THE UNIVERSITY OF MICHIGAN
INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING
SIMULATION AND CONTROL OF TRANSIENT FLOW
IN THE DIESEL INJECTION SYSTEM
Mohamed Fathy El-Erian
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy in the
University of Michigan
Department of Mechanical Engineering
1972
April, 1972
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To my wife and parents
ii

ACKNOWIEDGMENT
I would like to express my sincere appreciation to Professors
Jay A. Bolt and Benjamin E. Wylie, Co-Chairmen of my doctoral committee,
for suggesting this area of research. In particular, thanks are extended to Professor Bolt for his inspiration, guidance and valuable
advice throughout my graduate studies, to Professor Wylie for his
inspiration, guidance and valuable suggestions provided in numerous
discussions of the mathematical simulation and control techniques;
to Professor Victor L. Streeter for developing my initial interest
in studying transient flow problems and for his interest and cooperation throughout the course of the study; and to Professors Milton A.
Chace and Robert B. Keller for their participation and cooperation.
I am also indebted to Professor N. Abdou Henein for his sincere counsel during my undergraduate and graduate studies and for
developing my interest in the area of diesel engines.
The financial support of the U. S. Public Health Service,
and later the Environmental Protection Agency, is gratefully acknowledged. Without this support, this project could not have been completed. The financial assistance of the Chevron Research Company in
making possible purchase of needed equipment is also acknowledged.
I would like also to express my gratitude to the Mechanical Engineering
Department and the International Center of the University of Michigan
for their support in the form of tuition scholarships during my
graduate studies.
I would further like to extend my thanks to Mr. Bela Petry,
Mr. Arthur Bauer and Mr. Sam Onyegegbu, graduate students at the
University of Michigan for their able assistanyce during the course
111

of this study. The help of technicians and machinists in the Automotive Laboratory is also gratefully acknowledged.
For assistance in the preparation of the manuscript, I gratefully acknowledge the help of Dr. Ismail Eldumiati and Mx. Richard
Winsor for their valuable comments while editing the manuscript.
Thanks are also due to Miss Ruth Howard for typing the original manuscript, and to the staff of the Industry Program and the Office of
Research Administration of the University of Michigan for final preparation and publication of the manuscript.
Particular thanks are also due to my wife Magda for her
patience and understanding.
iv

TABLE OF CONTENTS
Page
ACKNOWLEDGMENT.....................iii
LIST OF FIGURES............. vii
LIST OF TABLES..............x..................... Xii
NOMENCLATURE..........................,,.. xiii
I. INTRODUCTION....1.....................................
1.1 Purpose and Background........1.........
1.2 Literature Review.............2
1.3 Scope of Investigation................. 9
II. TEST EQUIPMENT, INSTRUMENTATION AND EXPERIMENTAL
RESULTS...
2.1 Purpose of' The Experiment..,..,...,.11
2.2 General Description of the System..12
2.3 Instrumentation......... 18
2.4 Experimental Procedures. 26
2.5 The Experimental Results.. 29
2.5.1 The After-Injection Survey...... 30
III. BASIC EQUATIONS DESCRIBING THE DIESEL INJECTION
SYSTEM....................... 47
3.1 The Injection System Analysis ~~~~ 47
3.2 Basic Assumptions 0.... 0.....0.,............... 48
3.3 The Theoretical Formulation of the Model 50
3.3.1 Transient Flow in the Piping System 51
3.3.2 The Injection Pump...................... 57
3.3.3 The Fuel Injector....................... 61
IV. COMPARISON AND DISCUSSION OF THE SIMULATION AND
EXPERIMENTAL RESULTS...................,,........ 65
4.1 The Solution Technique......................... 65
4.2 Experimental Data for Comparison with the
Simulation Program Results..................... 68
4.3 Comparison of Results and Discussion........... 72
4.3.1 The Base Pressure...................... 84
4.3.2 The Mass Continuity.................. 85
4.3.3 The Effect of Variable Wave Speed... 87
4.3.4 The Effect of Distributed Friction.. 87
4.3.5 The Coefficient of Discharge........... 88
4.3.6 The Vapor Pressure...................... 88
v

V. THE DESIGN CONTROL PARAMETER AND FORMULATION OF THE
DESIGN PROGRAM...................................... 89
5.1 Introduction.............................. 89
5.2 Average Elastic Energy-The Control Parameter... 91
5.3 Description of the Design Method on the Pipe
Characteristic Plane........................... 95
5.4 Formulation and Solution of the Equations
Used in the Design Program...................... 102
5.4.1 Equations and Method of Solution at
Interior Points......................... 102
5.4.2 Equations and Method of Solution at
Pump-Pipe Boundary...................... 105
5.4.3 Equations and Method of Solution at
Injector-Pipe Boundary................ 106
5.4.4 Equations and Method of Solution of
Design Changes at the Pump.............. 110
5.5 Accuracy of the Design Program................. 114
VI. DESIGN PROGRAM RESULTS AND SIMULATION PROGRAM
VERIFICATIONS OF THE RESULTS......................... 118
6.1 Introduction................................... 118
6.2 Effect of the Average Elastic Energy Function
on the System Transient Pressures.............. 118
6.2.1 Average Elastic Energy and the Control
Valve Example 1.......................... 118
6.2.2 Average Elastic Energy and the
Redesigned Spill Port Example........ 122
6.3 Design Results and Verifications of the Control
Valve Example................................. 126
6.)4 Design Results and Verifications of the
Redesigned Spill Port Example *............... 130
VII. SUMMARY AND CONCLUSIONS......................... 145
REFERENCES -.......... o............... a 149
vi

LIST OF FIGURES
Figure Title Page
1 Diesel Fuel Injection System Test Equipment -
General View.................................. 13
2 Diesel Fuel Injection System Test Equipment -
Details of Pump, Pipe and Injector......... 14
3 Diesel Fuel Injection System Test Equipment -
Pump and Construction Details of Drive System... 15
4 Modified Injector and Its Instrumentation..... 16
5 Schematic Representation of Diesel Injection
System and Points of Pressure Measurement....... 17
6 Modified Pump Delivery Chamber.................. 21
7 Transducer Holder for the Injection Pipe Line... 22
8 Modified Injector Body and Nozzle.............. 23
9 Sectional View of Connector and Nozzle
Modification Details........................ 24
10 Oscilloscope Record of Transient Pressure in the
Injection Chamber and the Calculation of Ct
from the Trace................................ 28
11 Secondary Injection Zone in a Speed, Fuel
Delivery Plane............................... 31
12 Variation of Flow Resistance Coefficient with
Injected Flow 33
Injected Flow Rate.............................. 33
13 After-Injection Zone in a Speed, Load Plane..... 35
14 Effect of Load on Total Injection per Cycle for
Various Pump Speeds.36
15 Effect of Pump Speed on Total Injection per
Cycle for Various Load Conditions...............37
16 Effect of Load on 1Min Injection per Cycle for
Various Pump Speeds...................39
17 Effect of Pump Speed on Main Injection per Cycle
for Various Load Conditions.................. 40
vii

LIST OF FIGURES (CONT'D)
Figure Title Page
18 Effect of Load on After-Injection per Cycle for
Various Pump Speeds.............................. 41
19 Effect of Pump Speed on After-Injection per Cycle
for Various Load Conditions...................... 42
20 Effect of Load on Percent After-Injection for
Various Pump Speeds.........s...*.......... 44
21 Effect of Pump Speed on Percent After-Injection
for Various Load Conditions.................... 45
22 The Control Volume Used to Derive the Pipe
Equations................... 52
23 Characteristics in x-t Plane..................... 55
24 Sectional View of Injection Pump................. 59
25 Sectional View of Injection Nozzle............... 62
26 Oscilloscope Records of Transient Phenomena
in the Diesel Injection System................... 71
27 Pump Plunger Motion and Pump Port Areas; Rack
Control Setting = 0.509 in. 73
28 Comparison of Injection System Hydraulic Characteristics-Experimental and Computer Results,
800 RPM Pump Speed and 0.675 Rack Micrometer
(0.0818 lb. fuel injected/min. ).................. 75
29 Comparison of Injection System Hydraulic Characteristics-Experimental and Computer Results,
400 RPM Pump Speed and 0.509 Rack Micrometer
(0.0968 lb fuel injected/min. )................... 76
30 Comparison of Injection System Hydraulic Characteristics-Experimental and Computer Results,
800 RPM Pump Speed and 0.509 Rack Micrometer
(0. 1910 lb. fuel injected/min.).................. 77
31 Comparison of Injection System Hydraulic Characteristics-Experimental and Computer Results,
365 RPM Pump S'peed and 0.608 Rack Micrometer
(0.0514 lb. fuel injected/min. ).........y 78...

LIST OF FIGURES (CONT'D)
Figure Tit le Page
32 Comparison of Injection System Hydraulic Characteristics-Experimental and Computer Results,
405 RPM Pump Speed and 0.339 Rack Micrometer
(0. 1480 lb. fuel injected/min. )................. 79
33 Comparison of Injection System Hydraulic Characteristics-Experimental and Computer Results,
700 RPM Pump Speed and 0.426 Rack Micrometer
(0.216 lb. fuel injected/min.).................. 80
34 Comparison of Pressure in Pump Delivery Chamber,
Experimental and Computer Results for a Large
(900) Portion of Cam Shaft Angle................ 81
35 Sketch Showing the Method for Calculating the
Pipe Base Pressure.............................. 86
36 Schematic Representation of System Used to
Calculate the Average Elastic Energy............. 92
37 Transient Pressures and Average Elastic Energy
Versus Pump Cam Angle for Test No. 3 (Table III). 94
38 Injection System Performance on the Pipe x-t
Plane -99 —............................ 97
39 Design Method on the Pipe x-t Plane............. 99
1-0 Schematic Representation of the Control Valve
Position........................... 111
41 Simulation Check of Design Program Results
of Pump Delivery Chamber and Injector Transient
Pressures for Test No. 6 (Table IV)............. 115
42 Simulation Check of Design Program Results at
the Pump for Test No. 6 (Table IV).............. 116
43 Injection System Variables versus Pump Cam Angle.
Effect of Timing the Average Elastic Energy Drop.
The Control Valve Example, Test No. 3 (Table III) 120
44 Injection System Variables versus Pump Cam Angle.
Effect of the Shape of the Average Elastic Energy
Drop. The Control Valve Example, Test No. 6
(Table IV)...................,.... 121
ix

LIST OF FIGURES (CONT'D)
Figure Title Page
45 Injection System Variables versus Pump Cam Angle.
Effect of the Rate of the Average Elastic Energy
Drop. The redesigned Spill Port Example, Test
No. 6 (Table IV)......................123
46 Injection System Variables versus Pump Cam Angle.
Effect of the Shape of the Average Elastic Energy
Drop. The Redesigned Spill Port Example, Test
No. 6 (Table IV)...................... 124
47 Design Program Results of Injection System
Variables and Simulation Verification of these
Results. The Control Valve Example, Test No. 3
(Table III)..........-.-......... 127
48 Design Program Results of Injection System
Variables and Simulation Verification of
these Results. The Control Valve Example,
Test No. 5 (Table IV).......................... 128
49 Design Program Results of Injection System
Variables and Simulation Verification of these
Results. The Control Valve Example, Test No. 6
(Table IV).. -—................................. 129
50 Comparisons of Original Injection System Performance and Design Program Results of the Modified
System. The Redesigned Spill Port Example,
Test No. 4 (Table IV)............................ 132
51 Comparisons of Original Injection System Performance and Design Program Results of the Modified
System. The Redesigned Spill Port Example,
Test No. 5 (Table IV)........................ 133
52 Comparisons of Original Injection System Performance and Design Program Results of the Modified
System. The Redesigned Spill Port Example,
Test No. 6 (Table IV)........................, 134
53 Simulation Program Results of the Modified
Injection System. The Redesigned Spill Port
Example, Test No. 4 (Table IV)-................... 136
54 Simulation Program Results of the Modified
Injection System. The Redesigned Spill Port
Example, Test No. 5 (Table IV).................. 137

LIST OF FIGURES (CONT'D)
Figure Title Page
55 ~ Simulation Program Results of the Modified
Injection System. The Redesigned Spill Port
Example, Test No. 6 (Table IV).................. 138
56 Comparisons of Injection Chamber Pressures of
Original and Modified Systems. The Redesigned
Spill Port Example, Test No. 4 (Table IV)........ 139
57 Comparisons of Injection Chamber Pressures of
Original and Modified Systems. The Redesigned
Spill Port Example, Test No. 5 (Table IV)........ 140
58 Comparisons of Injection Chamber Pressures of
Original and Modified Systems. The Redesigned
Spill Port Example, Test No. 6 (Table IV). ~..... 141
59 Comparisons of Injection Chamber Pressures of
Original and Modified Systems. The Redesigned
Spill Port Example, Test No. 6 (Table IV)....... 143
xi

LIST OF TABLES
Table Title Page
I General Dimensions of American Bosch APEIB
Injection Pump.................................. 19
II General Dimensions of ADB-150S American
Bosch Injector............. 19
III Resume of Testing Conditions Used to Compare
with the Simulation Program.........0........... 69
IV Resume of Testing Conditions Used to Compare
With the Simulation Program and Used to Study
the After-Injection Phenomenon.................. 70
V Comparison Between Theoretical and Experimental
Results for Data Presented in Table III.......... 82
VI Comparison Between Theoretical and Experimental
Results for Data Presented in Table IV........... 83
xii

NOMENCLATURE
Symbol Meaning
A Pipe cross-sectional area, or area of opening at orifice
a Wave propagation velocity
Cd Discharge coefficient
Ct Time averaged flow resistance coefficient, defined in
Equation 2.1
Cvf Viscous friction coefficient for fuel leakage past the
needle
c As a subscript, refers to cylinder pressure into which
injection occurs
c.v. As a subscript, refers to control valve
D Pipe diameter
d As a subscript, refers to pump delivery chamber
E Injection system average elastic energy
F Force acting on needle or delivery valve
f Friction coefficient at valve or needle
f Darcy-Weisbach friction factor
As a subscript, refers to pump feed chamber
g Acceleration of gravity
h As a subscript, refers to the nozzle injection holes
i As a subscript, refers to nozzle injection chamber
INJ As a subscript, refers to equivalent pipe length of injector
volumes
J a ratio; J=fkt/2DA
K Bulk modulus of elasticity
k Spring static force
L Delivery pipe length
1 As a subscript, refers to nozzle lower chamber
xiii

NOMENCATURE (CONT'D)
Symbol Meaning
M A ratio; M-gA/ya
m I ss of valve or needle
Pump cam shaft speed
n As a subscript, refers to injector needle
p Pressure
P-t Time averaged pressure over the injection period
p As a subscript, refers to pumping chamber
PUMP As a subscript, refers to equivalent pipe length of the
pump delivery chamber volume
Q Volumetric flow rate
r Spring stiffness
Re Reynolds number
S Valve, needle or pump plunger displacement
t Time
TOT As a subscript, refers to total pipe length including
equivalent lengths of volumes at pump and injector
u As a subscript, refers to upper nozzle and delivery
chambers combined
V Velocity
volume of fluid enclosures in pump and injector
v As a subscript, refers to pump delivery valve
W Mass flow rate
w Weight of delivery valve or needle
W,Ws,Wd,
W1.W,6 As subscripts, refer to positions in the x-t plane
x Distance
xiv

NOMENCLATURE (CONT'D)
Symbol Meaning
X,X4,X5 As subscripts, refer to positions in the x-t plane
Y,Yd,
Y1..Y5 As subscripts, refer to positions in the x-t plane
Z,Z1. Z6 As subscripts, refer to positions in the x-t plane
Zd As a subscript, refers to the instantaneous flow in the
delivery pipe line at the pump delivery chamber
Zs As a subscript, refers to the instantaneous flow in the
supply pipe at the pump feed chamber
Zu As a subscript, refers to the instantaneous flow in the
delivery pipe at the injector
Specific weight of fluid
Ap Frictional pressure drop
AV Volume change
At Characteristic method time step
AL Injection period in degrees
e Pump cam angle in degrees
to Pipe wall shear stress
cp A time function representing the time rate of change of
pressure in the concentrated volumes at the pump and
injector

I. INTRODUCTION
1.1 Purpose and Background
The injection system of a diesel engine is of critical importance since it has a major influence on the combustion of the engine.
This is especially true today in view of the air pollution problem,
and the fact that combustion characteristics limit the present uses
of the diesel engine.
The diesel fuel injection system is an assembly of many complex and intricate mechanical components, each with specific functions. In addition to the behavior of individual components, the
interaction of these components has an important influence on the
ultimate operation of the system. However, the fundamentals of the
operating characteristics of some of the components and the interactions between these components are not fully understood. Consequently, much experimental trial-and-error development of injection
systems occurs among the diesel engine and equipment manufacturers.
The response of the fuel injection system is primarily dependent upon the action of the pump and the pressure wave propagation
phenomena in the delivery pipe line. The pump action with its delivery chamber and valve is not independent of the injector and delivery pipe line, since a complete system interaction takes place.
One of the most persistent injection system problems is related to wave phenomena in the high pressure line between the pump
-1

-2and nozzle assembly of the most popular type of injection system.
These pressure waves commonly result in a secondary opening of the
fuel injection nozzle following the normal injection, which is referred to as after-injection. This contributes to smoking of the engine.
This problem has been attacked in the past using experimental cut-andtry procedures with limited success. However, within the past decade,
procedures have been developed which permit a design or synthesis
approach to transient flow problems.
This study is divided into two major phases. The first phase
deals with the formulation and solution of the transient flow problem
in the diesel injection system. It includes a comparison of the
analytical results with experimental data taken on actual test equipment. The second phase is concerned with the investigation of an
analytical method to define means for control of the after-injection
phenomenon.
1.2 Literature Review
The common textbook approach, (17,22) employed to simulate
this problem is based on the use of a simplified form of the equation
describing the wave mechanism in the supply and delivery lines.
rThese simple approximations bear little resemblence to the performance of the true hardware in either theory or operation since it neglects many factors, including:
1. The change in geometry of fixed and moving parts.

