modelling of high-pressure fuel system for controller...

UPTEC F 19025

Examensarbete 30 hpJuni 2019

Modelling of high-pressure fuel system for controller development

Eric Pettersson

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Modelling of high-pressure fuel system for controllerdevelopment

Eric Pettersson

This master thesis treats the modelling of a common-rail direct fuel injection systemwhere pressure generation is decoupled from the injection process. It has beenshown that the fuel pressure plays a vital role for the general performance of theengine, affecting both emissions and efficiency, and it is carefully regulated to achieveoptimal performance at different operating points. In an attempt to facilitate thedevelopment of the responsible control algorithms, a simulation framework has beenrequested. A model describing the complete work cycle of the high-pressure fuel system isdeveloped and implemented in a Simulink environment. It is to a large extent basedon the underlying physics and constructed in a modular manner, which allows fordifferent engine configurations to be simulated. The modelled pressure signal iscompared to experimental data at different operating points with promising results incapturing the transient behaviour from a low-level perspective. Additionally, itmanages to replicate some of the pressure oscillations which has been observed inthe real system and it shows good response to changes in the input signals. However,there are some areas which are subject to improvement since capturing the staticpressure levels over longer drive cycles has proved to be a difficult task. Overall, the developed model serves as a starting point for future development andvalidation of control algorithms.

Keywords: Common-Rail Direct Injection, fuel system, water hammer, pressureoscillations, physical modelling, state-space representation

ISSN: 1401-5757, UPTEC F 19025Examinator: Tomas NybergÄmnesgranskare: Ken MattssonHandledare: Vaheed Nezhadali

ii

Populärvetenskaplig SammanfattningCommon-rail-systemet är ett e�ektivt bränslesystem som är vanligt förekommandebland moderna dieselmotorer. Den största fördelen gentemot utmanande teknolo-gier är dess förmåga att frikoppla insprutningarna från tryckuppbyggnadsprocessenvilket introducerar möjligheten till mer än en insprutning per insprutningstakt, nå-got som har påvisats ha en positiv inverkan på såväl motore�ektivitet samt utsläppav avgaser. Mängden bränsle som sprutas in i cylinderkammaren har en kraftig in-verkan på motorns prestanda och regleras noggrant genom att justera bränsletrycketsamt insprutningens varaktighet för varje arbetspunkt.

I detta examensarbete så har en modell av ett common-rail-system tagits framsamt implementerats i Simulink med syfte att underlätta utvecklingsprocessen avbränslesystemets styrsystem hos Scania. Modellen är till stor del baserad på denbakomliggande fysiken och är modulärt konstruerad vilket gör det möjligt att simulerasamt analysera olika hårdvarukonfigurationer. Den beskriver en stor del av bränslesys-temet och fokuserar främst på att fånga tryckförändringar i det gemensamma bränsleröret(common-rail) i samband med individuella insprutningar och pumpslag.

Den implementerade modellen fångar det generella beteendet hos det verkligasystemet och visar lovande resultat när det kommer till att beskriva enskilda tryck-förändringar i det gemensamma bränsleröret. Även de tryckoscillationer som ob-serverats i det verkliga systemet återskapas till viss del. Det visar sig dock vara ut-manande att modellera de statiska trycken vid olika arbetspunkter vilket resulterari en avvikelse i tryckuppskattningen när systemet simuleras under längre körcykler.

Avslutningsvis så är slutsatsen att den framtagna modellen är väl lämpad somett första steg i utvecklingsprocessen av framtida regleralgoritmer. På grund av denhöga beräkningskomplexiteten är den däremot inte anpassad för tillämpningar såsom virtuella trycksensorer då dessa simuleras i realtid.

iii

AcknowledgementsFirst of all, I would like to express my sincere gratitude to my thesis supervisorPh.D. Vaheed Nezhadali for his support and guidance during this thesis project.His extensive knowledge has been an important asset and I would not have beenable to accomplish this without him.

Besides my supervisor, I would also like to thank my colleagues and friends atScania for assisting me with their expertise, as well as my subject reader docent KenMattsson for his quick response and feedback. Finally, I wish to thank my familyfor their endless support which has made all of this possible.

Uppsala, June 2019Eric Pettersson

iv

NotationAbbreviations

AIM Active Inlet MeteringBDC Bottom Dead CenterCAD Crank Angle DegreeCI Compression IgnitedCR Common-RailCRDI Common-Rail Direct fuel InjectionECU Engine Control UnitEOI End Of InjectionEOTTL End Of Time To LeaveHPP High-Pressure PumpLPP Low-Pressure PumpMDV Mechanical Dump ValveOCV Outlet Check ValveODE Ordinary Di�erential EquationOP Operating PointPDE Partial Di�erential EquationSI Spark IgnitedSOI Start Of InjectionSOTTL Start Of Time To LeaveTDC Top Dead Center

General symbols

A Areaa AccelerationE Bulk ModulusF ForceI Currentk Spring ConstantL Lengthm Massneng Engine Speedp Pressureq Volumetric Flowfl Mass Density◊crank Crank AngleT TemperatureV Volumev Velocity‹ Damping Factorw Width

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objective and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Related Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 System Overview 52.1 The Compression Ignited Four-Stroke Cycle . . . . . . . . . . . . . . 52.2 The Common-Rail Direct fuel Injection System . . . . . . . . . . . . 6

2.2.1 The High-Pressure Pump . . . . . . . . . . . . . . . . . . . . . 72.2.2 The Active Inlet Metering Valve . . . . . . . . . . . . . . . . . 72.2.3 The Rail and Injectors . . . . . . . . . . . . . . . . . . . . . . 8

3 Method 103.1 Collecting Experimental Data . . . . . . . . . . . . . . . . . . . . . . 103.2 Modelling and Implementation . . . . . . . . . . . . . . . . . . . . . . 11

3.2.1 Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.2 Active Inlet Metering Valve Model . . . . . . . . . . . . . . . 133.2.3 High-Pressure Pump Model . . . . . . . . . . . . . . . . . . . 163.2.4 Rail Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.5 Injector Model . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Results and Discussion 274.1 Model Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1.1 AIM Valve Armature Stroke . . . . . . . . . . . . . . . . . . . 274.1.2 Pump Chamber Pressure Dynamics . . . . . . . . . . . . . . . 284.1.3 Rail Pressure Injection Response . . . . . . . . . . . . . . . . 294.1.4 Computational Demand and Model Speed . . . . . . . . . . . 29

4.2 Rail Pressure Validation . . . . . . . . . . . . . . . . . . . . . . . . . 304.2.1 High-Level Validation . . . . . . . . . . . . . . . . . . . . . . . 304.2.2 Low-Level Validation . . . . . . . . . . . . . . . . . . . . . . . 36

5 Sensitivity Analysis 425.1 Rail Pressure Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1.1 Fuel Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 425.1.2 Geometrical Parameters . . . . . . . . . . . . . . . . . . . . . 435.1.3 AIM Valve Control Signals . . . . . . . . . . . . . . . . . . . . 44

v

CONTENTS vi

5.2 Pressure Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6 Conclusions and Outlook 486.1 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

List of Figures

2.1 Overview of the CRDI fuel system. Adapted from c•Scania CV AB2013, Sweden, Reprinted with permission. . . . . . . . . . . . . . . . . 7

2.2 Conceptual illustration of the AIM valve and its associated pumpelement. The spring force and magnetic force are marked by Fspr andFm respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1 Projections of modelled bulk modulus. . . . . . . . . . . . . . . . . . 123.2 Projections of modelled mass density. . . . . . . . . . . . . . . . . . . 133.3 AIM valve current pulse and armature stroke. . . . . . . . . . . . . . 133.4 Force versus current relationship for the AIM valve armature. . . . . 153.5 Measured cam lift as a function of the crank angle. . . . . . . . . . . 183.6 Artificial partitioning of the rail. . . . . . . . . . . . . . . . . . . . . . 213.7 Required injector ontime as a function of injected fuel mass and rail

pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.8 Modelled injection rate-shape. . . . . . . . . . . . . . . . . . . . . . . 253.9 Injector drain leakage. . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1 Illustration of the AIM valve armature transitioning from being fullyopened to completely closed. The left figure corresponds to operatingpoint 1 and the right figure to operating point 9, see Table 3.1. . . . . 28

4.2 Pressure dynamics within one of the pump elements over the courseof 720o CAD. Rail pressure is shown as a reference level. . . . . . . . 28

4.3 Modelled rail pressure before, during and after a single injection forboth rail model approaches. . . . . . . . . . . . . . . . . . . . . . . . 29

4.4 Comparison between modelled and measured rail pressure during awork cycle covering each operating point in Table 3.1. . . . . . . . . . 31

4.5 Comparison between modelled and measured rail pressure during thetransitioning between operating points 1 and 2. Engine speed, totalcommanded injection amount and relevant AIM actuation times aredisplayed as well. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.6 Comparison between modelled and measured rail pressure during thetransitioning between operating points 5 and 4. . . . . . . . . . . . . 33



vii

LIST OF FIGURES viii

4.9 Modelled versus measured rail pressure at an engine speed of 1700rpm, pr ¥ 1480 bar and large injection quantities. . . . . . . . . . . . 36

4.10 Frequency spectrum of the measured and modelled pressure signal foroperating point 7 in Table 3.1. . . . . . . . . . . . . . . . . . . . . . . 37

4.11 Modelled versus measured rail pressure at an engine speed of 1100rpm, pr ¥ 1080 bar and small injection quantities. . . . . . . . . . . . 37


4.13 Comparison between modelled and measured rail pressure at 1100rpm, pr ¥ 950 bar and large injection quantities, see operating point4 in Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39


4.15 Comparison between a low-pass filtered model signal and experimen-tal data at operating point 4. . . . . . . . . . . . . . . . . . . . . . . 40

4.16 Comparison between modelled and measured rail pressure at 2200rpm, pr ¥ 1800 bar and small injection quantities. . . . . . . . . . . . 41

4.17 Frequency spectrum of the measured and modelled pressure signal foroperating point 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

List of Tables

3.1 Engine operating points. . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.1 Simulated time versus real time. . . . . . . . . . . . . . . . . . . . . . 30

5.1 Sensitivity analysis for fuel parameters. . . . . . . . . . . . . . . . . . 435.2 Sensitivity analysis for geometrical parameters. . . . . . . . . . . . . 445.3 Sensitivity analysis for small perturbations in tAIM,cd. . . . . . . . . . 455.4 Sensitivity analysis for small perturbations in SOTTL. . . . . . . . . 455.5 Sensitivity analysis for frequency of rail oscillations. . . . . . . . . . . 465.6 Sensitivity analysis for amplitude of rail oscillations. . . . . . . . . . . 47

ix

Chapter 1

Introduction

The purpose of this chapter is to give a brief background, define the objective andscope and present research related to this thesis.

1.1 BackgroundThe Common-Rail Direct fuel Injection (CRDI) system is an e�ective injection sys-tem among diesel engines with an advantage over other technologies due to its abilityto decouple the process of generating high pressure and the injections. This decou-pling allows for precise and controlled injections of the fuel [1] at the desired timesand intervals and introduces the possibility of pilot injections. Several parametersa�ect the amount of injected fuel, including the fuel pressure as well as the tim-ing and duration of the injection. A careful choice of these parameters has beenshown to increase the e�ciency of the engine, reduce the emissions and lower thecombustion noise [2].

A model of the fuel system that is ready to be integrated with Scanias alreadyexisting simulation framework of the engine has been requested. It would allowfor a virtual test environment which could facilitate the development of controlalgorithms. Additionally, it could also be used together with the embedded softwareas a first step towards a virtual pressure sensor for the rail. This would in turn openup the possibility of advanced software tools for hardware diagnostics.

