Resistance and Propulsion of Ships
MT512, Preliminary
Prof. Dr. Jr. G.Kuiper1
July 5, 1991
'MABJN, Maritime Research Institute Netherlands, Wageningen, Technical University Deift
Contents
1 1 2HulIforms
1.1 Displacement Hulls1.2 High Speed Ships 1.2.1 Planing Hulls 1.2.2 HydrOfoils
1.3 Air as carrier
1.3.1 Air Cushion Vehicles
1.3.2 Surface Effect Ships . .
1.4 Multihulls
1.4.1 Catamarans .
1.4.2
Swath ...
Propulsors
2.1 Propellers .
2.1.1 Controllable Pitch Propellers .
2.12 Overlapping Propellers
...
2.1.3 Contra Rotating Propellers .
2.1.4 Supercavitating Propellers
2.1.5 Surface Piercing Propellers 2.1.6 Agouti Propellers 2.1.7 Tipplates . . 2.18 Vane wheels 2.2 Ducted Propellers
...
2.2.1 Ringpropellers 2.2.2 Mitsui duct 2.3 Other Propulsors . . . 2.3.1 Voight-Schneider Propellers 2.3.2 Paddle-Wheels . . . 2.3.3 Pump Jets 2.3.4 Sails2.3.5 Other Types of Propulsion
17 18 26 30 30 31 31 35 38 9 9 11 14 115 17 17 18 18 21 21 23. 23 25 25 26 26 26 27 31 35
3 Resi8tance of simple. bodies
403.1 Non-dimensional Coefficients . .. 40
3.2 Flow Phenomena 43
3.3 Drag Components . . . 45
3.4 Drag and Wake 45
3.5 Sphere . . - 47
3.6 Flat plate perpendicular: to the flow
... ,.
...
. 483.7 Flat plate in the flow direction ..
...
483.8 Additional data,
...
493.9 Summary 50
4.
Resistance and Wake Distribution
514.1 Cross flow . 51
4.2 Separation 53
4.3 The Wake behind Simple Shiplike Bodies 56
441
Horse-Shoe Vortices
...
604.5 Ship Wake 60
4.6 Wake Fraction 82
5 Wave Resistance
665.1 The Kelvin Wave System . . . 66
5.2 Ship Generated Waves 67
5.3 Interference Effects 68 5.4 Non-dimensional Representation 72 5.5 Economical speed . . . 72. 5.6 Hull speed . . . 74 6
Scaling Rules
77 6.1Dimension Analysis...
78 6.2Scaling rules ...
. 80 6.3 Scale effects 827 Resistance Prediciion, using model tests
837.1 Elenients of ship resistance . 83
7.2 Scaling laws for Model Tests 84
7.3 Froudes. hypothesis 85
7.4 Determination of Resistance Components
...
. 857.5 Extrapolation of Resistance Tests . 90
7.6 Effective power . . 92.
7.7 Effects of Laminar Flow .
...
. 937.8
Wake Scale Effects ...
. ., . . 933
8 Resistance Prediction' using Statistical or Systematic Data
1008.1 General Considerations for Hull Design .. .. .. 100
8.2 Systematic Series . 101
8.3 Regression of available data 103
8.4 Design of Curve of Sectional Areas by Lap 106
8.5 The method of Holtrop and Mennen . . . 107
8.6 Example of Resistance Prediction
..
. 1098.7 'Resistance of Small Vessels
III
9 Equations of Motion
11291 The Continuity Eq:uation. . 113
9.2 The Equations of Motion . . .
... .
. . 1149.2.1 Rotation and Deformation
..., .
...
, 1169.2.2
Relation between Stresses and Strain ...117
9.2.3 Navier-Stokes Equations 118
9.3 A Simple Example 119
9.4 The Euler Equations . 120
9.5 The Bernoulli Equation . 121
9.6 Summary 121
110 Potential flow 123
10.1 Singularities in potential flow . . . .. . . . .. 124
110.2 A Simple Example of Potential Flow . 126
10.3 Forces on a Vortex . . 128
10.4 Biotand' Savart . 129
10.5 Panel methods 130
10.6 Summary 131
11 Flow Calculations
13311.1 Hess and Smith . . . 133
11,2 Michell Theory for, Wave resistance .
... 138
11.3 Dawson 141
11.4 N!avier-Stokes solutions.., . 145
11.5 Presentation of programs . . 147
12 Axial Momentum 'Theory
15212.1 Axial Momentum Theory 152
12.1.1 Efficiency . . . 155
12.2 Optimum Radial Loading Distribution . 156
13 The Propeller Geometry
15913.1 General Outline . . . 159
132.I NACA Definition of Thickness and Camber . 163.
13.2.2 Root and: Tip ...
. 16413.3 Pitch and Pitch Angle . . .. 164
1:3.4 Propeller Plane and Propeller Reference Line . 165
13.5 Rake 166
13.6 Skew
...
16613.7 Blade Contours and Areas .
... .
. . . 16813.8 Warped Propellers 170
13.9 The Propeller Drawing, . . . 170
13.iODescription of a P±opeller . . 171'
13.1iControllablè Pitch Propellers. .. . :. 173
14 Open Water Tests
. 17414.1 Open.. Water Performance 176.
14.2 Extrapolation of Propeller Characteristics:
18
14.2.1 The Equivalent Blade Section
... 178
14.3 Corrections for Reynolds Effects
...
17914.4 Example ...
. . . 18215 Systematic Propeller Series
. 184.15.1 Propeller design using B-series charts .. .. 1'85
15.2 Example . 187
15.3 The B - S diagrams
... .
. . 19015.4 Four Quadrant Measurements . . . 194
16 Profile Characteristics
19716.1 Profile characteristics . 197
16.1.1 The lift curve 197
16.1,2 The Pressure DistributiOn 198
16.L3 The Cavitation Bucket 199
16.1.4 The ideal angle of attack . . 202
16.1.5 Profile drag
...
20216.2 Profile Series . . 203
16.2i. Thickness distributions . .
... 203
16.2.2 camber distributiOns
... 203
16.2.3 NACA five digit series 203
16.3 NACA four digit series 205
17 Thin Profile Theory
209:17.1 Vortex Distributions . .
. 209
17.2 Source Distributions . . . ,. . 212
17.3 The Linearized Boundary Condition 213
5
17.5 Circulation 216
17.6 The Kutta Condition ... 217
17.7 A Flat Plate... 218
17.8 Thin Profiles with Camber 218
1.7.9 Leading Edge Suction Force . . .. 218
18 Cavitation
22118.1 Types of Cavitation 221
182 Detrimental effects of cavitation
...
. .. 22518.2.1 Erosion . . . 225
18.2.2 Noise, Radiation 226
18.2.3 Vibrations
... 227
18.2.4 Thrust Breakdown... 228
1.9 Lifting Line Propeller Design
23019.1 Induced Vélócities 230
19.1.1 Optimum circulation distribution . . 232
19.1.2 Induction factors . 233
19.2. Propeller design . .. .. 233
19.2.1 Lifting surface corrections . .. 234.
19.2.2 Viscous corrections
...
. . . . ... 23619.2.3 Extension of lifting line calculations . . 236
20 The Propulsion Test
23720.1 The Additional Towing Force 237
20.2 Overload Tests 238
20.3 Scaling laws 239
20.4 Propeller Hull Interaction 240
.20.4.1 Thrust Deduction
... ..
. . .. 24020.4.2 Taylor Wake Fraction .. . 241
20.5 Extrapolation . 242
20.6 Efficiencies .243
20.7 Variations on the Extrapolation Method . . .. 244
20.8 Example ..
...