-32. The change in fluid properties.
3. The dynamics of moving parts.
4. The coefficient of flow variations through different
passages in the system.
5. The flow friction in the supply and delivery lines.
6. The possible opening of vapor cavities.
In the existing research work, a great variety of' both theoretical and experimental procedures have been used to study the diesel
injection system. Prior to 1960, injection simulation studies were
limited by lengthy mathematical computations and graphical techniques.
They were only possible under many simplifying assumptions. This made
it impractical to apply theoretical simulation in the design stage
and led to experimental trial-and-error procedures.
One of the earliest significant contributions to fuel injection systems is due} to Davis and Giffen, (9) 1931. Their disus:;i.iLo
includes many of the significant variables involved in the system,
namely: fluid compressibility, elastic deformation, pressure wave
propagation, fluid friction, and pump and nozzle characteristics, including secondary injection. Ce Juhasz(10) 1937, used graphical
water hammer concepts to provide an analysis of a linear model of
typical simplified injection systems, including the elements of the
pipeline, pump, nozzle, and a fluid volume. On the other hand, Giffen
and Row, (13) 1939, theoretically solved the equations representing
the injection system, taking into account the effect of pressure

-4waves in the delivery pipe and the capacity effects of the volumes
located in the pump and nozzle system. They placed the differential
equations in finite difference form and found an algebraic expression
for the solution. This method of solution was limited to simple injection models because of the time required for mathematical solutions.
Knight, (18) 1960, introduced a model for viscous friction and
cavitation in the delivery pipe and used the same model for the pump
and nozzle system described by Giffen and Row.(13) His calculations
were performed using a digital computer.
Becchi,(4) 1962, used a model which comprised a detailed representation of the injector and the pump, but he neglected friction
in the delivery pipe and had no provision for possible occurrence of
vapor cavities. He solved the system of differential equations by
an iterative method after writing them in finite difference form.
Brown and McCallion, (8) 1967, combined Becchi's detailed
representation of the pump and injector with a model that included
viscous friction and possible cavitation in the delivery pipe. They
also considered a detailed modeling of the delivery valve as described by Stone(27) and solved the system of equations by another
iterative method.
The work of Walwijk, Van der Graaf, and Jansen, (30) 1969, is
also to be noted. Their experimental apparatus enabled them to
actually measure the motion of the delivery valve and injector

-5needle as well as the pressure in various locations in the system.
Particular attention was devoted to the motion of the delivery valve
in their simulation on a digital computer. A good correlation was
achieved between experimental and computed results.
Recently Becchi,(5) 1971, extended his model to allow for
variations in piping cross-sectional areas and possible opening of
vapor cavities. He also included the possibility of using a single
plunger distributor pump. Yamaoka, Saito and Okazaki, (33) 1971,
simulated an injection system of the by-pass type where the fuel
spill is controlled by a by-pass valve located in the pump delivery
chamber, and not by the commonly used spill port.
Many factors are likely to affect the accuracy of the injection model and have been discussed by many investigators. The value
of the residual pressure in the delivery pipeline is important for
a meaningful comparison between the model and experimental results.
In addition, a treatment of vapor pressure in the delivery pipeline
is also needed for a complete model. Kreith and Eisentadt,(20) 1956,
and Lichtarowicz, Duggins and Markland,(21) 1965, presented experimental results of the variation of the coefficient of discharge over
a wide range of Reynolds number and length to diameter ratio. Giffen
and Row, (13) 1939, cautioned of the danger of using coefficients of
discharge from the literature. They preferred to use experimentally
determined values for the particular nozzle under consideration.
The data of Gelalles, (12) 1931, in which he tested different nozzle

configurations, showed that the coefficient of discharge, besides
depending on length to diameter ratio and Reynold's Number, is also
greatly dependent on the configuration of the reservoir leading to
the nozzle holes.
The stability and convergence of the analytical solutions
are of prime importance. Henrici,(l5) 1964, discussed three different methods of numerical solution of a system of differential
equations: 1) the iterative solution of simultaneous algebraic
equations, 2) the expansion methods (Taylor's method or Runge Kutta
method), and 3) the numerical integration methods. The first and
second methods require the use of very small time steps and a prior
knowledge of the size of the time step. The third method includes
the predictor-corrector method which offers the advantage of an adjustable time increment, dependent upon a given error bound. This
particular advantage is of great value for reducing computation
time.
Experimental measurements of transient pressures, valve
movements, and transient discharges are of great importance in describing the injection system performance. The measurement of
pressure is possible by using piezo-quartz pressure transducers.
For the movement of valves, Bassi,(3) 1963, used a capacitive type
distance detector in measuring needle lift and a light source and
a photo cell to measure the relief valve movement.

-7-'ct inlrl;tarlrarl ouru f'low mrao;urcment is the riout c(Jaller4nirng
one. Ibrahim,(l6) 1964, used two methods of high-speed, mechanically operated collectors. In a third method he measured the pressure due to the injection in a filled volume with fuel, and deduced
the instantaneous flow by relating the pressure to the discharge
using the compressibility relation. He concluded that the third
method is the best provided that a high frequency pressure pick up
is used and enough damping of the secondary oscillations in the
measuring volume is ensured. Komarof, Iwan, and Kurt, (19) 1966, measured the distance travelled by a piston in a cylinder full of fuel
due to the introduction of injected fuel. This method has the advantage of discharging in a constant pressure while the previous
method is discharging in a highly varying pressure. Bosch,(16) 1966,
used a specially designed long tube to isolate one pressure pulse
and then related the intensity of the pulse to the instantaneous flow.
Considerable theoretical work has been conducted to control
the performance of hydraulic systems. Streeter and Wylie(29) used
the valve stroking technique for some large scale complex systems
and obtained good confirmation with experimental results. However,
little theoretical work has been done in the area of diesel injection
control. Most of the work has been experimentally oriented to obtain a desirable performance over a required range. Most often, the
system performance has been satisfactory for only a part of the range.

-8A study by Bradbury,(7) 1950, showed that after-injection invariably occurred at conditions of simultaneous high engine speed and
load. In addition, his studies on the relation between the specific
fuel consumption and break-mean-effective-pressure indicated the need
for large injector holes to achieve large output, and that small holes
were more adequate for part-loads. He concluded that small holes are
preferred over the whole range if it is possible to eliminate afterinjection at high outputs. Furthermore, Mansfield,(24) 1965, stated
that it is difficult if not impossible, for a pump to perform satisfactorily on a heavy-duty engine under all conditions of speed and load,
and that the high rates of pressure change, which must occur in all injection systems, lead to secondary injection.
Recently, Dolenc and Lees, (11) 1968, and Lustgarten and
Dolenc, (23) 1969, used a pump plunger with a stepped helix which provided a throttling effect during the early part of the fuel spill period. Their experimental results showed that the modified system had a
better performance than the original one. This was evidenced by less
after-injection and reduced cavitational damage. Anders, () 1971, used
a variety of shapes of the pump plunger helix and pump spill port. He
recommended the decrease of the dynamic flow delivery during the spill
period through a better design of the plunger helix and the pump spill
port, by using aerodynamically contoured ducts and helices.

-91.3 Scope of Investigation
The objective of this thesis is to conduct the following inve st igat ions:
1. A theoretical analysis on an actual Bosch type injection
system analyzing each component in terms of the basic
equations, and combining the analysis into a comprehensive digital computer simulation.
2. Measurement of the transient pressures and flow data
taken on an actual injection system, and comparing
these data with the computer simulation results.
3. Studying an analytical method to define means for control of the after-injection phenomenon.
The experimental apparatus is described in Chapter II. This
includes a description of the construction details, instrumentation and
experimental procedures. Factors affecting the accuracy of the theoretical model are emphasized. These factors include the pipe residual
line pressure and the coefficient of discharge through the nozzle holes.
The results of an experimental survey of the after-injection phenomenon
are presented toward the end of Chapter II.
In Chapter III a theoretical model of the fuel injection system is developed. A list of the assumptions used in the model is presented, and the importance of an adequate model is discussed. The
solution of the model is presented in Chapter IV. Experimental data is

-10compared with results from the analytical model, and the important
factors affecting the accuracy of the comparisons are discussed.
A theoretical investigation of a design parameter to control
the after-injection phenomenon is given in Chapter V. This includes
the formulation of a design program which utilizes the average elastic energy in the injection system as a controlling parameter. Two
examples are introduced to illustrate the usefulness of the design
program. The first deals with the elimination of after-injection
by adding a control valve in the pump delivery chamber. In the second example, the same goal is achieved by redesigning the pump
spill port. Results of both examples are presented in Chapter VI.
In this chapter the simulation program is used to check the results
obtained from the design program.

II. TEST EQUIPMENT, INSTRUMENTATION AND EXPERIMENTAL RESULTS
2.1 Purpose of the Experiment
There were several reasons for conducting experimental tests.
First, knowledge of some experimentally measured parameters is essential for an accurate determination of the theoretical system response.
Examples of these parameters are the system residual line pressure
and the flow coefficient of discharge through the nozzle holes.
Secondly, the computer simulation model results should be compared
with experimental data to check the validity of the assumptions and
techniques used in the study. A third reason is the need to study
the system performance, especially the undesirable phenomena of afterinjection and cavitation. The above reasons require a quantitative
determination of the time variant response of the predominant variables in the apparatus during a normal operating cycle.
The analytical simulation treats each component part in
great detail. It is not practical to measure all the variables,
therefore, a satisfactory confirmation between the theory and experiment is believed to be demonstrated if the theoretical results
agree with the experimental data using pre-selected variables. It
should be noted that these variables must be chosen to represent the
performance of the system adequately. In this study the experimentally determined system response was identified by the transient
-11

-12pressures, measured at specific locations, and by an overall measurement of the fuel input to the pump, the injected fuel and the
fuel leakages.
2.2 General Description of the System
A general view of the diesel injection test bench is shown
in Figure 1. This shows the injection pump mounted on a stand.
The pump was an American Bosch APE1B type and had a plunger diameter of 10 mmn. It was connected to the injector by a high pressure
pipe line 0.067 in. inside diameter, 0.25 in. outside diameter, and
36.4 in. long. The injector was an American Bosch ADB-150S type.
The pump drive system included a substantial flywheel to provide
uniform rotation and was driven by a variable speed dc motor. The
pump cam shaft speed was variable within the range of 100 rpm to
1000 rpm. The fuel rack was positioned by a micrometer that had a
travel of 0 to 1 inch, corresponding to maximum and minimum fuel delivery, respectively, with a minimum graduation of 0.001 inch.
References (2) and (3) were very helpful in the design and construction of the test equipment.
A detailed view of the pump, pipe and injector system is
illustrated in Figure 2, while Figure 3 shows the pump and construction details of the drive system. Figure 4 displays the injector
with modifications to allow for its instrumentation. Figure 5 is
a schematic representation of the diesel injection system with the

FUEL METERING STAND:
f // ~ ~':: STRAIN GAGE AMPLIFIER
NOZZLE:PIPE LINE
_ "/STRAIN GAGE -,
SPEED COUNTER.
Oii
l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l~~~~~~~~~~~~~~~~~~~~:
C"~~~~~~ uM:....:::: ~ ~~~~~~~~~ i::~
Pi- MP
LAROID CAMERAii
~...... ~ ~~~~~~~~~~AND
SCILLOSCOPE.'1:
Figure 1. Diesel Fuel Injection System Test Equipment-General View.

INJECTED FUEL 1
TO MEASURING EK
-0 FUEL TANK L
DE LIVVERY PIPE..........:::~:~~
-.-6i* a aa ai i a * r, rrr*** THREE WAY'.........x~:-:"::x ALV -~iii TRAIN GAGE.. CHARGE AMPLIFIERS
r i.*~~~............ ZERO-SWITCH Box
rrrl~~:~~~~l~~. ~~ ~ ~ ~ ~ ~~~~~~~vu....
r*J sr~~~~~~tr ~~~~:"4
I:*: i:t* r~i*~PUMP
i:*:il:*** i i r rr* r i, t r a,.i.~B~E UNIT (COVERED*
Az,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
NOZZLEa4 *a I~
ASSEMBLY`" "".....
MEASURING BEAKE
i::-* x: r**t.*~*i, ~ *~ —i- ".4* -Is of Pump, Pipe
Figare Diesel Fuel In L) e c tion System Test Equipment Detail~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a *
I~~ix rr~amd, Tnjector

TRANSDUCER #2;:;:;::
(DELIVERY CHAMBER); -& AM;. ^MODIFIED LVERY CHAMBER i
TRANSDUCER#.........
(FE E C EK MI ROMETER MAET E PICKUPi
40TMIN MAR~
3TIMING MARKI
TIGERING A
Figure 3. Diesel Fuel Injection System T'est Equipment - Pump and Construction
Details of Drive System.:E~~::~~i~ti~~i~ B~e~w8 U
ii-ii~iii i~i iiii-i-iii~iii~i- i —iii-iii~::ii:ii-iiiiiiiiil i H Ei:-~i:i -iii!!Asi:I
Imis,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-:ii-:: ii:-:i
FILTERL ~ i
1E1N1 -'~:"::::-~_
tTRIGGERING)~~~~~~IIGR -ti-I-~ — i
Dt ils fDie ytm

-16iDRA IN PIPE
L~EAKAGE
DELIVERY PIPE
COi:~i~ NNECTION
TRANSDERUCER
Ci/4............................
~Lh INJECTION CHAMBER
Figure 4. Modified Injector and Its Instrumentation.::~:rw j:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.....
t N3 E ~R A,EAIER(OZL ASMBY
TRANSDI~~~~~~~~~~~~~~~~~~~~~~~~~~~-::::::~
Figure 4. Modified Injector and Its Instrumentation.Y

-17STRAIN
GAUGE
TRANSDUCER TRANSDUCER
PIPE
TRANSDUCER #2
PUMP DELIVERY
CHAMBER
DELIVERY VALVE
PUMPING CHAMBER FEED CHAMBER
TRANSDUCER
SUPPLY PORT /1
/ t SUPPLY IDUCT g i -K RELIEF VALVE
SPILL PORT
FUEL FILTER
DELIVERY CHAMBER
TRANSDUCER #4
NOZZLE UPPER
CHAMBER
NOZZLE LOWER 5,'
CHAMBER FUEL
SUPPLY
TRANSDUCER #5 4 HOLES
INJECTION CHAMBER
Figure 5. Schematic Representation of Diesel Injection
System and Points of Pressure Measurement.

points of pressure measurement marked. The pump and injector general
dimensions are given in Table I and II, respectively. The pump delivery valve had an equivalent weight of.013 lb.; the spring force
on the seated valve was equal to 11 lbs.; the spring stiffness was
equal to 40 lbs/in. The nozzle needle had an equivalent weight of.02706 lb.; the spring force on the seated needle was equal to 86
lbs.; the spring stiffness was equal to 857 lbs/in. The needle
opening pressure was set under quasi-static conditions to 3000 lb/in.2
for all test runs. The injector nozzle discharged into a pressure
regrion of' otne atmosphere. The fuel used in all tests was Standard
Oil Company N1o. 2 diesel fuel, with a specific weight of.02986 lb/
in.3 at atmospheric pressure and 600F, a boiling point of 4500F and
an API gravity of 39.5.
Most of the above dimensions and properties were measured
and compared with the manufacturer's specifications. The measured
values were used in most cases while the manufacturer's data were
used only in cases where it was impractical to make an accurate measure tre nt.,' 2.3 Ins trwtr mentat; ion
The fuel pressure was measured using AVI piezo-quartz pressure transducers (type 7QP2500 a). The transducers were designed to
measure dynamic pressures up to 1500 atmospheres and were claimed to
e linear let' i l 1d\\:8- W ange within one percent of the full scale deflec

-19TABLE I
GENERAL DIMENSIONS OF AMERICAN BOSCH APE1B INJECTION PUMP
Length of supply duct = 23 inch
Diameter of supply duct =.234 inch
Volume of pump feed chamber (inlet gallery) =.7 in.3
Diameter of feed port =.107 in.
Diameter of spill port =.119 fin.
Maximum volume of pumping chamber =.0808 in.3
Diameter of delivery valve seat =.236 in.
Maximum volume of pump delivery chamber =.1637 in.3
TABLE II
GENERAL DIMENSIONS OF ADB-150S AMERICAN BOSCH INJECTOR
Volume of injector delivery chamber =.00772 in.3
No. of passages from delivery to nozzle upper chamber = 2
Length of passages =.76 in.
Diameter of passages =.069 in.
Volume of nozzle upper chamber =.004485 in.3
Length of passage from upper to lower chamber =.925 in.
Inside diameter of passage =.80 in.
Outside diameter of passage =.198 in.
Volume of nozzle lower chamber =.001 in.3
Volume of injection chamber =.001 in.3
No. of injection holes = 4
Hole length =.035 in.
Hole diameter -=.012 in.

-20Figure 5 shows the location of five pressure transducers
which were designed to measure the pressures at the following points:
the pump feed chamber, the pump delivery chamber, a location in the
high pressure pipe line near the injector, the nozzle upper chamber
and the injection chamber. The pump delivery chamber was modified
to accommodate the pressure transducer, and the modification details
are shown in Figure 6. Figure 7 illustrates the details of the connector used with pipe line transducer. The injector body and nozzle
were modified to house transducers No. 4 and No. 5. The details of
these modifications are given in Figure 8. To accommodate transducer
No. 4, the injector body and its nozzle retaining nut were modified,
and an injector retainer was added. To house transducer No. 5, the
nozzle tip was modified and a cap was added as shown in Figures 8
and 9. The addition of transducer No. 4 added a volume of less than
three percent to the nozzle upper chamber volume, and the addition
of transducer No. 5 added a volume of less than 10 percent to the
nozzle injection chamber. These volume additions were considered
tolerable in view of the great accuracy in measuring the pressure in
these very small volumes.
It was necessary to add a static pressure transducer to
establish a reference pressure. This was needed since piezo-quartz
transducers are of dynamic nature (measure pressure change only).
This was especially important to measure the residual pipe line pressure between successive injections, commonly called the base pressure.