1.2 Objective and ScopeThe main objective of this thesis is to develop a model of the high-pressure circuit ofthe CRDI system, mainly revolving around the High-Pressure Pump (HPP) and theCommon-Rail (CR). The model is supposed to be based on the underlying physicsand should be able to capture how the pressure within the pumping chambers andrail varies over time. Moreover, the model is supposed to describe the whole workcycle rather than being based on mean values since the dynamics within the cycleare crucial for future applications. More specifically, the model should

• to a large extent be based on the physical properties of the system such thatit is modifiable according to hardware and fuel properties,

1

1.3. RELATED RESEARCH 2

• take the AIM valve actuation times from a controller with feedback from railpressure as input,

• capture the pressure variations in the rail from each individual pump cycleand injection as well as the pressure changes in each pump element.

The model should be implemented in a Simulink environment and verified againstexisting data of the rail pressure generated in a test cell. Finally, a validationof the possibility of using the developed model for controlling purposes should beperformed.

This thesis will not put any focus on the development of a controller that canbe used together with the model nor on an detailed model of the injectors as thatis beyond the scope of this study. Furthermore, in order to limit the scope of thisreport, only a 6-cylinder engine configuration is described even though the modelshould be able to adapt other hardware configurations as well.

1.3 Related ResearchThe purpose of this section is to give an overview of previous studies related tothis thesis. Suggested methodologies and results are presented to give the reader aninsight into commonly encountered problems and assumptions.

Rodriguez-Anton, Casanova-Kindelan and Tardajos [3] show measured valuesof viscosity, density and vapour pressure for some commonly used fluids in dieselinjection systems, e.g. diesel fuel and normalised testing fuel. These physical prop-erties are of great importance in order to get an accurate model description of adiesel injection system as they have a direct impact on the pressure and are stronglycorrelated to the leakage flow between piston and cylinder etc. They present expres-sions for the di�erent properties together with the associated, empirically derived,constants.

Botwinska, Mruk and Krawiec derive a model of the high-pressure common-railsystem adapted for control applications in their study from 2016 [4]. The modelis based on the physical properties and dynamics of the system but neglects somemajor concepts such as the temperature dependency of the fluids properties sinceboth the kinematic viscosity and the modulus of elasticity are assumed to be constant(temperature independent).

In [1], Prinz et al. present a physical model of a common-rail system. The dieselfuel is modelled as an isentropic fluid and the authors suggest a physical descriptionof the fuel that is divided into three separate cases depending on the pressure. Theypresent a model of the pumping chamber where the inflow is regulated by pressuredependent mechanical valves in contrast to the HPP studied within this thesis wherethe fuel inflow to the pump elements is regulated by the AIM valve. The pressuredynamics inside the pump element is governed by an expression for the balance ofmass where three di�erent flows are considered: the inflow from the low-pressureside, the outflow to the rail and the leakage flow between cylinder and piston. Theleakage flow is modelled as laminar flow and is defined by a leakage coe�cient anda pressure di�erence.

1.4. THESIS OUTLINE 3

Wang, Zheng and Tian [5] propose a physical description of the high-pressurecommon-rail injection system that they divide into three sub-systems: the high-pressure pump, the common-rail and the injectors. The model of the pumpingchamber is similar to the one presented by Prinz et al., however somewhat sim-plified as the leakage flow between the cylinder and the piston is considered to beconstant. The results show a good correspondence between the developed modeland the reference model (AMESim) even though it seems to have some problemswith capturing the transients.

Qian and Liao [6] suggest a more advanced model of the high pressure pumpwhere they take structural deformations and nonisothermal flow at the interfaceleakages into consideration. Their work revolves around modelling the fluid in thepump chamber and rail as they derive a connection between the interfacial leakage,the volumetric e�ciency and the chamber pressure. The deformation of the cylinderas a result of pressure change is described by linear elastic theory, taking Young’smodulus, the Poisson’s ratio and the geometry of the cylinder into account. Thechange of fuel temperature in the chamber is assumed to only be dependent on thecompression work done by the piston in order to simplify the model, thus neglectingthe heat transfer process from cylinder to fuel etc. Furthermore, the leakage flowbetween piston and cylinder is considered to be laminar due to small Reynoldsnumbers and is described by lubrication theory.

Källkvist presents a model for an old version of the fuel system in his masterthesis at Scania [7]. The proposed model of the high pressure pump has similar char-acteristics to the model developed by Qian and Liao [6], taking the pressure inducedstructural deformation of the components into account. Furthermore, Källkvist sug-gests that the radial clearance between the piston and the cylinder is temperaturedependent due to the thermal expansion induced by the change in temperature.This dependency is taken to be linear and the temperature of the cylinder/pistonpair is assumed to be the same as the fuel temperature. The leakage flow betweenthe cylinder and piston is modelled as a combination of Poiseuille and Couette flow.

Roemer et al. [8] propose a physical description of the fluid force working on aplunger moving in viscous fluid. The force is assumed to consist of di�erent termsincluding the acceleration of surrounding fluid, the viscous shearing coe�cient andthe drag coe�cient together with additional frictional terms.

1.4 Thesis OutlineChapter 2: System OverviewIntends to give the reader an overview of the four-stroke cycle and the CRDI fuelsystem.

Chapter 3: MethodThorough explanation of the method and modelling process.

Chapter 4: Results and DiscussionGeneral characteristics of the model and validation against experimental data arepresented and discussed.

1.4. THESIS OUTLINE 4

Chapter 5: Sensitivity AnalysisStudy of the sensitivity to perturbations in parameters and input signals.

Chapter 6: Conclusions and OutlookPresents the conclusions that have been drawn based on the obtained results andthe discussion. Gives insight and recommendations of possible future work.

Chapter 2

System Overview

This chapter aims to give the reader a short introduction to the four-stroke cycleand a general overview of the CRDI system that has been the focus of this the-sis. Important concepts as well as commonly used expressions are presented andexplained.

2.1 The Compression Ignited Four-Stroke CycleThe engines modelled within the scope of this thesis falls under the category ofCompression Ignited (CI) four-stroke engines where the ignition is induced by theheat generated from compression of the in-cylinder gas mixture. This is in contrastto the Spark Ignited (SI) engines where an external spark plug is required to initiatethe combustion.

The four-stroke cycle can be divided into four di�erent strokes/processes whichtake place in the following order:

Intake stroke The piston starts at the Top Dead Center (TDC) and movestowards the Bottom Dead Center (BDC). When the volume increases, fresh airprovided by the intake manifold is drawn into the cylinder which counteracts theinduced pressure drop. As a result, the cylinder pressure is kept at a pressure closeto the pressure within the intake manifold.[9, p. 81]

Compression stroke The piston moves upwards from the BDC to the TDC,compressing the air within the cylinder. The rapid compression process results in asignificant increase in temperature and as the diesel fuel is injected into the cylinderthe air temperature is high enough for the air/fuel mixture to ignite without theneed of any external spark source. [9, p. 81]

Expansion stroke The work produced by the combustion process forces thepiston downwards. The exhaust valve is opened as the piston approaches the BDC,letting the exhaust gases escape the cylinder. This results in a decrease in the in-cylinder pressure. [9, p. 82]

Exhaust stroke Starting from the BDC, the piston moves upwards which forces

5

2.2. THE COMMON-RAIL DIRECT FUEL INJECTION SYSTEM 6

the remaining fluids to leave the cylinder volume. This leaves room for new freshair to get sucked in and completes the cycle. [9, p. 83]

The full four-stroke cycle is completed over the course of 720¶ Crank AngleDegrees (CAD) and it is often convenient to define the various events taking placeduring each cycle in terms of this specific unit. The crank angle is given by

Y]

[◊crank = neng2fi

60 [rad/s],◊crank =

st

0 ◊crankds = neng2fi

60 t [rad],(2.1)

where neng [rpm] is the engine speed.

2.2 The Common-Rail Direct fuel Injection Sys-tem

The CRDI system can be divided into two subsystems: the low-pressure circuit andthe high-pressure circuit. The low-pressure side of the system has the task of supply-ing the high-pressure side with filtered and water separated fuel at a stable pressure[9, p. 322]. This pressure level is in turn determined by the engine’s operating point.

The fuel is first drawn out of the main tank by the transfer pump, through afilter, and into a smaller storage tank. Thereafter, it is fed to the high-pressurepump (HPP) by the low-pressure pump (LPP) through another filter. The HPPhas the task of raising the fuel pressure of the low-pressure side of the fuel systemto the levels required in the high-pressure side. The desired pressure level in the raildepends on the engine’s operating point.

The highly pressurised fuel in the rail is distributed among the injectors whichthen inject it into the cylinders. Each injector is provided with a rapidly switchingsolenoid valve that is carefully controlled by the Engine Control Unit (ECU) sincethe timing and duration of the injections are crucial to achieve good performance.An overview of the CRDI system is seen in Figure 2.1 where components importantfor this thesis are marked.


MDVInjector

CR

Sensor

HPP

Figure 2.1: Overview of the CRDI fuel system. Adapted from c•Scania CV AB2013, Sweden, Reprinted with permission.

2.2.1 The High-Pressure PumpAs mentioned earlier, the HPP has the task of raising the fuel pressure of the low-pressure circuit to the levels required by the rail and injectors. This is a sensitiveand complex process that must be carefully controlled to keep the rail pressure atthe desired level, which in turn is determined by the instantaneous operating pointof the engine.

The HPP consists of two individual, but identical, plunger-based pump elements.The plungers are floating freely within the cylindrical pumping chambers but areforced upwards by the eccentrics of the cam during the compression stage. The twopump elements operate in opposite phases of each other so that the fuel is regularlydelivered to the rail.

The chamber volume varies with the cam profile, reaching its minimum valueat the TDC of the pump cycle. However, it is constructed in such a way that theplunger does not reach all the way up which leaves a small volume of fuel trappedat the top of the chamber during each compression stroke. This is referred to asthe dead volume, or Vdead, of the pump element. Furthermore, leakage flows can beobserved at the plunger/cylinder interface, reducing the e�ciency of the pump.

Each pump element is connected to the low-pressure side of the system by itsassociated AIM valve and to the rail by a mechanical spring loaded Outlet CheckValve (OCV). The OCV is kept closed by the spring force until the pressure di�er-ential is large enough for it to open, letting the highly pressurised fuel flow into therail.

2.2.2 The Active Inlet Metering ValveThe high-pressure circuit is connected to the low-pressure circuit via two ActiveInlet Metering Valves (AIM valves), one for each pump element of the HPP. Theseare actuators in the form of spring loaded electromagnetic solenoid valves controlledby the ECU. Each AIM valve is responsible for regulating the fuel flow between the


low-pressure side and its associated pump element and the setup is visualized inFigure 2.2.

Figure 2.2: Conceptual illustration of the AIM valve and its associated pump ele-ment. The spring force and magnetic force are marked by Fspr and Fm respectively.

The AIM valve is kept open by the spring and pressure forces during the de-compression/suction stroke of the pump so that fuel can flow from the low-pressurecircuit into the pump chamber. It can however be closed on demand by the ECUwhich typically is done during the compression stroke of the pump, forcing the fuelto stay within the pumping chamber to build up pressure. Being able to control theamount of fuel that gets trapped in the pumping chamber introduces the possibilityof regulating the amount of fuel delivered to the rail by the otherwise completelymechanical HPP.

Timing is vital and operating the AIM valve in an optimal manner is a complextask. There are variable actuator delays that depend on parameters such as pressureand engine speed that has to be taken into consideration in order to achieve goodperformance.

2.2.3 The Rail and InjectorsThe CR works as an accumulator of highly pressurised fuel, distributing it to theinjectors at the desired pressure. It is connected to the HPP through two separatepipes, one for each pump element, and to each injector. Furthermore, the numberof injectors corresponds to the number of cylinders.

