The interaction between diesel engines, ship and propellers during manouevring

The interaction between diesel engines,

ship and propellers during manoeuvring

Delft University of Technology

Ship Hydromechanics Laboratory

Library

Mekelweg 2, 2628 CD Delft

The Netherlands

Phone: +31 15 2786873 - Fax: +31 15 2781836 !C. ' ' -I '7-'1`=. enr NS: 4r, '...I'- ...'"-I

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-Paul Schulten

The interaction between diesel

engines, ship and propellers during

The interaction between diesel

engines, ship and propellers during

manoeuvring

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. dr.ir. J.T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op maandag 23 mei 2005 om 15.30 uur

door

Paulus Johannes Maria SCHULTEN

werktuigkundig ingenieur

Dit proefschrift is goedgekeurd door de promotoren:

Prof. ir. D. Stapersma

en:

Prof. dr.ir. T.J.C. van Terwisga

Samenstelling promotiecommissie:

Rector Magnificus

Prof. ir. D. Stapersma

Prof. dr.ir. T.J.C. van Terwisga

Prof. dr.ir. J.A. Pinkster

Prof. dr.ir. F.G.J. Absil Prof. dr.ir. R.S.G. Baert Prof. A.P. Roskilly, BSc, PhD Prof. N. Bose, BSc, PhD

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Delft University Press

P.O. Box 98 2600 MG Delft The Netherlands Telephone: + 31 15 27 85 678 Telefax: + 31 15 27 85 706 E-mail: infoOlibrary.tudelft.n1 ISBN 90-407-2579-9

Keywords: ship propulsion system, total model, uncertainty analysis Copyright ©2005 by Paul Schulten

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be reproduced or utilized in any form or by any means, electronic or mechanical,

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Delft University Press. Printed in the Netherlands

Voorzitter

Technische Universiteit Delft, promotor Technische Universiteit Delft, promotor

Technische Universiteit Delft

Koninklijk Instituut voor de Marine

Technische Universiteit Eindhoven

University of Newcastle upon Tyne

Memorial University

Preface

On the 28th of june 1914 the Archduke Franz Ferdinand, heir to the Austro-Hungarian

throne, was assassinated by Gavrilo Princip, a Serbian nationalist. This single act triggered a sequence of events that was to lead to the Great War. The course of this war was shockingly different from what people had expected with its four years of stalemate trench fighting and millions of victims.

The events that followed from Gavrilo Princip's assassination tell us that the conse-quences of dramatic actions are unpredictable and can be unexpectedly large. Or in the words of the German Great War veteran and author Ernst Ringer (1920): "That's the role of chance in war. More than elsewhere, small causes can have a vast effect."

1 Every action man or mankind undertakes has a sometimes surprisingly large but

ultimately unknown effect on the course of the world. Only if the action and

sur-roundings are extremely simple (e.g. not complex), a short term prediction can be made. Gavrilo Princip could safely assume that his shots, when aimed well, would kill Franz Ferdinand. The breaking out and course of the Great War however surely will not have been in his mind

I consider these to be universal principles. They do not only apply to the actions of man and mankind on the world stage, but also to complex technical systems, such as the ship - propeller - diesel engine combination. It is very difficult, if not

impossible, to accurately predict the dynamic behaviour of this system, especially when it operates under true operational circumstances where wind, current and waves play an important role.

In this thesis it is investigated how the wake in a turn, via the propeller, works through

to the inner variables of the diesel engine. Only by combining measurements with analytical models did I manage to shed a little bit of light on this complex system.

'Originally in German: "Zo spielt der Zufall im Krieg. Mehr als anderswo gilt hier: Kleine

Ursachen, groBe Wirkungen."

-As always, the research resulted in more questions than that real answers have been

provided.

Reading the above, the question arises what the purpose of human action and science then is. Why act in this world when the outcome of the action is unpredictable and why investigate technically complex systems if these investigations do not result in clear, immediately usable conclusions? The answer of course is that, although the outcome is unpredictable, our actions and investigations do have an effect. We have a moral obligation toward our fellow man and to the future generations to push the world in the right direction, to learn, to investigate and to try to create a better place than it is today, however uncertain and difficult the road is we have to take.

Contents

Preface

vii

1

Introduction

1

1.1 Research background and relevance 1

1.2 Research objectives 3

1.3 Thesis outlines 5

2 The ship mobility model

7

2.1 Introduction 7

2.2 Terminology 8

2.3 Literature 9

2.4 General modelling concept 10

2.5 Applied Ship Mobility Model 11

3 The diesel engine model

15

3.1 Introduction 15

3.2 Diesel engine modelling concepts 17

3.3 Concept of mean value diesel engine model 18

3.4 Cylinder model 22 3.4.1 Cylinder process 22 3.4.2 Gas exchange 25 . . . I.

...

. .

CONTENTS 7

Matching

71 7.1 Introduction 71 7.2 Definitions 73 7.3 Modelling objectives 74 7.4 Procedure 77 4 5

3.4.3 Cylinder model inputs and outputs

3.5 Discussion

The propeller and wake model

4.1 Introduction

1.2 Propeller performance in oblique flow - Gutsche model

4.2.1 Analytical calculations

4.2.2 Numerical results

4.3 Wake distribution in oblique flow

4.4 Implementation in Ship Mobility Model

The manoeuvring model

5.1 Introduction

5.2 Equations of motion

5.3 Hydrodynamic forces and moments: Fresim

5.4 Accuracy of Fresim 5.5 Discussion 34 35 37 '37 38 38 45 45 47 51 51 52 53 55 56 6

Uncertainty analysis

6.1 Introduction

6.2 Purpose of uncertainty analysis

6.3 Origins of uncertainty

6.3.1 Theory uncertainty

6.3.2 Parameter/variable uncertainty

6.3.3 Measurement uncertainty

.4 Mathematics

6.5 Uncertainty analysis in multidisciplinary modelling

59 59 60 60 62 63 64 65 68 .. - -.. . . . . . .

CONTENTS

7.5 Diesel engine model 78

7.5.1 Matching step flow resistance and power output. 78

7.5.2 Matching step 2: connecting front end 80

7.5.3 Matching step 3: connecting rear end 81

7.5.4 Part load behaviour 82

7.5.5 Sensitivity and uncertainty 83

7.6 Propeller model 86

7.6.1 Matching of parameters 86

7.7 Manoeuvring model 88

7.7.1 Matching of parameters 88

7.7.2 Sensitivity and uncertainty 89

7.8 Uncertainty of the total model 91

7.9 Discussion 93

8

Validation

95

8.1 Introduction 95

8.2 Model validity and accuracy 97

8.3 Validation of the diesel engine model 98

8.4 Validation of the propeller model 105

8.5 Validation of total model 106

8.5.1 103 rpm turning circle 106

8.5.2 70 rpm turning circle 112

8.6 Summary and conclusions 116

9 Examples

123

9.1 Introduction 123

9.2 Example A: diesel engine thermal loading 124

9.2.1 Static considerations 124

9.2.2 Dynamic results 130

9.2.3 Conclusions 134

9.3 Example B: constant KT control for cavitation reduction. 135

9.3.1 Background 135 .. .. , ..

....

. . . conclusions,

... .

...