Delivery
Pipe, End
Transducer *2
Figure o. Modified Pump Delivery Cham'ber.

Figure 7. Transducer Holder for the Injection Pipe Line.

INJECTOR BODY
SLEEVE -
TRANSDUCER #4
RETAINER - INJECTOR
ASSEMBLY
2 SET SCREWS ~ IR
TRANSDUCER #4
NOZZLE RETAINING
NUT (MODIFIED) BODY-NOZZLE
(MODIFIED)
CONNECTOR -.DRAIN PIPE
TRANSDUCER #5
CAP-RETAINER TRANSDUCER #5
Figure M. Modified Injector Body and Nozzle.

-24I
Nozzle Body
-Nozzle Spray Holes (4)
Transducer Connector
Transducer * 5
A <1. Sr. cCtiX(4lal View )f Connector andi Nr,'zlt Wl, dilicatiori
I. tails.

The static pressure transducer was of the strain gauge-type. It
was constructed and inserted in the pipe line directly above the
pump delivery chamber. This was done by reducing the pipe thickness through a one inch long section to.016 in. and measuring the
circumferential strain on the outside diameter using four strain
gauges connected in a four-arm bridge circuit. Some difficulties
were encountered as a result of vibration and outside interference
on the strain gauge circuit. This was overcome through building
an outside structure to envelope the reduced section, and act as
a vibration damper. All the pressure transducers were statically
calibrated using a dead weight tester.
The pump speed was measured using a Hewlett-Packard electronic counter, Type 512A. The cam angles were recorded every
three degrees using a disc with 120 equally spaced holes mounted
on the flywheel and an electromagnetic pick up (type 3010-AN made
by Electro-Mation Co.). Figure 3 shows some details of the cnam
angle measuring technique. A Tektronic 502A type dual beam oscilloscope fitted with a polaroid camera was used to record the pressure
traces and the cam angle position.
The net fuel flow to the pump was measured using a metering stand made by Waukesha Motor Co. (left side of Figure 1) which
consisted of a balance, a relay system and an electric clock. The
fuel actually injected was collected and weighed, and the difference between the two measurements gave the overall system leakage.

2.4 Experimental Procedures
This section deals with two basic objectives. One is the
measurement of parameters needed for the solution of the theoretical model of the injection system, namely, the residual pressure in
the pipe line and the flow resistance through the nozzle holes.
The other objective is to collect experimental data to compare with
the theoretical model results.
The residual pressure in the pipe line was measured during
each experiment by recording a dual trace representing the pressure
from the strain gauge transducer together with the reference zero
pressure. At the beginning and the end of each experiment, great
care was taken to ensure that the bridge circuit was balanced and
the zero reference line did not shift.
The average flow resistance coefficient through the nozzle
holes Ct was defined as:
Ct = (Cd x Ah)t (2.1)
where Cd is the commonly known coefficient of discharge (ratio of
act ua measured flow to theoretical flow neglecting friction), Al,
is the area of the nozzle holes, and the subscript t refers to
averaging over the injection period. This definition simplifies
the experimental procedure, since it requires the measurement of
one paranetcr Ct instead of measuring both Cd and Ah. This
is of special value if the area of the injection holes during

-27running conditions is in doubt. Figure 10 shows the details of the
average flow resistance coefficient measurement. First the beginning and end of the injection period were defined with the difference in degrees being the injection period AG. Then the injection
chamber pressure trace was averaged during this injection period
using the relation:
0AG
fpidg
(Pi)t 0 ~ — (2.2)
where Pi is the instantaneous pressure in the injection chamber
in lb/in.2 and (Pi)t is the average pressure in lb/in.2. Finally
the average flow resistance coefficient, in in. 2, was calculated
using the equation:
-.t = (2.3)
( (2g/y)1/2((p)) )1/2 A/6N)
where W is the injected mass flow rate in lbm/sec., g is the
acceleration of gravity in in./sec., y is the fuel specific
weight in lbm/in.3, Pc is the pressure into which injection
occurs, in psi, and N is the pump cam shaft speed in rpm.
For comparison with the theoretical model results, pressure traces from transducer No. 1 through No. 5 were recorded on
the dual-beam oscilloscope. The upper beam showed the output of
a particular transducer and the lower beam showed the cam angle
position. The data collected included pictures of a complete
cycle for each pressure transducer. Portions of the cycle during

INJECTION CHAMBER PRESSURE TRACE
5000 psi -
1_ _ I(PA
Ct W/((2g/r) 1/2
((Pi)t -Pc) X (A/6N))
Opsi
135~[ —; PUMP CAM ANGLE, DEGREES 1159~
AFTER BOTTOM DEAD CENTER
Figure 10. Oscilloscope Record of Transient Pressure in the Injection
Chamber and the Calculation of Ct from the Trace.

-29which injection occurs were magnified to ease the data reduction
process. During the pressure recording period the net fuel flow
to the pump was measured and the net mass of the fuel injected was
weighed. These two measurements were repeated several times during the course of running. The room and the injected fuel temperatures were also recorded. Usually the injected fuel had a higher
temperature (around 1200F) due to viscous friction.
Several steps were necessary in processing the data. These
included averaging the flows over the whole period of running, the
calculation of the overall fuel leakage and the tabulation of pressures from each pressure trace. These tabular pressures were used
for graphic representation of the results shown in this study.
2.5 The Experimental Results
The experimental data collected in this study can be divided
into three parts. The first is data of running conditions needed
for the purpose of comparisons between the experiment and the computer model. The second is data of running conditions needed for
the theoretical study of the after-injection phenomenon and means
of eliminating it. This data was used also for comparisons between
the experiment and the computer model, and is presented together
with the first data in Chapter IV. The third set of data which is
presented in this chapter is the data needed for an experimental
study of the injection system running under after-injection conditions.

-302.5.1 The After-Injection Survey
Bradbury(7) gave a region on the speed-fuel delivery plane,
Figure 11, in which after-injection occurs and outside of which it
does not occur. In his description of Figure 11 he defined point
X as the system design point. An increase in either fuel injected,
or operating pressures due to increased pump speed results in
after-injection. The after-injection is primarily cuased by occurrences at the pump, specifically with the manner in which the fuel
is opilled rcar the end of the injection cycle. The lower limit
line PAC rscults from a high spill rate due to the spill point being on thile fast part of the cam. For high fuel deliveries, on the
Utlcur hand, spilling occurs more toward the end of the cam lift
(where the cam velocity is low). This results in a low spill rate,
which in turn neutralizes the high pressures in the region above
PBD. Bradbury also mentioned that line PBD will be vertical for
pumps with constant cam speed near the end of the plunger lift.
In addition the after-injection zone may be bodily moved to the
right by increasing the area of the nozzle injection holes, or to
t-Ir l t-It by a partially plugged nozzle.'IJic pr evious discussion is of special value for the theoretical investigation of after-injection. It points to the important factors controlling this undesirable phenomenon. The injectioll system performance was therefore surveyed to identify the

225
~~~2OO ~ ~ ~ ~
200
B
N I
w: 3 175 1NJ ION
w
I //
a/
u'"' I H SCODR
w
L 125
II
575 600 625 2 650 675 $ 700 725 750
SPEED, R.P.M.
Figure 11. Secondary Injection Zone in a Speed, Fuel Delivery Plane.

-321. The region of operation in which after-injection is
certain to occur.
2. The magnitude of the after-injection problem.
In order to simulate after-injection conditions, the injection system described in Section 2.2 was tested with the injection holes
partially blocked to reduce the injection area to about 2/3 of the
original one. This condition commonly occurs in diesel engines
after short periods of operation, usually due to carbon blocking
of the injection holes.
The injection system was tested under a wide range of
operating conditions. The pump cam speed was varied from 100 rpm
to 1000 rpm with an increment of 100 rpm and the rack micrometer
was varied from a condition representing 20 percent of maximum
fuel delivery to a condition representing 80 percent of maximum
fuel delivery, with an increment of 10 percent. Extremely high
speed and high load conditions were not tested due to a fuel leakage problem around the injection chamber pressure transducer.
Pressure measurements were taken in the pump delivery, injector
upper and injection chambers. In addition the fuel flow to the
pump and the total injected fuel were measured.
The average flow resistance coefficient through the nozzle
holes was calculated in a manner similar to that described in
Section 2.4. Figure 12 shows that the measured average flow resistance coefficient varied within + 5 percent of.19 x 10-3 in..

American Bosch
APE 1 B- 100 P 6336 A Pump
ADB-1505/77-3610 Injector
0.3 Nozzle Holes Partially Blocked
U r Univ. of Michigan
z October 1971
V)
0.1
~ ~0.1 0.2 0.3 004
FLOW RATE, Ib/min
Figure 12. Variation of Flow Resistance Cof -ith Injeted Flow
0~~~ ~FO 0AE lbri
K~~Fgr 1.VrainoFlwRsitneCficntihIjcedFoRa.

This varieation is within the tolerance of the experimental measurement. Therefore, it is reasonable to conclude that the average
flow resistance coefficient is constant under all. test conditions.
Figure 13 shows the after-injection zone. The differences
between Figure 13 and Figure 11 are due to the difference in nozzle
injection areas, and because the pump used in the test rig had a
constant cam speed near the end of the pumping stroke.
Thleu relation between the total injection and the load is
linear and is shown in Figure 14. Each trace on the figure represents a constant speed line. The slight differences between these
lines are mainly due to a change in fuel leakage and throttling
effect at the pump ports. High speed tests are characterized by
short interval cycles; this results in lower fuel leakage and consequently higher total injection, when compared with lower speed
tests. Figure 15 shows the effect of the pump speed on the total
amount of Tuel injected for various load conditions. The speed has
little effect on the total amount of fuel injected per cycle. At
low loads, an increase of speed results in a slight increase in
the total amount of fuel injected per cycle. On the other hand,
at high loads, an increase in speed results in a slight decrease
in the total amount of fuel injected per cycle, due to the fact
that more fuel is dumped at the spill port. This effect is more
important at high loads than leakage.

American Bosch
APE I B- 100 P 6336 A Pump
ADB-1505/77-3610 Injector
Nozzle Holes Partially Blocked
Univ. of Michigan
October 1971
o 1.0
0
0.J
F0.8 After- Injection Region
0.6
L.
z 0.4
0
0.2
UL.
0.0
100 200 300 400 500 600 700 800 900 100
PUMP SPEED, rpm
Figure 13. After-Injection Zone in a Speed, Load Plane.

20
American Bosch
APE 1 B- 100 P 6336 A Pump
ADB-1505/77-3610 Injector
>? 15 Nozzle Holes Partially Blocked
Univ. of Michigan
October 1971
0
x 10 1000 rpm,5
0
I.J 50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
FRACTION OF MAXIMUM LOAD
Figure 14. Effect of Load on Total Injection per Cycle for Various Pump Speeds.

American Bosch
APE1 B- 100 P 6336 A Pump
ADB-1505/77-3610 Injector
w 30 Nozzle Holes Partially Blocked.j Univ. of Michigan
October 1971
25
&20 0.8 of Maximum Load
0
Z 1507
t; 0.6w I 0
z 0.5& 3 C
0 ~~~0.3
I I I IIj0.2Y
100 200 300 400 500 600 700 800 900 1000
PUMP SPEED, rpm
Figure 15. Effect of -pp Speed on Total Injection per Cycle
for Various Load Conditions.

-38The aznount of main injection is defined as the fuel injected during the first part of the cycle between the first nozzle
needle opening and its first closing. The effect of load on the
main injection/cycle is shown in Figure 16. Again each trace represents a constant speed test. At a fixed load, the lower the
speed the higher the main injection. This is due to the fact that
more after-injection occurs at high speeds, while the total injection is constant. In addition, Figure 17 displays the main injection as a function of pump speed for various load conditions. At
low loads, there is very slight effect of speed on the main injection due to the fact that after-injection does not occur at these
loads. This is contrasted with high load conditions where afterin2jectionl increases with increased speed and results in lower main
injection.
The amount of after-injection is defined as the quantity
of fuel injected after the main injection ends. Figure 18 shows
the effect of load on the amount of fuel after-injected per cycle.
It is seen from the lines of constant speed that after injection
starts earlier as the speed increases. In addition, the rate of
change of after-injection is smaller for lower speeds. In Figure
1t) thle data shown in Figure 18 is redrawn to show the effect of
speeld n tihe after-injection per cycle. At constant micrometer
setting after-injection starts at a certain speed, after which it
increases rapidly with speed. Finally, the rate of after-injection

20
American Bosch
APE 1 B- 100 P 6336 A Pump
iw | ADB-1505/77-3610 Injector 400 rpm
> 15 Nozzle Holes Partially Blocked
0o Univ. of Michigan / 500
October 1971 600
z
0
x 10
1000
z5
z
0 I I I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
FRACTION OF MAXIMUM LOAD
Figure 16. Effect of Load on Main Injection per Cycle for Various Pump Speeds.

American Bosch
APE I B- 100 P 6336 A Pump
w ADB-1505/77-3610 Injector
-' 30 Nozzle Holes Partially Blocked
Univ. of Michigan
October 1971
n 25
0.8 of Maximum Load
0 20
K
0 15 0.7
U 0.6
Z 10 A
0.5 n
0.3c 3
I 0.2
100 200 300 400 500 600 700 800 900 1000
PUMP SPEED, rpm
Figure 17. Effect of Pump Speed on Main Injection per Cycle for
Various Load Conditions.

American Bosch
APE 1 B- 100 P 6336 A Pump
ADB-1505/77-3610 Injector
w 6 Nozzle Holes Partially Blocked
Univ. of Michigan,;j 5p October 1971 900;;" 800
Z. 0700
1000 rpm
~~~x /x~~~ ~600
z 500
0 3
z 2
n,'x 400
w
U.
0.1 0.2 0.3 0.5 0.6 0.7 0.8 0.9 1.0
FRACTION OF MAXIMUM LOAD
Figure 18. Effect of Load on After-Injection per Cycle for Various Pump Speeds.

American Bosch
APE 1 B- O0 P 6336 A Pump
w ADB-1505/77-3610 Injector
J 6 Nozzle Holes Partially Blocked
>" | Univ. of Michigan
October 1971 0.7
V5
z
e I r 0.6
o 4 0.8 of
x Maximum Load L0.5
-3
Z 2
U ~/ 0.4, I
100 200 300 400 500 600 700 800 900 1000
PUMP SPEED, rpm
FiBgure 19. Effect of Pump Speed on AfIter-LDTjection per Cycle for
Various Load Conditions.

-43levels off at higher pump speeds. Figures 20 and 21 show the percentage of the after-injected fuel with respect to the total injection as a function of load and speed. Thirty-five percent of
the total fuel was after-injected as a result of combining high
speed and load conditions. Both figures show that the rate of increase of after injection decreases with increasing load at constant speed or increasing speed at constant load. This is mainly
due to the fact that at constant speed, the total injection increases at higher rates with respect to changes in load than the
after-injection. On the other hand at constant loads, the total
injection is essentially independent of speed, while the after
injection tends to go to a constant value only at high speeds.
The above survey of a diesel injection system indicates
that many hydraulic limitations affect the performance of the system as a result of after-injection. These limitations and their
effects are:
1. Injection systems are usually designed to operate at
fuel deliveries and injection pressures considerably
below their full capacities in order to avoid afterinjection. These low injection pressures limit fuel
atomization and penetration in the combustion chamber.
2. The optimum design point of injection systems is located critically close to the after-injection zone.
Any accumulation of carbon or fuel impurities on the

American Bosch
35 APE IB-100 P 6336 A Pump 1000 rpm 900
ADB-1505/77-3610 Injector 800
Nozzle Holes Partially Blocked
z 30 Univ. of Michigan
w October 1971
w 25 x~ 600
Lo 20 500
I-0. 0. 0. 0. 0. 06 07 0' i
ulO 400
5
_ _ _ _ _ _ _ _ _ _ _ 1
01 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
FRACTION OF MAXIMUM LOAD
Figure 20. Effect of Load on Percent After-Injection for Various Pup Speeds.

American Bosch 0.7
35
APE B- 100 P 6336 A Pump A
ADB-1505/77-3610 Injector
- 30 Nozzle Holes Partially Blocked
Z
w Univ. of Michigan
a: 25October 1971
w 25
a.
~F 0.8 of
0 20 Maximum Load
z 15
X
t- 10
5
100 200 300 500 600 700 800 900 1000
PUMP SPEED, rpm
Figure 21. Effect of Pump Speed on Percent After-Irnection for
Variouls Load Conditions.

-46nozzle holes changes the system performance drastically and will introduce large amounts of afterinjection. This results in a need for frequent servicing of the injection system.
From the above discussion it appears that the need is very
urgent for a theoretical design approach that could eliminate afterinjection by means other than increasing the nozzle injection area
or reducing the maximum cycle pressure. The analytical method used
in a dcsign approach to eliminate after-injection by changing some
of tlwm system time varying properties is presented in Chapters V
and VI.

III. BASIC EQUATIONS DESCRIBING THE DIESEL INJECTION SYSTEM
3.1 The Injection System Analysis
Until recently injection system design and modifications
have been based on experimental trial-and-error methods. Experimental methods used to control some of the undesirable phenomena
(after-injection and cavitation) that happen during the injection
process are tedious, expensive and frustrating.
From the basic equations describing the fuel injection
system, a computer model could be developed which would lessen the
effort, time and expense of development work. The computer model
could also be used as the basis for a design approach. The reliability of the design approach is dependent upon the accuracy of the
computer simulation program. The basic assumptions underlying the
simulation program should be fully understood and analyzed. The
validity of such assumptions will be indicated by the correlation
between the experimental data and the computer model results.
The diesel fuel injection system comprises four major components, namely: the fuel supply line, the pump, the delivery pipe
line and the injector. It should be emphasized that the performance
of each of these components depends on the other, i.e., a total system interaction takes place. Therefore, the equations describing
the whole system should be solved in a simultaneous manner.

