Bilge Vortex scale effect

3 SEP.

A RCHIEF

SYMPOSIUM ON

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

H0VIK OUTSIDE OSLO, MARCH 20. - 25. 1977

"BILGE VORTEX SCALE EFFECT"

By E. Huse

The Ship Research Institute of Norway The Ship Model Tank

Trondheim, Norway

SPONSOR: DET NORSKE VERITAS

PAPER 6/4SESSION i

cij

Lab.

y.

Scheepsbouwkunue

Technische Ho1eschool

BILGE VORTEX SCALE EFFECT.

by

E. Huse

The Ship Research Institute. of.Norwy The Ship Model Tank

SUMMARY.

From theoretical considerations it is tobe expected; that the Sasajiria-Tanaka

tnthod predicts the wake distribution scale effect fairly well for fine ships

and also for full ships with V-shaped afterbody sections. For single-screw

ships with full, U-shaped afterbodies, however, problems of scaling the wake

distribution may be expected due to the formation of bilge vortices.

The present investigation applies boundary layer suction at the aft shoulder

of a hull model with full, U-shaped afterbody sections. In this way a

thinner boundary layer., more. cónsistent with the full scale ship, is obtained..,

and the scale effect of the bilge vortices can be studied.

The cónclusion isthat when going from model to full scale the bilge vortices

move horizontally so that theirdistance from the centre plane of the propeller

disc is reduced by about 25 percent This is about half the motion predicted

by the Sasajima-Tanaka method for the frictional wake contours..

Furthermore, the bilge vortex centres move downward in full scale, a phenomenon

INTRODUCTION.

In the profession of ship model testing one of the main problems has always been, and still is, that the model tests can in general not be conducted at

correct Reynolds number. This means that för instance the boundary layer

thickness on the model is relatively much larger than on the full scale ship.

For the speed and power prognoses this difference can be taken into account

by various methods which are áll basically empirical. The procedure works

fairly well because large amounts of correlation data from ship trials are

at hand.

Turning now from the mean wake to the wake distribution, the situation is

quite different. _{Very little information on full scale wake dïstribution is}

aailable because, of course, such data are very expensive to produce.

However, the scale effect of the wake distribution is very important,

parti-cularly with respect to predictions of propeller induced vibratory forces

(see e.g. references 1 and 2) ad therefore deserves considerable attention.

Certain methods for theoretical calculation df the scale effect of the wake distributions havebeen suggested. They are all baed on rather crude

approximations, and there is a considerable demand for more refined methods

For instance, non of the existing theories seeñi to be able to predict the scale effects of bilge .vortices correctly.

The main purpose of the present paper is tó bring some ñew data on the scale

effect to be expected in connection with bilge vortices produced at the after-body of ships.

THEORETICAL CONSIDERATIONS.

A practical method for correcting the wake distribution for scale effect was

first suggested in ref. 4. This method is based upon the assumption that

the thickness of the boundary layer at the afterbQdy is proportional to the

frictional resistance coefficient. Knowing the difference ïn frictional

resistance coefficients between model and lull scale, basically from empirical data as mentioned above, one may thus correct the frictional part of the

wake distribution after first subtracting the potential part of the wake

distribution which can be determined by special tests. Certain modifications

to this method have been suggested later on, first in ref; 5 where it is suggested that the equi-velocity contours of the frictional wake distribution

are moved, not only towards the center plane, but more in a direction at

right angle to the hull surface. Furthermore, in ref. 6 a procedure has

been suggested which allows a certain degree of non-linearity to be taken into

account. Still, the method is based on acertain relationship between boundary

layer thickñess and frictional resistance. Non of these methods solv the

problem of possible scale effect in connection with bilge vortices.

Bilge vortices are most pronounced on U-shaped afterbodies with rather small

radius of. curvature at the bilges. For such a hull shape, the water flowing

from under the bottom of the hull is unable to follow the sharp curvature

around the bilges in the afterbody. Fig. i shows the flow line pattern of

such an extremely U-shaped afterbody. We see that at the upper part of the

bilge there is a separation zone. The water particles flowing from under

the bottom of the hull here leave the surface of the hull and flow into the

outer part of the propeller disc The region above this separation zone is

filled with water flowing from above, thus creating a downward flow close to

the hull surface as can be seen in Fig i This upward flow in the outer part

of the propeller disc combined with the downward flow in the inner part of

it represents arotationàf the flow into the propeller. This type äf rotation

is called a bilge vortex. The bilge vortex creates an exchange of water in

suçh a way that water particles in the boundary layer are transpOrted ot.it and

away from the hull while water particles fron outside the boundary layer are

transported intO the close vicinity of the. hull surface. These water

parti-des, from outside the boundary layer hav.e relatively large axial velocities.

