Knock Model Evaluation – Gas Engine

Nishchay Sharma

Master of Science Thesis MMK 2018: TRITA-ITM-EX 2018:600

KTH Industrial Engineering and Management

Machine Design

SE-100 44 STOCKHOLM

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Master of Science Thesis MMK 2018:

TRITA-ITM-EX 2018:600

Knock Model Evaluation – Gas Engine

Nishchay Sharma

Approved

2018-August-27

Examiner

Dr. Andreas Cronhjort

Supervisor

Dr. Johan Fjällman

Commissioner

AVL, Södertälje

Contact person

Jonas Modin

Sammanfattning Knack i en förbränningsmotor är en typ av onormal förbränning. Det är ett komplicerat fenomen

som beror på flera fysiska faktorer och resulterar i högfrekventa tryckoscillationer inuti

förbränningskammaren. Dessa oscillationer kan skada motorn och fenomenet hämmar motorns

effektivitet. Knack kan uppstå på två sätt i en Otto-motor och detta examensarbete kommer att

handla om självantändning. Självantändning, i detta fall, är när ändgasen börjar brinna utan att ha

blivit påverkad av flamfronten eller gnistan från tändstiftet. Det finns flera olika matematiska

modeller som i olika grader kan prediktera knackfenomenet. I detta examensarbete studeras några

av de tidigare publicerade prediktionsmodellerna för knack i Otto-förbränning och modelleras för

analys. Huvudsyftet med detta projekt är således att bedöma noggrannheten hos olika typer av

knackmodeller.

Extra fokus har lagts på empiriska korrelationsmodeller, särskilt till de som är baserade på kemisk

kinetik avseende förbränningsprocessen av metan. Dessa modeller förutsäger den tid det tar för

ändgasen att självantända, baserat på dess koncentration av luft och bränsle. Knackmodellerna

bedöms sedan utifrån det beteende som de förutsäger över motorns driftområde och dess

överensstämmelse med kända motorkalibreringsstrategier. Resultatet av knackpredikteringen för

de olika knackmodellerna utvärderas och valideras i en motorsimuleringsmodell i mjukvaran AVL

BOOST. BOOST-modellen kalibreras mot experimentellt uppmätta motortestdata.

Baserat på resultaten från de valda knockmodellerna så blev den modell som bäst korrelerar med

kända motorkalibreringsstrategier analyserad djupare. Den utvalda modellen var en ECM modell

och den utvärderas ytterligare med avseende på variation i predikterad knack-parameter. Detta

görs genom att modifiera två förbränningsparametrar: tändvinkel och förbränningsduration. Det

visade sig att modellerna predikterade en linjär ökning då tändningen tidigareläggs och ett linjärt

minskande vid längre förbränningsduration, vilket är i enlighet med motortestdata. Vidare visade

det sig att variationer i tändvinkel resulterade i en högre gradient i knackpredikteringen vid högre

motorbelastningar och korresponderande minskning vid lägre belastning.

Nyckelord: Knack, Otto-förbränning, Förbränningsmotor, Empiriska korrelationsmodeller,

BOOST, Förbränningsfasning, Tändvinkel, Förbränningsduration, Knackprediktering.

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Master of Science Thesis MMK 2018:

TRITA-ITM-EX 2018:600

Knock Model Evaluation – Gas Engine

Nishchay Sharma

Approved

2018-August-27

Examiner

Dr. Andreas Cronhjort

Supervisor

Dr. Johan Fjällman

Commissioner

AVL, Södertälje

Contact person

Jonas Modin

Abstract Knocking is a type of abnormal combustion which depends on several physical factors and results

in high frequency pressure oscillations inside the combustion chamber of a spark-ignited internal

combustion engine (ICE). These oscillations can damage the engine and hamper its efficiency,

which is why it is important for automakers to understand the knocking behavior so that it can be

avoided during engine operation. Due to the catastrophic outcomes of knocking a lot of research

has been done in the past on prediction of its occurrence. There can be several causes of knocking

but when it occurs due to auto-ignition of fuel in the end-gas it’s called spark-knock. There are

various mathematical models that predict the phenomenon of spark-knock. In this thesis, several

of the previously published knock prediction models for heavy-duty natural-gas engine are studied

and analyzed. The main objective of this project is to assess the accuracy of different types of

knock prediction models.

Amongst all the types of knock prediction models emphasize has been given to empirical

correlation models, particularly to the ones which are based on chemical kinetics pertaining to the

combustion process of methane. These are the models that claim to predict ignition delay time

based on concentration of air and fuel in the unburned zone of the cylinder. The models are

assessed based on the knocking behavior they represent across the engine operation range. Results

pertaining to the knock prediction models are evaluated in a 1D engine simulation model using

AVL BOOST. The BOOST performance prediction model is calibrated against experimentally

measured engine test-cell data and the same data is used to assess the knock prediction models.

The knock prediction model whose results correlate with experimental observations is analyzed

further while other models are discarded. Using the validated model, variation in knock occurrence

is evaluated with change in the combustion phasing. Two of the parameter that are used to define

the combustion phasing are spark-advance and combustion duration. It was found that when the

brake mean effective pressure is kept constant the knock prediction parameter increases linearly

with increase in spark advance and decreases linearly with increase in combustion duration. The

variation of knock prediction parameter with spark advance showed increasing gradient with

increase in engine torque.

Keywords: Knocking, Spark-Ignited, Internal Combustion Engine, Spark-Knock, Empirical

Correlation Models, BOOST, Combustion Phasing, Spark-advance, Combustion Duration, Knock

Prediction Parameter.

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ACKNOWLEDGEMENTS

“Extraordinary results require extraordinary efforts!”, these are the words that my parents have

sown in my character. First, I would like to thank them for always encouraging me to pursue my

passion and at the same time always reminding me to do it with complete devotion.

This thesis work has taught me the importance of guidance and team-work. For those two

invaluable lessons I would like to thank my supervisors Johan Fjällman and Johannes Andersen. I

have always grown from our discussions and their guidance has helped me to stay focused on

course in a complicated project where I could have easily digressed. Throughout the thesis they

have not only been working together with me but have also been acquainting me to the Swedish

culture. I find myself lucky to have them as my colleagues and have the utmost respect for them.

I would like to thank Dr. Andreas Cronhjort, his guidelines on the planning of a research project

have been extremely beneficial to me. It was through his feedback during the earlier project work

that I could learn from my mistakes as a student and then improve on them to put myself ahead as

an organized research professional.

Ludvig Adlercreutz has played a crucial role in realization of this thesis. His contribution with the

experimental data and trails on the test-cell engine proved as big stepping stones which laid the

foundation of this project. Not only did he help me to understand the working of test-cell and the

engine but also demonstrated knocking combustion experimentally. I envy his skills and hope that

I will be bestowed with more learning opportunities from him in the future. Hereby, I thank him

for his immense support.

I would also like to thank the friendly and motivated team members at AVL, especially my

department manager Jonas Modin. It was because of him that I never had to worry about any of

the organizational issues and could focus on my work. Moreover, he and other colleagues also

introduced me to a new sport “Innebandy” which made me feel like a part of the company and

among friends.

Throughout the project work, I met a lot of people at AVL and gained the experience of working

on a challenging research project. Being a part of the AVL team here has developed me

professionally and for that I express my sincere gratitude.

Nishchay Sharma

Stockholm, August 2018

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NOMENCLATURE

Notations

Symbol Description

τ Ignition delay time [s]

t Time [s]

Kc Knock prediction parameter [-]

Tu Unburned-zone temperature [K]

p Cylinder pressure [bar]

h Specific enthalpy [J/kg]

V Volume [bar]

cp Specific heat capacity at constant pressure [J/kg.K]

mb Mass of burned zone [kg]

mu Mass of unburned zone [kg]

….. …….

Abbreviations

SI Spark Ignition/Ignited

ICE Internal Combustion Engine

ECM Empirical Correlation Model

CKM Chemical Kinetics Model

CFDM Computational Fluid Dynamics Model

CI Compression Ignition/Ignited

CAD Crank Angle Degree [°]

TDC Top Dead Center

BDC Bottom Dead Center

AIT Auto-ignition Temperature [K]

EGR Exhaust Gas Recirculation

SCR Selective Catalytic Reduction

RON Research Octane Number

HC Hydrocarbon

CNG Compressed Natural Gas

LNG Liquified Natural Gas

RPM Revolutions per Minute [rpm]

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BMEP Brake Mean Effective Pressure

IVC Intake Valve Closed

SOC Start of Combustion

EOC End of Combustion

PR Propane Ratio

ER Equivalence Ratio

LHV Lower Heating Value [J/kg]

WHSC World Harmonized Stationary Cycle

CD Combustion Duration [°]

ROHR Rate of Heat Release [J/°]

CR Compression Ratio

… …

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TABLE OF CONTENTS

Sammanfattning (Swedish) i

Abstract (English) iii

Acknowledgements v

Nomenclature vii

Table of Contents ix

1 INTRODUCTION 1

1.1 Background 3

1.2 Purpose 7

1.3 Delimitations 7

2 LITERATURE REVIEW 9

2.1 Knock Prediction Models Based on Arrhenius Function 9

2.2 Knock Prediction Models Based on Chemical Kinetics 10

2.3 Knock Prediction Models Based on Thermodynamics 12

3 IMPLEMENTATION 14

3.1 Boost Model Calibration 15

3.2 Calculating Knock Prediction Parameter (Kc) 16

4 RESULTS 18

4.1 Models based on Ignition Delay Time 18

4.2 Calculating Knock Prediction Parameter (Kc) 20

5 ANALYSIS 22

5.1 Boost Model Calibration 22

5.2 Calculating Knock Prediction Parameter (Kc) 24

6 CONCLUSIONS 28

7 FUTURE WORK 29

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8 REFERENCES 30

APPENDIX A1: Kc vs CAD (KM1-KM10) 32

APPENDIX A2: Kc vs CAD (KM11) 38

APPENDIX B: Contour Plots of Knock Models 44

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1 INTRODUCTION

In this chapter, a brief introduction to the different types of ICEs and the properties of the fuels

used for them is presented. The working of spark-ignited engines is explained, which under certain

operating conditions undergo knocking. Different types of knocking phenomenon and their causes

are elaborated upon. Lastly, different ways to predict knocking are outlined.