The CR is equipped with a pressure sensor which collects real-time data as well aswith a Mechanical Dump Valve (MDV) that protects the system from reaching toohigh pressures. The MDV is mechanically pre-loaded and designed to open when therail pressure exceeds a certain value, setting an upper limit to the operating rangeof the system. After being triggered, it mechanically regulates the rail pressure tostay at a constant rail pressure.

The injectors are complex actuators that operate under strict requirements ofprecision and accuracy. They are supplied with fuel by the CR which they then injectdirectly into each cylinder. The injectors are regulated by rapidly switching solenoidvalves controlled by the ECU which allows for pre-injections (pilot injections) inaddition to the main injections. The characteristics of the injection process plays


a significant role for the evaporation of diesel in the cylinder, which in turn has adirect impact on the combustion process [9, p. 325].

The amount of fuel that is injected into the cylinder is regulated by the openingduration of the solenoid valve and the fuel pressure within the injector body, makingthe process sensitive to pressure changes in the CR. These pressure changes caneither be intentional, stemming from changes in the desired rail pressure, or can bethe result of unwanted pressure oscillations in the rail.

The pressure oscillations that has been observed in the CR can be explained bythe water hammer e�ect. A water hammer is the pressure wave originating fromsudden changes in fluid velocity [10] and is primarily caused by the rapidly switchinginjector flows and the pulsating flow from the HPP. As the injectors are closed itis possible to observe a pressure build-up due to the momentum of the fluid. Thiscreates a pressure wave propagating through the rail at the speed of sound which inturn is related to the bulk modulus and the density of the fluid. However, the waterhammer wave is attenuated by frictional forces and will eventually disappear.

The pressure oscillations in the CR must be taken into consideration as theyhave a direct impact on the injection process. Depending on the phase of the waveduring an injection, one can observe either overfueling or underfueling as a result ofthe water hammer e�ect.

Chapter 3

Method

This chapter aims to give a thorough explanation of the methodology and coversthe gathering of experimental data as well as the modelling approach. Some of thefigures are normalized due to confidentiality reasons.

3.1 Collecting Experimental DataExperimental data is collected from measurements carried out in an engine test cell.Since there are no sensors installed inside the pump chambers, the only availabledata is the signal collected by the pressure sensor situated on the rail. The signalis sampled at a fixed sampling frequency over the course of a full four-stroke cycle(720o CAD) or over longer drive cycles ranging over several operating points.

Data is collected at several di�erent engine operating points defined by the enginespeed, neng, and the rail pressure, pr. A wide range of operating points is necessaryfor a reliable performance evaluation of the model and the experimental data isrecorded at ten di�erent configurations covering almost the complete operating rangeof the system. The engine speed is varied within the interval neng ‘ [600, 2300] [rpm]and the rail pressure is varied within the interval pr ‘ [600, 1800] [bar]. Table 3.1shows the di�erent combinations.

Table 3.1: Engine operating points.

Test number neng [rpm] pr [bar]1 600 6002 600 8003 1100 9004 1100 9505 1100 10806 1700 14507 1700 14808 1700 17259 2200 180010 2300 1800

10

3.2. MODELLING AND IMPLEMENTATION 11

In addition to the measured pressure signal, also the control signals sent fromthe ECU to the AIM valves and injectors are recorded so that the same signals canbe used as input data to the computer model. These signals include the commandedamount of fuel to be delivered by the main and pilot injections as well as the relevantactuation times.

3.2 Modelling and ImplementationThis section intends to cover the complete modelling process of the CRDI systemin a systematic and thorough manner. Important physical and mathematical re-lations are presented for relevant fluid properties, physical components and otherphenomena.

3.2.1 Fluid PropertiesLiquids are often idealised by the assumption of complete incompressibility in themodelling of hydraulic systems, implying that properties such as the bulk modulusand mass density are invariant over the range of pressures that the system is subjectto. This is a valid assumption in certain applications and commonly seen for fluidpower systems operating in the range of 0-400 bar [2]. However, since the fuelpressure in the CRDI system is far out of this interval with pressures reachingover 2000 bar under normal conditions, it is no longer viable to assume constantproperties.

The dynamic fluid properties that is used for the modelling of the CRDI systemwithin the scope of this thesis is the bulk modulus and mass density of the dieselfuel. Furthermore, the diesel fuel is assumed to remain in its liquid phase during allthe modelled events. As a consequence, eventual cavitation is not captured by themodel.

Additionally, both the temperature in the whole system, T, and the pressure ofthe low-pressure circuit, plow are considered to be constant.

Bulk Modulus

The bulk modulus characterizes the compressibility of the fuel and is defined as theratio between an infinitely small pressure increase and the corresponding relativedecrease in volume [11],

E = ≠Vdp

dV. (3.1)

Rodriguez-Anton, Casanova-Kindelan and Tardajos [3] argue that the bulk modulusplays a significant role in the modelling of diesel injection systems and state thatthe use of a constant value measured at atmospheric pressure can result in pres-sure deviations of up to 20%. With this in mind, it is obvious that an accuraterepresentation is of high importance.

The bulk modulus of the diesel fuel is modelled by a second degree polynomialin two variables,

E(p, T ) = C1 + Cp1p + Cp2p2 + CpxT pT + CT 1T + CT 2T

2, (3.2)


where T is the temperature and p the pressure. The constants are used to parametrizethe specific fuel of use and have previously been fitted to measured data by Scania.Furthermore, it should be noted that equation (3.2) is only reliable for temperaturesand pressure levels within the operating range of the system. For very high pres-sures and/or temperatures, the second order terms will dominate and non-physicalbehaviour can be observed. One-dimensional projections of the temperature andpressure dependency of the modelled bulk modulus are seen in Figure 3.1.

40 60 80 100 120

T [oC]

1

2

3

4

5

E [

Pa

]

p = 2000 [bar]

p = 1500 [bar]

p = 1000 [bar]

p = 500 [bar]

0 500 1000 1500 2000 2500 3000

p [bar]

1

2

3

4

5

E [

Pa

]

T = 30 [oC]

T = 60 [oC]

T = 90 [oC]

T = 120 [oC]

Figure 3.1: Projections of modelled bulk modulus.

Mass Density

Based on the same reasoning as for the bulk modulus it is necessary to also considerthe variations in mass density. It has a direct impact on the flow through an orifice(see section 3.2.2) and thus indirectly a�ects the pressure levels within capacitivecomponents such as the pumping chamber and rail.

The mass density is defined as the mass per unit volume,

fl = m

V[kg/m

3], (3.3)

and is modelled in a similar manner to the bulk modulus by fitting a second degreepolynomial in two variables to measured data. The polynomial is defined as

fl(p, T ) = D1 + Dp1p + Dp2p2 + DpxT pT + DT 1T + DT 2T

2 (3.4)

and the constants Di have previously been determined by Scania. One-dimensionalprojections of the temperature and pressure dependency of the modelled mass den-sity are seen in Figure 3.2.


0 500 1000 1500 2000 2500 3000p [bar]

700

750

800

850

900

950

[kg

/m3]

T = 30 [oC]

T = 60 [oC]

T = 90 [oC]

T = 120 [oC]

40 60 80 100 120T [oC]

780

800

820

840

860

880

900

920

[kg

/m3]

p = 500 [bar]

p = 1000 [bar]

p = 1500 [bar]

p = 2000 [bar]

Figure 3.2: Projections of modelled mass density.

3.2.2 Active Inlet Metering Valve ModelModelling the AIM valve is a three-part process that can be divided into the followingdistinct areas: control signals that are sent to the AIM-valve, opening dynamics forthe valve armature and finally the fuel flow through it.

Control Signals

The solenoid in the AIM valve is activated by a pulse of current modelled as twoconsecutive square pulses. In reality, there are additional noise that slightly distortsthe signal. However, the influence of these disturbances is considered to be negligibleand a conceptual visualisation of the modelled current pulse can be seen in Figure3.3. The AIM valve armature stroke is included for reference.

Time

Armature stroke

Current pulse

tAIM,cd

Figure 3.3: AIM valve current pulse and armature stroke.

The current pulse has two distinct levels as can be observed in Figure 3.3. Thefirst and higher current level is intended to induce a strong electromagnetic fieldso that the duration of the transient behaviour is minimized. As the AIM valvearmature reaches its top position, the amplitude of the current is reduced since theelectromagnetic field just has to be strong enough for the valve to maintain its closedposition. Since the pressure forces within the pumping chamber rapidly increases,


quickly overcoming the counteracting spring and pressure force, the electromagneticforce eventually becomes superfluous and the current is cut o�.

From a model development perspective, it is advantageous to define some of thekey events taking place during the process illustrated in Figure 3.3. The momentwhen current is sent by the ECU to close the AIM valve is referred to as Start OfTime To Leave (SOTTL) and correspondingly the moment when the current is cuto� is named End Of Time To Leave (EOTTL). The full duration of the currentpulse, from SOTTL to EOTTL, is defined as tontime and the time interval betweenSOTTL and the moment when the current is decreased to the lower level is denotedtpullin.

Opening Dynamics

Modelling the opening dynamics of the AIM valve is focused on capturing the as-sociated actuator delays as they play an important role in the overall behaviour ofthe system. There are essentially two contributions to the total delay: a constantand a variable part. The constant delay, tAIM,cd, corresponds to the time betweenSOTTL and the solenoid getting activated and does not change between the operat-ing points, see Figure 3.3. This is in contrast to the variable part of the total delaywhich is associated with the transient behaviour that the valve armature displays asit is transitioning between being fully open and completely closed. In order to takethis into account, a natural approach is to consider the di�erent forces acting on thevalve armature and calculate the acceleration by the means of Newton’s second law.

The forces that are included in the model are the hydraulic pressure forces exertedby the highly compressed fuel, the electromagnetic force from the solenoid, the springforce and the contact forces between the armature and the physical stops restrictingits range of motion. This is an approximation that neglects the e�ect of di�erent jetforces stemming from the flow of fuel but also the e�ect of various friction forces.The resulting force acting on the AIM valve armature as it moves in-between thephysical stops, for displacements x ‘ (xmin, xmax), is given by

FAIM = Fm + Fhyd ≠ Fspr [N ], (3.5)

where the di�erent forces can be expressed asY___]

___[

Fm = f(I, x),Fhyd = ppAA,p ≠ plAA,l,

Fspr = kAIMx + CAIM .

(3.6)

The spring is assumed to be linear with a spring constant kAIM [N

m] and pre-load

CAIM [N] such that it can be described by Hooke’s law. AA,p [m2] is the cross-sectional area of the armature at the HPP side and AA,l [m2] is the cross-sectionalarea at the low-pressure side. The magnitude of the magnetic force, Fm, actingon the AIM armature is dependent on the amplitude of the current, I [A], runningthrough the solenoid as well as the instantaneous displacement of the armature itself.This is a complex relationship that is directly related to the geometry and physicalproperties of the involved components and the development of an accurate model


of the magnetic force is beyond the scope of this thesis. Such a model is howeverprovided by the manufacturer of the AIM valve and the characteristic behaviour isillustrated in Figure 3.4.

I

Fm

xmin

xmax

Figure 3.4: Force versus current relationship for the AIM valve armature.

Linear interpolation is used to construct a two-dimensional map with the arma-ture displacement on the first axis and the current amplitude on the second. Thismap is used to compute an approximation of the electromagnetic force and rangesover the domain [xmin, xmax]◊ [Imin, Imax].

Based on equation (3.5), Newton’s second law gives that the armature accelera-tion is computed by

FAIM = ma = md

2x

dt2 ≈∆ d2x

dt2 = 1m

FAIM . (3.7)

The armature displacement is obtained by integrating equation (3.7) two times.Additionally, the opening area of the AIM valve is assumed to be linearly pro-

portional to the displacement and is defined as:

AAIM = wAIM · (xmax ≠ x), (3.8)

where wAIM is the proportionality constant. This approximation of how the openingarea depends on the displacement originates from the lack of data over the AIMvalves geometrical properties. This is a simplification that is motivated by the factthat the transient behaviour has a relatively short time scale in comparison to theoverall duration of the fuel flow between the low-pressure side and the pump chamberand should not cause any significant loss in accuracy.

