Experiments with vortex generators to improve the flow over a ship's stern in order to reduce operational noise and vibration

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DEPARTMENT OF DEFENCE

AUSTRALIAN DEFENCE SCIENTIFIC SERVICE

AERONAUTICAL RESEARCH LABORATORIES

MELBOURNE VICTORIA

Aerodynamics Note 358

EXPERIMENTS WITH VORTEX GENERATORS

TO IMPROVE THE FLOW OVER A SHIP'S

STERN IN ORDER TO REDUCE

OPERATIONAL NOISE AND VIBRATION

N. MATHESON

UNCLASSIFIED

TECHNISCHE UNIVERSITET taboratorlum veer ScheephydromechanIca

kehlef

hiekekveg 2, 2226CD DeIft Wu 015-788873. Fat 018.781838 1 DEPARTMENT OF DEFENCE

AUSTRALIAN DEFENCE SCIENTIFIC SERVICE AERONAUTICAL RESEARCH LABORATORIES

AERODYNAMICS NOTE 358

EXPERIMENTS WITH VORTEX GENERATORS

TO IMPROVE THE FLOWOVER A SHIP'S

STERN IN ORDER TO REDUCE

OPERATIONAL NOISE AND VIBRATION

by

N. MATHESON

SUMMARY

During trials of a 31,000 t (30,000 ton) tanker unacceptable noise levels were measured in cabins near the stern and local structural vibration occurred in some adjacent areas especially at shallow draught. Both the noise and vibration were attributed to the operation of the propeller in a non-uniform velocity field. Wind

tunnel experiments using a reflex model

of

the ship showed that vortex generators

could make a marked improvement in the velocity distribution of the wake. Based on these tests a vortex generator Configuration was developed and fitted to the ship.

However, although there was a significant reduction in vibration, there was no

corresponding reduction in the noise levels in the cabins.

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DATUMe

CONTENTS NOMENCLATURE

2

1, INTRODUCTION 4

2. VORTEX GENERATOR DESIGN 4

3. EXPERIMENTAL PROCEDURE AND EQUIPMENT 4-7

(a) Model 5

(b) Equipment 5

4. MODEL EXPERIMENTS AND RESULTS 8-1 I

(a) No vortex generators - bare hull 8

(b) Six vortex generator systems 9

(c) Four vortex generator systems 9

(d) Two vortex generator systems 10

(e) Resistance of model 10

5. EXTRAPOLATION OF MODEL RESULTS TO THE FULL SIZE SHIP 12-15

(a) Vortex generator scaling 12

(b) Power required for the ship fitted with vortex generators 12

6. VORTEX GENERATOR SYSTEM FITTED TO THE SHIP 16

7. SHIP TRIALS WITH VORTEX GENERATORS 16

8. CONCLUSIONS 16 ACKNOWLEDGEMENTS 16 REFERENCES 17 APPENDICES 18-29 FIGURES DISTRIBUTION

SCD, spD, sP E

NOMENCLATURE

Thickness of vortex generator CD DI(112 pU2S) = Resistance coefficient

Resistance

Diameter of turbulence promoting studs

FN _{U/ Nig", = Froude number}

Acceleration due to gravity Height of vortex generator

Length scale (Length of ship or model) Length of vortex generator

PD Power delivered to propeller

PO, _{Measured power delivered to .the propeller during trials}

PE Effective power

Projection of the turbulence promoting studs from the surface of the model

Radius of propeller

RN UL/i; = Reynolds number

Radius from centre of propeller shaft in the propeller plane at which wake velocities were measured

Surface area

Thrust deduction fraction Freestream velocity

Axial wake velocity component in the propeller plane Wake fraction

a

Angle of incidence of the vortex generator to the local surface

streamline

Increment in CD, PD, _{and PE respectively caused by fitting vortex}

generators

Quasi-propulsive coefficient Hull efficiency

Open water propeller efficiency Relative rotative efficiency

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

Density

Kinematic viscosity Subscripts:

1,2,3 denote generator positions

V.G. denotes vortex generators fitted to the hull

INTRODUCTION

The Howard Smith tanker"M.T. Express" is a single screw ship built by the Newcastle State Dockyard, New South Wales, Australia, for the Australian Department of Transport. This vessel has a displacement of 31,000 t (30,000 ton), is 162.9 m (534 ft) long, has a 25.0 m (82 ft) beam, and a 9.2 m (30 ft) draught when fully loaded. The load design service speed is 16 knots.

The M.T. Express has similar lines to the Ampol tanker "W. M. Leonard" built a few years earlier but has a higher design service speed. The stern of the M.T. Express is also slightly more streamlined to improve the wake pattern and reduce the possibility of propeller cavitation, vibration, and noise problems, some of which occurred with the Leonard. However, even with this stern modification quite large variations in axial velocity over the propeller disc were measured during model tests'''. From these tests and subsequent cavitation performance calculations,' it was considered that cavitation on the propeller blade tips would be tolerable at the design pitch, but at higher power outputs cavitation and vibration might start to become troublesome.

Nevertheless, taken overall, it had been expected that the full scale ship would perform

satisfactorily since there was no positive evidence to show that it would not.

However, during sea trials, unacceptably high noise levels occurred in the aft cabins near the screw at the design speed of 16 knots. In addition, at shallow draught and high speeds, severe vibration occurred at the stern. Vibration was not considered a problem at full load draught. It was concluded that both noise and vibration were caused by the operation of the propeller in a non-axisymmetric velocity field which produced intermittent cavitation with the consequent propagation of very strong pressure pulses, in addition to cyclic variations in thrust and torque. The occurrence of severe cavitation has been previously shown to amplify the pressure pulses shed from the propeller blades and to be a major source of induced vibration and noise at blade rate frequency.4'5"6 The noise and vibration were also thought to be accentuated by the use of a controllable pitch propeller without rake or skew. Clearances between the propeller, rudder and stern were normal for this type of hull with an installed power of 13700kw (18300hp), and were not considered a contributing factor. Additional noise was also expected from the pressure fluctuations associated with the very thick turbulent boundary layer over the stern of the ship near the crew accomodation.

The Aeronautical Research Laboratories. Melbourne, were requested by the Shipbuilding Division of the Australian Department of Transport to investigate the problem in the low speed wind tunnel. The intention was to develop a set of vortex generators which would produce a more uniform velocity distribution in the plane of the propeller. This method hasbeen used in the past to reduce cavitation and propeller induced noise and vibration.7'8 Moreover, in view of the success in reducing vibration on the Lysaght Enterprise and Endeavour' it was expected that the problems with the M.T. Express would be satisfactorily resolved.

VORTEX GENERATOR DESIGN

Vortex generators operate by redirecting high velocity fluid along a helical path to mix with the sluggish boundary layer near the body surface. The increased energy of the fluid near the body surface counters, to some extent, the formation of a low energy boundary layer in an adverse pressure gradient.

Vane type vortex generators were used throughout the tests since they have been found to give good performance in the past.'° Well designed generators should produce a high level of effectiveness over a wide range of operating conditions, with only a low resistance penalty. Unfortunately these requirements are mutually conflicting and some compromise is necessary. Usually a number of tests are needed in order to refine the design to obtain the best solution for a particular problem.

An appropriate triangular planform was selected for the present generators because of its known efficiency in producing a strong vortex. The vortex generators had a thin symmetrical bi-convex spanwise section with a tapering section normal to the hull in order to provide adequate strength and rigidity. The generators were attached to the hull so that they were normal to the surface at approximately two-thirds of their length aft of the tip.

EXPERIMENTAL PROCEDURE AND EQUIPMENT

The investigation was carried out using a 1/60 scale, "reflex" or "mirror image" model of the below-waterline section of the hull mounted in the 2.7m (9ft) x 2.1m (7ft) low speed wind tunnel. The effects of Froude number cannot be represented using this method but were not considered to

be significant. The test Reynolds number based on model length between perpendiculars, was, in general, one ninetieth of full scale; this was the maximum attainable within the limitations of the wind tunnel. Surface flow visualization, wake surveys, and resistance tests were used to determine the effectiveness of different vortex generator systems. All tests were made without a propeller fitted to the model.

Apart from Froude number effects, mentioned above, the other main effects not simulated were propeller action, structural roughness, and hull fouling. Although the propeller has a favourable influence on the flow at the stern, both hull roughness and fouling are detrimental. Some allowance was made for these effects when extrapolating the model results to the full size ship.

Model

The principal ship particulars from which the 2.7m (9ft) model was scaled are given in Table I. Section lines, and bow and stern contours are shown in Figs. 1, 2, and 3 respectively. The stern arrangement with both rudder and propeller fitted is shown in Fig. 4. All tests were made with bilge keels, but without either the propeller or rudder fitted to the model.

The model was mounted in the wind tunnel on an external mechanical drag balance by means of a sting passing through the tunnel floor. A shroud was placed around the sting to reduce interference effects. The model was aligned with the airstream so that its horizontal plane of symmetry lay along the centreline of the tunnel.

Provision was made for tests in either the full load or ballast load condition since trim and displacement can influence the wake velocity distribution and hence the radiated noise and vibration levels. Studs, 0.90mm (0.035in)p x 3.2mm (0.125in)d spaced at 3.d were fitted to girth the model 150mm (6in) aft of the bow waterline endings to promote turbulent flow over its surface similar to that which occurs over the surface of the full size ship. Turbulence promoting studs of this design have been most successful in the past.11

Equipment

An external mechanical drag balance was used to measure the resistance of the model both with and without vortex generators. Local velocities in the plane of the propeller were measured using pitot probes connected to a multitube manometer. A total of four pitot tubes were mounted on an arm which could be rotated about the centre of the propeller shaft and also moved radially so that velocities could be determined at selected angular positions from the hub radius out to r/ R =

1.30.

