COMPUTER SIMULATION OF FUEL INJECTION FOR DIRECT … · BEng, ACGI. Thesis submitted for the degree...

Thermofluids Section,Department of Mechanical Engineering,

Imperial College of Science, Technology and Medicine,University of London.

IMPERIAL

COLLEGE

COMPUTER SIMULATIONOF

FUEL INJECTIONFOR

DIRECT-INJECTION DIESEL ENGINES

By

R J FairbrotherBEng, ACGI.

Thesis submitted for the degree ofDoctor of Philosophy

in the University of Londonand for the

Diploma of Membership of the Imperial College

BIBL

August, 1994

LONDON

UNIV

Abstract

ABSTRACT

Two simulation models of a fuel injection system used in a Direct Injection Diesel

Engine have been developed to provide information about the pressures and flow rates in

such a system. The first model simulates the flow in the nozzle only and the other covers

the pump, pipe and nozzle together. The partial differential equations and ordinary

differential equations representing the pressures and flow rates are solved using the

method of characteristics and the fourth order Runge Kutta method, respectively. The

models include the effects of nozzle needle bounce, cavitation, variable fuel properties

with pressure, spray angle, spray penetration and variable discharge coefficients.

The fuel injection system consists of a Bosch VE distributor-type pump

connected to Stanadyne multi-hole slim type injectors. Both computer models have been

experimentally validated from work performed on such a system set up on a Hartridge

1100 universal fuel pump test stand. Eight experimental parameters were measured using

a variety of techniques including piezo-resistive pressure transducers, linear variable

displacement transducers and capacitance transducers; these parameters include the

delivery valve lift as well as the needle lift. The most important fuel injection system

parameter, the injection rate, was measured using the Bosch long tube method.

The validation process showed that both models are able to simulate the pressure

profiles and flow rates in the system. The two models are particularly good at predicting

the start of injection, although the end of injection predictions are less accurate. The

pump-pipe-nozzle model has been used to find the most significant fuel injection system

parameters in relation to the injection rate profile. Parameters affecting the injection

timing, such as the high pressure pipe length and the nozzle opening pressure, are shown

to be the most significant, although the nozzle orifice area also exerts a significant effect

on the peak injection rate.

Overall, the models developed here can be used to improve the design of existing

fuel injection systems and reduce the development time of new systems by reducing the

number of experimental parameters required. They can also form an integral part of fuel

injection control in advanced direct injection diesel engines by supplying on line

information about injection timing and quantity, thus replacing the need for expensive

instrumentation.

1

Acknowledgments

ACKNOWLEDGMENTS

First and foremost I would like to thank Dr. C. Arcoumanis for his supervision

and support throughout the course of this work. I would also like to thank Mr. H. Flora

for his technical skill in making the experimental side of this work possible.

The significant contribution of Ford, Dunton in providing not only equipment and

support but useful discussions as well must also be acknowledged. My thanks to B.

French, T. Morris, R.Horrocks, P.Bostock and B.Shepard. I would also like to thank Dr.

Z.Bazari at Lloyd's Register for his contribution.

The kind donation of a Hartridge fuel pump test stand from Lucas Powertrain

was also a significant contribution to this work as was the financial support of the SERC.

The help of my fellow researchers in the Thermofluids section also proved

invaluable. I would particularly like to thank Dr. M.S.Baniasad for his significant

contribution and advice throughout as well as his experimental work that helped me to

get started. My thanks also to P. Cutter for being around to answer my computing

questions and E. Gavaises for his help in performing the parametric studies part of this

work. I would also like to wish E. Gavaises all the best for the future as he will be

continuing the development of the work presented here. I would also like to thank the

rest of the technical staff who helped me through this work. My thanks to P. Proctor, P.

Bruni and A. Finch.

I would also like to acknowledge the contribution of M. Knight and I. Stantham,

two third-year students sponsored by Ford who provided some useful assistance.

Finally, I would like to thank my parents for their support and encouragement

throughout the years.

2

Contents

CONTENTS

Abstract 1

Acknowledgments 2

Contents 3

List of Figures 6

List of Tables 10

List of Plates 11

Nomenclature 12

Chapter 1: Introduction 14

1.1 The Diesel Engine 151.1.1 Direct and Indirect Fuel Injection 15

1.2 The Fuel Injection System 161.2.1 Distributor Type Fuel Injection Pump (VE) 181.2.2 Other Systems 181.2.3 The Injection Process 191.2.4 Fuel Injection and Emissions 211.2.5 The Future for Fuel Injection Systems 231.2.6. Fuel Injection Simulation 24

1.3 Literature Review 251.3.1 Early Simulation Models 251.3.2 Methods of Solution 261.3.3 Leakage 271.3.4 Cavitation 281.3.5 Fuel Properties 301.3.6 Variable discharge coefficients 311.3.7 Spray Characteristics 321.3.8 Experimentation 321.3.9 Parametric Studies 331.3.10 Flexibility, User Friendliness and Modules 34

1.4 Outline of Thesis 34

Chapter 2 : Model Development 41

2.1 Introduction 42

3

Contents

2.2 Main Assumptions 43

2.3 Structure 44

2.4 Equations 462.4.1 Pump 492.4.2 Nozzle 51

2.5 Methods of Solution 532.5.1 Partial Differential Equations 53

2.5.1.1 Method of Characteristics 532.5.1.2 Finite Difference Scheme 59

2.5.2 Ordinary Differential Equations 602.5.2.1 Newton Raphson 602.5.2.2 Runge Kutta 61

2.6 Phenomena 622.6.1 Needle Bounce 632.6.2 Cavitation 632.6.3 Leakage 652.6.4. Friction Factor 662.6.5 Bulk Modulus 672.6.6 Density 682.6.7 Spray Angle 682.6.8 Spray Penetration 692.6.9 Variable Coefficients of Discharge 70

2.7 Model Programming 71

2.7.1 Library Routines 762.7.2 Nozzle Simulation 772.7.3 Pump-Pipe-Nozzle Simulation 81

2.8 Summary 85

2.9 Appendix 862.9.1 Fundamental Equations 862.9.2 The Effect of Pipe Wall Flexibility 872.9.3 Nozzle Bounce Equations 902.9.4 Variables for Density and Bulk Modulus Variations 94

Chapter 3 : Experimental Validation 9 '•

3.1 Introduction 96

3.2 Experimental Setup 96

3.3 Injection System Characteristics 1003.3.1 Fuel Injection Quantity 1003.3 2 Effective Plunger Travel 100

3.4 Measured Parameters 103

4

Contents

3.4.1 Control Lever Position 1043.4.2 Control Spool Position 1043.4.3 Pumping Chamber Pressure 1063.4.4 Delivery Valve Lift 1073.4.5 Line Pressure 1103.4.6 Needle Lift 1113.4.7 Injection Rate 113

3.5 Data Acquisition 116

3.6 Experimental Results 1203.5.1 Nozzle Simulation Validation 1223.5.2 Pump-pipe-nozzle Simulation Validation 123

3.7 Summary 125

Chapter 4: Parametric Studies 151

4.1 Introduction 152

4.2 Nozzle Simulation 152

4.3 Nozzle Forces 153

4.4 System Parameters 1544.4.1 Nozzle Orifice Area 1554.4.2 Nozzle Chamber Area 1564.4.3 Nozzle Chamber Volume 1574.4.4 Pipe Diameter 1594.4.5 Pipe Length 1604.4.6 Initial Nozzle Force 1614.4.7 Maximum Needle Lift 1634.4.8 Pumping Chamber Pressure 1644.4.9 Other Parameters 165

4.5 Applications 165

4.5 Summary 166

Chapter 5: Conclusions 180

5.1 Conclusions of the Computational Programme 181

5.2 Conclusions of the Experimental Programme 183

5.3 Recommendations for Future Work. 184

References 185

5

List of Figures

LIST OF FIGURES

1.1 Direct Injection 16

1.2 Indirect Injection 16

1.3 A Diesel fuel-injection system showing fuel flow 17

1.4 High pressure side of a Fuel Injection System 19

1.5 Hole type nozzle 21

1.6 Pintle nozzle 21

1.7 Schematic arrangement of an electronic control unit for fuel injection 24

1.8 Port Cavitation 29

1.9 Cavitation by centrifugal forces 29

1.10 Wave cavitation 29

1.11 Edge cavitation 29

2.1 Simulation schematics 45

2.2 Conservation of mass 46

2.3 Equilibrium of forces 47

2.4 Constant pressure valve 50

2.5 Schematic of a Stanadyne nozzle 52

2.6 Method of characteristics applied to the high pressure pipe 55

2.7 Grid for the finite difference method 60

2.8 A section of the high pressure pipe 64

2.9 Friction factor variation with Reynolds number 67

2.10 Fuel bulk modulus variation with pressure and temperature 67

2.11 Fuel density variation with pressure and temperature 68

2.12 Coefficient of discharge against lift for the seat passage 70

2.13 Coefficient of discharge against lift for the discharge holes 71

2.14 Window showing the programming software 72

2.15 Window showing the three simulation models 72

2.16 Building a Windows application 73

2.17 Dialog box showing project options 74

2.18 Dialog box showing C compiler options 75

2.19 Dialog box showing Linker options 75

2.20 Dialog box showing resource options 74

2.21 Dialog box showing project options 74

2.22 Nozzle data dialog box for nozzle simulation 79

2.23 Excel being used to examine a typical output file from the simulations 79

2.24 Computer program flow chart for the nozzle simulation 80

6

List of Figures

2.25 Time taken to run nozzle simulation on a 486DX2-50MHz PC

computer 81

2.26 Pump dialog box showing pump input variable and default values 82

2.27 Pipe dialog box showing pipe input variables and default values 83

2.28 Nozzle dialog box showing nozzle input variables and default values 83

2.29 Fuel dialog box showing fuel input variables and default values 84

2.30 Dialog box showing time taken to run pump-pipe-nozzle simulation

on a 486DX2-50M11iz PC computer 84

2.31 Computer program flow chart for pump-pipe-nozzle simulation 85

2.32 Control volume for continuity equation derivation 87

2.33 Tensile force in pipe wall 87

2.34 Schematic for nozzle impact 90

2.35 Example of the upper impact motion 91

2.36 Example of the lower impact motion 91

3.1 Schematic of instrumented fuel injection system 97

3.2 Experimental test rig 99

3.3 Fuel injection quantity per injection shot against speed and lever position 101

3.4 Plunger effective travel against speed and lever position 102

3.5 The effect of filtering the injection rate signal at 50% lever position,

1000rpm 129

3.6 The effect of filtering the injection rate signal at 100% lever position,

2000rpm 129

3.7 Control spool transducer calibration 105

3.8 Sample output from control spool transducer 105

3.9 Control spool position transducer 106

3.10 Pumping chamber pressure transducer 107

3.11 Sample output from pumping chamber pressure transducer 107

3.12 Delivery valve position transducer 108

3.13 Delivery valve transducer calibration 109

3.14 Sample output from delivery valve transducer 109

3.15 Line pressure transducer 110

3.16 Sample output from line pressure (pump end) transducer 111

3.17 Sample output from line pressure (nozzle end) transducer 111

3.18 Needle lift transducer 112

3.19 Needle lift transducer calibration 113

3.20 Sample output from needle lift transducer 113

3.21 Bosch injection rate meter 114

3.22 Injection rate meter calibration 115

7

List of Figures

3.23 Sample output from injection rate meter 116

3.24 Input options for data acquisition 117

3.25 Acquisition options for data acquisition 118

3.26 Input channel / gain list for data acquisition 118

3.27 Data acquisition using sample software 119

3.28 DT2839 board calibration 119

3.29 Fuel injection quantities at full lever position (100%) 127

3.30 Fuel injection quantities at part lever position (50%) 127

3.31 Fuel injection quantities at low lever position (20%) 127

3.32 Smoothed injection rate signal for 2000rpm, 100% lever position case 128



3.35 Experimental results for 500rpm, 100% lever position case 130










3.45 Comparison of simulated and experimental results, 450rpm,

0% lever position 140











4.1 Effect of pipe diameter variations on line pressure (nozzle end) 168

4.2 Effect of nozzle chamber area variations on line pressure (nozzle end) 169

4.3 Forces on the nozzle valve 170

4.4 Injection timing reference method 155

8

List of Figures

4.5 The effect of nozzle orifice area variations on the injection rate 171

4.6 The effect of nozzle chamber area variations on the injection rate 172

4.7 The effect of nozzle chamber volume variations on the injection rate 173

4.8 The effect of pipe diameter variations on the injection rate 174

4.9 The effect of pipe length variations on the injection rate 175

4.10 The effect of initial nozzle force variations on the injection rate 176

4.11 Effective flow area against needle lift 163

4.12 The effect of maximum needle lift variations on the injection rate 177

4.13 Pumping chamber pressure variations for the three test cases 178

4.14 The effect of pumping chamber pressure variations on the injection rate 179

9

List of Tables

LIST OF TABLES

1.1 Fuel injection characteristics and emissions 23

1.2 Previous fuel injection simulations 36,37

2.1 Boundary conditions used for pipe sections in the model 59

2.2 Typical values for determining spray angle 69

2.3 Typical values for determining spray penetration 69

2.4 Library routines in INJECT 77

2.5 Diesel fuel properties and fuel injection system parameters 87

2.6 Variables for density and bulk modulus variations 94

3.1 Calibration fluid 4113 properties 98

3.2 Fuel injection quantity per injection shot against speed and lever position 101

3.3 Plunger effective travel against speed and lever position 102

3.4 Bosch injection rate meter specifications 114

3.5 All test cases performed 120

3.6 Cases selected for model validation 120

3.7 Converting time to crankangle for the experimental results 121

3.8 Fuel injection quantities for nozzle simulation 123

3.9 Fuel injection quantities for pump-pipe-nozzle simulation 125

4.1 Fuel injection quantity variations with nozzle orifice area 156

4.2 Fuel injection quantity variations with nozzle chamber area 157

4.3 Timing variations with nozzle chamber area 157

4.4 Fuel injection quantity variations with nozzle chamber volume 158

4.5 Timing variations with nozzle chamber volume 158

4.6 Fuel injection quantity variations with pipe diameter 159

4.7 Timing variations with pipe diameter 159

4.8 Fuel injection quantity variations with pipe length 160

4.9 Timing variations with pipe length 160

4.10 Fuel injection quantity variations with initial nozzle force 161

4.11 Timing variations with initial nozzle force 162

4.12 Fuel injection quantity variations with maximum needle lift 163

4.13 Fuel injection quantity variations with pumping chamber pressure 164

4.14 Timing variations with pumping chamber pressure 165

10

List of Plates

LIST OF PLATES

1.1 Sectioned distributor head from a Bosch VE type pump 38

1.2 Delivery valve assembly (sectioned) 39

1.3 Delivery valve assembly components 40

3.1 Complete experimental set up 146

3.2 Hartridge 1100 fuel pump test stand with instrumented injection system 147

3.3 Instrumented fuel injection system 148

3.4 Instrumented distributor head (front view) 149

3.5 Instrumented distributor head (side view) 150

11

Nomenclature

NOMENCLATURE

A area.

a sound velocity.

acceleration.

Cd coefficient of discharge.

damping coefficient.

diameter.

diameter of discharge holes.

dt time step.

dx length step.

Young's modulus.

wall thickness.

friction factor.

gravitational acceleration.

clearance.

bulk modulus.

spring rate.

1 length of discharge holes.

mass.

pressure.

volumetric flow rate.

Re Reynolds Number.

spray penetration.

time.

V volume.

voltage.

velocity.

displacement.

velocity.

acceleration.

variation of volume.

fi compressibility

dynamic viscosity.

0 spray angle.

density

relative density

12

Nomenclature

Subscripts

c combustion chamber.

cavity.

d delivery chamber.

do delivery valve opening.

dv delivery valve.

fc feed chamber.

i sac volume.

position step integer.

j time step integer.

L last section of pipe.

liquid liquid properties.

mix mixture properties.

n nozzle chamber.

nv nozzle valve.

p plunger.

R reservoir.

sc section of nozzle valve.

u pumping chamber.

3 delivery valve chamber.

vapour vapour properties.

1 first section of pipe.

13

Introduction

1. INTRODUCTION

1.1 The Diesel Engine 151.1.1 Direct and Indirect Fuel Injection 15

1.2 The Fuel Injection System 161.2.1 Distributor Type Fuel Injection Pump (VE) 181.2.2 Other Systems 181.2.3 The Injection Process 191.2.4 Fuel Injection and Emissions 211.2.5 The Future for Fuel Injection Systems 231.2.6. Fuel Injection Simulation 24

1.3 Literature Review 251.3.1 Early Simulation Models 251.3.2 Methods of Solution 261.3.3 Leakage 271.3.4 Cavitation 281.3.5 Fuel Properties 301.3.6 Variable discharge coefficients 311.3.7 Spray Characteristics 321.3.8 Experimentation 321.3.9 Parametric Studies 331.3.10 Flexibility, User Friendliness and Modules 34

1.4 Outline of Thesis 34

14

Introduction

Chapter I

INTRODUCTION

If the engine is considered to be the heart of the car then the fuel injection

equipment (FIE) is the heart of the diesel engine. The FIE pumps the diesel fuel to the

engine required for it to function. It also influences the efficiency of the engine and most

of the engine characteristics are dependent on the performance of the FIE. The

importance of the FIE is such that most of the development of the diesel engine has been

closely linked over the years to the development of the FIE.

1.1 The Diesel Engine

The Diesel engine, also known as a compression-ignition engine, was conceived

by Dr. Rudolf Diesel in an attempt to improve on the relatively poor thermal efficiency of

the spark ignition engine by employing a higher compression ratio. During the

compression stroke of the engine the air in the combustion chamber is heated to such an

extent that when the fuel is injected it self-ignites. Injecting the fuel directly into the

engine proved unsatisfactory during the initial development of the engine and so

compressed air was used to force it into the combustion chamber. However, this air blast

injection method was cumbersome and expensive and was eventually replaced by a

mechanical system. The system that has been generally accepted was the 'jerk pump'

system in which an injection pump meters the fuel and injects it at high pressure through

small-hole injectors into the combustion chamber.

1.1.1 Direct and Indirect Fuel Injection

Unlike conventional petrol engines, also known as spark-ignition (SI) engines

employing carburetors, all diesel engines have fuel injection systems. The injection

method falls into one of two groups, either Direct Injection (DI) or Indirect Injection

(IDI). As the name suggests, direct injection refers to all systems in which fuel is injected

directly into the combustion chamber, see figure 1.1. In IDI engines a relatively rich

mixture of fuel is first ignited in a small pre-chamber or turbulence chamber, see figure

1.2., and this burning mixture then passes into the main combustion chamber, where it

mixes with the remaining compressed air and burns very efficiently.

Traditionally only IDI systems were used in passenger car diesels. This was due

to relatively smooth combustion, lower operating noise and the relatively low

requirements from the fuel injection system for achieving good fuel/air mixing at high

15

Injector

Fuel Spray

Piston

/a

Introduction

speeds. However, DI diesel engines consume 10-15% less fuel and, naturally, this has led

to the development of car engines with direct fuel injection into a piston-bowl located

eccentric to the piston axis.

Figure 1.1 : Direct Injection

Figure 1.2 : Indirect Injection

1.2 The Fuel Injection System

The fuel injection system of a diesel engine has to perform several functions:

• Meter the quantity of fuel injected.

• Accurately time the injection.

• Mix the fuel with the air in the combustion chamber in the shortest possible time.

The correct quantity of fuel must be injected to generate the required engine

torque. The injection timing affects performance, smoke levels, noise and exhaust

emissions and must be controlled to within ±1° crank angle to optimise these parameters.

And finally, the fuel has to be atomised to mix with the air in the combustion chamber

and this can be done using high injection pressures normally upto 1000 bar. The function

of the injection nozzle is to produce a finely atomised spray of fuel droplets that will mix

readily with the air and ensure complete combustion in the time available. The nozzle

outlet is controlled by a needle valve held against its seat by a stiff spring, which

determines the fuel pressure needed to lift the valve off its seat in order to initiate fuel

injection.

16

Introduction

1. Fuel tank

2. Fuel line (under vacuum)

3. Fuel filter

4. Injection pump

5. High pressure fuel line

6. Injection nozzle

7. Fuel return line (not under high pressure)

Figure 1.3: Typical Diesel fuel-injection system showing fuel flow direction.

To describe the fuel injection process and fuel injection system in more detail a

Bosch VE-type distributor pump will be used as an example, due to the fact that the

work described in this thesis involved such a pump. A complete fuel injection system is

made up of a low pressure section and a high pressure section; this is shown in figure 1.3

for the Bosch VE type distributor pump. The low pressure side consists of the fuel tank,

a filter, a supply pump and an overflow valve as well as several fuel lines. Its primary

17

Introduction

purpose is to condition and supply fuel to the injection pump and the high pressure side

of the system. However, it is the high pressure section which generates the pressure

necessary for injection that is the focus of this thesis, although the low pressure side has

been modeled as well. The high pressure section includes the pumping chamber, the

delivery valve, the high pressure pipe and the injection nozzle.

1.2.1 Distributor -Type Fuel Injection Pump (VE)

The VE distributor-type fuel-injection pump is used in passenger car Diesel

engines, tractors and light commercial vehicles with 3,4,5 and 6 cylinder engines with an

output of up to 20kW/cylinder, depending upon engine speed and combustion system.

The distributor pump has only one plunger and barrel assembly for all cylinders.

The plunger delivers the fuel by a reciprocating motion and distributes it to the individual

outlets by a rotary motion. The number of plunger strokes during one revolution of the

drive shaft corresponds to the number of engine cylinders. The drive shaft of the VE

pump rotates the cam plate, which is rigidly connected to the pump plunger, via the cross

coupling. The cams on the bottom surface of the cam plate roll over the rollers in the

rolling ring. This causes the plunger to reciprocate as well as to rotate, thus performing

both functions of delivery and distribution. The pump supplies fuel as long as the spill

port in the plunger remains closed during the working stroke. Delivery stops when the

spill port exits the control spool. The position of the control spool therefore determines

the effective stroke and the quantity of fuel injected. The position of the control spool

which slides along the plunger, is determined by the governor.

1.2.2 Other Systems

There are many other FIE systems which can perform the tasks of the fuel

injection system: For example, the in-line fuel injection pump has one plunger and barrel

assembly for each engine cylinder. The plunger is moved in the supply direction by a

camshaft driven by the engine and is returned by a plunger return spring. The overall

stroke of the pump plunger is fixed and the quantity of fuel is altered by varying the

plunger effective stroke. This is achieved by rotating the plunger, which has a helical

groove on its side, and changing the displacement of the plunger before the spill port is

opened.

Distributor pumps manufactured by Lucas and Stanadyne use inlet metering

control of the plunger displacement. In the case of the Lucas DPS pump the plungers are

mounted radially on the head of the rotor and operate within an internal cam ring

through rollers and shoes. The filling and delivery ports are incorporated in the rotor.

18

Fuel Lever and Governor

Feed Chamber

Control Spool

Spill Port

Plunger

Pumping Chamber

Delivery Pipe

Delivery Chamber

Delivery Valve

/ Delivery ValveChamber

PIPE

NOZZLEHigh Pressure Pipe

Nozzle Chamber

Nozzle Valve

Sac Volume

Introduction

Pumping commences when the plunger rollers strike the cam flank and the displacement

is determined by the outward position of the plungers at the point of inlet port closure.

On the other hand high pressure unit injectors consist of the pump and injector

together as one unit. Their principal advantage over pump-pipe-nozzle systems is their

higher injection pressures combined with accurate control of injected quantity although

their larger size makes installation into the cylinder head more difficult.

As an alternative, the Cummins PT fuel injection system incorporates inlet

metered pump-injection, fed from a common pressurised rail.

1.2.3 The Injection Process

Figure 1.4 : High pressure side of a fuel injection system

Figure 1.4 shows the high pressure side of a fuel injection system for the Bosch

VE type distributor pump connected to a hole-type nozzle. The pump part of the high

pressure side is also shown in Plate 1.1 at the end of this chapter. The photograph shows

a sectioned distributor head from a Bosch VE type pump. This sectioning was performed

at the beginning of the research programme to not only examine how the system works

but also measure the geometric characteristics of the system. Using this system as an

19

Introduction

example, the injection process will now be described in more detail: The plunger of the

fuel injection pump moves to decrease the volume of the pumping chamber under the

action of the cam plate. The increasing pressure in the pumping chamber opens the

delivery valve. A pressure wave then travels down the high pressure pipe at the speed of

sound (approx. 1400 m/s) towards the nozzle. When the pressure at the nozzle end

reaches sufficient magnitude to open the nozzle valve (nozzle opening pressure), fuel

flows into the sac volume and through the discharge holes into the engine cylinder. This

fuel is atomised as it enters the combustion chamber at high velocities and subsequently

ignites. Delivery of the fuel stops when the spill port at the pump end opens which results

in the pumping chamber pressure collapsing and the delivery valve closing. Depending on

the type of injection system used, the pressure left in the high pressure pipe is relieved to

ensure that:

• the injection nozzle closes quickly and fuel injection stops to prevent dribbling.

• oscillations in the high pressure pipe do not cause the nozzle to re-open or cause any

cavitation damage.

This relief operation can be performed by a collar which retracts a small amount

of fuel from the high pressure pipe; this is known as the retraction volume. However, for

high-speed, high-pressure systems a constant-volume relief valve is used which employs

small holes to damp the flow in the return direction. For even higher pressure systems, a

constant-pressure valve must be used; this reduces the pressure in the high pressure line

down to a specified static pressure by using a second non-return valve. A constant

pressure valve is used in the Bosch VE type distributor pump. Plate 1.2 at the end of this

chapter shows the delivery valve and valve stop in position on the sectioned head of a

Bosch VE type distributor pump. Plate 1.3 shows all the components of the delivery

valve assembly used in this system including the constant pressure valve.

It should be mentioned that the type of fuel injection nozzle used depends on the

engine type. DI engines, except for small stationary engines, are usually equipped with

multi-hole fuel injectors (see figure 1.5), while pintle injectors (see figure 1.6) with a

single annular hole of variable flow area are used in engines with IDI systems.

20

Nozzle chamber

Nozzle needle

Sac volume

NOT TO SCALE

Introduction

n = Fluid flow

Figure 1.5: Hole type nozzle Figure 1.6: Pintle nozzle

1.2.4 Fuel Injection and Emissions

Unfortunately, the diesel engine has a particularly bad reputation concerning

emissions due to the visible black smoke (particulates) produced under certain operating

conditions. However, this reputation is undeserved and there is increasing evidence that

advanced diesel engines are more environmentally friendly than the more widely used

petrol or spark ignition engines equipped with three way catalysts.

It's well known that the fuel injection system in diesel engines plays a vital role in

the combustion process. The fuel injection system controls and governs the timing,

duration and the amount of fuel that is injected into the combustion chamber. Therefore,

the performance of the engine depends to a great extent on the performance of the fuel

injection system used. The emissions or products of combustion, such as nitrogen oxides

(N0x), particulates and unburned hydrocarbons, depend also on the performance of the

fuel injection system and the degree of fuel/air mixing. This is particularly important

considering the urgent need to reduce these emissions and to comply with ever tightening

emission regulations.

Heywood (1988) explains that the burning during combustion in a typical DI

diesel engine has three distinguishable stages:

21

Introduction

1. Premixed or rapid combustion phase.

2. Mixing- controlled combustion phase.

3. Late combustion phase.

This burning is preceded by an ignition delay period which is the time between

the start of fuel injection into the combustion chamber and the start of combustion.

During the premixed phase the fuel injected during the ignition delay period, which has

mixed with air to within the flammability limits, burns rapidly in a few crank angle

degrees. There is a high heat-release rate during this phase. In the mixing controlled

combustion phase the burning rate is determined by the rate at which the mixture

becomes available for burning and, as a result, is primarily controlled by the fuel-air

mixing process. The final or late combustion phase continues well into the expansion

stroke due to unburnt fuel, soot or fuel rich products in the combustion chamber. The

heat release rate is lower during this phase. Oxides of nitrogen form in the high

temperature burned gas regions, within the combustion chamber, such as the flame front

but mainly in the postflame gases (The formation of oxides of nitrogen is essentially a

temperature dependent process). Particulates form in the rich core of fuel sprays within

the flame region and then oxidise when they come into contact with oxygen.

Unburnt hydrocarbons originate in regions where the flame quenchs such as chamber

walls or where there is incomplete mixing so that the mixture is either too lean or too

rich. Noise is controlled by the initial rapid heat release at the early point of combustion.

Carbon monoxide emissions are not as significant as in spark ignition engines as they are

controlled by the fuel/air equivalence ratio and diesels have leaner fuel/air mixtures than

spark ignition engines.

Start of injection, injection-sequence characteristics and fuel atomisation have an

important effect on toxic emissions and their formation. The start of combustion is

primarily determined by the start of injection. Retarded injection, for example, reduces

emissions of oxides of nitrogen while over-retarded injection increases the emissions of

hydrocarbons and particulates. Deviation of the start of injection from the nominal value

by 10 of crank angle can increase the emissions of NOx or HC by approximately 15%.

