate data from the

model test are taken into account (see section 5). It is the

authors' opinion that the wake distribution found by means of

model tests can be used primarily to judge whether the wake field is adequately homogeneous or not. A method for such an

evaluation is proposed by Odabasi and Fitzsimmons (3].

The wake data necessary for propeller and pressure varia-tion calculavaria-tions can be produced by multiplying the measured data with some coefficients taking the model scale into account.

It seems that doing anything else is just to hide our ignorance. 4.4. The, influence of stern form.

Most of the tests were made with a simplified ship stern

form. Some of the later tests were made with a modified stern

as shown in Fig. 8. There was no significant change in the

wake distribution (see Figs. 9 A og B).

4.5. influence of the rudder.

Because of the test technique used in the experiments most.

of the measurements taken were without rudder. Only at some of

the later tests the measurements were made when the model had a rudder fitted as shown in

Fig.

8. Figs. 9C and D show the test results for the two velocities 1,3 rn/s and 2,0 rn/s.

V.13tm/s î,-I. I\\'k i

"A

rT

¡CH

, w

i,.

j QO

\

I,!

_I

-n

IN

:.-WH eò L ___ ft

b y

rTl

V 2ß m,, SL

w

B I

LD

i

Fig.

9. Influence of stern

and rudder on wake distribution.

SMOOTh MOCEI. HALF StRIPE CF SAP FLLL STRIPE OF SAND

TOP OF DISC D(TRE CF DISC R.4BELOW CENTRE BOTTOM OF ffiO DISC

Fig.

10. Cross curves of the wake distribution at

The rudder does not change the general character of the wake

field, only the value is changed mainly because of the potential

wake field of the rudder. The mean increase of the axial wake

fraction at the observation points is for 1,3 rn/s approx. 0,016 and for 2,0 rn/s approx. 0,023.

5. Reliability of wake measurements.

It has always been difficult to carry out measurements of

wake with the five-hole pitot tube and the tests are very

time-consuming.

The time spent has been cut considerably by

intro-ducing the electronic and online computer techniques but new source of errors has also been introduced and tests must often

be repeated.

The tests described here involved many measurements; only

one parameter was changed at a time. The test period lasted

about half a year. The water temperature in the towing tank

increased from 13,8° C to 17,2° during the period but it is

assumed that this had no influence on the results. Some of the

measurements were repeated by running the model both as a

single-screw ship and as a double-single-screw ship without propeller bossings.

Consequently, the same wake field was measured twice at a certain

interval of time. This means that the measurements,

calcula-tions and computer interpolacalcula-tions were carried out without

being able to correlate them during the tests. Also the computer

programs used for single- and twin-screw ships are different.

The data can therefore be used as a basis for estimating the

uncertainty of the f lye-hole pitot tube technique.

If Figs. 7B and C are compared with Figs. 7G and H it is

seen that very great differences can exist

between

the

two sets

of measurements. The corresponding curves are even seen to

cross each other at angles of about 900. At some points the

difference in wake values is as big as 0,25. Normally the

ob-served difference is approx. ±0,05.

This means that the undulations of the wake curves often are more or less random and perhaps the "islands" with very high or low wake values do not exist in connection with a real

ship. Owing to this only the overall picture of the wake

distri-bution is to be relied upon and there is no reason to trust a

of small models must also be considered as having very little

significance in practice. 6. Conclusions.

The friction belt is decreased as the velocity is increased.

The contraction occurs more or less in a direction

perpen-dicular to the constant wake contours. However, some

irre-gularities at the top of the propeller were observed for

the model used in these investigations.

The constant wake contours are displaced when the

rough-ness is varied. The direction of the displacements is

more or less perpendicular to the contours. Increased

friction means increased wake. It is likely that the sanie

takes place when going from model to ship.

Moderate variation of the ship stern has little or no

influence on the wake distribution.

The rudder increases the wake but does not change the

distribution significantly.

The five-hole pitot tube measurement technique is

rela-tively unreliable.

It is necessary to carry out many measurements if a

rea-sonably safe determination of the wake is required. A

single standard test performed commercially could very easily ai7e a rather erroneous impression of the wake

distribution. An improved wake measurement technique is

very much needed. 7. References.

[i] Harvald, Sv. Aa.:"Wake of Merchant Ships. The Danish Technical Press,

Copenhagen, 1950.

[2] Hoekstra, M.:"Prediction of Full Scale Wake Characteristics Based on Model Wake Survey", Symposium on High Powered Propulsion of Large Ships,Netherlands Ship Model Basin,Publication No. 490, Wageningen

1974, Part i p. XII, 1.