The surface flow patterns were made visible using french chalk mixed with kerosene. This mixture was painted on the surface of the model immediately before the wind tunnel was started and the mixture allowed to flow under the action of surface shear, pressure and gravity forces. It was necessary to keep the air flowing around the tunnel for about fifteen minutes until the pattern dried. This method gave good results but unavoidable gravity forces have affected the pattern, especially at the stern, where surface shear forces are comparatively low. Therefore, some care must be exercised in their interpretation.

TABLE I

PRINCIPAL SHIP PARTICULARS

(Table 1 cont. next page) CONDITION Length between perpendiculars Breadth - moulded

Mean draught - moulded Trim at rest

Displacement - moulded Wetted surface coefficient Length displacement ratio Block coefficient

Maximum section coefficient Prismatic coefficient

Longitudinal centre of buoyancy from amidships

Half angle of entrance of waterline Length of entrance

Length of parallel middle body Length of run

Bilge radius Rise of Floor

Half flat of bottom of amidships Type of bow Shell plating LOAD 162.9 m (534.0 ft) 25.0 m (82.0 ft) 9.2 m (30.0 ft) Level 30,576 t (29,976 ton) 6.169 5.256 0.798 0.981 0.813 3.01 m (9.87 ft) Fore 31.0° 40.72 m (133.5 ft) 56.88 m (186.5 ft) 65.27 m (214.0 ft) 2.44 m (8.00 ft) 0.153 m (0.50 ft) 0.915 m (3.00 ft) Bulbous Flush welded BALLAST 162.9 m (534.0 ft) 25.0.m (82.0 ft) 6.1 m (20.0 ft) 0.61 m (2.0 ft) by stern 19,785 t (19,397 ton) 6.775 6.076 0.775 0.792 0.797 4.16 m (13.63 ft) Fore 37.5° 40.72 m (133.5 ft) 56.88 m (186.5 ft) 65.27 m (214.0 ft) 2.44 m (8.00 ft) 0.153 m (0.50 ft) 0.915 m (3.00 ft) Bulbous Flush welded 6

TABLE I (CONTINUED)

Design requirements

Machinery

Propeller

Stern

Full load service speed 16 knot

(U /N/L=- 0.692, FN = 0.232)

(Ballast service speed 17 knot)

Two V5V52/55 M.A.N. Diesel engines geared to one shaft.

Maximum delivered power 13,650 kW (18,300 hp)

corresponding to a fouled hull, minimum delivered power 8,420 kW (11,290 hp) corresponding to a clean hull. Shafting efficiency 0.93, and shaft speed 125 r.p.tn. (constant).

6.10 in (20.0 ft) diameter, 1.88 m (6.15 ft) boss diameter, four blades (R.H.) controllable pitch. Design pitch of 19° 20' at 0.7R corresponds to a delivered power of 10,970 kW (14,700

hp).

Clearances :

Trailing edge and rudder 0.81 m (2.65 ft)

Top of aperture - above tips 1.53 m (5.01 ft)

- forward of tips 2.82 m (9.24 ft)

Bottom of aperture - below tips 0.20 m (0.65 ft)

Closed aperture, semi-balanced rudder.

MODEL EXPERIMENTS AND RESULTS

Tests were made for some fifty systematicvariations in vortex generator number, position, angle of attack, rotational sense (counter or co-rotating vortices) and size to find the most effective vortex generator configuration. The majority of tests were made with the model in the full load condition. Initial generator design parameters and positions were chosen using the work reported by Lachman,'° and previous experience from similar tests on a model of sister ships Lysight Enterprise and Endeavour.9 Later tests were aimed at optimizing the generator design for a uniform velocity distribution into the propeller and low resistance penalty.

Following previous work,9 the vortex generator aspect ratio was kept constant at

approximately 1.1, while the height was changed from 6.4 mm (0.25 in) to 12.7 mm (0.50 in). These changes were coupled with variations in the number of generators from two (one port, one

starboard) to eight (four port and four starboard), and angles of incidence to the local surface flow from 12° to 30°. The longitudinal position of the generators was varied from approximately station 1 to station 2' /2. Transverse positioning varied from close to the keel centreline to the beam limits of the model. In all cases the position and size of the vortex generators were restricted so that they neither protruded beyond the maximum beam and draught of the hull not interfered with the

flow through the various seawater inlets and outlets.

The results of all tests are not discussed in detail. However, it was found that the generators were less effective if placed too far upstream because of the dissipation of their trailing vortices, or too near the stern because of the rapidly thickening turbulent boundary layer. To offset this loss of effectiveness larger generators with higher resistance penalties would be required in either of these positions. Generators were also found to be less effective if placed too close together or too far apart. A relatively small number of large generators performed better than a larger number of smaller ones.

Relevant surface flow patterns, wake velocities and resistance characteristics are presented in the following sections for the model without vortex generators and with vortex generators located at the best positions found for:

L Six vortex generators (three port and three starboard)

Four vortex generators (two port and two starboard) Two vortex generators (one port and one starboard)

Results are included for a range of generator size and angle of attack. Changes in incidence were made by pivoting each generator about its trailing edge. Similarly, generators of different size were attached with the position of their trailing edge fixed. Thus, a range of velocity distributions over the propeller disc are presented corresponding to different resistance penalties.

The majority of the axial velocity components were taken over the starboard side of the propeller disc with only a few measurements over the port side to check for symmetry. No significant asymmetry was found for any of the tests. The velocities in the propeller plane are expressed as a ratio of the effective forward speed of the model. All flow patterns and wake velocities were taken at a Reynolds number of 1.2 x 10' based on the length of the model between perpendiculars.

(a) No vortex generators - bare hull

The surface flow pattern over the stern of the model without vortex generators is shown in Fig. 5 for the full load condition and in Fig. 6 for the ballast condition. (The dark circular areas were caused by the flow pattern not completely drying where filler had been used to patch the model after vortex generators had been removed.)

The flow patterns in both loading conditions show a region of low energy flow extending from

approximately the propeller shaft centreline to the top of the propeller arch, and from

approximately station one-half to the aft waterline endings. Just above the turn of the bilge there is a separation line shown as a very dark region where all the french chalk has been swept from the surface by the high shear stresses associated with such a trailing vortex system:2

The axial velocity components over the propeller disc are shown in Figs. 7 and 8 for the full load and ballast draught respectively. These results are tabulated in Appendix A. In both loading conditions there were changes in the velocity ratio with angular position from about 0.40 to 0.90 over the outer twenty percent of the propeller radius. As the blades pass through this uneven velocity distribution fluctuating pressures and forces will be produced which may cause undesirable vibration and radiated noise at blade frequencies and higher harmonics. Overall, the velocity ratios in ballast draught were slightly smaller than in full load draught. However, in both

9

loading conditions the flow at the stern does not appear to be too unusual compared with other similar ships".

Six vortex generator systems

Tests with different generator configurations were aimed at creating the most uniform axial velocity distribution into the propeller without an excessive increase in resistance. After a number of tests a six vortex generator configuration (three port and three starboard) was found which gave quite good results. The positions of these generators are shown on a plan view of the port undersurface of the model in Fig. 9(a), and the sizes of the generators are given in Fig. 9(b). The girth dimensions to the tip and aft end of each generator in Fig. 9(a) relate to an angle of incidence of 20° to the local surface streamline.

The surface flow patterns with the vortex generators in Fig. 9 fitted to the hull are shown in Figs. 10 and 11 for the model in full load and ballast draught respectively. In both cases there was a marked straightening of the flow above the propeller shaft centreline forward of the propeller arch, compared with the surface flow patterns without vortex generators. The vortices associated with the separation line near the turn of the bilge are also less severe. Thus, some increase in axial velocity at the top and bottom of the propeller can be expected.

The axial velocity ratios over the propeller disc of the model at full load draught fitted with the six vortex generators shown in Fig. 9 are plotted in Figs. 12 and 13. Although these generators were considered to offer the best solution for a set of six, additional test results are included in Figs.

12 and 13 for the same size generators at angles of 17° and 25°, together with results for generators of heights h, = 12.7mm (0.50in), h2 = 10.7mm (0.42in), h3 = 8.4mm (0.33in), and h, = 8.4mm (0.33in), h2=6.4mm (0.25in), h3=6.4mm (0.25in), at an angle of incidence of 20°. All results are tabulated in Appendix B. An angle of incidence of 20° was considered the most suitable because the velocity ratios are relatively sensitive to reductions in incidence below 20°, whereas little change occurred for larger angles. Although the smallest generators hi = 8.4mm (0.33in), h2 = 6.4mm (0.25in), h3 = 6.4mm (0.25in), may be adequate, the larger generators h, = 10.7mm (0.42in), h2 = 8.4mm (0.33in), h3 = 6.4mm (0.25in), were chosen to allow some safety margin for unknown effects (such as rolling) when fitting the generators to the full scale ship. The largest generators were discarded because they did not increase the axial velocity ratios enough to justify the expected increase in resistance. Attempts made to improve the low velocity at the bottom of the propeller disc were relatively unsuccessful, and further increases in axial velocity above those shown in Fig. 12 could not be obtained. One aspect of the six vortex generator systems was that they produced unnecessarily large increaseinaxial velocity for 40°-..61-c.140° and r/ R-<..0.68, and

did not make any real improvement in the uniformity of the velocity distribution in this region. No six vortex generator system was found which created a more even velocity distribution simultaneously over both the inner region and the important outer region where maximum loading occurs.

Axial velocity ratios in ballast were taken with only the best set of generators for the full load draught, namely, h, = I 0.7mm (0.42in), h2 = 8.4mm (0.33in), h3 = 6.4mm (0.25in), at an angle of incidence of 20°. The results are plotted in Fig. 14, and tabulated in Appendix E. Although the wake velocity ratios were not quite-as good as those for the full load draught they were considered satisfactory. Additional tests were carried out at ballast draught to try and improve the velocity distribution further. However, only very small improvements resulted and the original set of generators were recommended as the most suitable.

