An Analytical Model of Spark Ignition Engine for Performance Prediction

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AN ANALYTICAL MODEL OF SPARK IGNITION ENGINE

FOR PERFORMANCE PREDICTION

MR.SITTHICHOK SITTHIRACHA

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE MASTER OF SCIENCE IN AUTOMOTIVE ENGINEERING

SIRINDHORN INTERNATIONAL THAI-GERMAN GRADUATE SCHOOL OF ENGINEERING

(TGGS)

GRADUATE COLLEGE

KING MONGKUT’S INSTITUTE OF TECHNOLOGY NORTH BANGKOK

ACADEMIC YEAR 2006COPYRIGHT OF KING MONGKUT’S INSTITUTE OF TECHNOLOGY NORTH BANGKOK



Name : Mr. Sitthichok Sitthiracha

Thesis Title : An Analytical Model of Spark Ignition Engine for

Performance Prediction

Major Field : Automotive Engineering

King Mongkut’s Institute of Technology North Bangkok

Thesis Advisors : Assistant Professor Dr.Suthum Patumsawad

Assistant Professor Dr.Saiprasit Koetniyom

Academic Year : 2006

Abstract

The objective of this thesis is to develop a mathematical model of spark ignition

engine based on cylinder-by-cylinder engine model which combines both physical

formulae, e.g. engine geometries, and empirical formulae, e.g. burning duration. The

engine performance, torque and power, can be calculated by integrating the pressure

inside cylinder within one engine cycle. The model is verified by data from 8 engine

models. It can capture torque and power characteristics very well. The overall errors

are in between -6% to 4%.

The model is used for simulating in order to predict the burning duration of the

alternative fuels. Furthermore, the model indicates the effects on η v when using these

alternative fuels too.

(Total 60 pages)

Keywords : Spark ignition engine, Gasoline engine, Engine modeling, Cylinder-by-

cylinder engine model, Engine simulation

______________________________________________________________Advisor

ii



ชื อ : นายสิทธิโชค สิทธิราชา

ชื อวิทยานิพนธ์ : แบบจําลองวิเคราะห์สําหรับการทาํนายสมรรถนะของเครื องยนต์ จุดระเบิดด้วยประกายไฟ

สาขาวิชา : วิศวกรรมยานยนต์ สถาบนัเทคโนโลยีพระจอมเกลา้พระนครเหนือ

ที ปรึกษาวิทยานิพนธ์ : ผูช้วยศาสตราจารย์ ดร ่ .สุธรรม ปทุมสวสัดิ ผูช้วยศาสตราจารย์ ดร ่ .สายประสทิธิ เกดนิยม ิ

ปีการศึกษา : 2549

บทคัดย่อ วัตถุประสงค์ของวิทยานิพนธ์นีคื อ เพื อพฒันาแบบจําลองทางคณิตศาสตร์ของเครื องยนต์จุด

ระเบิดด้วยประกายไฟบนพืนฐานของ แบบจําลองเครื องยนต์แบบสูบตอสูบ ซึ งรวมเอาทัง ่ ทฤษฎีทางกายภาพ เป็นตน้วา เรขาคณิตของเครื องยนต์ และทฤษฎีที ไดจ้ากการสังเกต เป็นตน้วา ่ ่ระยะเวลาการเผาไหม ้สมรรถนะของเครื องยนต์อันไดแ้ก แรงบิดและกาลัง สามารถคํานวณไดโ้ดย ่ ํการอินทีเกรตความดันในกระบอกสูบภายใตห้นึ งรอบการหมนุของเครื องยนต์ แบบจําลองได้ทดสอบเปรียบเทียบคากบเครื องยนต์ ่ ั 8 รุน พบวา สามารถทาํนายลกัษณะกราฟสมรรถนะของ ่ ่เครื องยนต์ไดเ้ป็นอยางด ีโดยมีคาผดิพลาดโดยรวมอยรูะหวาง ่ ่ ่ ่ -6% ถึง 4%

แบบจําลองนี ได้จําลองสถานการณ์เพื อท ีจะทาํนายระยะเวลาในการเผาไหม้ของเชือเพลิง ทางเลือกตางๆ ่ ยิงกวานัน แบบจําลองยังสามารถท ีจะอธิบายผลกระทบของการใช้เชือเพลิง ่ ทางเลือกที มีตอประสิทธิภาพเชิงปริมาตรไดอ้ีกดว้ย ่

(วิทยานิพนธ์มีจํานวนทงัสิน 60 หน้า)

คาํสาํคัญ : เครื องยนต์จุดระเบิดดว้ยประกายไฟ, เครื องยนต์เบนซิน, แบบจําลองเครื องยนต์,แบบจําลองเครื องยนต์แบบสูบตอสูบ ่ , การจําลองเครื องยนต์

________________________________________________ อาจารยท์ี ปรึกษาวิทยานิพนธ์

iii



ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to Professor Dr.Gyeung-Ho Choi

of Power Train Laboratory, Keimyung University, Republic of Korea and Assistant

Professor Dr.Noppavan Chananpanich of King Mongkut’s Institute of Technology

North Bangkok who are initiators of this story. My colleague and I had a chance to

have internship in the Power Train Laboratory under their allowance. This laboratory

brought me to the engine technology field. Until Associate Professor Dr.Suwat

Kuntanapreeda and Dr.Boonchai Watjatrakul went to visit us in South Korea. They

advised me to undertake this topic for my thesis. This thesis has been developed since

that point. After I came back to Thailand, this thesis is strengthened by many precious

comments and suggestions from Assistant Professor Dr.Suthum Patumsawad and

Assistant Professor Dr.Saiprasit Koetniyom. Thanks to all persons who are

mentioned here. And also the staffs of the Power Train Laboratory who took care of

us along 4 months of our visit in South Korea.

Sitthichok Sitthiracha

iv



TABLE OF CONTENTS

Page

Abstract (in English) ii

Abstract (in Thai) iii

Acknowledgement iv

List of Tables viii

List of Figures ix

List of Abbreviations and Symbols xii

Chapter 1 Introduction 1

1.1 Background 11.2 Objectives 1

1.3 Approach 1

1.4 Scope 1

1.5 Assumptions 2

1.6 Impacts or Benefits from Research 2

1.7 Thesis Outline 2

Chapter 2 Literature Review 32.1 Spark Ignition Engine 3

2.2 Modeling 5

2.2.1 Mean Value vs. Cylinder-by-cylinder Models 5

2.2.2 Limit of Physical Properties 5

Chapter 3 The Model 6

3.1 Model Overview 6

3.2 Crank Slider Model 8

3.3 Cylinder Pressure Model 8

3.4 Wiebe Function 9

3.4.1 Burning Duration 9

3.5 Heat Input 10

3.6 Air/Fuel Ratio 10

3.7 Heat Transfer 11

3.7.1 Heat Transfer Coefficient Correlations 11

v



TABLE OF CONTENTS (CONTINUED)

Page

3.8 Volumetric Efficiency 12

3.8.1 Flow through Valves 15

3.8.2 Valve Lift 16

3.8.3 Discharge Coefficient 17

3.8.4 Frictional Losses 17

3.8.5 Charge Heating 19

3.9 Residual Gas 19

3.10 Friction 21

3.11 Torque & Power 21

3.12 Minimum Spark Advance for Best Torque 21

3.13 Simulation conditions 22

3.14 Alternative Fuels 22

3.14.1 Ethanol-blended Gasoline or Gasohol 23

3.14.2 Ethanol 24

3.14.3 Compressed Natural Gas 24

3.14.4 Liquefied Petroleum Gas 25

Chapter 4 Model Validation and Sensitivity Analysis 26

4.1 Performance Validation 26

4.2 Sensitivity Analysis 31

4.2.1 Burning Duration 31

4.2.2 Discharge Coefficient 32

4.2.3 Frictional Losses 334.2.4 Charge Heating 34

4.2.5 Exhaust Gas Temperature 34

4.3 Combustion Duration of Alternative Fuels 35

4.3.1 Ethanol-blended Gasoline or Gasohol 35

4.3.2 Ethanol 37

4.3.3 Compressed Natural Gas 38

4.3.4 Liquefied Petroleum Gas 39

vi



TABLE OF CONTENTS (CONTINUED)

Page

Chapter 5 Conclusions and Suggestions 41

5.1 Conclusions 41

5.2 Suggestions 41

References 43

Appendix A Engine Specifications 45

Appendix B Matlab/Simulink Block Diagrams 50

Biography 60

vii



LIST OF TABLES

Table Page

3-1 Air/fuel ratios of many substances 11

3-2 Parameters for simulation 22

3-3 Summaries of major properties of gasoline, ethanol, E10 and E20 23

3-4 Summaries of major properties of methane, ethane, and natural gas 24

3-5 Summaries of major properties of propane, butane, and LPG 25

viii



LIST OF FIGURES

Figure Page

2-1 Schematic of gasoline engine 6

2-2 Basic four stroke cycle 3

2-3 Pressure-volume diagram of Otto cycle 3

3-1 Model overview 6

3-2 Model overview (continued) 7

3-3 Piston cylinder and geometries 8

3-4 Burned mass fraction characteristic 9

3-5 Effect of engine speed on flame-development angle 10

3-6 Comparison of surface-averaged heat flux variations predicted by CFD

calculations and empirical correlations 12

3-7 Volumetric efficiency versus mean piston speed for a four-cylinder

indirect-injection diesel and a six-cylinder spark-ignition engine 13

3-8 Effect on volumetric efficiency of different phenomena which affect

the air flow rate as a function of speed. Solid line is final volumetric

efficiency versus speed curve 14

3-9 Discharge coefficient of typical inlet poppet valve 17

3-10 Pressure losses in the intake system of a four-stroke cycle spark-ignition

engine determined under steady flow conditions 18

3-11 Assumption of remaining pressure after subtracted by pressure losses 18

3-12 Assumption of temperature inside manifold 19

3-13 Measured cylinder pressure pc, calculated cylinder-gas temperature T c,

exhaust mass flow rate em& , and measured gas temperature at exhaust port

exit T p, for single-cylinder spark ignition engine at speed = 1000 rpm 20

3-14 Assumption of exhaust gas temperature 20

3-15 Cylinder pressure versus crank angle for over-advanced spark timing (50°),

MBT timing (30°), and retarded timing (10°) and Effect of spark advance

on brake torque at constant speed and air/fuel ratio, at wide open throttle 22

4-1 Simulation results of Mercedes-Benz 250SE 26

ix



LIST OF FIGURES (CONTINUED)