-483.2 Basic Assumptions
The assumptions underlying the formulation of the injection
system equations are:
a. The flow passages (supply line, chambers, etc.) were
considered to be completely rigid. Elastic deformations of the different component parts of the system
due to action of the fluid pressure are negligible.
The error in the wave velocity as a result of neglecting pipe line deformation for the line defined earlier
was found to be less than 0.5 percent for the maximum
pressure variation (12,000 psi).
b. The effect of temperature and pressure on the fluid
density and bulk modulus of elasticity, together with
the effect of temperature on the fluid kinematic
viscosity have been taken into account. References
25 and 31 were helpful toward the determination of
those properties.
c. Fluid compressibility was introduced through the use
of a pressure dependent bulk modulus of elasticity.
This yielded a pressure dependent wave propagation
velocity that is a function of fluid compressibility
only.
d. Frictional effects were evaluated by considering the
loss during unsteady flow to be the same as the loss

-49for steady flow with the same velocity and i'luid
property. A friction-factor-resistance formulation
was used wherein the friction factor f is a function of the Reynolds number Re. For the laminar
range (Re < 2000), Hagen-Poiseuille's equation
(28)
gives: (28)
f -Re (3.1)
Re
For the turbulent range and transition zone
(Re > 2000), the Blasius equation for smooth pipes
gives: (28)
f = 03 (3.2)
Re/4
The frictional pressure drop was calculated using
the fo:rmula, (8)
8YL 22
AP= L( ) Q2 (3 3)'25g Q
where Ap is the frictional pressure drop, y is the
fluid specific weight, L is the pipe length, D is the
pipe diameter and Q is the rate of flow in the pipe.
e. A one-dimensional distributed parameter unsteady model
was used to describe the flow in the fuel pipe lines.
This implies that the parameters of system elasticity,
inertia and frictional losses are distributed along
the pipe length.

-50f. Whenever the pressure at any section on the pipe line
tended to drop below vapor pressure it was maintained
at vapor pressure and the formation of a vapor cavity
was assumed. The vapor cavity was permitted to grow
and collapse in accordance with the dynamic equations
and a local mass continuity balance.
g. The flow through the orifices was assumed to be noncavitating. Effects of fluid compressibility were
neglected along the orifice length. Orifice discharge
coefficients were based on steady-state data. References 14, 20 and 21 were used to give the coefficients
of discharge as a function of length over diameter
ratio and Reynolds number.
3.3 The Theoretical Formulation of the Model
The equations which describe the dynamic response of the
diesel injection system include four effects, namely: compressibility of elastic volumes, flow through orifices and passages,
dynamics of the moving parts and transient flow in the piping systern. These equations are grouped in three categories as follows:
the pipe lines (supply line and the high pressure delivery line),
the pump and the injector.

3.3.1 Transient Flow in the Piping System
Figure 22a shows the control volume used in the derivation
of the continuity equation. The net mass inflow through the control
volume boundaries must equal the rate of increase of mass inside the
control volume. This can be written in the following form:
yAV - [7AV + xAV 6 (yA~x) (3.4)
where:
A = pipe cross sectional area in in.2
V fluid velocity in in./sec.
6x incremental length of control volume
and x, t are the independent variables of distance and time, respectively.
Equation (3.4) can be expressed in the following form:(29)
8 +a t 0 (3-A)
where:
p = the fluid pressure in lb/in.2
and a is the wave propagation velocity in the fluid which is given
by:
a =gK (3.6)
where K is the fluid bulk modulus of elasticity - lb/in.2
Figure 22b shows the control volume used for the equation
of motion. The acting forces are the pressure and frictional forces.
The force due to the deformation of the piping material and the

- 52axx ax
A+8A
(a)A Control Volume Used for the Continuity Equation
t8 a t
pA+8
pAn |CA
A A+BVa
i(b) Control t Volume Used for the Equation of Motion.1,?t~',':.': (Xil[,r'ol Volume UTset'to'J>ri.ve t]h,; Pipe Equations.

-53gravitational force are neglected due to their very small values
compared to the pressure force. Therefore, the equation of motion
can be written as:
pA - (pA + A 6x) - xD x= A x dV (3.7)'uX.0 g dt
The following common expression for the steady state shear stress
TO is used (28)
qT xL f VI(3.8)
where
V = the fluid velocity.
Then Equation (3.7) can be expanded in the following form:(29)
Q + EA6 f QJQJ = o (3.9)
at 7 ax 2DA
The absolute value of Q and V are introduced to maintain the
correct direction of the shear stress with respect to the direction
of motion. In the derivation of Equations (3-5) and (3-9) the convective acceleration terms are dropped because their values are very
small compared to the other terms considered.
Equations (3.5) and (3.9) are partial differential equations with x and t as the independent variables, and p and Q
as the dependent ones. These two equations are converted into four
ordinary differential equations by use of he method of characteristics.(29) These ordinary differential equations can be transformed

into four algebraic equations by the use of a first-order finite
difference approximation method which results in:
Z -gA (pzpw) + fWtQ W = o (3.10)
2DA
xz - XW = aAt (3.11)
QZ Q (pz-py) + 2DAQY Y (3.12)
yay2DA
XZ - X= -apyt (3.1-3)
where At is the time increment. The pipe is divided into fixed
equally spaced sections of length Ax each, and the subscripts W,
Y and Z refer to positions in the x-t plane, as shown in Figure
23. It should be noted that Equation (3.10) is valid only along
the forward characteristic line, W-Z, as described by Equation
(3.11), while Equation (3.12) is valid only along the receding
characteristic line, YZ, as described by Equation (3.13). For
stability reasons it is necessary that the grid spacing Ax must
be -rcater thian or equal to the product of the wave speed a and
thel timne increment At
In general the analysis of any pipe line begins with known
conditions of pressure and discharge at time t=to. Then the transient pressures and discharges are calculated for time to + At at
-t;le. equally spaced sections which are separated by the grid spacing
Ax. By considering a pressure dependent wave speed, the slopes of

E
0
to+2At
<3 I — -ZX
to _ __\_/ I \n
O A C B L Length X
Fig... Ac. C' a:acteristics in x-v Par_.

the characteristic lines W-Z and Y-Z are dependent on the value of
the wave speeds at the points W and Y, respectively. In Figure
23, point W may be located at any place between A and C.
Therefore, an interpolation between the known points A and C is
required to find the conditions at point W. A similar interpolation is required at Y. In order to reduce errors resulting from
interpolation, a variable time increment is helpful. The choice
ol' tle2 time incremnent, at a certain instant, is based on the maxinmumr wave speed along the pipe line. As a result, the time increment may vary from one time to another.
In Figure 23 consider that the pressure and discharge are
known at each grid intersection along the horizontal line t = to.
The new values of pressure and discharge are calculated at a point
Z by Volving Equations (3.11) and (3.12). This procedure is valid
ic)r all interior points. At x=O, the C- line is used together
with the equations describing the boundary condition at x=O to
find the new boundary condition at t = to + At. Similarly for
x=L the C+ line is used together with the equation describing
the boundary condition at x=L.
For the fuel supply pipe line, the conditions at the
filter define the boundary equation at x=O. The large capacity
of ttle f'il]ter implies that the pressure is constant at this point.
Orn tie otiler f and, thle pump conditions define thle pipe boundary
equations at x=L. For the delivery pipe line, the pump equations

-57serve as the boundary equations at x=O. Similarly the injector
equations serve as the boundary equations at x=L.
3.3.2 The Injection Pump
In order to formulate the equations describing the injection pump, it is necessary to describe the following effects:
a. The fluid compressibility in various volumes is
calculated using the equation:
K APp (3.14 )
where
A = change in fluid volume
v = initial volume
Ap = change in fluid pressure
b. The fluid flow through the various orifices and
passages is described by:
Q= CdA P2-aP2) (3.15)
where Pi and P2 are the orifice upstream and downstream pressures respectively.
c. The equation of motion which describes the dynamic
action of mechanical moving parts such as the delivery
valve, is used in the following form:
F = m dV/dt (3.16)

-58where
F sum of all the forces in the direction of
motion, including pressure, frictional
and spring forces
m = mass of the mechanical part
V = velocity of the mechanical part
Figure 24 shows a cross sectional view of the injection
pump, including the major elements. The continuity equations combined with Equation (3.14) for the feed, the pumping, and the pump
delivery chambcers are given by Equations (3.17) through (3.19),
r'e spce -tl ive ly.
dpf Kf
dt f(Qzs - Q1 + 2 - Q4) (3.17)
dt - p+AvSvApSp (A V -AvVV+Q1-Q2-Q3) (3.18)
dpd Kd
dt b- dAS,~v(AvVv+Q3-QZd) (3.19)
dt ~d-AvSv
i reprcsents the valve or pump plunger displacement, and the sub-':riFptd (1t ~,' s re',present tihe I:_ow rates at; different points of the:ilcl-l:i (n a [np as illlustr'ated in Figure 2-. The subscripts f, p,
dc and v refer to conditions at the pump feed, pumping and delivery
chambers and the pump delivery valve respectively. The denominator
on tItw r-icilt hand side of Equation (3.18) represents the instantaneut;:: VKultl, (f L, e plumpi'nL g elwbllet' due to the effect of tile plunger
and delivery valve motions. Similarly the one in Equation (3.19)

-59QZd
Delivery Chamber
Transducer no.2
Pumping Chamber
QZS 17~L7~1 Relief Valve
Feed Chamber
Figure 24. Sectional View of Injection Pump.

-60gives the instantaneous volume of the pump delivery chamber due to
thle effect of the delivery valve motion. The flow rates through
different pump orifices are defined by:
Q1= CdlAl, I2g(pf-p)/y (3.20)
2 = Cd2A2 l2g(pp-pf)/7 (3.21)
Cd/AY 2g(Pp-Pd)/ y (3.22)
04=C A 4A~~~~- (3.23)
-_ CdA4 42g pf?' (3,23)
The numerical subscripts 1 through 4 refer to the pump intake port,
spill port, flow area around the delivery valve and pump relief
valve area, respectively.
Equation (3.16) applied to the pump delivery valve takes
the following form:
dVv = (av (Av(Pp-Pd)-kv-rvSv-fvVv) (3.24)
where
dS v
dv v (3.25)
dt
In the above equations the quantities k, r, fv and wv represent
the spring static force, spring stiffness, valve viscous friction
coefficient and valve weight, respectively.
The flow leaving the supply line and entering the pump
feed chamber, QZs' is described by Equation (3.10) in the following
form:

Q-s + Wsaws- (Pzs -Pws) + DA= 0 (3.26)
where the subscript Ws refers to known conditions in the supply
pipe at an earlier time increment and defined in a fashion similar
to Figure 23. Similarly the flow leaving the pump delivery chamber
and entering the fuel delivery pipe, QZd is described by i-unation
(3 13) in thle following form:
fydAt QYd1I Ydl (
QZd - gYd Yd(PZd-PYd) + dA= 0 (3 27 )
Y Ydayd2DA
where the subscript Yd refers to the known conditions in the supply
pipe at an earlier time increment and defined in a fashion similar
to Figure 23.
3.3.3 The Fuel Injector
The major elements of the fuel injector are shown in FJ:i cur
The.'J( continuity equat:Lons c:ombin(d with E quaLion (3.11) )I', 1,th(
delivery and nozzle upper chambers combined, nozzle lower charlbecr
and injection chamber are:
dt - KuA _S(Qz, uQ5 Q8AuAVn) (3.28)
dpl K1
d' l1+AlSn (Q5-Q6-A1Vn) (3.29)
dpi K.
dt +AiSn(Q6Q7-AiVn) (330)
The subscripts u, 1, i, and n refer to the nozzle delivery and
upper chambers, the nozzle lower chamber, the injection chamber,

-62Nozzle Delivery
Z u Chamber
Nozzle Upper
Chomber.Transducer no.4
Q5
_,,Nozzle Lower
Chamber
Injection Chamber
7Transducer no.5
FJg ure 25. Sectional View of Injection Nozzle.

and the injector needle. In the above equations the term v + AS
is the instantaneous volume due to the needle motion.
Flow rates with numerical subscripts refer to the orifice
flows shown in Figure 25 and are given by-:
= Cd5A5 <2g( p-p)/7 (3-31)
6 = Cd6A6 2g(P -pi)/r (3-32)
Q7 d7 A7 l2(ip )/y (3.33)
The leakage past the needle is given by
8 = CVfPu (3.34)
where CVf is a viscous flow coefficient which can be calculated
from Equations (3.1) and (3.3). The equations that describe the
needle dynamics take the following forms:
dn= -(Aupu+AlPl+Aii- kn- rnSn-fnVn) (33)
dt w(335
dS
= vn (3.36)
dt
The subscript n refers to conditions at the nozzle needle.
The flow leaving the delivery pipe line and entering the
injection delivery chamber, QZu' is described by Equation (3.10) in
the following form:

fwu - d + A ) Wd dWd 0 (337 )
Q -u oTj-aQ + + 2W d + -DA ) +....
7Wdad 2DA
where the subscript Wd refers to known conditions in the delivery
pipe line at an earlier time increment and defined in a fashion
similar to Figure 23.

IV. (C0MJI'AllI:i)JI AND DI[;CUS';ION 01' l'l ll: i)1lITJLA'I')l
AND EXPERIMEN\TAL ]RELIkTUL'["
The previous chapter dealt with the basic equations describing the injection system. This chapter considers the method
of solution of these equations. In addition, the computer simulation results are presented and compared with the experimental data.
A discussion of the parameters affecting the accuracy of the simulation model is given at the end of the chapter.
4.1 The Solution Technique
This section describes the method used to determine the
theoretical system response. This is achieved by solving three sets
of simultaneous equations representing the conditions at the supply
and delivery pipe lines, the pump and the injector. Equations (3.10)
and (3.12) describe the conditions in the pipe lines. The conditions at the pump are expressed by Equations (3.17), (3.18), (3.19),
(3.24) and (3.25). The unknown time dependent variables in these
equations are: the pressures in the pump feed, pumping and delivery
chambers, the delivery valve displacement and velocity, the flow
at the inlet of the pump feed chamber, and the flow at the exit of
the pump delivery chamber. Similarly Equations (3.28) through
(3.30), (3.35) and (3.36) represent the conditions at the injector.

The unknown time dependent variables in these equations are: the
pressures in the nozzle upper, lower and injection chambers, the
needle displacement and velocity, and the flow at the inlet of the
nozzle upper chamber.
Tlhe solution of the system equations begins with known
initial conditions in the pipe line, the pump, and the injector
at time t. The interior points for both the intake and delivery
pipes are calculated at time t + At using Equations (3.10), (3.12)
and th(e known initial conditions in the pipe line. The pump conditions are determined by solving the pump equations in conjunction
with Equations (3.26) and (3.27). The last two equations are the
C+ and C- equations at the pump-supply line boundary and the pumpdel iv-( ry inc boundary, respectively. Similarly, Equation (3-37)
i:. u( t(trU e tler with the injector equations to determine the conditions at the injector. It should be noted that Equation (3-37)
is the C+ equation at the delivery line-injector boundary.
The procedure for the numerical solution of Equations
(3.10), (3.12) is well documented in the literature.(29) The pump
and injector equations are solved numerically. Particular care
should be exercised to assure a true solution of each set of difI'erential equations because the boundary conditions at both the
pumIri, plrlI injrljC(', ar'(e c}langin extremely rapidly. A modified
pr'.li,c'K)r-cer'reuc'tur' mnethd(l by I-Iamrning(26) is used in this model.
Th'is method is a numerical integration method which makes use of

the knowledge of the system response at earlier times. It requires information from the pipe line during the step change.
This information is available by interpolation between known conditions in the pipe and by the use of Equations (3.10) and (3.12).
In this method the time step for solving the system differential
equations can be reduced below the fixed characteristic method
time step. The size of this reduction depends on a prescribed
accuracy level. Therefore, a relatively small time step is used
in that part of the cycle in which the transient contains high
frequency components, and the characteristic time step is used
over the major part of the cycle. This improves the computer program efficiency, an advantage which is not readily available in
either an iterative method or a Runge-Kutta method. The characteristic time step used in the simulation program was of the order of
0.0001 second, corresponding to a cam angle of about 0.48 degree
at 800 rpm.
The input data required for the solution of the injection
system must include a total description of the system geometric
configuration, properties of the system components and fluid properties described in Section 2.2. The forcing function of the entire system is the specified cam motion which drives the pump
plunge r.

-684.2 Experimental Data for Comparison with the Simulation
Program Results
This section deals with the test conditions used to compare the experimental data with the theoretical simulation results.
The object of the theoretical model is to be able to predict the
performance of the diesel injection system and the phenomena associated with its operation. Therefore, the test conditions should
cVewr Ij:i'fl rnt speeds and loads. Numerous experimental tests
thave t)( ^c1 ( c()olnducted ho( cover experirnmentally the range of conditions.
Some of these cases are presented in Tables III and IV. Table III
shows the testing conditions used to compare the experimental data
with the simulation results.(32) Test No. 1 had a high speed, low
load conditions and cavitation showed up in the pipe and injector
pressure traces. On the other hand, Test No. 2 had a lower speed
aod a higher load. In this test neither cavitation nor afteriinjectiorn occurred. Test No. 3 had combined high speed and load
conditions arid after-injection was detected. It is seen from Table
III that the average flow resistance coefficient Ct is reasonably
constant under all test conditions. Figure 26 shows a sample of
recorded traces for Test No. 3. The upper trace in each frame is
the pressure trace taken at each transducer location. The lower
trace correlates the pressure trace with the instantaneous position
of ti, caml during the p~umping cycle.