Odabasi, Y. and Fitzsimmons, P.A. "Alternative Methods for Wake Quality

Assessment", International Shipbuilding Progress ,Voi.25, February 1978, No. 282, p. 34.

Sasajima, H. and Tanaka,I.:"On the Estimation of Wake of Ships",Eleventh

International Towing Tank Conference, Tokyo, 1966, p. 140.

[5] ilòvi, V.:"A Five Hole Spherical Pitot Tube for Three Dimensional Wake Measurement", Hydro- and Aerodynamics Laboratory, Report No. Hy-3, Lyngby-Denmark, 1964.

(6] The 4th Research Committees:"Investigation into Effect of Fouling of a.

Ship and Propeller upon Propeller Performances of a Ship, The Report of the Shipbuilding Research Association of Japan, Tokyo,

APPENDIX

As mentioned in section 5 and in the

conclusion

_{6.e it was}

found that the measurements with the 5-hole _{pitot-tube are not}

reliable. Fig. A.l shows an example from

investigations

_at

David W. Taylor Naval Ship Research and Development Center

(ref. 7]. This figure shows a comparison between three _dif

fe-rent velocity measurement devices and it is seen that the

scat-tering of repeated meaSurements is considerable. _{At a distance}

of 60 ¡mn from the

cylinder

_{the difference in velocity}

measure-ments is as large as 1,5 rn/s. Tests in a rotational flow

indicate that the pitot-measurement _{can be distorted by the}

pressure in the vortices as mentioned by Müller in (ref. 8].

As also mentioned in the

conclusion

_{6.e an improved method} of measurement technique is needed _{because of:}

improved accuracy

possibility to meaSure the wake thefl the propeller is preáetit

possibility to measure without disturbing _{the flow field}

reduction in time and cost.

The one technique now emerging is the _{laser doppler}

velocity-meter LDV) technique. The technique is well known and most of the

necessary apparatus is available as standard equipment. _Halliwell

has described one way of adapting _{the LDV to ship science}

(ref. 9, 10 & li] and Kux has _{used the WV in full scale}

measure-ments on ships (ref. 12]. _{The Hamburg tank [HSVA] has taken}

delivery of a WV equipment in the _{autumn of 1978 and Fig. A.2} and A.3 show schematically the _{instrument and the mounting on}

the model, Fig. A.4 shows _{an alternative method to mount the}

instrument

if a big model capable of _{carrying the instrument}

cannot be used. _{This is the method also used by Halliwell.}

The WV-methods seem to have small or no disadvantages and

what is left now is only to develop _{the instrumentation} hard-ware so the instrument can be handled in _{an easy and fast way.}

Scragg, C.A. and Sandell, D.A.: "A statistical Evaluation of Wake Surway Techniques", Proceedings: International Symposium on Ship Viscous Resistance, SSPA, Gôteborg 1978.

Müller, A.: "Comparison of Pitot-Tube and LDA in a Rotational Plow",

Proceedings WA Symposium, Technical University of Denmark,

Copenhagen 1975.

(9] Ralliwéll, N.A.: "Laser Anemometry in Ship Hydrodynamics", The Naval

Architect, May 1976.

(io] Balliwell, N.A.: "A Towing Tank Laser-Doppler Anemometer", The Naval

Architect, July 1978.

[1.1] Halliwell, N.A. and Rizzo, J.E.: "The Application of Laser-Doppler Anemometry in Ship Science't, Proceedings IDA Symposium, Technical University of Denmark, Copenhagen 1975.

[12] Kux, J.: "Application of Laser-Velocimetry to Ship Flow-Field

Measurements ), Proceedings, International Symposium on Ship Viscous Resistance, SSPA, Gothenburg 1978.

Fig.A.l. Comparison between measuring devices.

O _HYDROTYPE 29 e o _o o O

a

AERO-TVPHOT-WIRE 28 o o o o o o o o 27 E

o

2 A

_o

o

A

o

o

a

o

o 25 A

g

..60 .30 0 30 60 POSITION (mm) CYLINDER tI

PHOTO MULTIPLIER

MODEL FREE TO HEAVE AND PITCH

BACI( SCATTERED BEAM

MEASURING POINT

LASER

PLATFORM MOUNTED ON MODEL

Fig.A.2. Principal sketch of a Laser Doppler Velocitymeter (HSVA).

MEASURING POINT MOVED

BY MOVING PLATFORM WITH LASER AND OPTIC

Fig.A.3. Mounting of the LDV on a ship model.

MEASURING POINT MOVED

BY ZOOM -OPTIC

/

/

MODEL FIXED TO CARRIAGE

/

/ 1 /

Fig.A.4. Mounting of the LOV on the towing carriage.