., 24620.8,1 Comparison with Resistance Test . . . 248
20.9 Extrapolation of the. example using, the Mann method . . 251
21 Propulsion calculations
. 255.
21.1 Flow around the hull . . . 255
21.2 Effective wake . . .. . 257
21.3 Cavitation tests 259
Preface
This text is a preliminary version of courses on 'ship resistance and propulsion for
Deift. University of Technology.
Structure of the course
The first part of the course is on resistance, the second part on propellers, the third part is on propulsion, which means both resistance and propulsion, interacting in the complete ship/propulsor combination. This sequence has been chosen because it
allOws a gradual introduction of the concepts' involved.
The prediction of resistance, propeller and propulsion characteristics are
ap-proached. in three ways:
By extrapolation from model test. results. By the use of systematic or statistical data.
By flow 'calculations
This sequence is natural since model tests form the basis for many systematic data sets. The development of computational fluids dynamics (CFD) has been rapid in
the last decade, so 'these methods. have become a considerable help in the prediction of the behaviour of ships at full scale. Model tests and computations are often
com-plementary, bOth having their advantages and disadvantages. Model. tests have, the
disadvantage, of possible scale effects, but have the advantage that complex flow
phe-nomena can be simulated. Calculations have the advantage that the flow can easily be calculated in detail and that variatiOns can be made rather easily To be able to make calculations it is generally necessary to make drastic simplifi'cations (inviscid flow e.g.,). An important aim of this course is to explain the complementary role of calculations and model tests.
The text is written in a sequence which allows sequential reading. The text is also to be used for different courses and' the. titles of the. chapters reflect these purposes.
References
Since this course is aimed at an understanding of the basic approach .of a topic, a
limited use of references has been made. In most cases users of this course will not yet
July 5, 1991, Preface 7
Introductory course MT512
The texts is written for an introductory course for students which have only basic
knowledge of mathematics and fluid dynamics. This course covers the basics of resis-tance and propulsion. The propeller inflow is simplified to an average uniform inflow
and the propeller loading is consequently assumed to be- stationary. The unsteady conditions will be dealt with in an advanced course (MT515).
Intermezzo's
The basic knowledge on fluid mechanics, required for the understanding of the intror ductory course, may not always be available. Therefore some chapters on the basics of fluid meëhanics, such as the equations of motion and its simplifications, notably potential flow and boundary layer flow, have been included. These chapters, which are not a part of the introductory course, are indicated as Intermezzo in the ob-jective. The reader who S: familiar with these topics can skip these chapters, others
can read them without going into great detail. The objective of these chapters. is to show the basic approach, not the details. Some equations are therefore worked out in one direction only. This makes it possible to avoid vector analysis, which is nearly unavoidable for the full three dimensional equations.
Additional data and questions
In the text some additional data, such as formula's which are often used, are printed in smaller letters. This text is only given for convenience when the reader is going to use the material: for his own purposes. It is not a part of the text and can be omitted. This is also done with questions at the end of a chapter.. The questions have been posed at the examS for the courses.
Important formula's or statements
Some conclusions, formula's or definitions are important throughout the text. In
order to recognize and retrieve these more easily, a box has been placed around the text involved.
G.Kuiper, Resistance and Propulsion, July 5, 1991 study literature of the subjects in depth. No efforts have been made to refer to the most recent literature For that the references in the Proceedings of the International Towing Tank Conference can be used. [61 The course is also not aimed at a full inventory of the practical experiences with the methods and concepts, treated in the course. For this the Principles of Naval Architecture [7] are more suitable. Instead the references have been selected for their ability to increase understanding of basic
concepts.
Further developments
This text is very prelimanary! The text will be further developed. in the future. Any comment can be helpful to improve it and will be very welcome.
Chapter 1
HüIiforms
Objective:
introduction of the hydrodnarnic features of some main types of ships and of the names used to describe these features. The names introduced in this chap-ter are written in italic The meaning of these names and the general properties ofthe concepts should be known.
ii
Displacement Hulls
The most common purpose of a ship is transport of cargo. For such ships the dis-placement hull is the most appropriate. The weight of the cargo and the fuel (tons
deadweight), together with the weight of the ship itself, is the displacement of the ship
(Achimedes' law). The movement of such a displacement ship requires little energy. in comparison with other means of transport, as long as the speed is limited. For bulk transport speeds of up to 16 knots'
The required energy per unit distance increases rapidly with the speed, so the speed is an important parameter fOr the hull form:. For large, fast displacement ships, speeds of up to 22 knots are found, with extremes of over to 30 knots for eig.passenger vessels and up to 40 knots for navy ships.
A characteristic hull form for slOw bulk transport is the tankerform (Fig 1.1).
The ideal form fOr the shipowner is a square shape, but the consequences of such a simple shape in terms of resistance are too large. So bow and stern are shaped such
'Although SI units should be used the speed of a ship is still expressed in knots, which is an
international or U.S. nautical mile of 1852 meter per hour. The U.K. nautical mile of 1:853.1:84 meter is also used Note that the nautical mile is different from the statute mile of 1609 344 meter, which is used for distances over land.
July 2, 1991, Hullforms 11
that the. volume, remains but the resistance is optimised. The form of the stern is determined by. the requirement of attached flow and proper inflow to the propeller. The shape of the .bow is strongly determined by the generation of waves.
Fort tanker it is t3pical that the ship is operated at two strongly different' drafts: loaded 'and ballast. The hull shape in these two conditions is quite different.
The shape 'of the bow is strongly affected by the fullness of the ship, which is
expressed in the biockcoefficient C8, defined' as
C-B Ii,
- LBT
.'I.'
with =disp1acement, b=length between perpendiculars, B=breadth en T=draft.
Far very full ships with blockcoefficients, over 0.80 a cylinderbow"is applied (See
Fig. i.2a). On many other ships a bulb is applied. Such a bulb is applied to decrease the generation of waves around the ship, as will be discussed later. The application of a bulb, on a tanker is difficult because of the two different drafts at which the ship. operates. A bulb is always: designed for t'he loaded draft.
With increasing speed the importance of wave generation increases, resulting in lower block coefficients and a frequent application of bulbs. Many different shapes have been designed, as shown in Fig. 1.2. A typical example of a fast displacement 'ship is a .containersh.ip." (Fig. 1.3). The bulb. is a common feature for this type of'.
ships. . .
'"
For ships with very high speeds' the bulb loses its 'effect and a sharp bow is applied.
(Fig. 1.4)
The form of the afterbody and the stern is strongly dependent.. on the position and the type of the propulsor. Some forms will be shown in chapter 2.
The displacement hull is by far the most common type of ship and in this. course mOst of the 'attention will be devoted to this type of ships.
1.2: High .Sp.ee.d Ships
...
-..
When a ship reaches high speeds this can be used to create lift. At high speeds a reduction of 'the displacement due to the extra lift' strongly affects thewave. generation
12 G.Kuiper, Resistance and Propulsion, July 2, 1991
a
e
Figure 1.2: Various bulbs
b
d
SS: S
,SS44
5SSS 55555 55 I S 5; s..ø
55 5 5 S 1"
S çss4 555 4 555
SzS5SSS-55 55 S SSS5 755 54. S 5S4;frS5 5 S55SSS S SS a. s5 '5. 5.55 55 s 414 S 55.55555.555 S.. 555 555; 5S4555555SçS5 555 SS S çS5S 5S 5S SSSS*
I S555 5555 14 5555S4S SSS SS SS S5 S54 S S Figure 1.3: Containership sJ '555 4S555 S July 2, 1991, Hullforms 13Figure 1.4: High speed displacement ship
S S
Figure 1.5: Spray generated by a planing hull
1.2.1
Planing Hulls
In case of planing there is a pressure build-up on the bottom of the ship, such that an upward force is generated. This can be obtained using a flat bottom, so little or no
deadrise. The water flowing along the hull is mainly flowing alongthe bottom and it is displaced downwards.