Four vortex generator systems

Tests were carries out with four vortex generators, (two port and two starboard), in an attempt to reduce the relatively large resistance penalty expected with six vortex generators, and to provide a range of wake patterns from which a set of generators could finally be chosen for the ship. The best results were obtained when the two aft generators (No. 3 pair) of the previous six vortex generator system were removed. Slightly better velocity distributions resulted when the second pair of generators were moved a little further aft, but this position was impracticable since the generators fouled the main engine cooling water inlets and outlets.

The surface flow patterns with the first and second pair of vortex generators in Fig. 9 fitted to the hull are shown in Figs. 15 and 16 for the model in full load and ballast draughts respectively. There was little difference between the surface flow patterns with four generators and the flow patterns in Figs. 10 and 11 with six vortex generators. Hence, similar increases in axial velocity over the propeller disc were expected for each set of generators.

The axial velocity ratios in the propeller plane of the model at full load draught fitted with the four vortex generators (No. 1 and 2 pair in Fig. 9) are plotted in Figs. 17 and 18. Additional velocity distributions are included in Figs. 17 and 18 for the same size generators at angles of 17°

and 25°, together with results for generators of heights hi 12.7tnrn (0.50in), h2 = 10.7mm

(0.42in), and hi = 8.4mm (0.33in), h2 = 6.4mm (0.25in), at an angle of incidence of 20°. These distributions show similar sensitivity to changes in generator size and incidence as the six vortex generator systems. All results are tabulated in Appendix C. Both the angle of incidence of 200, and heights of hi = 10.7mm (0.42in), h2= 8.4mm (0.33in), were chosen as the most suitable for the same reasons given when selecting the best six vortex generator system.

Axial velocity ratios for the model in ballast fitted with generators hi = 10.7mm (0.42in), h2= 8.4mm (0.33in), at an angle of incidence of 20° are shown in Fig. 14 and tabulated in Appendix E. As in the case of the six vortex generator system, these results were not quite as good in ballast as in full load draught, but are considered satisfactory. No axial velocity results were taken with any other four generator system in ballast.

Two vortex generator systems

An attempt was made to produce an acceptable velocity distribution with only two vortex generators (one port and one starboard). Although the results with two vortex generators were not considered satisfactory they are included for completeness. The positions of the generators found to produce the best wake velocity distribution are given in Fig. 19. Three generator sizes were tested with height of 6.4mm (0.25-in), 8.4mm (0.33in), and 10.7mm (0.42in), corresponding to the six vortex generator system in Fig. 9(b). The generators were set in turn at angles of incidence of 20° and 25°.

The surface flow pattern over the model at full load draught fitted with vortex generators of height hi = 8.4mm (0.33in) at an angle of incidence of 25° is shown in Fig. 20. As expected, the flow pattern is not as good as with four or six generators, but there is some improvement compared with the bare hull.

The axial velocity distributions in the propeller plane of the full load draught model fitted With each size of vortex generator at angles of incidence of 20° and 25° are shown in Figs. 21 and 22. These results are tabulated in Appendix D. Generators in the positions shown in Fig. 19 at an angle of incidence of 25° with heights hi = 8.4mm (0.33in), were considered the best of the two vortex generator systems. The axial velocity distribution with these generators attached to the model in ballast is shown in Fig. 14, and the results are tabulated in Appendix E. Like the results at full load, the axial velocity distribution in ballast was not as good with the two generators as it was with four or six generators.

Resistance of Model

The resistance of the model without vortex generators, and fitted in turn with each of the previously described generators, was measured using a mechanical drag balance. The majority of

the results were taken over a Reynolds number range of 8 x 106 to 12 x.106. Corrections were

applied for the interference effects of the shroud around the mounting sting, blockage, compressibility and the pressure gradient in the tunnel. The corrected results are plotted in Figs. 23, 24, 25 atid 26 for the six, four and two vortex generator systems attached to the model in both loading conditions. All results are tabulated in Appendix F.

The increase in resistance coefficient of the model with each vortex generator system at a Reynolds number of 10 is given in Table 2. As expected, variations in the angle of incidence, size, and number of generators cause corresponding changes in the resistance coefficients. These increases in resistance coefficient ranged from 3% for the smallest two generator system at 20°, to 11% for the largest six generator system at 20° incidence.

Table 2. Increase in resistance coefficient for the model fitted with each vortex generator system at RN =

Six vortex generator systems.

Four vortex generator systems.

Two vortex generator systems

11

SCD

Full load Ballast

a

(0)

h1=12.7mm (0.50in) h1=10.7mm (0.42in) h1=8.4mm (0.33in) hi=10.7mm (0.42in) h2=10.7mm (0.42in) h2= 8.4mm (0.33in) h2=6.4mrn (0.25in) h2= 8.4mm (0.33in) h3= 8.4mm (0.33in) h3= 6.4mm (0.25in) h3=6.4mm (0.25in) h3= 6.4mm (0.25in)

17 0.00017 20 0.00042 0.00026 0.00020 0.00024 25 0.00035 a (0) - bCD

Full load _ Ballast

hi=12.7mm (0.50in) h1=10.7mm (0.42in) h1=8.4mm (0.33in) h1=10.7mm (0.42in) h2=10.7mm (0.42in) h2= 8.4mm (0.33in) h2=6.4mm (0.25in) h2= 8.4mm (0.33in)

17 0.00016 20 0.00038 0.00024 0.00019 0:00024 25 0.00033 a (0) bCD

Full load Ballast

h1=10.7mm (0.42in) h1=8.4mm (0.33in) h1=-6.4mm (0.25in) h1=8.4mm(0.33in)

20 25 0.00016 0.00023 0.00010 0.00018 0.00014 0.00015

5. EXTRAPOLATION OF MODEL RESULTS TO THE FULL SIZE SHIP

In scaling the model results to the full size ship it is necessary to determine both the physical size of the generators and the change in power necessary to propel the ship at a given speed.

Vortex generator scaling

There are differences between the flow on the model and the ship caused by scale effects which exist because the Reynolds number of the model is only about one ninetieth of that for the full size ship. Additional differences between the flows are caused by both structural roughness and fouling

of the actual ship. A method of scaling which allows for these effects is required.

Geometric scaling from the model is one of the more obvious methods of determining the size of the vortex generators for the ship. However, if the vortex generators are scaled geometrically, stronger vortices will be created on the ship than on the model, because the boundary layer is relatively thinner and the generators consequently more effective. It, therefore seems more appropriate to scale the generators according to the relative boundary layer thickness between the model and ship.

Flat plate boundary layer theories were used to estimate the relative boundary layer thickness between the model and ship. These theories were expected to give a reasonable estimate of the relative boundary layer thickness even though they neglect the effects of the three dimensional nature of the hull. To maintain the same relative strength between the vortices on the model and ship the vortex generators should be scaled according to the displacement thickness of the boundary layers. Using this approach the relative displacement thickness of the boundary layer on the model was calculated to be 2.5 times the relative displacement thickness of the boundary layer on the "smooth" full size ship at 16 knots.

Structural roughness and fouling will increase the thickness of the boundary layer on the ship and offset scale effects to a large extent, especially after the ship has been in service for some time. The commonly accepted increase in skin friction coefficient of 0.0004'4 was used to allow for stfuctural and paint roughness effects. An additional increase of 30% of the effective power for the clean ship was added to allow for fouling. The relative displacement thickness of the boundary layer on the model will then only be 1.3 times the relative thickness required for similarity with the fouled ship at 16 knots. Using boundary layer thickness scaling the 8.4mm (0.33in) high vortex generators, for example, would become 380mm (15in) high on the ship instead of 510mm (20in) by direct geometric scaling. The increase in relative spacing between generators caused by boundary layer scaling was not expected to be important in view of the small changes involved. However, there are a number of additional factors, besides hull roughness, which should be considered.

Propeller action on the ship will induce a favourable effect on the performance of the generators by reducing pressure over the stern, hence reducing the effective boundary layer thickness. On the other hand, wavemaking will be detrimental to their performance by increasing the adverse pressure gradient over the stern. Of these two factors propeller action was estimated to be predominant. In addition, the motion of the ship (such as rolling) in a seaway will result in asymmetrical flow which may reduce the effectiveness of the generators. However, in very disturbed seaways the speed of the ship will be reduced for safety reasons, and both noise and vibration intensity will be reduced.

After taking into account the importance of keeping the power penalty as low as possible, and considering the known factors affecting the performance of the generators, it was decided to make the generators on the ship 0.80 of their geometrically scaled size. Therefore, for example, the 8.4mm (0.33in) high generators on the model would become 410mm (16in) high on the ship.

Power required for the ship fitted with vortex generators

Wavemaking and viscous resistance were considered separately when estimating the change in resistance of the ship caused by fitting vortex generators. It was assumed that the vortex generators will not cause any significant alteration to the wavemaking resistance because they are too far aft to influence the bow wave system which contains the majority of the wavemaking energy. Therefore, the only effect to be considered is the change in the viscous resistance of the hull. The increase in resistance coefficient of the model with each vortex generator configuration

at a Reynolds number of 10 is given in Table 2. It is assumed that these increases in resistance

coefficient remain constant and independent of RN, and that they can be applied directly to the ship fitted with vortex generators. The calculated increases in effective power for the ship using these constant increments in resistance coefficient are given in Table 3. Although all of the increases in effective power are within the allowable limits for the ship, it is far more important to estimate the

Table 3 Estimated increase in PE for the ship fitted with each vortex generator system. (Note: generator heights are applicable to the model).

Six vortex generator systems.