Figure Page

4-2 Simulation results of Mercedes-Benz 250E/8 27

4-3 Simulation results of Mercedes-Benz 250SL 27

4-4 Simulation results of Mercedes-Benz 280SE/8 28

4-5 Simulation results of Mercedes-Benz 280SL/8 28

4-6 Simulation results of Mercedes-Benz 300SEL/8 29

4-7 Simulation results of Mercedes-Benz 300SEL 29

4-8 Simulation results of Mercedes-Benz 600 30

4-9 Summarized relative errors from simulation results of 8 engines 30

4-10 Comparison between gasoline and +/-10 modified combustion range

without spark advanced adjusting 31

4-11 Relative errors of before and after adjusting the spark timing 32

4-12 Comparison between normal C D and +/-10% changing 32

4-13 Comparison between using and non-using C f 33

4-14 Comparison between using and non-using C heat 34

4-15 Comparison between normal and +/-50 K exhaust gas temperature 35

4-16 Effect of ethanol-blended fuel on volumetric efficiency 35

4-17 Combustion duration of gasoline, E10, and E20 29

4-18 Comparison between gasoline, E10, and E20 when using with unmodified

engine 36

4-19 Effect of ethanol as a fuel on volumetric efficiency 37

4-20 Combustion duration of gasoline, E10, E20, and E100 374-21 Effect of ethanol as a fuel on volumetric efficiency 38

4-22 Combustion duration of gasoline and CNG 38

4-23 Effect of ethanol as a fuel on volumetric efficiency 39

4-24 Combustion duration of gasoline and LPG 39

A-1 Performance curve of Mercedes-Benz 250SE 46

A-2 Performance curve of Mercedes-Benz 250SL 46

A-3 Performance curve of Mercedes-Benz 250E/8 47

A-4 Performance curve of Mercedes-Benz 280SE/8 47

x



LIST OF FIGURES (CONTINUED)

Figure Page

A-5 Performance curve of Mercedes-Benz 280SL/8 48

A-6 Performance curve of Mercedes-Benz 300SEL/8 48

A-7 Performance curve of Mercedes-Benz 300SEL 49

A-8 Performance curve of Mercedes-Benz 600 49

B-1 Main model 51

B-2 Cm block details 52

B-3 Engine geometry block details 52

B-4 Engine geometry/Vd block details 52

B-5 Engine geometry/A(CA) block details 52

B-6 Engine geometry/Crank geometry block details 53

B-7 Engine geometry/V(CA),Vc block details 53

B-8 Wiebe fn block details 53

B-9 Burn duration block details 53

B-10 P block details 54

B-11 P/Pratio block details 55

B-12 P/Lv fn block details 55

B-13 P/Cd block details 55

B-14 P/mdot block details 56

B-15 P/Cheat factor block details 56

B-16 P/Cf factor block details 56

B-17 Mw block details 57B-18 Residual mass block details 57

B-19 T block details 57

B-20 Heat tran block details 57

B-21 h block details 58

B-22 Work&Power block details 58

B-23 Work&Power/Work block details 58

B-24 Work&Power/FMEP block details 59

B-25 Work&Power/Effective power block details 59

xi



LIST OF ABBREVIATIONS AND SYMBOLS

Abbreviations

BDC Bottom Dead Center

CFD Computational Fluid Dynamic

CNG Compressed Natural Gas

CO Carbon Monoxide

DIN Deutschland Industrial Norm

ECU Engine Control Unit

EGR Exhaust Gas Recirculation

HC Hydrocarbon

HHV High Heating Value

HP Horsepower

LPG Liquefied Petroleum Gas

MBT Maximum Brake Torque

MWF Modified Wall Function

rpm Round per Minute

SAE Society of Automotive Engineers

SWF Standard Wall Function

TDC Top Dead Center

WOT Wide Open Throttle

Symbols

a Crank Radius A Exposed Combustion Chamber Surface Area

A R Reference Area

b Cylinder Bore

C D Discharge Coefficient

C f Frictional Loss Factor

C heat Charge Heating Factor

C m

Mean Piston Speed

xii



LIST OF ABBREVIATIONS AND SYMBOLS (CONTINUED)

Div Inlet Valve Diameter

Dv Valve Diameter

f Fraction of Heat Added

h Convection Heat Transfer Coefficient

HV Heating Value of Fuel

IVC Inlet Valve Close Angle After BDC

IVO Inlet Valve Open angle Before TDC

k Specific Heat Ratio

l Connecting Rod Length

Liv,max Maximum Inlet Valve Lift

Lv Valve Lift Function

mair,stoich Theoretical Amount of Air Requirement

m& Mass Flow Rate

ma Air Mass

N Engine Speed

p f Friction Mean Effective Pressure

pme Brake Mean Effective Pressure

pmi Indicated Mean Effective Pressure

pT Pressure at Restriction

p0 Upstream Stagnation Pressure

P Pressure Inside Cylinder

P e Effective Power Q Heat Addition

Qin Overall Heat Input

Qloss Heat Transfer

R Gas Constant

s Stroke

T g Temperature of Cylinder Gas

T exh

Exhaust Gas Temperature

T w Cylinder Wall Temperature

xiii



LIST OF ABBREVIATIONS AND SYMBOLS (CONTINUED)

T 0 Stagnation Temperature

V Cylinder Volume

V d Displacement Volume

Δθ Duration of Heat Addition

ε Compression Ratio

η v Volumetric Efficiency

θ Crank Angle

θ 0 Angle of Start of Heat Addition

ρ a Air Density

xiv



CHAPTER 1

INTRODUCTION

1.1 Background

Four-stroke spark ignition engine was developed by Otto in 1876. This engine

provided power output 3 HP. Since that point, the engine developing has been done

continuously over 100 years. Even now, some engines can provide power output more

than 1,000 HP.

However, developments of spark ignition engine along 100 years has been

conducting very slow due to lots of parameter, such as physical geometries (bore,stroke, crank radius, compression ratio), ignition advanced, valve timing, combustion

characteristic etc., influencing the performances. Many studies on effects of each

parameter were done by experiments. But this approach spent lots of expenses and

time such as building test engine, setting up laboratory, etc. Another approach is simulation method that allows engine designer to change

and test many different parameters without building real parts or even real engines.

The engine model can be used in various ways including designing engine control

system or ECU, designing transmission, etc. Although the computational model is

unable to obtain the exact characteristics because there are no perfect models and

there are many complex phenomena taking place in the engine, it simply estimates the

trend of those characteristics and effects with very low cost and less timeconsumption that is very helpful for speeding up the engine development process

before making real one.

1.2 Objectives

1.2.1 Develop a physically based, cylinder-by-cylinder spark ignition engine

model for predicting torque and power characteristics in order to study effects of

parameters such as engine geometries, fuel properties, valve timing layout, etc.

1.2.2 Predict the burning duration of alternative fuels such as Liquefied

Petroleum Gas (LPG), Compressed Natural Gas (CNG) and gasohol which are needed

information for simulation.

1.3 Approach

The engine model is developed under MatLab/Simulink which describes the

torque and power characteristics of the engine. The parameters, engine geometries

and valve timing layout, from existed gasoline engines are used. The model is

evaluated and compared with test data in order to determine the accuracy.

1.4 Scope

1.4.1 Use Matlab/Simulink for developing the engine model.

1.4.2 Gasoline is used for developing the model.

1.4.3 Outputs of the model are torque and power characteristics under full load

or wide open throttle (WOT) condition. For the alternative fuels, output is burning

durations.



1.5 Assumptions

1.5.1 The model will be derived from the spark ignition engine without turbo or

super charger and Exhaust Gas Recirculation (EGR) system.1.5.2 The engine uses multi-port injection system for adding fuels.

1.5.3 Fuel evaporates to be gas phase completely.

1.5.4 Fuel and air mix together perfectly.

1.5.5 Fuel-air mixture is assumed to be an ideal gas all the time.

1.5.6 There is no any effect of combustion chamber design.

1.5.7 Combustion chamber wall temperature is set at 400 Kelvin.

1.5.8 There is no effect of throttle body or there is no pressure drop at throttle

body due to WOT condition.

1.5.9 There are no effect of exhaust stroke and exhaust system.

1.6 Impacts or Benefits from Research The model which is developed under this thesis can be used for many purposes.

It can be used as an engineering tool in the development of the spark ignition engines.

The simulation can reduce the time consumption and costly tests needed in laboratory.

And also the model can be used for teaching a tool in the internal combustion engine

course.

1.7 Thesis Outline

The details of this thesis are shown as following

Chapter 1 Introduction

Chapter 2 This chapter explains of fundamental of spark ignition engine

and engine processes, review previous researches and theory of engine modeling

Chapter 3 Focusing on the performance prediction, this chapter describes

the model and theory of each component in details and

explanations of the alternative fuels

Chapter 4 Model validation by comparing to performance data from

vehicle manufacturer, analyze sensitivity when changing

parameters, and find out combustion duration of the alternative

fuels

Chapter 5 Conclusions and suggestions

2



CHAPTER 2

LITERATURE REVIEW

2.1 Spark Ignition Engine

The spark ignition engines are used in different applications, such as cars, boats

and small power generators. Depending on the field of application, the spark ignition

engine has certain structure and components which may differ from field to field. A

basic spark ignition engine used within the automotive industry has the following

structure and components as shown in Fig.2-1.

FIGURE 2-1 Schematic of gasoline engine [1]

The basic operation of a four stroke engine involves intake, compression,

expansion (or power), and exhaust strokes as shown in Fig.2-2. The piston starts at the

top, the intake valve opens, and the piston moves down to let the engine take in acylinder-full of air and gasoline. This is the intake stroke. Only the tiniest drop of

gasoline needs to be mixed into the air for this to work. Then the piston moves back

up to compress this fuel/air mixture. Compression makes the explosion more

powerful. When the piston reaches almost the top of its stroke, the spark plug emits a

spark to ignite mixture. The power generates from combustion and driving the piston

down. Once the piston hits the bottom of its stroke, the exhaust valve opens and the

exhaust leaves the cylinder to go out the exhaust pipe.



FIGURE 2-2 Basic four stroke cycle

With models for each of these processes, a simulation of complete engine cycle

can be built up and be analyzed to provide information on engine performances.

These ideal models that describe characteristic of each process are proposed. However

the calculation needs information from each state as shown in Fig.2-3a which

sometime could not obtain from real condition as shown in Fig.2-3b.

