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DEPARTMENT OF DEFENCE

DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION AERONAUTICAL RESEARCH LABORATORIES

AERODYNAMICS NOTE 376

THE WAKE VELOCITY AND RUDDER FORCE

ON A TANKER SHIP MODEL

by N. MATHESON

Bb!occk vm

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Af:""

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r L) A T Li M i SUMMARY

A propeller tunnel had been fitted to a 33,000 t (32,500 ton) bulk carrier to cure

cavitation, vibration and noise problems occurring previously. However, the ship's masters reported that the propeller tunnel had reduced manoeuverability especially when operating at low speed in shallow water. From a series ofwind tunnel tests with a model, a set of

vortex generators was developed which improved the flow over the stern and increased the side force produced by the rudder. It is anticipated that fitting corresponding generators

to the ship, together with the propeller tunnel and a 03 m (Ift) extension to the rudder,

will improve the manoeuverability compared with the original hull, when the rudder is set

at an angle greater than 25° with a 0 9 m (3 ft) underkeel clearance, and greater than

12° in a deep sea.

POSTAL ADDRESS: Chief Superintendent, Aeronautical Research Laboratories, Box 4331 P.O., Melbourne, Victoria, 3001, Australia.

A R-001-275 TEcJffiISCHE UNIvEftsrr tabaratodum voor Scheepuhyd,omechafljca Archief

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CONTENTS Page No. NOMENCLATURE INTRODUCTION i EXPERIMENTS EQUIPMENT 2

EXPERIMENTAL RESULTS FOR THE MODEL 3

4.1 Bare hull 3

4.2 Model fitted with a propeller tunnel 4

4.3 Model fitted with vortex generators 5

4.4 Model fitted with larger rudder, vortex generators, and the propeller tunnel 6

4.5 Model resistance 6

4.6 Model yaw tests 7

APPLICATION OF MODEL RESULTS TO THE FULL SCALE SHIP 8

5.1 Scaling of the vortex generators and rudder extension 8

5.2 Additional power required 8

5.3 Predicted manoeuvering characteristics of the ship 9

CONCLUSIONS 9

REFERENCES 10

APPENDICES

li

FIGURES 31

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NOMENCLATURE b Thickness of vortex generator CD D/(4pU2S) = Resistance coefficient Cy Y/(pU2S) = Side force coefficient

D Resistance

h Height of vortex generator Length between perpendiculars

¡ Length of vortex generator

PD Power delivered to propeller

PE Effective power R Radius of propeller

RN ULpp/v = Reynolds number

r

Radius from centre of propeller shaft, in the propeller plane,

at which velocities were measured S Surface area of model (excluding rudder)

U Freestream velocity

u Axial velocity component of the flow in the propeller plane Y Side force

Angle of incidence of rudder measured from the centreline of the modelpositive when trailing edge of rudder is moved to starboard

ß Model yaw anglepositive when stern of model is moved

to port

Cy Increase in Cy

û Angular position in the propeller plane at which axial velocities were measured. (Origin at top dead centre and measured as positive in a clockwise direction when viewed from aft) y Kinematic viscosity

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INTRODUCTION

Cavitation, vibration, and noise problems have occurred on a 33,000 t (32,500 ton) single screw tanker recently built in Australia for coastal operation. The ship is 173 m (566 ft) long,

has a 250m (820ft) beam and a 98 m (322 ft) draft when fully laden, and a service speed

of 16 kn. The problems were attributed to the propeller working in an uneven velocity distri-bution, and it was considered that they could be overcome by making the wake velocity more uniform. To do this, a propeller tunnel was designed and fitted to the ship. However, the ship's masters complained that under some conditions they now had difficulty in steering the ship. In particular, in the fully laden condition with underkeel clearances between approximately I m

(33 ft) and 4m (l3 I ft), difficulty was experienced in manocuvering at speeds between about

two and six knot. The loss of steerage was more severe when the ship was decelerating between

six and two knot under following or quartering sea conditions. Although procedures were developed which partly overcame these reported adverse steering characteristics it was feared that an accident might occur, especially during berthing, where these conditions commonly

exist and where maximum manoeuverability is usually required.

The Aeronautical Research Laboratories were asked by the owners of the ship to investigate the problem and to try and develop a simple method, possibly using vortex generators, to modify

the wake velocity and improve the steering characteristics of the ship without major structural

modifications.

EXPERIMENTS

The investigation was made using a reflex model of the hull tested in the low speed wind tunnel. The experiments were carried out in a number of separate parts. First, to determine the effects of the propeller tunnel, the axial velocity distribution of the flow through the propeller

plane and the forces generated by the rudder were measured with the hull as originally designed,

and then with the model fitted with the propeller tunnel. Second, a number of tests were made to try and develop a set of vortex generators which would improve the velocity of the fluid into the propeller and over the rudder. The vortex generators must create a velocity distribution of

the flow into the propeller which will produce satisfactory vibration and cavitation characteristics

as well as increasing the manoeuvering forces generated by the rudder.

The model tests were initially carried out in the 'deep water' condition, and then with

simulated underkeel clearances of 37 m (12 ft), and 09 m (3 ft). Deep water tests with vortex

generators were necessary in order to make sure that the velocity distribution of the flow into

the propeller would minimize cavitation and vibration. This was important because the ship

operates predominantly at its design speed in deep seas.

Surface flow visualization, wake surveys, resistance and side force (generated on the model by placing the rudder at incidence) measurements were made to investigate the steering, cavitation

and vibration problems. Some tests were also made with the model set at various small yaw angles to determine the effect of the propeller tunnel on stability. The wake survey, side force, and flow visualization tests were all made at a Reynolds number of approximately 10 based on model length. Yaw tests were carried out at a slightly lower Reynolds number of mately 8 x 106. Resistance tests were made over a range of Reynolds number from

approxi-mately 25 x 106 to 1 5 x 10v. The rudder was not fitted to the model during the resistance

or yaw tests. All of the experiments were made with the model corresponding to amaximum

draught of 98l m (322 ft) for the full scale ship, and without a propeller. Froude number

effects were not simulated since a reflex model of the below waterline section of the hull was

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Manoeuvering and stability tests, such as Dieudonne's spiral manoeuvre, the zig zag

manoeuvre and the turning circle test, usually employed to demonstrate the steering charac-teristics of models tested in manoeuvering basins (or the full scale ship in a seaway), could not

be carried out since the model was rigidly mounted in the wind tunnel with its longitudinal axis

along the centreline of the working section. However, it was considered that the tests proposed

would be sufficient for present purposes.

3. EQUIPMENT

The investigation was carried out using a 1/5933 scale reflex model of the below-waterline

section of the hull mounted in a 27 m (9 ft) x 2 I m (7 ft) low speed wind tunnel on an external

mechanical drag balance.

The principal ship particulars from which the model was scaled are given in table 1. Section lines, and the stern arrangement with the propeller and rudder fitted are shown in figures 1 and 2

respectively. The propeller tunnel as originally designed is shown in figure 3. After the tunnel

had been fitted to the ship it was found that although the actual dimensions of the tunnel appeared

to be correct, the aft end of the tunnel was lower than originally intended as shown in figure 4.

TABLE i

Principal ship particulars

(a) Dimensions:

Length overall

l726 m (5660ft)

Length between perpendiculars

136m (5365 ft)

Lengthsections 0 to 10 1628 m (5340 Lt)

Sections apart 1628 m (534ft)

Length at 9 15 m (30 Lt) draft waterline l668 m (5472 ft)

Breadth moulded 25O m (82O ft)

Depth moulded to upper deck l29 m (42.3 ft)

Load draft maximum

98l m (322ft)

Rise of floor 0.15 m(O.5Oft)

Radius of bilge 244 m (8M ft)

Load displacement at maximum draft 33,000 t (32,500 ton)

Wetted surface coefficient to 9 15 m

(30 ft) draft waterline 6 151 Block coefficient to 915 m (30 ft)

draft waterline

080l5

Type of bow Bulbous

(b) Machinery:

Two 16 cylinder turbocharged Crossley SEMI Pielstick PC2V. Maximum 8,000 BHP (Metric) at 520 R.P.M., coupled to a single

shaft.

