CHAPTER I INTRODUCTION
Ships (with the exception of submarines that move totally under water) move both in water and in air. The forward motion of the vessel is opposed by resistance forces from the air and the water. These forces, called “drag “ drag forces” forces” r equire equire the ship to exert a force directed forward (“thrust (“ thrust”” force) to overcome them in order to make the ship cruise in water and in air. The devices that impart the thrust forces on the hull are called the “ propulsors”. propulsors”. The most most widely used propulsor propulsor is the screw propeller or one of its variants. It is of utmost importance for the ship designer to determine the components of ship resistance accurately and reduce them as much as possible, and also to select the optimum propulsor to provide the necessary necessary thrust for a given ship speed. The science of ship propulsion is involved with the investigation of the sources of those drag forces and their relations with ship speed, hull geometry, hull condition, relative sea state, etc. and with the design of ship propulsors that are required to impart opposing forces to overcome them with the minimum loss of energy possible. An important issue is the selection of an ideal propeller and the ideal propeller rotational speed (revolutions per minute) for a given hull and engine. Except the case of low speed Diesel engines, where the propeller revolutions are equal to engine crankshaft revolutions, the designer has to install a reduction gear between the propeller shaft and the engine. The selection of this reduction gear to provide a reduction in shaft rotational speed to match the engine and propeller is also an important issue of the engineer.
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CHAPTER II RESISTANCE OF SHIPS
When a ship floating in water is towed by an external means, forces acting in the opposite direction to the direction of motion, will be created both on the underwater part (exposed to seawater) and the upper part (exposed to air) of the hull. Those forces forces are proportional to the mass density of the surrounding surrounding fluid, water or air. However, since the mass density of the water is much larger than that of the air (about 800-850 times in ambient conditions), only the underwater part is taken into account (except for cases like fast planning craft and hovercraft).
COMPONENTS OF SHIP RESISTAN RESISTANCE CE
The resistance (or, towing force) of a ship is the force required to move the ship on a straight course at a given constant speed. This total resistance can be analysed by dividing it into several components. These components are influenced by a number of conditions, conditions, and interact interact with each other in a complex way. way.
For engineering purposes, the calm water
resistance of a hull on a straight course and in an unconfined mass of water can be divided into two main components: 1. Bare hull resistance 2. Appendage resistance
Calm water resistance of a hull = Bare hull resistance + Appendage resistance BARE HULL RESISTANCE
Bare hull resistance resistance is the main component component of the resistance in most most ships. It can be assumed assumed that it is the sum of four main components: 1. Frictional resistance: A ship experiences a frictional force between its exterior underwater hull surface (“wetted” surface) and the surrounding water water as it advances on a straight path. This component stems stems from the friction between water particles and the surface of the hull. 2. Wave making resistance: As a ship advances in water, it creates a moving pressure field around it. This pressure field, which moves moves together with the ship, causes causes the free surface of the sea sea to be disturbed. These disturbances of free water surface propagate propagate away from the ship in forms of a wave system. An energy is required for the creation of this wave system. The energy expended for the creation of those waves waves can be accounted as the source of resistance which is called “wave making resistance”. 3. Eddy resistance : An ideal inviscid fluid flows around a submerged submerged body in smooth streamlines. streamlines. However, an actual actual fluid (water for the case of underwater hull and air for the case of superstructure and fittings) cannot always flow along those smooth streamlines. streamlines. A boundary layer, due to friction with the water particles particles and the hull surface is
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formed. This boundary layer is turbulent turbulent in nature over most of the length of the hull. In areas areas around the hull surface where the water particles are forced to experience a rapid slowing down (i.e., decelerate), decelerate), these particles in the boundary layer cannot follow the flow contour and separate, forming a number of eddies. An observer at a location close to the stern of a ship or a small small boat can easily see see those eddies. The formation of those eddies require a sizeable amount amount of energy. Eddy resistance arises arises from the energy expended in forms of eddies about the hull. 4. Wind (air) resistance: As air flows about the above-water above-water part of the ship, i.e., about about the main hull, superstructure superstructure and the deck fittings, frictional and eddy resistances form with mechanisms similar to that of the water-related resistances. Although wind resistances resistances of classical hull forms are much much smaller than the water resistance, resistance, wind resistance can reach reach to higher values for the case of fast vessels: vessels: It can be a major component component of the resistance in hydrofoil, hovercraft or wing-in-ground effect t ype vessels. Due to their nature, frictional and eddy resistances are summed up together and called “viscous resistance”. resistance”. Therefore, total resistance is the sum of viscous viscous and wave-making wave-making resistances. For fast vessels, air resistance resistance should also be included. For slow and medium speed ships:
Frictional resistances + Eddy resistances + Wave-making resistances = Bare Hull Resistance Viscous resistance For high speed ships:
Frictional resistances + Eddy resistances + Wind resistance + Wave-making resistances = Bare Hull Resistance Viscous resistance APPENDAGE RESISTANCE
Appendage resistance is the resistance of components other than the hull itself: rudder, shaft brackets, shaft, propeller, nozzles and flow regulating devices, bow and stern thrusters, sonar dome, bilge keels, roll stabilizers, etc. These resistances are mainly viscous in nature.
In practice, appendage resistance of each component is calculated
separately and added on the bare hull resistance. Appendage resistance gains importance especially on warship hull forms. Appendage resistance (other than the hull itself) = Rudder Resistance + Shaft Brackets Resistance + Shaft Resistance + Propeller Resistance + Nozzles Resistance Resistance + Flow Regulating Devices Resistance +
Viscous resistances
Bow and Stern Thrusters Resistance + Sonar Dome Resistance + Bilge Keels Resistance + Roll stabilizers Resistance + etc.
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DIMENSIONAL ANALYSIS
Dimensional analysis is the most invaluable tool of the engineer searching for relationships between the interactions of various factors influencing influencing a complex situation. A typical example example is the resistance of a ship in i n calm water: The resistance force of a ship, proceeding in the sea at calm weather encounters, is related intuitively to R (dimension: MLT-2) The density of seawater (dimension: ML-3) -1 Speed of the ship in relation to the mass of seawater V s s (dimension: LT )
Characteristic dimensions of the ship, where the waterline length of the ship is a good representative L s (dimension: L)
Gravitational acceleration: acceleration: The waves that are propagated propagated on the surface surface of the sea are mainly mainly produced by the difference in the specific specific weights of the air and the water. water. In practice, the specific specific weight of the seawater is about 800-850 times that of the ambient air and only the specific weight of the seawater is taken into account.
, and = g
since was taken into account formerly, formerly, g is is taken t aken (Dimension: (Dimension: LT-2) Viscosity of the seawater, However, viscosity
= , and also since that
was taken into account formerly, (the kinematic
is taken into account (Dimension: L2T-1)
R aV sb Lcs g d e
Solving for the powers,
Or
This system does not have have a unique solution since it has three equations equations and five unknowns. unknowns. However, any solution should comply the relations:
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Hence, the relation for the ship resistance resistance becomes:
R V s2 L2s gLV
2
d
VL
1
e
Where the powers d and e are to be determined by experimental means. L s2 is directly pr oportional oportional to the “wetted” surface area of the hull for “geosim” (geometrically (geometrically similar) hulls. Therefore, one can write:
R 1 2
V s2 S
gL V L f 2 s , s s V s
The right hand side of this last equation can be lumped as a dimensionless coefficient called “resistance coefficient”, or, “total resistance coefficient”, coefficient”, C T.
R 12 Vs2 S C T Noting that the two main main parameters parameters of C T T are the square of the i nverse of the:
Froude number,
and the Reynolds number
and hence:
It can be concluded that the two geometrically similar models (geosims) of different sizes, but having the same Reynolds and Froude numbers do have the same total resistance coefficients, C T unless the two T. Unfortunately, this is not possible unless geosims are identical. identical. In other words, to test the entire hydrodynamic hydrodynamic properties properties of a 350 m. tanker we should should have a model of 350 m, which is not possible. This difficulty can be circumvented circumvented by a testing procedure applied in present day towing tanks, developed after the pioneering work of Sir William Froude in the second half of the 19th century. Despite the latest developments in numerical procedures, hull forms are developed by a number of hydrodynamic testing procedures involving involving towing tests in model tanks.
MODEL TESTING IN TOWING TANKS
For a ship and its geosim model to be tested hydro-dynamically in a test facility to have the same component of resistance, resistance, either Reynolds or Froude numbers numbers should be equal. Denoting the ship and the model model with the subscripts s and m , for the equity of the Reynolds numbers, i.e., for the equity of inertial forces to viscous resistance components (sum of frictional resistance and eddy resistance coefficients) coefficients)
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Re s V s Ls s Vm V s If the testing environment is water,
m =
Rem
Vm Lm , or
m
Ls m
Lm s
and:
s
V m V s
L s
or
Lm
V s L s
V L m
m
For the equity of the Froude numbers, i.e, for the equity of wave-making wave-making resistance coefficient,
Fr s
Fr m
V s
g s Ls
V s V m
V m gm Lm
, or since g m = g s,
L s Lm
If the Reynolds numbers of the ship and its model have to be the same (Reynolds number similarity) assuming that the test is made in water as well, ensuring
s
=
L s Lm and a model scale of
m
10
is to be used, one gets the result
V =10 =10 V m m s s. In other words, the model should be towed in a tank at 100 m/s if the condition of Reynolds number similarity
for a ship speed of 10 m/s is to be met. On the other hand, if the Froude numbers of the ship and the model are to be the same (Froude number similarity), , one assuming the acceleration of gravity is the same both in the sea and at the location of the testing facility, ie, g s s = g m m
gets the testing speed for the model as V m = V s words, the model model should be towed at 3.62 m/s if if the s / 10 . In other words, condition of Froude number similarity for the ship speed of 10 m/s should be met. Among the various parameters involved, a parameter that is most sensitive to the environmental conditions is the kinematic viscosity of the water. In terms terms of temperature temperature t (in centigrade) and salinity s (in percentage), kinematic viscosity in m2/s can be expressed as:
106 0.014 s 0.000645t 0.0503 t 1.75
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For daily calculations of ship hydrodynamics, a well-accepted value for kinematic viscosity: (For seawater)
= 1.188 10-6 m2/s and
(For freshwater)
= 1.139 10-6 m2/s
Both being values at 15 oC. A well-accepted value for the acceleration of gravity at sea level is g is g = 9.80665 m/s2.
FROUDE’S TESTING METHOD
Sir William Froude, back in 1868, has developed a testing procedure, assuming that the coefficient of resistance of the ship is composed of two components: components: 1. Coefficient of frictional resistance, C F
: This coefficient is the coefficient coefficient of resistance of a straight, smooth flat
plate having the same length as the ship and towed in the sea at the same speed as the ship. It is obvious that C F is a function of the Reynolds number only. 2. Coefficient of residual resistance, C R R
: It is assumed that this coefficient is a function of the Froude number
only. It is obtained by the Froude number testing of a small scale model model of the ship and subtracting the coefficient coefficient of frictional resistance of the smooth flat plate having the same length as the model. It is assumed that the model and the ship have the same coefficients coefficients of residual resistance. resistance. It is obvious that the coefficient of residual resistance resistance shall include wave-making and eddy resistance components, and shall also include the differences between the frictional resistance of a flat plate and the t he actual hull. EXAMPLE PROBLEM Question
A 100 m. long mono-hull, mono-hull, displacement type frigate is to be tested by Froude’s Froude’s testing procedure. procedure. A 1/20 scale geosim geosim model is prepared and towed at various speeds representing representing the speeds of the ship from 3 to 30 knots. Underwater surface surface area of the bare-hull ship is 1800 m 2. Water in the towing tank is freshwater freshwater at 20oC and the seawater salinity is 2.5%, temperature is 18oC. a. Find the towing speed of the model corresponding to the ship speed of 25 knots. b. If the force measured to tow the model at this speed is 110 Newton, estimate the resistance of the prototype ship by
Froude’s method c.
Estimate the ideal power to propel the ship at that speed.
Solution a. The ship model should have the same wave-making characteristics as the “prototype” ship, ie.
Fr s = Fr m V s gL s
Vm gLm
Vs Ls
Vm Lm
Vm V s
Lm L s
Vs
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Vm
25 knts 20
5.59 knts 2.876 m / s
Where: 1 Knt = 1 nautical mile (nm)/hr (1 nm = 1852 m., 1 hr = 3600 s) b. Underwater surface surface area of the model shall be 1800/ 1800/ 2 = 1800/202 = 4.5 m2. Therefore, the total resistance coefficient
of the hull shall be:
C Tm
RTm 1 2
2
Vm S m
110 N 0.5 1000 kg / m
3
2.876 ms
1
2
4.5 m
2
0.005911
The viscous component of the resistance can be found from the Reynolds number of the model: Re m
Vm Lm m
For the freshwater model tank at 20 oC, m = 1.002 1.00210-6 m2/s. The Reynolds number of the model shall hence be Rem =1.4351 107. The coefficient of friction of the hull surface surface shall then be estimated estimated from the so-called ITTC line (an empirical relation, to be discussed later):
C Fm
0.075 Re m 2 log10 Re
0.002820
2
The coefficient of residual resistance of the hull shall hence be:
C Rm
CTm C Fm 0.0059 0.005911 11 0.0028 0.002820 20 0.0030 0.003091 91
It is now hypothesized that the residual resistance coefficients coefficients of the model and the prototype ship are the t he same, ie., C Rs =0.003091 The kinematic viscosity of the seawater ( s s =2.5) at 18 oC shall, from the relation above be s=1.037 =1.03710-6 m2/s. The Reynolds number of the prototype ship shall be:
Re s
V s Ls s
(25 (25 1852/ 1852/ 3600 3600)) 100 100 1.03 1.037 7 10
6
1.240 109
Therefore, Therefore, using the same ITTC relation for the coefficient of friction of the proto-type proto-type ship’s hull,
C Fs
0.075
log10 Re s 2
2
0.001491
And the total coefficient of resistance of the ship shall then be:
CTs
CFs C Rs 0.0014 0.001491 91 0.0030 0.003091 91 0.0045 0.004582 82
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The total resistance of the ship shall be: R s
12 sVs2 SsC Ts 2
12 1025 kg m3 25knts 1852m. / knts / 36 3600 s / hrs 1800 m2 0.004582 699.163 kN c.
The “ideal” power to propel the bare-hull bare -hull ship at that speed shall be, with no energy loss to the sea or air by the propulsion system is termed as “effective power” (as shall be outlined in the following ch chapter) and shall be:
P s ,i
Pe RTs Vs 699.163 kN 12.861ms 1 8992 kW 9000 kW
SHORTCOMINGS SHORTCOMING S OF FROUDE’S TESTING TESTIN G PROCEDURE
1. The hull of the ship is assumed to be a rectangular flat plate, having the same length as the ship’s waterline length. This is not true since the hull is a three-dimensional body with variations both on the shape of the wetted underwater surface, causing divergence or convergence of streamlines and has significant pressure gradients along the streamline. 2. The hull of the ship and the model are not smooth in hydro-dynamical hydro-dynamical sense. 3. The wave-making components and the eddy-resistance component of the hull are lumped into the so-called so- called “residual resistance”. WaveWave -making resistance resistance is mainly a function of the Froude number and the ship’s geometry. geometry. Eddy resistance is a f unction unction of the ship’s Reynolds number and the ship’s geometry.geometry.- like adding apples and pears together. As can be seen, Froude’s testing procedure is a crude approximation and is discontinued in modern towing tanks. However, it was a historical breakthrough in ship science.
ITTC 1978 TESTING METHOD
International Towing Tank Conference (ITTC), has developed a procedure taking the criticisms of the Froude method listed above into account. They have re-divided the residual residual resistance coefficient coefficient of Froude into wave-making wave-making and form (or eddy resistance) components: components:
C R Re, Fr CW Fr C form Re Although lacking physical exactness (wave-making resistance resistance is influenced significantly by the boundary layer formation on the hull, which is dependent on Reynolds number and hull form and frictional resistance is influenced by the waveform on the hull to some degree), degree), this procedure is accurate accurate enough for engineering purposes. purposes. Therefore, the total resistance coefficient coefficient of the hull shall be:
CT
CF Re C form Re CW F r
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The frictional and form resistance coefficients, both being functions of t he Reynolds number, are often lumped together in form of “viscous resistance coefficient” and the form resistance is assumed to be a constant multiple of the coefficient of frictional resistance:
Where the factor 1+k is termed as “form factor” correction. Form factor k can be found from the analysis of the towing tank results, as well as from various empirical formulae for the form factor. The results in the literature reveal reveal that the form factors are the functions of coefficients coefficients of form (C , C , B B P P ) of the hull. Typical values can can be as high as 1.60 (for small, full form vessels vessels such as slow speed speed barges), C M M , C A , C VP VP =0.40 =0.40 is a typical value. = 0.05 for slender, fast ships like destroyers where for tankers (C value. It can be as low as k = B 0.80) k (C 0.45). Small marine marine craft craft with high beam to length (B/L) ratios also have high coefficients of form. A first B
approximation for form factor can be found from the empirical formula by Watanabe:
k
0.095
25.6 C B 2
L B
B T
An experimental procedure procedure using towing tank results is developed by Prohaska. Based on the discussions above, International Towing Tank Conference has developed an empirical procedure that can be outlined as follows: . Test the model 1. Construct a small scale geosim model model for the ship, with a scaling ratio of =L /L model in the towing tank s m
with a set of speeds corresponding to the real ship, with corresponding speeds speeds yielding the same Froude number (Fr = V )1/2 = V )1/2 ). Obtain the coefficients . /(gL /( /(gL /( coefficients of resistance resistance C s s gL s m m gL m Tm Tm for the set of speeds, V m m
2. From the set of results corresponding to low speeds, deduce the form factor (By the method proposed by Prohaska, which shall be described later). 3. Find the coefficient of friction of the model hull from the ITTC relation:
C Fm
0.075 Rem 2 log Re
2
4. Find the values of model wave-making resistance coefficient:
CWm
CTm (1 k )CFm
5. It can be deduced that C Wm Wm = C Ws Ws. Therefore, the coefficient of total resistance of the bare-hull ship can be obtained from:
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6. Resistance coefficient for the appendages can be added to obtain the total coefficient of resistance for the appended hull.