The collisions between the armature and the physical stops that restrict its rangeof motion give rise to contact forces that are not included in equation (3.5). Theseforces are modelled indirectly by the assumption of perfectly inelastic collisionswhere all the kinetic energy is dissipated as suggested by Prinz et al. in [1].

Orifice Flow

As the valve opens, the pressure di�erential (�p) induces a flow of fuel through it.The valve orifice act as a restrictive component and can be compared to a resistor in


an electrical circuit. However, in contrast to the linear relationship given by Ohm’slaw, fuel flow is often non-linear.

The flow is approximated to be incompressible, inviscid and steady-state andcan therefore be described by Bernoulli’s equation seen in equation (3.9) [12],

||v||2

2 + gz + p

fl= constant, (3.9)

where v is the fluid velocity, g the gravitational acceleration and z the elevationabove a reference plane. Equation (3.9) is valid along a streamline and by definingan upstream point (1) as well as a downstream point (2) on the same streamline itholds that

||v1||2

2 + gz + p1fl

= ||v2||2

2 + gz + p2fl

. (3.10)

Neglecting the di�erence in elevation above the reference plane and assuming one-dimensional flow gives that

v212 + p1

fl= v

222 + p2

fl, (3.11)

which together with the continuity of mass,

q = A1v1 = A2v2 =∆

Y]

[v1 = q

A1

v2 = q

A2

, (3.12)

gives that

q = A2

ııÙ2(p1 ≠ p2)/fl

1 ≠ A22/A2

1= A2

Û1

1 ≠ A22/A2

1

Û2(p1 ≠ p2)

fl, (3.13)

where q is the volumetric flow. Defining C =Ò 1

1≠A22/A2

1and introducing the dis-

charge coe�cient CÕd, defined as the ratio between the actual flow and the theoretical

flow, results in

q = A2CCÕd

Û2�p

fl= A2Cd

Û2�p

fl, (3.14)

where Cd = CCÕd. Equation (3.14) is frequently used in similar applications to model

the flow through an orifice, see for example [1], [7], [13] and [14]. Equation (3.15) is amodified version of equation (3.14) that is better suited for implementation as it al-lows for fuel flow in both directions. Furthermore, the mass density is approximatedby applying equation (3.4) to the mean pressure, i.e. fl = fl(p1+p2

2 ), as suggested byPrinz et al. [1]. The coe�cient Cd is set to a standard value of Cd = 0.67 since theflow is assumed to be turbulent but the exact geometry of the valve is not known.

q = sgn(�p)CdA

Û2|�p|

fl[m3 · s

≠1]. (3.15)

3.2.3 High-Pressure Pump ModelAs stated in section 2.2.1, the HPP consists of two separate pump elements. Sincethey are only distinguished from each other by the phase they operate in, it is con-venient to create a model of a generic pump element with the phase as a parameter.


This model aims to capture the pressure dynamics within the pumping chamber aswell as the fuel flow through the OCV and is naturally divided into these separateareas.

Pump Chamber

The pump chamber is modelled as a capacitive component by adopting a lumped pa-rameter approach. It is approximated by a single control volume whose size evolvesduring the pump cycle in accordance with the cam profile. This is a simplificationwhich reduces the original Partial Di�erence Equation (PDE) in both time and spaceto an Ordinary Di�erential Equation (ODE) without any spatial dependency [11,p. 32]. The modelled pressure then corresponds to the spatially averaged pressurein the chamber.

Starting from the definition of the bulk modulus in equation (3.1) it is possibleto rearrange the expression and divide by an infinitesimal time-step dt to get anexpression for the pressure dynamics:

dp

dt= ≠E

V

dV

dt. (3.16)

Here, V is the instantaneous volume of the fuel inside the control volume and itstime-derivative can be expanded into two di�erent terms, separating the e�ect ofin-/outflow of fuel from the e�ect of the mechanically induced volume change of thepump chamber:

dpp

dt= Ep

Vp

3 ÿ

i

qi ≠ dVp

dt

4. (3.17)

The term representing the total flow of fuel can in turn be expanded into the di�erentflows considered in this model: the inflow through the AIM valve and the outflowthrough the OCV. The resulting expression is seen in equation (3.18) where thedirection of flow is defined by the sign.

dpp

dt= Ep

Vp

3qp,in ≠ qp,out ≠ dVp

dt

4, (3.18)

The subscript p indicates that these quantities are associated with the pump cham-ber and equivalent expressions to equation (3.18) are suggested by [1], [4], [5] and[13] among others.

The chamber volume, Vp, is a function of the cam lift, lcam, which is relatedto the crank angle, ◊crank, by the cam profile. The cam profile studied within thisthesis has a sinusoidal characteristic and is approximated by the general expressionin equation (3.19),

lcam = B + Asin(Ê◊crank + „), (3.19)

where B is the bias, A the amplitude, Ê the angular frequency and „ the phase.These constants are determined by doing a least square fit of equation (3.19) to themeasured data of the cam profile seen in Figure 3.5. The measurements are evenlyscatted over only one quarter of the cam profile due to the symmetric property ofthe sinusoidal wave.


crank

l ca

m

Figure 3.5: Measured cam lift as a function of the crank angle.

The pump chamber has a cylindrical shape and its volume is linearly dependenton the cam lift according to equation (3.20),

Vp = Vmax ≠ Aplungerlcam, (3.20)

where Aplunger is the cross-sectional area of the plunger and Vmax is the maxi-mum possible chamber volume, obtained at the BDC of the pump. It is definedas Vmax = Vdead + Aplungerl

max

cam.

Outlet Check Valve

There are many similarities between the OCV and the AIM valve as both of themact as restrictive components, regulating the flow of fuel. However, the OCV is notsubject to any electromagnetic force in contrast to the AIM valve, implying that itoperates under the influence of mechanical forces only since the gravitational e�ectis ignored. This simplifies the modelling process substantially and the total forceconsidered to act on the OCV when it is moving freely between the physical stopsis given by

FOCV = Fhyd ≠ Fspr, (3.21)where Fhyd is the hydraulic force and Fspr the spring force given by

Y]

[Fhyd = ppAOCV,p ≠ prAOCV,r,

Fspr = kOCV x + COCV .(3.22)

The subscripts p and r denote the pump chamber side and rail side of the OCVarmature respectively. p and A corresponds to pressure and cross-sectional area,kocv is the spring constant, x is the armature displacement and Cocv is the pretensionof the spring. Newton’s second law gives that

d2x

dt2 = 1mocv

(ppAOCV,p ≠ prAOCV,r ≠ kOCV x ≠ COCV ). (3.23)

The opening area is assumed to be linearly proportional to the displacement andis given by

Aocv = wocvx. (3.24)


Additionally, the volumetric flow through the valve is modelled by the same equationfor orifice flow as for the AIM valve, see equation (3.2.2).

The displacement is mechanically restricted to the interval [xmin, xmax] and thecollision between the valve disc and the valve seat is approximated to be completelyinelastic, just as for the AIM valve.

E�ciency Map

The real HPP su�ers from e�ciency losses due to leakage flows at the plunger/cylin-der interface, fuel temperature increase from compression work and cavitation in thepump chamber which reduces the e�ective volumetric e�ciency substantially. Previ-ous work on the topic shows di�erent approaches to the leakage modelling problem,suggesting solutions ranging from constant leakage models in [5] to fully dynamicmodels based on lubrication theory in [6]. However, since the exact geometry of thepump studied within this thesis is unknown, the latter approach is not feasible.

An alternative approach is to create an e�ciency map for the pump by comparingthe ideal model with experimental data at several operating points, lumping thee�ect of leakage flow, varying temperature and cavitation together. As the e�ciencyhas been observed to vary with both pressure and engine speed, a two-dimensionalmap with respect to these two quantities is suitable. It is created by performing alinear least-square fit to data from operating points 1, 3, 5, 7 and 9 in Table 3.1,leaving the others for verification.

3.2.4 Rail ModelModelling the rail concerns the task of capturing the variations in fuel pressure. Thisincludes both the static pressures as well as the dynamics taking place during pumpevents and injections. Similar to the model of the HPP, the rail model is dividedinto separate areas: rail volume and MDV. Furthermore, two di�erent modellingapproaches of the rail volume are studied: with and without spatial dependency.

Mechanical Dump Valve

Since the purpose of the MDV is to act as a mechanical safeguard, preventing the railpressure from reaching dangerous levels, it is not necessary to model it accuratelyin order to capture the rail pressure during normal operating conditions. However,since the model is intended to be used for controlling and development purposesthe functionality of the MDV still has to be included. This is accomplished bya PI controller that aims to hold the rail pressure around a constant setpoint byregulating the flow qMDV out of the rail. Similar to the real system, the MDV flowis triggered at a high pressure value corresponding to the upper allowed limit ofoperation for the fuel system.

Rail Volume

In the first approach to model the rail volume, it is modelled as a capacitive com-ponent in an equivalent manner to the pump chamber in section 3.2.3. It is defined


as a single control volume for which the fuel pressure is described by,

dpr

dt= Er

Vr

3qr,in ≠ qr,out ≠ dVr

dt

4= Er

Vr

3qr,in ≠ qr,out

4, (3.25)

where the time derivative of the rail volume is zero since the structural deformationsinduced by the high pressures are neglected. The flow into the rail, qr,in, correspondsto the pulsating flow from the HPP and its two pump elements while the flow outof the rail, qr,out, is defined as the sum of injector flow and eventual flow throughthe MDV according to

Y]

[qr,in = qp1,out + qp2,out,

qr,out = qninj

i=1 qinj,i + qMDV .(3.26)

Apart from the volume of the cylindrically shaped rail, the modelled volume alsoincludes the connecting pipes between HPP and rail, rail and injectors as well asthe injector bodies:

Vr = VP toR + VR + VRtoI + VI . (3.27)

Since the spatial variations are neglected, these di�erent physical compartments canbe lumped together to form a storage volume with a fluid capacitance correspondingto the total capacitance of all the individual components.

The single control volume approach is a good choice if simplicity and reducedcomputational complexity is vital. It aims to model the spatially averaged pressurewithin the rail which is useful for controlling applications. However, it does notintend to capture the pressure oscillations within the rail stemming from the pul-sating pump flow and the water hammer e�ect. This phenomena are crucial from adevelopment point of view, which raises the need of an extended model of the railvolume.

Rail Volume with Spatial Dependency

An alternative way of addressing the rail modelling problem is to construct an arti-ficial partitioning of the rail where it is divided into several smaller compartments.Each compartment is represented by a control volume where the pressure is givenby the same first order ODE as before,

dpi

dt= E(pi)

Vi

3qin ≠ qout

4, (3.28)

where the index i refers to a specific element. The partitioning takes place in thedimension along the rail, thus neglecting the pressure variations over the cross-sectional area.

The rail studied within this thesis is constructed for a 6-cylinder engine and hassix separate connections to the injectors in addition to its two connections to theHPP. The control volumes are centred around the connecting pipes as well as thepressure sensor and the partitioning of the rail into 19 separate elements is illustratedin Figure 3.6, where the number of elements stems from geometrical properties of


the real rail. Furthermore, the volumes of connecting pipes and injector bodies areincluded by adjusting the cross-sectional area, Ai, of the corresponding elements.

Figure 3.6: Artificial partitioning of the rail.

