Thesis of Dr. Kacper Kwasniak

Figure 11 Conventional vs Saleri engine port timings

Saleri Engine

Combustion Cycle

Analysis

Author: Kacper Kwasniak

Supervisor:DrMorayKidd

In partial fulfilment of the Degree Requirements

of

MEng Mechanical Engineering at

School of Mechanical, Aerospace and Civil Engineering The University of Manchester

May 2022

TABLE OF FIGURES 3

ABSTRACT 4

DECLARATION 5

INTELLECTUAL PROPERTY STATEMENT 5

NOMENCLATURE 6

1. INTRODUCTION 8

   1. AIMS & OBJECTIVES 9

   2. RELEVANCE OF THE PROJECT TO THE AUTOMOTIVE INDUSTRY 10

   3. LITERATURE REVIEW 11

2. SALERI ENGINE DESIGN 13

   1. DOUBLE DIAMETER PISTON 14

   2. SECONDARY CHAMBER 15

   3. VALVE TIMING 16

      1. COMBUSTION 17

      2. EXPANSION 17

      3. EXHAUST BLOWDOWN 17

      4. SCAVENGING 18

      5. COMPRESSION 18

      6. CRANKCASE COMPRESSION 18

3. METHODOLOGY 19

   1. ENGINE DESIGN PROCESS 19

   2. ANALYTICAL ANALYSIS WITH EMPIRICAL SUPPORT 20

4. ENGINE CYCLE MODELLING THEORY 20

   1. ZERO-DIMENSIONAL SYSTEM 20

   2. SINGLE-ZONE COMBUSTION MODEL 22

   3. SUB-MODELS 23

      1. MASS FRACTION BURNED 23

      2. COMBUSTION STOICHIOMETRY 23

      3. THERMODYNAMIC PROPERTIES 24

      4. CYLINDER GEOMETRY 25

      5. SCAVENGING 26

5. MATLAB CODE 28

   1. NUMERICAL SOLUTION 28

   2. SALERI ENGINE PERFORMANCE EVALUATION 29

6. RESULTS DISCUSSION 30

Table of Figures

Figure1Huyghens'gunpowderengine(Sher,1989)8Figure2Timelineoftwo-strokeenginedevelopment(Sher,1989)8Figure3Exhaustgasdecomposition(Kirkpatrick,2021)10Figure4CrosssectionofSaleri engine13Figure5Pressuredifferencecheckvalve(Oliver,2008)14Figure6Doublediameterpistonandthesecondarychamber14Figure7Saleriengine backandsideview14Figure8Secondarychambercreatedbythedoublediameterpiston15Figure9Symmetricalporttiming(Pattakon,2014)16Figure10Loopscavengedtwo-strokeengineportpositioning (Blair,1996)16Figure11ConventionalvsSaleriengineporttimings17Figure12 Rolls-Royce enginedesignprocess(Jones, et al.,2002)19Figure13Input/outputdirectionsofenginesimulation(Krishnan,2003)21Figure14Controlvolumeofasinglezonemodel(Caton,1999)22Figure15Cylindergeometryschematic25Figure16Massflowdiagramofscavengingperiodinatwo-strokeengine (Sher,1989)26Figure17Perfectmixingchargingefficiencyvsdeliveryratiograph(Sher,1989)27Figure18MATLABcodeflowchart28Figure19Pressurevscrankanglegraph30Figure20 Temperaturevscrankanglegraph31Figure21Deliveryratiovschargingefficiencygraphs32Figure22Initialprojectplandraftedinsemester137Figure23Projectplandraftedduringsemester238

Abstract

A new type of two-stroke engine was patented by Remo Saleri. Its 3 cylinders are arranged in an equilateral triangle, therefore the intake of air into a cylinder comes from a crankshaft of a piston, which is 120 crank angle degrees before it. Pistons are designed to have bottom diameter larger than the top bore in order to increase the compressive capabilities. This project contributes to the development of his engine by analysing and comparing its in-cylinder pressure curve and scavenging with a conventional two-stroke engine. Single-zone combustion, compression and single-zone perfect mixing scavenging are modelled mathematically and a MATLAB code created to aid the computations. Calculations showed that Saleri engine has lower pressure trace comparing to a typical two-stroke, however exhibited significantly better scavenging performance, by having a 1.3 delivery ratio and charging efficiency 0.9 greater than that of a simulated conventional two- stroke. Further engine development direction was suggested by the means of a parametric study and prototype building validation process.

Declaration

I, Kacper Kwasniak, declare that all content presented below is a result of my own work. Any piece of knowledge or information not belonging to me, was properly referenced.

Intellectual Property Statement

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Nomenclature

a, m

Wiebe's function constants

AFac

Air-to-fuel ratio

BDC

Bottom dead centre

cp

Specific heat at constant pressure

CVC

Crankcase valve closes

CVO

Crankcase valve opens

EOC

End of combustion

EVC

Exhaust valve closes

EVO

Exhaust valve opens

h

Specific enthalpy

IVC

Intake valve closes

IVO

Intake valve opens

LHV

Lower heating value of fuel

m

Mass of mixture

ma

Mass of fresh air

mb

Mass of burned gasses

Mmolar

Molar mass

mo

Reference cylinder mass

N

Number of moles of mixture

p, P

Pressure

Q

Total heat transfer

Qin

Total combustion heat

Qw

Heat transferred to walls

R

Mass specific gas constant

Runiv

Universal gas constant

SOC

Start of combustion

T

Temperature

TDC

Top dead centre

U

Internal energy

V

Volume

Vd

Instantaneous volume

W

Work performed

Xb

Mass fraction burned

γ

Specific heat ratio

Δθ

Combustion duration

ηc

Charging efficiency

ηcomb

Combustion efficiency

θ

Crank angle

θsoc

Start of combustion angle

λ

Delivery ratio

1. Introduction

If a two-stroke engine was defined as 'an engine, which fires every revolution', the first design of its kind can be traced back to as early as 1680, when Huyghens designed a machine using gunpowder, to provide motoring power (Sher, 1989).

Since then, greatest automotive minds were developing the designs. Even Nicolaus Otto's four- stroke design from 1876 didn't force two-strokes out of the picture and further features (such us various types of scavenging, piston orientation or turbocharging) were still appearing on patent applications. The timeline of two-stroke engine development is presented below:

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1. Aims & Objectives

Objective:CompareperformanceofSalerienginetwoaconventionaltwo-strokeengine,withregardsto in-cylinder pressure and scavengingprocess.

In order to fulfil the objective, the following aims should be achieved:

Aims:

• AnalyseSaleriengine'scycle.

• Constructamathematicalmodeltoquantifyperformanceparameters.

• Compareresults witha conventionaltwo-strokeengine.