CONTENTS

9.3.2 Constant Kt controller. 136

9.3.3 Modelling results 137

9.3.4 Conclusions and recommendations 143

10 Conclusions and recommendations

145

10.1 Validity of the Ship Mobility Model 146

10.2 Smart-buying sub-models 149

10.3 Case studies 151

10.4 Recommendations 152

A Derivation of diesel engine model formulas

155

A.1 Volume element 155

A.2 Resistance element 158

A.3 Induction 160

B Model and physical parameters

165

B.1 Diesel engine model 165

B.2 Propeller model 180

B.3 Manoeuvring model 181

C Part load behaviour diesel engine model

185

Bibliography

198

Nomenclature

199

Summary

205

Samenvatting

208 Acknowledgements 211

Curriculum Vitae

213

...

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

1

Introduction

"The birth of an idea is that happy moment when every-thing appears possible and reality has not yet entered into the problem."

Rudolph Diesel

1.1

Research background and relevance

In the period 1984 - 1997 a number of actions have been performed that can be

regarded as the foundations of the research written down in this thesis. First of all, in a continuous cooperation between the Royal Netherlands Naval College and Delft University of Technology, a mean value diesel engine model has been created. The development of this model, in various appearances, has taken nearly 15 years and in

fact is still continuing. It started with a simple thermodynamic description of the

cylinder process and evolved to a model where all elements of the diesel engine, from air filter to exhaust, are modelled.

Another development was the Dynaship project, undertaken at the Royal Netherlands Naval College. In this project, a mobility model of a Multipurpose Frigate was de-veloped in which not only the manoeuvring of the frigate was included, but also the

-CHAPTER 1. INTRODUCTION

,diesel engine On the form of a lookup table) and the combinator curves. The model could be 'sailed' via a (simulated) control position on the bridge and even the choice between cruising diesel engines and main gas turbines could be made..

A third development was the creation of a well validated ship manoeuvring model

by the Maritime Research Institute Netherlands (MARIN). In this model (called

`Fresiml the motions of the ship in calm water conditions in 4 degrees-of-freedom,, he. surge, sway, roll and yaw, are predicted using a full non-linear model based on the main particulars of the ship.

Finally, the operation of propellers in oblique flow (e.g. in a turn) was experimentally investigated by MARIN. Analytical treatment of the propellers makes it possible to

calculate the effects of the varying wake on the resulting thrust and torque of the

propellers. This effect is fundamentally different for the inner and outer propeller of a twin-shaft ship in a turn.

Although all mentioned developments deal with the same system (the mobility of

the engine - propeller - ship system), they still are separated developments and are

examples of the 'traditional' system analysis. In this traditional analysis the

engi-neer, model builder or researcher stays within his own field of expertise. As soon as boundaries have to be crossed and the modeller needs information from other fields of expertise, simplified models are chosen for those "foreign' parts. As an example, to simulate the load on a marine diesel engine, often a simple static resistance curve is used instead of the true marine environment (6-degrees-of-freedom dynamic manoeu-vring in waves and under the influence of waves).

In recent years however, this traditional system engineering approach is being chal-lenged by more holistic and true total system engineering. Three developments are responsible for this fact. Firstly, the development of the personal computer and its in-credible increase in memory and computing power make it possible to simulate large, complex systems. Apart from a number of special systems or special mathematical operations, nearly all modelling can be done by commercially available hard- and software. Secondly, due to automation and the use of electronic and other complex technologies, individual components and the systems they are part of tend to get more" complex. For adequate functioning of a component, a good component design is not sufficient: The component has to function correctly within the mobility 1 system. To evaluate this, a system approach is required.

"Closely related to this is the third reason for the growing interest in total system simulation: the attention for the in-service operation of the mobility system. The

reason for this is that it is the experience of (naval) ship owners that, when sailing in true operational circumstances (wind, waves and continuous manoeuvring), the wear of the components was higher than ,expected, resulting in higher maintenance costs

1A definition of 'mobility' is given in section 2.2.

-1.2. RESEARCH OBJECTIVES

and longer engine downtimes. This thesis deals with the development and validity of a holistic model of the mobility system, with a focus on manoeuvring in calm water. The relevance and applicability of this model can be found in many ways. The model

could be used to evaluate existing systems and to gain insight in the fundamental

functioning of the mobility system and its components. The answers to these 'why' questions (why is the outer propeller overloaded in a turn, why is the diesel engine temperature higher in a turn?) might prove valuable in the troubleshooting process

of an existing system and provides a better general understanding of the system.

Another type of question is related to the design of systems. The model can be used for the 'what if' question. What if a different propeller or diesel engine is used? What are the effects on the diesel engine if the maximum rudder angle is enlarged? Also

more innovative and conceptual questions are possible: what if I control the ship

speed instead of the shaft speed?

Apart from the development and analysis of the model, in this thesis also examples of a 'why' and a 'what if' questions are given, see the next section for further details.

1.2

Research objectives

This research consists of three objectives: to develop a model of the mobility function of a ship and assess its uncertainty, to gain knowledge of the process of creating a

multi-disciplinary model and finally to show the applicability of the model in the

analysis and design of the propulsion system.

Elaborating on the first objective, the focus not only lies on the interaction between

the various components, but also on the behaviour of the individual components within the system. With the model it should be possible to look into a problem

related to a certain component and then assess the effects on the other components. This line of thought -the simultaneous assessment of all affected components- is a basic philosophy of this research. Therefore, in the initial development of the model, special emphasis on one specific sub-system should be avoided as much as possible. When in the end the model is used, shifts in attention can occur.

Because the model consists of sub-models originating from different fields of expertise

(diesel engine, ship manoeuvring, ship propulsion), no single person can develop all sub-models. The developer of the total model acts as a system integrator and 'smart-buys' models from the specialists who in their turn have to present (or 'smart-sell') their model in terms of output, applicability and modelling concept. This topic is also addressed in this thesis and forms the second research objective. Summarizing, the first objective is to have a model and to determine it's validity, the second objective is to gain knowledge on how to develop such a complex model. This second research question will not be addressed in a specific chapter, but will be discussed throughout

CHAPTER 1. INTRODUCTION

the whole thesis. A summary is given in chapter 10 where the research questions are

answered.

The third part of the research is to demonstrate the use of the model by investigating two specific problems. The focus does not lie on this part, but it is merely used as an example of the possibilities and limitations of the model. The examples presented are an investigation of the thermal loading and possible overloading of the diesel engine

in a turn and the development of a constant KT controller (meant for cavitation

reduction). This latter could be favorable to the propeller in terms of cavitation. The model is used to assess the effects of such a control regime on the rest of the system. In this research the author fulfills two roles: as system integrator and as developer of a specific sub-model: the diesel engine model. Because of this the diesel engine receives more attention in this thesis than the other elements.

The objectives as discussed above translate into the following specific research

ques-tions.

1. What is the validity2 of the total model with respect to: diesel engine variables (torque, temperatures, pressures), ship manoeuvring variables (ship velocities, shaft speed), propeller variables (torque, thrust).

2. How is a complex total simulation model developed when the system engineer has to smart-buy sub-models?

3. Can the model be used to address the following questions:

Is the diesel engine thermally overloaded in a turn, and if so, what is the

mechanism?

What is the effect of a constant KT controller, used for cavitation reduc-tion, on the diesel engine and on the manoeuvring capabilities?

Summarised answers to these questions are given in chapter 10 (`Conclusions and recommendations').

Finally, at this stage it must already be noted that the matching and validation

elements concern the model without controllers (engine governor and higher order mobility controller or Toortstuwings Regel Automatiek VRA' in Dutch). This is achieved by using measured outputs of the controllers (fuel rack position and pitch

angle) as input to the model. Only with the two examples presented in chapter 9

(simple) controllers are introduced.