The flow of fuel between two control volumes is given bydqi

dt= Ai

fl(pi)Li

3pi≠1 ≠ pi

4≠ ‹qi, (3.29)

where ‹ is a damping factor which takes di�erent frictional losses into account. If it isset to zero, energy will be conserved in the system and the pressure waves in the railwill continue to propagate without anything damping them. Combining equation(3.28) and equation (3.29) for each control volume results in a system of 38 coupledODEs that describe the pressure and flow dynamics within the rail. However, thissystem is reduced to 37 ODEs since there is no flow q1 due to the physical boundaryof the rail.

Equation (3.28) and equation (3.29) are general expressions and have to beadapted to each individual control volume. There are five di�erent cases, start-ing with left boundary:

dp1dt

= ≠E(p1)V1

q2, (3.30)

then right boundary:Y__]

__[

dp19dt

= E(p19)V19

3q19 ≠ qMDV

4,

dq19dt

= A19fl(p19)L19

3p18 ≠ p19

4≠ ‹q19,

(3.31)

elements connected to an injector:Y__]

__[

dpi

dt= E(pi)

Vi

3qi ≠ qi+1 ≠ qinj,i

4,

dqi

dt= Ai

fl(pi)Li

3pi≠1 ≠ pi

4≠ ‹qi,

, i = 2, 4, 6, 8, 16, 18, (3.32)

elements connected to the HPP:Y__]

__[

dpi

dt= E(pi)

Vi

3qi ≠ qi+1 + qp,i

4,

dqi

dt= Ai

fl(pi)Li

3pi≠1 ≠ pi

4≠ ‹qi,

, i = 12, 14, (3.33)


and generic elements:Y__]

__[

dpi

dt= E(pi)

Vi

3qi ≠ qi+1

4,

dqi

dt= Ai

fl(pi)Li

3pi≠1 ≠ pi

4≠ ‹qi,

, i = 3, 5, 7, 9, 10, 11, 13, 15, 17. (3.34)

This system of 37 coupled ODEs can be implemented in Simulink directly. How-ever, this is in many cases not preferred due to the large computational complexityand complicated structure. An alternative and commonly used approach is to lin-earise the system around an operating point and adopt a state-space representationinstead.

State-Space Representation and Linearisation

A linear and continuous-time system can be written in state-space form by definingthe relationship between input and output according to equation (3.35),

Y]

[

˙x = Ax + Bu,

y = Cx + Du,(3.35)

where x(t) ‘Rn is the vector of states, u(t) ‘Rp is the vector of inputs, y ‘Rq is theoutput vector and A ‘Rn◊n, B ‘Rn◊p, C ‘Rq◊n and D ‘Rq◊p are the system matrix,input matrix, output matrix and feed-through matrix respectively [15, p. 31]. Forthe sake of this application, C has only one non-zero element: the diagonal elementcorresponding to the pressure state in the control volume with the sensor, which isset to one. Additionally, D is zero in this case as there is no direct feed-through.

Since each control volume in the partitioning of the rail is defined by a system oftwo ODEs describing the pressure and flow, it is natural to choose these variables asstates. Furthermore, the flow through each injector, from each pump element andthrough the MDV are chosen as inputs to the system:

x(t) =

S

WWWWWWWWWWWWWWWWWWWU

p1p2q2p3q3.

.

.

p19q19

T

XXXXXXXXXXXXXXXXXXXV

, u(t) =

S

WWWWWWWWWWWWWWWWU

qinj,1qinj,2qinj,3qinj,4qinj,5qinj,6qp1qp2

qMDV

T

XXXXXXXXXXXXXXXXV

. (3.36)

Based on the definition of the state vector and input vector in equation (3.36), it isnow possible to express the system as

˙x = f(x, u), (3.37)

where f is a non-linear vector function containing the right-hand side of the ODEsin equation (3.28) and (3.29) for each state:


f(x, u) =

S

WWWWWWWWWWWWWWWWWWWWWU

≠E(p1)V1

q2E(p2)

V2

3q2 ≠ q3 ≠ qinj,1

4

A2fl(p2)L2

3p1 ≠ p2

4≠ ‹q2

.

.

.

E(p19)V19

3q19 ≠ qMDV

4

A19fl(p19)L19

3p18 ≠ p19

4≠ ‹q19

T

XXXXXXXXXXXXXXXXXXXXXV

(3.38)

In order to write the system in the state-space form given by equation (3.35), itfirst has to be linearised due to the non-linear expressions for the bulk modulus andmass density as well as the cross terms. This is accomplished by Taylor expandingf(x, u) around the operating point (x0, u0), neglecting terms of order higher thanone, and introducing the deviation variables defined by equation 3.39 [16, p. 117].

Y]

[�x := x ≠ x0,

�u := u ≠ u0.(3.39)

The system can now be written as

˙x ¥ f(x0, u0) + ˆf

ˆx

----x=x0u=u0

�x + ˆf

û

----x=x0u=u0

�u (3.40)

and the state vector x is obtained by solving the system in equation (3.41) for �x,� ˙x = A0�x + B0�u, (3.41)

where

A0 :=

S

WWWWWWU

ˆf1ˆx1

ˆf1ˆx2

· · · ˆf1ˆx37

ˆf2ˆx1

. . . ...... . . . ...

ˆf37ˆx1

· · · · · · ˆf37ˆx37

T

XXXXXXVx=x0u=u0

, B0 :=

S

WWWWWWU

ˆf1û1

ˆf1û2

· · · ˆf1û9

ˆf2û1

. . . ...... . . . ...

ˆf37û1

· · · · · · ˆf37û9

T

XXXXXXVx=x0u=u0

. (3.42)

It is convenient to choose (x0, u0) such that f(x0, u0) = 0, i.e. (x0, u0) shouldpreferably be an equilibrium point to f(x, u), which is accomplished by letting p0,i

= p ‘R , q0,i = 0, and u0,i = 0.

3.2.5 Injector ModelThe injectors are complex components whose characteristics have a direct impacton the static levels and transient behaviour of the rail pressure, but also on thepressure oscillations induced by the water hammer e�ect. An authentic model ofthe injection process that attempts to describe the spatial pressure variations in theinjector bodies and the instantaneous injection rate is beyond the scope of this thesisdue to its complexity. Therefore, focus is only placed on capturing the quantity andduration of each injection.


Injection Duration

The duration of an injection is dependent on two parameters: commanded amountof injected fuel (Qcom [mg]) and rail pressure. Just as expected, it holds that anincrease in Qcom corresponds to an increase in the injection duration while an in-crease in pr has the opposite e�ect. This relationship is hardware dependent andempirical studies of the behaviour at di�erent operating points have been carriedout at Scania previous to this thesis. The result of these studies is visualised in thetwo-dimensional map seen in Figure 3.7. Linear interpolation is applied between thegrid points and it is evident that the injection duration has a non-linear dependencyon both Qcom and pr.

0

1

0.33

t inj

0.75 1

0.66

Rail pressure Injected fuel mass

0.660.5

1

0.330.250

Figure 3.7: Required injector ontime as a function of injected fuel mass and railpressure.

The rail pressure used for computing the duration is the instantaneous value ofpr as the injection is about to take place.

Rate of Injection

The mapping in Figure 3.7 provides su�cient information for computing the averagerate of injection over the course of one injection according to equation (3.43),

Y_]

_[

qinj = Qcom

tinjt ‘ [tSOI , tEOI ],

0 otherwise,(3.43)

but does not give any information about the transient behaviour. Here, SOI denotesStart Of Injection and EOI denotes End Of Injection. The exact characteristics ofthe injection rate over time, commonly referred to as the rate-shape, has a directimpact on the pressure oscillations related to the water hammer e�ect but is notknown for the studied system. However, a first step towards a better model of theactual rate-shape is to add some transient behaviour to the square pulse given by


equation (3.43) in order to mimic the opening and closing of the injector valves.This is accomplished by introducing a first-order transfer function,

G(s) = 1·injs + 1 , (3.44)

transforming the original square pulse according to Figure 3.8. The transfer functionis parametrized by the time constant of the system, ·inj, which is calibrated to mimicthe real-world behaviour.

Time

q

Original

Transformed

Figure 3.8: Modelled injection rate-shape.

Drain Leakage

In addition to the main flow running through the injectors, it is import to include thedrain leakage associated with each injection to model the static pressure levels aftereach event accurately. The amount of drained fuel, Qdrain [mg], is approximatedby an in-house developed model that based on pr and Qcom estimates the totalamount of drained fuel during the corresponding injection. The mapping functionis illustrated in Figure 3.9.

Figure 3.9: Injector drain leakage.

The estimation of Qdrain is added to Qcom in equation (3.43) to construct anexpression for the e�ective average injection rate:

Y_]

_[

qinj = Qcom+Qdraintinj

t ‘ [tSOI , tEOI ],0 otherwise.

(3.45)


The final rate-shape used for each injection is thus given by the square pulse inequation (3.45) transformed by the first order system in equation (3.44).

Chapter 4

Results and Discussion

This chapter intends to present and discuss the behaviour of the implemented modeland the obtained results. It is divided into two separate sections, covering themodel characteristics in general as well as the rail pressure validation. Just as forthe methodology chapter, some of the figures are normalized due to confidentialityreasons.

4.1 Model CharacteristicsThis section is meant to exhibit the general behaviour of the model with focus onthe parts considered to have a major impact on the whole system: the openingdynamics of the AIM valve as well as the pressure dynamics within the pump cham-bers and rail. Since the only experimental data that is available comes from the railpressure sensor, it is not possible to directly verify the behaviour of the remainingcomponents. However, it is still useful to present the modelled signals and analysetheir characteristics.

4.1.1 AIM Valve Armature StrokeAs explained in section 3.2.2, the main focus when modelling the AIM valve is tocapture the actuator delays associated with the armature stroke. The timing ofclosure is vital for the general performance of the pump, which in turn directlya�ect the rail pressure. The variable delay is dependent on the forces acting uponthe armature and is expected to vary with both engine speed and pressure level.

The modelled transition between the physical limits is illustrated in Figure 4.1for operating points 1 and 9. The constant delay between SOTTL and the solenoidgetting activated is marked by the two dotted lines furthest to the left in eachsubfigure. After this initial delay, the armature quickly accelerates until reaching itsmaximal displacement. It should be noticed how it instantaneously comes to a fullstop as it hits the physical barrier due to the assumption of a fully inelastic collision.

27

4.1. MODEL CHARACTERISTICS 28

Timex

min

xmax

Dis

pla

cem

en

t

Timex

min

xmax

Dis

pla

cem

en

t

t2 t

1tAIM,cd t

AIM,cd

Figure 4.1: Illustration of the AIM valve armature transitioning from being fullyopened to completely closed. The left figure corresponds to operating point 1 andthe right figure to operating point 9, see Table 3.1.

Furthermore, the model displays a di�erence in the variable armature strokedelay of approximately 16% between the two operating points which indicates thatit is a�ected by the engine speed and pressure level. It is however not possible tovalidate this specific number due to the lack of experimental data.

4.1.2 Pump Chamber Pressure DynamicsThe pressure development within each pump chamber plays a major role for theoverall operation of the high-pressure circuit. Figure 4.2 shows the modelled dy-namics given by equation (3.18) for the first pump element. The left figure covers awhole four-stroke cycle while the right figure shows one pump cycle in greater detail.In addition to the chamber pressure, the modelled rail pressure is also included as areference level. The periodic increase in rail pressure that can be observed betweenthe pump chamber pressure peaks is associated with the second pump element whosepressure level is not included in Figure 4.2.

0 180 360 540 720

Crank angle [deg]

0

0.2

0.4

0.6

0.8

1

Pre

ssure

pp1

pr

150 200 250

Crank angle [deg]

0

0.2

0.4

0.6

0.8

1

Pre

ssure

pp1

pr

Figure 4.2: Pressure dynamics within one of the pump elements over the course of720o CAD. Rail pressure is shown as a reference level.