Saleri engine is so far a concept, which requires validation. Focusing the analysis on suspected areas of better performance stated in the objective is one of many steps contributing to its design development. In order to achieve the aims required to complete the objective, first the valve timing of the engine is analysed and contrasted with that of the conventional two-stroke. Secondly, a MATLAB code based on engine modelling theory is produced to support the quantitative analysis of performance. Finally, the results achieved by both types of engines are discussed comparatively to assess, if Saleri's design has potential to be competitive in the automotive industry. More on project's methodology in Section 3.

1. Relevance of the project to the automotive industry

Currently, due to strive for greener solutions and protection of the world's climate, engineers are looking for more efficient and less polluting power units in the automotive industry. Conventional two-strokes engine struggle with reaching net emissions standards due to troubling scavenging period, which leads to recirculating exhaust gases back to combustion chamber, leading to dissociation of the combustion species at higher temperatures. It leads to formation of highly harmful CO and NO molecules, which are responsible for deterioration of global climate.

Figure3Exhaustgasdecomposition(Kirkpatrick, 2021)

If there is a shadow of opportunity to discover a more fuel efficient, less polluting engine, which could substitute current solutions, without a doubt it is worth pursuing.

1. Literature Review

   • (Blair, 1996) – Contains wide range of information on two-stroke engine design, ranging from description of mechanical features or engine types over the years and mathematical models to analyse performance of every important area of interest. The author in great detail outlines the two-stroke scavenging process, stating its significance to the performance of the engine.

   • (Caton, 2016) – Extensively presents engine modelling theory, including empirically supported results for validation. His methods are a collection of fundamental tools, which constitute basis for creating zero and multidimensional systems and allow engineer to decide on methods appropriate for their applications.

   • (Caton, 1999) – The author focuses here on explaining spark-ignited engine combustion modelling, presenting equations prepared for numerical solving and includes exemplary graphs with results for validation of various achieved parameters.

   • (Heywood & Sher, 1999)– The authors in great detail explain important aspects of two- stroke internal combustion engine behaviour using examples of real engines. Some of the empirical data and constants were adopted from their work for the purpose of this dissertation, considering their discoveries are widely used in literature.

   • (Jones, et al., 2002) – This report presents an insight into the design process used by one of the largest engine manufacturers – Rolls Royce. Their approach to early design stages was followed in the methodology of this dissertation, by creating a tool for engine analysis, mimicking their Genesis and RRAP packages.

   • (Kirkpatrick, 2021) – Describes engine modelling theory focusing on the chemical aspect, discussing high temperature combustion and the use of wider range of available fuels. Explains how to implement NASA polynomial functions in numerical analysis of combustion modelling.

   • (Krishnan, 2003) – A comprehensive lecture on different types of combustion models, ranging from single to multi-zone schemes. Provides a list of necessary assumptions to make said modelling possible.

   • (McAllister, et al., 2011) – The authors covered the phenomenon of ignition and combustion chemistry of various fuels, depending on temperature, composition and

equivalence ratios. Ignition initial conditions for combustion modelling suggested in their research were adopted in this project.

• (McBride & Gordon, 1994) – Using experimental data, McBride & Gordon prepared constants of polynomials for evaluating properties such as: enthalpy, specific heat at constant pressure and entropy of chemical species present during combustion of fuels. Their work facilitated the evaluation of those properties in computer programmes.

• (Mohammed, et al., 2019) – The authors created a mathematical model for crank-rocked engine analysis and validated the results on a dynamometer. Their approach for single-zone combustion modelling was review and utilized for the similar purpose of this dissertation.

• (Oliver, 2008) – Numerical analysis of a two-stroke engine was performed, with an experimental validation from a flowbench setup. His suggestion of the use of pressure check valves was implemented in the design of Saleri engine, as a harmonious addition to the concept.

• (Pattakon, 2014) – Wide collection of two-stroke designs and their description, including two-stroke conventional and unconventional port timings, concept ideas for opposing piston or rotary crankcase engines. The author also covers inventions of blade valves, variable timing systems and crankless engines.

• (Perini, et al., 2010) – Report covering modelling of two-zone combustion adapted for numerical solving with hydrogen fuel blend. It includes the hydrogen addition effect on combustion flame propagation, therefore expanding the theory to quasi-dimensional. Studies effects of various combustion parameters on the chemical composition of exhaust gases.

• (Saleri, 2019) – The patent of Saleri engine, describing its mechanical operation and is the foundation and main motivation for this project topic.

• (Sher, 1989) – Deeply covers the topic of two-stroke engine scavenging , studying various models, from simple one-zone perfect mixing to more complex multi-zone such as Bensons or Maekawa's two and three zonal schemes.

• (Wiebe, 1962) – The author covers the fundaments of heat release modelling in combustion engines, by presenting the first of its kind theoretically proven function for mass fraction of fuel burned. Wiebe's research helped propel the internal combustion modelling and design

for years to come. His theory was later expanded to double and triple Wiebe's functions for even better increase in accuracy.

The following content presents the combination of theory drawn from the above literature, which was adjusted to achieve the aims & objectives stated for this project.

1. Saleri Engine Design

The engine comprises of 3 cylinders, arranged in an equilateral triangle and operates on a two- stroke cycle. Figure 1 and Figure 2 present the cross-sectional, back and side view of the engine

1.

Crankcase (1,2 and 3)

2.

Double diameter piston (1,2 and 3)

3.

Cylinder wall

4.

Crankcase inlet valve

5.

Cylinder inlet valve

6.

Connecting rod

7.

Crankshaft (1,2 and 3)

8.

Sparkplug

9.

Secondary chamber

10.

Exhaust port

11.

Inlet port

12.

Fuel injector

13.

Exhaust cam follower

Figure4 CrosssectionofSaleriengine

Figure 5 Pressure difference check valve (Oliver, 2008)

Figure7Salerienginebackandsideview

1. Double diameter piston

Figure 6 Double diameter piston andthesecondary chamber

Bottom part of the piston has a larger diameter than bore of the top part (Figure 6). Whilst increasing the inertial mass of the component it also manifests a different compression and

scavenging behaviour, both of which are a subject of later numerical analysis. On the contrary to a typical two-stroke engine, during a compression stroke the cylinder inlet valve remains opened for the most of the stroke, because the predecessing cylinder is during the power stroke travelling downwards and further compresses the air in the chamber of the cylinder being in the compression stroke. A pressure difference check valve (Figure 5) described in (Oliver, 2008) is a perfect solution to accommodate such flow regulation. It has smaller discharge coefficent and occupies less space than a reed valve.