This high sensitivity implies that the start of injection must be precisely determined. Fuel

injected into the combustion chamber after the main combustion phase may reach the

exhaust system unburned and thus increase the hydrocarbon and particulate emissions.

Post-injection (dribble or secondary injection) must be prevented to stop hydrocarbon

emissions from increasing. Increasing the injection rate increases NOx emissions but

decreases particulate emissions and explains the current trend for increased injection

pressures. The controlling physical process being the rate of fuel-air mixing in the

combustion chamber.

22

Introduction

Table 1.1, below shows a summary from Takaishi et al (1990) of the effect of

injection parameters on emissions, fuel consumption and noise.

Fuel Injection Characteristics

Demand Injection Rate Injection Timing Injection Pressure Normality of

injection

Prevention of

irregular injection

Low Combustion

noise

Reduction of

initial injection

rate

Delay in the low

speed region

-------

Low smoke and

particulate

emissions

Improvement in

mode of injection

cut-off

Delay in the low

speed region

Raise mean

injection pressure

Prevention of

secondary

injection

Prevention of

irregular &

secondary

injection

Low fuel

consumption

Improvement in

mode of injection

cut-off

Advance in the

high-speed region

Raise mean

injection pressure

Table 1.1 : Fuel injection characteristics and emissions from Takaishi et at (1990).

One example of the advances in emissions technology is the use of exhaust gas

recirculation (EGR). This is the case where exhaust gas is mixed with the intake air to

reduce the oxygen concentration in the charge and, thus, lower the combustion

temperature and reduce the formation of nitrogen oxides (N0x). In addition the quantity

of exhaust gas can be varied. Other methods to reduce emissions associated with the fuel

injection system, include high pressure injection, injection timing retard, two-stage and

pilot injection which also allow reduction of the combustion noise resulting from the

relatively large amount of fuel burned in the premixed combustion phase.

1.2.5 The Future for Fuel Injection Systems

The application of electronic controls to fuel injection has been made possible by

the recent advancements in electronic and microprocessor technology. This application is

well suited because, using the example of the Bosch VE type pump, the mechanical

governor which controls the control spool position is cumbersome and has a limited

number of inputs. An electronic actuator can be used to move the control spool to the

required position after receiving the necessary information from an electronic control unit

(ECU). This in turn uses information from several transducers to measure controlling

parameters such as the engine speed and air inlet temperature. A schematic for such a

system is shown in figure 1.7.

23

Coolant temperature EGR Control—

ElectronicControl

Unitn Start Aid Option

Timing Control

Manifold Pressure

Engine speed

Crankshaft reference

4-1]Throttle sensor

Fuel Control

41=1n

Introduction

Figure 1.7 : Schematic arrangement of an electronic control unit for fuel injection.

The ECU can also be used to control the injection timing, as well as the fuel

injection quantity, with the use of another actuator. The timing mechanism of the Bosch

VE type pump involves the rotation of the circular cam plate which drives the plunger.

The use of ECU s enables a large number of input signals to be processed. This,

in turn, allows groups of characteristic function curves to be implemented which would

be impossible to achieve mechanically. In addition, other vehicle systems such as the

exhaust gas recirculation(EGR) can make use of the signals output by the ECU to allow

control of the percentage of EGR as a function of the engine operating condition.

1.2.6. Fuel Injection Simulation

The importance of fuel injection simulation in the development of fuel injection

equipment and better understanding of combustion and pollutant formation has been

recognised for some time and several computer models have already been developed. A

computer simulation can be used to improve existing FIE systems as well as analysing

the injection characteristics of new and innovative systems. Fuel injection models can be

used to examine variables not easily obtained by experimentation and to quantify the

effect of new emerging parameters such as increased injection pressures. They can also

be used to expand the scope of existing diesel engine performance simulation codes and

multi-dimensional computer models of diesel combustion and exhaust emissions.

To simulate a fuel injection system, the pressures and flows throughout the

system must be calculated and the wave propagation between the pump and nozzle must

be adequately simulated. Thus, the core of any computer simulation involves solving the

24

Introduction

equations governing the fluid flow in pipes and the dynamics of the mechanical

components. Probably the most important feature of any simulation is the degree of its

experimental verification and special emphasis has been given to this point in the present

research programme.

The early stages of this work involved stripping and examining a typical fuel

injection system which was done not only to understand its mode of operation but also to

obtain the necessary geometric data, such as the size of the relevant chambers, which are

needed for modeling.

1.3 Literature Review

The fundamental aspects and equations of fuel motion which are common to all

existing simulation models will be covered in more detail in Chapter 2: Model

Development.

This review of FIE simulation models starts by covering the early fuel injection

simulation attempts and then goes through the important parts of fuel injection

simulation which include the methods of solution of the equations involved and flow

phenomena like leakage and cavitation as well as the experimental work done to validate

these models.

As will become clear later, some of the terminology has been modified in this

thesis relative to that used by various authors. This is not only to maintain consistency

with the rest of the thesis when referring to particular components but also to be correct

in terms of the measurement of injection pressure. For example, some authors have

referred to the line pressure at the nozzle end as the injection pressure. The inaccuracy of

this statement will become more clear in the later chapters on experimental validation and

parametric studies.

1.3.1. Early Simulation Models

Giffen and Rowe (1939) is the earliest paper found that relates directly to fuel

injection simulation and sets the foundations for many future simulation models. Their

model is initially divided into three main parts representing the fuel injection system,

namely the pump, pipe and nozzle. The system selected is an in-line pump connected to a

hole-type nozzle. The method of solution was limited by the lack of computer technology

at the time and proves to be very awkward. In common with future work, the high

pressure pipe was handled by selecting two parameters, in this case the pressure and

velocity, and solving the relevant equations. The pressure is handled by dividing the

pressure waves into forward (pump to nozzle) and reverse (nozzle to pump) waves and

resolving them accordingly. Only one parameter was used to validate the model and that

25

Introduction

was described as the nozzle pressure although there is no experimental diagram to

indicate the measurement position. The agreement with the simulation was reasonable.

Knight (1960) has taken advantage of the development of digital computers to

expand on the work of Giffen and Rowe (1939). A finite difference scheme has been

used to solve the high pressure pipe flow equations; the pipe itself is divided into ten

sections. However, the only model validation has been against the pipe line pressure at a

station in the pipe. More recent simulation attempts are discussed below in terms of the

solution methods used and the flow phenomena examined but are also summarised in

Table 1.2.

1.3.2. Methods of Solution

Fuel injection systems must first and foremost be able to cope with the

compressibility of the fuel. It is this property that ensures that the flow out of the nozzle

does not follow exactly the displacement of the pumping plunger. In fact this

phenomenon has caused a lot of problems in the initial development of fuel injection

equipment (Gilkin, 1985). In a similar win any computer simulation must be able to cope

with this phenomenon. Using an example from Schweimer et al (1987), in order to bring

a dead volume of 3000mm 3 to a pressure of 300 bar the fuel density must be increased

by 3% or the volume reduced by 90mm 3 ; these 90mm3 are equal to three times the full

load injection quantity of a small passenger car diesel engine. In theory, it is necessary to

make a distinction between isothermal and adiabatic compressibility. Since however the

compression cycles occur so rapidly that heat losses to the walls can be neglected and

adiabatic compressibility has therefore been assumed for calculation purposes

(Schweimer, 1987).

The equations describing the various parts of the fuel injection system fall into

two main groups. The first includes equations for the pump and the nozzle; these consist

of the conservation of mass and the equilibrium of forces and are simultaneous ordinary

differential equations (0.D.E. ․). These form the boundary conditions for the flow in the

high pressure pipe which is governed by both the conservation of momentum and the

conservation of mass. These equations are quasi-linear hyperbolic partial differential

equations (P.D.E. ․) and require different numerical techniques to solve from those in the

pump and injection nozzle.

Although the equations used to describe the fuel injection system are generally

agreed upon, the numerical methods used to solve them vary considerably. The

techniques used to solve these equations can be arranged into three groups: A delay line,

finite difference or the method of characteristics. The generally accepted view is that the

finite difference schemes can handle discontinuities or cavitation better than the method

of characteristics although the method of characteristics is superior in handling boundary

26

Introduction

conditions. The delay line technique is the simplest of the three but it is considered to be

the least accurate. It is interesting to note that out of the three techniques the method of

characteristics has been more widely used.

In the case of the delay line method, the flow in the high pressure pipe is handled

by using the laws of fluid propagation by pressure waves, i.e.

p = I a. vg

This implies that

1. The intensity, p, of the pressure waves is proportional to the velocity,v,

of the fluid.

2. The disturbances propagate in the elastic system with the sound velocity,

a. From this it can be stated that the waves starting from any point in the

equipment, at the moment 1, will reach a point distant x, in 1+x a time.

Schweimer et al. (1987) have suggested that an acoustic approximation is more

effective than the method of characteristics as long as the attenuation of waves is

correctly taken into account.

A more recent trend in fuel injection simulation has been followed by Marcic

(1993) and Smith and Timoney (1992). Their approach has been to simulate the nozzle

only and use experimentally measured parameters as inputs to these models. These inputs

can consist of the line pressure (nozzle end), the needle lift or even the combustion

chamber pressure. The use of experimental inputs reduces the modeling requirements and

reduces the need for 're-tuning' constants generally associated with variables such as fuel

leakage. However, it must be noted that this type of model (Arcoumanis et al., 1993)

although more accurate in predicting the injection rate has severe limitations when it

comes to parametric studies. This is due to its reliance on experimental inputs and will be

discussed in more detail in Chapter 4.

1.3.3. Leakage

There are two areas of the fuel injection system that are considered to be

sensitive to leakage. One is the pumping chamber, Where fuel can leak to the feed chamber

which is at a much lower pressure during the pumping process, and the second is the

nozzle chamber, where fuel can flow past the needle towards the spring assembly.

However, in the latter case fuel leakage is not totally undesirable since it lubricates the

27

Introduction

various mechanical components. Nevertheless, it is important to bear in mind this specific

type of flow when considering fuel injection simulation.

Despite its importance not all previous models have included leakage. For

example, Schweimer et al. (1987) have neglected the leakage losses on the basis of the

short duration of the injection period, and some have not attempted to simulate it but

simply fitted the results to some experimental data (Henien, 1975). In four cases where

the leakage has been simulated (Aguirre (1992), Wannenwetsch and Egler (1985),

Marcic and Kovacic (1985) and Gibson(1986)), it is either expressed as a flow rate or a

pressure drop. In particular all the equations agree in that:

(i) the leakage flow rate is proportional to (clearance)3.

(ii) the leakage flow rate is proportional to pressure.

In the case of Marcic and Kovacic (1985) the leakage from the pumping chamber

has been considered but not the leakage at the nozzle. In a later paper by the same author

(Marcie, 1993) which concentrates on a nozzle simulation, he claims that the leakage

flow between the needle and nozzle body was always less than 1% of the injected fuel

and can thus be neglected.

1.3.4. Cavitation

In a flowing fluid like the diesel fuel within the fuel injection system, under

certain operating conditions, areas of low pressure can occur locally. If this pressure falls

below the vapour pressure of the diesel fuel there will be local boiling and vapour

bubbles will form. This phenomenon is known as cavitation and can cause serious

problems because when the vapour bubbles collapse in areas of higher pressure, they do

so suddenly. If this should occur in contact with a solid surface, very serious damage can

result due to the very large force with which the liquid hits the surface. Cavitation in a

fuel injection system has been shown to cause erratic fuel delivery and, on a smaller

scale, poor atomisation of the fuel leading to increased smoke emissions, injector fouling

and even misfire (Meier et al., 1989).

In simulation models the vapour pressure is generally assumed to occur at zero

pressure even though its actual value is slightly above zero. This difference is assumed to

be insignificant considering the magnitude of the pressures involved in diesel fuel

injection. This assumption is not made in all cases but Yamaoka (1973) has showed in

the discussion of his paper that this assumption can cause an inaccuracy of only 0.001%

in the predicted fuel quantity and can be neglected.

The usual method used in computer simulations is to assume that cavitation

occurs when the pressure falls below zero and remains zero while cavitation takes place.

28

1 Sr

Introduction

The cavity volume is calculated using the mass continuity equation and cavitation ends

when this volume drops to zero. During cavitation the density, bulk modulus as well as

the propagation speed of sound in the fuel are adjusted accordingly.

Schweimer et al. (1987) have made a distinction between four types of cavitation

occurring in fuel injection systems. Port cavitation (figure 1.8) occurs at the end of the

pipe and tends to produce a large vapour pocket. There is also cavitation by centrifugal

forces (figure 1.9) when cavitation can occur on the inside radius of a curved section.

Wave cavitation (figure 1.10) occurs when pressure waves in the high pressure pipe

interact during the injection process to reduce the pressure below the vapour pressure.

And finally, edge cavitation (figure 1.11) where the fluid can cavitate coming off an edge

or sharp corner. In most cases cavitation is associated with the low pressure region in a

recirculating flow and as such any design efforts to reduce flow separation can lead to

lower chances of cavitation taking place.

Figure 1.8 : Port Cavitation Figure 1.9 : Cavitation by Centrifugal Forces

Figure 1.10 : Wave Cavitation

Figure 1.11 : Edge Cavitation

= Cavitation

Cavitation has been identified as one of the major uncertainties in fuel injection

simulations and numerous techniques have been applied in an attempt to overcome this

problem. Schweimer et al. (1987) have suggested that it is important to carry out

cavitation calculations on the basis of mass. A calculation on the basis of volumetric flow

29

(1.3)

Introduction

values leads to non-conservation of mass and, thus, small losses of mass can lead to large

losses of pressure.

Takaishi et al. (1987) have presented an experimental technique for detecting

cavitation using a piezoelectric sensor which detects ultrasonic waves generated by

cavitation. This has been tried because the increasing demands on fuel injection systems

for higher line pressures also increase the possibility of cavitation. It is also interesting to

note that cavitation could be artificially generated by altering pump speed, fuel injection

quantity, retraction volume, nozzle orifice area and pipe diameter thus highlighting the

need for careful selection of these parameters. Cavitation and erosion were found to be

worst at the nozzle end of the high pressure pipe but may also take place in the injection

hole downstream of the sac volume.

Gibson (1986) and Russell and Lee (1994) have suggested a novel approach to

the problem of cavitation by using relative density and pressure as the key parameters

when solving the pipe flow equations. This allows the model to handle both condensation

and vapourisation in the system without the need to use separate routines. Alternatively

Yamaoka (1973) has introduced a new variable called the variation of volume, Y, defined

as

Y = fiVp +V, (1.2)

This approach can also be used when cavitation occurs due to the inclusion of Tic,

the volume of the cavities during the period of cavitation.

1.3.5. Fuel Properties

The most important fuel properties in fuel injection simulations are density, bulk

modulus and, to a lesser extent, viscosity. Density and bulk modulus jointly determine

the speed of sound and, hence, the speed of propagation of the pressure waves in the fuel

injection system according to the following relationship:

This has obvious implications for the correct timing of the injection events.

Considering that fuel injection pressures can go up to 1000 bar, an important question is

whether the variation of these properties with pressure and even temperature should be

taken into account. When no variations are taken into account, the prevailing argument is

that the property changes are small enough to be insignificant or that an increase in

pressure will lead to an increase in temperature and these have opposite effects on the

30

Introduction

fuel properties (density rises with pressure but falls with an increase in temperature, thus

giving rise to the same bulk modulus). Where the variation of these properties is taken

into account, the equations developed by Dow and Fink (1940) have been invariably

used. Kumar (1983) showed that using variable density and bulk modulus did not affect

the duration or timing of the signals but did reduce their peak values.

Another factor which can affect the speed of sound in a fuel injection system is

the pipe wall rigidity. Out of all the simulations examined, only Parsons and Harkins

(1985) have considered this effect. This is probably due to the fact that he was examining

large marine diesel engines where the increased dimensions of the fuel injection system

used would make this a significant factor. Pipe wall flexibility and its relation to this

work is discussed in more detail in the Appendix to Chapter 2 on Model Development.

The friction factor, f, which is contained in the conservation of momentum

equation for pipe flow can be calculated individually for each time step using the local

Reynolds number and surface roughness. This calculation is based on data provided by

the Moody diagram.

1.3.6. Variable Discharge Coefficients

Considerable work has been done on the flow through nozzle discharge holes.

This part is particularly relevant to simulation work when the discharge coefficients are

considered since the primary output of any fuel injection simulation model is the injection

rate or the flow rate through the discharge holes. This flow rate, Q, is directly

proportional to the discharge coefficient of the nozzle orifices, i.e.,

aCd

A similar situation applies to the flow through orifices within the fuel injection

system such as the flow through the nozzle seat and into the sac volume.

Smith and Timoney (1992) have determined the instantaneous Cd from the

Reynolds number, Re, of the flow through the holes and the non-dimensional pressure

drop or cavitation number across them. This was based on the work of Bergwerk (1959)

who performed a large number of steady flow tests using two lapped steel orifice plates

with reamed holes of 0.25mm and 0.5mm and an lid ratio of 2.5. By varying the injection

pressure and the back pressure independently, he was able to determine the discharge

coefficient of the nozzle holes as a function of both the Reynolds number and the

cavitation number.

Xu et al (1992) have recognised that the discharge coefficient of two reduction

areas of the fuel passage in the nozzle, that is, the needle seat opening passage and the

discharge holes, are both necessary for the solution of the flow equations in the nozzle.

31

Introduction

They even suggested that constant discharge coefficients such as those used by many

simulation models (an approximate Cd value of 0.7 is common) are not sufficient for

accurate prediction of the pressures and flow rates. In addition, they have noted that the

discharge of the seat passage has been neglected in many simulations and this may have

affected the accuracy of the calculations.

1.3.7. Spray Characteristics

Considering that one of the uses and aims of fuel injection simulations is to

improve the combustion process and reduce emissions, it is logical for such a simulation

to be able to provide useful data on the injection spray characteristics as well. This has

been recognised by previous researchers like Scullen and Hames (1978) who included in

the simulation the calculation of the spray penetration and Sauter mean diameter of the

injected spray in addition to the pressures and flow rates throughout the system. Diesel

transient sprays and their characteristics are a huge topic in its own right and most

simulation models have used empirical correlations such as those developed by, for

example Xu et at (1992).

1.3.8. Experimentation

A definite distinction should be made between those models that have been

validated against experimental data and those that have not. Even for those models that

have been validated, it is important to consider which were the validation parameters and

the methods used to measure them. Scullen and Hames (1978) have suggested that the

key elements of FIE validation are the fuel output per stroke, the start of injection and

the injection duration. All three of these can be obtained from the injection rate profile

which is a quantity easily measurable in test rigs but not inside engines.

Because there is a wide variety of fuel injection equipment from in-line pumps to

unit-injectors and from pintle to hole-type nozzles, the previous work to validate

simulation models has been carried out on a similarly wide range of systems. The systems

themselves can be set up on running engines or on purpose built test rigs.

Most researchers have recognised the limiting factors of every piece of

instrumentation. The most important of these being that it is almost impossible to

measure something without changing its previous value. This is particularly relevant to

the measurement of the pressure in the sac volume of a hole-type fuel injection nozzle.

This is probably the most important parameter in fuel injection systems as this is

effectively the last pressure the fuel experiences before entering the combustion chamber.

Henien (1975) even went as far as using no direct pressure transducer measurements, so

as not to affect the fuel injection characteristics, but used strainkauges to measure the

32

Introduction

pressures in an N-50 unit injector mounted in the cylinder head of a 2-stroke Detroit

Allison 2-53 engine.

Probably the easiest parameter to measure in a pump-pipe-nozzle fuel injection

system is the line pressure. This can be done with a special adapter to hold the transducer

or it can be clamped onto the high pressure pipe with a small hole drilled in the pipe at

that location. Erdmann and Schlinder (1982) employed a Kistler 4065A1000 transducer

to measure the line pressure since they could measure both the static and dynamic

pressure allowing examination of the residual pressure variations. Calibrated strain gages

attached to the high pressure pipe can also measure the line pressure. Nearly all

experimental validations of simulation models have measured the line pressure at some

point. Another common parameter measured is the injector nozzle needle lift. This is

typically done with a Hall-effect sensor or an inductance probe. The pumping chamber

pressure is usually measured when a Bosch VE-type distributor pump is used since the

pump design allows relatively easy access for the transducer to be mounted on the wall

of the pumping chamber. Where the injection rate has been measured, the Bosch long

tube method has invariably been used to determine the injection rate profile. The more

recently developed Zeuch method has yet to be used to validate fuel injection simulations

although it offers some advantages relative to the Bosch method (Arcoumanis et al,

1992). When the injection rate profile has not been measured, the average fuel injection

quantity is either measured by counting the time the system takes to consume a given

amount of fuel or by measuring the volume of a number of injections into a burette.

Suzuki et al. (1982) suggested a method of measuring the delivery valve lift on an

in-line pump. This has involved adding an aluminum stick to the top of the delivery valve

which will pass in and out of a coil contained in an extended delivery valve stop.

However, this technique goes against the principle of unaffecting the parameter under

investigation since it not only adds mass to the delivery valve but together with the

extended valve stop, affects the flow patterns in the delivery valve chamber.

The validation cases for the simulation models usually cover the full operating

range of speeds and lever positions. The major differences identified between the

experimental and simulation values include the injection timing, the rate of pressure rise

and the injection rates (Kumar, 1983).

1.3.9 Parametric Studies

Once a model has been programmed and validated, it is ready to be used for

parametric studies. That is to say, it can be used to examine the fuel injection process and

determine which parameters affect the injection characteristics and to what degree.

Kumar et al. (1983) have performed extensive parametric studies with their pump-pipe-

nozzle model and a list of the parameters they examined is given below:

33

Introduction

• Residual pressure

• Nozzle opening pressure

• Pump plunger diameter *

• Retraction volume *

• Friction Loss

• High pressure pipe diameter*

• High pressure pipe length

• Spill port diameter *

• Nozzle orifice area *

• Combustion chamber pressure

• Pump speed

• Nozzle valve inertia

• Nozzle valve maximum lift

Those parameters which are indicated by (*) were found to exert the most

significant effect on the injection characteristics. Aguirre et al. (1992) also performed

parametric studies and agreed with the significance of the spill port diameter, nozzle

orifice area and plunger diameter but suggested that the high pressure pipe length is also

significant in determining the injection characteristics.

1.3.10. Flexibility, User Friendliness and Modules

Another important feature of fuel injection models that has generally been

recognised is the structure and format of the programming involved. Wannenwetsch and

Egler (1985) have highlighted the importance of user-friendliness for a simulation code.

This included interactive data input, engineering as opposed to mathematical descriptions

of the system and stable mathematical methods. In a similar fashion to Goyal (1978), the

different parts of the fuel injection system were divided up into modules. Each module is

independent but can be linked together with any number of different modules to form a

complete fuel injection system. This makes it relatively easy to handle design changes or

even completely different systems. The modules used by Wannenwetsch and Egler

(1985) have included containers, pressure-driven valves, flow passages, short pipes (no

wave propagation), pipes, laminar flow (e.g. for leakage) and pairs of valves.

1.4 Outline of Thesis

The engine group at the Mechanical Engineering Department of Imperial College

has done considerable work in the field of combustion analysis, mixture formation and

34

Introduction

spray characteristics for diesel engines over the last twenty years. However, to date little

or no work has been done on the modeling of the fuel injection process up to the point at

which the fuel is introduced to the combustion chamber. This thesis presents another

attempt to simulate diesel fuel injection systems. However, using ideas suggested by

Goyal (1978) and Wannenwetsch and Egler (1985) the simulation model has been

structured in a modular format allowing flexibility to simulate various FIE systems. It has

also taken advantage of the recent developments in computer technology with the

simulation being written in QuickC and using the Windows operating system. In addition

an attempt was made to validate the model using the maximum possible number of

measured parameters._The thesis begins by introducing fuel injection systems and reviews the previous

literature on fuel injection simulations. The next chapter entitled Model Development

concentrates on the theory and techniques of simulation and covers the computational

side of the research programme. This is followed by a chapter on Experimental

Validation which describes in detail the experimental work and the data obtained to

validate the simulation model. This chapter is followed by the Parametric Studies which

involve using the models developed to examine the effect of different parameters on the

injection characteristics. The Thesis rounds off by summarising the main conclusions of

the work and offering recommendations for future work.

35

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i3

Model Development

2. MODEL DEVELOPMENT

2.1 Introduction 42

2.2 Main Assumptions 43

2.3 Structure 44

2.4 Equations 462.4.1 Pump 492.4.2 Nozzle 51

2.5 Methods of Solution 532.5.1 Partial Differential Equations 53

2.5.1.1 Method of Characteristics 532.5.1.2 Finite Difference Scheme 59

2.5.2 Ordinary Differential Equations 602.5.2.1 Newton Raphson 602.5.2.2 Runge Kutta 61

2.6 Phenomena 622.6.1 Needle Bounce 632.6.2 Cavitation 632.6.3 Leakage 652.6.4. Friction Factor 662.6.5 Bulk Modulus 672.6.6 Density 682.6.7 Spray Angle 682.6.8 Spray Penetration 692.6.9 Variable Coefficients of Discharge 70

2.7 Model Programming 712.7.1 Library Routines 762.7.2 Nozzle Simulation 772.7.3 Pump-Pipe-Nozzle Simulation 81

2.8 Summary 85

2.9 Appendix 862.9.1 Fundamental Equations 862.9.2 The Effect of Pipe Wall Flexibility 872.9.3 Nozzle Bounce Equations 902.9.4 Variables for Density and Bulk Modulus Variations 94

41

Model Development

Chapter 2

MODEL DEVELOPMENT

2.1 Introduction

The aim in simulating fuel injection systems is to accurately predict the pressures

and flow rates at different points within the system. The most important is the fuel

injection rate into the combustion chamber, the output of the system. This does not

require the solution to a large number of complicated fluid mechanics equations but can

in fact be done using a few basic principles, such as the conservation of mass, the

conservation of momentum and the equilibrium of forces. The complications and

differences between existing models arises in the solution to the differential equations

from applying these principles.

The simulation and modeling work described in this report are based on a typical

pump-pipe-nozzle system (A Bosch VE type distributor pump connected to Stanadyne

multi hole-type nozzles by high pressure pipes). The simulation work began by

attempting to model the entire high pressure side of the fuel injection system

(Arcoumanis and Fairbrother, 1992). However, it was found easier to develop first a

model of the nozzle alone, then to add in a dynamic model for the needle motion and

finally extend the modeling to cover the whole fuel injection system. Two simulation

models are presented in this thesis: A pump-pipe-nozzle simulation which uses a

pumping chamber pressure profile as an input and simulates the flow throughout the

system and a nozzle simulation which uses a line pressure (nozzle end) profile and

simulates the needle motion and the flow in the nozzle only.

The Model Development chapter of this thesis covers the theory and

computational part of the work. It begins by going through the assumptions behind the

models and follows on with the program structure. These sections are then followed by

the equations used to predict the pressures and flow rates in the various parts of the fuel

injection system and how these equations are solved. Some alternatives to the methods

used and important phenomena included in these models are also described. These range

from the needle bounce equations to the correlations used for variable discharge

coefficients. The chapter then finishes by describing the simulation programs themselves

and some of the techniques used in their programming. The most notable being the use

of the Windows operating system and dialog boxes for user interaction.

42

Model Development

2.2 Main Assumptions

To develop the models described in this thesis it was necessary to make a number

of assumptions. This was done to allow the application of certain equations, reduce the

complexity of the programming required and increase the speed of the simulation. The

assumptions made are listed below:

1) All flow is assumed to be one dimensional.

The flow in all the pipe sections and chambers is assumed to be one dimensional.

The principal advantage of this assumption is that it dramatically reduces the

number and complexity of equations required.

2) All chambers are treated as concentrated volumes.

This means that the physical conditions, such as pressure, are assumed to be

constant throughout a particular volume. It also means that no account of the

shape of that volume is taken into account. This assumption is reasonable

considering the small size of the chambers and the high pressures involved in fuel

injection equipment.

3) The high pressure pipe connecting the pump and nozzle is divided into sections and

the pressure within each section is assumed constant.

This effectively means that the pipe is divided up into a series of connected

concentrated volumes. By selecting a suitable length of pipe section this reduces

the computation required and output data without effecting the accuracy of the

simulation significantly.

4) Fuel temperature remains constant at 40°C.

The temperature of the fuel will change within a fuel injection system particularly

in the nozzle of a firing engine. However, for the conditions on a test rig as was

used to validate the different models described here, the effect of the temperature

on the fuel propérties was considered to be insignificant. The effect of higher

temperature on the fuel is to lower both its bulk modulus and density.

5) Feed chamber pressure is constant during an injection cycle.

This is the boundary condition for the pumping chamber in the fuel injection

pump. In reality this pressure will change with speed from about 2 bar at idle to 7

or 8 bar at maximum speed for the Bosch VE type pump[Automotive Handbook,

Bosch, 19861. These variations are considered to be small enough in comparison

to the injection pressures to be ignored.