An Engine is defined as a device that converts one form of energy in to another (Ganesan, 2008).

Generally, in an engine it is the chemical energy of a fuel that is converted into useful mechanical

work by combusting the air-fuel mixture in a controlled manner.

Based on their construction and working principles engines can be classified as rotary type and

reciprocating type. An example of a modern rotary type engine would be a Mazda RX7 rotary

engine which was originally invented by Felix Wankel (Heywood, 1988) and an example for

reciprocating type engine would be Spark-Ignited (SI) engines which is based on Otto Cycle

(1876). Another classic example of reciprocating type engines is Compression-Ignited (CI)

engines which are based on Diesel Cycle (1892) (Çengel and Boles, 2015). In the automotive

industry, most of the vehicles use reciprocating type engines apart from that there have been a few

vehicles based on electric drivelines. In a reciprocating engine the air-fuel mixture is burned in a

cylinder that has a reciprocating piston which translates along the axis of the cylinder. The piston

transmits power to the driveshaft through the connecting rod and crank mechanism (Heywood,

1988). Since, the fuel is burned internally in a closed space in these engines, they are called as

‘Internal Combustion Engines’. Figure 1 shows the basic geometry and construction of an SI

engine:

Figure 1. Geometry and construction of an SI Engine (Ganesan, 2008)

Conceptually, as far as the combustion of fuel in SI and CI engines is concerned oxygen (from the

air) is necessary but SI and CI engines have different ways of igniting the fuel in presence of air.

Conventionally in an SI engine the air and fuel are mixed outside the cylinder and then inducted

into the cylinder. This pre-mixed charge is ignited by a spark plug later in the engine cycle. While

in a CI engine, only air is inducted into the cylinder which is then compressed to a high pressure

and temperature before the injection of fuel, the high temperature of the surrounding compressed

air auto-ignites the injected fuel. Auto-ignition is the tendency of the fuel to spontaneously ignite

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in presence of air without any external source of energy at a given temperature (Johansson, 2014).

It is due to this difference in auto-ignition properties of petrol and diesel that qualifies them as

suitable fuels for SI and CI engine respectively.

Most of the modern SI and CI engines operate on the four-stroke cycle. Each stroke is marked by

the motion of the piston from one extreme position to another. Moreover, during the piston

movement, from one extreme to another, the crank shaft rotates by an angle of 180°. Thus, the

completion of an entire four-stroke cycle, amounts for 720° crank angle degrees (CAD). Since this

work is specifically about SI engine, the construction and general working principle of a four-

stroke SI engine is discussed below.

Figure 2 shows the four strokes during an engine cycle (Ganesan, 2008) respectively. As per Figure

2, the four strokes of an SI engine can be described as:

1. Intake stroke: Suction of the air-fuel mixture starts when the piston is at the Top Dead Center

(TDC); top most position of the piston in the cylinder. Here the intake valve opens and piston

moves down, this downward piston motion results in suction of air through the intake port

inside the cylinder until the piston reaches the Bottom Dead Center (BDC).

2. Compression stroke: The intake valve closes after the intake stroke. The charge induced in

the cylinder is then compressed by the upward motion of the piston as the piston moves from

BDC to TDC. During the end of this stroke, when the piston is moving towards TDC, the

spark plug ignites the compressed charge.

3. Power or Expansion stroke: With both intake and exhaust valve still closed, the ignited air-

fuel mixture at high pressure pushes the piston down to BDC hence doing work on the piston.

This is the only stroke amongst all the four strokes that leads to power generation.

4. Exhaust stroke: After the expansion stroke, the exhaust valve opens when the piston is at

BDC and is starting to move towards TDC. Upward motion of piston pushes the exhaust gas

through the exhaust port and out of the cylinder.

Figure 2. Working principle of a four-stroke SI Engine (Ganesan, 2008)

The type of fuel plays a crucial role in determining the suitable ignition strategy to be used for its

efficient combustion. As mentioned earlier, one of crucial fuel properties is its tendency to auto-

ignite, this tendency is physically represented by the fuel’s Auto-Ignition Temperature (AIT); it is

the temperature at which the fuel gets ignited in presence of oxygen in its surrounding. The value

of AIT poses as one of the most important parameters for when the design of an SI engine is

concerned. This is because if the fuel has a low AIT then it limits the compression ratio of the

engine and a lower compression ratio leads to lower pressure and temperature at the end of

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compression stroke which reduces the power output and hence efficiency of the engine (Ganesan,

2008). The power delivery and efficient fuel combustion of an ICE is highly dependent on its

geometrical construction. For example, thermodynamically, the efficiency of an ICE depends on

the compression ratio; ratio of maximum cylinder volume to minimum cylinder volume during an

engine cycle (Heywood, 1988). But increasing the compression ratio increase the temperature of

the charge at the end of compression stroke which leads to auto-ignition of fuel resulting in

abnormal combustion.

There is another important aspect of an ICE that has been the area of enormous amount of research

work for decades now: emissions. The quest of designing an ICE with less harmful emissions

without affecting its performance has been a challenge for engineers. To mitigate the harm caused

to the environment by emissions after combustion, numerous after-treatment technologies have

been developed like Exhaust Gas Recirculation (EGR) and Selective Catalytic Reduction (SCR).

EGR is the recirculation of a portion of the exhaust gas after cooling into the cylinder along with

the fresh charge, this reduces the temperature in the combustion chamber and hence the formation

of harmful oxides of nitrogen (NOx) emissions. But there is also a downside of using excessive

EGR because it increases the formation of soot particles (Heywood, 1988). While, SCR is a device

that is used to chemically reduce the emitted NOx to nitrogen and water (Johansson, 2014). Apart

from all the methods mentioned above, one of the most basic requirements to deal with emissions

is to have a clean and efficient combustion of fuel, which is easier said than done since there are

possibilities of abnormal combustion amongst other challenges.

Another solution that has been explored by researchers for reduction of harmful emissions from

an ICE is the use of unconventional fuels instead of gasoline and diesel. The present thesis

specifically considers the use of natural gas as a fuel for heavy-duty SI engines. Since the fuel is

burned in an SI-engine that are susceptible to knocking, the focus of this thesis is on the

phenomenon of knocking which is defined as a type of abnormal combustion. This phenomenon

hampers the combustion process and reduces the engine efficiency, in worst cases it may damage

the engine as well. In the next sections, the motivation, background and purpose of this research

work are outlined in detail.

1.1 Background

Most of the heavy-duty automotive applications are powered by diesel engines. The emission

legislations are very tough and for the heavy-duty automotive industry this means complex and

expensive after treatment systems for the diesel engines. An alternative approach to this problem

is to use gas-engines because natural gas as a fuel has numerous advantages. For example; it is

composed mainly of methane (CH4) so it has 75% carbon mass compared to petrol and diesel

which have 86-88%. It produces less CO2 per unit of energy as compared to petrol and diesel, it

has a high-octane number (RON 110-130) and hence can be used in an engine with high

compression ratio (at least when compared to petrol engine). Since, natural gas has a higher auto-

ignition resistance it requires a higher spark energy for ignition as compared to other hydrocarbons

(HCs). Its higher flammability range allows the engine to operate on a lean fuel mixture. However,

being gaseous leads to lower volumetric engine efficiency since the air breathing capacity of the

engine is reduced. Moreover, the lower energy density requires vehicle onboard storage in

compressed (CNG) or liquefied (LNG) form leading to issues with the heavy pressurized storage

cylinders (McLean and Lave, 2002). Still, considering the overall evaluation, natural gas comes

out as a better fuel compared to gasoline and diesel.

Natural gas as a fuel is a potent prospect for the heavy-duty automotive industry, but incorporation

of this fuel in the powertrains based on existing ICEs has its own peculiar challenges. One of these

challenges is knocking, to understand knocking in a better way at first the combustion process is

to be analyzed in detail. Conceptually, for a natural gas engine the combustion process is like that

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of a conventional gasoline engine: mixing of the air and fuel in the intake system, induction of air-

fuel and EGR mixture into the cylinder, mixing of the inducted charge with the left over residual

gas from the previous engine cycle. Then, as mentioned in the earlier section the four-stroke engine

cycle takes place, where power is generated by combustion of the charge via an electric discharge

from the spark plug that initiates the ignition (Heywood, 1988). Taking a deep dive into the

phenomenon of combustion, the burning of the fuel starting from the time of spark can be divided

sequentially into the following stages:

1. Spark initiation or electrical discharge: A high potential difference across the electrodes of

the spark plug leads to electrical breakdown of air in the gap between them. Thus, leading

to a spark in the combustion chamber. This occurs during the compression stroke, usually

around -30° to -20° CAD for part load, -10° to 0° CAD in case of full load. This spark forms

a localized high temperature zone which initiates the combustion of the compressed charge

in the cylinder. The local high temperature gas near the spark plug forms plasma and within

the plasma surface the chemical reaction starts to form radicals from the reactants.

2. Start of combustion and early flame development: When the number of radicals formed

reach beyond a critical number a chain reaction is started which leads to formation of more

radicals by consuming the reactants. In the next chapter, the chemical reactions forming

radicals are discussed in detail.

3. Flame propagation: The increase in reactant consumption due to chain reactions propagates

the reaction zone further away from the spark plug. The intensity and movement of the

reaction zone is influenced by various factors like local air-fuel composition, inert gas

fraction (EGR and residual gas), turbulent-laminar flow profile, in cylinder motions – squish,

tumble and swirl etc. This propagating reaction is called a flame front. The mixture of air,

fuel, EGR and residual gas in the unburned zone is called end-gas. Relevant to this project,

one of the most important parameters is the flame speed. The flame propagation can be

categorized based on its speed, namely: (1) laminar flame speed; (2) expansion speed; and

(3) turbulent flame speed. At first, the flame front propagates with laminar flame speed

which is determined by the reactivity of the charge due to the fact that the charge velocity

around the spark plug is very low. Areas with high turbulence in the cylinder increase the

flame propagation speed due to relatively faster intake of unburned gas into the reaction

zone. The velocity at which the unburned gas enters the reaction zone is defined as the

turbulent flame speed. The laminar flame speed is around 0.2-0.5 m/s, whereas the effective

flame propagation in turbulent regime ranges from 10-50 m/s. Moreover, the burned zone is

at a higher temperature as compared to the unburned zone, due to which there is thermal

expansion. This thermal expansion leads to even higher flame speed which is also called as

the expansion speed. The expansion speed of the flame front can be twice as high as the

turbulent flame speed (Johansson, 2014).