1. Secondary chamber

As a result of the double diameter piston a secondary chamber is created between the top face of the larger diameter piston base and the shelf in the cylinder walls. Saleri suggested this [Grab your reader's attention with a great quote from the document or use this space to emphasize a key point. To place this text box anywhere on the page, just drag it.]

feature could be used for lubrication, placing a small valve in the cylinder wall to allow for the

Secondary chamber

Figure 8 Secondary chamber created by thedoublediameterpiston

intake of oil and additional piston grooves for supplying the oil to the gudgeon pin (Saleri, 2019).

The chamber may serve as a blow-by barrier between the combustion chamber and the crankcase. During power stroke, a small amount of exhaust gases usually slips through the piston rings and

reaches the crankcase exposing it to chemicals which hinders its performance. Releasing unwanted blow-by gasses through the cylinder wall instead of the crankcase will mitigate some of its negative effects.

1. Valve timing

Cylinder intake and exhaust port timings in a typical two-stroke crankcase compression engine are determined by the height of the ports relative to the piston's BDC and therefore have a symmetrical port timing around BDC.

Figure9 Symmetricalporttiming (Pattakon,2014) Figure10Loop scavengedtwo-

stroke engine port positioning (Blair,1996)

Saleri engine is a lot more flexible when it comes to port timing. It isn't restricted by fixed intake and crankcase ports in the cylinder walls but uses poppet valves, controlled by profiled crankshafts to regulate all the airflows. In this paper however, we will be considering crankcase and inlet valves as previously described pressure difference check valves, therefore their opening and closing times are governed by the adequate chamber pressures to ensure zero backflow.

Port timings for conventional engine are adopted from (Pattakon, 2014) and (Heywood & Sher, 1999), Saleri engine timing are based on the former with adjustments according to its mechanical design. Both schemes are conveniently presented in Figure 11 and described below:

1. Combustion

SOC → EOC

For both engines happens between [-10° : 30°]. The combustion model used in this paper is further demonstrated in Chapter 4.2. A good assumption of ignition timing at -10° and combustion duration of 40° was suggested in ( (Heywood & Sher, 1999).

1. Expansion

EOC → EVO

For both engines happens between [30° : 115°]. Burned fuel mixture of high pressure end temperature expands and does work on the piston.

1. Exhaust blowdown

EVO → IVO

For both engines happens between [115° : 135°]. When exhaust valve opens, pressure difference between exhaust manifold and cylinder chamber forces the leftover gases out of the system.

1. Scavenging

IVO → IVC/EVC Conventional Engine

For conventional engine happens between [135° : 225°/245°]. Both cylinder intake and exhaust valves are opened. Fresh air is forced into the cylinder chamber pushing out burned gas, increasing purity of the trapped charge before the next combustion. Period between IVC and EVC is called Exhaust Displacement, during which a small portion of the trapped charge is forced out of the control volume by the piston movement. Theoretical model for exhaust scavenging for a two-stroke engine is presented in greater detail in Chapter 4.3.5.

IVO → EVC Saleri Engine

First minor difference between the two designs. In this case scavenging starts at [135°] and lasts until [245°], due to intake port being opened for a much longer period than in a traditional engine. The reason behind it is explained in the next point.

1. Compression

EVC → SOC Conventional Engine

Freshly delivered air and some leftover residual exhaust gases are compressed by the piston between [245° - 350°]. For a zero-dimensional engine model it is reasonable to assume that at the end of this period the fuel is injected forming homogeneous combustible mixture.

EVC → IVC/SOC Saleri Engine

This period contributes to the biggest difference between the two cycles. Between EVC and IVC [245° : 300°] the air is compressed by the piston 1 travelling upwards and piston 2 travelling downwards due to volumes of crankcase 2 and combustion chamber 1 being interconnected by the opened inlet valve. When piston 2 reaches BDC, the inlet valve of cylinder 1 closes and the trapped charge is further compressed by only piston 1 IVC → SOC [300° - 350°].

1. Crankcase compression

Conventional Engine

Crankcase inlet port opening is typically regulated either by the piston position (however disc and reed valves systems are also known). As a result, a mirrored timing around TDC exists (in this case

-50° BTDC and +50° degrees ATDC). Between IVC and CVO [-135° : -50°] a negative (lower than atmospheric) pressure in the crankcase is created allowing for rapid air intake to the crankcase volume. The timing of both CVO and CVC has to be appropriately tuned to ensure the greatest net mass of air intake during this period for further crankcase compression between CVC and IVO [50° : 135°].

Saleri Engine

Due to crankcase linkage with the cylinders which are 120° ahead of them in the cycle and check valve flow regulation, in Saleri engine crankcase compression occurs only between CVC and IVO [120° : 135°], however in exchange for such short compression period the downward motion of piston 2 contributes to combustion chamber compression of piston 1.

1. Methodology

1. Engine design process

Inspiration for the approach chosen for the Saleri engine analysis was drawn from Rolls-Royce's engine design process for military aircraft presented in the Figure 12 below:

Figure 12Rolls-Royceenginedesignprocess(Jones,etal.,2002)

Preliminary concept definition stage determines the initial functional attributes and sets initial direction for the whole endeavour (Jones, et al., 2002). This step was already completed by Saleri, who provided the idea and description of his engine (Saleri, 2019).

This paper contributes to the preliminary design stage. The aim is to increase knowledge about the engine and deliver a tool to aid further development as well as prototyping. Rolls-Royce uses a self-developed programmes called Rolls-Royce Analysis Programme [RRAP] and Genesis. They are engineering tools designed to accept general parameters of engines and with some simplified assumptions provide calculations for performance prognosing (Jones, et al., 2002).

Following Rolls-Royce's approach, a theoretical performance model is presented in the following sections with a MATLAB code, as a preliminary design tool, enabling engineers to perform calculations specific for Saleri engine.

1. Analytical analysis with empirical support

Experimental substance in this project was deemed impossible due to time and budget constraints. Prototype manufacturing would not only be costly, but the first iteration would had little chance of being fully operational due to highly conceptual nature of the design, therefore Saleri engine's performance parameters are compared to a conventional two-stroke cycle of the same geometry and other relevant input empirical parameters drawn from literature.

1. Engine Cycle Modelling Theory

It is a widely researched area with models varying in complexity, computational speed and application. It is crucial to select appropriate methods for desired aims. Models can be classified into 3 main categories:

1. Zero-dimensional system

This model disregard spatial parameters, significantly reducing the complexity. It provide systems of ordinary differential equations for working fluid properties derived from 3 general thermodynamic equations.