However, in order order to account for the inaccuracies inaccuracies incurred during the testing testing procedure, a factor factor called
“correlation allowance” allowance” can also be used. used. Correlation allowance allowance (C (C A) has a typical value value of 0.00040. This correlation correlation allowance takes the roughness of the hull and the laminar area near the bow of the model, etc. into account. Therefore,
7. The resistance of the full-scale ship and the ideal power required to propel it at a given speed (effective power) can be calculated.
EXAMPLE PROBLEM: Question
A 100 m. long monohull, displacement type frigate is to be tested by ITTC 1978 testing procedure. procedure. A 1/20 scale geosim model is prepared and towed at various speeds representing representing the speeds of the ship from 3 to 30 knots. Underwater surface surface area of the bare-hull ship is 1800 m2. Water in the towing towing tank is freshwater. freshwater. a. If the force measured to tow the model at a speed corresponding corresponding to 25 knots i s 110 Newtons and at the corresponding
speed to 3 knots is 1.24 Newtons, estimate the resistance of the ship by ITTC 1978 method. b. Estimate the ideal power to propel the ship at 25 knots speed. Assume that the total (lumped) drag coefficient of the
appendages appendages are 0.004000 and t heir total surface area is 50 m 2. Solution
From the previous problem, it is known that the model is to be towed at a speed of V m =2.876 m/s and the coefficient of resistance is C Tm resistance of the hull, one needs to know the form factor. In the Tm =0.005961. In order to separate the total resistance absence of other experimental experimental results, following logic is used: “At low Froude numbers, wave-making wave-making resistance vanishes, where the entire model resistance is almost viscous in nature. Therefore, Therefore, the total resistance coefficient can be taken equal equal to viscous resistance coefficient coefficient at low Reynolds numbers.” For 3 knots, corresponding model speed shall be: V m= 3 /201/2 = 0.6708 knots = 0.3451 m/s. And the model model hull’s Reynolds number: Rem = V = V m Lm / m =1.7722 106
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Therefore, Therefore, the coefficient of friction shall be, assuming an all-turbulent friction over the model hull (!) shall be: C Fm Re-2)2 = 0.004180 Fm= 0.075/(log10 Re-2) On the other hand, total resistance coefficient, coefficient, from the measured values, shall be: C Tm = RT/(1/2 V V m2S m) =1.24/(0.5 =1.24/(0.5 1000 0.345124.5) =0.004628 C vm Tm = R vm From which the form factor is obtained to be equal to: 1+ k = = C vm vm/C Fm Fm =0.004628/0.004180 =1.1072 Now, one can can revert to the model at speed speed corresponding to 25 knots, where, from the previous previous problem: problem: V m = 2.8758 m/s, Rem=1.4351 107,
C Fm Fm= 0.002820,
C Tm Tm = 0.005911
Coefficient of model viscous resistance shall be: C vm (1+k) C Fm vm = (1+k) Fm =1.1072 0.002820 = 0.003122 In the absence of surface roughness of the model surface and appendages, wave-making wave-making resistance shall be: C wm – C vm 0.005911 – 0.003122 0.003122 =0.002789 wm= C Tm Tm – C vm = 0.005911 – Now, one can can proceed to the full scale ship. ship. For Vs= 25 knots (12.861 m/s), Res = 1.240 109, C FS FS = 0.001491 C vs vs = (1 + k ) C FS FS = 1.1072 0.001491 = 0.001651 Coefficient of wave-making wave-making resistance, equal to that of the model: C ws =C wm ws =C wm = 0.002789 Therefore, Therefore, the bare-hull resistance of the ship shall be: C Ts (1+k ) C Fs Ts = (1+k Fs + C A+ C ws ws= 0.001651 + 0.00040 + 0.002789 = 0.004840 2 RTs= ½ V V s 2S sC Ts Ts = 0.5 1025 12.861 1800 0.004840 = 738.518 kN
However, the resistance of appendages (either separately for each or by a lumped approximation) should be added. 2 RApp =1/2 V Vs 2 S App 50 0.004000 = 16.954 kN. App C App App = 0.5 1025 12.861 50
The resistance of the ship, by the t he ITTC 1978 method, is: RTot= 738.518 + 16.954 =755.472 kN. The power required (“effective” or “tow“tow -rope” power) is: PE = R TVs= 9716.21 kW
The determination of effective power is usually the first step i n the design of the propulsive system of the t he ship. DETAILED DISCUSSION OF RESISTANCE COEFFICIENTS FRICTIONAL RESISTANCE
The source of of frictional resistance resistance is the viscosity of water. water. To understand the frictional frictional resistance, resistance, one has first to understand the frictional resistance of an idealized ideal ized ship, a flat plate (“equivalent flat plate”), having the same length and surface area, moving in the water with the same velocity U as as the ship. Water particles particles adjacent adjacent to the surface of the flat flat plate moving in water will “stick” on the plate surface surface and will be dragged dragged together together with the plate. At some distance distance vertically away away from the plate, water will will attain a velocity less than than the ship’s speed U , increasing with the vertical distance from the wall and finally will be asymptotically equal to U , i.e., not be influenced by the existence of the plate.
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This can be analyzed by assuming a zero-velocity flat plate and a flow of water with a freestream velocity of U . The =0) =0) up to the location where the u(y) layer of water away from the surface of the flat plate (y
called “boundary layer”. The distance
associated with the condition u ( )
condition is satisfied is condition U
U is U is satisfied is called “the boundary
layer”. The momentum of of water lost within the boundary layer is the origin of frictional resistance. In practice, frictional resistance of the ship is influenced by a number of effects- Reynolds number, surface roughness, pressure gradients, gradients, three dimensional effects, waves created by the ship....
y U(y)U
U
r e y a L y r a d n u o B
u(y) =0
Fig. Definition of a boundary layer By the nature of the flow, boundary layer flows can be classified into two: 1. LAMINAR BOUNDARY LAYERS
Laminar boundary layers are described as the boundary layers where the flow of water particles take place smoothly, with a given order. This has been explained by some authors as the flow of “sheets” or “laminae” of fluid at different speeds. ) = As the sheet adjacent to the wall satisfies the condition u(0) =0 and the layer at the edge of the boundary layer u( ) = U ,
the different laminae are assumed assumed to slide each over the other. As each of the laminae slide on the other, shear shear forces occur opposing the motion. This is accounted by the loss of fluid momentum, momentum, and is accounted by a drag force force opposing to the flow. This drag force is the “laminar friction” and is equal to the shear force on the lamina adjacent to the wall. Laminar boundary layers layers lose the stability described above under certain conditions. In general, laminar boundary layers layers are stable for:
Low velocities
Short distances
High kinematic viscosities
is This condition dictates that the quantity U x/ is small. This is the Reynolds number, number, alternatively alternatively defined as as the non-
dimensional ratio of inertial forces to laminar forces within the boundary layer. The laminar boundary layer layer loses its stability at high Reynolds numbers and in the presence of external disturbances. disturbances. A well-accepted criterion for transition from laminar to non-laminar (i.e., turbulent) flow is Re 5105. The stability of laminar boundary layers is also dependent on pressure gradients on the body. Obviously, for the equivalent flat plate representing the ship, at the familiar speeds involved, laminar flow region is smallabout 8 cm. from the bow for a 15 knot speed. However, for a small ship model tested in a towing tank at lesser speeds,
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laminar boundary layer layer extends further on the bow relative to ship’s length length and can cause erroneous erroneous results. This region is minimized by inducing an early transition on the model - by sandpaper roughening of the bow, by the usage of studs mounted on the bow or, by the usage of a trip-wire along the depth before the bow. Laminar boundary layers are also important in propellers, where the dimensions are smaller than the vessel by one or two orders of magnitude. 2. TURBULENT BOUNDARY LAYERS
One can safely assume that the entire boundary layer on the full-size (prototype) ship and the equivalent flat plate are turbulent, by neglecting the contribution of the short laminar laminar region. Turbulent boundary layers are characteriz characterized ed by the externally chaotic nature of the flow, where the order between laminae is totally lost and the flow is characterized by the mean flow and the flow of eddies imposed imposed on it. The energy of the mean mean flow is dissipated in form of eddies, and the associated loss of momentum of the flow is accounted by higher values of friction when compared with the laminar flow. The transition from laminar to turbulent flow is not abrupt- small patches of turbulence are created in the laminar region initially, and in the areas of higher Reynolds numbers, turbulent patches increase in size and finally dominate the entire flow. Turbulent boundary layer can be represented by a “power law”: 1
y n U u
Where u is is the mean velocity within the boundary layer, y layer, y is is the distance from the wall, U is is the free-stream velocity, is the boundary layer thickness. The power n has a value between 7 and 9.5, increasing with Reynolds number and affected by surface roughness. roughness. Coefficient of friction friction in turbulent flow is is computable by by a number number of “correlations”, “correlations”, i.e., i .e., empirical formulae. The frictional shear force, w of the t he flow on the flat plate can be expressed conveniently by a coefficient of friction, C f :
1
w U 2C f 2
And the overall drag force on one side on a flat plate by the overall coefficient of friction, C F : L
C F
D 1 2
2
U L
1 2
2
U C f dx
0
1 2
2
U L
1 L L
C dx f
0
The overall coefficient of friction of flat plates have been investigated by several authors in the past- where reported as a function of the Reynolds number of the plate.
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Fig. Coefficient of friction of a flat plate for laminar l aminar and turbulent boundary layers
Fig. Coefficient of friction of a flat plate, as adopted by the t he ATTC (Schoenherr) and ITTC (1957 Madrid) conferences conferences and two authors
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Reynolds numbers involved for ships can be high for a large and fast ship (aircraft carrier or containership), it can be in the range 3 ~ 5 109. For this range, range, correlations correlations based based are are used to predict the hull frictional resistance. resistance. One wellwellaccepted is the Schoenherr formula, accepted by the American American Towing Tank Conference in 1947:
0.242 C F
log10 Re L C F
However, a relation later adopted by the International Towing Tank Conference in 1957 that was more general and more widely accepted is:
C F
0.075
log10 Re 2
2
Although these coefficients represent flat plate coefficients of friction, they are for hydrodynamically smooth surfaces. The additive constant C A= 0.00040 , which is added to the viscous resistance coefficient C V is a rather crude approximation for the effects of hull surface roughness and for the inaccuracies involved by the model to ship extrapolation procedure outlined above.
VISCOUS PRESSURE (FORM) RESISTANCE
To understand the viscous pressure resistance, one should know about D’Alambert’s paradox - one of the main concepts of classical hydrodynamics, expressed literally as: “For a body immersed in a uniform flow of an inviscid fluid, pressure shall rise in the areas where the flow slows down and shall increase in the areas areas where the flow accelerates, accelerates, according according to the law of Bernoulli. The in-flow direction components of the pressure pressure forces created created on the fore part will have a net positive (backward) drag effect. effect. On the other hand, the high pressure pressure area in the stern will form negative-drag negative-drag forces (forces (forces in the forward direction). direction). Those two forces are equal equal in magnitude” magnitude” D’Alambert’s paradox states that the two net drag forces (acting in forward and backward directions) will cancel each other and the body shall experience experience no drag. However, due to viscosity of water, water, skin friction and eddy formation behind the body, there is a significant drag component. component. Equivalent flat plate approach approach can be used to calculate this drag force partially. For all streamlined bodies moving in water, talking with the ship terminology, the bow and stern are the areas of high pressure and the amidships area is a low pressure area. Therefore, for the forward quarter of the ship, the flow will encounter a favorable pressure gradient - from high pressure area to low pressure area. On the contrary, the stern quarter, especially the stern of the ship, shall encounter an unfavorable pressure gradient - the fluid will be forced to flow from low pressure to high pressure pressure area. This is associated associated with the drop of local local shear force close close to the stern and then afterwards, the reversal reversal of the flow within the boundary layer. layer. The complicated complicated flow will therefore shall not be attached attached to the wall and separate, leaving a flow area with eddies at the stern. This flow area, with the velocity defect is called
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“ship’s wake”. For a ship with a separated flow, equivalent flat plate approach is not sufficient to account for the viscous drag force for reasons explained explained above. above. The net difference difference shall be be a force-directed force-directed sternwards, called the “viscous pressure drag”. drag”.
Fig. Boundary layer on a hull
Fig. Boundary layer velocity profiles on the hull An important component of eddy viscosity is the formation of “bilge vortices” at the stern of the ships, especially full form ships or ships having sterns with rapid changes changes of curvature. The energy of bilge vortices are are accounted by extra values of viscous pressure drag, as well as they are the causes of uneven wakes- a cause of propeller-induced vibrations and propeller inefficiency.
Fig. Formation of bilge vortex
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Also, the equivalent flat plate approach the representation of the ship’s underwater surfaces by the equivalent flat plate involves a number number of inaccuracies: inaccuracies:
deviations from the flat flat plate shape, causing causing divergence or convergenc convergencee of
streamlines, streamlines, pressure gradients, crossflow effects on the hull, change of the t he underwater shape by the surface wave profile on the ship... cause extra additions to the coefficient of friction. Viscous pressure gradient, being a function of the Reynolds number and the boundary layer formation on the hull, is hypothesized to be a constant multiple of the frictional drag of the hull, is expressed as:
CVP
kvp C F
Lumping the three dimensional effects on the hull together, t ogether, the viscous resistance coefficient becomes:
CV
1 k C F
Where (1+k (1+k ) is the “form coefficient”. Form coefficient coefficient is assumed to be unaffected by the Reynolds number (scale (scale and ship speed) and hull roughness effects. effects. In practice, obtaining of the form coefficient coefficient is made by extrapolating the total ship resistance measurements to zero speed (where the wave making resistance becomes equal to zero).
R C lim 0 R 0 C
1 k lim Fn
T
F
Fn
F
A well-accepted procedure is the Prohaska’s method , where the total t otal resistance coefficient of the ship model normalized by the coefficient of resistance of the equivalent equivalent flat plate (C (C T T /C Fo) is plotted as the ordinate and the abciassa is the fourth power of the Froude Froude number, number, also normalized normalized by the coefficient coefficient of resistance resistance of the equivalent flat plate plate ( Fn Fn4 /C Fo).
Fig. Prohaska’s Prohaska’s method for obtaining the form factor
WAVE MAKING RESISTANCE
Pressure variations variations on the hull surface are also the reason for the formation formation of surface waves waves created by the ship. The pressure rises about the bow and stern parts of the hull compared with the still water pressure. These high pressure areas cause rise of the free surface in those parts, which propagate propagate away from the hull in the form of a wave array. The energy
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carried away from the ship in form of waves is the origin of wave resistance. The outward energy energy flux of the waves at a control volume surrounding the ship at distances sufficiently away from the ship, divided by ship speed is defined as the wave making resistance.
RW
E wave V s
A simple explanation of the wave creation is by the assumption of a simple, streamlined, ship-like body moving in an ideal (inviscid) fluid, applicable both for gas and liquid flows. The velocity of fluid moving on the body shall be “zero” at two “stagnation points”: one on the forward end and a nd one on the rear end. end. The regions near the stagnation stagnation points shall have velocities of flow less less than the velocity of body. According to the law of Bernoulli, Bernoulli, those low velocity areas areas shall have pressures pressures above the ambient pressure. pressure. The velocity of flow near amidships shall be higher than the velocity velocity of the body, and hence the pressure pressure there shall be lower than the ambient. The pressure areas areas forward and astern will will sum up to force values that are equal and opposite to each other and hence the resistance in an infinite, inviscid fluid shall be equal to “zero” (D’Alambert’s (D’Alambert’s paradox). However, if the body is moving on the free surface of a liquid, all points along the streamline shall shall have the same pressure, pressure, the ambient atmospheric atmospheric pressure. In this case, high pressure areas (bow and and stern) shall be associated with a rise in free surface, and low pressure areas (amidships) by a drop in free surface, also in accordance accordance to the law of Bernoulli:
v2
2 g
constant
Therefore, Therefore, there shall be a wave system travelling together together with the ship-like body: A wave crest in the bow, a wave trough in the amidships and another wave crest crest at the stern. This is called “the primary wave wave system”.
Fig. Pressure and velocity fields giving rise to the primary wave system of a streamlined body
In real ships, the high and low free surface distributions created created by bow and stern are radiated outwards from the ship, and the wave pattern will be highly dependent on the Froude number.
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The first scientific investigations investigations are owed to Lord Kelvin Kelvin and Dr. Michell, in the late 19th century. century. Lord Kelvin has formulated the wave wave pattern of a simple point source source travelling on the free water water surface. This wave pattern pattern is the wellknown “Kelvin wave pattern”, as can be seen in th e figure below:
Fig. Kelvin wave pattern
As can be observed from the figure above, two series of waves are created: One set of diverging waves moving away from the point source and another set of transverse waves waves following the point source. Both of these waves are contained within two straight lines, = arcsin (1/3) = 19.5 o from the direction of travel. Lord Kelvin has assumed that a ship can be represented by a “source”, or by an hypothetical point that produces an outward flow of water (i.e., a creator of radially outward streamlines). streamlines). Mathematical Mathematical analysis shows that wave making making resistance of this “Kelvin source” shall be:
RW
1
2
V 2 2
2
A cos3 d
2
Where A ( ) is is the wave amplitude. V s 4. The behavior of a ship in the far field obeys the Kelvin pattern, One can deduce that R that RW A2V s2, and also A also A V V s , RW V
although it is inaccurate to model the ship by a point source in the near field. As this simplified analysis indicates, frictional resistance increases with roughly the square of the ship s peed, while wave making resistance increases with the fourth power of the ship speed (rather, the Froude number). This fact is more more complicated by the fact that the bow, stern and discontinuities on and slightly below the waterline surface have wave patterns of their own, interacting with each other.