Four vortex generator systems.

Two vortex generator systems

13

a (0)

3PE

Full load-16 knot Ballast-17 knot

h1=12.7mm (0.50in) h2=10.7mm (0.42in) hl= 8.4mm (0.33in) 1.11=10.7mm (0.42in) h2= 8.4mm (0.33in) h3= 6.4mm (0.25in) h1=8.4mm (0.33in) h2=6.4mm (0.25in) h3=6.4mm (0.25in) h1=10.7mm (0.42in) h2= 8.4mm (0.33in) h3= 6.4mm (0.25in) 17 20 25 7201W (970hp) 290kW (390hp) 450kW (600hp) 600IcW (810hp) 340kW (460hp) 400kW (540hp) SPE

a Full load-16 knot Ballast-17 knot

(0)

hi=12.7mm (0.50in) hi=10.7mm (0.42in) hi-=8.4mm (0.33in) h1=10.7mm (0.42in) h2=10.7mm (0.42in) h2= 8.4mm (0.33in) h2=6.4mm (0.25in) h2= 8.4mm (0.33in)

17 ' 280kW (370hp)

20 660kW (880hp) 410kW (550hp) 330kW (440hp) 400kW (546hp)

25 570kW (760hp)

(0)

SPE

Full load-I6 knot Ballast-17 knot

1=10.7mm (0.42in) h1=8.4mm (0.33in) h1=6.4mm (0.25in) hi=8.4mm (0.33in)

20 25 280kW (370hp) 400kW (530hp) 170kW (230hp) 310kW (410hp) 240kW (320hp) 250kW (340hp)

increase in delivered power because this is the additional power which the engines must develop. Changes in the power delivered to the propeller to maintain a given speed with the vortex generators fitted cannot be accurately found from the present wind tunnel tests because propulsion factors are not available. However, in view of the importance of the parameter an estimate of its increase was made using the following method. First, the relative rotative efficiency,

nR, and open water propeller efficiency, owere assumed to remain unchanged when vortex

generators were fitted to the hull. The quasi-propulsive coefficient, given by equation (I), will

therefore be dependent only on hull efficiency, n

'77D PE.IPD nif 77R ( I)

Secondly, it was assumed that the thrust deduction fraction, t, remains constant. Thus the hull efficiency, given by equation (2), will be dependent only on the wake fraction, w. Finally,

77=(l-t)

(1 - w) (2) the wake fraction was assumed to be independent of Reynolds number and Froude number enabling the wake fractions found from the model tests to be applied directly to the ship. The delivered horsepower for the ship with vortex generators was then calculated from equation (3).

PD,G.= (1 - wv.G.) / (1 - w) [PDT + (PEKG.-. PE) PDT I PE] (3) Power data, used in equation (3), were supplied by the Department of Transport and are given in Table 4.

Table 4 Predicted and trial PD and PE for the full size ship.

Actual trials power results were not available for the ship in ballast so it was assumed that the trials PD in ballast and full load are in the same ratio as the predicted PO values from towing tank tests.

The calculated increase in PD above the trial power is given in Table 5 for the ship in full load and ballast for each set of vortex generators. Obviously, the large increases in delivered power necessary with some vortex generator configurations makes them unacceptable.

14

Full Load - 16 knots Ballast - 17 knots

P E= 6,090kW (8,160hp) PD = 8,360kW (11,200hP) PDT= 10,150kW (13,600hp) P E= 6,510kW (8,720hp) PD = 8,950kW (12,000hp) PDT= [10,8201(W (14,500hp)]

Table 5 Estimated increase inPDfor the ship fitted with each vortex generator system. (Note: generator heights are applicable to the model)

Six vortex generator systems.

Four vortex generator systems.

Two vortex generator systems.

15

(0)

813r,

Full load-16 knot Ballast-17 knot

h1=12.7mm (0.50in) h2=10.7mm (0.42in) 113= 8.4mm (0.33in) h1=10.7mm (0.42in) h2= 8.4mm (0.33in) h3= 6.4mm (0.25in) h1=8.4mm (0.33in) h2=6.4mm (0.25in) h3=6.4rnm (0.25in) 111=10.7mm (0.42in) h2= 8.4mm (0.33in) h3= 6.4mm (0.25in) 17 20 25 4,400kW (5,900hp) 1,800kW (2,400hp) 3,400kW (4,500hp) 3,900kW (5,200hp) 3,000kW (45000hp) 3,300kW (4,400hp) ,

a

(0) (513D

Full load-16 knot Ballast-17 knot

h1=12.7mm (0.50in) h2=10.7mm (0.42in) h1=10.7mm (0.42in) h2= 8.4inm (0.33in) hi=8.4mm (0.33in) h2=6.4mm (0.25iri) h1-=10.7mm (0.42in) h2= 8.4mm (0.33in) 17 20 25 3,100kW (4,200hp) 1,300kW (1,700hp) 1,900kW (2,500hp) 2,800kW (3,800hp) 1,600kW (2,200hp) 2,500kW (3,300hp) a (0) SPD

Full load-16 knot Ballast-17 knot

11i=10.7mm (0.42in) h1=8.4mm (0.33in) h1=6.3mm (0.25in) h1=8.4mm (0.33in)

20 25 1,400kW (1,900hp) 2,100kW (2,800hp) 1,000kW (1,400hp) 1,600kW (2,200hp) 1,400kW (1,900hp) 1,600kW (2,100hp)

VORTEX GENERATOR SYSTEM FITTED TO THE SHIP

Initially, it had been decided that a power penalty corresponding to a speed loss of between 3/4 and 1 knot could be tolerated for the ship fitted with vortex generators. A 3/4 knot speed loss would correspond to 1,600kW (2,200hp) for the fully loaded ship at 16 knot, and 2,500k W (3,300hp) for the ship in ballast at 17 knot.

From a comparison of all the results it was considered that the four vortex generator system lb= 10.7mm (0.42in), h2= 8.4mm (0.33in), at a= 200, shown at model scale in Fig. 9, produced the most suitable velocity distribution into the propeller within the allowable power limits. This set of vortex generators was scaled and fitted to the full size ship. It was estimated that the vortex generators would absorb 1,900kW (2,500hp) at 16 knot full load, and 2,500kW (3,300hp) at 17 knot ballast, with corresponding speed losses of approximately 0.8 knot and 0.7 knot. A 13mm (0.5 in) doubling plate was welded between the hull plating and the base of each generator as required by the American Bureau of Shipping. Inspections during fitting revealed that the No 2. pair of generators might cause fouling of the engine water cooling inlets and outlets. Although calculations indicated that no serious fouling would occur, the generators were, in fact, moved bodily 0.38m (1.25ft) further outwards from the keel centreline as a safety precaution. In addition the No. 1 pair of generators was moved out a further 0.08m (0.25ft). These changes were not expected to cause any significant alteration in the wake velocity distribution. The final positions and sizes of the vortex generators fitted to the ship are given in Fig. 27.

SHIP TRIALS WITH VORTEX GENERATORS

Ship trials with vortex generators fitted to the hull were carried out in deep water off the coast of New South Wales between Sydney and Newcastle in good weather conditions during January 1975. The trial resUlts were disappointing because noise levels in the aft cabins remained unchanged through the normal audible frequency range. Significant reductions in noise levels did, however, occur above 16,000 hertz and below 60 hertz. It was concluded that the noise was now predominant at propeller shaft revolutions and not at blade passing frequency. However, the origins of the noise at shaft frequency remained unknown. Overall, it was considered that the high noise levels in the aft cabins were associated more with their position which was unusually far aft, as required by the owner, rather than any abnormality in the propulsion system.

One favourable outcome of fitting the generators was the reduced vibration of the ship, particularly at light draught where the vibration had been more noticeable. Although full details of the power absorbed by the generators are not available, the power increases were somewhat lower than estimated and were well within allowable limits.

CONCLUSIONS

A system of vortex generators, designed from tests of a reflex model of a ship in a wind tunnel, produced significant improvements in the axial velocity distribution over the propeller disc of the model. These vortex generators were scaled to the ship where similar improvements in wake velocities were expected to reduce both the noise level in the aft crew quarters and vibration at shallow draught. Although the generators were successful in reducing vibration to an acceptable level at shallow draught, they did not produce any change in the audible noise levels in the cabins.

ACKNOWLEDGEMENTS

The author wishes to thank all of the many people who assisted with the project. In particular, Mr. R. Campbell and Staff from the Australian Department of Transport (Shipbuilding Division), Prof. P.T. Fink from the University of New South Wales, (Member of the Australian Shipbuilding Board), and Miss D.A. Lemaire from the Aeronautical Research Laboratories, for their very helpful suggestions and discussions throughout the project.

17 I.

REFERENCES

"Wake Survey, Resistance and Propulsion".

Unpublished N.P.L. Ship Division report for the

Shipbuilding Division of the Australian Department of Transport. Project No. 51.2.101, 12 July 1972.

2. "Propeller Water Tunnel Experiments". Unpublished

N.P.L. Ship Division report for the Shipbuilding

Division of the Australian. Department of Transport, Project No. 30.25, 26 April 1972.

3. "Hydrodynamic Propeller Loading and Cavitation

Performance". Det Norske Veritas Report No. 74-75-C for the Shipbuilding Division

of the Australian

Department of Transport, 9th April 1974.

4. Marten, J.D. van "The Effect of Cavitation on the Interaction between

Propeller and Ship's Hulr. Int. Shipbuilding Prog.,

Vol.19, Jan. 1972.

5. Oossanen, P. van

"A Method

for Minimizing the Occurrence of

Cavitation on Propellers in a Wake". IM. Shipbuilding Prog., Vol.18, Sept. 1971.

6. Huse, E. "Pressure

Fluctuations on the

Hull Induced by

Cavitating Propellers". Publication No 111 of the

Norwegian Ship Model Experiment Tank, Trondheim, March 1972.