4. Flame quenching: Under normal combustion circumstances, the advancing flame reaches

the cylinder wall thus consuming all the charge present in the cylinder. The flame reaches

the walls at around 15° CAD. Even when the entire combustion chamber is ablaze by the

flame there is still approximately 25% of the charge that is yet to burn. Thus, the combustion

continues around the combustion chamber till around 25° CAD. Ultimately, all the charge

gets burned which extinguishes the flame (Heywood, 1988).

Depending upon the engine operating conditions, the duration of flame development and

propagation typically lies between 30° and 90° CAD. This is typically the case when the

combustion is normal. In SI engines, the abnormal combustion phenomenon can occur in many

ways but in the present thesis work the phenomena of knocking is explored, which when severe

may lead to catastrophic engine damage. When it is not severe, it limits the engine performance

and generates noise. Knocking got its name due to the type of noise that it transmits through the

engine body and it can occur due to two reasons; localized auto-ignition in the unburned zone and

surface ignition. The auto-ignition in the unburned zone creates another flame front which then

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collides with the normal combustion flame front (see figure 3). This causes high intensity pressure

oscillations in the combustion chamber, thus, making knocking an acoustic phenomenon. Surface

ignition, on the other hand, is the burning of the charge due to a hot spot on the combustion

chamber walls. The hot spot can be an overheated spark plug or valve, hot cylinder wall or a heated

scrapped oil deposit. Any source of combustion other than the normal spark ignition classifies as

surface ignition, see figure 4. When the surface ignition occurs before the spark discharge, it’s

called as pre-ignition. Contrarily, when it occurs after the spark discharge, it’s called as post-

ignition. It should be noted that surface ignition can lead to knocking, especially pre-ignition.

Moreover, several plausible combinations of knock and surface ignition can occur depending upon

various parameters like, pressure and temperature of end-gas, spark advance, combustion phasing,

in-cylinder turbulence, etc. (Heywood, 1988).

Figure 3. Auto-ignition of end-gas that eventually leads to knocking (Hpcomb.kaust.edu.sa, 2018)

The repeated occurrence of auto-ignition of end-gas instead of normal combustion is called spark-

knock. Although, knocking is a highly sporadic phenomenon and varies greatly from one engine

cycle to another. It is possible to have knocking at the same operating conditions repetitively for a

certain number of cycles and none during other cycles. As far as spark-knock is concerned, it can

be controlled by changing the combustion phasing. This can be done by changing the spark

advance which is defined as the CAD value during the latter part of the compression stroke at

which spark discharge from the spark plug ignites the charge. When the spark advance is retarded

both the knock severity and intensity decrease. Concurrently, advancing the spark event increases

the possibility of knocking (Heywood, 1988).

Figure 4. Various types of surface-ignition (Hpcomb.kaust.edu.sa, 2018)

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The root cause for occurrence of spark-knock is the auto-ignition of the end-gas ahead of the flame

front. The auto-ignition happens because the end-gas reaches at or beyond the AIT of the fuel. To

understand how and why this happens, it is essential to emphasize on the thermodynamics involved

in the combustion process. Based on the first law of thermodynamics, if the end-gas is considered

as an open system, then its internal energy (which is directly related to the temperature) can only

be increased in two ways: (1) adding heat to the system; (2) doing work on the system (Çengel and

Boles, 2015). There are several ways in which heat and work are added to the end-gas.

Chronologically, they occur as:

• After the induction of the charge in the cylinder during the intake stroke, the piston

compresses the charge during the compression stroke before the spark discharge from the

spark plug. This volumetric work done by the piston increases the temperature and pressure

of the entire charge.

• Spark-ignition occurs late during the compression stroke initiating the combustion of fuel.

The fuel burning in the reaction zone releases heat to the surrounding end-gas. It should be

noted that during this time, the piston moving towards TDC still continues to compress the

charge, hence adding work. Moreover, the combustion of fuel leads to increase in pressure

and temperature of the reaction zone along with expansion of burned gas. The high-pressure

reaction zone pushes the end-gas, thus compressing end-gas further.

• Cylinder wall around the combustion chamber is at high temperature due to constant

exposure to heat release from combustion. Same is the case with piston top and exhaust

valves. The portion of end-gas close to these hot physical boundaries gets heated from them.

On top of that, the same portion of end-gas, since located farthest away from the spark-plug

experiences the maximum compression work and heat addition from the propagating

reaction zone (Heywood, 1988).

As described above, knocking is a complex abnormal combustion phenomenon which affects the

engine in terms of performance and in worst case damages its parts thus stalling the engine. Due

to this knocking has been a topic of research and exploration for a long time, where the area of

interest has been prediction of its occurrence for a given engine operating condition. The prediction

of occurrence of knocking has been done majorly through three different types of models:

1. Empirical Correlation Models (ECMs): these models predict knocking by using empirical

correlations that have been tuned to experimentally acquired data. The advantage of using

these types of models is that they can be tuned to work for any engine if the parameters used

are independent of the engine geometry. However, the accuracy of prediction of occurrence

of knocking from these models is not very high. Interestingly, some of the empirical

correlation models use the fundamentals of chemical kinetics while others are based on

purely mathematical expressions and curve fitting. Apart from these, there are several other

models which take into consideration the variation of thermodynamic parameters during the

engine cycle to predict knocking. The mathematical expressions on which all these models

are based require inputs in terms of physical and thermodynamic parameters. These

parameters are related to the combustion process, composition of the charge in the cylinder

and the concomitant state of end-gas.

2. Chemical Kinetics Models (CKMs): the combustion process is nothing but a chemical

reaction where the fuel is oxidized. These models use the chemical reactions involved in the

oxidation of the fuel. The chemical oxidation of fuel involves numerous intermediate

reactions as well as radicals. CKM models rely entirely on the chemical kinetics

fundamentals to evaluate the concentration of reactants and products to predict the

possibility of auto-ignition in the end-gas. Most of the CKMs involve iterative numerical

methods to calculate the mass fraction of the chemical species.

3. Computational Fluid Dynamics Models (CFDMs): the physical parameters that define the

state of the end-gas can be estimated by solving the Navier-Stokes equations. In a CFDM,

for a given engine geometry, the combustion process can be simulated. The simulations to

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solve the Navier-Stokes equation are based on various numerical approximations, e.g.

Reynolds-Averaged Navier–Stokes (RANS) equations, Large Eddy Simulation (LES), etc.

Setting up a combustion case and solving the RANS equations for it using different types of

iterative solution methods can result in evaluation of parameters of interest. The only

drawback with CFDMs is that they are highly geometry dependent and for every engine

operating point a separate simulation is to be run.

1.2 Purpose

Numerous researchers have proposed knock prediction models for gas engines, the problem with

these models is that they claim to predict knocking accurately but their predictions do not coincide

with the experimental observations. Therefore, the first and the foremost objective of this thesis is

to evaluate the accuracy of end-gas auto-ignition claimed by a selected few knock prediction

models. To check the accuracy of a given knock prediction model its results are to be compared

with previously acquired experimental data.

Through a thorough literature survey several knock prediction models are were shortlisted for

chosen for evaluation. They were then analyzed and compared with each other in terms of their

accuracy. Out of the assessed models the ones with plausible results are to be used for further

analysis by performing simulations while changing the spark timing and combustion duration. The

engine modelling is to be done in BOOST.

Out of the three mentioned categories of knock prediction models in the previous section ECMs

are the focus of the current work. On that basis, the following research questions have been

formulated. These research questions are aimed to explicitly define the objectives of the thesis:

• What are the different types of ECMs currently available that can be used to predict knocking

in gas engines?

• What are the thermodynamic assumptions and considerations these models are based on?

According to these models, what are the parameters on which knocking depends? Can these

parameters be related to other physical parameters e.g. fuel concentration?

• Which ECMs show plausible knocking behavior?

• How does the knocking behavior vary with change in parameters like spark advance and

combustion duration?

1.3 Delimitations

As mentioned in the previous section, prediction of knocking can be done by using three different

types of models. In this project the target is to assess a zero-dimensional (0D) ECM. 0D models

have no geometric dependency rather they only have time dependency (Holzbecher, 2012). Apart

from the type of models there are several other assumptions as well as limitations that have been

deliberately imposed to get a better understanding of the complex knocking behaviour. These

assumptions and limitations are:

1. Fuel consideration: The fuel of interest is natural gas but we are using pure methane, both

for the ease of modelling but also for the easier chemical estimations. To model the

combustion phenomenon as close as possible to reality, the use of a certain fraction of

propane in the fuel should be considered, but in this work the fuel is assumed as pure

methane. This is because it has been found that the presence of propane changes the kinetics

of methane combustion (Lifshitz et al., 1971).

2. Only spark-knock consideration: Knocking is an abnormal combustion phenomenon which

is highly complex in nature, one of the factors that adds to its complexity is the cause that

leads to knocking. As discussed earlier, there can be several causes that may lead to

8

knocking, e.g. spark-knock and surface ignition (especially pre-ignition). In this work, the

aspect of auto-ignition of end-gas is studied and modelled. No emphasise has been given to

the surface ignition phenomenon, except that the cylinder wall temperature is considered

when the heat transfer in the combustion chamber is analysed in BOOST.

3. No acoustics involved: Another aspect that has not been considered in this work is the

acoustics of knocking. This is because the work is focused on predicting the occurrence of

knocking, that is, for a given engine operating condition will there be knocking or not? While

the acoustics on the other hand come into play when knocking is occurring already because

it is signified by oscillation of cylinder pressure.