Those individual waves are sometimes sometimes augmenting, augmenting, sometimes
cancelling each each other, depending on the shape of the hull and the Froude number. Roughly, a ship wave system system is the superposition of:
The bow- beginning with a wave crest
Forward shoulder – shoulder – beginning beginning with a wave trough
After shoulder – shoulder – beginning beginning with a wave trough
The stern- beginning with a wave crest
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Fig. Bow and stern waves on a ship, wave making and frictional resistances (V (V in in knots, L knots, L in in feet)
The most prominent of those waves waves is the bow wave. Bow wave is mainly determined determined by the half-angle of entrance of the free water surface. Therefore, whenever high wave making resistance values are a challenge for the ship designer, the main option should be lovering the entrance angle of the vessel - as is the case for various warship and fast commercial (passenger (passenger ship, containership, etc.) forms. On the other hand, sleek entrances lower the deadweight capacity capacity of the ship. Therefore, in ships that have to carry cargoes at acceptably lower speeds, sharp bow shapes are replaced by almost cylindrical or bulbous bows. Bulbous bows have the ability to reduce wave making making resistances at relatively lower Froude number ranges. (Less than F n = 0.25). Many of present present day cargo ship forms are are characterized characterized by either cylindrical cylindrical or bulbous bows or higher higher coefficients coefficients of form (crude oil carriers, carriers, bulk cargo cargo carriers, OBO’s, OBO’s, etc.) Due to the interaction i nteraction of those different waves, the total wave system will be highly nonlinear: with pronounced humps at about F about F n =0.30 and F and F n = 0.50, and an intermediate trough at about F about F n = 0.35.
Fig. Wave resistance versus Froude number An analytic expression, more sophisticated than the assumption of Kelvin source for a given hull was given in 1898 by Michell, for a hull whose fore-aft direction lies along the x- axis and z- is the vertical ordinate:
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Rw
4
V 2
A i
2
2 1
1
e
2 z ix
A
2
d
f x, z dz dx
S
Where: : is the dummy variable of integration,
V : is the ship speed, : is the density of seawater, =V 2 /g : : g is the t he gravitational acceleration, acceleration,
S : is the underwater hull surface below the calm water line and y = y = f(x,z) f(x,z) : is the t he hull surface offset from the centerline plane in the ythe y- (athwart (athwart ship) direction. Modern digital techniques model the ship as a number of sources and sinks distributed along the hull surface on discrete panels. Accurate predictions of wave pattern is possible, but however, mainly due to the neglecting of viscosity effects, some errors exist. Although partially corrected by empirical empirical viscosity corrections (boundary (boundary layer formation), errors still prevail. Therefore, model model towing tank experiments experiments are are still an indispensable indispensable part of hydrodynamic hydrodynamic analysis analysis of the ships. ships. Ship wave system also has an effect on the viscous resistance components of the ship, by inducing velocities along the streamlines and by a non-straight path on the free water surface.
BULBOUS BOW FORMS
Many merchant ships produced during the last few decades have a bulbous bow form. Bulbous Bulb ous bow form is a means of reducing the wave-making resistance of the ship, where at the designed service speed of the vessel. Wave trough of the bulbous bow cancels cancels the bow wave wave crest, thereby reducing the wave-making wave-making resistance resistance significantly. significantly. This effect has been been known for centuries, as is visible by the resistance decrease decrease of ram-bow type warships of the past. A number of bulbous bow shapes have have been produced: produced: Pear-shaped, Pear-shaped, inverted pear-shaped, pear-shaped, elliptical elliptical cross section, section, cylindrical, etc. etc. It is obvious that the desired effect of the bulbous bow takes place at the proper operating speed and at the proper immersion of the bulb: which means means the effect effect of bulb is also dependent dependent on the loading condition of the vessel.
Fig. Simplified explanation of the effect of bulbous bow on wave-making
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Since the stern part of a ship is also a high pressure area, which is responsible for the formation of stern waves, a plausible approach shall be the fitting of stern bulbs as well. Although designs involving stern bulbs have been made, they they have not been so popular since the gains obtained are marginal compared to the bow bulb and the high cost of manufacturing of a stern bulb. It has also been proposed to replace bulbous bows by wing-like foils that emulate the same pressure distribution and waveform.
TRANSOM STERN FORMS
Transom sterns sterns are widely used in almost all ship types, replacing the cruiser cruiser stern forms. The main reason reason for the use of transom stern in merchant ship forms where F r <0.3 is the ease of manufacture and hence lower cost. The transoms of those ships are above the waterline, waterline, and do not have any hydrodynamic hydrodynamic effect. However, for high speed speed marine craft, transom stern is for the reduction of wave-making wave-making resistance. The effect of transom is by increasing the virtual length of the ship and hence increasing increasing the Froude number. The depth of transom below the waterline should should be about 10-15% for Fr Fr 0.5 and 15-20% for Fr for Fr 0.5.
STERN WEDGES AND STERN FLAPS
As a ship reaches to speeds corresponding to Froude numbers of about 0.40 and above, bow wave gains dominance and as a result, the ship trims trims backward. This results in another component component in wavewave-making making resistance: the component of ship’s weight in the direction of propulsor propulsor thrust. This can be remedied remedied by fitting of trim-reducing mechanisms mechanisms.. The first one is the stern wedge, fitted to warship warship hull forms. The function of the stern wedge wedge is deflecting the streamlines streamlines downward to produce an upward force component, component, hence creating a forward trimming moment to reduce the trim by stern. The same effect is achieved in high speed planning hulls by hydraulically-controlled stern flaps.
Fig. Stern wedge of a frigate
Apart from the classical viscous, wave-making, wave-making, appendage and air resistances, resistances, certain components of resistance on certain hull forms forms arise. Those are: are:
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WAVE BREAKING RESISTANCE
Another component of wave resistance is the “wave breaking resistance”, which can be significant in full form ships (tankers, bulk carriers, carriers, barges, etc.) and the bow has a bluff shape. The bow of the ship can collide with the bow wave before it propagates into the sea, causing it to break and release its energy. energy. The energy of the broken waves is dissipated by viscous effects. Therefore, wave breaking resistance is viscous in nature, although it is mainly a function of Froude number.
Wave-breaking phenomenon can be prevented by making the radius of curvature r of of the bow form such as r V s2/50, where r is is in meters and V in in m/s. Wave breaking resistance can be observed in the wakes of such ships, as two visible white rows extending backwards from the stern (white color comes from the air bubbles entrained as the wave breaks).
SPRAY RESISTANCE
In very fast vessels, high pressure at the forward stagnation point causes an upward spray of water, also resulting in an energy loss that can be significant. significant. This spray resistance, resistance, if not prevented by the shaping shaping of the bow, can be deflected deflected downwards by spray-rails, hence reducing the unwanted effect.
WIND (AIR) RESISTANCE
The aerodynamic resistance of the upper parts of the main hull and the superstructure, masts, funnels, antennae, etc., also viscous in nature, can become appreciable at higher speeds and can have a significant effect both in propulsion and steering characteristics characteristics at higher wind speeds. speeds. Due to the boundary layer effect effect of the sea surface, surface, the higher the component is located, the higher the velocity becomes, according to the power law:
u z U ref
z z ref
7.5
Where the reference wind velocity U ref is evaluated at the standard reference height z height z ref above the sea level, l evel, usually 10 m. ref is ref above Wind resistance is a function of the wind direction and ship speed. At calm weather, the wind blows from the bow and the wind resistance is a function of the ship speed alone. alone. In this case,
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Rwind
1
airVs2 ATr C x 2
Where A Tr is the transversal projected area of the ship. A typical value of the wind-resistance coefficient coefficient is C x = 0.8.
APPENDAGE RESISTANCE
The principal appendages to the hull are the rudder(s), shaft bossings or shaft brackets, the shaft and the propeller, struts, bilge keels, roll stabilizing fins, sonar dome, bow thruster.... All of those items contribute to the underwater resistance and their drags are calculated separately. The calculation procedure procedur e is similar to the hull itself. Each appendage can be modelled by a frictional frictio nal and a form coefficient.
Therefore, both the wetted surface area and the geometry of the
appendage are important. The breakdown of components of a bare-hull ship is presented below graphically. graphically.
Following table shows the relative contributions of resistance components of bare hull resistance:
Type of resistance Friction R Friction R F Wave R Wave RW Eddy R Eddy R E Wind R Wind Rw
Percentage of total barehull resistance High speed ship Low speed ship (Container (VLCC) vessel) 45 90 40 5 5 3 10 2
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IN-SERVICE RESISTANCE COMPONENTS
The discussion of the ship resistance explained above applies only to the calm-water resistance of a ship cruising on an infinitely deep water and on on a straight course, without reverting to use her rudder. rudder. Furthermore, Furthermore, the ship is assumed to have a clean and uncorroded hull, as it is newly launched to the sea and “even“even-keeled” (without any fore or astern trim). In real life, it is not always possible to obtain obtain those situations. In-service situations situations are discussed discussed below.
WAVE ADDED RESISTANCE
A ship in a seaway generally encounters a speed speed loss. One part of this speed loss is due to captain’s initiative of lowering the ship speed so as to encounter waves at a lower velocity or change of course for a more favorable wave direction (“Voluntary” speed loss). The other part is due to the increase of ship resistance resistance due to the diffraction and reflection of waves, as well as the motions of the ship to cause the ship deviate deviate from the hydro-dynamically favorable favorable position. This is a complicated problem of engineering, since too many parameters are involved: Wave height, ship speed, relative direction of waves, and ship length relative to wavelength, bow shape, ship hull shape, draft, wind speed and direction. Approximate formulae for the wave-added resistance are given by Townsin and Kwon in form of speed loss for a given power as:
V C C ship V
Where C is a factor considering the predominant direction of wind and waves, angle measured measured from bow, as well as is the sea state in Beaufort scale, BN: C = 1
for = = 0-30o
C 1.7 – 0.03 0.03(BN – (BN – 4) 4)2 = 1.7 –
for = 30o – 60 60o
C 0.9 – 0.06 0.06(BN – (BN – 6) 6)2 = 0.9 –
for = = 60o – 150 150o
C 0.4 – 0.03 0.03(BN – (BN – 8) 8)2 = 0.4 –
for = = 150o – 180 180o
C ship is a factor considering the ship type: C ship= 0.5 BN + BN6.5/ (2.7 2/3) for tankers, laden C ship= 0.7 BN + BN6.5/ (2.7 2/3) for tankers, ballast C ship= 0.7 BN + BN6.5/ (2.2 2/3) for containerships containerships Where:
: is the t he displacement displacement volume in cubic meters.
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SHALLOW WATERT ADDED RESISTANCE
A ship cruising in shallow waters will encounter an increase increase of resistance. This is due to two effects: 1. Due to the increase of draft and trimming of the ship (usually by stern) by the effect of sea floor (“Squat”), ( “Squat”), and 2. Due to the change of the wave pattern formed by the ship. The effects of shallow water water have been calculated calculated and given in forms of curves. A well-accepted calculation calculation procedure is due to Schlichting, as given in the following chart, where: Ax
: Maximum ship sectional area (usually equal to CM)
H
: Water depth
V
: Ship speed in infinitely deep water
EXAMPLE
Question-1
A tanker, 300 m. in length, 50 m. in breadth, 25 m. in draft has a midship section area coefficient of C M = 0.99. Her service speed speed is 15 knots. She enters to a shallow area area of depth 40 meters. Estimate her her final speed.
Solution-1
A x = C M B B T T = = 0.99 50 25 = 1237.5 m2
A x
h
0.88
V = 15 knots =7.717 m/s 2 V /gh =0.152 /gh =0.152
Therefore, Therefore, speed loss due to shallow water shall be 12 % (approx.), and the speed shall drop to 13.2 knots.
Fig. Schlichting’s curves for relative speed loss in shallow water
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STEERING RESISTANCE
In a real sea environment, with the presence of external disturbances like waves and winds, the ship is forced out of her straight course. During this turn, the ship experiences experiences a yaw motion, which increases increases the frontal area of of underwater surfaces to forward motion, and the rudder is used to set the ship back into position - thereby adding a lift-induced drag to the forward motion motion of the ship.
The result is a sinusoidal sinusoidal motion, and can can also be studied studied by statistical means. means.
Obviously, steering resistance increases in harsh weather conditions, where the ship is deflected from her original course by external wind wind and wave effects. effects.
HULL ROUGHNESS
Hull roughness can either be in the form of bio-roughness, that is, biological fouling (by underwater algae and animal forms), or by the deterioration of hull material by corrosion and the hull paint. A relation to predict the hull roughness effect of a painted hull on frictional and hence on viscous resistance for large ships is the equation proposed by Townsin for 10-30 knots range: 1 h 13 C F 10 44 L 10 Re 3 0.125 3
Where h is the mean apparent hull roughness roughness of 50 mm. long samples. A new ship has roughness roughness values of about 100120 microns, while a 25 year old vessel can have have about 1000 microns, even if no biological fouling exists. It can be observed that roughness penalty is proportional to the one-third power of the relative hull roughness, h/L h/L and gains a relative importance in larger vessels such as VLCC’s and large bulk carriers. EXAMPLE Question-1
A LWL = 100 m. ship with a service speed of 16 knts has an average hull roughness of 250 microns. Find the final coefficient of friction. Solution-1 = Re = Re =V V s L LWL / = 7.937 7.937108
C Fsmooth Fsmooth = 0.001575 (by ITTC 1957 relation) CF= 44 4410-3[(250 [(25010-6/100)1/3-10 -10(7.937 (7.937108)-1/3] + 0.000125 = 0.000247 CF rough = 0.001822 As can be seen, even a smooth-looking hull surface, with 250 microns of roughness, can have a relative roughness penalty of 16% due to hull roughness. The roughness of larger (low Froude number) number) hulls, where most of the ship resistance is viscous, plays a significant role in ship operations. Keeping the roughness at a minimum can result in significant savings savings
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in ship operations.
Needless to say, say, the growth of macro-organisms macro-organisms on the hull surface (marine (marine algae, mussels, mussels,
tubeworms, tubeworms, barnacles, etc.) will have a detrimental detrimental effect on the t he fuel bill of a marine vehicle.
ADDED RESISTANCE DUE TO SUBSURFACE WAVES
In certain areas of the seas, like the Scandinavian fiords or the estuaries of rivers, a stratification in the water beneath the ship can occur: A layer of low density fresh water can be on the surface and another layer of high density seawater can be at some distance below below the surface. A pressure disturbance disturbance travelling on the free surface, surface, such as caused caused by a slow moving ship, will create a system of internal waves between the two subsurface layers, taking their energy from the vessel. Those internal waves waves shall have an amplitude (in height) that is larger than the surface waves that the vessel vessel creates, thereby increasing the ship resistance a few times than it should be in open seas. Fortunately, these waves cannot travel faster than about (say) 5 knots and a vessel travelling more than five knots will very likely not be affected by those subsurface waves.
ICE-BREAKING RESISTANCE
Icebreaker ships, as well as the vessels that are required to operate in the Arctic and Antarctic areas, or inland waterways of Europe and North America during winter months, have often to navigate in seas where the surface of the sea is covered with a sheet of ice. The thickness of this ice sheet can vary and those ships are classified separately with more stringent safety requirements by the classification societies depending on the approximate thickness of permissible ice thickness. The bow form of those vessels are designed to break this sheet of ice and open way for the vessel itself or the vessels to follow it. In such cases, the wave pattern pattern of the ship will be supressed and another another resistance component, component, “icebreaking “icebreaking resistance” resistance” shall arise.
The detailed detailed analysis analysis of this ice-breaking ice-breaking resistance is complex, involving complicated
mechanisms mechanisms of fracture mechanics mechanics and often requiring towing tests performed in towing tanks with frozen free surfaces.
PRELIMINARY ESTIMATION OF SHIP RESISTANCE
Although the most accurate way of determining the resistance of a given hull form is by a series of model tests, it is usually sufficient to make an estimate of ship resistance resistance by empirical methods in the preliminary design phase. Model tests are costly and time-consuming. time-consuming. However, there are methods methods for the preliminary estimate estimate of ship resistance with acceptable acceptable accuracies accuracies in the preliminary design phase. Those methods can be classified classified as:
Methods that are based on systematic systematic model series
Methods that are based on model experiments
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METHODS THAT ARE BASED ON SYSTEMATIC MODEL TESTS
Methods that are based on systematic model tests are based on a series of hull forms, where main parameters are systematically systematical ly varied and the variations in resistance parameters are expressed in forms of curves. For a given design project, a suitable series is selected, main parameters parameters related to ship size, deadweight, speed, etc. are determined and the residual resistance is estimated estimated by interpolation from a series of curves. Frictional resistance can be calculated calculated from the ITTC 57 formula. Examples of such series are the Taylor, Series 60, SSPA, Taggart, NPL, NTUA and ITU Fishing Boat series. Since the number of parameters parameters relevant for a ship form are excessive excessive (C ( C B , C P , C M , C A , C VP , L/B, B/T, LCB, LCF, VP parameters parameters related to bulb, transom t ransom and stern form, half angle of entrance, length of run, number of screws, number of rudders, etc), only main parameters are selected (usually C B , L/B, B/T , LCB).
METHODS THAT ARE BASED ON MODEL EXPERIMENTS
Methods that are based on model experiments are obtained from the databanks containing the results of model tests of various hull forms. forms. They are also also for the calculation calculation of residual residual resistance coefficient. coefficient. Most well-known are the LapLapKeller, Danckwardt, Guldhammer-Harvald diagrams, Holtrop-Mennen Holtrop-Mennen and Hollenbach’s method.
The first three
methods rely on diagrams, diagrams, while the last two relies on empirical correlation correlation formulae. Form factor (k (k ), ), wave making resistance, resistance, and also ship’s wake coefficient and thrust deduction coefficient coefficient is obtained. A simple computer program can be used to evaluate evaluate these formulae for a given hull form. form.
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CHAPTER III PROPULSION OF SHIPS
More than 99% of present day ships are propelled by screw propeller or one of its variants:
Controllable and reversible pitch propeller (CRPP)
Tandem propeller
Contra-rotating propellers
Trans-cavitating Trans-cavitating propellers
Super-cavitating Super-cavitating propellers
Ventilated propellers
Grimm vane wheel propellers
Ducted propellers
Kappel propeller,
CLT (contracted and loaded type) propellers,
Podded drives, etc.
Other propulsors (waterjet, airscrew, paddle wheel, cycloidal propellers) have had limited usage on certain types of vessels. Magneto-hydrodynamic Magneto-hydrodynamic propulsion, a promising alternative to mechanical mechanical propulsors, is still in the development stage. One can also mention sails (classical sails, rigid sails, kite sails, Flettner rotors) that use wind-power as a means of propulsion as other other viable supplementary supplementary propulsion systems. systems.