A flat bottom is very sensitive to waves. To reduce this sensitivity a sharp bow is applied, which gradually changes into a flat bottom (see Fig. 1.4). The flat bottom ends in a flat stern, the transom stern. To increase the downward displacement of the water in the afterbody and to control the trim a trim wedge is sometimes applied.
The bottom of the trim wedge is a continuation of the transom stern. The trim wegdes are also made as adjustable flaps extending from the flat bottom.
Planing also generates excessive spray, which has been found to cause a higher
resistance.(see Fig. 1.5) Sprayrails are therefore used to reduce the spray. These rails are a kind of longitudinal spoilers on the hull, which deflect the spray downward.
_SS5
V5SS5
The amount of planing can vary. A small planing force can be generated by using chines. Extreme planing is used in speedboats and racing boats.
J4
July 2, 1991, Hullforms 15
I
Figure 1.6: Surface Piercing Hydrofoil
1.2.2
Hydrofoils
When the lift is generated by foils under the hull the ship is called a hydrofoil. The foils can pierce through the water surface, thus ensuring stability. In such a case these are called surface piercing hydrofoils. (Fig. 1.6).
Another type of hydrofoil is fully submerged (Fig. 1.7). In that case the stability and the trim have to be maintained by actively controlled fins.
Hydrofoils are applied in the speed range up to 40 knots. Especially the fully submerged hydrofoils are rather insensitive to waves, as long as the hull is not hit by green water. Hydrofoils have been driven with propellers generally. 2 The shafts, which extend from the hull into the water, are a source of high resistance, while the propeller thrust is not exactly in the forward direction due to the angle of the shafts. This is being improved by using propellers in front of or behind the main hydrofoil, which are driven with Z-drives (see chapter 2).
The distribution of the load over the front and rear hydrofoils can differ. When the
front foil carries only a very small part of the load this is called a canard arrangement as in the case of airplanes with the stabiliser in front of the wing instead of at the
tail.
2These propellers are often supercavitating propellers, see chapter 2
16 G.Kuiper, Resistance and Propulsion, July 2, 1991
/
it,
--Figure 1.7: Submerged hydrofoil
July , 1991, Hullforms 17
Figure 1.8: Air Cushion Vehicle
1.3
Air as carrier
1.3.1
Air Cushion Vehicles
Air can carry the weight of the ship when maintained at a high enough pressure. This pressure is built up in an air cushion, which is maintained below the vessel by skirts around the ship (Fig. 1.8). In such a case the ship is called an air cushion
vehicle or ACV. Losses of air will occur in waves or due to forward speed, so the air pressure has to be maintained with air compressors.
An ACV still has a displacement which is equal to the weight of the total ship. The pressure inside the cushion times the area of the cushion has to be equal to the total weight or displacement. An ACV therefore does not float above the water, as it does on land. The total resistance of an ACV is lower than that of a displacement ship due to the lower friction and partly because of the more favorable wave forms.
Typical for an ACV is its amphibious character: it can operate both on land and in the water. The propulsion therefore is generally by air propellers.
1.3.2
Surface Effect Ships
When the amphibious character is not required the loss of air under the skirts can be
reduced by using fixed sidewalls. These also improve the behavour in waves (Fig. 1.9).
Such ships are called Surface Effect Ships or SES. They can be used for very high speeds of up to 60 knots. The largest SES vessels nowadays have a length of about 50 meter and a speed of near 100 knots (US-Navy). In waves the speed reduction, however, is larger than e.g. with hydrofoils and it occurs at lower sea states.
18 G.Kuiper, Resistance and Propulsion, July 2, 1991
Figure 1.9: Surface Effect Ship
1.4
Multihulls
1.4.1
Catamarans
Stability at high speeds is a general problem. When a stable platform is required
a double hull ship or catamaran can be used . An example is a passengerferry
(Fig. 1.10). The small breadth of the hulls reduces the generation of waves,although the wetted area is almost doubled in comparison with a monohull, which increases the frictional resistance. In waves a catamaran is restricted because of the risk of hitting the water with the superstructure. Its response to waves will also be larger than e.g. hydrofoils because it is in fact a displacement ship. Efforts have been made to improve the riding qualities of a catamaran by special bow shapes, such as the wavepiercer. The effects still have to be proven.
1.4.2
Swath
A variation on a catamaran is a Small Waterline Area Twin Hull or -SWATH ship (Fig. refswathl).
In that case the displacement is brought far below the waterline, thus reducing the waterline area to a minimum (Fig. 1.12). As a result the vessel will react only sligtly on waves, so it offers a stable platform in waves. A disadvantage is of course that it is very sensitive to changes in loading or even to forward speed. A SWATH
4 -k , A '5 Figure 1.10: Catamaran Figure 1.11: SWATH July 2, 1991, Hullforms 19 -4
'5-20 G.Kuiper, Resistance and Propulsion, July 2 1991 DWL
\
AFT STA II 17 II " 11 20 21 22Figure 1.12: Cross section of SWATH hull
therefore often has active fins, for control of trim and stabili:ty. These fins can also be
used for further roll reduction.
Literature for further reading.
Several afterbody forms and their relative mçrit are. given by Vossnack and Voogd [31 A very rough estimate of the relative power requirements of various high speed
concepts is given by Dorey. [1].
Questions
Give. a sketch of the cross section 'of'the main foil of a surface. piercing and a fully submerged
hydrofoil.. Discuss the arguments in choosing each of these configurations.
'Describe the principle of an SES. Discuss why such a vessel is applied and compare its
Chpter 2
Propuisors
Objecflve
Introduction of various types of propuisors for ships and the mainprop-erties of these. The names of the propulsors are written in ita1ic The meaning of these names and the general properties of the concepts should be known.
The amount of concepts for ship propulsion is large. The most important criterion for a propulsor is its efficiency. The efficiency varies widely over the various types of propulsors, but the screw propeller has not yet been equalled in most cases.
The propulsor is generally mounted behind the hull. This is because of efficiency: the Water which is set into motion by the friction along the ship is brought to rest again by the propeller action, which means that less energy is left behind' in the water behind the ship.
A risk for every propulsor operating at high rotational velocities is cavitation This occurs when the local pressure in the fluid is lower than the vapor pressure
due to local high velocities. Regions with vapor occur e.g. on the propeller blades, such as occurs extensively in Fig. 2.5. When these vapor filled (not air filled) cavi-ties arrive in regions ith a higher pressure they collapse violently, causing erosion (Fig. 2.1). Strong dynamic behaviour of large cavities also generate vibrations in the ship structure.
2.1
Propellers
The most common propulsor is the screw propeller. The number of blades and the blade geometry can differ widely, as will be discussed extensively in this course.
The propeller is located behind the hull. The traditional afterbody shape is such that the hull ends in a screw aperture in front of the propeller, while the rudder stock forms the after part of the propeller aperture.