(c) Propeller:

Four blade, controllable pitch, 6MO m (l969 ft) diameter, 140

R.P.M. at service speed.

(d) Speed:

Full load service speed 16 kn.

(e) Stern arrangement:

Closed aperture, semi balanced rudder, chord 396m (13 ft), span 648 m (21 25 ft).

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To correctly simulate shallow water conditions experienced by the ship it would be necessary

to use a moving false floor and a moving false ceiling (moving ground boards) mounted in

the wind tunnel below and above the model respectively. However, since the tunnel is not equipped

with such a moving boundary system, a fixed false floor and ceiling were used to approximate underkeel clearances of 37 m (12 ft) and O9 m (3 ft). Each board was placed at a very small divergent angle to the flow in an attempt to allow for the boundary layer growth.

Vane type vortex generators were selected for the tests because they have been found to perform very well under the conditions likely to be experienced on a ship hull1'2'3'4'5. While these generators are effective over a wide range of conditions, a number of tests are usually

required to refine their design. All of the generators had a triangular planform and were attached at right angles to the surface of the model at about two-thirds of their length aft of the upstream tip. Local axial velocities in the plane of the propeller were measured with a rake of pitot probes

connected to a multi-tube manometer. The resistance of the model and the side force generated by the rudder were measured on an external mechanical drag balance. French chalk mixed with

kerosene was used for the surface flow visualization tests. Care must be employed in interpreting the resulting flow patterns because gravity forces can become significant.

4. EXPERIMENTAL RESULTS FOR THE MODEL

In the following sections, details of the test results are given for the model with and without

the propeller tunnel, and with various vortex generator systems. The results are given for the

model with simulated full scale underkeel clearances of O9 m (3 ft), 37 m (12 ft) and in a

deep sea. 4.1 Bare hull

Initially, the axial velocity distribution of the flow in the propeller plane, the surface flow pattern, the side force generated by the rudder, and the resistance of the model were found for

the hull as it was originally designed.

The axial velocity distribution of the flow into the propeller at four radius ratios of

nR = I

23, 096, 068 and 04l are shown in figure 5 for the deep sea condition, and in figures

6 and 7 for simulated underkeel clearances of 37 m (12 ft) and 09 m (3 ft) respectively. The experimental results are tabulated in appendix I.

In the deep sea case, the axial velocity distribution of the flow through the propeller disc showed the usual low values near the top and bottom dead centre position associated with a

single screw ship which has a closed aperture. At nR = I 23 the velocity ratio varied from 026 at 0 = 00 to 093 at O = ± 100°, and then remained constant to 0 = ± 180°. Near the tip of the propeller disc at nR = 096 the velocity ratio varied gradually from 032 at 0 = 0° to 092 at O = ±120°, but decreased abruptly from 084 at 0 = ± 1600 to O24 atO = ± 1800. Further

towards the centre of the propeller disc at nR = 068 the velocity ratio variation was much

smaller but there were a number of 'humps' and 'hollows' in the distribution. Near the hub, at

nR = 04l the velocity ratio varied from 035 at O = 00 and increased to a maximum value of 040 at O = ±20° before decreasing through a number of small 'humps and hollows' to 008 at O = +180°.

There was little difference between the corresponding velocity distributions for the deep

sea and 37 m (l2ft) clearance conditions at radius ratios of l23 and 096. At nR = 068

differences in the velocity distribution occurred near the top dead centre where low values occurred for a 37 m (12 ft) clearance, and at O = +60° where a 'trough' in the velocity

distri-bution occurred in the deep sea condition. At r/R = 04l for O between +(0° to 60°) much

higher velocities were produced in a deep sea than with a 37 (12 ft) clearance, although similar

results were obtained for other values of 0. However, taken overall, the axial velocity distributioins for both cases were very similar.

Comparison between corresponding results in figure 5 and figure 7 indicates that the axial velocities with a 09 m (3 û) clearance are much lower than the axial velocities in a deep sea. Over the top segment of the propeller disc reverse flow or separation occurred with a 09 m

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blade tip. However, the velocity of the flow over the lower segment of the propeller disc, for O between approximately +(160° to 180°) was somewhat higher for a 09 m (3 ft) underkeel clearance than in a deep sea.

Overall, the velocity distributions indicate that lower control forces will be produced by the rudder with a 09 m (3 ft) underkeel clearance compared with both a 3-7 m (12 ft) clearance and a deep sea where similar control forces are expected to be produced.

The surface flow patterns over the stern of the model shown in figure 8 confirm the relative

differences in the axial velocity distributions of the flow in the plane of the propeller. It should be noted that the patterns were formed on the upper section of the reflex model and that the

gravity force on the flow visualization fluid acts from the keel to the waterline. In all three cases

there appears to be some separation of the flow from the surface of the model. With deep seas, separation mainly occurs below the propeller shaft and produces low axial velocities in the propeller disc for O between +(160° to 180°). For a 3-7 m (12 ft) clearance the separation region is approximately equally located above and below the propeller shaft, but for a 0-9 m

(3 ft) clearance the separation area is greatest above the propeller shaft. In addition, the separation

region extends much further upstream with a 0-9 m (3 ft) clearance than with a 3-7m (12 ft)

clearance or a deep sea, and is the cause of the reverse flow found in the propeller plane.

The side force coefficients generated by placing the rudder at various angles of incidence are shown in figure 9, and tabulated in appendix 2. The results in figure 9 are the average coefficients

found by placing the rudder at equal angles of incidence to port and starboard. At a rudder angle of 20° the side force coefficient for a 3-7 m (12 ft) underkeel clearance was 6% greater than in a deep sea, but, with a 0-9 m (3 ft) clearance the side force coefficient was only 39% of that produced in a deep sea. This large reduction in side force coefficient caused by the rudder

working in a low velocity field might lead to manoeuvering problems in shallow Water. However, because of the interference effects caused by the boundary layer on the fixed ground boards, the

side force coefficients measured for a 0-9 m (3 ft) clearance may be lower than if the correct conditions had been simulated, for instance, by using moving ground boards. Comparable results between deep and shallow underkeel clearances therefore need to be interpreted with

caution.

4.2 Model fitted with a propeller tunnel

The axial velocity distributions for the model fitted with the designed propeller tunnel, and

with the propeller tunnel fitted to the ship are shown in figures 5, 6 and 7 for the deep sea, 37 m (12 ft) and 09m (3 ft) underkeel clearance conditions respectively. The experimental results are tabulated in appendix 3.

In a deep sea, and with a 37 m (12 ft) underkeel clearance there was little difference between

the velocity distributions for each propeller tunnel. However, with a 0-9 m (3 ft) underkeel clearance the velocity of the fluid through the propeller disc was slightly lower for the tunnel as originally designed. Slightly smaller sideforce coefficients were therefore expected with this tunnel fitted to the model.

The axial velocity ratios for the propeller tunnel fitted to the model in a deep sea, and with

a 37 m (12 ft) underkeel clearance were greater than those for the bare hull over the outer region

of the propeller disc for O between approximately ±(0 to 60°). Over the inner section of the propeller disc there was no improvement for O between ±10°. However, for a 0-9 m (3 ft) underkeel clearance, the reverse flow region which occurred near the hub in the upper segment of the propeller disc was virtually eliminated by fitting the propeller tunnel. In each case, there was little difference between the axial velocity distributions over the lower part of the propeller

disc with the propeller tunnel fitted compared with the bare hull. Overall, the velocity distributions were more uniform with the propeller tunnel fitted.

The surface flow patterns over the stern of the model with the propeller tunnel fitted are

shown in figure lO. No significant difference could be detected between the surface flow patterns

for the two propeller tunnels. The flow pattern for the model in a deep sea was similar to the corresponding pattern for the bare hull, but with a 37 m (12 ft) clearance there was a slightly smaller separation region above the propeller shaft. For a 0-9 m (3 ft) underkeel clearance, there was little difference between the flow patterns obtained for the bare hull and with the

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propeller tunnel fitted. In this case the surface flow pattern did not reflect the significant

improve-ment in the axial velocity distribution of the flow in the propeller plane found from the wake

survey.