(a) (b)

FIGURE 2-3 Pressure-volume diagram of Otto cycle: (a) ideal; (b) real

Overall engine work can be determined by integrating the area under the

pressure-volume diagram. So many previous works concerned mainly prediction the

pressure inside the combustion chamber [2, 3, 4]. But the pressure and volume are

influenced by engine geometries during variation of crank angle. So the pressure and

displacement volume are needed to convert as functions of crank angle. Kuo [3] and

Kirkpatrick [5] proposed the method that can calculate the pressure and volume at anycrank angle. The combustion process can be described by simple correlation, Wiebe

function [6].

The results from Kuo [3] and Zeng et al [4] indicated that heat transfer from

inside the cylinder to engine cooling water had much influences on the pressure inside

the cylinder. So the heat transfer function is needed to take into account in the model.

Many researches reported that the mass of mixture that flows into the cylinder

during intake stroke is a very importance parameter [1, 2, 3], [6] because it affects

amount of fuel which mixes with the air. This mass can be determined by combining

the ideal gas law and volumetric efficiency. However it is very difficult to evaluate

because they are affected by many factors, such as manifold geometries and valve

timing [6]. So Eriksson et al [2] and Kuo [3] assumed that the pressure inside

4



manifold and inside the cylinder are the same, and neglect effect of volumetric

efficiency. But Kuo [3] used corrective equation from real experiment to compensate

the errors. While Zeng et al [1] took the effect of volumetric efficiency into account.However the data were obtained from the real experiment and stored in a 3-dimension

table by relation between engine speed and intake manifold pressure.

It can say that combining of those methods that are mentioned above can predict

the engine performances precisely only if some testing data are known, mainly the

volumetric efficiency. So this thesis tries to use the one-dimension flow model to

predict the volumetric efficiency in order to reduce the testing data dependence.

2.2 Modeling

There are numerous ways of describing reality through a model [7, 8]. Some are

more complex than others and the different approaches may differ in both structure

and accuracy. Choosing the model depends on the particular situation and especiallythe field of application. The model classifications are summarized follow.

2.2.1 Mean Value vs. Cylinder-by-cylinder Approaches

When considering the cylinder, two main approaches can be found. The most

common use is mean value engine method. The mean value method defines number

of cylinders as one which occupies whole displacement volume. The fluctuating flow

through the inlet port is modeled by average value over a cycle. The dynamics of

speed, engine torque, pressure build-up in the inlet and exhaust manifolds are the

aspects of most interest in this approach.

Another method to the mean method is the cylinder-by-cylinder engine

approach. Unlike the mean method, it describes each cylinder individually and

generates for example a torque signal with each individual combustion pulse present. Normally the mean model is sufficient enough for use in processes such as control

system design. But in engine performance development aspect, the cylinder-by-

cylinder method is better because this method derives from engine geometries, which

is very useful for improving and optimizing the engine in the future.

2.2.2 Limit of Physical Properties

There are a number of approaches available when deciding on the basis of a

model. Physical equation theoretically describing the system is the most common

method since it creates a general model working for many operating areas. Its

drawback is that reality might be difficult to describe correctly in theory.

Another common approach bases on the model entirely on measurements. The

measured data is stored as a table of two or more dimensions in a so called black boxdepending on input signals. This approach often provides an accurate result since it is

based directly on empirical formulation. However it is only defined for a limited

region. A combination of both approaches is commonly used. The main basis of the

model rests on physical equations. And empirical equations are used to model certain

complexities.

5



CHAPTER 3 THE MODEL

In this chapter the model is described in detail. The engine to be modeled is a

gasoline engine which has no EGR and turbo system. The chosen model bases on the

pressure inside the cylinder prediction. There are two main approaches to consider;

mean value and cylinder-by-cylinder models. Since the objective of this thesis intends

to develop the model which can describe effects of each parameter on the engine

performance, the cylinder-by-cylinder approach is used in order to achieve this goal.

Another consideration for model selection is limited by physical properties.Since there are no perfect equations which can describe phenomena in the engine,

both physical and empirical formulae are used in the model.

3.1 Model Overview

FIGURE 3-1 Model overview

Start

RPM Stroke Bore Conn. Rod Comp.Ratio Spark Angle

Heating ValueA/F RatioConn. RodIVOIVC k

Liv Div Tw No. Cylinder

Find mean

piston speed

Find displacement

volume

Find compression

volume

Find Temperature

of gas in cylinder

Find residual mass

θ = -360

θ = 180 No Yes

A

B

C

End

D

Find cylinder

volume, Eq.3-1

Find exposed combustion

chamber surface area, Eq.3-2

Find exhaust gas

temperature, Eq.3-21

Find total heat

input, Eq.3-7

Wiebe Function,

Eq.3-4

Heat release,

Eq.3-5 Find heat transfer coefficient,

Eq.3-10

Find pressure

increment, Eq.3-3

Find total heat

transfer, Eq.3-8

Find pressure inside

cylinder by integrating



FIGURE 3-2 (CONTINUED)

θ = θ + 1

A

B

)1/(

0 1

2−

⎥⎦

⎤⎢⎣

⎡

+≥⎟⎟

⎞⎜⎜⎝

⎛ k k

Critic

T

k p

p

0 p

pT =0 p

pT

0 p

pT = )1/(

1

2 −

⎥⎦⎤

⎢⎣⎡

+

k k

k

C

No

Yes

P e

D

Find valve lift

function, Eq.3-16

Find valve curtain

area, Eq.3-14Find discharge

coefficient, Eq.3-18

Find frictional loss

factor, Eq.3-19

Find charge heating

factor, Eq.3-20

Find flow-in mass,

Eq.3-15

Find total flow-in mass

by integrating

Find pressure that belongto flow-in mass

Find friction loss,

Eq.3-22

Find indicated mean

pressure, Eq.3-23

Find effective

pressure, Eq.3-24

Find effective power,

Eq.3-25

7



Fig.3-1 and Fig.3-2 shows the overview of the model. Engine geometries, such

as bore, stroke, compression ratio, etc., are calculated to obtain physical information

such as displacement volume, area and volume variation as function of crank angle,etc. That information will be used for cylinder pressure prediction with another line of

information about heat input. Heat energy needs data from amount of flow in mass

and burn characteristic which is described by Wiebe function. Predicted pressure will

be used to determine temperature inside cylinder and also heat transfer from cylinder

to wall chamber. Rate of heat loss will be fed back to the pressure prediction function.

Resulted pressure will be converted to indicated mean effective pressure subtracted by

mean friction, then work and power will be known finally. The Matlab/Simulink

block diagrams of the model are shown in Appendix B. The details of each module

are described in following section.

3.2 Crank Slider ModelThe volume of the piston cylinder can be determined as a function of crank

angle from the compression ratio (ε ), the stroke ( s), bore (b) and connecting rod

length (a). The geometric parameters of the piston cylinder can be described by the

crank slider model which is represented in Fig.3-3.

FIGURE 3-3 Piston cylinder and geometries

The equations of volume and area that relate to crank angle are described as

following equation [5]:

])sin(cos1[21

)( 2

1

2

2

θ al θ

al V

ε-V V d d

−⎟ ⎠ ⎞⎜

⎝ ⎛ −−++=θ Eq.3-1

])sin(cos1[22

)( 2

1

2

2

2θ

a

l θ

a

l sπ bb

π A −⎟

⎠

⎞⎜⎝

⎛ +−++=θ Eq.3-2

3.3 Cylinder Pressure Model

This model is derived from the first law of thermodynamics. The pressure is

derived as a function of crank angle also [5].

θ θ θ d dV

V P k Q

d Q

V k

d dP

loss −⎟ ⎠ ⎞⎜

⎝ ⎛ −∂−= 1 Eq.3-3

8



θ d

dV can be determined from Eq.3-1 by taking derivative with respect to the

crank angle (θ ). The Wiebe function for the burn fraction is used for θ d Q∂ .

3.4 Wiebe Function ( f )

The mass fraction burned profiles as a function of crank angle in each individual

cycle shown in Fig.3-4. It has a characteristic S-Shape. The rate at which fuel-air

mixture burns increases from a low value intermediately following the spark

discharge to a maximum about halfway through the burning process and then

decreases to a close to zero as the combustion process ends.

FIGURE 3-4 Burned mass fraction characteristic

A functional form often used to represent the mass fraction burned versus crank angle curve is the Wiebe function:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟

⎠

⎞⎜⎝

⎛

Δ

−−−=

3

05exp1)(θ

θ θ θ f Eq.3-4

The heat release ( Q∂ ) over the crank angle change (Δθ ) is:

θ θ d

df Q

d

Qin=

∂Eq.3-5

Then take the derivative of the heat release function ( f( θ )), with respect to crank

angle, beingθ d

df from Eq.3-4.

3.4.1 Burning Duration (Δθ )Mixture burning rate is influenced by engine speed. It is well established that

the duration of combustion in crank angle degrees only increases slowly with

increasing engine speed. Fig.3-5 shows how intervals of burning characteristics are.

The burning rate throughout the combustion process does not increase linearly as

engine speed. Additionally, increasing in-cylinder gas velocities (e.g. with intake

generated swirl) increases the burning rate. Increasing engine speed and introducingswirl both increase the levels of turbulence in the engine cylinder.

9



(a) (b)

FIGURE 3-5 Effect of engine speed on flame-development angle

(a) 10% and 90% burn [6] and (b) 100% burn [9]

However, the swirl characteristic is not able to determine easily depending onmanifold geometries and piston head design. Therefore, the results in Fig.3-5a, which

obtained from experiment, are used to estimate the burning duration (Δθ ) for gasoline.

951.39)1000

(886.19)1000

(6189.1 2 ++−=Δ N N

θ for 1000 ≤ N ≤ 6000 Eq.3-6

3.5 Heat InputOverall heat input can be determined by using heating value of fuel and amount

of mass which is drawn into cylinder.

stoichair

IVC

IVOin

m

d m HV

Q,1

)(

+=

∫ θ θ

Eq.3-7

Values of final mass fraction burned usually are in the range 93% to 98% due to

the fact that not all of the fuel is burned [6]. Kuo [3] used 95%. So this value is

applied to Qin.

3.6 Air/Fuel Ratio

In internal combustion engines, the air-fuel ratio refers to the proportion of air and fuel present during combustion. The chemically optimal point at which this

happens is the stoichiometric ratio. Examples are shown in Table 3-1.

For gasoline fuel, the stoichiometric air/fuel mixture is approximately 14.6

times the mass of air to fuel. This is the mixture that modern engine management

systems employing fuel injection attempt to achieve in light load cruise situations.

Any mixture less than 14.6 to 1 is considered to be a rich mixture, any more than 14.6

to 1 is a lean mixture.