-3-peak at the center plane in the upper part of the propeller disc. Thus a

certain degree of bilge vorticity may have a beneficialinfluence on the

wake distribution.by reducing the wake peak at the center plane. (See e.g.

ref. 3). If the bilge vortex gets too strong, however, it will in itself represent a wake peak in the outer part of the propeller disc and may cause

trouble in the form of vibratory forces and cavitation. Since it represents

a certain energy loss it will also lead to increased hull resistance.

Since bilge vortices are important with certain beneficial as well as

detri-mental features it is of interest to know what possible scale effects there

may be in connection with it. Applying the Sasajima/Tanaka method (ref. 4.)

directly after for instance determining the potential part of the wake distri-bution by towing the model in reversed direction will lead to the bilge vortex being treated as part of the frictional wake and will thus move towards' the center plane by the same amount. as the equi-velocity contours of the frictional wake. This is of course not necessarily correct because there are other

physical phenomena governing the behaviour of the bilge vortices,.

Direct calculation of the complete boundary layer development and, bilge vortex

formation on the hull surface is today practically impossible. _Numerical

proce-dures for the calculation of boundary layer development generally available

today are only applicable under conditions where there are no flow separation

and no significant cross-flow. Both phenomena may be significant in connection

with bilge vortex formation. If one starts with the model boundary layer and

model bilge vortex as known input data, aiming only at calculating what effect

the reduced boundary layer thickness in' full scale should have o the bilge

vortex, the situation seemsslightly brighter, but only slightly. If the center

of the bilge vortex is well outside the boundary layer one might as a basic

approximation assume that the center line of the bilge vortex will coincide

with the direction of the general potential flow. Starting at the position of

the center of the bilge vortex at the propeller disc on the model one could

possibly calculate thepotential flow line in upstream direction from that point,

ending at a sort, of effective position of generation of the bilge vortex, a '

position which would be somewhere 'around the aft shoulder of the hull. At that

position one would have to estimate how much this point of generation moves

towards'the hull surface as' the boundary layer decreases to a.value corrésponding

to full scale cOnditions. The last stage

_of

=4-the potentiàl flow line and thus end up at a point in =4-the propellèrdisc,

thus seeing how much, the vortex has been displaced toward the propeller center

due to the thinner boundary layer in full scale. During the computational

process along the potential flow line one would have to také the boundary layer of model and full scale, respectively, into account by displacing the hull surface in the way which is quite commonplace in connection with

cal-culation of potential flow outside the boundary layer of solid bodies. The

main problem in this process would be, besides of 'the interaction between

the vortex and the boundary layer, to detemine the effective displacement

of the point of generation towards the hull at the aft shoulder. This could

possibly be obtained from empirical data of the type to be given later in

this report. The author has made no serious attempt at carrying out this

computational process. From the above physical reasoning, one would expect

that the displacement of the bilge vortex center towards the center' plane,

as one moves from model scale to full scale boundary layer thickness, would

be somewhat less than the displacement of the equi-velocity contours of the

frictional wake.

The vertical displacement of the center of the bilge vortex taking place as one moves from model to full scale can possibly be predicted by a physical

reasoning based on application of images. In the case of a vortex with its

axis parallel to a solid wall as shown in Fig. 2 the effect of this wall can

be described as equivalent to 'that of an image vortex. The velocity induced

by this image vortex will tend to displace the original vortex in the downward

direction for the direction of circulation shown in Fig 2 The situation

indicated in Fig 2 corresponds to a bilge vortex in the vicinity of the hull

surface If now the bilge vortex under full scale conditions gets closer to

the hull surface than under model conditions, the image effect will also become

stronger, tending to move the vortex faster downward. ' The cnclusion therefore

is that if the scale: effect lead to a certain displacement of the bilge vortex towards the hull surface in full scale,then it will also move downward ',in full scale compared to the. model case.

SCALE' EFFECT OF BILGE VORTICES, EXPERIMENTAL PROCEDURE.

