11P1997-3
SHIP HYDRODYNAMICS
AND HULL FORMS,
AN INTRODUCTION
MARITIME
RESEARCH
INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
2 RESISTANCE 4
2.1 Flat-Plate Resistance 9
2.2 Wave Resistance 10
2.3 Form factors 12
2.4 Other Components 14
3 FLOW AND WAKE 15
3.1 Flat plate in the direction of the flow 15
3.2 Potential Flow 17
3.3 Resistance of bodies 17
3.4 Cylinder perpendicular to the flow 18 3.5 Flow and pressure distribution over a ship's hull 20
3.6 Wake Distribution 24
4 PROPULSION 30
4.1 Thrust deduction 30
4.2 Propeller Action and Wake Fraction 31
4.3 Simple Momentum Theory for a Propeller in Open Water 31
4.4 Propeller Open-Water Characteristics 34 4.5 Efficiency Components and Propulsion Factors 36
4.6 Typical Propulsion Factors 37
4.7 A prediction Formula for the Wake Fraction 39
4.8 The Quality of the Propulsor 40
5 HULL FORM DESIGN 42
5.1 Ferries and cruise liners 44
5.1.1 Fullness 45
5.1.2 LCB 45
5.1.3 Bulbous bows 45
5.1.4 Lines 46
5.1.5 Propellers and rudders 46
5.2 High block ships 46
5.2.1 Forebody form 47
5.2.2 Afterbody form 51
5.2.3 Choice of LCB 53
5.3 Slender single-screw ships 54
5.3.1 Forebody 55
5.3.2 Classical afterbody forms 55
5.3.3 Barge type forms 62
5.4 High speed mono hulls 66
5.4.1 Special elements of high speed craft 70
5.4.2 Appendages of high speed craft 73
5.4.3 Systematic series of high-speed craft 75
6 SUMMARY 80
CONTENTS
Page
RESEARCH INSTITUTE
NETHERLANDS
1 INTRODUCTION
Ship Hydrodynamics and Hull Forms - An Introduction
;UZI
In this introductory training course module several hydrodynamic features of a ship are treated and in particular we shall see how the design of the shape of a ship's hull is
related to the dynamics of the fluid.
By tradition, the hydrodynamics are studied by model experiments through which, by iteration, the hull form is optimised by the designer in collaboration with the staff of the model test institution. These days, there is a rapid growth of computational tools and by
the application of Computational Fluid Dynamics, or CFD, several iterative cycles of the experimental optimisation can be dispensed with, still using the same experience of
designers and staff.
The aim of studying the hydrodynamic properties of ships is to build better ships. Of course, there are always many design constraints and operational limitations, many of
which are of a non-hydrodynamic nature. Moreover, in all research programmes there is
a limitation of time and budgets. Nevertheless, the aim to acquire a better ship from the viewpoint of the a propulsive power should be pursued always. Present developments
point towards an increased influence of limitations posed by vibration, noise, sea keeping and manoeuvring characteristics.
The area in which attention is paid to the propulsive performance of a ship, usually in
calm water, is commonly referred to as Ship Powering or Powering Performance. In the field of Ship Powering there are two matters of interest to be predicted:
the speed the ship will attain for a given power supplied by the propulsionplant,
and
the rotation rate of the propeller at which this given power is absorbed.
These two basic matters are the very reason for most Ship Powering experiments in
towing tanks. Related areas are the development of hull forms, propulsors, the prevention of vibration and noise, etc.
In the next chapters we shall look into the resistance of a ship, the flow pattern, the wake distribution, the propulsion properties and, only briefly, into the propulsor action itself with emphasis on the interaction with the hull. In the last chapter we shall discuss the various design hydrodynamic features of four types of ships and in particular we
shall indicate how basic principles of resistance, propulsion and flow are present here. In
particular, the relationship between the hydrodynamic characteristics and the hull form
MARITIME
RESEARCH INSTITUTE
NETHERLANDS
2 RESISTANCE
A moving ship experiences resistance from the water and, to a smaller degree, from thE
air. The resistance depends on the forward speed according to a complicatec
relationship. A propulsive force, called the thrust, is needed to balance the resistance o the ship. Resistance forces are normally expressed in Kilo-Newtons (kN). The forcE supplied to the ship by pulling it forward at a steady speed V is the resistance R. ThE
power is the work done per unit of time. This power to tow the ship is called the effectivE power, PE. The speed of sea going ships is usually expressed in knots, 1 knot =
0.514447 m/sec. Other quantities are expressed in SI-units. To find the power suppliec
to towing a ship in Kilo-Watts (kW), the speed has to be given in m/sec. Thus: PE(kW): V (m/s) R (kN)
There are three ways to determine the resistance of a ship:
model experiments in a towing tank and extrapolation of the results to full-scalE
values,
computational methods based on hydrodynamic theory, and full-scale experiments on the actual ship.
Predictions of the absolute value of the resistance of a ship should be made with som( reservation. The actual resistance can not be verified experimentally. Only in a fey
research cases some ships were towed and speed and resistance measurements wen
made. Nevertheless, the resistance of a ship is treated in our profession as if it is afixe(
quantity in principle to be known accurately. In reality, the resistance of a ship cannot lo(
determined by experiments on full scale in an accurate manner. Only the magnitude o
the propulsive power can be measured on a ship with a reasonable accuracy. Hence
the resistance of a ship should be considered rather as a component of the tote propulsive power supplied to the propeller. In this respect, the magnitude of th( resistance depends on the applied scale-effect corrections on the wake and thi
propeller performance. As a consequence, since these scale effect corrections are nc
well defined, the resistance becomes an uncertain parameter.
There are several methods of dividing the propulsive power into components. It depend
on the definitions and consistency of these components whether resistance data of tw
ships can really be compared. The procedure of measuring the resistance of a real shil is only of academic interest to us.
Statistical methods are based almost fully on the results of model experiments. Thes
model test results have to be made non-dimensional. Thenthese results can be used i
a more general
way. Therefore,a framework for presenting the
data innon-dimensional form is to be set up. In several cases, the statistical methods hay been verified by correlation with results of full-scale measurements. The extrapolatio methods for model experiments always include some empirical factors which wer obtained from model-to-ship correlation studies. It is known that when the same shi model is tested in two towing tanks slightly different results are found. Therefore, th
correlation factors in the extrapolation methods are towing tank dependent. Ship Hydrodynamics and Hull Forms - An Introduction
RESEARCH
INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
16
V
;WI
There are different ways to define and to measure the resistance of a ship or of its model. We shall discuss three ways of definition.
First, there is the classical way by the tow rope. Through the tow rope a forward force is
exerted which balances the hydrodynamic resistance, provided there is steady motion. A second way to define the resistance is by considering the pressure difference over the
forward and the aft part of the ship, and to add the effect of the longitudinal component of the tangential stresses imposed on the hull surface by the water. This approach turns
to the basis of ship resistance: the pressure distribution over the hull and, in addition, the
tangential frictional stresses. The latter are caused by the viscosity of the water. This
definition of the resistance as the sum of the pressure and friction forces leads
automatically to the subdivision of the resistance into pressure and frictional resistance. From a practical viewpoint, measurements of the frictional stresses and. the pressure distribution over the hull are too complicated. Nevertheless, for optimising hull forms, the distribution of the pressure over the hull is the most important information to the designer. Computational methods can provide this information. This explains the success of these methods, which have now become available on a routine basis.
