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]
viii 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 (K
c) 16
4 RESULTS 18
4.1 Models based on Ignition Delay Time 18 4.2 Calculating Knock Prediction Parameter (K
c) 20
5 ANALYSIS 22
5.1 Boost Model Calibration 22
5.2 Calculating Knock Prediction Parameter (K
c) 24
6 CONCLUSIONS 28
7 FUTURE WORK 29
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8 REFERENCES 30
APPENDIX A1: K
cvs CAD (KM1-KM10) 32
APPENDIX A2: K
cvs 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
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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).
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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 = ∫0𝑡1𝜏
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)
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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)3.402𝑝−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 → 𝐶̇𝐻3+ 𝐻𝑂2̇ } (chain initiating) (5) 𝐶̇𝐻3+ 𝑂2 → 𝐶𝐻2𝑂 + 𝑂̇𝐻 } (chain propagating) (6)
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𝑂̇𝐻 + 𝐶𝐻4 → 𝐻2𝑂 + 𝐶̇𝐻3 } (chain propagating) (7) 𝑂̇𝐻 + 𝐶𝐻2𝑂 → 𝐻2𝑂 + 𝐻𝐶̇𝑂 } (chain propagating) (8) 𝐶𝐻2𝑂 + 𝑂2 → 𝐻𝑂2̇ + 𝐻𝐶̇𝑂 } (chain branching) (9) 𝐻𝐶̇𝑂 + 𝑂2 → 𝐶𝑂 + 𝐻𝑂2̇ } (chain propagating) (10) 𝐻𝑂2̇ + 𝐶𝐻4 → 𝐻2𝑂2+ 𝐶𝐻3 } (chain propagating) (11) 𝐻𝑂2̇ + 𝐶𝐻2𝑂 → 𝐻2𝑂2+ 𝐻𝐶̇𝑂 } (chain propagating) (12) 𝑂̇𝐻 → 𝑤𝑎𝑙𝑙 } (chain terminating) (13) 𝐶𝐻2 → 𝑤𝑎𝑙𝑙 } (chain terminating) (14) 𝐻𝑂2̇ → 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 𝑂̇𝐻 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
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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):
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𝐾
𝑐=
(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):
𝐾
𝑐=
((ℎ𝑠𝑡−ℎ𝑡)∗𝑚𝑢
𝑉𝑡 )
(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.
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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_Pow Low Speed
BMEP [bar]
Engine Speed (RPM)
LOAD
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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.
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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 (K
c)
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
Cylinder Pressure [bar]
CAD [°]
Experimental Boost
Difference
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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.
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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