22 G.Kuiper, Resistance and Propulsion, July 2, 1991)
I
8 SSSS S45S4
a %S,S 'S' S 'Si' / SS '' 'S,' Sç5S,5 SS '"S - _i 7' :-- '-:;-'4"Figure 2.2: propeller' with open stern
called an open stern,, as shown in Fig. 2.2. An' arrangement with the propeller shaft extending under a flat siern und'er a small atigle is typical for Navy 'ships and other fast ships. The shaft is supported by brackets (Fig. 2.3). in 'large twin screw ships like passenger ships the shafts are covered by bossings
In fastships the engine arrangement can be as shown in 'Fig. 2.4, where the shaft is
driven from behind through a gearbox or where the shaft is replaced by a rectangular
drive.
2.1.1
Controllable Pitc'h Propellers
The thrust, and, consequently the speed of the ship, is controlled' by the propeller
revolutions in case of a fixed pitch propeller Backing'is done by reversing the engine. In case of a controllable pitch propeller or CPP reversing occurs 'by changing the pitch with constant revolutions in the same direction. This is specifically favourable in.case
of high skew Also the ship speed can be controlled by the pitch instead of by the number of revolutions. The hub of a CPP is of course complicated'. and expensive, while the hub diameter is also larger than that of a fixed pitch propeller. This is a
disathantage for huib, and blade' root cavitation;
2.1.2
Overlapping Propellers
For large ships with high. speed's the thrust is distributed over two or more 'propellers.
This configuration has a lower efficiency because the propellers operate outside the region of the highest wake. To increase the efficiency the twin propellers can be brought together as close 'as possible, with one propeller slightly ahead of the' other. July 2, 1991, Propulsors 23
24 G.Kuiper, Resistance and Propulsion, July , 1991)
Figure 2.3: Shafts with brackets
S 54S 555 5 555,S55, S'S Sr *" '5 iSS, 5,
Figure 2.5: Supercavitating Propeller
The blades can than overlap and the twin screw arrangement approaches a single
screw arrangement. The propellers can in principle rotate in opposite direction, so that a contra rotating arrangement is approached.
2.1.3
Contra Rotating Propellers
A rotating propeller also induces a rotating motion in its wake. This is lost energy. In order to gain this energy two propellers behind each other are used at the same shaft. These propellers turn in opposite directions, thus eliminating each others' rotating wake. The construction is of course very complicated. Also the two propellers close together can cause shaft vibrations.
2.1.4
Supercavitating Propellers
When cavitation occurs extensively, e.g. at very high rotation rates of the
pro-peller, it is advantageous to use blade sections which generate a long sheet cavity at one side of the blade, about two times the chordlength of the blades. These propellers are called supercavitating propellers (Fig. 2.5). Because cavitation implodes far be-hind the blades the danger of erosion is absent, at the cost ofa drastically reduced
efficiency.
26 G.Kuiper, Resistance and Propulsion, July 2, 1991)
2.1.5
Surface Piercing Propellers
When the draft is too small for a normal propeller to operate tunnels are applied in the hull to lead the water upwards to the propellers. When this is also insufficient the prcpellers are allowed to operate partly submerged. Such propellers are called surface piercing propellers. The geometry of the blades is generally skewed to soften
the impact of the blades on the water surface and the exit from the water. Air
suction will decrease the efficiency of the submerged blades, so the efficiency will be considerably lower than that of submerged propellers.
2.1.6
Agouti Propellers
A special way to control cavitation is to supply air to the cavity. The cavity will then contain air. together with vapor and on implosion the..air will cushion the collaps. As a result the radiated noise of the cavitation is lower than without air supply. The amount of air supplied is very critical', because an overdose of air will increase the
cavity volume drastically.
The air, is supplied through small holes at the leading edge of the blades. A restricted supply of air will not affect the efficiency of the propeller. An Agouti system is used on navy ships only.
2.1.7
Tipplates
An increased loading of the blade tips would be beneficial to' efficiency, but the flow around the tips prevent such a heavy loading. In order to prevent such a flow around the tips tipplates have been applied.. Because this would also reduce the strength of the tip vortex these propellers are also called Tip Vortex Free Propellers or TVF Propellers. It is, however,, very difficult to locate the tip plates properly in the wake behind the hull. Moreover, the tip vortex tends to occur in the corners between the tip plates and the blades. These propellers have mostly been applied in combination with a duct. Their effect is still to be proven.
2.1.8
Vane wheels
A large propeller diameter is often benificial for efficiency. When an increase ofan
existing diameter is benificial or when the diameter of the' main propelér is. restricted
a vane wheel can be applied. This is a kind of propeller,, which runs freely downstream
of the main propeller. (Fig. 2.6). The inner part of the vane wheel, the impeller part or turbine part, .has a pitch such that the vane wheel is driven by the wake of the main propeller. The outer par.t of the blades of the vane wheel, the propeller part, has a different pitch, which causes the vane wheel to generate. thrust at these radii.
The mimer of revolutionsor rpm of the vane wheel will be different from that of the
4
--Figure 2.6: Vane wheel
main propeller. (In German the vane wheel is called after its designer the "Grimmse Leitrad"). The concept is patented.
2.2
Ducted Propellers
At high propeller loadings a duct can increase efficiency (Fig. 2.7). A duct gener-ates part of the total thrust due to its interaction with the propeller. This is the case with an accelerating duct (Fig. 2.8a) , in which the flow velocity is increased due to
the duct. The duct shape can also cause the flow to be decelerated (Fig 2.8b). This suppresses cavitation, but decreases the efficiency. A decelerating duct is therefore suitable for navy ships only, and there it is rarely applied.
The gap between the blade tips and the duct has to be small for a proper inter-action of propeller and duct. This makes the construction of the duct more difficult, especially the very large ducts on e.g. tankers.
The flow along heavily loaded ducts may separate from the duct, which decreases their effect and increases their resistance. A method to reduce this type of separation is the application of slots at the exit of the duct (see Fig. 2.9).
Due to manufacturing considerations ducts are generally rotationally symmetri-cal. The wake behind the hull, however, is not symmetrical and a-symmetrical ducts have been designed to make the flow into the propeller more uniform.
I
28 G.Kuiper, Resistance and Propulsion, July , 1991)
decelerating
S7
Figure 2.7: Ducted Propeller
accelerating
July 2, 1991, Propulsors 29
Figure 2.9: Duct with trailing edge slots (Courtesy v.Cunsteren and Ceiling, Deift, the Netherlands)
30 GKuiper, Resistance and Propulsion, July 2, 199)
C-A.I1
An
llIr4.
--
--I I I I
m I iIr 1uIllu iW
--Figure 2.i'O: Dynamic positioning
Ducted propellers are used in a wide. range of applications of heavily .laded pro-pellers, suëh as for dynamic positioning (Fig. 2.10)' and for active rudders(Fig, 2.11).
instead of an a-symmetric duct other types of fins or ducts can be applied to make the propeller inflow more uniform. These ducts or fins are applied at some distance upstream of the propeller. Generally they accelerate the retarded flow in the upper part of the. propeller plane. A. patented concept is the "Schneegiuth Duct", as shown. in Fig 2 12 Variations are possible, as in Fig 2 1'3
2.2.1
Ringpropellers
A variation on the ducted propeller is the rzngpropeller indexringpropeller This is a duct similar to the normal duct, but now 'the duct is connected to the propeller blades and rotates with it This eliminates the gap between blades and' duct, but at the cost of a greatly increased viscous resistance. The efficiency of a ringpropeller is. therefore relatively lOw.
2.2.2
Mitsui duct
The position of the propeller' of a ducted propeller is generally inside the duct. The' propeller can also be moved towards the exit of the duct without too much loss of efficiency. Such a positiOn is appropriate when a duct 'is used as a retrofit, that is an improvement 'afterwards. It should be kept in mind, however, that the application of a duct in front of an existing propeller will change the propeller loading 'and may
2.3.2
Paddle-Wheels
Figure 2.11: Active rudders
require another propeller design. Mitsui has patented such retrofits with duct, the combination is therefore also called a "Mitsui Duct".