There are several things to notice in Figure 4.2, with the most obvious one being

4.1. MODEL CHARACTERISTICS 29

the occurrence of negative chamber pressures at the end of each pump cycle. Eventhough this is allowed from a mathematical point of view, it implies that somethingis missing in the physical model. The most probable explanation is that there iscavitation present in the real system during the expansion phase of the pump cyclethat is not accounted for. Both the modelled bulk modulus and mass density relyon the assumption that the fuel remains in its liquid state.

Another thing to notice in Figure 4.2 is how the chamber pressure rises abovethe rail pressure for a short moment before quickly decreasing to then follow the railpressure during the remaining compression phase of the pump. This can partiallybe explained by the preloaded spring keeping the OCV closed but is also a�ectedby the inertia of the valve armature and the associated opening delay.

4.1.3 Rail Pressure Injection ResponseThe response to the rapid change in rail pressure induced by a single injection isillustrated for both rail models in Figure 4.3. The spatially dependent approachgives rise to pressure oscillations which eventually disappear due to the dampingfactor in equation (3.29). As the amplitude of the oscillations approaches zero, it isevident that the same static pressure is captured by both models.

Another thing to notice in Figure 4.3 is the small o�set between the initialpressure drop of the models. The spatially dependent model responds slightly slowerto the injection than the spatially averaged model since the pressure sensor and theinjector are not connected to the same control volume, creating a more realisticbehaviour.

0 0.005 0.01 0.015 0.02 0.025 0.03

Time [s]

594

596

598

600

602

pr [

bar]

Spatially dependent rail model

Spatially averaged rail model

Figure 4.3: Modelled rail pressure before, during and after a single injection for bothrail model approaches.

4.1.4 Computational Demand and Model SpeedThe implemented model shows a significant computational demand as the time-stephas to be short enough for it to capture the rapid dynamics of the system, e.g. thetransient behaviour displayed by the valves. Furthermore, as stated by Huhtalaand Vilenius in [2], the combination of high pressures and small volumes causes

4.2. RAIL PRESSURE VALIDATION 30

the system to become sti�. This numerical di�culty causes most explicit solversto become impractical as they require an excessively reduced time step and a moresuitable alternative might be to use an implicit solver to discretize the probleminstead, due to their larger stability region. However, the fixed-step explicit solverODE45 manages to solve the system with acceptable accuracy with a time step of10≠6 and Table 4.1 shows the measured time for three di�erent simulations.

Table 4.1: Simulated time versus real time.

Test number Real time [s] Simulated time [s]1 5 125.02 5 126.13 5 124.1

The simulations are carried out in Matlab R2017b in accelerated mode on acomputer running Windows 10 with Intel(R) Core(TM) i7-8850H CPU @ 2.60GHz.On average, it takes about 25 seconds to simulate a drive cycle of one second.

4.2 Rail Pressure ValidationThe main part of the model validation consists of comparing the modelled railpressure with the experimentally measured pressure signal sampled by the sensorin the rail. This process is divided into di�erent stages as there are essentially twodi�erent aspects of the validation: high-level and low-level.

4.2.1 High-Level ValidationThe high-level validation is focused on the model’s ability to capture the rail pressureover longer drive cycles. This is studied by letting the model be subject to the sametime dependent input signals as the real system, analysing how the average railpressure levels evolve over time. The simulations are performed with the spatiallyaveraged rail model since the pressure oscillations are of no interest in this case.

Figure 4.4 shows a comparison between the modelled and measured rail pressureover a longer drive cycle of 200 seconds where each operating point in Table 3.1is included. In addition to the pressure, the figure also displays how the enginespeed, injected amount of fuel, SOTTL, tontime and tpullin varies during the drivecycle with the purpose of showing how changes in the pressure signal can be linkedwith changes in the input signals. The model manages to reproduce the generalcharacteristics of the experimental signal with a mean deviation of approximately6.2%, even though the instantaneous deviation is larger at some operating points.

The stationary pressure level at each operating point is determined by the per-formance of the HPP in relation to the amount of fuel injected into the cylindersand a stable rail pressure is achieved when there is a perfect balance between them.Thus, the most probable cause of the o�set between the modelled and measuredrail pressure is an inaccurate estimation of the amount of fuel delivered to the rail,


which can be considered to mainly depend on an inadequate HPP e�ciency map.This map intends to capture the impact of the plunger/barrel leakage, temperatureincreases induced by rapid compression as well as cavitation e�ects but it seemslike the linear least-square approach does not manage to capture the variations withperfect accuracy. A more suitable alternative might be to model these e�ects dy-namically instead. An incorrect estimation of the injected amount of fuel is unlikelysince that part of the model is based on in-house models that have been verifiedprevious to this thesis work.

Figure 4.4: Comparison between modelled and measured rail pressure during a workcycle covering each operating point in Table 3.1.


Four di�erent transitions seen in Figure 4.4 are studied separately and a compari-son between the modelled and measured rail pressure signal as the system transitionsbetween operating point 1 and 2 is given by Figure 4.5. The comparison shows thatthe model underestimates the average rail pressure before, during and after the tran-sition. The o�set that can be observed between the modelled and measured signalstarts around 12.5% but increases during the transition, reaching 25% as the signalsstabilizes around 600 and 800 bar respectively.

0

500

1000

1500

2000

ne

ng [

rpm

]

0

0.33

0.66

1

Qto

t

neng

Qtot

500

600

700

800

900

pr [

bar]

Measured pr

Modelled pr

0 2 4 6 8 10 12

Time [s]

0

0.5

1

SO

TT

L

0

0.5

1

Tim

e

SOTTL

tontime

tpullin

Figure 4.5: Comparison between modelled and measured rail pressure during thetransitioning between operating points 1 and 2. Engine speed, total commandedinjection amount and relevant AIM actuation times are displayed as well.

Figure 4.6 shows the transition between operating points 5 and 4 and in contrastto the behaviour seen in Figure 4.5, the model seems to overestimate the pressure


level initially. As Qtot increases, one can observe that both pressure signals starts todecrease. However, the model displays a more significant reaction to the changinginput signals which results in the modelled rail pressure dropping below the measuredsignal before finally stabilizing slightly above it. This behaviour is assumed to bepartially explained by the linear least-square approximation of the e�ciency mapwhere the sign of the deviation between the modelled and actual e�ciency variesbetween the operating points.

The relative o�set between the two pressure signals is lower in comparison to thetransition seen in Figure 4.5, staying below 10% during the complete transition.

0

500

1000

1500

2000

ne

ng [

rpm

]

0

0.25

0.50

0.75

1

Qto

t

neng

Qtot

900

950

1000

1050

1100

1150

pr [

ba

r]

Measured pr

Modelled pr

0 1 2 3 4 5 6 7 8 9 10

Time [s]

0

0.25

0.50

0.75

1

SO

TT

L

0

0.25

0.50

0.75

1

Tim

e

SOTTL

tontime

tpullin

Figure 4.6: Comparison between modelled and measured rail pressure during thetransitioning between operating points 5 and 4.

The transition between operating points 8 and 6 is seen in Figure 4.7 and as


previously observed for other operating points, the modelled system does not manageto accurately capture the exact rail pressure level over time. However, for thisspecific case, the deviation between the modelled and measured signals stays below10%.

Furthermore, the model shows good response to changes in the input signalsand follows the measured signal with an almost constant o�set as Qtot increases andSOTTL decreases during the first part of the comparison. When SOTTL suddenlyincreases around four seconds into the drive cycle, the model exhibits a rapid pressuredrop similar to the one of the experimental signal.

0

500

1000

1500

2000

ne

ng [

rpm

]

0

0.25

0.50

0.75

1

Qto

t

neng

Qtot

1300

1400

1500

1600

1700

1800

pr [

ba

r]

Measured pr

Modelled pr

0 1 2 3 4 5 6 7

Time [s]

0

0.33

0.66

1

SO

TT

L

0

0.33

0.66

1

Tim

e

SOTTL

tontime

tpullin


The fourth and final individual transition is seen in Figure 4.7 where the system


transitions between operating points 6 and 7, increasing the rail pressure from 1450to 1480 bar. Initially, the model underestimates the stationary pressure at operatingpoint 6 with about 8% but as Qtot and SOTTL starts to increase and decreaserespectively, this o�set is reduced to approximately 4% at operating point 7.

0

500

1000

1500

2000

neng [rp

m]

0

0.25

0.50

0.75

1

Qto

t

neng

Qtot

1300

1350

1400

1450

1500

1550

1600

pr [

bar]

Measured pr

Modelled pr

0 1 2 3 4 5 6

Time [s]

0

0.20

0.40

0.60

0.80

1

SO

TT

L

0

0.33

0.66

1

Tim

e

SOTTL

tontime

tpullin


Overall, the model shows good response to changes in the input signals which isa promising result for controller development applications.


4.2.2 Low-Level ValidationIn contrast to the high-level validation, the low-level validation treats the detaileddynamics observed over the course of one four-stroke cycle. This includes thetransient response to individual pump events and injections and both rail modelapproaches are analysed and compared with measured data at di�erent operatingpoints.

Since this kind of validation does not specifically focus on the model’s ability tomimic the static rail pressure levels, SOTTL is slightly adjusted for the modelledsystem such that it stabilizes around the same pressure as the real system. Theexact correction is stated for each studied operating point.

Spatially Averaged Rail Model

The spatially averaged rail model is compared to the experimental data at twospecific operating points. The first corresponds to an engine speed of 1700 rpm,rail pressure around 1480 bar and large injection quantities inducing considerablepressure drops, see operating point 7 in Table 3.1. A comparison in the time domainbetween measured and modelled signal is visualised in Figure 4.9 where SOTTL isdecreased by 7% for the modelled signal.

0 80 160 240 320 400 480 560 640 720

Crank angle [deg]

0

0.2

0.4

0.6

0.8

1

pr

Experimental data

Model

Figure 4.9: Modelled versus measured rail pressure at an engine speed of 1700 rpm,pr ¥ 1480 bar and large injection quantities.

The model seems to be able to capture the transients associated with each pumpevent and injection quite well but lacks the ability to model the pressure oscilla-tions just as expected. This observation is even more obvious when comparing thefrequency spectrum of both modelled and measured signals, see Figure 4.10.


0 0.2 0.4 0.6 0.8 1

Frequency

0

1

2

3

4

5

6

Am

plit

ud

e [

ba

r]

Experimental data

Model

Pump

frequency

Injection

frequency

Figure 4.10: Frequency spectrum of the measured and modelled pressure signal foroperating point 7 in Table 3.1.

The two largest peaks correspond to the frequency of the injectors and the HPP,although with a slight deviation due to the low resolution of the spectrum. Theseare modelled well. However, as indicated by the time domain comparison in Figure4.9, the model does not manage to capture the higher frequencies stemming fromthe water hammer e�ect.

The same comparison is performed for another operating point at an enginespeed of 600 rpm, a rail pressure around 1080 bar and small injection quantities (seeoperating point 5 in Table 3.1). The time domain comparison is seen in Figure 4.11where SOTTL is increased by 2% for the modelled signal.

0 180 360 540 720

Crank angle [deg]

0

0.2

0.4

0.6

0.8

1

pr

Experimental data

Model

Figure 4.11: Modelled versus measured rail pressure at an engine speed of 1100 rpm,pr ¥ 1080 bar and small injection quantities.

The experimental data in Figure 4.11 displays oscillation of equal or greateramplitude than the pressure increase/decrease induced by individual pump eventsand injections. This implies that the spatially averaged model is not as well suitedfor this operating point as for the one seen in Figure 4.9, even though it still managesto follow the average pressure with promising results.


The discrepancy between the modelled and the measured signal can also beobserved in the frequency domain, see Figure 4.12. Just as for operating point 7,both the pump and injection frequencies are modelled well. However, the model’sinability to capture the oscillations is evident.