There are at least three principally different 'procedures for investigation of

measuring the full scale wake ahead of the propeller, comparing, the results

with corresponding model tests. This would immediately seem to be the best

way. However, it is also the niöst expensive way, and the problem of obtaining

accurate measurements in full scale is considerable. A second possibility

is tö run geosirn tests with models from for instance 1 meter length up to the

order of 10 meters or more. The disadvantage of this method is that one

covers only a very limited range of Reynolds numbers, and full scale conditions are still far away.

A third possibility, which has béen applied at The FIorwegian Ship Model Tank consists in simulating, at the afterbody of a model, inflow conditions

corre-sponding to a large range of Reynolds number. Tests with an eight meters long.

hull model were carried out in three stages, first with boundary layer suction

applied so as to reduce the boundary layer thickness in the inflow to the

afterbody of the model, secondly tests were done with artificially increased

boundary layer thickness obtained by fitting wire mesh to decelerate the

water flow at the bow of the model. Thirdly tests were done with the ordinary

naked model. Thus the idea is to simulate boundary layer thicknesses at the

afterbody of the model covering a very large range of Reynolds number from that

of the full scale ship down to a model size much smaller than the eight meter

model.

The technique of boundary layer suction has been applied once before,, ref. 7,

but then on a very small model and with the observations being done far aft of

the propeller disc

TEST PR0GRPJ1 AND INSTRUMENTATION.

For each, of the three cases mentioned above the behaviour of the bilge vprtex

was investigated by means of the. fo1lowin test prog'am:

Measurement of velocity distribution in the bòundary layer at a

section behind the position of boundary layer suction. Wake survey in way of the propeller plane by pitot tubes. Tuft grid test in way of the propeller plane.

All tests were done during towing of model at a speed corresponding to 9.22

Type of ship tanker

Deadweight . about 220.000 TDW

Block coefficient 0.81

Ship length 312 m

Ship breadth. 46.4 m

Draught at condition tested, AP 10.0 ni

Draught at condition tested, FP 7.8 ni.

Propeller diameter 8.8 m

Model scale ratio 1/40

The afterbody lines plan and sections are shown in Fig. 3. The. sections of

the model have, been made rather extremely U-shaped and the radius of curvature

at the afterbody bilge has been made rather small. In this way one obtains

a very significant bilge vortex formation, much more pronounced than one will find on most s,hps.

Fig. 4 shows the position of the area over which boundary layer suction takes

place. This area is çovered by a perforated steel plate flush with the surface

of. the model. The section-wise extension of this plate is along the girth from

30mm below the still water line WL I on both sides of the hull, model. The

longitudinal extension of the plate is 200 mm, at a position between sections

2 and 2. This plate forms the outer wall of a closed box fitted inside the

model. From this box. water is pumped out at a rate of 2570 liters per minute,

model scale. ..

At Section 2 (see Fig. 4) altogether 9 velOcity probes wer fitted for measuring

the velocity distribution in the boundary layer and outside it. Each probe

conststs of twO tubes measuring total head añd static pressure, each tube being 2 mm outer diameter.

Wake surveys in way of the propeller plane were carriéd but by means of ordinary

Prandtl tubes during towing of the model

Tests with tuft grid were also carried out in way of th.e prope.11ér plane. The distance between tùfts is 15 mm in horizontal as well as vertical direction.

times from behind. As an example Fig. 5 shows two photographs taken wïth and without boundary layer suction, respectively.

The Prandtl tubes have been calibrated for various angles of inflow, so that

the tuft grid photographs in combination with the Prandtl tube readings. give

the complete 3-dimensional wake distribution,.

PRE5ENTATION AND .DISCUSSION OF RESULTS.

Fig. 6 a, b and c show the velocity distribution measured t Section 2, with

wire meshes at the bow, for the naked model, and with boundary layer suction

applied. It can be seen that the wire meshes at the bow have produced a

vèlocity distribution which is not a very realistic simulation of boundáry

layer flow. The flow has been retarded at too large distances from the hull.

This is due to the particular mesh configuration chosen, consisting of

altogether 4 meshes, extending at rightangles from the hull surface to

distance vàrying from.3 to 15 cm.

Due to the unrealisticflowfield the results obtainedwitn wire meshes at the

bow will nòt be stressed so much in the subsequent disçussion. As a

reconimen-dation for possiblefùture application of this testing technique, the author

would suggest to fit wire meshes to the surface of the model covering for

in-stance the complete forward half of the hull This might produce a flow at

the afterbody, simulating in a more satisfactory way the flow around a very

snial i model.

