Marine Propulsion

Modelling and Simulation of Marine Power and Propulsion Systems

Melvin Loh (113807) Page 1

1.0 INTRODUCTION

Diesel-Electric Propulsion (DEP) systems is beneficial in several ship applications with a varying velocity profile, such as supply vessels, floating production vessels, drill-ships, shuttle-tankers, ice-breakers, naval ships and cruise liners. The basic idea of DEP systems is to replace the main diesel propulsion engines with electric motors, and split the power production into several smaller diesel-generators (DG). Electrical motors can be designed with a very high efficiency throughout the whole range of operation with respect to both speed and power outputs, in contrast to the diesel engine that has a clear peak in efficiency around its nominal working point.

Powering and performance have always been the key aspects in the design process of any vessel. Small crafts in particular are often either produced and run on tight budgets or designed under consideration of maximum performance. Scaled model testing in the towing tank is the most accurate method available of almost any vessel to obtain the vessel resistance. It has the advantage of providing a definitive answer compared to the tested models drag under repeatable constraints, as well as giving the opportunity of studying flow over the hull. The downside is the amount of time and money involved in producing and testing models at the required levels of accuracy, especially if any kind of optimisation process is involved. This generally leaves this method out of reach for the average small boat designers; it is only commonly used in a particularly important or novel project for an initial or final check of a hull form design. Computational fluid dynamics is a similar story with a need for a vast outlay in capital and time required to achieve the levels of accuracy needed to make the process useful. Therefore regression based methods will be used for this project.

Main advantages of DEP system are as follows: Improved life cycle cost by reduced fuel consumption and maintenance, especially where

there is a large variation in load demand. By running a specified number of DG at optimum for every load condition, the overall fuel consumption is reduced compared to conventional diesel propulsion, even including losses due to the additional electrical link;

Reduced vulnerability to single failure in the ship system and possibility to optimise loading of prime movers (diesel generator or gas turbine);

Higher flexibility in terms of engine room arrangement as the DEP system takes less space, and the diesel generators could be placed on any suited place. This implies the possibility of noise reduction, and to use the engine room arrangement to influence the ship stability. As compared to diesel engine with the same rated power, the electrical motor is far quieter;

Improved manoeuvrability by utilizing azimuthing/podded propulsion for faster response in manoeuvring; and

Simplified maintenance. Since with optimal running of DG, the need for maintenance decreases and by using several DG, maintenance can be performed for one generator set while maintaining almost normal operation.



These advantages should be weighted up against the present penalties, such as: Increased investment costs. However, this is continuously subject for revisions, as the cost

tends to decrease with increasing number of units manufactured; Additional components (electrical equipment generators, transformers, drives and

motors/machines) between prime mover and propeller increase the transmission losses at full load; and

For operational and maintenance personnel, a higher number and new type of equipment are involved and therefore, training are required.

High availability of power, propulsion and thruster installations, as well as safety and automation systems, are the key factors in obtaining maximum operation time for the vessel.

1.1 Scope of project This project focused on diesel-electric propulsion. The principal aim of the project is to develop a software program for the design of marine power system for DEP, compromising of a diesel engine as the prime mover powering the diesel generator to the electrical motors driving the propeller shaft. The types of propulsor in the propulsion system were excluded from this project. The software is developed by dividing the project into eight stages:

1. Limitation check for Holtrop and Lahtiharju resistance prediction algorithm; 2. Resistance prediction using Holtrop method; 3. Resistance prediction using Lahtiharju method; 4. Required power for Generators and electrical motors; 5. Generators selection; 6. Fuel consumption analysis; 7. Range and Endurance analysis; and 8. Plots.

1.2 Objectives The main objective is to develop a marine power and propulsion computer program in LabVIEW. When given ship resistance information, perhaps through regression based methods such as Holtrop and Lahtiharju or known curves, this analysis tools will be capable of exploring power options for diesel generators or electrical motors. Fuel consumption, range and endurance analysis will be presented based on the selected generator. The program will determine a solution that is the best match to the ship operating profile.

1.3 Research Methodology

For the first half of the project, the research work began with the understanding and familiarization of the background and conducting literature review on the ship resistance fundamental and theory, methods for ship resistance predictions as well as background knowledge of diesel-electric propulsion. All the background information is collected from past research papers on diesel-electric propulsion and regression based methods and ship resistance books.



After conducting literature review, mathematical models of the software was created in order for the software to be developed. For regression based methods, Holtrop and Lahtiharju were chosen for this research. Numerical examples from the Holtrop and Lahtiharju papers were used to verify with the software developed. After that, R/V G.O. Sars is used for the final verification to validate the required power for the diesel generators and electrical motors from the ship specifications. At the data analysis stage, it will be presenting the plots in LabVIEW in order for future users to optimize the full usage of the software. Towards the last stage of the project, it will be entirely project write-up. The flowchart of the research methodology as described is shown in Figure 1-1.

Figure 1-1: Flowchart of the research methodology



1.4 Literature Review

Electrical installations are present in any ship, from powering of communication and navigation equipment, alarm and monitoring system, running of motors for pumps, fan or winches, to high power installation for electric propulsion

Electric propulsion is an emerging area where various competence areas meet. Successful solutions for vessels with electric propulsion are found in environments where naval architects, hydrodynamic and propulsion engineers, and electrical engineering expertise cooperate under constructional, operational, and economical considerations. Optimized design and compromises can only be achieved with a common concept language and mutual understanding of the different subjects. It is the aim to give engineers with marine competence and background the necessary understanding of the most important electro-technical subjects used in design and configuration of ships with electric propulsion.

The concept of electric propulsion is not new; the idea originated more than 100 years ago. However, with the possibility to control electrical motors with variable speed in a large power with compact, reliable and cost-competitive solutions, the use of electrical propulsion has emerged in new application areas during the 80s and 90s.

Electric propulsion with gas turbine or diesel engine driven power generation is used in hundreds of ships of various types and in a large variety of configurations. Installed electric propulsion in merchant marine vessels was in 2002 in the range of 6-7GW, in addition to a substantial installation in both submarine and surface war ship applications.

At present, electric propulsion is applied mainly in various types of ships: cruise vessels, ferries, DP drilling vessels, thruster assisted moored floating production facilities, shuttle tankers, cable layers, pipe layers, icebreakers and other ice going vessels, supply vessels and war ships. There is also a significant on-going research and evaluation of using electric propulsion in new vessel designs for existing and new application areas (Adnanes, 2003).



1.4.1 Resistance Prediction Methods

In the industry, there are many techniques as shown in Figure 1-2, which can be used in determining ship resistance.