0 0.2 0.4 0.6 0.8 1

Frequency

0

0.2

0.4

0.6

0.8

1

1.2A

mp

litu

de

[b

ar]

Experimental data

Model


Overall, the spatially averaged rail model performs well and manages to captureeach individual pump event and injection with good accuracy.

Rail Model with Spatial Dependency

The validation of the second rail model, where the spatial dependency is taken intoconsideration, is performed in a similar manner to the first rail model approach.Figure 4.13 shows a comparison with experimental data at operating point 4 with anengine speed of 1100 rpm, rail pressure around 950 bar and large injection quantities.SOTTL is increased by 4% to match the static pressure level of the real system.

Similar to the averaged rail model, the spatially dependent model manages tocapture the transients associated with each pump event and injection with promisingaccuracy. Furthermore, it gives rise to pressure oscillation similar to those observedin the experimental data stemming from the water hammer e�ect and the pulsatingflow from the HPP. The amplitude of these oscillations is slightly overestimated,especially after the injections, which is most likely explained by the simplified injec-tion rate-shape presented in section 3.2.5. This is further indicated by the sensitivityanalysis in section 5.2 which shows that even small changes in ·inj have a significantimpact on the amplitude of the oscillations.


0 180 360 540 720

Crank angle [deg]

0

0.25

0.50

0.75

1

pr

Experimental data

Model

Figure 4.13: Comparison between modelled and measured rail pressure at 1100 rpm,pr ¥ 950 bar and large injection quantities, see operating point 4 in Table 3.1.

Another thing to notice in Figure 4.13 is that there seems to be additional high-frequency oscillations present in the modelled signal. This is further confirmed bythe frequency spectrum seen in Figure 4.14.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Frequency

0

1

2

3

4

5

Am

plit

ud

e [

ba

r]

Experimental data

Model


Figure 4.14 confirms that there are additional oscillations in the modelled signalwith high frequencies, just as observed in the time domain comparison. The originof these peaks is not easy to establish, but they might be the result of the artificialpartitioning itself. Since the size of each control volume varies, so will also theassociated fluid capacitance and this might result in the pressure wave being partiallyreflected at the interfaces between them. This e�ect is especially pronounced for theelements containing additional volumes of pipes and/or injector bodies.

Overall, there is a great resemblance in the frequency spectrum between themodelled and experimental signals. In addition to capturing the pump and injection


frequencies with good accuracy, the spatially dependent model also manages toreproduce the frequency peak close to 0.2 on the normalised frequency axis.

Since the high-frequency peaks in the modelled signal are considered redundantfor the model, it is interesting to study the correspondence with experimental datain the time domain for a low-pass filtered model signal. This is illustrated in Figure4.15 where the higher frequencies are damped and it is evident that the modelledsignal fits the experimental one better after the low-pass filtration.

0 180 360 540 720

Crank angle [deg]

0

0.25

0.50

0.75

1

pr

Experimental data

Model

Figure 4.15: Comparison between a low-pass filtered model signal and experimentaldata at operating point 4.

Another time domain comparison between modelled and measured rail pressuresignal is seen in Figure 4.16 for operating point 9, where SOTTL is increased by1.5% to match the static pressure level. This operating point di�ers from the oneseen in Figure 4.13 in both engine speed and pressure level, but also in the amount ofinjected fuel. The slightly smaller injection quantity results in pressure oscillationsof the same magnitude as the pressure changes induced by individual pump eventsand injections, making it hard to distinguish any trend.

The model makes a good attempt in capturing the oscillations and manages toreproduce some of them with good accuracy. However, just as observed for theprevious operating point, it appears like it gives rise to additional high-frequencyoscillations.


0 180 360 540 720

Crank angle [deg]

0

0.20

0.40

0.60

0.80

1

pr

Experimental data

Model

Figure 4.16: Comparison between modelled and measured rail pressure at 2200 rpm,pr ¥ 1800 bar and small injection quantities.

Furthermore, the frequency spectrum corresponding to Figure 4.16 is given byFigure 4.17 which once again shows the higher frequencies.

0 0.20 0.40 0.60 0.80 1

Frequency

0

0.5

1

1.5

2

2.5

3

Am

plit

ud

e [

ba

r]

Experimental data

Model

Figure 4.17: Frequency spectrum of the measured and modelled pressure signal foroperating point 9.

Here it can also be seen that there are some low-frequency peaks in the exper-imental signal that are not produced by the model, explaining the deviations seenin the time domain comparison. Since these frequencies are not observed in themodelled signal, it is probable that they originate from geometrical properties ofthe real rail that are neglected by the one-dimensional partitioning.

The relatively small o�set between the modelled and measured frequency peakassociated with the water hammer e�ect, situated around 0.15 on the normalized fre-quency axis, is most likely explained by a discrepancy between modelled and actualfuel properties at this specific operating point. Since the temperature is consideredconstant within the modelling framework, it is the most probable candidate.

Chapter 5

Sensitivity Analysis

This chapter aims to give an insight into how the output of the model is a�ected bysmall perturbations in di�erent input signals and parameter values. There are vari-ous techniques for analysing the sensitivity of the model, including both theoreticaland empirical approaches. However, due to the complexity of the system studiedwithin this thesis, an empirical study is preferred.

The sensitivity analysis in this chapter covers two di�erent areas: rail pressurestability and pressure oscillations. It is meant to work as a guideline for calibrationand analysis of the modelled system.

5.1 Rail Pressure StabilityA stable rail pressure is achieved when the pressure drop induced by the injections isperfectly counterbalanced by the fuel fed into the rail by the HPP. This is a sensitiveprocess and small disturbances in parameters and/or control signals can have a majorimpact on the overall behaviour of the system. The deviation from the stable railpressure after a simulated time of 1 s is recorded for six di�erent perturbations inselected parameters/control signals at four distinct operating points: 1, 2, 7 and 8in Table 3.1. One parameter is varied at a time while the others are kept constantat their nominal values.

Furthermore, the parameters and control signals are categorized into three sepa-rate areas according to their underlying characteristics: fuel properties, geometricalparameters and control signals.

5.1.1 Fuel PropertiesThe fuel parameters include the constant pressure of the low-pressure circuit, themodelled bulk modulus and mass density as well as the fuel temperature. Table5.1 summarizes the result of the sensitivity analysis, showing the observed deviationafter 1 s for each perturbation.

42

5.1. RAIL PRESSURE STABILITY 43

Table 5.1: Sensitivity analysis for fuel parameters.

Deviation [%]Gain OP1 OP2 OP7 OP8

plow 0.85 0.0 0.0 0.0 0.00.90 0.0 0.0 0.0 0.00.95 0.0 0.0 0.0 0.01.05 0.0 0.0 0.0 0.01.10 0.0 0.0 0.0 0.01.15 0.0 0.0 0.1 0.0

E 0.85 -2.6 -2.6 -3.3 -5.40.90 -1.8 -1.7 -2.1 -4.90.95 -0.9 -0.9 -1.0 -2.21.05 0.8 0.9 1.0 1.11.10 1.6 1.8 1.8 0.91.15 2.4 2.7 2.6 -0.1

fl 0.85 -4.5 -16.1 -11.7 -5.50.90 -2.8 -10.2 -7.4 -3.40.95 -1.3 -4.9 -3.5 -1.61.05 1.2 4.5 3.2 1.41.10 2.3 8.6 6.1 2.61.15 3.3 12.3 8.8 3.7

T 0.85 5.9 9.2 5.8 2.70.90 3.8 6.0 4.0 0.20.95 1.9 2.9 2.0 1.51.05 -1.9 -2.7 -2.2 -4.41.10 -3.6 -5.1 -4.4 -6.31.15 -5.2 -7.3 -6.8 -8.4

Based on the observed deviations seen in Table 5.1 it appears like plow has a verysmall impact on the overall behaviour of the system. This is in contrast to E, fl andT for which small perturbations propagates all the way to the rail pressure. Therelationship between small variations in these quantities and the observed deviationin rail pressure seems to follow an almost linear trend for all operating points exceptthe last one.

5.1.2 Geometrical ParametersIn addition to the parameters a�ecting the fuel properties, there are parameters di-rectly associated with the physical geometry of the system: AA,p, AA,l and Vdead. Theparameters related to the AIM valve armature, AA,p and AA,l, a�ect the hydrostaticforce in equation (3.5) and thus also its opening dynamics while small perturbationsin Vdead have a direct impact on the pump chamber pressure described by equation(3.18). The results from the sensitivity analysis are seen in Table 5.2.

5.1. RAIL PRESSURE STABILITY 44

Table 5.2: Sensitivity analysis for geometrical parameters.


AA,p 0.85 -0.1 -0.1 -0.2 -0.70.90 -0.1 -0.1 -0.1 -0.40.95 0.0 0.0 -0.1 -0.21.05 0.0 0.0 0.1 0.21.10 0.1 0.1 0.1 0.31.15 0.1 0.1 0.2 0.4

AA,l 0.85 0.1 0.1 0.1 0.30.90 0.1 0.1 0.1 0.20.95 0.0 0.0 0.0 0.11.05 0.0 0.0 0.0 -0.11.10 -0.1 -0.1 -0.1 -0.21.15 -0.1 -0.1 -0.1 -0.4

Vdead 0.85 2.2 1.6 1.1 -0.40.90 1.5 1.1 0.7 -1.30.95 0.8 0.5 0.4 -0.51.05 -0.9 -0.5 -0.4 -3.11.10 -1.7 -1.0 -0.7 -3.41.15 -2.5 -1.6 -1.1 -4.1

wAIM 0.85 0.1 0.2 0.4 0.60.90 0.1 0.1 0.2 0.40.95 0.0 0.1 0.1 0.21.05 0.0 0.0 -0.1 -0.31.10 -0.1 -0.1 -0.2 -0.61.15 -0.1 -0.1 -0.3 -0.9

wOCV 0.85 0.0 -0.3 -0.4 -2.60.90 0.0 -0.1 -0.1 -2.50.95 0.0 0.0 0.0 -2.51.05 0.0 -0.1 0.0 -2.21.10 0.0 -0.1 0.0 -3.31.15 0.0 -0.4 0.0 0.0

It is evident that the geometrical parameters does not have as big impact onthe system as the fuel parameters. Vdead appears to be the most influential and thedeviations show an almost linear relationship to the perturbations, just as observedin Table 5.1, but with a smaller proportionality constant.

5.1.3 AIM Valve Control SignalsThe timing of the electric pulse triggering the AIM valve solenoid determines theamount of fuel getting trapped within the pump chamber, thus regulating the pres-sure levels indirectly. Table 5.3 and 5.4 show the sensitivity of the modelled system

5.2. PRESSURE OSCILLATIONS 45

towards small perturbations in the constant delay tAIM,cd and SOTTL.

Table 5.3: Sensitivity analysis for small perturbations in tAIM,cd.


tAIM,cd 0.85 0.39 0.4 0.5 0.60.90 0.26 0.3 0.3 0.60.95 0.13 0.1 0.2 0.41.05 -0.13 -0.1 -0.2 -0.71.10 -0.26 -0.3 -0.3 -1.81.15 -0.40 -0.4 -0.5 -3.3

Table 5.4: Sensitivity analysis for small perturbations in SOTTL.

Deviation [%]O�set [CAD] OP1 OP2 OP7 OP8

SOTTL -3 18.9 20.9 6.9 11.2-2 12.1 13.7 4.8 7.6-1 5.7 6.9 2.5 1.21 -6.1 -7.1 -2.7 -7.22 -11.2 -14.2 -5.7 -12.33 -16.2 -21.4 -8.9 -20.4

The large sensitivity to changes in SOTTL is not unexpected as it has a directimpact on the amount of fuel getting trapped in the pump chamber and thus alsoon the rail pressure. This can also be observed in the high-level validation in section4.2 where a change in SOTTL drastically changes the stable rail pressure level.