43

Model Development

6) Constant damping and delivery valve discharge coefficients (Cd= 0.7).

For simplicity constant values for the damping coefficients of both the delivery

and nozzle valve are used However, although a constant coefficient of discharge

at the delivery valve is reasonable the variation of the discharge coefficients in the

nozzle, with respect to needle liji, are accounted for in these models. This is at

least partly due to earlier work which suggested the inadequacy of using constant

discharge coefficients at the nozzle (Arcoumanis and Fairbrother, 1992).

7) The friction factor in unsteady flow is the same as in steady flow.

The correlations developed for friction factor in steady flow are assumed to be

valid for unsteady flow as well. An example of these correlations are given by

Streeter and Wylie (1983).

8) Compression is assumed to be adiabatic.

This assumption comes from Schweimer et al (1987) who suggested that the

injection process was relatively short and so heat transfer could be ignored.

2.3 Structure

The fuel injection system can be broken down into three main elements. These

are volumes, pipes and valves. The volumes or chambers include the pumping chamber,

both the delivery and delivery valve chambers, the nozzle chamber and the sac volume.

The pipes are the delivery pipe, the high pressure pipe and the nozzle pipe. The valves

are the delivery valve and the nozzle valve. There are two advantages in being able to

break the fuel injection system down in this manner. Firstly it reduces the programming

required as each element can be solved using the same principles. And secondly, it allows

the programmer to structure the model using a modular format. This means that each

part or element can be kept independent of another except at the points at which they

meet. These points are known as the boundary points and require the solution of

boundary conditions. These will be covered in more detail later. This independence has a

particular advantage when considering future development and the simulation of different

systems, such as unit injectors, which are made up of the same type of elements with

different geometric parameters.

Figure 2.1 shows the simulation schematics for both models presented here and

indicates how they are both made up of the three types of elements mentioned above.

44

PUMP-PIPE-NOZZLE SIMULATION

Pumping chamber

Delivery pipe

Delivery chamber

Delivery valve

Delivery valve chamber

High pressure pipe

Nozzle chamber

'Nozzle' pipe

[..>< Nozzle valve

rj-Sac Volume

Discharge holes

NOZZLE SIMULATIONHigh pressure pipe (small section)

Nozzle chamber

[1---'Nozzle' pipe

I>< Nozzle valve

ri :4Sac Volume

Discharge holes

KEY

= Pipe

><_ = Valve

= Volume

Model Development

Figure 2.1 : Simulation schematics

45

Model Development

2. 4 Equations

Once the fuel injection system has been broken down into different elements

equations to predict the pressures and flow rates must be found. For the volumes the

conservation of mass can be used. The equilibrium of forces can be used for the valves

and pipe flow can be handled with the continuity and momentum equations. Another

important equation to be used is the orifice flow equation. This is used for some of the

boundary conditions and even the final output, the injection rate (The discharge holes in

the nozzle being modeled as orifices).

I. Conservation of mass.*

Figure 2.2: Conservation of mass

The pressure, p, in a volume of size, V, as shown in figure 2.2 is given by the

relationship,

dp . K

dt V

( Q

'

_- U

'Id+ Ax (2.1)

Rate of change of = Bulk modulus (Net inflow + Rate of decrease in

pressure in section Volume volume)

EQ(2.1) is an ordinary differential equation.

2. Equilibrium of forces

Figure 2.3 shows the schematic of a valve and the forces acting on that valve.

These forces consist of the fluid pressure exerted by the pressurised fuel, the valve inertia

*see section 2.9.1 on page 86

46

P2

4,111111M1r,

A

0

Model Development

and the spring forces made up of the initial spring force, the spring force due to the

additional compression of the spring caused by the valve opening and the damping force

of the spring.

Figure 2.3 : Equilibrium of forces

Resolving the forces on the schematic of a valve shown if figure 2.3 gives,

mx+cx+kx+F = p2 A2 — (2.2)

inertia + damping + spring + initial = resultant

force force pressure force

EQ(2.2) can be solved for x, the valve lift, providing the other values are known.

For the fuel injection simulation work the primary importance of calculating the valve

lifts is to determine the flow areas through the valves for the fuel. The relationship

between the valve lift and the flow area can be taken from the valve geometry.

The equilibrium of forces equation EQ(2.2), like the conservation of mass

equation EQ(2.1), is an ordinary differential equation (0.D.E.).

47

(2.4)c I 2 2 I 49 f , 1

QIQI = 00 p a 2DA

Momentum:*

Model Development

3. Pipe Flow

The continuity and momentum equations used to model pipe flow are described

below:

Continuity: * cl) + A elo .0

a 1:v 2 a (2.3)

The continuity equation states that the time rate of increase of mass within a

control volume is just equal to the net rate of mass inflow to the control volume.

The continuity equation assumes that the pipe walls are inelastic. This is

discussed in the Appendix to this chapter which shows that this assumption causes an

inaccuracy of only 1% in the speed of sound in the pipe. and only 2% in the pressure in the pipe.

The momentum equation states that the resultant force acting on a control

volume is equal to the time rate of increase of linear momentum within the control

volume plus the net efflux of linear momentum from the control volume. Gravitational

effects on the momentum equation are ignored.

Both the continuity and momentum equations are partial differential equations

(P. D . E. s).

4. Orifice Flow

The orifice flow equation used is given by:

Q = I P' P2 1CdA113-(pi—p2)A -P21 P

where p i and 112 are the pressures on either side of an orifice of area A and p is

the fuel density. Cd is the discharge coefficient and is made up from the velocity

coefficient, Cv, which is the ratio of the actual velocity to the theoretical velocity and the

coefficient of contraction, Cc; which is the ratio of the orifice area to the jet area.

EQ(2.5) allows for flow in both directions through the orifice by a directional coefficient

made up of the pressures on either side of the orifice (this coefficient will be either +1 or

-1).

*see section 2.9.1 on page 86

(2.5)

48

± CdAdoll-p(17,1— Pv)

Flow

through (2.7)

delivery valve

Model Development

The actual equations used in the simulation are now listed for each part of the

injection system

2.4.1 Pump

1. Conservation of fuel in the pumping chamber.

A vP P

Change in pumping

chamber volume

due to the

plunger motion

dpuV„+

di K

Compression

of

fuel in the

pumping chamber

CdA,11-2(p.— pfc)P

Flow through

the

Spill port

dQd„, , ‘+ 1 lil

di

Flow through

the (2.6)

Outlet port

2. Continuity of flow in delivery chamber.

Adv Vdv ±

Change in

delivery chamber

volume due to

valve motion

Cd Adoep (Pu — Pa)

Flow into

delivery

chamber

dpd Vd

dt K

Compression

of fuel

in

delivery chamber

3. Continuity of flow in delivery valve chamber.

+ C- d Adoll-2 (Pv — Pd)

P

Flow through

delivery valve

A vdv dv

Change in

delivery valve

chamber volume

dpvVv

dt K

Compression of

fuel in delivery

valve chamber

+dQ, (i)

dt

Flow into

high pressure (2.8)

pipe

C

IBI)LONDON

UM V

49

Constant pressurevalve spring Locator Ball bearing Delivery valve

Delivery chamber

Delivery valve chamber

//

g'maw0000

0

II

D 0 0

%0-000.000.%%Me

War

Model Development

4. Equilibrium of forces on delivery valve.

AdPd = AdPv + Fat, + C Vdv dv + k dv X dv + mdvad,,

Fuel pressure Fuel pressure Intial spring Damping Spring force Inertia

force from force from force on

delivery chamber delivery valve valve

chamber

Figure 2.4: Constant pressure valve

The continuity equations for both the delivery chamber and the delivery valve

chamber (EQs(2.7) & (2.8)) must take into account the constant pressure valve. The

operation and function of this pressure valve were described in the Chapter 1:

Introduction and shown in plates 1.2 and 1.3. The constant pressure valve used in the

Bosch VE type pump is shown above in figure 2.4 and consists of a one way valve at the

end of a hole through the centre of the delivery valve itself The opening pressure of this

valve was determined by using a pop test normally used to determine the opening

pressures of nozzles. The opening pressure of this valve was measured at approximately

20 bar. Therefore, in the model, the valve is considered to be open if the pressure in the

delivery valve chamber is 20 bar greater than the pressure in the delivery chamber. The

flow through the constant pressure valve is approximated by the orifice flow equation

EQ(2.5).

(2.9)

50

Model Development

2.4.2 Nozzle

5. Conservation of fuel in the nozzle chamber.

dQL(l) dp„V„dan(i) = + An v,, +di di K di

Flow into nozzle Compression Change in Flow into

chamber from of volume first section (2.10)

high pressure fuel in nozzle of nozzle of' nozzle'

pipe chamber chamber pipe

6. Conservation of fuel in the sac volume.

dg(l) ,_ dP, V, + Cd 21,4-2 (p,— pc)di dt K P

Flow into sac Compression of Injection Rate

volume from fuel in Flow rate through

last section of sac volume discharge holes

'nozzle' pipe

(2.11)

7. Equilibrium of forces on nozzle valve.

P. A. ± P1( 21. — = F„„ + c„,v„„ + +

Pressure force Pressure force Initial Force Damping Spring Force Inertia (2.12)from fuel in from fuel in

nozzle chamber sac volume

51

From high pressure pipe

1

Nozzle needle

Nozzle chamber

Section B-B'

Nozzle outer casing

Fuel passage

Nozzle needle

,

,

,Sac volume

Section A'-A

Model Development

Figure 2.5: Schematic of a Stanadyne nozzle

During the initial development of the model the nozzle was simulated as two

connected volumes with a valve between them, representing the nozzle valve. However,

it was decided to include a pipe section between the nozzle chamber and the sac volume.

This was considered to be particularly relevant for the Stanadyne nozzles used in this

work. A diagram of such a nozzle is shown in figure 2.5 above and shows there is a

significant pipe section between the nozzle chamber volume and the sac volume.

However, the flow areas for the high pressure pipe and this 'nozzle' pipe are not only of

different size but different cross section as well. The high pressure pipe has a circular

cross section for the flow area while the nozzle pipe has an annular cross section. This

can be seen by comparing sections A-A' and B-B', respectively, in figure 2.5. This was

52

Model Development

simulated in the models by using a larger friction factor for this nozzle pipe section in

proportion to the greater wetted perimeter of the cross section. However, there is scope

for further work in simulating this annular flow more accurately.

The equations describing the flow and dynamics in the pump and nozzle are all

ordinary differential equations and are solved simultaneously using the fourth order

Runge-Kutta method. The method of characteristics is used to solve the partial

differential equations for the pipe sections (i.e. the continuity and momentum equations).

2.5 Methods of Solution

The model, put in simple terms, is a pipe with two separate boundary conditions

at either end. The pipe equations are partial differential equations (P.D.E. ․) and can be

solved using the method of characteristics or a finite difference scheme. However, both

these methods need information to solve for the end or boundary conditions. This

information is provided by the pump and nozzle equations which are ordinary differential

equations (0.D.E. ․). Two methods for solving 0.D.E.s are described here - the Newton-

Raphson and Runge - Kutta methods and two methods for solving P.D.E.s are described

- the method of characteristics and a finite difference scheme. The method of

characteristics and the Runge-Kutta method are described in more detail as these are the

techniques used in the models in this work.

The methods used were selected on the basis of ease of programming and

accuracy (including stability). However, this is far from being an exhaustive list of

numerical techniques available to solve these types of equations. Press et al's (1992)

book Numerical Recipes in C : The Art of Scientific Computing provides more

information on the methods used here as well as other alternatives.

2.5.1 Partial Differential Equations

2.5.1.1 Method of Characteristics

The method of characteristics is a graphical or numerical finite difference

technique used to solve systems of non-linear partial differential equations such as the

continuity and momentum equations EQ(2.3) and EQ(2.4) for pipe flow. If both are

equal to zero, we can also write,

OQ A Op f±p Ox Ox01 + 1 + pa

4 (3/, 0Ot 2DA - Ot

(2.13)

where X is a non zero quantity to be determined. EQ(2.13) can be rearranged to become

53

Model Development

A .1. 1 Op _i_t_e3p)+( e 3 Q + 0Q i) i_ f Qv., 0

apa22 Ox Ot Ox 2DA

Now if we let

dr _ a2 _ A

dt — T -

(2.14)

(2.15)

the terms in parentheses become total derivatives and EQ(2.14) becomes

(2.16)A A dp ± c1Q ± fp a' dl di 2DA QIQI=°

From EQ(2.15) we obtain the required conditions for 2; that is

A= ±a (2.17)

and the differential equation EQ(2.16) is valid in the independent variable space

(x,i) only when EQ(2.17) is satisfied [ This is particularly important to note when the

speed of sound, a, changes as would occur during cavitation]. EQ(2.17) defines lines in

the independent variable space (x,/) which are called characteristic lines. The line

associated with A.— +a is called the C+ characteristic; that associated with 2---a is called

the C- characteristic.

Along the C+ characteristic defined by A=a, we have

A A dP + dQ- ± f QIQI= 0 and —dx ap dia 2 di di 2DA

Along the C- characteristic defined by A—a, we have

_ A A dp ± d() + f Qio 0

= _ drand — = —a

p a 2 di di 2DA I 1 di

(2.18)

(2.19)

These equations can be developed into an efficient finite-difference scheme if we

assume that the relatively small frictional resistance term is constant over local regions in

dx and di.

If we consider the independent variable space (x,t) associated with a length of

pipe, we can consider discrete lengths along the pipe dx and discrete time steps di. We

can use EQ(2.18) along with the C+ characteristic lines and we can use EQ(2.19) along— _the C- characteristic lines shown in figure 2.6. EQs(2.16), (2.18) and (2.19) are all odes_ .. _along the characteristics.

54

Time,t

t+dt-t_

C+/,\CDistance,x

PUMP PIPE NOZZLE

R Pa= —A

R= "ad,2DA2

(2.22)

(2.23)

Model Development

Figure 2.6 : Method of characteristics applied to the high pressure pipe.

If we know conditions everywhere at time to we can integrate EQ(2.18) and

EQ(2.19) over a time step di to give

A I0along C+: – _p,,)+(Q, – Q,_ 1 ) + fdla-10-11 =

p a 2DA

= a.dt

along C-: --A

(p,– p,,,)+(Q, – =Q.1) + p a 2DA

xi – x1+1 = –a.dt

(2.20)

(2.21)

For numerical stability,dx adt.[For convenience the time step in the simulations was set to match the data

acquisition speed from the experimental data (see section 3.5). This results in a timestep of 0.004ms or 4,us which, in turn, results in a length step of about 5mm (assuminga, the speed of sound, is approximately 1400m/s).]

For convenience we can now define

55

,(C+ (t)— p -,(1 dt))Q,(i + d t ) = (2.31)

Model Development

so that EQ(2.20) and EQ(2.21) become

along C+: p = p, 1 — B(Q, — Q,)— RQ,_ 1 1Q1-1 I (2.24)

along C-: p, = B(Q, — 424. 1 ) — Ra+11Q+11

(2.25)

These can be rewritten as follows to emphasize the time-stepping procedure:

along C+ p,(t + dt) = C + (t)— BQ,(t + dt) (2.26)

where,

C+ ( 1 ) = 13,1(0 + BQ,_1( 1 ) — RQ, 1(1)1Q,_1(1)I

(2.27)

along C-: p,(1 + dt) = (0+ BQ,(1 + dt) (2.28)

where,

C (0= p,+1 (1)-Ba+1(1)+RQ1.1 (012+1(01

(2.29)

Note that C+ and C- can be calculated from known conditions at any time 1.

At any interior point i, EQ(2.26) and EQ(2.28) can be solved simultaneously to

obtain the pressure and flow at time 1+ dt. This yields

, (C+ ( t) + 01)) p,(t + dt) =

2(2.30)

where C+ and C- depend only on the conditions existing at time I.

At the pipe boundaries, only one of the equations [EQ(2.26) or EQ(2.28)] can be

used. The condition at the boundary can be used to obtain the remaining required

condition. If the boundary condition at the downstream end is a closed valve allowing no

flow we know Qi(t+dt) — 0 and EQ(2.26) then yields

pa (t + dt) = C + ( t) (2.32)

If the boundary condition is a constant pressure PR reservoir at the upstream end,

we know pi(t+dt) =PR and EQ(2.28) then yields

56

N (PR —C (1)) Q(t +do.

B(2.33)

Model Development

Similar boundary conditions can be derived for other cases of interest.

At the upstream end of a pipe EQ(2.28) provides one equation for the two

unknowns Q, the flow rate, and p, the pressure. Another equation or condition is

required to solve these unknowns. This condition may be a constant value of one of the

parameters, such as a constant pressure reservoir, a specified variation of one of the

variables with time, an algebraic relationship between the variables or even a relationship

in the form of a differential equation. The simplest boundary condition is one in which

one of the variables is given as a function of time or held constant. A direct solution of

EQ(2.28) for the other variable at each time step provides a complete solution of the

interaction of the fluid in the pipeline and the particular boundary. This includes the

appropriate reflection and transmission of transient pressure and flow waves that arrive

at the pipe end. Complex systems can be visualised as a combination of single pipelines

that are handled as described above, with boundary conditions at the pipe end to transfer

the transient response from one pipeline to another and to provide interaction with the

system terminal conditions.

A valve at the downstream end is an important boundary condition used by the

simulation and is derived below:

Using the orifice flow equation,

Q. Cd A .11-2

.pP

From EQ(2.26),

p = C+ —B.Q

:. Q= Cd A ll—p2 (C+ — BQ)

Rearranging EQ(2.36) gives,

r 11j02 ± [B(Cd A) 2 ]Q [C- (Cd A) 2 ] 0

L2 P P

(2.34)

(2.35)

(2.36)

(2.37)

57

Model Development

From the solution to quadratic equations, namely,

if, ax2 + bx + c = 0

—b±Vb 2 —4acthen, x =

2a

B(CdAY +

11(B(Cd A) )2 2C+ (CdAY :. Q = (2.38)

P P P

and from EQ(2.35)

p=C" —B.Q (2.39)

If the valve is closed then the flow rate, Q, will be zero,

Q=0

p=C+

A similar derivation can be performed for a valve at the upstream section giving,

and,

,Q _ MCd AY 4. iii[B ( Cd AY)

2 + 2C- (Cd A)2

P P P(2.40)

p=C- + B.Q (2.41)

Other boundary conditions can be derived for changes in cross-section, junctions

of two or more pipes, valves in a pipeline or even an accumulator. These are not used in

these models but some are likely to be used as the models develop and become more

detailed, particularly for changes in cross-section. A usefiil description of these

conditions are given by Streeter and Wylie (1983).

In the pump-pipe-nozzle simulation there are three pipe sections each requiring

two boundary conditions. These are the delivery pipe between the pumping chamber and

the delivery chamber. The high pressure pipe between the delivery valve chamber and the

nozzle chamber. And finally, the nozzle pipe between the nozzle chamber and the sac

volume. A full list of the boundary conditions used in the simulation are given overleaf in

table 2.1.

58

Model Development

Pipe Upstream Downstream

Delivery Pipe Valve at upstream end Pressure equals the delivery

chamber pressure

High Pressure

Pipe

Pressure equals the

delivery valve chamber

pressure

Pressure equals the nozzle chamber

pressure

Nozzle Pipe Pressure equals the

nozzle chamber

pressure

If the nozzle valve is closed then

the flow rate is zero. If the nozzle

valve is open then it acts as a valve

at the downstream end.

Table 2.1 : Boundary conditions used for pipe sections in the model.

2.5.1.2 Finite Difference Scheme

The method of characteristics is not the only method available to solve the

P.D.E.'s Alternatives include finite difference schemes which will be covered here briefly.

This involves placing EQ(2.3) and EQ(2.4) in finite difference form:

From EQ(2.3),

K= + Q+1 .) (2.42)

Aiox

From EQ(2.4),

P".j — Po f . Vi.iA1dt2 V1 (2.43)2Q. n= —

Pdx 2Dpp 0 c-i.j-I

]+[

The grid below helps to explain the finite difference scheme. i and j are integers

and are used to represent time and distance steps, respectively.

59

dx

i+11

dti _ i+1

Model Development

Time, t

Distance,x

Figure 2.7: Grid for the finite difference method.

Again this method can cope with everything except the boundary conditions.

2.5.2 Ordinary Differential Equations

The problem is to solve a set of first order ordinary differential equations having

the general form

dy,(x) fi(xo, y = 1,...,N (2.44)

where the functionsfi in the right hand side are known.

The basic method for solving an initial value problem is this: Rewrite the dy's and

dx's in EQ(2.44) as finite steps dy and Ax, and multiply the equations by Ax. This gives

algebraic formulas for the change in the functions when the variable x is stepped by one

step size dr.

EQs(2.6)-(2.9) and EQs(2.10)-(2.12) are ordinary differential equations and can

be solved by any one of a number of numerical methods.

2.5.2.1 Newton-Raphson

If x is an approximation to the solution for f(x)=0 then,

f(x) (2.45)

is a better approximation provided there is no horizontal tangent to the curve

between the two iterative steps (e.g. x i & x2). This is a very simple method but relies on

60

dy f(r y)

dx(2.46)

Model Development

a good initial guess to the correct solution. This method was successfully used by Kumar

et al (1983), although this author found the need for a good initial guess to the correct

value as too much of a restriction.

2.5.2.2 Runge-Kutta

This method propagates a solution over an interval by combining information

from several Euler-style steps. The basics of the Runge-Kutta (fourth order) method for

the numerical solution of ordinary differential equations are shown below:

ki = Ax„,y„)

k2 = &.f (x + 0 .5 dx,y + 0.5k1)

k3 = Ox. Ax„ + 0 .5 x,y +0.5k2)

1c4 = Ox. f(x„ + ex , y„ -F k3)

ey = +2k2 + 2k3 + k4 ) (2.47)

The equations for the delivery valve section of the pump will be used as an

example to show how this method is used.

The three equations for the delivery valve section are:

EQ(2.7).Continuity of flow in delivery chamber

EQ(2.8).Continuity of flow in delivery valve chamber

EQ(2.9).Equilibrium of forces on delivery valve

EQ(2.9) is used to determine the valve lift, if any, and hence the area of the

delivery valve opening (A do) . EQs (2.7) & (2.8) are rearranged as follows:

EQ(2.7) becomes,

dpd K A= — = — fidvVd,, — Cd Adoe(pu_ Pd) — Ad Vdv —Cd Ado ll— (Pd — Pv)

2

dt Vd(2.48)

61

Model Development

EQ(2.8) becomes

A 2 ( da)dPv – K (A v + C Ado li—kpv —pdr--F2 =

(2.49)

These equations are then expressed in finite difference form and solved

simultaneously using the Runge-Kutta method, as follows:

rkl 1 = dt.F109,(j),pd(j))

_rk 211 ,pd(i)+rk212)r k21= dt.F1(pv(j)

rk31

_rk221 ,pd( j).* rk222)= di. Fl(p„(j)

+

rk41 = di Fl(p„(j)+ rk3 1, pd ( j)+ rk32)

dpd(i) = --6-1 (rkl 1+ 2.rk21+ 2. rk3 1+ rk41)

rk12 = dt. F2(19,(j), pa(j))

rkll ,pdrk12)rk22= dt.F2(19,0)

(j)+

2 2 )rk21 rk222)

rk32 = di. F2(p,,(j)+-2 ,pdk +—

rk42 = di. F2(19,(j)+ rk3 1, pd (j) + rk32)

dp„(j)= -k(rk12 + 2.rk22 + 2.rk32+rk42)

Pd(J) = Pd(i) P,,(.1)= Pv(.1) + dPv(i)

To start the method approximations for the delivery chamber pressure (pd) and

delivery valve chamber pressure (pv) are required. The calculated values for the previous

time step or the initial values are considered to be sufficient for this purpose. The method

is time-consuming as it requires several evaluations of the function and provides no easily

obtainable information about truncation error. However, the step size can easily be

changed and it's relatively easy to program into a computer.

To start the solution all the initial conditions for the fuel injection system must be

specified : All valves are closed and the spill and inlet ports for the plunger are both

unobstructed. The plunger is at its lowest position (i.e. the pumping chamber volume is

at its maximum value) and this is defined as zero displacement for the plunger.

2.6 Phenomena

In addition to the solution of the flow equations and the force calculations several

features to enhance the accuracy and detail of the models have been included. These are

described below:

62

Model Development

2.6.1 Needle Bounce

A model of the nozzle bounce was included not only to achieve a more accurate

and realistic needle lift profile. The end of injection and dribbled fuel has been cited as

one of the possible causes of particulate emissions due to incomplete combustion in the

decaying flame and needle bounce has been suggested as one possible cause of this

dribbled fuel.

The model of needle bounce relies upon a dynamic mechanical analysis which

uses the fracture mechanics technique of contact stiffness to model the impact process.

The equation used EQ(2.50) is derived in the Appendix,

2m, v - [V4m,(k1+k2)–

x[ , = m1

V4m,(k, + k2)–e 2 sin

2m1 1+ 0) (2.50)

All the values in this equation can be taken from the system geometry or the

impact conditions except k2, the contact stiffness. Since k2 is the variable governing the

modeling of the actual impact process, the top and bottom impacts will have discrete k2

values associated with their respective impact geometry's and conditions. Currently the

only way to determine these values is from the appropriate experimental data on the

impact oscillation. Since the original intention was to examine the effect on the injection

rate of the needle bounce this was not considered to be a major problem. Although there

is scope for further work in this area to determine the contact stiffness without relying on

experimental data.

The contact stiffness is obtained from EQ(2.51),

= 4m1 co l + c12 L.".2

4/n1

and,

(2.51)

2gW I = — (2.52)

.vihere T is the time period of the oscillation measured from the experimental

data.

2.6.2 Cavitation

Cavitation was discussed in Chapter I: Introduction and occurs when the

pressure of the fluid reaches the vapour pressure at approximately zero bar. This results

in the formation of cavities, which are filled with vaporised fluid and reduction locally of

the speed of sound and bulk modulus, although the density decreases only slightly

63

KMiX = K — K . .1+

vapour hquid

Kliquid

ratio

Kvapour(2.54)

Model Development

Figure 2.8: A section of the high pressure pipe.

One method to deal with cavitation is when the pressure at a particular section

falls to zero ( the vapour pressure ) the fuel pressure is set equal to zero and the cavity

volume is calculated from,

VccnnOr (Qom, en)di

(2.53)

The bulk modulus and density are adjusted using the following equations:

Vratio is the ratio of the volume of liquid fuel in the section to the total volume of

the section.

P vapour + 1 P— 'liquid {

a p o u r v}

p liquid pvliquid

where,

Kliquid(Kmix - Kvapour)[

Kliquid - Kvapour

V=

mix. . .rmia x

'° mix

(2.55)

(2.56)

(2.57)

K mix

EQ(2.54) and EQ(2.55), in turn, give the speed of sound at that point,

Initially the above method provided reasonable results. However, as the model

developed instabilities in the numerical methods occurred due to cavitation. This

manifested itself as high frequency oscillations on the predicted pressure traces. A very

64

Model Development

simple alternative to the above method was tried which involved setting both the

pressure and flow rates at a section experiencing cavitation to zero. This restored

stability to the numerical methods although no measure of the accuracy of this technique

was available. Another approach used by Gibson (1986) and Russell and Lee (1994)

involves the use of the relative density as the controlling parameter in place of the

pressure.

The cavities collapse as a result of high frequency pressure variations. This

means, therefore, that the process in a fuel injection system is different from the steady

flow situation. It is also important to bear in mind that diesel fuel is a mixture of liquids

of different boiling points which respond differently to pressure fluctuations in the

injection system.

Cavitation in the nozzle should also be considered since there is evidence that it

has a strong effect on spray development. Depending on the local pressure in the sac

volume, an appropriate factor can be introduced to reduce the exit area of the holes

during cavitation; this will modify the exit momentum of the fuel which is the main factor

controlling spray penetration and atomisation in the combustion chamber of diesel

engines.

2.6.3 Leakage

Gibson (1986), Marcic and Kovacic (1985) and Scullen and Hames (1978)

highlighted the importance of simulating leakage in the fuel injection system. This

particularly applies to the pumping chamber where the high pressures necessary to cause

injection are generated.

Considering the problems associated with the simulation and validation of

leakage it was decided to ignore leakage at the nozzle. This is backed by evidence that

leakage at the nozzle is minimal (Marcic, 1993).

The pump-pipe-nozzle simulation relies on an experimentally measured pumping

pressure profile which removes the need for leakage simulation for the pumping

chamber. This also removes the need for arbitrary coefficients although ideally a model

could eventually be developed of the pumping chamber which includes a validated

leakage term. Some of the possible leakage terms suggested by the literature are listed

below,

p. (2.58)

-Aguirre (1992).

65

fl u 3 . p – (ye • yo)6,u.v.hQ = g

2 (Y, + Yo)(2.60)

0< Re < 2000

2000 < Re < 4000

(2.62)

Re � 4000

Re=plv

—II

(2.63)

Model Development

/AP =

h2(2.59)

-Wannenwetsch and Egler (1985).

ye = slot height (high pressure)

yo = slot height (low pressure)

-Marcic and Kovacic (1985).

ir.h 3 . p Q=

3p ln 0 (2.61)

0= [calculated from radius of port and distance from port]

-Gibson (1986).