ENGINE POWER
To understand about ship propulsion, one should start with the energy produced by the engine, starting with the chemical energy contained within the fuel.
By the combustion of the fuel within the cylinders of the main propulsion engine (for Diesel and Otto-cycle engines), chemical energy of the fuel is converted into thermal energy (for steam and gas turbine ships, combustion takes place in the boiler and in the combustion chamber, respectively). respectively).
A certain proportion of this energy is released to the environment, while the remaining part is converted into mechanical energy.
Some of this mechanical energy is used for compressing the working substance (air, for the case of internal combustion engines and gas turbines, and water, for the case of steam engines).
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The time-rate at which this energy is produced, being the result of the thermodynamic process taking place in the cylinders, is called “indicated “indicated power ”. ”.
This energy is the result of combustion of fuel.
Unfortunately, not all of this energy is obtained from the engine: frictional losses within the engine bearings and the piston-cylinder arrangement, arrangement, as well as auxiliary systems taking their power from the engine, consume some of the indicated energy.
The time-rate of energy obtained from the engine crankshaft is called “ brake power ”. ”. If the lower-heating value* (energy ( energy released by a proper combustion of the fuel, provided that water produced by the combustion is exhausted in vapour form) form) of the fuel is q LHV LHV and the specific fuel consumption ( fuel consumed per unit brake power, in one hour of operation) operation) of the fuel is sf c then then the overall efficiency of the engine shall be:
OA
P B m f qLHV
3600 sfc qLHV
A typical value of lower heating value for high cetane number Diesel engine fuels (an (an example is Marine Diesel Oil ) is 43 MJ/kg, where heavier bunker oils have 40-42 MJ/kg qLHV’s.
Modern low-speed marine Diesel engines can have overall efficiencies of about 52%, while the overall efficiency of an outboard gasoline engine is typically about 30%.
A common method of relating HHV to LHV is:
HHV = LHV + h v x (nH2O, out /nfuel, in) Where:
hv
: is
the heat of vaporization of water,
nH2O, out
: is
the moles of water vaporized vaporized and
nfuel, in
: is
the number of moles of fuel combusted.
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TRANSMISSION TRANSMISS ION OF ENGINE POWER
For the case of most marine propulsion systems, with the exception of low speed Diesel engines and reciprocating steam engines (which (which are obsolete now), now), the rotational speed of the engine crankshaft is too high for being directly coupled to the ship’s ship’s propeller. propeller. Therefore, Therefore, a REDUCTION GEAR to to reduce the engine crankshaft rotational speed to the proper propeller rotational rotational speed is required. required. [To give an idea: the shaft revolutions of a steam turbine is about 3000-5000 revolutions per minute (rpm), while the propeller revolutions revolutions required required for a single-screw single-screw tanker is about about 80 rpm.] rpm.] Reduction gears, if used, have energy losses of about 1%.
The ratio of the power at the reduction gear output to the engine brake power is called “Gearing Efficiency ”, where a typical value is 0.99.
G
P S P B
Where: P s is called the shaft power.
For low speed Diesel engines, where there is no reduction gear:
G =1.00
Most engines are placed some distance away from the stern tube. Within the shaft tunnel connecting the engine room to the stern tube, a number of shaft shaft bearings are located to support support the shaft. A small amount of energy (typically (typically about 0.5 percent) is lost lost in those bearings. bearings.
Time rate of energy carried up to the stern tube entrance is called “torsionmeter power ”. Since in some ships it is obtained from the shaft torque measured by a device called “torsionmeter”, p laced immediately before the stern stern tube.
Therefore, the efficiency of bearings from the engine to torsionmeter is expressed in terms of “bearing efficiency ”.
B
P trm P S 33
Where: P trm trm is the torsionmeter power, equal to the product of the measured by the torsionmeter torque, Q trm trm and the shaft
rotational speed, 2 n .
Ptrm
Qtrtrm 2n Qtrm
rpm 30
Where: n is the shaft revolutions per second.
In Diesel-electric ships, there are no reduction gears gears or intermediate bearings. In those ships, energy supplied by the main propulsion engine used to generate electricity by a generator directly coupled to t o the engine crankshaft and the propeller shaft is driven by an electric drive motor motor utilizing that electrical energy. energy. Therefore, in Diesel Diesel electric ships, the product of gearing and bearing efficiencies can be expressed as the product of generator’s, electrical transmission’s and electrical motor’s efficiencies. efficiencies.
The shaft is lead to the sea by passing through a bearing with a watertight shaft seal. se al. This bearing bearing is called called the “sterntube”. A small portion (about (about 0.5 %) of energy is lost as the shaft passes passes into the sea.
The energy, finally delivered to the propeller is called “delivered power ( P D)”. Therefore, a “stern-tube “stern-tube efficiency” efficiency” can be be defined:
St
P D P trm
The efficiencies mentioned above, starting from the engine crankshaft output to the sea can be incorporated into a single, “transmission efficiency (
tr)”
For mechanical transmission:
tr
P D P B
G B St
For Diesel- electric (also turbo-electric) propulsion:
tr generator electricaltr ltransmission motor St 34
COMPONENTS OF PROPELLER EFFICIENCY
( P Unfortunately, not all of the energy delivered to the propeller ( to overcome the total D) is converted into useful work to resistance of the ship.
The useful part of the energy, or the rate of energy to be imparted to the ship if it were towed by an imaginary rope, free of other effects is called “effective power” power ” which is equal to the power of an “ideal propulsor”.
P E
1
RT VS Vs3 SC T 2
Effective power ( P E) is related to the delivered power ( P D) by means of a parameter called “quasi-propulsive efficiency” efficiency ” (
QP
QP).
P E P D
Unfortunately, quasi-propulsive quasi-propulsive efficiency is significantly lower than the unity, with typical values in the range 0.70-0.50.
The efficiency that would define the engine brake power to the effective power is the “propulsive efficiency (
P)”
35
P
P E P B
tr QP
Quasi propulsive efficiency is the product of three components, or or “efficiencies”. “efficiencies”. In order to understand understand propeller action, one should take a look at the three components of the quasi-propulsive efficiency. efficiency.
HULL EFFICIENCY
The purpose for which which the propeller of the ship ship is installed is the production of a forward forward thrust. While developing developing the forward thrust, the propeller operates in a location near the stern post which is highly turbulent with eddies separated from the hull. The average average value of the water water stream incident incident to the propeller is somewhat somewhat less than the speed of the ship. This is measured by “wake surveys” conducted on the ship models, where an an example is shown below. As can be noticed, the wake distribution can deviate significantly both in radial and angular positions over the propeller disk, and is not necessarily necessarily symmetrical even on a symmetrical hull form.
Fig. Wake survey conducted on a =6 ship model of a single screw vessel (A Victory-type ship)
Although that velocity changes changes over the disc area of the propeller, it is possible to take an average value. That average velocity is called “advance velocity (V A)”. Advance velocity velocity can be related to the ship speed by a factor factor called “wake coefficient (w )”.
V A
1 wV S
Wake coefficient coefficient is highly variant over the t he propeller disk. However, for engineering calculations, calculations, an area-averaged value can be taken over the propeller disk, called “ mean wake”:
w r , dr d w dr d A
A
36
Wake coefficient coefficient can be thought as to be composed of tthree hree parts: 1. Potential wake (the ideal value that the wake would be if it were in an inviscid fluid), 2. Viscous wake (due to the fact that the propeller operates inside the highly turbulent boundary layer at the stern) and the 3. Waveform wake (which is a small portion of the wake except in high speed vessels, due to the induced velocities of the waveform about the ship). The wake is mainly dependent on the hull form: 1. Full form ships, with block coefficients of C B = 0.80 or more, like tankers, bulk carriers, etc. have wake coefficients
w = 0.40~0.30 range, 2. High speed vessels with streamlined forms have lower wake coefficients. 3. Twin screw ships have lower wake coefficients, typically about 0.05. 4. The larger the propeller diameter, the smaller the wake coefficient shall be.
THRUST
The thrust that the propeller develops should be slightly larger than the ship resistance: As the propeller operates behind the stern, it draws a mass mass of water through the propeller propeller disc. This creates a “suction effect” on the hull, reducing the effect of the forward thrust thrust of the same propeller. Therefore, forward forward thrust T is is related to the ship resistance R T by:
RT
1 t T
Where the parameter t is called “thrust deduction coefficient ”. It is in the range 0.15 0.15-0.0. Also the higher values are associated with full form ships and lower values with thin hull forms and twin screw vessels. The thrust power, P T that should be supplied by the ship shall then be:
PT
VA T (1 w) V s
RT
1 t
P E 1 t
1 w If one calls the parameter parameter in the denominator of the last equation equation as the “ hull efficiency (
H
H)”:
t P E 1 w P T 1
It is interesting to note that for most ships, hull efficiency efficiency can have have values greater greater than unity. This paradox can be resolved by regarding it as a correction correction factor, rather than an efficiency. efficiency. (In fact, hull efficiency is a momentum momentum recovery factor: Energy of the propulsive power power lost in the wake is recovered recovered by the propeller.)
37
HOW DOES A PROPELLER WORK?
A screw propeller is so-called since as it advances advances in the water by a rotary motion, it acts like a screw. However, However, its speed of advance is less than it should be if it were to advance in a solid environment. This discrepancy is measured measured by defining a “propeller slip”. Slip ratio is the relative relative deviation of advance advance made by by the propeller propeller operating in seawater to that of a propeller operating operating in an ideal (solid) (solid) environment. environment. In mathematical terms:
s
Deviation Deviation from the advance of an ideal screw Advance of an ideal screw
If evaluated evaluated on “per unit time” basis:
s
P n V A P n
1
VA Pn
1
VA P (n D) D
1
J P D
Where the dimensionless parameter J = V A /n D is called “advance coefficient”, P : is the pitch and D : is the propeller disc diameter and
number of revolutions revolutions of the propeller per per second. n : is the number
The parameter P/D (propeller pitch over propeller disc diameter) is one of the main parameters defining the geometry of the propeller. Propeller slip is the measure how well well the propeller performs behind a ship. A zero slip propeller is associated associated with an optimum propeller, but however, however, it produces no forward thrust. Therefore, one should should design for a propeller which will operate with the minimum minimum possible slip. A ship operator should seek seek for the conditions of a minimum minimum slip as well. However, it is not always possible possible to know the ship’s wake beforehand. beforehand. The amount of average average wake in which the propeller operates operates is usually not known. An “apparent slip ratio” is defined instead.
sapp
1
V S P n
It is related to the actual slip ratio by:
38
sapp
s w 1 w
Or,
s sapp 1 w
w
It should be taken into account that, for full-form ships where the wake coefficient w is large, apparent slip ratio can attain negative negative values. In general, general, slip is lowest lowest in calm water for a clean hull. As the hull gets gets rougher, or the ship encounters heavy heavy seas, apparent slip gets larger. Therefore, monitoring monitoring of apparent slip ratio can give the ship operators about the operating condition of the ship.
EXAMPLE PROBLEMS
Question-1
A ship on a voyage between two ports travels a distance distance of 2400 nautical miles in eight days. During the voyage, voyage, the ship is found to make a total of 820 000 revolutions. revolutions. If the pitch of the propeller is 6 metres, metres, calculate the slip. Solution-1
Theoretical Theoretical advance of the ship:
Ltheoretical= P n = n = 6 m/rev. 820 820103 rev. = 4 920 000 m. Actual advance of the ship:
Lactual = 2400 n.m. 1852 m/n.m. = 4 444 800 m. Apparent slip =
s a
L 4920000 100 1 theoretical 100 1 9.66% Lactual 4444800
Question-2
During a passage on a straight course, a bulk carrier is observed to make a speed of 14.7 knots from the ship’s log . The propeller revolutions are 90 revolutions per minute and the propeller pitch is at its maximum setting of 4.70 metres. Calculate the apparent slip you should enter to the log. Solution-2
s a
V 100 1 s 100 P n
V s = 14.7 nm/hr 1852 m/nm /3600 s/hr = 7.562 m/s n = 90 rev/min /60 s/min. =1.5 rev/sec.
s a
7.562 562 V 100 1 s 100 100 1 100 7.26% 1 4.70m. 1.5 s P n
39
A negative apparent apparent slip can be surprising at the first look. But however, for a full form ship such as a bulk carrier, the advance velocity velocity of propeller is considerably considerably less than the ship speed, as defined defined by the wake coefficient. coefficient. For a wake coefficient of 0.40, typical for a full form ship, the true slip becomes about 35% - which is a typical value. What produces the forward thrust, reason d’etre of d’etre of a propeller, is the pressure difference created between between the two sides of a rotating, airfoil shaped blade. A positive pressure field dominates dominates on the “face” of the blade (astern-looking (astern-looking part) and a negative pressure field on the “back” (forward looking part) of the blade. The difference between between those pressures, integrated integrated on the propeller disc area, is the thrust. The useful work created by the propeller is the product of thrust and the speed of advance. Hence the “open“open-water efficiency” of the propeller is given by:
o
PT P D
T V A
2 Q n
Before getting into the further analysis of propeller thrust and torque, one should look into the laws of similitude for propellers.
LAWS OF SIMILITUDE FOR PROPELLERS
For a propeller operating in non-cavitating condition, the thrust developed by the propeller can be related to a number of parameters: parameters:
Mass density of water,
Propeller size, described by the diameter, D diameter, D
Propeller pitch, P pitch, P (for (for a given propeller diameter , P/D)
Number of blades blades , Z
Speed of advance, V A
Acceleration Acceleration due to gravity, g gravity, g
Speed of rotation, n
Pressure in the ambient field, p field, p
Viscosity of water,
Since we are looking for the laws of similitude for two geometrically similar propellers pitch, diameter and number of blades will also also be similar. Therefore, propeller pitch and number number of blades blades are deleted deleted from the above list. Writing:
T
f a , Db ,V c , g d , ne , p f , g A
In terms of dimensions:
MLT 2
a
c
d
e
f
ML3 Lb LT 1 LT 2 T 1 ML1T 2 ML1T 1
g
-3a+b+c+d – f – f – g g -c-2d-e-2f-g MLT-2 =Ma+f+g L-3a+b+c+d – T
40
This will lead to the system of equations:
a b c 1 0 0 0 0 1 1 1 3 1 1 1 0 1 1 d 1 e 0 0 1 2 1 2 1 2 f g h Solving and rearranging the result,
T
1 2 Where =
D 2V A2
gD nD p f 2 , , 2 , V V V V D A A A A
is the kinematic viscosity. viscosity.
From this last equation, one can deduce that two propellers that are geometrically similar but different in size will have the same non-dimensional thrust coefficient coefficient (T /½
2 2 D V A ) provided that all the parameters that appear on the right hand
side are equal. One can recognize recognize that the first term is the square of the inverse of the Froude number number and the last term the inverse of the Reynolds number. Like as was previously done for ship models, a model scale relating the model-size model-size and full scale (ship size) propeller is defined:
DS D M
P S P M
The equity of the first term that appears on the right hand side implies that the Froude numbers of both propellers are the same. This requires requires that: that:
V A, S V A, M
Froude number similarity is required for modeling the propeller-free surface interaction. For two propellers having the same Reynolds number,
1
V A, S V A, M
Reynolds number similarity is required if both the model and the ship (prototype) propellers have the same viscous resistance coefficient coefficient as they t hey advance in the water.
41
The third term, p/ V A 2 , means that the two geosim propellers should operate at the same ambient ambient pressure. This similarity is meaningful if there is cavitation phenomena. phenomena.
The second term in parenthesis is the inverse of the advance coefficient, J = V described in the previous section. described /n D A Stating that the advance coefficients of two geosim models are the same is equivalent to stating that the slip ratios should be the same, same, as well. For the advance advance coefficient coefficient similarity,
J M
J S VS
nS DS
V M nM DM
Arranging, and assuming that the Froude number similarity holds as well,
nS
n M
D M V A, S DS V A, M
DS
D M V A, S
V A, M
nS n M
1
Therefore, Therefore, model propellers should be run at a higher speed than the t he prototype ship speed. For the thrust developed by the propeller,
T TS T M
D 2V A2 2
2
D V S S 3 DM V M
The thrust power supplied by the propeller is P=T V A . So that for the model and prototype ship propellers,
PT , S PT , M
TS V A, S
3.5
TM V A, M
The torque delivered to the propeller shall be:
Q
QS Q M
P n
P T , S nM PT , M
nS
4
Therefore, Therefore, an acceptable way of expressing the thrust and t he shaft torque of propellers in non-dimensional form are:
C T
T 1 2
D 2V A2 42
C Q
Q 1 2
D3V A2
J= V This set of non-dimensional characteristics are expressible to the base J=V . C are directly applicable to are A / n D T T and C Q Q
the propellers of seagoing ships, but for example, for tugs towing heavy load while advancing very slowly, they tend to infinite values. Therefore, Therefore, a more widely accepted set set of non-dimensional propeller propeller characteristics characteristics is obtained by replacing V A by a multiple of propeller tip speed, nD: nD:
K T
K Q
T 2
n D
(Thrust coefficient) 2
Q 2
n D
(Torque coefficient)
4
The efficiency of a propeller operating in open water (in a uniform flow field) shall be:
O
Thrust power power Delivered power
T V A
2n Q
J
KT
2 K Q
Propeller characteristic charts, K charts, K T T , K Q and O are customarily prepared as a function of advance coefficient and propeller geometry. Propeller characteristics characteristics are drawn drawn with K T T , K Q and O as the ordinate and J as the abciassa, for different propeller blade numbers, Z numbers, Z , pitch ratios ( P/D) P/D) and for f or different expanded-area ratios.
Fig. An example of propeller characteristics characteristics chart (Wageningen B4-55)
As a general rule, fast vessels have higher P/D ratios (1.0 or more), while low speed ships have lower P/D ratios.