10

M a s s B u r n ( × 1 0 0 ) %



TABLE 3-1 Air/fuel ratios of many substances

3.7 Heat Transfer

Generally there are three modes of heat transfer in the combustion engine.

Conduction - Conduction in solid matter is caused by molecular movement. Thedriving physical characteristic is the thermal conductivity. The heat flow in the

combustion chamber walls occurs through heat conduction.

Convection - Convection is a term for heat transfer occurring in a moving fluid.

The exchange of heat between the coolant or combustion gas and the combustion

chamber wall occurs through convection. The velocity and the degree of turbulence of

the moving fluid determine the degree of heat transfer via the convection.

Radiation - Heat transfer through occurs in the form of electromagnetic waves.

The energy of the radiation is proportional to T 4. Radiation is only relevant in the

combustion chamber and only short period of time during and after combustion when

high gas temperatures are present.

In spark ignition engines, the primary heat transfer mechanism from thecylinder gases to the wall is convection, with only 5% from radiation. Using a

Newtonian model, the heat loss to the wall is given by:

Qloss = hA(T g -T w) Eq.3-8

When determining the heat release term (θ d

Q∂) the heat loss to the walls has to

be taken into account. Substitute Eq.3-5 and Eq.3-8 in Eq.3-3, the pressure over crank

angle now becomes:

θ θ θ d dV

V P k T T

N hA

d df Q

V k

d dP

w g in −⎥⎦⎤⎢⎣

⎡ −−−= )(6

1 Eq.3-9

3.7.1 Heat Transfer Coefficient Correlations (h)

The heat transfer coefficient is needed in order to calculate heat loss from the

cylinder in Eq.3-8. For design purposes, simplified analyzes are often performed

using empirical heat transfer correlations such as Annand, Woschni and Hohenberg.

These give at most estimates of the surface-averaged heat transfer coefficient, which

are defined in terms of the bulk gas temperature and used with this to calculate

surface-averaged or total heat flux. Annand assumed a constant characteristic gas

velocity equal to the mean piston speed, while Woschni assumed that the average gas

velocity should be proportional to the mean piston speed. Hohenberg examined

Woschni’s formula and made changes to give better predictions.

11



Kleeman et al [10] compared these empirical correlations with Computational

Fluid Dynamic (CFD) prediction by using Standard Wall Function (SWF) and

Modified Wall Function (MWF) methods. Both SWF and MWF are boundary layer models which have been employed to calculate wall shear and heat transfer in CFD.

SWF derives the near-wall velocity and temperature profiles from a Couette flow

analysis, assuming steady one dimensional flow and ignore the variation within the

layer of the fluid thermophysical properties (e.g. density, viscosity, thermal

conductivity). The use of SWF in CFD calculation of engine heat transfer generally

leads to underprediction of the wall heat flux. So MWF is developed further for using

in engine simulation by taking the fluid thermophysical properties into account. The

results are shown in Fig.3-6.

FIGURE 3-6 Comparison of surface-averaged heat flux variations predicted by CFD

calculations and empirical correlations [10]

The results from [10] showed that the MWF method gave the most accurate

results. So using these simple correlations will introduce some errors. However MWF

can only be obtained from CFD because the CFD program can calculate the

instantaneous local heat fluxes which are not uniform throughout the combustion

chamber, while this thesis assumes the charge are burned completely throughout thecylinder at the same time. According to the results in Fig.3-6, the Hohenberg

correlation is selected because it is closest to MWF and also there is no empirical

form for MWF. The Hohenberg correlation is following equation [4].

8.04.08.006.0 )4.1(130 += −−m g C T P V h Eq.3-10

3.8 Volumetric Efficiency (ηv)

The intake system – the air filter, carburetor, and throttle plate (in a spark

ignition engine), intake manifold, intake port, intake valve – restricts the amount of air

which an engine of given displacement can induct. The parameter used to measure theeffectiveness of an engine’s induction process is the volumetric efficiency (η v).

12



Volumetric efficiency is only used with four-stroke engines which have distinct

induction process. It is defined as the volume of air which is drawn into the intake

system divided by the volume which is displaced by the piston, Eq.3-11. Typicalmaximum values of volumetric efficiency for naturally aspirated engines are in the

range 80 to 90%. The volumetric efficiency for diesels is somewhat higher than the

spark ignition engines as shown in Fig.3-7.

d a

av

V

m

ρ η = Eq.3-11

FIGURE 3-7 Volumetric efficiency versus mean piston speed for a four-cylinder

indirect-injection diesel and a six-cylinder spark-ignition engine [6]

According to Fig.3-7, there are no such a model can predict the trend of the

volumetric efficiency exactly because it is affected by the following fuel, engine

design and engine operating variables:

1. Fuel type, air/fuel ratio, fraction of fuel vaporized in the intake system, andfuel heat of vaporization

2. Mixture temperature as influenced by heat transfer

3. Ratio of exhaust to inlet manifold pressures

4. Compression ratio

5. Engine speed

6. Intake and exhaust manifold and port design

7. Intake and exhaust valve geometry, size, lift and timings

The manifold and valve geometry design has great effects on the volumetric

efficiency since the designs of each engine model have never been the same. So this

thesis tries to develop the model in order to predict η v caused by the different valve

design.

13



FIGURE 3-8 Effect on volumetric efficiency of different phenomena which affect

the air flow rate as a function of speed. Solid line is final volumetric

efficiency versus speed curve [6]

The shape of volumetric efficiency can be explained by Fig.3-8. It is affected by

many different phenomena. Non-speed-dependent effects (such as fuel vapor

pressure) drop the volumetric efficiency below 100% (curve A). Charge heating in the

manifold and cylinder drops curve A to curve B. It has greater effect at low enginespeeds due to longer gas residence time. Frictional flow losses increase as the square

of engine speed, and drop curve B to curve C . At higher engine speeds, the flow into

the engine during at least part of intake process becomes choked. Once this occurs,

further increases in speed do not increase the flow rate significantly so volumetric

efficiency decreases sharply (curve C to D). The induction ram effect at higher engine

speeds which occurs from inertia of mixture raises curve D to curve E . Late inlet

valve closing, which allows advantage to be taken of increased charging at higher

speeds, results in a decrease in the volumetric efficiency at low engine speeds due to

backflow (curve C and D to F ). Finally, intake and/or exhaust tuning can increase the

volumetric efficiency (often by substantial amount) over part of the engine speed

range, curve F to G. The terms which appear in Fig.3-8 are described as following.Frictional losses – During the intake stroke, the pressure in the cylinder is less

than atmospheric pressure due to friction in each part of the intake system. This total

pressure drop is the sum of the pressure loss in each component of the intake system:

air filter, carburetor and throttle, manifold, inlet port, and inlet valve.

Ram effect – The pressure in the inlet manifold varies during each cylinder’s

intake process due to the piston velocity variation, valve open area variation, and the

unsteady gas-flow effects that result from geometric variations. At high engine

speeds, the inertia of the gas in the intake system as the intake valve is closing

increases the pressure in the port and continue charging process when the piston slow

down around BDC and starts the compression stroke. This effect becomes

progressively greater as engine speed is increased.

14



Back flow – Because the inlet valve closes after the start of the compression

stroke, a reverse flow of fresh charge from the cylinder back into the intake can occur

as the cylinder pressure rises due to piston motion toward TDC. This reverse flow islargest at the lowest engine speeds. This phenomenon cannot be avoided due to

choosing the inlet valve closing time for taking advantage of the ram effect at high

speeds.

Tuning – The time-varying inlet flow to the cylinder causes expansion waves to

be propagated back into the inlet manifold. These expansion waves can be reflected at

the open end of the manifold (at the plenum) causing positive pressure waves to be

propagated toward the cylinder. If the timing of these waves is appropriately arranged,

the positive pressure wave will cause raising the pressure at the inlet valve above the

nominal at the end of intake process. This will increase the inducted air mass and be

described as tuned. This phenomenon can occur in exhaust system also.

Charge Heating - According to the conduction heat transfer, the heat inside thecylinder transfers to inlet manifold via connecting ports and intake valves. This heat is

absorbed by air/fuel mixture directly and makes the mixture expand its volume due to

increasing of temperature. Finally, the volumetric efficiency decreases automatically.

Generally, the residence times, length of inlet manifold and manifold geometries are

the main factors which influence how much heat can be transferred to the mixture.

Choking - Choked flow of a fluid is caused by the Venturi effect. When a

flowing fluid at a certain pressure and temperature flows through a restriction (such as

the hole in an orifice plate or a valve in a pipe) into a lower pressure environment,

under the conservation of mass the fluid velocity must increase for initially subsonic

upstream conditions as it flows through the smaller cross-sectional area of the

restriction. At the same time, the Venturi effect causes the pressure to decrease.Choked flow is a limiting condition which occurs when the mass flow rate will not

increase with a further decrease in the downstream pressure environment.

3.8.1 Flow through Valves

The valve is usually the most important flow restriction in the intake and the

exhaust system of four-stroke cycle engines. In this thesis considers only the intake

valve in order to determine η v. The mass flow rate through a poppet valve is usually

described by the equation for compressible flow through a flow restriction, Eq.3-12.

This equation is derived from a one-dimensional isentropic flow analysis, and real gas

flow effects are included by means of an experimentally determined discharge

coefficient (C D).

5.0/)1(

0

/1

05.0

0

0 11

2

)( ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −

−⎟⎟ ⎠

⎞⎜⎜⎝

⎛ =

− k k

T

k

T R D

p

p

k

k

p

p

RT

p AC m& Eq.3-12

When the flow is choked, the pressure ratio (0 p

pT ) will not lower than the

following value so called critical pressure ratio.

)1/(

0 1

2−

⎥⎦

⎤⎢⎣

⎡

+=⎟⎟ ⎠

⎞

⎜⎜⎝

⎛ k k

Critic

T

k p

pEq.3-13

15



For the mass flow of the mixture into the cylinder through the intake valve, p0 is

ambient pressure, and pT is the cylinder pressure [6], [11]. T 0 is ambient temperature.

For A R, the most convenient reference area in practice is the so called valve curtainarea since it varies linearly with valve lift and is simple to determine [5, 6].

A R = vv L Dπ Eq.3-14

Eq.3-12 should be converted into a function of crank angle also by dividing

with 6N same as Eq.3-9.