With the exception of Wannenwetsch and Egler (1985) the leakage has been

expressed as a flow rate and all three terms agree that leakage is proportional to the third

power of the clearance and the first power of pressure,

leakage flow rate oc 173

leakage flow rate oc p

2.6.4 Friction Factor

The friction factor in the momentum equation for the pipe flow is allowed to vary

as a function of Reynolds number. This variation is shown below for a smooth pipe.

, 64J =

Re

f = 0.32 + (0.008( Re– 2000

4000

f = O. 316

Re°25

66

2000 30001000 50004000

Reynolds Number

30°C

40°C

50°C

00 200 400 600 800

Pressure, bar

1000

1 + ap— bp'K=

a —2bp(2.64)

Model Development

Figure 2.9 : Friction factor variation with Reynolds number.

2.6.5 Bulk Modulus

The bulk modulus is allowed to vary as a function of pressure and is shown

below in figure 2.10 for the range 0-1000 bar and temperatures of 30, 40 and 50°C.

Figure 2.10 : Fuel bulk modulus variation with pressure and temperature.

The formula used for this variation was proposed by Dow and Fink (1940) and is

given below. The values of a and b are temperature dependent but are assumed to be

constant in this simulation. The values of a and b are given in the Appendix to this

chapter.

67

oo0

200 400 600 800 1000

Pressure, bar

30°C

40°C

50°C

9 = 0.05( DPaA2 P)P.

4

(2.66)

Model Development

This equation is used to determine the bulk modulus unless the pressure is zero

or less at which point cavitation occurs and the bulk modulus is determined using the

approximations described in section 2.6.2.

2.6.6 Density

Fuel density is also allowed to vary as a function of pressure again using a

formula suggested by Dow and Fink (1940).

p= po tl+ap—bp2 } (2.65)

As for the variation of bulk modulus a and b are temperature dependent

constants determined by Dow and Fink (1940) and given in the Appendix to this chapter.

However, it is important to note that the change in density with pressure is not as

marked as that of the fuel's bulk modulus. This variation is shown in figure 2.11 which

also shows the effect of temperature variations.

Figure 2. 11: Fuel density variation with pressure and temperature.

Again, EQ(2.65) is used to determine the fuel density unless the pressure is zero

or less at which point the equations for cavitation are used.

2.6.7 Spray Angle

The spray angle correlation used in the models is given by Xu et al (1992).

68

I

I � t6 •• S = 2.95(— NI DtApi ,---

Pa(2.68)

Model Development

Symbol Description Typical Value

D Discharge hole diameter 0.1717*104m

Pa Density of gas 20 kg/m3

Pa Viscosity of gas 1.7*104 Pa sA p Pressure drop across nozzle 200 bar

Table 2.2 : Typical Values for determining spray angle.

These figures give a spray angle, 0 of 35 degrees.

2.6.8 Spray Penetration

The empirical expressions used to determine spray penetration are again those

suggested in Xu et al (1992):

0 �. I <tb : S=0.39 2Apt

(2.67)Pi

th = 28.65 ,PIDV p„A p

t , = time to break -up of spray

(2.69)

Based on the values given in Table 2.3,

t, = 0.065ms and S =1.7mm at t,

Symbol Description Typical Value

D Discharge hole diameter 0.1717*104m

Pa Density of gas 20 kg/m3

p Density of liquid 840 kg/m3

A p Pressure drop across nozzle 200 bar

Table 2.3: Typical values for determining spray penetration.

69

•n•n•

0

0.02

0.04 0.06

0.08

0.1

mm

00

Model Development

2.6.9 Variable Coefficients of Discharge (Xu at al, 1992)

Variable coefficients of discharge for the nozzle seat and discharge holes have

been used, with the coefficient dependent on the needle lift. In comparison to the

common assumption of a constant coefficient of discharge (0.7) the effect is to reduce

the injection rate at low needle lift which is in agreement to experimental observations

(Arcoumanis and Fairbrother, 1992).

Figure 2.12 shows the relationship between the needle lift and the coefficient of

discharge for the seat passage.

Figure 2.12: Coefficient of discharge against lift for the seat passage.

Although figure 2.12 shows the discharge coefficient going to zero at zero lift, in

reality the discharge coefficient would tend to unity as zero lift is approached, since the

flow becomes laminar at the seat when the flow area becomes very small. However,

because the effective flow area is very small the discharge coefficient is allowed to fall to

zero at zero valve lift as this small flow area has a negligible effect on the simulation

results.

The equations for the relationship shown in figure 2.12 are given below,

Cd = 195 x lift lift.� O. 0038mm

Cd = + Ar lift + A 2 .1ift 2 + A3 1ift 3 + 24410 4 + Aslift s O. 0038mm < lift O. 059 mm

Cd = 0.70898+1.53025.10 lift > 0.059mm

(2.70)

70

00

0

VD

0

et

0

C•1

0

0

0 0.02 0.04 0.06 0.08 0.1

Lift, mm

Model Development

Ao = O. 48021

AI = 82.759

4 = —5.3413 x103

A3 = 1.3984 x 105

A4 = —1.6239 x 106

A, = 6.9753 x 106

Figure 2.13 shows the relationship between the needle lift and the coefficient of

discharge for the discharge holes.

Figure 2.13 : Coefficient of discharge against lift for the discharge holes.

The equations for the relationship shown in figure 2.13 are given below,

Cd =I5 lift

d

Cd = 0. 4 + 0. 63 Lld

lift � 0.0278.d

lift > 0.0278.d

(2.71)

2.7 Programs

The software chosen to write the simulation programs was selected bearing in

mind the desire for a flexible model with a modular format which is also easy to use. The

initial development work was carried out using a FORTRAN program but something

more flexible and user friendly was required for the later models. The software used was

71

QuickCase:W Image Editor Dialog EditorOCIWin

FIGS:Pump-pipe-nozzle

Simulation

Fl CS: N ozzleand Needle

Simulation

Fl CS: NozzleSimulation

Simulations

Model Development

Microsoft's QuickC for Windows Version 1.00. The icons for this software and the

associated tools are shown in figure 2.14 as they would appear in the Windows operating

system.

Figure 2.14 : Window showing the programming software.

The Image Editor allows the creation of icons and cursors to be associated with

the program. Figure 2.15 shows the icons for the FICS simulation codes which can easily

be selected with a mouse when they are required to run. FICS is the name used to refer

to the simulation models and stands for Fuel Injection Computer Simulation. The Dialog

Editor is used to create dialog boxes which will be discussed in more detail later. The use

of dialog boxes was one of the main attractions of using QuickC for Windows as it

makes the models very quick and easy to use. QuickCase:W creates the simulation

window including the menu items and drop down menus.

Figure 2.15 : Window showing the three simulation models.

It is interesting to note that the same technique of using dialog boxes in the

Windows operating system is used by Data Translation to run their data acquisition

boards. This will be discussed in Chapter 3: Experimental Validation.

72

QuickC for WindowsResource CompilerQuickC for Windows

Linker

Create the source files

Image Editor Dialog Editor

I

Create the icon Create the dialog boxesfor the application for the application

Create the module-definition file

C librariesWindows libraries

QuickC for WindowsCompiler

FICS • Flu SIonvAntInn

Edk lope lystem RUM &WU tiliP

.EXE •

aCO as

Model Development

QuickC for WindowsResource Compiler

The result is a Windows application

Figure 2.16 : Building a Windows application.

Figure 2.16 shows how a Windows application is built up using Microsoft's

QuickC for Windows. Initially the source files are created. These consist of the main

code given the extension '.C' and the header file or files with the extension '.H'. The main

code consists of the routines for simulating the pressures and flow rates. These will be

described for the nozzle and pump-pipe-nozzle simulations, together with flow diagrams,

later. The header files contain supplementary information such as the array dimensions.

These are compiled together to form the object file, given the extension '.OBJ'.

This is then linked with the module definition file and libraries to form an executable file.

73

Project

[

Program Type

0 Windows EXE1 0 QuickWin EXE

0 Windows DLL 0 DOS EXE[

Build Mode

0 aebug

0 ReleaseI Help 1

Model Development

This executable file is compiled with the resources to give the final executable Windows

application. The resources consist of dialog boxes and icons made with the help of the

Dialog Editor and Image Editor, respectively. These two editors are supplied with

QuickC for Windows. The Image Editor is essentially cosmetic but the Dialog Editor and

the dialog boxes it can create are one of the big advantages of this software. These

dialog boxes allow the simulations to be quick and easy to use and means they can be

used without a knowledge of programming as there is no need to alter the code or re-

compile the files.

Two simulations have been programmed for simulating fuel injection to date.

These are a nozzle simulation and a pump-pipe-nozzle simulation. The former uses

experimentally measured line pressures while the latter relies on pumping chamber

pressures as an input.

The programming techniques and options used to write the simulation codes are

described briefly below. Further details about programming windows and the methods

used here can be found in Hipson,P.D (1992).

Figure 2.17 : Dialog box showing project options.

Figure 2.17 shows the project options: QuickC for Windows organises projects

or types of program into four basic types. Windows EXE is a Windows program and is

selected for the simulation codes presented in this thesis. The one exception to this is the

library INJECT which uses the Windows DLL option (Dynamic Link Library). A DLL is

a library linked at program-execution time. They have two advantages; the first is that

applications can share a single copy of an executable function, so, for example, the

nozzle simulation and pump-pipe-nozzle simulation can share the routine used to

determine the fuel density as a function of pressure. The second advantage is that if the

function is improved the DLL can be updated and the applications can take advantage of

the improvement without being recompiled or relinked. The DLL INJECT used by the

simulation codes in this thesis and the routines it contains is described in more detail in

section 2.7.1. The build mode is set to Debug as the release option is only used when the

program is fully debugged and completed.

74

1 3 Ld

Customize C Compiler Options

[

Debug Options

1E1 EodeVietv Info

0 Ppinter Check

0 Incremental Compile[

Release Options Optimizations

0 OD 0 Off 0 Full

El Suppress Stack Check Options >>

OK[ C Language

0 ANSI Compatible

0 MS Extensions

LargeICancel I

I Help I[

Global OptionsMemory Model:

Warning Level:

Project

— Global Options

ignore Case

El Extended Dictionary

0 Ignore efault Library

atack Size:

Alignment:

110000

116

Debug Options

(3] CodeView Info

O CV 3.X Format

O Map File

OK

I_Help

— No Release Options --

Customize Linker Options

Options >>

Project

Model Development

Figure 2.18 : Dialog box showing C compiler options.

Figure 2.18 shows the C compiler options: The Memory Model can either be

small, compact, medium or large. Ideally the smallest possible model should be selected

for speed. However, due to the large number of variables and the large arrays associated

with inputting the experimental data into the simulation the largest possible memory

model size available has been chosen. In fact even the large memory model is not

sufficiently large to accommodate the number of variables needed for a simulation of the

pumping chamber pressure as well. This problem can be overcome by the use of Visual

C++ which has a huge memory model not available to QuickC for Windows.

For C language, MS extensions is selected as this allows the use of more

features. ANSI compatibility is only selected if there is a concern over portability. As the

program is currently built in debug mode only the debug options have an effect on the

compiling of the program. These include Codeview Info, which includes information the

debugger uses to help debug the program and Incremental Compile which allows the

compiler to recompile the parts of the source file that have changed. This increases the

speed of the compile stages.

Figure 2.19 : Dialog box showing Linker options.

75

Project

Customize Resource Options

OK

OK

ICancel

Help

Custom Options:

Defines:

J

[El Windows Protect Mode Only

IE Disable Load Optimization

Cancel I

I Help I

Model Development

Figure 2.19 shows the Linker options: Ignore Case tells the linker to ignore the

case of the external symbols it's searching for. The Extended Dictionary option allows

the linker to use the extended dictionary contained by most library files. Stack Size is the

stack allocation for the program. The Alignment used is the default value for Windows

applications, 16-byte boundaries.

Figure 2.20 : Dialog box showing resource options.

Figure 2.20 shows the resource options. These include searching the path

specified for include files, allowing the program to run only in Standard mode or 386

Enhanced mode and disable the load optimization so that the file is not reorganized.

2.7.1 Library Routines

In addition to the use of a modular format in the programming to make the

simulations as flexible as possible, a library of routines has been built up. This library has

been called INJECT and consists of a number of common routines used by both the

nozzle and pump-pipe-nozzle simulations. Both simulations can use the same library

routines and simply call the routine with one line of code in the simulation. This has the

added advantage of cutting down on the size of the programming code dedicated to each

simulation code. It also helps in the process of setting up models of varying design or

even completely different systems. Table 2.4 shows the routines that are currently

available in INJECT, although it is intended that this library of routines expands as the

simulations are developed.

76

Model Development

Name Function Equation

EQ(2.5)orifice Calculates the flow through an orifice

bounce Calculates the oscillation associated with the needle

impact

EQ(2.45)

friction Calculates the friction factor as a function of Reynolds

number

EQ(2.57)

modulus Calculates the bulk modulus of the fuel as a function of

pressure

EQ(2.58)

density Calculates the density of the fuel as a function of

pressure

EQ(2.59)

seatcd Calculates the coefficient of discharge for the nozzle

seat as a function of needle lift

EQ(2.64)

holecd Calculates the coefficient of discharge for the nozzle

holes as a function of needle lift

EQ(2.65)

Table 2.4 : Library routines in INJECT

In table 2.4 the name refers to the programming name which is used to call the

routines from the main code. The function describes what it does and the equation refers

to the equation number used in this thesis that the routine performs.

2.7.2 Nozzle Simulation

The nozzle simulation begins by reading into the program the system geometry

selected by the user with the dialog boxes. These include the size of the nozzle discharge

holes and also the properties of the fuel to be simulated. Figure 2.21 shows an example

of one of these dialog boxes, the nozzle data dialog box. Also at this time the program

settings, such as the simulation run time are read into the program. This is all included in

the subroutine INPUT which also reads in the experimental line pressure and chamber

pressure data files. These files are one dimensional ASCII files and can be selected using

another dialog box, figure 2.22. Once all the necessary input to the program has been

carried out the program moves onto the INITIAL subroutine. This initialises all the

arrays in the program so that the valves are all closed, the flow rates are equal to zero

and the pressures equal the residual pressure. The residual pressure is set from the run

conditions selected or can even be calculated by running the program over a number of

cycles, although this is very time consuming. The program then moves onto the core of

the simulation which, for the nozzle simulation, consists of the PIPE and NOZZLE

subroutines. For each time step these routines calculate the pressures and flow rates in

the pipe between the input line pressure and the nozzle or for the nozzle itself,

77

System Run Results HelpPipe..

fuel..

Impact Equivalent StiffnessUpper. Nim • 106

Lower, Nirn • 1o-6

125.0 1

17.0

Cancel

File Edit Input

Nozzle Data

Area of noz. orifices (total). mm-2

Area of noz. valve (closed). mre2

Area of noz. valve (open), minA2

Area sub. to charn pressure, mre2

Initial force nozzle valve, mN

Stiffness of noz. valve spring. Wm

Length of discharge hole. mm

Mass of nozzle valve. kg

Vol. of nozzle chamber. mie3

Vol. of injection chamber, mm's3

FICS : Nozzle Simulation

10.127

17.95

19.95

10.005

1315

11.25

6.68

210000

149200

1.0

Maximum nozzle valve lift. mm 0.32

Damping coef. of valve, Naha 50

Comb. chain. pressure, kPa 100

Dia. of discharge holes, mm 0.211 1

Model Development

respectively. If at any time the pressure falls to zero, cavitation occurs and the cavitation

routine takes over until the cavity is calculated to collapse. Both these subroutines can

access the library functions in the library INJECT at any time they wish. The OUTPUT

subroutine organizes the results for the pipe and nozzle separately and writes them to

external files, together with a time value, so that they can be examined later. Finally, the

STEP routine advances the time by the selected time step which also matches the time

step of the selected input data files. It also rearranges the arrays and returns to the PIPE

subroutine to calculate the pressures and flow rates for the next time step. A time step of

4i..ts is used as this corresponds to the acquisition sampling rate used experimentally and

it also provides the required stability for the method of characteristics. However, if the

time has reached the selected run time chosen by the user the program stops and the

simulation data can be examined. Figure 2.23 shows Excel being used to examine a

typical output file from a simulation run. The flow diagram for the nozzle simulation

which summarises this process is shown in figure 2.24. For a time step of 41.1s the

simulation typically takes less than one minute to complete a run when running on a

486DX2-50MHz PC computer with a maths co-processor, see figure 2.25. The maths

co-processor is really the essential element of the computer being used in terms of speed

as the simulation is effectively solving mathematical equations one after another.

Figure 2.21 : Nozzle data dialog box for the nozzle simulation.

78

System Run Results HelpFile Edit

I OK I

[ Cancel IIre.dat

Open File Name:

Files in cAroblquickclnozzle

p501000.datpa.datpb.datpc.datpnaidle.datpnf1000.dat

Model Development

FICS : Nozzle SimulationInput

Line Pressure...

Cylinder Pressure...

Line Pressure Input File

MOW

1Figure 2.22 : The simulation window including the dialog box with the cylinder pressure

input file.

File EditMicrosoft Excel

Formula Format Data gptions Macro Window Help

um 0 'Normal I 13 0 DEMO DOOM 12_0,1 1:11:6-,

. MEM omen ocin o ORM

Al I Time

PIPEOUT.XLS CI

12

Time • P[1]0.80.80.80.81.30.80.8

Q[1]-47.3-47.3-47.3-47.3

0-47.3-47.3

P[Mid]1.31.31.31.31.31.30.8

Opid) P[End]000000

-47.3

Q[End]1.31.31.31.31.31.31.3

0000000

0.0040.0080.0120.016

0.020.0240.028

345678

[1L1

Reedy I r-r---iNITar-i- 1---

Figure 2.23 : Excel being used to examine a typical output file from the simulations.

79

—Dialog Boxes—INPUT

Line pressure &chamber pressure

data files

Settings

PipeData

NozzleData

FuelData

INITIAL

NOZZLE

STEPt=t+dt

if t =tmax, then end

OUTPUT

PIPE •

Library Functions

INJECT

_ Output Files

PIPEpressures and flow rates

NOZZLEpressures and flow rates

needleli ft

Model Development

if pressure <= 0

Cavitation

if pressure <= 0

Figure 2.24: Computer program flow chart for the nozzle simulation.

80

Model Development

file EditFICS : Nozzle SimulationInput System Run Results

C11:1Help

111

Tt

1.

4=1 Golation

red pt and

zle a'stemline p

4.

. 2.

Simulation running I

2 Complete : 100.0

Time taken in s: 58.7

MEI

.1,1

Figure 2.25 : Time taken to run nozzle simulation on a 486DX2-50MHz PC computer.

2.7.3 Pump-Pipe-Nozzle Simulation

As the name suggests this simulation covers all the high pressure side of a pump-

pipe-nozzle fuel injection system. Currently the system is set up for a distributor pump

connected to a hole type nozzle typical of DI diesel engines, but it is also capable of

simulating in-line pumps, pintle-type nozzles and unit injectors provided all the important

geometric parameters are available.

The set-up and structure of the pump-pipe-nozzle simulation is very similar to the

nozzle simulation. Once loaded, the required conditions for a particular run can be set up

using the program's dialog boxes. The four main dialog boxes for selecting the geometric

and physical parameters to be used in the pump-pipe-nozzle simulation are shown in

figures 2.26- 2.29. These dialog boxes also show the default values for the pump, pipe,

nozzle and fuel, respectively. The settings for each run (i.e. run time, initial residual

pressure and pump speed) are also set using a dialog box. An input file containing further

details for the simulation, such as the length/time step, is read in just before the

simulation is started.

After the pumping chamber pressure input file has been selected the program

initialises the arrays in the same way as the nozzle simulation. Then separate subroutines

PUMP, PIPE and NOZZLE calculate the pressures, flows and valve displacements

throughqut the system before advancing the time and restarting the cycle. If at any point

the pressure falls below zero, the cavitation routine is called and adjusts the fuel

properties. The calculated values are printed to separate output files which can be

examined once the run has finished. These ASCII data files can then be graphed for

easier examination while the main results are printed in a dialog box at the end of each

run to provide a quick summary of the results. A typical simulation run covering one

81

Inputfile Edit

95.0 1

19.6

38.5

129400

17350

10.0018

1450

Model Development

injection cycle of 4ms takes about 1.5 minutes to complete. This is shown in figure 2.30

and is again quoted for a 486DX2-50MHz PC computer with a maths co-processor.

The operation of the program is summarised in the flow chart shown in figure

2.31. This can be compared to the earlier flow diagram for the nozzle simulation, figure

2.24, which shows that the two simulations are very similar. In fact the pump-pipe-nozzle

simulation contains just one extra module to simulate the pump pressures and flow rates.

This highlights the advantage of using a modular structure as the same modules can be

used in different simulations of varying scope or different combinations could be used to

simulate systems of markedly different design.

CI FICS : Pump-pipe-nozzle SimulationSystem Run Results Help

Pump..Pipe..Nozzle..fuel..

Pump Data

OK

Area of plunger. me2

Delivery valve area[closed), mm's2

Delivery valve arealopen). mm's2

Initial force on del valve. mN

Delivery valve spring rate, NM

Mass of delivery valve. kg

Vol of del valve chamber, me3

1

Vol of pumping chamber. mm's3

Vol of delivery chamber. mm's3

Pressure relief volume. mre3

Max delivery valve lift. mm

Delivery pipe length. mm

Area of delivery pipe. me2

Damp coeff of del valve. Ns/m

ICancel I

638

160

200

12.5

125

13.14

10.0062

Figure 2.26 : Pump dialog box showing pump input variables and default values.

82

FICS : Pump-pipe-nozzle Simulation C11:1file Edit Input System Run Results Help

Pump..

Pipe- ig

Nozzle..fuel..

Nozzle Data

Nozzle orifice area, mm-2

Nozzle valve area(closed], mm-2

Nozzle valve area(open), me2

Area of chamber pressure. mm-2

Initial force nozzle valve. mN

Nozzle valve spring rate, Plim

0.127

7.95

9.95

16.60

1210000

1149200

Mass of nozzle valve. kg

Vol of nozzle chamber. me3

Vol of injection chamber. mie3

Max nozzle valve lift. mm

Damping coeff of valve, Nilm

Chamber Pressure. kPa

ICancel

10.005

1315

11.25

10_32

150

[3000

Model Development

FICS : Pump-pipe-nozzle Simulation 1112

file Edit Input system Run Results HelpPump..Pipe..Nozzle..Fuel..

El.,

I .F\

Internal pipe

Pipe length.

Pipe Data

diameter, mm 1106 1

mm 1350 1

OK I Cancel I

-4

Figure 2.27 : Pipe dialog box showing pipe input variables and default values.

Figure 2.28 : Nozzle dialog box showing nozzle input variables and default values.

83

FICS : P mp-pipe-nozzle SimulationFile Edit Input system Run Results Help

eump..Pipe..Nozzle..Euel..

Fuel Data

Density, kg/me3 •1 0A-7

Bulk Modulus, kPa-lr6

Kinematic viscosity, cSt

8.40

11.5

13.3

All properties at 1 bar 40 deg C

I OK I ICancel I

Model Development

Figure 2.29: Fuel dialog box showing fuel input variables and default values*

FICS : Pump-pipe-nozzle Simulation aFile Edit Input System Run Results Help

a

E

11!F•

=.1 GGo

Simulation running I

Z Complete : loao

Time taken in s: 1015

ICancel I

.41,i Figure 2.30: Dialog box showing time taken to run the pump-pipe-nozzle simulation on

a 486DX2-50MHz PC computer.

The properties are input at 1 bar 40°C as the property variations with pressure are related to thevalues at 1 bar and a constant temperature of 40°C is assumed throughout the system.

84

PumpData

PipeData

NozzleData

FuelData

PUMP

• if pressure <= 0

if pressure <= 04 •

•CavitationPIPE

A

if pressure <-0. . . .NOZZLE

_ Output Files

PUMPOUTPUT pressures and flow rates

delivery valve lift

PIPEpressures and flow rates

STEPt = t +dt

if t tmax, then endNOZZLE

pressures and flow ratesneedlelift

Library FunctionsINJECT

—Dialog Boxes —

[—SettingsINPUT

Pumping chamberpressure data file

INITIAL

Model Development

Figure 2. 31: Computer program flow chart for the pump-pipe-nozzle simulation.

2.8 Summary

Two models based on the conservation of mass, the equilibrium of forces and the

conservation of momentum have been presented. The ordinary and partial differential

equations have been solved using the fourth order Runge Kutta method and the method

of characteristics, respectively. The models are one dimensional and consist of a nozzle

simulation and a pump-pipe-nozzle simulation to predict the pressures and flow rates in

a typical fuel injection system used in direct injection diesel engines. Several features

have been included such as needle bounce, cavitation and variable discharge coefficients

to enhance the accuracy of the models' predictions. The models have been structured in a

modular format to make them flexible and programmed using Microsoft's QuickC for

Windows to make them user friendly.

85

Model De elopment

2.9 Appendix

2.9.1 Fundamental Equations

lhe ('Hmc'I-V011(07 of .1,1cos for ( ' unCC1711-CliCcl Ivol11111CS

I . or an chamber n, n hose wItinIc changes from I' at time / to I" , ,/t at tulle I at as a result of the

ard motion of a plunger of area .4 through a distance c/x. the equation for consers ation of mass is_

Final mass - initial mass net addition of mass

C

p cip)( I cit . ) (,fl.- m

Neglectin g second order terms, ss dun g c/1" -flay_ introducing pressure via the bulk modulus

definition so I ttaa.. c.p ,p and cons crung to \ (flume flo\s rates b‘ di \ iding each in bs p

(1' / K Adv. 0,

\\Inch gi\ es EQ(2 I) on page 46

• c ("or-minim . 14:glamon

From Streeter and Wv he( )983) the fundamental form of the continuo equation is.

, er'N,v + pa- = o

( 3c a a

The convective term ‘.6p/Ox is usuall y much smaller than 6prOt and can be neglected. This was

shown to be true for fuel injection simulation b y Kumar et al (1983). The equation can also be

expressed in terms of volumetric flow rates b y multipl y ing b y the cross sectional flow area. A. This

gives.

(7) A (2) 0

ixr

\\ hid ) is the same as FQ(2.3) on pai4e 48

111C AIM)1C111111)1 14.Olamor?

A g ain, from Streeter and \V\ lie (1983) the fundamental form of the momentum equation is.

(:-.\.• I (j9 VV - = 0

(-)f p (7A- 21)

In waterhammer applications the on term v 6v/6x is generallv much smaller than 6s , 1 6t and

\\ill be omitted The omission of the cons cense term in the momentum equation s‘ as sho\sn b\ Kumar et

al (1984) to haxc a ne g li g ible effect on their fhel injection simulation results

In a simular manner to the commun.\ equation. cons ertin g to \ olumetric flos\ ratcs time 1110111cM11111

equation becomes,

)A 1j) f _ () 0

p ( -3k- 2 DA --

\\hich is the same as EQ(2 4) on page 48

N(‘

1 for fluids of low compressibilit\

1 dA 1 dpA dt +—p dt +

(2.74)

Model Development

2.9.2 The Effect of Pipe Wall Flexibility

Applying the unsteady continuity equation to the control volume, which

represents a section of the high pressure pipe connecting the pump to the nozzle, in

figure 2.32,

Figure 2.32: Control volume for continuity equation derivation

0 0--(pAV)OX = (pAciic) (2.72)

in which d:c is not a function of t. Expanding the equation and dividing through by the

mass (pAdx) gives,

V OA 1 OA V Op 1 Op OV--+--+--+--+—=0A & Aa pOxpâ a (2.73)

The first two terms are the total derivative (I/A) d4/di, and the next two terms

are the total derivative (I p) dp di, yielding,

The first term deals with the elasticity of the pipe wall and its rate of deformation

with pressure; the second term takes into account the compressibility of the liquid.

pD

Figure 2.33 : Tensile force in pipe wall.

87

(2.75)

(2.76)

(2.77)

(2.78)

(2.79)

From the definition of bulk modulus of elasticity of fluid

dp dp K= =

dV /V dp/p

and the rate of change of density divided by density yields,

1 dp 1 dp

p dt K dt

From EQ(2.76) and EQ(2.78), EQ(2.74) becomes

1 dp(, K D) et, „-- i +-- + — =uK dt E e a

1 +(K / E)(D / e)c. 1

K / pa2 = (2.80)

Model Development

For the wall elasticity the rate of change of tensile force per unit length is (D/2)dp di; when divided by the wall thickness e, it is the rate of change of unit stress (D/2e)dp di; when this is divided by Young's modulus of elasticity for the wall material, the rate

of increase of unit strain is obtained, (D/2eE) dp/dt. After multiplying this by the radiusD 2, the rate of radial extension is obtained; finally, by multiplying by the perimeter ff.D,the rate of area increase is obtained:

and hence

dA _ D dp D irD

dt — 2eE dt 2

1 dA = D dp

A dt eE dt

It is convenient to express the constants in this equation in the form,

where a is the speed of sound in the fluid.