Figure 1-2: Ship resistance evaluation methods and examples (Carlton, 2007)

Model testing method is the most widely used and applied among others since it uses models with similar characteristic to the ship and applicable to any kinds of ships. Meanwhile, the two other methods are effective and used for prediction and can be used for a ship that has similar particulars to such a group. However, numerical methods are more time effective compared to model-testing. Table 1-1 and Table 1-2 show the methods available for planning hull and displacement ships.



Table 1-1: Methods for planning hulls (Carlton, 2007) Savitsky (Pre-planning)

This algorithm is useful for estimating the resistance of a planning hull before it gets onto the plane; i.e. its pre-planning resistance.

Savitsky (Planning) Used for estimating the resistance of planning hulls when in the planning speed regime.

Blount and Fox (Planing)

Used for estimating the resistance of planning hulls when in the planning speed regime. The algorithm is based on the Savitsky planning method with improvements to the algorithm at hump speed, the speed at which the vessel just begins to plane. The method is considered superior to the Savitsky planning method for vessels that have varying deadrise angles in the afterbody, or has a varying beam in the afterbody (i.e. not prismatic).

Lahtiharju Used for estimating the resistance of planning hulls when in the planning speed regime.

Wyman

A universal formulation used for calculating the resistance of hull forms in both planning and displacement modes. The original method was set out by Wyman results in an engine power being calculated. As such, for Hullspeed to accurately predict the hull resistance, an overall efficiency must be added in the efficiency dialog. The overall efficiency accounts for losses between the power developed at the engine (brake power) and the effective power (hull resistance).

Table 1-2: Methods for displacement ships (Carlton, 2007)

Holtrop This algorithm is designed for predicting the resistance of tankers, general cargo ships, fishing vessels, tugs, container ships and frigates.

Compton This algorithm is designed for resistance prediction of typical coastal patrol, training or recreational powerboat type hull forms with transom sterns operating in the displacement and semi-planning regimes.

Fung

This algorithm is applicable for resistance prediction of displacement ships with transom stern hull forms (generally used for larger vessels than Compton). The regression is based on data from tests on 739 models at the David Taylor model basin and consists over 10 000 data points, Fung and Leibman (1995).

van

Ortmerssen Useful for estimating the resistance of small ships such as trawlers and tugs.

Series 60 Used for estimating the resistance of single screw cargo ships.



1.4.2 Holtrop and Mennen Resistance Prediction Algorithm

The mathematical model first made its appearance in 1977. This was followed a year later by an improved model which made allowance for bulbous bows and an improvement in estimating resistance of large waterplane area coefficient ships. The model was then extended in order to improve the power prediction of ships with a high block coefficient and a low length breadth ratio and slender naval ships (Holtrop & Mennen, 1982). Despite this, predictions for high-speed craft (Fn > 0.5) were often incorrect and in an attempt to rectify this, the data sample was extended to include the Series 64 hull forms and then re-analyzed (Holtrop, 1984). The 1982 mathematical model was developed from 191 random model experiments and full-scale data, which increased to 334 for the 1984 model.

1.4.3 Lahtiharju Resistance Prediction Algorithm In an attempt to extend existing series to higher block coefficients and beam draught ratios, the VTT Ship Laboratory Technology Research Center of Finland carried out tests on a series of four round bilge and two hard chine models based on the NPL parent form. The results of these tests together with the NPL series data, the SSPA tests on sma1l fast displacement vessels and the results of existing VTT tests on suitable models were statistically analysed. In developing the regression equations, a total of 65 round bilge and 13 hard chine models were used. Separate equations were developed for the round bilge and for the hard chine vessels, however; only the round bilge method is applicable to this study.

1.4.4 Main Components of Diesel-Electric Propulsion

Prime Mover The source for power is most often a generator set driven by combustion engine which is fuelled with diesel or heavy fuel oil. Occasionally one can find gas engines, and also gas turbines, steam turbines or combined cycle turbines, especially for higher power levels, in light high-speed vessels, or where gas is a cheap alternative (e.g. waste product in oil production, boil-off LNG carriers, etc.) In a diesel-electric propulsion system, the diesel engines are normally medium to high-speed engines, with lower weight and costs than similar rated low speed engines that are used for direct mechanical propulsion. Availability to the power plant is of high concern and in a diesel electric system with a number of diesel engines in a redundant network; this means high reliability but also sophisticated diagnostics and short repair times (Adnanes, 2003).

Generators The majority of new buildings and all commercial vessels have an AC power generation plant with AC distribution. The generators are synchronous machines, with a magnetizing winding on the rotor carrying a DC current, and a three-phase stator winding where the magnetic field from the rotor current induces a three-phase sinusoidal voltage when the rotor is rotated by the prime mover. The frequency f (Hz) of the induced voltages is proportional to the rotational speed n (RPM) and the pole number p in the synchronous machine:

(1.1) 2 60p nf =



1.4.5 Past Research

For a marine propulsion system design, the number of potential Power & Propulsion (P&PS) solutions is increasing all the time as new types of mechanical and electrical technologies become available. The different options and the complexities of vessel operations lead to a large number of variables to assess.

In May 2010, BMT Defence Services developed a marine P&P analysis tool, Ptool, to allow designers to establish the vital P&PS parameters and to identify the best sub-sets of solutions quickly with the least input information. Ptool uses a library of P&PS equipment data to reduce the need for initial data. A ship definition file contains much of the bounding input data.

The various P&PS options are defined in separate files to allow unique configuration and equipment set-ups to be analysed. Ptool provides graphic output and report generation of key data parameters. These outputs include budget estimates of physical and cost information for the purposes of comparison and cost benefit analysis.

The approach is therefore one of matching the propulsion solution to the ships operating speed profile. Ptool is most valuable for ships with varying electrical loads across ships speeds and those with a wide range of operating speeds.

Ptool make use of a library of generic engine, motor, converter and propulsor data to reduce the date entry required. Data from several different diesel and gas turbine engine suppliers is recorded. This is the specific fuel and lub oil consumption for an engine as well as the NOx and smoke emission levels.

Performance curves for a range of propulsor devices are also recorded in a library for easy option definition. The electric motor and convertor technologies are defined by generic performance characteristics such as their operating efficiency over speed or load conditions (Buckingham, 2010).



1.5 Outline of Thesis

Chapter 2.0 presents the resistance and propulsion background information and formulas involved. Two regression based methods Holtrop and Lahtiharju were selected and the formulas and limitations were presented. The mathematical models of Holtrop and Lahtiharju are also presented in this chapter.

Chapter 3.0 presents the background information of diesel-electric propulsion and each component in it. The mathematical model of DEP is also presented.