The side force coefficients found for the model with each propeller tunnel are plotted with the results for the bare hull in figure 9. The experimental results are tabulated in appendix 4. The percentage change in the side force coefficients is listed in table 2 for the model with the rudder at an angle of incidence of 200; the result with the "as fitted" propeller tunnel is used

as the basis for comparison for each underkeel clearance. In a deep sea the "as designed" model

propeller tunnel produces slightly greater side force coefficients than the "as fitted" tunnel however, the reverse occurs in shallow water. In each case fitting a propeller tunnel increases the side force coefficients compared with the bare hull. The greatest improvement occurs with

the 09 m (3 ft) clearance. This is in agreement with the wake survey results where a much greater

relative increase in velocity was produced in the propeller plane for a 09 m (3 ft) clearance than for a 37m (12 ft) clearance or a deep sea.

TABLE 2

Percentage change in the side force coefficients with the rudder at 200 incidence

(The results for the model with the propeller tunnel as fitted to the ship are used as the basis

for comparison)

4.3 Model fitted with vortex generators

The propeller tunnel was removed from the model and a series of tests were made with a number of different sets of vortex generators attached to the stern. The size and location of the

vortex generators was constrained so that they did not protrude beyond the maximum beam and

draught limits of the model. This reduces the possibility of accidental structural damage to the

generators on the ship especially when it is operating in shallow channels.

Increases in the side force coefficient of up to 45% were achieved (compared to the model with the propeller tunnel fitted) by increasing the velocity of the flow in the regions O

to 40°) and O = ±(160° to 180°). However, overall, the axial velocity distribution in the wake was less uniform than obtained with the propeller tunnel because large increases in the axial

velocity were also produced for O = +(50° to 150°). These high velocities could lead to increased

vibration and Cavitation. The use of vortex generators alone was therefore not considered

appropriate.

The propeller tunnel corresponding to that fitted to the ship was reattached to the model and further tests carried out with vortex generators fitted over the stern. While improvements

Model configuration % Change in Cy Deep sea 37 m (12 ft) clearance 09 m (3 ft) clearance Barehull

Designed propeller tunnel

Fitted propeller tunnel Fitted propeller tunnel plus

four vortex generators

Fitted propeller tunnel, plus

four vortex generators,

plus 03 m (I ft) addition to trailing edge of rudder

67

+25

Base (Cyzzzzl2OXlO4)

+200

+3l6

9i

31

Base (Cyoo131X104)

+153

+267

189

38

Base

(Cy53x104)

+l69

±246

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disc could be achieved, the overall effect was to make the velocity distribution less uniform. This increased non-uniformity was mainly caused by attempts to improve the velocity through

the upper section of the disc, Effort was therefore concentrated on using vortex generators to

increase the velocity of the flow through the lower section of the propeller disc. While a significant improvement in the axial velocity of the flow to the lower section of the rudder could be achieved

by using a free hanging (open aperture) rudder instead of a solepiece, this was not acceptable as it would involve major structural modifications. The axial velocity distributions for the most

suitable vortex generator system found are shown in figures II, 12, and 13, for the model corresponding to deep sea conditions, 37 m (12 ft) underkeel clearance and a 09m (3 ft)

underkeel clearance respectively. The experimental results are tabulated in appendix 5. The size and location of these vortex generators are shown in figure 14. The choice between the different vortex generator systems was based on a compromise between the uniformity of velocity

distri-bution of the flow into the propeller and the increase in side force produced by the rudder.

In all three cases, the low velocity over the lower segment of the propeller disc was significantly improved. It was considered that the changes in the velocity distribution produced by the vortex generators would not have any adverse effects on stern vibration or propeller cavitation.

The surface flow patterns obtained with the vortex generators fitted to the hull are shown in figure 15. These flow patterns show that the vortex generators have reduced the separation region over the lower section of the stern near the keel compared with the propeller tunnel alone as shown in figure 10. In addition, comparison of the flow patterns over the rudder in figures 10 and 15 shows that the vortex generators have reduced the large component of the

velocity of the fluid towards the keel which occurred when the propeller tunnel alone was fitted to the model.

The side force coefficients for the model fitted with vortex generators are shown in figure 9.

The experimental results are tabulated in appendix 6. As indicated in table 2, with the rudder set at 20° incidence, fitting the vortex generators produces a 20% increase in the side force coefficient in a deep sea, and 15.3% and 16.9% increase for underkeel clearances of 3'7 m (12 ft) and 0'9 m (3 ft) respectively. While a 17% increase in side force is significant for the most important case of 0'9 m (3 ft) underkeel clearance, it was not considered sufficient to

completely overcome the problem of lack of manoeuverability in shallow water. 4.4 Model fitted with larger rudder, vortex generators, and the propeller tunnel

To try to further increase the side force generated by the rudder an extension equivalent to 0'3 m (1 ft) full scale was added to the trailing edge of the rudder. For the ship, this would essentially consist of a flat plate welded to the rudder. A larger extension would have been

preferable, but could not be allowed for reasons of classification.

The side force coefficients for the model with the propeller tunnel, vortex generators, and the addition to the rudder are plotted in figure 9 with the previous results. The experimental

results are tabulated in appendix 7. Table 2 shows that the side force coefficient for the important

0'9 m (3 ft) underkeel clearance case is now 25% greater than for the model corresponding to the ship with the propeller tunnel. With a 37m (12 ft) underkeel clearance, and in a deep sea, the side force coefficients are now 27% and 31% greater than originally obtained.

4.5 Model resistance

The resistance of the model fitted with the propeller tunnel, and with vortex generators plus the propeller tunnel, was measured over a range of Reynolds number using a mechanical drag balance. The results were corrected for the interference effects of the shroud around the mounting column, blockage and the longitudinal pressure gradient in the tunnel. The resistance coefficients are plotted in figure 16 and tabulated ¡ri appendix 8.

The increase in resistance coefficient for each case, compared with the result for the model with the propeller tunnel corresponding to the tunnel fitted to the full scale ship, is given in table 3 for a Reynolds number of l0. There was virtually no difference between the resistance coefficients for the model with the propeller tunnel as designed and as fitted. However, adding the vortex generators produced a small increase in the resistance of the model which varied from 2% in a deep sea condition, to 1 3% with a 0'9 m (3 ft) underkeel clearance. As expected, the resistance of the model in shallow water was much greater than in a deep sea.

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TABLE 3

Percentage change in the resistance coefficients for the model at RN = IØ7

(The results for the model fitted with the corresponding propeller tunnel on the ship are used

as the basis for comparison)

4.6 Model yaw tests

Fitting a propeller tunnel, or vortex generators, to the stern of the model will increase the directional stability since these appendages increase the effective area in the vertical plane through the longitudinal centreline. To determine this stabilizing effect the side force on the

model was measured at yaw angles from 00 to +8° in the deep sea case, and at yaw angles from

00 to ±40 with simulated full scale underkeel clearances of 3 7 m (12 ft) and 09 m (3 ft). Physical

constraints prevented the model being tested at higher yaw angles.

The side force coefficients for the model at various constant yaw angles both with and without

the propeller tunnel, and with the propeller tunnel and vortex generators attached to the stern, are plotted in figure 17 and tabulated in appendix 9. The results in figure 17 are the average

coefficients found by placing the model at equal yaw angles to port and starboard.

The results show that the sideforce coefficients for the model with the propeller tunnel, and with both the propeller tunnel and vortex generators, are approximately the same for each of the three underkeel clearance cases tested. This indicates that fitting vortex generators has

little effect on the directional stability of the model. However, fitting the propeller tunnel

increases the sideforce coefficients compared with the bare hull. Within the rather narrow limits

of the tests it appears that above about one degree yaw the increase in side-force coefficient caused by fitting the propeller tunnel is approximately constant with angle of yaw for each

underkeel clearance. These sideforce increments are listed in table4. As shown in figure 17, the

side force coefficient is much greater with a small underkeel clearance than in the deep sea

condition.