𝐶𝑜𝑛𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑛𝑒𝑟𝑔𝑦

𝑑𝑈 =𝜕𝑄− 𝜕𝑊+ 𝜕𝐻 (1)

𝐼𝑑𝑒𝑎𝑙 𝑔𝑎𝑠 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛

𝑝𝑉 =𝑚𝑅𝑇 (2)

𝐶𝑜𝑛𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑚𝑎𝑠𝑠

𝑑𝑚 =∑𝑑𝑚𝑖 (3)

Depending on the aims and resources of a simulation, there are two possible directions of analysis:

Figure13 Input/outputdirectionsofenginesimulation(Krishnan,2003)

Top scheme is chosen for this dissertation, due to missing cylinder data.

It is up to the engineer to make reasonable assumptions and balance reduction in complexity against robustness and accuracy when creating engine models. Sets of the following assumptions were adopted from literature, to help manipulate above equations:

• Working mixture is homogenous in its own zone (no gradient exists throughout the volume).

• Thermodynamic parameters are changing only with respect to time or crankshaft angle.

• Enthalpy of injected fuel is omitted.

• Gases follow the ideal gas relation.

• Crevice and wall heat losses are neglected.

• Constant cylinder wall temperature.

• Chemical composition of burned gases is maintained frozen.

(Krishnan, 2003), , (Stepanenko & Kneba, 2019)

1. Single-zone combustion model

Figure 14 represents one control volume, defining volume of the combustion chamber, filled homogeneously with working fluid. Temperature and pressure vs crank angle functions are derived from aforementioned general equations and the use of sub-models (described later in this chapter). According to (Mohammed, et al., 2019) for a spark ignited engine during combustion, rate of change of cylinder pressure is described as:

Single-zone model has low computational cost and is capable of predicting basic engine performance parameters, therefore it was selected for the purpose of this dissertation.

1. Sub-models

Combustion model is often accompanied by several sub-models, evaluating additional thermodynamical or mechanical processes. They are used to further constrain the model, increasing accuracy, or focus on investigating specific areas of engine performance.

1. Mass fraction burned

Due to direction of analysis chosen in Section 3.1, a model for mass fraction of fuel burned is required. The most widely used by researchers is Wiebe's function, formulated by Ivan Wiebe, who as one of the first, described chain chemical reactions with relation to mass burning rate for use in internal combustion engines:

Properties of burned and unburned gas mixture may now be calculated using relations described in the following section.

1. Thermodynamic properties

1. Scavenging

Characteristic for two-stroke engine is the scavenging period occurring when both intake and exhaust ports are opened during downward piston motion. Fresh air charge replaces exhaust gases in the chamber. Efficiency of his process is an important performance parameter of two-stroke engines. It influences emission levels, fuel consumption and output power.

Figure 16 Massflowdiagramofscavengingperiod inatwo-strokeengine (Sher,1989)

Figure 16 Mass flow diagram of scavenging period in a two-stroke engine Figure 16 portrays the mass exchanges during scavenging period. Fresh delivered charge splits into the charge retained in the cylinder when ports close and short circuited portion, which escapes with the exhaust gases via exhaust outlet. Small percentage of residual exhaust gases are 'circling' the centre of the diagram. This is the fraction that is always present during the whole cycle (during combustion as residual gas and during scavenging as unwashed portion of combustion products).

The following parameters are used to analyse the scavenging process:

In this analysis, a single-zone perfect mixing model will be used. When the fresh charge enters the cylinder it is assumed that it instantly mixes with the cylinder contents and an equivalent mass of the exhaust gasses at the same instantaneous purity leaves the chamber. Additionally, both gases obey the ideal gas law at constant and equal specific heats. No heat transfer between the fresh charge and exhaust gasses is considered during the scavenging period. The following equation for describing the process is then formulated:

𝜂𝑐 = 1 − exp(−𝜆) (21)

(Sher, 1989)

It links the amount of fresh charge delivered miwith that retained in the cylinder after ports close ma. Resultant curve of the above relation is presented in Figure 17 below.

Figure17Perfectmixing chargingefficiencyvsdeliveryratiograph(Sher,1989)

The model accurately depicts the nature of scavenging, which can never be perfect - the charging efficiency value approaches unity. Higher than unity values of delivery ratio may be achieved by means of air charging.

1. MATLAB Code

1. Numerical solution

Using theory presented in Section 3 a MATLAB code included in the Appendices C, D, E and F was formulated. Schematic of its operation is demonstrated in Figure 18:

Figure18MATLABcodeflowchart

Convergence mechanism is based on two values: residual mass fraction f and exhaust temperature at the end of expansion stroke TEVO. Both of those values are used at the beginning of the compression calculation. Delta of initial and final values is calculated and the process is repeated if they do not meet the convergence criteria. List of engine input data is included in the model code in Appendix B and C. For integration of differential equations in-built MATLAB function ode45is used, which is a pre-programmed Runge-Kutta 4th order ODE solver.

1. Saleri engine performance evaluation

The algorithm is run for two engines:

• Saleri engine with dimensions specified in the delivered CAD model.

• Conventional two-stroke engine cycle with the same dimensions as the above Saleri engine.

The only difference between the 2 cases will be in the valve timing and pressure trace/scavenging parameters, which analysis is the objective of this dissertation.

1. Results discussion

1. Pressure

Figure19Pressurevscrankanglegraph

Saleri engine's pressure trace is significantly under the conventional two-stroke engine curve. As a result, the engine will have noticeably lower power and torque on the whole range of rpms. The issue of such difference lies in the lower pressure during compression, due to lower compression ratio of the added crankcase volume. It is apparent that Saleri cycle in its current version is not competitive with current two-stroke performance.

Pressure curve has a dip around 10 CAD. This is caused by the single-zone combustion model differential pressure equation, which has a slow initial increase, due to lagged exponential mass fraction burned function. A more accurate two-zone combustion algorithm would help with reshaping current pressure trace.

1. Temperature

Figure 20 Temperaturevscrankanglegraph

Temperature graphs correlate with pressure values and its tendencies. Lower pressure implies less entrapped air, therefore less fuel to combust resulting in lower temperatures of the cycle.

Contrary to in-cylinder pressure, temperature of gasses do not have a direct influence on the power curve, however many aspects of engine operation such as: heat losses, crevice losses, combustion efficiency and combustion flame propagation (Heywood, 2018) do influence the gas temperature. Separate piece of work, with more detailed model for burned gas composition (for example using a two-zone combustion model) must be performed to focus on analysing the aforementioned factors, as they are out of scope for the current project.

1. Scavenging

Figure21Deliveryratiovschargingefficiencygraphs

Scavenging parameters is where the Saleri engine seems to shine. Despite having lower intake blowdown period (initial scavenging at the opening of the intake valve) it presents massive delivery ratio potential, resulting in higher value of charging efficiency by 0.9. Delivery ratio final value greater than unity indicates supercharging behaviour, despite being a naturally aspirated engine.