5.2 Pressure OscillationsPressure oscillations in the rail can be characterized by their frequencies and am-plitudes. These characteristics are a�ected not only by fuel properties, but also byhardware attributes related to rail geometry and the injection rate-shape. The sensi-tivity to small perturbations in these quantities/parameters is studied by analysingthe frequency spectrum of the rail oscillations after a single injection, varying oneparameter at a time. Frequency and amplitude are recorded for the two main peaksobserved in the spectrum and the observed deviations from the nominal values areseen in Table 5.5 and 5.6 for two di�erent operating points: 600 and 1600 bar.

Based on the observations in Table 5.5, it is clear that the frequency of thepressure oscillations is a�ected by changes in the fuel’s properties. The distinguish-able trends are intuitive as an increasing bulk modulus results in higher frequencieswhile an increasing mass density or temperature has the opposite e�ect. The same


behaviour can be recognized for both operating points, displaying only minor di�er-ences.

Table 5.5: Sensitivity analysis for frequency of rail oscillations.

Deviation [%]600 bar 1600 bar

Gain Peak 1 Peak 2 Peak 1 Peak 2E 0.85 -7.7 -7.8 -7.8 -7.8

0.90 -5.1 -5.1 -5.2 -5.10.95 -2.4 -2.4 -2.6 -2.61.05 2.4 2.6 2.4 2.51.10 4.8 4.9 4.8 4.91.15 7.2 7.3 7.2 7.2

fl 0.85 8.4 8.5 8.4 8.50.90 5.5 5.4 5.4 5.40.95 2.7 2.7 2.6 2.61.05 -2.4 -2.4 -2.4 -2.51.10 -4.6 -4.6 -4.6 -4.71.15 -6.7 -6.7 -6.8 -6.7

T 0.85 9.4 9.4 6.2 6.30.90 6.3 6.1 4.2 4.20.95 3.1 3.1 2.0 2.01.05 -2.9 -3.0 -2.0 -1.91.10 -5.8 -5.8 -3.8 -3.91.15 -8.4 -8.5 -5.6 -5.6

·inj 0.85 0 0 0 00.90 0 0 0 00.95 0 0 0 01.05 0 0 0 01.10 0 0 0 01.15 0 0 0 0

L 0.85 17.6 17.7 17.7 17.70.90 11.1 11.1 11.1 11.10.95 5.3 5.3 5.2 5.31.05 -4.8 -4.7 -4.8 -4.81.10 -9.2 -9.1 -9.1 -9.11.15 -13.0 -13.1 -13.1 -13.1

Even though the injection rate-shape, parametrized by ·inj, appears to have noimpact on the frequencies, the same cannot be said for the amplitudes seen in Table5.6. An aggressive rate-shape with similar appearance to a square pulse gives riseto larger pressure oscillations in comparison to a more smooth alternative.

Also the fuel properties a�ect the amplitudes of the oscillations. However, it isnot possible to distinguish any obvious trends from the data in Table 5.6.


Table 5.6: Sensitivity analysis for amplitude of rail oscillations.

Deviation [%]600 bar 1600 bar

Gain Peak 1 Peak 2 Peak 1 Peak 2E 0.85 -10.7 -7.2 -15.3 -18.2

0.90 -25.2 -4.3 -6.6 -2.00.95 -14.9 -10.7 -17.0 -19.91.05 1.5 4.0 -17.6 -11.71.10 5.6 -26.9 -16.2 -4.31.15 8.5 -27.1 7.6 14.5

fl 0.85 -13.9 -12.9 -3.6 -6.20.90 -19.3 -28.3 -9.3 -26.70.95 2.1 -16.2 -5.8 -5.11.05 1.6 -21.8 2.2 -19.01.10 2.8 20.1 -3.6 -22.21.15 4.8 -0.3 -12.1 5.5

T 0.85 1.7 10.3 -17.1 3.00.90 -14.0 20.7 -18.5 -0.90.95 -3.4 16.8 4.3 3.61.05 -0.7 -9.5 -3.5 -25.81.10 -9.0 0.3 -7.6 -4.01.15 -10.6 4.1 -6.2 -31.1

·inj 0.85 7.7 12.8 9.3 13.90.90 5.1 8.2 6.1 9.00.95 2.5 4.1 2.9 4.31.05 -2.4 -3.8 -2.9 -4.11.10 -4.9 -7.3 -5.6 -7.71.15 -7.2 -10.6 -8.3 -11.3

L 0.85 -15.9 13.5 -18.9 -9.40.90 -4.7 13.5 4.9 -13.20.95 6.5 -8.1 3.5 1.91.05 -19.6 10.8 -7.0 -24.51.10 -24.3 -8.1 -13.3 01.15 -2.8 -27.0 -4.2 -1.9

Chapter 6

Conclusions and Outlook

A model of the high-pressure circuit in the CRDI system is developed and imple-mented in a Simulink environment. It describes the individual events taking placewithin the four-stroke cycle, covering the transient behaviour associated with eachpump cycle and injection. Furthermore, the model is to a large extent based onthe underlying physics and constructed in a modular manner which allows for dif-ferent engine configurations to be simulated. It takes the same input signals as thereal system does and is ready to be integrated in the already existing simulationframework.

When compared to experimental data, it can be observed that the model hasproblems capturing the instantaneous performance of the HPP. This results in adrifting rail pressure when the model is subject to the same AIM actuation times asthe real system and is most likely explained by the lack of accuracy in the e�ciencymap. Additionally, the model shows a high sensitivity towards small perturbationsin SOTTL and another possible cause to the drifting phenomena is that the variableactuator delays are not captured well enough. However, by slightly adjusting thevalue of SOTTL, the model is able to mimic both the transient behaviour and thestatic levels seen in the experimental data with good agreement.

Both the spatially averaged rail model and the rail model with spatial depen-dency capture the static pressure levels after each event with good accuracy. Addi-tionally, the latter gives rise to pressure oscillations with similar characteristics tothose observed in the experimental data. Most peaks align well in the frequencyspectrum, although with some deviation. However, in addition to the expected fre-quencies, the model gives rise to additional oscillations of higher frequencies as well.This is most likely explained by the partitioning of the rail into several control vol-umes itself and how volumes of connecting pipes and injectors are included. Betteragreement with experimental data is seen if the modelled signal is low-pass filteredfirst. Furthermore, the additional low-frequency oscillations that are not capturedby the model are assumed to originate from the geometrical properties of the realrail that are not considered in the one-dimensional partitioning.

The developed model serves as a step in the direction towards model baseddevelopment and is suitable as a first stage in the verification process of futurecontrol algorithms due to its good response to changes in the inputs signals. Dueto the short time scales that has to be resolved in combination with the sti�ness of

48

6.1. OUTLOOK 49

the system causing the model to be computationally demanding, it is however not agood choice for applications running in real time such as a virtual pressure sensor.

6.1 OutlookThe most challenging part of the modelling process is to capture the performanceof the HPP since it is dependent on the instantaneous operating point of the en-gine. The e�ciency map utilized within this thesis has its advantages in beingcomputational inexpensive and easy to implement but lacks in accuracy. A possi-ble improvement would be to extend the implementation with physical models ofthe plunger/cylinder interface leakage, temperature increase induced by rapid com-pression and cavitation process taking place within the pumping chambers. Theadditional computational cost might be compensated by the increased ability tocapture the static pressure levels.

Even though the spatially dependent rail model manages to capture several fre-quencies in the pressure signal with promising accuracy, there are still some im-provements that should be considered. Based on the frequency spectrum in Figure4.17, it appears like there are two additional frequencies present in the experimentalsignal that are not captured by the model. As previously stated, these frequenciesare most likely stemming from the geometrical properties of the real rail and a firststep in the development of a more advanced model would be to take this into con-sideration. This could for example be accomplished by an artificial partitioning inmore than one dimension, facilitating the management of the additional volumesassociated with the pipes and injectors.

The current injector model approximates the rate-shape of each injection with asquare pulse transformed by a first order system. An obvious improvement wouldbe to model the injection process based on the underlying physics, considering bothhardware properties and variations in the fuel pressure inside each injector body.This would allow for a more realistic rate-shape where the transient behaviour as-sociated with the opening dynamics of the injector valves is included. As seen inthe sensitivity analysis, this would have an impact on the amplitude of the pressureoscillations as well and it could possibly reduce the observed discrepancy.

Bibliography

[1] Katharina Prinz, Wolfgang Kemmetmüller, and Andreas Kugi. Mathematicalmodelling of a diesel common-rail system. Mathematical and Computer Mod-elling of Dynamical Systems, 21(4):311–335, 2015.

[2] Kalevi Huhtala and Matti Vilenius. Study of a common rail fuel injectionsystem. In Automotive and Transportation Technology Congress and Exposition.SAE International, oct 2001.

[3] L. M. Rodriguez-Anton, J. Casanova-Kindelan, and G. Tardajos. High pressurephysical properties of fluids used in diesel injection systems. In CEC/SAESpring Fuels & Lubricants Meeting & Exposition. SAE International, jun 2000.

[4] Botwinska, Katarzyna, Mruk, Remigiusz, and Krawiec, Lukasz. Modelling ofthe work processes high-pressure pump of common rail diesel injection system.E3S Web Conf., 10:00126, 2016.

[5] H.P. Wang, D. Zheng, and Y. Tian. High pressure common rail injection systemmodeling and control. ISA Transactions, 63:265 – 273, 2016.

[6] Dexing Qian and Ridong Liao. Theoretical analysis and mathematical mod-elling of a high-pressure pump in the common rail injection system for dieselengines. Proceedings of the Institution of Mechanical Engineers, Part A: Jour-nal of Power and Energy, 229, 01 2014.

[7] Kurt Källkvist. Fuel pressure modelling in a common-rail direct injection sys-tem. Master’s thesis, Linköping University, Vehicular Systems, 2011.

[8] Daniel B. Roemer, Michael M. Bech, Per Johansen, and Henrik C. Pedersen.Optimum design of a moving coil actuator for fast-switching valves in digitalhydraulic pumps and motors. IEEE/ASME Transactions on Mechatronics,20(6):2761–2770, 2015.

[9] Lars Eriksson, Lars Nielsen, Inc Books24x7, Fordonssystem, Linköpings univer-sitet, Tekniska fakulteten, and Institutionen för systemteknik. Modeling andcontrol of engines and drivelines, volume 9781118479995. Wiley, Chichester,West Sussex, United Kingdom, 1st edition, 2014.

[10] V. L. Streeter and E. B. Wylie. Waterhammer and surge control. Annual Reviewof Fluid Mechanics, 6(1):57–73, 1974.

[11] Rolf Isermann. Engine Modeling and Control. Springer Verlag, DE, 2014.

50

BIBLIOGRAPHY 51

[12] 1931-2016 Nordling, Carl and 1952 Österman, Jonny. Physics handbook forscience and engineering. Studentlitteratur, Lund, 8., [rev.] edition, 2006.

[13] Paolo Lino, Bruno Maione, and Alessandro Rizzo. Nonlinear modelling andcontrol of a common rail injection system for diesel engines. Applied Mathe-matical Modelling, 31(9):1770 – 1784, 2007.

[14] Christophe Gauthier, Olivier Sename, Luc Dugard, and Guillaume Meissonnier.Modelling of a diesel engine common rail injection system. IFAC ProceedingsVolumes, 38(1):188 – 193, 2005. 16th IFAC World Congress.

[15] Torkel Glad and Lennart Ljung. Control Theory. CRC Press, 1 edition, 2018.

[16] Maurcio C. de Oliveira. Fundamentals of Linear Control: A Concise Approach.Cambridge University Press, New York, NY, USA, 1st edition, 2017.

modelling of high-pressure fuel system for controller...

Documents