43
RELATIVE ROTATIVE EFFICIENCY
From the discussions above, it is apparent that the quasi-propulsive efficiency is obtainable by the multiplication of the open-water efficiency efficiency and the hull efficiency. efficiency. However, A ship’s propeller propeller will operate with a higher Reynolds number than the model, resulting that for most cases the boundary layer on the model propeller is dominantly laminar and the boundary layer on the ship propeller is dominantly turbulent. turbulent. This is mainly from from the boundary boundary layer on the propeller blade and is called “scale effect”. The wake field in which which the propeller operates operates in is uneven. Therefore, Therefore, the velocity incident to a propeller propeller blade behind a ship varies greatly as it rotates and has a high degree of ambient turbulence, promoting an earlier laminar to turbulent transition, as well as having a pre-swirl before it enters into the propeller disk. “in-behind” conditions will introduce a difference These “indifference to the model to ship correlation. To account for this difference,
the concept of “relative rotative efficiency” (
RR )
is introduced:
QP O H RR Typical values of relative rotative efficiency are about 0.98 for twin-screw ships and within 1.00-1.07 range for single screw ships.
44
NOTES ON PROPELLER GEOMETRY
Propeller blades can vary between 2 and 7 (propellers used in small boats and yachts usually have 2 - 3 blades, twin screw ships 3-4 blades, while larger single screw vessels have 4 - 7 blades).
FIXED PITCH PROPELLERS
Fixed pitch propellers used on single-screw ships are designed to operate in the clockwise direction when viewed from
the stern, and twin-screw ships have an outward rotation (starboard propeller rotates in clockwise and port side propeller rotates in counterclockwise counterclockwise direction). The hub diameter of a propeller propeller is about 1/5 th of the propeller disc diameter for a fixed pitch propeller and 1/3 rd for a variable pitch propeller. As a reference for further discussions, a figure to illustrate various definitions of propeller geometry is included below.
45
PROPELLER THEORIES
A ship’s propeller works by creating a forward thrust. This forward thrust has been explained explained by a number of theories: Momentum Theory: Momentum created by the acceleration of water passing through the propeller disk. Blade Element Theory: Forward thrust created by the lift l ift forces created by the airfoil-shaped sections of Propellers. Vortex Theory: Circulations caused by the vortex system on the blades and within the vortices shed to the propeller
slipstream. Lifting line Theory: Vortex theory based on assumption that each propeller blade is represented by a single bound
Vortex. Advanced Vortex theory , Lifting surface theory or Vortex lattice methods: that the surface of a propeller blade is
represented represented by a number of discrete vortex elements.
MOMENTUM THEORY OF PROPELLERS
Consider that the propeller is modelled by a disc (“actuator disc”), immersed perpendicularly to a free free-stream -stream of velocity V A. The function of this actuator disc disc is to impart an an extra momentum momentum to the mass of fluid that passes passes through it. The resulting pressure distribution is a low pressure area immediately before and a high pressure area immediately after the propeller. The pressure far ahead and far behind the propeller shall have the ambient values. The propeller race column (“slipstream”) (“slipstream”) will experience a contraction contraction due to the condition of continuity. The propeller is assumed assumed to have an infinite number of blades and the thrust is assumed to be distributed un iformly over the propeller disc.
Momentum equation: V m a
T m V a U
The thrust developed by the propeller shall be:
T
p A D p1 p1 AD 46
Where: A D is the propeller disc area. area. Equivalently, Equivalently, it is also equal to the change change of momentum as the water passes through it. Denoting the axial axial velocity on the propeller disc increases increases to the value V A +U - far behind the propeller,
T Where: m
Q V A U VA QU
Q is the t he mass flow rate of water passing through the propeller disc. Q A D V A U D
The thrust work done by the propeller should be equal to the net change of kinetic energy within the fluid:
1 2 QU V A U D Q VA U D VA2 2 Solving, one can get:
U 2U D Defining the open water efficiency of the propeller as the ratio:
O
Useful work obtained Total work expended
T V A T V A U D
1 1 a
Where a = U D /U A. An alternative way of writing this relation in terms of non-dimensional coefficients is by expressing the parameter a as a function of thrust coefficient(s):
2
o
1 1
8 KT J 2
2
1 1
4C T
From the relation above, it is understood that low values of propeller loading, i.e., propellers with a larger diameter for the same thrust or propellers developing lesser lesser thrusts will have better open water efficiencies. An open water efficiency of unity (an ideal case) is obtained when the propeller delivers a zero thrust (K T T =C T =0). The foregoing analysis neglects the fact that the water leaving the actuator disc encounters a rotation as it deforms into the propeller slipstream. For a propeller angular speed of rotation of , the value of tangential speed of rotation can be expressed as a’ r . Incorporating that into the analysis analysis above, the ideal ideal value of open water efficiency efficiency shall be:
o
1 a 1 a
This momentum theory neglects the effects of finite number of blades, effects of viscosity of water and unevenness of thrust distribution along the blades in the radial direction. “Blade element element theory” is proposed for for a better analysis of marine propellers. However, for a better understanding understand ing of the blade element theory, one has to know the basic concepts of airfoil/hydrofoil theory.
AIRFOIL/HYDROFOIL AIRFOIL/HYDR OFOIL THEORY- BASICS
A propeller blade element can be explained by seeing it as a “ lifting surface”. A two-dimensional two-dimensional airfoil immersed in a flow of a real fluid shall experience a change in flow velocities along the blade and shear stresses along the path of the
47
fluid. The resulting pressure pressure distribution along the plate by the law of Bernoulli Bernoulli shall give rise to a nonzero force, force, in a direction direction perpendicular to the direction of flow of the fluid, called “lift”. Certain two-dimensional two-dimensional sections called “airfoils” have been found to produce large values of lift forces. The shear stresses shall shall also give rise to another force, in the direction of of the flow of fluid, called “drag”. This drag can be analyzed analyzed in a way similar to ship ship hulls - it has a main frictional component and a “form” component and is affected affected by surface roughness. (Propeller blade drag can also have Froude number, shock wave and cavitation effects effects under certain circumstances.) circumstances.)
Airfoils form the basis of many
engineering applications- aircraft wings, helicopter rotors, lifting foils of hydrofoil craft, airscrews and marine propellers, ship and aircraft rudders, fans, screw pumps, as well as certain water and wind turbines operate on this principle. L (Lift)
D (Drag)
Fig. An airfoil section A symmetrical airfoil section with a chord length of c will will produce a lift force L provided that the flow has a certain angle with its nose-tail line. line. This angle angle is called “angle of attack” .
C L
L 1 2
U 2c
2
Where: U
: is the free stream velocity.
An engineering application of a symmetrical foil is the ship’s rudder.
Fig. An example of a symmetrical symmetrical airfoil- ship’s ship’s rudder
However, most airfoils used in present day engineering applications are nonsymmetrical nonsymmetrical airfoil shapes, ship’s propeller blade blade sections being an example. example. The parameter parameter that determines non-symmetricity is the camber camber line. As a result of nonsymmetricity, symmetricity, a lift is developed even at at zero angles of attack. attack. In other words, zerozerolift condition is satisfied if the angle of attack on a cambered blade is negative.
Fig. Geometry of an airfoil with camber, indicating zero-lift zero-lift angle
48
In this case, lift developed by an isolated, two-dimensional airfoil in a uniform stream is given by:
C L 2 L 0 Where L0 cascade (for example, example, as is the case of a propeller with a finite L0 is the zero angle of attack. For an airfoil in a cascade number of blades), both the zero-lift angle and the slope of the lift coefficient versus angle of attack curve are reduced. Together with the three dimensional effects (a hydrofoil and a propeller blade are not two dimensional, they have a certain amount of span), the lift coefficient (C (C L) versus angle of attack ( ) relationship are seen in the figure below. Above a certain angle of attack (typically about 12-15 degrees), the flow about the back of the blade shall separate, resulting in a loss of lift and severe vibrations.
Fig. Lift coefficient versus angle of attack for awing BLADE ELEMENT THEORY
Blade element theory recognizes that the propeller blades are airfoils in shapes specially designed for cavitation-free operation. At a radius x radius x =2r/D from =2r/D from the propeller axis of revolution, differential forces and moments for a blade element can be expressed as:
49
dL dD Z cos i sin i dr dr dr dQ dL dD Z r sin i cos i dr dr dr dT
Where: dT
: is the thrust and
dQ
: is the t he torque developed by a differential cylinder sheet of thickness dr , and
dL and dL and dD : are the differential lift and drag of the blades developed along the same cylinder for Z -bladed -bladed propeller. Defining a so-called so-called “glide angle” as:
dL
tan
dD
C D C L
dr 2 cos sin i dQ 1 ZcrV R2C L dr 2 cos dT
1
ZcV R2C L
cos i
From these results, the open water efficiency of a propeller blade element can be written as:
O
V A dT
dQ
O
VA
cot i
2nr
tan tan i
This last form of the open water efficiency can be assumed to be constant along the radial direction of the blade, and therefore, an acceptably accurate representation representation of the blade can be taken at the representative non-dimensional non-dimensional radius x radius x 0.7-0.75. The problem is defining the axial axial and radial inflow factors factors a and a’ on the blade.
VORTEX THEORY OF PROPELLERS
Vortex theory (circulation theory) assumes that the lift developed by the blades is caused by a vortex distribution along the blade. The velocity differential differential around the blades, which is the producer of the lift forces, can be expressed expressed in terms of a vortex. The velocity on the blades can be expressed as:
V R
V A r uinduced induced U c
50
Where u induced induced is the sum of axial and rotational induced velocities and U c is the circulation velocity on the blade. V A is the velocity of advance (velocity of water incident to propeller due to forward ship speed) and the term velocity due to the rotation rotation of the propeller. propeller. The circulation circulation
r is the
(vortex strength) along the blade is defined defined as:
U c d s
The circulation and the lift generated by an airfoil section can be related by the relation:
dL dr
U
Known as the Kutta-Joukowsky Kutta-Joukowsky theorem. theorem. Thus, the generation of the lift is related related to the circulation, or, to the velocity distribution around the blades.
Fig. Vortex formation along a propeller blade
The vortex vortex extending radially along the blade blade rotates together with the blade. This is called “the bound vortex line”. However, according according to the theorem of Helmholtz, a vortex li ne should either extend to infinity or should end on a fixed or free surface. surface. In order to account for the radial variation along the blade, differential vortex elements elements should be shed at radial locations along the blade. Therefore, Therefore, vortex line(s) around a propeller propeller blade should extend backward backward from the blade, also helicoidal helicoidal in shape. The most important important of those shed vortices vortices is in the location where where the most drastic drastic change in circulation happens- blade blade tip. In most cases, the propeller propeller vortex system can can be thought to be composed of a bound vortex, a tip vortex and a hub vortex, located at the center of the propeller stream tube and extending axially backward (axial vortex line).
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Fig. Bound vortex, tip vortex and axial (hub) vortex lines
Despite this simplification, for an accurate model of a screw propeller, it should be taken into account that the thrust distribution and hence the circulation are not constant in the radial radial direction. For the radial change change of circulation, circulation, it is assumed that a vortex filament is shed to the propeller slipstream with a vortex strength equal t o:
r 0
dr r
0
0
Fig. Vortex system shed from a propeller- basis of lifting line theory
Propeller vortex theory is based based on the analysis of the flow field around a propeller propeller blade. The fluid velocity at a point ) by ) by a vortex filament is found by the application of the Biot -Savart law: P(x, y, z
u ( x, y , z )
r 0 R d l 3 4 C R
. Where R Where R is is the distance between the differential element element dl and and point P(x , y, z) z)
The first form of the vortex theory is the lifting line theory, starting with the works of L. Prandtl and S. Goldstein and developed to perfection by Hermann Lerbs, where each blade is represented by an radially-extending bound vortex line. However, this theory has a shortcoming for broad marine propellers where the flow is forced to a curved path along the
52
blade width as it passes through t hrough the propeller. Therefore, more developed class of propeller analysis methods are the lifting surface methods or vortex lattice methods, where the surface of the propeller is modelled by a collection of
vortices, discretized both radially and along the chord lines (almost always to be performed by numerical methods, and calculation software for such purposes are available).
Fig. Vortex lattice model of a propeller
CAVITATION CAVITAT ION OF PROPELLERS
The generation of lift on the propeller blade is mainly due to the low pressure pressure area on the back of the propeller. If the pressure on the blade gets sufficiently low, cavities filled with water vapour form on the blade surface. This takes place when the pressure becomes lower than the vapour pressure corresponding to the ambient water temperature. temperatur e. This phenomenon is called “cavitation”. Cavity bubbles suddenly form on the blade surface where the pressure at that location is below the vapour pressure of water, and also disappear very rapidly where the pressure rises above that vapour pressure. The very rapid growth and collapse of the bubbles are the source of pulse loads on the propeller surface, surface, which may be the reason of erosion erosion of the material, as well as unwanted unwanted sources of sound and vibration. Cavitation is also a source of reduction of the thrust developed by the propeller.
Assuming a foil immersed in a freestream of velocity U. The pressure pressure at a point P on the foil, p foil, pP shall be related to the local velocity V , freestream velocity U and and the t he ambient pressure p pressure p by by the law of Bernoulli:
p 12 U 2
p P 12 V 2 53
The normalized form of the pressure difference between the point P and the ambient is defined by the number
p P 1 2
p
U 2
pP p q
1 2
:
V 2 U 2 q
Also, a cavitation number (“Thoma” number), defined as:
p pv q
Where: P
), ), + h : is the local (ambient) pressure at a point on the propeller hub (p = p Atm Atm + h
h
: being water depth at the propeller hub,
p v
: is
the vapour pressure of water at the ambient temperature temperature and the parameter
q =½ n U 2: is the dynamic pressure, based on the free stream velocity, U .
Cavitation occurs when the pressure is p p P v. In terms of normalized coefficients where
is the condition of
cavitation to take place. Cavitation initially forms as the blade tip cavitation around the blade tip vortices, followed by a vortex extending from the hub. Later, a sporadic vortex vortex on the blade forms, which can develop to cover a wider area area and finally can cover the entire blade surface. surface. This last case case is called “super “super cavitation”. cavitation”.
Fig. Wing tip and hub vortex cavitation on a propeller
Cavitation can be prevented or reduced for a given pr opeller blade by:
Shaping of the blade to produce the same lift without letting too high pressures to occur on the blade (This is achieved by the preference preference of “round-back ” sections over the airfoil sections)
Avoidance of high values of angle of attack
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Avoidance of changes in the direction and magnitude of flow velocity incident to the propeller (i.e., operating the propeller in a field field of uniform velocity) velocity)
Avoidance of roughness on blade surfaces
Operating the propeller at deeper waters
Operating at the propeller at lower ambient temperatures
High values of angle of attack correspond to propellers loaded above the design values. Therefore, avoidance of extra loading, extra-low draughts, and maintenance of propeller smoothness are contributing factors to propeller cavitation.
Fig. Pressure distribution on a round-back blade section For a propeller designer, designer, a cavitation-free operation operation is ensured by the avoidance avoidance of extra-loads on the blade. blade. For this purpose, a well-accepted well-accepted procedure is after Burrill, who prepared charts as a function of the cavitation number at the representative representative radius x radius x = = 0.7.
0.7 R
p A pv
h 2 1 V A2 0.7nD 2
Where pA is the atmospheric pressure and h is the water water depth at at the propeller propeller centerline. By selecting selecting appropriate numbers for the seawater at 10oC in metric units, cavitation number becomes: becomes:
0.7 R
195.31 195.31 19.02 19.02h V A2 4.836n2 D2
The ordinate of the diagram is the thrust load per unit blades, normalized by dynamic pressure force on propeller projected area: area:
c
T 1 2
A pV 0.72
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Fig. Burrill diagram for cavitation susceptibility
An estimate of the propeller projected blade area, from the developed area is:
A P A D
1.067 7 0.22 0.229 9 1.06
P D
The thrust can be estimated from:
T
P E
1 t VS
P D QP
1 t VS
Another widely-used criterion for the selection of the minimum propeller expanded area ratio for cavitation-free operation is the Keller’s relation:
Ae A0
1.3 0.3 Z T k p0 pv D 2
Where: A0 : is the propeller propeller disc disc area area ( A A0 = ¼ D2), k
: is a constant depending on ship hull form, varying from k = 0 for a twin-screw, fine form warship to k = 0.4 for a single screw merchantman.
p0 -pv
: is the factor for the pressure pressure at the propeller centerline. centerline. The following following table is the vapour pressure pressure of seawater
for various temperatures. temperatures.
Temperature, oC Vapour pressure, pv (Pa)
0
5
10
15
20
25
30
35
40
610.8
871.8
1227.1
1704.0
2336.9
3166.6
4241.4
5622.2
7374.6
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The propeller of a vessel, operating in an uneven wake field is more susceptible to cavitation than one operating in a wakeless environment. environment. The angle of attack to the blades will change during each rotation of the blade due to the changing local velocity of advance. advance. A remedy is to use a highly skewed propeller, propeller, or use of a raked propeller to increase increase the clearance between between the propeller and the sternpost.
PADDLE EFFECT
Paddle effect is a factor that deviates deviates a ship from its straight path even for calm water- rudder at amidships condition. condition. For a right-hand rotation propeller (a propeller rotating in clockwise direction when viewed from aft), the blades at the lowermost position have a slightly higher drag than the ones at the uppermost position, causing a net thrust that pushes the stern to starboard starboard side. side. Therefore, Therefore, the ship’s ship’s course deviates towards the port side. This effect This effect is more pronounced in shallow waters, such as ports and inland waterways. waterways. The same ship, when moves moves astern, the stern is pushed to port side. In order to have the same effect for a controllable-reversible pitch propeller (CRPP) of a single screw ship when astern maneuvering maneuvering is necessary, necessary, CRPP propellers are made to rotate counterclockwise counterclockwise (both forward and astern) when viewed from aft.