7. Vossnack, E. and "Developments of Ship's Afterbodies, Propeller Excited

Voogd, A. Vibrations". Proceedings of the second Lips Propeller

Symposium, Drunen, Holland, May 10-11, 1973. 8. Huse, E. "Stern Fins can Reduce Vibration and Noise".

NSFI-Nytt, Vol.2, 1973.

9. 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.

10. "Boundary Layer and Flow Control". Edited by G.V.

Lachman, Pergamon Press, Oxford, London, 1961.

Ii. Matheson, N. and "Experimental Determination of the Components of

Joubert, P.N. Resistance of a Small 0.80 CB Tanker Model"., J.S.R.,

Vol. 17, 1973.

Maskell, E.C. "Flow Separation in Three Dimensions".

R.A.E. Report No. Aero 2565, November 1955.

13. Nadler, J.B. and

"Analysis of Experimental Wake Data in Way of

Cheng, H.M.

Propeller Plane of Single- and Twin-Screw Ship

Models". Trans. S.N.A.M.E., Vol.73, 1965.

14. "Principles of Naval Architecture". Edited by J.P.

Comstock, The Society of Naval Architects and Marine Engineers, New York, 1967.

APPENDIX A

Axial velocity component ratios in the propeller plane of the model without vortex

generators at full load and ballast draught.

18 0 i Degree) u/ U r/R = 1.23 r/R = 0.96 r/R = 0.68 r/R = 0.41 Full Load Ballast Full Load Ballast Full Load Ballast Full Load Ballast 0 _0.33

-

_{0.38 0.37 0.40 0.38 0.36 0.37} 10 0.41

-

0.49 0.46 0.49 0.46 0.42 0.44 20 0.55

-

0.60 0.52 0.56 0.50 0.48 0.49 40 0.67 0.60 0.72 0.58 0.60 0.55 0.50 0.53 60 0.80 0.66 0.81 0.69 0.64 0.60 0.45 0.60 80 0.89 0.82 0.88 0.80 0.69 0.65 0.40 0.58 100 0.92 0.92 0.92 0.83 0.71 0.62 0.39 0.51 120 0.93 0.95 0.93 0.82 0.67 0.49 . 0.39 0.47 140 0.94 0.95 0.92 0.72 0.52 0.44 0.38 0.41 160 0.94 0.94 0.72 0.53 0.38 0.41 0.22 0.29 170 0.94 0.87 0.43 0.37 0.39 0.39 _. 0.31 0.34 180 0.93 0.83 0.34 0.34 0.19 0.30 0.13 0.25

APPENDIX B

I. _{Axial velocity component ratios in the propeller plane of the model at full load draught fitted}

with six vortex generators 111 = I0.7mm (0.42in), /12 _{= 8.4mm (0.33in), h3 = 6.4mm (0.25in), at}

angles of incidence of 17°, 200 and 25°.

19 o u/ U r/R = 1.23 r/ R = 096 r/ R = 0.68 r/R = 0.41

(Degree) a= a= a= a= a= a= a= a= a= a= a= a=

170 20° 25° 170 20° 25° 170 20° 25° 170 20° 25° 0 0.39 0.50 0.55 0.44 0.54 0.58 0.45 0.54 0.55 0.39 0.49 0.50 10 0.45 0.51 0.58 0.50 0.66 0.67 0.50 0.63 0.61 0.43 0.55 0.53 20 0.53 0.56 0.61 0.65 0.72 0.74 0.59 0.68 0.68 0.46 0.58 0.57 40 0.68 0.74 0.79 0.77 0.81 0.83 0.72 0.78 0.77 0.57 0.62 0.60 60 0.83 0.84 0.85 0.85 0.87 0.88 0.81 0.84 0.85 0.62 0.69 0.68 80 0.90 0.90 0.89 0.90 0.89 0.90 0.88 0.89 0.89 0.64 0.73 0.73 100 0.92 0.92 0.92 0.92 0.92 0.92 0.90 0.92 0.92 0.63 0.75 0.76 120 0.93 0.93 0.93 0.92 0.92 0.92 0.85 0.92 0.92 0.59 0.72 0.73 140 0.94 0.93 0.93 0.93 0.93 0.93 0.71 0.92 0.92 0.45 0.57 0.57 160 0.93 0.94 0.94 0.89 0.93 0.93 0.42 0.66 0.65 0.33 0.39 0.41 170 0.94 0.94 0.93 0.56 0.71 0.76 0.39 0.41 0.40 0.30 0.34 0.34 180 0.94 0.94 0.94 0.38 0.41 0.44 0.35 0.37 0.37 0.30 0.34 0.34

APPENDIX B (CONT.) 2.

Axial velocity component ratios in the propeller plane of the

model at full load draught fitted with various six

vortex generator systems at an angle of incidence of 20"!

0 u/ U r/R = 1.23 r/ R = 0.96 r/R = 0.68 r/ R = 0.41 (Degree) hi=.8.4mm(0.33in) hi=12.7mm(0.50in) hi=8.4mm(0.33in) hi=12.7mm(0.50in) hi=8.4mm(0.33in) hi=12.7mm(0.50in) ,h1=8:4mm(0.33in) hi=12.7mm(0.50in) h2=6.4mm(0.25in) ' h2=10.7mm(0.42in) h2=6.4mm(0.25in) h2=10.7mm(0.421n) h2=6.4rnm(0.25in) h2=10.7mm(0.42in) h2=6.4mm(0.25in) h2=10.7mm(0.42in) , h4=6.4mm(0.25in) Ill= 8.4mm(0.33in) h3=6.4mm(0.25rn) 113= 8.4mrn(0.331n) h,=6.4mm(0.25in) th= 8.4mm(0.33in) h1=6.4rnm(0.25in) h,= 8.4mm(0.33in) 0 0.45 0.50 0.55 , 0.53 0.54 0.52 0.49 0.48 10 0.49 0.60 0.63 0.64 0.63 .0.60 0.54 0.50 20 0.52 0.68 0.68 0.74 0.69 0.68 0.58 0.54 40 0.67 . 0.81 0.78 '0.84 0.77 0.79 0.63 0.58 60 0.81 087 0.86 0.89 0.84 0.86 0.70 0.67 80 0.89 0.90 0.89 0.90 0.89 0.90 0.74 0.75 100 0.92 0.91 0.92 0.91 0.92 ' 0.91 0.76 0.77 120 140

0.93,

0.93 0.93 0.93 0.92 0.93 0.93 0.93 0.92 0.92 0.92 0.92 0.71 0.55 0.76 0.60 160 0.94 0.94 0.93 0.93 0.59 0.70 0.41 0.40 170 180 0.94 0.94 0.94 0.94 0.52 0.40 0.79 0.45 0.41 0.38 0.40 0.36 0.36 , , 0.36 0.34 0.34

APPENDIX C

1. Axial velocity component ratios in the propeller plane of the model at full load draught fitted with four vortex generators h1 = I0.7mm (0.42in), h2 = 8.4mm (0.33in), at angles of incidence of 17°, 20° and 25°. 21 u/ U 0 _{r/R = 1.23}

_{r/R = 0.96}

_{r/R = 0.68}

_{r/R = 0.41} (Degree)

a= a= a= a= a-

a= a= a= a= a= a=

170 20° 25° 170 20° 25° 170 200 25° 170 20° 25° 0 0.48 0.50 0.51 0.49 0.49 _ 0.49 0.48 0.48 0.49 0.42 0.43 0.43 10 0.48 0.60 0.62 0.54 0.58 0.58. 0.52 0.54 0.55 0.43 0.47 0.47 20 0.67 0.70 0.69 0.65 0.68 0.67 0.60 0.62 0.62 0.49 0.53 0.53 40 0.77 0.79 0.78 0.77 0.78 0.79 0.71 0.73 0.73 0.51 0.53 0.52 60 0.84 0.85 0.85 0.84 0.86 0.86 0.80 0.82 0.83 0.52 0.52 0.52 80 0.90 0.89 0.90 0.90 0.90 0.90 0.86 0.88 0.88 0.53 0.57 0.55 100 0.92 0.91 0.92 0.91 0.91 0.91 0.90 0.90 0.91 0.53 0.56 0.58 120 0.93 0.92 0.92 0.93 0.92 0.92 0.88 0.90 0.91 0.49 0.56 0.56 140 0.93 0.93 0.94 0.93 0.93 0.93 0.72 0.84 0.87 0.40 0.44 0.45 160 0.93 0.93 0.94 0.88 0.92 0.93 0.40 0.47 0.50 0.26 0.30 0.31 170 0.93 0.93 0.94 0.48 0.55 0.62 0.36 0.36 0.36 0.28 0.29 0.29 180 0.94 0.94 0.94 0.39 0.39 0.39 0.37 0.37 0.37 0.33 0.34 0.33

APPENDIX C (CONT.) 2.

Axial velocity component ratios in the propeller plane of the model at full load draught fitted with various four

vortex generator systems at an angle of incidence of 20°.