88

K / pa2

=1 +(K / E)(D / e)c,

17848%

Model Development

Symbol Property Value

K Bulk Modulus 1.5GPa

P Density 840kg/m3

E Young's Modulus 206GN/m2

D Pipe Diameter 6mm

e Pipe Wall Thickness 2mm

Table 2.5 : Diesel Fuel Properties and fuel injection system parameters.

If we take typical Diesel fuel properties and the geometry of the system being

used in this work, as shown in Table 2.5, it's possible to examine the effect of pipe

elasticity.

First assume the pipe is rigid (i.e E tends to infinity)

2 Ka =—P

.*.a=1336m/s

Taking into account pipe flexibility (i.e. E not equal to infinity)

.a = 1+0.0218

...a=1322m/s

Therefore, the effect of pipe flexibility is to reduce the speed of sound within the

high pressure pipe by about 1%.

From the definition of bulk modulus,

dp = —KdV

together with EQ(2.76) this gives,

KDdp = —(--)p

eE

where dp represents the reduction in pressure caused by the pipe expansion due

to the pressure p. Therefore the expansion of the pipe will reduce the pressure by

approximately 2%.

V

89

Model Development

2.9 Nozzle Bounce Equations

Figure 2.34 shows the schematic of a nozzle needle impacting on either the seator the top stop.

Figure 2.34: Schematic for nozzle impact

Resolving the forces gives,

m, x, + c, xi + x, (lc, + k2 ) — k2 x2 —Ins+ kb. = 0 (2.81)

Using an auxiliary equation gives,

m/12 + cl ),+(ki + k2 ) = 0

—c, ± Vc12 — 4m, (k, + k2 )

x = Ae all ± Be 121 +C.F.1

Where C.F. is the complimentary fimction.

X1 = a+ flt + xt2

x, =/3+2t

xi =2x

Equating coefficients of t 2, t and constants,

A-1.2 =2m

90

Model Development

z=0

/3= 0

+k a:. a = mlg 1

=x F.C=k,+ k2 1 .

•- x i = Ae A i t +B2' +mig+klaki+k2

which may be written as,

- 114m,(k1+k2)—c g+k812x = Xe 2"" sin t +0)+

m,,

kl+k2(2.82)

This is in fact a decaying sin oscillation about a median position defined by the

value of the complimentary function. The boundary conditions for the top and lower

impact of the nozzle needle can now be assessed to determine X.

For the upper impact, motion is of the form shown in figure 2.35.

Figure 2.35: Example of the upper impact motion

Thus, 4)upper

For the lower impact, motion is of the form shown in figure 2.36.

Figure 2.36 : Example of the lower impact motion

91

Model Development

Thus, 4)lower = n

P= 2m,

V4m1 (k, + k2 ) — c;q=

xi = Xe -P1 sin(qt + 0)

For the upper impact,

x, = OA = v,t = 0

x, = 0 = Xe -`) sin 0

sinck = 0 which agrees with figure 2.35.

il = —pXe -pi sin(qt + 0)+ Xe -P'sqcos(q1+ 0)

v = Xe-°qcos(0)

e° —> 1 and cos(0) —> 1

vX =—

9

Which is equivalent to

2m1v

V4m1(k1+k2)—c12

For the lower Impact,

x, = 0, il = —v, 1 = 0

xl = 0 = Xe -° sin 0

ci

2m,

X—

92

Model Development

x, = —v = Xe °qcos(g)

C° --> 1 and cos( 70 —> —1

... X =vq

Thus in summary,

2m, v

V4m1(k1+k2)-4

Therefore the full equation for needle bounce is,

x 1 =2m1 v

[---1

e 2"i/ sin12114m1(kl+k2)— c

nl kl 8 (2.83)t + 0 + ig+,.V4m, (k, + k2 )— c12 2m1 k1+k2

The complimentary function will be ignored since it is equivalent to a constant

vertical shift and it is solely the oscillation about a median position which is of interest.

This gives a final equation to be used for the simulation of the nozzle bounce,

X—

2m, v - --- `i € 114m1(ki+k2)— c12x, =[ I , e 2"" sin t +k 0)

V4m1 (k i +k2 )—c; 2m1(2.84)

93

Model Development

2.9.4 Variables for Density and Bulk Modulus Variations

Table 2.6 below gives the values of the two variables, a and b, used by Dow &

Fink (1940). These variables are used to determine the variation of the density and bulk

modulus of most oils with pressure. The paper was written in 1940 and has been used by

most previous simulations. The original values were determined for Fahrenheit and

lbf7in2 . The converted values in Table 2.6 have been provided for the same correlation

but using centigrade and bars.

Original Converted

°F a*10-6 b*10 -11 °C a*10 5 b*10 820 3.96 7.30 -6.67 5.75 1.5430 4.02 7.00 -1.11 5.83 1.4740 4.08 6.80 4.44 5.92 1.4350 4.14 6.60 10.00 6.01 1.3960 4.19 6.40 15.56 6.08 1.3570 4.24 6.20 21.11 6.15 1.3180 4.29 6.00 26.67 6.22 1.2690 4.34 5.80 32.22 6.3 1.22100 4.38 5.70 37.78 6.36 1.20110 4.42 5.50 43.33 6.41 1.16120 4.46 5.40 48.89 6.47 1.14130 4.50 5.30 54.44 6.53 1.12140 4.53 5.10 60.00 6.57 1.07150 4.56 5.00 65.56 6.62 1.05160 4.59 4.90 71.11 6.66 1.03170 4.61 4.80 76.67 6.69 1.01180 4.63 4.70 82.22 6.72 0.99190 4.64 4.60 87.78 6.73 0.969200 4.66 4.50 93.33 6.76 0.948210 4.67 4.40 98.89 6.78 0.927220 4.68 4.40 104.44 6.79 0.927

Table 2.6: Variables for density and bulk modulus variations.

94

Experimental Validation

3. EXPERIMENTAL VALIDATION

3.1 Introduction 96

3.2 Experimental Setup 96

3.3 Injection System Characteristics 1003.3.1 Fuel Injection Quantity 1003.3.2 Effective Plunger Travel 100

3.4 Measured Parameters 1033.4.1 Control Lever Position 1043.4.2 Control Spool Position 1043.4.3 Pumping Chamber Pressure 1063.4.4 Delivery Valve Lift 1073.4.5 Line Pressure 1103.4.6 Needle Lift 1113.4.7 Injection Rate 113

3.5 Data Acquisition 116

3.6 Experimental Results 1203.5.1 Nozzle Simulation Validation 1223.5.2 Pump-pipe-nozzle Simulation Validation 123

3.7 Summary 125

95


Chapter 3

EXPERIMENTAL VALIDATION

3.1 Introduction

Before the models presented here can be used they must be experimentally

validated. This involves comparing the predicted values against experimentally measured

parameters. This chapter describes the experimental part of this work and highlights how

each separate parameter was instrumented. Careful note is made of likely inaccuracies of

the measured values to the actual values. This is because it is almost impossible to

measure something without altering the value you're measuring.

The chapter begins by covering the whole of the experimental setup before going

on to detail the instrumentation of each measured parameter. The experimental results

are then presented and used to validate both the pump-pipe-nozzle and the nozzle

simulations.

3.2 Experimental Setup

The fuel injection pump used is a Bosch VE type distributor pump (code VE 4/11

F 2250 RTV 11675). It is designed for use on a turbocharged 4 cylinder direct injection

diesel engine. This was connected to four Stanadyne pencil type nozzles with high

pressure pipes (350mm length and 1.2mm diameter). The nozzles are PN2-LM

Stanadyne pencil type nozzles and are also for use on a turbocharged 4 cylinder direct

injection diesel engine. Where necessary these components or identical versions were

taken apart and/or sectioned to examine not only their mode of operation but also to

obtain the geometric information necessary for the simulation models.

Some simulation work had been done before the experimental rig was set up„This

proved to be advantageous in deciding which parameters should be instrumented and

measured to validate the different models. Figure 3.1 shows a simplified schematic of the

injection system used and the eight parameters selected for instrumentation. These were

selected on the basis of several criteria. These included the ease of instrumentation, the

importance for validating the models and, probably most important of all, the accuracy

with which they could be measured without altering their actual values.

96


1. Lever position

2. Control spool position

3. Pumping chamber pressure

4. Delivery valve lift

5. Line pressure: pump end

6. Line pressure: nozzle end

7. Needle lift

8. Injection rate

Figure 3.1 : Schematic of instrumented fuel injection system

The actual instrumentation of this system was helped by the kind donation of a

Hartridge 1100 fuel pump test stand by Lucas Powertrain Systems. A diagram of the

97


experimental test rig is shown in figure 3.2. This shows the Bosch VE type pump (b)

connected to the Hartridge fuel pump test stand (a). The pump itself is connected via

four high pressure pipes of equal length to four identical Stanadyne injection nozzles.

Three of these are fed into a dummy block (c) which returns the fuel to the Hartridge

fuel pump test stand where it is either returned to the fuel tank for recirculation (after

filtering) or fed into separate burettes (f) so that the fuel injection quantity can be

measured. One of the Stanadyne nozzles (d) is instrumented and injects into a Bosch

injection rate meter (e) before the fuel is returned to the fuel tank of the Hartridge or fed

into a burette. All the measured parameter transducers(1-8) are powered by the

transducer power supply (g) which is also connected to the data acquisition board's

connection terminal (h) which in turn is connected to a 486DX2-50M1-Iz PC computer

(i). The computer can display and record data from any or all the measured parameters.

The techniques for measuring each of the parameters is described in more detail later.

The experimental set up is also shown in plates 3.1-3.5 at the end of this chapter.

Plate 3.1 shows a picture of the complete experimental set-up, plate 3.2 show the

instrumented fuel injection system set-up on the Hartridge 1100 fuel pump test stand and

plate 3.3 shows the instrumented fuel injection system on its own. Plates 3.4 and 3.5

show the instrumented distributor head of the Bosch VE type pump from two different

views. The line pressure (pump end) transducer, the delivery valve transducer

connections, the pumping chamber pressure transducer and the control spool position

connections are shown in both of these plates.

Property Unit Value Method ofDetermination

Density at 40°C g/ml 0.840 ISO 3675Kinematic viscosity at 40°C mm2/s 2.45 to 2.75 ISO 3104Bulk Modulus at 40°C GPa 1.5 ISO 6073

Table 3.1 : Calibration fluid 4113 properties.

The fuel used in the instrumented pump is calibration fluid 4113. The properties

for the fluid are given in table 3.1, above. Using the Hartridge test stand and its ability to

measure the fuel temperature, care was taken to maintain a constant value of 40°C fuel

temperature for all the experimental tests. This was to assure that the assumption in

Chapter 2 : Model Development of a constant fuel temperature of 40°C was as accurate

as possible.

98

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3.3 Injection System Characteristics

The first tests performed on the experimental test rig were to determine both the

fuel injection quantity and the effective plunger travel, or governor response, against

speed and lever position. These could then be used to analyse the system performance

and select the experimental test cases.

The following two pages show the effective plunger travel or control spool

position and the fuel injection quantity per shot against speed and lever position. A figure

is provided with each one for quick visualisation together with a table for more detailed

values or analysis.

Both sets of data were taken from the experimental setup on the Hartridge test

stand using steps of 100rpm pump speed. The lever position was done in steps of 10%

from 0% (minimum lever position or idle) to 100% (maximum fuel lever position). The

factory settings on the pump were used to determine the minimum and maximum lever

position. The lever position was measured using the potentiometer which will be

described in section 3.4.1. The voltage output from the potentiometer was measured

with a digital volt meter.

3.3.1 Fuel Injection Quantity

The fuel injection quantity per shot was measured over the full operating

conditions of the pump. The quantity itself was measured using the burettes of the

Hartridge test stand which metered 100, 200, 500 or 1000 shots from the instrumented

Stanadyne nozzle into a burette. The fuel injection quantity per shot was then easily

obtained by simply dividing the measured quantity by the number of shots. At very low

speeds the quantity became erratic and difficult to measure so a minimum speed of

200rpm pump speed was selected. Figure 3.3 shows that even at this speed there is some

variation in the quantity in relation to the smooth response at the other speed and lever

position conditions.

3.3.2 Effective Plunger Travel

The plunger effective travel or control spool position was measured using the

calibrated LVDT described in section 3.4.2. The output voltage was read with a digital

volt meter and converted to an effective plunger travel using the calibration values.

Figure 3.4, showing the plunger effective travel, also shows the governor response

to various speed and lever position conditions.

100


Figure 3.3: Fuel injection quantity per injection shot against speed and lever position.

Lever Position (56)SPolK4rPm 0 10 20 30 40 50 60 70 80 90 100

200 575 5549 51,5 54,8 -MP ,,,,,P1,9 18,§ 47,8 4$) 5 55,9 55,ii300 5 44.5 45.3 43.0 45.8 43.3 40.5 42.5 41.0 41.0 55.5 41.0400 ,, 21,8 36.9 39.2 40,9 394 3E4 33.0 36,0 ,e,§ 40,8 104500 ' 0.0 9.8 24.3 37.6 38.0 37.7 36.7 37.0 38.9 36.8 36.4600 9,9 4.9 20,6 31%4 36,4 4,37.‘fl 36,0 236,1 0.$ 104 364700 -, 0.0 9.7 19.0 28.8 34.5 35.4 34.6 35.0 35.4 34.7 34.2800 0,.0 9j 16.8 ,26.3 324 33,6/ 4.8 02,4 .,81.g 2,,12-.J 3f.6,900 0.0 8.3 14.5 23.4 30.4 31.6 31.0 30.8 31.0 30.4 30.21000 ' 0.0 7.6 14.1 22.3 28.7 ,28,0 28.0 28.2 28,1 274 081100 0.0 6.2 12.9 20.6 26.8 27.8 28.0 27.6 27.9 27.7 27.41200 0,0 , 0.0 12,0 19.2 24,4 26,8 27,2 26.8 26.5 267 26,61300 , 0.0 0.0 11.7 18.2 22.3 25.6 25.4 25.5 25.6 25.7 25.61400 0.0 0.0 11.5 18.0 22.2 ;5.6 0,g 26.0 25.7 25.8 25,71500 0.0 0.0 11.9 18.1 22.0 25.4 25.4 25.3 25.4 25.3 25.31800 , 0,0 OM 1 t1 1 7,3 ;1.g4 25,0 0,4 20,P 25,0 264 )26,t1700 0.0 0.0 13.4 18.0 22.0 25.4 26.5 26.6 26.4 26.6 26.71800 0,0 0,0 0 , 1 0,7 224- 0,4 46,0wA47,0 2p/ 40.1 10,41900 0.0 0.0 12.8 19.0 22.2 26.6 27.0 27.3 27.1 27.6 27.72000 0,0 CO 0,0 4,7 .1.0 S4G,2014 04 272 17,, )20,02100 0.0 0.0 0.0 0.0 9.0 19.0 25.3 26.8 26.6 26.8 27.22200 /0,0 0.0 0,0 0.0 0,9 6,8 15.8 24.6 28.1( 274 1742300 0.0 0.0 0.0 0.0 0.0 0.0 0.0 13.8 21.0 26.4 26.92400 040 ,0.0 0,0 0.0 0,9,00 0,9 941,m2 ,29,0 26.02500 ' 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.2 16.42600 om 0.0 om om om 0.0 dm 110 m clo dm

Table 3.2 : Fuel injection quantity per injection shot against speed and lever position.

101

Plunger 1.5Effective

Travel (mm)

0.5


Figure 3.4 : Plunger effective travel against speed and lever position.

Lever Position MASpo.d, rpm 0 10 20 30 40 50 ' 70 80 90 100 ,

0 ;,98 ' .40 2,23 '2,18 g-3 5 243 ,,M, ,z19 'zio ;4)9 gy1 a100 2.09 2.27 2.23 2.19 2.18 2.16 2.14 2.14 2.12 2.11 2.13200 5,4 1A4 1,0 5,6 144 141 14f f() 1,20 1 .26 Afl,300 1.21 1.41 1.36 1.33 1.31 1.30 1.29 1.28 1.27 1.25 1.28

400 .0,1 04 1A4 AO f,lf 549,IAA1,,10,fga,,U4lo fiAl500 0.34 0.82 1.04 1.29 1.32 1.30 1.29 1.28 1.27 1.25 1.28600 049 0773 0 .04 f•gj 141 JA I149 Ws 1-0 f. 2$ JO700 0.27 0.70 0.91 1.18 1.32 1.31 1.29 1.28 1.28 1.25 1.28800 P44 0.67 0.58 1,35 ),Og 10 1.0 1,48 148 f.45 5,0900 0.20 0.63 0.85 1.12 1.31 1.31 1.29 1.28 1.27 1.26 1.281000 O6 0-55 On 5,00 149 1,3t 520 f,g8 347 /,5 5451100 0.13 0.55 0.78 1.04 1.25 1.31 1.29 1.28 1.27 1.26 1.291200 0,4 0,53 9,74 J.Pf 1,45 Or f9 1028 J47 1.2a 4,29'1300 0.13 0.53 0.74 0.99 1.19 1.32 1.31 1.29 1.28 1.27 1.291400 944 0,54 P/74 Q,P0 1,35 1 35 04 141 LU -1930 1,331500 0.15 0.54 0.74 0.99 1.18 1.38 1.38 1.36 1.36 1.34 1.361600 9.18,, 06 9,76 5,99 118 ,),,” f,4f A,C,44CO339 1,0 011700 0.22 0.59 0.79 1.01 1.20 1.41 1.45 1.43 1.42 1.41 1.431800 040 0,01 0,0,,,00 ,j,41 1,44 t48 1,48 frj,41 1,45 1,481900 0.00 0.48 0.77 1.06 1.26 1.47 1.51 1.52 1.51 1.49 1.522000 0.00 4..9,00 9O4 Ali ).,10 5.49 1,55 154 1.54 5,54 1,572100 0.00 0.00 0.00 0.08 0.50 0.93 1.52 1.58 1.56 1.57 1.592200 0.00 0,00 0.00 9,60 0.09 6.13 A98 tits 1,56 5.56 59;2300 0.00 0.00 0.00 0.00 0.00 0.00 0.25 0.70 1.39 1.57 1.572400 0,00 „ 0)90 040 9.00 00 p.06 9,00 0,00 0,60 fof 1,58,2500 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.26 0.892600 two 0.00 0.00 000 0.00 0.00 0.00 om 0.06 ()Ad Obo

Table 3.3 : Plunger effective travel against speed and lever position.

102


3.4 Measured Parameters

This section covers the methods used to instrument and measure individually

each of the selected parameters. A diagram of the experimental techniques as well as the

calibration of the transducers and a sample output are provided for each parameter.

Baniasad (1994) showed that there was a problem with the filtering of the

injection rate signals which causes a shift in the time base. This was investigated before

performing the experimental tests as this data would be used to validate the timing

predictions of the simulation models and so needed to be as accurate as possible. Figuresill

3.5 and 3.6 show the effect of filtering on the injection rate signal at 50% lever position,

1000rpm and 100% lever position, 2000rpm. Both cases were taken from the

experimental test rig shown in figure 3.2 and plate 3.1 and the data was acquired using

the apparatus and methods described in section 3.5. The filtered injection rate profiles are

shown together with the line pressure (nozzle end) measured at the same time as the

different injection rate profiles but unfiltered. These line pressures are included to show

that the shift in the time base on the injection rate is not caused by variations in the

triggering point but are purely due to the different filtering settings. If the triggering

point was different the line pressures would also show a shift in the time base. For both

cases filtering has two major effects on the injection rate profile. The first is fairly

obvious and is to smooth the profile, this smoothing being greater the lower the low pass

filtering frequency goes. The second is less obvious and is to shift the time base so as to

delay the experimentally measured start of injection. The difference between the

20.5kHz, 101cHz and 5k1.-Iz signals is small although they show the trend of delaying the

start of injection as the filtering frequency decreases. The 2IcHz signal shows a significant

shift in the signal and leads to the recommendation of avoiding filtering at this level if

filtering is required. Because the simulation models need accurate experimental data for

all the parameters it was decided to perform no filtering, if possible, on any of the

measured parameters so as to avoid any time shift of the form described above. Also by

avoiding filtering all the measured information about the signal, including noise, is

recorded. This was also backed by the use of differential inputs (see section 3.5) to

minimise the noise on all measured channels. The one notable exception to this was the

delivery valve lift transducer signal which was of very low voltage and was

indistinguishable from noise if the signal wasn't filtered.

This study also highlights the excellent repeatability of the measured signals: This

can be seen by looking at the measured line pressures in figures 3.5 and 3.6 and seeing

that there is no change in either the timing or the profile. For each case the four line

pressure signals were measured during different injection cycles.

*see figures 3.5 and 3.6 on page 129

103


3.4.1 Control Lever Position

The control lever or fuel lever position is measured using a 1 kf/ servo mount

potentiometer with a conductive plastic (RS 173-552) which provides almost infinite

resolution. This is mounted on the top of the Bosch VE type pump and connected to the

fuel lever with a flexible coupling with no backlash. The maximum and minimum lever

position are left at the factory settings and the potentiometer gives a reading of 1.2 volts

over this range. The voltage is read with a digital volt meter and expressed as a

percentage of the maximum fueling position (i.e. 100% lever position is when the lever is

against the maximum lever position stop and 0% lever position when the lever is against

the minimum lever position stop)

3.4.2 Control Spool Position

The position of the control spool, which is determined by the governor and sets

the effective plunger travel, is measured using a linear variable displacement transducer

(LVDT). A probe is attached to the control spool via a plate and moves with the control

spool. The movement of this probe in and out of the coils which form part of the LVDT

can be detected, measured and converted into a signal representing the effective plunger

travel. A schematic of the instrumentation can be seen in figure 3.9. It is also useful to

refer to plate 1.1 showing a photograph of the plunger and control spool as well as the

distributor head. The LVDT itself is attached to the distributor head of the pump and the

probe passes into the feed chamber through a hole in the distributor head. It is important

to note that the feed chamber is under pressure ( 3 to 8 bar, depending on pump speed ).

As a result of this a grove is cut into the nylon bush supporting the probe and pressure

relief holes are made in the casing for the transducer. This allows the pressurised fuel to

flow to all parts of the transducer and insures all components experience the same

pressure from all directions. The connections for the control spool position transducer on

the distributor head of the pump are shown in plates 3.4 and 3.5 at the end of this

chapter.

The probe and plate add some weight to the control spool although this is not

considered to be significant. However, the surface area of the attaching plate is liable to

have some affect on the measured signal. The surface area of the plate is shown in

Section A-A' of figure 3.9. This is particularly relevant at spill when fuel will rush out of

the spill ports at high pressure, the fuel flow against the plate moving the control spool.

The control spool position was calibrated in relation to the spill point with the

plunger at the bottom of the cam profile. The spill point being the point at which the spill

ports are just uncovered by the control spool.

104

• Measured

Best Fit

0

CV

CO

*v(uL

%-4 -2 0 2 4 6

8

Effective Plunger Travel, mm


Figure 3.7: Control spool transducer calibration.

Figure 3.7 shows the calibration graph for the control spool transducer from

which the relationship between the voltage and the effective plunger travel can be

determined. This relationship is given below,

V = —EPT(mm)+ 6.875

(3.1)

Figure 3.8 : Sample output from control spool transducer.

Figure 3.8 shows a typical voltage output from the control spool transducer. The

signal is fairly noisy although filtering is avoided to prevent a shift in the time base.

105

.444,44440.4.1141...Insulator

A' •

Spill holes

Plunger

Distributor head

RDP Transducer

Outer casing \

(

Pressure relief hole

Coils

Nylon bush

nA

Control Spool

Attaching plate

Probe


Figure 3.9: Control spool position transducer.

3.4.3 Pumping Chamber Pressure

The pumping chamber pressure is measured with a Kistler 4065A1000

piezoresistive pressure transducer fitted into the timing screw. This is shown in figure

3.10 and also in plates 3.4 and 3.5 at the end of this chapter. The timing screw itself had

to be enlarged slightly to accommodate the transducer. The timing screw works by

adjusting the size of the pumping chamber and changing the pressure profile in the

chamber. Therefore great care was taken to insure that the addition of the pressure

transducer didn't change the factory setting for the pumping chamber volume.

106

Plunger Pumping Chamber Pressure Transducer Timing Screw


Figure 3.10 : Pumping chamber pressure transducer.

Figure 3.11: Sample output from pumping chamber pressure transducer.

A typical voltage output for an injection period is shown in figure 3.11. The

pressure transducer is pre-calibrated and gives 1V per 100bar of pressure, which gives,.

V = 0.01 x pressure(bar)

(3.2)

3.4.4 Delivery Valve Lift

The delivery valve lift is measured using a capacitance technique. Out of all the

instrumented parameters this proved to be the hardest to measure and took the most

development work. The final and most successful method was to remake the delivery

107

).To highpressurepipe

Frompumpingchamber

Inner capacitor sleeve

Delivery valve

Outer capacitor sleeve

Capacitor connectionsk- ----

Valve stop

Washer [push fit]

Outer casing


valve stop out of a machinable ceramic and fix two brass cylindrical sleeves to the end of

the stop. The two sleeves do not touch and are separated by a thin layer of araldite. The

outer cylindrical capacitor sleeve needs to be grounded to the outer casing and this

achieved by using a washer with a push fit. The weakest part of the instrumentation is the

capacitor connections which have to pass through the outer casing. The hole needed for

these connections is carefully sealed with araldite insuring the bubbles in the araldite have

been removed. However, due to pressures in the valve assembly during injection this

sealing eventually fails insuring that the transducer has a finite life span. This

instrumentation is shown in figure 3.12 and the connections for the transducer are shown

in plates 3.4 and 3.5 at the end of this chapter. This can be compared to a photograph of

an uninstrumented delivery valve shown in plate 1.2.

The capacitor attached to the valve stop forms part of a tuned circuit and the

motion of the valve into the field generated by the two capacitor plates can be detected

from this tuned circuit. This technique for measuring the delivery valve is new and

previously unreported in the literature. However, several factors have to be taken into

account. Any change in the dielectric, that is the fuel between the capacitor sleeves and

the delivery valve, will also affect the signal in addition to the valve movement.

Figure 3.12 : Delivery valve position transducer.

The delivery valve lift transducer was calibrated by setting it up on a small lathe

and slowly opening the delivery valve, with a probe, in small steps so that it gets closer

108

,T

8----•____

en a a .

a*

B0)ik._z CNJ

>

r- -

0

Measured

0 0.5 1 1.5 2 2.5

Distance, mm


to the valve stop and the capacitor sleeves. The results of the calibration are shown in

Figure 3.13. The distance on the x axis corresponds to the opening of the delivery valve.

Unfortunately, the signal is not linear and operates in the least sensitive region. This is

logical enough as the transducer will be more sensitive to the valve motion as it gets

closer to the capacitor sleeves.

Figure 3.13 : Delivery valve lift transducer calibration.

An example of a typical output from the transducer is shown in figure 3.14. The

voltage decreases as the valve gets nearer to the capacitor (i.e. when the valve opens) so

the voltage profile has to be inverted to get the delivery valve lift profile. The voltage

values themselves are converted into a delivery valve lift using the calibration values

shown in figure 3.13.

Figure 3.14: Sample output from delivery valve transducer.

The delivery valve signal is the only one which is filtered due to the low voltage

and the relatively high amount of noise with the signal. The signal is filtered at 2.01cHz

109


low pass and the example output given in figure 3.14 has been filtered in this way.

However, because the signal has been filtered it is important to bear in mind the time

shift that will be associated with this filtering.

3.4.5 Line Pressure

The line pressure at both ends of the high pressure pipe is measured using a

Kistler 4065A1000 identical to that used to measured the pumping chamber pressure.

The transducer is attached to the high pressure pipe by a clip adapter which essentially

clamps onto the pipe. The transducer can then measure the pressure through a small

pressure taping in the high pressure pipe. However, because the line pressure transducer

relies on being clamped to the high pressure pipe some leakage is almost inevitable. This

manifests itself as an occasional drip of fuel from the transducer. Obviously this effect

will be greater as the pressure increases. This was not considered to be a major problem

although it's important to bear in mind that the transducers will tend to under predict the

pressures particularly at high levels. This problem was noticed when the transducer was

clamped to a bent section of the high pressure pipe. This highlights the need to keep the

high pressure pipe as straight as possible.

Figure 3.15 shows the line pressure transducer and how it is clamped onto the

high pressure pipe with a clip adapter. Plates 3.4 and 3.5 also show this clip adapter for

the line pressure (pump end) transducer although the line pressure (nozzle end)

transducer uses an identical clip adapter.

Figure 3.15 : Line pressure transducer.

110


As with the pumping chamber pressure transducer the transducer is pre-calibrated

and gives an output of 1V for every 100bar of measured pressure. Typical voltage

profiles for both the line pressure (pump end) and line pressure (nozzle end) are given in

figure 3.16 and 3.17.