1. Applications

Analysis of Saleri engine at preliminary design stage so far showed, that the engine might not achieve highest levels of performance and be competitive in i.e. peak power domain with similar engines in its field, however great potential was exhibited in overall engine efficiency. Outstanding scavenging parameters are responsible for lower emissions and better fuel efficiency comparing to a conventional two-stroke engine. With the current tendencies in the automotive industry shifting from high RPM, powerful engines to more efficient power units in order to lower carbon emissions, Saleri engine fits perfectly.

1. Limitations

Most significant hindrance was lack of experimental data, which would help with model validation and tuning of empirical constant specific for Saleri engine. In-cylinder pressure tracer or lambda sensors at exhaust are two simple tools, which help eliminate any inaccuracies with mathematical model and provide basis for deeper engine investigation. It is understandable that at current

development stage, with restricted budget, prototype manufacturing was impossible, however is definitely the next recommended step in the design process.

Engine simulation theory is an immensely broad and complicated subject, requiring specialised knowledge and experienced engineering intuition. This project would benefit with input and manpower of wider array of engineers with varying experience to increase the accuracy of results and expand covered areas of engine simulation.

Professional available packages for engine simulation (i.e. GT-Power, Ricardo WAVE) are unfeasible for simulating concept engines, such as Saleri's design. They are inapt for preliminary design stage work, where all the innovations are impossible to model within conventional boundaries of engine theory. Should modelling Saleri engine in one of those softwares be possible, it would provide wide array of useful data and validation capabilities, however for now separate, design-specific analytical modelling must be pursued.

This dissertation is the first piece of work ever prepared on Saleri engine. Lack of applicable literature to this exact design proved extremely challenging to contrive an applicable model using only theory available for conventional engines. No design specific literature validation or referencing was possible.

1. Future work

Pursuit of manufacturing a scaled model of Saleri engine will prove most valuable for the development process. It will help validate the potential scavenging and efficiency discoveries, as well as provide solid data for analysis.

Saleri engine does have likely advantages over conventional two-stroke engine. Suggested way of further investigation is a parametric study, where arrays of parameters such as: top to bottom diameter ratio, displacement, fuel used are changed and the results compared, in order to discover possible hidden performance. Aforementioned parameters were held fixed in this dissertation, therefore their influence was not analysed.

In order to expand engineering team working on Saleri engine development, it is a reasonable idea to suggest for example the aforementioned parametric study as a 4th Year project, where with greater amount manpower and budget development could be propelled forward, using the discovery of potential scavenging performance of Saleri engine in this dissertation.

Model used in this project can be further expanded to account for heat transfer and frictional effects. Appropriate sub-models implementable for conventional two-strokes engines, which can be applicable to Saleri's design are outlined in (Heywood, 2018) and (Blair, 1996). More accurate two-zone combustion model, such as one presented in (Perini, et al., 2010), could be used to obtain more accurate results of in-cylinder pressure trace and study exhaust gas composition. At lower temperatures there is less dissociation of exhaust products and smaller fraction of harmful NO species are generated, which could overturn the lower temperature trace described in Section 5.2 into an advantage.

1. Conclusions

The comparative analysis of Saleri engine with a conventional two-stroke showed, that in-cylinder pressure trace is lower, indicating potential lower power and torque curves. Better performance was discovered in the scavenging area, where the concept engine exhibited characteristics indicating supercharging behaviour (delivery ratio reaching values of 1.3). It indicates that there is potential for Saleri engine to be more fuel efficient and produce less emissions than typical two- strokes.

Further direction for engine development was suggested, especially the parametric study, which has the ability to tune engine geometry and provide dimensions for future prototype building.

1. Project management review

Due to the concept nature of Saleri design and the fact that this project is the first piece of analysis performed on the engine, the dissertation underwent many minor and major rescoping throughout the year. It proved distracting and hindered focusing on the same aims and objectives from the beginning. More time should have been allocated for developing the MATLAB code, especially troubleshooting, which consumed a significant amount of time during the last month preceding submission date.

The plan created at the beginning of semester 1 (included in Appendix A) was too general to be followed throughout the year, however with research performed before the start of semester 2, a new more accurate version was drafted. Despite changes to the scope of the project, the new plan was followed with respect to deliverable section of the report, which helped with staying on track

to finish the submission on time. Dr Moray Kidd proved invaluable with his advices to help shape and plan the project and many thanks are directed towards him for his input.

References

Blair, G. P., 1996. Designand SimulationofTwo-StrokeEngines.s.l.:s.n.

Caton, J. A., 1999. Comparisonsofinstructionaland completeversionsofthermodynamic enginecyclesimulations for spark-ignition engines, s.l.: s.n.

Caton, J. A., 2016. AnIntroductiontoThermodynamicCycleSimulationsforInternalCombustionEngines. s.l.:s.n.

Heywood, J. B., 2018. Internal Combustion Engine Fundamentals. Second Edition ed. s.l.:s.n. Heywood, J. B. & Sher, E., 1999. TheTwo-StrokeCycle Engine. s.l.:s.n.

Jones, M., Bradbrook, S. & Nurney, K., 2002. A Preliminary Engine Design Process for anAffordableCapability, s.l.: s.n.

Kirkpatrick, A. T., 2021. Internal Combustion Engines Applied Thermosciences. Fourth Edition ed. s.l.:s.n.

Krishnan, S., 2003. ME418 CombustionEngines Course. Alabama: s.n.

McAllister, S., Chen, J.-Y. & Fernandez-Pello, C., 2011. Fundamentals of CombustionProcesses.s.l.:s.n.

McBride, B. J. & Gordon, S., 1994. ''CoefficientsforCalculatingThermodynamicandTransportPropertiesof Individual Species,s.l.: NASA.

Mohammed, S. E., Baharom, M. B., Aziz, A. R. A. & A., E. Z. Z., 2019. Modelling ofCombustion Characteristic of a Single Curved-Cylinder Spark-Ignition Crank-Rocker Engine,s.l.: s.n.

Oliver, P. J., 2008. ANUMERICALINVESTIGATIONOF,Ontario: s.n.

Pattakon, 2014. Pattakon. [Online] Available at: https://www.pattakon.com/

Perini, F., Paltrinieri, F. & Mattarelli, E., 2010. A quasi-dimensional combustion model for performance and emissions of SI engines running on hydrogen-methane blends. ScienceDirect.

Saleri, R., 2019. Enginewithcooperatingpistonsbasedonatwo-strokecycle.WIPO. Sher, E., 1989. Scavenging TheTwo-StrokeEngine,s.l.: s.n.

Stepanenko, D. & Kneba, Z., 2019. Thermodynamic modellin of combustion process of theinternalcombustion engines-an overview, s.l.: s.n.