TIALE III
RESUMSE OF TESTING CONDITIONS USED TO CO i3ARE WITH THE SIMULATION PROGRAMi'-'
Rack Micr.* Total Fuel Base
Test Speed Setting Injected P-essure Ct CavitaNo. lp n b/mmn. 2
NO. rpm in. lb/min. psi in. tion Inieztion
800.675.o818 1100.000185 Yes
2 400.509.0966 -.oo86 NoooN
3 8oo.509.191 1400.000178 No
Test load
*Rack M1vicr-(,omaete-r setting, in. =1 - axmt load
MrxL-n-xrnq oad

TABLE IV
REST-hI OF iES0IIiG COKDITIOiTS USED TO CO1-TAKE 0I1-1. 11- SIMULATION I EC3RA
AlTED USED TO SiDlY THE AFTEiR-INJECTIOU LI OITLON4
% After
Rack Miocr. Total Fuel Base After- Injection
Test Speed Setting Injected Pressure Ct Injection of Total
No. rpm in. lb/m. psi in. lb/min. Injection
4 365.608.054 1300.000127.0055 10.19
5 405.350.148 2000.000126.0343 23.18
6 700.426.216 2500.000128.0796 36.85

-71OP
u.,, M0
CCL otr _o-o
C./)
i;.. X b. 1 6. s.. s t.ii; t l, s s t i s t l i
11350 11800
PUMP INLET CHAMBER RESIDUAL LINE PRESSURE
(Transducer No. 1) (Strain Gage Transducer)
LU
Il 356 180~ 1135~ 1180~
I~lo ll 0 III ar
0 - O -_
LU
Orr
11350 1180~ 135~ 16580
INJECTION UPPER CHAMBER INJECTION CHAMBER
(Transducer No. 4) (Transducer No. 53)
PUMP CAMSHAFT ANGLE
Figure 26. Oscilloscope Records of Transient Phenomena
in the Diesel Injection System.

-72A smaller injection area was used for the tests presented
in Table IV. This was necessary to produce after-injection so that
this phenomenon could be simulated and then theoretically investigated. Test Nos. 4, 5, and 6 were chosen to represent low, medium
and high speed and load conditions, respectively. It is seen from
the table that a simultaneous increase of speed and load results in
an increase in after-injection.
The experimental data obtained with this equipment were
Lighly reproducible. This includes not only the system residual
prnessure and injected volume in each cycle but also individual pressure spikes in the recorded traces. These spikes may at first
appear to be random. After injection and temporary conditions of
vapor pressuyre were also very reproducible traits of certain operating condition.
As indicated in Section 4.1, the forcing function of the
entire system is specified by the cam motion driving the pump plunger.
Figure 27 shows the pump plunger lift during the pumping part of the
cycle, togrether with the uncovered area of the spill port for Test
1.3 Comparis on of Results and Discussion
A compariison between experimental data and the theoretical
model results for the six testing conditions listed in Tables III
anid IV is presented in this section. The results for the pressure

N.012.6
C)
w
z.010
Spill Port Completely
H~~
Uncovered b
0
a.008 Intake Ports Spill Port Begins
a. Cov ered To Uncover-
a..0If r
UO~~~~- w
C 004t\ I/.
o a.J
w a-0,
cr_
J.002
0
0
C)
z
0 01
135 140 145 150 155 160 165 170 175 180
PUMP CAM ANGLE, DEGREES
Figure 27. Pump Pliuo:er:i: and Pump Port Areas; Rack f
Setting =..

-74variation at four locations, namely: the delivery chamber, the
pipe end, the nozzle upper chamber and the injection chamber are
given in Figures 28 through 33. Also, theoretical results for the
pressure variation at the pumping chamber and the pump delivery
valve and nozzle needle motion are included in the same set of
figures. In addition, a comparison of experimental and simulated
results in the pump delivery chamber for a larger pump cam angle
is shown in Figure 34. These results are from the same test conditions as those shown in Figure 30. All the injection system
variables are presented as functions of the pump cam angle for the
portion of the cycle in which fuel injection occurs. The computer
model results, together with the experimental data for the system
residual pressure and the injected fuel for each of the six cases
considered, are listed in Tables V and VI.
It is seen from the previous comparisons that the analytical model agrees reasonably well with the experimental data. This
gener'ates confidence in the underlying assumptions and techniques
used in developing the model.
A cause and effect study of the injection system response
is possible by examining any of the presented cases (Figures 29
through 34). For example, the pressure in the pumping chamber begins tj rise slowly because the ports are still partly uncovered.
W'o1(nr 1EthX ports atre covrerd, theak pressuore rises rapidlly. Tl:Je pre' -
urlle nr ti(e p-urip deliver'y ckhamber rises when the delivery valve

- 0.08. EXPERIMENTAL DATA 0.016
~ — 0.06 PUMP 0 0.012
u- DELVERY x xxxxx COMPUTER MODEL 0
0.04- DELIVERY'ET 08 ~
ALvE RESULTS- w
004 EVALI' INJECTOR NEEDLE 0 —-04
0........ox'......... xxxxx xx x x x x x x x x x x- o
6000 0
6000 VALVE OPEN.
4000
PUMPING CHAMBER
0................................... 6000
4000
DELIVERY CHAMBER 4000
00 <....... NO.. 2000
4000 PIPE END,.4OO0. I.NO. 3
10 10 10 10186000
NOZZLE UPPER000
NO. 4
x.................. 2 2000
6000- "' 0
4000
Results., 00 RPM 0ump Speed and o.67s
2000Rack MicrINJECTION CHAMBER
NO. 5
min.).(2

-76*2o 0.08 - P MP..... - _EXPERIMENTAL DATA_ 0.016 t
-M 0.06PU x~x-xx.x. XX.""."" COMPUTER MODEL 0.012 j
0.06 -...........
-004 _DELIVERY.. RESULTS - 0008
VALVE... INJECTOR004
O. 0.02-'. NEEDLE/ —-'
O _.......... xx KX.. -......xxx XXXXXX KXX XXXX X X X X X X 0
6000
VALVE OPEN.
4000 -
2000 -
PUMPING CHAMBER
0O -6000
DELIVERY CHAMBER 000
NO. 2
6= 4000-4000 PIPE END
cr 000
6000
4000
2000_. t INJECTION CHAMBER
NO. S5
130 140 150 160 170 180
PUMP CAM ANGLE, DEGREES':iuru'~ 2). Comparison of Injection System Hydraulic
Characteristics-Experimental and Computer
Results, 400 RPM Pump Speed and 0.509
Rack Micrometer (0.0968 lb. fuel injected/

-77EXPERIMENTAL DATA
xxxxxxx COMPUTER MODEL
RESULTS z
_ 0.08 PUMP 0.016!:
- "0.06 DELIVERY..x x x-xx INJCTOR 0.012
V 0.04V. x NEEDLE x 10.008 W
-J 0,.02 -0.004
x x.
0..............x xxx xxxx 0
10000
VALVE OPEN
5000PUMPING CHAMBER
0 ~..~................................. 0000
DEUVERY CHAMBER
NO. 2 -5000
In 10000- -0
a..0 10000.<\ NOZZLE UPPER
/ \ NO. 4 - 5000
10000- -0
5000. INJECTION CHAMBER
01 40 15070
130PUMP CAM ANGLE, DEGREES160 170
PUMP CAM ANGLE, DEGREES
Figure 30. Comparison of Injection System Hydraulic
Characteristics-Experimental and Computer
Results, 800 RPM Pump Speed and 0.509
Rack Micrometer (0.1910 lb. fuel injected/
min. )(32)

_z --— EXPERIMENTAL DATA
- 0.08-.......... COMPUTER MODEL - 0.016 Lu
O-06- PUMP,KKXKK ~ RESULTS - 0.012 -
DELIVERY. x.
j 0.04 VALVE xN 0.008 L4
L, K INJECTOR NEEDLE
0.02 L L 0.00L
0.................. x x X o,,,r(XxXXXXXXXI(
4000 "
2000. PUMPING CHAMBER
135 46000".6
DELIVERY CHAMBER 4000
NO. 2
2000
U5 cn ~~~~~~PIPE END
4000 b i, NO. 3
_ 20006
_m O- - 6000
NOZZLE UPPER -
4000
NO. 4
2000
6000!
4000- INJECTION CHAMBER
NO. 5
135 140 145 150 155 160 165
PUMP CAM ANGLE, DEGREES
ipf-urc 31. Comparison of Injection System Hydraulic
Characterist ics —xperimental and Computer
Results, 365 RPM Pump Speed and 0.608
Rack Micrometer (0.054 lb. fuel injected/
min.).

-79EXPERIMENTAL DATA z
xxxxx COMPUTER MODEL
— Z.08 PUMP.... xXXX XKXXRESULTS 0.016
0.0~t PUMP XXXX XX.. Ux-x x 0 0 2
0.064 DELIVERY X INJECTOR 000
--'
80000, x NEEDLE, 0.004 w
_ 3' x Kxxx~xxx4Xx N XXXXXXO Z
"D c LoPUMPING CHAMBER
o.. I I I I I
135 140 145 150 155 160 165 170
PUMP CCHAM ANGLE, DEGREES
M.......Rack Micrometer (...148 lb. f.uel injected/
8000).
_ D ELIVERY~/~Z ~CHAMBNOZEUER -
"'"""~' NO. 4'n 40004
-8000 - -0
_~~~''~ INJECTIO CPPER
NO. 3
-000
PUMP CAM ANGLE, DEGREES
Rack Kicrmeter (0.48000.fulijet.............

-80EXPERIMENTAL DATA
Zi~~ i ~ ~;:'x.: COMPUTER MODEL -
0.08- PUMP ESULTS 0.016 LL
- 0.06 DELIVERY x x x.K K K K K;K"xRESULTS 0 016
8000.
VAE DELIVERY CHAMBER
7. 0.04 " 0
__i 0.02 INJECTOR
j. -000 0.004 L.
LJ x x NEEDLE.
8000......
PUMPING CHAMBER
4000
2000....'...................................... 12000
DELIVERY CHAMBER
NO. 2 8000
40 00~4 ~ 14000
5 12000 - 0
a' 8000s -'u PI PE END
t3ac froer (.1 l.feiNO. 3t
(n 4000- t )
Cr..
O_
NO. 4,
1350~~~~~ 140 145- 1 1 4000
INJECTION CHAMBER
J000 NO. 5
4000 -
135 140 145 150 155 160 165 170 175 180
PUMP CAM ANGLE, DEGREES
1,itnrc' 33- Cr,,~pa' ison of Injection System Hydraulic
Characteristic — Experi menta l and Computwer'
iebsul'ts,'(()0 I<PM Pump Speed anrd 0.)4-20
Rack Micrometer (0.216 lb. fuel injected/
min. ).

PUMP DELIVERY CHAMBER
NO. 2
6000 -.
EXPERIMENTAL DATA
V 4000 a —COMPUTER MODEL
LU I / RESULTS
cn 2000
130 140 150 160 170 180 190 200 210 220
PUMP CAM ANGLE, DEGREES
Figure 3L. Comparison of Pressure in PLrlp Delivery Chamber, Experimental and
Computer Results for a Large (90~) Portion of Cam Shaft Angle.

TABLE V
COI4PARISON BETWEEN THEORETICAL AND EXPERIMENTAL RESULTS FOR
DATA PRESE=TED IN TABLE III
Experimental Data Simulation Data
Rack Micr. Injected Base Injected Base
Test Speed Setting Fuel Pressure Fuel Pressure
No. rom in. in.3/cycle psi in.3/cycle psi
1 8oo 0.675 0.00340 1100 0.00357 1490
2 4oo 0.509 0.00805 - 0.00840 2000
3 800 0.509 0.00796 14oo 0.00789 16oo

TABLE VI
COMPARISON BETWETEN THIEORETICAL AND EXPERDVIENTAL RESUILTS FOR
DATA PRESENTED IN TABLE IV
Experimental Data Simulation Results
Rack Micr. Injected Base Injected Base
Test Speed Setting Fuel Pressure Fuel Pressure
No. rpm in. in.3/cycle psi in.3/cycle psi
4 365 o.6o8 o.oo493 1300 0.00511 1400
5 405 0.350 0.01218 2000 0.01193 1988
6 700 0.426 0.01029 2500 0.01011 2430

-84opens, and drops with the delivery valve closing. The nozzle needle
opens after the pressure in the nozzle upper chamber exceeds the injector opening pressure of 3000 psi. This causes the nozzle upper
chamber pressure to drop temporarily and the injection chamber pressure to begin to rise at the instant of needle opening. The needle
motion and nozzle pressure are easily correlated for cases with afterinjection. The wave reflection phenomena and the time delay in
pressure wave travel are made clear by comparing pressures at different locations.!~.3.1 The Base Pressure
The base pressure is the steady state pressure in the delivery pipeline between two consecutive cycles. It is important to
establish this pressure as a known reference value. A suitable reference is established if vapor pressure is reached during any part
of the cycle since this value is readily determined. In cases
where vapor pressure does not occur, the base pressure was measured
by the use of the strain gauge transducer mounted on the delivery
pipe lirin. The experimentally determined base pressure was used to
start each) computer run. The simulation ends after the pump delivery valve and the nozzle needle close with no possible reopening
in the considered cycle. At this point it is possible to evaluate
tihe average pressure in the system by the use of pressures along
the pipe line, in the pump delivery chamber and in the injector.

Figure 35 illustrates the method used for the base pressure evaluation. In this figure LPUMP and LINJ are additional lengths
equivalent to the corresponding volume in the pump and injector, respectively. If the average system pressure after the cessation of
fuel supply and injection is different from the initially used base
pressure, a new value of base pressure is estimated and the run is
repeated. Usually one extra trial was needed to satisfy the condition that the assumed base pressure is equal to the resulting one.
For a meaningful agreement between the model and the experiment the measured base pressure should be within a limited error
bound from the theoretically determined one. In Tables V and VI
the error bound is of the order of 300 psi. This value is within
the tolerance of the experimental measurement, taken with this particular strain gauge transducer.
4.3.2 The Mass Continuity
A gross mass continuity balance provides a good check on
any fluid transient problem solved with numerical techniques. The
experimental data included a measurement of the fuel supply to the
pump and the injected fuel. Actual leakage that occurs in the system is available by subtraction. The leakage usually did not exceed
three percent of the injected fuel. Similarly, the computer model
accumulates the volume pumped, injected, and the leakage volume. A
comparison between the experimental and computer model results of

p
PIPE BASE PRESSURE' —N
LTOT
i _ Iiii
PUMP DELIVERY CHAMB INJECTR
LpUW L
Ige 35.SLTOwTi + L UMe + LINJ t
Figure 35. Sketch Showing the Method for Calculating the Pipe Base Pressure.

-87the injected fuel is shown in Tables V and VI, where it is seen
that the mass continuity checked well within less than 4.5 percent
of the injected fuel. Any discrepancy between the assumed and resulting base pressure in a simulation run usually gives rise to
continuity errors in the simulation.
4.3.3 The Effect of Variable Wave Speed
The variation in wave speed is due to the variation in the
bulk modulus of elasticity. A reference modulus is found from the
experimental recordings of the initial operating conditions in the
test runs. The variation in the modulus is used as cited in the
literature.(31) A change in pressure between 0 and 12,000 psi results in a change of wave speed between 4017 and 4391 ft/sec. Very
little improvement in the timing of pressure peaks was achieved
using variable wave speed. Therefore, it is justifiable to use
constant wave speed values in the simulation program for the above
pressure range.
4.3.4 The Effect of Distributed Friction
Friction is present as viscous losses, and it controls the
rate of attenuation of the residual pressure waves in the system
after the end of injection. Friction has a slight effect on the
shlape of the initial pressure build-up in the system during the injection period. Also the variations inl the friction factor with
Reynolds number slightly affect the simulation results.

-884.3.5 The Coefficient of Discharge
Simulation results are greatly affected by values of the
coefficient of discharge at some key locations. The most important
of these is the coefficient of discharge of the nozzle holes. The
coefficients of discharge of flow past the pump delivery valve and
the nozzle passage leading to the injection chamber are also important. The value of these coefficients are difficult to estimate
from the literature due to their unusual geometric configurations.
Best results in simulation are obtained by the use of factors determined where possible from the measured pressure transient response as described in Section 2.4. The variation of the coefficientss of discharge with Reynolds number has a slight effect on the
simulation results. It was shown experimentally (Section 2.5.1)
that thie coefficient of discharge of the injection nozzle holes is
reasonably constant during all test conditions.
4.3.6 The Vapor Pressure
Vapor pressure is detected on the recorded pressure traces
by a flat-bottom-trace for a short period of time. The computer
mod(l wats able to reproduce the sane condition by not permitting
tl( prlessu-r to drop below vapor pressure, and by assuming a local
vapor cavity formation. The size of this cavity is computed from
a mass continuity balance. The vapor pocket collapses when the
pressure exceeds vapor pressure. At this point homogeneous fuel
is assuned at the former pocket.