TABLE 4

Increase in sideforce produced by fitting the propeller tunnel to the model

7 Model Configuration % Change in CD Deep sea 3 .7 m (12 ft) clearance 09 m (3 ft) clearance Fitted propeller tunnel

Designed propeller tunnel

Fitted propeller tunnel plus

four vortex generators

Base (CD=O.00404)

00

+20

Base (CD=O 00552)

04

+1 8 Base (CD=O 00602)

00

±13

Underkeel clearance Increase in model sideforce (Cy) Deep sea

37m(l2ft)

09m(3ft)

25 X l0

28 x l0

32x 10

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Assuming that the increase in sideforce produced by fitting the propeller tunnel acts at the

propeller tunnel, then an additional stabilizing moment will be produced which resists any

change in heading. There is also a stabilizing effect caused by the increased resistance with the propeller tunnel fitted. However, at a yaw angle of 4°, this latter effect is only about 5% of that produced by the increase in sideforce, and is neglected in the following discussion.

To counter the increased stabilizing moment created by the propeller tunnel an additional force, or disturbing moment, must be produced by the rudder to maintain the same turning ability. This, of course, can be achieved by increasing the rudder incidence. For example, in the worst case, with a 09 m (3 ft) clearance, figure 9 indicates that a rudder incidence of 20°

produces a sideforce coefficient of 43 x When the propeller tunnel is fitted the sideforce

coefficient produced by the rudder at the same incidence is increased to 53 x 10, an increase

of I 0 x l0-. However, the propeller tunnel has a stabilizing influence on the vessel, and table 4

indicates that the sideforce coefficient produced by the rudder must be increased by 3 2 >< l0 to maintain the same turning moment. From figure 9, this larger sideforce coefficient of 75 x 1 O

can be achieved by increasing the rudder incidence to 28°. Corresponding increases in rudder incidence of only 24° need to be applied for both the deep sea, and 3-7m (12 ft) clearance cases. A similar analysis for other rudder angles can be made using the results in figure 9.

By fitting vortex generators, and adding an equivalent of U-3 m (I ft) full scale to the

trailing edge of the rudder the increase in rudder incidence can be reduced. Again, for example,

consider the 09 m (3 ft) clearance case with an initial rudder angle of 20°, then the sideforce

coefficient is now 66 x 10. To produce the required coefficient of 7-5 x l0- the rudder

would need to be set at only 22°. Rudder angles greater than 25° produce increased sideforce, and hence greater turning moment, than originally obtained for the model without the propeller

tunnel. Likewise, for the deep sea, and 37 m (12 It) clearance cases, increased turning moments will be produced for rudder angles greater than 12° and 14° respectively.

It should be remembered that the previous discussion neglects the dynamic effects of

manoeuvering, such as yaw velocity, yaw acceleration, and cross coupling effects, which can be

important in certain manoeuvres.

5. APPLICATION OF MODEL RESULTS TO THE FULL SCALE SHIP

The results of the model tests presented in the previous sections must now be applied to

the full scale ship. This involves determining the size and location of the vortex generators to be fitted to the ship, the increase in power required in fitting the generators, as well as the

manoeu-vering characteristics produced by fitting the generators and the extension to the trailing edge of the rudder.

5.1 Scaling of the vortex generators and rudder extension

Differences in the flow over the model and ship exist because the ship operates at a Reynolds

number which is approximately one hundred times greater than the Reynolds number at which the model could be tested. Both hull fouling and structural roughness cause differences in the flow over the ship compared with the flow over the smooth model tested in the wind tunnel. In addition, other factors not represented in the model tests, such as propeller action,

wave-making, and ship motions also influence the real flow. Taking all of these factors into account3'5, it was nevertheless estimated that the vortex generators and the size of the addition to the trailing

edge of the rudder should be geometrically scaled from the model to the ship. The location and

size of the most suitable set of vortex generators described previously in sections 4.3 and 4.4 are

shown in figure 18 for the full scale ship. In addition to the vortex generators, as described in section 4.4, the trailing edge of the rudder should be extended aft by 0-3 m (1 ft) on the ship.

5.2 Additional power required

Fitting vortex generators to the hull will require an increase in power to be delivered to the

propeller to maintain the service speed of 16 knot. Unfortunately, the propulsion factors

necessary to determine this increase in power cannot be found from tests in the wind tunnel. However, in order to gain some indication of the extra power required, a very simple approach

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was adopted, where it was assumed that the alteration in the wake fraction, and the increase in resistance coefficient produced by fitting the vortex generators, were the only factors contri-buting to the increase in power5. In addition, it was assumed that these factors remain constant

and that they are directly applicable to the ship fitted with vortex generators. Using this method,

it was estimated that fitting the vortex generators to the ship with the propeller tunnel would require an increase in delivered power of 3% to maintain 16 knot in a deep sea.

5.3 Predicted manoeuvering characteristics of the ship

The actual turning characteristics of the ship cannot be predicted from data obtained

from the wind tunnel tests. However, the changes in manoeuverability which occur when the ship is modified in the same way as the model can be estimated from the wind tunnel data. A

complete picture of the changes which occur cannot be obtained since the dynamic effects (yaw velocity, yaw acceleration, and cross coupling effects) could not be simulated in the model tests.

Nevertheless, after considering the effects that these factors are likely to have on manoeuver-ability, it was estimated that the addition of the propeller tunnel, vortex generators, and the

extension to the rudder, would produce the same percentage changes in the side force coefficient on the ship as on the model. Therefore, fitting the propeller tunnel, vortex generators and rudder

extension to the ship can be expected to improve manoeuverability, compared with the bare hull, when the rudder is set at an angle greater than 25° and the underkeel clearance is 09 m (3 ft). In a deep sea, and with a 37 m (12 ft) clearance, increased manoeuverability can be

expected for rudder angles greater than 12° and 14° respectively.

6. CONCLUSIONS

The following conclusions are drawn from the wind tunnel tests.

Compared with the bare hull, fitting the propeller tunnel to the model produced a more

uniform axial velocity distribution of the flow into the propeller by increasing the velocity

in the upper region of the propeller disc. In addition, the tunnel increased the side force coefficients generated by the rudder by approximately 7% for a simulated deep sea,

10% for a simulated underkeel clearance of 37 m (12 ft), and by 23% with a simulated clearance of 09 m (3 ft).

For small underkeel clearances, the side force coefficients for the model fitted with a propeller tunnel as fitted to the ship were slightly greater than those produced with the

propeller tunnel as originally designed. However, the reverse occurred in simulated deep

waters. Both propeller tunnels produced similar axial velocity distributions of the flow in the propeller plane.

A set of vortex generators was developed for use with the model fitted with both the propeller tunnel and an addition to the trailing edge of the rudder of 03 m (1 ft) full scale. Compared with the model fitted with the propeller tunnel alone, the addition of

the vortex generators and the extension to the rudder increased the side force coefficients produced by the rudder by 32% for a simulated deep sea, 27% for a simulated underkeel

clearance of 37 m (12 ft), and by 25% for a simulated clearance of 0-9m (3 ft). The vortex generators also slightly improved the uniformity of the velocity distribution of

the flow through the propeller disc.

Fitting the propeller tunnel to the model produced an increase in directional stability

which was countered to a limited extent by an increase in side force coefficient generated

by the rudder. However, within the range of yaw angles tested, adding to the rudder and fitting vortex generators to the model with the propeller tunnel, increased the side force coefficient (or turning moment) compared with the bare hull, provided the rudder incidence was greater than 25° for a simulated underkeel clearance of 09 m (3 ft), or

14° for a simulated clearance of 37 m (12 ft) and 12° for a simulated deep sea. A similar situation is expected to occur when the vortex generators and the addition to the trailing edge of the rudder are directly scaled and fitted to the ship with the existing propeller tunnel.

The addition of vortex generators to the ship with the propeller tunnel is expected to require an increase in delivered power of 3% for a fully laden ship to maintain 16 knot

(13)

REFERENCES

Lachman, G. V. (Editor)"Boundary layer and flow control". Pergamon Press, Oxford,

London, 1961.