2.3
Other Propulsors
2.3.1
Voight- Schneider Propellers
A very special propulsor is the Voight-Schneider Propeller (Fig. 2.14). a number of "knifes" on a rotating plate. These "knifes" can rotate on this plate and their
position is such that they are always perpendicular to the radials from a moving centerpoint P, as shown in Fig. 2.15. When this centerpoint is in the center of the blade circle there is no resulting force (Fig. 2.15c). When this centerpoint is moved a thrust is generated perpendicular to the direction in which the centerpoint is shifted. The main asset of a Voight-Schneider Propeller is that in that way the thrust can be applied in all directions, just by moving the centerpoint. Rudders and shafts can be omitted. This can be used e.g. for tugs or supply boats, for which manoeuvring is important. Its efficiency,however, is lower than that of an open propeller due to
the fact that the blades generate thrust over part of the revolution only, while the viscous resistance is present over the whole revolution.
Voigth Schneider propellers can be mounted under a flat bottom. For protection
some cover is sometimes applied (Fig. 2.14).
32 G.Kuiper, Resistance and Propulsion, July 2, 1991)
4
i% f
Figure 2.13: Flow improving fins
July 2, 1991, .Propulsors 33
Lii1r
34 G.Kuiper, Resistance and Propulsion, July 2, 1991)
3 Q D
;
Figure 2.16: Paddle wheel
a a
/
Figure 2.17: Pumpjet
The oldest form of mechanical propulsion after the sails is the paddle wheel Contrary to the propeller, which uses lift for propulsion, a paddle wheel uses drag, which at higher speeds is less efficient. The blades. of a paddle wheel are most effective
in the lowest position, in other positions they also generate a vertical force. So. a
paddle wheel has to be large, with only a small immersion. In order to improve the entrance and exit of the blades in and from the water, the blades have been made rotating by. a system of rods. This made the wheel very complicated, however.
2.3.3
Pump Jets
The basic mechanism of propulsion is acceleration of water This cannot only be done by e.g. a propeller outside the hull, but also by a pump inside the hull. The water is sucked in from the bottom of the ship, js accelerated inside the ship by a pump and 'leaves the ship at the stern. This has many advantages when a propeller is too sensitive to damage, or when a propeller is dangerous (e.g. rescue vessels). Also in shallow waters a pumpjet can be useful. The inner surface of the pump system is large and the velocities inside are high, so the viscous losses are high too. 'The efficiency is therefore lower than that of an open propeller.
2.3.4
Sails
The oldest sails were square rigged, using drag as the thrust force,just as the paddle wheels later (Fig. 2.18). Sailing towards the wind is not possible with this
rigging. Before the steam engine took over longitudinal sails were also used. "When
the energy crisis hit, some modern sail' designs were made of both form, either as
additional power or as main propulsor. (Figs'. 2.19' and 2.20'). The use of computer controlled setting8 of the sail can highly improve their operation. The development of racing yachts as the 12 meters, used for the America's Cup, can' provide more
36 G.Kuiper, Resistance and Propulsion, July 2, 1991) - / 1 - - -3__,, 4 --.-- ----q
;",
38 G.Kuiper, Resistance and Propulsion, July 2, 1991)
Figure 2.20: Modern square rigged sailing ship
experimental and theoretical experience with sails. Sails will only become attractive
when the fuel price rises again considerably.
2.3.5
Other Types of Propulsion
When a cylinder rotates in wind a thrust force is generated. This effect resembles sailing. The rotating cylinders are called Flettner Rotors, after their original designer. Flettner rotors have been applied on experimental ships only (Fig 2.21). A major problem is the mechanical connection of the rotor to the hull, where the ship motions cause very large forces and moments.
Even more esoteric types of ship propulsion are ramjets, which are an analogy of
jet engines. In a water jet hot compressed air is injected in a water stream, and the expanding air accelerates the flow in the engine.
Nature has often been an example for technology (although the airplane only became practical after the bird wing motion was abandoned). Fish propulsion has
also been an example. In this case a flat plate makes sinusoidal motions perpendicular
to the direction of the ship. The construction is very complicated, ofcourse.
A variation on the fish propulsion is Weiss-Fogh propulsion. This is simply a flat plat which moves between two walls in a direction perpendicular to the direction of motion of the ship. The angle of the plate is varying with its position, so that the water is pressed towards the rear during the motion of the plane. As with fish propulsion this is mainly of theoretical importance.
The same is true for magneto-hydrodynamic propulsion . In this case a strong magnetic field accelerates the flow in a magnetic duct. In principle no moving parts
Figure 2.21: Flettner rotor propulsion
are required for this type of propulsion. The high electrical resistance of sea water makes the efficiency extremely low, however. It still has to be developed for other fluids with more suitable properties.
Questions
Describe the function of a duct. Give three variations of the duct geometry or location and indicate the reasons for these variations.
Describe the basic difference between square rigged sails and paddle wheels on the one hand, and propellers or longitudinal sails on the other.
Discuss the reasons for application of a contra rotating propeller a supercavitating propeller a waterjet
Chapter 3
Resistance of simple bodies
Purpose:
Briefintroduction of non-dimensional formulatIon and of many hydro dynamic concepts such as wake,,drag, boundary layer and separation. These concepts will be used in the discussion of ship resistance. intermezzo.3.1
Non-dimensional Coefficients
To understand. the physics of the flow around a ship it is useful to look first to the flow around simpler bodies, such as a cylinder.. A cylinder is a simple body because it can, be described by a single parameter: the diarneter.(2r where r is the radius). As will be seen the flow around a cylinder is not simple. at all.
Each cylinder has its own"resistance. Still there is a need to compare the resistance
of cylinders of various diameters at various velocities. Experiments show that the resistance of a cylinder is approximately proportional with the square of the velocity
and with the square of the diameter. The resistance of a cylinder of an arbitrary diameter at an arbitrary velocity can than be reduced toa single number by defining a drag coefficient Cd:
,r!_
IlI /2pV2S
where Rdrag(N), V=velocity(m/sec), p=specific rnass(kg/m3) and S is the frontal area of the cylinder (rn2). (We will use R for the drag or resistance of the cylinder instead of D, which is also commonly used. In naval architecture D is used for the propeller diameter, howeverThe,radius and diameter of the cylinder will be indicated with r and d.)
Looking at the dimensioii of .the drag coefficient it can easily be found that its is 1. That means that the drag coefficient is a real coefficient, because it is
non-dimensional. Each cylinder,whatever the size or the velocity, has in the same
100 80 60 40 C0 20 10 8 I 4 2 02 0.1
July 3, 1991, Simple bodies 41
0(mn) o 0.05. 0.J 10. Dy 7.9 Weiilsbergef o 42.0 aao Jx.0 Thxj-g&,e,p lamb 2 4 6 8i00 2 4 8 2 6 6 6' 88103 2 4 .6 81047 4 6 8ioS 2 4 va
Figure 3.1: Drag coefficient of a, cylinder
As will be shown later this means that the flow has to be similar in all cases, whih is true when there are no other parameters for the drag than the size and the speed. When the. drag coefficient o'f a certain cylinder is measured at various velocities a curve like Fig. 3.1 is found, with the velocity as the abcissa instead of R,,f. It is noted at first glance that the drag coefficient is not a constant! The assumption that the drag is proportional with V2 is therefore only valid for small variatiOn's of V. So there are other parameters iiivolved in the drag of a cylinder. Systematic tests will show that the drag coefficients of cylinders with the same product Y.d are the same. When the temperature is varied the viscosity of the fluid is changed and systematic' tests will show that the drag coefficient of all' cylinders will collaps on one line when plotted on the abcissa Vd/'v where ii kinematic viscosity of the fluid(m2/sec). This parameter is calkd the Reynolds number:
Vd £1
(3.2)
Again it can be found that the Reynolds number is non-dimensiOnal, so that in Fig. 3.1 all parameters are expressed non-dimensionally.