V. THE DESIGN CONTROL PARAMETER AND FORMULATION
OF THE DESIGN PROGRAM
5.1 Introduction
After-injection is usually caused by uncontrolled transients
after the end of the main injection. A survey of this phenomenon,
together with the factors affecting it, were presented in Chapter II.
Many experimental trial and error methods have been used to control
this phenomenon with limited success. These methods included changing the nozzle injection area or the delivery pipe diameter with the
goal of reducing the injection pressures, and consequently, afterinjection. The lack of success in using these methods can be attributed to the fact that these design changes are time invariant and
hence do not suit the transient nature of the problem. More success
could be achieved by studying the time varying parameters of the system. Examples of these parameters are: the instantaneous area of
the spill port during the spill period and the cam motion.
Prior to the 1960's, control of objectionable transients in
hydraulic systems was achieved by using simulation methods in which
the performance of time varying control devices (i.e., valves) are
assumed and the system resulting performance is obtained. The control device characteristics are changed until acceptable performance
is achieved. These methods proved to be inconvenient, tedious and
many times inadequate even for simple systems.
Recently new design procedures referred to as "Valve Stroking"(29) have been developed. In these procedures, hydraulic systems
-89

-90are synthesized by specifying a transient enabling the calculation
of a desired time varying boundary condition which is then used to
determine the required design changes. This is a more direct
approach which leads to sophisticated control techniques not attainable by the previous methods.
This work included a study to apply valve stroking techniques to the diesel injection system in order to control residual
transients after the uncovering of the pump spill port. This study
centered around the investigation of the desired pressure and flow
boundary conditions required to eliminate after-injection. The concept provided a better understanding of the controlling parameters
in the system. However, it did not lead to feasible design changes.
This is mainly due to the rapidly varying nature of the system pressure and flow boundary conditions, and to the passive type elements
in the system which respond to internal driving forces rather than
to externally forced conditions.
The difficulties encountered in trying to achieve feasible
design changes by using valve stroking techniques led to the seeking
of a design parameter which does not exhibit erratic behaviour. It
was noted that the variation of the system stored elastic energy
during the injection cycle is a smooth function of time. This characteristic makes it a good candidate for a system control parameter.
An investigation using the system stored elastic energy as a control parameter is presented in the remaining sections of this

-91chapter. The results of this investigation are presented in
Chapter VI.
5.2 Average Elastic Energy —The Control Parameter
In this study the term average elastic energy will be
used to define the average pressure stored in the injection system at an instant of time. It should be noted that this pressure
has the units of energy per unit displaced volume at the boundaries. Two examples are given to illustrate this definition.
First, a moving frictionless piston in a liquid filled cylinder
exerts work on the liquid. This energy is stored in the elastic
deformation of the liquid. The same energy could be used to
drive the piston back to its initial position. The second example is drawn from unsteady liquid flow in a frictionless pipe.
In this example, elastic energy is stored in a liquid column due
to the compression of the column. This energy is released as
kinetic energy by the expansion of the column.
The dotted system in Figure 36 is the system used to
calculate the injection system average elastic energy. This system includes the fluid in the pump delivery chamber, in the injector delivery, upper and lower chambers and in the delivery
pipe line. In this figure, p and LTOT are the same as defined
in Figure 35. The average elastic energy at an instant is calculated in the same manner in which the base pressure was calculated
in Secion 4.3.l.

SPILL PORT
A/'r'L - E.. I
PLUNGER DELIVERY VALVE INJECTOR
NEEDLE
fpdx
AVERAGE ELASTIC ENERGY
LTOT
Figure 36. Schematic Representation of System Used to Calculate the Average
Elastic Energy.

-93It can be visualized that the pump adds energy in the form
of flow work at the delivery valve end. This energy is stored in
the pipe line and volumes of the system as elastic energy. Part
of this energy is released at the injection nozzle during the injection period. If excessive uncontrolled elastic energy remains
in the system following the closure of the pump delivery valve, it
will be released at the nozzle resulting in after-injection.
The average elastic energy, together with pressures in
the pump delivery chamber and nozzle upper chamber for Test No. 3,
(Table III) are displayed in Figure 37- All the traces begin at
the point when the spill port begins to open. In Region I, the
average elastic energy drops because of spilling at the pump spill
port plus the energy release due to injection at the nozzle. Region II begins when the delivery valve closes. The energy-drop in
this region is due to injection at the nozzle only. Region II
ends when the nozzle needle begins to close, while Region III coincides with the period of needle closure. For this region slight
increase in elastic energy might occur due to the effect of work
done by the needle compressing the fuel during its downward motion.
When the needle finally closes, the nozzle upper chamber pressure
is lower than the needle opening pressure. However, the intermediate elastic energy in Region IV is high, thus causing the pressure
at the nozzle upper chamber to increase as the pressure wave reflects in the closed system. When this pressure reaches the

-94- 8000
>: 6000 AVERAGE ELASTIC ENERGY
cr \ IN THE SYSTEM
LLI
LL 4000 Intermediate
o Energy Residual
~_ —.... Energy in
o3 2000 the Line:13::m nz: m
Needle Needle
Reopen Reclosed - 8000
-6000 a
Valve w
Port PU NOZZMP DELIVERY CHAMBER
Ld \ Clos ing Needle Opening
Open 4000Period
Or
2000 a8000
i0- 6000 NOZZLE UPPER CHAMBER
Needle
GUl \ Needle Opening
O _4000 Closn Pressure
2000
Nee le Closing
150 155 160 165 170 175
PUMP CAM ANGLE, DEGREES
F]':]lir' 37. Trwa-~sient Pressures and Average Elastic
EMne rg,y Versus Punp Cam Angle for Test
No. 3 (Tab:le III).

-95needle opening pressure, the needle opens and the system elastic
energy drops during Region V. Later on, the upper chamber pressure drops below the needle closing pressure and the needle closes.
At this point, the system elastic energy finally reaches the residual energy. The elastic energy stays constant during Region VI
until the next cycle begins.
The average elastic energy trace in Figure 37 gives a
better understanding of the after-injection phenomenon. The manner
in which this energy drops during the spill period seems to control the behavior of residual transients in the injection system.
For example, a rapid energy drop in Region I will cause a rapid
closing of the delivery valve, which means a higher intermediate
energy and therefore an increased after-injection. On the other
hand, a very slow drop during the spill period will lead to prolonged injection periods. Control of undesirable transients seems
possible by releasing the average elastic energy in a controlled
manner.
5-3 Description of the Design Method on the
Pipe Characteristic Plane
The investigation of a specific case of after-injection
begins with recording experimental data of the actual test condition. Then the simulation program is used to simulate this condition. Comparisons are made between theoretical results and experimental data to check the validity of the assumptions and

techniques used in this study. The results and comparisons of four
cases of after-injection (Tests No. 3 through 6) were presented in
Chapter IV. The design program presented in this section serves
the purpose of finding means to eliminate after-injection. This
is achieved by utilizing a controlled release of the stored elastic
energy in the system. The resulting alterations in pressure and
flow patterns are calculated and translated into feasible design
changes, using the design program.
Figure 38 represents the pipe characteristic plane (x-t
plane). An instant of time is represented by a horizontal line,
while a vertical line represents a specific location along the
pipe. The line AJ represents the location of the pump delivery
chamber, and the line BI represents the location of the injector
delivery chamber. On the other hand, line ED represents the
instant of time at which the negative wave, resulting from the
spill at the pump, reaches the injector. Also line HG represents the instant of nozzle needle closing. Three important events characterize the performance of the diesel injection system
and are given on Figure 38. First, the plunger helix begins to
uncover the spill port at point C. Then the pump delivery valve
is totally closed at F. Finally, the nozzle needle is totally
closed at G. On this figure, the distance AC is the wave travel
time and BD is twice the wave travel time.

-97u) t
4 J....:_ I,. -.- J I',I, i
m I
PUMP m DELIVERY PIPE, INJECTOR
DELIVERY —-, DELIVERY
CHAMBER _ _ l__ CHAMBER
Figure 38. Injection System Performance
on the Pipe x-t Plane.
0> J~ ~ o h Pp -tPae

-98The design method is illustrated on Figure 39, which is
similar to Figure 38, but includes more details of the solution
procedure. In this figure, the distance between the vertical
lines represents a pipe section of length Ax, while the distance
between the horizontal lines is the characteristic method time
step At. The data needed by the design program includes a cornplete description of the injection system geometric configuration
and properties. Simulation program results of pressure and flow
along the line BD are specified for the design program. Also a
control period beginning at point C together with a controlled
average elastic energy function are specified. The choice of the
length of the control period and the energy function during this
period depend on the injection system properties and the choice
of the controlling device. Further discussion of this subject
will be presented in Chapter VI.
Several regions are given on Figure 39 to simplify the
presentation of the solution method. The solution procedure in
Region I begins with known pressure and flow conditions at all
points along the vertical line BD. Conditions at points lying
on another vertical line adjacent to BD are calculated by the
use of the pipe characteristic equations in a manner illustrated
by the triangle ZlY1Wl. In this triangle, pressure and flow
conditions are known at Y1 and W1 and are not known at Z1.
It should be noted that Z1W1 is the C+ characteristic line