PROPELLER SELECTION
Modern shipyard practice is to select a propeller from a series used by manufacturers, rather than a custom-designed propeller. Usually, the starting starting point of the design is the selection of the propeller propeller type for the particular application. application. The next step is usually the selection of the propeller diameter, which is often dictated by the draft or the required propeller immersion. Alternatively, the engine power delivered to the propeller(s) and the engine revolutions can be the given parameter. The number of blades is mainly determined by vibration considerations, taking the fact that the main harmonic of the propeller-induced vibrations is n Z into account. In general, the lower the number of blades and the lower the propeller disk area ratio ( A E /A0), the better the efficiency become. P/D ratio P/D ratio A A E /A0 ratio are also to be selected for the propeller revolutions and the diameter. diameter. Minimum value of disk area ratio is often dictated by the t he cavitation-free operation requirement. A well-accepted set of propeller series are the series of Maritime Research Institute of Netherlands (MARIN), known as Wageningen series, which have become a standard in assessment of propellers. Producers which use other propeller series also have followed the example of Wageningen series in preparing charts for propeller selection. As well as representing the propellers in the familiar K T T, 10 K Q, o versus J format, they also have prepared propeller selection charts. charts. Wageningen propeller propeller series are classified classified as A, B and C, where B-series being the most widely used for classic, fixed pitch non-cavitating screws. A Wageningen series propeller is named with:
An initial name, “Wageningen A, B or C”,
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A number following the letter A , B or C, for the number of blades ( Z Z ), ),
A two digit number for the expanded area ratio (in percent), followed by an hyphen.
Thus, “Wageningen B4B4-55” propeller refers to a Wageningen B series propeller with four blades and A E /A0 = 0.55. Still the pitch ratio, P/D ratio, P/D is is required to specify a particular particular propeller of the series. It should be taken into account that the series are obtained with models of 24 cm. diameter, seawater and Reynolds number effects should be taken into account when selecting the particular screw. The first step of propeller selection for a given ship is the determination of the diameter. The diameter should be selected selected as large as possible, but the tip of the t he blade should not approach to the water surface in order to avoid free surface effects and “ventilation” (sucking (sucking of atmospheric air to the low pressure area on the propeller back) as it rotates. For most ship forms, D/T forms, D/T = 0.7 is a reasonable reasonable first approximation. P/D ratio P/D ratio should also be selected as high as possible for a high open water efficiency. efficiency. Most high speed speed ships have P/D have P/D ratios ratios of more than 1.0, while heavy-loaded propeller vesels such as tankers and bulk carriers have P/D have P/D ratios ratios of about 0.7. Propeller selection charts, based on the analysis of propeller characteristics have been prepared both for the unknown diameter ( K Q /J 5)1/4, known as BP1 chart or for known diameter ( K Q /J 3)1/4, known as BP2 chart. A separate separate chart is prepared prepared for each A each A E /A0 value. Propeller selection selection is to be made at full service speed- full displacement displacement condition for a given ship type.
EXAMPLE Question-1
A ship has a service service speed of 20 knots. Effective power power is found to be 9600 kW. The ship is to be propelled by a single single shaft, with a 7.5 m. m. immersion. The wake coefficient at the propeller location is found to be w = 0.20 and the thrust deduction coefficient t = = 0.15. The relative rotative efficiency efficiency is taken to be 1.05. Select the Wageningen B series propeller for this application. Solution-1 quasi-propulsive ive coefficient is selected to be The quasi-propuls
0.75. Therefore, the delivered power to the propeller shall be P 0.75. be P D
= = QP
QP P = = P E / = 12800 kW. Power correction for seawater is made: P’ made: P’ D = 1.025 P D = 13120 kW. kW. Q Propeller diameter was selected to be the largest possible 6.4 m. to give enough clearance and submergence. A four bladed propeller (Z = 4) was chosen. The inflow velocity velocity to the propeller propeller shall be: V A =20.0 nm./h. 1852 m./nm./3600 s./h. (1 - 0.2) = 8.231 m/s.
The input value to the chart shall be:
3 K Q P D 13120 10 W 3 0.5420 J 2 D 2V 3 kg 2 3 A 2 1025 3 6.4m 8.321m / s m 1
4
1
4
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From the propeller charts (B p2 class) of the B4 class, using the values that lie on the optimum open water efficiency line, following data were obtained: B4-40
B4-55
B4-70
B4-85
0.665
0.66
0.66
0.65
0.64
P/D
1.07
1.04
1.04
1.1
1.23
1/J
1.22
1.22
1.23
1.22
1.20
0
B4-100
As can be observed, for larger expanded area ratios, hence immunity from the cavitation is achieved at the expense of open water water efficiency. efficiency. To decide on a proper value of expanded area ratio, Keller’s relation is to be used:
A E A0
1.3 0.3 Z T k p0 pv D 2
Since this is a fast vessel, k = = 0.2 is taken. taken. For the water water temperature, temperature, 25oC value ( p Pa) is taken. Thrust value value pv = 3166.6 Pa) is calculated from the effective power as:
T
P E
1 t V s
1 0.15
9600 kW 20 knts 1852 m. / nm
1097.70 kN 3600 s / h.
The pressure at the propeller hub shall be:
p0
patm gh 101325 Pa 1025kg / m3 9.81m / s 2 7.5m. 176739.4 Pa
Therefore,
A E A0
1.3 0.3 4 1097.70 kN 0.2 0.2 0.58 0.586 6 2 2 176739.4 3166.6 N / m 6.4 m
This value is slightly larger than the expanded expanded area ratio of of B4-55 propeller.
By interpolation, suitable suitable propeller
characteristics characteristics (one to be ordered to the manufacturer) are found to be: 0 =0.6945, P /D = /D = 1.04, 1/J = = 1.22 or J or J = = 0.820. Propeller revolutions revolutions for the selection selection of engine and the reduction reduction gear
are:
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n
V A JD
8.321 m / s 0.82 0.820 0 6.4 6.4 m
1.586 rev / s or 95.1 rpm.
As a check, H = (1-t)/(1-w) =(1-0.15)/(1-0.20) (1-t)/(1-w) =(1-0.15)/(1-0.20) = 1.0625 QP = 0.6945 0.69451.0625 1.06251.05 = 0.77 QP= 0 H RR RR =
Which is acceptably close to the initial assumption, QP QP = 0.75
Question-2
A cargo ship is to be installed with a main main propulsion engine to deliver 4750 kW to the propeller propeller at 100 rpm. The desired service speed of the ship is going to be V S=15 knots, and for the hull form selected, w = 0.25 and t = 0.12. Select a propeller, together together with the restriction restriction that the diameter diameter shall not exceed exceed 6.0 m. m. with an immersion immersion of 7.0 m.
Solution-2
V S S= 15 knots = 7.717 m/s. V A = (1-w) V S = (1 - 0.25) 0.25)7.717 = 5.7875 m/s. S = n = 100 rpm/60 =1.667 rev/s.
Q
P D
2 n
4750 kW 2 1.667 s 1
453.592 kN .m 1
4 1 K Q Q n3 453592 N .m 1.667 s 0.750 J 5 V 5 5 A 1025 kg / m3 5.7875 m / s 1 4
3
An initial A initial A E /A0 = 0.55 assumption assumption is made. made. From the appropriate appropriate BP1 (B4-55) chart (shown above), 0=
0.637, P/D = 0.84, 1/J =1.70 =1.70 were obtained.
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The diameter shall then be: =V =V A /Jn = /Jn = 5.8775 5.87751.70/1.667 = 6.00 m. D As a check for the appropriateness appropriateness of the B4-0.55 B4 -0.55 screw, H = (1-t)/(1-w) =(1-0.12)/(1-0.25) (1-t)/(1-w) =(1-0.12)/(1-0.25) =1.1733
Assuming RR RR = 1.00, QP 0 H RR0.637 1.1733 1.17331.00 = 0.7474 QP T= P E / [V S (1-t)]=P (1-t)]=P D QP /[V S ( 1-t)] = 522.776 kN QP /[V S (1-t)] =
Again, using Keller’s relation:
A E A0
1.3 0.3 Z T = 0.4 and k with k = p0 pv D 2
p0 = patm + g g h = h = 101325 Pa +1025 kg/m39.81 m/s27.00 m. =171711.8 Pa Assuming that the ambient temperature is 25oC, such that p that pv = 3166.6 Pa,
A E A0
1.3 0.3 4 522776 N 0.4 0.6154 2 171711.75 3166 .7 N / m2 6 m.
Which is higher than the assumed A assumed A E /A0=0.55. Using B4-70 chart, chart, 0= 0.675, P/D 0.675, P/D = = 1.00, 1/J = = 1.32 values are obtained.
=V =V A /Jn = /Jn = 5.8775 5.87751.32/1.667 = 4.65 m. D Interpolating, the proper values for the propeller to be installed are: 0=0.654
,
P/D = 0.91
,
D = 5.41m.
CONTROLLABLE-REVERSIBL CONTROLLABL E-REVERSIBLE E PITCH PROPELLERS (CRPP)
As can be seen from the propeller characteristic curves, higher operating speeds require higher pitch ( P/D ( P/D)) ratios, while lower speeds can be attained with lower values of P/D. P/D. Therefore, control control of ship speed within within a range can be made by the change of propeller propeller pitch. For the reverse operation operation of the ship, the propeller blades are are given a reverse pitch while keeping the direction direction of propeller revolutions revolutions unchanged. unchanged.
In most practical practical cases, this is achieved achieved by a hydraulic
mechanism placed placed inside the propeller hub. The hydraulic pitch changing mechanism mechanism can be remotely controlled from the bridge, thereby giving the captain captain of the ship a good control over his vessel. vessel. Many of the high-speed Diesel propelled propelled ships and gas turbine driven ships use this option since the engine is operated at more fuel-efficient high revolutions at lower speed ranges and the need for shaft or engine revolutions reversing mechanisms mechanisms are obviated. For the higher speed ranges beyond a certain certain speed, ship speed is controlled by increasing of shaft revolutions. revolutions. The condition that propeller revolutions is kept constant for a range of speed is advantageous if shaft generators are used to provide electric power. The main disadvantage is that the open water efficiency of CRPP’s are slightly lower due to the use of a non -optimum pitch for most of speed ranges and that the hub is considerably larger, resulting a reduction of blade areas for the same diameter and an increase increase in friction. There is also a restriction on the blade chords, chords, so as not to block the pitch reversing operation.
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Fig. Internal parts of a controllable-reversible controllable-reversible pitch propeller
The preference preference of CRPP’s is increasing increasing despite the higher higher initial cost and mechanical mechanical complexity.
Pitch control
philosophy can be also applied to nozzle, trans-cavitating and super-cavitating propellers. The main disadvantage disadvantage is the increased degree of sophistication and the requirement that the propeller hub is larger in diameter (about 0.3 D, as
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opposed to about 0.2 D in conventional conventional propellers). propellers). Also, propeller chord chord length at its maximum maximum location x’ location x’ = 2r/D cannot be increased above Dx’/Z value value since the blades cannot cannot be reversed if so designed. designed. This requirement requirement sets a limit to the projected area ratio equal to unity.
NONCONVENTIONAL SCREW PROPELLERS
The general theory of screw propellers has been developed for cases other than the optimal conditions that were assumed. Those are the provision of additional thrust, need to operate at very high speeds where the cavitations is unavoidable, conditions to avoid the unevenness of the wake distribution and designs to provide extra economy.
NOZZLE PROPELLERS
Fig. Comparison of nozzle shapes and velocity distributions for accelerating and decelerating nozzles
Nozzles placed around the blade tips can be accelerating nozzles, to provide extra thrust or, decelerating nozzles, to operate the propeller at higher static pressures and thus reducing the probability of cavitation. cavitation. The comparison comparison of two types of nozzles nozzles is shown below.
Kort nozzle propeller
Fig. A Kort nozzle on a tug
The blades of nozzle propellers are broader at the tip giving the blade a paddle-like appearance (“Kaplan” propellers), in contrast with the elliptical-pear elliptical-pear shaped blades of the conventional conventional propellers. They can also be combined combined with rudders rudders to provide better steering properties. The most well-known accelerating accelerating nozzle-propeller nozzle-propeller combination is the Kort nozzle propeller. The extra thrust provided by the nozzle makes it an attractive choice for tugs, river push-boats and trawlers where an extra pulling force at lower speeds speeds is required, as well well as some tankers. tankers. In some Kort nozzles, nozzles, the nozzle body is made made integral with the hull. In some nozzles, Kort nozzle is made to cover only the upper part of the propeller. For vessels that are likely to maneuver often in the astern direction, the nozzle is shaped symmetrically, so as to give a positive thrust in both forward and astern directions. Decelerating nozzles are installed in fast vessels like destroyers, high speed passenger liners, etc. where the cavitations occurrence occurrence is imminent. The action of the nozzle is to reduce r educe the local velocities and hence increase increase the static pressure,
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thereby offsetting the cavitations cavitations inception. However, the nozzle nozzle produces a negative thrust and, being an appendage, appendage, an additional drag. Hence, the thrust demand demand from the propeller is increased to overload the propeller (increase (increase K K T, while forcing the propeller to operate at a lower J lower J value). value). This effect offsets the gains offered offered by the decelerating nozzles nozzles and therefore the usage is limited. Both types of nozzles have the advantage of providing the propeller a protection against striking to the sea bottom or to the banks, from ice damage, or from ropes.
TRANSCAVITATING PROPELLERS
Fig. A Transcavitating Transcavitating propeller
Transcavitating Transcavitating propellers are also used used in high speed craft. They are identified with broad blades, usually numbering in 3 -4, where the expanded area ratio can be more than unity. The blade sections are thin and of round-back round-back type, ensuring an an even distribution of pressure. pressure. Higher values of expanded expanded area ratios reduce the the thrust per blade area and hence give the opportunity to offset the cavitation inception at higher speeds.
SUPERCAVITATING PROPELLERS
In cases where the pressure on the blade backs drop to regimes such that the operating regime of trans-cavitation is exceeded, Supercavitating and ventilated propellers are used. Super cavitation is the case where the entire entire blade back is covered with a cavitation cavitation sheet. By letting the cavity sheet to cover cover the entire blade back back (suction side) surface, surface, detrimental effects effects of cavitations are avoided. However, since the pressure pressure drops on the back does not produce any further forward thrust in this case, the face (pressure side) of the blades are required to provide thrust. The blade profile is designed to have a wedge-shaped profile to ensure this condition.
Fig. A Supercavitating propeller in a cavitations tunnel
Fig. A Supercavitating propeller blade section
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VENTILATED VENTILAT ED (SURFACE-PIERC (SURFACE-PIERCING) ING) PROPELLERS
In propellers operating with high velocities on their back and close to the free surface of water, some air is sucked to the low pressure pressure region. This air-cavity air-cavity performs the same same function as the Super-cavitation Super-cavitation cavity cavity for the propeller. In practice, such such propellers are are made to operate operate with only the lower lower portion of the propeller in water, thus it is only the lower portion producing the required thrust.
They are placed behind the transom of high speed, planning boats.
This
configuration enables the elimination of underwater appendages: appendages: shaft, shaft struts, rudder and most of the t he propeller itself. Also by the lessening of draft-related restrictions, propeller diameters can be made larger, compensating the loss of the thrust provided by the unimmersed part of the propeller. The drive is steerable, and has the function of a rudder.
TANDEM PROPELLERS
In cases where the radius of propeller is limited by draught or similar conditions, one remedy is the use of tandem propellers. More than one (usually two) sets of screws screws are placed on the same shaft, shaft, one after the other, both providing
some thrust. The propeller in behind behind should have a larger pitch and should be slightly smaller smaller in diameter since it it operates in the wake of the forward forward one. The energy of rotation of the slipstream slipstream of the propeller will be larger in this case. The thrust demand from the propeller is thus divided into two propellers, enabling the use of smaller diameters. diameters.
Fig. Tandem propellers on a model
65
CONTRA-ROTATING PROPELLERS
Contra-rotating propellers are designed to use use the rotational energy energy in the slipstream of propellers. Two tandem
propellers are installed on two coaxial shafts, rotating in opposite directions. Since the slipstream rotations of two propellers are also in opposite directions, the rotation of the first one in fore is cancelled by the second one astern, ther e shall not be a significant rotation in the ultimate wake in the ideal case, and hence higher efficiencies – efficiencies – about about 6 % more than that of an equivalent conventional conventional screw propeller- can be attained with lesser diameters. This configuration has been been widely used in torpedoes in the past. Their application to large ships has caused caused problems related to bearings and reduction gears. gears. However, they have have found a good application in small boats.
Fig. An application of contra-rotating propeller
Fig. A contra-rotating propeller on a large ship
Volvo D6-310/DP engine package for small fast craft
OVERLAPPING PROPELLERS
Overlapping propellers involve the use of two propellers where where the propeller disc areas areas are designed to overlap. overlap. The
two propellers rotate in the same direction, letting the slipstream induced velocities of one in front being used by the one in behind.
Fig. Overlapping propellers
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GRIMM VANE WHEEL
Grimm vane wheel has a propeller, usually with 4-5 blades coupled to an engine and a freely-rotating wheel right astern
with a larger number of blades and concentric concentric with the main propeller. The freely rotating wheel wheel (vane) has a 20 % larger diameter. The inner parts of the freely-rotating freely-rotating wheel serve as a turbine, turbine, gaining the energy of rotational rotational and axial induced velocities. The recovered energy energy is used to provide an extra thrust, more on the tips of the blade.
Fig. Grimm vane wheel
Some recent recent Grimm vane wheel propeller propeller installations have the freely rotating vane vane installed on the rudder horn. This configuration eliminates the problems related to mounting the two screws on the same shaft.
BLADE TIP VORTEX REDUCED PROPELLERS
Fig. Tip-vortex reduced propellers (CLT- left, Kappel propeller- right) The vortices shed by the propeller are concentrated at the blade tips, as witnessed by the fact that the first stage of cavitation cavitation is the blade tip cavitations. cavitations. If the propeller tips are shaped to lessen this loss of energy, gains in propeller efficiency shall be obtained. Various designs have been made to obtain this- ring-nozzle propellers, tip-vortex free (TVF) propellers, contracted and loaded tip (CLT) propellers, Kappel propeller are some. Energy savings of about 5% have been reported.
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PROPELLERS WITH BOSS CAP FINS (PBCF PROPELLERS) PBCF propellers employ a similar idea to blade tip vortex reduced propellers, this time to reduce the blade root (or hub)
vortex. A series of small blades, also aerofoil aerofoil in shape and having the same number of blades as the main propeller are placed about the propeller propeller hub, creating creating a vortex system opposite to that of the hub vortex while creating creating a forward thrust. This concept is also reported to attain efficiency increases increases of about 4-5%. 4 -5%.