A third method of resistance definition is to consider the energy left behind in the water after the passage of the ship. The energy behind a ship, or its model, consists of the energy radiated by the free surface waves and in the kinetic energy left in the wake behind the ship. The latter is caused by viscous effects. Conservation of energy and
momentum requires that the momentum loss behind the ship must be equal to the
viscous resistance and that the energy dissipated by the radiating waves must match the wave resistance. The total resistance defined in either way must be equal to that
defined any of the other approaches.
For practical work in the towing tank, the designer has to work with the total model resistance only. By model resistance experiments the distinction into the various components has to be made by an analysis of the results. This distinction is essential for two reasons:
Each component follows its own scaling rule and,
The influence of the hull form on the various components is different and to
identify potential areas for hull form improvement the magnitude of the different
components needs to be assessed.
Often, the knowledge of the
total model resistance is supplemented by visual observations of the wave pattern. In some cases, additional measurements of the energy loss behind the ship model can be made to identify the major sources of some of the resistance components.MARITIME
RESEARCH
INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
The three ways of definition of the resistance are shown in the following figure. Three definitions of the resistance
friction
R = Rpressure + R friction
R determined from fluid energy
In practice, unfortunately, the total measured energy behind a ship model does not fully
balance the power supplied to the ship model.
When we speak of resistance in this module we refer to the resistance of a ship, or of its model, as the tow rope force pulling the ship at a steady speed. So we adhere to the first definition.
For prediction of the resistance, a subdivision into components of different origin is usually made. For each of these components a prediction is made, either by model
experiment or by a statistical analysis of old model test data. The following subdivision is
quite common:
R = RF Rw + RVIsc. Form + RAir RRoughness RApp
16
0
(41Z]
P
RESEARCH INSTITUTE
Ship Hydrodynamics and Hull Forms - An Introduction
16 0 ;AV,'
We distinguish between two types of extrapolation methods: Classical methods (A) and form factor methods (B). Methods (A) implicitly suppose the viscous form resistance RviscForm to be proportional to the wave resistance. In methods (B) the viscous form resistance is considered proportional to the flat plate resistance and this component is
expressed explicitly by the form factor.
Methods (A) do not distinguish between the wave resistance and the :viscous form resistance. The sum of the wave and viscous form resistance is usually referred to as the residuary resistance. These methods (A) follow exactly William Froude's original
concept of the flat plate. We speak of these methods as classical methods.
Methods (B) are commonly referred to as form factor methods. The ratio (proportion factor) of the viscous form resistance and the flat plate resistance is called the form
factor. Form factors are usually referred to as 1 + k.
1+ k =1 + RViscFoml Rf
The flat plate resistance is also referred to as the frictional resistance. This is because
the resistance of a flat plate can be only of frictional origin. According to Froude's
original concept, the frictional resistance of a ship is equal to that of the resistance of a flat plate. This plate must have an equal surface area, equal length and be towed at the same forward speed. This is the equivalent flat plate. Strictly speaking, the frictional
resistance of a ship is not equal to that of the corresponding flat plate. The pure frictional resistance, which is the sum of the longitudinal tangential stresses exerted on the hull, is
slightly larger than the resistance of the equivalent flat plate. We shall see why the flow
around a hull form differs from that along a flat plate.
Not only the flat plate resistance is somewhat different from the frictional resistance. Also, the pressure resistance, which is the resultant longitudinal force caused by the difference in pressure at the fore and after body, is not equal to the wave resistance.
The pressure resistance includes a part of viscous origin. Therefore, the pressure resistance is larger than the pure wave resistance.
The form factor, mentioned earlier in this paragraph, accounts for both differences, viz.: the difference between the pressure and wave resistance, and
the difference between the flat plate and the frictional resistance. -where: RE = Flat plate resistance
= Wave resistance
Rw
RVisc. Form
(B)
from
= Viscous resistance (A) RAir = Air resistance
RRoughness = Resistance due to hull roughness
MARITIME
RESEARCH INSTITUTE
NETHERLANDS
The sum of these two differences make up the component viscous form resistance. In
form factor methods the assumption is made that this viscous form resistance is
proportional to the resistance of the flat plate. This assumption is used in the
extrapolation of the results of model experiments and sometimes in defining resistance
components for statistical purposes.
Often, the distinction is made between 2 and 3-dimensional methods, thus indicating
methods without and with a form factor, respectively.
The various resistance components
Resistance components
It is noted that in practice the components RA,,, RRpughness and RApp are not always taken into consideration separately.
Resistance data of ships and models are usually made non-dimensional by dividing the resistance by 1/2 p V2 S. S is the wetted surface area of the ship at rest. This wetted
surface area is not the true wetted area but the longitudinal component.
The non-dimensional resistance coefficient of a ship is smaller than that of its model at corresponding speeds. The difference is called resistance scale effect. Corresponding speeds are speeds for which the Froude numbers of the ship and that of the ship model
are equal: Fns = Fn,
Ship Hydrodynamics and Hull Forms - An Introduction
0 M
Cause
,
Effect
Form factor
methods
Classical methods
4/MO ViscosityFriction
Appendages
AppendagesRoughness
Roughness
Flat plate
Flat plate
Viscous form
Residuary
Pressure
Waves ' Wave Air.
Air drag
_ AirRESEARCH INSTITUTE
NETHERLANDS
The Froude number Fn is the major non-dimensional speed parameter in hydrodynamic
ship research. It is defined as: V
Here, V is the speed, g is the acceleration of the gravity and L is a typical length. At
equal Froude numbers the gravity wave pattern is geometrically similar and, as a natural consequence, the wave resistance per unit displacement weight is the same.
2.1
Flat-Plate Resistance
The flat-plate resistance is usually calculated by means of the ITTC-19g7 model-ship
correlation line:
1 1 0.075
RF = p v2 S CF =p v2 S (
log Ra - 2)2
This formula is not a genuine flat-plate resistance formula but in model-to-ship
extrapolation it serves as such. For several decades the discussion has been going on
which formulation of the flat plate drag provides the most consistent model-ship correlation. There is some uncertainty about the level of the flat plate friction in the range of the very high Reynolds' numbers and doubts about the slope of the ITTC-1957 formulation in the range of low towing tank Reynolds' numbers. A comparison with some other formulations of the flat plate resistance, taken from "Principles of Naval Architecture", is shown here:
Various formulations of the flat plate resistance coefficient C,
0 009 0 008 0007 0.006 _ 0 005 0 004 0 003 0 002
Ship Hydrodynamics and Hull Forms - An Introduction
t111T] 1-1 T. TC LINE ---A TIC. LINE ATTC LINE *0.0004
160 ;011
i 0 075 ( LOG.° Ti-212 0 242 100,0 Cr) ,fc7, 0 066 ---- HUGHES LINE C10 CLOG, R.-2031! T-T -r-r-rri TI 1111 I.T.T C. LINE ---- AT TC LINEMARITIME RESEARCH INSTITUTE
NETHERLANDS
2.2
Wave Resistance
A typical wave resistance curve is shown in the figure with typical ranges for various
ship types indicated. Both the resistance and the non-dimensional resistance curves are shown as a function of the Froude number
V
This non-dimensional coefficient Fr, governs the wave pattern generated by a certain ship. This coefficient also serves in model experiments to attain equal wave patterns on
model and full scale by doing model experiments at equal Froude number.