5.0/)1(

0

/1

0

5.0

0

0 11

2

)(6 ⎪

⎭

⎪⎬⎫

⎪

⎩

⎪⎨⎧

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −

−⎟⎟ ⎠

⎞⎜⎜⎝

⎛ =

− k k

T

k

T R D

p

p

k

k

p

p

RT N

p AC

d

dm

θ Eq.3-15

Eq.3-9 doesn’t consider about mass flow into cylinder. It determines pressure

different based on pressure at previous crank angle. But the pressure inside cylinder is

influenced not only by volume variation, incoming mass also. So Eq.3-15 is

integrated to obtain amount of mass over a crank angle degree and then finding the

pressure of mixture inside cylinder by using ideal gas equation of state, mRT PV = .

The pressure is added with integrated pressure from Eq.3-9 to obtain pT in Eq.3-15.

3.8.2 Valve Lift

The fundamental the valve lift design is to satisfy an engine breathing

requirement at the design speeds. However, it is philosophies and secrecies of each

carmaker. One of the valve lift design uses polynomial function, for example,Hermann, McCartan and Blair (HMB) technique [12] uses up to 11th order

polynomial functions. The alternative approach is the G. P. Blair (GPB) method [12]

which considers jerk characteristic of valve motion.

Which method is employed depends on how smooth of the lift and/or

acceleration diagrams are otherwise the forces and impacts on the cam follower

mechanism will be considered. In other words, a good mathematical smoothing

technique within the valve lift design process is absolutely essential, may be degree

by degree level. So this thesis assumes to use cosine function for valve lift instead in

order to reduce complexity as following equation:

2

)cos1()(

max,θ += iv

v

L L Eq.3-16

180

)5402(

++

++−=

IVC IVO

IVC IVO θ π ϕ Eq.3-17

16



3.8.3 Discharge Coefficient (C D)

Fig.3-9 shows the results of steady state flow tests on a typical inlet valve

configuration with a sharp-cornered valve seat. The discharge coefficient based onvalve curtain area is a discontinuous function of the valve-lift/diameter ratio. The

three segments shown correspond to different flow regimes as indicated. At very low

lifts, the flow remains attached to the valve head and seat, giving high values for the

discharge coefficient. At intermediate lifts, the flow separates from the valve head at

the inner edge of the valve seat as shown. An abrupt decrease in discharge coefficient

occurs at this point. The discharge coefficient then increases with increasing lift since

the size of separated region remains approximately constant while the minimum flow

area is increasing. At high lifts, the flow separates from the inner edge of the valve

seat as well. Typical maximum values of valve-lift/diameter ratio are 0.25.

Although the flow through valve is dynamic behavior, it has been shown that

over the normal engine speed range, steady flow discharge coefficient results can beused to predict dynamic performance with reasonable precision. The averaged

equation which obtained from the results in Fig.3-9 is shown as Eq.3-18.

FIGURE 3-9 Discharge coefficient of typical inlet poppet valve [6]

6913.0)(5999.2)(248.31)(13.143)(47.190 234 +−+−=iv

v

iv

v

iv

v

iv

v D

D

L

D

L

D

L

D

LC Eq.3-18

3.8.4 Frictional Losses

Takizawa et al [13] made an experiment to measure pressure losses due to

friction across the air cleaner, carburetor, throttle and manifold plenum of a standard

four-cylinder automotive engine intake system. The results are shown in Fig.3-10.

However, the parameters which are used to calculate the pressure losses still

unknown, mainly frictional factor for each component. So a frictional loss factor (C f )is introduced to adjust p0 in Eq.3-15. The products of C f and p0 are assumed as shown

in Fig.3-11. The basis of C f is assumed to be a function of engine speed linearly inorder to reduce complexity as following equation.

Average

17



986923.0)1000

(019738.0 +−= N

C f for 1000 ≤ N ≤ 6000 Eq.3-19

FIGURE 3-10 Pressure losses in the intake system of a four-stroke cycle spark-

ignition engine determined under steady flow conditions [13]

86

88

90

92

94

96

98

100

0 1000 2000 3000 4000 5000 6000 7000

Engine Speed, RPM

R e m a i n i n g P r e s s

u r e ,

k P a

FIGURE 3-11 Assumption of remaining pressure after subtracted by pressure losses

18



3.8.5 Charge Heating

As mentioned in Sec.3.8, the residence times, length of inlet manifold and

manifold geometries are the main factors which influence how much heat can betransferred to the mixture. However, the length and geometries of manifold cannot be

determined easily and the mixture velocity is dynamic behavior. So a charge heating

factor (C heat ) is introduced to apply with T 0 in Eq.3-15. The assumption is defined that

temperatures inside manifold are in between cylinder wall temperature and ambient

temperature. The products of C heat and T 0 are assumed as shown in Fig.3-12, 373 K at

1000 rpm and 308 K at 6000 rpm. The basis of C heat is assumed to be a function of

engine speed linearly in order to reduce complexity as following.

2953.1)1000

(043624.0 +−= N

C heat for 1000 ≤ N ≤ 6000 Eq.3-20

260

280

300

320

340

360

380

0 1000 2000 3000 4000 5000 6000 7000

Engine Speed, RPM

T e m p e r a t u r e I n s i d e M a n i f o l d , K

FIGURE 3-12 Assumption of temperature inside manifold

3.9 Residual Gas

The residual gas affects volumetric efficiency and engine performance directly,

and efficiency and emissions through its effect on working fluid thermodynamic

properties [6]. The residual gas is primarily a function of inlet and exhaust pressure,

speed, compression ratio, valve timing, and exhaust system dynamics. However, the

equation which can describe the magnitude of residual gas is still unknown. So this

thesis assumes that the amount of residual gas can be determined by using the idealgas equation of state, mRT PV = at TDC which is a function of exhaust pressure,

compressed volume, exhaust gas molecular weight, and exhaust gas temperature. The

exhaust pressure is between 1 and 1.5 atm [3]. So it is selected at 1.5 atm. The exhaust

gas molecular weight is 30.4 g/mol.

Caton and Heywood [14] measured cylinder pressure, calculated cylinder gas

temperature and exhaust mass flow rate, and measured gas temperature at the exhaust

port exit for a single-cylinder spark ignition engine at 1000 rpm. The results of [14]

are shown in Fig.3-13. According to Fig.3-13, the exhaust gas temperature at 1000

rpm can be assumed starting at 900 K. The exhaust temperatures along other engine

speeds are calculated at point 4 in Fig.2-3a under ideal process. The increments of

temperature at point 4 on each engine speed are added to 900 K as shown in Fig.3-14.And the exhaust gas temperature equation is obtained from those results as following.

19



21.676)1000

(49.279)1000

(9.51)1000

(3955.3 23 ++−= N N N

T exh for 1000 ≤ N ≤ 6000

Eq.3-21

FIGURE 3-13 Measured cylinder pressure pc, calculated cylinder-gas temperature

T c, exhaust mass flow rate em& , and measured gas temperature at

exhaust port exit T p, for single-cylinder spark ignition engine at speed

= 1000 rpm [14]

0

200

400

600

800

1000

1200

1400

0 1 2 3 4 5 6 7

Engine Speed, RPM

E x h a u s t G a s T e m p e r a t u r e , K

FIGURE 3-14 Assumption of temperature inside manifold

20



3.10 Friction

Friction losses influence the indicated power and useful output, the brake

power. Barnes-Moss [15] tested several four-stroke cycle four cylinder SI engines between 845 and 2000 cm3 displacement at wide-open throttle. The total friction work

per cycle (and thus the friction mean effective pressure) for a given engine geometry

will vary with the engine speed as following equation.

97.0)1000

(15.0)1000

(05.0 2 ++= N N

p f for 1000 ≤ N ≤ 6000 Eq.3-22

3.11 Torque & Power

To determine the overall performance, indicated mean effective pressure is used

[16]. The indicated mean effective pressure represents the work per combustion cycle

normalized by the displacement volume also called specific work. This valueindicates amount of maximum available power that can generate from single cylinder.

d

miV

PdV p

∫= Eq.3-23

The engine has to overcome the friction loss. So the available output becomes:

f mime p p p −= Eq.3-24

Effective power can be determined by following equation.

d mee V p N P ⋅⋅= 5.0 Eq.3-25

Finally, torque can be determined by following relation.

30

NT P e

π = Eq.3-26

3.12 Minimum Spark Advance for Best Torque (MBT)

The charge of the air/fuel is burned by a flame-front beginning at the spark plug.

The flame starts a kernel with a rather slow rate of expansion, but once a small

percentage of the charge is ignited, the combustion process accelerates at a faster rate.

Due to the very slow initial reaction rates, ignition must occur before TDC. This is the

"advance" in ignition and is measured in degrees of crankshaft rotation. The best

advance depends on design and operating conditions. This value is called “Minimum

Spark Advance” which will produce the maximum torque at a given operating

condition of speed and load of a given engine combination. In most cases the spark

advance curve can be advanced several degrees before torque begins to drop off. If

"knock" occurs, advance can be determined. The advance is referred to as "knock

limits". The fuel octane, camshaft profile and/or the compression ratio will need to beaddressed before maximum output can be achieved.

21



(a) (b)

FIGURE 3-15 (a) Cylinder pressure versus crank angle for over-advanced spark

timing (50°), MBT timing (30°), and retarded timing (10°). (b) Effectof spark advance on brake torque at constant speed and air/fuel ratio,

at wide open throttle [6]

3.13 Simulation conditions

The conditions for simulation are summarized in Table 3-2.

TABLE 3-2 Parameters for simulation

Parameters Value

Ambient Pressure 1 atm

Ambient Temperature 298 K Mean cylinder wall temperature 400 K [11, 17]

Specific heat ratio (k ) 1.3 [3, 6]

Air molecular weight 28.97 g/mol

Air density 1.2 kg/m3

Gasoline molecular weight 114 g/mol

Gasoline heating value 44,000 kJ/kg

Gasoline air/fuel ratio 14.6:1

In real engine test (SAE, DIN standard), the performance of engine is measured

with all accessories and standard intake and exhaust systems. All parameters which

affect to the volumetric efficiency due to using those systems are taken into accountas well. Although the temperature inside manifold is varied from 308 to 373 Kelvin

due to the heat transfer from cylinder (Sec.3.8.4) which affects to density of air, the

air density is still kept constantly at 1.2 because the volumetric efficiency is measured

comparing to the ambient condition.

3.14 Alternative Fuels

By researches of many scientists, quantity of petroleum in the world has a limit

and it cannot be renewed. 70% of petroleum is consumed in transportation and it is

increasing every year. With this rate, the petroleum will deplete from the world one

day in the near future. So many countries are searching the other sources of energy to

replace the petroleum in long run. Furthermore, improvement of air quality is another objective too.