Figure 3.16: Sample output from line pressure [pump end] transducer.

Figure 3.17: Sample output from line pressure [nozzle end] transducer.

3.4.6 Needle Lift

Unfortunately due to the design of the Stanadyne nozzles selected for this

experimental work it was impossible to use the widely used Hall effect needle sensor.

Therefore a probe was attached to the top of the needle with the other end inserted into a

coil, see figure 3.18. This has the slight disadvantage of adding some weight to the

needle but this was not considered to be significant.

111

Coil

Probe

Nozzle outer body

-7 - - 7) 00 o0 00 000

0Needle spring

0 00 00 0o o-o o

0 C)

JTop of Nozzleneedle


The needle lift transducer was calibrated in steps of 0.1mm upto 4mm lift. This is

shown in figure 3.19 which shows there is a linear relationship between the voltage and

the lift given by,

V = 4.8118 x needlelift (mm) (3.3)

Due to the large pressures that build up in the nozzle before it opens (e.g. the

Stanadyne nozzles used here have an opening pressure of about 250bar ) the nozzle

components tend to expand slightly. This results in the probe moving in the coil and the

needle lift transducer measuring a signal before the needle actual opens. The same

problem occurs with the Hall effect needle sensor and is unavoidable. An indication of

this effect is shown in figure 3.20 which shows a sample voltage output from this

transducer. However, this effect becomes clearer when the experimental data is

compared to the simulation results.

Figure 3.18 : Needle lift transducer.

112

L()

111,00410406•••••••••••~................n••••••n•nnn

T

4

0 2 4 6 8 10 12

Time, ms

to


Figure 3.19 : Needle lift transducer calibration.

Figure 3.20: Sample output from needle lift transducer.

3.4.7 Injection Rate

The injection rate from the instrumented Stanadyne nozzle is measured with a

Bosch long tube injection rate meter. As the name suggests this involves injecting the

fuel from the nozzle into a long tube or pipe and measuring the pressure at the nozzle

end of the pipe with strain gages. The long tube is intended to remove the pressure wave

associated with the injection of fuel into the tube so that the instantaneous pressure can

be measured. This is shown in figure 3.21.

113

Pressure gauge

Regulator Valve

Orifice Plate

Back Tube

Strain gages

Injector


Figure 3.21 Bosch injection rate meter.

The critical design parameters for the Bosch injection rate meter are,

1. Diameter of the back tube

2. Length of the back tube

3. Wall thickness of the back tube

4. Orifice diameter at the end of the back tube.

5. Opening pressure of the relief valve at the end of the back tube

The pipe dimensions used are shown in table 3.4.

Parameter Dimension

Diameter of back tube 6.5mm

Length of back tube 7.3m

Orifice diameter 0.7mm

Table 3.4 : Bosch injection rate meter specifications.

The wall thickness should be sufficiently high to avoid any change in the speed of

sound in the back tube. This is discussed in more detail in the Appendix to Chapter 2:

Model Development in relation to the effect of pipe flexibility on the speed of sound in

the high pressure pipe. The opening pressure of the relief valve or the back pressure in

the long tube section of the meter can be adjusted by the regulator valve shown in figure

3.21. The back pressure is chosen to simulate the combustion chamber pressure to get a

similar situation as possible to a real diesel engine. A back pressure of 30 bar was used

for all the test cases and was input into the simulation modeling as being the combustion

chamber pressure.

114

U•

1U•

••

I

•

U

• Measured

Best Fit

0 20 40 60 80

Pressure, bar

III

0

NT


From the injection meter specifications the fuel injection rate is then given by,

dq . A, p

di ap

A l = 33.2*10-6m2

a= 1336 m/s

p= 825kg/m3

...—dq

= 3 x 10 11 p[m 3 I s]di

EQ(3.4) gives the relationship between the injection rate and the pressure. The

pressure can itself be determined by calibrating the injection rate meter on a Budenburg

Gauge which uses known weights to give known pressures. The calibration for the

injection rate meter, performed on such a gauge, is given below in figure 3.22.

(3.4)

Figure 3.22: Injection rate meter calibration.

Figure 3.22 shows that there is a linear relationship between the pressure and the

measured voltage. The best fit relationship is,

p = 15.75.V

... --q-d = 47.25 x V[mm 3 I ms]di

Figure 3.23 gives a typical measured injection rate profile with a maximum

voltage change of about 0.6V which in turn corresponds to an injection rate of

28mm3/ms. Figure 3.23 also shows that the signal is reasonably noisy although, as

mentioned a the beginning of this section, no filtering is done to avoid shifting the time

base.

115


Figure 3.23: Sample output from injection rate meter.

The development work on using this technique at Imperial College was done by

Baniasad (1994) who gives a more detailed analysis of the selection and use of this

injection rate meter in his thesis.

3.5 Data Acquisition

The data acquisition system selected to acquire the data was the DT2839 board

from Data Translation. This was installed into a 486DX2-50M1-Iz PC computer that was

also used for the computing work described in Chapter 2: Model Development. A

summary of this boards' analog to digital conversion features are given below,

• 32 single-ended or 16 differential inputs.

• 12 bits resolution.

• 1MHz throughput, single channel, 4161cYlz multi-channel (gain=1).

The board is also capable of digital to analog conversion, digital input or output

and has two programmable clocks. Although these features were not required for this

work.

116

Triggered Scan[Triggered Enable

OK

Input Options

[

Interface ModeO Single Ended0 Differential

[

Clock Source0 InternalO External

Trigger Source[O InternalO External

Range 1-10.0V to 10.0VIA

[

Encoding 0 Offset Binary0 2's Complement


Figure 3.24 : Input options for data acquisition.

Figure 3.24 shows the input options for the DT2839 data acquisition board. The

interface mode refers to the way the transducers are connected to the board. Differential

inputs have two connections; the transducer signal and earth. By combining these two

signals any noise the transducer signal experiences will also effect the earth signal. The

board then measures the difference between the two, hence differential inputs. Single

ended inputs use a common earth signal for all channels. Differential inputs were selected

for this work to eliminate as much noise as possible and because there was no restriction

on the number of connections available. The DT2839 board can receive 16 differential or

32 single ended inputs. In this case a maximum of 8 channels were required. No external

clock was required so the internal clock is used but an external trigger consisting of a

pulsed TTL signal from the drive shaft of the pump is required. A transducer range from

-10V to +10V was selected to accommodate all the transducers used and the encoding

used was binary (i.e. the data written to the hard disk of the computer is in binary

format). This binary data has to be converted to decimal so that the measured voltages

can be examined and converted to their relevant dimensions using the calibration values.

The data was converted to decimal using a simple program using the same software as

the simulations, Microsoft's' QuickC for Windows. These decimal values representing the

voltages were then read into Microsoft Excel and into a spreadsheet specifically set up to

convert the measured voltages into valve lifts, pressures or flow rates.

117

— Input Options

El Disable Input

0 Display Data

12:1 Write to File

Data Flow:

0 Burst

0 Continuous

Ii L±..1

Input Data Transfer

Sampling Frequency

N umber of Buffers

Buffer Size

DMA Channels

[250000.0

1314000

Output Options

0 Disable Output

0 live DMA

0 Sine0 Squaie

0 rle

Acquisition Options

ICancel I


Figure 3.25: Acquisition options for data acquisition.

Most of figure 3.25, which shows the acquisition options for the DT2839

software, is self explanatory. The buffer size (4000) refers to the number of data points

to be acquired. So sampling at a frequency of 250kHz (as shown in figure 3.25) 16ms of

data will be acquired and saved to a file. The time step between individual data points

will be 0.004ms or 41.ts which matches the time step in the simulation programme.

Figure 3.26: Input channel/gain list for data acquisition.

The input channels and any gain settings are selected using the dialog box shown

in figure 3.26. The current settings are for 6 channels of data to be acquired (channels 0

to 5) with a gain of 1 on each channel. For the board settings a gain of 1 for each

experimentally measured parameter was used throughout this work. Using this dialog

box any number of the eight instrumented system parameters can be analysed.

118

DT-Open Layers C Example - 0T2839 BOARDConfigure Start! SingleValue... CounterTimer... ViewOutput! Help

Data

8

4

0

4

5 10 15 20 25 30 35 40 45

V

Input Buffers done:Output Buffers done:

Milliseconds30

• Measured

Best Fit

•

IA

•A

J."

,E7Lj

1000 2000 30000 4000

•

Hexadecimal Values


Figure 3.27 : Data acquisition using sample software.

Figure 3.27 shows a typical display on the computer screen during data

acquisition. Just one channel is being analysed which in this case is the line pressure

(nozzle end). Although data has been acquired over a 50ms period this can be

manipulated later so that the important period (15 to 35ms) can be analysed in more

detail.

Figure 3.28 : DT2839 board calibration.

Figure 3.28 shows the calibration for the DT2839 data acquisition board when its

set to receive transducer voltages in the range -10V to 10V. The hexadecimal values

119


along the bottom of the graph have been converted to decimal for plotting. The

calibration shows that the resolution of the data acquisition board is 0.005V.

3.6 Experimental Results

Table 3.5 lists all the test cases done on the experimental test rig. These cases

were performed to cover the whole performance range in terms of speed and lever

position. From these cases three were selected for validation purposes and these are

shown in table 3.6.

Lever Position, % Pump Speed, rpm Fueling', mm3100 500 36.40100 1000 27.80100 1500 25.30100 2000 26.5050 500 37.7050 1000 28.0050 1500 25.4020 500 24.2520 1000 14.10

0 [idle] 450 7.00Table 3.5: All test cases performed.

Lever Position, % Pump Speed, rpm Fueling', mm3100 2000 26.5050 1000 28.00

0 [idle] 450 7.00

Table 3.6: Cases selected for model validation.

There is a problem with the repeatability of the idle case not associated with the

other two cases. This is because the 0% lever position at 450rpm (idle case) is on a steep

part of the curve in both the fuel injection quantity map (figure 3.3) and the effective

plunger travel map (figure 3.4). This means that a small variation in either the speed or

lever position can have a significant effect on both the effective plunger travel and fuel

injection quantity. As a result of this, the injection rate profile will also be different.

Fortunately, the other two cases of 50% lever position, 1000rpm and 100% lever

position, 2000rpm lie on a fairly smooth part of the map and are nowhere near as

sensitive to such changes. The two methods of determining the fuel injection quantity

(i.e. the burette measurement and the integration of the injection rate signal) rely on good

repeatability for accurate results as it is impossible to measure the same shot in a burette

as that used to generate the injection rate signal. The burette quantity is determined by

I As measured with the burettes on the Hartridge test stand

120


averaging the fuel injection quantity over hundreds of injections and as such it is not

directly comparable to the single-shot injection rate measurement.

The measured values for each of the eight parameters are presented together on

one page for each of the test cases. With the exception of the lever position, which

remains constant over the injection period, the same time base is used for each

parameter. A 4ms period is used for each set of results which are plotted against time

rather than crank angle. Table 3.7, below, can be used to convert the time to crank angle

for each of the different speed settings.

Time, ms

Pump speed 1 2 3 4

2000rpm 12.0 24.0 36.0 48.0

1000rpm 6.0 12.0 18.0 24.0

450rpm 2.7 5.4 8.1 10.8

Table 3.7: Converting time to crank angle for the experimental results.

The results are shown in figures 3.35 - 3.44 and several useful observations for

each of the measured parameters can be made from these results alone.

The control spool position remains constant until or just before the spill point.

The spill point is the point at which the spill ports are just uncovered by the control

spool. The spill point on the graphs will be the point at which the pumping chamber has

reached its maximum pressure and begins to fall. This fall cannot be the result of the

plunger going over-the-nose of the cam profile as the maximum lift from the cam is

2.3mm and, therefore, the plunger will always uncover the spill ports before it reaches

the top of the cam profile. After the spill point the control spool position oscillates

slightly, this effect becomes greater as the speed and lever position increase which also

means it increases with the pumping chamber pressure at the spill point. There is also a

tendency for the spool to be dragged along with the motion of the plunger. This is shown

as an increase in the plunger effective travel on the graphs. It is hard to say what part the

problems associated with the control spool instrumentation (see section 3.4.2) play in

these motions, although the flow against the attaching plate and the movement of the

spool which this causes is likely to become more pronounced as the pumping pressure at

the spill point increases.

Two simple, but important, observations can be made regarding the pumping

chamber pressure profiles. Firstly, the rate of increase of the pumping chamber pressure

which will effect the beginning of injection events is controlled by the pump speed.

Secondly, the maximum pumping pressure or spill point is determined by the lever

position. This will affect the timing of the end of injection events and injection quantity.

121


As was mentioned in section 3.4.4 the delivery valve lift proved very hard to

instrument and limited confidence was placed in its results. However, the delivery valve

must open between the time the pumping chamber pressure begins to rise and the time

the line pressure (pump end) begins to rise. For all the experimental cases the transducer

did exactly that. However, due to the low measured voltages the signal becomes almost

too small to measure at low speed and lever position (see figure 3.44). The delivery valve

signal also shows some unexpected negative values in the second half of the injection

period. One possible explanation for this is the result of cavitation in the dielectric (i.e.

the fuel) between the capacitor plates and the delivery valve.

Both line pressures on the high pressure pipe show some interesting results. In

nearly all cases the pressure is actually magnified by the time it reaches the nozzle end of

the pipe. This is due to the interaction of the pressure waves that are set up in the high

pressure pipe by the injection process. The lack of high pressure oscillations and no

measured points of zero pressure in the pipe after injection suggest that the constant

pressure relief valve is managing to prevent cavitation in the high pressure pipe. This is

highly desirable from a practical point of view but from a simulation point of view some

cavitation would be advantageous so that it could be simulated.

The only problem with the needle lift signal appears to be the transducer

measuring a lift before it actually rises. This is because it is reasonable to assume that the

needle will rise just before the injection begins.

The Bosch long tube method used to measure the injection rate appears to be

good at predicting the start of injection, although the pressure waves introduced into the

tube make the resulting signal quite noisy. As was mentioned before, filtering was

avoided as it shifts the time base and the most important thing for the simulation was

judged to be the timing of events.

3.6.1 Nozzle Simulation Validation

The validation of the nozzle simulation involved inputting the experimentally

measured line pressure (nozzle end) into the model for each of the three selected

validation cases. The simulated output is then compared to the measured values of the

needle lift and the injection rate.

Figures 3.45 to 3.47 show the comparison of simulation and experimental results

for the three validation cases for the nozzle simulation. The comparisons for the three

selected test cases are shown together on the same time base. The line pressure (nozzle

end), which is the input to the model, is shown at the top of each page and shaded in

gray.

Now that the experimental and simulated needle lift profiles are compared the

initial lift on the experimental data can clearly be seen. This is most noticeable on the idle

case (figure 3.45). It is also important to notice how this initial needle lift matches up

122


with the rise in the line pressure for each of the three cases. This is further evidence to

suggest that the rising line pressure in the nozzle, and not actual needle lift, causes this

signal. The time the needle lift begins to rise sharply matches well with the simulated

needle lift as does the magnitude of the needle lift even when the needle doesn't reach the

maximum lift. The end of the needle lift profile is also matched well with the possible

exception of the 50% lever position, 1000rpm (pump speed) case. The needle oscillations

have been matched to the experimental data using the techniques described in section

2.6.1 and so do not provide a good judge of the accuracy of the nozzle simulation.

Therefore, overall the nozzle simulation provides an accurate prediction of the needle lift

profile for all the validation cases and evidence suggests the simulation even gives a more

accurate prediction of the start of the needle lift than the experimental data.

Because the timing of the needle lift is accurately predicted so is the start of the

injection. The injection rate profile is also predicted accurately although the

predicted magnitude is slightly less for all cases and the simulation also predicts an earlier

end to the injection rate than is suggested by the experimental data. This could be due at

least partly to a similar problem associated with the pump-pipe-nozzle simulation where

the simulation methods used accurately predict the timing of the interference of pressure

waves but tend to under predict the magnitude. This will be discussed in more detail later

for the pump-pipe-nozzle simulation. The injection quantities for the three validation

cases for the nozzle simulation are shown in table 3.8, below.

Case

lever position,

pump speed

Burette

mm3

Integrated

mm3

Simulation

mm3

0%, 450rpm 7.00 4.35 4.7

50%, 1000rpm 28.00 32.80 22.70

100%, 200Orpm 26.50 29.80 21.00

Table 3.8 : Fuel injection quantities for nozzle simulation.

3.6.2 Pump-pipe-nozzle Simulation Validation

The validation of the pump-pipe-nozzle simulation involved inputting the

experimentally measured pumping chamber pressure into the model for each of the three

selected validation cases. The simulated output is then compared to the measured values

of the other transducers. As for the nozzle simulation the selected cases for validating the

model are shown together on one page using the same time base.

Figures 3.48 to 3.50 show the comparison of simulation and experimental results

for the three validation cases for the pump-pipe-nozzle simulation. The pumping

123


chamber pressure, which is the input to the model, is shown at the top of each page and

shaded in grey.

As was mentioned earlier the greatest confidence in the measured delivery valve

lift was associated with the start of its lift. This matches well for all three validation cases

with the simulation results. The maximum valve lifts and the first half of the lift profiles

also match well but the second half and valve closure time are significantly different.

However, due to experimental techniques used it is impossible to say which is the more

accurate without further study.

Therefore, the first measured signal for the pump-pipe-nozzle simulation

validation that can be used with some confidence is the line pressure (pump end). As

with the delivery valve lift the time the line pressure begins to rise and the first half of the

profile match well. The peak pressures also match well although the pressure for the

second half of the profile drops too quickly. This in turn could be associated with an

inaccurate prediction of the delivery valve lift closure.

The timing of line pressure (nozzle end) is predicted accurately for all cases as is

the profile. Although, at the higher lever positions particularly, the magnitude is under

predicted. A similar situation occurred for the nozzle simulation where timing of the

interaction of forward and reflected waves was accurate although the magnitude was

under predicted. This under prediction is greater for the pump-pipe-nozzle simulation

where a greater pipe length is simulated. This suggests the method for simulating the

pipe flow is good for the timing of the pressure waves but not the magnitude. Whether

this is a problem with the method of characteristics or the magnitude of various

parameters needs further examination. The effect of removing the friction factor from the

pipe sections in the model was to increase the peak pressures by approximately 2%.

As for the nozzle simulation the needle lift profile is accurate and potentially a

better predictor of the start of needle lift than the experimental results. This is possible

even if the line pressure (nozzle end) is not so accurate as the needle lift will be at its

maximum value above a certain pressure level. Where the needle doesn't reach its

maximum value, as in the idle case (figure 3.44), the needle lift profile matches well with

the experimental values as long as the simulated and experimental line pressures (nozzle

end) match well.

The start of injection is accurately predicted again due to the accurate predict of

the start of the needle lift. Because the line pressure (nozzle end) is under predicted so is

the magnitude of the injection rate which, for all three cases, is predicted to end before

the experimental values suggest it should. The fuel injection quantities for the validation

of the pump-pipe-nozzle simulation are shown in table 3.9 for comparison.

124


Case

lever position,

pump speed

Burette

mm3

Integrated

mm3

Simulation

mm3

0%, 450rpm 7.00 4.35 4.61

50%, 1000rpm 28.00 32.80 22.5

100%, 200Orpm 26.50 29.80 21.97

Table 3.9 : Fuel injection quantities for pump-pipe-nozzle simulation.

Both simulation models failed to predict the oscillations seen in the injection rate

profiles. When these measured profiles were integrated to find the injection quantity it

was also found that the integrated signal over predicted the measured burette quantity

for nearly every case. Therefore, the profiles were manipulated to remove the oscillations

in the measured injection rate and integrated again. Both the original and smoothed

signals for three cases are shown in figures 3.32 - 3.34. These re-integrated values which

represent the fuel injection quantity and the burette values were then found to match

fairly well. Figures 3.29 - 3.31 show the comparison of the burette, original integrated

signal, the smoothed integrated signal and the simulation values for 100%, 50% and 20%

lever position. This is evidence to suggest that these oscillations are not present in the

actual injection rate profile and are due to the measurement technique. There is also

evidence to suggest that the oscillations in the injection rate profile are linked to the

needle bounce. This is because the oscillations in the injection rate only occur when the

needle reaches its maximum value and bounces. However, if such a link does exist the

previous method of smoothing and re-integrating the signal suggests that the magnitude

is much smaller than in the measured profiles.

3.7. Summary

In this chapter an instrumented fuel injection system consisting of a Bosch VE

type pump connected to four Stanadyne nozzles has been presented. Eight parameters

have been measured; the fuel lever position, the control spool position, the pumping

chamber pressure, the delivery valve lift, the line pressure at both ends of the high

pressure pipe, the needle lift and the injection rate. The control spool position and

delivery valve lift transducers are most notable as they use previously undocumented

techniques. The data from the transducers was acquired using a high speed data

acquisition board in the same computer used for the simulation models. The experimental

data from these measurements have been used to validate the nozzle simulation and

pump-pipe-nozzle simulation presented in Chapter 2: Model Development. This

validation shows that the models are good at predicting the start of injection although the

end of injection predictions are less accurate. As a result of this the fuel injection

quantities are also slightly under predicted. This is primarily because the models predict

125


the timing of pressure wave interactions well but tend to under predict the magnitude.

Evidence is also given suggesting that the oscillations in an unfiltered injection rate signal

from a Bosch long tube meter don't represent actual injection.

126

A

500 1000 1500

—6— Burette

—a— Integrated signal

Integrated signal(smoothed)

Simulation1n1

Pump Speed , rpm

Burette

Integrated signal

Integrated signal

(smoothed)

0 Simulation

500

1000

Pump Speed, rpm

111111ft


en

•—n

0

—6— Burette

Integrated signal

o

Integrated signal

(smoothed)0

Simulation

500 1000 1500 2000

Pump Speed, rpm

Figure 3.29 : Fuel injection quantities at full lever position (100%)

Figure 3.30 : Fuel injection quantities at part lever position (50%)

Figure 3.31 : Fuel injection quantities at low lever position (20%)

127

tP1

3 40 1 2

1=1

00.1

4

0 1 2 3.\

4

Time, ms

0 1 2 3 4

08

Time , ms


Tune, ms

Figure 3.32: Smoothed injection rate signal for 2000rpm, 100% lever position case.

Figure 3.33: Smoothed injection rate signal for 1000 rpm, 50% lever position case.

Figure 3.34: Smoothed injection rate signal for 1000 rpm, 20% lever position case.

128

50% lever, 1000rpm

20.5 kHz

10 kHz

5 kHz

2 kHz

0

1

2

3

4

Time ,ms

50% lever, 1000rpm

00cr

00rs1

0

100% lever, 2000rpm

20.5 kHz

10 kHz

5 kHz

2 kHz

00ON

00n0

00rn

0

100% lever, 2000rpm


Figure 3.5 : The effect of filtering the injection rate signal at 50% lever position, 1000rpm

Figure 3.6 : The effect of filtering the injection rate signal at 100% lever position, 2000rpm

129

SPEED : 500 rpm (pump speed]LEVER POSITION : Full [1. 100%]FUELING : 36.4 mm 3 (Burette) & 42.5 mm 3 (Integrated signal)

0CD

0LO

0 FL0

7. Needle lift

0 a;cr)

og

E

0-73

8. Injection rateZ "

9

...nnnn•n

90

1

2

3

4

Time,ms

co

03

Co

Co

0

9

00


Figure 3.35 : Experimental results for test case 100% lever position, 500rpm.

130

LC)

1

2

3

4

Time,ms

CO

0


5. Line pressure - pump end

6. Line pressure - nozzle end-

-----------N"-- \ y---------,

o

o(.0

8. Injection rate

o

ci

cl9

0LC)N

0LON


SPEED : 1000 rpm [pump speed]LEVER POSITION: Full [1. 100%1FUELING : 27.8 mm 3 (Burette) & 30.1 mm 3 (Integrated signal)


131

'2. Control spool position

_


_

o

U")

00CD

ooTr

00CV

_

-

_

•,,,Im....

-

4. Delivery valve Ilt -

_

nozzle end -


6. Line pressure -

0Co

o

•••

000,

0LC)CV

1 2 3 4


SPEED : 1500 rpm [pump speed]LEVER POSITION : Full [1. 100%]FUELING : 25.3 mm 3 (Burette) & 29.2 mm 3 (Integrated signal)

Time, ms


132



csi


5. Line pressure -

6. Line pressure -

co

7. Needle lift

8. Injection rate

itt/VV`voNf 0

3 41

2

Time,ms

9


SPEED : 2000 rpm [pump speed]LEVER POSITION: Full [1. 100%[FUELING : 26.5 mm 3 (Burette) & 29.8 mm 3 (Integrated signal)

Figure 3.38 : Experimental Results for test case 100% lever position, 2000rpm.

133

oocoI



LoCs/

6


.1-"...5. Line pressure - pump end I

6. Line pressure - nozzle end

1111n•n

------- \

2

Time, ms

1 3 4

o_ LI,N

o- Lo(NJ

-

oco

7. Needle lift

98. Injection rate


SPEED : 500 rpm [pump speed]LEVER POSITION : Middle [1. 50%1FUELING : 37.7 mm 3 (Burette) & 43.3 mm 3 (Integrated signal)


134

9

_

-

_

oLi"N

00co

0IDV'

ooel

oL).-

o

oc%,

c64. Delivery valve lift

pump end

nozzle end

5. Line pressure -

6. Line pressure -

8. Injection rate

1

2

3

0Locv.—

000.—

0 "rtiis).oN ,i.

is0 in

o0 oin IL-

OLo04

oTt


SPEED : 1000 rpm [pump speed]LEVER POSITION: Middle [1. 50%]FUELING : 28 mm 3 (Burette) & 32.8 mm 3 (Integrated signal)

Time,ms


135

ooco

Csi—I— 2. Control spool position

00(-4


Tr

o

N

o o

4 -

co _o

co --o

-

oc.i

7. Needle lift _

8. Injection rate

2

Time. ms

-

_

10 3 4

—ooo—

0LC)N


SPEED : 1500 rpm [pump speed]LEVER POSITION : Middle [1. 50%]FUELING : 25.4 mm 3 (Burette) & 28.75 mm 3 (Integrated signal)

Figure 3.41: Experimental results for test case 50% lever position, 1500rpm.

136

oco

7. Needle lift

8. Injection rate

o

2 3 41




_

_

_

a:0

in

CNJ

Time,ms




SPEED : 500 rpm [pump speed]LEVER POSITION : Low [1. 20%]FUELING : 24.25mm3 (Burette) & 14.1 mm 3 (Integrated signal)


137

ooco



4. Delivery valve lift-

5. Line pressure - pump end I


401Ir -

1

2

3

4

Time, ms

-

o

_


SPEED : 1000 rpm [pump speed]LEVER POSITION : Low [1. 20%]FUELING : 14.1 mm 3 (Burette) & 7.2 mm 3 (Integrated signal)


138

ooCo


.............n••••n•n••••••••"........"..........


........n•n•nnnn•n ,aveL 0

0

1

2

3

4

Time, ms

oco

0

0

N

-

0

N

cio

rii.0a'sIncn

:12

CI-

\I,.

-

oo

oont-

oocn

00N

.4.

_


,..•=0............."-


nozzle end6. Line pressure -

oo,

-


SPEED : 450 rpm [pump speed]LEVER POSITION: Idle [1. 0%]FUELING : 7 mm 3 (Burette) & 4.35 mm 3 (Integrated signal)


139

0

1

2

3

4

ci

INPUT: Line Pressure [nozzle end]

.8:4 200

11i

100

300

Needle Lift

Injection Rate

Time, ms

1 2 3 4

0 1 2 3 4


SPEED: 450rpm [pump speed] LEVER POSITION: 0%FUELING: 7.0mm 3 (Burette) & 4.35mm 3 (Integrated signal)

Simulation

Experimental

Figure 3.45 : Comparison of simulated and experimental results for test case 0% lever position, 450rpm.

140

00to

o0c.,

,r0"\— ..."•••%.

0

1 2 3 4

•zr

o

9 0

2

3

4

cno

o

0

1

2

3

4

Time, ms

co

o

o.-

-

SPEED: 1000rpm [pump speed] LEVER POSITION: 50%FUELING: 28.0mm 3 (Burette) & 32.8mm 3 (Integrated signal)I-- Simulation

Experimental I


Needle Lift

Injection Rate



141

0 1

2

3 4

Time, ms

0 ._......n,..........„,,,.....

SPEED: 2000rpm [pump speed] LEVER POSITION: 100%FUELING: 26.5mm 3 (Burette) & 29.8mm 3 (Integrated signal)I- Simulation Experimental


Needle Lift

Injection Rate

0 1 2 3 4

o

.—9

2 43


Figure 3.47 : Comparison of simulated and experimental results for test case 100% lever position, 2000rpm

142


SPEED: 45Orpm[pump speed] LEVER POSITION: 0% [idle]FUELING: 7mm 3 (Burette) & 4.35mm 3 (Integrated signal)

Simulation Experimental

0 INPUT: Pumping chamber pressure oocs,;II.0 0

0

I.. CN7on 0U) O .

oCf)

RI0 .C1004 11;

ki0 tn0CO)

o.........._ ......._ 0

U)od

EE

g

111>To °>t'0>

z"-0coo

c43

ooco

c160 J20 ••tt e

7(I)

1'o

ei

0 o.N VC

n

Delivery valve lift

Line pressure ['a u p end]

w-W-Alia

111hIMMII.