_ 0 u/ U r/R = 1.23 r/R = 0.96 r/R =1/68 r/12 = 0.41 (Degree) hi=8.4mm(033in) h1=12.7mm(0.50in) h,=8.4mm(0.33in) h, =12.7rnm(0.50in ) hc=8.4mm(0.33in) 11,=11.7mm(0.50in) h, =8.4inm(0.33in) h1=12.7mm(0.50in) h2=6.4mm(0:25in) h,=10.7mm(0.42in) h2=6.4mm(0.25m) h!=10.7mrn(0.421n) h2=6.4mm(0.25in) h2=-10.7mm(0.421n) h2=6.4mm(0.25in) h2=10.7mm(0.421h) 0 0.44 0.52 0.49 0.49 0.49 0.48 0.46 .0.43 ,10 - 0.54 0.62 061 0.59 0.58 0.55 0.50 0.48 20 0.64 0.70 068 0.68 0.63 062 0.54 0.50 40 0.73 0.82 0.77 082 0.73 . 0.75 0.55 0.50 60 80 0:81 0.87 0.87 0.89 0.83 088 0.87 090 0.80 0.86 0.83 0.89 , 0.55 0.55 0.51 0.58 100 0.87 0.92 0.88 09l 0.86 0.91 0.55 0.62 120 0.92 0.92 0.91 092 -0.90 0.92 0.51 , 0.60 140 . 0.93 0.93 092 . 0.92 0.81 0.88 0.41 0.47 160 0.93 0.94 0.92 0.93 0.43 0.53 0.29 , 0.33 170 0.94 0.94 0:48 0.64 0.37 0.36 0.29 0.30 180 0.94 0.94 \ 0.37 0.41 0.37 0.35 0.36 0.30

APPENDIX D

I. Axial velocity component ratios in the propeller plane of the model at full load draught fitted with various two vortex generator systems at an angle of incidence of 25°.

23 0 (Degree) u/ U r/R =1.23 r/RI=0.96

r/R=0.68

r/R= 0.41 111=6.4 h,=8.4 111=10.7 111=6.4 h1=8.4 h1=10.7 1)1=6.4 h1=8.4 h1=10.7 111=6.4 h1=8.4 h1=10.7 mm mm mm mm mm mm mm mm mm mm mm mm

(0.25in) (0.33in) (0.42in) (0 25w) (0.33i.n) (0 42w) (0 25w) (0.33in) (0 42w) (0.25in) (0 33w) (0.42in)_

0 0.41 0.43 0.43 0.47 0.47 0.43 0.47 0.47 0.42 0.43 0.42 0.35 10 0.48 0.57 0.57 0.58 0.60 0.54 0.55 0.56 0.50 0.49 0.49 0.40 20 0.55 0.63 0.69 0.66 0.67 0.68 0.63 0.63 0.61 0.53 0.53 0.49 40 0.63 0.69 0.76 0.74 0.77 0.78 0.72 0.73 0.72 0.53 0.53 0.50 60 0.80 0.81 0.83 0.82 0.84 0.86 0.79 0.80 0.80 0.52 0.52 0.48 80 0.88 0.88 0.90 0.88 0.88 0.90 0.84 0.85 0.86 .0.52 0.52 0.49 100 0.92 0.92 0.92 0.92 0.92 0.92 0.87 0.89 0.88 0.51 0.52 0.51 120. 0.93 0.93 0.93 0.93 0.93 0.93 0.83 0.87 0.87 0.43 0.46 0.45 140 0.94 0.94 0.93 0.92 0.93 0.9,3 0.67 0.75 0.74 0.38 0.38 0.37 160 0.94 0.94 0.93 0.90 0.92 0.91 0.43 0.44 0.42 0.23 0.29 0.27 170 0.94 0.94 0.93 0.51 0.57 0.52 0.38 0.36 .0.36 0.32 0.29 0.29 180 0.94 0.94 0.94 0.34 0.35 0.35 0.32 0.32 0.35 0.24 0:30 0.32

APPENDIX D (CONT.)

2. Axial velocity component ratios in the propeller plane of the model at full load draught

fitted with various two vortex generator systems at an angle of incidence of 200.

24 0 (Degree) u/ U r/R = 1.23 r/R = 0.96 r/R = 0.68 r/R = 0.41 h1=8.4 111=10.7 111=8.4 h1=10.7 hi=8.4 111=10.7 111=8.4 111=10.7 mm mm mm mm mm mm mm mm

(0.33in) (0.42in) (0.33in) (0.42in) (0.33in) (0.42in) (0.33in) (0.42in)

0 0.42 0.43 0.44 0.43 0.43 0.41 0.28 0.32 10 0.58 0.57 0.58 0.54 0.54 0.51 0.43 0.38 20 0.65 0.67 0.66 0.67 0.62 0.60 0.50 0.47 40 0.70 0.76 0.77 0.78 0.71 0.69 0.50 0.48 60 0.82 0.83 0.84 0.85 0.78 0.77 0.48 0.46 80 0.88 0.90 0.88 0.90 0.84 0.83 0.48 0.45 100 0.92 0.92 0.92 0.92 0.84 0.85 0.46 0.43 120 0.93 0.93 0.93 0.93 0.81 0.82 0.40 0.40 140 0.94 0.94 0.94 0.93 0.65 0.68 0.37 0.34 160 0.94 0.94 0.88 0.89 0.42 0.42 0.25 0.26 170 0.94 0.94 0.50 0.58 0.38 0.36 0.28 0.29 180 0.94 0.94 0.34 0.34 0.30 0.34 0.28 0.32

APPENDIX E

Axial velocity component ratios in the propeller plane of the model at ballast draught fitted with six, four, and two vortex

generators. u/U r/R=I.23 r /R=0.96 -r/ R=0.68 r / R=0.41 B al= , /0° a = 25° a = 20° a = 25° ' a = 20° a = 25° a = 20° -a = 25° -(Degree) h ,=10.7mm hi =10.7mm h1=8.4mm h1=10.7mm 111=10.7mm h1=8.4mm ht=10.7mm h 1=10.7mm hi=8.4mm h 1=10.7mm 111=10.7mm hi=8.4mm (0.42in) (0.42in) (0.33in) (0.42in) (0.42in) (0.33in) (0.42in) (0.42in) (0.33in) (0.421n) (0.421n) -(0.33in) h2= 8.4mm h2= 8.4mm h2= 8.4mm h2= 8.4mm h2= 8.4mm h2= 8.4mm h2= 8.4mm h2= 8.4mm (1133in) (0.33in) (0.33in) (0.33in) (0.33in) (0.331n) (0.33in) (0.33n) 113= 6.4rnm h3= 6.4mm 113= 6.4mm . h3= 6.4mm (0.25in) (0.251n) (0.25in) (0.251n) 0

-0.44 0.50 050 0.48 0.50 0.50 0.46 0.48 0.45 10

-0.44 0.59 ' 0.57 0.48 0.57 0.57 0.49 0.49 0.50 20

-0.52 0.66 0.61 0.60 0.65 0.65 0.56 0.55 0.56 40 0.56 0.59 0.58 0.60 0.73 0.65 0.73 0.71 0.71 0.67 0.62 0.62 60 0.69 0.74 0.62 078 0.80 ' 0.74 080 0:78 0.76 070 0.64 0.64 80 0.88 0.88 0.84 0.87 0.86 0.84 0.85 0.83 0.81 0.74 0.64 0.61 100 0.92 0.92 0.90 0.91 0.91 0.88 0.88 0.86 0.79 0.74 0.60 0.54 120 0.94 0.94 0.94 0.93 0.94 0.92 0.90 0.80 0.65 0.63. 0.52 0.46 140 0.94 0.94 0.95 094 ' 0.86 0.89 0.80 0.57 0.50 0.55 0.46 0.43 160 0.94 0.94 0.94 0.88 0.78 0.66 0.49 0.46 0.45 0.44 0.35 0.31 170 0.94 0.94 0.92 0.55 0.45 0.43 0.49 0.45 0.43 0.43 0.39 0.37 180 0.94 0,94 0.92 0.40 0.39 0.39 0.43. 0.45 0.41 0.39 0.38 0.35

APPENDIX F Resistance coefficients

I. Resistance coefficients for the model without vortex generators.

26

Full load Ballast

RN X 10-6 CD X 103 RN X 10-6 CD X 103 3.39 3.91 8.25 3.91 3.90 4.25 9.06 3.87 4.98 4.25 9.79 3.82 5.64 4.13 10.61 3.79 7.06 3.97 11.88 3.75 8.05 3.90 8.87 3.85 9.61 3.83 10.50 3.79 11.63 3.78

APPENDIX F (CONT.)

2. Resistance coefficients for the model fitted with six vortex generators.

27

hi = I0.7mm (0.42in), h2 = 8.4mm (0.33in), h3 = 6.5mm (0.25in)

Full load Ballast

a = 17° a = 20°

a =25°

a = 20° RN X 10-6 CD X 103 RN x 10-6 CD x 103 RN x 10-6 CD x 103 RN x 10-6 CD X 103 8.14 4.06 8.24 4.19 8.24 4.24 8.13 4.16 8.96 4.03 9.00 4.13 9.00 4.19 8.92 4.14 9.71 3.97 9.60 4.06 9.76 4.16 9.70 4.05 10.51 3.94 10.51 4.02 10.44 4.16 10.48 4.02 11.77 3.87 11.77 3.98 11.82 4.07 11.79 4.01 a -= 20° Full load 111=8.4mm (0.33in) h1=12.7mm (0.50in) h2=6.4mm (0.25in) h2=10.7mm (0.42in) h3=6.4mm (0.25in) h3= 8.4mm (0.33in) RN x 10-6 CD x 103 RN X 10-6 CD X 103 8.35 4.10 8.27 4.30 9.17 4.01 8.96 4.30 10.00 3.99 9.84 4.26 10.76 3.98 10.69 4.18 12.01 3.91 11.95 4.14

APPENDIX F (CONT.)