22



Many road-tests on the alternative fuels are done to prove these potentials.

However, there are a few on analytical studies. So this thesis would like to study the

alternative fuels in analytical aspect. This section is going to mention about thealternative fuels, such as LPG, CNG and alcohol-blended gasoline in details and how

the model is applied to study these fuels.

The model needs lots of parameter which are distinguished as shown in Fig.3-2,

engine geometries, valve geometries, fuel properties, and engine operating condition,

in order to predict the performance. However, the alternative fuel properties in details

are still unknown, mainly the combustion duration. So the studies are set to predict the

combustion range of these alternative fuels by comparing between the output

performances and simulated values which the data are obtained from previous

researches. The model is used to explain the volumetric efficiency in order to

determine effects of using those alternative fuels too.

The previous researches are selected under specific condition. They have tostudy the using both gasoline and one of alternative fuels on the same engine in order

to compare the information. The gasoline engine model which is developed under this

thesis uses parameters of the engine in order to determine the spark advanced angle.

With additional information of specific spark advanced setting on each alternative

fuels, the burning duration can be determined.

3.14.1 Ethanol-blended Gasoline or Gasohol

Ethanol (ethyl alcohol) and methanol (methyl alcohol) are two types of alcohol

fuels. The use of pure alcohols in internal combustion engines is only possible if the

engine is designed or modified for that purpose. However, in their anhydrous or pure

forms, they can be mixed with gasoline in various ratios for use in unmodified

automobile engines. Typically, only ethanol is used widely in this manner, particularly since methanol is toxic.

E10, also frequently called gasohol, is a fuel mixture of 10% ethanol and 90%

gasoline by volume that can be used in the internal combustion engines of most

modern automobiles. However, not enough scientific tests have been done to

determine if E10 is harmful to older cars' fuel systems. It has been introduced

nationwide in Denmark and Thailand, and will replace high octane pure gasoline in

Thailand by 2007.

E20 contains 20% ethanol and 80% gasoline. This fuel is not yet widely used in

the world. Since February 2006, this is the standard ethanol-gasoline mixture sold in

Brazil, where concerns with the alcohol supply resulted in a drop in the ethanol

percentage, previously at 25%. Flexible-fuel cars are set up to run with gasoline insuch concentration range and few will work properly with lower concentrations of

ethanol. The properties of E10 and E20 are compared in Table 3-3.

TABLE 3-3 Summaries of major properties of gasoline, ethanol, E10 and E20 [18]

Properties Gasoline Ethanol E10 E20

Heating value (kJ/kg) 44,000 27,000 41,900 40,000

Stoichiometric air/fuel ratio 14.6 9 14 13.5

23



Al-Farayedhi et al [19] investigated the effect of using unleaded gasoline–

ethanol blends on typical SI engine performance in order to replace leaded gasoline.

He founded that using of ethanol-blended fuel increase spark timing by average -1degree for E10 and -6 degree for E20 when comparing to gasoline. And also the

engine brake thermal efficiency is improved when compared to the leaded fuel.

3.14.2 Ethanol

Ethanol fuel is an alternative to gasoline. Anhydrous ethanol or ethanol without

water can be blended with gasoline in any concentration up to pure ethanol (E100) to

reduce the consumption of petroleum fuels, as well as to reduce air pollution. In

Brazil, ethanol-powered and flexible-fuel vehicles are manufactured to be capable of

operation by burning hydrated ethanol. In addition, flexible-fuel vehicles can run on

any mixture of hydrated ethanol and gasoline, as long as there is at least 20% of

ethanol. A few flexible-fuel systems, like the Hi-Flex, used by Renault and Fiat, can

also run with pure gasoline.Renault Clio is one of many vehicle models which are sold in Brazil. It is

equipped by Hi-Flex technology which allows using pure ethanol as fuel with full

efficiency due to the automatic adjustment on engine system. The power curve of Clio

increases only 1 horsepower throughout engine speed range when using ethanol. And

also, information from [20] indicates that the proper timing for an ethanol engine is

five to eight degrees advanced from the optimum gasoline setting.

3.14.3 Compressed Natural Gas (CNG)

CNG is a substitute for gasoline or diesel fuel. It is considered to be an

environmentally "clean" alternative to those fuels. It comprises mainly methane (CH4)

and ethane (C2H6). It is stored and distributed in hard containers, usually cylinders,

and keeped under high pressure. In response to high fuel prices and environmentalconcerns, compressed natural gas is starting to be used in light-duty passenger

vehicles and pickup trucks, medium-duty delivery trucks, and in transit and school

buses. The properties of natural gas are shown in Table 3-4

TABLE 3-4 Summaries of major properties of methane, ethane, and natural gas [21]

Properties Methane

(CH4)

Ethane

(C2H6)

Natural Gas

(CH3.76) [20]

Heating value (kJ/kg) 50,100 47,400 49,500

Stoichiometric air/fuel ratio 17.16 16 16.9

Mello et al [21] evaluated the maximum horsepower in many vehicles which

were converted to use both natural gas and gasoline, so called “bi-fuel vehicle”. They

founded that there is substantial drop in horsepower 13-17% when using the natural

gas with electronically lambda control. However, emissions are reduced dramatically.

The drop of power came from using of gas mixer which restricts air flow through

manifold. And also the natural gas is gaseous fuel which occupies a larger volume

than liquid fuel. It causes reduction of η v. Not only that, spark advanced angle is

needed to increase about 21-25 degree in order to obtain the maximum output due to

low burning rate.

24



3.14.4 Liquefied Petroleum Gas (LPG)

LPG comprises primarily propane (C3H8) and mixed by butane (C4H10). LPG is

mainly used in household, industries and transportation respectively. LPG can be produced from crude oil and natural gas. However, the composition between propane

and butane depends on the sources. The characteristics of LPG are summarized in

Table 3-5.

TABLE 3-5 Summaries of major properties of propane, butane, and LPG [22]

Properties Propane

(C3H8)

Butane

(C4H10)

LPG

(97.6%C3H8) [21]

Heating value (kJ/kg) 46,000 45,400 45,900

Stoichiometric air/fuel ratio 15.6 15.4 15.6

Caton et al [22] developed a dedicated LPG fueled engine from production car.They founded that torque drops about 10-12% when using LPG without any enhanced

modification. The reason of performance reduction came from using the gaseous fuel

which decreases η v. For spark timing, LPG needs an advanced spark timing usually

around +10 degree due to slower burning rate [23].

25



CHAPTER 4

MODEL VALIDATION AND SENSITIVITY ANALYSIS

This chapter presents and describes results acquired through simulations made

with the model. The results are compared to data which appear in vehicle technical

manual in order to prove the accuracy.

4.1 Performance Validation

This section shows the results of simulation comparing to test data from 8

engines. All engine geometries are obtained from Mercedes-Benz model year 1969which are summarized in Appendix A. The model is simulated between 1,000 to

6,000 rpm of engine speed range.

0

20

40

60

80

100

120

1000 2000 3000 4000 5000 6000Engine Speed, RPM

P o w e r , k W

0

50

100

150

200

250

300

T o r q u e , N m

Power

Power(Sim)

Torque

Torque(Sim)

FIGURE 4-1 Simulation results of Mercedes-Benz 250SE



0

20

40

60

80

100

120

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

0

50

100

150

200

250

300

350

T o r q u e ,

N m

Power

Power(Sim)

Torque

Torque(Sim)

FIGURE 4-2 Simulation results of Mercedes-Benz 250SL

0

20

40

60

80

100

120

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

0

50

100

150

200

250

300

350

400

T o r q u e , N m

Power

Power(Sim)

Torque

Torque(Sim)

FIGURE 4-3 Simulation results of Mercedes-Benz 250E/8

27



0

20

40

60

80

100

120

140

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

0

50

100

150

200

250

300

350

400

T o r q u e ,

N m

Power

Power(Sim)

Torque

Torque(Sim)

FIGURE 4-4 Simulation results of Mercedes-Benz 280SE/8

0

30

60

90

120

150

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

0

80

160

240

320

400

T o r q u e ,

N m

Power

Power(Sim)

Torque

Torque(Sim)

FIGURE 4-5 Simulation results of Mercedes-Benz 280SL/8

28



0

30

60

90

120

150

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

0

80

160

240

320

400

T o r q u e ,

N m

Power

Power(Sim)Torque

Torque(Sim)

FIGURE 4-6 Simulation results of Mercedes-Benz 300SEL/8

0

30

60

90

120

150

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

0

80

160

240

320

400

T o r q u e ,

N m

Power Power(Sim)

Torque

Torque(Sim)

FIGURE 4-7 Simulation results of Mercedes-Benz 300SEL

29



0

40

80

120

160

200

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

0

200

400

600

800

T o r q u e , N m

Power

Power(Sim)

Torque

Torque(Sim)

FIGURE 4-8 Simulation results of Mercedes-Benz 600

According to the results from Fig.4-1 to Fig.4-8, torque and power

characteristics at low and high speed are almost the same to reference data for all

cases. There are some cases greater at high speed. But all graphs are lower at midrange. When considering relative errors which are summarized from simulation

results of 8 engines in Fig.4-9, overall errors are in between -6% to 4%. But at low

and high engine speed, the error values are in positive side. While the error values in

negative side occur in mid engine speed.

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 1000 2000 3000 4000 5000 6000 7000

Engine Speed (RPM)

%

FIGURE 4-9 Summarized relative errors from simulation results of 8 engines

30



According to the results, the model can interpret the output engine performance

very well. The errors might come from inadequate information which has to be

assumed such as pressure losses in the intake system, temperature inside manifold,exhaust gas temperature, etc. And also some effects which are not included in the

model such as tuning, ram effect, exhaust stroke, and exhaust valve. However, the

next section is going to determine the effects of each parameter in order to find which

parameter has to be studied seriously in the future.

4.2 Sensitivity Analysis

This section is going to determine the sensitivity of the model affected by each

parameter.

4.2.1 Burning Duration

This section is going to determine the effects of changing the gasoline burning

duration from Eq.3-6 by increasing and decreasing 10 degree of burning durationwhile keeping the optimum gasoline spark advanced setting.