1.3

Thesis outlines

This thesis consists of ten chapters and three appendices in which the total model is described, validated and used. The development of the model is based on the cruising engine operation of the Air Defense and Command Frigate (in Dutch luchtverdedig-ings en Commando Fregat' or LCF), currently in service with the Royal Netherlands

Navy. The LCF has a length of 130.2 m, a displacement of approximately 5800 tonnes and in cruising condition is powered by two Wartsila 16V26 sequentially turbocharged diesel engines. The LCF is propelled by two 4.95 meter diameter propellers, each

pro-peller being driven by one diesel engine. For higher speeds the LCF is equipped with two gas turbines. The gas turbine operation is not considered in this research.

In chapter 1 the research background, the research objectives and the outlines of

the thesis are written down. The important aspect of this chapter is the formulation of the research objectives as they in fact dictate the outlines of the research and this

thesis.

Chapter 2 deals with the concept of the 'Ship Mobility Model'. The relation between the various sub-models is shown and the model boundaries are determined.

The details of the three most important sub-models are presented in chapter 3(diesel

engine model model), chapter 4 _{(propeller model) arid} chapter 5 (manoeuvring

model). The manoeuvring model has not been developed by the author and chapter 5 is limited to a general description of the theory of manoeuvring and the way the applied model fits into this field. Because details of the model cannot be given (it

is a commercially used and therefore protected model), an important part of this

chapter is the presentation of this model in terms of output, validity and applicability. The concept of the diesel engine model, its background and its details are described more extensively because the development of the diesel engine model was part of the research. Chapter 3 therefore is more elaborate then the other two model description

chapters. The propeller model is based on a combination of three parts: standard

propeller performance characteristics (KT-KQ-J), implementation of the effects of

oblique propeller inflow and implementation of the effects of a varying wake in a turn.

In chapter 5 these theories and their combination are presented.

In chapter 6_{some background concerning uncertainty analysis and the way it is to}

be used in multidisciplinary modelling and simulation is presented. This is slightly different from the uncertainty analysis in measurements although the physical and mathematical foundations are the same.

Chapter 7deals with the matching of the model. For each of the three sub-models the matching of the parameters is extensively described, including the determination of the uncertainty in of the model outputs. The validation of the model is performed

using independent total system measurements and is described in chapter 8. The

CHAPTER 1. INTRODUCTION

end result of this chapter is la, presentation of the validity of the model for each of the target variables.

The application of the model in the form of two examples is given in chapter 9. The examples are the use of the model in investigating the thermal loading of the diesel engine in a turn and the development of a constant KT control 'system.

In chapter 10. the conclusions and recommendations are presented.

In appendix A the derivation of important formulas used in the diesel engine model

are presented. Appendix B shows the static part load behaviour of the diesel engine

The ship mobility model

"It is a mistake to try to look too far ahead. The chain of destiny can only be grasped one link at a time."

Sir Winston Churchill

2.1

Introduction

Since multi-disciplinary modelling involves the input of different fields of expertise (or

experts), clear and unambiguous communication is essential. This communication not only involves the used vocabulary but also an agreement on the model boundaries and structure.

As always in models of complicated systems, the Ship Mobility Model consists of different levels. The higher levels will focus on the total system and the deeper one gets into the model, the more the sub-models will represent components. Although there is no sharp borderline between a system and a component description, in total system modelling they have different functions.

CHAPTER 2. THE SHIP MOBILITY MODEL

The high level system concepts are needed to ensure a clear communication between the specialists. In fact, it defines where the world of one specialist ends and where the world of the other begins. The system concepts should be agreed on by all. On a component level, the specialist defines the model and its architecture. Although

the specialist is free to design his or hers own concept, two conditions are to be

satisfied. Firstly, the model should fit in the overall system. Secondly, the concept should be logical, clear and transparent. Others using the model should be able to assess the philosophy and physical concepts on the basis of the layout.

In this chapter, the Ship Mobility Model is introduced on a system level. The philo-sophy and details of the most important sub-models are presented in the next three

chapters.

Another aspect of clear communication is the use of a consistent vocabulary. The general definitions making up the standard vocabulary are found in every textbook

on the subject and there is little controversy over them. Therefore they are only

briefly addressed in the following paragraph.

2.2

Terminology

A physical system usually is made up of several sub-systems. These sub-systems

can either be single components or consist of a number of components. Also a sub-system can be based on a certain functionality instead of on a physical object. An

example is a ship (system) which consists of a large number of components (e.g.

diesel engine, rudder, shaft). A number of these components make up a sub-system (the drive train consisting of diesel engine, gearbox, shaft and propeller). Of course these considerations can be made at various levels: the diesel engine in itself is also a

(sub)-system consisting of various components.

A mathematical model is a (simplified) representation of a system. A model can consist of several sub-models that represent the sub-systems. A simulation is an

imitation of a physical process using the model.

A (sub-)model is quantitatively characterized by parameters. During a simulation the parameters remain constant. The inputs and outputs of the simulation are variables that change during the simulation.

In this thesis the following terms relating to the movement of a ship will be used:

ship movement, ship manoeuvring, hydrodynamic forces and moments, ship propulsion

and ship mobility. The pure motions of the ship, without looking at causes or at the details of the ship are referred to as 'ship movement'. Ship movement is part of 'ship manoeuvring' which primarily deals with the 'hydrodynamic forces and moments'

architecture, the term 'ship propulsion', is part of the ship manoeuvring and deals with that part of the ship that produces the thrust force (e.g. propeller or water jet) and as such are part of the hydrodynamic forces. In marine and mechanical engineering 'ship propulsion' or the 'propulsion system' usually denotes the mechanical system that converts a primary energy source to a thrust force (e.g. diesel engine, gearbox, shaft and propeller).

In this thesis the relevant expression is 'ship mobility' which incorporates all the areas described above. Ship mobility thus deals with all (sub)-systems that contribute to the eventual movement of the ship, from primary energy source to ship motion.

2.3

Literature

An early example of a total ship model where diesel engine, propeller and ship ma-noeuvring are combined is the model by Droste (1984). In this model the focus lies on the propeller. The diesel engine is modelled as a single formula and only longitudinal movement (surge) is regarded.

Most research in recent years that deals with the total system is limited to one-degree-of-freedom manoeuvring and relatively simple diesel engine modelling. The role of the diesel engine model is to provide torque and no research questions regarding the internal behaviour of the diesel engine can be answered. Examples are the models of Bonivento et al. (2002) and Izadi-Zamanabadi and Blanke (1999) who use it to investigate fault-tolerant control.

The diesel engine receives more attention in the models used by Grimmelius and Sta-persma (2000), van Terwisga (1998) and van Spronsen and Tousain (2001). They all

used instances of the same model which includes one-degree-of-freedom manoeuvring and a mean value diesel engine model. Van Spronsen and Grimmelius investigated the overloading of the engine in seaway while van Terwisga focused on the hydrodynamic

aspects of the system in general and specifically on cavitation on the propeller. The model used in these references is the direct predecessor of the model presented in this paper.

The fact that the concept of the Ship Mobility Model is not limited to a diesel engine-propeller driven ship is illustrated by Hansen et al. (2001) and Haller (2001) who both constructed a total ship model for a diesel-electric podded drive.

The models found in literature that are most comparable with the model used in this thesis are the models of Benvenuto and Kyrtatos. Benvenuto et al. (2001) have ob-tained acceptable results with a three-degrees-of-freedom manoeuvring model (surge, sway and yaw) combined with a propeller model and a two zone diesel engine model. Considerable research has been performed by Kyrtatos (Kyrtatos and Koumbarelis,

1991, 1993; Kyrtatos, 1994, 1997; Kyrtatos et al., 1999) who, for a number of different

CHAPTER 2. THE SHIP MOBILITY MODEL

research questions, uses total models in which crank-angle diesel engine models are

combined with one, two or three-degrees-of-freedom manoeuvring models.