001.11

0

'a 2.0

:ii 83 ,_.

I- 8o. —,.0

C 07.. 0

C?

oou?

cn E6 E

e._a,

4)ci 41

cf.'

-Line pressure (nozzle

_

endl

Needle lift

_

oN

(I)

RE

E °Cl;

10r=

o

oN

U)E

0 E— Ea4...63cc

o

4

Injection rate

, n- -- — __ __ _

0 1

_ _ __ —

2 3

Time, ms

Figure 3.48: Comparison of experimental and simulation results for test case 0% lever position, 450rpm.

143


SPEED: 1000rpm [pump speed] LEVER POSITION: 50%FUELING: 28mm' (Burette) & 32.8mm 3 (Integrated signal) Simulation Ex erimental

o INPUT: Pumping chamber pressureo o

oLo L.toxio ei

• in =N in

V)

11.'o.

o

inob3n

2.; 0m Lf)in esi11)

II.'a.

_.......

in

aEE

— aw>

TOa u.)

41) a._liCI

L)

ooo—

o t

iCD mCD lau) 0

8.o ID

(NI '...1

Delivery valve lift

nIII

Line pressure [pu p end

I

oo0

... 0CI 0.0 cy)

E;=cn

I'0.4.1 oco:i C7

00

cii)

Na

in0 E

E

m eCi 0

:6ti)coz

ci

-.

f;

Line pressure (noz- le end]

Needle lift

_ .

0

0E

mE 0E CNI

U,—cocc

0

0

0 Pm t.

0Cn1 E

6.0 ••-•, ,0

cc

0

4

Injection rate

/

A

N

0 1 2 3

Time, ms


144


SPEED: 2000rpm [pump speed] LEVER POSITION: 100%FUELING: 26.5mm 3 (burette) & 29.8mm 3 (Integrated signal) Simulation Ex erimental

0 INPUT: Pumping chamber pressure ooco

to.0

i. 013 00 it0Ea.

'

A

co..

AIL

o

ZO

.0

0 vio zCr in

00

it

r.)ci

EE u)

� d0)>

To °>

to>

'713 0o

Cl

ci3

ooo.- .0

i'3to)v)

04)o ct.-Lo

a)c:J-

o

Delivery valve lift

Line pressure [pu p end]

0oo,

,co 0

.13 0in

E

=wv, 0EO.(1) 0C 0

..3 u?

ooo.—

oN

cio

Lf) E° E

o �Cr) n

d Ø-Ts(1)

Ow

d

o

9

Line pressure [nozzle end]

Pa— . ...._ _

-

_

Needle lift—

1••nn•n

oLn

E

"E u..,E IN

6-....e ,

cc

0

EvanE

(.411) E

a;-co

c c

Injection rate

2

Time,

_ Alilithh\3

ms

4

o_

1

Figure 3.50 : Comparison of experimental and simulation results for test case 100% lever position, 2000rpm.

145

Parametric Studies

4. PARAMETRIC STUDIES

4.1 Introduction 152

4.2 Nozzle Simulation 152

4.3 Nozzle Forces 153

4.4 System Parameters 1544.4.1 Nozzle Orifice Area 1554.4.2 Nozzle Chamber Area 1564.4.3 Nozzle Chamber Volume 1584.4.4 Pipe Diameter 1594.4.5 Pipe Length 1604.4.6 Initial Nozzle Force 1614.4.7 Maximum Needle Lift 1624.4.8 Pumping Chamber Pressure 1644.4.9 Other Parameters 165

4.5 Applications 166

4.5 Summary 166

151

Parametric Studies

Chapter 4

PARAMETRIC STUDIES

4.1 Introduction

One of the advantages of a fuel injection system model is that it can be used to

examine the effect of different system geometne on the performance of that system. For

example it can be used to determine the effect of high pressure pipe length variations on

the fuel injection rate and timing. Such an investigation using experimental methods

would certainly be more time consuming and expensive. It is this examination of the

effect of various parameters that is termed a parametric study.

This chapter begins by explaining the unsuitability of using the nozzle simulation

for parametric studies. A preliminary investigation of the forces on the nozzle is then

carried out to determine the most likely parameters to have a significant effect on the

needle lift and, therefore, the injection rate. These parameters include the nozzle chamber

area, the nozzle chamber volume, the high pressure pipe diameter, the high pressure pipe

length and the initial force on the nozzle valve. The effects of these parameters on the

injection rate, particularly the injection timing and injection quantities, are then discussed

in turn. For each parameter examined the same three test cases used at the validation

stage are used and the injection rate profiles for each varied parameter are presented

together at the end of the chapter.

4.2 Nozzle Simulation

Before using the pump-pipe-nozzle simulation to perform some parametric

studies on some typical fuel injection parameters, evidence will be given of the

unsuitability of using a nozzle only model with experimental inputs for parametric

studies.

The problem with the nozzle only model is that it uses an experimentally

measured line pressure (nozzle end) as an input and this input cannot change if the

system geometry is changed, it is a fixed input. However, in reality a change in such

geometre.5 like the nozzle chamber volume or pipe diameter would actually change the

line pressure profile. Such changes would invalidate the results from such a parametric

study. This is unfortunate as the nozzle simulation is more accurate in predicting the

system performance due to the smaller number of required inputs and modeling

requirements. The pump-pipe-nozzle simulation itself can be used to show how the line

pressure profile changes with various geometric variations.

152

Parametric Studies

Figure 4.1 shows the effects, obtained from the pump-pipe-nozzle simulation, of

varying the pipe diameter on the line pressure (nozzle end) for each of the three

validation cases. If the nozzle simulation was used to examine the effect of pipe diameter

variations the model would not include these variations as the line pressure (nozzle end)

is the input to the simulation. Therefore, the results would be invalid. This is just one

example of how a change in the system geometry effects the line pressure (nozzle end).

Figure 4.2 shows the effects, again obtained from the pump-pipe-nozzle simulation, of

varying the nozzle chamber area on the line pressure (nozzle end). The other parameters

investigated here would also have an effect on this signal so the nozzle simulation was

not used for the parametric studies, only the pump-pipe-nozzle simulation.

4.3 Nozzle Forces

Before beginning the parametric study for real it is worth looking at the different

forces acting on the nozzle valve during a typical injection cycle. This will give a good

idea of which parameters are likely to be most significant in determining the needle lift

profile and, therefore, affect the injection rate.

Figure 4.3 shows the forces acting on the nozzle valve for the three validation

cases. This shows that the most significant forces acting on the nozzle come from the

pressurised fuel and the initial compression of the spring. The force from the pressurised

fuel in the nozzle chamber (1 in figure 4.3) acts on the section of the needle in the nozzle

chamber which has a reduced diameter and is directly proportional to the pressure in the

nozzle chamber as the area it acts on will be constant. However, the force from the

pressurised fuel in the sac volume (2 in figure 4.3) will dramatically increase when the

nozzle valve opens not only due to the increased pressure but also because of the greater

exposed area at the tip of the nozzle needle as this is the area that the pressure acts upon.

The initial force on the nozzle valve (3 in figure 4.3) comes from the initial compression

of the spring when the nozzle valve is closed. Therefore, this force is constant and is

noticeably larger than the extra force on the nozzle valve caused by the additional

compression of the nozzle spring when the nozzle valve opens (5 in figure 4.3). This

additional spring force also shows the needle lift timing and profile for each case as this

force is directly related to the needle lift. For the idle case (0% lever position, 450rpm)

the initial spring force is actually higher than the force from the pressurised fuel in the

nozzle chamber due to the relatively low pressure. The needle valve only manages to

open in this case due to the combined force from the pressurised force in both the nozzle

chamber and the sac volume. It is interesting to note the negligible force from damping

and inertia (4 & 6 in figure 4.3) for all three cases. This will mean that any parameters

offecting these forces only, such as the damping coefficient of the nozzle spring, will

have no effect on injection.

153

Parametric Studies

From this study it can be seen that the parameters which will be most significant

in determining the needle lift and, influence the injection rate, will be the ones which have

a significant effect on these forces. These will include any which change the force from

the pressurised fuel whether by changing the pressure or the effective area it acts on. Any

parameters which change the initial force on the valve from the spring will also be

significant.

4.4 System Parameters

The most important parameter in an injection system is the injection rate as this

determines the start, the quantity and the end of the fuel introduced into the combustion

chamber. Therefore, the parametric studies concentrate on the effects on the injection

rate. The variations of the line pressure at both ends of the high pressure pipe, the nozzle

valve lift and the pressure in the nozzle chamber were also examined. However, the

effects on the injection rate alone are presented here for clarity and because the effects

on these other parameters can be deduced from the variation in the injection rate. For

example, if the nozzle valve opens earlier the injection will start earlier and, similarly, if

the nozzle valve closes earlier the injection will end earlier. If the nozzle chamber

pressure rises quicker then the injection will begin earlier as the time to reach the nozzle

opening pressure will be shorter.

For each of the parameters studied a percentage variation of ±20% in their value

was used for consistency, although it is important to bear in mind that for some

parameters this may be a geometrically small change. This is particularly true in the case

of the nozzle orifice area. One exception to this is for the pumping chamber pressure

variations where a 10% change is used. Two features of the injection rate profile are

concentrated on; the timing of the start of injection and the injection quantity. These are

summarised in tables for each of the studied parameters. For the timing of injection the

start of the rise of the pumping chamber pressure is used as a reference point for all the

cases. This is because the pumping chamber pressure will rise just as the plunger begins

to rise on the cam profile. This means, therefore, that the injection timing can be

referenced to the cam profile. This is shown in figure 4.4 below.

154

- - Pumping pressure - Injection rate

0

2

3

Time, ms

•••

• ' ••

. •,I.

I.

• I•

'II

a•

-

.. II

%

, a • • ' 11111111g— .I.

O. .. • ••

tri

c•-)

Parametric Studies

Figure 4.4 : Injection timing reference method.

The injection process in a pump-pipe-nozzle system is a fairly complex process

even when it's assumed to involve one dimensional flow. This is because as the pressure

waves travel down the high pressure pipe they are reflected, at least partially, when they

reach the nozzle and interact with the forward pressure waves still traveling towards the

nozzle. This is also why the process has to be simulated by computer as the interaction of

all these pressure waves has to be calculated. This process naturally becomes more

complicated the longer these pressure waves last as would occur at low speeds. That is

one reason why the idle case is more complicated and shows different effects for the

variation of some parameters in comparison to the other two test cases. The idle case is

also more sensitive to parametric variations due to the slower pressure rise and because

the pressure generated is just sufficient to open the nozzle. In fact for the idle case the

needle doesn't actually reach the maximum needle lift.

For some of the results from the parametric study it is hard to deduce the exact

reasons for the variations due to the complexity of the process, as described above. It is

interesting to note that the difficulties invariably occur with the idle case. However, due

to the validation of the model carried out in Chapter 3: Experimental Validation which

covered the full speed and lever position range a good deal of confidence is placed on

the results generated in the study. This is particularly true for the timing where the

validation process showed that the start of injection could be accurately predicted.

4.4.1 Nozzle Orifice Area

The nozzle orifice area refers to the cross-sectional flow area of the discharge

holes. As would be expected the primary effect of the nozzle orifice area variations is on

the injection quantity. This is due to a higher injection rate associated with the greater

155

Parametric Studies

flow area. This comes directly from the orifice flow equation (EQ(2.5)) which states that

flow rate is directly proportional to flow area. Table 4.1 shows that the injection quantity

variations are similar for all cases.

Quantity, mm3 Nozzle Orifice Area, mm2

Lever position,

Pump speed

0.101 (-20%) 0.127 0.153 (+20%)

0%, 450rpm 4.12(-11%) 4.61 4.85( +5%)

50%, 1000rpm 19.34(-14%) 22.50 25.04(+11%)

24.40(+11%)100%, 2000rpm 18.88(14%) 21.97

Table 4.1 : Fuel injection quantity variations with nozzle orifice area.

The nozzle orifice area variations have no effect on the start of injection or the

end of injection. There is one exception to this; the end of injection for the idle case (0%

lever position, 450rpm). For this case the smaller nozzle orifice area results in the rate of

pressure drop being slightly smaller due to the smaller flow area. This in turn results in

the nozzle closing pressure being reached slightly later and, hence, there is a slightly

longer injection period.

The injection rate profiles for the nozzle orifice area variations are shown in

figure 4.5 at the end of this chapter.

4.4.2 Nozzle Chamber Area

Nozzle chamber area refers to the effective area of the nozzle needle that the

pressure in the nozzle chamber acts on to open the nozzle valve. Therefore, variations in

this area will have a direct effect on the nozzle opening and closing pressures. The force

from the pressurised fuel in the nozzle chamber was shown in figure 4.2 and is one of the

more significant forces acting on the nozzle valve. A larger nozzle chamber area will

result in the nozzle opening earlier as the force required to open the nozzle will be

reached earlier as less pressure will be required in the nozzle volume to provide the

force. The fuel injection quantity variations with nozzle chamber area are shown in table

4.2, below.

156

Parametric Studies

Quantity, mm3 Nozzle Chamber Area, mm2

Lever position,

Pump speed

5.34 (-20%) 6.68 8.02 (+20%)

0%, 450rpm n/a 4.61 7.75(+68%)

24.09(+7%)

22.86(+4%)

50%, 1000rpm 20.01(-11%) 22.50

100%, 2000rpm _ 20.80(-5%) 21.97

Table 4.2 : Fuel injection quantity variations with nozzle chamber area.

The fuel injection quantities increase with increasing nozzle chamber area as the

decreased nozzle opening and closing pressures allow the nozzle valve to remain open

longer and so increases the injection duration. Figure 4.6 shows that the peak injection

rates are almost unaffected. For the idle case the decreased nozzle chamber area results

in the nozzle failing to open. The pressure acting on the nozzle chamber area being

insufficient to open the nozzle valve. The increased nozzle chamber area has a similar

effect for the idle case as the other two cases although the effect is more pronounced as

the longer duration of the pressure profile associated with the low speed means the lower

opening pressure has a more significant effect. The closing pressure change is not so

significant as this is dependent on the spill rate not the speed.

Time, ms Nozzle Chamber Area, mm2

Lever position,

Pump speed

5.34 (-20%) 6.68 8.02 (+20%)

0%, 45Orpm 2.372(+11%) 2.132 n/a

50%, 1000rpm 1.316(+8%) 1.220 1.172(-4%)

0.908(-3%)100%, 2000rpm 0.980(+5%) 0.932

Table 4.3 : Timing variations with nozzle chamber area.

The timing variations with nozzle chamber area are shown in table 4.3. The

decreased nozzle opening pressure associated with an increased nozzle chamber area

result in an earlier start to injection. This is true for all three test cases although the effect

is more significant for the idle case where the low speed with be associated with a slower

rate of pressure rise.

The injection rate profiles for the nozzle chamber area variations are shown in


157

Parametric Studies

4.4.3 Nozzle Chamber Volume

The nozzle chamber volume variations will affect the rate of change of the

pressure in the nozzle chamber in accordance with the conservation of mass (EQ(2.1)).

This states that the rate of change of the pressure will increase with a decreased volume

size and vice versa. This applies to both a rising and falling pressure and assumes the

flow rates in and out of the volume are unchanged. Table 4.4 shows the fuel injection

quantity variations with nozzle chamber volume.

Quantity, mm3 Nozzle Chamber Volume, mm3

Lever position,

Pump speed

252 (-20%) 315 378 (+20%)

0%, 450rpm 3.34(-28%) 4.61 5.58(+21%)

22.86(+2%)

22.44(+2%)

50%, 1000rpm 21.8(-3%) 22.50

100%, 2000rpm _ 21.42(-3%) 21.97

Table 4.4: Fuel injection quantity variations with nozzle chamber volume.

For all cases the fuel injection quantity increases with increased nozzle volume

although the effects are far more pronounced for the idle case than the other two where

the changes are almost negligible. With the exception of the idle case, the peak injection

rates and, in fact, the profile are hardly affected by the volume variations. However, the

idle case shows an increasing peak injection rate and duration with increased volume

which explains the more significant fuel quantity variations. This could be due to the

effect of volume variations on the rate of pressure rise being more significant at the low

speed where the pressure duration will be longer.

Time, ms Nozzle Chamber Volume, mm3

Lever position,

Pump speed

252 (-20%) 315 378 (+20%)

0%, 450rpm 2.412(+2%) 2.376 2.364(-0.5%)

1.260(+3%)

0.956(+3%)

50%, 1000rpm 1.196(-3%) 1.228

100%, 2000rpm 0.904(-3%) 0.932

Table 4.5: Timing variations with nozzle chamber volume.

Table 4.5 shows the timing variations with nozzle chamber volume. As would be

expected the smaller volume size results in an earlier start of injection due to an increased

rate of pressure change. However, the effects are not large and for the idle case the

situation is reversed although, again, the effects are not large.

158

Parametric Studies

The injection rate profiles for the nozzle chamber volume variations are shown in


4.4.4 Pipe Diameter

Variations in the high pressure pipe diameter affect the flow in the pipe in a

similar manner to orifice flow. That is, a greater diameter or cross-sectional area

allowing a greater flow rate and vice versa. However, the situation is more complicated

for the pipe flow where the change in flow rate will also effect the timing of pressure

waves and their interactions in the pipe. Table 4.6 shows the effect of the pipe diameter

variations on the injection quantity.

Quantity, mm3 Pipe Diameter, mm

Lever position,

Pump speed

0.96 (-20%) 1.2 1.44 (+20%)

0%, 450rpm 5.87(+27%) 4.61 7.12(+54%)

22.21(-1%)

21.34(-3%)

50%, 1000rpm 21.93(-3%) 22.50

100%, 2000rpm 22.41(+2%) 21.97

Table 4.6: Fuel injection quantity variations with pipe diameter.

With the exception of the idle case there is a negligible effect on the injection

quantity. However, figure 4.8 shows that the injection rate profile does change with pipe

diameter. The peak injection rate decreases with decreasing pipe diameter but this is

compensated for, in relation to the injection quantity, by an increased injection duration.

This can be directly associated with the change of flow rates in the pipe. However, for

the idle case the injection quantity actually increases for both the 20% increase and 20%

decrease in pipe diameter. The changing flow rates and their effect on pressure wave

interactions is one possible explanation for this phenomena.

Time, ms Pipe Diameter, mm

Lever position,

Pump speed

0.96 (-20%) 1.2 1.44 (+20%)

0%, 450rpm 2.324(-5%) 2.372 2.252(-5%)

1.196(-2%)

0.908(-3%)

50%, 1000rpm 1.292(+6%) 1.220

100%, 2000rpm _ 1.004(+8%) 0.932

Table 4.7: Timing variations with pipe diameter.

Table 4.7 shows the timing variations with pipe diameter for the three test cases.

With the exception of the idle case, an increased pipe diameter results in an earlier start

159

Parametric Studies

to injection. This is due to the increased flow rates resulting in the nozzle chamber

pressure reaching the nozzle opening pressure earlier. For the idle case the injection

begins earlier for both the reduction and increase in pipe diameter. The earlier start of

injection associated with the increased pipe diameter agrees with the other two cases.

However, the earlier start of injection for the decreased pipe diameter is somewhat

unexpected although the decreased flow rates and the associated increased line pressure

is a possible explanation for this phenomena. The idle case being more sensitive to such

events than the other two cases.

The injection rate profiles for the nozzle orifice area variations are shown in


4.4.5 Pipe Length

The pipe length refers to the length of the pipe section between the delivery valve

chamber in the pump and the nozzle chamber. The primary effect of changing the pipe

length is to change the timing of injection. A longer pipe length delays the start of

injection and a shorter pipe length causes the injection to start earlier. This is because the

pipe length changes the time the pressure wave takes to travel down the pipe to the

nozzle. Tables 4.8 and 4.9 show the change of fuel injection quantity and timing with

pipe length, respectively.

Quantity, mm3 Pipe Length, mm

Lever position,

Pump speed

280 (-20%) 350 420 (+20%)

0%, 450rpm n/a 4.61 6.32(+37%)

22.72(+1%)

22.23(+1%)

50%, 1000rpm 22.53(0%) 22.50

100%, 2000rpm 21.22(-3%) 21.97

Table 4.8 : Fuel injection quantity variations with pipe length.

Time, ms Pipe Length, mm

Lever position,

Pump speed

280 (-20%) 350 420 (+20%)

0%, 450rpm n/a 2.376 2.384(+0.5%)

1.292(+5%)

0.904(-3%) ,

50%, 1000rpm 1.176(-4%) 1.228

100%, 2000rpm 0.876(-6%) 0.932

Table 4.9: Timing variations with pipe length.

For the 50% lever position, 1000rpm case and the 100% lever position, 2000rpm

case there is a negligible effect on the injection quantity. In fact figure 4.9 shows that the

160

Parametric Studies

injection profiles are hardly changed for these cases by varying pipe length. Again the

most dramatic effect is on the idle case (0% lever position, 450rpm). Somewhat

surprisingly the reduction of the pipe length by 20% has resulted in the nozzle valve

failing to open. One possible explanation for this is that the shortened pipe length has

effected the timing of the interaction of forward and reflected pressure waves in such a

way that the pressure in the nozzle chamber never reaches the nozzle opening pressure.

When the pipe length is increased by 20% the timing is hardly effected although the

injection quantity increases due to a larger peak injection rate and a longer injection

duration. Again the effect on the timing of the interaction of pressure waves in the high

pressure pipe is one possible explanation for this phenomena.

The injection rate profiles for the pipe length variations are shown in figure 4.9 at

the end of this chapter.

4.4.6 Initial Nozzle Force

The initial nozzle force is the force acting on the nozzle valve to keep it closed.

This force comes from the initial compression of the needle spring set up in the nozzle.

As was shown in figure 4.2 the initial nozzle force is one of the significant forces acting

on the nozzle valve. As a result of this it has an effect on the nozzle opening and closing

pressures; a higher initial nozzle force resulting in larger nozzle opening and closing

pressures. In fact for the idle case (0% lever position, 450rpm) the effect of increasing

this force by 20% is such that the pressure built up in the system is insufficient to open

the nozzle valve and, hence, no injection. Table 4.10 shows the effects of initial nozzle

force variations on the injection quantity for the three test cases.

Quantity, mm3 Initial Nozzle Force, N

Lever position,

Pump speed

72 (-20%) 90 108 (+20%)

0%, 450rpm 9.04(+96%) 4.61 n/a

50%, 1000rpm 24.56(+9%) 22.50 20.18(-10%)

20.60(-6%)100%, 2000rpm _ 23.18(+6%) 21.97

Table 4.10 : Fuel injection quantity variations with initial nozzle force.

The fuel injection quantity invariably increases with decreased force. This is

because the decreased nozzle opening and closing pressures result in the needle valve

remaining open for longer and increasing the duration of injection. The effect is

noticeably stronger for the idle case (0% lever position, 450rpm) where the pressure will

be lower but will last longer. The peak injection rate is almost unaffected by the force

changes. This situation is similar but reversed for an increased force.

161

Parametric Studies

Table 4.11 shows the effect of these force changes on the injection timing.

Time, ms Initial Nozzle Force, N

Lever position,

Pump speed

72 (-20%) 90 108 (+20%)

0%, 450rpm 2.052(-14%) 2.376 n/a

50%, 1000rpm 1.140(-7%) 1.228 1.312(+7%)

0.984(+6%)100%, 2000rpm 0.876(-6%) 0.932

Table 4.11: Timing variations with initial nozzle force.

As expected the lower force allows the nozzle valve to open earlier and the larger

force keeps the nozzle valve shut slightly longer. Again the effect is most notable for the

idle case ( 0% lever position, 450rpm ). For the idle case the start of injection is affected

significantly more than the end of injection. This is because the rise of the pressure,

which determines the start of the injection, is speed dependent and the fall of the

pressure, which controls the end of injection, is determined by the spill rate which is

similar for all three test cases.

The injection rate profiles for the initial nozzle force variations are shown in


4.4.7 Maximum Needle Lift

It is important to bear in mind the relationship between the effective flow area

through the valve and the valve lift when performing a parametric study. This is because

this area will increase with valve lift upto a critical value beyond which it can not

increase. This critical value will be the cross-sectional flow area of the 'nozzle' pipe (i.e.

the pipe section between the nozzle chamber and the sac volume). This area was shown

in the section B-B' in figure 2.5. The relationship between the valve lift and the effective

flow area for the Stanadyne nozzle used in this work is shown in figure 4.11, overleaf.

The effective area shows a sudden transition from a linear rise to a constant value. In

reality, there will actually be a smooth change between the two, i.e. there will be a radius

on the curve between the linear rise and the constant value. However, this was not

considered to be significant in relation to the state of the model at present.

162

0

0.1

0.2

0.3

0.4

•cr

Needle Lift, mm

Parametric Studies

Figure 4.11 : Effective flow area against needle lift.

This shows that the critical valve lift is 0.1mm when the effective flow area has

reached its maximum value of 0.5mm2. The maximum valve lift used in the

experimentation was 0.32mm, well above the critical value. Therefore, if a parametric

study was performed in a similar manner to the previous parameters in this chapter then

no change in the effective flow area would be experienced and their would be no change

in the injection rate profile. To insure that the effective flow area was varied four values

were used upto and including the critical value. These values were 0.025mm, 0.050mm,

0.075mm and 0.1mm. The effect of these variations on the fuel injection quantity are

shown in table 4.12, below.

Quantity, mm3 Maximum needle lift, mm

Lever position,

Pump speed

0.025 0.050 0.075 0.100

0%, 450rpm 2.95 3.95 4.32 4.52

50%, 1000rpm 14.26 17.61 19.81 21.42

100%, 200Orpm 14.17 17.19 19.20 21.00

Table 4.12 : Fuel injection quantity variations with maximum needle lift.

For all the test cases the greater the maximum needle lift the greater the fuel

injection quantity due to the greater effective flow area. The maximum needle lift has no

effect on the start of injection and the increased fuel injection quantities are primarily due

to an increase in the peak injection rates. However, the injection duration is also slightly

longer as the maximum needle lift is increased due to the needle valve taking longer to

close for a larger lift. The rate of valve closure being consistent for each case.

The injection rate profiles for the maximum needle lift variations are shown in


163

Parametric Studies

4.4.8 Pumping Chamber Pressure

The pumping chamber pressure is the input to the model and was manipulated to

simulate variations of +1- 10% in the pressure profile. This manipulation was done using

the spreadsheet software (Microsoft Excel) which was also used to examine the output

files. The whole pressure profile was increased or decreased by 10% so the peak

pumping chamber pressure as well as the rate of pressure rise was changed. Figure 4.13

shows the three different pressure profiles used for each of the three test cases.

There were two main reasons for conducting a parametric study on variations in

the pumping chamber pressure profile. The first was to see how sensitive the injection

rate is to variations in the measurement of this pressure, these variations taking the form

of experimental errors. Secondly, because the model has been shown to be particularly

good at measuring the start of injection a possible application of using the pumping

chamber pressure alone to provide information for an electronic control unit has been

suggested. Therefore, it is important to see how sensitive to variations in the pumping

chamber pressure the injection quantity and timing are.

Quantity, mm3 Pumping chamber pressure

Lever position, -10% no change +10%

Pump speed

0%, 45Orpm n/a 4.61 5.19 (+13%)

50%, 1000rpm 21.00 (-7%) 22.50 25.00 (+11%)

100%, 2000rpm 19.97 (-9%) 21.97 23.27 (+6%)

Table 4.13 : Fuel injection quantity variations with pumping chamber pressure.

Table 4.13 shows the fuel injection quantity variations with pumping chamber

pressure. The fuel injection quantity increases with increased pumping chamber pressure

for all cases. This increase is of similar or greater magnitude to the changes in the other

parameters even though the pumping chamber pressure is varied by only 10% in

comparison to the 20% figure used for the other parameters. This is because the

increased pumping chamber pressure not only increases the injection duration but the

peak injection rate as well. This is due to the increased rate of pressure rise and the

increased peak pressure, respectively. However, for the idle case the reduction of the

pumping chamber by 10% has resulted in the nozzle valve failing to open. This is due to

the decreased pumping chamber pressure failing to generate sufficient pressure at the

nozzle to open the valve.

164

Parametric Studies

Time, ms Pumping chamber pressure

Lever position, -10% no change +10%

Pump speed

0%, 450rpm n/a 2.376 2.265 (-5%)

50%, 1000rpm 1.278 (+4%) 1.228 1.178 (-5%)

100%, 2000rpm 0.952 (+2%) 0.932 0.912 (-2%)

Table 4.14: Timing variations with pumping chamber pressure.

Table 4.14 shows the timing variations with pumping chamber pressure. For all

cases the increased pumping chamber pressure causes an earlier start to injection as the

rate of pressure rise is higher thus reducing the time required to reach the nozzle opening

pressure. There is a similar but reversed situation for decreases in the pumping chamber

pressure.