Fig. PBCF fitted on a propeller
PINNATE PROPELLER
The wake field field behind the ship is nonuniform nonuniform both in radial and in tangential directions. directions. Radial variation can can be accounted by changing changing the propeller blade pitch in radial direction. However, as the propeller propeller rotates, a point on the propeller experiences experiences different values of incident axial velocities. In a single-screw single-screw vessel, at the 12 o’clock position the axial velocity is low, increasing ar 3 o’clock and 9 o’clock positions and again reducing to lower values at 6 o’clock position. To accommodate accommodate for this change in i n V A, the pitch of the blade is made to lessen as it passes through the 12 o’clock position and increase thereafter wards, reaching to its maximum at the 3/9 o’clock positions by an internal mechanism.
Fig. Distribution of wake coefficient on the propeller disc area
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PROPELLERS WITH PRE-AND POST-SWIRL VANES
The fact that some of the energy absorbed by the propeller is lost by slipstream rotation has led researchers to improve fins. The placement of rudder efficiency by straightening the flow in the propeller slipstream using post-swirl vanes or fins
behind the propeller propeller also serves serves for the same same purpose.
Pre-Swirl Vanes or Grothues Spoilers placed before the propeller give the velocity field ahead of the propeller a pre-
rotation that cancels the slipstream rotation, also preventing the so-called so-called “bilge vortex” which greatly increases the ship’s form factor, k (i.e., (i.e., its viscous form drag).
Fig. A Grothues spoiler
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PRE-PROPELLER STATOR
Fig. A pre-propeller stator
Pre-propeller stators provide a favorable, favorable, non-rotating flow field to t o the propeller, which compensates the penalty of extra-drag.
ASYMMETRIC STERN FORMS
Fig. An asymmetric stern form
Asymmetric Asymmetric stern forms have a V-shaped after-body after-body on one side and a U- shaped after-body on the other. The resulting inflow to the propeller is a reduced tendency for bilge-vortex generation on the side with V-shaped form and a prerotation before the propeller. These two effects effects add up to improve the propulsive performance, performance, meriting in powering reductions in the 5-10% range.
WAKE EQUALIZING DUCTS
Wake-equalizing ducts (WED) are used to concentrate the flow to the upper parts of the propeller disc to equalize the
wake. This results in the reduction of bilge vortices vortices and more more efficient operation of the propeller. Examples Examples are the Schneekluth nozzle and Mitsui duct.
Fig. Stern flow with and without WED (Left) and a WED on a ship
POST-PROPELLER STATORS
Another way of of improving propeller efficiency efficiency is to prevent the rotation rotation of post-propeller flow in the slipstram. slipstram. It has been noted that ships with rudders in the propeller race have better efficiency. Despite the added drag of such devices, post-propeller devices devices have have improved efficiencies. efficiencies.
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One of the most widely accepted post-propeller stator types is the concept of thrust fin, which generate some some thrust using the axial and rotational energy of the propeller slipstream. slipstream.
Fig. Post-propeller fins
Rudder horns with twisted leading edges have the same effect as a thrust fin.
Such a configuration also reduces reduces the the susceptibility susceptibility to rudder
cavitation.
RUDDER BULBS
Apart from the axial and rotational velocity components of the propeller slipstream, there is also a radial component which is caused by the slipstream contraction. contraction. Rudder bulbs act to reduce reduce the radial component component of the propeller slipstream.
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STEERABLE PROPELLERS AND PODDED PROPELLERS
Steerable propellers are used in small boats- with power ranges of less than 1 kW ( ( 1.3 HP) to several several hundred kilowatts
per shaft. The engine and the propeller are made in one unit in most cases. Removable Removable units are preferred in smaller craft, while a fixed engine is used in larger larger applications. The propeller drive assembly assembly is mounted on the stern transom and also performs as the rudder.
Fig. Steerable propeller
Podded propulsors are produced for larger vessels with higher power ranges. They give the designer an appreciable
flexibility by removing restrictions related related to draft and propeller placement. Usually the pods are given the option for a 360o turn- called “azimuthing propellers” and also perform as the rudder. Propellers are installed installed at locations where where thrust deduction and uneven wake are eliminated. eliminated. Two propellers (usually contrarotating) contrarotating) can be mounted on either side of the pod- one in the “pulling” and one in the “pushing” mode. mode. In single propeller per ship usage, the propellers propellers are mounted as forward forward looking (in the “pull” mode) to enable enable operation in a relatively relatively even wake possible. possible.
Power
transmission to the propeller shaft can be mechanical, mechanical, hydraulic and electrical, thanks to the axial flux-permanent magnet electric motor technology. technology. Propeller blades can can also be placed in a nozzle. nozzle.
Fig. Podded propellers on a ship
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Fig. An Azipod system integrated with a single-screw ship- creating a pair of counter rotating propellers
HIGHLY SKEWED PROPELLERS
Highly skewed skewed propellers are being being widely used in many many applications. They make the operation of a propeller propeller at locations where uneven uneven wake distributions are present. present. The main advantages advantages of high skew angles are the reduction in unsteady bearing forces, reduction in unsteady pressure forces and increased cavitations inception speeds, i.e., reduced susceptibility to cavitations. The only known disadvantages disadvantages are related to strength considerations. considerations.
Fig. Propeller outlines with 0o, 360, 72o and 1080 skew
Highly skewed propellers are used in a wide range of applications ranging from large tankers to submarines.
SYSTEMS OTHER THAN SCREW PROPELLERS
CYCLOIDAL PROPELLERS
Cycloidal propellers have vertical vertical shafts and vertically extending blades mounted on a rotating disk. The blades are also of round back type, as most of the marine propellers are and are mounted on the bottom part of the hull, not necessarily necessarily at the stern. Their usage obviates the use of a separate rudder. In other words, they are used both as rudders and propellers.
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The angles of attack of the blades to the flow are changed by a pitch-control mechanism to adjust the resultant thrust of the blades to the desired direction. Two types of Cycloidal propellers exist: Kirsten-Boeing and Voith Schneider propellers.
Fig. Kirsten-Boeing propellers (left) and Voith-Schneider propellers (right)
In Kirsten-Boeing propellers, each blade makes one half turn (180o) about its axis for one full revolution (360o turn) of the propeller. In Voith-Schneider propellers, each each blade makes makes one full turn for each each revolution of the propeller. If the vessel is moving on a straight course, the path of each of the blades is epicycloidal in shape, hence giving the n ame “Cycloidal propeller”.
Fig. Arrangement Arrangement of blades in a VoithSchneider propeller
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WATER-JET PROPULSION
Water-jets are the propulsors for smaller high speed craft, alternative to the use of Supercavitating and surface piercing
propellers. By making the water-jet steerable, they give the ship an extra maneuverability. Additionally, if the water-jet is reversed by a scoop, a very effective, but simple reversing system is acquired.
Fig. Main parts of a water-jet propulsion unit
The analysis of a water-jet water-jet propulsion unit is made by the momentum momentum theory, similar to that of propellers. propellers. By taking two control surfaces, one sufficiently ahead and one sufficiently behind the water-jet unit, and neglecting the change of vertical location of water mass, forward thrust provided by the jet becomes:
T
m V j Vs
Where V S and V j are the speeds of the ship and the water-jet for a fixed observer. Useful work done by the water-jet unit:
PU
T VS mQV mQVS V j V S
The amount of kinetic energy lost in discharge becomes: becomes:
KE Loss
12 m V j V s
2
Efficiency of water-jet propulsion unit becomes:
PU PU
KELoss
m V j m V j
V s
Vs 12 m V j VS
2
2V S Vj
V S
As it becomes obvious from this last equation, for high efficiencies ship speed should approach to the speed of the water jet. This is possible by either a very fast ship or a slow water-jet. In this latter case, the thrust t hrust obtained shall be small unless the mass mass flow rate is large. large. This in turn is obtained by a large diameter diameter water-jet. A large diameter diameter water-jet is possi ble ble by placing the unit outside the hull. This is called a “pump-jet”. Pump-jet Pump-jet concept is now used in submarine propulsion.
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Fig. Water-jets on a ship
Fig. Water-jet operation 1- Forward, 2- Reverse
AIRSCREWS
Airscrews, similar to that used in aircraft, are used in hovercraft, wing in ground effect vehicles and in vessels that operate in very shallow waters and marshes. Analysis of airscrew airscrew (or air-jet) propulsion propulsion is the same same as screw propellers, the main problem being the low density of air. For obtaining large flow rates, large diameter airscrews and/or high flow velocities should be used, both resulting in safety and sound problems.
Therefore, those
systems are not used in vehicles that have to operate near urban areas.
PADDLE WHEEL PROPULSION
Fig. Paddle wheels with feathering arrangement arrangement
Side and stern paddles were widely used in the 19 th century, but their usage declined after after the introduction introduction of more convenient convenient screw screw propellers. propellers.
In
principle, their operation relies on the drag forces experienced by a series of paddles mounted on a wheel. By arranging the paddles to “feather”, “feather”, i.e., ensuring entrance and exit into the water so as to obtain minimum frontal area, optimization of efficiency efficiency has has been possible. possible. Usually, best best efficiencies are obtained by large sized sized paddle wheels. wheels. This requires slow moving moving engines. Paddles can be either either stern or side mounted. mounted. Since their operation operation is closely related to the location l ocation of free water surface, their performance performance drops rapidly in heavy seas and their their operation is optimum only at a certain certain draft. draft.
This
requires high amounts of ballasting when the ship is not laden, thus is uneconomic for cargo vessels. Paddles impose an extra width on the beam of the ship, which is also a restriction on t heir application.
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SCULLING (FISHTAIL) PROPULSION
Fig. Fishtail propulsion
Sculling propulsion is the propulsive means by which many species of fish, as well as cetaceans cetaceans (whales and dolphins) propel themselves themselves in water. water.
Also, it is used used by
swimmers using using fins. It is based upon the creation creation of a series series of vortices behind behind a “tail”, created by pressure differences on the two sides of the tail, where the vortices induce a backward stream of flow. The momentum change caused caused by that flow creates a forward thrust. This swimming mode has been been investigated by researchers researchers studying the means of ship propulsion. It has also been applied in small boats.
MAGNETO-HYDRODYNAMIC MAGNETO-HYDR ODYNAMIC (MHD) SHIP PROPULSION P ROPULSION
Magneto-hydrodynamic ship propulsion is simple in principle- it depends on the so-called Lorentz force of the electrical theory. If an electric current, expressed as the vector J is passed through a conducting fluid, in a magnetic induction
field of B , a body force of F (force per unit volume) is created on the fluid particles, expressed by the equation:
F J B For the maximum value of this body force, the angle between the current and the magnetic induction fields should be 90 degrees. The body force can can be used to create a displacement displacement of the mass of the fluid, so as to pump pump the electrically conductive liquid or to create a forward thrust for a marine vessel. In spite of its simplicity and its advantages of not requiring any moving parts, this concept has no practical use in marine propulsion so far. However, its advantages advantages have have led the researchers researchers worldwide worldwide to work on this concept. Very high values values of currents and/or magnetic magnetic fields pose a challenge challenge for this technology technology to develop. The practical applications applications shall be possible if the technology technology of superconductivity superconductivity at at practically achievable achievable temperatures temperatures becomes becomes available. available.
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PROPELLER MATERIALS
A propeller has to endure the high propulsive thrust loads of the ship as it operates. Therefore, it has to be strong, nondeformable and be suitable to work in the corrosive marine environment. environment. Several materials materials have been used to fulfill those tasks. Aluminum: Aluminum has an allowable maximum tensile strength of up to 0.34 MPa, and is by far the most popular
material used for outboards and stern drive recreational boat propellers. It is inexpensive, has good strength and is easily repaired. Stainless Steel: Stainless steel, both chromium chromium and austenitic (nickel) type, has a tensile strength of up to 0.55 MPa. Due
to their higher strength, stainless steel propellers can be made thinner thinner for better efficiency. However, the repair cost of stainless steel propellers is high. Propellers of icebreakers and some high speed vessels (Transcavitating(Transcavitating- Supercavitatingventilated propellers) are made of stainless steel. Plastic and Composite Materials: Plastic and composite material propellers flex considerably under high loads and
cannot be repaired if damaged. Use of advanced composite materials is expanding for various vessels, from small boats to large merchant and warships. They offer the advantage of having cavitations damage resistance, they are lightweight and silent. Manganese Bronze : Manganese bronze has a tensile strength of up to 0.44 MPa and is the most widely used material for
all ship types and sizes. Manganese bronze propellers can cause corrosion on steel hull surfaces in seawater. Therefore, the use of cathodic protection is necessary necessary for almost all ships using bronze propellers. Nibral (Nickel, Aluminum, and Bronze): Nibral has a tensile strength of up to 0.65 MPa and is very durable. Nibral is
typically used on high performance military and pleasure craft with high horsepower and high rpm's. Cast iron:
Cast iron, with gray, gray, nodular and spheroidal spheroidal graphite types are also also used in propeller propeller production for
applications like colliers and smaller smaller ore carriers. Their strength is about half that of manganese bronze. bronze.
PROPELLER ROUGHNESS
Fig. The Rupert gauge
One of the as pects of maintaining the smoothness of ship‘s underwater surfaces, often overlooked is the maintenance maintenance of the smoothness smoothness of propeller propeller surfaces. surfaces. Maintenance Maintenance of propeller smoothness also has an importance on fuel economy. economy.
Manufacturers Manufacturers deliver
propellers polished up to ISO Class S requirements. requirements. However, propellers can roughen in service. Propeller roughness can be the result of biofouling (growth of plant and animal forms on propeller surface) or from erosion of blades, mainly due to cavitations, but also due to mechanical mechanical damage due to cable chaffing, grounding, sea sea ice, etc. In the past, a practical method method for the assessment assessment of propeller roughness has been been developed- the Rupert Rupert gauge. It is a comparison test, with where where an accurate accurate comparison can be made made by finger nails.
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Rupert gauge has six surfaces- from A representing a smooth propeller blade surface to F, with a substantial roughness. Professional “propeller “propeller polishing teams” can perform polishing either when t he ship is dry-docked dry-docked or at port, using divers. By polishing the propeller blades up to Rupert A standard, substantial fuel savings can be achieved.
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CHAPTER IV PROPELLER-HULL-ENGINE PROPELLER-HULL -ENGINE INTERAC INTERACTION TION
One of the most important issues of ship design is the selection of a proper propulsion system- i.e., the best combination of engine, reduction gear and propeller, to supply the required thrust at the best optimum torque and engine revolutions. Also, the engine selection process should include the extra power requirement due to in-service conditions: sea state, hull and propeller roughening and fouling, towing, etc. A ship designer has a number of choices for engine, each each with its relative merits and drawbacks. Like all other phases of the design process, selection selection of the proper engine system is mainly mainly a compromise. Presently available available technologies for designers are: 1. High and medium speed Diesel engines 2. Directly coupled low speed Diesel engines 3. Steam turbines (both fossil and nuclear fueled) 4. Gas turbines 5. Electric drives, where the prime mover (electric generation) can be any of the above. Electric power can both be alternating or direct current type. 6. Combinations of gas turbines with Diesel, steam, gas turbines and electric drives (CODOG, CODAG, COGOG, CODAD, COSAG, COGAS, CODLAG, CONAG). 7. Novel power systems systems such as solar panels, panels, fuel cells, cells, Stirling engines, etc. etc.
The use of wind power, which is historically the oldest of non-human power propulsion systems can be used together with any of those t hose propulsion systems.
TORQUE-ENGINE SPEED RELATIONSHIP FOR THREE PRINCIPAL PROPULSION ENGINE TYPES
The engine has to provide a certain torque to the shaft at a given number of revolutions. All engines have different shaft shaft torque-engine speed characteristics. characteristics.
Fig. Torque-engine speed relationship for three principal propulsion engine types
80
As can be seen, the Diesel engine provides an almost constant torque for a given fuel setting over the operating range, while steam turbine systems have decreasing and gas turbine systems have increasing torque characteristics as the engine revolutions increase. increase. Electric propulsion propulsion motors have characteristics characteristics depending depending on the type of windings windings used. Following discussion will mainly cover Diesel engines; however, same logic can be applied to other propulsors as well.
The lower speed (propeller revolutions per minute) of a Diesel engine is mainly limited by the so-called “smoke condition”, i.e., by the lowest engine speed speed at which proper combustion combustion can be maintained. maintained. Upper speed is limited by the sufficiency of fresh intake air, cooling and lubricating system performance.
The power at which the engine shall operate safely for an unlimited time is called “Maximum continuous rating”, MCR. *** MCR. *** Diesel engine shaft output torque is directly related to the mean effective pressure, which is a function of the pressure-volume ( p-v) p-v) relationship during a power cycle. This p-v relationship and thus the shaft output torque is mainly determined by the amount of fuel injected per cycle, and relationship thus by increasing the fuel setting one gets different levels of mean effective pressure.
ENGINE SPEED (n) AND POWER (P)
Since engine output (“brake”) power is related to torque by the relationship PB = Q n, power output for different levels of fuel setting (different mean effective pressures) are shown as follows:
Upper limit of operation 110% MCR
P
, r e w o P
Maximum continuous rating (MCR) Lower limit of operation (”Smoke limit”)
75%MCR
50% MCR
Area of operation Iddling
Engine speed, n
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Within the operational speeds of a ship equipped with a fixed pitch propeller, the “advance coefficient”, coefficient”, J of the propeller ) of the propeller remains constant. remains constant; this means that the speed of advance (V a constant. Also, the wake coefficient coefficient a
of the ship is also constant during this range, and therefore propeller rotational speed is directly proportional to the ship speed. If the engine is directly connected connected to the propeller or through a gearbox with a constant gear ratio, the power power taken from the engine is directly proportional to the third power of t he ship speed and hence propeller revolutions, n : 3 3 1 V D SC 3 3 1 1 3 S C P P V SC J n 3 2 2 2 1 w 1 w a
B
P E
P
s
T
T
P
T
P
In this last equation, all the terms contained in the square brackets are assumed to be constant for a fixed pitch propeller. Therefore,
The engine power shall also be a function function of the third power of the engine speed, n. This is known as the “propeller law”. When the two relations describing the engine (brake) power versus propeller revolutions are plotted on the same graph ( P P B versus n), it ), it is apparent that they shall intersect at the origin (no engine revolutions) and at a given point. This point is the “operation point” of point” of the engine. Operating power can be determined for a number of fuel settings and proper propeller revolutions can be predicted from the propeller curve- engine set of curves data.