If the Ship Mobility Model as used in this thesis is compared with the models found in literature, the following fundamental differences are found:

The manoeuvring is based on a state of the art manoeuvring model designed by MARIN and includes four-degrees-of-freedom movement: surge, sway, roll and

yaw.

The propeller model incorporates the effects of oblique inflow as well as differ-ences in wake between the inner and outer propeller.

A very sophisticated and information rich diesel engine model is used. This is also the case in the Benvenuto and Kyrtatos models but the model used in this thesis has the potential to be much faster while containing the same amount of information as will be shown in chapter 3.

2.4

General modelling concept

The general concept of the Ship Mobility Model is shown in figure 2.1. It does not only

apply to the system as investigated in this thesis (a twin shaft diesel engine-propeller driven frigate) but represents the concept of most ship propulsion systems, save for a few exotic concepts. The general Ship Mobility Model consists of 5 sub-models.

Ship Movement. In this sub-model the six degrees-of-freedom equations of mo-tion are modelled. The inputs of this sub-model are the hydrodynamic forces, the outputs are positions, speeds and accelerations in the various directions. Active Forces and Moments. In this sub-model the directly controllable forces and moments that actively move the ship are calculated. The final outputs are the (thrust) forces generated by the propulsors (e.g. classic propeller, azimuth thruster or podded thruster). The propulsors are driven by some kind of engine. Engine and propulsors are linked via the rotational dynamics.

Passive Forces and Moments. In this sub-model the forces and moments that are generated because of the (relative) ship velocities are calculated. Examples are rudder forces and moments, resistance forces and moments and stabilizer

forces and moments.

Disturbances. In this sub-model the effects of wind and waves (uncontrollable inputs) are modelled.

,1.

.3.

ACTIVE FORCES AND MOMENTS engine rotor dynamics propulsor multiple input MOBILITY CONTROL SHIP MOVEMENT 1 f"--surge

yaw PASSIVE FORCES sway AND MOMENTS

rudder forces hull forces roll pitch heave DISTURBANCES wind waves

Figure 2.1: Concept of the Ship Mobility Model.

5. Mobility Control. This refers to the system that translates the command given by the operator to setpoints for the active and passive forces sub-systems. This translation can be either direct, via a combinator curve, or via a true control sys-tem following a certain control strategy. In this case the inputs to the mobility control system can be every set of measurable parameters of the ship mobility system. The mobility control system is not the only control system. Controllers usually are found at every level of the system. Recognition of the controllers and the level they operate at is essential for a clear and unambiguous model structure.

Note that the 'hydrodynamic forces and moments' are calculated in two sub-models: the active and passive forces and moments sub-models.

2.5

Applied Ship Mobility Model

From the general Ship Mobility Model as presented in the previous paragraph, the

actual model as used in this thesis can be derived. The model is based on a twin

shaft, diesel engine-propeller driven frigate whose physical layout is presented in figure

2.2. The five sub-models of the general Ship Mobility Model are implemented in the

APPLIED SHIP MOBILITY MODEL 2.5.

CHAPTER 2. THE SHIP MOBILITY MODEL

Rudder Propeller Shaft Gearbox Diesel engine

Figure 2.2: Physical layout of LCF frigate.

following way:

Ship movement is calculated with four-degrees-of-freedom equations of motion:

surge, sway, yaw and roll. Because the model is restricted to calm water condi-tions, pitch and heave and their influence on the other motions are considered

to be negligible.

The active forces and moments sub-model is divided in a starboard and a port side. The models for both sides are equal and consist of a diesel engine model, a propeller model and a rotational dynamics model.

The passive forces are calculated using the (commercial) program Tresim', de-veloped by MARIN. Fresim calculates the hydrodynamic forces and moments (including the rudder forces and moments) based on four-degrees-of-freedom manoeuvring. The propeller forces and moments are also calculated by Fresim, but these results are not used. Instead, an improved propeller model is used. -1. The Ship Mobility Model is only evaluated in calm water and calm weather

conditions. The disturbances are not directly modelled (i.e. the 'disturbances' sub-model is empty). Indirectly, the disturbances resulting in added resistance are accounted for by using a service margin (an addition to the hull resistance following from towing tank tests).

5. In its basic form, the model has no intelligent high level control system. The mobility control sub-model just produces the appropriate setpoints to the diesel engine model and the propeller model. In fact, the only true control systems in the Ship Mobility Model are the governor and the pitch controller as used in chapter 9.

The mathematical relations between the various sub-models are best illustrated using

figure 2.3 in which the mathematical relations for a one-degree-of-freedom 1

manoeu-vring ship are shown. The two main elements are the integrator blocks. The 'ship

Shaft Rotation Dynamics

VA

2.5. APPLIED SHIP MOBILITY MODEL

Disturbances

Figure 2.3: Block diagram of longitudinal ship dynamics (Stapersm,a, 2004).

translation dynamics' block calculates the ship speed by integrating the force balance between ship resistance and propeller thrust using Newton's second law.

d (m u)

dt =-

F.,

Fship

1

(Fprop Fship) dt uo (2.1)

The loop is closed because the ship resistance depends on the output of the integrator

(ship speed).

The 'shaft rotation dynamics' block calculates the shaft speed by integrating the

torque balance between engine torque and propeller torque, again using Newton's

second law.

d (27/ n)

dt op 1

n =

(Meng 11-1prop) dt no Disturbances Ship Resistance (2.2)

'Figure 2.3 also shows the concept of a multi-degrees-freedom manoeuvring model if u is

consi-dered to be a velocity vector and Fsh, a forces and moments vector.

Commandl,

ndem Propulsion Odem Pitch

Governor Control Control

System System pro, Diesel Engine Propeller Torque Propeller Thrust A I Ship Translation Dynamics = ₊

CHAPTER 2. THE SHIP MOBILITY MODEL

The loop is closed because the engine torque depends on the output of the integrator (shaft speed).

Both loops (the 'ship speed loop' and the 'shaft speed loop') are linked through the propeller which provides (required) torque and (delivered) thrust. The output of the propeller depends on the advance coefficient J who in its turn depends on the outputs of the main integrators.

The final elements of the system are the controllers that translate the commands to setpoints for the propulsion engine and the pitch.

The three main sub-models (highlighted in figure 2.3) are discussed in chapter 3 (diesel

engine model), chapter 4 (propeller model) and chapter 5 (manoeuvring model). No-tice that the right highlighted block in figure 2.3 only involves the 'hydrodynamic forces and moments'. Still, in chapter 5 the manoeuvring model is described which, besides the hydrodynamic forces and moments, also involves the ship movement. In

figure 2.3, this ship movement is represented by the right integrator. Concerning

the diesel engine model, something similar could be done. The diesel engine model could be extended with the shaft rotational dynamics, creating the diesel engine drive model. However, since the shaft rotational dynamics are straightforward and need no further elaboration, chapter 3 deals with diesel engine core model only.

Summarizing, there is a slight unbalance in the treatment of the left and the right loops

of figure 2.3. The right loop is referred to as the manoeuvring model (so including the integrator) while the left loop is referred to as the diesel engine model (so without the integrator). Only in chapters 7 and 8 is the diesel engine drive model (so including the integrator) in some cases used.

The other sub-models in figure 2.3 (governor, propulsion control system, pitch control

system) are outside the scope of this thesis. Only when examples of the applicability of the model are presented in chapter 9, simplified models for the governor and pitch control are introduced.