Typical wave resistance curves
Ship Hydrodynamics and Hull Forms - An Introduction
FRIGATES FISHING BOATS / TUGS FERRIES CONTAINERS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fn WAVE 0.8 0.0 1.0 WAVE AHING
For a certain Froude number the magnitude of the non-dimensional wave resistance depends on the ratio of the main dimensions, the form coefficients and on the shape of the hull form. Unfortunately, these dependencies are complicated, difficult to predict by theory. These dependencies are the very reason of model testing and adhering to the
concept of corresponding speeds, implying equal Froude numbers on the model and the actual ship.
Most notable is the main hump at a Froude number of Fn = 0.5. This main hump is
found on the resistance curve of almost any ship which is able to pass this critical speed.
When going from left to right in this diagram we indicate how the wave-pattem changes.
If we watch a ship, running at a Froude number of about 0.1, we see hardly any waves except for some diverging waves at the bow. Up to this speed there is hardly any wave
RESEARCH INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
At a Froude number of about 0.15 a clear rise of the bow wave and a depression at the forward shoulder will be seen. A Froude number of 0.15 corresponds to the service
speed of many high block ships. At this Froude number the wave resistance is still
comparably small. Even for the fullest hull forms, as those of VLCC's, the magnitude of
the wave resistance is of the same order as the still-air resistance. Between the diverging waves and the hull and also behind the ship a system of transverse waves has
developed. This wave system travels along with the ship at the same speed. The wave
length of the transverse waves is:
= 27ca V2 = 21t FL (Deep water)
Waves generated by a not fully immersed bulbous bow, are visible throughout the speed
range. At high speeds the bulb waves are often reduced by bow waves and effects of running trim. Due to the forward speed the ships settles and trims by the bow up to a
Froude number of about 0.4.
At a Froude number of about 0.2, which is the service speed of many coastal vessels and other merchant ships of moderate fullness, the wave pattern as described above is more fully developed. These ships are more slender than those operating at a Froude
number of 0.15 to reduce the magnitude of the wave resistance. The energy radiated by the transverse waves, in particular the stern wave, is becoming relatively more important
in this range of the speed. Attention should be paid to the interference of bow and
fore-shoulder wave systems.
At speeds corresponding to a Froude number of 0.25 the wave resistance is quite
important. Splashing, breaking and some spray at the bow is usually present. A Froude
number of 0.25 is typical for a sea-going ferry, a cruise liner or a container ship.
Interference of bow and stern waves is becoming important at Froude numbers of about 0.3. At this speed a significant and unwanted interference hump on the resistance curve
is often found. The transverse waves carry a large part of the energy away. Froude numbers of 0.3 are typical for fishing vessels, tugs in free running condition and the
cruising speed of naval vessels as frigates.
At Froude numbers just over 0.4 the wave length of the transverse wave system
becomes in the order of the length of the ship. This results into a sharp increase of the wave resistance until the main hump is reached at a Froude number of 0.5. Ships of moderate fullness generate a pronounced wave system. A slight increase of the length of these ships and a corresponding fullness reduction to preserve displacement and
capacity is extremely beneficial from a powering point of view.
At the hump speed of Fn = 0.5 the ship sails in her own wave and only-transom type ships designed with a flat afterbody are able to pass the main hump. Then, the ship is
MARITIME
RESEARCH INSTITUTE
03=3
which the ship is lifted and the resistance flattens off. The range of speeds greater than
Fn = 0.5, is often referred to as the high speed range.
The transverse waves become relatively unimportant at speeds beyond the main hump at a Froude number of Fn = 0.5. Apparently, the generation of waves of a length greater
than the size of the ship does not occur.
At a Froude number of about 1 the planing speed range is entered. The dynamic lift is fully developed here and carries the weight of the ship to a great extent. Here, the wave resistance is gradually becoming less important in a relative sense. The wave pattern is reduced to a narrow V-pattern. The angle of the V-pattern decreases as the speed is
raised.
2.3
Form factors
The form factors, as mentioned before, reflect the influence of the velocity and pressure distribution on the viscous resistance. Both pressure and friction effects are accounted
for by the form factor, the total being the viscous form resistance. In principle, form
factors can be determined from model experiments. Establishing their magnitude is not always easy and their use is not universally accepted. One of the reasons for a lack of
enthusiasm for form factors is the uncertainty of its experimental determination. Typical values of the form factor are:
Ship Hydrodynamics and Hull Forms - An Introduction
Notice that the lower figures apply to good hull forms. A low form factor indicates that the additional friction and pressure resistance of viscous origin is small. The magnitude
of the form factor is dependent primarily on the fullness and on the form of the afterbody.
It is noted that the level of the form factor depends on the formulation of the flat plate
friction.
Form factors were introduced in the analysis of model experiments on ships more than
40 years ago. It was ascertained from the earliest days that Froude's original flat plate concept was only an approximation of the truth. This approximation, that the viscous resistance of a ship is equal to the frictional resistance of that of a flat plate, is almost
perfectly correct for very slender ships and throughout the decades Froude's conception
has proven to be a sound basis for extrapolation of model test results, particularly for
slender forms.
,.
Cb < 0.7 : 1+k= 1.10 -1.15
0.7<Cb <0.8 : 1+k= 1.15-1.20
RESEARCH INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
16
V
;41§11Why have form factors been introduced ? First, it was discovered that particularly for
large ships of great fullness negative allowances were to be applied to match the results of speed trials to the model experiments when extrapolated by means of Froude's
method. In general, the allowances applied in extrapolation methods were ascribed only to effects of hull roughness in the early days of model experiments, thus ignoring errors, if any, in the extrapolation method. Through the introduction of all-welded hulls in the middle of the twentieth century lower allowances for roughness must have resulted but
negative roughness contributions were thought inconceivable. Lower and lower
allowances, up to -25 to -30 per cent and even lower, were found for the largest ships
that were built.
A second argument for the introduction of form factors is the observation that predictions
based on tests on models of different size deviate systematically when extrapolated by means of the classical method of Froude. The results of the largest models are more favourable than those of the smallest models. These results indicate that the steepness of the extrapolator, the Cv-curve as a function of the Reynolds' number, is too small at
model scale.
At this point it was concluded that in the extrapolation of the resistance a fundamental error was made by over-estimating the full scale resistance by the same amount. The
introduction of the form factor made the results of the correlations consistent again. It is no surprise to see that particularly in countries as Japan, where many high block ships
are built the introduction of the form factor was well accepted. In countries as the United States of America, where mainly slender ships were built, the use of form factors was
not stimulated.
These arguments from a practical point of view were in addition to the more theoretical
reasons:
The frictional resistance of a ship's hull is larger than that of a flat plate of equal length, wetted area surface and towed at the same speed. The local velocities are slightly higher due to the three-dimensional hull form.
The pressure distribution around the hull as e.g. determined in potential flow
causes that the boundary layer flow causes a pressure difference over the hull which results into a force component in astern direction. The pressure loss at the
afterbody contributes particularly to this effect. So, a part of the pressure resistance of viscous origin is not regarded if only the flat plate drag is considered.