3. Resistance coefficients for the model fitted with four vortex generators.

28

hi = 10.7mm (0.42in), h2 = 8.4mm (0.33in)

Full load Ballast

a = 17° a = 20° a = 25° a = 20° RNX 10-6 CD X 10. X 10-6 CD X 103 RN X 10-6 CD X 103 RNX 10-6 CD X 103 _ 8.25 4.04 7.56 4.22 8.16 4.21 7.95 4.20 9.00 3.99 8.11 4.13 8.85 4.17 9.06 4.11 9.73 3.97 8.96 4.11 9.71 4.14 9.79 4.07 10.54 3.95 9.58 4.04 10.50 4.13 10.73 4.00 11.65 3.90 10.58 4.03 11.65 4.06 11.89 3.99 11.70 3.97 a = 20° --Full load hi = 8.4mm '(0.33in) hi = 12.7mm (0.50in) h2 = 6.4mm (0.25in) h2 = 10.7mm (0.42in) RN A 10-6 CDX 103 RN .X 10-6 CD .X 103 8.27 4.10 8.22 4.25 8.96 4.05 8.95 4.22 9.90 4.00 9.77 4.18 10.73 3.95 10.62 4.16 11.96 3.92 11.88 4.12

APPENDIX F (CONT.)

4. Resistance coefficients for the model fitted with two vortex generators.

29

a = 25°

_

Full load - Ballast

111 = 6.4mm (0.25in) 111 = 8.4mm (0.33in) 111 = 10.7mm (0.42in) hl = 8.4mm (0.33in)

-.RN x 10-6 Co x 103 RN x 10-6 Co x 104 .RN x 10-6 Co x 103 RN x 10-6 CD X 103 8.27 4.03 8.23 4.06 8.13 4.16 8.27 4.06 9.03 4.01 9.10 4.03 8.82 4.10 9.06 4.00 9.81 3.97 9.88 3.98 9.71 4.03 9.80 3.99 10.72 3.91 10.49 3.97 10.52 4.02 10.76 3.93 11.96 3.86 11.80 3.88 11.67 3.95 11.90 3.92

a =

20° Full load

= 8.4mm (0.33in) III = 10.7mm (0.42in)

RN X 10-6 CD X 103 RN X 10-6 CD X 1b3 8.30 3.98 8.24 4.07 8.96 3.98 8.90 4.03 9.86 3.92 9.71 3.98 10.73 3.87 10.44 3.94 11.84 3.82 11.73 3.92

SHIP BODY SECTION LINES.

7

BOW CONTOUR AND WATERLINE ENDINGS'.

8.2 m (27 ft.) 13.7 m (45 ft.) 9.2 m (30 ft.) L.W.L. 4.6 m (15 ft.) 0.9 m (3 ft.) 0 Station ,No. 8% 91/4 9 9% 10 F.P.

13.7'm (45 ft.)

STERN CONTOUR AND WATERLINE ENDINGS.

L.W.L. m

(45 ft)

_{al k°}

. Ng)

0

11

. Station No. 0 1/4 1/2 1 A.P. 9.2 m (30 ft.) 4.6 m (15 ft.)

0

Station No:

Ii

I>

II:

m xi

'Ii

0

1 I :Z I I

0

i

I

-I

-71 T. i 61 CO -1=h 00 1.53 m (5.0 fit.) 3.57 m (11.7 ft.) 1/4 1/2 0.20 m (0.65 ft.)

PROPELLER AND STERN ARRANGEMENT.

1181m

2.56 m (8.4 ft.)

FLOW PATTERN OVER THE STERN OF THE FULL LOAD DRAUGHT MODEL

-,...

--'';

FLOW PATTERN OVER THE STERN OF THE BALLAST DRAUGHT MODEL

WITHOUT VORTEX GENERATORS.

1.0 _0.8

u/U

0.6 0.4 0.2

MIND =MED MIMI :WINN.

=MI 411=1=11=11 =NEMO r/R = 1.23 r/R = 0.96 r/R = 0.68 r/R = 0.41 NIMS. 111/1 MOD O. 0 I I I I i I 1 I 1 I 1 1 t i 1 0 20 40 60 80 100 120 140 160 180

AXIAL VELOCITY DISTRIBUTION, IN THE PROPELLER PLANE OF THE MODEL WITHOUT VORTEX GENERATORS

1.0 _0.8 u/U 0.6 0.4 0.2 0.0 20 40 , 60 80 100 0 0 120 140 160

AXIAL VELOCITY DISTRIBUTION IN THE PROPELLER PLANE OF THE MODEL WITHOUT VORTEX GENERATORS

AT BALLAST DRAUGHT.

11. 1 107 mm 93 mm (4.20 in) (3.65 in)

0

d°

Generator No. 3

(a) Vortex generator location

132 mm (5.20 in) (1 135 mm (5.30 in)

0

fl terllne 41 mm _{(1.60 in)} s 118,mm (4.65 in)

0

Generator No. 2 2 Station No. 20 mm _{(0.80 in)} 161 mm (6.35 in)

0

Generator No. 1 146 mm (5.75 in)

0

Note:

Similar generators are fitted to opposite side of hull. Changes in angle of incidence are made _{by pivoting generators about their} trailing edge. Position of the trailing edge is the same for all generator sizes: 0 = Girth measurement.

LOCATION AND SIZE OF THE SIX VORTEX GENERATOR SYSTEM

FITTED TO THE MODEL AT AN ANGLE OF INCIDENCE OF

20°. . XI

0

0

--n m 6") co ' 01 CO CO

Shape to surface curvature and attach to hull. Forward edge of generator

Note:

Generator.is attached normal to hull surfaceat two-thirds _{.generator length aft otforward tip.}

(b) Vortex generator dimensions.

Generator

No.

b

1 3

38.1 mm _{' (.1.50 in)} 30.5 mm (1.20 in) _{. 22.9 mm} ,(0.90 in);

; 107 mm (0:42 in) : 8.4 mm (033 in) 6.4 mm , (0.25 in)

FLOW PATTERN OVER THE STERN OF THE FULL LOAD DRAUGHT MODEL FITTED WITH SIX VORTEX GENERATORS hi = 10.7 mm (0.42 in)

w 04(1 rrl

0

0

"r1 M C4 .1 01 co

FLOW PATTERN OVER THE STERN OF THE BALLAST DRAUGHT MODEL FITTED WITH SIX VORTEX GENERATORS hi = 10.7 mm (0.42 in),

20 40 60 80 00 100 (a) FIR = 1.23

AXIAL VELOCITY DISTRIBUTIONS IN THE PROPELLER PLANE OF THE MODEL AT FULL LOAD DRAUGHT FITTED WITH SIX VORTEX

GENERATORS h1 = 10.7 mm (0.42 in), h7 = 8.4 mm (0.33 in), h3 = 6.4 mm (0.25 in), AT

ANGLES OF INCIDENCE OF 17°, 20°, 25°. 120 140 160 180 1.0 ₀₁₈ u/U 0.6 0.4 0.2 0.0

../."

011.°./ 1011. o' 0 4/ 03111.111 No = 17°

a

= 20°

a= 25°

vortex generators 1111=15 INIMMENS 11.MMOR=NNB 011IND ,11

1:0 - 0.8 u/U 0.6 0.4 0.2 20 _ 40 1 I 1 60 1131=.1=MMII fib 011 Me= 41H MEM 111,' 41=1 (b) r/R = 0.96 a = 17° a = 20° (X = 25° No vortex generators -1 1 1 80,

0°

100_ 120 146 160 180

u/U 1.0 0.8 0.6 0.4 0.2 0.0 ...---..-1 I

.

_.../

.... ...,, ... .... .... ...-. ... .... ...

N

\ \

/

N

\

/

%

a

= 17° ..--...

a

= 20° 1

a

= 25°

-% % No vortex generators I I i I i 180 160 140 20 40 60 80 00 100 (c) r/R 0.68 120 0 - 0 z

1.0 _{0.6 0.4 0.2 0.0}

INIMI=1

MEMO Mmil . a = 17° LX = 20° a = 25° No vortex generators I I (d) r/R = 0.41 ...ar. 1 %

/

% .1=MI 0 20 40 60 80 00 100 120, 140 160 180 -14, 0.8 u/U

u/U 1.0 0.8 0.6 0.4 0.2 0.0

-,

Z

.9

e

.

..

- ...--_....,

/

I /

_/

e

e

= 8.4 mm (0.33 in), h2 = 6.4 mm = 103 'mm (0.42 in), h2 = 8.4 = 12.7 mm (0.50 in), h2 = 10.7

vortex generators. _______I____

[

I (0.25 in), h3 mm (0.33 in), h3 mm (0.42 in), I = 6.4 mini (0.25 =6.4 mm (0.25 h3 = 8.4 mm '(0.33 I

/

/

in) in) in) h1 No _L_____I 1 0 20 40 60 80

00

100 120 140 160 180

(a) r/R =123

AXIAL VELOCITY DISTRIBUTIONS IN THE PROPELLER PLANE OF THE MODEL AT FULL LOAD DRAUGHT FITTED WITH VARIOUS

06

0.4 0.2 0.0 (b) r/R = 0.96 , ,

../

...

..

.... ...

r

... ...

e

... I...0" % 1 .

,

_/

,

/

/

,7

h1 = h1 = h1 = No vortex I 8.4 mm (0.33,in), 10.7 mm (0.42 12.7 mm (0.50,in), generators ' I i h2 = 6.4 mm in), ih2 =8.4 mm h2 = 10.7 mm ' i I . , (0.25 in), h3 = (0.25 in), h3 (0.42 in), h3 , i I 6.4 mm (0.25 in) ₌6.4 mm (0.25 in) -=8.4 mm _{(0.33 in)} I A % % % 1

-\

%.

..

--- ---

I II' - I I , 1 I 0 20 40 60 80 00 100 120 -140 160 180 0.8 u /U

(c) r/R = 0.68 ,

- ...

--.... -,.. *.i. %. . ....

/

,. h = 8.4 mm (0.33 in), h = 6.4 mm (0.25 in), mm ( 0.25 in).

.