4. Emphasis on when knocking starts to occur: The prediction of occurrence of knocking has

two important aspects; (1) predicting the CAD at which knocking starts to occur which is

otherwise called as the ‘knock onset’, (2) predicting the intensity of the knocking

phenomenon which is the amplitude of the pressure oscillation that knocking is going to

result in. In this work the modelling is focused on the prediction of knock onset, but the

possibility of estimating knock intensity has not been considered. To relate this to the

pressure oscillations due to knocking, the focus is to predict the point of time at which the

oscillations begin (knock-onset) and not the amplitude of those oscillations (knock

intensity).

5. Consideration of spark-advance only in terms of CAD: Another essential aspect that is

directly related to knocking is the spark advance. In this work, the influence of spark advance

on knock onset is emphasized upon but not on knock intensity. Rather, the spark advance is

considered as an event that controls the combustion phasing. Spark advance has only been

considered in terms of CAD to assist in marking the beginning of combustion of fuel at any

engine operating point.

6. Air-fuel ratio consideration: In an engine the air-fuel ratio varies with respect to the

operating conditions, this variation in the air-fuel ratio also plays a crucial role when it comes

to knocking. An air-fuel mixture is called lean which has more than the required amount of

air to burn the fuel completely. Contrarily, if the amount of air required to burn the fuel is

lower, then the mixture is called rich. Whereas, a stoichiometric mixture has the exact

amount of air required to burn the fuel completely. It has been observed that, lean mixtures

have a higher tendency to knock as compared to rich mixtures. This is because lean mixtures

attain higher temperature at the end of the compression stroke as compared to stoichiometric

and rich mixtures (Grandin et al., 2002). This leads to more heating of the end-gas and may

also lead to surface ignition (especially pre-ignition). Therefore, for the sake of simplicity,

the air-fuel mixture is considered as stochiometric. The stoichiometric air-fuel ratio (by

mass) for pure methane is 17.23, whereas for natural gas it is 14.5 (Heywood,1988).

9

2 LITERATURE REVIEW

In this chapter, the summary of existing knowledge and former performed research about ECMs

used for knock prediction is presented. Several types of knock prediction models in the ECM

category have been identified and mentioned. A comparative analysis of these models has been

done which outlines their similarities and differences. The physical and numerical parameters that

these models consider are analyzed and discussed.

Most of the knock predicting ECMs are based on ‘ignition delay time’ which is defined as, “A key

physicochemical property of combustible fuel-air mixture used for engines running on various

principles. The time or the turn angle of a piston engine crankshaft from the start of fuel injection

into the combustion chamber to the instant of appearance of flame (cold flame glow) or rise of

pressure in the chamber due to heat evolution upon combustion of the fuel is considered as the

ignition (spontaneous ignition) delay time.” (Keshavarz et al.,2013). By some authors like,

Heywood (Internal Combustion Engine Fundamentals, 1988) the ignition delay time is also

referred as induction time. The parent correlation on which most of ECMs are based that uses

ignition delay time to predict the onset of auto-ignition in end gas is (Livengood and Wu, 1955):

𝐾𝑐 = ∫1

𝜏

𝑡0

𝑑𝑡 = 1 (1)

In the above equation, 𝐾𝑐 is the knock prediction parameter and signifies onset of knocking at the

time when its value reaches 1, τ is the ignition time delay and t is the elapsed time from start of

compression (closure of intake valve) to auto-ignition. τ has been estimated in several ways by

several approaches: (1) by fitting the engine’s experimental data to an Arrhenius function

(Reference 99 in chapter 9 by Heywood, 1988); (2) by chemical kinetics that consider the oxidation

of the fuel, which in this case is methane. There are several models that are studied and analysed

in this thesis that use these approaches for estimation of ignition delay time.

2.1 Knock Prediction Models based on Arrhenius Function

The Arrhenius function that is used for matching the experimentally measured data is:

𝜏 = 𝐴𝑝−𝑛exp (𝐵

𝑇𝑢) (2)

Here 𝑝 is the cylinder pressure, 𝑇𝑢 is the unburned zone temperature and 𝐴, 𝑛 and 𝐵 are constants

which depend on the fuel type. In general, the accuracy of knock prediction models based on this

equation is ambiguous and depends upon how the parameters 𝐴, 𝑛 and 𝐵 are calibrated with the

experimentally obtained data (Heywood, 1988). To minimize the error in prediction of knock least

square method is used for optimization of the parameters (Douaud and Ezyat, 1978). The following

sets of values for the constant parameters were proposed by researchers to predict occurrence of

knocking based on equation (2):

Table 1. ECMs based on Arrhenius function

Model No. A n B Reference

KM1 0.021 1.7 3800 (Elmqvist-Möller, 2006)

KM2 0.0071 1.325 3296 (Elmqvist-Möller, 2006)

KM3 32.87 1.7 3800 (Douaud and Ezyat, 1978)

KM4 0.985 0.887 6167 (Soylu, 2005)

10

Amongst the models mentioned in Table 1, the ignition delay time estimation in knock prediction

model KM3 is based on the following equation, it should be noted that this equation gives the

ignition delay time in milliseconds:

𝜏 = 17.68 (𝑂𝑁

100)

3.402

𝑝−1.7𝑒𝑥𝑝 (3800

𝑇𝑢) (3)

In equation (3), ON stands for the octane number of the fuel which is 120 for methane. (Heywood,

1988). From equation (3) it is observable that ignition delay time is dependent on the octane

number which in turn is a fuel property, this supports that accuracy of the knock prediction model

is sensitive to the type of fuel. This high dependency of the accuracy of knock prediction models

on the type of fuel also forces to consider the fact that fuels used for running the engine are not

pure and when two or more different types of hydrocarbons are present in the fuel then the

parameters of the knock prediction models need to be calibrated accordingly. As far as dependency

on the quality of fuel is concerned, the parameter 𝐵 for only KM4 considers the ratio of propane

present in the natural gas. The following equation shows how the propane ratio and equivalence

ratio are considered in the evaluation of 𝐵 (Soylu, 2005):

𝐵 = (−0.575 + (10.058 ∗ 𝑃𝑅 − 54.053 ∗ 𝑃𝑅2)) ∗ 𝐸𝑅 + (1.456 + (−8.703 ∗ 𝑃𝑅 + 43.615 ∗

𝑃𝑅2)) ∗ 7000 𝐾 (4)

In equation (4), PR is propane ratio by mass and ER is the equivalence ratio of the charge inducted

in the cylinder.

It should be noted that KM1 was developed based on equation (3) which is same as for KM3, the

only difference was that KM1 was developed for an engine running on gasoline fuel while the

parameters in KM3 are corresponding to methane. Moreover, the parameters in KM2 were

obtained from the optimization of parameters in KM1, this was done to improve the accuracy of

knock prediction by KM1 (Elmqvist-Möller, 2006). Therefore, the parameters in KM1 and KM2

need to be calibrated and optimized if the models are to be used for knock prediction on a methane

fuelled engine.

Apart from the dependency on the fuel properties like propane ratio and octane number as well as

other curve fitting parameters it is also observable that for models KM1-KM4 the ignition delay

time reduces with increase in cylinder pressure and the temperature of the unburned zone.

Consequently, from equation (1) it is straightforward that decrease in the ignition delay time

increases the value of knock prediction parameter, thus suggesting higher possibility of knocking.

2.2 Knock Prediction Models based on Chemical Kinetics

Chemical kinetics theory for study of knocking is based on the fact that combustion in an engine

is nothing but the chemical oxidation reaction of fuel with oxygen present in air. The chemical

reaction mechanism is complex for the process of combustion, since it not a single or even few-

steps process but consists of numerous concurrent reactions called as chain reactions. There is an

initiation step in the chain reactions which results in formation of highly reactive intermediate

species called as radicals which are produced by dissociation of stable molecules like fuel and

oxygen. Radicals formed in the initiation step react with the reactants to form intermediate

products and new radicals which continue the chain reactions. There are some reactions which

result in generation of two radicals by consuming one, these are called as chain branching

reactions. While, the termination reactions are those which mark the end of chain reactions by

consuming the radicals such that no more radicals are left. The following reactions explain the low

temperature oxidation of methane (Glassman, 1996):

𝐶𝐻4 + 𝑂2 → ��𝐻3 + 𝐻𝑂2 } (chain initiating) (5)

��𝐻3 + 𝑂2 → 𝐶𝐻2𝑂 + ��𝐻 } (chain propagating) (6)

11

��𝐻 + 𝐶𝐻4 → 𝐻2𝑂 + ��𝐻3 } (chain propagating) (7)

��𝐻 + 𝐶𝐻2𝑂 → 𝐻2𝑂 + 𝐻��𝑂 } (chain propagating) (8)

𝐶𝐻2𝑂 + 𝑂2 → 𝐻𝑂2 + 𝐻��𝑂 } (chain branching) (9)

𝐻��𝑂 + 𝑂2 → 𝐶𝑂 + 𝐻𝑂2 } (chain propagating) (10)

𝐻𝑂2 + 𝐶𝐻4 → 𝐻2𝑂2 + 𝐶𝐻3 } (chain propagating) (11)

𝐻𝑂2 + 𝐶𝐻2𝑂 → 𝐻2𝑂2 + 𝐻��𝑂 } (chain propagating) (12)

��𝐻 → 𝑤𝑎𝑙𝑙 } (chain terminating) (13)

𝐶𝐻2 → 𝑤𝑎𝑙𝑙 } (chain terminating) (14)

𝐻𝑂2 → 𝑤𝑎𝑙𝑙 } (chain terminating) (15)

However, there is a change in the above reaction mechanism when high temperature oxidation of

methane occurs. This is because the 𝐻2𝑂2 molecule does not dissociate into ��𝐻 radicals at lower

temperature, the dissociation is significant only above 900K (Glassman, 1996). Thus, the chain

reaction mechanism changes with the increase in temperature and hence it becomes relevant to the

study of combustion in a gas engine since the temperature in the burned zone at certain operating

conditions can reach above 2500 K. Therefore, apart from the low temperature oxidation of

methane the reaction mechanism at high temperature needs to be considered as well. Following

reactions showcase the major reaction path for oxidation of methane at high temperatures

(Glassman, 1996):

𝐶𝐻4 + 𝑀 → 𝐶𝐻3 + 𝐻 + 𝑀 (16)

𝐶𝐻4 + 𝑋 → 𝐶𝐻3 + 𝑋𝐻 (17)

𝐶𝐻3 + 𝑂2 → 𝐶𝐻3𝑂 + 𝑂 (18)

𝐶𝐻3 + 𝑂2 → 𝐻2𝐶𝑂 + 𝑂𝐻 (19)

𝐶𝐻3𝑂 + 𝑀 → 𝐻2𝐶𝑂 + 𝐻 + 𝑀 (20)

𝐻2𝐶𝑂 + 𝑋 → 𝐻𝐶𝑂 + 𝑋𝐻 (21)

𝐻𝐶𝑂 + 𝑀 → 𝐻 + 𝐶𝑂 + 𝑀 (22)

𝐶𝐻3 + 𝐶𝐻3 → 𝐶2𝐻6 (23)

𝐶𝑂 + 𝑂𝐻 → 𝐶𝑂2 + 𝐻 (24)

In the above reactions, 𝑀 represents a chemically stable molecule while 𝑋 on the other hand

represents any of the radicals like 𝐻, 𝑂𝐻 and 𝑂.