Chapter 4.0 shows the software development of this project. The rationale and structures are also presented in this chapter.

Chapter 5.0 shows the testing and analysis of the software. Validation of R/V G.O. Sars is shown in this chapter to prove the accuracy of the software developed.

Chapter 6.0 discusses about the project, accuracy of regression based methods, limitations of the software and the verifications.

Finally in Chapter 7.0 and 8.0 presents concluding remarks and future works are drawn.

Chapter 9.0 shows the bibliography and works cited.

Appendix A presents the ship specifications of R/V G.O. Sars and SV290.

Appendix B presents the block diagram of the VIs developed.

Appendix C presents the user manual for the software.



2.0 RESISTANCE AND PROPULSION THEORY

This chapter describes the basic principles and theory of resistance of a ship that includes frictional, pressure and wave resistance, and the effects of these resistances. There are also two resistance prediction algorithms that are used in the industry to predict the resistance of a ship based on the operating profile or ship coefficients: Holtrop and Lahtiharju.

Translation of a hull through water requires a force. This force is called the resistance: it is the force that is required to tow the ship at a specified speed (without the propulsor). The thrust developed by the propulsion system has to overcome the resistance of the ship. Figure 2-1 shows the ship resistance and its breakdown. The total resistance consists of three components:

Frictional resistance is the force that is the resultant of tangential forces acting on the hull as a result of the boundary layer along the hull;

Pressure resistance is the force that is the resultant of the normal forces on the hull, due to the difference in the pressure in front of and behind the moving ship. The pressure losses become significant when the boundary layer separates from the hull at the stern of the ship; and

Wave resistance is the drag that is the result of waves generated by the moving ship. The kinetic and potential energy in the waves has to be generated by the propulsion system.

Figure 2-1: Components of ship resistance (Carlton, 2007)



Figure 2-2: Different types of ships resistance speed curve (Stapersma & Woud, 2002)

Figure 2-2 shows various resistance-speed relations. For higher speeds, the resistance curve will be steeper; curves of type (2) may be encountered. Planning craft and swath (small waterplane area twin hull) ships may have curves that are more like (3).

2.1 Hull Resistance

Translation of a hull through water requires a force. This force is called the resistance. It is the force that is required to tow the ship at a specified speed (without the propulsor). The thrust developed by the propulsion system has to overcome the resistance of the ship. The total resistance consists of three components:

Frictional or viscous resistance is the force that is the resultant of the tangential forces acting on the hull as a result of the boundary layer along the hull;

Form or pressure resistance is the force that is the resultant of the normal forces on the hull, due to the difference in the pressure in front of and behind the moving ship. The pressure losses become significant when the boundary layer separates from the hull at the stern of the ship; and

Wave resistance is the drag that is the result of waves generated by the moving ship. The kinetic and potential energy in the waves has to be generated by propulsion system.

(2.1)

It is often acceptable to assume that the ships resistance is roughly proportional to the square of ship speed vs relatively low speeds.

(2.2)

Total resistance R Frictional Pressure Wave Resistance= + +

21 SR c V=



The power required to tow the ship at ship speed vs with resistance R is the effective towing power PE. Using the assumed proportionality of resistance and ship speed squared, effective power is as a first approximation proportional to the cube of ship speed.

(2.3)

(2.4)

2.1.1 Non-dimensional Resistance CE

In hydromechanics, total resistance is usually written in non-dimensional form CT.

(2.5)

where = density of water (kg/m3) As=Wetted surface of the hull (m2) Usually, the wetted surface As is not readily available. Therefore, a more practical coefficient is used: Specific resistance CE.

(2.6)

By defining specific resistance CE, a ship is assigned a value that indicate resistance characteristic depending, amongst others on ship size, speed and hull form.

The Reynolds number Re and the Froude number Fn represent the viscous (friction) and dynamic (waves) effects on resistance (and power), respectively.

Therefore, the dependency of CE on the Reynolds and Froude numbers means that CE depends on speed and size.

2.1.2 Relationship between c1 and CE

(2.7)

(2.8)

In particular, the dependency on the Froude number means that the propulsion power can change with speed more rapidly than is predicted by the cube law. The cube law is only valid for low Froude numbers (Fn=0.1-0.2).

.E sP R v=

31.E sP c v=

20.5T s sRCA v

=

1 233 3

EE

s

PCv

=

1 233 3E E sP C v=

1 23 3

1 Ec C =



2.2 Propulsion

The function of a propulsor is to deliver a thrust force T to overcome the resistance R of the hull. The power needed to overcome R at speed vs is the effective power PE, already defined in equation (2.3):

The power as delivered by the propeller in water at velocity of advance vA with useful output T is the thrust power PT (per propeller): (2.9) Another important effect is that the velocity of the water at the propeller does not equal the ships speed: the entrained water in the boundary layer around the ship has a certain forward speed. The boundary layer at the ships stern has a considerable thickness and normally the propeller is completely within the region where the water velocity is affected by the hulls presence. As a result the advance velocity vA of the propeller relative to the water is smaller than the ships vs.

The difference between ships speed and advance velocity in front of the propeller, as a ratio of ships speed is called the wake factor w:

(2.10)

From this definition the advance velocity as experienced by the propeller can be expressed in terms of the ship speed: (2.11)

2.2.1 Hull Efficiency

As a result of thrust deduction and wake factor, the sum of the thrust power PT of all the propellers does not equal the effective power PE. The ratio of effective power to propulsive power is called the hull efficiency H, clearly all differences between the towed and propelled hull are contained within this factor:

(2.12)

(2.13)

2.2.2 Propeller Efficiency

In order to deliver thrust at a certain translating speed, power must be delivered to the propeller as torque Q and rotational speed: (2.14) The index O stands for open water and refers to the fact that propellers normally are tested in open water tank or tunnel. During the open water test, open water propeller efficiency can be measured:

T AP T v=

s A

S

v vw

v

=

( )1A sv w v=

sEH

p T p A

R vPk P k T v

= =

11H

t

w =

2o p pP Q Q n pi= =



(2.15)

The open water propeller efficiency lies in the range of 0.3 for inland ships to 0.7 for frigates. In reality, i.e. behind the ship, the torque Mp and thus the power Pp actually delivered to the propeller are generally slightly different as a result of the non-uniform velocity field in front of the actual propeller.