Wiebe, I. I., 1962. Progressinenginecycle analysis:Combustionrateandcycleprocesses,s.l.: s.n.

APPENDIX A – Initial and revised project plan

Figure22Initialprojectplandraftedinsemester1

Figure23Projectplandraftedduringsemester2

APPENDIX B – Table of polynomial coefficients for combustion species

200K < T < 1000K

Isooctane

CO2

H2O

N2

O2

a1

15.9899273

4.63659493

2.67703787

2.95257626

3.66096083

a2

0.055318479

0.00274132

0.002973183

0.001396901

0.000656366

a3

-1.95E-05

-9.96E-07

-7.74E-07

-4.93E-07

-1.41E-07

a4

3.12E-09

1.60E-10

9.44E-11

7.86E-11

2.06E-11

a5

-1.85E-13

-9.16E-15

-4.27E-15

-4.61E-15

-1.30E-15

a6

-35875.7973

-49024.9341

-29885.8938

-923.948645

-1215.97725

1000K < T < 6000K

a1

0.815737338

2.35677352

4.19864056

3.53100528

3.78245636

a2

0.073264396

0.008984597

-0.002036434

-0.000123661

-0.002996734

a3

1.78E-05

-7.12E-06

6.52E-06

-5.03E-07

9.85E-06

a4

-6.94E-08

2.46E-09

-5.49E-09

2.44E-09

-9.68E-09

a5

3.22E-11

-1.44E-13

1.77E-12

-1.41E-12

3.24E-12

a6

-30477.2862

-48371.9697

-30293.7267

-1046.97628

-1063.94356

Table1 Polynomialcoefficientforcombustionspecies(McBride& Gordon,1994)

APPENDIX C – MATLAB code for conventional two-stroke engine

clc clear close all

% --- CONSTANTS ---

format long

bore = 0.0524; % bore [m]

a = 0.02895; % half stroke [m] stroke = a*2; % stroke [m]

l = 0.180; % connecting rod length [m]

Vmax = 1.41771e-04; % cylinder BDC volume [m3] Vhead = 1.69094e-05; % cylinder TDC volume [m3] Vdis = 1.24862e-04; % cylinder displaced volume [m3] Ahead = 0.0031746422; % cylinder head area [m2]

CR = 6.31091; % compression ratio [ND] step = 1; % computational step [deg] thetaIVO = 135; % [deg]

thetaIVC = 225; % [deg] thetaEVO = 120; % [deg] thetaEVC = 240; % [deg] thetaSOC = 350; % [deg] thetadur = 40;

thetaEOC = thetaSOC + thetadur; % [deg] mwiebe = 5; % [ND]

awiebe = 2; % [ND]

Tamb = 303; % ambient air temperature [K] Twalls=350; % cylinder wall temperature pamb = 101325; % ambient air pressure [Pa] rpm = 2000; % RPM [rev/min]

AFR = 14.7; % [ND]

LHV = 2237500; % Lower Heating Value of Isooctane [J/kg] Rhoair = 1.225;

Runiv = 8.314; % universal gas constant [J/mol*Kel]

molmasair = 0.21*property(1,5,4)+0.79*property(1,4,4); % molar mass of air [kg/mol]

molmasexh = 0.02859375; % molar mass of exhaust gas [kg/mol] (stoichiometric and complete combustion isooctane)

molmasaf = 0.030251239669421; % molar mass of air-fuel mixture (stoichiometric isooctane) [kg/mol]

Rexh = Runiv/molmasexh; % specific gas constant for exhaust gas stoichiometric and complete combustion isooctane) [J/kg*K]

Rfuel = property(1,1,5); % specific gas constant for fuel [J/kg*K]

Rair = Runiv/molmasair; % specific gas constant for air [J/kg*K]

isooctmasaf = 0.0624;

o2masaf = 0.2186;

n2masaf = 0.7190;

h20masexh = 0.0885;

co2masexh = 0.1923;

n2masexh = 0.7191;

convergenceT = 101;

convergencef = 0.06

Texhevo = 600 ;% INITIAL VALUE f = 0.1; % INITIAL VALUE

while convergencef > 0.05 && convergenceT > 100

Vinst =@(theta) vainst(theta,'v'); dVdtheta = @(theta)

(bore^2*pi*((a*pi*sin((pi*theta)/180))/180 + (a^2*pi*cos((pi*theta)/180)*sin((pi*theta)/180))/(180*(l^2 - a^2*sin((theta*pi)/180)^2)^(1/2))))/4;

Ainst =@(theta) vainst(theta,'a');

% COMPRESSION

pevc = pamb;

Tevc = (1-f)*Tamb + f*Texhevo; Vevc = Vinst(thetaEVC);

R = Runiv/(f*molmasexh+(1-f)*molmasaf); m = pamb*Vevc/(R*Tevc);

mexh = m*f; maf = m*(1-f);

mair = maf/(AFR+1); mfuel = maf/((1/AFR)+1);

cp = (1- f)*(isooctmasaf*property(Tevc,1,1)*property(Tevc,1,5)+o2masa f*property(Tevc,5,1)*property(Tevc,5,5)+n2masaf*property(Tev c,4,1)*property(Tevc,4,5))+f*(h20masexh*property(Tevc,3,1)*p

roperty(Tevc,3,5)+co2masexh*property(Tevc,2,1)*property(Tevc

,2,5)+n2masexh*property(Tevc,4,1)*property(Tevc,4,5)); gamma = cp/(cp-R);

itercomp = 1;

for theta= thetaEVC:step:thetaSOC

T = Tevc*(Vevc/Vinst(theta))^(gamma-1); p = pevc*(Vevc/Vinst(theta))^(gamma); pcomp(itercomp)=p;

Tcomp(itercomp)=T; itercomp=itercomp+1;

end

% COMBUSTION

Xb =@(theta) 1-exp(-awiebe*((theta- thetaSOC)/(thetadur))^(mwiebe+1));

dXbdtheta = @(theta) (awiebe*exp(-awiebe*((theta - thetaSOC)/thetadur)^(mwiebe + 1))*(mwiebe + 1)*((theta - thetaSOC)/thetadur)^mwiebe)/thetadur;

Qtotrel=mfuel*LHV;

dQindtheta = @(theta) Qtotrel*dXbdtheta(theta);

%Ainst(theta)*1000*(500-Twalls)*30/(rpm*pi)%(T;

dpdtheta = @(theta,p) (- gamma*p/Vinst(theta))*(dVdtheta(theta))+((gamma- 1)/Vinst(theta))*(dQindtheta(theta));