The injection rate profiles for the pumping chamber pressure variations are shown

in figure 4.14 at the end of this chapter.

4.4.9 Other Parameters

The mass of the needle valve only effects the inertia of the nozzle valve as the

model currently stands. This was shown to have a negligible effect in figure 4.2 so valve

mass variations have no effect on the injection rate profile.

Although the spring rate determines the initial valve force it is used in the model

to only calculate the additional force on the valve caused by the valve opening and

further compressing the spring. This additional force was shown in figure 4.2 to have a

small effect on the nozzle forces in comparison to the initial valve force and the nozzle

chamber area so was not included in this study. The effect of these variations will be

similar to the initial nozzle force and nozzle chamber area variations but smaller.

Interestingly the variations in the sac volume provided no variations in the

injection rate. This is because the small size of the sac volume resulted in the percentage

changes used in this parametric study causing only a small physical change. The

assumptions of one dimensional flow and concentrated volumes being used to simulate

chambers, which means that no account of the shape of the chamber is accounted for,

also result in the sac volume variations having a negligible effect. However, this does

highlight the need to expand the model of the nozzle as sac volume variations are well

known to affect injection characteristics.

165

Parametric Studies

4.5 Applications

The simulation presented and used in this thesis have several applications. The

first comes direct from the parametric study presented in this chapter. That is that it can

be used to examine the effect of the variation of parameters on the injection rate and

even other injection process characteristics such as the line pressure and needle lift. Such

a study using experimental methods would clearly be more time consuming and

expensive. The simulation can also examine the variation of parameters which cannot be

measured experimentally due to restricted access or the inability to measure the

parameter without significantly changing its value. The models can be used independently

or in conjunction with experimental data thereby reducing the required number of

experimental parameters.

The simulations can also be used in conjunction with existing combustion models

to provide accurate information on the timing and quantity of fuel injected as currently

these are typically used as inputs to such models. This will extend the scope of such

simulations to include the fuel injection system.

One application which arose directly during development of the models was the

possibility of using the code to determine fuel injection timing and quantity just from the

pumping chamber pressure signal. The pumping chamber pressure signal could then be

measured and used as an input to an electronic control unit (ECU) to provide such

information rather than measuring the line pressure and or the needle lift.

4.6 Summary

The nozzle simulation based on an experimentally measured line pressure is

unsuitable for use in a parametric study. This is because the line pressure input cannot

vary with parametric changes as would occur in reality. This effect was shown using the

pump-pipe-nozzle simulation.

The most significant forces acting on the nozzle were shown to be from the

pressurised fuel although the initial force from the nozzle spring was also shown to be

significant particularly for the idle case (0% lever position, 450rpm) when the pressures

are relatively low. From this the parameters which would have the most effect on the

needle lift and, therefore, the injection timing and duration could be deduced.

The most significant parameter for determining injection quantity and peak

injection rate was found to be the nozzle orifice area which provided significantly large

changes for relatively small physical differences. However, variations in the nozzle orifice

area have no effect on the injection timing. Increasing the nozzle chamber area increased

the injection quantity and caused an earlier start to injection. Increasing the nozzle

chamber volume increased the fuel injection quantity and caused the injection to begin

166

Parametric Studies

slightly earlier. Increasing the pipe diameter had a negligible effect on the injection

quantity and caused the start of injection to begin earlier. Increasing the pipe length also

had a negligible effect on the injection quantity but delayed the start of injection.

Increasing the initial nozzle force reduced the injection quantity and delayed the start of

injection. Changing the maximum needle lift so that the maximum effective flow area

reduced also reduced the injection quantity but had no effect on the timing.

For all the parametric studies the idle case (0% lever position, 450rpm) proved to

be the most difficult to handle and caused different effects to those described above. This

is because of the relatively long time that the pressure signal lasts at low speed and

because at idle the pressures being generated are just sufficient to open the nozzle.

167

Parametric Studies

1..al

.0

1..=col41.iL.am

0.96mm (-20%) 1.44mm (+20%)1.2mm

c)c)ON

0

I

100% lever, 2000rpm

S

c)

CD

C..

en

0

.

....

...,..•‘

0 1 2

Time, ms

3 4

1...vs-a

i.=V2WI41.16.

0.4

.0<0

4

vz.

cQ

50% lever, 1000rpm

•zi-

C>0eV

..

0 1 2

Time, ms

3

C0

1...as c).0 c)

CA4.71...=

4n 0<Leu. 0

rzi .--n

0

4

. .0% lever, 450rpm

.. .•

.

..

•

.

.

.... '

.. . .

.. 'S

.- .. .

`...

0 1 2

Time, ms

3

Figure 4.1 : Effect of pipe diameter variations on line pressure (nozzle end).

168

Parametric Studies

1...os

az.

s...=rnGolel)I.

gt4

5.341=12 (-20%) 8.02mm2 (+20%)6.68mm2

c)CON

c,0

100% lever, 2000rpm

v)

0c)

• • •

(...)

CI

40 1 23

Time, ms

1...0:

C1...=tAWI4146,

Covz,

c)

I

.... ,•. .

50% lever, 1000rpm

C)C,

0

‘..

0 1 2

Time, ms

3 4

CPS

.'eV1.=CA4.)

0.1

CC

4

..0 C

I.

,....,

0

esi

C)C)

.

l .. .,.

A.....-...;IloiNK1. A --.

0% lever, 450rpm

0 1 2

Time, ms

3

Figure 4.2 : Effect of nozzle chamber area variations on line pressure (nozzle end).

169

Parametric Studies

4.174.)1..

- -- 4 5 • 61 - - - - 2 3

c)c))c)

c)c)

1w•s

•

.

.

1100% lever, 2000rpm

-4-

el

0 -

0

..

.. ..

-

•'S

2

Time,

aa

• a

'

ms

.,..._Lie...,....:.:

31 4

Z

uL.0

Wm

CC

4

•zi-

0esi

0

1 ,,.....

• .,

.

.

50% lever, 1000rpm

.. = •

iI

• = •

ai

•

-"a

.•• ='•• •• •••••• n • • • ••• •• •••••"..

0 1 2

Time, ms

3

CC(-)

4 c>csi

c.o1.0 0

4T• 0

CD

4

I0% lever, 450rpm

C

'

. •• •

M 0 = = =====

s•

sa •

•••• timm..1••••

0 I 2

Time, ms

3

1. Force from pressurised fuel in nozzle chamber.2. Force from pressurised fuel in sac volume.3. Initial force on valve from spring.4. Damping force of spring.5. Spring force due to nozzle opening.6. Inertia.

Figure 4.3 : Forces acting on the nozzle valve.

170

Parametric Studies

i

E

4.

.-4,..,eU

• nn10

on1

4

- - - - 0.101mm2 (-20%) 0.127mm2 0.153mm2 (+20%)

C

IFa),

-1- i100% lever, 2000rpm

C

a

.-

0r

0 1 2 3

Time, ms

g1

E

4...,

C.?4)._,.

Cen

pi ...,AS.,....k

50% lever, 1000rpm

.„,

. ,._.

C II,0 1 2 3 4

Time, ms

CCA

E

nE

E

.... c,4 —00..—..:c.,4,._,0•_.

C

G.

0% lever, 450rpm

0 1 2 3 4

Time, ms

Figure 4.5 : The effect of nozzle orifice area variations on the injection rate.

171

Parametric Studies

g

Eo;

1:4co•...4...cotu

•—,c

•—n

- - - - 5.34=2 (-20%) 8.02mm2 (+20%)6.68mm2

oTr I

100% lever, 2000rpm

rsi

oII

—..

1

C

0 1 2

Time, ms

3 4

g,.

Eo;

4..

.4=...,.-,.-

C

4

Icn

50% lever, 1000rpm

pi

.

1

.

I...

. I

0 1 2

Time, ms

3

CcsiE

.,

E0.;

IF14 CC4.-C0WCW

• n1CIni

0

4

10% lever, 450rpm

0 1 2

Time, ms

3

Figure 4.6 : The effect of nozzle chamber area variations on the injection rate.

172

Parametric Studies

ifte

Eor

4=.

.....c.,..—,.—

- - - - 252mm3 (-20%) 378mm3 (+20%)315mm3

o,:r

es),

I100% lever, 2000rpm

(9

c>\

_

.

\

\

0 1 2

Time, ms

3 4

i..k

Ec;4'cdcc

.4.4Ca•a.--$c

n—•

C

4

(--)

Ien

• \

50% lever, 1000rpm

(-1

.. .

.

.

C

.1

••.

.s

IA

0 1 2

Time, ms

3

E1

E

4.0

4..

7_1,.,.

.—,C

0.1

C

4

(-1

c

—

cp •

• .

0% lever, 450rpm

...•.

...1

•

.

.

.

1

I _ IT

0 1 2

Time, ms

3

Figure 4.7 : The effect of nozzle chamber volume variations on the injection rate.

173

Parametric Studies

i9.'ssc4c0. or4.0Cd4/

• ..•0

I.n4

- - 0.96mm (-20%) 1.44nun (+20%)1.2mm

c).1-

es:,)

I100% lever, 2000rpm

c,

, , .- ..

rl

C.

....

•''''.

C)

/8

88

•

Ili, .

0 1 2

Time, ms

3 4

g1E

47

4

.....U..-,0-

eD

4

en

c,r.4

.

'. -

50% lever, 1000rpm

8

/

..

•.

.,

I,

. .

.•

0 1 2

Time, ms

3

CNI

E1

ECvsc,

0.=)..*:U40

.—,0

In1C)

4

, •i

g.

0% lever, 450rpm

Time,

2

ms

.8

8iiI//

LI

30 1

Figure 4.8 : The effect of pipe diameter variations on the injection rate.

174

0

0% lever, 450rpm

- - - - 280nun (-20%)

350nun

420mm (+20%)

0

1

2

3

4

Time, ms

0

1

2

3

4

Time, ms

0

I 2 3 4

Time, ms

1

11.

100% lever, 2000rpm

r.....

.

I

l..

aa

•

••I

1aIa*a

I a A

50% lever, 1000rpm

I ..

• .

1. ..• .•

•..

..1

., A

0V'

0re)

0NI

0,—.

0

0en

0Cl

vn1

0

Parametric Studies

Figure 4.9 : The effect of pipe length variations on the injection rate.

175

- - - - 72N (-20%)

90N

108N (+20%)

0

2

3

4

Time, ms

0

1

2

3

4

Time, ms

0

1

2

3

4

Time, ms

1100% lever, 2000rpm

117Aa Oa

i.

50% lever, 1000rpm

II

I

I

.

".

. 111144,I

0% lever, 450rpm

I••sa•

I•I•e

esaa•I ,

•

Il 1

0•rl-

0ce)

0C.4

0vnI

0

0en

0CA

0,—.

0

0cs1

0

Parametric Studies

Figure 4.10 : The effect of initial nozzle force variations on the injection rate.

176

Parametric Studies

i1

E

...:

gco

*4.0c.oa.)

..-5cit

- 0.075nun 0.1mm- 0.025mm 0.05nun

c)•zr

o4111

100% lever, 2000rpm

(.4

cp

0 1

/

.

• ••• n a

.•

a

3 42

Time, ms

EØk

E

a.

•ImiCa0

CW

• .$0

/nI

o

4

en1

50% lever, 1000rpm

,

0-

0 1

/

32

Time, ms

tr,.--.

i 0%..,s

E °tu*0alg00 ir)

'4...c.4eu

• —,c1.0

c) -

4

lever, 450rpm

.

•1

0 1

Time,

2

ms

..

.

3

Figure 4.12 : The effect of maximum needle lift variations on the injection rate.

177

± 0%- - - " -10% +10%

0

1

2

3

Time, ms

0

1

2

3

4

Time, ms

0

1

2

3

4

Time, ms

1

100% lever, 2000rpm

..

.

0

I

50% lever, 1000rpm

aa

P

10 .%•

a ' '

.0"NrolC

0% lever, 450rpm—

,"' •

s.I

a

• - a

Ia

a r.a

t

, . .z :

0

Parametric Studies

Figure 4.13 : Pumping chamber pressure variations for the three test cases.

178

al

I 0% lever, 450rpm

0CV

00 1 2 3 4

0

± 0%- '' '' - -10% +10%

0

1

2

3

4

Time, ms

0

1

2

3

4

Time, ms

Time, ms

1

100% lever, 2000rpm

,

AI,.

• •••

50% lever, 1000rpm

•••

•

•

\

0en

0CV

0

0

0CA

Parametric Studies

Figure 4.14 : The effect of pumping chamber pressure variations on the injection rate.

179

Conclusions

5. CONCLUSIONS

5.1 Conclusions of the Computational Programme 181

5.2 Conclusions of the Experimental Programme 183

5.3 Recommendations for Future Work. 184

180

Conclusions

Chapter 5

CONCLUSIONS

5.1 Conclusions of the Computational Programme.

The single most important conclusion of this work is that it is possible to simulate

adequately the high pressure side of a production pump-pipe-nozzle thel injection system

used in direct-injection diesel engines. This can be achieved by dividing the system up

into volumes, pipes and valves and using basic principles such as the conservation of

mass, the equilibrium of forces, orifice flow and the continuity and momentum equations

for the pipe flow. These equations which are either ordinary or partial differential

equations can be solved with the 4th-order Runge Kutta method or the Method of

Characteristics, respectively.

It is also possible using currently available software packages to make such a

simulation quick, easy to use and to eliminate the need for detailed programming

knowledge. The simulation presented here used Microsoft's QuickC for Windows. This

allowed the use of dialog boxes not only to select the geometric parameters but also to

select any input files required for the simulation run. This means the programs can be run

by people who have no programming experience. The models were also structured in a

modular format for flexibility; this means that the programming for each separate element

of the fuel injection system was kept independent from the others except at their

boundaries.

Several features were incorporated into the models to enhance their accuracy.

These included nozzle or needle valve bounce to provide a more realistic needle lift

profile despite the fact that the predictions were based on experimental data. Leakage at

the nozzle was ignored although several correlations were examined for incorporation

into the pumping chamber; however, at this stage of development, a pumping chamber

pressure input file was used to remove the need for simulation of fuel leakage. Friction

factor was allowed to vary as a function of the Reynolds number and the fuel properties

were allowed to vary with pressure. Spray characteristics based on previous correlations

were used together with variable discharge coefficients which decreased the fuel injection

rate at low needle lifts, in agreement with experimental observations.

The simulation of cavitation has been a major problem not only in this work but

also in all previous attempts to simulate the complete fuel injection system. Previously

developed correlations were used with some success although the simple approach of

zeroing the pressure and flow rate at the point of cavitation has provided some

encouraging results. Unfortunately, from a simulation point of view, the experimental

181

Conclusions

system used a Bosch VE type pump connected to Stanadyne pencil-type nozzles showed

no sign of large scale cavitation. Therefore, there was little or no opportunity to examine

the validity of the correlations used in the simulation programme.

Although the development time for the computer simulation models was longer

than the time to set up and analyse the data from the experimental rig, such models offer

numerous advantages over experimental methods. Once the model has been developed

and validated the time to simulate new FIE designs or different FIE systems is expected

to be significantly lower than the time to set-up new experimental rigs. This will naturally

provide huge savings in cost but the data obtained will also be more extensive since with

a simulation it is possible to examine the variation of parameters throughout the system

regardless of the ability or inability to properly instrument them. Using the work done

here let's compare as an example the experimental and computational work performed.

Eight experimental parameters were measured and, by using only the test rig system data

obtained at only these eight points can be analysed whereas the simulation programme

can provide data at any desired point in the system. In addition the computer generated

signals do not suffer from noise which in turn eliminates the need for filtering which has

been shown to affect the time base of the measured signal.

On the other hand, there are serious limitations in the use of the nozzle simulation

programme using experimental data as input with respect to parametric studies. This is

because this input to the simulation is fixed and cannot react to the parametric changes as

would occur in reality. However, the pump-pipe-nozzle simulation could be used for

parametric studies and showed some interesting results. The most significant parameter

for determining injection quantity and peak injection rate was found to be the nozzle

orifice area which provided significantly large changes for relatively small geometric

differences. However, variations in the nozzle orifice area have no effect on the injection

timing. Increasing the nozzle chamber area has resulted in an increase of the injection

quantity and an earlier start of injection. Increasing the nozzle chamber volume increased

the fuel injection quantity but caused the injection to begin slightly earlier. Increasing the

pipe diameter had a negligible effect on the injection quantity and caused the start of

injection to begin earlier. Increasing the pipe length also had a negligible effect on the

injection quantity but delayed the start of injection. Increasing the initial nozzle force

reduced the injection quantity and delayed the start of injection. Changing the maximum

needle lift so that the maximum effective flow area was reduced, also reduced the

injection quantity but had no effect on the injection timing. From all the parametric

studies examined in this research programme the idle case (0% lever position, 450rpm

pump speed) proved to be the most difficult to simulate and caused some opposite

effects to those described above. This is probably due to the relatively long time that the

pressure signal lasts at low speeds which means prolonged time for the interaction of the

182

Conclusions

pressure waves and the fact that at idle the pressures being generated are just sufficient

to open the nozzle making it more sensitive to parametric variations.

5.2 Conclusions of the Experimental Programme

The experimental side of this work involved instrumenting a Bosch VE type

distributor pump to measure eight parameters which were used to validate the complete

pump-pipe-nozzle simulation as well as the nozzle simulation developed in this work.

This validation has shown that the models are capable of predicting the start of injection

accurately but less so the end of injection. As a result of this, the fuel injection quantities

were slightly under predicted. A possible explanation is that the models predict well the

timing of pressure wave interactions but tend to under predict their magnitude.

The experimental results obtained over the full speed and lever position range of

the pump have shown that it is important to be careful with the terminology when

referring to pressures throughout the injection system. In previous simulations the line

pressure (nozzle end) has been referred to as the injection pressure but this is not

accurate. Not only is there a time difference between the line pressure (nozzle end) and

the actual injection pressure at the sac volume but their profiles are also different. The

injection pressure has been obtained from the Bosch injection rate meter which

unfortunately cannot be used in a running engine.

An experimental technique using a capacitor transducer has been used to measure

the delivery valve lift with some degree of success. This technique involved remaking the

delivery valve stop of a Bosch VE type pump and placing two capacitor sleeves in its

place. The developed method has the advantage of adding no weight to the valve and to

introduce no change to the size or shape of the delivery valve chamber. However, it is

sensitive to changes in the fuel between the capacitor and the delivery valve as well as to

the movement of the delivery valve. This was considered to be a problem particularly

when cavitation occurs in the delivery valve chamber which is likely to occur at spill or

just after.

The needle lift transducer signal was found to rise before the start of the actual

needle lift. This was shown to be due to the build up of pressure in the nozzle causing the

probe and the coil used to measure the lift to move in relation to each other.

Finally, the signal from a Bosch injection rate meter tended to over predict the

fuel injection rate when the signal was not filtered: The oscillations observed in the

unfiltered signals from the Bosch meter were removed and the signals re-integrated to

calculate the fuel injection quantity. These new values were found to match more closely

the burette measurements of the fuel injection quantity averaged over 500 consecutive

injections.

183

Conclusions

5.3 Recommendations for Future Work

The pump-pipe-nozzle simulation programme should be extended to include

simulation of the pumping chamber pressure based on upstream geometric data. This will

involve determining the various port openings in relation to the plunger angle as well as

the cam profile for the plunger lift. This approach will eliminate the need for

experimental inputs and will allow the examination of other system parameters such as

the cam profile. The major problems to be encountered in extending the simulation in this

way will be the extra variables in the program which is already near its limit, the

determination of the various port openings accurately, as any variations are likely to have

a significant effect and the simulation of leakage. Fuel leakage was examined in this work

and several correlations were used but there was no reliable way of validating these flows

using the current system.

Further work on the prediction of cavitation in the model is also recommended,

especially within the nozzle discharge holes where emerging evidence is suggesting that

cavitation at this point can affect the spray formation. The problem with the current

experimental system is that no large scale cavitation has been detected and the available

details of the model at the nozzle end do not allow the simulation of cavitation in the

discharge holes. This leads to the recommendation for increasing the details of the nozzle

simulation, particularly the flow in the sac and the discharge holes. However, this will

require 3D modeling of the sac volume which is time consuming and expensive but

highly desirable.

Developing the current method for determining needle bounce so that

experimental data is not required would also be advantageous and further work on the

experimental set-up, particularly the delivery valve lift transducer, would prove useful. A

possible alternative to using the capacitance transducer for the delivery valve lift is an

inductance transducer and this approach is recommended.

Finally, due to the limitations of the PC system in terms of the number of

variables that can be used and the recommendation for extending the model at both the

pump end to simulate the pumping chamber and the inclusion of 3D modeling at the

nozzle end, a switch to a workstation-based UNIX system may be necessary. This will

also have the advantage of being more compatible with existing combustion and emission

simulations which generally use this system.

184

References

REFERENCES

Aguirre,I.A., Quiros,A.L. and Rodriguez,J.V., Computer Simulation of Diesel Fuel

Injection Equipments, SIA Paper No 92003, International Congress on 'The Powertrain:

development and future', Valencia, 14-15 May, 1992.

Arcoumanis,C. and Baniasad,S.M., Analysis of Consecutive Fuel Injection Rate Signals

Obtained by the Zeuch and Bosch Method, SAE International Congress and Exposition,

SAE paper 930921, 1993.

Arcoumanis,C., Baniasad,S and Fairbrother,R.J., Simulation of Fuel Injection Under

Diesel Engine Conditions, Proc ICCME, Shiraz, Iran, 1993.

Arcoumanis,C., Baniasad,S and Gibbins,J.R., Measurement and Analysis of Injection

Rate Variations in DI Diesel Engines, IMechE Seminar on 'Diesel Fuel Injection

Systems', April 1992.

Arcoumanis,C. and Fairbrother,R.J., Computer Simulation of Fuel Injection Systems for

DI Diesel Engines, SAE 922223, 1992.

Baniasad,M.S., Analysis of Fuel Injection Rate in Diesel Injection Systems, PhD Thesis,Imperial College(London), January 1994.

Becchi,G.A., Analytical Simulation of Fuel Injection in Diesel Engines, SAE paper

710568, 1971.

Bergwerk,W., Flow Pattern in Diesel Nozzle Spray Holes, Proc. IMechE Vol 173

No.25, 1959.

Bosch, Automotive Handbook, 2nd Edition, Delta Press Limited, 1986.

Dow,R.B. and Fink,C.E., Computation of some Physical Properties of Lubricating Oils

at High Pressures. Part I, Journal of Applied Physics Vol. II, p353-357, May 1940.

El-Erian,M.F., Wylie,E.B. and Bolt,J.A., Analysis and Control of Transient Flow in the

System. Part 1 - The Analytical Control Method. Part 2 - Design Results of Controlled

After - Injection, University of Michigan, SAE Paper 730662, 1973.

185

References

Erdmann,H-D and Schindler,K-P, Experimental and Theoretical Analysis of Injection

Systems of Diesel Engines, IMechE Conf, Paper C125/82, 1982.

Gibson,D. H., A Flexible Fuel Injection Simulation, SAE paper 861567, 1986.

Gibson,D.H., Dionne,P.J. and Singhal,A.K., A Numerical Model for Elastohydrodynamic

Analysis of Plunger and Barrel Clearances in Fuel Injection Equipment, SAE Paper

900823, 1990.

Giffen,E. and Rowe,A.W., Pressure Calculations for Oil Engine Fuel Injection Systems,

Proc. IMechE, Vol 141, 1939.

Gilkin,P.E., Fuel Injection in Diesel Engines, Automobile Chairman's Address, 1985.

Goyal,M, Modular Approach to Fuel Injection Simulation, SAE paper 780162, 1978.

Henein,N.A., Singh,T. and Rozanski,J., Characterisation and Simulation of a Unit

Injector, SAE paper 750773, 1975.

Heywood,J.B., Internal Combustion Engine Fudamentals, McGraw-Hill, 1988.

Hipson,P.D., Using QuickC for Windows, Que Corporation, 1992.

Kegl,B., Zambare,V.V., Cernej,A.and Dobovisek,Z., A Parametric Study of Fuel

Injection Performance by Calculation, IMechE Diesel Fuel Injection Systems Seminar,

April 1992.

Knight,B.E., Fuel Injection System Calculations, Proc. Auto Div., IMechE, No 61,

1960-61.

Koike,M., Imai,K., Yamada,M., Kamiya,M. and Yanagihara,H., Simulation of Abnormal

Fuel Injection in Diesel Engines, SAE paper 900345, 1990.

Krepec,T. and To,C.H., Optimization of Diesel Injectors Using Computer Aided

Technique, SAE Paper 881855, 1988.

Kumar,K., Gaur,R.R., Garg,R.D. and Gajendra Babu,M.K., A Finite Difference Scheme

for the Simulation of a Fuel Injection System, SAE paper 831337, 1983.

186

References

Kumar,S. and Watson,H.C., A Regression Model for Describing the Fuel Injection of

Diesel Fuel. Seed Oils and the Methyl Esters of Seed Oils, IMechE, 1989.

Lee, Hang-Kyung, Modelling Rotary Diesel Fuel Injection Equipment with Rate Control

to Reduce Noise and Emissions, PhD Thesis, University of Southampton, May 1994.

Marcic,M. and Kovacic,Z., Computer Simulation of the Diesel Fuel Injection System,

SAE paper 851583, 1985.

Marcic, M., Computer Simulation of the Diesel Fuel Injection Nozzle, SAE paper

930925, 1993.

Matsuoka,S., Yokota,K., Kamimoto,T. and Igoshi,M., A Study of Fuel Injection

Systems in Diesel Engines: Parts I & II, SAE papers 760551&760552, 1976.

Meier,G.E.A., Chaves,H. and Bode,J., The Influence of Cavitation on Spray Formation

of Diesel Injection Nozzles, 89 AutoTech Exhibition & Congress, Integrated Diesel

European Action (IDEA) I, C399/13 Seminar, 1989.

Parsons,M.G. and Harkins,R.W., Investigation of Fuel Injection System Cavitation

Problems on the MV James R Barker . MV Mesabi Miner and MV William J. De

Lancey, Marine Technology, Vol 22, No 3, pp 219-237, July 1985.

Press,W.H., Teukolsky,S.A., Vetterling,W.T. and Flannery,B.P., Numerical Recipes in C

: The Art of Scientific Computing, Second Edition, Cambridge University Press, 1992.

Romig,B.E., Strunk,R.D. and Weinert,M.S., Performance Comparison of Unit Injector

and Pump-Line-Nozzle Injection Systems, SAE Paper 840274, 1984.

Russell,M.F. and Lee,H.K., Modelling Diesel Injection Rate to Control Combustion

Noise, IMechE Conf. 'Vehicle NVH & Refinement', 1993.

Schweimer,G.W. , Schlindler,K.P. and Oetting,H., The Physics of Fuel Injection in

Diesel Engines, International EAEC Conference on New Developments in Power Train

and Chassis Engineering, Strasbourg, 3-5 June 1987.

Scullen,R.S. and Hames,R.J., Computer Simulation of the GM Unit Injector, SAE paper

780161, 1978.

187

188

References

Smith,W.J. and Timoney,D.J., Fuel Injection Rate Analysis - A New Diagnostic Tool for

Combustion Research, SAE paper 922224, 1992.

Streeter,V.L. and Wylie,E.B., Fluid Mechanics, McGraw-Hill, 1983.

Suzuki,K., Honda,A., Shizuo,S. and Kibune,M., Study of Abnormal Fuel Delivery

Characteristics in High Pressure Injection Syatems, Nippondenso Co Ltd & Aichi

Prefecture, SAE paper 821073, 1982.

Takaishi,T., Tateishi,M. and Kunimoto,E., Dynamic Response of Fuel Injection System

of Diesel Engines, IMechE Seminar on Engine Transient Performance, November 1990.

Takaishi,T., Tateishi,M., Kunimoto,E., Matsuo,T., Nagae,Y. and Oikawa,H., Prediction

of Cavitation Erosion in Diesel Engine Fuel Injection Systems, SAE paper 871631, 1987.

Vogel,W., Simulation von Einspritzvorgangen auf dem Kleinrechner, MTZ 1974 35,

pp282-287, 1974.

Wannenwetsch,P. and Egler,W., A User-Friendly Program System for Digital Simulation

of Hydraulic Equipment, SAE paper 850532, 1985.

Wylie,E.B., Bolt,J.A. and El-Erian,M.F., Diesel Fuel Injection System Simulation and

Experimental Correlation, SAE paper 710569, 1971.

Xu,M., Nishida,K. and Hiroyasu,H., A Practical Calculation Method for Injection

Pressure and Spray Penetration in Diesel Engines, SAE Paper 920624, 1992.

Yamaoka,K. and Saito,A., Computer Technique for Evaluation of Cavitation

Characteristics of Certain Phases of Fuel Injection in Fuel Injection System, SAE Paper

730663, 1973 (with Discussion).

COMPUTER SIMULATION OF FUEL INJECTION FOR DIRECT … · BEng, ACGI. Thesis submitted for the degree...

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