-3

The diesel engine model

3.1

Introduction

A typical layout of a turbocharged inter-cooled marine diesel engine is shown in

fig-ure 3.1. The Wartsila 16V26ST engine, on which the matching and validation is

based, resembles this engine but has two fundamental differences. First, the Wartsila 16V26ST is equipped with sequential turbocharging. This means the engine has two

turbocharging units. In full load both units are used while in part load one unit is

turned off. The advantage is that if the diesel engine operates in part load, the remain-ing turbocharger operates closer to its nominal load condition. The second difference is the bypass valve which, if open, short circuits the output of the compressor(s) and the outlet receiver. Part of the air then bypasses the cylinder.

"All generalizations are false, including this one."

Dwight D. Eisenhower

'Part of the text in this chapter is reprinted with permission from SAE Paper # 2003-01-0219

CHAPTER 3. THE DIESEL ENGINE MODEL

silencer

Figure 3.1: Turbocharged and inter-cooled diesel engine (Klein Woud and Staperpna, 2002).

The model described in this chapter primarily relates to the engine concept shown in figure 3.1, so without sequential turbocharging and a bypass valve. Since these elements are only measured in status quo, e.g. without switching from one to two

turbocharging units and opening/closing of the bypass valve, modelling of this

switch-ing and openswitch-ing/closswitch-ing has not been performed. A more extensive study, includswitch-ing details of the sequential turbocharging control, has been performed by Boetius and Baan (1998). A few relevant details are presented in this chapter and in chapter 7. The model concept focuses on a 4 stroke engine (the Wartsila 16V26ST is a 4-stroke engine). A 2-stroke engine version of the model has been developed and described by Dijkstra (2003a).

The diesel engine model as used in this research is the result of a development process

that included a number of research studies at different stages. At the start of the PhD-research, a model of the Wartsila 16V26ST, developed by Boetius and Baan (1998)

and Baan (1998), was available. Apart from restructuring the model, the major

contribution by the author was the revision of the modelling of the gas exchange. Because of this, the gas exchange model receives a lot of attention in this thesis and

inlet filter

3.2. DIESEL ENGINE MODELLING CONCEPTS

is described in great detail in section 3.4.2. Of the other model parts, only relevant details are presented and reference is made to literature.

3.2

Diesel engine modelling concepts

The field of diesel engine modelling is as extensive as there are applications: every

design process or research project has its own fit-for-purpose model. Still, only a

limited number of modelling concepts can be recognised. According to Brace (1996) a distinction should be made between analytical and empirical models. The various analytical models have in common that they consist of a set of algebraic and differen-tial equations. The difference between the models is the volume size and the time step for which these equations are solved. Since simulation time increases as the volume or time discretization increases, there usually is a trade-off between the amount of information a model contains, the accuracy and the simulation speed.

The empirical models usually are fast and, depending on the availability of measure-ments, accurate. They consist of lookup-tables or best-fit polynomials in which the measured data is stored. This approach however has two disadvantages. First, the models are not generic. They are meant to replace a specific engine and are used to analyze the (dynamic) behaviour of that specific engine. As soon as the engine para-meters change, for instance simple scaling up or down, it is unclear how the measured data should be treated. Secondly, it is not possible to generate engine data other than is measured e.g. it is not possible to ask questions to the model. A further distinction between the various empirical diesel engine model concepts is given by Brace (1996).

The clear distinction between the analytical and empirical models is not found in

practice. Every analytical model at some level incorporates empirical parts.

Regarding the analytical models, five main areas can be recognized. In order of

complexity:

CFD models.

Phenomenological multizone models,

Filling and emptying / crank angle models,

Mean value models,

Transfer function models.

The computational fluid dynamics models are usually intended to model the processes in the cylinder. The combustion chamber is divided into tens of thousands of volumes or elements (a fine grid) and the basic equations between these volumes or elements

CHAPTER 3. THE DIESEL ENGINE MODEL

are then solved. They provide very detailed information of the internal processes and require powerful computers and long computing times.

If the combustion chamber is divided in a smaller number of control volumes (in the order of 10, a coarse grid) the computing time can be dramatically reduced.

Further, if not only the basic continuity-, momentum and energy equations are used but also some phenomenological equations, e.g. for reaction rate and heat transfer, a phenomenological multi-zone model is obtained. An example of a phenomenological multi-zone model is the model by Stiesch and Merker (1998).

The CFD-based models and the phenomenological multi-zone models are intended to provide detailed information of the cylinder process or part of the gas flow and usually only includes the cylinder and/or the inlet and outlet ducts.

With the filling and emptying models the control volumes are the various components

of the diesel engine, e.g. the cylinder, compressor and air intake. With steps in

the order of magnitude of a crank angle (hence the alternative name crank angle

models), the (differential) equations governing the processes between the elements are solved. The cylinder process is modelled using the fundamental energy equation

and a combustion (rate) model. Furthermore, other in-cylinder and in-cycle processes are modelled with a varying complexity. For instance, Zweiri et al. (2001) include extensive inertia and friction models, resulting in detailed cycle information.

If a complete diesel engine model is to be included in a larger system, say for instance

the drive train of a ship or a vehicle (including load and environmental influences), the in-cycle variations usually are not of primary interest. The focus lies on overall engine

parameters such as manifold temperatures and pressures, turbocharger speed, air-fuel ratio and maximum cylinder pressure that can be generated by a mean value model. These models basically have the same origin as the filling and emptying models but since the time step is in the order of one revolution, the discrete in-cylinder processes that take place within a revolution have to be replaced by mean value models. If the internal mechanisms of the engine are of no interest at all, but only the engine-output is needed, one could settle for a transfer function model. The engine is merely

represented by a simple second or higher order system in which some basic dynamical

aspects (e.g. delay time between injection and torque build-up) are incorporated.

3.3

Concept of mean value diesel engine model

The concept of both the crank angle diesel engine model and the mean value diesel engine model is shown in figure 3.2 from which the following observations can be

FPftme.

I

Inlet

i volume

nturbo

1.3. CONCEPT OF MEAN VALUE DIESEL ENGINE MODEL

tf

f I

TT

T

[...1 L...j

_ p Turbine Silencer 1.-p,

Figure 3.2: Concept of crank angle model and mean value model.

The primary inputs of the model are engine speed neg and fuel fuel rack

po-sition X. The secondary inputs are the ambient conditions parnb andTamb and

the cooling water temperature Tcw. The primary output of the engine is engine torque Meng. The primary inputs are directly fed into the cylinder sub-model, the primary output directly comes out of the cylinder sub-model. Torque cal-culation therefore takes place in the cylinder sub-model.

The compressor and turbine are mechanically linked. Integrating the difference in compressor torque Menn, and turbine torque Au, results in the turbocharger rotational speed nturbo which is also an input to both the compressor and the turbine models.

The inlet volume, the air cover, the inlet receiver, the outlet receiver and the

silencer volume are modelled as a series of control volumes. In the control

volumes the instantaneous mass is calculated by integrating the net mass flow (conservation of mass). Integrating the net energy flow associated with the mass flows results in the instantaneous temperature (conservation of energy). The incoming mass flows have their own temperature, the outgoing mass flow have

a temperature that is equal to the instantaneous temperature of the element.

The instantaneous pressure of the element now can be calculated using the ideal gas law. The formulas are presented in appendix A.1.