[theta,pcomb]=ode45(dpdtheta,[thetaSOC:step:thetaEOC], p); itercomb=1;

for theta=thetaSOC:thetaEOC

Tcomb(itercomb)=Vinst(theta)*pcomb(itercomb)/(m*R); itercomb=itercomb+1;

end

%EXPANSION

Teoc=Tcomb(length(Tcomb)); peoc=pcomb(length(pcomb));

iterexp = 1;

for theta = (thetaEOC-360):step:thetaEVO

T = Teoc*(Vinst(thetaEOC)/Vinst(theta))^(gamma-1); p = peoc*(Vinst(thetaEOC)/Vinst(theta))^(gamma);

pcomb=pcomb'; ptotal=[pcomp, pcomb, pexp];

ttotal=[Tcomp, Tcomb, Texp]; xxx=(thetaEVC-360):(thetaEVC+242-360); figure

plot(xxx,ptotal,'r') title('Pressure vs Crank angle') xlabel('Crank Angle [deg]') ylabel('Pressure [Pa]')

figure plot(xxx,ttotal,'r')

title('Temperature vs Crank angle') ylabel('Temperature [K]') xlabel('Crank Angle [deg]')

figure plot(delratioxx,chargeffxx,'r')

APPENDIX D - MATLAB code for Saleri engine

clc clear close all

% --- CONSTANTS ---

format long

bore = 0.0524; % bore [m] bore2= 0.1048; % larger bore [m] a = 0.02895; % half stroke [m] stroke = a*2; % stroke [m]

l = 0.180; % connecting rod length [m]

Vmax = 1.41771e-04; % cylinder BDC volume [m3] Vhead = 1.69094e-05; % cylinder TDC volume [m3] Vdis = 1.24862e-04; % cylinder displaced volume [m3] Ahead = 0.0031746422; % cylinder head area [m2]

step = 1; % step [deg] thetaIVO = 135; % [deg] thetaIVC = 300; % [deg] thetaEVO = 120; % [deg] thetaEVC = 240; % [deg] thetaSOC = 350; % [deg] thetadur = 40;

thetaEOC = thetaSOC+thetadur; % [deg] mwiebe = 5; % [ND]

awiebe = 2; % [ND]

Tamb = 303; % ambient air temperature [K] Twalls=350;

pamb = 101325; % ambient air pressure [Pa] rpm = 2000; % RPM [rev/min]

AFR = 14.7; % [ND] LHV = 2237500;

rhoair=1.225;

Runiv = 8.314; % universal gas constant [J/mol*Kel]

molmasair = 0.21*property(1,5,4)+0.79*property(1,4,4); % molar mass of air [kg/mol]

molmasexh = 0.02859375; % molar mass of exhaust gas [kg/mol] (stoichiometric and complete combustion isooctane)

molmasaf = 0.030251239669421; % molar mass of air-fuel mixture (stoichiometric isooctane) [kg/mol]

Rexh = Runiv/molmasexh; % specific gas constant for exhaust gas stoichiometric and complete combustion isooctane) [J/kg*K]

Rfuel = property(1,1,5); % specific gas constant for fuel [J/kg*K]

Rair = Runiv/molmasair; % specific gas constant for air [J/kg*K]

isooctmasaf = 0.0624;

o2masaf = 0.2186;

n2masaf = 0.7190;

h20masexh = 0.0885;

co2masexh = 0.1923;

n2masexh = 0.7191;

convergenceT = 101;

convergencef = 0.06

Texhevo = 600 ;% INITIAL VALUE f = 0.1; % INITIAL VALUE

while convergencef > 0.05 && convergenceT > 100

Vinst =@(theta) vainst(theta,'v'); dVdtheta = @(theta)

(bore^2*pi*((a*pi*sin((pi*theta)/180))/180 + (a^2*pi*cos((pi*theta)/180)*sin((pi*theta)/180))/(180*(l^2 - a^2*sin((theta*pi)/180)^2)^(1/2))))/4;

Ainst =@(theta) vainst(theta,'a'); Vbott=@(theta) abs((stroke-(a+l-(l^2-

a^2*(sind(theta))^2)^(1/2) - a*cosd(theta)))*pi*bore2^2/4); Vcrank= 7.068583470577034e+05;

% COMPRESSION

pevc = pamb;

Tevc = (1-f)*Tamb + f*Texhevo;

Vevc = Vinst(thetaEVC)+Vbott(thetaEVC)+Vcrank; R = Runiv/(f*molmasexh+(1-f)*molmasaf);

cp = (1- f)*(isooctmasaf*property(Tevc,1,1)*property(Tevc,1,5)+o2masa f*property(Tevc,5,1)*property(Tevc,5,5)+n2masaf*property(Tev c,4,1)*property(Tevc,4,5))+f*(h20masexh*property(Tevc,3,1)*p roperty(Tevc,3,5)+co2masexh*property(Tevc,2,1)*property(Tevc

,2,5)+n2masexh*property(Tevc,4,1)*property(Tevc,4,5)); gamma = cp/(cp-R);

itercomp1 = 1;

for theta= thetaEVC:step:thetaIVC T =

Tevc*(Vevc/(Vinst(theta)+Vcrank+Vbott(theta)))^(gamma-1);

p = pevc*(Vevc/(Vinst(theta)+Vcrank+Vbott(theta)))^(gamma);

pcomp1(itercomp1)=p; Tcomp1(itercomp1)=T; itercomp1=itercomp1+1;

end pivc=p; Tivc=T;

Vivc=Vinst(thetaIVC); itercomp2=1;

for theta= thetaIVC:step:thetaSOC

T = Tivc*(Vivc/Vinst(theta))^(gamma-1); p = pivc*(Vivc/Vinst(theta))^(gamma); pcomp2(itercomp2)=p; Tcomp2(itercomp2)=T; itercomp2=itercomp2+1;

end psoc=p; Tsoc=T;

m = psoc*Vinst(thetaSOC)/(R*Tsoc); mexh = m*f;

maf = m*(1-f);

mair = maf/(AFR+1); mfuel = maf/((1/AFR)+1);

% COMBUSTION

Xb =@(theta) 1-exp(-awiebe*((theta- thetaSOC)/(thetadur))^(mwiebe+1));

dXbdtheta = @(theta) (awiebe*exp(-awiebe*((theta - thetaSOC)/thetadur)^(mwiebe + 1))*(mwiebe + 1)*((theta - thetaSOC)/thetadur)^mwiebe)/thetadur;

Qtotrel=mfuel*LHV;

dQindtheta = @(theta) Qtotrel*dXbdtheta(theta);%- Ainst(theta)*50*(500-Twalls)*30/(rpm*pi)%(T;

dpdtheta = @(theta,p) (- gamma*p/Vinst(theta))*(dVdtheta(theta))+((gamma- 1)/Vinst(theta))*(dQindtheta(theta));