(2.16)

The ratio between open water power (or torque) and actually delivered power (or torque) is called the relative rotative efficiency:

(2.17)

2.2.3 Propulsive Efficiency

It is common practice to define the total propulsive efficiency to embrace all effects hull and propeller discussed up to now. So, the propulsive efficiency must be defined as the quotient of the previously defined effective power PE delivered to the hull and the power actually delivered to all the propellers PD. The total propulsive efficiency is defined as:

(2.18)

With the definitions of hull efficiency H, open water propeller efficiency o, and relative rotative efficiency R the following chain of partial efficiencies arises:

(2.19)

in which the hull efficiency can further be expressed in thrust deduction t and wake fraction w:

(2.20)

2.2.4 Non-dimensional delivered power coefficient CD

Not only effective towing power PE but also delivered power PD is increasing with the cube of ship speed, if it is assumed that the total efficiency D remains almost constant at ship speeds other than nominal ship speed, as shown by the following relations:

(2.21)

12

T Ao

O p

P T vP Q n pi

= =

2p p p p pP M M n pi= =

oR

p p

P QP M

= =

ED

D

PP

=

D H o R =

11D o R

t

w =

1 21 233 3

33 3E sED D s

D D

C vPP C v

= = =



in which the non-dimensional delivered power coefficient CD is by definition:

(2.22)

(2.23)

2.2.5 Propeller Law

The relation between the power delivered to a propeller Pp and shaft (or propeller) speed np is known as the propeller law. From experience, it is known that shaft (rotational) speed is almost linearly proportional to the ships translating speed:

(2.24)

It can be shown that the delivered power is not only proportional to the cube of ship speed but also to the cube of shaft speed. This is called the propeller law.

(2.25)

then:

(2.26)

That is: propeller torque is proportional to the square of the shaft speed. There were two assumptions in the derivation of the propeller law:

The propulsive efficiency remains constant in off-design conditions; and Shaft speed is linearly proportional to translating speed.

2.3 Propulsion Chain

Shaft losses are expressed in terms of shaft efficiency, which is defined as:

(2.27)

The shaft loss typically is 0.5 to 1 percentage at nominal power. Ps is the shaft power, i.e. the power delivered to the shaft that is connected to a propeller and Pp is the power delivered to the propeller.

(2.28)

2 1 23 33 3 3

D D ED

Ds s

P P CCv v

= = =

1 23 3

2 Dc C =

3p sn c v=

323 32

433

pDp s p

p p p

c nP cP v c nk k k c

= = = =

34 5 2

2p

p pp

c nM c n

npi

= =

p ps

s s

P MP M

= =

2s s p s pP M M n pi= =



Engine brake power PB is the power developed by the engine is defined by:

(2.29)

where MB is the engine torque, e is the angular velocity of the engine shaft and ne is the engine speed. If there is no gearbox, brake power equals shaft power. If however, transmission includes a gearbox, gearbox losses are expressed in terms of gearbox efficiency, taking into account the number of engines per propeller shaft ke:

(2.30)

i is the gearbox reduction ration indicating the ratio of engine speed to propeller speed:

(2.31)

The gearbox losses are moderate (1% to 2%) for one-step reduction gearboxes in medium-speed diesel installations and they may be high (3% to 5%) for complex gearboxes with two or three reduction stages such as currently applied in multi-engine installations.

The total transmission efficiency is defined as the ratio of delivered power to brake power. With the definition of shaft and gearbox efficiency, total transmission efficiency can be written as the product of these two.

(2.32)

To complete the power chain from the moving ship to the fuel in the tanks, the last step is effective engine efficiency. It is defined as the ratio of engine output and heat input:

(2.33)

Effective engine efficiency accounts for all engine losses in the conversion of chemical energy in fuel to the mechanical energy in the rotating output shaft of the engine.

Figure 2-3 presents the propulsion chain: the overview of powers and efficiencies from resistance to brake powers.

2B B e B eP M M n pi= =

1s ps sGB

e B e B e e B

M nP Mk P k M n k M i

= = =

e

p

nin

=

1 1p p p sTRM s GB

e B e B s e B

P M M Mk P k M i M k M i

= = = =

Be

f

PQ =



Figure 2-3: Propulsion Chain: Overview of powers and efficiencies from resistance to brake power (Stapersma & Woud, 2002)



2.4 Holtrop (1984/1988) One of the methods which are used to predict the resistance of a full displacement hull form is Holtrop 1988. This algorithm is designed for predicting the resistance of tankers, general cargo ships, fishing vessels, tugs, container ships and frigates. However, there are some limitations for this prediction method and will be mentioned in Section 2.4.12.

This resistance prediction method is one of the techniques widely used in prediction of resistance of displacement and semi-displacement vessels. Like all methods, however, this technique is limited to a suitable range of hull form parameters. This algorithm is designed for predicting the resistance of tankers, general cargo ships, fishing vessels, tugs, container ships and frigates. The algorithms implements are based upon hydrodynamic theory with coefficients obtained from the regression analysis of the results of 334 ship model tests.

In their approach to establishing their formulas, Holtrop and Mennen assumed that the non-dimensional coefficient represents the components of resistance of a hull form. It might be represented by appropriate geometrical parameters, thus enabling each component to be expressed as a non-dimensional function of the sealing and the hull form.

This resistance prediction method was presented based on a regression analysis of random models and full-scale test data. A Froude number dependency of the form factor was introduced with the objective to improve the accuracy of the prediction. The prediction method was carried out as shown:

(1 )Total F APP TR W B AR R Yk R R R R R= + + + + + + (2.34)

2.4.1 Froude Number

The Froude number is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. For vessel, it is an important parameter with respect to the ship drag, or resistance, including the wave making resistance.

(2.35)

The coefficient Y as shown in Table 2-1 was varied for several fixed values of the Froude numbers and for each Froude number a regression analysis of the wave resistance was made in order to match the numerical model to the measured data. In Figure 2-4, it shows the Froude number dependency of the form factors.