Clements, R. E."The control of flow separation at the stern of a ship model using vortex generators". Trans. R.I.N.A., Vol. 107, 1965.

Matheson, N."Wind tunnel studies of a ship model using vortex generators to improve

wake velocities". Department of Supply, Australian Defence Scientific Service, Aeronautical Research Laboratories, Aerodynamics Note 347, April 1974.

Chang, P. K."Control of flow separation: energy conservation, operational efficiency, and

safety". Hemisphere Publishing Corporation, Washington, London, 1976.

Matheson, N."Further studies on a ship model fitted with vortex generators to improve

the velocity distribution of the flow into the propeller". Department of Defence, Australian

Defence Scientific Service, Aeronautical Research Laboratories, Aerodynamics Note 359, 1975.

(14)

APPENDIX i

Axial velocity component ratios of the flow in the propeller plane of the model (without propeller tunnel or vortex generators)

1.1 Deep sea e (°) u/U

nR = 1 23

r/R = 096

r/R = 068

r/R = 04l

O

026

032

038

035

12

039

0.45

044

038

24 O53 051

044

040

48

067

061

031

033

72

082

076

038

024

96

091

088

060

026

120

093

092

069

026

144

094

093

068

019

168

093

068

031

010

180

094

024

015

009

12

042

042

039

038

24

056

048

0'42

032

48

069

0-50 0-25 0-28

72

0-83 0-68 o-32 0-19

96

0-93 0-85 0-55 O-19

120

0-94 0-91 0-66 0-20

144

0-94

092

0-58 0-13

168

0-94

080

0-30

007

180

0-95 O-24 0-15 0-08

(15)

APPENDIX i (Continued) 1.2 37m (12 ft) Underkeel clearance 12 o (°) u/U r/R = 1-23 r/R = 0-96 nR = 0-68 r/R = O-41

O O-26 O-27 O-26 O-12

12 0-48 0-49 0-40 0-23 30 0-68 0-61 0-48 0-26 48

076

0-68 0-53 0-24 66 0-81

076

0-60 0-24 84 0-87

082

0-68 0-25 102 0-94 0-88 0-73 0-27 120 0-98 0-93 0-76 0-26 138 1-00 0-95 0-73 0-22 156 1-01

094

0-59 0-15 168 1-00 0-74 0-35 0-10 180 0-96 0-28 0-17 0-09

12

0-46

035

0-25 0-10

30

0-71 0-58 0-40 0-18

48

0-80 O-68 0-49 0-21

66

0-86 0-75 O-58 O-22

84

0-90 O-81 0-65 0-23

102

0-95 0-87 0-70 0-25

120

0-98 0-91 0-74 0-23

138

1-00 0-93 0-71 0-19

156

1-01 0-92 0-58 0-15

168

O-99 0-86 O-39 O-il

(16)

1.3 0-9 m (3 ft) Underkeel clearance APPENDIX i (Continued) 6 (0) u/U nR = 1-23 r/R = O-96

r/R = 068

r/R = O-41 O 0O9

ve

ve

ve

12

Oi3

ve

ve

ve

24 0-26 0-07

ve

ve

36 0-38

016

ve

ve

48 0-44 0-25 0-05

ve

60 0-59

037

013

ve

72 0-63

046

023

O-03 84 0-63 0-52 0-31 0-06 96 0-59 0-55

040

0-10 108 0-53 0.55 0-45 0-14 120

046

0-53 0-48

016

132 0-40 0-51 0-46 0-17 144 0-36 0-50 0-42 0-16 156 0-36 0-42 0-37 0-14 168 0-44 0-40 0-28 0-14 180 0-49 0-38 0-30 0-16

12

0-23

ve

ve

ve

24

0-38 0-16

ve

ve

36

054

0-31 0-10

ve

48

0-65 0-47 0-24 0-02

60

0-70 0-59 0-36

008

72

0-71

062

0-44 0-14

84

0-69 0-62 0-49 0-19

96

0-64 0-59 0-52 0-23

108

0-55 0-54 O-53 O-26

120

O-47 0-49 0-52

027

132

O-38 O-45

050

O-27

144

03!

0-41 0-47 0-26

156

O31 O-40 O-43 O-24

168

0-40 0-41 O-37 O-20

(17)

APPENDIX 2

Side force coefficients for the model (without propeller tunnel or vortex

generators) fitted with the standard rudder

Deep sea 3 7 m (12 ft) Underkeel clearance 09 m (3 ft) Underkeel clearance (°) Cy x 1O x (°) Cy X lOE' (°) Cy X 10

00

Oil

00

007

00

014

46

253

92

559

76

139

76

423

l54

-882

123

250

l23

656

219

1313

170

353

170

951

286

1588

219

467

2I9

1255

92

520

286

609

286

l584

154

907

76

161

46

228

2l9

1382

123

278

76

392

286

1797

17O

370

123

643

219

478

170

935

286

620

219

1218

286

1568

(18)

APPENDIX 3

Axial velocity component ratios of the flow in the propeller plane of the model fitted with a propeller tunnel.

3.1 Propeller tunnel as designed

3.1.1 Deep sea 0 (°) u/U

r/R = i 23

r/R = 096

r/R = O68

r/R = 041

O

-

04O

035

O30 12

-

049

047

O35 24

053

051

040

48

065

060

042

040

72

081

O70

036

O3l 96

091

O86

057

028

120

094

091

063

026

144

094

O92

051

O12 168 O84

050

O24

006

180

093

025

021

008

12

-

046

044

032

---24

053

051 04O

48

066

059

043

042

72

083

068

033

032

96

093

085

055

030

120

095

092

065

030

144 0.95

092

055

020

168

09l

074

030

004

180

093

026

021

009

(19)

APPENDIX 3 (Continued) 3L2 3-7 m (12 ft) Underkeel clearance 16 o (°) u/U

r/R = 123

r/R = O-96 r/R = O-68 r/R = O-41

O

-

O-42 O-31

016

12

-

0-49 0-42 0-23

30

-

o-63 0-52 0-33

48 0-77 0-68 0-55 0-35

66 0-80 0-73 0-55 0-32

84 o-86 O-80 O-59 O-30

102 0-94 O-86 O-63 O-29

120 0-98 0-90 0-62 0-25 138 1-00

091

O-56

017

156 1-00

088

O-43 0-11 168 0-96 O-62 0-29 0-10 180 0-93 0-28 0-23 0-10

12

-

O-46 0-40 O20

30

-

O-64 O-52 O-31

48

0-81 0-70 0-55 0-33

66

O-86 0-74

059

O-32

84

0-90 0-80 0-62 0-30

102

0-94 0-86 O-66 O-30

120

0-99 O-90 O-68 O-27

138

1-00 0-92 O-62 O-19

156

1-01 0-89 0-48 0-11

168

0-97 0-68 0-34 0-08

(20)

APPENDIX 3 (Continued) 3J.3 O-9m (3 ft) Underkeel clearance

8 (0) u/U

r/R=1-23

r/R=0-96

r/R=0-68

r/R=O-41

O

-

O-32 O-19

ve

12 0-33 0-23

ve

24

-

0-36

024

0-09 36 0-39 0-21 0-13 48 0-60 0-38 0-21 0-13 60 0-60 0-43 0-26 0-15 72 0-64 0-50 0-31 0-15 84 0-63 0-55 0-36

014

96 0-59 0-57 O-38 O-11 108 0-52 0-55 0-39 0-08 120 0-45 0-53 0-38 0-07 132 0-39 0-51 0-37 0-09 144 o-38 0-49 0-33 0-10 156 0-40 0-43 0-31 0-11 168 0-43 0-36 o-26 o-12 180 0-47 0-26 0-22 O-13