As far as occurrence of knocking is concerned, according to Semenov’s theory, the air-fuel mixture

auto-ignites when the energy released by the chemical reactions is more than the amount of heat

that is lost to the surroundings. This results in a situation like self-heating which ultimately leads

to auto-ignition (Glassman, 1996). Several researchers have experimentally performed and

analysed the process of auto-ignition of methane, particularly in shock tubes. From these

experimental studies researchers have claimed to understand the influence of one or more reactions

in driving the process of oxidation of methane. Using the chemical kinetics approach these

researchers have empirically derived relationship between ignition delay time and concentration

of methane in the air-fuel mixture. For example, Seery and Bowman developed a chemical kinetics

model that uses numerical integration method to evaluate the thermodynamic properties of the gas

mixture during the combustion process. There are other similar experimental studies as well which

represent the dependence of ignition delay time on concentration of methane and air present in the

mixture, these studies are based on experiments conducted in a shock-tube to study oxidation of

12

methane. These studies propose that the ignition delay time can be expressed in the following way

as shown in equation (25):

𝜏 = 𝐴. 𝑒(

𝑇𝑎𝑇𝑢

). [𝑂2]𝑥. [𝐶𝐻4]𝑦 (25)

If the evaluated ignition delay time from equation (25) is substituted in equation (5) then the knock

prediction parameter can be estimated. Here 𝑥 and 𝑦 are the exponents for mole density (in

mole/cu.cm) of oxygen and methane in the end-gas respectively and 𝑇𝑎 is the activation

temperature which is equal to the activation energy 𝐸𝑎 divided by the ideal gas constant 𝑅.

Activation energy is the amount of energy that needs to be added to the reactants to initiate a

chemical reaction amongst them (Glassman, 1996). The activation energy to initiate the fuel

oxidation reaction is provided by the spark event in an SI engine.

The following set of values for the parameters 𝑥, 𝑦 and 𝑇𝑎 are proposed by the corresponding

authors to determine the ignition delay time for methane based on chemical kinetics:

Table 2. ECMs based on chemical kinetics function

Model No. A x y Ta Reference

KM5 7.65E-18 -1.6 0.4 25900 (Seery and Bowman, 1970)

KM6 3.62E-14 -1.03 0.33 23400 (Lifshitz et al.,1971)

KM7 2.50E-15 -1.02 0.32 26700 (Tsuboi and Wagner, 1974)

KM8 1.19E-18 -1.94 0.48 23333 (Cheng and Oppenheim, 1984)

KM9 4.40E-15 -1.03 0.33 26360 (Grillo and Slack, 1976)

KM10 4.99E-14 -1.31 -0.38 9575 (Petersen et al.,1999)

Based on the values of parameters in Table 2, it can be commented that across different models a

parameter’s value changes significantly. E.g., the value of 𝑦 is positive for all the models except

KM10. Extended analysis on this based on equation (25) reveals that if 𝑦 is negative, then the

concentration of methane in end-gas is inversely proportional to ignition delay time. A further

analysis on the same reveals that the ignition delay time is dependent on the engine load, because

more number of moles of fuel (higher molar density!) are burned in the same cylinder volume at

high engine loads if the engine speed is kept constant. Thus, it would be an interesting exploration

to know which of the models here are correct and what is their corresponding value of 𝑦. Similarly,

there are different values of 𝑇𝑎 for different models, this can be accounted to the fact that

researchers have used different values of activation energy for oxidation reaction of methane

(Lifhitz et al., 1971). The value of parameter 𝑇𝑎 for all the models are approximately 2.5 times to

that in KM10. This is expected to cause huge differences in the evaluation of ignition delay time

for KM10 as compared to other models in this category because 𝑇𝑎 has an exponential influence

on the value of ignition delay time.

2.3 Knock Prediction Models based on Thermodynamics

The model based on thermodynamics considers that the pre-reactions in end-gas must become

sufficiently intense and release enough energy to cause auto-ignition of a portion of the mixture

that is yet to be consumed by the propagating flame. These types of models consider two-zones

combustion for analysis and evaluation of the thermodynamic parameters; burned zone and

unburned zone. Based on the total energy released due to pre-reactions activity in the unburned

zone per unit volume the following dimensionless knock criteria to predict occurrence of knocking

was formulated (Karim and Gao, 1992):

13

𝐾𝑐 =(

𝐸𝑛𝑒𝑟𝑔𝑦 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑒𝑛𝑑𝑔𝑎𝑠 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛𝑠

𝑉𝑜𝑙𝑢𝑚𝑒)

𝑡

(𝐸𝑛𝑒𝑟𝑔𝑦 𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑐𝑜𝑚𝑏𝑢𝑠𝑡𝑖𝑜𝑛

𝑉𝑜𝑙𝑢𝑚𝑒)

𝑡0

(26)

In the above equation (18), when the energy released by end gas reactions is evaluated using

change in enthalpy of the unburned zone from start of combustion to any time 𝑡 the following

expression is obtained which evaluates the knock prediction parameter (Shrestha, 1999):

𝐾𝑐 =(

(ℎ𝑠𝑡−ℎ𝑡)∗𝑚𝑢𝑉𝑡

)

(𝑚𝑜ℎ𝑜

𝑉𝑜)

(27)

In equation (27), ℎ𝑠𝑡 is the specific enthalpy of the charge at start of combustion, 𝑚𝑢 is the

unburned zone mass, ℎ𝑡 is the specific enthalpy of the unburned zone at time 𝑡 after start of

combustion, ℎ𝑜 is the effective heating value of the fuel and 𝑚𝑜 is the initial or total mass, 𝑉𝑜 is

the cylinder volume at the start of combustion and 𝑉𝑡 is the volume of the unburned zone after

time 𝑡 has elapsed after the start of combustion. This model has been referred as KM11 from here

onwards in this text. It should be noted that according to KM11, the time 𝑡 at which value of the

𝐾𝑐 becomes equal to or more than 1.5 signifies the onset and further occurrence of knocking.

Following the approach proposed by Karim and Gao, their two-zone thermodynamic model has

been implemented and tested by several researchers to determine the safe operating conditions for

gas engines that avoid knocking (Saikaly et al., 2008). Although it has been found that different

chemical kinetics schemes are used for the same two-zone thermodynamic model, like by Saikaly

et al. and Attar. Due to the use of different chemical kinetics schemes different numerical solutions

are obtained for energy released in the end-gas reactions. Hence, the thermodynamic parameters

in equation (27) would have different values with different chemical kinetics schemes. This is

similar to what was observed in case of models based on chemical kinetics in the previous section

where different models proposed different values of parameters for the same fundamental

equation. This once again highlights the underlying problem of not having accurate knock

prediction models because the chemical reactions in the end-gas are not fully understood. E.g., to

evaluate the parameters in equation (27), Attar uses the chemical kinetics scheme that predicts the

energy released by end-gas reactions using a 155 reaction steps and 39 species. Whereas, the

chemical kinetics scheme implemented by Saikaly et al. uses 325 equilibrium reactions and 53

species, this scheme was proposed by (Smith et al., GRI-Mech). It should be noted that, these

different chemical kinetics schemes are not evaluated in this thesis.

There is another model which follows the approach laid out by Karim and Gao, the interesting

highlight of this model is that the following differential equation has been proposed to evaluate

the value of 𝐾𝑐 (Sierra Parra et al., 2017):

𝑑𝐾𝑐 =1

𝑉[𝑉𝑐 ∗ 𝐶𝑅

((ℎ𝑠𝑡−ℎ𝑢)𝑑𝑚𝑏+𝑚𝑢∗𝑐𝑝,𝑢∗𝑑𝑇𝑢)

𝐿𝐻𝑉− 𝐾𝑐 ∗ 𝑑𝑉] (28)

In the above equation (28), 𝑑𝑚𝑏 is the change in mass of burned zone, 𝑐𝑝,𝑢 is the constant pressure

specific heat capacity of the unburned zone, ℎ𝑠𝑡 − ℎ𝑢 is the change in specific enthalpy of the

unburned zone since after spark, 𝑉 is the cylinder volume with respect to which the equation is to

be integrated to obtain 𝐾𝑐. However, it was observed that the proposed differential equation (28)

is dimensionally incorrect and that’s why this model is discarded from study in this thesis.

14

3 IMPLEMENTATION

The approach followed to calibrate an existing BOOST engine performance prediction model

against experimentally obtained data has been explained. How the engine simulation boost model

has been used to evaluate the value of knock prediction parameter (Kc) proposed by 11 selected

models (KM1-KM11) has been described briefly.