The control volumes are connected via resistances. In a resistance element

the mass flow rit is calculated as a function of pressure difference using the

momentum equation. If applicable, heat exchange results in a difference between

Silencer volume X Fuel I.- pump non, CYLINDER I

ikon, Air ñicau Inlet Cylinder fir

Cover receiver volume

t

flf

Corn P'1.2 Cha kLI I - Air," Inlet JpLCylinderCylinder Outlet

I Cooler valves valves

I Outlet th receiver 1 Meng n twto 1.,

CHAPTER 3. THE DIESEL ENGINE MODEL

Tin and Tout (e.g. in the charge air cooler). The standard formulas of a resistance

element are shown in appendix A.2.

M _

f

Pout Resistance 1 71, 11'7-0, 1 Volume Tin

Figure 3.3: Resistance and volume element.

The main difference between the crank angle models and the mean value models is the way the cylinder process is treated. With the filling and emptying models, the thermodynamical processes in the cylinder are regarded at each crank angle. The flow through the cylinder is calculated in the same way as was done in the other volume elements. The heat input in the cylinder volume is achieved by using a sophisticated (but still phenomenological) combustion model that calculates the heat release at each

crank angle.

In the mean value models the cylinder volume as such is left out and combined

with the cylinder inlet- and outlet resistances. The dynamical (cylinder) volume and inlet/outlet valves are replaced by analytical models for the cylinder process and the gas exchange. The advantage is that instead of a crank angle time scale a revolution time scale can be used during the simulation, theoretically increasing the simulation

speed with a factor 400 or so. The downside is that analytical models have to be

developed which in fact are the solutions to the original differential equations of the crank angle model. An example of such a solution is given in appendix A.3 where the induction model is derived.

Although a mean value diesel engine model does not provide information on a crank angle scale, it still predicts the same information in terms of number of signals. Ex-amples are: mass flow, turbocharger speed, inlet receiver pressure and temperature, maximum cylinder pressure and temperature, outlet receiver pressure and tempera-ture, engine torque, exhaust gas temperature.

STELLINGEN

behorende bij het proefschfift

The interaction between diesel engines ship anti propellers during manoeuvring

van

Paul 'Schulten

23 mei 2005

Technische Universiteit Delft.

De aanname dat gedurende een manoeuvre het transversale volgstroomveld in de onderste helft van het schroefvlak versterkt wordt met een factor anderhalf terwijl dit in de bovenste helft van het schroefvlak gelijk blijft, blijkt goed te werken voor de voorspelling van het koppel van de buitenste schroef van een dubbelschroef

schip met open assen.

[Dit proefschrifq

2

De uitlaatgassen temperatuut is een van de meest ingewikkelde en comPlexe grootheden van de dieselmotor. Een beter begrip van deze grootheid volgt na simulatie aangezien het maken van een simulatiemodel dwingt tot het uitvoeren

van metingen en analytische beschouwingen. Juist door de combinatie van simulatie, meting en theoretische analyse lukt het om het dynamisch gedrag enigszins te verklaren Dit principe ('stimulatie door simulatie') geldt voor alle

complexe technische systemen.

[Dit proefschrift],

3

Het varen met een constante stuwkrachtcoefficient-regeling is gunstig voor het uitstellen van cavitatie van de schroef, het voorkomen van therrnische overbelasting

van de dieselmotor en heeft een beperkt effect op de manoeuvreereigenschappen van het schip.

,[Dit proefschrifq

4

De uitvoer van eon complex model kan Met eenvoudig gededuceerd worden 1

5

De onzekerheidsanalyse is bedoeld om de betrouwbaarheid van een model te bepalen. Minstens zo relevant is de betrouwbaarheid van de onzekerheidsanalyse.

6

Naast gestructureerde documenten is bij het construeren van een complex simulatiemodel de mondelinge communicatie tussen de diverse specialisten van

essentieel belang.

7

Het gebruik van confidentiele gegevens beInvloedt de wetenschappelijke

openbaarheid in negatieve zin. Een proefschrift dat gebaseerd is op niet openbare

confidentiele gegevens is daardoor niet wetenschappelijk.

8

Gebrek aan ervaring kan worden gecompenseerd door karakter en talent. Gebrek aan talent kan worden gecompenseerd door ervaring en karakter. Gebrek aan

karakter zal echter nooit worden gecompenseerd door talent en ervaring. 9

Aangezien de toekomst niet te voorspellen is, zijn de lessen uit het verleden alleen zinvol voor vandaag en niet voor morgen.

10

Langdurige polarisatie is alleen nuttig bij magneten en zonnebrillen.

Deze stellingen worden verdedigbaar geacht en zijn als zodanig goedgekeurd door de promotoren.

PROPOSITIONS

appended to the thesis

The interaction between diesel engines, ship and propellers during manoeuvring

by

Paul Schulten

23 mei 2005

Delft University of 'Technology

The assumption that during a manoeuvre the transversal wake field in the lower half of the propeller plane will be multiplied by a factor 1.5 while it remains the same in the upper half, turns out to be adequate for the prediction of the torque of

the outer propeller of a twin-propeller ship with open shafts.

[This thesis]

2

The exhaust gas temperature is one of the most difficult and complex variables of the diesel engine. Better understanding of this quantity follows from simulation

since the creation of a simulation model forces measurements and theoretical evaluations. Because of the combination of simulation, measurement and theoretical analysis it is possible explain the dynamic behaviour of the exhaust gas

temperature to a certain extend. This principle ('stimulation through simulation')

is valid for all complex technical systems.

[This thesis]

3

Sailing with a constant thrust-coefficient controller is favorable for the delay of cavitation of the propeller, the prevention of thermal loading of the diesel engine

and has limited effect on the manoeuvring properties of the ship.

[This thesis]

4

5

Uncertainty analysis is meant to assess the reliability of a model. Just as important is the reliability of the uncertainty analysis.

6

Apart from structured documents, oral communication between the various specialists is essential when constructing complex simulation models.

7

The use of confidential information has a negative effect on scientific transparency. )2(

A thesis that is based on non-public confidential information therefore is not

scientific.

8

Lack of experience can be compensated by character and talent. Lack of talent can be compensated by experience and character. Lack of character however will never

be compensated by talent and experience. 9

Since the future is unpredictable, the lessons from the past are useful only for today and not for tomorrow.

10

Prolonged polarisation is only useful for magnets and sunglasses.

These propositions are regarded as defendable, and have been approved as such by the supervisors.

3.3. CONCEPT OF MEAN VALUE DIESEL ENGINE MODEL

The details of the cylinder model (cylinder inlet valves, cylinder volume and cylinder

outlet valves in figure 3.2) are presented in section 3.4. In the remainder of this section

the other elements are briefly described.

Fuel pump. The fuel pump is modelled using the following relation:

th fuel = X nen, (3.1)

With this relation the fuel flow depends linearly on the engine speed neng and the fuel rack position X.

Air filter and silencer.

The air filter and the silencer are modelled as standard resistance elements. From the pressure differences over the elements the mass flows

directly are calculated following equation A.33 for compressible flow.

Inlet volume, air cover and silencer volume.

The inlet volume, air cover and

silencer volume have one input mass flow and one output mass flow. The

instan-taneous temperatures and pressures of the elements follow from equations A.19 and

A.21.

Compressor. The compressor model is based on the compressor map provided by

the manufacturer. In this map the compressor isentropic efficiency Ths and volume flow

Qcon, are stored as function of the pressure ratio pacIpir. From the inlet conditions

pi, Ti, and Ri, the mass flow

outlet temperature Tc0m and the compressor torque Mc°, are calculated 2.