0

20

40

60

80

100

120

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

Gasoline

+10 deg-10 deg

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

%+10 deg

-10 deg

(a) (b)

FIGURE 4-10 Comparison between gasoline and +/-10 degree modified combustion

range without spark advanced adjusting (a) output power; (b) relative

power gain

Results from Fig.4-10a indicate that power curves are almost the same when

increasing and decreasing 10 degree of combustion range. When considering the

relative power gain in Fig.4-10b, 10 degree increasing reduces power gradually from

1.4% to 2.0%, while 10 degree decreasing raises power gradually up to 0.9%

maximum except at low speed. These results roughly indicate that shorter combustion

time brings better performance to engine. The wave-liked curves cause from

inappropriate spark advanced timing. So adjusting the spark timing is the next thing to

study.

31



-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1000 2000 3000 4000 5000 6000Engine Speed, RPM

%

+10 deg

-10 deg

+10 deg optimum

-10 deg optimum

FIGURE 4-11 Relative errors of before and after adjusting the spark timing

According to Fig.4-11, adjusting the optimum spark timing increases power in

both cases. For 10 degree increasing, power shifts up average 0.5% due to more 5

degree advanced adjusting. And 10 degree decreasing case, power shifts up average

0.7% due to less 5 degree advanced adjusting. It can conclude that changing of

combustion duration affects to the output performance. But it does not affect much

and also it has no any effect to η v. Only one thing affected is the spark advanced

angle.

4.2.2 Discharge coefficientThis section is going to determine the effects of changing the discharge

coefficient from Eq.3-18 by increasing and decreasing 10%.

0

20

40

60

80

100

120

140

1000 2000 3000 4000 5000 6000

Engine Spee d, RPM

P o w

e r , k W

Normal

+10% Cd-10% Cd

-10

-8

-6

-4

-2

0

2

4

6

8

10

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

%

+10% Cd

-10% Cd

(a) (b)

FIGURE 4-12 Comparison between normal C D and +/-10% changing

(a) output power; (b) relative power gain

32



According to Fig.4-12a, output powers do not look different much at low and

mid engine speed. But at high engine speed, less C D value causes lower power than

normal, while greater C D value causes greater power than normal. When consideringrelative power gain in Fig.4-12b, less C D value causes more power a bit at low and

mid engine speed, while greater C D value causes less power. For high engine speed,

the results are explicitly the same as in Fig.4-12a.

When considering Eq.3-15, less C D value causes less pT due to less mass flow

into the cylinder during intake stroke. With this reason, total mass flow in is increased

a bit at the end of intake process. But at high speed, lesser magnitude of pT does not

affect to mass flow rate any more due to choking which limits the mass flow rate. So

less C D value limits mass flow into the cylinder itself. The greater C D value gives

opposite results to the explanations above. However, changing of C D alters the output

performance very much only at high engine speed about +/-10%.

4.2.3 Frictional LossesThis section is going to determine the effect of non-applying frictional loss

factor (C f ) in Eq.3-15. p0 is kept at 1 atm constantly. Changing of p0 affects η v mainly.

So η v graph is considered in order to explain the effect.

0

20

40

60

80

100

120

140

160

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r ,

k W

With Cf

Without Cf

50

60

70

80

90

100

110

0 1000 2000 3000 4000 5000 6000 7000

Engine spee d, rpm

n v , %

Without Cf

With Cf

(a) (b)

FIGURE 4-13 Comparison between using and non-using C f

(a) output power; (b) η v

The using of ambient pressure gives the maximum possible power and

maximum η v to the engine. It is clearly that non-applying of the frictional losses

causes more power according to Fig.4-13a. When considering Fig.4-13b, η v curve is

increased also. The difference of η v increases gradually throughout the engine speed

range due to the assumption which defines more pressure drop for more speed.

However, η v increases up to 100.8% which might cause from accumulative sum of

error. The lower values of η v are still under interferences of charge heating, back flow

effect at low speed, and choking effect at high speed. So C f applying in Eq.3-15 is

reasonable.

33



4.2.4 Charge Heating

This section is going to determine the effect of non-applying charge heating

factor (C heat ) in Eq.3-15. T 0 is kept at 298 K constantly. Changing of T 0 affects η v mainly. So η v graph is considered in order to explain the effect.

0

20

40

60

80

100

120

140

1000 2000 3000 4000 5000 6000

Engine Spee d, RPM

P o w e r , k W

With Cheat

Without Cheat

50

60

70

80

90

100

110

0 1000 2000 3000 4000 5000 6000 7000

Engine speed, rpm

n v , %

Without Cheat

With Cheat

(a) (b)

FIGURE 4-14 Comparison between using and non-using C heat

(a) output power; (b) η v

The using of ambient temperature gives the maximum possible power and

maximum η v to the engine. It is clearly that non-applying of the charge heating causes

more power according to Fig.4-14a. When considering Fig.4-14b, η v curve is

increased also. The difference of η v reduces gradually throughout the engine speed

range due to the assumption which defines less heat transfer for more speed.

However, η v increases up to 101.6% which might cause from accumulative sum of

error. The lower values of η v are still under interferences of frictional losses, back

flow effect at low speed, and choking effect at high speed. So C heat applying in Eq.3-

15 is reasonable.

4.2.5 Exhaust Gas Temperature

The exhaust gas temperature, Eq.3-21, is used to determine the residual masswhich is affected to η v as mentioned in Sec.3.9. This section is going to determine the

effects of changing the exhaust gas temperature (T exh) by increasing and decreasing

temperature 50 K.

34



0

20

40

60

80

100

120

140

1000 2000 3000 4000 5000 6000Engine Spee d, RPM

P o w e r , k W

Normal

+50 K Texh-50 K Texh

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

1000 2000 3000 4000 5000 6000

Engine Spee d, RPM

%

+50 K Texh

-50 K Texh

(a) (b)

FIGURE 4-15 Comparison between normal and +/-50 K exhaust gas temperature

(a) output power; (b) relative power gain

According to Fig.4-15a, output powers are almost the same in both cases. When

considering Fig.4-15b, Increasing of T exh raises power up to 0.85%, while reduction of

T exh reduces power up to 0.14%. Increasing of T exh reduces the residual mass

according to ideal gas equation of state, mRT PV = , and increases η v. While

reduction of T exh gives opposite results. These results agree with explanations in [6].

4.3 Combustion Duration of Alternative fuels

This section is going to interpret the results of simulation in order to determine

the combustion duration of the alternative fuels.

4.3.1 Ethanol-blended Gasoline or Gasohol

60

65

70

75

80

85

90

0 1000 2000 3000 4000 5000

Engine speed, rpm

n v , %

Gasoline

E10

E20

FIGURE 4-16 Effect of ethanol-blended fuel on volumetric efficiency

35



0

20

40

60

80

100

120

0 1000 2000 3000 4000 5000

C o m b u s t i o n D u r a t i o n , d e g

Gasoline

E10

E20

FIGURE 4-17 Combustion duration of gasoline, E10, and E20

Using of ethanol-blended gasoline introduces increasing of η v by average 2.7%for E10 and 4.3% for E20 as results in Fig.4-16. The results agree with [19].

Increasing of η v can compensate reduction of heating value and cause toque and

power gain. However, conditions of air/fuel ratio in [19] are rich mixture in all cases

which increase η v greater than stoich condition due to the excess fuel. So η v might be

lower than simulation results around 0.5-1% at stoich condition.

According to information of spark timing, it’s clear that combustion duration

increases in parallel as percentage of ethanol increase throughout engine speed range

as shown in Fig.4-17. The equations of combustion duration are shown below.

For E10

271.41)1000

(479.20)1000

(6429.1 2 ++−=Δ N N θ for 1000 ≤ N ≤ 6000 Eq.4-1

For E20

343.50)1000

(443.21)1000

(8571.1 2 ++−=Δ N N

θ for 1000 ≤ N ≤ 6000 Eq.4-2

10

20

30

40

50

60

70

80

90

100

110

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

P o w e r , k W

Gasoline

E10

E20

0

0.5

1

1.5

2

2.5

3

1000 2000 3000 4000 5000 6000

Engine Speed, RPM

%

E10

E20

(a) (b)

FIGURE 4-18 Comparison between gasoline, E10, and E20 when using withunmodified engine (a) output power; (b) relative power gain

36



In Thailand, the gasohol is introduced through nation for a while. However, the

effects of using gasohol are still questioned. So the scenario is set to determine effect

of using E10 and E20 with unmodified spark ignition engine. The results are shown inFig.4-18. According to Fig.4-18a, the output powers seem to be almost the same. But

when considering in details, using gasohol brings more power both E10 and E20 as

shown in Fig.4-18b. The maximum power gains are about 2% for E10 and 2.5% for

E20 at low engine speed and gradually reduce through high engine speed. According

to the results, E10 and E20 can replace gasoline immediately in aspect of

performance. Nevertheless, the maximum efficiency cannot be achieved. However,

real experiments are needed to confirm the simulation results because the condition of

scenario is set to run under stoich condition which the ECU might not handle much

different air/fuel ratio of E20. This effect occurs also in transient driving. Many

drivers may feel that their vehicles have less acceleration when using E10. It causes

from ECU of feedback fuel control system getting “hesitation”. So if the ECU is not

designed to be smart enough, this problem might appear even steady state running.

4.3.2 Ethanol

40

50

60

70

80

90

100

0 1000 2000 3000 4000 5000 6000 7000

Engine speed, rpm

n v , %

Gasoline

E100

FIGURE 4-19 Effect of ethanol as a fuel on volumetric efficiency

0

20

40

60

80

100

120

0 1000 2000 3000 4000 5000


Gasoline

E10

E20

E100

FIGURE 4-20 Combustion duration of gasoline, E10, E20, and E100

37



Using of ethanol as a fuel increases η v by average 7.2% as results in Fig.4-19.

Although increasing of η v can compensate reduction of heating value, the power and

torque do not take advantages much due to very low heating value and lowcombustion rate when comparing to gasoline. According to the results in Fig.4-20, the

combustion duration of ethanol does not much difference to E20. It might conclude

that the combustion lengths of E20 to E100 are almost the same. Only stoichiometric

air/fuel ratio is different which can be controlled by the Flex-fuel technology. The

equation of combustion duration is shown below.

For E100

787.52)1000

(178.21)1000

(6843.1 2 ++−=Δ N N

θ for 1000 ≤ N ≤ 6000 Eq.4-3

4.3.3 Compressed Natural Gas (CNG)

60

65

70

75

80

85

90

2500 3500 4500 5500

Engine speed, rpm

n v , %

Gasoline

CNG

FIGURE 4-21 Effect of CNG as a fuel on volumetric efficiency

0

20

40

60

80

100

120

140

160

0 1000 2000 3000 4000 5000


Gasoline

CNG

FIGURE 4-22 Combustion duration of gasoline and CNG

38



According to Fig.4-21, it’s clear that using of gaseous fuel and gas mixer

introduce η v reduction as mentioned in [21]. It decreases about average 6.9%. Fig.4-

22 shows the combustion duration of CNG comparing to gasoline. The combustionrange of CNG is almost twice time of the gasoline. So when considering to use CNG

in both bi-fuel and dedicated system, spark timing adjusting is recommended. For bi-

fuel system, electronic control box is needed to control the spark timing during using

of CNG. The equation of CNG combustion duration is shown below.