BOOST is a fully integrated IC engine 1D simulation software. It can simulate a wide variety of

engines, 4-stroke or 2-stroke, spark or auto-ignited. A virtual engine model created in BOOST can

be used for prediction of engine performance, analysis of gas exchange, study of combustion and

emissions. For this thesis, the assessment of knock prediction models was done using a 1D virtual

engine model developed in BOOST. In that 1D engine model, the 0D (only time dependent) knock

prediction models were incorporated in relation to the combustion process. Then the knock

prediction parameter was evaluated for all the knock prediction models separately by running the

engine cycle simulations in BOOST.

The BOOST engine model was calibrated using the steady state data collected from a single-

cylinder heavy-duty natural gas test engine. The data was captured at the load points which are a

part of the World Harmonized Stationary Cycle (WHSC) test cycle. WHSC test is a well-known

standard steady-state engine dynamometer schedule (DieselNet, 2018). There were in total 13

different engine operating conditions which are represented by the points marked in the following

plot in figure 5:

Figure 5. WHSC engine test steady-state operating points

The single cylinder engine cycle simulations were run in BOOST to replicate the engine

performance which was experimentally obtained by running the engine on the 13 operating points

represented in Figure 5. The BOOST model was calibrated using experimentally obtained data

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

P12

Max_PowLow Speed

BM

EP

[bar

]

Engine Speed (RPM)

LOAD

15

from the test cell engine. It should be noted that running the engine in the test cell to acquire

experimental data was not in the scope of this thesis, rather the experimental data available from

previously conducted tests was used as a reference for modelling. The technical specifications of

the single cylinder test engine that was used to design the model in BOOST are (see table 3):

Table 3. Technical specifications of the heavy-duty natural-gas engine

No. of Cylinders 1

Compression Ratio (CR) 12

Swept Volume 2 L

Using the engine test cell data corresponding to operating points mentioned in Figure 5 and engine

specifications from Table 3 the following 1D engine model was designed in BOOST (see figure

6):

Figure 6. Engine cycle simulations model in BOOST

3.1 BOOST Model Calibration

The most important test cell data that was used to calibrate the engine cycle simulations model in

BOOST was the in-cylinder pressure trace. The in-cylinder pressure was measured from the test

cell engine and recorded in crank angle resolution for all 13 operating points mentioned in figure

5. These measured in-cylinder pressure traces were averaged for at least 10 engine cycles and then

the averaged pressure traces were used for calculating parameters related to combustion such as:

(1) start of combustion (SOC), (2) combustion duration (CD), (3) Wiebe function shape parameters

(Wiebe,1956), (4) rate of heat release (ROHR) and (5) CAD corresponding to 5%, 10%, 50% and

90% mass fraction burned.

16

The BOOST simulations were performed using the ‘Multiple Vibe 2-Zone’ combustion model.

Choosing a two-zone combustion model allowed calculation of thermodynamic as well as physical

parameters in both burned and unburned zone. Using a two-zone combustion model was important

because it enabled the detection of auto-ignition in the unburned zone, thus, allowing the

possibility to analyse spark-knock if it occurred in the engine simulations.

The above-mentioned data was used to calibrate the BOOST engine model. Following plot shows

the comparison between an experimentally measured cylinder pressure trace and the cylinder

pressure trace obtained by BOOST (see figure 7):

Figure 7. Experimental and simulation cylinder pressure trace comparison against CAD

As shown in Figure 7, a good correlation was observed between the experimentally measured

cylinder pressure trace and a pressure trace obtained from simulations. The plots of cylinder

pressure trace comparison for the remaining 12 operating points showed similar coherence

between experimental and BOOST simulation values.

3.2 Calculating Knock Prediction Parameter (Kc)

The physical and thermodynamic parameters 𝑇𝑢, 𝑝 and ℎ𝑢 that are required to calculate the knock

prediction parameter (𝐾𝑐) were taken from the BOOST simulations, this was done for all 11 knock

prediction models separately. For models based on the Arrhenius function and chemical kinetics

the ignition delay time was calculated at each operating point. Moreover, enthalpy was the

parameter of interest for the thermodynamic model (KM11). Since it was also essential to

understand if the knock prediction models can determine the CAD at which knock occurs 𝐾𝑐 for

all the models was calculated in crank angle resolution.

-360 -300 -240 -180 -120 -60 0 60 120 180 240 300 360

Cyli

nder

Pre

ssure

[bar

]

CAD [°]

Experimental

Boost

Difference

17

The value of 𝐾𝑐 determines whether the engine is going to knock or not. Therefore, it is important

to understand its variation to predict knocking successfully. For understanding this variation,

firstly the critical value of 𝐾𝑐 is to be established as a reference and secondly the variation is to be

studied with respect to that reference. From the literature review we know that the critical value of

𝐾𝑐 which signifies occurrence of knocking is 1 for KM1-KM10 and is 1.5 for KM11.

There are two ways of understanding the behaviour of 𝐾𝑐:

1. Variation of 𝐾𝑐 with respect to crank angle during an engine cycle especially from closure

of intake valve till end of combustion. This will be helpful in determining if the knock

prediction model correctly predicts knocking or not. Moreover, it will also show how does

𝐾𝑐 grow with respect to crank angle during the engine cycle.

2. Variation of 𝐾𝑐 with respect to engine operating conditions like load and engine speed. This

will be helpful in determining which model shows plausible occurrence of knocking for an

operating point and at which CAD, moreover how does the knocking characteristic vary with

change in engine operating condition.

Graphs pertaining to the two analyses mentioned above are shown later in this text.

18

4 RESULTS

In this chapter the evaluated results of all the selected knock prediction models (KM1-KM11) are

presented. Firstly, the variation in important parameters like ignition delay time against crank

angle is presented. Secondly, variation in 𝐾𝑐 with crank angle for all the models is presented for

comparison and analysis.

Out of the 11 models selected for assessment 10 are based on ignition delay time theory proposed

by Livengood and Wu, these models are KM1-KM10. For these models, 𝐾𝑐 is evaluated from

closure of intake valve till end of combustion (see equation 1). A similar evaluation is done for 𝐾𝑐

in case of model KM11 which is based on thermodynamic parameters. It should be noted that

according to model KM11, the knock prediction parameter directly depends on the change in

specific enthalpy of the end-gas.

Plots of 𝐾𝑐 for all the knock prediction models KM1-KM11 are shown for an operating point so

that the models can be compared to each other and their accuracy can be assessed at the same time.

Models which showed plausible results are further analyzed in the next chapter using contour plots

of their 𝐾𝑐 on the engine operating range.

4.1 Models based on Ignition Delay Time

For models KM1-KM10, the knock prediction parameter (𝐾𝑐) depends on ignition delay time, thus

it is essential to understand how the ignition delay time varies during the engine cycle. Figure 8

shows the ignition delay time with respect to crank angle for the ‘Low Speed’ operating point:

Figure 8. Ignition delay time with respect to Crank Angle as per models KM1-KM10 for Low Speed

19

Since 𝐾𝑐 is evaluated from the beginning of compression till the end of combustion the variation

in ignition delay time with respect to crank angle in this time frame is of interest and is shown in

figure 9. From figure 9, it is evident that models from the same category such as KM1-KM4 have

the same trend of 𝜏 because of the similar mathematical formulation (see equation 3). While on

the other hand, 𝜏 for models belonging to chemical kinetics category KM5-KM9 show different

trend since they are based on a different mathematical formulation (see equation 25). However, it

is also observable from figure 9 that the plot for ignition delay time given by model KM10 has

more similarities to the graphs of KM1-KM4 than with KM5-KM9. Another observation from

figure 9 is that there is huge variation (peak values range approximately from 102-1022) in the

estimation of ignition delay time proposed by all these models with respect to crank angle. Models

based on the Arrhenius function (KM1-KM4) tend to estimate relatively lower values of ignition

delay time whereas models based on chemical kinetics (KM5-KM9) tend to estimate high values.

The only outlier amongst the chemical kinetics models is KM10, which shows ignition delay time

values like that of models based on the Arrhenius function.

Figure 9. Ignition delay time with respect to crank angle (from intake valve closure to end of combustion)

Figure 9 shows variation in 𝜏 with respect to crank angle for models KM1-KM10 and this is the

information that will be used in determining if there is occurrence of knocking at the considered

operating point (in this case – Low Speed) or not. This will be done by evaluating 𝐾𝑐 using 𝜏 as

per equation 1. Then the evaluation of 𝐾𝑐 for all models needs to be compared to check which

Chemical Kinetics

Arrhenius Function

KM10

Ign

itio

n D

ela

y T

ime

[s]

20

models show reasonable results. It should be noted that during experiments the engine did not

show any characteristics of knocking while it was run using the WHSC load points. No knock was

therefore observed on any of the 13 operating points which are used for assessment of the knock

prediction models. From this information it would be easier to observe that which knock prediction

models emulate the experimental observations and which do not. This leaves only the plausibly

correct knock prediction models to be considered as reliable for further combustion analysis. In

figure 10 𝐾𝑐 is evaluated for models KM1-KM10 and represented along with the heat release curve

to indicate the combustion process. The plots of 𝐾𝑐 for models KM1-KM10 for the remaining 12

operating points are presented in Appendix-A1.

Figure 10. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (Low Speed)

Out of all the models based on ignition delay time, KM10 gave the best plausible results since its

outcomes strongly agreed with the experimental observations. This is because the value of 𝐾𝑐 for

KM10 was less than 1 for all the operating points thus showing that the there is no knocking,

whereas, the other models did not show such results.

4.2 Model based on Thermodynamics

Apart from the evaluated 10 knock prediction models based on ignition delay time calculation,

there is another model represented by KM11 which hypotheses prediction of knocking based on

21

thermodynamic parameters (see equations 26 and 27). According to the formulation of 𝐾𝑐 as per

model KM11, 𝐾𝑐 is directly proportional to change in specific enthalpy of the end-gas during

combustion and inversely proportional to the total heat release by combustion. Moreover, in case

of KM11 the critical value for 𝐾𝑐 is 1.5 while its 1 for models KM1-KM10.

The variation of 𝐾𝑐 as per KM11 is plotted in figure 11 for the ‘Low Speed’ operating point. As

far as the results pertaining to KM11 go, the model has shown that none of the operating points

are knocking because for all the operating points the value of 𝐾𝑐 has been found to be less than the

defined critical value. Thus, from initial observations of the results the model KM11 shows a good

compatibility with the experimental results.