12

0-39 0-26 0-09

24

-

0-43 0-24 0-15

36

-

0-45 0-24 0-15

48

0-65 0-48 0-28 0-15

60

0-66 O-54 0-35 0-15

72

0-69 0-60 0-43 0-18

84

O-67 0-62 0-48 0-20

96

0-61 0-60 0-49 0-20

108

0-54 0-56 0-49 0-20

120

0-46 0-52 0-49 0-19

132

0-37 0-48 0-46 0-19

144

0-32 0-46 0-44 0-20

156

0-33 0-46 0-37 0-19

168

0-43 0-42 0-32 0-16

180

0-46 0-27

023

0-14

(21)

APPENDIX 3 (Continued) 3.2 Propeller tunnel as fitted

3.2.1 Deep sea 18 û (°) u/U

r/R = i 23

nR = 096

nR = 068

nR = 041

O

-

043

037

029

12

-

050

047

O33 24

054

051

O39 48

066

060

043

041 72

082

068

036

031 96

093

086

057

O28 120

094

092

062

027

144

094

092

O48

009

168

081

O47

023

006

180

093

027

022

006

12

-

045

045

034

24

-

053

052

041

48

068

061

045

043

72

082

069

036

034

96

093

086

055

031

120

095

093

067

032

144

095

094

o-56

023

168

0-88 0-76 0-31 0-02

180

094

0-28 0-23

005

(22)

APPENDIX 3 (Continued) 3.2.2 3-7m (12 ft) Underkeel clearance û (°) u/U r/R = 1 -23 r/R = 0-96 nR = 0-68 nR = 0-41 O

-

0-44 0-31

015

12 0-51 0-43 0-24 30

-

0-64 0-53 0-34 48 0-77 0-68 0-55 0-35 66 0-81 0-73 0-54 0-32 84 0-87 0-80 0-58 0-30 102 0-94

087

0-62 0-29 120 0-96 0-87

061

0-25 138 1-00 0-91 0-54 0-15 156 1-0! 0-89 0-46

011

168

100

0-77 0-34 0-11 180 0-94 0-29 0-23 0-10

12

-

0-46 o-42 o-20

30

-

0-67 0-54 0-32

48

0-79 0-72 0-58 0-35

66

0-87

075

0-59 0-34

84

091

081

0-62 0-32

102

0-95 0-87 0-67 0-31

120

099

0-91 0-68

028

138

1-00 0-92 0-62 0-19

156

1-01

089

0-48 0-10

168

0-96 0-70 0-34 0-09

180

0-93 0-28 0-23 0-11

(23)

APPENDIX 3 (Continued) 3.2.3 0-9 m (3 ft) Underkeel clearance 20 0 (°) u/U r/R = 1-23 r/R = 0-96 r/R = 0-68 r/R = 0-41 0

-

O-32 O-21

ve

12

-

0-34 0-23

ve

24

-

0-36 0-26

009

36

-

039

0-23

012

48 0-60 0-39 0-24

014

60

062

0-43 0-28

014

72 0-63 0-51

035

0-15 84 0-63 0-56 0-39 0-13 96 0-59 0-57 0-40 0-12 108 0-53 0-56 0-40 0-08 120 0-46 0-54 0-41 0-08 132 0-42 0-52

040

0-10 144 0-42 0-49 0-38

012

156 0-40 0-43 0-32

012

168 0-43 0-36 0-28 0-14 180 0-48 0-26 0-28 0-16

12

-

0-39 0-27 0-13

24

0-44 0-26 0-17

36

0-47 0-26 0-17

48

0-64 0-50 0-29 O-16

60

0-68 O-55 O-36 0-17

72

0-69 0-60 O-44 O-18

84

0-66 0-62 0-48 0-20

96

O-61 0-60 0-50 0-20

108

0-54 0-56 0-50 0-20

120

0-46 0-53 0-50 0-22

132

0-38 0-49 0-46 0-20

144

0-33 O-47 0-44 0-20

156

0-35 0-46 0-38 0-19

168

0-45 0-42 0-32 0-18

180

O-48 0-28 0-28 0-17

(24)

4.2 Propeller tunnel as fitted

APPENDIX 4

Side force coefficients for the model fitted with a propeller tunnel and the standard rudder.

4.1 Propeller tunnel as designed

Deep sea 3 7 m (12 ft) Underkeel clearance 0 9 m (3 ft) Underkeel clearance (0) Cr X 10 (0) Cy X 10 (0) Cy X 10 0.0

014

00

O2O

00

021

46

312

92

53l

l73

76

503

154

907

123

284

123

757

2l9

1438

17O

426

l70

1021

286

1917

219

551

219

1371

92

492

286

704

286

1709

154

943

T6

209

46

225

2l9

1380

123

320

76

442

286

1828

170

440

123

726

219

5'56

170

1054

286

718

219

1380

286

1791 Deep sea 3 7 m (12 ft) Underkeel clearance 09 m (3 ft) Underkeel clearance (°) Cy X 10 (0) Cy X 104

()

Cy X 10

00

018

00

023

00

015

46

309

92

576

76

156

76

462

154

1026

123

275

123

720

219

l494

170

426

170

957

286

1989

219

548

219

1293

92

551

286

747

286

l675

154

943

76

203

231

2L9

1399

123

35l

76

426

286

l850

170

490

123

7.45

219

620

170

1043

286

768

219

1293

286

1725

(25)

APPENDIX 5

Axial velocity component ratios of the flow in the propeller plane of

the model with the propeller tunnel as fitted and four vortex generators.

5.1 Deep sea o (°) u/U

r/R= l-23

r/R=096

r/R=0-68

r/R=0-41

O

-

0-42 0-35 0-28 12

048

0-45 0-32 24

-

0-53

052

0-38 48

066

0-59 0-49 0-48 72 0-80

063

O-34 0-33 96 O-91 O-66 0-29 0-27 120 0-94 0-79 0-43 0-15 144 0-95 0-93 0-72 o-28 168 0-95 0-91

072

0-44 180 0-96 0-52 0-56 0-46

12

-

0-47 0-48 0-34

24

-

0-54 0-52 0-42

48

-

O-60 0-42 0-42

72

0-83 0-66 0-34 0-35

96

0.93 0-73 0-30 0-31

120

0-96 0-81 0-38 0-17

144

0-95 0-93 0-70 0-22

168

0-96 0-92 0-72 0-45

180

0-96 0-53 0-56 0-46

(26)

APPENDIX 5 (Continued) 5.2 3-7m (12 ft) Underkeel clearance

û

(°)

u/U

r/R = 1-23 r/R = O-96 r/R = O-68 r/R = O-41

o

-

0-45 0-32 0-17

12

-

0-52 0-43 0-24

30

-

U-65 O-54 U-34

36

-

O-67 o-55 U-36

48 0-76 0-68 0-56 U-36 66 0-80 0-72 0-55 0-34 84 0-86 0-77 0-51 0-30 102 o-93 0-73 0-34 0-22 120 o-97 0-71 0-30 0-02 138 1-01 0-90 0-54 0-21 156 1-01 0-95 0-80 U-43 168 1-00 0-91 0-77 0-54 180 0-97 0-54 0-54 0-53

12

0-54 0-42 O-22

30

-

0-67 U-53 O-31

48

0-79 0-72 0-56 0-34

66

U-85 O-74 U-56 O-33

84

U-89 O-79 U-56 O-30

102

0-94 0-81 0-47 0-23

120

U-96 O-76 O-32 O-03

138

U-99 O-84 U-43 O-12

156

1-UI O-93 U-68 O-32

168

1-UO O-92 U-71 O-45

(27)

APPENDIX 5 (Continued) 53 09 m (3 ft) Underkeel clearance 24 e (°) u/U nR = 1-23 r/R = O-96 r/R = O-68 r/R = 0-41 O O-33 O-19

ve

12 0-34 0-24

ve

24 0-40 0-26 0-12 36 0-40

023

0-14 48 0-60 0-39 0-25 0-16 60 0-59 0-42 0-26 0-16 72 0-62 0-48 O-30 O-14

84 0-63 O-52 O-29 O-IO

96 0-59 0-53 0-26 O-04

108 O-54 O-51 O-20 O-02

120 0-48 0-49 0-22 0-04

132 O-43 0-50 0-28 0-16

144 0-40 O-49 O-38 o-22

156 O-38 0-48 0-43 O-26

168 0-43 0-48 O-41 0-31

180 0-49 O-42 0-36 0-34

12

-

039

0-26 0-14

24

-

O-43 O-26 O-18

36

-

0-46 0-26 O-18

48

0-64 0-48 O-29 O-18

60

0-65 0-53 0-34 O-18

72

0-68 0-59 0-37 0-18

84

0-67 0-62 0-37 0-17

96

0-61 0-59 O-36 0-13

108

0-55 0-55 0-34 0-11

120

O-48 0-51 0-36 0-15

132

0-40 0-47 0-43 0-23

144

0-33 0-47 0-48 0-32

156

0-32

045

0-48 0-38

168

0-44 0-46 0-43 0-38

180

0-49 0-43 0-37 0-35

(28)

APPENDIX 6

Side force coefficients for the model with the propeller tunnel as fitted, four vortex generators, and the standard rudder.