Both effects cause that the drag of viscous origin is higher than according to Froude's concept. How much is the viscous drag greater than the flat plate drag ? According to
the form factor concept the viscous drag Rv is equal to: Rv = (1+k) RF
MARITIME
RESEARCH INSTITUTE
r=lt=
Ship Hydrodynamics and Hull Forms - An Introduction16
AZI
How can 1+k be determined? There are some approaches to determine 1+k from the
results of the model test. If we carry out the resistance test at sufficiently low speeds the assumption can be made that the wave resistance vanishes according to a simple
relationship of the Froude number. However, the accuracy of the experimental form
factor is often insufficient.
An important conclusion about form factors is that they give not only consistency but also uncertainty because their level is sometimes difficult to assess. Therefore, they are
not always applied with enthusiasm and the merits of using the form factor implies only a small gain in accuracy, if any, over the more classical methods of earlier times.
2.4
Other Components
The other resistance components, appendage resistance sometimes excepted, are usually small under typical trial conditions. At this stage we shall just mention a few
typical percentages.
The air resistance is usually not more than 2-3 per cent. Notice, that this is the still air resistance, which is different from the wind-added resistance! Effects of hull roughness should not be larger than 3-5 per cent for new-built ships of good finish. Appendage
drag varies from 2 per cent in single-screw ships to more than 20 per cent in
multiple-screw planing ships with raked exposed shafts. Merchant twin-screw ships with open, exposed shafts show an appendage drag in the order of 10-15 per cent of the
RESEARCH INSTITUTE
Ma=1=1
3 FLOW AND WAKE
The flow pattern around a ship and the resistance experienced are complicated matters.
Much of the flow around a ship can be explained, if first a study is made of the flow
around bodies of more simple form. Also the representation of the real flow by a
hypothetical flow will clarify many features of the actual flow. We shall look into some simple bodies. For the moment we shall neglect effects of the free surface. For details
and a more in-depth study reference is made to the handbooks on hydrodynamic theory. (e.g. Glauert, The Elements of Aerofoil and Airscrew Theory", from which several paragraphs in this chapter were taken.)
3.1
Flat plate in the direction of the flow
First, we look into the flow and drag of a flat plate in the direction of the flow. If there were no viscosity, the flow would not notice the plate and pass it without any transfer of
energy and there would be no resistance at all.
All real fluids possess the property of internal friction or viscosity by virtue of which tangential stresses may occur at the surface of separation of two adjacent fluid
elements. These tangential stresses are zero when the fluid is at rest, and in general
they depend on the relative velocity of the adjacent fluid elements. When the fluid moves in layers in this manner, it is said to be in laminar motion. This definition of the tangential force due to viscosity is based on the conception that the frictional force depends on the
relative velocity of the adjacent fluid elements and is justified by the accuracy of the
results which can be deduced from it.
When two parallel layers of fluid are moving in the same direction with different velocities, the surface of separation is a vortex sheet and the elementary vortices of this
sheet act as roller bearings between the two layers of the fluid. The tangential stress at the surface of separation is intimately related to this vortex sheet and the workwhich must be done against the tangential stress is represented by the dissipation of energy which occurs in the vortices. To complete the definition of the nature of a viscous fluid it is necessary to consider the conditions at a solid boundary. The motion of the fluid over
the surface of a body will cause a finite tangential force on the surface and it follows that
the layer of fluid immediately in contact with the surface must be at rest relative to the
surface, for if this condition were not satisfied, the velocity gradient would tend to infinity at the surface and the tangential force would also tend to infinity unless the coefficient of
friction between solid and fluid were indefinitely small compared with that between two
fluid layers. This condition of zero slip at a solid boundary is confirmed by experiments. Close to the surface of the flat plate, the velocity of the fluid must change rapidly to meet the zero slip condition at the wall. The thin layer, in which this occurs, is called the boundary layer, a concept due to Prandtl. Only in the boundary layer- the viscosity manifests itself.
Ship Hydrodynamics and Hull Forms - An Introduction
MARITIME
RESEARCH INSTITUTE
NETHERLANDS
In the boundary layer the velocity of the fluid rises rapidly from zero to its value in the
free stream, and however small the viscosity may be, the viscous force retains its importance in this layer.
The boundary layer theory has been applied by H. Blasius to the determination of the
laminar flow along a flat plate and of the resulting frictional drag. Measuring the
coordinate x along the plate from the leading edge, the thickness of the boundary layer
is shown to be proportional to:
X V
Blasius' solution corresponds to laminar flow along the plate and will represent the actual flow at low values of the Reynolds' number only.
At higher Reynolds' numbers, the streamlines begin to waver at a certain point from the leading edge. The paths of the flow particles become irregular. This is called turbulence and the change from the laminar flow to this state of turbulence is called transition.
Osborne Reynolds was the first to do systematic experiments into the nature of
turbulence and the parameters governing the transition. In the following diagram the
frictional coefficients for both laminar and turbulent boundary layers on smooth flat plates are shown together with some intermediate lines.
The line of turbulent friction is due to Von Karman, who derived this line for flat plates from empirical data on turbulent pipe flow. The intermediate lines shown in the next figure, which was taken from "Principles of Naval Architecture", account for the flat plate partially being covered by a laminar, and by a turbulent boundary layer. The variation in
the intermediate lines point to a variation in streamwise position of the transition. Flat plate resistance for laminar and turbulent flow
3Q09
3008
0.037
0 315 %\\\
Cia4
Ship Hydrodynamics and Hull Forms - An Introduction
4 CO33 /-*N
/
,,C,,TYPICALTRANSITION LINES/.
. Q 33Z 031 0 1,11, 135 op` I I I I alPRANOrL VON KARMAN CF 0072(V4,) I
BLASIUS C, 1.527C.,4)-1 LAMINAR FLOW Rn
IIL
I I ioRESEARCH INSTITUTE
NETHERLANDS
To avoid this variation of the transition from model to model, turbulence tripping is usually applied in towing tank experiments.
The frictional resistance of a plate with a turbulent boundary layer varies roughly
proportional to the speed to the power 1.825. This was discovered by Froude from his experiments on flat plates. The exponent found by Froude corresponds closely to the exponent of 0.2 used in the rule of the non-dimensional friction coefficient according to
Von Karman.
3.2
Potential Flow
Theoretical hydrodynamics often uses the concept of potential flow, a hypothetical, irrotational fluid without viscosity. For many ship flow problems the potenflal flow model is sufficiently accurate, in particular, if the pressure distribution over the hull is studied. The representation by the potential flow is even more realistic if the free surface waves are included. If these free surface waves are not included a body, irrespective of its shape, will not experience any resistance in potential flow. This is referredto as the Paradox of d'Alembert. A major achievement of the potential theory is the law of
Bernoulli. This well known law states that the total head is constant. The total head is
the sum of the pressure in the fluid and contributions both from gravitational forcesand
from the velocity of the fluid. In other words, it states that along a streamline kinetic energy per unit of volume (1/2 p V2) can be changed into potential energy (pressure wise and gravitational) without energy loss. If the streamlines originate from an area of equal pressure and equal velocity, the total head is constant over the entire potential
flow field.