For CNG

405.72)1000

(976.27)1000

(4286.2 2 ++−=Δ N N

θ for 1000 ≤ N ≤ 6000 Eq.4-4

4.3.4 Liquefied Petroleum Gas (LPG)

60

65

70

75

80

85

90

0 1000 2000 3000 4000 5000

Engine spee d, rpm

n v ,

%

Gasoline

LPG

FIGURE 4-23 Effect of ethanol as a fuel on volumetric efficiency

0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000


Gasoline

LPG

FIGURE 4-24 Combustion duration of gasoline and LPG

39



The results agree as mentioned in [22] when using gaseous fuel. η v decreases

about 3% average as shown in Fig.4-23. Caton et al [22] used sequential LPG gas

injection system for delivering fuel which sacrifices some performance due to the η v reduction. Combustion duration of LPG is greater than gasoline in Fig.4-24 and still

less than CNG. Nevertheless, using of LPG needs electronic control box in order to

adjust the spark timing as well. The equation of LPG combustion duration is shown

below.

For LPG

571.58)1000

(762.21)1000

(8095.1 2 ++−=Δ N N

θ for 1000 ≤ N ≤ 6000 Eq.4-5

40



CHAPTER 5

CONCLUSIONS AND SUGGESTIONS

5.1 Conclusions

An analytical model of spark ignition engine has been constructed based on

cylinder-by-cylinder engine model which combines both physical formulae, e.g.

engine geometries, and empirical formulae, e.g. burning duration. The engine

performance, torque and power, can be calculated by integrating the pressure inside

cylinder within one engine cycle.

In engine modeling, the model needs design parameters from real engine. It isthe same as 3-D engine model which needs the perfect 3-D geometry of combustion

chamber, valves, and ports in order to achieve the accuracy. The parameters which are

usually provided by commercial brochures are not enough for engine modeling.

The model is verified by data from 8 engine models. It can capture torque and

power characteristics very well. The overall errors are in between -6% to 4%. But the

error values at low engine speed occur in positive side, while most of error values

occur in negative side at mid and high engine speed. These errors might cause from

calculation itself, many assumptions and unknown phenomena which are not

considered yet such as the tuning, ram effect, exhaust stroke, and exhaust valve, etc.

There are significant changes to the performance curves when changing the

parameters which affect η v, for example, pressure and temperature. So η v affectsdominantly to the performance shapes because it represents how much the fuel is

drawn into the cylinder. But the prediction of η v is still very difficult. It is combined

result from a lot of parameters and many phenomena. If those phenomena can be

realized, the accuracy can be achieved.

The simulations in order to predict the burning duration of the alternative fuels

express many interesting information. All alternative fuels in this thesis have greater

combustion durations when compare to gasoline. Furthermore, the model indicates the

effects on η v when using these alternative fuels. Using of ethanol and ethanol blended

fuel can increase η v due to high latent heat value of ethanol itself. While using LPG

and CNG reduce η v due to gaseous fuels.

5.2 Suggestions

Eq.3-3, which is used for predicting the pressure inside cylinder, is derived from

close cycle. Kirkpatrick [5] made assumptions that compression and power strokes are

close system due to all valves closing and neglecting effects of incoming mixture

which is drawn into cylinder. Only Qin is considered as input for Eq.3-3. But Qin can

be determined only if mixture mass is known. Therefore, 1-D mass flow model, Eq.3-

12, is applied by comparing between ambient pressure and pressure inside cylinder.

Then pressure is determined to by amount of flow-in mass and fed back to pressure

comparing loop. However, the ambient pressure and also the ambient temperature are

influenced by frictional losses and charge heating respectively. So both topics should

be studied more in order to make better assumptions. For residual mass, theassumption should include other parameters as described in [6].



For part load condition, the throttle body model is needed to integrate into the

engine model. However, the real geometries of the throttle body, e.g. close angle,

maximum angle, inside throttle body diameter, are needed also in order to calculatethe mass flow through the throttle itself.

All equations which describe the combustion range of the alternative fuels

should be verified by experiment in order to prove model prediction accuracy.

However, the results from experiments may deviate from the predictions caused by

proportion of fuel mixture and also testing conditions.

In order to predict the output performance of engines which use the alternative

fuels, the model is needed to be revised due to the different technique of fuel

dispensing system, e.g. gas mixer, gas injector.

42



REFERENCES

1. Zeng, P. and Assanis, D. N. “The Development of a Computer-Based Teaching

Tool for Internal Combustion Engine Courses.” Proceedings of IMECE

2004. (2004).

2. Eriksson, L. and Andersson, I. “An Analytic Model for Cylinder Pressure in a

Four Stroke SI Engine.” SAE 2002 Transactions Journal of Engines. (2002)

: 726-733.

3. Kuo, P. S. “Cylinder Pressure in a Spark Ignition Engine: A Computational

Model.” Journal of Undergraduate Science. (1996) : 141-145.

4. Zeng, P., et al. “Reconstructing Cylinder Pressure of a Spark-Ignition Engine for

Heat Transfer and Heat Release Analyses.” Proceedings of ASME ICEF

2004. (2004).

5. Kirkpatrick, Allan. Internal Combustion Engine Thermodynamic. Available

from: http://www.engr.colostate.edu/~allan/thermo/page6/page6.html [2005,

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44



APPENDIX A

Engine Specifications



This appendix summarizes all engine specifications which are used for

simulation in this thesis

A.1 Mercedes-Benz 250SE (Model Year 1969) No. of Cylinders : 6

No. of Valves per Cylinder : 2

Displacement (cc.) : 2,500

Bore × Stroke (mm.) : 82 × 78.8

Compression Ratio : 9.3 : 1

Intake Valve Open before TDC (degree) : 11°

Intake Valve Close after BDC (degree) : 53°

Maximum Valve Lift (mm.) : 8

Inlet Valve Diameter (mm.) : 41.2

FIGURE A-1 Performance curve of Mercedes-Benz 250SE

A.2 Mercedes-Benz 250SL (Model Year 1969)

No. of Cylinders : 6



Bore × Stroke (mm.) : 82 × 78.8






FIGURE A-2 Performance curve of Mercedes-Benz 250SL

46



A.3 Mercedes-Benz 250E/8 (Model Year 1969)


No. of Valves per Cylinder : 2Displacement (cc.) : 2,500

Bore × Stroke (mm.) : 82 × 78.8




Maximum Valve Lift (mm.) : 8.5


FIGURE A-3 Performance curve of Mercedes-Benz 250E/8

A.4 Mercedes-Benz 280SE/8 (Model Year 1969)




Bore × Stroke (mm.) : 86.5 × 78.8




Maximum Valve Lift (mm.) : 8.5


FIGURE A-4 Performance curve of Mercedes-Benz 280SE/8

47



A.5 Mercedes-Benz 280SL/8 (Model Year 1969)



Bore × Stroke (mm.) : 86.5 × 78.8






FIGURE A-5 Performance curve of Mercedes-Benz 280SL/8

A.6 Mercedes-Benz 300SEL/8 (Model Year 1969)




Bore × Stroke (mm.) : 86.5 × 78.8






FIGURE A-6 Performance curve of Mercedes-Benz 300SEL/8

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A.7 Mercedes-Benz 300SEL (Model Year 1969)



Bore × Stroke (mm.) : 85 × 88





Inlet Valve Diameter (mm.) : 49

FIGURE A-7 Performance curve of Mercedes-Benz 300SEL

A.8 Mercedes-Benz 600 (Model Year 1969)




Bore × Stroke (mm.) : 103 × 95

Compression Ratio : 9 : 1

Intake Valve Open before TDC (degree) : 2.5°

Intake Valve Close after BDC (degree) : 52.5°



FIGURE A-8 Performance curve of Mercedes-Benz 600

49



APPENDIX B

Matlab/Simulink Block Diagrams



51

F I G U R E B

- 1 M a i n m o d e l



FIGURE B-2 Cm block details

FIGURE B-3 Engine geometry block details

FIGURE B-4 Engine geometry/Vd block details

FIGURE B-5 Engine geometry/A(CA) block details

52



FIGURE B-6 Engine geometry/Crank geometry block details

FIGURE B-7 Engine geometry/V(CA),Vc block details

FIGURE B-8 Wiebe fn block details

FIGURE B-9 Burn duration block details

53



F I G U R E B - 1

0 P b l o c k

54



FIGURE B-11 P/Pratio block details

FIGURE B-12 P/Lv fn block details

FIGURE B-13 P/Cd block details

55



FIGURE B-14 P/mdot block details

FIGURE B-15 P/Cheat factor block details

FIGURE B-16 P/Cf factor block details

56



FIGURE B-17 Mw block details

FIGURE B-18 Residual mass block details

FIGURE B-19 T block details

FIGURE B-20 Heat tran block details

57



FIGURE B-21 h block details

FIGURE B-22 Work&Power block details

FIGURE B-23 Work&Power/Work block details

58



FIGURE B-24 Work&Power/FMEP block details

FIGURE B-25 Work&Power/Effective power block details

59



BIOGRAPHY

Name : Mr.Sitthichok Sitthiracha

Thesis Title : An Analytical Model of Spark Ignition Engine for

Performance Prediction

Major Field : Automotive Engineering

Biography

Mr.Sitthichok Sitthiracha has studied in King Mongkut's Institute of

Technology North Bangkok (KMITNB) since vocational school. It was first time for

him studying automotive vehicle. After that he studied Mechanical Engineering in

KMITNB. As undergraduate, he joined the cooperative education program which

gave chance to him for working in automotive industry about one year. Along the one

year program, he worked in many positions such as manufacturing & process

engineer, product engineer, and quality engineer. Then he got a bachelor degree in

Mechanical Engineering in 2003. After one year of graduate, he decided to study

Master degree in Automotive Engineering in KMITNB also. He was selected to have

an internship in South Korea about LPG retrofit on heavy duty truck engines and

engine testing for 4 months. He earned many experiences about engine technology

through practicalities which become the inspiration for this thesis.

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An Analytical Model of Spark Ignition Engine for Performance Prediction

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