Piv rhCOM = Q COM (3.2) Ri, _LT,

)'

1

,)

(

TC0771

=T+

1 -.- . (PCL' (3.3) 7/is Pir

PCOM thcom (Cp,iv ' Cp.com Team)

Mcorrt = (3.4)

27r nturbo 27f _ntarbo

The sequential turbocharging is modelled by multiplying the compressor mass flow corn with a factor 2 if both turbocharging units are running If the bypass is open, the flow from the turbocharger to the outlet receiver is calculated from the pressure

difference par pa, using the resistance formulas.

'The specific heats c and Cp,com in equation 3.4 are determined at the temperatures of the associated flows (7', and Tom). Strictly speaking this is incorrect since the temperatures should be

temperature differences relative to the reference temperature and the specific heats should be mean values over that temperature difference, see appendix Al..

CHAPTER 3. THE DIESEL ENGINE MODEL

Charge air cooler.

'The charge air cooler model is adopted from Boetius and Ban

(1998). It consists of two stages (a high temperature stage and a low temperature

stage) where the gases, heated from the compression in the compressor, are cooled

using two cooling water flows..

Inlet and outlet receiver.

In the mean value modelling concept the flow through the cylinder is divided in a number of discrete flows as will be explained in section 3.4. These flows then are thermodynamically mixed in the inlet and outlet receiver using the standard volume element equations, in this case with more than one input and output.

Turbine... Instead of using a lookup table,, the turbine has been modelled using the generic turbine map developed by Dijkstra (2003b). This generic turbine map has been matched to the Wartsila 16V26ST engine using the procedure as 'described in

chapter 7 resulting in values for the turbine flow riztur and temperature Ttur. . From

this, the turbine torque Mt is 'calculated as:

Ptur ihtur l(Cp,or ' T Or - Cp,tur '

Mtur =

ZIT - nturbo. 27r _nturbo.

Again, the specific heats are determined at the temperatures of the associated flows and the effects of the reference temperature Tref are neglected see appendix A..

3.4

Cylinder imodel

In a mean value model the cylinder process is divided in a number of discrete processes: inflow, combustion, scavenging, blowdown, outflow as is shown in figure 3.4. For each

of these processes mean values of mass flow, temperature, composition, pressure and work are calculated using only algebraic functions. The various mass flows are then

thermodynamically mixed in the outlet receiver (or in the inlet receiver in case of

backflow) resulting in the entry condition for the turbine.

3.4.1 Cylinder process

The modelling of the cylinder process is based on a theoretical 6-point Seiliger process.

This process (numbers 1 to 6 in figure' 3.4) consists of polytropic compression (1-2), isochoric combustion (2-3), isobaric combustion (3-4), isothermal combustion (4-5)1 and polytropic expansion (5-6). The shape of the process primarily depends on the combustion parameters a, 6 and ie.. For these ,parameters the following engine

(3.5)

1kCylinderPressure Pori IL BDC 3 b4 TDC El°BDC I 10 TDC I EC

Figure 3.4: Diesel process divided in discrete processes.

speed dependent and fuel flow dependent (e.g. load dependent) equations have been

developed: (XN neng

± X) '

rid ' qcb a = 1 + et, T2 X6 gcb

bb = b a = 1+

Cp C

=T4

e

a,r

These models are based on measurements by Schulten (1997, 1998) on a MAN 4L20/27

diesel engine that were later verified and fitted to the Wartsila 16V26ST engine by Boetius and Baan (1998) and Baan (1998) using measurements from Wartsila. In the calculation of a, bb and c, the following considerations are made:

The heat input in the Seiliger cycle qi, is less than the energy in the fuel q

because of incomplete combustion (expressed by the combustion efficiencynth)

and the heat loss to the cooling water (expressed by the heat release efficiency

rig) rh, fHO

qin=qcbqq=qfr7cbr)q=

71, 71q Mi 3.4. CYLINDER MODEL BDCIIC (3.6) (3.7) (3.8) (3.9) EXHAUST SC*/ , INDUCTION CYLINDER GAS PROCESS EXCHANGE Crank Angle

CHAPTER 3. THE DIESEL ENGINE MODEL

From the total heat input q, and the heat inputs q23 and q34 during stages 2-3 and 3-4 (see table 3.1), the heat input during q43 stage 4-5 can be calculated.

'445 qin q23 (434 (3.10)

The ignition delay Yid is calculated using the equation by Hardenberg and Hase

(Heywood, 1988).

The factor Xb is calculated as:

Xb = C1 ± C2 ne,g (3.11)

neng,TLOM

The heat release efficiency is calculated as:

Qloss

qcb

The mean heat loss flow Qi053 is:

i nen9

loss = a Ac b (Tg,cb Tw,cb) t3_5

The calculation of the mean values of the heat transfer coefficient the wall

area Acb, the gas temperature Tg,,b and the wall temperature Tu,,,b as well as the time from 3 to 5 t3_3 is described in (Boetius and Baan, 1998).

The combustion efficiency is a function of the air excess ratio A according to:

{

(0.9 + 0.1 elm) - A

A < 1

ricb =

0.9 + 0.1 e,

1< A < As,,,

1 A > A,,,

The air excess ratio A is the ratio of the amount of available air and the amount of air that is minimally required to burn all fuel (the stoichiometric amount). At a certain air excess ratio Asm the amount of air is insufficient for complete combustion and the engine starts to smoke.

Once the parameters a, b and c are known, the temperatures, pressures and work in the various stages of the Seiliger cycle can be calculated, see table 3.1.

The result is that the work generated in the Seiliger cycle can be calculated as a

function of trapped conditions rill, pi, T1, fuel flow riv and engine speed Tien,.

(3.14)

(3.12)

3.4. CYLINDER MODEL

Table 3:1:e Seiliger cycle calculations.

3..4.2 Gas exchange

The gas exchange is defined by 4 discrete processes (numbers 6-7 and I-VI in figure 3.4). During each process certain amounts of mass are involved and by multiplying these masses with the engine frequency fenfl

neng

Jeng k

the mean value mass flows are obtained. The mass flows involved in the gas exchange are shown in figure 3.5 (inlet mass flows) and 3.6 (outlet mass flows)..

In figure 3.5, the mass flow Thi is trapped in the cylinder at the start of the cylinder

process when the inlet closes. A small part of this mass flow is the result of incomplete

scavenging during the previous gas exchange: ihres. The rest however is fresh in the

cylinder:

The fresh gases that enter the cylinder can be divided in two parts. When both the inlet and outlet valves are opened, scavenge gases flow through the engine as a result of the pressure difference between inlet and outlet receiver. Part of this scavenge flow' (7hr et) will be retained in the cylinder because at a certain point the outlet receiver

closes. The second part of the fresh gases consists of the gases that are induced

because of the piston movement when only the inlet valve is opened

(3.15) 1 Volume V Pressure P Temperature I T Work' w Heat q 1-2 IA, = re_{v2 p i}2., _ nc T> =1- -1 7'. W12 = ma. 2-3 L VI -_V2 Ea =a_P2

_{,-, =a}

-,2 .- , q23 = 6,23(T3 T2) 3-4I I

i"-,4 = b_.,3 FLA. ,_ 1_7,3' l'i._T3 b

= -w34 = R34 (T4 T3), 1734 = 4,34 (T4 T3) -I

5=o'

1 4 P5

=c

1 T5 W45 = R45 T4 In C

q4=

R45 T4 ln.c.

ii 5-6 Il(i = 7-=_bc P-u- = (r4bcre

P5 _ -I , RL = (rclbcre-1 R56 (T6 T5 ) n.a.. W56 = ,, 1 R (T2 -T1) 1

-CHAPTER 3. THE DIESEL ENGINE MODEL Mres(idual) ihslip VTDC vs thret(nined thcvl sc(avenge

Figure 3.5: Inlet mass flows of a 4-stroke diesel engine.