3.3
Resistance of bodies
In a real fluid a body experiences a drag or a resistance opposite to the velocity vector.
The resistance is often expressed in a non-dimensional form by means of the drag
coefficient Cd. Resistance
P V2A
2
Cd usually implies that the area A transverse to the flow direction is used in expressing
the drag in a non-dimensional way.
Cd =
Ship Hydrodynamics and Hull Forms - An Introduction
MARITIME
RESEARCH INSTITUTE
=13=1
Ship Hydrodynamics and Hull Forms - An IntroductionThe large variation of Cd for some types of bodies is related to the flow patterns. Flow
patterns may change considerably with varying Reynolds number. It is unusual to
express the hydrodynamic resistance of a ship in terms of Cd.
3.4
Cylinder perpendicular to the flow
The next figure, taken from Schlichting's "Grenzschicht-Theorie", shows the drag
coefficient of a circular cylinder perpendicular to the flow as a function of the Reynolds' number, here defined as: VD/v
Drag coefficient of a circular cylinder perpendicular to the flow
100 60 40 20 CD 10 6 4 2 0.6 04 02 01
SOME TYPICAL Cd VALUES
Flat plate (square) 1.10
Flat plate (rectangular with 1:4 sides) 1.19
Sphere 0.1 - 0.5
Circular cylinder (high Reynolds number) 0.3 - 1.2 Streamlined bodies (ships under water!) 0.04 - 0.1
Above-water part of a ship 0.7 - 0.8
lot 10' 104 10' 10' 10'
R
At very low Reynolds' numbers, where viscosity effects are dominant, the drag
coefficient is quite high. It decreases gradually until at Rn = 1000 the level of Cd = 1 is reached. In this range of Reynolds' numbers the flow separates from the cylinder. This causes a wide wake which gradually narrows with increasing Reynolds' number. Over the range of Reynolds' numbers from 1000 to 2 * 105 the separation point lies close to 80 degrees from the front. The laminar boundary layer leaves the surface of the body
RESEARCH INSTITUTE
=3=
and after separation it is referred to as a free-stream shear layer. This free-stream shear layer becomes unstable and there is transition to turbulence. As the Reynolds' number increases further, the transition point shifts upstream towards the point of separation. At a certain Reynolds' number there is re-attachment of the free-stream turbulent flow, just downstream of the separation point. At the circular cylinder this abrupt change occurs at
a Reynolds' number of about 2*105. The small region of separation is called a separation bubble. The turbulent boundary layer separates again, but since the wake is quite
narrow it is not surprising to see that the drag coefficient is small. A further increasing
Reynolds' number will eliminate the separation bubble. The transition shifts to the
surface of the body. The drag coefficient increases steadily towards a constant level of
about 0.6 at the highest Reynolds' numbers.
At low Reynolds' numbers the flow is called sub-critical. At high Reynolds' numbers the flow is called super-critical. In both ranges of the Reynolds' number there is periodic
shedding of vortices at the sides of the wake. These vortices are called the Von Karman
vortices. They appear in a regular flow in a zigzag pattern behind the cylinder. They are
visualised by the wavering flag on a pole. The pressure in the separated zone at the rear
end of the cylinder is called the base pressure. Effects of base pressure are present on
bodies with fully separated flow.
The circular cylinder discussed shows a complicated flow pattern. This is primarily determined by the pressure distribution:
Pressure distribution over a circular cylinder
_
--1
-1
3
Ship Hydrodynamics and Hull Forms - An Introduction
-IExperimental
/.
Theoretical
..._ t t0
450
900
1350
Angle from Nose of Cylinder
.160 k.td
_
MARITIME
RESEARCH INSTITUTE
=
Ship Hydrodynamics and Hull Forms - An Introduction160 AZ1
_
The pressure distributions shown in this diagram, which is due to Glauert, clearly reveal the difference between real and potential flow. In potential flow the pressure coefficient is 1 at the nose and also at the rear of the circular cylinder. In both these conditions of
zero local velocity, the pressure increases to stagnation pressure. At the front, the
agreement between the potential flow and real flow conditions is almost perfect. At the
rear end, however, the stagnation pressure is not attained. The high velocity at the sides
of the cylinder, theoretically twice the upstream velocity in potential flow, does not really occur. In real flow the deep pressure drop predicted in potential flow is not found. In the
separated flow with the wide wake, the pressure recovery is far from ideal. The
asymmetry in the pressure distribution in the real flow is the very reason for the greater
part of the resistance. Frictional drag is of minor importance if blunt bodies with
separation are considered. Nevertheless, the origin of the drag is of viscous nature.
Note that with a symmetrical pressure distribution, as in potential flow, there is no
pressure resistance. t.
3.5
Flow and pressure distribution over a ship's hull
Most features discussed for the cylinder perpendicular to the flow are present at a ship as well. The pressure distribution over a ship shows the same character. The values
attained by the pressure coefficient are less extreme along the hull, thanks to the
streamlined form. The pressure drop in areas of large convex curvature (shoulders) is present as at the cylinder. Along the parallel middle body the velocity is only a small fraction higher than the ship speed. This causes that the pressure coefficient is only
slightly negative. Towards the stern there is an adverse pressure gradient. An adverse pressure gradient means an increasing pressure when travelling downstream. As in the case of the cylinder, the stagnation pressure is not attained in reality. A negative pressure gradient, sometimes referred to as an adverse gradient, will cause the boundary layer to become thicker. Then the velocities in the flow near the surface
become smaller. Separation is characterised by zero velocities or reverse flow. The
effect of the pressure gradient applies to both laminar and turbulent boundary layers. On full scale ships only turbulent boundary layers are important. On model scale laminar flow may occur easily. Undefined location of transition to turbulence or unwanted
separation are the main reasons why attempts are made to avoid laminar flow in towing tanks. Turbulence tripping and choosing the largest possible models within practical
RESEARCH INSTITUTE
Pressure distribution over a fine and a full hull form
Ship Hydrodynamics and Hull Forms - An Introduction
vP*
The adverse pressure gradient may cause the boundary layerto separate from the hull. At blunt ship forms severe separation may be present, particularly on model scale. On model scale the Reynolds' numbers are lower by a factor of about 100 and viscous
effects, including separation are usually larger. On a streamlined three-dimensional hull form there is always separation, but this type of separation was not discussed in
describing the flow around the circular cylinder. The flow around the cylinder can be
regarded as two-dimensional because at each cross-section the flow pattern will be the
same. A ship form is three-dimensional and also the flow-pattern in potential flow will show a typical three-dimensional pattern. A pressure gradient perpendicular to the streamlines is quite common. On a ship form there is three-dimensional separation, usually along a vortex line. The three-dimensional separation along a vortex line is
initiated by a cross flow in the boundary layer. Some typical flow patterns on simple ship hulls are shown in the following figures.
A a
V.