Deep sea

37m (12 ft)

Underkeel clearance 09 m (3 ft) Underkeel clearance (°) Cy X lO (°) Cy X 10 (°) Cy X 1O

00

_Ø.Ø3

00

012

0'O

011

76

.._5.37

92

673

76

214

123

887

l54

1l99

123

354

170

1223

219

1733

ITO

540

2l9

1549

286

2292

219

726

286

2064

92

604

286

971

76

49O

154

1035

76

242

123

873

2l9

1577

123

376

170

1246

286

2156

l70

492

219

1647

219

687

286

2172

286

915

(29)

APPENDIX 7

Side force coefficients for the model with the propeller tunnel as fitted, four vortex generators, and an equivalent addition of O3 m (1 ft) full scale to the trailing edge of the rudder.

26 Deep sea 3 7 m (12 ft) Underkeel clearance 09 m (3 ft) Underkeel clearance (°) Cy X 1O (°) Cy X lO (°) Cy X lOi 0O +OO2 0O

007

00

O07

5.5

356

82

662

68

234

110

815

I52

l238

138

473

166

1307

224

1939

195

645

224

19O0

284

259O

254

851

284

247O

82

568

3l6

1038

5.5 3.31

152

1196

68

184

110

812

224

1919

138

412

l66

1299

284

252O

195

643

224

l803

254

868

284

2412

3l6

1129

(30)

APPENDIX 8

Resistance coefficients for various configurations of the model.

8.1 Propeller tunnel as fitted

Deep sea

37m (l2ft)

Underkeel clearance

09m (3ft)

Underkeel clearance RN x 10-6 CD >< l0 RN x 10-6 CD x 10 RN x 10-6 CD x l0

239

472

1071

549

234

690

328

483

1154

544

3'36

683

568

439

1128 541

464

660

743

42!

1O3O 55O

527

649

869

412

1114

547

629

634

930

410

lI88

544

711

623

988

407

1262

539

804

618

248

478

904

609

3.57 4.74 9.93

603

4l9

460

1076

598

487

451 1161 591

547

4.44 1220 591

610

4.35

284

698

664

4.31

376

674

823

417

4.75

653

883

413

576

640

9.47

406

672

629

9.67 4'07 7.53

622

918

409

859

613

791

4i8

708

424

632

431

566

442

505

448

4.54

458

394

468

307

488

1047

403

(31)

APPENDIX 8 (Continued)

8.2 Propeller tunnel as designed

8.3 Propeller tunnel as fitted plus vortex generators

28 Deep Sea 37 m ((12 ft) Underkeel clearance 09 m (3 ft) Underkeel clearance RN x106 CD >< 1O RN x 106 CD x 1O RN >< 106 CD >< 1O

585

438

lO73

546

1057 5.97

652

429

1146

544

ll78

593

727

423

l224

54O 1265

588

859

413

1037

547

933

6O6

705

4.74

ll89

5.39 1001

604

789

417

1258

538

1128

594

849

412

9l4

408

986

4'04 Deep Sea

37m (l2ft)

Underkeel clearance

09m (3ft)

Underkeel cleara nce RN >< l06 CD >< l0

RN x106 CD x 10

RN >< 106 CD X 10

823

422

1103

558

1072

602

887

418

1l80

555

II78

598

9.45

4l4

1259

549

l264

5.94

796

4-24 10-57

559

9-98 6-09 8-59 4-20

Il-44

5-53 11-33 6-01

914

416

12-22

552

12-25 5-95

973

413

12-95 5.49 10-02

409

(32)

9.2 3-7m (12 ft) Underkeel clearance APPENDIX 9

Side force coefficients for the model at various fixed yaw angles.

9.1 Deep sea

p

(°)

Cy X 10 Bare hull Propeller tunnel

as fitted

Propeller tunnel as fitted plus vortex generators

8

9-77 10-20 9-98

6

4-68 5-28 5-20

4

1-98 2-32

218

2

0-89 1-05 1-05 0

0-02

004

004

2

0-84

0-99

129

4

2-26

236

2-58

6

5-55

5-54

5-62

8

10-67

1084

10-82

B (°) Cy X 10

Bare hull Propeller tunnel as fitted

Propeller tunnel as fitted plus vortex generators

4

9-78 10-72 10-65

3

6-95 7-56 7-57

2

4-04

486

4-92

1

142 2-28

236

O

002

0-02 0-03

2-22

2-12

2-08

2

4-44

4-26

4-20

3

7-26

7-06

7-04

4

1070

1018

10-10

(33)

APPENDIX 9 (Continued) 9.3 09 m (3 ft) Underkeel clearance 30 ß (°) Ci' X l0

Bare hull Propeller tunnel as fitted

Propeller tunnel as fitted plus vortex generators

4

14'62 1472 1470 9.44 1030

985

2

551

546

510

1

279

298

254

o I

245

292

324

2

523

582

640

3

930

956

9.55

4

1438

l462

1480

(34)

Upper deck FIG. i

SHIP SECTION LINES

93;/'

7

/

91/4 14.64 m (48 ft) 12.20 m (40 ft) 9.81 m (32.2 ft)

- L,WL.

3.32 m (24 ft) 4.88 m (16 ft) 2.44 m (8 ft)

(35)

10.99 m (36 ft) 9.81 m (32.2 ft)

LW. L.

7.32 m (24 ft) 3.66 m (12 ft) Base line

FIG. 2

PROPELLER AND STERN ARRANGEMENT

I

3.50 m (11.5 ft)

A.RO

1/2 3I Station no.

(36)

10.99 m (36 ft) 9.81 m (32.2 ft) L.WL.

I

L

7.32 m (24 ft)

3.66m(l2ft)

p Base line

--,-

--J

j 'I I' t I t I J I p I i i

I---r

'TI,

-,

p1

Upper intersection with shell Lower

interSe°.

6.10 m (20.01 ft) Station no. FIG. 3

PROPELLER TUNNEL AS DESIGNED (a)

Location of propeller tunnel

7.90 m (25.91 ft) 3i

II

J I 1/5 1/4 1/2 5í o A'F'.

(37)

0.705 m (2.31 ft)

-l.185m(3.89ft)

-w-I View A on Fig. 3a FIG. 3 cont.

(b) Plan view of propeller tunnel

o

0.743m(2.44ft)

Station no. 0.652 m (2.14 ft)

__

1/8 1/4 1/2 3/4

(38)

Angle of side plate over length of propeller tunnel

h'-230 (1590m (1.94 ft) 4 6.145m

'i

(20.l6ft) I

'

'

I L 1 6.450 m )

i'

(21.l6ft

4

'I

/1

0.60m

/

/ p

(1.97 ft)

i/1'

0.90 m (2.95 ft) $

/

tt

11.100m 3.74m (36.41 (12.27ft)

/

5.78 m(18.96ft) 1/8 1/4 3, 1/2 5i 3/4

/

/ / /

/

/r/

/

Station in way of propeller 13.715 m (44.99 ft) 15.103 m (49.54 ft) Base line 14.400m (47.23 ft.) Station no. 6.100m (20.01 ft) 7.900m (25.91 ft) T

(39)

0.610m (2.00 ft.) 1.08 m (3.54 ft)

L

4-0.153m (0.50 ft) Rudder 0.318 m (1.04 ft)

t

Rudder Propeller tunnel

(a) Propeller tunnel as designed

Base line

(b) Propeller tunnel as fitted

Base line

Propel ter tunnel

Lower intersection with shell

Lower intersection with shell

FIG. 4 DIFFERENCES BETWEEN THE PROPELLER TUNNELAS DESIGNED AND AS FITTED

(40)

1.0 0.8 0.6 0.4 0.2

O

FIG. 5

AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODEL IN A SIMULATED DEEP SEA

(a) r/R= 1.23

-/

I

/

/

/

/

/

tunnel as fitted tunnel as designed

-'

1l

i

I

/

/

/

Propeller _____ Propeller

-

Barehull - 160 -120

-80

-40

O 90 40 80 120 160

(41)

FIG.5cont.