Referring to Figure 2-5, the standard deviation Rm between the total measured and calculated model resistance was used to determine the value of Y for each Froude number analysed.

sn

VFgL

=



Table 2-1: The standard deviation of the model resistance, the Y-values and the number data points (Holtrop, 1988)

Fn Y Rm (%) n 0.100 0.9300 3.89 123 0.125 0.9395 3.41 207 0.150 0.9513 3.83 236 0.200 0.9500 3.78 167 0.250 0.8744 4.80 172 0.300 0.7500 6.54 151 0.350 0.5625 7.40 112 0.400 0.3800 4.69 75 0.450 0.2844 3.59 60 0.500 0.2200 3.17 49 0.600 0.1000 2.87 45 0.800 0.0000 2.92 43

Figure 2-4: Froude number dependency of the form factor (Holtrop, 1988)



Figure 2-5: The standard deviation between measured and calculated RM is shown for various Froude numbers investigated as a function Y (Holtrop, 1988)

2.4.2 Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two forces for given flow conditions and the formula is shown as:

(2.36) where: for fresh water = 1.13910-6 m2/s for sea water = 1.18310-6 m2/s

se

V LR

=



2.4.3 Form coefficients

Form coefficients are important parameters to help compare hull forms as well: Block coefficient is the ratio of the immersed volume of a vessel to the product of its immersed draft, length and beam and is shown as:

(2.37)

Midship coefficient is the ratio of the largest underwater section of the hull to a rectangle of the same overall width and depth as the underwater section of the hull and is shown as:

(2.38) Prismatic coefficient is the ratio of the immersed volume of the hull to a volume of a prism with equal length to the ship and cross-sectional area equal to the largest underwater section of the hull (midship section) and is shown as: (2.39)

Waterplane coefficient expresses the fullness of the waterplane or the ratio of the waterplane area to a rectangle of the same length and breadth and is shown as:

(2.40)

2.4.4 Frictional Resistance RF

The frictional resistance RF is the major part of the total viscous resistance of a ship. The area of the wetted surface S and the coefficient of the frictional coefficient CF determine its magnitude.

(2.41)

(2.42)

(2.43)

(2.44)

In the form-factor formula LR is a parameter reflecting the length of the run according to:

(2.45) The coefficient c12 is defined as:

When T/L > 0.05:

B P MWL

C C CL B T

= =

mM

ACB T

=

PPP m

CL A

=

wWP

PP

ACL B

=

210

0.075[log ( ) 2]F

n

CR

=

20.5F S FR S V C=

(2 ) (0.453 0.4425 0.28620.003467 / 0.3696 ) 2.38 /

M B M

WP BT B

S L T B C C CB T C A C

= + +

+ +

0.924971 13 12

0.521488 0.6906

(1 ) [0.93 ( / )(0.95 ) (1 0.0225 ) ]

R

P P

k c c B LC C lcb

+ = +

+

[1 0.06 / (4 1)]R p p pL L C C lcb C= +



(2.46)

When 0.02 < T/L < 0.05: (2.47)

When T/L < 0.02: (2.48)

The coefficient c13 accounts for the specific shape of the afterbody and is related to the coefficient Cstern according to: (2.49)

According to Figure 2-6, the typical values of Cstern are shown.

Figure 2-6: Typical values of Cstern (Holtrop, 1988)

2.4.5 Appendage Resistance RAPP

The appendage resistance can be determined from:

(2.50)

0.222844612 ( / )c T L=

2.07812 48.2( / 0.02) 0.479948c T L= +

12 0.479948c =

13 1 0.003 sternc C= +

220.5 (1 )APP S APP eq FR V S k C= +



Table 2-2: 1+k2 values used for streamlined flow-orientated appendages (Holtrop, 1984)

Approximate 1+k2 values

Rudder behind skeg 1.5-2.0

Rudder behind stern 1.3-1.5

Twin-screw balance rudders 2.8

Shaft Brackets 3.0

Skeg 1.5-2.0

Strut bossings 3.0

Hull bossings 2.0

Shafts 2.0-4.0

Stabilizer fins 2.8

Dome 2.7

Bilge keels 1.4

The equivalent 1+k2 values is shown in Figure 2-6 for a combination of appendages is determined from:

(2.51)

2.4.6 Wave Resistance RW (Fn >0.55) The wave resistance formula was derived for the speed range Fn > 0.55:

(2.52)

(2.53)

(2.54)

(2.55)

The coefficients c2, c5, d and have the same definition for all Froude Number: (2.56)

(2.57)

22

(1 )(1 ) APPeq

APP

k SkS

++ =

20.55 17 2 5 3 4exp[ cos( )]dW n nR c c c g m F m F = +

0.9d =

2.00977 1.406921.3346

17 36919.3 2ML

c CL B

=

0.326869 0.6053753 7.2035( / ) ( / )m B L T B=

2 3exp( 1.89 )c c=

1.5

30.56

[ (0.31 )]BT

BT F B

Ac

B T A T h=

+



(2.58)

When L/B < 12: (2.59)

When L/B > 12: (2.60)

(2.61)

When L3/ < 512: (2.62)

When 512 < L3/ < 1726.91: (2.63)

When L3/ > 1726.91: (2.64)

2.4.7 Wave Resistance RW (Fn < 0.4) (2.65)

(2.66)

When B/L < 0.11: (2.67)

When 0.11 < B/L < 0.25: (2.68)

When B/L > 0.25: (2.69)

(2.70)

(2.71)

51 0.8

( )T

M

Ac

B T C

=

1.446 0.03( / )PC L B =

1.446 0.36PC =

3.294 15 0.4 exp( 0.034 )nm c F =

15 1.69385c =

1/315 1.69385 ( / 8) / 2.36c L= +

15 0c =

RW 0.4 = c1 c2 c5 g exp[m1Fnd + m2 cos(Fn2 )]

c1 = 2223105 c73.78613(T / B)1.07961(90 iE )1.37565

c7 = 0.229577(B / L)0.33333

c7 = B / L

c7 = 0.5 0.0625L / B

iE = 1+ 89 exp[(L / B)0.80856 (1 CWP )0.30484(1 CP 0.0225lcb)0.6367 (LR / B)0.34574 (100 / L3)0.16302 ]

m1 = 0.0140407(L / T ) 1.75254(1/3 / L) + 4.79323(B / L) c16



When CP < 0.8: (2.72)

When CP > 0.8: (2.73)

(2.74) When L3/ < 512: (2.75)

When 512 < L3/ < 1727: (2.76)

When L3/ > 1727: (2.77)

2.4.8 Wave Resistance RW (0.4 < Fn < 0.55)

(2.78)

2.4.9 Additional pressure of bulbous bow near the water surface RB

The additional resistance due to the presence of a bulbous bow near the water surface is determined from:

(2.79)

(2.80)

(2.81)

c16 = 8.07981CP 13.8673CP2 + 6.984388CP3

c16 = 1.73014 0.7067CP

m2 = c15 CP2 exp(0.1Fn2 )

c15 = 1.69385

1/315 1.69385 ( / 8) / 2.36c L= +

15 0c =

0.55 0.40.4 0.55 0.4

(10 4)( )1.5

n W WW W

F R RR R

= +

2 3 1.5

2

0.11exp( 3 )(1 )

B ni BTB

ni

P F A gRF

=

+

0.56( 1.5 )

BTB

F B

AP

T h=

2( 0.25 ) 0.15ni F B BT SVF

g T h A V=



2.4.10 Additional Pressure Resistance of Immersed Transom Stern RTR

In a similar way the additional pressure resistance due to immersed transom can be determined:

(2.82) The coefficient c6 has been related to the Froude number based on the transom immersion: When FnT < 5: (2.83)

When FnT > 5: (2.84)

FnT has been defined as:

(2.85)

2.4.11 Model-Ship Correlation RA

The model-ship correlation RA with (2.86)

describes the effect of the hull roughness and the still-air resistance. From an analysis of results of speed trials, which have been corrected to ideal trial conditions, the following formula for the correlation allowance coefficient CA was found: (2.87)

When TF/L 0.04: (2.88) When TF/L > 0.04: (2.89)

260.5TR S TR V A c=

6 0.2(1 0.2 )nTc F=

6 0c =

2 / ( )nT T WPVF

gA B BC=

+

20.5A S AR V S C=

0.16 42 40.006( 100) 0.00205 0.003 / 7.5 (0.04 )A BC L L C c c= + +

4 /Fc T L=

4 0.04c =



2.4.12 Limitations

The Holtrop and Mennen resistance prediction algorithm is valid for a variety of hull forms ranging from tugs to trawlers to naval vessels. The Froude numbers will range from 0.05.to 1. However, there are some limitations in Holtrop: The correlation factor is constant but is calculated based on regression method within the specified Froude number or speed ranges.

The Holtrop prediction algorithm is also favourable to certain limits of hull dimensions. The limitations of the hull dimensions referring to Table 2-3.

Table 2-3: Limits of applicability for Holtrop and Mennen (Holtrop, 1984) Parameter Minimum Maximum CP 0.55 0.85 L/B 3.9 15 B/T 2.1 4.0

2.4.13 Mathematical Modelling of Holtrop Resistance Prediction Algorithm

Figure 2-7: Mathematical Modelling of Holtrop Resistance Prediction Algorithm

Based on the mathematical model of Holtrop as shown in Figure 2-7, user will understand the flow of the Holtrop resistance prediction algorithm developed. The very first input of the software will be the vessel operating profile or ship coefficients and through the Holtrop resistance prediction algorithm, the result will be the total resistance of the vessel and effective power.



2.5 Lahtiharju (1991) Lahtiharju is a reliable resistance prediction method which is used to predict the resistance of a planning hull. Extensive systematic resistance tests were carried out with all models, including typical hard chine planning hull form. Resistance prediction equations were developed by using regression analysis, which was based on parameters and resistance data if some older systematic series, the new series and suitable models from the records (Lahtiharju, et al., 1991).

With all the models tested, the volumetric displacement Froude number, Fn, is defined by:

(2.90)

2.5.1 Hard Chine Craft

The analysis of hard chine craft was carried out by using the main dimensions and the resistance test results of only 13 vessels. Thus the equation is a supplement to the Savitsky method in the pre-planning regime. The parameters in the equation are the ratios of main dimensions (L, B, T and ) and the ratio of transom area AT/AX. The new formula is a second order function of Fn. The number of variables is six.

The values of the regression coefficients and the parameters are given in Table 2-4. Because the models in the analysis did not form any systematic series and the number of the models was very small, the coefficient of determination is only 0.9687. The general form of the resistance prediction equation for hard chine craft in the pre-planning speed regime is:

(2.91)

(2.92)

(2.93)

(2.94)

1/3S

n

VFg

=

3 62

100000 0 1 12 4

/T i i n i i ni i

R A A P A P F A P F = =

= + + +

( )2100.075

log 2F nC

R=

1/3

5

1000032.264

1.2817 10

n

n

LFR

=

( ) 2100000 2/3100000

0.5T T F A F ncorr

R R SC C C F

= +



Table 2-4: Parameters and coefficients of the resistance equation for hard chine vessels (Lahtiharju, et al., 1991)

Coefficient = 1 i Pi Ai 0 1 -0.03546471

1 /T3 0.00129099

Coefficient = Fn i Pi Ai 2 1/3/L 0.51603410 3 (L/T)2 -0.00010596

Coefficient = Fn2 i Pi Ai 4 (L/1/3)2 -0.00090300 5 (L/1/3)3 0.00017501 6 (B/L).(AT/AX) -0.02784726

The total resistance is calculated in exactly the same way as for round bilge vessels. At low speeds, resistance is calculated by using the Mercies-Savitsky method. When the speed is larger than Fn =1.8, equation (2.91) is used up to planning regime. After that, the Savitsky equation is applied. Small experimental corrections have been made to the Mercier-Savitsky and Savitsky methods, because they slightly underestimate the resistance according to previous examinations.



2.5.2 Limitations

The Lahtiharju resistance prediction algorithm is valid for vessel speeds corresponding to displacement Froude number Fn in the range of 1.8 to 3.3. However, Lahtiharju is favourable to certain limits of hull dimensions, these limits are shown in Table 2-5:

Table 2-5: Limits of applicability for Lahtiharju (Lahtiharju, et al., 1991) Type of Hull Forms Round Bilge and Hard Chine Vessels L/1/3 4.49 to 6.81 L/B 2.73 to 5.43 B/T 3.75 to 7.54 AT/AX 0.43 to 0.995

2.5.3 Mathematical Modelling of Lahtiharju Resistance Prediction Algorithm

Figure 2-8: Mathematical Modelling of Lahtiharju Resistance Prediction Algorithm

Based on the mathematical model of Lahtiharju as shown in Figure 2-8, user will understand the flow of Lahtiharju resistance prediction algorithm developed. The very first input of the software will be the vessel operating profile or ship coefficients and through the Lahtiharju resistance prediction algorithm, the result will be the total resistance of the vessel and effective power.



3.0 DIESEL-ELECTRIC POWER AND PROPULSION

This chapter deals with the diesel-electric power and propulsion in a DEP vessel. Once the diesel generators translate mechanical energy to electrical energy, the electrical power will be translated from the diesel generator to a list of electrical components like the switchboard, transformer, frequency converter and electrical motors for propulsion. In order to determine the power required for the diesel generator and electrical motors, typical electrical and propeller efficiency are used in this project. Each components of the DEP system are explained in this chapter as well to gain an in-depth knowledge of how the DEP system works and functions.

Figure 3-1: Three comparative concepts of a Ropax vessel showing how space can be utilized with electric propulsion and podded propulsion (Adnanes, 2003)

The advantages of the DEP were highlighted in the earlier chapter. High availability of power, propulsion and thruster installations, as well as safety and automation systems, are the key factors in obtaining maximum operation time for the vessel. The safety and automation system required to monitor, protect, and control the power plant, propulsion and thruster system, becomes of increasing importance for a reliable and optimum use of the installation. Figure 3-1 shows the vessel layout of diesel-mechanical, diesel-electric and pod propulsion.