MARITIME
RESEARCH INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
Pressure distribution along streamline No. 4
COL 12 10 4 0
kaNrwma ialmasin
IRITIMIOMMINIMMEME111111
IIIIIMIMIWAMPILIIMIN71511111
INISWAIMINEVIIIM.VMOMMI
IMIPAIFILMAIIIM110117/1710.1
CWL 6 4 2 0Model Experiment
Pot. Theory 0.0 * -0.2. 0.4 0.6 0.8 1.0 1.2 1:4 1.8 2.0 2.2 2.4 2.6 X (m)livAlatd
MARITIME
RESEARCH INSTITUTE
=
Ship Hydrodynamics and Hull Forms - An IntroductionTypical flow patterns behind hull forms
54 2
,
43 1 ... ....\
\
\SIIIII
\tillti I
soli
1X1f IttIII
1 I 2..///1IIIIIII.
4 S - / / I 1 I 1 I 1 5,
7 ., , 7, IIII.III,I
.... ... .., ....`''. /4 / / / / ft
t/
, / /
I .... .. ..,/1
t tI
/
...."\\..../ /
/
# 1 1, / / / /
/
1,
1 I I/ /
/
I e ...-/
I I f I 8 I I///III I
I I , I 4fl I4
IIIII,lo
3 V16 V atZI
-_..---
----
...17.
--.I...
---...1..
...
....
//...._
----
1/
/71_
\ I
/ /
//
4/
`-- \ k
1/
/
,
/ f \/..__\\
1 .../.-//
/
/
/
/
\ \_._
./ //
/ / /
t I,
/ I / / / .. / 1,
/ I\
\
I s g i-MARITIME
RESEARCH
INSTITUTE
=
3.6 Wake Distribution
The flow pattern caused by the potential flow, the boundary layer, flow separation, either 2-dimensional or in the form of a vortex-type flow leads to a wake behind the ship. In this
area of reduced velocities the propulsor is working. As we shall see later the wake
contributes to the efficiency of the propulsion, but the inhomogeneity of the flow may lead to propeller cavitation, vibration and noise. Especially for high-powered ships the
designer of the hull form aims at achieving an homogeneous wake distribution as possible. This applies particularly to single-screw ships where the wake distribution often becomes critical.
If we compare traditional hull forms it can be illustrated how vortices separation at the
afterbody can be generated on purpose to the advantage
of making the wake
distribution more uniform. This is done to avoid vibration and propeller cavitation problems. At this stage we shall not discuss the influence of the wake onpropeller-induced vibration further. The three hull forms shown in the next figure generate different wake distributions
Three hull forms to generate different wake distributions Ship Hydrodynamics and Hull Forms - An Introduction
,-RESEARCH
INSTITUTE
Ship Hydrodynamics and Hull Forms - An Introduction
V - STERN
MARITIME
RESEARCH INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
In the next example, a Ro-Ro ship, it is shown how a relatively small change in the form of the afterbody affects the wake distribution. In the next figure the three hull forms are shown. The bottom picture is an intermediate form between the middle one and the as-built form shown on top. The model wake patterns for the design draught of 10.00 m
are shown in the following figure.
RESEARCH INSTITUTE
2=2
TAT. 0
Ship Hydrodynamics and Hull Forms - An Introduction
Body plan, fore and aft contours of ship model Nos 5492, 5492A and 5492B and
curves of sectional areas for a ship draught of 10.000 m on F.P. and 10.000 m on
A.P.
5492
16 0
;kid
S TAT. 20 .
MARITIME
RESEARCH INSTITUTE
NETHERLANDS
Circumferential distribution of axial velocity component
1 .0 0-5 0.0 1.0 0-5 0.0
IC
00
Ship Hydrodynamics and Hull Forms - An Introduction
s-Li9 t A
\,
\ 1.015 0 948 \0.812\\,k
s.0577 0-0 45.0 90-0 25.3 i80Postion angle (TOP)
0 .0 45.0 90 -0
RESEARCH INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
As can be seen, the depth of the 12 o'clock wake peak in the axial flow is deepest for the as-built form. The intermediate form causes a wake field with an intermediate wake
peak. Apparently, the thick, round forms below the shaft help to form longitudinal vortices (three dimensional separation) by which fluid of higher axial velocity is transferred to the top sector of the propeller disc. The difference in propulsive power, if
any, between the three forms was found to be hidden in the normal band width of measuring inaccuracy.
MARITIME
RESEARCH INSTITUTE
NETHERLANDS
4 PROPULSION
The resistance force of the ship, R, determined from either a model resistance test or predicted from systematical series data, or calculated by empirical/statistical methods, has to be compensated by a propelling force to maintain the steady forward motion of the ship at a certain speed, V. This balancing propelling force in forward direction is
called the "thrust", T. Supplying this thrust force is the very purpose of the propeller.
4.1
Thrust deduction
The thrust force is always greater than the resistance, leaving aside one or two special cases. Only when the thrust force is applied without affecting the pressure distribution over the ship's hull, the resistance force and the thrust force are equal. In normal ships,
the propulsor is located in the vicinity of the hull. Then, the action of the propulsor affects
the pressure on the hull, at least locally at the afterbody. The difference between the thrust and the resistance is called the thrust deduction force. This refers to a certain fraction of the thrust which is not effectively used to overcome the resistance. Because the thrust deduction force appears to be a certain fraction of the total thrust, rather than a fixed fraction of the resistance, it is defined as such: tT. The thrust deduction fraction,
t, or the thrust deduction factor as it is also called, is thus defined as:
T-tT=T(1-t)=R-F,
or: t = (F - R + TyrHere, R is the resistance, T is the thrust and F is a tow-rope force acting on the ship in forward direction. In model experiments this force F has a certain value, but on a freely sailing ship F = 0. On a ship towing an object F is negative. Typical values of the thrust
deduction fraction are:
Ship Hydrodynamics and Hull Forms - An Introduction
1+7'0 ttzi
Since the thrust deduction is a loss factor in the propulsive performance it is the task of the designer of the hull and the propulsor to achieve a thrust deduction fraction t as low
as possible.
From load variation tests on model scale it has become clear that an increase of the
propeller loading leads to a reduction of the thrust deduction fraction.
-Configuration t
Single-screw ships of great fullness 0.20-0.25 Slender single-screw ships 0.16-0.22 Twin-screw ships, normal fullness 0.10-0.15 Slender twin-screw ships 0.07-0.12 In bollard condition (V= R =0!) 0.02-0.05
4.2
Propeller Action and Wake Fraction
Usually, the thrust is provided by a rotating screw propeller at the stem. This propeller which rotates at a rotative speed of n revolutions per second experiences a torque Q, while giving its thrust T in axial forward direction. The action of the propeller of diameter
D is described in a non-dimensional manner by the following three coefficients:
The velocity Vaa is the speed of advance of the propeller. If there is no ship ahead of the
propeller we call this hypothetical condition the "open-water condition. We imagine the
propeller moving steadily forward in axial direction at the speed of advancd-Vad.
In a propeller open-water experiment in a towing tank the speed by which the driving
unit with the propeller fitted is moving forward is this speed of advance Vad. In reality, the
propeller is fitted to a ship which sails at a speed V. Then, the propeller advances at a lower speed relative to the water. The speed of advance of the propeller is lower
because the hull in front of the propeller causes a wake. This more realistic condition of
the propeller is called the "behind" condition. The fraction by which the speed of
advance of the propeller is lower than the ship's speed is called the "wake fraction". It is also called the Taylor wake fraction. It is indicated by w. Thus, w = 1-VadN. If in the advance coefficient the ship speed V is used instead of Vad, the advance coefficient, which is not the real advance coefficient of the propeller any more, is then called the
"apparent advance coefficient", J' or J,. By definition: J/J' = 1 - w.