If a profound look is taken at the formulation of 𝐾𝑐 as per KM11 it is understood that spark timing

plays a very crucial role in predicting occurrence of knocking (see equation 27). This is because

the change in enthalpy (ℎ𝑠𝑡 − ℎ𝑡) is zero until the spark event and if no spark is given during an

engine cycle then there will be no combustion, thus no knocking! This has been observed

experimentally as well, when the charge in the engine is not ignited by a spark there is no knocking.

In addition to that, (ℎ𝑠𝑡 − ℎ𝑡) represents how the specific enthalpy of the end-gas changes after

the spark event, hence taking into consideration the variation in amount of energy that is contained

by the end-gas per unit mass. If this energy contained by the end-gas is high enough to cause auto-

ignition then there will be knocking otherwise the end-gas will be consumed by the propagating

flame front.

Figure 11. 𝐾𝑐 and heat release with respect to CAD for KM11 (Low Speed)

Based on KM11, the 𝐾𝑐 is evaluated for all operating points and their graphs are presented in

Appendix-A2.

22

5 ANALYSIS

The evaluated results are analyzed to assess all the models and subsequently show which one of

them is best suitable for knock prediction in a natural-gas engine. Finally, for the best available

model the variation in 𝐾𝑐 is studied with respect to spark advance and combustion phasing.

Using the evaluated results of all the models and comparing them with experimentally obtained

data the knocking behavior was understood, this was done with the help of contour plots and in-

cylinder pressure traces which were measured from test cell engine. E.g., at certain operating

points some of the pressure traces which were obtained from the test cell engine showed very small

pressure oscillations (<10 bar from peak to peak) during few engine cycles. But these oscillations

were eliminated when an average of all the pressure trace was taken for calibration of the BOOST

model. Therefore, when the simulation results for the same operating points (with little pressure

oscillations) showed knocking tendency it was established that the knock prediction model

correctly predicts the occurrence of knocking at these operating points. Moreover, to get a better

insight into the knocking behavior contours were plotted for 𝐾𝑐 against the engine operating

conditions defined by brake mean effective pressure (BMEP) and engine speed. Contours

corresponding to models KM4 and KM10 were found to show realistic knocking behavior with

variation in engine operating conditions.

5.1 Knocking Behaviour – Contour Plots

Figure 12 shows the variation of 𝐾𝑐 with engine operating conditions for model KM4. From this

figure, the value of 𝐾𝑐 increases with BMEP when engine speed is constant.

Figure 12. Variation in 𝐾𝑐with engine operating conditions as per KM4. Red circle highlights the region which is

most susceptible to knocking and corresponds to high load and low engine speed operating condition

4,5

55,5

6

6,5

6,5

7

7,5

8,5

5 5

5,5

6

7

7,5

8

8,5

7,8794

5,4563

6,9368

8,3099

4,2663

7,8568

4,8931

6,3922

7,9331

6,4758

4,351

6,90628,987

BM

EP

[b

ar]

→

Engine Speed [RPM] →

23

This is because when the engine operates at higher loads parameters like pressure, temperature and

heat released due to combustion are increasing. This high temperature and pressure in the cylinder

also increase the chances of knocking in the end-gas because at higher pressure the auto-ignition

temperature of air-methane mixture decreases (Caron et al., 1999). It is to be noted that 𝐾𝑐 is

highest in the region where the engine operates at high load and low engine speed (marked by the

red circle in figure 12). This is because when the engine operates at low speed the turbulence

intensity in the cylinder is low and results in lower flame propagation speed during combustion.

The lower flame propagation speed allows more time for the end-gas to auto-ignite, hence resulting

in knock (Johansson, 2014). Moreover, the value of 𝐾𝑐 is above the critical limit of 1 across the

entire engine operation range, this indicates that model KM4 needs to be calibrated.

In figure 13 which corresponds to KM10, a similar trend as KM4 was observed for 𝐾𝑐.

Highlighting the fact that the engine is more susceptible to knocking at higher loads and lower

engine speeds (marked by the red circle in figure 13). The contour plot of model KM10 also shows

a region at medium-high speed where 𝐾𝑐 is higher (marked by the black circle in figure 13). This

means that when the engine is operated to deliver higher power at high loads the chances of

knocking increase. This is because, to deliver higher power more fuel is burned which leads to

higher heat release rate and subsequently higher temperatures in the cylinder resulting in an

increased chance of auto-ignition in the end-gas. Furthermore, the value of 𝐾𝑐 is below the critical

limit of 1 across the entire engine operation range indicating that there is no knocking. This rightly

matches with the experimental observations because none of 13 operating points showed knocking

in the test-cell engine.

Figure 13. Variation in 𝐾𝑐with engine operating conditions as per KM10. Red and black circles highlight the high

load engine operating conditions which are highly susceptible to knocking

Amongst all models based on ignition delay time only KM4 and KM10 showed reasonable

knocking behaviour. Contour plots for all the remaining models are presented in Appendix-B.

Apart from the models based on ignition delay time there was a model namely KM11 which was

based on thermodynamic parameters. In case of KM11, it was found that none of the 13 operating

0,2

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0,55

0,6

0,7

0,2 0,2

0,25

0,3

0,35

0,4

0,45

0,5

0,55

0,6

0,6

5

0,7

0,63328

0,24198

0,50542

0,67749

0,14149

0,6628

0,21058

0,44678

0,72957

0,43507

0,17082

0,570030,77399

BM

EP

[b

ar]

→

Engine Speed [RPM] →

24

points were knocking which coincided with experimental observations. However, from the contour

plot for KM11 it was established that the knocking behaviour shown by the model is incorrect (see

figure 14). This is because the contour plot indicates that the engine is most susceptible to knocking

in the low-mid load region and low-mid engine speed range (marked by black circle in figure 14).

Since this knocking behaviour shown by KM11 does not agree with the experimental observations,

this model is discarded for further analysis.

Only model KM10 was chosen for further analysis of the knocking behaviour with respect to

combustion phasing. This is because none of the models other than KM4 and KM10 showed

correct knocking behaviour across the engine operating range. Furthermore, to achieve better

accuracy with KM4 the model had to be calibrated. Thus, amongst all models KM10 comes out

on top and was used for further analysis of the knocking behaviour with respect to combustion

phasing.

Figure 14. Variation in 𝐾𝑐with engine operating conditions as per KM10. According to this model the engine

operating range that is most susceptible to knocking is the black circle which is around low-mid engine load

5.2 Variation in Kc with Combustion Phasing

According to Wildhaber combustion phasing can be defined as, “The time in the engine cycle,

specifically the compression and expansion strokes, where combustion occurs. A change in

combustion phasing causes a change in combustion duration” (Wildhaber, 2011). Combustion

phasing plays a crucial role not only on the efficiency of an engine but also in determining if the

engine is going to knock or not. The effect of combustion phasing on knocking can be found by

changing the combustion phasing and evaluating its influence on 𝐾𝑐. There are two ways in which

the combustion phasing can be changed:

1. By changing the spark advance: If the spark advance is increased the chances of knocking

increases and if the spark is retarded then the risk of knocking reduces. The spark advance

then plays a crucial role in determining the efficiency of the engine and it is needed to

0,7

0,75

0,8

0,8

0,85

0,85

0,85

0,9

0,95

0,95

10,

70,75

0,8

0,8

0,85

0,85

0,85

0,9

0,9

0,9

0,95

1

0,9467

0,8923

0,8209

0,7311

0,8092

0,8209

0,9795

1,0359

0,9313

1,0341

0,8882

0,76670,9674

Engine Speed [RPM]→

BM

EP

[b

ar]

→

25

extract higher power but then the engine should be calibrated such that it does not reach

the knocking limits. It has also been found that by using cooled EGR the maximum BMEP

of the engine can be increased with advance in spark timing (Grandin et al., 1998).

2. By changing the combustion duration: When the combustion duration is long then it means

that it takes a longer time to burn the inducted charge in the cylinder, meaning that the

flame propagation speed is low. Slow combustion allows more time for the end-gas to auto-

ignite and to avoid knocking the flame propagation should be fast. Controlling the

combustion duration is extremely difficult. Therefore, generally EGR is added in the

charge to increase the time of end-gas auto-ignition, addition of EGR dilutes the unburned

gas mixture and reduces the peak temperatures thus requiring longer time for the end-gas

to heat up to auto-ignition temperatures (Heywood, 1988). This allows the propagating

flame front to consume the end-gas before it auto-ignites (Wang et al.,2017).

The chosen knock prediction model KM10 is used for analysing the influence of spark advance

and combustion duration on 𝐾𝑐. To maintain consistency in the simulations and to make a direct

comparison of the results BMEP was kept constant for every operating point and then the spark

advance and combustion duration were separately changed from their original value. The variation

in 𝐾𝑐 is plotted for a change of ±5° of CAD (step size 1°) in spark advance and combustion duration

respectively. In the following figure 15, the variation in 𝐾𝑐 with change in spark advance for all

the operating points is shown. It was found that 𝐾𝑐 increases linearly with spark advance and the

gradient of 𝐾𝑐 versus spark advance is approximately 6 times steeper at higher engine loads as

compared to lower loads.

From figure 16, it can be seen that 𝐾𝑐 decreases linearly with increase in combustion duration.

This is because the simulations were run by keeping the BMEP constant and in that case when the

combustion duration is increased then the peak pressure inside the cylinder would reduce hence

decreasing the possibility of knocking.

The BMEP was kept constant while analysing the impact of combustion phasing (both spark

advance and combustion duration) on 𝐾𝑐 so that it could be understood how the combustion

phasing influences knocking when the same power is extracted from the engine. The throttle angle

was varied to keep the BMEP constant while the combustion phasing was modified to carry out

this analysis. Throttle angle was chosen as a parameter to vary in the simulations because it is

practically possible to control, if in case there is any experimentation to be performed in future for

validation of this analysis.