Anyhow, the velocity distribution obtained by boundary layer suction is according

to Fig 6 realistic enough, and this is naturally the most important case to

be compared with the naked model.

Fig.7 a, band c show the axial wake distributjon with wire meshes at the bow,

for naked model, and with boundary layer suction, respectively The wake value

-8

where

VA = axial inflow velocity, measured by Prandtl tube in combination with the tuft grid,

VM = model speed.

When comparing Figs. 7 b and c we see that the boundary layer suction has

displaced the wake contours of w = 0.7, 0.6, 0.5 and 0.4 in the upper part of

the propeller disc in such a way that their distance from the centerplane has

been reduced by nearly 50 percent. This .s fairly accurately the same

dis-placement as one obtains when predicting the full scale wake of this ship from

the model wake by the Sasajima-Tanaka method. This indicates that by the

boundary layer suction we have succeeded in establishing a flow field around

the afterbody which is fairly similar to that of the full scale ship.

The effect of boundary layer thickness on the position of the bilge vortices can now be seen from the tuft grid photographs, for instance shown in Fig. 5.

Due to a certain flow instability the position of the centre of the bilge vortex

shows some fluctuation. Fig. 8 shows the positions of the bilge vortex centre

for the three different test conditions. The positions plotted in Fig. 8 are

mean positions obtained from a number of tuft grid photographs taken at each

test condition. We see that the boundary layer suction has reduced the distance

of the bilge vortex centre from centre plane of the hull by about 25 percent,

compared to the naked model case. This corresponds to about half the

displace-ment predicted by the Sasajima-Tanaka method. Furthermore we see that the

boundary layer suction has moved the bilge vortex centre downward,which is in

accordance with our theoretical considerations.

CONCLUSIONS.

When going from model to full scale, the centres of the bilge vortices of the

large tanker tested move horizontally so that their distance from the centre plane i

the propeller disc is reduced by about 25 percent. This is about half as much

as the iso-wake contours of the viscous wake would move according to the

Sasajima-Tanaka method.

Furthermore, a pronounced downward displacement of the bilge vortices has also been observed, a phenomenon which can be explained by theoretical considerations.

When calculating the wake distribution scale effect correction for ships

with significant bilge vortex formation, the bilge vortices should be

con-sidered as a separate contribution to the total wake distribution. For

a complete scale correction procedure they should be displaced downward and

toward the centre plane. The results of the present investigation may be

taken as approximate guidelines for the degree of displacement, but similar investigations on more models should be carried out to establish more general criteria.

REFERENCES.

Ruse, E., "Cavitation Induced Hull Pressures, Some Recent Developments

of Model Testing Techniques", NSMB Symposium on High Powered Propulsion

of Large Ships, Wageningen 1974 (Also available as NSFI Report R-35.74.

Wereldsma, R., "Dynamic Behaviour of Ship Propellers", Internationale

Periodieke Pers, Rotterdam 1965. (Doctoral Thesis, Delft Technical University).

Huse, Erling, "Effect of Afterbody Forms and Afterbody Fins on the Wake Distribution of Single-Screw Ships", NSFI Report R-31.74, 1974.

Sasajima, H. and Tanaka, I., "On the Estimation of Wake of Ship", 11th ITTC, Tokyo 1966.

Hoekstra, M., "Prediction of Full Scale Wake Characteristics based on Model Wake Survey", Symposium on High Powered Propulsion of Large Ships,

Wageningen 1974.

Dyne, G., "A Study on the Scale Effect on Wake, Propeller Cavitation and

Vibratory Pressure at Hull of two Tanker Models", Transaction SNAME, Vol. 82, 1974.

Tagori, T. et al., "An Experimental Study on the Stern Bilge Vortices of

Full Hull Form", Selected Papers from Journal of Soc. Nay. Arch. of Japan, Vol. 4, 1970.

t

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Fig. 1.

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Fig. 2. Effect of "image" vortex.

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downward motion due to image vortex

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POSITIONS OF TUBES ON MODEL.

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Position of boundary. 'layer s:ucton

-and velocity measurement probes..

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boundary layer suction applied, upper

photograph, and without, lower photograph.

o o 1.0

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20

40

60

80

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distance from huLl surface

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Fig. 6a. Velocity versus distance from surface of

hull model at Section 2. O naked model

( wire meshes fitted at bow boundary layer suction

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Onaked model

X wire meshes fitted at bow L. boundary layer suction

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160°

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600

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