That means that the
drag coefficient is a function of the Reynolds number' only and that Fig. 3,. 1 has a universal meaning for all possible cylinders, which is exactly the purpose of expressing'
42 G!Kuiper, Resistance and Propulsion, July 3, 199i
subcritical flow
supercriticai flow
July 3 1991, Simple bodies 43
separation
Figure 3.3: Velocity profiles in a laminar boundary layer
3.2
Flow Iheno.mena
Now we can focus on the physics behind Fig. 3.1. At very low Reynolds numbers the dtag cofficient is high and it decreases gradually until one at R, = 1000. The flow pattern corresponding to this range of conditions is given in Fig. 3.2a. At very low Reynolds numbers the boundary layer flow around the cylinder is laminar and separatesnearly at the location of maximum thickness. This separation lócation.grad-ually moves downstream at higher Reynolds numbers (for one cylinder at a constant temperature this means at higher velocities) and as a result the width of thewake behind the cylinder decreases gradually. This condition is caikd the subcritical
con-dition. The wake consists of regularly shedded vortices, which are called the Karnzan vortices.
At a Reynolds value of about half a million there is a sharp decrease. in the drag
coefficienL This is the critical conditiOn and this change has to do with the 'transition
of the boundary layer from laminar to turbulent flow before separation occurs. The flow pattern changes, as shown in Fig. 3.2b: separation occurs much further down stream on the cylinder and the wake decreases in width and depth.
A boundary layer is the region close to the wall of a body where strOng velocity gradients occur. At Reynolds numbers above 1000 this region is thin relative to the diameter of the cylinder. in laminar flow the particles in the boundary layer are
gliding, smoothly over each other, so that no motions perpendicular to the flow .occur.
In a turbulent flow the smooth motions disappear and violent motions perpendicular to the. direction of the motion occur.
44 G.Kuiper, Resistance and Propulsion, July 3, 1991
boundary layer
Figure. 3.4: Velocity gradient in laminar and turbulent boundary layer
separation has to be be understood. This is shown for the two-dimensional case in Fig. 3.3. At the wall the flQw is attached to the wall(the no slip condition) and
there-fOre has the same velocity as't'he wall.. Close to the wall the e1ocity increases rapidly
and the large shear. causes frictional resistance. The slope of the velocity profile at the wall is a measure of the drag force on .the wall. In 1 laminar bounda.ry layer the velocity of the layers close to the wall is strongly reduced, so that the inner layers. are
stopped and when the pressure increases in the flow direction ( an adverse pressure gradient) the flow can even reverse. In that case laminar separation occurs.
The effect of traiisition to turbulence is .a strong exchange of impuls between the various layers. of the boundary layer. As a result the inner layers will be accelerated by the impuls of the outer layers and the outer layers will be decelerated So the veloci.ty gradient in the boundary layer changes, as shown in Fig. 3.4. The slope of the velocity profile. increases significantly, thus delaying the moment. at. which this
slope becomes infinite and separation o.ccurs After some time the turbulent bound-ary layer will of course also be retarded and turbulent separation will take place.
Now the effect of the Reynolds number on the cylinder drag can be understood: after transition to turbulence the flow in the turbulent boundary layer remains at-tached much longer until turbulent separation takes place. This reduces the width01
the wake behind the cylinder because the pressure recovery at the rear, .of the cylinder
is better, as shown in Fig. 3.5. The base pressure in the supercritical condition is
significantly higher.
--3
Fzouu7. Circular Cylinder: oompariaon of th..an, friction, and preurediatribution at
varioue Reynólde numbers. . .:., Re = 10.x 10';---, Re
= 26.x 10'; --,R, =86x
= 36x 10'.
Figure 3.5: Pressure distribution on a cylinder
3.3
Drag Components
The force on the cylinder can be decomposed into pressure forces perpendicilar to the cylinder (the pressure from Fig.. 3.5) and friction, forces parallel to the cylinder surface. The integration of the drag component of the pressure forces can be called the pressure drag or form drag. The integration of the drag coefficient of the friction forces is called the frictional drag. These two drag components are not independent in case of a cylinder. Flow separation at any location on a body generates form drag. At the critical Reynolds üumber the form drag of a cylinder decreases strongly and
the viscous d:rag increases slightly.
304
Drag and Wake
The drag force on a body can be related with the wake behind the body.. To illustrate
this we. use the laws of conservation of mass and momentum.
Consider again a cylinder,as.in Fig. 3.6 A cylinder is used there, but the shape of the body is irrelevant For sake of simplicity the body is two dimensional, so the flow is
identical in every plane parallel to the drawing. A control volume. is defined with plane
A (width 2a)upstream of the body, where the velocity is U everywhere. Downstream
July 3, J99}J, Simple bodies 45
#0 I
f
\
I
tit/.t
0a
2
46 G.Kuiper, Resistance and Propulsion, July 3, 1991
This relation will be used later.
The drag force R on the body is related with the loss of momentum Over the control volume. Momentum is entering the control volume through plane A. The volume per unit time entering plane A is. 2aU. (Note that this is per unit length of the cylinder, the dimension of the volume is thus kg/s ecm instead of kg/sec) Its momentum is p2aU2. in plane .B momentum is leaving the contrOl volume. At an arbitrary position. y relative to the centerline a flow volume udy passes plane B. The momentum leaving plane B can therefOre be written as
M0 = pLu2dy
p0
Figure 3.6: Control volume around a body
a plane B (width 2b)is chosen, where the velocity is u(y). The outer boundaries are streamlines, which means that no fluid passes through these boundaries. The outer boundaries are taken at such a distance from the body that the velocity in plane B is equal to U near the boundary. This makes it possible to assume. a fluid pressurePu everywhereover the control volume. (Note that this is not evident in the region where the velocity u is smaller than U. it is an assumption, often made for convienience!) This assumption means that there is no pressure force acting on the control volume.
Assuming incompressible fluid the law of conservation of mass requires that
Since, the drag force is the only force present and since there is no resultant pressure force the drag is equal to the loss of momentum over the control volume So:
R=p2aU2-
u2dy Using eq.. 3.3. this can be written aéR.=
-
u)dy (3.4)Since the integrand is zero outside the wake region (because U - u = '0) the choice of .b is not important. So eq. .3.4 can be used over the wake region only, where U.'
A further simplification' can be obtained w:hen it is assumed that the wake velocity u is not too much different from the incoming velocity U In that case (U - u)2 0
and thus it can be derived that U(U - u). = u(U - u). So eq. 3.4. can be written as
R= pUJb(U u)'dy
(3.5)In this case the drag is thus directly related with the velocity deficit behind the body.
3.5
Sphere
The flow around acylindr, is two-dimensional(x,y). The flow around a sphere is three dimensional(x,y,z), but in a special way it is rotationally symmetric Mathematically this is still two-dimensional in cylinder coordinates '(x,r). The drag coefficient of a sphere has a character which is. similar to that of a cylinder. The drag coefficient approaches 0.4 in the subcritical range, which is until around R = 3.105. in the.
supercritical range the drag coefficient drops. until about 10.. 1. The Karman vortices
are absent on: a sphere.