The merits of electrical propulsion include the ease of control which it provides giving an excellent manoeuvring capability together with an ability to operate economically and for lengthy periods at reduced speed and power. The principle disadvantage of electrical drive has been that it is much expensive in first cost than the geared alternative. This economic disadvantage is compounded by the fact that the mechanical efficiency is lower, leading to increased fuel consumption and cost. Bringing all the electrics together in one system along with some reduction in relative cost of electric propulsion systems have combined to reduce the extra cost of todays electrical propulsion and it is now the favoured system for large cruise liners, research vessels, ice breakers, on which its many operational advantages outweigh any residual extra cost. The differences between conventional diesel propulsion and diesel-electric propulsion system are shown in Figure 3-2.

Figure 3-2: Layout diagram of Conventional and Diesel Electric Propulsion System (Adnanes, 2003)



3.1 Overview of Diesel-Electric Propulsion

The main difference between the marine and a land-based electrical power system is the fact that the marine power system is an isolated system with short distances from the generated power to the consumers, in contrast to what is normal in land-based systems where there can be hundreds of kilometres between the power generation and the load, with long transmission lines and several voltage transformations between them. The amount of installed power in vessels may be high and this gives special challenges for the engineering of such systems. High short circuit levels and forces must be dealt with in a safe manner. The control system in a land-based electrical power system is divided in several separated sub-systems, while in a vessel; there are possibilities for much tighter integration and coordination. The main components of DEP are shown as:

Figure 3-3: Main components of Diesel-Electric Propulsion (B&W, 2011)

The function of the electric power plant is to supply electric power to a great diversity of electric consumers. The electric consumers, or electrical systems, include systems that are vital to the ships operation, and safety of crew and passengers; e.g. lighting, communication, navigation and mission specific systems. Because of the importance of reliable operation of these electrical systems, regulatory bodies provide ample rules and regulations for configuration and design of electrical power plants and their components. Figure 3-4 shows the layout diagram of DEP.



Figure 3-4: Layout of Diesel-Electric Propulsion (B&W, 2011)



3.2 Mathematical Modelling of Diesel-Electric Propulsion

Figure 3-5: Relationship between resistance and PIN

Figure 3-6: Mathematical Model of DEP system in software

From the previous mathematical model of Holtrop and Lahtiharju, the output will be the resistance. According to Figure 3-5, the relationship between resistance and power are presented. So from the calculated results, using equation (2.3), the effective power will be generated and dividing by the assumed propeller efficiency, PIN of the DEP system will be achieved. After that, using the typical efficiencies in Table 3-1 and mathematical model of DEP as shown in Figure 3-6, the software will calculate the required generators and electrical motors power loads based on the number of generators and electrical motors selected. The development of the software will be discussed in Chapter 4.0.



3.3 Prime Mover

In a DEP system, the diesel engines are normally medium to high-speed engines, with lower weight and costs than similar rated low speed engines that are used for direct mechanical propulsion. Most common is the use of a diesel engine to drive the generator due to its good performance characteristics and low fuel costs. Main electric power supply systems of 50 Hz require a prime mover with a speed of 750, 1000 or 1500 rpm, 60 Hz-systems require 900, 1200 or 1800 rpm. High speed diesel engines need high quality fuels, whereas engines that run 750-1000 rpm can usually operate on cheaper heavy fuel. This gives them an advantage from a fuel cost point of view.

Figure 3-7: Caterpillar 3512B Diesel Engine

Gas turbines are also used for electric power supply systems. Figure 3-7 shows a Caterpillar 3512B diesel engine. It has a robust diesel strength design prolongs life and lowers owning and operating cost. Besides that, it has a broad operating speed range and with a separate circuit aftercooler to provide industry-leading ambient capability; ease-of-cooling system integration and enables sea water cooling. A steam turbine is rarely used to drive a generator (turbo-generator), nowadays. It has advantages though, when the propulsion system includes a steam plant, or when sufficient steam is generated by the energy in exhaust gases.



3.4 Diesel Generators

The generator is driven by a prime mover converts mechanical energy to main electric energy. Manufacturers usually combine the generator, prime mover and auxiliary systems, such as reduction gear (if required) and lubricating oil system, to a generator set.

Most common are AC generators. If a DC main electric system is required, as on a submarine, AC generators will still be used in combination with rectifiers. The type of generator (frequency, voltage) and number of generators are determined by the electrical load analysis, redundancy requirements and other rules and regulations provided by regulatory bodies. For electric powers up to 2500kW, AC generators with frequency/voltage of 50Hz/400V or 60Hz/440V (three phase) are generally installed. If the required electric power is higher, high voltage generators are implemented (voltage of 3.3 or 6kV). Often, the generator capacity is not given as real power (kW) but as the apparent power (kVA), the product of current and voltage, because the current required from the generator determines the dimensions due to heating of the windings.

A two-pole generator will give 60Hz at 3600 RPM, a four-pole at 1800 RPM and a six-pole at 1200 RPM.

50Hz is obtained at 3000 RPM, 1500 RPM and 1000 RPM for two, four and six-pole machines;

A large medium speed engine will normally work at 720 RPM for 60 Hz (10 pole generator) or 750 RPM for 50 Hz networks (8 pole generators);

The DC current was earlier transferred to the magnetizing windings on the rotor by brushes and slip rings;

Modern generators are equipped with brushless excitation for reduced maintenance and downtime;

The brushless excitation machine is an inverse synchronous machine with DC magnetization of the stator and rotating three-phase windings and a rotating diode rectifier. The rectified current is then feeling the magnetization winding; and

The excitation is controlled by an automatic voltage regulator (AVR), which senses the terminal voltage of the generator and compares it with a reference value.



3.5 Electrical Motors

Electrical motors are the most commonly used device for conversion from electrical to mechanical power and is used for DEP, thrusters or station keeping, and other on-board loads such as winches, pumps, fans etc. Typically, 80-90% of the loads in ship installation are electrical motors.

An electric motor can be directly connected to the network, and such direct-on-line (DOL) motors are normally three-phase asynchronous, or induction motors. The asynchronous motor has a rugged and simple design, where the three-phase stator windings are similar to a generator stator winding. The rotor is cylindrical, with a laminated iron core and a short-circuited winding similar to the damper winding in a synchronous machine. At no-load, the voltages imposed to the stator winding will set up a magnetic field in the motor, which crosses the air gap and rotates with a speed given by the frequency of the imposed voltages, called synchronous frequency, fs. Hence, the synchronous speed ns:

(3.1)

As the shafts get loaded, the rotor speed will decrease, and there will be induced currents in the rotor winding since they are rotating relatively to the synchronous rotating magnetic field from the stator windings. One defines the slip, s, as the relative lag of motor speed to the synchronous speed ns:

(3.2)

Hence the slip varies from 0 (no load) to 1 (block rotor). The slip at rated load is normally below 0.05 (5%) for most motor design, and even lower (2-3%) for large motors.