-99_ J I,0~ ~~
REGION IY
0!I H G~'
II~~~~~~~~~~(
REGION lf l
X Y5
aO-WO E
EA9N4~~~~~~ W~Imm
lx I I -Z w
C y0
awj
OW L REY I II e f I t
z U Z3Z i 1 i,
a" ZE L
REGION I
QI
Figure 39. Design Othod on the Pipe x-t Plane.
w
I.I
~~~~~~~~~~~~A
B,1 -
X SO x L
Fpigue3.Dsgto on th Pipe x~- taory Pfalane.l^% I

-100and Y1Z1 is the C- characteristic line. When the conditions at
all points lying on a vertical line are calculated, the calculation proceeds to points on the next adjacent vertical line. Calculations in Region I end when the pressure and flow at point C
are known.
In Region II, calculations begin at t = L/a + At. At
this instant, pressure and flow conditions are known for all pipe
locations except the boundary point W2. Conditions at this
boundary point are calculated by making use of the assumed instantaneous average elastic energy together with an equation from the
pipe C= characteristic line. At t = L/a + 2At, pressures and
flows are known at all points except at Z2 and Z3. At this
point of time, conditions at the interior point Z2 are calculated by utilizing the known pressures and flows at W2 and Y2
together with the pipe characteristic equations along the C+
line W2Z2 and the C line Y2Z2. Conditions at Z3 are calculated in the same manner described for W2. This procedure
continues by advancing to the next step, calculating the interior
points, and then calculating the boundary point along the line CE.
Calculations in this region end by calculating pressures and flows
at all points along the horizontal line ED
Calculations in Region III proceed by calculating all
pressures and flows at time t prior to calculating these conditions at time t + At. This is done by first calculating the

-101interior points in the same manner previously described for point
z2 in lRegion II.'lThen, conditions at the injector boundary point
along the line DG are calculated by solving the injector equations
(previously described in Section 3.3.3) together with the pipe
characteristic equation along the C+ line illustrated by the line
W4Z4. Finally the pump boundary point along EH is calculated.
During the control period, this calculation is performed in the
same manner described for W2. After the end of the control period,
the compressibility equation [Equation (3.14)) describes the conditions in the pump delivery chamber and is used together with the
pipe C- characteristic equation to determine the pressure and
flow at the pump boundary. This C_ line is illustrated by the
line Y5Z5. Similarly, the compressibility equation [Equation
(3.14)] relates the pressure and flow in the combined injector chambers after the needle is completely closed. This equation is used
together with the pipe C+ characteristic equation to determine
the pressure and flow at the injector boundary in Region IV. In
this region, the interior points and pump boundary point are calculated in the same manner described for Region III. Since the design program objectives are to eliminate undesirable system characteristics (after-injection and cavitation), no provision has been
made to simulate these characteristics.

-1025.4 Formulation and Solution of the Equations
Used in the Design Program
Having described the solution procedure on the x-t plane,
attention is now given to the formulation and solution of equations
used in the design program. These equations are divided into four
major groups; namely, interior point equations, pump-pipe boundary
equations, injector-pipe boundary equations, and equations of design changes at the pump.
5.4.1 Equations and Method of Solution at Interior Points
On Figure 39, Z1 represents an interior point in Region
I at time t and pipe location x with known pressure and flow
conditions at W1 and Y1. W1 is located at time t + At and
distance x + ZAx, while Y1 is located at time t - At and distance x + Ax. The pressure and flow conditions at Z1 are
found by using Equations (3.10) and (3.12). Equation (3.10) represent the C+ characteristic line Z1W1 and is written in the
following form:
fzl AtQzl Qzll
Q - QZ1 + gA (PWl-PZl) + 2D= 0 (51)
YZlaZ1
Also, Equation (3.12) represent the C- characteristic line Y1Z1
and is written in the following form:
z - Y P f(PZ yP) + fytQy1 2 0 (5.2)
QZ 1 7lay 1- 2DA

-103For convenience, the variables M and J are defined in the following forms:
M = gA (5 3)
ya
and
J 2DA (5.4)
M and J are functions of the pressure and flow conditions.
Therefore the subscripts are associated with them to identify these
conditions. It should be noted that these variables are positive
and have an order of magnitude of 0.001 for the particular system
under consideration. Eliminating pZ1 from Equations (5.1) and
1
(5.2) yields:
B1 - B2QZ + B3Qz1Qz 0, (55)
where
1 = %YQlB + Mz~%Q + ZM1M11 Pw11 - Mz J%%Q Y (5.6)
B2 = (Z1 + M) (5.7)
and
B3 = MylJz1 (5.8)
For positive QZ the general solution of Equation (5.5) is:
IQZ1.= (5.9)
and for negative QZ1, the solution becomes:
B2 + + 4B1B3(5
- 213...... (5.10)

-104It should be noted that B3 is much less than B2, B2 and B3
are always positive and the product B1B3 is much less than the
square of B2. In order to avoid very high orders of magnitude
of QZ1, Equations (5.9) and (5.10) become:
Q IB1 B2 - B - 41BJJB3 (5.11)
B1 2B3
In Equation (5.11), the sign of B1 describes the sign of the
flow QZ1. Then the pressure pZ1 is calculated by substituting
Qzl in Equation (5.1) or Equation (5.2).
The calculation procedure at the interior points in
Regions II, III and IV is essentially the same. This procedure is
illustrated by the calculation of pressure and flow conditions at
point Z2, (Figure 39). Z2 represents an interior point at a
time t and a pipe location x. The pressure and flow conditions
at the adjacent points W2 and Y2 are known. W2 is located at
time t - At and distance x - Ax, while Y2 is located at
time t - AT and, distance x + Ax. Equations (3.10) and (3.12)
are used to calculate the pressure and flow at Z2 and can be
written in the following form:
QZ2 - QW2 + Mw2(PZ2-Pw2) + JW2QW2QW21 Q = (5.12)
7,2 - - MY2(PZ2PY2) + JyQyY2QY2 Y21 (5-13)
Subtracting Equation (5.12) from Equation (5.13) results in:

-105Jy2QY2 QY2 1 - JW2QW2 QW21 + MI2PW2 + MY2PY2 + 2 - QY2
Z2 MY2 + 2
(5.14)
The flow Q2 is calculated by substituting for Pz2 from Equation (5.114) into Equation (5.12) or Equation (5.13).
5.4.2 Equations and Method of Solution
at the Pump-Pipe Boundary
Calculation procedure of the pressure and flow conditions
at this boundary takes advantage of computed pressure and flow
conditions in the remainder of the pipe length. Calculation of
these conditions, at a point Z3, (Figure 39), is given as an
illustrative example for this procedure. Assume that Z3 is located on the horizontal line t = t3. The pressure at Z3 is
calculated from the average elastic energy defined in Section 5,2
and by Figures 35 and 39 and is expressed as:
LTOT
pz3 = (Et3 x LTOT pt3 dx)/LPUM (5-15)
LPUMP
where E is the specified instantaneous average elastic energy,
and the other variables are previously defined. The flow at Z3
is calculated by substituting pz3 in the pipe C- characteristic
equation [Equation (3.12)], and is given by
3 3 3 Y3 Y33

Outside the control period interval, the compressibility
equation [Equation (3.14)] relates the pressure and flow in the
pump delivery chamber. The calculation procedure at the pump
boundary is illustrated by calculating the pressure and flow at
the point Z5 (Figure 39). The finite difference form for the
compressibility equation at this point is given by:
PZ5-Px5 K
5 = -(QZ5+QX5 (5.17)
In addition, the C- characteristic equation [Equation (3.12)]
can be written as:
QZ = Y + My(PZ -PY JY QY lQY (5.18)
5 5 5 5 5 5 5 5
In the above equations subscripts refer to locations on the x-t
plane (Figure 39). Equations (5.17) and (5.18) are two algebraic
equations in two unknowns, and can be solved simultaneously to
give pz5 and Q5
5.11.3 Equations and Methods of Solution
at the Injector-Pipe Boundary
The injector equations were presented in Chapter III.
They were solved using the predictor corrector method in the simulation program. From the simulation results presented in Figures
28 through 33, the following observations are noted: (1) The
nozzle needle stays at its highest position (0.013 inch) until
the negative wave that results from the opening of the spill port
reaches the injector. (2) The needle begins to close when the

-107pressure at the injector reaches the needle closing pressure.
(3) During the needle closing period, the needle velocity is
fairly constant. Therefore, it was decided to simplify the solution procedure in the design program by assuming a needle motion
in accordance with the above three observations.
In the design program, it is assumed that the needle lift
is 0.13 inch at the point D, in Figure 39. The needle stays at
that lift until the pressure at the injector in Region III starts
to drop below the needle closing pressure. At this point, the
needle starts to close. The needle velocity is constant during
its closing period. The magnitude of this velocity was taken
from the above-mentioned simulation results. Therefore, a prescribed needle motion dependent on the pressure at the injector
is given in Region III, Figure 39, and the needle equations are
dropped. It should be stated that this procedure is not necessary
and was used only to expedite the solution procedure.
The remaining injector equation [Equations (3.28), (3.29)
and (3.30) ] are of the following form:
= cp(t) (5.19)
dt
where Tp(t) is a function of time representing the right-hand
side of these equations. Such equations can be written in the
following finite difference form:
P2-P1 P(tl) + P(t2) (5.20)
2+0

-108where the subscripts 1,2 refer to the beginning and end of the time
period At. The left-hand side of Equation (5.20) is the pressure
slope, while the time function on the right-hand side is averaged
during the time period. The algebraic equations expressed by
Equation (5.20) are solved together with the pipe C+ characteristic equation [Equation (3.37)] using an iterative method. This
method is illustrated by using the points W4, X4 and Z4 on the
x-t characteristic plane (Figure 39). On this figure pressure and
flow conditions are known at W4, X4 and are to be calculated at
Zl). F'irst, the prcszurc at Z4 (nozzle upper chamber pressure)
is assumed. As a first approximation, this pressure is assumed to
be the same as that at X4. Substituting this value, Equation
(3.37) can be solved for the flow at Z4 (flow entering the injector upper chamber). Similarly, substituting PZ4 and QZ4,
the finite difference form of Equation (3.28) can be solved for
the nozzle lower chamber pressure. Using the above known pressures and flow, it is possible to calculate the pressure in the
nozzlc injection chamber by two means. The first is by using
Equation (3.29) and the second is through solving Equation (3.30).
If the assumed pressure at Z4 happens to be the same as the true
solution of these equations, the two calculated values of the pressure in the injection chamber should be the same. However, this is
a very uncommon situation. Therefore, the difference between the
two calculated pressures is used as an error function and the

-109solution is repeated by assuming a new pressure at Z4, which is
obtained by adding an increment of + 200 psi to the previously assumed value of pressure. The sign of the increment depends on the sign of the error. This procedure is repeated until
a change in the error sign is indicated. At this point a NewtonRaphson converging method(l5) is used to obtain the solution. This
technique proved to be very efficient. It greatly improves the
convergence of the solution; in most cases no more than five iterations to reach a solution were needed.
After needle closing, the injector equations are dropped.
The compressibility equation [Equation (3.14)] for the combined injector chambers (delivery, upper and lower) at point Z6 (Figure
39) is given in the following finite difference form:
PZ6 - PG K
At + 2( + )(Q6 +G (5.21)
Equation (5.21) is solved with the pipe C+ characteristic equation:
Z6 - 6 + Mw6(PZ6 P- 6) w6w6QW61 (5.22)
The solution of Equations (5.21) and (5.22) gives the pressure and
flow at Z6. In this equation the subscripts G, W6 and Z6
represent points on the x-t characteristic plane (Figure 39).

-1105.4.4 Equations and Method of Solution
of Design Changes at the Pump
So far, the design program has used an assumed average
elastic energy profile and known initial conditions to calculate
pressure and flow conditions in the whole x-t plane given in
Figure 39. To make use of these conditions, they must be translated into feasible design changes in the injection system.
Two design changes aimed at the elimination of afterinjection are suggested at the pump. The first example is a controlled relief valve in the pump delivery chamber which opens to
release the excessive elastic energy at the correct instant. The
second is a redesign of the pump spill port area to release the
elastic energy in a controlled manner. In both examples, the calculated pressure and flow data at the pump-pipe boundary during
the control period are used as added boundary conditions to the
pump equations. The solution of these equations provides the required design change. The equations used in both examples are
given in this section. Design program results of these examples
are given in Chapter VI.
The control valve used in the first example is illustrated by Figure 40. It is assumed that this valve does not open
while the delivery valve is open. Therefore, the equation representing the pump delivery chamber [Equation (3.19)] is modified to:
dpd Kd
= - ~j(Qc.v. + Q~d) (5.23)
dt --- ('' d)

SPILL PORT DELIVERY VALVE
r.t2 g e -----------— ___JIJEE
INJECTOR NEE(LE
PLUNGER
CONTROL VALVE
Figure 40. Schematic Representation of the Control Valve Position.

-112where Q is the flow through the control valve and is given
by:
Qc.v. = Cdc.v.AcOv Y (5.24)
The subscript c.v. refers to the control valve and the other
terms were previously defined. The calculated pressures and flows
Pd and QZd at the pump-pipe boundary during the control period
are used together with a reasonable value of the valve coefficient
of discharge to give the needed area of flow through the valve.
A value of 0.7 was used for Cdc.v
The second example determines a pump spill port area from
the known pump-pipe boundary conditions (Pd. Zd)' This is done
by first solving the pump delivery chamber equation [Equation (3.19)]
together with the delivery valve motion equations [Equations (3.24)
and (3.25)]. Each of these equations can be written in a form
similar to Equation (5.19). The finite difference form used in the
solution takes the following form:?2-P!
2Pl = c(P(t2) (5.25)
where the subscripts 1 and 2 refer to the beginning and end of the
time period At. The left-hand side is the slope and the time fiunction on the right-hand side is calculated at the end of the period.
It was found that the use of average values for the right-hand side
during the period results in divergence of the solution due to the

-113Iighly varyirng natu're of the delivery valve velocity during the
closing period. This is in contrast with the needle motion where
the needle velocity is very stable during the needle closing period.
Extreme variations in the delivery valve velocity during the closing period result from the use of light valve spring and the fact
that the acting pressure force (pd-Pp ) is small and is highly varying. Converging solutions were obtained by using the finite difference form given by Equation (5.25).
In the finite difference form of Equations (3.19), (3.21),
(3.25), P and an d d are known from previous calculations, and
pp, Sv and Vv are the unknowns to be determined. An iterative
method and a convergence technique similar to that described for
the injector-pipe equations given in Section 5.3.4 was used to determine these unknowns.
The calculated pressure in the pumping chamber pp together with the calculated valve motion (Sv, Vv) are used in the
finite difference from [given by Equation (5.25)] of the pumping
chamber equation [Equation (3.18)] to determine the spill port
area. For this equation, the feed chamber pressure pf was
assumed using previous simulation results. A value of 150 psi was
used in all cases for pf. It should be noted that the spill
port area is highly insensitive to the value of pf because pf
is much less than pp during the major part of the spill.

-1145.5 Accuracy of the Design Program
The procedure presented in the previous sections utilized
an assumed average elastic energy function during a control period
to determine the injection system performance and to propose design
changes. Some assumptions and solution techniques were used to
accomplish this objective. It is important to illustrate the accuracy of the design program compared with the simulation program result s.
Average elastic energy curves for Tests No. 3 through 6
(Tables III and IV) were computed using the simulation program results for the injection system pressures. These curves were given
as data to the design program and the injection system performance
was calculated. Results from the design program were compared to
the simulation program results. In all cases, the design program
results were in very good agreement with the simulation program.
A sample of these comparisons are given in Figures 41 and
42 for Test No. 6 (Table IV). In Figure 41, the upper trace is
the average elastic energy calculated from the simulation results
and used in the design program. Three other traces for the pressures in the pump delivery chamber, nozzle upper chamber and injection chamber are also illustrated on the same figure. Figure
42 gives comparisons of calculated results at the pump. The design program results in this figure were determined using the procedure given for the second example in Section 5.3.5. There is

-115~o o o DESIGN PROGRAM
-SIMULATION PROGRAM _
1000 -
AVERAGE ELASTIC ENERGY _8000 U
IN THE SYSTEM U6000
4000
410000
PUMP DELIVERY CHAMBER i10
wJ60t
(1)400
2000rC
a:
NOZZLE UPPER CHAMBER 12000
I000
6000 _
o INECTI 2000 CrH
0
12ooo
U)
_ Io o - I I I
d. 80PUMP CAM ANGLE, DIHAMBER
of Pump Delivery Chamber and Inj ctor
LL!
a.
0150 152 154 156 158 160
PUMP CAM ANGLE, DEGREES
Figure 41. Simulation Check of Design Program Results
Transient Pressures for Test No. 6 (Table IV).

-116o o o DESIGN PROGRAM
-- SIMULATION PROGRAM
8000
at~ \ ~PUMPING CHAMBER
4000
O-.08.07
PUMP DELIVERY VALVE -.06
-.05.04 -.03.02
-.0 I
0
0.z 004
< m-'.003
VJ.002.j -001 PUMP SPILL PORT
_~.001 - y
o
150 152 154 156
PUMP CAM ANGLE, DEGREES
Figure 42. Simulation Check of Design Program Results
at the Pump for Test No. 6 (Table IV).

-117essent-ially no difference between the simulation and design program
results. The minor differences in Figures 41 and 42 result from
using two different approximate solution methods.

VI. DESIGN PROGRAM RESULTS AND SIMULATION PROGRAM
VERIFICATIONS OF THE RESULTS
6.1 Introduction
The previous chapter dealt with the formulation of the design
program and two examples were given to illustrate its usefulness. In
both examples, the system average elastic energy was used as a control
parameter in the design program. This chapter considers the application of the design program to both examples. A study of the system
performance as a function of the timing and the shape of the injection
system average elastic energy function during the control period is
given for both examples.
Certain constraints were imposed on allowable design changes
made to eliminate after-injection. It was decided that the performance
of the injection system during the main injection period should be
maintained. This implies that the injection chamber pressure should
not be seriously altered during the main injection and the system
base pressure also should not be seriously altered.
6.2 Effect of the Average Elastic Energy Function
on the System Transient Pressures
6.2.1 Average Elastic Energy and the Control Valve Example
As described in Section 5.3.5, the first example deals with
the use of an additional control valve in the pump delivery chamber,
which is used to release the system elastic energy in a controlled
manner. In order to maintain the performance of the system during
main injection, it was decided not to alter the original system
average elastic energy function during this period. Also the
-118

system average elastic energy must reach the system base pressure by
the end of the control period. This elastic energy drop will be
achieved by using the additional control valve, Figure 40. Several
elastic energy alterations as applied to example No. 1 are given in
Figures 43 and 44. These figures illustrate the effect of the system
average elastic energy on the resulting transient pressures at the
pump delivery and the injector upper chambers. All traces on these
figures begin at the beginning of the control period, and the solid
traces represent the system performance without alterations. The
appearance of high residual energy on the solid traces and the existence of negative pressures in some of the traces are due to the fact
that after-injection and cavitation were not accounted for in the
design program.
Two alterations are given on Figure 43 to illustrate the
dependence of pressure on the time of initiating the elastic energy
drop. The results given on this figure represent Test No. 3 (Table
III, Figures 30 and 37). The circles represent an elastic energy drop
starting at the point of delivery valve closing, while the triangles
represent an energy drop starting at the point of needle final closing.
From comparisons of resulting pressures at the nozzle upper chamber,
the following is clear: The first alteration (given by circles)
results in added cavitation. Also, after-injection is liable to
occur since the residual pressures at the injector are not damped.
The second alteration (given by triangles) results in damping the
residual pressures and therefore, after-injection does not occur.
Also, no cavitation is detected in the second example. Thus it
can be concluded that an elastic energy drop beginning at the point

-1208000
a0
~^ 6000r\ AVERAGE ELASTIC ENERGY
Z 40 IN THE SYSTEM
w 4000
2000 - 0ooOOOOOdAooooo=owoo
0
8000
\ _ 0~~~6000
PUMP DELIVERY CHAMBER I|
\c')J4000 200
080000,,,8a 6000o S /.:s-60, 6000 NOZZPMPDLEIPERY CHAMBER
a- 42000o _2000
0 CAM NG &~LE, DIEGRE EAS
AAA& )0000 A0
ex: 2000
0igure 43.0Injectio System Var versu0 0Pm
0 0 o~ ~0
0
-2000
150 155 160 165 170 175
PUMP CAM ANGOZZLE, DEGRESCHAMBER
Cam Agrle. Efect of Timing the Av-: raf
J ~.....,'I' I.... I': )

-1218000
a. AVERAGE ELASTIC ENERGY
IN THE SYSTEM
>- 6000
(0
LU
w 4000 o: 0;A00
oooooooo oooooooOOOOOO
u 2000
w - 8000
PUMP DELIVERY CHAMBER
6000 _
AAw
00 A "' 4000
a A * 4AAAAA uJ
Ooftoo oo~ ooo oooo o
-.",o -2000 n
12,000- 0
10,000
NOZZLE UPPER CHAMBER
8000
aj 16000 -
Cam Angle. ES.AA
co 4000-A
&A 00o A o0
2000 A
0150 155 160 165 170 175
PUMP CAM ANGLE, DEGREES
Figure 44. Injection System Variables versus Pump
Cam Angle. Effect of the Shape of the
Average Elastic Energy Drop. The Control Valve Example, Test No. 6 (Table IV).

-122of final needle closing is desirable. Several other trials have
confirmed this conclusion.
Several shapes of elastic energy drop were studied and three
of them are given in Figure 44. Results on this figure are for Test
No. 6 (Table IV, Figure 33). In this figure, all alterations begin
at the point of final needle closing. The three elastic energy
alterations are represented by dots, triangles and circles. By comparing pressures at the nozzle upper chamber, it is clear that the
average elastic energy function represented by the circles results
in damping the residual pressures and thus eliminates the possibility
of after-injection. The other two alterations reduce the magnitude
of the residual pressures but do not eliminate after-injection.
6.2.2 Average Elastic Energy and the
Redesigned Spill Port Example
As described in Section 5.3.5, the second example dealt with
redesiging the pump spill port. The object of the new design was to
release the U high elastic energy in the system by controlling the fuel
spilling at the port. To allow this, the pump delivery valve must be
open during the control period. This can be done by using slower
rates of energy release and delivery valves with high unloading
volumes.
Several choices of average elastic energy functions are given
in Figures 45 and 46. Results on both figures are for Test No. 6
(Table IV and Figure 33). Traces on these figures are used to
illustrate the effect of the average elastic energy on the transient
pr (,:,urs l in the sy tem. Three of' these functions are given on
lfigure'c and are used to illustrate the ei'f'ect o' charging the r'at

-1238000
C]:: 60000. 6000 0.A AVERAGE ELASTIC ENERGY
Z I0 N THE SYSTEM
4000 0
-J
8000
-.. -PUMP DELIVERY CHAMBER 6000
8- 000 _, A\.
~~~~~~~~0 02000-0 A
8~-000~
aPU MP ZZLE UPPLIVER CHAMBER
r o4000 A A 0 0 u
CaA AA 0a0 of,,00200
I ~~~~~~~0,00~~~0 A
2_8000 A
L~V~ I II
150 155 160 0 7 0
I.LJ 6000 00000 A AM A
0AE A A LA
150 155 160 165 170 175
PUMP CAM ANGLE, DEGREES
Figure 45. Injection System Variables versus Pump
Cam Angle. Effect of the Rate of the
Average Elastic Energy Drop. The redesigned Spill Port Example, Test No.
6 (Table IV).

,,, -00'0 & ~
8000 I
r6000 0 AVERAGE ELASTIC ENERGY
w 000 IN THE SYSTEM
z 0
4000 0.
2000
LLI
000 8000
00
CLt~~~~~~ ~ L L)
Wt~. 6000 60
0 NOZZPUMP DELIVERY CHAMBER
w 00 44000 A
@,0(~
oL A ".00.0 02000 0A
8000 - ~0
w' 6000 o X
150 1 55 160 165 170 1
PUMP CAM ANGOZZLE UPPE, CHAMBERDEGREES
Cam Angle. Effect of the Shape of the
iesine pill Port Exaple. Test N.
46 (Tnjable IV) ~ ~ )

-125of elastic energy drop near the end of the control period on the
resulting transient pressures. It is seen from this figure that the
solid trace represents a desirable solution, while the opposite is
true for the cases represented by circles and triangles. The triangles represent a very slow drop of the elastic energy function.
The very slow drop results in high residual pressures at the nozzle
upper chamber which will prolong the main injection period. The
circles represent a relatively fast elastic energy drop. This change
results in high nozzle upper chamber pressures which leads to afterinjection. The solid trace of the elastic energy function results
in damping the residual pressures and eliminating the possibility
of after-injection.
Figure 46 is intended to illustrate the effect of manner of
variation of average elastic energy on the resulting transient pressure. Three functions are given to demonstrate this effect. All
three functions on this figure have'the same beginning and end points
for the average elastic energy function. The solid average elastic
energy trace represents a desirable solution since it results in
damping the nozzle upper chamber pressures, therefore eliminating
after-injection. The other two traces (triangles and circles) have
less damping effect on the transient pressures than the solid line
trace.
Usually no more than four trials were needed to achieve a
desirable average elastic energy trace for both examples. It should
be noted that the procedures described here for the formulation
and application of the design program are general and could be used
with any injection system. However, the results presented here

-126apply only for the specific injection system described in this
study.
6.3 Design Results and Verifications
of the Control Valve Example
The previous section presented a study of the effect of
timing and shape of the average elastic energy function on the system
residual pressures. In this study, the average elastic energy curve
given by circles in Figure 44 represented a desirable solution for the
after-injection problem. As mentioned before, this solution is
achieved by adding a control valve in the pump delivery chamber in
ordter to r eleaLse the system average elastic energy in the controlled
mannler. The area of flow past the control valve is calculated by the
design program in the manner described in Section 5.4.4.
Design program results and simulation program verification of
these results are presented in this section for Tests No. 3, 5 and 6
(Tables III and IV) and are given in Figures 47, 48 and 49, respectively.
On these figures, the circles represent results obtained by the design
program, while simulation program verification of these results are
illustrated by solid traces. The traces include the system average
elac;tLic encrtly, pressures in the pump delivery chamber and injector
uppfe(-r chaLmbe.r and the aurea of flow through the control valve. It should
be noattel thlat a simple valve motion was used in the simulation program.
As a result, the valve area is described by a linear opening of the valve,
a constant maximum opening area and a linear closing. This area was
obtained by averaging the design program results for the control valve,e11as LIs shown on ligures 4r7 through 49.

-127o o-o DESI GN PROGRAM
— SIMULATION PROGRAM - 0.0006 z
0000 000
0 -0
CONTROL VALVE 0 0.0002
8000- 0 <
cn
Q>6000
(9
Z 4000 AVERAGE ELASTIC ENERGY
W | IN THE SYSTEM
-I
(n 2000
C0- _ 8000
PUMP DEUVERY CHAMBER 6000
4000,0, 0000 00
0o200 0
LLI 1 NOZZLE UPPER CHAMBER
t- 155 i ~ f0
BO~.oo -000
150 155 160 165 170 175
PUMP CAM ANGLE, DEGREES
Figure 47. Design Program Results of Injection System
Variables and Simulation Verification of
These Results. The Control Valvr E xample,
Test No. 3 (Table III)

-128ooooDESIGN PROGRAM
-- SIMULATION PROGRAM LCONTROL VALVEi -0 o 02
8000 -0 <
03
>: 6000 -
Z AVERAGE ELASTIC ENERGY
_c 4000 - u~IN THE SYSTEM
-)
on 2000
_J
O_ 8000
-6000
PUMP DELIVERY CHAMBER W
4000 cn
-2000 0
0
8000
_i 6000
6000g 4000 _ \ NOZZLE UPPER CHAMBER
Cr)
X 2000 0 0
0
I I.I....1
152 156 160 164
PUMP CAM ANGLE, DEGREES
Figure 48. Design Program Results of Injection System
Variables and Simulation Verficiation of
These Results. The Control Valve Example,
Test No. 5 (Table IV).