The ship’s resistance can increase by a number of reasons:
Increased hull fouling
Heavy weather
Towing of another vessel
Changes in draught, etc.
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This results with a different propeller curve, corresponding to a higher C T propeller speed and and the engine engine power T. Both the propeller shall be involuntarily reduced. In order to compensate, the engine fuel setting should be increased. increased.
In order to take account the in-service conditions, the engines are selected to provide the required speed: In calm weather; clean hull; clean propeller conditions typically at 85% MCR (i.e., at the power to provide 85% of the maximum continuous power), where also maintaining the maximum fuel efficiency (i.e., lowest sfc) . The 15% discrepancy is called the “service margin”. When margin”. When selecting the engine, specific fuel consumption at a given brake power (bsfc) is also taken account in order to provide fuel efficiency. efficiency.
In ships equipped with controllable-reversible pitch propellers, same considerations apply, this time it is the P/D ratio (which is closely related to the advance coefficient J at at low propeller loadings) that is changed to change the ship speed.
1 D 3 SC T 3 3 1 3 P B P P E P V s SC T P n J 3 2 2 1 w 83
In such ships, the engine is operated at constant revolutions within the range of economic operation, while the pitch angle of the propeller is altered to achieve the speed control.
Engine Power, P
B
P/D = 1.2 P/D = 1.0 P/D = 0.8
Propeller revolutions, n
It should be noted that increasing the pitch increases the ship speed, speed, while also increasing the power requirement. requirement. Similarly, in many of the merchant ships where the service speed and hence propeller revolutions are constant, main engine power can be used to generate generate electricity, via a shaft-driven generator. generator. This power takeoff shall, in general, general, be constant independent independent of speed, hull resistance, resistance, etc. Operating point can be obtained obtained by shifting the propeller curve vertically upwards by the power absorbed by the generator.
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EXAMPLE
Question-1
A VLCC tanker has a propeller designed to operate with J with J = = 0.70. The ship’s average average wake wake coefficient coefficient is w = 0.35 and thrust deduction coefficient t =0.05. =0.05. The ship is equipped with a two stroke stroke low speed Diesel Diesel engine with 10 cylinders, cylinders, bore = 0.80 m, stroke length = 2.8 m, brake mean effective pressure = 1.6 MPa, at MCR. The ship has a wetted surface area of 32600 m2 and total resistance coefficient coefficient of 0.0023. Find the a) Trial propeller revolutions, b) Ship speed, c) Engine power .
Solution-1
Engine
P B
LANn 1.6 106 N / m 2 2.8m p B LANn
4
cyl n 2.2519 107 n 0.8m2 10cyl
Hull-propeller combination
P E 12 V S 3 SC T P B
V S
3 V S SC T 1 t 2 tr o RR 1 w
JnD Jn D
1 w 1025
kg 3
P B
J 3 D 3 SC T
2
2 tr o RR 1 w 1 t
n3
0.7 3 7m 3 32600m 2 0.0023
m n3 2 2 0.99 0.50 1.0 1 0.35 1 0.05
P B
P B
2.2755107 n3
Equating the two functions for P for P B, B,
a) Propeller revolutions
n
2.2519 10 7 2.2755 10
7
689 rpm 0.9948 revs / s 59.689
b) Ship speed
V s
JnD
1 w
0.7 0.9948 7 1 .35
7.499 499 m / s 14.58 knts
c) Engine power
2.2519107n =22.519 =22.5190.9948 = 22.402 MW P B = 2.2519
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CHAPTER V ESTIMATION OF THE FUEL CONSUMPTION OF SHIPS
The effective power of a ship was defined previously as the power to overcome the drag force acting on t he hull resisting the forward motion:
P E RT V S
1
V s3 SC T 2
The total drag force acting on the hull with a wetted surface area can be expressed as:
1
R T V s2 SC T 2 Where: : Ship speed in metres/second metres/second
V s s
: Mass density of seawater seawater (assumed to be 1025 kg/m3 for standard seawater) seawater) S
: Wetted surface area of the hull, im square metres
C T T
: Total dimensionless dimensionless drag coefficient coefficient of hull hull (a typical value value for a ship with clean clean hull is 0.0020)
By geometrical considerations, considerations, wetted surface area of a ship is assumed to be related to the displacement displacement volume by:
S k 1 2 / 3 For the standard seawater, it can also be written as:
S k 2 2 / 3 Where:
: is the displacement tonnage. tonnage.
Therefore,
P E
1 2 / 3V 3 k C s 2 T 2
The brake power demand from the engine of the ship will be:
P B
P E
P D P B
P E P D
P E P E P D
P E QPC TR
P D P B Or,
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P B
k 2 C T 2 / 3 3 V s 2 QPC TR
The first term in parenthesis is assumed to be constant for a given ship at moderate operating conditions. Therefore, Therefore, using the convenient units (kW or HP for power, tons for displacement displacement and knots for ship speed),
P B
2 / 3V S 3 C Adm
Where:
C Adm Adm
: is
the so-called Admiralty constant.
EXAMPLE PROBLEM
Question
A ship of 15000 tons displacement displacement has a speed of 14 knots. If the Admiralty constant constant of this ship is 410 (based on kW), Find the power ( P P B) developed by the engine.
Solution
a) The power (P ) developed by the engine B B
P B
2 / 3V S 3 C Adm
150002 / 3 14 3 410
4070 kW .
) ESTIMATION OF FUEL CONSUMPTION ( m
P m bsfc B
bsfc C Adm
2 / 3V s3
Fuel consumption per day ( FCPD) FCPD) shall be:
bsfc 2 / 3 3 V s FCPD FCPD 24 C Adm 87
The first term in parenthesis is named as the “fuel coefficient” ( FC ): ):
FCPD FCPD FC 2 / 3V s3 For a constant fuel coefficient, where the Admiralty coefficient and the specific fuel consumption of the engine are assumed to be constants,
FC
2 / 3 V s3 FCPD FCPD
Two different voyage conditions of the same ship with different weights and speeds can be related in terms of fuel consumption characteristics as:
FC
21 / 3V S 31 FCPD1
22/ 3V S 32 FCPD2
Or,
FCPD1 FCPD2
1 2
2/3
V 1 V 2
3
VOYAGE FUEL CONSUMPTION
Fuel consumption per voyage (Voyage fuel consumption) is:
VFC VFC FCPD FCPD Num Number ber of days at sea If the distance to be made good during the voyage is L nautical miles between the ports of departure and arrival, and with a constant or average speed of voyage, V s : Number Number of days at sea sea
L
24 V S
Total amount of fuel to be consumed at sea during the voyage is:
VFC FCPD
L
24 V S
FC 2 / 3V S 3
L
24 V S
k 3 FC 2 / 3V S 2 L
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Therefore, voyage fuel consumptions of two voyages, each with a given displacement, speed and with a given distance can be compared as:
1 VFC VFC 2 2 VFC VFC 1
2/3
2
V L 1 1 V 2 L2
EXAMPLES
Question-1
A vessel with a displacement of 12250 tons consumes 290 tons of fuel when cruising at a speed of 15 knots on a voyage of 2850 nautical miles. Estimate Estimate the quantity of fuel to t o be consumed by the same ship for a voyage of 1800 nautical miles at a speed of 13 knots and at a displacement of 14200 tons.
Solution-1
1 VFC 2 2 VFC 1
2/3
2
V L 1 1 V 2 L2
1 = 12250 tons 2 = 14200 tons V1= 15 knots
V2 = 13 knots
L1 = 2850 n.m.
L2 = 1800 n.m.
VFC1 = 290 tons
VFC2 = ?
290 tons fuel VFC 2
12250 tons tons 14200
2/3
2
15 knots 2850 n.m. knots 13 1800 n.m.
= 151.8 tons fuel VF C 2 2 =
Question-2
A ship cruising with a full load displacement of 15000 tons and at a speed of 12 knots consumes 15 tons of fuel per day. After giving her cargo, she is ballasted to a displacement displacement of 6000 tons. The captain reduces the speed speed to 11 knots to save fuel. How much fuel does the the ship consume per day day in the ballasted condition?
Solution-2
FCPD FCPD1 FCPD FCPD2 1 = 15000 tons
1 2
2/3
V 1 V 2
3
2 = 6000 tons
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V 1 = 12 knots
V 2 = 11 knots
FCPD1 = 15 tons/day
FCPD2 = ?
15 tons / day FCPD FCPD2
15000 tons tons 6000
2/3
12 knots knots 11
3
= 6.27 tons/day FCPD 2 2 =
Question-3
A twin screw ship cruises with 11.5 knots at an optimum setting of engine. As a result of an engine failure, she has to go to a shipyard for repairs. The failed engine is disengaged disengaged from the propeller shaft and the propeller propeller is set to freely windmill. With the same engine setting setting on the unfailed engine and with the same displacement, displacement, how much speed speed does she make?
Solution-3
For a given ship at a given condition,
P B
k V 3
or, 3
V P k 1 2 V 2 P 1
or,
P V2 V 1 2 P 1
1
3
For one engine operating, P operating, P 2 =1/2 P 1 1/3 V 2 2 11.5 0.5 = 9.1 knots
Question-4
A 15 year old Panamax bulk carrier ( ( = 58000 t, 46000 DWT, L BP = 193 m, B = 32.2 m, T= 11.2 m, C B = 0.82) is going to be dry-docked. dry-docked. A roughness survey survey conducted conducted reveals that she has an an average average hull roughness of 480 microns. microns. The shipyard proposes to apply a dry-docking procedure involving shot-blasting of the entire underwater hull and re-paint it with a coating system costing 15 USD/m2, with a guarantee that the ship shall maintain an underwater roughness of 200 microns over the next dry-docking period. Make a feasibility assessment of the proposal assuming: a.
The time till the next dry-docking is 24 months,
b.
She is laden with an average of 75% cargo capacity by weight over the operating period,
c.
The service speed is 15.5 knots, 85% MCR, where the MCR rating is 11000 MW,
d.
She is at sea 260 days per year,
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e.
Engine specific fuel consumption is 170 gr/kW.hr,
f.
The bunker used is IFO 380, costing about 600 USD/ton
Make use of the formula for the t he wetted hull surface:
S 1.7 LT
T
Solution-4
The first step is the estimation of hull wetted surface:
S 1.7 LT
T
1.7 LT C B LB
1.7 193 m 11.2 m 0.82 193m 32.2m 8771 m2 However, for a 75% cargo, DWT = (1 – (1 – 0.75) 0.75) DWT = 0.25 0.2546000 = 11500 t
’ = - DWT = 58500 – 58500 – 11500 11500 = 47000 t
Service displacement tonnage:
Service wetted surface area:
S
S
2 3
2 3
47000 S 8771 7580m2 58500 Hull resistance elements:
V s = 15.5 knts = 15.5 nm/h 1852 m/s /3600 s/h = 7.974 m/s Re = V s L/ L/ = 7.974 m/s 193 m/ 1.188 1.18810-6 m2/s = 1.295 109 C F = 0.075 0.075(log Re-2)-2 = 0.001483
k 0.095
25.6 C B
L B
2
B T
0.095
25.6 0.82
193
2
32.2
0.25
32.2 11.2
C v = (1 + k) C F = 1.25 0.001483 = 0.1854
Other components of viscous resistance:
C app app = 0.0002 (Assumed to be 10% of C v), CA = 0.0004
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h 44 10 Re L 1 3
C
F
1 3
0.125 10 3
480 10 6 10 44 9 193 1.295 10 1 3
1 3
C 0.000317
for h
480
C 0.000167
for h
200
F
F
0.125 10 3
For 480 micron roughness:
C T = C W + C v + C A + C app T = W + app +C F C T = C W + 0.001854 + 0.00040 + 0.0002 +0.000317 T = W + C T = C W + 0.002771 T = W + Assuming C V = 0.80 (typical for a bulk bul k carrier), C T = 0.003464 V /C T T =
Effective power:
P E
12 V 3 SC s
T
12 1025kg / m3 7.974 m / s 3 7580 0.003464 6.823 106W 6.823MW Assuming an overall propulsive efficiency P (from engine outlet to sea) of 0.75, P B =P E /P = 6.823/0.75 =9.097 MW
The fuel consumption with 480 microns roughness:
FC = sfc = sfc P B 24 h/day 260 days/yr 2 yrs = 0.170 kg/kW.h kg/kW.h9097 kW kW24 h/day h/day260 days/yr 2 yrs = 19.300 19.300106 kg = 19300 tons
For the 200 microns roughness (per the shipyard’s proposal):
C T,200 (C F, -C F,200 ) = ) = 0.003464 – 0.003464 – (0.000317 – (0.000317 – 0.000167) 0.000167) = 0.003314 0.003314 T,480 – ( T,200 = C T,480 F, 480 -
P E
12 V 3 SC s
T
12 1025kg / m3 7.974 m / s 3 7580 0.003314 6.527 106 W 6.527MW P B =P E /P = 6.527/0.75 =8.703 MW
Fuel consumption with 200 microns roughness:
FC = sfc = sfc P B 24 h/day 260 days/yr 2 yrs = 0.170 kg/kW.h kg/kW.h8703 kW kW24 h/day h/day260 days/yr 2 yrs = 18.464 18.464106 kg = 18464 tons
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Difference between between two roughnesses = 19300-18646 = 654 tons In terms of money: 836 tons 600 USD/t = 392400 USD
Cost of painting:
If the entire bottom is painted, including the “ bottom” bottom” area S S 8771 + 200 2 =9171 m2 Cost = 9171 m2 15 USD/m2 = 137565 USD
Savings in fuel bill by the painting:
392400 -137565 = 254835 USD (Approx. twice the cost)
Question-5
A 318,000 DWT tanker has a displacement displacement of 390,000 tons (laden condition) and and 218,000 tons (ballast). Her service speed is 17 knts, achieved by an engine of 27000 kW power at service in the laden condition. She uses the same service speed for ballasted condition. Her electric Diesel generator generator provides 800 kW, unchanged with speed, and uses marine Diesel oil (MDO). She is engaged in a trade route route of 7000 nautical miles, and the time she spends at port is 7 days for a round trip. The fuel prices are 600 USD/ton USD/ton for HFO, HFO, and 1000 USD/ton for MDO. The total costs costs of ship ship except the fuel amount to 6,000,000 USD/year, unchanged unchanged with operating condition. Freight rate is 12 USD/ton for this route. By a sudden crisis in world politics, the oil prices escalate escalate and HFO costs 1100 USD/ton and MDO 1850 USD/ton. USD/ton. The shipping company has has made a decision to reduce the service service speed of the fleet from 17 knots knots to 12.5 knots. Assess the economic consequences of this decision, assuming that the freight rate and other costs are unchanged. Assume that the fuel carried is 95% of the DWT and sfc
main engine
= 0.176 kg/kW.h, sfc
generator =
200 gr/kW.h, unchanged for the practical
speed range. Assume no fuel fuel is consumed while in port.
Solution-5
Power requirement for the ballast condition: 2 3
2
218 10 3 0.6786 b 3 P l l 390 10
P b
3
;
P b
0.6786 27000kW 18321kW
Before the price price escalation: escalation:
Fuel consumption per hour: = = ( P×sfc×HFO P×sfc×HFO price) price) main + ( P×sfc×MDO P×sfc×MDO price) price)gen F C
= 27000kW×0.176 kg/kW.h ×10-3 t/kg×600 USD/t +800×0.2×10-3×1000 = 3011 USD/h (laden) = 18321 ×0.176×10-3×600+800×0.2×10-3×1000 = 2095 USD/h (ballast)
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One leg of voyage:
7000nm/17 knts = 412 hrs = 17. 2 days (take 18 days, incl. delays)
Duration of one round trip: 2 × 18 + 7 = 43 days Round trips per year: 365/43 = 8.49 rtips (take 8.5 rtrips/year) Fuel cost per round trip: 3011 USD/h×18d×24h/d + 2095USD/h×18 2095USD/h×18 d×24 h/d =2,205,800 USD/rtrip Fuel cost per year: 2205800×8.5 =18,750,000 USD/yr Total operating costs: (18.75+6) (18.75+6) × 106 = 24.75×106 USD/yr Earnings per year: (318000×0.95) t/rtrip ×8.5× 12 USD/t = 30,814,000 USD/yr Net profit: 30.81×106 - 24.75×106 = 6.06 ×106 USD/yr
After the price price escalation: 3
P B B = k
3 V s s
k
3 =P ) =P / / B1 B1 / (V S2 B2 B2
3 (V s2 )
3 V S 2 12.5 P B1 P B 2 P B1 39 7 P B1 0.40 P B1 0.397 V 17 S 1
Fuel consumption per hour: = = (P × sf price) main + (P × sf price) F C sf c ×HFO price) sf c ×MDO price)
gen
= 0.40×27000 0.40×2700 0 kW ×0.176 kg/kW.h ×10-3 t/kg×1100 USD/t +800×0.2×10-3×1850 = 2387 USD/h (laden)
= 0.40×18321 ×0.176×10-3×1100+800×0.2×10-3×1850 = 1715 USD/h (ballast) One leg of voyage:
7000nm / (12.5) knts = 560 hrs =23.3 days 24 days
Duration of one round trip : 2 × 24 + 7 = 55 days Round trips per year: 365/55 = 6.64 rtrips/year rtrips/year (Take 6.5 rtrips/yr) Fuel cost / round trip:
FCPRT = 2387× 24 d×24h/d + 1715×24×24 = 2,362,752. USD/rtrip Fuel cost per year: = 2,362,752 USD/rtrip × 6.5 rtrips = 15.358×106 USD/yr Total operating costs: 15.358 + 6 = 21.358 million USD/yr Earnings per year: (318000×0.95)t/rtrip × 6.5 rtrips/yr × 12 USD/t =23,564,000 USD/yr Net profit: 23,564 – 23,564 – 21.358 21.358 = 2.206 Million USD/yr The net profit has been greatly reduced….
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