At very low Reynolds numbers (R,1 ( 1) the drag of a sphere is much higher than that of a cylinder and can 'be written as
R = 3:7rzdV
or
R = 24/R,,
The flow at these low Reynolds numbers', where. dynamic forces are negligible and
viscous forces dominate, is called Stokes flow
July 3, 1991, Simple bodies 4
.020 .305 .006 .007 .006 C0 .005 .304 00 .002
Figure 3.7: Drag coefficients of a flat plate
3.6
Fiat, plate perpendicular to .the flow
The flow around a cylindrical flat plate perpendicular to the flow is siniilar to that of a sphere, except that the location of separation is fixed. So the drag, coefficient will
not depend on. the Reynolds number very much and remains one over a very wide region of Reynolds numbers larger than 1000. In terms of form drag and frictional drag such a flat plate has only pressure drag.
When the plate makes an angle to the flow the drag coefficient can 'be taken as that of the plate perpendicular to the flow, when the area is taken as the projected area perpendicular to the flow (the frontal area)
3.7
Flat plate in the flow direction.
A flat plate in the direction of the flow is a special condition in which no form drag occurs and only frictional drag is present. A special element in the boundary layer growth over the flat plate is that the pressure is constant over the length of the plate. The drag coefficient of a flat plate is given in Fig. 3.7. At the critical Reynolds number a drag increase occurs because separation is now absent and the transition of the boundary layer to turbulence increases the drag. The transition to turbulence
occurs over a wide range of Reynolds numbers,depending on very slight disturbances in, the flow or on the surface.
The length scale in Fig'3.7 is now the length of the plate Apart from the Reynolds number based on this length a local Reynolds number can be defined, based on the position x along the .plate. (x measured from the leading edge of the plate or,better,
48 G.Kuiper, Resistance and Propulsion, July 3, 1991
.00'
'0
CI' = F
pV2
where F is the local friction force on a unit surface. This translates into a drag coefficient of a flat plate of
1.328.
Cd
-
(3.9)where.! stands for the Ienght of the plate.
July 3, 1991., Simple bodies 49
from thestart of the laminar boundary layer). This Reynolds. number will be
in-dicated as where . In general the lenght scale in the exit Reynolds
number will be given as an index to R.
3.8
Additional data
Since the fiat plate boundary layer is used in many circumstances some data of the laminar and
turbulent boundary layer in zero pressure gradient will be given below.
Laminar flow The thickness of the boundary layer 6 is defined as the distance to the wall at
which the velocity is 99% of the uniform inflow velocity V. The boundary layer thickness is
±
5j'
(3.6)So the boundary layer thickness increases with In non-dimensional notation the boundary layer thickness can be written as R,,5 =
Compared to the rnviscid flow, where the outer velocity V starts immediately at the wall, there is a loss of flow volume in the boundary layer. This loss of volume is expressed as the displacement thickness 6. The decrease of volume due to the boundary layer can be written as:
V51 = - u)dy. (3.7)
where u is the velocity in the boundary layer at a distance y from the wall. The displacement
thickness can now be written as
0.34
= 1
The local friction coefficient is proportional to the slopeof the velocity distribution perpendicular to the wall. This local friction coefficient is.
1
=a!:-;
0.664
(38.)
50 G.Kuiper, Resistance and Propulsion, July 3,. 1991
Turbulent flow: An approximation of the velocity distribution in the turbulent boundary layer derived from pipe flow is the so-called 1/7th power law. In that case the velocity distribution in the boundary layer is always
= (
V
'6'
The boundary layer thickness can then be written as
6 = O37zR1*
This means that the boundary layer thickness increases with z instead with -.J in laminar flow. The turbulent boundary layer will therefore be thicker than the laminar one
The displacement thickness can easily be derived using the. 1/7th power law to be öi The local friction coefficient can be written as
Cj OO576(R) (3.12)
and the drag coefficient based on a plate of length 1 and unit width
Cd= O.O72(R,) (3A3)
A survey of experimental drag coefficients of simple bodies is given by S.F.Hoerner [8].
3.9
Sumniary
The resistance of a body can be expressed in non-dimensional terms as the resistance
coefficient Cd
-
1/2pV2S The resistance coefficient of a submerged. body is found tobe dependent on the Reynolds numberR, only. The dragcoeficient e.g. of a
cylinder varies with the Reynolds number depending on the type of separation which takes place In the subcritical condition laminar separation occurs In the supercrztzcal condition turbulent separation occurs The turbulent boundary layer remains attached after transition and the form drag or pressure resistance of the cylinder is greatly
reduced; The frictional drag increases because the turbulent boundary layer has a
greater drag coefficient.
The magnitude of the wake behind a body can be related directly with the resistance
of the body.
(3.10)
Chapter 4
Resistan.c.e and Wake Distribution
Objective:
A description of the magnitude and the structure of the propeller inflowof the flow phenomena which determine this structure.
The propeller operates generally in the wake behind the ship.. The uniformity of the wake in the propeller plane is important for a smooth operation of the propeller. Therefore the wake distribution over the propeller plane is often measured at model
scale.
The structure of the wake reflects the flow phenomena around the hull'. in order to be able to recognize some wake patterns and to be able to improve the wake distribution it is necessary to understand the relation between flow and wake. First some flow phenomena will 'be described. After that the relation with wake measurements will
be given.
4.1
Cross flow'
Consider a boundary layer, as on a flat plate. in three dimensions there is not only a. pressure gradient in the flow direction, but also in a direction perpendicular to the flow. As a result the velocity vectors in the boundary layer will not remain in one plane, but will change direction towards the low pressure region when approaching the wall'. This is shown in 'Fig. 4.1. 1
The streamlines outside the boundary layer will therefore have another direction than the streamlines at the wall. This fact is to be remembered when paint is used at the surface of a model hull' to find the direction of the flow around the ship, e.g. for the application of fins or stabilisers.
'All figures in the remainder of this chapter: courtesy of 'M.Hoekstra
52 GKuiper, Resistance and Propulsion, July. 3, 1991
Figure 4.1: Velocity vectors in a 3D boundary layer
VISCOUS REGION IN EXTERNAL STREAM SURFACE OF SEPARATION (BUBBLE) LINE OF SEPARATION ilIiidUIt IlIltillililpilIl
tIhbIIH LIIS1IrING S1REAIALINES
- ILl
SURFACE OF SOLID BODY
Figure 4.3: Transverse separation on a ships hull
4.2
Separation
Separation occurs in a three dimensional space (3D) in two different manners. The first is similar to 2D separation ,.where the flow velàcity decreases until zero and
becomes negative. This situation is shown in Fig. 4.2. The separation line runs in transverse direction relative to the local flow. On ship hulls this type of separation has to be avoided, because it increases the drag, just as in 2D flow on a foil. Regions where such unwanted separation can occur are specifically the regions in front of or
above the working propeller., as shown. in Fig. 4.3.
In 3D the flowlines can also converge because the body becomes smaller. In that case the fluid moves away from the surface simply because of the law of continuity (Fig. 4.4). The flowlines in such a region will exhibit a separation line in streamwise direction, as shown in Fig. 4.5. Such separation lines cannot be avoided and the design of a good ship hull is mainly the control of these separation lines, so that t:he wake behind the ship remains as small and uniform as possible.