.

h3 = 6.4 ... ...,, h1 = 107 mm (0.42 in), h2 = 84 mm (0.33 in), h3 = 6.4 mm (0.25 in). % _, 1 h1 = 12.7 mm (0.50 in), h2 = 10.7 mm (0.42 in), _ -h3

-8'4 mm (0.33 in). No vortex generators. 20 40 60 80 00 100 120 140 160 180 1.0 0.8 u/U 0.6 0.4 0.2 0.0

u/U 1.0* 0.8 0.0 0.4 0.2 0.0 (d) r/R = 0.41 I , I I

I

, I , I 'I I I , 1 .

...

, . -. ....

T-...,_

1 , .

-IM1 IM lft OM OS OW4OM, 41=1 fti, MO .0 Oft ... . .ft "Oft....

-hi = 8.4 mm (0.33 in), h2 = 6.4 mm (0.25 in), h3 =6.4 mm (0.25 in) UNftImMIIIIIM

-

h = 10.7 mm (0.42 in), h2 = 8.4 mm (0.33 in), h3 = 6.4 mm (0.25 in)

/ .

A li = 12.7 mm (0.50 in), h2 = 10.7 mm (0.42 in), h3 = 8.4 mm (0.33 in) ! ,

----No vortex generators. I I 1 I 1 I 1 1 L , I 1 I I 1 1 ! 1 140 1:60 20 40 60 80 00 100 180 120 0

180

#

'4.. %

.

...

#

#

,

#

#

## I

-

_. -. = 84 mm (033 . . = 10.7 mm ,(0.42 = 10.7 mm (0.42 = 6.4 mm (0,25 No vortex generators. h h3

.

in), a = 25° in), h2 = 8.4 in), h2 = 8.4 in), a =20° mm (0.33 in),, mm (0.33 in), ,

-,

a

= 20°

-h

-20 40 .60 80

0°

100 120 140 160 (a) r/R = 1.23

AXIAL VELOCITY DISTRIBUTIONS IN THE PROPELLER PLANE OF THE MODEL AT BALLAST DRAUGHT WITH SIX, FOUR

AND TWO VORTEX GENERATOR SYSTEMS.

1.0 0.8

u/U

I 1 I I .... I ....

---.

I I

...

I ,

-....

.--'..-..7/

....

...-.../

,.., 4, .0

.

/

'

....

..

.

\

\

1

\

....e;''.

-h 1 h1 h1 h3 No =8.4 mm (0.33 = 10.7 mm (0.42 = 10.7 mm (0.42 = 6.4 mm (0.25 vortex generators I

I

in), a

= 25° in), h2 = 8.4 in), h2 = 8.4

in), a

= 20° mm (0.33 in), mm (0.33 in), I

\

a

= 20°

\

\

\

%

\

\

\

-\

% '11

...

-I i I 1

-0 20 40 60 80

0°

1'00 120 140 160 180 (b) r/R = 0:96 1.0 _0.8 u/U 0.6 0.4 0.2 0.0

-...

\

\

\

I

\

\----

\

I ....

-

. ... ....-.... ...

,

... ....t N. **. .0

/.

.0' P h = 8.4 mm (0.33 in), mm (0.42 in), mm (0.42 in), (0.25 in)' generators

a

= 25° h2 = 8.4 mm h2 = 8.4 mm CE= 20° , (0.33 in), a = 20° (0.33 in), _

...

i hi = 10.7 h = 10.7 113 = 6.4mm No vortex

--

-

--0 20 40 60 80

0°

100 (c) r/R = 0.68 1.0 0;8 u/U 0.6 0.4 0.2

ao

120 140 160 1180

1.0 0.8 u/U 0.6 0.4 0.2 0.0 (d) r/R = 0.41 I I 1 i -I I , . I i I I I I i 1 . I . ... MZEN=...0 . .41.440%%. ...b..%. .. 1 ... ...

-

---1.---e

,

e

../

... '

....-.... ....-... .... .0, -. .111/.. ... ... ... ... I

...

..

..., ... .... , '1'....,... ... .... -... ... .... -.. ..,. "...

"1...

.N...

-"...

...

.. hi h1 h1 h3 No = 8.4 mm (0.33

=10.7 mm

(0.42 = 10.7 mm (0.42 = 6.4 mm (0.25 vortex generators. I I in), CY = 250 in), h2 = 8.4

in), h2 =8.4

_{in), a =}

20° I I ,

mm (023 in),

mm (0.33 in); I 1

a =

20° -I I ....

% -

...

--%

A

-. . -I I

-I

-

-I

-I I 0 20 40 60 80 00 100 120 140 160 180

FLOW PATTERN OVER THE STERN OF THE FULL LOAD DRAUGHT MODEL FITTED WITH FOUR

VORTEX GENERATORS

-FLOW PATTERN OVER THE STERN OF THE MODEL AT BALLAST DRAUGHT FITTED WITH FOUR VORTEX GENERATORS

,u/U 1.0 0.8 0.6 0 1 20 40 a = 17° a = 20°

a = 25°

--- No vortex generators

IMO 1111 i I I 1 I 1 I

I-60 80 00 100 120 140 160 180 (a) rill = 1.23

AXIAL VELOCITY DISTRIBUTIONS IN.THE PROPELLER PLANE OF THE MODEL-AT FULL -LOAD DRAUGHT FITTED WITH FOUR

_

VORTEX GENERATORS h1 = 10.7 mm (042 in), h2 = 84 mm (0.33 in), AT ANGLES OF INCIDENCE OF

17°, 20° AND 25°.

1.0 0.8 0.6 0.4 0.2 0:0 40

a 17°

a =20°

= 25° No vortex generators 60 80. 00 100 (b) r/R = 0.96 Lommism 120 140 160 180 -n

u/U 1.0 _0.8 0,6 . 0.4 0.2 0.0 0 60. , .1MNIMMI .1.=111 1111M

..i...= sm.

sme. 80

0°

100 (c) r/R = 0.68

a= 17°

a= 20°

q= 25°

No `vortex generators 120 S. S. 140 160 awd 180

20 40 60 80

0°

100 (d) r/R = 0.41 , ... ...

7---r"

... ... .. ...,

N

.,,,...

-.

. .

..., _.

...,

... .

..

a

= 17°

a

= 20° vortex generators

/

t

% ...; NO '1.0 0.8 u/U 0.6 0.4 0.2 0.0 120 140 160 180

u/U

1.0 0.8 0.6 0.4 0.2 0.0 AXIAL VELOCITY DISTRIBUTIONS IN THE PROPELLER PLANE OF THE MODEL AT FULL LOAD DRAUGHT FITTED WITH VARIOUS

SIZE FOUR VORTEX GENERATOR SYSTEMS AT AN ANGLE OF INCIDENCE OF 20°.

1 I 1 I 1 1 I I ,

,

-0/

/

.0'

-../

./

.

/

./.

/

_/

/

# /

/

-/

/

_/

.-

---, =8.4 mm (0.33 in), h2 = 6.4 mm (0.25 in)

,

....

,

h1 7 107 mm (0.42 in), h2 = 84 mm (0.33 in) h1, = 12.7 mm (0.50 in), h2 = 10.7 mm (0.42 in)

r--

---,---No vortex generators

--I I

I1

I i I I I I I I 20 40 60 -80 190 100 120 140 160 180 (a) r/R =1,.23.

I I I I I

_

I ...- -. I 1

-\

_

\

/

./

/

.,

..

/

_ % = 8 4 mm (0.33 in), h2 = 6.4 mm (0.25 in) mm (0.42 in), h2 = 8.4 mm (0.33 in) I

-hi = 10.7 12.7 mm (0.50 in), h2 = 10.7 mm, (0.42 in) OM MD h1 =

---No vortex generators , ,

\

, I I

III ill Ii

II 1 1 20 40 60 80 00 100 120 1140 160 180 (b) r/R = 0.96 1.0 0.8 0.6 0.4 0.2 0.0

1.0 _0.8 u/U 0.6 0.4 0.2

₀₀

0 20 40 60 80 00 100 (0 r/F1 = 0;68-120 140 160 180 1 1 ' 1 . . 1 1

...--"7

1 1 , ...4%,%S. ! '""""" ,sa.

\

\

\

t

1 . . ....

--.

7

1 ... ..,. .... ... ... .

7

, . ... -.0 .- ... ... ... .... ... , .... .... . . ...#

/

.... .0 ... ... h1 = h1 = h1 = I No vortex 8A mm (0.33 in), 10.7 mm (0.42 12.7 mm (0.50 generators 1 I . . h2 =6.4 mm in), h2 = 8.4 mm _ in), h2 = 10.7 rum .1 I , (0.25 in) (0.33 in) (0.42 in) ' I A . . 1

t

% 1 _ab4 -I

=

-I , 1 1 , I 1' .

r , r

... ...

... I =I / I° I. GOO 0.4.

,...

ft

...

NO h1 hi No I =8.41mm (0.33 = 10.7 mm (0.42 = 12.7 mm (0.50 vortex generators 1 I me a mo. in), h2 = 6.4 in), h2 =

84

in), h2 = 10.7'mm I I mm (0.25 in) mm (0.331in) (0.42 in) I ... I % masa& Ime .., 0,

/

I -I 1 % %.

---1 I 1 0 20 40 60 80

0°

loci

120 140 160 180 (d) r/Fi = OAT

10

0.8 u/U 0.6 0.2 0.0

Note:

'Similar generator is fitted on opposite side of hull. Changes in angle of incidence are made by pivoting generator about its trailing edge. Position of the trailing edge is the same for all generator sizes. 0 = Girth measurement.

1111111 terllne 5 mm (0.20 in) 2 150 mm _{(5.92 in)} 1

0

4=11 133 mm _{(5.25 in)}

0

Station" No. Generator No. 1

FLOW PATTERN OVER THE STERN OF THE FULL LOAD DRAUGHT MODEL FITTED WITH TWO VORTEX GENERATORS