(b) r/R=O.96

-F

i

,.

j

y

-

- - :flTj1uI

160

120

- 80 - 40 O 40 BO 120 160 00 1.0 0.8 u/U 0.6 0.6 0.2 O

(42)

1.0 0.6 0.4 0.2 O FIG. 5 cont. (c) r/R = 0.68 Propeller Propeller

tunnel as fitted tunnel as designed

hull

--- Bare

_

N

I

I

\d

'

t

\

d

/

/

/

/

Ib t t t -I k I I I I I

I

Ib - 160

120

- 80

40

O 60 80 120 160 00 0.8

(43)

1.0 0.6 0.4 0.2 O - 160 -120 -80

-60

O 00 FIG.5cont. (d) r/R=O.41 40 80 120 160

Propeller tunnel as fitted Propeller tunnel as designed Bare hull

-s,.

/

/

/

4

/

-_% 'I.._

--,

/

's. s.. s.

-.-..--s..

-J

---I I I L I -I s. 's.. 0.8 u/U

(44)

T

I

I

/

I

/

/

-t t I I I I g a

I

I

tunnel as fitted tunnel as designed

% -g g

/

Propeller

---i

Propeller Bare hull

I t I

-8

-60

O 60 80 120 160 00 FIG. 6

AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODE,L WITH A SIMULATED FULL SCALE UNDERKEEL CLEARANCE OF 3.7 m (12 ft).

(45)

1.0 0.8 u/U 0.6 0.6 0.2 FIG.6cont.

(b) r/R0.96

/

F

-

.-%% s' 's'.' -f

'

/

---.

t'

s 5.. ... 0

/

-.

/

/

p

'7

t%

V

f i i

i

i i a

-as fitted as designed I ¡ I Propeller tunnel .5 I I

/

g L

Propeller tunnel Bare hull

I i i I - 160

120

80

- 60 O 00 60 80 120 160

(46)

- 160 -120 -80

-60

O 00 FIG.6cont.

(c) r/R0.68

40 80 12

I

- -

/

-s s s s s

/

-/

/

/

-. .s. I

/

I

\

s ¼

,/

/

1 -t L t I t I

'

-J

/

/

/

I I

Propeller tunnel Propeller tunnel Bare hull i

I

as fitted as designed

(47)

1.0 0.8 u/U 0.6 0.6 0.2 - 160

120

80

40

o Q0

FIG.6cont.

(d) r/R=O.41 60 80 12 6

Propeller tunnel as fitted

as designed

-Propeller tunnel

---Barehull

--

-

/-- /-- a

-I I

W,

/

I I i

N

I

(48)

00

FIG. 7

AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODEL WITH A SIMULATED FULL SCALE UNDERKEEL CLEARANCE OF 0.9 m (3 ft).

(a) r/R = 1.23

/

/

/

I

/

/

I

I

/

g I

//

h I I

I

I

/

I

tunnel as fitted tunnel as designed

Propeller Propeller Bare hull

I .

I

/

\ .1

i - 160

120

- 80 - 40 O 40 80 120 160 1.0 0.8 0.6 0.4 0.2 O

(49)

1.0 0.8 u/U 06 0.4 0.2 o 40 O 00 FIG.7cont.

(b) r/R=O.96

40 80 120 160

-as fitted as designed

Propeller tunnel Propeller tunnel Bare hull

(50)

-1.0 0,8 0.6 0.4 0.2 O - 160

12

B

- 40 O 00 FIG. 7 cont. (c) nR = 0.68 40 BO 120 160 as fitted as designed tunnel

Propeller tunnel Propeller

-

--Bare hull

//

-.

0

I

/

/

1

,.

J I I I -I

/

I

i

/

/

/

L

/

I -t

(51)

1.0 0.6 0.4 0.2 o 00 FIG. 7 cont.

(d) nR

0.41

Propeller tunnel as fitted

as designed

-Propeller tunnel Bare hull

-- 160

120

80

60

o 60 BO 120 160 0.8 u/U

(52)

> Cu

o

FIG. 8

FLOW PATTERN OVER THE STERN OF THE MODEL WITH BARE HULL

(53)

FIG. 8 cont.

(54)

FIG. 8 cont.

(55)

cyx

20 15 lo

5 o

vortex generators and rudder extension

Propeller tunnel as fitted plus

o 5 10 15 20 25 30 FIG. 9

SIDE FORCE COEFFICIENTS FOR THE MODEL

(a) Simulated deep sea

Bare hull

O

Propeller tunnel as fitted

+ Propeller tunnel as designed

A

Propeller tunnel as fitted plus vortex generators

(56)

25

cyx

20 15 10 5 o lO p u Bare hull Q

Propeller tunnel as fitted

+

Propeller tunnel as designed

A

Propeller tunnel as fitted plus vortex generators Propeller tunnel as fitted plus vortex generators and rudder extension

D 5 lo is 20 25 30 o FIG. 9 cont.

(57)

k

1O

Bare hull

o Propeller tunnel as fitted

-f-Propeller tunnel as designed

A

Propeller tunnel as fitted plus vortex generators

D

vortex generators and rudder extension

Propeller tunnel as fitted plus

5 lo 15 20

25 30 FIG. 9 cont.

(58)

FIG. lo

FLOW PATTERN OVER THE STERN OF THE MODEL WITH THE PROPELLER TUNNEL AS FITTED

(59)
(60)

-n P Q o cf) CD o- o- CD -I CD CD CD D) C) CD o 4,

p

()

Gravity force

(61)

00

FIG. 11

AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODEL IN A SIMULATED DEEP SEA.

(a) r/R = 1.23

L'

-L I I i I i

tunnel as fitted tunnel as fitted generators

I i I Propeller Propeller - _____ I I plus vortex I I - 160 -120 - 80

-60

O 40 80 120 160 1.0 0.8 u/U 0.6 0.4 0.2 O

(62)

0.6 0.4 0.2 O 00 FIG. 11 cont. (b) r/R = 0.96

/

j

j

as fitted as fitted generators

I

N

/

A7

I _1zf I

_lnt

I nA i

Propeller tunnel Propeller tunnel

I I --plus vortex i I I ILV LU 80 120 160

(63)

1.0 0,8 (1/U 0.6 0.4 0.2 O FIG. 11 cont. (c) nR = 0.68

tunnel as fitted tunnel as fitted

vortex generators

/

/

'\

/

Propeller Propeller plus

/

/

\

/

/

\

/

w

I I I -I f I I o 00 40 80 120 160

(64)

1.0 0.6 0,2 90 HG. 11 cont. (d) nR = 0.41 as fitted as fitted generators

-Propeller tunnel Propeller tunnel plus vortex

-

>Ti'T

- ILU 40 80 120 160

(65)

1.0 0.8 u/U 0.6 0.4 0.2

0

FIG. 12

AXIAL VELOCITY DISTRIBUTION OF THE FLOW IN THE PROPELLER PLANE OF THE MODEL WITH A SIMULATED FULL SCALE UNDERKEEL CLEARANCE OF 3.7 m (12 ft.)

(a) nR = 1.23 I I I t I I

Propeller tunnel as fitted

tunnel as fitted generators

i I

-Propeller

-I I plus vortex i I

4

o Q0 40 80 120 160

Cytaty

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