Two examples of such a ty.pe of separation are shown in Fig. 4.6 for two different
54 G.Kuiper, Resistance and Propulsion, July 3, 1991
Figure 4.4: Thickening of stream tube in converging flow
STREAMLINE IN EXTERNAL STEAM
SURFACE OF SEPARATION
SURFACE OF SOLID BODY
Figure 4.5: Streamwise separation
,VISCOUS REGION
SEPARATION LINE ATTACHMENT LINE
LIMITING STREAMLINES
Figure 4.6: Longitudinal separation at bow
56 G.Kuiper, Resisiance and Propulsion, July 3, 1991 CWL 5 4 4 CWL
--
S. I -.5.- I,
--'- -5--, ,__,__S,%
/ /
,,,
- .5.5 'I
ii
I I' .5 , / /.% ' \ / I! S S S. - - , ,Figure 47: Wake behind a U-shaped huilform.
ships. In the first case the separated flow forms a kind of bubble, in the second case the separation line rolls up and forms a vortex, which in this case is a bilge vortex. Sometimes more than one vortex of different direction is generated at various posi-.tions on the hull.
Separation at the bow, as shown in Fig. 4.6,is suppressed by proper bow design. Such vortices are, however, stronger and nearly inevitable around the 'afterbody. The increase in pressure along the afterbody stimulates separation. The vortices originating from the bilge near the end of the parallel middlebody are characteristic and are therefore called bilge vortices.
4.3
The Wake behind Simple Shiplike Bodies
Some' simpler forms' will be helpful for 'a good' understanding of the wake generation. Consider a simple hull'fórm with U-shaped frames , as in Fig. 4.7 The water will be. pressed sideways in this case,' causing higher flow velocities at the sides than under' thekeel. The pressure at the sides of the ship will be lower than at the bottom. TheBODY PLAN
TUFT GRID
cwI-CWL , , _ - I / I I 2 4 5 I / I
- "
'
I I I I'
' ' IIj
Ii
% '.-_, ,, I
I % S - / ,. I I I S '. - I BODY PLAN TUFT GRID AT A.P.Figure 4.& Wake behind a pram-type huilform
flow will go from bottom to side and a bilge vortez will form which rotates clockwise.
This vortex shows up at the aft perpendicular as shown.
Another simplified extreme form is t:he Pram-type hull shown in Fig. 4.8. The water will be forced down and the lowest pressure occurs here at the bottom, so that a vortex with counterclockwise direction is generated. The vortex rolls up under its own induction and Shows up in the near wake as shown.
In these simple cases separation may be suppressed considerably by combining U-shaped and Pram-type huilform, as shown in Fig. 4.9. In this case the amount of energy which is left in the wake wil be minimal. No separation occurs and the wake will be completely due to the velocity distribution in the boundary layer along the hull. This body will have the lowest resistance because a minimum of energy has been left in the wake. The main component of the resistance will be frictional
58 C.Kuiper, Resistance and Propulsion, July 3, 1991 cwl 4 CWL
_____-,,.,_,, p
--
F, I___//
I V I I I I- -- ,
, , , / , I I- -
, /1 I I - I I , , /f /
/ I I I - I I I I I I I I I I I! I eODY PLAN TUFT GRID AT A.P.,MODEL A MODEL B MODEL C MODEL 0 RESISTANCE SHIP SPEED
Figure 4.10: Effect of variation of bilge vortex on resistance
resistance. The form drag will be small, 2
The effect of separation on the resistance is large. in Fig 4.10 the bilge radius is systematically reduced from model A to D, which means a reduction of the strength of the bilge vortex.. The corresponding resistance curves show that the effect on
resistance is considerable.
2see chapter 7 for a definition of these resistance 'components
July .9, 1991, Wake 59
A
60 G.Kuiper, Resistance and Propulsion, July 3, 1991 UNEO SURFACE OF SEPARATION
4IIIIII-IpP
SEPARATION STREAMLINE oF SEPARATIO'44frSURFACE FLOW PATTERN
Figure 4.11: Horseshoe vortex around a strut
44 Horse-Shoe Vortices
A different type of separation should be mentioned:horse shoe vortices These are formed when a strut or fin attaches to a surface with a boundary layer. In this case also 3D separation takes place., but in a special way. A vortex developes around the front of the strut and because of its form this is called a horseshoe vortex. An, example of it is given in Fig. 4.11, These vortices are also transported with the flow
and will arrive in the wake also, further complicating the wake structure.
4.5
Ship Wake
The wake behind a ship generally has a complicated structure because it is the result of the retardation of the flow in the ship's boundary 'layer 'and of many separated
flows around the hull. The wake behind a ship i generally only measured in the
propeller plane, which may be only a fraction of the total wake. The wake at the propeller plane without the propeller action is cilled the nominal wake.
The representation of the wake in the propeller planeis done by representing the axial,tangential and radial velocity components separately. An example of the axial wake distribution as a simple diagram is given in Fig 4.12. The axial velocities are
3The occurrence of this of type of vortices makes the application of tip plates on apropeller
July 3, 1991, Wake 61
R.I39
1
0 go- 13
POSITION ANGLE
Figure 4.12: Example of axial wake distribution
expressed as a fraction of the ship speed. A rather complicated wake peak is present in this figure in the top position of 180 degrees. The radial and tangential compo-nents of the wake can be plotted in a similar way
Another way to plot both axial and tangentil components of the wake is shown in Fig. 4.1:3. The axial wake distribution is given as contourplots, in which thelow
speed regions reflect the core of the vortices in the wake. The tangential flow veloci-ties are plotted as a vector diagram, in which the same vortical structures should be
visible.
The relation between the shape of the hull and the wake structure is complicated. in Fig. 4.14 three variations of the same afterbody areshown. The wake structure in
the propeller plane is shown in Fig. 4.15. In general a hull shape with small curva-tures will shed few separated vortices and will generate a smoother wake, This is the
case with a V-shaped hullform, which shape will have the lowest resistance. However.,
the non-uniformity of the flow in the propeller plane is large and a large portion of the wake passes outside the propeller plane, which decreases the total efficiency, as will be discussed later. A U-shaped huilform has more longitudinal separation and therefore has a more uniform propeller wake, since the boundary layer from the ship is rolled-up into the propeller plane. This U-shaped huilform will have a higher re-sistance, but the interaction with the propeller may offset this., as will be discussed later. A further increase of the uniformity of the axial wakefield can be obtained
62 G.Kuiper, Eesistance and Propulsion, July 3, 1991 0 0)0 o oo 0)0k 010 a,. 0 0_so 0.70 o .o o o o '0 o 70 I) 70 010 1 f2W fro 7rR2'Jo Jrh
Figure 4.13: Example of plotting, the wake
using a bulbous stern,, where local separation lines from the bulb will roll-up an make
the wake more uniform.
The determination of the ship's resistance and wake is generally done by model experiments. Model tests do not always show clearly why some forms are' better than others and cakulation techniques become available nowadays to 'calculate
cer-tam 'aspects of the 'flow around the ship's hull. Both experimental and 'calculation
techniques are necessary to design an optimum huilform.
4.6
Wake Fraction
As discussed in chapter 3 the velocity deficit behind t'he ship is a measure 'for the
resistance It should be kept in mind that this is true when the wake is measured until the velocity reaches the undisturbed velocity. The area 'of the wake may be much larger than the propeller plane, in which the nominal wake is defined.
The velocity deficit in the 'propeller plane can be integrated over the propeller
plane. This' results in an advance velocity' Va. 'in the wake.
Figure 4.14: Variations of the huilform NOMINAL WAJ(E, V STERN U - STERN BULBOUS STERN July 3, 1991, Wake 63
Figure 4.15: Effect of hull form variation on the axial wake