26

Figure 15. Variation in 𝐾𝑐 with respect to spark advance for all operating points. Operating points are colour coded

based on load.

y = -0.0088x + 0.0852

y = -0.0589x + 0.3349

0,00

0,20

0,40

0,60

0,80

1,00

1,20

-22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0

Kc

[-]

SOC [ ]

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

P12

Max_PowLow Speed

BM

EP

[bar

]

Engine Speed (RPM)

LOAD

27

Figure 16. Variation in 𝐾𝑐 with respect to combustion duration for all operating points. Operating points are colour

coded based on load.

y = -0.0034x + 0.2508

y = -0.0177x + 1.4383

0,00

0,20

0,40

0,60

0,80

1,00

1,20

25 30 35 40 45 50 55

Kc

[-]

Combustion Duration [°]

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

P12

Max_PowLow Speed

BM

EP

[bar

]

Engine Speed (RPM)

LOAD

28

6 CONCLUSIONS

Outcomes and findings of the thesis are laid out in this section. Arguments are proposed in lieu of

the outcomes. The findings are compared with previously conducted researches.

The phenomenon of knocking is sporadic and is difficult to predict. There are a several types of

ECMs that can be used to predict the occurrence of knocking in an SI engine. Out of all the types

of models available, three types of knock prediction models are assessed in this thesis: (1) models

based on the Arrhenius function, (2) models based on chemical kinetics and (3) model based on

thermodynamics. The assessment of the models was done using 1D engine simulations in BOOST.

The simulated results are compared to experimental observations from a test-cell engine.

Among all the 11 different knock prediction models, it was found that two models showed

plausible knocking behaviour and have results that agree with the experimental observations.

These two models are:

1. KM4 – this is a model based on the Arrhenius function (Soylu,2005)

2. KM10 – this is a model based on chemical kinetics (Petersen et al., 1999)

Out of these models KM10 is the best because its results agree with the experiments. Since KM10

is based on the ignition delay time estimation provided by Petersen it can be concluded that his

formulation to evaluate the ignition delay time is correct (see equation (25) and table 2). It was

also observed that of all the models based on chemical kinetics it was only model KM10 which

claimed that the ignition delay time is inversely proportional to the fuel molar density, hence,

indicating that 𝐾𝑐 depends upon load. This is because the fuel molar density increases with increase

in load at constant engine speed and it has been observed experimentally that at higher loads the

engine is more susceptible to knocking.

Based on the assessment of all the models, KM10 was chosen to analyse the variation in knocking

parameter with a change in combustion phasing and at the same time ensuring that the BMEP

delivered by the engine is kept the same. From this analysis it was found that the knock prediction

parameter increases linearly with spark advance and decreases linearly with an increase in

combustion duration. Another observation was that the change in knock prediction parameter with

spark advance is dependent on engine load, at higher loads a high gradient between 𝐾𝑐 and spark

advance is observed while at lower loads the curve has less slope.

29

7 FUTURE WORK

There are potential areas that can be explored based on the thesis, what can be done further in

the field of knock prediction models is presented in this chapter.

There are always a few constraints and limitations that make technical exploration difficult in

research projects. Based on this work, there are few areas which are interesting to tap into but were

not explored due to several limitations. The author recommends that the following can be a good

extension to the current work:

1. Natural gas a fuel occurs in nature as a mixture of several gases, but in this thesis the fuel

was assumed as pure methane. There are claims that presence of gases like propane change

the combustion properties and knocking behaviour of the fuel. Thus, for future work it is

recommended to use the fuel as a mixture of methane and propane.

2. Model KM4 showed plausible knocking behaviour but was not correct in terms of

evaluation of the knock prediction parameter. This model can be calibrated and then used

to predict knocking.

3. The experimental results are available for only 13 operating points which are used to assess

and analyse different types of knock prediction models. More test cell data can be acquired

to further analyse and then quantify the knocking behaviour. The quantification should be

done in such a way that the values of 𝐾𝑐 are able to distinguish between no knock,

borderline knock and sever knock.

4. The focus of the thesis was on spark-knock and surface ignition was not considered for

simulations. As an extension, surface ignition can also be taken into consideration.

30

8 REFERENCES

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exchange system and knock prediction (Licentiate dissertation). KTH, Stockholm. Retrieved from

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Conversion and Management, 46(1), p.130.

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Technical Paper Series, 922366.

Attar, A. (1997). Optimization and knock modeling of a gas fueled spark ignition engine. Ph.D.

Thesis. The University of Calgary. pp.66-79.

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SI engines through heat transfer evaluation. International Journal on Interactive Design and

Manufacturing. Springer Paris, pp. 1–11. doi: 10.1007/s12008-017-0452-6.

Seery, D.J., Bowman, C.T. (1970). An experimental and analytical study of methane oxidation

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Lifshitz, A., Scheller, L., Burcat, A., Skinner, G.B. (1971). Shock-tube investigation of ignition in

methane-oxygen-argon mixtures. Combustion and Flame, 16. p.331.

31

Tsuboi, T., Wagner, H.G. (1974). Homogeneous thermal oxidation of methane in reflected shock

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32

APPENDIX A1: Kc v/s CAD (KM1-KM10)

Figure A1-1. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P2)

Figure A1-2. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P3)

33

Figure A1-3. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P4)

Figure A1-4. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P5)

34

Figure A1-5. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P6)

Figure A1-6. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P7)

35

Figure A1-7. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P8)

Figure A1-8. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P9)

36

Figure A1-9. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P10)

Figure A1-10. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P11)

37

Figure A1-11. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (P12)

Figure A1-12. 𝐾𝑐and heat release with respect to CAD for models KM1-KM10 (Max_Pow)

38

APPENDIX A2: Kc v/s CAD (KM11)

Figure A2-1. 𝐾𝑐and heat release with respect to CAD for model KM11 (P2)

Figure A2-2. 𝐾𝑐and heat release with respect to CAD for model KM11 (P3)

39

Figure A2-3. 𝐾𝑐and heat release with respect to CAD for model KM11 (P4)

Figure A2-4. 𝐾𝑐and heat release with respect to CAD for model KM11 (P5)

40

Figure A2-5. 𝐾𝑐and heat release with respect to CAD for model KM11 (P6)

Figure A2-6. 𝐾𝑐and heat release with respect to CAD for model KM11 (P7)

41

Figure A2-7. 𝐾𝑐and heat release with respect to CAD for model KM11 (P8)

Figure A2-8. 𝐾𝑐and heat release with respect to CAD for model KM11 (P9)

42

Figure A2-9. 𝐾𝑐and heat release with respect to CAD for model KM11 (P10)

Figure A2-10. 𝐾𝑐and heat release with respect to CAD for model KM11 (P11)

43

Figure A2-11. 𝐾𝑐and heat release with respect to CAD for model KM11 (P12)

Figure A2-12. 𝐾𝑐and heat release with respect to CAD for model KM11 (Max_Pow)

44

APPENDIX B: Contour Plots of Knock Models

Figure B1. Variation in 𝐾𝑐with engine operating conditions as per KM1

Figure B2. Variation in 𝐾𝑐with engine operating conditions as per KM2

1

1

1,5

2

2,5

3

3,5

4

1

1,5

2

2,5

3

3,5

4

3,8536

1,0607

2,6407

3,969

0,7884

3,0846

0,9759

1,9975

3,8406

1,992

0,8429

2,99223,8048

BM

EP

[b

ar]

→

Engine Speed [RPM] →

1,5

2,25

3

3,75

4,5

5,25

1,5

2,25

3

3,75

4,5

5,25

6

6,0326

1,6604

4,1339

6,2132

1,2342

4,8287

1,5277

3,127

6,0122

3,1184

1,3196

4,68415,9562

BM

EP

[b

ar]

→

Engine Speed [RPM] →

45

Figure B3. Variation in 𝐾𝑐with engine operating conditions as per KM3

Figure B4. Variation in 𝐾𝑐with engine operating conditions as per KM5

2,25

3

3,75

4,5

5,25

6

2,25

3

3,75

4,5

5,25

6

6,3424

2,305

4,5952

6,5769

1,9536

5,0918

2,1617

3,5832

5,9496

3,6779

1,9592

4,83316,2995

BM

EP

[b

ar]

→

Engine Speed [RPM] →

0,02

0,02

0,03

0,03

0,04

0,04

0,04

0,05

0,05

0,02

0,02

0,03

0,03

0,04 0,0

5

0,01768

0,04170

0,03035

0,02359

0,01214

0,06358

0,03200

0,05681

0,03764

0,05022

0,02094

0,034400,05541

BM

EP

[b

ar]

→

Engine Speed [RPM] →

46

Figure B5. Variation in 𝐾𝑐with engine operating conditions as per KM6

Figure B6. Variation in 𝐾𝑐with engine operating conditions as per KM7

0,004

0,0060,0080,01

0,01

0,004

0,006

0,006

0,008

0,008

0,01

0,00366

0,01172

0,00635

0,00464

0,00409

0,01167

0,00897

0,01168

0,00696

0,01058

0,00622

0,006700,01011

BM

EP

[b

ar]

→

Engine Speed [RPM] →

22

3

3

4

4

2

2

3

3

4

1,0299

4,494

2,1252

1,4131

1,2395

4,2405

3,2833

4,4381

2,2135

3,8668

2,1499

2,17263,4862

BM

EP

[b

ar]

→

Engine Speed [RPM] →

47

Figure B7. Variation in 𝐾𝑐with engine operating conditions as per KM8

Figure B8. Variation in 𝐾𝑐with engine operating conditions as per KM9

0,3

0,4

0,4

0,4

0,5

0,10,2

0,3

0,3

0,4

0,5

0,20769

0,30901

0,30288

0,26419

0,09789

0,60285

0,24293

0,49228

0,41271

0,43593

0,16113

0,363520,54824

BM

EP

[b

ar]

→

Engine Speed [RPM] →

0,0020,002

0,003

0,003

0,004

0,004

0,004

0,002

0,002

0,003

0,003

0,004

0,00125

0,00505

0,00245

0,00167

0,00154

0,00493

0,00380

0,00506

0,00263

0,00452

0,00254

0,002550,00413

BM

EP

[b

ar]

→

Engine Speed [RPM] →