4.3
Simple Momentum Theory for a Propeller in Open Water
The action of a single propeller can be explained by looking atan "actuator disk". In this
actuator disk model, which is a very simple model of a real propeller, the finite number of
blades have been replaced by a disc. This disc produces thrust in axial direction. In the
actuator disc model there are no effects of viscosity. The energy supplied to the actuator
disk is transferred to thrust without any loss of energy. Nevertheless, the efficiency of this propulsor is not equal to 100 per cent. The reason is that the actuatordisk
acceler-ates the fluid. Behind the actuator disc an area of increased velocities is generated. This area is called the "slipstream". The kinetic energy left in the slipstream is the very cause
of the efficiency not being equal to 1, even if the energy supplied to the propeller is converted to thrust without losses. The ratio of the work done by the thrust, which is equal to the product of the thrust and the speed at which the actuator distadvances, T V, in relation to the energy left in the slipstream is a straightforward measure of the
effi-Advance coefficient J = Vad/(n D),
Thrust coefficient KT = T/(p n2 D4) and the Torque coefficient K0 = Q/(p n2 D5).
RESEARCH INSTITUTE
MARITIME
RESEARCH
INSTITUTE
Ship Hydrodynamics and Hull Forms - An Introduction
This efficiency is called the "ideal efficiency", because of the hypothetical nature of the actuator disk. This simple actuator disk model also exhibits the concept of the "induced
velocity". The induced velocity is the velocity caused by the propulsor.
V (1) Po
Pkvi 0 M
V.v P. AP (2)The pressure force exerted on the flow by the propeller as a reaction to the thrust 1 gives Ap = T/A. Assuming potential flow ahead of the propeller (1) results according tc
Bernoulli into:
Fli = po + 1/2 p V2 = p + 1/2 p (V + v)2
Similarly downstream of the propeller (2):
H2 = pa + 1/2 p (V +v1)2 =p + Ap + 1/2 p (V+ v)2
Subtracting these equations gives: Ap = FI2 - Hi = p (V + 1/2 vi)
Momentum added to the flow through the disc is equal to the exerted force: T = A p (V + v) v1
In combination with Bernoulli:
p=pvi(V+1/2Vi)=p(V+V)Vi
V
Vv
RESEARCH INSTITUTE
This results into vt = 2 v and T = 2 p A (V + v) v The increase of the kinetic energy per unit of time is:
E =1/2pA(V+v)((V+v1)2-V2}
=2pA(V+v)2v=T(V+v)
This is the work done on the fluid by the thrust. This is equal to 2 it 0 n for a rotating propeller if there is no loss. The useful work done by the thrust per unit of time is T V.
The ideal efficiency is the ratio of the useful work done to the total work done:
=
TV
V71
T (V +v) V +v
We can express the induced velocity in terms of thrust loading. We solve v from T = 2 A p (V + v) v, using A = 1/4 n D2, with D being the propeller diameter, we find:
V
y
8 T2 2
21+
Y2, OrV
n V Dp
v 1., 8 Kt
--\7=y2 1+7c--ij -y2
Notice that KT/J2 is equal to T/(p D2 V2).
8/7c KT/J2 is called the thrust loading coefficient, whichis usually indicated by C. At zero
speed the thrust loading coefficient Ct is infinite, but the induced velocity remains finite
and can be evaluated:
v= I
2T,
ornD
2=.\1-2Kt
niDD`
The ideal efficiency expressed in terms of the thrust becomes:
2
=1+,ii+Ct
Ship Hydrodynamics and Hull Forms - An Introduction
MARITIME
RESEARCH INSTITUTE
NETHERLANDS
From this simple actuator disk model, some important conclusions can be drawn, which
will help us to understand the action of propulsion:
The axial velocity far upstream is equal to the advance speed. The axial velocity is increased by the induced velocity. The induced velocity in the final slipstream is
twice the induced velocity in the actuator disk.
This acceleration causes a contraction of the stream through the actuator disk. The law of mass conservation requires that the slipstream converges towards a final cross section. The contraction of the flow through the actuator disc is larger if the
thrust loading is greater.
At zero speed (bollard condition) the loading coefficient Ct is infinite. The ideal
effi-ciency mis zero. Nevertheless, the induced velocity attains a finite value.
At zero loading the efficiency reaches the value of 1. This implies that the induced velocity is zero. A zero loading requires an infinitely large propeller. Apparently, the
efficiency of the propulsion depends on the size of the propeller.
Ahead of the actuator disc is an area of reduced pressure. A body (a ship's hull) placed here will experience this low pressure at the after end. In real flow this will
cause extra pressure resistance of the body in the form of thrust deduction.
The efficiency of the propulsion depends on the slipstream velocity in a reverse
way. The highest efficiency is attained if the velocity in the slipstream is small. Apparently, it is more beneficial to accelerate a large amount of water to a low velocity than to give a large velocity to a small amount.
If there is a wake, as behind a ship, the highest efficiency is reached by accelerating
the retarded flow to its original velocity. In this way the energy left behind the ship is minimum. Then not only the propeller efficiency is regarded, also the propeller-hull
interaction is taken into account.
4.4
Propeller Open-Water Characteristics
By testing a single propeller the open-water characteristics are obtained. Usually, they
are expressed in the form KT-KQ-J. The efficiency of the propeller is: Vad K-r
TIP° = 2 71: n= 2IT Ko
It is appropriate to compare the efficiency of a propeller in an open-water experiment with the ideal efficiency of the actuator disk. This comparison must be made at corre-sponding thrust loadings. In the next figure the efficiency of a real propeller is compared
to the efficiency of the actuator disk.
RESEARCH INSTITUTE
03:1=
1.0 Q8r
Q6 Q4 02Ship Hydrodynamics and Hull Forms - An Introduction
1 6 V AZ1
This propeller has four blades (Z = 4) and a pitch-diameter ratio of one. In general, it appears that a well designed propeller will achieve a propeller efficiency equal to the ideal efficiency reduced by approximately 0.175. The difference between the ideal and
actual efficiency, which is almost independent of the loading over a wide range, is
caused by:
rotational losses, viscous losses,
losses originating from the finite number of propeller blades, and losses due to the radial load distribution not being optimum.
The rotation of the propeller causes an efficiency loss through the kinetic energy of the
rotational components of the induced velocity. These are obviously present in the action
of a rotating screw propeller. They are not considered in the simple axial actuator disk
model. In the actuator disc model the thrust and induced velocity are axial, whereas in a real propeller each propeller blade generates lift almost perpendicular to the blades. So,
the lift on the blades is associated with an induced velocity almost perpendicular to the blades. Hence, in the case of the rotating propeller theinduced velocity has a rotational
component. Since at the inner part of the propeller the pitch angle is highest, the
rotational component of the induced velocity is highest here. Therefore, the rotational
losses occur primarily in the central part of the propeller disc.
<
MARITIME
RESEARCH INSTITUTE
NETHERLANDS Ship Hydrodynamics and Hull Forms - An Introduction
Further departures between the ideal efficiency and the actual propeller efficiency are caused by the frictional losses which occur when a real propeller works in a viscous fluid. Blade roughness contributes further to the viscous losses. These viscous losses originate from the frictional and form drag of the blade sections. It will be no surprise to see that the viscous losses occur for the greater part in the outer area of the propeller
where the circumferential velocities are highest.