Because of the valve overlap a considerable part of the gases flows through the engine

(rhsi,p) and the total scavenge flow rils, thus consists of a part that 'slips' through

the cylinder and a part that is 'retained' in the engine. The mass flow that is trapped in the cylinder at the end of the scavenge phase (when the outlet closes) is denoted Thsct, (scavenge-trapped).

Finally, the total amount of gases rit, that enter the engine is the scavenge flow 'tits, plus the induction flow rilid.

In figure 3.6, the mass flow that takes part in the blowdown process (rhbld) is the mass flow in the cylinder at the end of the Seiliger process, Th.bld = Th6- =7771 + 7h f. When

the exhaust valve opens, an amount rhbid_out immediately exits the cylinder during the blowdown process 6 - 7, leaving fri7 in the cylinder. Both rh6 and 7.117 occupy

volume VE0. They are drawn equal length in figure 3.6, but they are not equal mass: Th6 = rn7 + Thbld-out The gases left in the cylinder (Th7) are subject to the exhaust stroke during which only rhex, will be expelled. The total amount Thbid_out+rhe.rp is

denoted 7i2exh. The remaining part in the cylinder Ths,(0) is the starting condition for

the scavenge phase. During scavenging, an amount rhsiip + rhleft exits the cylinder, Thle ft being the amount of gas that entered the cylinder during the previous cycle (e.g. 'left' over from Th6 and not exhausted by the `blowdown' or 'expelling' and not becoming 'residual'). After scavenging, of the original mass only Thre, still is in the cylinder. This means that an amount ri-16 -thres has been driven out. The total mass

2 11.7tr(apped)= rh1 1 .111 sctr EC _{thind(uction)} IC TDC V BDC BOG -. a

3 Filsc(0) -sc-out = = Ph,-F tit f m. 10 _{1;11exp(elled) 1E01} 161 BDC Mlikl thout CYLINDER MODEL

Figure 3.6: Outlet mass flows of a 4-stroke diesel engine.

flow that exits the engine now can be obtained: Mout = rhscolit + rhexh = Thin + rhf

Calculation of mass flows

The mass m1 that is trapped in the cylinder at the start of the cylinder process is

calculated by:

Pi,'Vic

17/1 = (3.16)

1

The total trapped mass flow riti of the engine then is:

Pir 'VIC

J (3.17)

/Li /1

The mass flow drawn in by the piston movement Th d is:

rh,fld = ritnd

The induction efficiency ilid is a function of the valve timing (i.e. volumes at the closing of the inlet and exhaust valves) and the ratio temperature and the cylinder temperature at the closing of the inlet

VIC VEC T1

Mres Mleft Meth

'us//p cvl-out TDC VBDC _V TDC Vs nind = VIC

Td

(3.18) of the cylinder of the induction valve: (3.19) 3.4..

=

eng

CHAPTER 3. THE DIESEL ENGINE MODEL

During the induction process, the pressure loss is assumed to be zero (pind = P1 =

Pir). The total scavenge flow Ms, can be calculated using the resistance-flow for-mula (equation A.33) if the pressure ratio pir /pop and the upstream pressure and

temperature are known.

The trapped mass after scavenging equals (refer to figure 3.5):

1- sc-tr = ihind (3.20)

The amount of residual mass Titres in the cylinder is determined by the effectiveness'

of the scavenge process:

'thres (1 - 71ret) (3.21)

In this equation rivet is a factor indicating the mentioned effectiveness and is calculated

assuming perfect mixing of the cold scavenge flow with the hot gases present in the cylinder. Further details are presented in the paragraph 'Scavenging'.

'The scavenge mass flow rhs, can be calculated using the standard resistance element equation presented in A.2 which for the scavenge flow becomes:

msc = (tt(15) A _'N/RirPir_Tir qf (3.22) The W-function is a function of the pressure ratio/Air/ Poi- and is calculated according'

to equation A.35.

With MI, and Titres known, the following mass flows. now can be easily

calculated:

As stated before the mass flow that takes part in the outlet phase of the gas 'exchange.. 'S.

7-116 = rhbid = rhf (3.27)

The part of this mass flow that does not immediately exit the cylinder during the

blowdown continues the polytropic expansion (stage 5-6 of the Seiliger process). Be-cause the pressure and temperature at the end of this expansion (pr = por, Tor) are

= rhres (3.23)

rhret = rhscir rhres (3.24)

rhslip = 'Thee rhret (3.25)

7hid Thse + rhind 0,261

=

known as will be shown in the paragraph Blowdown and exhaust', the resulting mass flow can be calculated:

pa" VED

R17 = hug

T7

Since the blowdown in the idealized process in figure 3.4 is assumed to occur

instan-taneously, volume 177 equals volume VE 0 . The mass flow Mbid_out then is:

rhbld out = th6 1.47

At the end of the exhaust stroke, the resulting mass in the cylinder m5(0) is:

Por Vto

72,4 sc(0) = J eng

R(0) T7

The massflow rilexp then is:

thexp = th7 th8c(0)

Recalling that Thieft is the mass flow that entered the cylinder during the previous

cycle and leaves during scavenging:

rhle f t thsc(0) Titres (3.32)

Finally:

rhexh = thexp ± Thudout (3.33)

r hsc out = rhslip rhle ft (3.34)

rhcyl out = 7-46 thres (3.35)

rhout = rh7, Th

f

(3.36)

Mass partition and composition

With the mass flows known, it is now possible to review the compositions of these

massflows. These compositions are of interest because they determine the air excess

ratio and the properties of the gases. First however a distinction has to be made

between the partition and the composition of a certain massflow. The composition x

is defined as the ratio of pure air or combustion air ri-ica and the total mass flowrittot:

rizca x = rhtot 3.4. CYLINDER MODEL (3.28) (3.37) (3.29) (3.30) (3.31)

CHAPTER 3, THE DIESEL ENGINE MODEL

ri7reS

1

qhni

Figure 3.7: Scavenge model: efficiencies 7fret, 71,nd and ilscav

In figure 3.7 the partitions of Thi are given. First, Thi is divided in Thin,' and Thsc_tr

using the previously defined induction efficiency

Secondly, a further division of ritsc_tr (the mass flow in the cylinder after

scaveng-ing, see equation 3.20) can be made using the efficiency 77t (equation 3.21). The

calculation of 71r,t is presented in the paragraph 'Scavenging'.

The composition of a certain mass flow will be smaller than unity in case of presence of (stoichiometric) combustion gases rh. The combustion gases emerge because of

the burning of fuel and typically consist of CO2, SO2, H20 and other gases and

particles. Excess air that was present in the cylinder during combustion and still is after combustion is not a part of the combustion gases. Consequently:

1 x = (3.38)

rhiot

and

rhtot = Thca Thcg (3.39)

Apart from the (chemical) composition of a mass flow, also the (flow) origin of its partitions can be considered. If for instance the mass flow in a cylinder consists of

part rhA that enters the cylinder at time A and a part rhB that enters the cylinder

at time B, then the partition riA is the ratio of rhA and the total mass flow:

riA =

Th A + Th13

ThA _(3.40)

From the given equations it is clear that the composition x is not the same as the

partition n since mass flow Th A can consist of air and combustion gases. The

calcula-tion of the mass flows in the previous paragraph was based on 77t and ihrid. In fact

these efficiencies are partitions as defined above.