[theta,pcomb]=ode45(dpdtheta,[thetaSOC:step:thetaEOC], p); itercomb=1;

for theta=thetaSOC:thetaEOC Tcomb(itercomb)=Vinst(theta)*pcomb(itercomb)/(m*R); itercomb=itercomb+1;

end

%EXPANSION

Teoc=Tcomb(length(Tcomb)); peoc=pcomb(length(pcomb));

iterexp = 1;

for theta = (thetaEOC-360):step:thetaEVO

T = Teoc*(Vinst(thetaEOC)/Vinst(theta))^(gamma-1); p = peoc*(Vinst(thetaEOC)/Vinst(theta))^(gamma); pexp(iterexp)=p;

Texp(iterexp)=T; iterexp=iterexp+1;

end

pevo=pexp(length(pexp)); Tevo=Texp(length(Texp));

%When Exhaust valve opens

%AT EVC

mevo=m*pamb/pevc;

%Crankcase pressure

Vcrank=@(theta) 7.068583470577034e-05 + Vbott(theta); pcrankivo=pamb*(Vcrank(120)/Vcrank(thetaIVO))^(gamma); Tcrankivo=Tamb*(Vcrank(120)/Vcrank(thetaIVO))^(gamma-1); deltaminject=Vcrank(thetaIVO)*(pcrankivo- pamb)/(R*Tcrankivo);

mdel=@(theta) deltaminject + pamb*Vscav(theta)/(R*Tcrankivo); delratio=@(theta) mdel(theta)/(Vdis*rhoair); chargeff=@(theta) 1- exp(-delratio(theta));

mivo=mevo*(Vinst(thetaIVO)/Vinst(thetaEVO)); thetascav=thetaIVO:thetaIVC; Vscavxx=zeros(1,thetaIVC-thetaIVO+1); mdelxx=zeros(1,thetaIVC-thetaIVO+1); delratioxxsal=zeros(1,thetaIVC-thetaIVO+1); chargeffxxsal=zeros(1,thetaIVC-thetaIVO+1);

iterscav=1;

for theta=thetaIVO:thetaIVC

APPENDIX E – Sub program for retrieving thermodynamic properties of species

function property = property(T, id, prop)

% id = 1 isooctane

% id = 2 CO2

% id = 3 H20

% id = 4 N2

% id = 5 O2

% prop = 1 cpoveR

% prop = 2 H0ToverRT

% prop = 3 S0ToverR

% prop = 4 molarmass

% prop = 5 R specific constant Runiv = 8.314; % J/Kel*mol

if T > 1000

if id == 1 % isooctane

molarmass = 0.1142; % kg/mol

a = [1.59899273E+01 5.53184790E-02 -1.95267072E-05 3.11779172E-09 -1.85312577E-13 -3.58757973E+04 -

6.01161414E+01];

R = Runiv/molarmass; elseif id == 2 % CO2

molarmass = 0.044; % kg/mol

a = [4.63659493E+00 2.74131991E-03 -9.95828531E-07 1.60373011E-10 -9.16103468E-15 -4.90249341E+04 -

1.93534855E+00];

R = Runiv/molarmass; elseif id == 3

molarmass = 0.018; % kg/mol

a = [2.67703787E+00 2.97318329E-03 -7.73769690E-07 9.44336689E-11 -4.26900959E-15 -2.98858938E+04

6.88255571E+00];

R = Runiv/molarmass; elseif id == 4 % N2

molarmass = 0.028; % kg/mol

a = [2.95257626E+00 1.39690057E-03 -4.92631691E-07 7.86010367E-11 -4.60755321E-15 -9.23948645E+02

5.87189252E+00];

R = Runiv/molarmass;

elseif id == 5 % O2

molarmass = 0.032; % kg/mol

a = [3.66096083E+00 6.56365523E-04 -1.41149485E-07 2.05797658E-11 -1.29913248E-15 -1.21597725E+03

3.41536184E+00];

R = Runiv/molarmass; end

elseif T <= 1000

if id == 1 % isooctane

a = [8.15737338E-01 7.32643959E-02 1.78300688E-05 - 6.93589620E-08 3.21629382E-11 -3.04772862E+04

2.41509994E+01];

molarmass = 0.1142; % kg/mol R = Runiv/molarmass;

elseif id == 2 % CO2

a = [2.35677352E+00 8.98459677E-03 -7.12356269E-06 2.45919022E-09 -1.43699548E-13 -4.83719697E+04

9.90105222E+00];

molarmass = 0.044; % kg/mol R = Runiv/molarmass;

elseif id == 3 % H20

a = [4.19864056E+00 -2.03643410E-03 6.52040211E-06 - 5.48797062E-09 1.77197817E-12 -3.02937267E+04 -8.49032208E-

01];

molarmass = 0.018; % kg/mol R = Runiv/molarmass;

elseif id == 4 % N2

a = [3.53100528E+00 -1.23660987E-04 -5.02999437E-07 2.43530612E-09 -1.40881235E-12 -1.04697628E+03

2.96747468E+00];

molarmass = 0.028; % kg/mol R = Runiv/molarmass;

elseif id == 5 % O2

a = [3.78245636E+00 -2.99673415E-03 9.84730200E-06 - 9.68129508E-09 3.24372836E-12 -1.06394356E+03

3.65767573E+00];

molarmass = 0.032; % kg/mol R = Runiv/molarmass;

end

end

a_1 = a(1);

a_2 = a(2);

a_3 = a(3);

a_4 = a(4);

a_5 = a(5);

a_6 = a(6);

a_7 = a(7);

cpoverR = a_1+a_2*T+a_3*T^2+a_4*T^3+a_5*T^4;

H0ToverRT = a_1+a_2/2*T+a_3/3*T^2+a_4/4*T^3+a_5/5*T^4+a_6/T; S0ToverR = a_1*log(T)+a_2*T+a_3/2*T^2+a_4/3*T^3+a_5/4*T^4+a_7;

if prop == 1

property = cpoverR; elseif prop == 2

property = H0ToverRT; elseif prop == 3

property = S0ToverR; elseif prop == 4

property = molarmass; elseif prop == 5

property = R;

end end

APPENDIX F – Subprogram for calculating instantaneous volume and area of combustion chamber

function va = vainst(theta,id) bore = 0.0524; % bore [m]

a = 0.02895; % half stroke [m]

l = 0.180; % connecting rod length [m]

x = a+l - (l^2-a^2*(sind(theta))^2)^(1/2) - a*cosd(theta); Vhead = 1.69094e-05;

Ahead = 0.0031746422;

if 

id == 'v'

va = Vhead + x*pi*bore^2/4; elseif id == 'a'

va = Ahead + pi*bore^2/4+pi*bore*x;

end end