The last two causes of losses in relation to the uniformly loaded actuator disk are the
effects of the finite number of propeller blades and radial variations of the propeller
loading. It can be shown theoretically that any non-uniformity in the distribution of the
induced flow field corresponds to a certain loss of efficiency. The finite number of blades
can be regarded as such. Also non-optimum radial load distributions contribute to the non-uniformity of the induced flow field. The kinetic energy of such a non-uniform flow field is always larger than that in a uniform flow field containing the same momentum. So, from a left-energy point of view the highest number of blades is beneficial.
Unfortu-nately, the frictional losses increase as the number of blades increases, both by increasing blade area and also by higher specific drag coefficients of the sectional profiles.
4.5
Efficiency Components and Propulsion Factors
The propulsive efficiency 11D is the ratio between the effective power and the power absorbed by the propulsor. Thus lip = PE/PD. PE is the power required to pull the ship forward by a tow rope. PD is the "delivered power", which is absorbed by the propulsor.
The coefficient rip is also called the "quasi-propulsive coefficient" (QPC), the total efficiency or the efficiency of the propulsion.
It is natural that the propeller efficiency is an important part of the propulsive efficiency. And, indeed, a change in the quality of the single propulsor will almost automatically lead to a corresponding change of the propulsive efficiency im. It is usual to express the propulsive efficiency into efficiency elements and propulsion factors as below. Indices
"o" refer to open-water conditions.
.
(R F)V =T(1 t)V
2rcQn
2TcQn =TV(1w)(1t)
T0V(1 w) Q0T 1 t
2 it Q n (1 w)
2 rc Qon QoT 1w
(11p) (11H)(ii)
(%)
(11K) < J KT° Ka. KT 1_ t =2TEK0o Ko KT. 1w
(110) (11R) (T1H)RESEARCH INSTITUTE
23=1=1
Ship Hydrodynamics and Hull Forms - An Introduction16 V AZI
This simple algebraic subdivision shows first how the propulsive efficiency fia is divided into the propeller efficiency lip and the hull efficiency 111.4, with rifi= (1-t)/(1-w). Next, it
shows how the propeller efficiency is divided into a propeller open-water efficiency 1-1,0
and the "relative-rotative efficiency", iiR. The quality of the propulsion arrangement can
either be a matter of the propulsor itself, or of the hull-propulsor interaction, or both. The definition of the wake fraction is decisive here. A low wake fraction causes a high
propeller efficiency but also a low hull efficiency, and reverse. In Chapter 4.8 we shall
pay further attention to this aspect.
There are three principal ways to determine the wake fraction:
The "nominal wake". An averaging of the local axial velocities over the propeller
disk. The ship, or its model, is towed at the correct speed without a propeller fitted. "Wake based on torque identity". The wake is then determined from the J/J'-ratio
found from Ka-identity. Then the propeller experiences the same torque in open water as in behind condition when rotating at the same rate.
"Wake based on thrust identity". As in 2., but instead of torque, the thrust is used.
This is the most common definition of the wake fraction. In this case the rela-tive-rotative efficiency reduces to the ratio of the torques in open and behind conditions at equal rotation rate and thrusts.
Wake fractions determined by 2. or 3. are called "effective wake" fractions. The concept of "effective wake" implies that the influence of the propeller action on the stern flow is incorporated. Notice, that the induced velocity itself is not a part of the effective wake
fraction. For this reason the effective wake can essentially not be measured.
Measurements of the flow always contain the induced velocities. The effective wake can be derived by subtracting the calculated induced velocities from the measured flow field.The induced velocity is present in both the open-water and in the behind condition. In nominal wakes effects of the propeller action are absent. If wake fractions are used without further specification, we suppose them to be effective wake fractions based on thrust identity.
4.6
Typical Propulsion Factors
It is quite practical to make an assessment of the propulsion factors and efficiency components. Some typical values are:
Configuration w
Single screw, high block forms, laden 0.40-0.55 Single screw, high block forms, ballast 0.50-0.65 Single screw, moderate fullness, laden 0.30-0.45
MARITIME
RESEARCH INSTITUTE
Ship Hydrodynamics and Hull Forms - An Introduction
ffiriTaTI
These are values often found in the towing tank. They are typical model values. Wake fractions found at the actual full-scale ships are lower, particularly behind conventional single-screw hull forms. For this type of arrangement the difference between the model and the full-scale wake fractions is about 0.05-0.25, depending on the scale ratio and the magnitude of the wake itself. The differences in wake fractions are ascribed to the difference in Reynolds' number between model and ship leading to a relatively thinner
boundary layer on the ship. This thinner boundary layer leads to a lower viscous
resistance and this naturally involves a smaller momentum loss than on the model. So, the comparatively smaller viscous resistance of the ship is responsible for the smaller
wake fraction found at full scale. The difference is called "wake scale effect".
The same principle causes the wake fraction to be correlated to some degree to the viscous resistance in a more general sense. This mechanism allows that the propeller recovers the loss of momentum of the hull to some extent. It also shows that a poor resistance performance is improved often by the propulsor action to a certain degree. The designer should ultimately aim at a situation in which the flow behind the hull which
carries the momentum loss associated with the viscous resistance, i.e. the viscous wake, is accelerated by the propeller again to its original speed, thus leaving a minimum of kinetic energy in the water when the ship has passed.
A combination of the given figures for the wake fraction with the earlier given values of
the thrust deduction, can readily give some useful values of the hull efficiency. As a rule:
Behind single-screw ships of conventional propeller arrangement the hull efficiency is
greater than 1. For high-block ships values of 1.5 occur, particularly in ballast conditions,
where even higher figures are found sometimes. More usual is 1.1-1.2. Slender ships and ships with an open-shaft arrangement have hull efficiencies of about 1. Twin-screw ships, commonly fitted with exposed shafts, usually have hull efficiencies between 0.9
and 1.
In all cases the relative-rotative efficiency TIR is about 1. A deviation of more than 3 per
cent is exceptional. Apparently, the relationship between the thrust and torque of a propeller is hardly affected by putting a large body as a ship just in front of the propeller!
The relative-rotative efficiency is by its definition the change of the propeller efficiency when going from open-water to the behind-ship condition. An rjR-value larger than 1 implies that the propeller "works better in the behind than in the open-water condition. Hence, the relative-rotative efficiency potentially expresses to which extent the radial
load distribution of the propeller has been matched to the wake distribution. Therefore,
the relative-rotative efficiency is influenced by the radial distributions of the wake and the propeller pitch. As a consequence the relative-rotative efficiency need not
to be
independent of the propeller. Behind single-screw ships with a pronounced radial wake
distribution R-values of wake adapted propellers are be found which are about 1 pei cent higher than those of twin-screw ships with exposed shafts, behind which the radia'
wake distribution is much more homogeneous. Unfortunately, in experimental
relative-rotative efficiencies these effects are often obscured by measuring inaccuracy anc
systematic departures of open-water and propulsion test conditions.
The observation that there is a scale effect on the wake fraction, tells us that, as e consequence, there will be also a scale effect on the hull efficiency. Both the wake anc