60/ 2

ss

fn

p

=

s

s

n ns

n

=



3.5.1 Asynchronous (Induction Motors) The asynchronous or induction motor is the workhouse of the industry. Its rugged and simple design ensures in most cases a long lifetime with a minimum of breakdown and maintenance. The asynchronous motor is used in any applications, either as a constant speed motor directly connected to the network, or as a variable speed motor fed from a static frequency converter.

The induction motor is characterized by simplicity, reliability, and low cost, combined with reasonable overload capacity, minimal service requirements, and good efficiency.

An induction motor utilizes alternating current supplied to the stator directly. The rotor receives power by induction effects. The stator windings of an induction motor are similar to those of the synchronous machine. The rotor may be one of two types. In the wound rotor motor, windings similar to those of the stator are employed with terminals connected to insulated slip rings mounted on the shaft. The rotor terminals are made available through carbon brushes bearing on the slip rings. The second type is called the squirrel-cage rotor, where the windings are simply conducting bars embedded in the rotor and short-circuited at each end by conducting end rings.

Figure 3-8: Asynchronous (Induction) motor construction (Wildi, 2006)



3.5.2 Synchronous Motors

Synchronous electric motors are AC motors that operate at fixed frequency of the system. These motors require direct current (DC) for excitation and have a low starting torque, and therefore synchronous motor suitable for use beginning with low load, such as air compressors, frequency changes and the generator motor. Synchronous motor is able to correct the power factor of the system and usually used in energy power systems that use a lot of electricity.

The synchronous machine is normally not used as a motor in ship applications, with exception of large propulsion drives, typically > 5 MW directly connected to propeller shaft, or > 8-10 MW with a gear connection. In power range smaller than this, the asynchronous motor is normally cost-competitive. The design of a synchronous motor is similar to that of a synchronous generator. It is normally not used without a frequency converter supply for variable speed control in ship applications.

Synchronous motors are like induction motors in that they both have stator windings that produce a rotating magnetic field. Unlike an induction motor, the synchronous motor is excited by an external DC source and, therefore, requires slip rings and brushes to provide current to the rotor. In the synchronous motor, the rotor locks into step with the rotating magnetic field and rotates at synchronous speed. If the synchronous motor is loaded to the point where the rotor is pulled out of step with the rotating magnetic field, no torque is developed, and the motor will stop. A synchronous motor is not a self-starting motor because torque is only developed when running at synchronous speed; therefore, the motor needs some type of device to bring the rotor to synchronous speed.

A synchronous motor may be started by a DC motor on a common shaft. When the motor is brought to synchronous speed, AC current is applied to the stator windings. The DC motor now acts as a DC generator and supplies DC field excitation to the rotor of the synchronous motor. The load may now be placed on the synchronous motor. Synchronous motors are more often started by means of a squirrel-cage winding embedded in the face of the rotor poles. The motor is then started as an induction motor and brought to ~95% of synchronous speed, at which time direct current is applied, and the motor begins to pull into synchronism. The torque required to pull the motor into synchronism is called the pull-in torque.



Figure 3-9: Synchronous motor construction (Wildi, 2006)

Synchronous motor has four main parts, rotor, stator, dc excited, and stator frame. Large machines include additional parts for cooling the machine, supporting the rotor, lubricating and cooling the bearings, and various protection and measurement devices.



3.6 Power Flow and Power Efficiency

Figure 3-10: Power flow in a simplified electric power system (Adnanes, 2003)

The prime movers e.g. diesel generators or gas turbines supply a power to the electric generator shaft. The electric motor, which could be the propulsion motor, is loaded by a power from its connected load. The power flow in diesel-electric propulsion is shown in Figure 3-10. The power lost in the components between the shaft of the diesel engine and the shaft of the electric motor is mechanical and electrical losses which gives heat and temperature increase in equipment and ambient and the typical values of electrical efficiencies in DEP system according to Table 3-1.

(3.3)

out outElectrical

in out losses

P PP P P

= =+



Table 3-1: Typical values of electrical efficiencies in DEP system (Adnanes, 2003)

Typical values of electrical efficiencies Generator 0.95 0.97 Switchboard 0.999 Transformer 0.99 0.995 Frequency Converter 0.98 0.99 Electric Motor 0.95 0.97 Diesel engine shaft to electric propulsion motor shaft 0.88 0.92

3.7 Ship Fuel Consumption

Fuel economy is important, not only because of the direct operational cost consequences for a diesel plant operator, but also in view of the ultimate scarcity of fossil fuel and the direct link with the emission of pollutants.

The measurement for fuel economy is specific fuel consumption, SFC. The specific fuel consumption is by defining the fuel consumption of the engine related to brake power.

f

B

msfc

P=

i

(3.4)

The specific fuel consumption will have a value of sfc 220 160g/kWh. By multiplying the specific fuel consumption with the power, the fuel consumption of the ship per unit time can be obtained:

f Bm sfc P= i

(3.5) The fuel consumption per mile covered can be found by dividing the fuel consumption per hour by the speed:

f

s

mfcmv

=

i

(3.6)



3.8 Range and Endurance

When given the amount of fuel F onboard and the fuel consumption per mile, fcm as a function of ship speed the following can be determined:

Range: How far can the ship get as a function of speed? Endurance: How long can the ship sail as a function of speed?

If the amount of fuel available on board is F then the range is the inverse of fuel consumption per mile:

FR fcm= (3.7)

Figure 3-11: Range of a typical frigate of 3300 tonne displacement with mechanically driven CODOG installations (Stapersma & Woud, 2002)

Figure 3-11 shows a typical curve of the range of the example ship as a function of speed. Range is the inverse of fuel consumption per mile, so if there is an optimum for fuel consumption, there is an optimum range as well.



Endurance is important in case a ship has to stay present in a certain area. It is linked to range as follows:

s

REv

= (3.8)

Figure 3-12: Endurance of the example ship (Stapersma & Woud, 2002)

Figure 3-12 gives the endurance of the example ship for which the previous figure gave the range. There is a step when changing from main to cruise engines. A marked difference with the range is that endurance always increases when ship speed decreases. In fact the maximum occurs exactly at zero ship speed.

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Marine Propulsion