-1290.0008
00o oo o DESIGN PROGRAM z
0 0- aSIMULATION PROGRAM 0.0006
CONTROL VALVE\ 00.0004 <
0.0002 c
v, &~~~~~00
03 80006
z AVERAGE ELASTIC ENERGY
W, 4000 IN THE SYSTEM
400
J 2000
8000
03
a_
PUMP DELIVERY CHAMBER -6000 -j::
D
O3
4000 _
12,000- 0Oo0000000 2000
10 000-
0
a:
~ 6000 — NOZZLE UPPER CHAMBER
40000 00
0000
0~~0 0000 000
150 155 160 165 170
PUMP CAM ANGLE, DEGREES
Figure 49. Design Program Results of Injection System
Variables and Simulation Verification of
These Results. The Control Valve Example,
Test No. 6 (Table IV).

-130In all the cases presented, the control valve starts to open
when the needle finally closes. The maximum opening area differs from one
case to the other with the combined higher load and speed condtions
requiring larger areas of flow through the control valve than the relatively
lower speed and load conditions. The valve opening periods for Tests No.
5 and 6 (Figures 48 and 49) are both 1.2 millseconds. However, these
periods are different in terms of cam angle degrees due to the speed
difference between the tests. The valve opening period for Test No. 3
(Figure 47) is 2 milliseconds. This is greater than for Tests No. 5
and 6 primarily because of the relatively low base pressure associated
with this test.*
The average elastic energy traces on Figures 47 through 49
result in the damping of the system residual pressures and therefore
eliminating after-injection. It should be emphasized that the injection
characteristics during the main injection period are not altered since
the average elastic energy function during this period znd the system
base pressures are not changed. Simulation program results verify the
design program predictions. Small differences between design and simulation results can be attributed to the use of simple valve motion in
the sirnulation program.
6.4 Design Results and Verifications
of the Redesigned Spill Port Example
The formulation and solution of the equations used with this
example were presented in Section 5.4.4. Later, a study on the effect
of the average elastic energy function of the system residual pressures
*This test uses a different nozzle area than Tests No. 5 and 6.

-131was presented in Section 6.2.2. In this study, the solid line average
elastic energy trace on Figures 45 and 46 represented a desirable solution
to the after-injection problem. This solution is achieved by redesigning
the pump spill port in order to release the system elastic energy in
the desired controlled manner. The new areas of flow of the pump
spill port are calculated in the manner described in Section 5.4.4.
Design program results together with the simulation program verifications.
of these results are presented in this section for Tests No. 4 through
6 (Table IV).
The original system performance was illustrated in Figures
31 through 33. A comparison between this performance and the modified
system as calculated by the design program is given in Figures 50
through 52 for Tests No. 4 through 6, repsectively. On these figures,
the solid traces represent the original system performance while the circles
represent the modified one. Comparisons are given for the system average
elastic energy, the pump spill port areas, the pump delivery valve
motion and for pressures in the pump delivery and nozzle upper chambers.
As mentioned previously, the design program utilizes a controlled'unction
for the average elastic energy to calculate the performance of the
modified system. It can be seen from the above mentioned figures that the
design changes result in damping the residual pressures and eliminating
after-injection. Most of the elastic energy release is done at the pump
by keeping the pump delivery valve oepn for longer periods compared
to its original performance. This is accomplished by the relatively smaller
areas of the modified spill port and by using dELivery valves with
higher unloading volume.

-132" 6000
_ - SYSTEM WITHOUT CHANGES
w4 ooooo SYSTEM WITH CHANGES
z 4000W, 0% AVERAGE ELASTIC ENERGY
( 2~000 00o~~~~ IN THE SYSTEM
2000 —
)<
- 0.012 w
SPILL PORT < 00o
0.008 _o
BEGINS TO OPEN PUMP SPILL PORT 00.
0.004 w J
00000 ooo000000ooooooaoooooo00ooo 0000 0000 000 L. 0.08-
w 0.06 - ~ 0o00,> 0 ~OoPUMP DELIVERY VALVE
000 oooo o
0.04-) ~c~ OOOo~
w 0.02
-0
w O
00o PUMP DELIVERY CHAMBER W
06000 U
60000
F- J \NOZZLE UPPER CHAMBER
aG 2000- 0 -
00 000000 0 000
oo~o0 400000
(/)
u -2000
145 150 155 160
PUMP CAM ANGLE, DEGREES
Figrure 50. Comparisons of Original Injection System
Performance and Design Program Results of
the Modified System. The Redesigned
Spill Port Example, Test No. 4 (Table IV).

-133a 8000 - SYSTEM WITHOUT CHANGES; - 00 00000 SYSTEM WITH CHANGES
D 6000 00
z 6000 \ ~~~~~o00 AVERAGE ELASTIC ENERGY
~00 IN THE SYSTEM
z4000_ -
~ 20000 ~~~7~~~~~~~~~~~~~~o~~~~~~10000000000002
W O_ <
SPILL PORT _ 0.008 o 0
BEGINS TO OPEN PUMP SPILL PORT - cr0.004 W -
O0.~. 00~> a_
0(
0000 0000000000
Z L
~ ~Oaooooo00
-J 0.06 0
w 0_ PUMP DELIVERY VALVE
0.04 0 ooo(
>^~1> 00~o UM ELVRYCH 000 000
0 0 ~O O o o o o ~ ~ 2 0
& 0.02]
0-0 8000
X 6000 PUMP DELIVERY CHAMBER 6000 ~
60000
4000, —ooooooo-oooooooo
0000000000 ~2000 r
8000- ~oo
0 NOZZLE UPPER CHAMBER 0
a. 6000 5 Co o
cr 4000-
c) 2ooo- 0
165 160 165 170
PUMP CAM ANGLES, DEGREES
Figure 51. Comparisons of Original Injection System
Performance and Design Program Results of
the Modified System. The Redesigned
Spill Port Example, Test No. 5 (Table Iv)

oa 8000; - SYSTEM WITHOUT CHANGES
~' - xo% ooo, SYSTEM WITH CHANGES'r 6000 t_
W 4000 ~O AVERAGE ELASTIC ENERGY
Ou -_ ~~00 IN THE SYSTEM
cn 2000 SPILL PORT -o.012 0 0
BEGINS TO OPEN i
0r~~ I /t 1~~~~0.008 oo
O- 0
wO/ PUMP SPILL PORT 0.00J
I 0.004 >
O - o a ~~
0000
w 0.06 _~
0 0.04 PUMP DELIVERY VALVE
>0Oo
w 0.02 00o
w o ~o 0 8000
PUMP DELIVERY CHAMBER- C)
6000 u0
0~o~D~o ~4000
12000- ~"o%00 2000 w
010000 0
-a. o % NOZZLE UPPER CHAMBER
w 8000
03X ~~~~~0
4 6000ooo \/'o oo 0
0- 4000 00
__0 0I
2000 o0e 0Co0000o *
I 0 000 I I I'
150 155 160 165 170 175 180
PUMP CAM ANGLE, DEGREES
Figure 52. Comparisons of Original Injection System
Performance and Design Programn Results of
the Modified System. The redesigned Spill
Port Example, Test No. 6 (Table IV).

-135IJ:]ll the ascs, a d(Il:ivcr-y valve diameter of'.3('/3 in.lch wals ueJd(1
instead of the original diameter of 0.236 inch. It should be noted
that the resulting system base pressure for the modified system is the
same as the original one, and that the resulting pressures at the injector
for the modified system differ slightly from the original one.
It can be seen from Figures 50 through 52 that the resulting
area of the pump spill port starts with linear opening and then reaches
a constant value. In Figure 52, the spill port area begins to increase
again near the end of delivery valve closing. The cornstant opening of the
spill port, is nearly the same in all cases (0.0011 inch2).'TherefJor(e,
it is possible to describe a common spill port area as a function ol'
pump plunger lift for all the reported cases. Such a common description
is not possible in terms of time or pump cam angle because of the
difference in speed for each test.
A common area was used in the simulation program in order to
verify the design program results. These verifications are given in
Figures 53 through 58. Figures 53 through 55 illustrate the simulation
program results of the injection system using the modified spill port
area for Tests No. 4 through 6 (Table IV). Also, comparisons between the
oritgirnal and the modilfied systems are given in Figure 56 through 58 ior
the spill port areas and the injection chamber pressures. Simulation results
and the comparisons which are given on Figures 53 through 58 verify tile
success of the proposed design changes toward eliminating after-injection.
IFrom comparing the nozzle upper chamber pressures in Figure 53 through
55 wi th corresponding original system pressures in Figures 31 through 33,
it is clear that the proposed design changes have resulted in damping
these pressures without changing the final system base pressures.

-1360.08 - 0.016 U. 0.06o DELIVERY O';';'.O..oo 0.012'
t- 0.04 VALVE.....0.... -0.008 J. 0.02 o0 NEEDLE - 0.004
W 0 ---— 0000000-.- i
0 O w
LJ ot......s O O O Oo~ 00. o o 0 -o o 0o0 o o o o o o o o o o o- O
4000
PUMPING CHAMBER
2000
0 -6000
DELI VERY CHAMBER 00
-2000
6000_ -0
Li. 4000
2000t~~~~~ /PIPE END
~ 2000
4000
NOZZLE UPPER
2000
6000 - 0
4000
2000_ INJECTION CHAMBER
135 140 145 150 155 160 165
PUMP CAM ANGLE, DEGREES
Figure 53. Simulation Program Results of the Modified
Injection System. The redesigned Spill
Port Example, Test No. 4 (Table IV).

-137-.08. -.016
-"o o o o" ~ ~ o o ooo -.012
t- -.012
L..04- DELIVERY.j;. 0.008
-J +VALVE.'. 00
_.0-. - NEEDLE.02- all.~~~~'. 004 -
C:) Oo o o b o oO b. o0o o o 0o Q oPUMPING CHAMBER
400O
8000
DELIVERY CHAMBER
~ _0) ~-4000
| PIPE END|
4000I
NOZZLE UPPER
3000- _ O0
4000 _ / NJECTION CHAMBER
135 140 145 150 155 160 165 170
PUMP CAM ANGLE, DEGREES
F:igure j4. Simulation Program Results of the Modified
Injection System. The Redesigned Spill
Port Example, Test No. 5 (Table IV).

-138-8_.....Z....... -.016
DELIVEIRIY..oee;;'o oo''.e o. o o eo 0 e 0i. - U.
Uc DELIVERY O... ooooo o 012
- o.0_VALVE. ~08.
I O.004_
C).o0ooo 0o 000@ ~ ~ ~ ~00000000000000000000000 w
PUMPI NG CHAMBER
12Q00
8000
DELIVERY CHAMBER
4000
8000~~~~~~~~~ 0
I Pi-PE END _
w
NOZZLE UPPER CHAMBER - 8000
4000
83001 f\ I
4000 INJWECTION CHAMBER
135 140 145 150 155 160 165 170 175 180
PUMP CAM ANGLE, DEGREES
Figure 55. Simulation Program Results of the Modified
Injection System. The Redesigned Spill
Port Example, Test No. 6 (Table IV).

SYSTEM WITHOUT CHANGES
< 0.012- oooooSYSTEM WITH CHANGES IN
w THE SPILL PORT AREA
0 0.008
-i 0.006 PR
w 00 PUMP SPILL PORT
> &: 0.004
0.002 00000 0
D 0 0 -0
6000 H( La
L 4000
D> INJECTION CHAMBER
~3 2000 0
0. 00
0
135 140 145 150 155 160 165
PUMP CAM ANGLE, DEGREES
Figure 5c. CooariJsons of Injection Chazber kressires of Original
anT ZI~Izified Systems. The edees'ied Spill PDort
Kx~nple, Test No. 4 (Table IV).

SYSTEM WITHOUT CHANGES
N 0.010 oooooSYSTEM WITH CHANGES IN
wO O THE SPILL PORT AREA
cr 0.006
w 0 0.006
W - PUMP SPILL PORT
0.002
o 0
Z U)0.002
0 U. 1 _6 0 00000 0 0 00 00 0 000
0 0
8000 -
too0 INJECTION. CHAMBER
tr):3 4000
C,)
a. 0
a.0 000 000 00000000
135 140 145 150 155 160 165 170
PUMP CAM ANGLE, DEGREES
Figure 57. Comparisons of In ection Chamber Pressures of Original
and Modified Syste-s. The Redesigned Spill Port
Example, Test XIc. 5 (Table IV).

SYSTEM WITHOUT CHANGES
z"
P~- 0.012 ooooooSYSTEM WITH CHANGES IN
THE SPILL PORT AREA
0.008
W Ju PUMP SPILL PORT
>amj
0 IL
Uu, 0.004
Zb I ^d00 0000000000000
0
a 12,000
CId
D 8000 INJECTION CHAMBER. 4000 Ib
0 000000000
I I I~~~~~~~~~~ I1
135 140 145 150 155 160 165 170 175 180
PUMP CAM ANGLE, DEGREES
Figure 5=. Comparisons of Injection Charber Pressures of Original
and Mosdified Systems. The Pedesi zned Spill Port
Example, Test No. 6 (Table LV'

-142Modified spill port areas are drawn as function of pump cam
angle and are compared with the original areas on Figures 56 through
58. As mentioned previously, these modified areas will appear the
same if they are drawn as functions of pump plunger lift. On the
same set of figures, comparisons between the injection pressure characteristics for the modified and original systems indicate that slight
differences occur for Tests No. 4 and 5 while a relatively bigger difference was observed with Test No. 6. It should be noted that Test
No. 6 has high speed and load conditions and high system base pressure
(2400 psi). This relatively high base pressure is higher than the
needle closing pressure (2200 psi). Therefore, it can result in prolonging the injection period as seen from Figure 58. Better results
for the system injection pressures were obtained by using a different
area for the spill port as seen in Figure 59. The choice of this new
area was directed toward lowering the system base pressure. This was
achieved by using higher uncovering rates for the spill port near the
end of injection while keeping these areas the same as those on Figure
58 for the early part of the spill. The system base pressure for the
results given on Figure 59 was found to be 1600 psi.
The modified spill port area associated with Test No. 6 and
given on Figure 59 was used in the simulation program to investigate
its effect on Tests No. 4 and 5. This area resulted in lowering the
base pressures for these tests and slightly improved the injection
pressure characteristics. However, extreme lowering of these base
pressures at a combined low load and speed conditions (Test No. 4) results in reaching vapor pressures. It should be noted that mechanical
damage due to vapor bubble collapse is less harmful at combined low
speed and load conditions than at the combined high speed and load

z =' SYSTEM WITHOUT CHANGES
W 0.012 000000 SYSTEM WITH CHANGES IN
THE SPILL PORT AREA
O e 0.008
Ll
wI PUMP SPILL PORT
0.004 0 0
~o~~o~ 000
12,000
w 8000
PU: MINJECTION CHAMBER
U) o
w 4000
0
I I I I I I I
135 140 145 150 155 160 165 170 175 180
PUMP CAM ANGLE, DEGREES
Figure 59. Comparisons of Injection Chamber Pressures of Original
and Modified Systems. The Redesigned Spill Port
Example, Test No. 6 (Table IV).

-144conditions.(23) Therefore, vapor pressures can be allowed to occur at
the low load and speed conditions.

VII. SUMMARY AND CONCLUSIONS
The primary objectives of this thesis were to achieve a
good understanding of the theory describing the diesel injection
system and to use this understanding to develop a theoretical control method by which design changes could be determined to eliminate undesirable system characteristics (i.e. after-injection).
In this study, the after-injection phenomenon was experimentally surveyed. Then a computer simulation model was developed
to predict the theoretical system performance. The results from
the computer simulation were compared with experimental data taken
on actual test equipment. Then, an investigation of a theoretical
control parameter was carried out which led to the formulation
of a design program that used the injection system average elastic energy as the control parameter. Two injection system design
changes were investigated. The first was the addition of a control valve in the pump delivery chamber which is used to release
the system excess elastic energy in a controlled manner and eliminate after-injection. The second change centered on re-designing
the pump spill port to control the rate of fuel spill in order to
eliminate after-injection. The results of both changes were determined and were verified using the simulation program.
The study included three major phases; namely, experimental
survey of the after-injection phenomenon, computer simulation of the
injection system, and the theoretical control of the after-injection
-145 -

phenomenon. Specific conclusions related to each phase of study are
given and will hopefully contribute to the development of future
injection systems. These conclusions can be summarized as follows:
1. Currently used injection systems of the Bosch type
are usually designed to operate at fuel deliveries
and injection pressures considerably below their
full capacities in order to avoid after-injection.
These low injection pressures limit fuel atomization and penetration in the combustion chamber.
2. The optimum design point of injection systems is
located critically close to the after-injection
zone. Any accumulation of carbon or fuel impurities on the injection holes changes the system
performance drastically and introduces large
amounts of after-injection.
3. The computer model presented herein improves on
existing injection system models by using the
characteristic method to solve the exact partial
differential equations representing the wave propagation phenomena in the pipe lines. It also includes the effect of variable wave speeds and uses
a variable time increment solution technique
(predictor-corrector method). These features
improve the accuracy and efficiency of the
simulation model.
4. The computer model presented here accurately
simulates the injection system perfoMrimance.

-147This is demonstrated in Tables III and IV by
a mass continuity check within 4.5 percent and
by a base pressure check within 300 psi. The
accuracy of the system pressures is demonstrated
by the good correlation between the experimental
and theoretical model results as shown in Figures
28 through 34. Therefore, the analytical model
can be confidently used to study the diesel injection system and the phenomena associated with its
performance.
5. The injection system average elastic energy is
a useful control parameter. It can be used to
eliminate undesirable system characteristics.
This was demonstrated in this thesis by eliminating after-injection. Further use of this
concept can improve other injection system characteristics. This concept can also be applied
to other similar complex systems which are characterized by high frequency internal and external
boundary conditions and which cannot be controlled using existing valve stroking techniques.
6. The control method presented allows a theoretical
systematic design improvement of injection systems for the first time. This has been demonstrated
by two examples in which the injection system pressures after the end of the main injection were controlled in order to eliminate the after-injection

-148phenomenon. Such knowledge many be helpful in improving future injection systems and may lead to
improved combustion and reduced exhaust emissions.
7. The pump spill port or an additional valve in the
pump delivery chamber can be properly designed to
eliminate after-injection. This can be done without seriously altering the injection system performance during the main injection period.

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